source,target Given the low sigual-to-noise ratio of the echo iu the images iu both bands. we consider our unucertaimties to be quite conservative.," Given the low signal-to-noise ratio of the echo in the images in both bands, we consider our uncertainties to be quite conservative." Tere we provide an analysis of the echo and its origin., Here we provide an analysis of the echo and its origin. We note that this analvsis differs from that preseuted by Sueenuan (2005)., We note that this analysis differs from that presented by Sugerman (2005). We have determined that SN 2003ed is at the exact ceuter of the liebt echo. with uncertainty «0.2 pixel (ο 005}. through comparison of our Suapshot images to the ACS FI35W images obtained by Suuutt et al. (," We have determined that SN 2003gd is at the exact center of the light echo, with uncertainty $< 0.2$ pixel $< 0{\farcs}005$ ), through comparison of our Snapshot images to the ACS F435W images obtained by Smartt et al. (" 200L). when the SN was siguificauth brighter.,"2004), when the SN was significantly brighter." The SN itself therefore must be the source of the eclio. which we observe at age f£ after explosion and age 7 after optical maximum.," The SN itself therefore must be the source of the echo, which we observe at age $t$ after explosion and age $\tau$ after optical maximum." The observed echo is the product of the iuput, The observed echo is the product of the input "where N, is the number of true cluster satellite galaxies and is the number of projected field galaxies.",where $N_c$ is the number of true cluster satellite galaxies and $N_f$ is the number of projected field galaxies. " We can introduceNy the fraction of real cluster satellite as fe(z)=Ne/(Ne+Ng), the BCG alignment from true cluster members as Ye=—45 and the BCG alignment from the projectedκ0;/N. field galaxies as Yyp-Yo0;/N,—45."," We can introduce the fraction of real cluster satellite as $f_c(z) = N_c/(N_c + N_f)$, the BCG alignment from true cluster members as $\gamma_c=\sum_{i=0}^{N_c}\theta_i/N_c - 45$ and the BCG alignment from the projected field galaxies as $\gamma_f=\sum_{j=0}^{N_f}\theta_j/N_f - 45$." " Substitute these definitions into Equation 5 and take ensemble average of the clusters, we will have: where (...) denotes the average over the cluster ensemble."," Substitute these definitions into Equation \ref{gamma_m} and take ensemble average of the clusters, we will have: where $\left<...\right>$ denotes the average over the cluster ensemble." " As the mean alignment signal from the field is consistent with zero, the alignment parameter y from the true cluster satellites is related to the measured one through the redshift dependent fraction f.(z)."," As the mean alignment signal from the field is consistent with zero, the alignment parameter $\gamma$ from the true cluster satellites is related to the measured one through the redshift dependent fraction $f_c(z)$ ." " To the first order approximation, we can separate f.(z) into two parts as f.(z)=feonstXf(z), where fronst is a redshift independent component of the fraction, indicating the “intrinsic” fraction of true satellite based on color selection."," To the first order approximation, we can separate $f_c(z)$ into two parts as $f_c(z) = f_{const} \times f(z)$, where $f_{const}$ is a redshift independent component of the fraction, indicating the “intrinsic” fraction of true satellite based on color selection." " f(z) is the redshift dependent part, corresponding to the effect we described above."," $f(z)$ is the redshift dependent part, corresponding to the effect we described above." " Then, the redshift dependence of the measured alignment will be mainly determined by f(z)."," Then, the redshift dependence of the measured alignment $\gamma$ will be mainly determined by $f(z)$." " In the GMBCG catalog, we also measured a weighted richness, which takes into account the different degree of overlaps between red sequence and the field galaxies at different redshift (?).."," In the GMBCG catalog, we also measured a weighted richness, which takes into account the different degree of overlaps between red sequence and the field galaxies at different redshift \citep{haocat}." The difference between weighted richness and the direct member count richness is a good estimator of the number of projected galaxies due to the effect described above., The difference between weighted richness and the direct member count richness is a good estimator of the number of projected galaxies due to the effect described above. The fraction of contamination can therefore be estimated by the ratio of this difference to the direct member count richness., The fraction of contamination can therefore be estimated by the ratio of this difference to the direct member count richness. " In Figure 20,, we plot the fraction of contamination (1— (f(2))) as a function of redshift in bins of size 0.05."," In Figure \ref{fig:fcz}, we plot the fraction of contamination $1 - \left$ ) as a function of redshift in bins of size 0.05." The fraction is almost constant except for the lowest redshift bin., The fraction is almost constant except for the lowest redshift bin. " Again, this cannot explain away the dependence of y on redshift as shown in Figure 10 and Figure 19.."," Again, this cannot explain away the dependence of $\gamma$ on redshift as shown in Figure \ref{fig:gammaz} and Figure \ref{fig:gammaz25}. ." " Therefore, after considering all the possible systematics known to us, the measured redshift dependence of still cannot be explained."," Therefore, after considering all the possible systematics known to us, the measured redshift dependence of $\gamma$ still cannot be explained." " In ?,, the authors also reportedΥ a different BCG alignment between one low redshift bin (0.08 - 0.26) and another high redshift bin (0.26 - 0.44), which is consistent with the results we find here."," In \citet{ostholt10}, the authors also reported a different BCG alignment between one low redshift bin (0.08 - 0.26) and another high redshift bin (0.26 - 0.44), which is consistent with the results we find here." We measure the satellite alignment and BCG alignment based on a large sample of photometrically selected galaxy clusters from the SDSS DR7., We measure the satellite alignment and BCG alignment based on a large sample of photometrically selected galaxy clusters from the SDSS DR7. We detect a satellite alignment only when we use the isphotal PAs., We detect a satellite alignment only when we use the isphotal PAs. " As we noted in §3.3, the isophotal PA tends to trace the outer profile of the galaxy while the model fit PAs tend to trace the inner part of the galaxy."," As we noted in 3.3, the isophotal PA tends to trace the outer profile of the galaxy while the model fit PAs tend to trace the inner part of the galaxy." A direct interpretation of the measurement results could be that the outer part of the satellite galaxy is more susceptible to the the gravitational torque and thus shows an orientation preference toward the BCG., A direct interpretation of the measurement results could be that the outer part of the satellite galaxy is more susceptible to the the gravitational torque and thus shows an orientation preference toward the BCG. However the inner part of the galaxy is not affected much by the tidal torque and does not show preference toward the BCG., However the inner part of the galaxy is not affected much by the tidal torque and does not show preference toward the BCG. The measured discrepancy of the satellite alignment from different PAs could be a manifestation of the twisting of galaxy shape from inner part to outer part., The measured discrepancy of the satellite alignment from different PAs could be a manifestation of the twisting of galaxy shape from inner part to outer part. " However, another possibility of this discrepancy could be that the light from BCG contaminates the measurement of the PA based on the isophote fit to the outer region of the galaxy and lead to a ""artificial"" alignment."," However, another possibility of this discrepancy could be that the light from BCG contaminates the measurement of the PA based on the isophote fit to the outer region of the galaxy and lead to a “artificial” alignment." " By comparing the dependence of ó on BCG apparent and absolute magnitudes, we favor the latter explanation."," By comparing the dependence of $\delta$ on BCG apparent and absolute magnitudes, we favor the latter explanation." " This means that, though the tidal torque within the galaxy cluster may induce the satellite alignment, we are not yet able to detect them based on our current SDSS data."," This means that, though the tidal torque within the galaxy cluster may induce the satellite alignment, we are not yet able to detect them based on our current SDSS data." It will be definitely an interesting question to address with the forthcoming high quality data such as that from the Dark Energy Survey , It will be definitely an interesting question to address with the forthcoming high quality data such as that from the Dark Energy Survey \citep{des05}. "For the BCG (?)..alignment, by introducing the alignment parameter y, we detect a strong redshift and BCG absolute magnitude dependences of the alignment."," For the BCG alignment, by introducing the alignment parameter $\gamma$, we detect a strong redshift and BCG absolute magnitude dependences of the alignment." The redshift dependence cannot be explained by our known systematics., The redshift dependence cannot be explained by our known systematics. This result implies that the BCGs orientation is a dynamically evolving process and gets stronger as the cluster system evolves., This result implies that the BCGs orientation is a dynamically evolving process and gets stronger as the cluster system evolves. " For the dependence of y on the absolute magnitude of BCG, our result is qualitatively consistent with the conclusion that clusters with BCG dominance show stronger BCG alignment in (?).."," For the dependence of $\gamma$ on the absolute magnitude of BCG, our result is qualitatively consistent with the conclusion that clusters with BCG dominance show stronger BCG alignment in \citep{ostholt10}." " Furthermore, based on a subsample of the BCGs whose stellar masses are available, we show that the BCG alignment signal becomes stronger as the BCG stellar mass increases."," Furthermore, based on a subsample of the BCGs whose stellar masses are available, we show that the BCG alignment signal becomes stronger as the BCG stellar mass increases." This result indicates that more massive BCGs lower absolute magnitude) are more likely to align with (withthe major axes of clusters., This result indicates that more massive BCGs (with lower absolute magnitude) are more likely to align with the major axes of clusters. We must take great caution when interpreting the dependence of y on BCG absolute magnitude and stellar mass since the purity of the cluster sample may also depend on the BCG absolute magnitude and stellar mass., We must take great caution when interpreting the dependence of $\gamma$ on BCG absolute magnitude and stellar mass since the purity of the cluster sample may also depend on the BCG absolute magnitude and stellar mass. " As the cluster purity decreases, the alignment signal will decrease too."," As the cluster purity decreases, the alignment signal will decrease too." " The faintest two bins in Figure 14 show null alignment signal, which may also be due to the significantly decreased cluster purity."," The faintest two bins in Figure \ref{fig:gamma_ramag} show null alignment signal, which may also be due to the significantly decreased cluster purity." " Nevertheless, we can still see a trend that y increases as the BCG absolute magnitude increases by looking at the bright end of the samplewhere we are confident about the cluster purity."," Nevertheless, we can still see a trend that $\gamma$ increases as the BCG absolute magnitude increases by looking at the bright end of the samplewhere we are confident about the cluster purity." Evaluating the cluster purity variation w.r.t BCG absolute magnitude turns out tobe difficult, Evaluating the cluster purity variation w.r.t BCG absolute magnitude turns out tobe difficult "seen more transparently in the density-corrected V,,,,. method.",seen more transparently in the density-corrected $\vmod$ method. The real advantage here is that V4. need only be calculated for each galaxy using the selection r-band Petrosian magnitudes after which the GLF (or GSMF) can be determined straightforwardly using different photometry., The real advantage here is that $\vmod$ need only be calculated for each galaxy using the selection $r$ -band Petrosian magnitudes after which the GLF (or GSMF) can be determined straightforwardly using different photometry. When calculating the GLF in a different band (or the GSMF) there is no colour bias in a bin unless a population with a certain colour is only visible over a reduced range of luminosity (mass) within the bin., When calculating the GLF in a different band (or the GSMF) there is no colour bias in a bin unless a population with a certain colour is only visible over a reduced range of luminosity (mass) within the bin. " Note also the GAMA DDP sample is highly complete, which means thatthe calculation of Padp is robust."," Note also the GAMA DDP sample is highly complete, which means thatthe calculation of $\rho_{\rm ddp}$ is robust." " Figure 7 shows a comparison between V,,.x and Vinax.", Figure \ref{fig:volumes} shows a comparison between $\vmod$ and $\vmax$ . " For example, note the flattening of V;,.x in G12 brighter than —15.2 (red line)."," For example, note the flattening of $\vmod$ in G12 brighter than $-15.2$ (red line)." This corresponds to the overdensity at z~0.022 with the underdensity beyond., This corresponds to the overdensity at $z\simeq0.022$ with the underdensity beyond. Brighter galaxies can be seen further but the corrected volume rises slower than the standard Vinax because the DDP is underdense beyond., Brighter galaxies can be seen further but the corrected volume rises slower than the standard $\vmax$ because the DDP is underdense beyond. " In order to estimate GLFs, the completeness is assumed to be unity(c;— 1) in this paper with the area of the survey being 143deg? (one third of this for each region)."," In order to estimate GLFs, the completeness is assumed to be unity$c_i=1$ ) in this paper with the area of the survey being $143\,\sqdeg$ (one third of this for each region)." Figure 8 shows the 7-band GLF computed using the different volume correction methods., Figure \ref{fig:compare-methods} shows the $i$ -band GLF computed using the different volume correction methods. " The V;,4,, method produces much better agreement between the regions than the standard Vinax method.", The $\vmod$ method produces much better agreement between the regions than the standard $\vmax$ method. " The remaining difference between the regions, below <105L in particular, may be the result of the GLF varying between environments or uncertainties in the distances."," The remaining difference between the regions, below $<10^{8}\Lsun$ in particular, may be the result of the GLF varying between environments or uncertainties in the distances." The grey lines in Fig., The grey lines in Fig. 8 represent the GLF using a combined volume over all regions., \ref{fig:compare-methods} represent the GLF using a combined volume over all regions. " This is obtained by modifying paap(Z1i;Zmax,i)Vmax,i in Eq."," This is obtained by modifying $\rho_{\rm ddp}(z_1; z_{{\rm max},i}) \, V_{{\rm max},i}$ in Eq." " 4 to be a sum over all three regions for each galaxy with zmax,; being different in G09+G15 (r« 19.4) compared to G12 (r« 19.8) (see also Avni&Bahcall1980 for combining samples with different effective volumes)."," \ref{eqn:density-correction} to be a sum over all three regions for each galaxy with $z_{{\rm max},i}$ being different in G09+G15 $r<19.4$ ) compared to G12 $r<19.8$ ) (see also \citealt{AB80} for combining samples with different effective volumes)." " Hereafter, this combined V;,4, is used."," Hereafter, this combined $\vmod$ is used." Note also we show GLFs using solar luminosities because we are working towards the GSMF., Note also we show GLFs using solar luminosities because we are working towards the GSMF. The S/N in the 2-band is significantly higher than the SDSS z-band or any of the UKIDSS bands for galaxies in our sample., The S/N in the $i$ -band is significantly higher than the SDSS $z$ -band or any of the UKIDSS bands for galaxies in our sample. Thus we use the i-band as the fiducial band from which to apply stellar ratios., Thus we use the $i$ -band as the fiducial band from which to apply stellar mass-to-light ratios. First we start by looking at the 7-band and comparing the GLF taken with different photometric apertures., First we start by looking at the $i$ -band and comparing the GLF taken with different photometric apertures. " Figure 9((a) shows the {-ραπά GLF using photometry from (i) SDSS pipelinePHOTO,, (ii) as run by Hilletal.(2011) and (iii) as run by Kelvinetal.(2011)."," Figure \ref{fig:compare-lf-magtype}( (a) shows the $i$ -band GLF using photometry from (i) SDSS pipeline, (ii) as run by \citet{hill11} and (iii) as run by \citet{kelvin11}." ". For comparison, the result from Lovedayetal.(2012) at z«0.1 using Petrosian magnitudes and SWML method is also shown The difference between the GLFs in Fig. 9(("," For comparison, the result from \citet{loveday12} at $z<0.1$ using Petrosian magnitudes and SWML method is also shown The difference between the GLFs in Fig. \ref{fig:compare-lf-magtype}( (" a) are generally small except for the The z<0.1 GAMA volume is known to be underdense by about with respect to a larger SDSS volume (see fig.,a) are generally small except for the The $z<0.1$ GAMA volume is known to be underdense by about with respect to a larger SDSS volume (see fig. 20 of Driver 2011)) whereas the z«0.06 GAMA density is similar to the SDSS volume., 20 of \citealt{driver11}) ) whereas the $z<0.06$ GAMA density is similar to the SDSS volume. The faint end differences in Fig. 9((, The faint end differences in Fig. \ref{fig:compare-lf-magtype}( ( a) are generally not significant eerror bars in Fig. 8)),a) are generally not significant error bars in Fig. \ref{fig:compare-methods}) ). " At the bright end, the differences are because the apertures and Sersic fits are recovering more flux from early-typegalaxies than the Petrosian aperture."," At the bright end, the differences are because the apertures and Sersic fits are recovering more flux from early-typegalaxies than the Petrosian aperture." Figure 9((b) compares the GAMA result using Petrosian magnitudes with results using the SDSS NYU-VAGC low-redshift sample (0.0033«z 0.05; Blantonetal. 2005b))., Figure \ref{fig:compare-lf-magtype}( (b) compares the GAMA result using Petrosian magnitudes with results using the SDSS NYU-VAGC low-redshift sample $0.0033 < z < 0.05$ ; \citealt{blanton05nyuvagc}) ). " Ignoringthe differences below 10"" L, which are because of the differing magnitude limits, the Blantonetal.(20054) GLF (DR2) gives a higher number density below 10°Lo."," Ignoringthe differences below $10^{7.5}\Lsun$ , which are because of the differing magnitude limits, the \citet{blanton05} GLF (DR2) gives a higher number density below $10^{9}\Lsun$ ." This can be at least partly explained by the distances used., This can be at least partly explained by the distances used. " The NYU-VAGC uses distances from the Willicketal.(1997) model, tapering to"," The NYU-VAGC uses distances from the \citet{willick97} model, tapering to" The LIGAS survey (Neugebauer et al.,The IRAS survey (Neugebauer et al. 1984) discovered many ultraluminous infrared galaxies (ULIICGs) that emit the bulk of their energy. in infrared. (LR) photons., 1984) discovered many ultraluminous infrared galaxies (ULIRGs) that emit the bulk of their energy in infrared (IR) photons. Since their bolometric Luminosity and the number density are as high as those of quasars. ULIRCGs are among the most energetic objects in the universe.," Since their bolometric luminosity and the number density are as high as those of quasars, ULIRGs are among the most energetic objects in the universe." The most fundamental problem vet to be solved is the energy source of the extremely intense infrared. emission., The most fundamental problem yet to be solved is the energy source of the extremely intense infrared emission. NGC 6240. a gravitationallv ineracting svstem with a complex optical morphology (Fosbiuv Wall 1979: Fried Schulz 1983). is à very interesting example of ULIRG.," NGC 6240, a gravitationally interacting system with a complex optical morphology (Fosbury Wall 1979; Fried Schulz 1983), is a very interesting example of ULIRG." Lts bolometric luminosity reaches 2.4.1Y? L. (Weight. Joseph. Meikle 1984: z=0.0245 and Lo=50 km s.1 1 are assumed).," Its bolometric luminosity reaches $2.4\times10^{12}$ $L_{\odot}$ (Weight, Joseph, Meikle 1984; z=0.0245 and $H_0=50$ km $^{-1}$ $^{-1}$ are assumed)." NGC 6240 is outstanding in several respects., NGC 6240 is outstanding in several respects. lis Ils 10S(1) at 2.121j/n and Fell] 1.64421. line luminosities and the ratio of Hs to bolometric luminosities are the largest. currently known (e.g.. van der Werf ct al.," Its $_2$ $1\rightarrow0S(1)$ at $\mu$ m and [FeII] $\mu$ m line luminosities and the ratio of $_2$ to bolometric luminosities are the largest currently known (e.g., van der Werf et al." 1993)., 1993). Further. its stellar velocity dispersion of 360 kms is among the highest values ever found ina galaxy centre (e.g. Dovon et al.," Further, its stellar velocity dispersion of 360 km/s is among the highest values ever found in a galaxy centre (e.g., Doyon et al." 1994)., 1994). The energv source. of the huge li luminosity is controversial., The energy source of the huge IR luminosity is controversial. Many. HV spectroscopic suclies (e.g. Genzel ot αἱ., Many IR spectroscopic studies (e.g. Genzel et al. 1998: Riceway et al., 1998; Ridgway et al. 1994: Ricke et al., 1994; Rieke et al. 1985: Weight ot al., 1985; Weight et al. 1984) have suggested that main energy. source of the Ji emission is starburst: activity. which is presumably a super-starburst induced by a merger of two galaxies (Joseph Wright 1985: Chevalier Clege 1985).," 1984) have suggested that main energy source of the IR emission is starburst activity, which is presumably a super-starburst induced by a merger of two galaxies (Joseph Wright 1985; Chevalier Clegg 1985)." The erouncbased: optical spectrum can be classifier as LINER. and iJa interpreted as a resut of shock heating (lleckman ct al.," The ground-based optical spectrum can be classified as LINER, and is interpreted as a result of shock heating (Heckman et al." 1987)., 1987). On the other iand. a significant contribution [roni an active galactic nuceus (ΑΝ) similar to Sevfert. ealaxies was also discovered rom ΕΙ spectroscopy (DePov ct al.," On the other hand, a significant contribution from an active galactic nucleus (AGN) similar to Seyfert galaxies was also discovered from IR spectroscopy (DePoy et al." 1986)., 1986). Another hint o ian AGN in NGC 6240 is the presence of compact bright radio cores (Carral et al., Another hint of an AGN in NGC 6240 is the presence of compact bright radio cores (Carral et al. 1990. but see Colbert et al., 1990 but see Colbert et al. L994)., 1994). HST discovered a core that is excited higher than LINER. (Itafanelli et al., discovered a core that is excited higher than LINER (Rafanelli et al. 1997)., 1997). X-ray observation provides an important tool. for investigating both the starburst and AGN activity., X-ray observation provides an important tool for investigating both the starburst and AGN activity. imaging from the VLA FIRST survey (Beckeretal.2003) shows strong emission both in the companion bulge and outside the primary bulge. but not within the primary bulge.,"imaging from the VLA FIRST survey \citep{becker.helfand.ea:first} shows strong emission both in the companion bulge and outside the primary bulge, but not within the primary bulge." The primary bulge is much redder than the bulge of any other blue-centered galaxy and has an Ho equivalent width of only iin emission. despite a very blue region immediately surrounding the red core (Fig.," The primary bulge is much redder than the bulge of any other blue-centered galaxy and has an $\alpha$ equivalent width of only in emission, despite a very blue region immediately surrounding the red core (Fig." 1) and integrated EW(Ha) ~ 6.5 iin emission., 1) and integrated $\alpha$ ) $\sim$ 6.5 in emission. Thus although its identifies NGC 5541 as a rare high-luminosity blue-centered galaxy. its low-luminosity companion probably has more similarities to the rest of our blue-centered galaxy sample than NGC 5541 does.," Thus although its identifies NGC 5541 as a rare high-luminosity blue-centered galaxy, its low-luminosity companion probably has more similarities to the rest of our blue-centered galaxy sample than NGC 5541 does." NGC 5875A has no UZC companion. but its 2MASS color-composite image reveals a large region with distinct JHK-color on the northeast side of the galaxy. resembling à merging companion.," NGC 5875A has no UZC companion, but its 2MASS color-composite image reveals a large region with distinct JHK-color on the northeast side of the galaxy, resembling a merging companion." NGC 7752 appears to be in direct contact with the tidally distorted spiral arm of its larger companion. NGC 7753.," NGC 7752 appears to be in direct contact with the tidally distorted spiral arm of its larger companion, NGC 7753." The arm ts not easily visible at the scale and contrast of Fig., The arm is not easily visible at the scale and contrast of Fig. |., 1. "positive. correspondinglv Aj, takes smaller. value and. A, is around 0.5.","positive, correspondingly $\lambda_{\rm b}$ takes smaller value and $\lambda_{\rm g}$ is around $0.5$." For stars more massive (han 124M.. A even drops below 0.5 for most J.," For stars more massive than $12M_\odot$ , $\lambda$ even drops below $0.5$ for most $R$." " The extreme case in our calculation is lor 20... stars. in which both Aj, and A, evolve to be =3 is clue to the increased SE cllicleney by metal cooling within the galaxies., This suggests that the enhanced GSMF at $z=3$ is due to the increased SF efficiency by metal cooling within the galaxies. Again. the apparent enhancement. in he number of low-mass galaxies in the N216L10mc run compared to the N216L10 run is somewhat dependent on he threshold. density of grouping. therefore it. should. be interpreted with caution.," Again, the apparent enhancement in the number of low-mass galaxies in the N216L10mc run compared to the N216L10 run is somewhat dependent on the threshold density of grouping, therefore it should be interpreted with caution." As the accretion of GM onto galaxies become more ellicient al ο<3 clue to the increased. LGAL cooling by the metals. we expect that the total harvonic mass of galaxies would be more enhanced at 2=1 than at 2=3.," As the accretion of IGM onto galaxies become more efficient at $z<3$ due to the increased IGM cooling by the metals, we expect that the total baryonic mass of galaxies would be more enhanced at $z=1$ than at $z=3$." Figure S. shows the Αποκ at.=3 anced 2=1 in the N288L234 series. and it clearly demonstrates that this expectation is true.," Figure \ref{fig:MF_comp_N288L34} shows the MFs at $z=3$ and $z=1$ in the N288L34 series, and it clearly demonstrates that this expectation is true." " Here we show only the range of Ala,28.2«107AJ... which corresponds to the limiting mass of 32 gas particles."," Here we show only the range of $\Mgas \ge 8.2\times 10^8\,\Msun$, which corresponds to the limiting mass of 32 gas particles." The general trend in the three (star. gas. and total barvon) MES is similar to that we saw in Figure 7.. although the cillerence at 23 between the N288L34 and N288L34mc runs is slightly smaller than in the N2IGLIO series due to poorer resolution.," The general trend in the three (star, gas, and total baryon) MFs is similar to that we saw in Figure \ref{fig:MF_comp}, although the difference at $z=3$ between the N288L34 and N288L34mc runs is slightly smaller than in the N216L10 series due to poorer resolution." Fieure SIP shows most. prominently the enhancement of the total barvonic ME at 2=1 in the N288L34mc run owing to the metal cooling., Figure \ref{fig:MF_comp_N288L34}f f shows most prominently the enhancement of the total baryonic MF at $z=1$ in the N288L34mc run owing to the metal cooling. In panels (ο) Cf). the N288L34 run actually has a longer tail at he most massive-enc than the N288L34mc run.," In panels $e$ ) $f$ ), the N288L34 run actually has a longer tail at the most massive-end than the N288L34mc run." The reason for this feature is not fully clear. but it may. be related to the balance between IGM aceretion and feedback.," The reason for this feature is not fully clear, but it may be related to the balance between IGM accretion and feedback." Owing to metal cooling. IGM accretion rate increases in the mc. run. and the SER. is also enhanced. leading to a stronger feedback.," Owing to metal cooling, IGM accretion rate increases in the 'mc' run, and the SFR is also enhanced, leading to a stronger feedback." The amount of mass loss is greater in low mass galaxies. but the net heating of IGM is more significant for massive galaxies.," The amount of mass loss is greater in low mass galaxies, but the net heating of IGM is more significant for massive galaxies." The mc run has stronger feedback. therefore its feedback. heating may become more significant than ICM acerction for very massive galaxies.," The 'mc' run has stronger feedback, therefore its feedback heating may become more significant than IGM accretion for very massive galaxies." The significant IM. heating suppresses the growth of massive-cnd of mass function [from z=3 to >=| and results in shorter tail for the mc run at z=1 as shown in Figure Sec.f. For a fixed galaxy baryonic mass. the enhancement of star formation bv metal cooling would. decrease the gas mass paction. fa.οAdww/Adivaven.," The significant IGM heating suppresses the growth of massive-end of mass function from $z=3$ to $z=1$ and results in shorter tail for the 'mc' run at $z=1$ as shown in Figure \ref{fig:MF_comp_N288L34}e e,f. For a fixed galaxy baryonic mass, the enhancement of star formation by metal cooling would decrease the gas mass fraction, $\fgas \equiv M_{\rm gas} / M_{\rm baryon}$." Figure 9 shows fax. as a function of galaxy stellar. mass for the N2IGLIO series., Figure \ref{fig:GFrac_evol_N216L10} shows $\fgas$ as a function of galaxy stellar mass for the N216L10 series. ancl (a) shows the data only from. N216L10mc run at >=A. and cach data point corresponds to a simulated galaxy.," Panel $a$ ) shows the data only from N216L10mc run at $z=3$, and each data point corresponds to a simulated galaxy." " To characterise the distribution. we compute the ollowing two quantities in cach logarithmic stellar mass xn: ""average and ""median."," To characterise the distribution, we compute the following two quantities in each logarithmic stellar mass bin: `average' and `median'." " The ‘average’ is the ratio of otal gas mass to total barvonic mass for all the galaxies in cach mass bin. Le... 7,οπμ "," The `average' is the ratio of total gas mass to total baryonic mass for all the galaxies in each mass bin, i.e., $\sum_{i}^{} M_{\rm gas, i} / \sum_{i}^{} M_{\rm baryon, i}$." "The ""median? case is simply the median of fa.. values in cach mass bin.", The `median' case is simply the median of $\fgas$ values in each mass bin. " Both quantities show a similar trend. however. there is a sharper clrop-olf at. Aa;&2.5101AL. for the ""median case in Figure 9aa. This mass-scale corresponds to 32 star xwiicles in the N2IGLIO series."," Both quantities show a similar trend, however, there is a sharper drop-off at $\Mstar \simeq 2.5 \times 10^{7}\,\Msun$ for the `median' case in Figure \ref{fig:GFrac_evol_N216L10}a a. This mass-scale corresponds to 32 star particles in the N216L10 series." " We find tha there are many galaxies with fur.=0 above this mass-scale. which causes the sharp drop-olf in the ""median. line."," We find that there are many galaxies with $\fgas = 0$ above this mass-scale, which causes the sharp drop-off in the `median' line." Below this imiting mass. galaxies are not resolved. well. which results in an underestimate of star formation and an overestimate of fas.," Below this limiting mass, galaxies are not resolved well, which results in an underestimate of star formation and an overestimate of $\fgas$." M we had a higher resolution simulation with finer xuticle masses. this limiting mass-scale would shift to a ower mass.," If we had a higher resolution simulation with finer particle masses, this limiting mass-scale would shift to a lower mass." Therefore the location of this sharp drop-olf is currently determined by the resolution of our simulation., Therefore the location of this sharp drop-off is currently determined by the resolution of our simulation. Llowever. dark matter halos would stop forming stars at some lower limiting halo mass. if we had an infinitely hieh-resolution simulation. This lower limit to the galaxy mass is presumably. determined. by the photoevaporation of gas by the UV. background: radiation (tees1986:Efstathiou2004:Pontzenctal.2008:Okamotoet 2008).," However, dark matter halos would stop forming stars at some lower limiting halo mass, if we had an infinitely high-resolution simulation, This lower limit to the galaxy mass is presumably determined by the photoevaporation of gas by the UV background radiation \citep{Rees:86, Efstathiou:92, Quinn.etal:96,Gnedin:00, Nagamine.etal:04-dla, Pontzen.etal:08, Okamoto.etal:08}." .. Recent works suggest that star formation could be suppressed. by the UV backgroundin halos with Mya;1°ALR at zm3.," Recent works suggest that star formation could be suppressed by the UV backgroundin halos with $M_{\rm halo} \lesssim 10^9\,\Msun$ at $z\sim 3$." " Galaxies with Auc2101AM. would reside in. halos with Alas2210""AL..."," Galaxies with $\Mstar \simeq 2 \times 10^{7}\,\Msun$ would reside in halos with $M_{\rm halo} \approx 2\times 10^9\,\Msun$." " ""Phe N216LI0 series would resolve such a halo with ~280 dark matter particles. and its mass resolution is actually close to the astrophysical limit [or dwarl galaxy formation at z3."," The N216L10 series would resolve such a halo with $\sim 280$ dark matter particles, and its mass resolution is actually close to the astrophysical limit for dwarf galaxy formation at $z\sim 3$." Therefore the sharp drop-oll in sas UU Mau&2sLOτAL. may not be so far [rom the truce answer.," Therefore the sharp drop-off in $\fgas$ at $\Mstar \simeq 2 \times 10^{7}\,\Msun$ may not be so far from the true answer." We find that fya. increases with decreasing Maas at al recishifts. regardless of metal cooling ancl wind effects.," We find that $f_{gas}$ increases with decreasing $\Mstar$ at all redshifts, regardless of metal cooling and wind effects." “Phis trend. is qualitatively consistent with current observations., This trend is qualitatively consistent with current observations. Erbctal.(2006). estimate the eas fraction as a function of stellar mass using the rest-frame UV-selected star-forming ealaxics at z2. and show that the eas fraction decreases with increasing stellar mass.," \citet{Erb.etal:2006} estimate the gas fraction as a function of stellar mass using the rest-frame UV-selected star-forming galaxies at $z \sim 2$, and show that the gas fraction decreases with increasing stellar mass." And using the mean gas ane stellar mass. they find the average ων~0.35. which agrees with the predicted: gas fraction for massive galaxies in our simulation.," And using the mean gas and stellar mass, they find the average $f_{gas} \sim 0.35 $, which agrees with the predicted gas fraction for massive galaxies in our simulation." In accdition. Gehaetal.(2006). reported. tha the average neutral gas fraction is Cfi)=0.6 for the loca chvarl ealaxies selected. from the Sloan Digital Sky Survey.," In addition, \citet{Geha.etal:06} reported that the average neutral gas fraction is $\langle \fgas \rangle = 0.6$ for the local dwarf galaxies selected from the Sloan Digital Sky Survey." " In our N216L10 series with metal cooling. the ""average reaches 0.6 for galaxies with AL,210AJ. αἱ 4."," In our N216L10 series with metal cooling, the `average' $\fgas$ reaches 0.6 for galaxies with $\Mstar \simeq 2\times 10^7\,\Msun$ at $z=3$ 4." " 10bb.ο, dshowtheredshi flevolutiono flan.for the N216L10 series."," \\ref{fig:GFrac_evol_N216L10}b b,c,d show the redshift evolution of $\fgas$for the N216L10 series." " In the runs with metal cooling (N216L10me and N216LI0mw). fas. is lower than in the N2IGLIO run bv 20—30% at all redshifts. for galaxies with λα=10710"" A4.."," In the runs with metal cooling (N216L10mc and N216L10mv), $\fgas$ is lower than in the N216L10 run by $20-30$ at all redshifts for galaxies with $\Mstar = 10^{7.5} - 10^9\,\Msun$ ." This result. suggests. that the metal cooling reduces. a. OWlng to more efficient. star formation., This result suggests that the metal cooling reduces $\fgas$ owing to more efficient star formation. The values of. fi; seem to be more convergent . ⋜∐↿↓↕⋖⋅⊔↓⋜↧⊳∖⊳∖↓∖⇁⋖⋅⊣⊾↓⊔⇂∪∫∖⋯↙⇁↓∪⇀∪⋅∃⊳↓⊔⋯," The values of $\fgas$ seem to be more convergent at the massive-end $\Mstar > 10^9\,\Msun$ )." "⇂∠⊔↿↓∪⊔⊳∖∖⋎⋖⊾∐⊔∠⇂"" .. ⋅"," In addition, we find" This paper has been concerned with the ellect of PSF anisotropy patterns on systematic errors in weak lensing surveys.,This paper has been concerned with the effect of PSF anisotropy patterns on systematic errors in weak lensing surveys. We have suggested the use of galaxy shapes measured in disünct exposures to estimate shear correlations as a way of eliminating the systematic error due to non-recurrent PSF patterns., We have suggested the use of galaxy shapes measured in distinct exposures to estimate shear correlations as a way of eliminating the systematic error due to non-recurrent PSF patterns. showed that recurrent PSF patterns can be accurately measured using a Principal Component Approach.," \citet{Ja05} showed that recurrent PSF patterns can be accurately measured using a Principal Component Approach." " By using these two techniques in lensing pipelines, systematic errors due to generic PSF patterns can be interpolated (and therefore corrected) to high accuracy."," By using these two techniques in lensing pipelines, systematic errors due to generic PSF patterns can be interpolated (and therefore corrected) to high accuracy." " In planning a large-area cosmic shear survey, we have shown that the key factors that enable accurate PSF corrections are: sufficiently many well-measured stars in all parts of the sky; 5-10 exposures per poinüng; sufficiently [ew important principal components, which cannot exceed the number of stars per exposure."," In planning a large-area cosmic shear survey, we have shown that the key factors that enable accurate PSF corrections are: sufficiently many well-measured stars in all parts of the sky; 5-10 exposures per pointing; sufficiently few important principal components, which cannot exceed the number of stars per exposure." " In addition, the principal components can be estimated better if dense stellar fields are imaged on regular intervals, and if there are few changes in the instrument over the course of the survey (as these can introduce new principal components)."," In addition, the principal components can be estimated better if dense stellar fields are imaged on regular intervals, and if there are few changes in the instrument over the course of the survey (as these can introduce new principal components)." Another consideration [or minimizing the number of important principal components is to keep the observing conditions as stable as possible., Another consideration for minimizing the number of important principal components is to keep the observing conditions as stable as possible. " For each underlying physical cause of PSF variation, one can essentially do a Taylor expansion of the PSF pattern with respect to that variable."," For each underlying physical cause of PSF variation, one can essentially do a Taylor expansion of the PSF pattern with respect to that variable." The PCA will need a separate component [or each term in the Taylor expansion which has a significant amplitude., The PCA will need a separate component for each term in the Taylor expansion which has a significant amplitude. Thus. one should try to keep such variations (eg.," Thus, one should try to keep such variations (eg." " locus error, component misalignments, mirror flexure, etc.)"," focus error, component misalignments, mirror flexure, etc.)" small enough that one or two terms in the expansion are sufficient to adequately describe the elTect on the PSF pattern., small enough that one or two terms in the expansion are sufficient to adequately describe the effect on the PSF pattern. One can estimate what limits are sufficient through spot-diagram ray-tracing programs., One can estimate what limits are sufficient through spot-diagram ray-tracing programs. The second goal of this paper was to provide a formalism to estimate residual systematics due to PSF errors., The second goal of this paper was to provide a formalism to estimate residual systematics due to PSF errors. The ingredients needed to apply our formalism are an estimate of typical PSF power spectra and of the number of significant principal components of PSF patterns., The ingredients needed to apply our formalism are an estimate of typical PSF power spectra and of the number of significant principal components of PSF patterns. " For planned surveys, this is best accomplished by generaüng PSF patterns in à given exposure by ray tracing through the telescope opucs."," For planned surveys, this is best accomplished by generating PSF patterns in a given exposure by ray tracing through the telescope optics." Mock surveys can then be generated by modeling the atmosphere and the variation of instrumental parameters over the course of the survey., Mock surveys can then be generated by modeling the atmosphere and the variation of instrumental parameters over the course of the survey. The resulung models of PSF patterns can be used with the formalism of to find telescope parameters and survey strategy that minimize residual systematics., The resulting models of PSF patterns can be used with the formalism of \\ref{pca} to find telescope parameters and survey strategy that minimize residual systematics. " The difficulty in gelling reliable estimates of residual systematics will be in including all relevant factors which may affect the PSF, many of which may be subtle and hard to anticipate."," The difficulty in getting reliable estimates of residual systematics will be in including all relevant factors which may affect the PSF, many of which may be subtle and hard to anticipate." But the benefit of such an exercise is the ability to optimize instrument and survey parameters for lensing measurements., But the benefit of such an exercise is the ability to optimize instrument and survey parameters for lensing measurements. " Further, once data is taken, comparison of the measured principal components with the models will help validate the error analysis."," Further, once data is taken, comparison of the measured principal components with the models will help validate the error analysis." " Our formalism can be applied to survey data to estimate residual systematic errors,", Our formalism can be applied to survey data to estimate residual systematic errors. " If systematics turn out to be significant, empirical estimation allows one to incorporate them in the error budget lor cosmological parameters."," If systematics turn out to be significant, empirical estimation allows one to incorporate them in the error budget for cosmological parameters." " In addition, the following tests provide independent checks of the estimate of systematic errors [rom survey data (note that at least the latter two tests can be applied to model PSF patterns for planned surveys as well):"," In addition, the following tests provide independent checks of the estimate of systematic errors from survey data (note that at least the latter two tests can be applied to model PSF patterns for planned surveys as well):" local universe.,local universe. When the R3 distribution is considered. we find the models produce too large a fraction of simulated sources having HR3=-|.," When the $HR3$ distribution is considered, we find the models produce too large a fraction of simulated sources having $HR3 = -1$." This is most probably caused by the over-abundance of very faint sources produced by the simulations. related to the XLF mismatch.," This is most probably caused by the over-abundance of very faint sources produced by the simulations, related to the XLF mismatch." These sources are detected just above the flux limit in the softer bands. but have count rates which fall below the background level in the hardest band. and hence are measured to have HR3x-|.," These sources are detected just above the flux limit in the softer bands, but have count rates which fall below the background level in the hardest band, and hence are measured to have $HR3 \approx -1$." The statistical analysis strongly rejects the R=ACLy) model. in agreement with the findings of a recent study by Treisteretal. (20043... which was based on deep multi-wavelength data in the GOODS fields.," The statistical analysis strongly rejects the $R=R(L_X)$ model, in agreement with the findings of a recent study by \citet{treister04}, which was based on deep multi-wavelength data in the GOODS fields." These authors tested the //6(Vjj) model of etal. (2003)... alongside a simpler /CVjj). but found that the latter provided a much better description of the data.," These authors tested the $f(N_H)$ model of \citet{ueda03}, alongside a simpler $f(N_H)$, but found that the latter provided a much better description of the data." " By examining the subset of sources satisfying the ""hard"" selection criteria. we can compare the distributions of absorption above logN;,=22 that are found in the sample with those predicted bythe models."," By examining the subset of sources satisfying the “hard” selection criteria, we can compare the distributions of absorption above $N_H = 22$ that are found in the sample with those predicted bythe models." " We have carried out 3D-KS and KS tests on ARI. HR2. and HR3. as before. but only for the ""hard"" selected subsets of the sample and simulations."," We have carried out 3D-KS and KS tests on $HR1$, $HR2$, and $HR3$, as before, but only for the “hard” selected subsets of the sample and simulations." The 3D-KS test rejects each of the ΟΛ) models with high confidence. (both with and without a reflection component included in the model spectra).," The 3D-KS test rejects each of the $f(N_H)$ models with high confidence, (both with and without a reflection component included in the model spectra)." We haveexamined the individual KS test results to determine the source of this large disparity., We haveexamined the individual $KS$ test results to determine the source of this large disparity. We find that the KS probabilities for the best fitting 6=8 model. (with the absorbed power-law spectral model). are 0.0003. 0.76. and 0.12. for HRI. HR2 and HR3 respectively.," We find that the $KS$ probabilities for the best fitting $\beta=8$ model, (with the absorbed power-law spectral model), are 0.0003, 0.76, and 0.12, for $HR1$, $HR2$ and $HR3$ respectively." The equivalent probabilities when an additional reflection component isincluded in the model spectra are 0.0002. 0.77. and 0.29.," The equivalent probabilities when an additional reflection component isincluded in the model spectra are 0.0002, 0.77, and 0.29." " The KS test probabilities do not vary greatly between the different /6N;,) models (excepting the A=0 model).", The $KS$ test probabilities do not vary greatly between the different $f(N_H)$ models (excepting the $R=0$ model). " The HA2 and HAS distributions of all the ΟΛ) models (excepting the A=QO model) provide rather good matches to the HA? and HR3 distributions found in the ""hard"" subset of the sample.", The $HR2$ and $HR3$ distributions of all the $f(N_H)$ models (excepting the $R=0$ model) provide rather good matches to the $HR2$ and $HR3$ distributions found in the “hard” subset of the sample. " The ditferences between the ""hard"" subsets of the JON) models are small. due to the rapid decline in the selected fraction of “input” sources for high absorbing columns (see fig. 39)."," The differences between the “hard” subsets of the $f(N_H)$ models are small, due to the rapid decline in the selected fraction of “input” sources for high absorbing columns (see fig. \ref{nh_det_frac}) )." This acts to diminish the importance of the ditferences between the JON) models above Ny=107 72., This acts to diminish the importance of the differences between the $f(N_H)$ models above $N_H = 10^{22}$ $^{-2}$. The addition of a reflection component to the spectral model improves the KS probability for HR3 by a factor of ~2., The addition of a reflection component to the spectral model improves the KS probability for $HR3$ by a factor of $\sim 2$. " We see that the mismatch between the AAI distributions is much worse in the ""hard"" subset. compared to the sample as a whole."," We see that the mismatch between the $HR1$ distributions is much worse in the “hard” subset, compared to the sample as a whole." " This appears to be due to the overproduction of simulated sources having HAL=I. which is more pronounced in the ""hard"" sub-sample."," This appears to be due to the overproduction of simulated sources having $HR1 = 1$, which is more pronounced in the “hard” sub-sample." " The fraction of the ""hand"" sample with HRI=| is for the field. but ~40% for the model populations."," The fraction of the “hard” sample with $HR1 = 1$ is for the field, but $\sim 40\%$ for the model populations." The disparity could be explained if a number of the heavily absorbed AGN have an additional soft X-ray component in their spectra., The disparity could be explained if a number of the heavily absorbed AGN have an additional soft X-ray component in their spectra. In order to reproduce the distribution of HAL. this phenomenon should occur in around of the heavily absorbed sources.," In order to reproduce the distribution of $HR1$, this phenomenon should occur in around of the heavily absorbed sources." A number of absorbed AGN with excess soft emission have been observed by other authors in samples of spectroscopically identified X-ray sources (e.g. Caccianigaetal.2004... Pageetal. 2005).," A number of absorbed AGN with excess soft emission have been observed by other authors in samples of spectroscopically identified X-ray sources (e.g. \citealt{caccianiga04}, \citealt{page05}) )." This excess component could be due to intense starbursts in the host galaxy. or to ditfuse emission surrounding anAGN embedded in a galaxy cluster.," This excess component could be due to intense starbursts in the host galaxy, or to diffuse emission surrounding anAGN embedded in a galaxy cluster." Alternatively. it could be scattered radiation from the central engine of the absorbed AGN.," Alternatively, it could be scattered radiation from the central engine of the absorbed AGN." " For the simplest toy model of a torus with uniformly density. and a typical opening angle. &,. the fraction of AGN that are heavily absorbed is approximately coste,)."," For the simplest toy model of a torus with uniformly density, and a typical opening angle, $\theta_o$, the fraction of AGN that are heavily absorbed is approximately $cos(\theta_o)$." " So. if we use the size of the ""hard"" fraction of the sample as a measure of the number of absorbed AGN. we can infer a rather wide opening angle of 4,~67."," So, if we use the size of the “hard” fraction of the sample as a measure of the number of absorbed AGN, we can infer a rather wide opening angle of $\theta_o \sim 67\degr$." " However. this estimate does not take into account the effect of the drop in the selection function toward high Αμ. and can only be seen as an upper limit on &,."," However, this estimate does not take into account the effect of the drop in the selection function toward high $N_H$, and can only be seen as an upper limit on $\theta_o$." " We estimate the relative selection function for hard sources by counting the fraction of simulated ""hard"" input sources that have output counterparts relative to that for all input sources.", We estimate the relative selection function for hard sources by counting the fraction of simulated “hard” input sources that have output counterparts relative to that for all input sources. " Applying this correction to the sample. we predict an ""hard"" fraction of ~ 0.8. implying an opening angle of &,~ 37°."," Applying this correction to the sample, we predict an “hard” fraction of $\sim 0.8$ , implying an opening angle of $\theta_o \sim 37\degr$ ." " If in our correction for the relative selection function. we exclude those sources with absorbing column above log),= 24. where our sample constrains the models only weakly. then we find &,= 52°."," If in our correction for the relative selection function, we exclude those sources with absorbing column above $N_H = 24$ , where our sample constrains the models only weakly, then we find $\theta_o \sol 52\degr$ ." We are also able, We are also able "Mens/Mxray is not only a function of d, but also depends very strongly on R, (or the arc radius r4,).","$m_{\rm lens}/m_{\rm xray}$ is not only a function of $d$, but also depends very strongly on $R_x$ (or the arc radius $r_{\rm arc}$ )." " Apparently, each cluster in our sample has quite different rare."," Apparently, each cluster in our sample has quite different $r_{\rm arc}$." " Probably, other mechanisms than the offset effect should play important roles, and the lensing-X-ray mass discrepancy may not be just from one mechanism, but a combination of many effects: (1) The central regions of clusters may be still undergoing dynamical relaxation, and the X-ray gas may not be in good hydrostatic equilibrium."," Probably, other mechanisms than the offset effect should play important roles, and the lensing-X-ray mass discrepancy may not be just from one mechanism, but a combination of many effects: (1) The central regions of clusters may be still undergoing dynamical relaxation, and the X-ray gas may not be in good hydrostatic equilibrium." " Therefore, large errors could be induced in the X-ray measurement of cluster cores, especially for unrelaxed clusters. ("," Therefore, large errors could be induced in the X-ray measurement of cluster cores, especially for unrelaxed clusters. (" 2) The spherical models are too simple to reflect the real mass distribution of clusters.,2) The spherical models are too simple to reflect the real mass distribution of clusters. " The use of more realistic mass model could reduce the lens mass within the arc radius by up to 40%, though values of ~20% are more typical (Bartelmann 1995; Allen 1998). ("," The use of more realistic mass model could reduce the lens mass within the arc radius by up to $40\%$, though values of $\sim 20 \%$ are more typical (Bartelmann 1995; Allen 1998). (" "3) The presence of substructures may complicate our simple spherical lens model, and hence could be a main source of uncertainties in ens.","3) The presence of substructures may complicate our simple spherical lens model, and hence could be a main source of uncertainties in $m_{\rm lens}$." The absence of the secondary arc-like images in most arc-cluster systems may indicate the limitations of the spherical mass distribution in the central regions of clusters., The absence of the secondary arc-like images in most arc-cluster systems may indicate the limitations of the spherical mass distribution in the central regions of clusters. It should be noted that the mass ratios we obtained here are slightly higher than Allen (1998) and Wu (2000) because they unfortunately used a Hubble constant of Ho=50kms!Mpc!.," It should be noted that the mass ratios we obtained here are slightly higher than Allen (1998) and Wu (2000) because they unfortunately used a Hubble constant of $\rm H_0=50 \, km \, s^{-1}Mpc^{-1}$." The use of Hy)=70kms!Mpc! here will of course make the mass discrepancy problem more pronounced.," The use of $\rm H_0=70 \, km \, s^{-1}Mpc^{-1}$ here will of course make the mass discrepancy problem more pronounced." " It should be noted that the gas represents only a 10% perturbation due to the small ratio of gas-to-DM in the central region, likewise the offset of the gas is only a small perturbation (less than 10%) to the otherwise concentric matter density or potential."," It should be noted that the gas represents only a $10\%$ perturbation due to the small ratio of gas-to-DM in the central region, likewise the offset of the gas is only a small perturbation (less than $10\%$ ) to the otherwise concentric matter density or potential." It is unlikely to create a factor of two difference in the lensing-derived enclosed masses within an arc., It is unlikely to create a factor of two difference in the lensing-derived enclosed masses within an arc. " To illustrate the lensing effect of the offset perturbation and triaxiality, we show the critical curves in Figure 4."," To illustrate the lensing effect of the offset perturbation and triaxiality, we show the critical curves in Figure 4." " The solid curves indicate the critical curve of circular NFW plus 6 model without offset, the dotted curves indicate the critical curve of elliptical NFW plus 6 model with offset d=10""."," The solid curves indicate the critical curve of circular NFW plus $\beta$ model without offset, the dotted curves indicate the critical curve of elliptical NFW plus $\beta$ model with offset $d=10''$." " The square and cross denote the center of dark matter and the hot gas, respectively."," The square and cross denote the center of dark matter and the hot gas, respectively." " For the NFW profile, c=4.3,r, 516kpc; for the 6 model, B=0.65,r.150kpc."," For the NFW profile, $c=4.3, r_s=516 \rm kpc$ ; for the $\beta$ model, $\beta=0.65, r_c=150 \rm kpc$." We also introduce the triaxiality with the ellipticity e=0.15 and position angle 6=30°., We also introduce the triaxiality with the ellipticity $e=0.15$ and position angle $\theta=30^{\circ}$. " We also assume the lens and source redshifts z;=0.3, z,=1."," We also assume the lens and source redshifts $z_l=0.3$, $z_s=1$." We can see that the predicted critical curves (dotted lines) have very similar sizes as the predicted critical curves for a benchmark model (solid lines) with the same mass DM and gas mass but in concentric spheres., We can see that the predicted critical curves (dotted lines) have very similar sizes as the predicted critical curves for a benchmark model (solid lines) with the same mass DM and gas mass but in concentric spheres. Early studies have suggested that statistically unrelaxed clusters have larger mass discrepancies than relaxed clusters (Allen 1998; Wu 2000; Richard et al., Early studies have suggested that statistically unrelaxed clusters have larger mass discrepancies than relaxed clusters (Allen 1998; Wu 2000; Richard et al. 2010)., 2010). As Shan et al. (, As Shan et al. ( "2010) have reported, the clusters with large offset of d>10” are all unrelaxed clusters.","2010) have reported, the clusters with large offset of $d>10''$ are all unrelaxed clusters." " If such offsets exist and are big, then they must come into play in our dynamical studies of galaxy cluster, and should not be ignored, especiallyfor unrelaxed clusters."," If such offsets exist and are big, then they must come into play in our dynamical studies of galaxy cluster, and should not be ignored, especiallyfor unrelaxed clusters." Several near-infrared surveys (Muenchetal.2001:Oliveira and mid-infrared measurements (Comerónetal.2000:Persi2000;Testietal.2002;Natta2002:Apa2002) indicate the presence of disks around Brown Dwarfs (BDs).,"Several near-infrared surveys \citep{Muench01,Oliveira02,Liu03,Jayawardhana03} and mid-infrared measurements \citep{Comeron00,Persi00,Testi02,Natta02,Apai02} indicate the presence of disks around Brown Dwarfs (BDs)." In contrast to infrared emission. submillimeter and millimeter emission 15 certainly always optically thin and is an excellent measure for the total dust mass.," In contrast to infrared emission, submillimeter and millimeter emission is certainly always optically thin and is an excellent measure for the total dust mass." An early attempt to detect millimetre continuum emission also from very low-mass stars and suspected BDs was done by Andre&Montmerle(1994)., An early attempt to detect millimetre continuum emission also from very low-mass stars and suspected BDs was done by \citet{Andre94}. . Probably the most sensitive observationof this kind was carried out by Carpenter(2002) using the OVRO interferometer. however at a relatively long wavelength.," Probably the most sensitive observationof this kind was carried out by \citet{Carpenter02} using the OVRO interferometer, however at a relatively long wavelength." We carried out the first successful search for dust continuum emission associated with confirmed BDs. using the bolometer arrays SCUBA at the JCMT and MAMBO at the IRAM 30-m telescope.," We carried out the first successful search for dust continuum emission associated with confirmed BDs, using the bolometer arrays SCUBA at the JCMT and MAMBO at the IRAM 30-m telescope." The survey led to the detection of cireumstellar dust around the two young BDs CFHT-BD-Tau 4 and 6613. which have ages below 10 Myrs.," The survey led to the detection of circumstellar dust around the two young BDs CFHT-BD-Tau 4 and 613, which have ages below 10 Myrs." In the case of field BDs we obtained upper mass limits of a few Moon masses of dust., In the case of field BDs we obtained upper mass limits of a few Moon masses of dust. For BDs in the Pleiades the mass limits are less strict and range 4+ and 7 Earth masses., For BDs in the Pleiades the mass limits are less strict and range 4 and 7 Earth masses. We should note that the data presented for CFHT-BD-Tau 4 together with other ground-based and ISO data allowed the first detailed discussion of a complete spectral energy distribution of a BD. ranging from optical to millimeter wavelengths (Pascuecietal.2003).," We should note that the data presented for CFHT-BD-Tau 4 together with other ground-based and ISO data allowed the first detailed discussion of a complete spectral energy distribution of a BD, ranging from optical to millimeter wavelengths \citep{Pascucci03}." . The detection of these amounts of circumstellar material around two young BDs makes the formation of planets or even planetary systems around BDs a possibility., The detection of these amounts of circumstellar material around two young BDs makes the formation of planets or even planetary systems around BDs a possibility. Therefore. search strategies for planets should include BDs.," Therefore, search strategies for planets should include BDs." In the case of imaging surveys. they might even be the best targets.," In the case of imaging surveys, they might even be the best targets." In. addition. the detection of significant amount. of circumstellar dust carries important information about the formation processes of BDs.," In addition, the detection of significant amount of circumstellar dust carries important information about the formation processes of BDs." These detections. together with the discovery of quite a number of BD binaries (Bouyetal.2003:Burgasseretal. 2003).. do not support fragmentation of circumstellar disks as the general process for BD formation.," These detections, together with the discovery of quite a number of BD binaries \citep{Bouy03,Burgasser03}, do not support fragmentation of circumstellar disks as the general process for BD formation." Other formation scenarios for BDs (Bateetal.2003:Reipurth&Clarke2001:Watkinsetal.1998) include ejection from multiple systems and erosion of star-forming cloudlets by stellar winds and UV radiation from massive stars.," Other formation scenarios for BDs \citep{Bate03, Reipurth01,Watkins98} include ejection from multiple systems and erosion of star-forming cloudlets by stellar winds and UV radiation from massive stars." Disks will certainly have different structures depending on the formation mechanism., Disks will certainly have different structures depending on the formation mechanism. However. statistics 1s still poor and information about the disk structure from. interferometric observations are needed before one can put more definite observational constraints on BD formation scenarios.," However, statistics is still poor and information about the disk structure from interferometric observations are needed before one can put more definite observational constraints on BD formation scenarios." To search for circumstellar material around BDs. we selected relatively young BDs with an age of a few Myrs because these objects should have the highest probability to be associated with disk material.," To search for circumstellar material around BDs, we selected relatively young BDs with an age of a few Myrs because these objects should have the highest probability to be associated with disk material." The nine selected objects are located in Taurus. the & Orionis cluster. IC 348. and the Upper Scorpius OB association (Martínetal.2001:BéjarNajitaetal.2000:Luhman1999;Ardila 2000).," The nine selected objects are located in Taurus, the $\sigma$ Orionis cluster, IC 348, and the Upper Scorpius OB association \citep{Martin01,Bejar01,Najita00,Luhman99,Ardila00}." . For the first three regions. additional selection criteria were the previous detection of Ha emission (Martínetal.2001).. the presence of X-ray emission (Mokler&Stelzer2002;PreibischZin-necker 2001). and the requirement that the objects should be as isolated as possible in order to avoid confusion during the observations with single-dish telescopes.," For the first three regions, additional selection criteria were the previous detection of $\alpha$ emission \citep{Martin01}, the presence of X-ray emission \citep{Mokler02,Preibisch01}, and the requirement that the objects should be as isolated as possible in order to avoid confusion during the observations with single-dish telescopes." The three BDs in the Taurus star-forming region are among the youngest BDs of our target list., The three BDs in the Taurus star-forming region are among the youngest BDs of our target list. They have ages of about MMyr (Martínetal. 2001).., They have ages of about Myr \citep{Martin01}. . The object CFHT-BD-Tau 4 shows the highest Ha emissionamong the Taurus BDs (Martín 2001).. emits X-ray radiation (Mokler&Stelzer2002) and shows mid-infrared excess emission (Pascuecietal. 2003)..," The object CFHT-BD-Tau 4 shows the highest $\alpha$ emissionamong the Taurus BDs \citep{Martin01}, , emits X-ray radiation \citep{Mokler02} and shows mid-infrared excess emission \citep{Pascucci03}. ." small effect of seeing on the spectrophotomoetry should. not significantly: allect our estimates of the CALR evolution as it does not appear to increase with redshift. or to fainter luxes.,"small effect of seeing on the spectrophotometry should not significantly affect our estimates of the CMR evolution as it does not appear to increase with redshift, or to fainter fluxes." Llowever. Figures 1 and 2) also show that the mean GapeeGrab increases with redshift. as does the scatter in his quantity.," However, Figures \ref{sf-z} and \ref{sf-seeing} also show that the mean $g_{spec}-g_{fib}$ increases with redshift, as does the scatter in this quantity." This is not related to seeing but might be oe a separate problem with the SDSS spectrophotometry., This is not related to seeing but might be be a separate problem with the SDSS spectrophotometry. Further investigation of the gasgrip Olset found. it was correlated with the spectral type classification xvameter. being much greater lor redder galaxies with more negative (ligure 3)).," Further investigation of the $g_{spec}-g_{fib}$ offset found it was correlated with the spectral type classification parameter, being much greater for redder galaxies with more negative (Figure \ref{sf-eclass}) )." Note the I2/850 sample all have eclass<0 with a mean of -0.1275., Note the E/S0 sample all have $\rm eclass\leq 0$ with a mean of -0.1275. In the red-band the mean FaeePip is also correlated witheclass. although the elfect is smaller and does not increase strongly with redshift.," In the red-band the mean $r_{spec}-r_{fib}$ is also correlated with, although the effect is smaller and does not increase strongly with redshift." " The dependence on is obviously non-linear and might be better described as eclass"".", The dependence on is obviously non-linear and might be better described as $^2$. To understand why gi; might be alfected byeclass. especially at higher redshifts. we examine the spectra. of four representative [2/50 galaxies of dillerenteclass. all at 2om0.25.," To understand why $g_{spec}$ might be affected by, especially at higher redshifts, we examine the spectra of four representative E/S0 galaxies of different, all at $z>0.25$." Figure 4. illustrates that a more negative eclass is associated with a lower lux in the rest-frame UV. which at these redshifts is observed in the g-band.," Figure \ref{z0.3spec} illustrates that a more negative eclass is associated with a lower flux in the rest-frame UV, which at these redshifts is observed in the $g$ -band." The spectra are particularly noisy at the blue end of the observed: g-band. near 4000A.," The spectra are particularly noisy at the blue end of the observed $g$ -band, near $4000\rm \AA$." " Flux variations [rom noise at the blue end of the spectrum. would. produce correlated. variations in gio, andeclass.", Flux variations from noise at the blue end of the spectrum would produce correlated variations in $g_{spec}$ and. Bul the trend in (gap—drio? With redshift implies that this scatter is not symmetric. but skewed.," But the trend in $\langle g_{spec}-g_{fib}\rangle $ with redshift implies that this scatter is not symmetric, but skewed." As a result. [or spectra with very low signal/noise at these wavelengths. the integrated. «ων Hux is. on average. underestimated. by a few times 0.01 mags.," As a result, for spectra with very low signal/noise at these wavelengths, the integrated $g_{spec}$ flux is, on average, underestimated by a few times 0.01 mags." Although the reason for this discrepancy in the SDSS spectrophotometry is not known. we can try to correct. for it as follows.," Although the reason for this discrepancy in the SDSS spectrophotometry is not known, we can try to correct for it as follows." " We begin by assuming that the olfset between the spectra-cerivecd and. fiber magnitude is not. directly sensitive to redshift or wavelength. but depends only (i) the signal/noise in the spectrum. averaged: across the (ii) the tilt of the spectrum across the band. represented bv eclass. (11) à cross-term (eclass"" signal/noise)"," We begin by assuming that the offset between the spectra-derived and fiber magnitude is not directly sensitive to redshift or wavelength, but depends only (i) the signal/noise in the spectrum, averaged across the (ii) the tilt of the spectrum across the band, represented by $^2$ (iii) a cross-term $^2\times$ signal/noise)." bias toward a negative flux.,bias toward a negative flux. There are (wo reasons for the larger error in the measured. growth rate for this run: 1) the equilibrium: velocity gives rise to mumerical diffusion due to the motion of the Πα variables with respect to the grid: and 2) since the erowing modes are being advected in the azimuthal direction. the maximum growth does not occur at the grid scale.," There are two reasons for the larger error in the measured growth rate for this run: 1) the equilibrium velocity gives rise to numerical diffusion due to the motion of the fluid variables with respect to the grid; and 2) since the growing modes are being advected in the azimuthal direction, the maximum growth does not occur at the grid scale." The latter effect can be seen in Figure 8:5 several grid cells are required [or a well-resolved wavelength., The latter effect can be seen in Figure \ref{f8}; several grid cells are required for a well-resolved wavelength. " In order to resolve smaller wavelengths. we have repeated (his run with £,=6. 3 and 1.5."," In order to resolve smaller wavelengths, we have repeated this run with $L_y = 6$ , $3$ and $1.5$." " The results are plotted in Figure 7 alongwith the results [rom the £,=12 run.", The results are plotted in Figure \ref{f7} alongwith the results from the $L_y = 12$ run. " The measured erowth rate lor the £,=1.5 run is 0.0024.", The measured growth rate for the $L_y = 1.5$ run is $0.0924$. To quantify the ellects of numerical diffusion. we have performed a series of tests similar to Run 2 (external potential in a rotating ΠΙΟ) bul with an overall boost in the azimuthal direction.," To quantify the effects of numerical diffusion, we have performed a series of tests similar to Run 2 (external potential in a rotating frame) but with an overall boost in the azimuthal direction." Figure I0. shows measured growth rates as a function of boost al three different nunmerical resolutions., Figure \ref{f10} shows measured growth rates as a function of boost at three different numerical resolutions. The largest boost magnitude in (his plot corresponds to the velocity at the mininium in V2 for a run with q=1.5., The largest boost magnitude in this plot corresponds to the velocity at the minimum in $N_x^2$ for a run with $q = 1.5$. This highlights the importance of the fluid velocity. wilh respect to the grid in determining numerical camping in ZEUS., This highlights the importance of the fluid velocity with respect to the grid in determining numerical damping in ZEUS. To investigate the effect of differential rotation upon the growth of Chis instability. we have performed a series of simulations with nonzero q.," To investigate the effect of differential rotation upon the growth of this instability, we have performed a series of simulations with nonzero $q$." Intuitively. one expects the instability to be suppressed when the shear rate is greater than the growth rate. iie. for Ri2—1.," Intuitively, one expects the instability to be suppressed when the shear rate is greater than the growth rate, i.e. for ${\rm Ri} \gtrsim -1$." Figure 11. shows growth rates from a series of runs with Α΄ranin>=—0.01 and small. nonzero values of q al three numerical resolutions.," Figure \ref{f11} shows growth rates from a series of runs with $N_{x,min}^2 = -0.01$ and small, nonzero values of $q$ at three numerical resolutions." This ligure clearly demonstrates our main result: convective instability is suppressed bv dillerential rotation., This figure clearly demonstrates our main result: convective instability is suppressed by differential rotation. The expected growth rate from linear theory (/LN2] ab q= 0) is shown in Figure Ll as a dotted line., The expected growth rate from linear theory $\sqrt{|N_x^2|}$ at $\qe = 0$ ) is shown in Figure \ref{f11} as a dotted line. If there is a racial position where g(r)=0 (ie. Ri= —2€). ve at that position looks similar (ο (hat of the previous runs (very little deviationfrom a straight line): these measurements are indicated on the plot with solid points.," If there is a radial position where $\qe(x) = 0$ (i.e., ${\rm Ri} = -\infty$ ), $v_t$ at that position looks similar to that of the previous runs (very little deviationfrom a straight line); these measurements are indicated on the plot with solid points." For q20.055 there is no longer any point where g(r)=0: in that case vj was measured at the radial average between the minimum in .V26r) and (he minimuni in g(r). since (his is where the maximum growth occured.," For $q \gtrsim 0.055$ there is no longer any point where $\qe(x) = 0$; in that case $v_t$ was measured at the radial average between the minimum in $N_x^2(x)$ and the minimum in $\qe(x)$, since this is where the maximum growth occured." The data for these nmeasurenienis. which are indicated in Fieure 11 with open points. is not as clean as it is for the runs with Ri=—o (see Figure 12)).," The data for these measurements, which are indicated in Figure \ref{f11} with open points, is not as clean as it is for the runs with ${\rm Ri} = -\infty$ (see Figure \ref{f12}) )." All of the growth rate measurements in Figure were obtained by a least-squares fit of the data in the range |xLO? 2$ galaxies using the HST NICMOS camera have yielded varying results, largely due to different selection criteria." For example. Papovichetal.(2005) studied the rest-frame optical morphologies of a flux-limited sample of galaxies at zzc2.3 and found that they are generally irregular. Toftetal.(2005).," For example, \cite{pap05} studied the rest-frame optical morphologies of a flux-limited sample of galaxies at $z \approx 2.3$ and found that they are generally irregular. \cite{tof05}," . on the other hand. investigated the rest-frame optical and UV morphologies of distant red galaxies (DRGs) in the Hubble Ultra Deep Field (HUDF). and found both galaxies with irregular morphologies and galaxies with smooth morphologies.," on the other hand, investigated the rest-frame optical and UV morphologies of distant red galaxies (DRGs) in the Hubble Ultra Deep Field (HUDF), and found both galaxies with irregular morphologies and galaxies with smooth morphologies." Additionally. they showed that the rest-frame optical morphologies of these galaxies are much more regular and centrally concentrated than the rest-frame UV morphologies.," Additionally, they showed that the rest-frame optical morphologies of these galaxies are much more regular and centrally concentrated than the rest-frame UV morphologies." With the advent of the Wide Field Camera 3 (WFC3). with its vastly improved sensitivity and resolution compared NICMOS. it has become possible to analyze the rest-frame optical structure of high redshift galaxies with an unprecedented level of detail.," With the advent of the Wide Field Camera 3 (WFC3), with its vastly improved sensitivity and resolution compared to NICMOS, it has become possible to analyze the rest-frame optical structure of high redshift galaxies with an unprecedented level of detail." Cameronetal.(2010) have used data from the first year of observations of the HUDF and the Early Release Science Field to classify the rest-frame UV and optical morphologies of galaxies up to z—3.5., \cite{cam10} have used data from the first year of observations of the HUDF and the Early Release Science Field to classify the rest-frame UV and optical morphologies of galaxies up to $z\sim 3.5$. These authors confirm results by e.g. Krieketal.(2009)... who showed that massive galaxies at formingz>2.3 can galaxiesbe separated into two distinct classes: blue star with irregular morphologies on the one hand. and red quiescent galaxies with smoother morphologies on the other.," These authors confirm results by e.g. \cite{kri09}, who showed that massive galaxies at $z\approx 2.3$ can be separated into two distinct classes: blue star-forming galaxies with irregular morphologies on the one hand, and red quiescent galaxies with smoother morphologies on the other." In this Letter. we extend the previous results using the full two-year ultradeep near-infrared (NIR) imaging of the HUDF taken with the HST WFC3.," In this Letter, we extend the previous results using the full two-year ultradeep near-infrared (NIR) imaging of the HUDF taken with the HST WFC3." These data are the deepest ever obtained in the NIR and make it possible to analyze the morphologies. colors and structure of galaxies to z~3 in the rest-frame optical.," These data are the deepest ever obtained in the NIR and make it possible to analyze the morphologies, colors and structure of galaxies to $z\sim 3$ in the rest-frame optical." Using the incredible sensitivity and angular resolution of the WFC3 images we analyze the rest-frame optical surface brightness profiles of à mass-selected sample of galaxies at z—2., Using the incredible sensitivity and angular resolution of the WFC3 images we analyze the rest-frame optical surface brightness profiles of a mass-selected sample of galaxies at $z\sim 2$. We use these profiles to derive structural parameters such às size and profile shape. and obtain rest-frame colorprofiles.," We use these profiles to derive structural parameters such as size and profile shape, and obtain rest-frame colorprofiles." We study the correlations between these parameters as a function of redshift in order, We study the correlations between these parameters as a function of redshift in order using S seconds in order to search for faster variations.,using 8 seconds in order to search for faster variations. The correctIv-phased baselines are added to produce. effectively. a phased-array response: since the position of the source is adequately known. the in-phase component then represents an unbiased estimate of its [lux density.," The correctly-phased baselines are added to produce, effectively, a phased-array response; since the position of the source is adequately known, the in-phase component then represents an unbiased estimate of its flux density." The typical rms noise on a single 32-seconcl sample when observing in this moce is 6 mJv., The typical rms noise on a single 32-second sample when observing in this mode is 6 mJy. " Since the estimates are unbiased. the noise level reduces as the square root of the integration time,"," Since the estimates are unbiased, the noise level reduces as the square root of the integration time." guez et ((1995) show a map of nearby sources. inclucling the region (45.0|0.06 which has a total Dux. density. of about 5 Jv at this frequency.," guez et (1995) show a map of nearby sources, including the region G45.46+0.06 which has a total flux density of about 5 Jy at this frequency." I. lies about 12 aremin from 11915|105 (compared with a full-width to hallpower primary beam of 6 aremin)., It lies about 12 arcmin from 1915+105 (compared with a full-width to half-power primary beam of 6 arcmin). Using the IE with the pointing centre on 11915|105 an image of the region shows a response of some 3 mJv at the position of the LL LE region., Using the RT with the pointing centre on 1915+105 an image of the region shows a response of some 3 mJy at the position of the H II region. " Since 11915|105 is variable and the observations are in any case usually too short for satisfactory mapping. there is à very small aciditional uncertainty in the flux censities when observing in the ""phased. array’ mode: values below about 1 nv may be unreliable."," Since 1915+105 is variable and the observations are in any case usually too short for satisfactory mapping, there is a very small additional uncertainty in the flux densities when observing in the `phased array' mode; values below about 1 mJy may be unreliable." Some observations were mace in a slightly more extended array. when this problem is not significant.," Some observations were made in a slightly more extended array, when this problem is not significant." The data presented bere run from 1995 Aug LO to 1996 Dee 31., The data presented here run from 1995 Aug 10 to 1996 Dec 31. Individual observations were of varving duration. typically between Lh and 6h.," Individual observations were of varying duration, typically between 1h and 6h." During intervals of pronounced activity it was often possible to observe every day., During intervals of pronounced activity it was often possible to observe every day. Fig., Fig. 1 shows some 9000 points. cach one being a 5-min integration. over the the whole of this time.," 1 shows some 9000 points, each one being a 5-min integration, over the the whole of this time." The overall pattern o£ variations is apparent from this plot. although the details are not.," The overall pattern of variations is apparent from this plot, although the details are not." Fig., Fig. 2 shows a series of individual observations. illustrating the range of behaviours observed.," 2 shows a series of individual observations, illustrating the range of behaviours observed." Particular features include: 1., Particular features include: 1. Smoothlyv-varving flux density. during major [lares with decav times of hours or davs., Smoothly-varying flux density during major flares with decay times of hours or days. The lare starting near ALJD 50275 (1996 July) was characterised. by smooth variations of lux density until it had almost disappeared. at which time the emission became much more crratic.," The flare starting near MJD 50275 (1996 July) was characterised by smooth variations of flux density until it had almost disappeared, at which time the emission became much more erratic." 2., 2. Quasi-periodic oscillations (QPOs) and isolated short Hare events. a selection of which is shown in Fig," Quasi-periodic oscillations (QPOs) and isolated short flare events, a selection of which is shown in Fig." : these are discussed further below., 2; these are discussed further below. 3., 3. Very low flux densities between active periods (e.g. ALJD 50105 — 50220. big.," Very low flux densities between active periods (e.g. MJD 50105 – 50220, Fig." 1)., 1). 'hese remarkable features were first observed in late 1995. ancl reported in LAU. Circulars (Pooley 1995. 1996).," These remarkable features were first observed in late 1995, and reported in IAU Circulars (Pooley 1995, 1996)." One other example has also been reported by guez Mirabel (1997)., One other example has also been reported by guez Mirabel (1997). We note the following features: 1., We note the following features: 1. Phe periods! vary in the range ο 40 min., The `periods' vary in the range 20 – 40 min. The most [requentIy-observed. periods are close to 40 min ancl 25 min: the event reported by guez Mirabel (1097) hack a period. of 30 min., The most frequently-observed periods are close to 40 min and 25 min; the event reported by guez Mirabel (1997) had a period of 30 min. " “Phere are clear instances when a change in the period occurs during an observation (ος, 1996 Alay 26. 1996 Sep 15). and there are also instances when the gap between the maxima is erratic."," There are clear instances when a change in the period occurs during an observation (e.g. 1996 May 26, 1996 Sep 18), and there are also instances when the gap between the maxima is erratic." Isolated. peaks can be characterised. by à. rise-time close to 5 min ancl a decay which is approximately exponential with a time-constant between 12 and. 25 min., Isolated peaks can be characterised by a rise-time close to 5 min and a decay which is approximately exponential with a time-constant between 12 and 25 min. When the peaks are close together. they appear as (quasi-sinusuoidal variations. although it is often observed. that the rise is more rapid than the fall of each evele.," When the peaks are close together, they appear as quasi-sinusuoidal variations, although it is often observed that the rise is more rapid than the fall of each cycle." We suggest that the events themselves are similar. and they are trigecred by releases of energy. on some short time-scale.," We suggest that the events themselves are similar, and they are triggered by releases of energy on some short time-scale." The amplitudes of the individual peaks seldom exceed. 100 mJv (the maximum Ilux density. recorded in the whole of this dataset is 170 mJ)., The amplitudes of the individual peaks seldom exceed 100 mJy (the maximum flux density recorded in the whole of this dataset is 170 mJy). Individual sequences of oscillations, Individual sequences of oscillations halo velocity dispersion can ellectively produce a mildly or non-evolving relation.,halo velocity dispersion can effectively produce a mildly or non-evolving relation. " We show that this is indeed the case for the empirical scaling that we adopt in this paper with a,xa during mergers.", We show that this is indeed the case for the empirical scaling that we adopt in this paper with $\alpha_* \propto \sigma^{-3}$ during mergers. A more physical model might appeal to AGN growth and feedback which are much less ellicient in low mass galaxies. thereby inhibiting quenching. while in massive galaxies. the central black holes are already fully grown and are responsible for quenching the SER.," A more physical model might appeal to AGN growth and feedback which are much less efficient in low mass galaxies, thereby inhibiting quenching, while in massive galaxies, the central black holes are already fully grown and are responsible for quenching the SFR." Inhanced merging at high redshift provides the SSER boost that also lends itself to generating enhanced oa{ο in the resulting massive galaxies., Enhanced merging at high redshift provides the SSFR boost that also lends itself to generating enhanced $\alpha/Fe$ in the resulting massive galaxies. " We predict that there should be rare low mass a/f'e ""refugees"".ὃν perhaps companions of massive IE7ECis. that have avoided the final merging fate and eas blow-out. but nonetheless carry chemical traces of their enhanced SSER. history."," We predict that there should be rare low mass $\alpha/Fe$ ""refugees"", perhaps companions of massive ETGs, that have avoided the final merging fate and gas blow-out, but nonetheless carry chemical traces of their enhanced SSFR history." The role of AGN remains to be elucidated., The role of AGN remains to be elucidated. Quenching of star formation is Commonly attributed to AGN., Quenching of star formation is commonly attributed to AGN. This may be the case for massive galaxies at hieh redshift., This may be the case for massive galaxies at high redshift. Llowever AGN may also play a role in boosting star formation in the low mass systems where the SSER is enhanced., However AGN may also play a role in boosting star formation in the low mass systems where the SSFR is enhanced. A future test of the role of ACGN will be to examine the residuals of a sample with measured AGN accretion rates and star formation rates in order to see whether for example the Ecdcington ratio correlates. (boosting) or anti-correlates (quenching) with SSER., A future test of the role of AGN will be to examine the residuals of a sample with measured AGN accretion rates and star formation rates in order to see whether for example the Eddington ratio correlates (boosting) or anti-correlates (quenching) with SSFR. " Our results suggest. that the majority of galaxies with AZ,©10° M. atoc9d are interacting svstenis.", Our results suggest that the majority of galaxies with $M_* \ltsim 10^{9}$ $_{\odot}$ at $z > 4$ are interacting systems. This prediction. can be tested with future upcoming observational missions. and should. provide a strong test on the carly build-up of galaxies.," This prediction can be tested with future upcoming observational missions, and should provide a strong test on the early build-up of galaxies." In a follow-up paper. we will investigate the individual contribution from. merger triggered star-bursts and GN. with respect to accretion-driven star formation in the context of a full semi-analytic niocel.," In a follow-up paper, we will investigate the individual contribution from merger triggered star-bursts and AGN with respect to accretion-driven star formation in the context of a full semi-analytic model." The authors would like to thank Dan Stark for kindly providing the observational data in electronic. form. and useful comments on the draft., The authors would like to thank Dan Stark for kindly providing the observational data in electronic form and useful comments on the draft. SIX. acknowledges MM from the the Itoval Society Joint Projects Grant 0500523., SK acknowledges support from the the Royal Society Joint Projects Grant JP0869822. "The radio pulsation search at the position of hhas been carried out by using the 25-m radio telescope at Nanshan, operated by Urumqi Astronomical Observatory (UAO).","The radio pulsation search at the position of has been carried out by using the 25-m radio telescope at Nanshan, operated by Urumqi Astronomical Observatory (UAO)." The observing system has a dual-channel cryogenic receiver that receives orthogonal linear polarizations at 18 cm., The observing system has a dual-channel cryogenic receiver that receives orthogonal linear polarizations at 18 cm. " After mixing down to an intermediate frequency, the two polarizations are each fed into a filter bank of 128 contiguous channels, each of width 2.5 MHz."," After mixing down to an intermediate frequency, the two polarizations are each fed into a filter bank of 128 contiguous channels, each of width 2.5 MHz." " The outputs from the channels are then square-law detected, filtered and one-bit sampled at 0.5 ms interval."," The outputs from the channels are then square-law detected, filtered and one-bit sampled at 0.5 ms interval." The data streams of all 256 channels are written to disk for subsequent off-line processing., The data streams of all 256 channels are written to disk for subsequent off-line processing. " For more details about this system, please refer to Wang et al. ("," For more details about this system, please refer to Wang et al. (" 2001).,2001). " In our observation, we did not find any convincing signal and we placed an upper-limit for any pulsed radio emission of 0.1 mJy at the position ofJ202131."," In our observation, we did not find any convincing signal and we placed an upper-limit for any pulsed radio emission of 0.1 mJy at the position of." 0+402645.. We have also searched for any radio counterpart for wwith the data from the NVSS database. (, We have also searched for any radio counterpart for with the data from the NVSS database. ( Condon et al.,Condon et al. 1998)., 1998). " Interestingly, we have identified radio excesses within the y—ray error circle of (see Figure 7))."," Interestingly, we have identified radio excesses within the $\gamma-$ ray error circle of (see Figure \ref{nvss1}) )." A 6x arcmin? close-up view centered on the nominal y—ray position of rreported in Abdo et al. (, A $6\times6$ $^{2}$ close-up view centered on the nominal $\gamma-$ ray position of reported in Abdo et al. ( 2009a) is displayed in Figure 8..,2009a) is displayed in Figure \ref{nvss2}. Radio contours calculated at the levels between 10—25 mJy/beam are overlaid., Radio contours calculated at the levels between $10-25$ mJy/beam are overlaid. We have identified a feature with a size of about 3 arcminx1.5 arcmin in the center of this radio map., We have identified a feature with a size of about 3 $\times$ 1.5 arcmin in the center of this radio map. The peak of this radio feature is found to be at the south-east from the position ofJ202131., The peak of this radio feature is found to be at the south-east from the position of. "0+402645.. Apart from the aforementioned feature, another radio excess extends for ~3 arcmin from tto the north-west."," Apart from the aforementioned feature, another radio excess extends for $\sim3$ arcmin from to the north-west." Adopting the FWHM of the beam and the rms fluctuation of the image of 45 arcsec and 0.45 mJy/beam respectively (cf., Adopting the FWHM of the beam and the rms fluctuation of the image of 45 arcsec and 0.45 mJy/beam respectively (cf. Condon et al., Condon et al. " 1998), we estimated the flux densities at 1.4 GHz of the southeastern and the northwestern features to be 139+4 mJy and 85+2 mJy respectively."," 1998), we estimated the flux densities at 1.4 GHz of the southeastern and the northwestern features to be $139\pm4$ mJy and $85\pm2$ mJy respectively." " These correspond to (5.84+0.17)x10!"" ergs cm~? s! and (3.57+0.08)x10!"" ergscm ? s! for an effective bandwidth of 42 MHz respectively.", These correspond to $(5.84\pm0.17)\times10^{-17}$ ergs $^{-2}$ $^{-1}$ and $(3.57\pm0.08)\times10^{-17}$ ergs $^{-2}$ $^{-1}$ for an effective bandwidth of 42 MHz respectively. It is interesting to notice that iis located approximately in between this two features., It is interesting to notice that is located approximately in between this two features. " If such alignment is confirmed, this will suggest a possible bipolar outflow from the pulsar."," If such alignment is confirmed, this will suggest a possible bipolar outflow from the pulsar." " Unfortunately, the limited angular resolution of NVSS data does not allow us to conclude this possible alignment."," Unfortunately, the limited angular resolution of NVSS data does not allow us to conclude this possible alignment." Future observation with the dedicated high resolution aperture synthesis by VLA can help us to confirm (or refute) this suggested scenario., Future observation with the dedicated high resolution aperture synthesis by VLA can help us to confirm (or refute) this suggested scenario. With the already publicly available data of the y—ray LAT All-Sky survey we have carried out an analysis of ccentered at the accurate X-ray position derived by analyzing data (see Sec 2.1)., With the already publicly available data of the $\gamma-$ ray LAT All-Sky survey we have carried out an analysis of centered at the accurate X-ray position derived by analyzing data (see Sec 2.1). We have studied its y—ray spectral and temporal properties in details., We have studied its $\gamma-$ ray spectral and temporal properties in details. In order to get the most significant results for the spectral analysis we took all available events from the start of the LAT All-Sky survey 4 August 2008 until 26 September, In order to get the most significant results for the spectral analysis we took all available events from the start of the LAT All-Sky survey 4 August 2008 until 26 September see (heir Fig.,see their Fig. 2: Belt et al. (, 2; Bett et al. ( 2007). see their Fie.,"2007), see their Fig." 13)- the axis ratio q used in (he present paper is equal to the ratio of the semi-major axes c/a in (hese papers., 13)- the axis ratio $q$ used in the present paper is equal to the ratio of the semi-major axes $c/a$ in these papers. Thus. either M31 is an unsual galaxy. or the simulations need to include additional physics such as the ellect of barvons that could affect the shape of the halo.," Thus, either M31 is an unsual galaxy, or the simulations need to include additional physics such as the effect of baryons that could affect the shape of the halo." Further. a moderate variation in HI gas dispersion results in a less flattened halo as shown in Section 5. point 3.," Further, a moderate variation in HI gas dispersion results in a less flattened halo as shown in Section 5, point 3." The III scalehight constraint. as applied in this paper is ideally suited for application to gas-rich. late-tvpe spiral galaxies with an extended III disk.," The HI scalehight constraint as applied in this paper is ideally suited for application to gas-rich, late-type spiral galaxies with an extended HI disk." " In order to be useful as a constraint. the IHE scale height data should be available bevond 3 - 4 HR, and even Father out in the galaxy."," In order to be useful as a constraint, the HI scale height data should be available beyond 3 - 4 $R_{d}$ and even farther out in the galaxy." This is where the disk gravitational force begins to drop out and the dark matter halo takes over., This is where the disk gravitational force begins to drop out and the dark matter halo takes over. We note that obtaining the II scale height data is an observationallv challenging task (Sancisi Allen 1979). and therein lies the main diffieultv in using this method.," We note that obtaining the HI scale height data is an observationally challenging task (Sancisi Allen 1979), and therein lies the main difficulty in using this method." As far as our work is concerned. the observational data (Braun 1991) gives only three data points bevond Ro — 3424.," As far as our work is concerned, the observational data (Braun 1991) gives only three data points beyond R = $R_{d}$." " We consider the region only bevond R = 342, following the Galaxy case (Naravan et al.", We consider the region only beyond R = $R_{d}$ following the Galaxy case (Narayan et al. 2005)., 2005). Also. the irregularity or the scatter in (he observed data in (he inner region suggests the presence of a bar or spiral arn or some unknown structure. and is therefore excluded from the analysis.," Also, the irregularity or the scatter in the observed data in the inner region suggests the presence of a bar or spiral arm or some unknown structure, and is therefore excluded from the analysis." In Fig.G we illustrate the above point by plotting (he halo surface density within the I scale heieht. as well as the corresponding values for the bulge. stars. and HII gas versus the radius.," In Fig.6 we illustrate the above point by plotting the halo surface density within the HI scale height, as well as the corresponding values for the bulge, stars, and HI gas versus the radius." For using the III scale height constraint. the vertical [orce close to the galactic mid-plane is needed. (his is why the surface density of the halo within the ILE scale height is included.," For using the HI scale height constraint, the vertical force close to the galactic mid-plane is needed, this is why the surface density of the halo within the HI scale height is included." This figure shows that the halo surface density just begins to take over the stellar density at the point bevond which we do not have any observed data., This figure shows that the halo surface density just begins to take over the stellar density at the point beyond which we do not have any observed data. Availability of more data points in (he outer parts. with lower error-bars. is (hus clearly desirable aud would vield a üghter constraint on the halo shape and the density prolile.," Availability of more data points in the outer parts, with lower error-bars, is thus clearly desirable and would yield a tighter constraint on the halo shape and the density profile." The calculated rotation curve does not depend on (he shape ol the halo (q)., The calculated rotation curve does not depend on the shape of the halo $q$ ). All the q values give equally good fits to the observed data., All the $q$ values give equally good fits to the observed data. Surprisingly. the 47 minima for the rotation curve and the IL} scale height data. taken separately. lie on different regions of the grid.," Surprisingly, the ${\chi}^2$ minima for the rotation curve and the HI scale height data, taken separately, lie on different regions of the grid." The best-fit to the rotation curve alone gives high values of the central density and small values of core radius., The best-fit to the rotation curve alone gives high values of the central density and small values of core radius. The best-fit to the scale height data. on the other hand. gives a lower central density and a larger core radius.," The best-fit to the scale height data, on the other hand, gives a lower central density and a larger core radius." Geehan et al. (, Geehan et al. ( 2006) obtained a best-Lit pj of 0.033 ΔΙ. * (somewhat higher than the value we get) and /2. of 8.2 kpe. probably. because they had used (he rotation curve as the only constraint.,"2006) obtained a best-fit $\rho_{0}$ of 0.033 $_{\odot}$ $^{-3}$ (somewhat higher than the value we get) and $R_{c}$ of 8.2 kpc, probably because they had used the rotation curve as the only constraint." We. on the other hand. have used (wo complementary constraints: (he planar one involving the," We, on the other hand, have used two complementary constraints; the planar one involving the" the rest-frame UV range. in particular the mid-UV.,"the rest-frame UV range, in particular the mid-UV." The first high : red galaxies detected were two fait radio sources frou the Licden-Berkcley Deep. Survey (LBDS): LBDS 53N091 (2—1.55) aud LBDS 53W069 (2 —1.13) (Duulopetal.1996:Spiurad1997:Dun-lopetal. 1999).," The first high $z$ red galaxies detected were two faint radio sources from the Lieden-Berkeley Deep Survey (LBDS): LBDS 53W091 $z=$ 1.55) and LBDS 53W069 $z=$ 1.43) \citep{dunlop96,spinrad97,dunlop99}." . The aualvsis of these svstenis was soon a subject of much debate., The analysis of these systems was soon a subject of much debate. " For instance. Spinradctal.(1997) determined an age of 3.5 Cyr for LBDS 53N091. which posed complicatious to explain galaxy formation ""under au Eiustein-De Sitter universe."," For instance, \citet{spinrad97} determined an age of 3.5 Gyr for LBDS 53W091, which posed complications to explain galaxy formation under an Einstein-De Sitter universe." This age was soon contested bv a seres of authors (Druzual&Alaeris1997:IIleapetal.1998:Yi2000) that derived much vounger ages (<2 Cyr). which allowed for more comfortable estimates for the formation redshift (i£) of the galaxies.," This age was soon contested by a series of authors \citep{bruzual97,heap98,yi00} that derived much younger ages $<$ 2 Gyr), which allowed for more comfortable estimates for the formation redshift $z_{F}$ ) of the galaxies." Subsequeu analvses revived the polemic by coufinüus the first deteriunuations. bo. ascribing ages du excess of 3 Cyr (Nolanetal.2003:PFerreras&Yi 2001).," Subsequent analyses revived the polemic by confirming the first determinations, i.e. ascribing ages in excess of 3 Gyr \citep{nolan03,ferreras04}." Aside frou the different inethodologies used for the age deteruriuations. Hf was clear that our poor knowledge of the UV spectrum of the prestunably well understood. MS sars (emsPeterson.Dorman&Rood2001) was (aud still is to some extent) a major drawback that hews prevented the unambiguous deterumination of the main properties (age and chemical colmposition) of these distant svstenis.," Aside from the different methodologies used for the age determinations, it was clear that our poor knowledge of the UV spectrum of the presumably well understood MS stars \citep[e.g.,][]{peterson01} was (and still is to some extent) a major drawback that has prevented the unambiguous determination of the main properties (age and chemical composition) of these distant systems." More receutlv. a series of deep surveys have Όσοι conducted. (Cimattietal.2002:Abraham2001:MeCarthyetal.2001) and now iuclude well over 300 svstenis with similar spectrophotometric properties as those of the prototypical LBDS S3WoO9L.," More recently, a series of deep surveys have been conducted \citep{cimatti02,abraham04,mccarthy04} and now include well over 300 systems with similar spectrophotometric properties as those of the prototypical LBDS 53W091." Ciiiattietal(2008) presenteκα what perhaps is the best spectrum represeutative of distant red objects., \citet{cimatti08} presented what perhaps is the best spectrum representative of distant red objects. Within the Galaxy Mass Assembly ultra-deep Sky. Survey (CALASS) program. thev selected 13 passive galaxies (with 1.3<2 2.0) ou the basis of their red UV color. defined as the magnitude differcuce between two bauds (cach of LOO wwidtl) centered at 200 Yand 3300A.. aud coustructed astacked spectrum that totalled nearly 500. hours of observing time at the Χαν Large Telescope.," Within the Galaxy Mass Assembly ultra-deep Sky Survey (GMASS) program, they selected 13 passive galaxies (with $1.3 < z < 2.0$ ) on the basis of their red UV color, defined as the magnitude difference between two bands (each of 400 width) centered at 2900 and 3300, and constructed a spectrum that totalled nearly 500 hours of observing time at the Very Large Telescope." By conrpariue that spectra with single stellar populations (SSPs) from several population svuthesis codes (Bruzuall&Charlot2003:Maraston 2005).. they determined. from the rest-frame UV alone. ages that ranged from 0.7 to 2.8 Cir aud metallicities in the range 0.2 to 1.5 Z..," By comparing that spectrum with single stellar populations (SSPs) from several population synthesis codes \citep{bruzual03,maraston05}, they determined, from the rest-frame UV alone, ages that ranged from 0.7 to 2.8 Gyr and metallicities in the range 0.2 to 1.5 $Z_{\odot}$ ." By adding to the comparison near and iid IR photometric data. thewv significantly constrained the ages to L1.6 Cov and fonud that Z=Z.. provided the best results.," By adding to the comparison near and mid IR photometric data, they significantly constrained the ages to 1–1.6 Gyr and found that $Z=Z_{\odot}$ provided the best results." Iu Fig. 3..," In Fig. \ref{fig:gmass_seds}," we show the CALASSstacked spectrum of the 13 red galaxies (black) together with three different SSPs of various ages and chemical compositions., we show the GMASS spectrum of the 13 red galaxies (black) together with three different SSPs of various ages and chemical compositions. As a qualitative demonstration of the AMD in the UV. we uote that the observed spectrum is verv simular to the iuiddle two SSP fluxes constructed with quite differcut parameters.," As a qualitative demonstration of the AMD in the UV, we note that the observed spectrum is very similar to the middle two SSP fluxes constructed with quite different parameters." It is bevoud the scope of this paper to discuss any detail ou the procedures so far delevoped to establish the age and chemical composition of distant systems., It is beyond the scope of this paper to discuss any detail on the procedures so far delevoped to establish the age and chemical composition of distant systems. We. nevertheless believe that iu general the spectroplotometiic analysis of distant objects has been carried out with stella libraries that might be inadequate. in particular concerning the spectral resolution and capabilities of represcuting real stars.," We, nevertheless, believe that in general the spectrophotometric analysis of distant objects has been carried out with stellar libraries that might be inadequate, in particular concerning the spectral resolution and capabilities of representing real stars." Back in 2002 the Stellar Atmospheres aud. Populatious Research Group (GrAPEsfor its designation in spanish at the Tustituto Nacional de Astrofisica. Ópptica Y Llectróunuica initiated a project aimed at providiug updated stellar tools for the analvsis of the UV spectra of a varietv of stellar agerceates. mainly evolved ones.," Back in 2002 the Stellar Atmospheres and Populations Research Group (GrAPEs–for its designation in spanish) at the Instituto Nacional de sica, Ópptica y Electrónnica initiated a project aimed at providing updated stellar tools for the analysis of the UV spectra of a variety of stellar aggregates, mainly evolved ones." The overall project consists iu four main steps. παλ] aj- the creation of a theoretical stellar database that we have calledUVBLUE?.. br the conrparison of such data base with observational stellar data. c)- the calculation of a set of svuthetic SEDs of SSPs :id their validation through a comparison with observations of a salmple of Galactic globular clusters. d)- construction of models for dating local cllipticals aud distant τος ealaxies.," The overall project consists in four main steps, namely a)- the creation of a theoretical stellar database that we have called, b)- the comparison of such data base with observational stellar data, c)- the calculation of a set of synthetic SEDs of SSPs and their validation through a comparison with observations of a sample of Galactic globular clusters, d)- construction of models for dating local ellipticals and distant red galaxies." In Chavez(2009).. we prescuted a παπα of the results obtained im steps (a) and (b) aud the reacer is referred. to that paper aud the original references for a detailed description of the project (Rodriguez-Merinoetal.2005:Chavezct 2007).," In \citet{chavez09}, we presented a summary of the results obtained in steps (a) and (b) and the reader is referred to that paper and the original references for a detailed description of the project \citep{lino05,chavez07}." . Tn what follows. we elaborate on the third step.," In what follows, we elaborate on the third step." Iu Chavezetal.(2009) we presented the first theoretical analysis of the UV integrated spectra of evolved SSPs (seealsoMarastonetal.2009.forvounepopulatiouxs).., In \citet{chavezetal09} we presented the first theoretical analysis of the UV integrated spectra of evolved SSPs \citep[see also][for young populations]{maraston09}. We focused on particular absorption lines aud bleuds to establish. through the use of spectroscopic imdices. their ychavior iu terms of age and chemical composition.," We focused on particular absorption lines and blends to establish, through the use of spectroscopic indices, their behavior in terms of age and chemical composition." We identified several interesting tendencies. such as the ow general scusitivity of the indices to age aud the remarkably distinct behavior of the indices Fe 2332 and Fe 2102. at super solar regimes (in fact. we xopose these indicesas a promising tool to establish he age in moetal-nrich svstems).," We identified several interesting tendencies, such as the low general sensitivity of the indices to age and the remarkably distinct behavior of the indices Fe 2332 and Fe 2402, at super solar regimes (in fact, we propose these indicesas a promising tool to establish the age in metal-rich systems)." Svuthetic iudices were compared to IUE low resolution observations of prototypical, Synthetic indices were compared to IUE low resolution observations of prototypical deposition of a significant amount of charges in pixels along the row during the serial read-out process.,deposition of a significant amount of charges in pixels along the row during the serial read-out process. These “streak” events were removed by using the program in CIAO., These “streak” events were removed by using the program in CIAO. The total available times for cach observation. after the scereeniug. are listed iu Table 1..," The total available times for each observation, after the screening, are listed in Table \ref{obslog}." (Jausenctal.2001) also observed SN 1987À aud the 30 Dor region several times: the satellite has a spatial resolution of ~1 and a relatively wide FOV with the radius of15'.," \citep{jansen} also observed SN 1987A and the 30 Dor region several times; the satellite has a spatial resolution of $\sim$ and a relatively wide FOV with the radius of." . We selected wo observations (Observation ID = 0101660301. aud 0113020201: hereafter Obs.3 aud 1D. which cover 303 Dor C and are relatively free from Ligh backeround fares due o low-enerev protous.," We selected two observations (Observation ID = 0104660301 and 0113020201; hereafter Obs.3 and 4), which cover 30 Dor C and are relatively free from high background flares due to low-energy protons." The observed dates and argeted positious are shown in Table 1.., The observed dates and targeted positions are shown in Table \ref{obslog}. In both observations. only the metal oxide seuiconductors (MOS) CCDs. which have au cucrey range of L110.0 keV and a similar cucrey resolution toChandra. αποetal.2001) were operated in the ull-fiaue mode with the medium filter (Stephanetal.1996:Villa199s) for blocking ultra-violet photous.," In both observations, only the metal oxide semiconductors (MOS) CCDs, which have an energy range of 0.1–10.0 keV and a similar energy resolution to, \citep{turner} were operated in the full-frame mode with the medium filter \citep{stephan,villa} for blocking ultra-violet photons." The data reductions aud analyses were nade using the Staudard Analvsis System (SAS: Watson et al 2001) version SLA: we performed the basic pipeline process following the SAS enide., The data reductions and analyses were made using the Standard Analysis System (SAS; Watson et al 2001) version 5.4.1; we performed the basic pipeline process following the SAS guide. The background level was larecly changed. particularly in Obs.," The background level was largely changed, particularly in Obs." L. heuce we removed the data with a high backeround level (20.6 cuts + iu the 10.015.0 keV baud).," 4, hence we removed the data with a high background level $>$ 0.6 cnts $^{-1}$ in the 10.0–15.0 keV band)." The exposure times in cach observation after the screeniues are listed in Table 1.., The exposure times in each observation after the screenings are listed in Table \ref{obslog}. Fieve l1 shows the soft (0.72.0 keV) and hard (2.0.7.0 keV) wand iuages around 30 Dor C. in which the two observations (Obs.1 and 2) are combined with a correction of the exposure times.," Figure \ref{images} shows the soft (0.7–2.0 keV) and hard (2.0–7.0 keV) band images around 30 Dor C, in which the two observations (Obs.1 and 2) are combined with a correction of the exposure times." A clear shell-like structure with a radius of ~ (UoLO pevadius at the 50 kpc distance) is seen in both bands., A clear shell-like structure with a radius of $\sim$ $R\sim 40$ pc-radius at the 50 kpc distance) is seen in both bands. Iu detail. however. the uorphologies are differeut from) each other: the eutire shell is seen im the soft baud. whereas he hard N-vavs are visible oulv at the western vat.," In detail, however, the morphologies are different from each other; the entire shell is seen in the soft band, whereas the hard X-rays are visible only at the western part." Catalogned SNRs. the Wouevcomb nebula (SNR 69.3) and SN 1987À are also seen uaiulv iu the soft baud (see Figure 1)).," Catalogued SNRs, the Honeycomb nebula (SNR $-$ 69.3) and SN 1987A are also seen mainly in the soft band (see Figure \ref{images}) )." The Nav catures of these objects have been reported with (Deunerlotal.2000) and (Burrowseal.2000:Parket2002:Michael monitoring observatious.," The X-ray features of these objects have been reported with \citep{dennerl} and \citep{burrows,park,michael} monitoring observations." Iu addition to the diffuse structure. sole poiut-like sources are found inside 30 Dor C. The exposure time of the observations are short. most of the data suffer from a high background. and the spatial resolution is not sufficient.," In addition to the diffuse structure, some point-like sources are found inside 30 Dor C. The exposure time of the observations are short, most of the data suffer from a high background, and the spatial resolution is not sufficient." " Ποσο, we concentrated on the data for the point-source search anc analysis."," Hence, we concentrated on the data for the point-source search and analysis." " At first. point sources were searched for with heweedetect softwarcin the 0.58.0 keV baud Πμασος, then manually iuspectecd for any spurious oomt-like structure due mainly to a part of he diffuse enmuüssiou."," At first, point sources were searched for with the in the 0.5–8.0 keV band images, then manually inspected for any spurious point-like structure due mainly to a part of the diffuse emission." We lus found six poiut sources with a significance level of 7.06. as shown in Figure 1 aud Table 2..," We thus found six point sources with a significance level of $>$ $\sigma$, as shown in Figure \ref{images} and Table \ref{point}." For these six yolut sources. we searched for optical. infrared. and radio counterparts. and found that three (No.l. 3. aud. 1) coincide at the yositions of the xiehtest star clusters: a. 2. and 5 (Lortet&Testor198 L).," For these six point sources, we searched for optical, infrared, and radio counterparts, and found that three (No.1, 3, and 4) coincide at the positions of the brightest star clusters: $\alpha$, $\beta$, and $\gamma$ \citep{lortet}." . We therefore checked further for any N-ray endssion from the other clusters (8. €. aud C). which are also members of the OB association LII 90 (Lucke&Hodge1970). eunconipassed. by the 30 Dor € shell.," We therefore checked further for any X-ray emission from the other clusters $\delta$ , $\epsilon$, and $\zeta$ ), which are also members of the OB association LH 90 \citep{lucke} encompassed by the 30 Dor C shell." ILowever. we fouud no excess N-ravs frou these clusters at the 236 limit.," However, we found no excess X-rays from these clusters at the $\sigma$ limit." We also searched for N-aay counterparts fromROSAT PSPC aud URI catalogues (Iaberl&Pictsch1999:Sasaki.Haberl.&Pictsch 2000).. but found no candidate.," We also searched for X-ray counterparts from PSPC and HRI catalogues \citep{haberl,sasaki}, but found no candidate." Tn the observatious. we can see that the diffuse structure consists of several shell fraeineuts (see Figure 1)). aud the whole structure is widely spread over the two observed regions with different configurations of the CCD types (back- and frout-illunated).," In the observations, we can see that the diffuse structure consists of several shell fragments (see Figure \ref{images}) ), and the whole structure is widely spread over the two observed regions with different configurations of the CCD types (back-illuminated and front-illuminated)." Therefore. a spectral analvsis ou allof the diffuse structure is technically and scientifically complicated.," Therefore, a spectral analysis on allof the diffuse structure is technically and scientifically complicated." For this reason. we divided the diffuse structure iuto four regions (hereafter shells ÀD). as shown in,"For this reason, we divided the diffuse structure into four regions (hereafter shells A–D), as shown in" The resultiugC» abundance is lavecrOo for ugher trial eniperature.,The resulting abundance is larger for higher trial temperature. This is a result of the fact that Iv shell clectrous are increasingly stripped off for higher eniperatures. and hence a higher mon abundance is necessary to account for the observed equivaleut width.," This is a result of the fact that $K-$ shell electrons are increasingly stripped off for higher temperatures, and hence a higher iron abundance is necessary to account for the observed equivalent width." The sunallest abuudauce is obtained to be 2.11.17 at a eniperature of 7 keV. which impies the lower limut of the abundance to be 1.35.," The smallest abundance is obtained to be $\pm 1.1\odot$ at a temperature of 7 keV, which implies the lower limit of the abundance to be $\odot$." Note. however. that this is a very conservative lower limit. aud the abundance based on the iron omission line is probably several times as large as that of Solar composition.," Note, however, that this is a very conservative lower limit, and the abundance based on the iron emission line is probably several times as large as that of Solar composition." This is in conurast to the abundances of CVs which have recently been measured to be xub-Solar. such as 0.63+0.087. for (Fujimoto alc Tshida 1997). 0.1105+ for (Ishida 1997). alc ~O.L+ for SS Cre (Done and Osborne 1997).," This is in contrast to the abundances of CVs which have recently been measured to be sub-Solar, such as $0.63\pm 0.08\odot$ for (Fujimoto and Ishida 1997), $0.4^{+0.2}_{-0.1}\odot$ for (Ishida 1997), and $\sim 0.4\odot$ for SS Cyg (Done and Osborne 1997)." A lint for a larger abuudance than Solav is obtained only for (Misaki 1996)., A hint for a larger abundance than Solar is obtained only for (Misaki 1996). Since we have obtained the abundance iu the previous section. we have next calculated the bolometric Iuuinositv of the hard N-vav componcut.," Since we have obtained the abundance in the previous section, we have next calculated the bolometric luminosity of the hard X-ray component." To do this. we have adopted the volune enüssivitv formmlas of the optically thin plasma approximated by MeCray (1987). but modified to take iuto account the abundance effects.," To do this, we have adopted the volume emissivity formulas of the optically thin plasma approximated by McCray (1987), but modified to take into account the abundance effects." where T5 is the plasiua temperature in 109 Ik. The first term on the right haud side is the volume emissivitv for the line cussion which is proportional to the abundance., where $T_6$ is the plasma temperature in $10^6$ K. The first term on the right hand side is the volume emissivity for the line emission which is proportional to the abundance. The secoud term represeuts that oftιο frec-free. CLUSSIOL., The second term represents that of the free-free emission. Note that the first terii is ereater tiui the second teri. in the rauge T«2 seV. The bolo1ieric linunosity of the uud component Ly is obtained by A+EM. where EM is the emission measure obtained from the spectral fitting or the 0.5 keV component aud the hard excess couponcut separately by asstuuing a distance to the source.," Note that the first term is greater than the second term in the range $T < 2$ keV. The bolometric luminosity of the hard component $L_{\rm H}$ is obtained by $\Lambda \cdot EM$, where $EM$ is the emission measure obtained from the spectral fitting for the 0.8 keV component and the hard excess component separately by assuming a distance to the source." The πιοαν thus calculated for the trial teniperatures is otted in the lower pancl of Fig., The luminosity thus calculated for the trial temperatures is plotted in the lower panel of Fig. " 8. showiug a rather Hat dependence witi temperature in the 730 keV range: Ly-06Ls1079 cre 1,", \ref{AbLumi} showing a rather flat dependence with temperature in the 7–30 keV range: $L_{\rm H}=0.6-1.4\times 10^{30}$ erg $^{-1}$. Note hat we have not corrected for reflectionfro t1ο white dwarf surface;, Note that we have not corrected for reflectionfrom the white dwarf surface. One can do this by dividiug the above value by 1]ex where ay is the hard N-rav albedo., One can do this by dividing the above value by $1+a_X$ where $a_X$ is the hard X-ray albedo. Ins 3... we have obtained the lower lait of the bolometric huninosity othe blackbo«v component Zip to be 2«1077 erg s+ fromROSAT aud siuniltaucous spectral fitting.," In 3.4, we have obtained the lower limit of the bolometric luminosity of the blackbody component $L_{BB}$ to be $2\times 10^{32}$ erg $^{-1}$ from and simultaneous spectral fitting." This mcais LaLp>το., This means $L_{\rm S}/L_{\rm H} > 140/<\cos \theta> $. If we also takeICE daadu O accollat x5) Lpp Is constraine iutherauge2 B5«107 ere sf. aud heuce £LsfLy=(110SJO0)/—cos> is obtained.," If we also take data into account 3.5), $L_{BB}$ is constrained in the range $2-5\times 10^{32}$ erg $^{-1}$, and hence $L_{\rm S}/L_{\rm H} = (140-830)/<\cos \theta>$ is obtained." Note that wute dyvarf atuosphere models could possibly reduce the himunosity of tιο soft conrponeut. aud thus also LfLy.," Note that white dwarf atmosphere models could possibly reduce the luminosity of the soft component, and thus also $L_{\rm S}/L_{\rm H}$." Ins XL we have derived the temperature of the soft blackbody comipoueut to he 15!* eV. The best fit value is outside the usual range derived bv Szkody (1995). namely 2015 eV. Iun estimating the blackbody teiiperature. Szkody (1995) assumed a thermal bremssstrallhime component with a temperature of 10 keV for the lard X-ray. componcnut.," In 3.4, we have derived the temperature of the soft blackbody component to be $15^{+7}_{-5}$ eV. The best fit value is outside the `usual' range derived by Szkody (1995), namely 20–45 eV. In estimating the blackbody temperature, Szkody (1995) assumed a thermal lung component with a temperature of 10 keV for the hard X-ray component." However. based on our data we have found a spectral compoucut which can be represented by a R&SS spectrum with KT~ 0.5 keV. The R&SS component with such low cluperature has a forest of wou cussion lines in the L81l keV baud caused by the mon L-shell rausitious (Ravinond and Suuth 1977).," However, based on our data we have found a spectral component which can be represented by a S spectrum with $kT \sim$ 0.8 keV. The S component with such low temperature has a forest of iron emission lines in the 0.8–1 keV band caused by the iron L-shell transitions (Raymond and Smith 1977)." ence. a significant amount of the flux iu the 0.52 keV. baud is attributed to the ow temperature R&SS compoucut iu our nocelline.," Hence, a significant amount of the flux in the 0.8–2 keV band is attributed to the low temperature S component in our modelling." Note that this cannot happen if we asstue a thermal xemisstrahluug component with a temperature of 10 keV. As a result. the Dlackbody teiiperature. becomes lower han the estimates in Szlsodyv (1995).," Note that this cannot happen if we assume a thermal bremsstrahlung component with a temperature of 10 keV. As a result, the blackbody temperature becomes lower than the estimates in Szkody (1995)." Iu analvzingROSAT data. oue usually assumes the cluperature of the hard X-ray. component to be arouud 20 keV (Ramsay 1991. for example).," In analyzing data, one usually assumes the temperature of the hard X-ray component to be around 20 keV (Ramsay 1994, for example)." As shown rere. however. this may cause a huge svstemiatic error in evaluating the Iuuiuositv aud the temperature of the soft dlackhody component.," As shown here, however, this may cause a huge systematic error in evaluating the luminosity and the temperature of the soft blackbody component." We preseuted ταν data of obtained byΑρα., We presented X-ray data of obtained by. From the light curves we find ouly uareinal evidence for orbital intensity modulation which is seen in the light curve below 0.5 keV characterized by the sharp aud deep munima., From the light curves we find only marginal evidence for orbital intensity modulation which is seen in the light curve below 0.5 keV characterized by the sharp and deep minima. Frou this energy depenence. we couclude that the intensity modulation is caused mostly bv photoelectric absorption in the pre-shock accretion column. and the accreting pole moves around on the hemisphere visible from the observer. consistent with the conclusions from Cremer. Remillard Notch (1998).," From this energy dependence, we conclude that the intensity modulation is caused mostly by photoelectric absorption in the pre-shock accretion column, and the accreting pole moves around on the hemisphere visible from the observer, consistent with the conclusions from Greiner, Remillard Motch (1998)." " It is possible that the line of sight absorber is partly ionized or has adistribution in Ny, in the range S107! 7.", It is possible that the line of sight absorber is partly ionized or has adistribution in $N_H$ in the range $^{21}$ $^{-2}$ . The X-raw spectruni can be represented by a two teniperature oXticallv thin thermal plasiuna emission model, The X-ray spectrum can be represented by a two temperature optically thin thermal plasma emission model and { then corresponds to the cooling radius (eg Crawford Fabian 1995b).,and $R$ then corresponds to the cooling radius (eg Crawford Fabian 1995b). The second. model emploved is a projected ]xing law. with index fixed at -1.5. and the core radius. /? and normalization left as free parameters.," The second model employed is a projected King law, with index fixed at -1.5, and the core radius $R$ and normalization left as free parameters." Given the errors inherent in whether such simple models truly characterize the extended: emission. we do not convolve the extended emission models with the PSE.," Given the errors inherent in whether such simple models truly characterize the extended emission, we do not convolve the extended emission models with the PSF." The relative normalization between the PSE and extended components are not always very well determined. so we also derive. what should. be regarded: as a lower limit to the presence of any extended component by assuming the nuclear emission accounts for all the lisht in the X-rav core.," The relative normalization between the PSF and extended components are not always very well determined, so we also derive what should be regarded as a lower limit to the presence of any extended component by assuming the nuclear emission accounts for all the light in the X-ray core." We fit the PSE to the quasar racial profile within the inner 15 aresec and then subtract this model and [fit the residuals by cach of the cluster models., We fit the PSF to the quasar radial profile within the inner 1–5 arcsec and then subtract this model and fit the residuals by each of the cluster models. We execute these 5 model fits to the profiles out to a radius of 50 arcsec (11 data points). vielding 10. S. and 9 degrees of freedom for the psf onlv. psf|extended component mocdels. and the fit of the extended component model to the residual after subtraction of the normalised URL PSE.," We execute these 5 model fits to the profiles out to a radius of 50 arcsec (11 data points), yielding 10, 8, and 9 degrees of freedom for the psf only, psf+extended component models, and the fit of the extended component model to the residual after subtraction of the normalised HRI PSF." We then repeat the fits to the profile out to à racius of 100 aresec (15 data points). vielding 14. 12 and 13 degrees of [reedom to the fits as above.," We then repeat the fits to the profile out to a radius of 100 arcsec (15 data points), yielding 14, 12 and 13 degrees of freedom to the fits as above." The fitting analvsis is carried out. first for cach quasar image in the absence of any wobble correction. and then for the images corrected using cdilferent phase intervals.," The fitting analysis is carried out first for each quasar image in the absence of any wobble correction, and then for the images corrected using different phase intervals." The detailed results are summarized in Table 2. where the is given for each fit.," The detailed results are summarized in Table 2, where the $\chi^2$ is given for each fit." We tabulate the fit parameters of the profile fits out to a radius of 50 arcesec and then LOO aresee in turn: Z? (in aresec) representing either the break in the broken power-law mocel. or the core radius in the Wing law model: the integrated. luminosity from the extended component as a percentage of the total Iuminosity ol the X-ray source: the X-ray luminosities (in the observed nergv. band) of. the quasar component (LyONO ) and that “the cluster component (LA) assuming a power-law of οποίο index 2 and thermal bremsstrahlung emission at a emperature of AZ=4keV respectively. (," We tabulate the best-fit parameters of the profile fits out to a radius of 50 arcsec and then 100 arcsec in turn: $R$ (in arcsec) representing either the break in the broken power-law model, or the core radius in the King law model; the integrated luminosity from the extended component as a percentage of the total luminosity of the X-ray source; the X-ray luminosities (in the observed energy band) of the quasar component $L_X^{QSO}$ ) and that of the cluster component $L_X^{cl}$ ) assuming a power-law of photon index 2 and thermal bremsstrahlung emission at a temperature of $kT=4\keV$ respectively. (" At the redshift Sour quasars this observed. band. carries about half of the rolometric Luminosity for the thermal spectrum.),At the redshift of our quasars this observed band carries about half of the bolometric luminosity for the thermal spectrum.) The errors ave derived from propagating the Ay7=1 confidence limits of the fit parameters., The errors are derived from propagating the $\Delta\chi^2=1$ confidence limits of the fit parameters. Errors are not shown when the fit was insulliciently robust to extract errors on all parameters of interest., Errors are not shown when the fit was insufficiently robust to extract errors on all parameters of interest. Table 2. however. demonstrates the full range of values obtained from the ten model fits employed. for cach of the phase intervals ancl allows one to assess the variation of cach parameter from the svstematic uncertainties of PSE normalization and extended component model emploved.," Table 2, however, demonstrates the full range of values obtained from the ten model fits employed for each of the phase intervals and allows one to assess the variation of each parameter from the systematic uncertainties of PSF normalization and extended component model employed." A comparison of some of the better fits to the radial profile of cach quasar (those shown in bold font in Table 2) are displayed in Figure 2.., A comparison of some of the better fits to the radial profile of each quasar (those shown in bold font in Table 2) are displayed in Figure \ref{fig:profs}. These plots clearly show that there are significant dillerences between the PSE-onlv [it to the profile. and the fits that. include a model. for. extended emission.," These plots clearly show that there are significant differences between the PSF-only fit to the profile, and the fits that include a model for extended emission." In all this analysis we necessarily assume that any extended component is both centred on the quasar (in no case do we see any evidence for a secondary. oll-centre »eak). and derive its properties such as scale and luminosity assuming that itis at the redshift of the quasar.," In all this analysis we necessarily assume that any extended component is both centred on the quasar (in no case do we see any evidence for a secondary off-centre peak), and derive its properties such as scale and luminosity assuming that it is at the redshift of the quasar." The present data cannot rule out a contribution to he extended component of X-ray emission from the active nuclei of close companion galaxies to cach of the quasars., The present data cannot rule out a contribution to the extended component of X-ray emission from the active nuclei of close companion galaxies to each of the quasars. Such emission. would. of course. provide further support or a clustered environment.," Such emission would, of course, provide further support for a clustered environment." The probability of getting an Unassociated X-ray source within an aperture of 1 square areminute centred. on a quasar is less than LO’. at the lux level of the extended: emission.," The probability of getting an unassociated X-ray source within an aperture of 1 square arcminute centred on a quasar is less than $10^{-3}$, at the flux level of the extended emission." Vhus there is little chance of the extended. emission component being due to contamination by fore- or back-ground sources., Thus there is little chance of the extended emission component being due to contamination by fore- or back-ground sources. Given dis proximity. to ἃ verv luminous source of photoionizaton. the low ionization state observed in the spatially extended. oxygen line emission around. this 3C48 ος Fabian et al (LOST) to deduce a high density environment around this quasar.," Given its proximity to a very luminous source of photoionizaton, the low ionization state observed in the spatially extended oxygen line emission around this 3C48 led Fabian et al (1987) to deduce a high density environment around this quasar." The inferred eas pressure οἱ 10 wwithin oof the quasar core is consistent with confinement of the extended: emission-line region. by an intracluster mediunr There is. however. no strong evidence for a rich cluster of ealaxies [from optical images (Yee. Green Stockman 1986: Yates etal 1989).," The inferred gas pressure of $\times10^5$ within of the quasar core is consistent with confinement of the extended emission-line region by an intracluster medium There is, however, no strong evidence for a rich cluster of galaxies from optical images (Yee, Green Stockman 1986; Yates etal 1989)." The fit to the radial profile is substantially improved by he addition of an extended component. the best fits being obtained in all cases when this is represented by a Ixing law.," The fit to the radial profile is substantially improved by the addition of an extended component, the best fits being obtained in all cases when this is represented by a King law." The extended component requires à very consistent value for he core radius A of around 5-6 aresee in all fits (1 arcsec corresponds to at the redshilt of the quasar*)). and. accounts. for 10-16 »r cent of the total X-ray source.," The extended component requires a very consistent value for the core radius $R$ of around 5-6 arcsec in all fits (1 arcsec corresponds to at the redshift of the ), and accounts for 10-16 per cent of the total X-ray source." The full variation of its uminositv is 5.—10«l0tteres+o. with most of the values derived being to the lower end of this range.," The full variation of its luminosity is $5-10\times10^{44}$, with most of the values derived being to the lower end of this range." This quasar lies in a densely clustered. environment (Ellingson 1991: Llintzen 1984). and the racio source has a very complex structure suggestive of dellection. ancl distortion of the radio jet. to. the south-east by. some external medium.," This quasar lies in a densely clustered environment (Ellingson 1991; Hintzen 1984), and the radio source has a very complex structure suggestive of deflection and distortion of the radio jet to the south-east by some external medium." The two sides of the radio source show asymmetric Faraday depolarization. which can be interpreted as due to cdilfering lines of sight through a depolarizing cluster medium (Carrington. Conway Leahy 1991).," The two sides of the radio source show asymmetric Faraday depolarization, which can be interpreted as due to differing lines of sight through a depolarizing cluster medium (Garrington, Conway Leahy 1991)." Crawford. Fabian (1989) inferred a high gas pressure of over 3.LO {from the ionization state of the extended. line emission, Crawford Fabian (1989) inferred a high gas pressure of over $3\times10^{5}$ from the ionization state of the extended line emission spends most of its time and emits most of its gravitational radiation while waiting for an encounter rather than curing an interaction. we only include gravitational radiation between encounters.,"spends most of its time and emits most of its gravitational radiation while waiting for an encounter rather than during an interaction, we only include gravitational radiation between encounters." To isolate this effect. we run simulations both with and without gravitational radiation.," To isolate this effect, we run simulations both with and without gravitational radiation." We include gravitational radiation by utilizing orbit-averaged expressions for the change in seminmajor axis « and eccentricity € with respect to time (Peters1964): and where rp and mag OngZ iy) are the gravitational masses of the binary pair., We include gravitational radiation by utilizing orbit-averaged expressions for the change in semimajor axis $a$ and eccentricity $e$ with respect to time \citep{p64}: : and where $m_{0}$ and $m_{1}$ $m_{0} \ge m_{1}$ ) are the gravitational masses of the binary pair. Were C is (he eravitational constant. and ¢ is the speed of light.," Here $G$ is the gravitational constant, and $c$ is the speed of light." The orbital elements are evolved until (he next encounter takes place. at a time that we choose randomly from an exponential distribution with a mean encounter time. (Tone)=1/(neso). where n is the number density of objects in the clusters core. vy is the relative velocity. ancl σ is (he cross-section of the binary.," The orbital elements are evolved until the next encounter takes place, at a time that we choose randomly from an exponential distribution with a mean encounter time, $\left<\tau_{\mathrm{enc}}\right> = 1/\left$, where $n$ is the number density of objects in the cluster's core, $v_{\infty}$ is the relative velocity, and $\sigma$ is the cross-section of the binary." If we assume the mass of the binary mg+mq29mo. then where ry is (he maxinmun considered close approach of mis to the binary's center of mass.," If we assume the mass of the binary $m_{0} + m_{1} \gg m_{2}$, then where $r_{p}$ is the maximum considered close approach of $m_{2}$ to the binary's center of mass." For a thermal distribution of stellar speeds. ος=(nusma).Uus. Where mass=O4AL is (he average mass of the main sequence star and 04; is (ie main sequence velocity dispersion.," For a thermal distribution of stellar speeds, $v_{\infty} = \left( m_{\mathrm{avg}} / m_{2} \right)^{1/2} v_{\mathrm{ms}}$, where $m_{\mathrm{avg}} = 0.4~\msun$ is the average mass of the main sequence star and $v_{\mathrm{ms}}$ is the main sequence velocity dispersion." In our simulations. the second term of Eq. 3..," In our simulations, the second term of Eq. \ref{crosssection}," gravitational focusing. dominates over the first.," gravitational focusing, dominates over the first." Averaging over velocity (assiuned to be Maxwellian) we find We then subject the binary to another encounter using orbital parameters adjusted by both the previous encounter and (he gravitational radiation emitted between the encounters., Averaging over velocity (assumed to be Maxwellian) we find We then subject the binary to another encounter using orbital parameters adjusted by both the previous encounter and the gravitational radiation emitted between the encounters. This sequence of encounters continues until (he binary merges due to gravitational wave emission., This sequence of encounters continues until the binary merges due to gravitational wave emission. If orbital decay is not being caleulated. then we determine that the binary has mergedwhen the randomly drawn encounter time is longer than the timescale to merger. which is approximately," If orbital decay is not being calculated, then we determine that the binary has mergedwhen the randomly drawn encounter time is longer than the timescale to merger, which is approximately" [actor and is the jet comoving energy density with proton number density i!pedet,"factor and is the jet comoving energy density with proton number density $n'_{\rm p, \, jet}$." In the rest frame ol the jet head. the ram-lorce of the ambient medium is where paup=ΠρΠω Is the density of ambient gas around the jet head. is (he advanced. Lorentz [actor of the jet head and μι is the cross-section area of a bow-shock at the end of the jet (ΙΟ ean be larger than the cross-section area of the jet itself. Ajay=πι ).," In the rest frame of the jet head, the ram-force of the ambient medium is where $\rho_{\rm amb} = m_{\rm p} \, n_{\rm amb}$ is the density of ambient gas around the jet head, $\Gamma_{\rm head} \equiv (1 - \beta_{\rm head}^2)^{-1/2}$ is the advanced Lorentz factor of the jet head and $A_{\rm head}$ is the cross-section area of a bow-shock at the end of the jet (which can be larger than the cross-section area of the jet itself, $A_{\rm jet} = \pi R_{\rm jet}^2$ )." Hlere we neglect pressure of the non-thermal component within the outer lobe. what will be justified below.," Here we neglect pressure of the non-thermal component within the outer lobe, what will be justified below." " The ram-force of the ambient medium is balanced by the momentum flix of the jet. where Ty=(1—92,)|? is the bulk Lorentz factor of the jet as measured in the rest frame of the head."," The ram-force of the ambient medium is balanced by the momentum flux of the jet, where $\Gamma_{\rm rel} \equiv (1 - \beta_{\rm rel}^2)^{-1/2}$ is the bulk Lorentz factor of the jet as measured in the rest frame of the head." With relation Preter=TheatPict(7j—na) One can therefore find expression for the advance velocity of the jet head where In the non-relativistic Limit with head$ 2 s) bursts with massive core-collapse progenitors (Woosley 1993) that are commonly accompanied by luminous and broad-lined Type Ic supernovae (Watson et al. 2007)., 2007). CRB 060505 has a burst leusth of —1 s. but notably lacks evidence of an accomipauviusg supernova.," GRB 060505 has a burst length of $\sim$ 4 s, but notably lacks evidence of an accompanying supernova." Investigations into the host properties of GRD 060505 strongly disagree on the nature of the xoeenitor., Investigations into the host properties of GRB 060505 strongly disagree on the nature of the progenitor. Itis unclear whether GRB 060505 originates roni a conipact-object merger. a niswive core-collapse supernova. or a new class of loue-duration GRBs with 10 associated supernovac.," It is unclear whether GRB 060505 originates from a compact-object merger, a massive core-collapse supernova, or a new class of long-duration GRBs with no associated supernovae." The nature of CRB 060505 nay have important implications for our classification iid understanding of GRB progenitors., The nature of GRB 060505 may have important implications for our classification and understanding of GRB progenitors. GRB 060505 was observed on UTC 2006 May 5 by he Swift Burst Alert Telescope (BAT)(ITulliueer et al., GRB 060505 was observed on UTC 2006 May 5 by the Swift Burst Alert Telescope (BAT) (Hullinger et al. 2006: ealxyPalmer et al., 2006; Palmer et al. 2006). associated with the : = SNO 2d0FCRS SI73Z112 (Colless et al.," 2006), associated with the $z$ = 0.0889 galaxy 2dFGRS S173Z112 (Colless et al." 2002: Ofek et al., 2003; Ofek et al. 2006: Thóune et al., 2006; Thönne et al. 200642: Fvubo ct al., 2006a; Fynbo et al. 2006)., 2006). It was initially categorized as a loue-duration GRB based on its ~ ls burst leugth (I&ouveliotou et al., It was initially categorized as a long-duration GRB based on its $\sim$ 4 s burst length (Kouveliotou et al. 1993)., 1993). Thoune Fyubo (2007) fud a lower metallicity and higher rate of star formation at the CRB 060505 burst site when compared with other regions of the host ealaxy., Thönne Fynbo (2007) find a lower metallicity and higher rate of star formation at the GRB 060505 burst site when compared with other regions of the host galaxy. Recent investieatious sugeest that long-duratiou GRBs are associated with lovAnetallicitv star-forming environments (Stanek et al., Recent investigations suggest that long-duration GRBs are associated with low-metallicity star-forming environments (Stanek et al. 2006. Sollerman ct al.," 2006, Sollerman et al." 2005. Fruchter et al.," 2005, Fruchter et al." 2006. Ikewlev et al.," 2006, Kewley et al." 2007. Brown et al.," 2007, Brown et al." 2007). supporting a core-collapse progenitor scenario for CRB 060505.," 2007), supporting a core-collapse progenitor scenario for GRB 060505." Ou the other hand. GRD 060505 mav be the product of à compact-object iierger with a louger-than-average burst duration.," On the other hand, GRB 060505 may be the product of a compact-object merger with a longer-than-average burst duration." Short- aud lone-duration CRBs are separated by a burst-duration cut-off of 2 s but there nav be some overlap between these two classes of progenitor events: short-burst progenitors have a chance of vieldiug a burst longer than (IIorvátth 2002).," Short- and long-duration GRBs are separated by a burst-duration cut-off of 2 s, but there may be some overlap between these two classes of progenitor events; short-burst progenitors have a chance of yielding a burst longer than 4 s (Horvátth 2002)." Additional support for a conmpact-object merecr xoeenitor for GRB 060505 /includes the progenitor evolutionary timescale. the spiral nature of the lost ealaxy. and the brightuess of the burst reeion.," Additional support for a compact-object merger progenitor for GRB 060505 includes the progenitor's evolutionary timescale, the spiral nature of the host galaxy, and the brightness of the burst region." Ofek et al. (, Ofek et al. ( 2007) calculate an upper limit of 10 Alyy for he progenitor birth-to-explosiou timescale of the GRD 160505 event.,2007) calculate an upper limit of 10 Myr for the progenitor birth-to-explosion timescale of the GRB 060505 event. While this age linut docs not rule out the xossibilitv of a core-collapse progenitor. such a timescale is also consistent with the mereine of two neutron stars or a neutron star-black hole merger. both of which are conrpact object merecr scenarios associated with short musts(Belezvuski et al.," While this age limit does not rule out the possibility of a core-collapse progenitor, such a timescale is also consistent with the merging of two neutron stars or a neutron star-black hole merger, both of which are compact object merger scenarios associated with short bursts (Belczynski et al." 2006)., 2006). The host galaxy of CRB 160505 is categorized as an She spiral. which is uuusual or a lone-duration GRB host ealaxy (Thoune Fyubo 2007).," The host galaxy of GRB 060505 is categorized as an Sbc spiral, which is unusual for a long-duration GRB host galaxy (Thönne Fynbo 2007)." Fruchter et -- al.(, Fruchter et al. ( 2006) found that loue-diuratiou GRBs favor the reeions of their host galaxies hat are associated with coucentrated populations of young nassve stars (vau deu Παιν Yoon 2007).,2006) found that long-duration GRBs favor the brightest regions of their host galaxies that are associated with concentrated populations of young massive stars (van den Heuvel Yoon 2007). The GRB 060505 progenitor region is relatively faint compared to its host ealaxy. supporting a conipact-object merecr progenitor(Ofek et al.," The GRB 060505 progenitor region is relatively faint compared to its host galaxy, supporting a compact-object merger progenitor (Ofek et al." 2007)., 2007). " Alternatively, GRB 060505 may. beloug to a new class of long-duration GRBs with no associated supernovae."," Alternatively, GRB 060505 may belong to a new class of long-duration GRBs with no associated supernovae." The distribution of knowu GRB burst durations sugecst the existence of a third category of CRBs(Mukhlerjee ot al., The distribution of known GRB burst durations suggest the existence of a third category of GRBs (Mukherjee et al. 1995. Tlorvatth 2002).," 1998, Horvátth 2002)." GRB 060505 is often compared with CRB 06061 La ~102 s burst(Bartheliuv et al.," GRB 060505 is often compared with GRB 060614, a $\sim$ 102 s burst (Barthelmy et al." 2006) classified as a long GRD with no apparent superuova counterpart - both have been proposed as represents exaluples of a new class of CRBs d.(Fyubo ct al., 2006) classified as a long GRB with no apparent supernova counterpart - both have been proposed as representative examples of a new class of GRBs (Fynbo et al. 2006 Jakobsson Fyubo 2007. ine ct ," 2006, Jakobsson Fynbo 2007, King et al." 2007)., 2007). Schaefer Xiao (2006) sugeest that GRB 060505 is a backeround event that hasbeen associated with 2dFCRS S173Z112 bv coincidence., Schaefer Xiao (2006) suggest that GRB 060505 is a background event that has been associated with 2dFGRS S173Z112 by coincidence. However. Watson et al. (," However, Watson et al. (" 2007) estimate that the superposition. of the burst directlv over a star-formüng region of low iuctalliitv would be nureasonably serendipitous.,2007) estimate that the superposition of the burst directly over a star-forming region of low metallicity would be unreasonably serendipitous. " There are several reasous to believe that the progenitors of long-duration bursts would favor low-metallicity environments,", There are several reasons to believe that the progenitors of long-duration bursts would favor low-metallicity environments. Mass loss in late-tvpe massive stars. driven by radiation pressure on spectral lines.," Mass loss in late-type massive stars, driven by radiation pressure on spectral lines," while the characteristic timescale of the radiative processes is below 200s (Oke.Giver&Searle1962... Buonauraetal. 1985)).,"while the characteristic timescale of the radiative processes is below $200\mbox{s}$ \citealt{oke1}, \citealt{buon1}) )." The cllect of the variable effective. gravity can be characterized. by our Condition HL. which provides information whether QSAA may. be assumed.," The effect of the variable effective gravity can be characterized by our Condition II, which provides information whether QSAA may be assumed." The limits are 4.5ems2/25008ο”«14200ems.7/2500s.," The limits are $4.5\mbox{cms}^{-2}/2500\mbox{s} < \vert \partial g_{\rm e}/\partial t \vert < 14200 \mbox{cms}^{-2}/2500\mbox{s}$." ‘Phe upper Limit comes from the rising branch of the light curve. when the main shock hits the atmosphere.," The upper limit comes from the rising branch of the light curve, when the main shock hits the atmosphere." In general. the photometric input of the present method is identical with that of the DW. method.," In general, the photometric input of the present method is identical with that of the BW method." In. order to obtain the fundamental parameters. radial velocity data and their. problematic conversion to. pulsation velocities are notnecessary.," In order to obtain the fundamental parameters, radial velocity data and their problematic conversion to pulsation velocities are notnecessary." On the other hand. 9 and. fy must be differentiated numerically. dilferential quotients are sensitive to the non-valicity of QSAA.," On the other hand, $\vartheta$ and $h_0$ must be differentiated numerically, differential quotients are sensitive to the non-validity of QSAA." Our photometric and byerodvnamic considerations revealed empirical quantitative conditions to| find the phase intervals of the pulsation when static model atmospheres of Ixurucz(L997) are satisfactory to derive the variable and non-variable physical parameters. of the pulsating atmosphere., Our photometric and hydrodynamic considerations revealed empirical quantitative conditions to find the phase intervals of the pulsation when static model atmospheres of \citet{kuru1} are satisfactory to derive the variable and non-variable physical parameters of the pulsating atmosphere. Outside these intervals. dyvnamical mocel atmospheres are necessary to refine the parameters from QSAA. which is beyond the scope of the present. paper.," Outside these intervals, dynamical model atmospheres are necessary to refine the parameters from QSAA, which is beyond the scope of the present paper." The fundamental parameters d. A. Αν ECBV) were determined. using photometric quantities onlv. in phases when the QSAA is à good approximation (ie. both Conditions L and Ll were satisfied).," The fundamental parameters $d$, ${\cal M}$, $[M]$, $E(B-V)$ were determined using photometric quantities only in phases when the QSAA is a good approximation (i.e. both Conditions I and II were satisfied)." Phe values obtained from averaging over the entire pulsation evele can be considered as a first approximation only. because QS.AA was assumed in all phases regardless of it being à good or poor approximation.," The values obtained from averaging over the entire pulsation cycle can be considered as a first approximation only, because QSAA was assumed in all phases regardless of it being a good or poor approximation." The large error of Ley and (Ady) originates [rom Ad/d.1 of our best value. *] in Table 2.., The large error of $L_{\rm eq}$ and $\langle M_V \rangle$ originates from $\Delta d/d \approx .1$ of our best value $[\ast]$ in Table \ref{tab2}. To give an impression on the accuracy of inverting the CBVGe: photometry to physical. parameters. the comparison star DD. |67 TOS was used. because its colours are similar to those of SU Dra (Bareza2002.. Table 3).," To give an impression on the accuracy of inverting the $UBV(RI)_C$ photometry to physical parameters, the comparison star BD +67 708 was used, because its colours are similar to those of SU Dra \citealt{barc0}, Table 3)." The results are M]=O77x03. ΗΕV)=000. 9=(1.9132-.002)-10.2? rad loeg—3.504501. 7.= 7505475I. The errors are roughly in the same order of magnitude as those of SU Dra when Conditions E and LE are satisfied.," The results are $[M]=-0.77\pm .03$, $E(B-V)=.000$, $\vartheta=(1.913\pm .002)\times 10^{-10}$ rad, $\log g=3.59\pm .01$, $T_{\rm e}=7505\pm 5$ K. The errors are roughly in the same order of magnitude as those of SU Dra when Conditions I and II are satisfied." Figs., Figs. . 3cc. d demonstrate that significant corrections must be added to £e. P? ifthe true pulsation velocity and acceleration are required. at QO1 is satisfied. multiple images can occur only when the source is located within Yer= Yee). where cu is determined. from thelensing equation (eq.|23]]),"even if $\kappa_c>1$ is satisfied, multiple images can occur only when the source is located within $y_\mathrm{cr}=y(x_\mathrm{cr})$ , where $x_\mathrm{cr}$ is determined from thelensing equation (eq.\ref{lenseq1}] ])" with dy/d.r=0 Or .r«O0 (this is similar to lensine by NEW halos)., with $dy/dx=0$ for $x<0$ (this is similar to lensing by NFW halos). For a singular clensity profile such as the SIS and NEW profiles. the central value is divergent. so &>1 is always satisfied. ancl nuulüple images can be produced [or any given mass.," For a singular density profile such as the SIS and NFW profiles, the central value is divergent, so $\kappa>1$ is always satisfied, and multiple images can be produced for any given mass." For densitv profiles with a finite soft core such as the NTIS profile. however. the condition #>1 requires that only halos with nass ereater (han a certain value (determined by &.=1) can produce multiple images.," For density profiles with a finite soft core such as the NTIS profile, however, the condition $\kappa>1$ requires that only halos with mass greater than a certain value (determined by $\kappa_c=1$ ) can produce multiple images." " This is Clearly shown in Figure 1. where (hree curves lore. =1.1.1.05. and 1.0 are plotted. aud when s,=1.0. only one image is produced."," This is clearly shown in Figure 1, where three curves for $\kappa_c=1.1, 1.05$, and $1.0$ are plotted, and when $\kappa_\mathrm{c}=1.0$, only one image is produced." Iu lensing statistics. this requirement will limit the populations of lensing halos to quite a small fraction.," In lensing statistics, this requirement will limit the populations of lensing halos to quite a small fraction." Such a conclusion is valid for any lensing halos with a finite soft core. which is discussed in detail later.," Such a conclusion is valid for any lensing halos with a finite soft core, which is discussed in detail later." " When quasars at redshift 2, are lensed by foreground CDM halos of galaxies ancl clusters ol galaxies. the lensing probability for image separations larger (han A@ is 1984:Schneider.Ehlers.&Faleo1992) where ος) is the redshilt distribution for quasars approximated by a Gaussian model with a mean of 1.27 and a dispersion of 0.95 (IIelbieetal.1999:Marlow2000:etal.2002:Myers 2003)... DP(2) is the proper distance from the observer to thelens located at redshilt z. 5(M.2) is the physical number density of virialized dark halos of masses between 4M and A4M. and B(M.z)isthe magnification bias."," When quasars at redshift $z_{\mathrm{s}}$ are lensed by foreground CDM halos of galaxies and clusters of galaxies, the lensing probability for image separations larger than $\Delta\theta$ is \citep{turner,schne} where $\mathcal{P}(z_\mathrm{s})$ is the redshift distribution for quasars approximated by a Gaussian model with a mean of 1.27 and a dispersion of 0.95 \citep{helbig1999,marlow2000,chae02,myers}, $D_{\mathrm{L}}^\mathrm{p}(z)$ is the proper distance from the observer to thelens located at redshift $z$, $\bar{n}(M,z)$ is the physical number density of virialized dark halos of masses between $M$ and $M+dM$, and $B(M,z)$ is the magnification bias." The physical number density n(M.z) is related to the comoving number density n(M.z) by n(M.z)=nCAl.2)(1uz) the latter is originally given by Press&Sehechter(1974).. ancl the extended: versionis nCM.z)dM=(poM)fGCM.z)dM. where py is the current mean mass density of the universe and is (he mass function for which we use (he expression given by Jenkinsοἱal.(2001).," The physical number density $\bar{n}(M,z)$ is related to the comoving number density $n(M,z)$ by $\bar{n}(M,z)=n(M,z)(1+z)^3$; the latter is originally given by \citet{press74}, and the extended versionis $n(M,z)dM=(\rho_0/M)f(M,z)dM$, where $\rho_0$ is the current mean mass density of the universe and is the mass function for which we use the expression given by \citet{jenki}." ". In {his expression. A,=0,.f2)/ACAL). in which 9.(2) is the overdensity threshold lor spherical collapse αἱ τους z and ACAL) is the rms of the present variance of the f[Inctuations in a sphere containing a mean mass AL."," In this expression, $\Delta_{\mathrm{z}}=\delta_c(z)/\Delta(M)$, in which $\delta_c(z)$ is the overdensity threshold for spherical collapse at redshift $z$ and $\Delta(M)$ is the rms of the present variance of the fluctuations in a sphere containing a mean mass $M$." " The overdensity threshokl is given by for the ACDM cosmology(Navarro.Frenk.&White 1997).. where is the linear growth function of the density perturbation (Carroll. 1992).. in which g(r)=0.5r(1/70+200%/140—22/140+P"")* and O(z)=On4+2)°/[L-O402 z:)7]."," The overdensity threshold is given by $\delta_c(z)=1.68/D(z)$ for the $\Lambda$ CDM cosmology\citep{nfw97}, , where $D(z)=g[\Omega(z)]/[g(\Omega_{\mathrm{m}})(1+z)]$ is the linear growth function of the density perturbation \citep{carroll}, , in which $g(x)=0.5x(1/70+209x/140-x^2/140+x^{4/7})^{-1}$ and $\Omega(z)=\Omega_{\mathrm{m}}(1+z)^3 /[1-\Omega_{\mathrm{m}}+\Omega_{\mathrm{m}}(1+z)^3]$ ." When we caletdate the variance of the fluctuations ANC(M). we use the fitting formae for the CDM power spectrum P(/)=AET?(&) given by," When we calculate the variance of the fluctuations $\Delta^2(M)$ , we use the fitting formulae for the CDM power spectrum $P(k)=AkT^2(k)$ given by" cwarfs.,dwarfs. We limit the discussion to models with solar metallicity., We limit the discussion to models with solar metallicity. The sedimentation parameter of the cloud mocel is fixed at foo=3. which gives a good representation of far-red and photometry of L dwarls (Marley. et al.," The sedimentation parameter of the cloud model is fixed at $f_{\rm sed}=3$, which gives a good representation of far-red and near-IR photometry of L dwarfs (Marley et al." 2002: Bureasser οἱ al., 2002; Burgasser et al. 2002) and of (he ammonia cloud deck of Jupiter as well (Ackerman Marley 2001)., 2002) and of the ammonia cloud deck of Jupiter as well (Ackerman Marley 2001). For simplicity. we do not take into account the possibility of cloud disruption near the L/T boundary (Durgasser et al.," For simplicity, we do not take into account the possibility of cloud disruption near the L/T boundary (Burgasser et al." 2002)., 2002). The combination of ΗνΑς: photometry aud IRS spectroscopy with eround-based optical and near-IR. data will give the complete spectral energy distributions (SED) of many brown cdwarfs., The combination of IRAC photometry and IRS spectroscopy with ground-based optical and near-IR data will give the complete spectral energy distributions (SED) of many brown dwarfs. Empirical bolometric corrections immediately follow as well as the bolometric Iuminosity for objects with known parallaxes., Empirical bolometric corrections immediately follow as well as the bolometric luminosity for objects with known parallaxes. An independent determination of Tig (e.g. by fitting spectra wilh models) will give the eravily. radius. and mass of individual brown dwarts.," An independent determination of $\Teff$ (e.g. by fitting spectra with models) will give the gravity, radius, and mass of individual brown dwarfs." " lt is well known that in the far-red and near-IR. the brightness temperature 7j, οἱ brown clwarls varies stronglv with wavelength due to (he high. contrast between. opacity windows and molecular absorption bands."," It is well known that in the far-red and near-IR, the brightness temperature $T_{\rm br}$ of brown dwarfs varies strongly with wavelength due to the high contrast between opacity windows and molecular absorption bands." " This is still true in the mid-IR. up to about jam. thereafter T1, gradually decreases to stabilize at ~75% of Tir bevond jam. Only near jan and near sau does Tj, become as large as Tig."," This is still true in the mid-IR up to about $\,\mu$ m, thereafter $T_{\rm br}$ gradually decreases to stabilize at $\sim$ of $\Teff$ beyond $\,\mu$ m. Only near $\,\mu$ m and near $\,\mu$ m does $T_{\rm br}$ become as large as $\Teff$." For 4Slogg(ces)5.5. the pressure ad (he mid-IR. photosphere stavs between 0.1 and bar. depending mostly on wavelength. aud surface gravitv and least on Zi.," For $4 \wig< \log g \,({\rm cgs}) \wig< 5.5$, the pressure at the mid-IR photosphere stays between 0.1 and $\,$ bar, depending mostly on wavelength and surface gravity and least on $\Teff$." Basically. the mid-IR spectra of brown clwarls ave formed al PSTey and pressures of about bar.," Basically, the mid-IR spectra of brown dwarfs are formed at $T\wig< \Teff$ and pressures of about $\,$ bar." " Figure 1 identifies (he mid-IR molecular absorbers in a sequence of spectra from 600 (o 2400Ix. By Dar. the most important. absorber is H3O (throughout the entire spectral range. except for two strong molecular bands due to CLL, and δι."," Figure 1 identifies the mid-IR molecular absorbers in a sequence of spectra from 600 to $\,$ K. By far, the most important absorber is $_2$ O throughout the entire spectral range, except for two strong molecular bands due to $_4$ and $_3$." Devond jn. all features are due to H5O0. with the exception of a lew weak NII4 bands between 32 and jn for models with TirS800 IN. In the high-7iy spectra. the fundamental band of CO at sam and a weak TiO band at jm are the only features not originating from Π.Ο. The step in the spectrum ~6.5 jm is a IH5O0 feature.," Beyond $\,\mu$ m, all features are due to $_2$ O, with the exception of a few weak $_3$ bands between 32 and $\,\mu$ m for models with $\Teff \wig< 800\,$ K. In the $\Teff$ spectra, the fundamental band of CO at $\,\mu$ m and a weak TiO band at $\,\mu$ m are the only features not originating from $_2$ O. The step in the spectrum $\sim 6.5\,\mu$ m is a $_2$ O feature." The TiO band disappears at 2200Ix but the CO band persists down to 900IX in these cloudy models.," The TiO band disappears at $\,$ K but the CO band persists down to $\,$ K in these cloudy models." As Zi decreases. new molecular bands appear and steacily increase in strength.," As $\Teff$ decreases, new molecular bands appear and steadily increase in strength." The pam band of NI; appears at I. This band is very broad and dominates the spectrum from 3.5 to 1640n ab Teg500 Ix. Weaker bands of NI appear al 900Ix (5.5. Tyan) and 800IN (8.9 jan).," The $\,\mu$ m band of $_3$ appears at $\,$ K. This band is very broad and dominates the spectrum from 8.5 to $\,\mu$ m at $\Teff \le 800\,$ K. Weaker bands of $_3$ appear at $\,$ K (5.5 – $\,\mu$ m) and $\,$ K (3.9 – $\,\mu$ m)." The former is superimposed on a, The former is superimposed on a corresponding to the four main molecular clouds in the whole region.,corresponding to the four main molecular clouds in the whole region. Therefore. assuming that each of the four molecular clouds is made from material at the same distance. which ts reasonable given the localized morphology of the emission. each clump is assumed to be at the same distance as the cloud it belongs to (see Table 3)).," Therefore, assuming that each of the four molecular clouds is made from material at the same distance, which is reasonable given the localized morphology of the emission, each clump is assumed to be at the same distance as the cloud it belongs to (see Table \ref{param_nubi}) )." This leaves the question of the ambiguity. which we discuss in Sect. ??..," This leaves the question of the ``near-far ambiguity”, which we discuss in Sect. \ref{starformationassociation}." The spectrum of the emission of each identified clump was obtained by integrating the 'CO(I-0) data cube in the channels of the emission of the clump. over the area enclosed by the deconvolved contour level of the CO 1-0) emission.," The spectrum of the emission of each identified clump was obtained by integrating the $^{13}$ CO(1-0) data cube in the channels of the emission of the clump, over the area enclosed by the deconvolved contour level of the $^{13}$ CO(1-0) emission." The spectra of clump co4 and clump col9 have been derived from the higher velocity resolution (0.5 uns !) data-cube. as discussed in the previous section.," The spectra of clump co4 and clump co19 have been derived from the higher velocity resolution (0.5 km $^{-1}$ ) data-cube, as discussed in the previous section." The parameters of each clump were determined by fitting a Gaussian profile to each produced spectrum., The parameters of each clump were determined by fitting a Gaussian profile to each produced spectrum. Line profiles showing more than one velocity component were analyzed by fitting more than one Gaussian component. in order to remove the contribution to the emission by other clumps along the line of sight from the emission coming from the clump of interest.," Line profiles showing more than one velocity component were analyzed by fitting more than one Gaussian component, in order to remove the contribution to the emission by other clumps along the line of sight from the emission coming from the clump of interest." The results of this analysis are reported in Table 3.., The results of this analysis are reported in Table \ref{param_nubi}. Figure 4. shows the APEX 870 ym continuum emission from the same region we observed in the 'CO(1-0) emission line (see Fig. 1))., Figure \ref{identif-cont} shows the APEX 870 $\mu$ m continuum emission from the same region we observed in the $^{13}$ CO(1-0) emission line (see Fig. \ref{integr_tot}) ). The data are part of the ATLASGAL project 2009))., The data are part of the ATLASGAL project ). The white ellipses represent: 1) the GMC surrounding G19.61-0.23. which is the 33-48 km s! ⋯⋃∣⊜∁∐∣⋅≏∐⋪⊱⊺∐⋋⋖∁∣∪⋯↿⊐⇅∐⋋∁∐⋋⋋⊜∐≣∏⊱⊜∁↾↜∎⋅≱∎⋅≱∷," The white ellipses represent: 1) the GMC surrounding G19.61-0.23, which is the 33–48 km $^{-1}$ molecular gas (cloud 2) discussed in Sect. \ref{kinematics};" and 2) the km s! molecular gas (cloud 3) discussed in Sect., and 2) the 54--63 km $^{-1}$ molecular gas (cloud 3) discussed in Sect. ?? (see also Fig. 1))., \ref{kinematics} (see also Fig. \ref{integr_tot}) ). We decided to use a threshold of 10 «c to identify the different sources in the continuum emission., We decided to use a threshold of 10 $\sigma$ to identify the different sources in the continuum emission. In this way. we identified in the APEX continuum emission 14 sources. which aree shown in Fig.," In this way, we identified in the APEX continuum emission 14 sources, which are shown in Fig." 4. with their respective labels., \ref{identif-cont} with their respective labels. " Most of the APEX continuum sources have counterparts in one of the FCRAO ""CO(I-0) clumps (see also Fig.", Most of the APEX continuum sources have counterparts in one of the FCRAO $^{13}$ CO(1-0) clumps (see also Fig. A3 in the Online Material Sect).," \ref{CO-apex-spitzer} in the Online Material Sect.)," with the exception of sources C8 and C9., with the exception of sources C8 and C9. Source C8 ts associated with significant emission in the 'CO(1-0) line. but over a region slightly to the south of C8 (see Fig. A3).," Source C8 is associated with significant emission in the $^{13}$ CO(1-0) line, but over a region slightly to the south of C8 (see Fig. \ref{CO-apex-spitzer}) )." " The ""CO(1-0) emission in this case corresponds to CO clump co7. which “contains” the APEX sources C8 and C7."," The $^{13}$ CO(1-0) emission in this case corresponds to $^{13}$ CO clump co7, which “contains” the APEX sources C8 and C7." " We thus assume for both C8 and C7 the distance corresponding to ""CO 8.", We thus assume for both C8 and C7 the distance corresponding to $^{13}$ CO 8. " C9 is associated with ""CO emission at 62 km s∣ and hence probably to cloud 3.", C9 is associated with $^{13}$ CO emission at 62 km $^{-1}$ and hence probably to cloud 3. Moreover. given the lower resolution of the 'CO data. the continuum sources C3 and C4 correspond both to clump co3 in the FCRAO CO(I-0) emission.," Moreover, given the lower resolution of the $^{13}$ CO data, the continuum sources C3 and C4 correspond both to clump co3 in the FCRAO $^{13}$ CO(1-0) emission." Column 8 of Table 4 indicates the counterpart. if any. of each APEX continuum source. as identified from the comparison between the CO emission and the APEX continuum emission.," Column 8 of Table \ref{param_cont} indicates the counterpart, if any, of each APEX continuum source, as identified from the comparison between the $^{13}$ CO emission and the APEX continuum emission." " It 1s worth noting that the two maps (""CO map and APEX continuum maps) have significantly different resolutions. with the APEX resolution being 182 at 870 ym and the FCRAO resolution being 46” at the frequency of the 'CO(1-0) line."," It is worth noting that the two maps $^{13}$ CO map and APEX continuum maps) have significantly different resolutions, with the APEX resolution being $18.\!\!^{\prime\prime}2$ at 870 $\mu$ m and the FCRAO resolution being $^{\prime\prime}$ at the frequency of the $^{13}$ CO(1-0) line." Therefore it is not surprising that the sources identified in the APEX contiuum emission are more compact than the CO clumps (as seen also in Fig. A3)., Therefore it is not surprising that the sources identified in the APEX continuum emission are more compact than the $^{13}$ CO clumps (as seen also in Fig. \ref{CO-apex-spitzer}) ). Moreover. the 870 uim continuum emission probably traces dense cores embedded in the CO(I- 0) clumps.," Moreover, the 870 $\mu$ m continuum emission probably traces dense cores embedded in the $^{13}$ CO(1-0) clumps." " For the APEX continuum sources that have a counterpart in the FCRAO ""CO(I-0) emission. we assume as distance the one of the corresponding '*CO(CI-0) clump."," For the APEX continuum sources that have a counterpart in the FCRAO $^{13}$ CO(1-0) emission, we assume as distance the one of the corresponding $^{13}$ CO(1-0) clump." The obtained distances are reported in col., The obtained distances are reported in col. 9-10 of Table 4 (see Sect.," 9-10 of Table \ref{param_cont} (see Sect." ?? and Table 3)., \ref{identif} and Table \ref{param_nubi}) ). One of our aims ts to compare the properties of the molecular clumps with and without star formation within them., One of our aims is to compare the properties of the molecular clumps with and without star formation within them. " With this in mind. we have compared images from the GLIMPSE 2003)) and MIPSGAL mid infrared surveys 2005)) with both ATLASGAL maps and our FCRAO ""CO data (supplemented by the BU-FCRAO GRS)."," With this in mind, we have compared images from the GLIMPSE ) and MIPSGAL mid infrared surveys ) with both ATLASGAL maps and our FCRAO $^{13}$ CO data (supplemented by the BU-FCRAO GRS)." " It is worth recalling that the MIPSGAL 70 jm survey has a ""beam"" of 18"". which is comparable to that of ATLASGAL."," It is worth recalling that the MIPSGAL 70 $\mu$ m survey has a “beam” of $18^{\prime\prime}$, which is comparable to that of ATLASGAL." Moreover. the GLIMPSE 8 um data traces PAH emission excited by UV from OB stars close to GMCs whereas the 24 iim MIPSGAL radiation often traces dust heated by embedded proto-stellar objects.," Moreover, the GLIMPSE 8 $\mu $ m data traces PAH emission excited by UV from OB stars close to GMCs whereas the 24 $\mu$ m MIPSGAL radiation often traces dust heated by embedded proto-stellar objects." Also. the 4.5 uum GLIMPSE data has been found often to trace molecular hydrogen emission associated with outflows.," Also, the 4.5 $\mu$ m GLIMPSE data has been found often to trace molecular hydrogen emission associated with outflows." In Fig., In Fig. " A3 (online. version). we superpose FCRAO ""CO and ATLASGAL maps to Spitzer images at 3.6. 8 and 24 um. One sees here that there are several ATLASGAL sources associated with strong continuum emission in the Spitzer bands."," \ref{CO-apex-spitzer} (online version), we superpose FCRAO $^{13}$ CO and ATLASGAL maps to Spitzer images at 3.6, 8 and 24 $\mu$ m. One sees here that there are several ATLASGAL sources associated with strong continuum emission in the Spitzer bands." Table 5. summarizes these associations (within 1) as well as the information about maser emission and HII regions close to the positions of continuum emission., Table \ref{SFassociations} summarizes these associations (within $^{\prime}$ ) as well as the information about maser emission and HII regions close to the positions of continuum emission. Not surprisingly. there is strong mid infrared emission from the vicinity of clumps Cl and C2 which are associated. with the HII region complex G19.61-0.23 but one also notes strong emissio associated with the C7/C8 complex and with CI2.," Not surprisingly, there is strong mid infrared emission from the vicinity of clumps C1 and C2 which are associated with the HII region complex G19.61-0.23 but one also notes strong emission associated with the C7/C8 complex and with C12." In all of these cases. it is reasonable to assume that there is an embedded cluster of young stars producing ultra-violet radiation responsible for exciting the PAH and small grain emission observed at 8 and 24 jim. Less obvious in Fig.," In all of these cases, it is reasonable to assume that there is an embedded cluster of young stars producing ultra–violet radiation responsible for exciting the PAH and small grain emission observed at 8 and 24 $\mu$ m. Less obvious in Fig." is the fact that in many cases there are point-like (< 6 are sec.), \ref{CO-apex-spitzer} is the fact that in many cases there are point-like $<$ 6 arc sec.) continuum sources at 24 jm close to the ATLASGAL 870 micron peaks., continuum sources at 24 $\mu$ m close to the ATLASGAL 870 micron peaks. It is noticeable that there are 3 ATLASGAL sources without clear 24 pm counterparts and we presume this implies a relatively low dust temperature (below 25 K)., It is noticeable that there are 3 ATLASGAL sources without clear 24 $\mu$ m counterparts and we presume this implies a relatively low dust temperature (below 25 K). These are perhaps similar to the infrared dark clouds (RDCs) observed associated with star-forming regions closer to the sun but lacking a strong infrared background., These are perhaps similar to the infrared dark clouds (IRDCs) observed associated with star-forming regions closer to the sun but lacking a strong infrared background. We note also that we have searched without success for extended emission in the 4.5 μπι IRAC band of the type often found associated with outflows in nearby star-forming regions., We note also that we have searched without success for extended emission in the 4.5 $\mu$ m IRAC band of the type often found associated with outflows in nearby star-forming regions. Finally. all the ATLASGAL sources show association with extended Spitzer," Finally, all the ATLASGAL sources show association with extended Spitzer" posterior probability distribution (asvimmnetric).,posterior probability distribution (asymmetric). Note that these asvanmnietric distributions arereal ancl not mathematical artifacts: they properly represent our knowledge of the distance and radius. which is not true for least-squares or maximunm-likelihood calculations on the same data.," Note that these asymmetric distributions are and not mathematical artifacts; they properly represent our knowledge of the distance and radius, which is not true for least-squares or maximum-likelihood calculations on the same data." The latter methods assume svinmeltric errors by their verv nature., The latter methods assume symmetric errors by their very nature. Because this situation prevails for only a lew stars in this sample. ancl only for stars with large errors. il has little οδοί on the weighted mean ratios of distances ancl radii quoted in the previous secon.," Because this situation prevails for only a few stars in this sample, and only for stars with large errors, it has little effect on the weighted mean ratios of distances and radii quoted in the previous section." As we did with the distances and radii themselves. we begin by examining the behavior of theratio of the Bavesian uncertainty {ο the linear-bisector uncertaintv for the same Cepheid.," As we did with the distances and radii themselves, we begin by examining the behavior of the of the Bayesian uncertainty to the linear-bisector uncertainty for the same Cepheid." In Figures 7 and 8 we show these ratios for the distance and radius uncertainties plotted against /ogP?., In Figures \ref{sigmadist} and \ref{sigmarad} we show these ratios for the distance and radius uncertainties plotted against $log P$. Unwelghted least-squares fits in these figures vield There is no apparent dependence of these ratios on pulsation period., Unweighted least-squares fits in these figures yield There is no apparent dependence of these ratios on pulsation period. Plots of the ratios ol the distance uncertainties against distance and of the ratios of the radius uncertainties against radius are similarly uninformative., Plots of the ratios of the distance uncertainties against distance and of the ratios of the radius uncertainties against radius are similarly uninformative. The two ratios are. however. highly correlated with each other (22= 0.99) as shown in Figure 9..," The two ratios are, however, highly correlated with each other $R = 0.99$ ) as shown in Figure \ref{sigma_sigma}." Thus the underlviug cause of the larger uneertainties in the Davesian calculation is likely (ο be the same for the distance uicertaintv and radius uncertainty., Thus the underlying cause of the larger uncertainties in the Bayesian calculation is likely to be the same for the distance uncertainty and radius uncertainty. In section 2.1 we noted that the linear-bisector caleulation does not treat (hevariables problem rigorously nor does il properly propagate uncertainty through (he racial velocitv integration., In section 2.1 we noted that the linear-bisector calculation does not treat the problem rigorously nor does it properly propagate uncertainty through the radial velocity integration. The second of these issues will certainly lead to an underestimate of the uncertainties in (he computed clistances and radii., The second of these issues will certainly lead to an underestimate of the uncertainties in the computed distances and radii. Because the Bavesian MICAIC caleulation correctly address these (vo computational issues. we interpret the large ratio of Bavesian to bisector uneertain(y as measuring the amount bv which the linear-biseetor errors have been underestimated.," Because the Bayesian MCMC calculation correctly address these two computational issues, we interpret the large ratio of Bayesian to bisector uncertainty as measuring the amount by which the linear-bisector errors have been underestimated." This interpretation is supported by the fact (hat of the liear-bisector uncertainties isfarger (han ils Bavesian counterpart., This interpretation is supported by the fact that of the linear-bisector uncertainties is than its Bayesian counterpart. Our second result is (hat the linear- calculation underestimates the uncertainties in distance ancl in radius substantially. amounting to factors of 1.46.7 for this dataset.," Our second result is that the linear-bisector calculation underestimates the uncertainties in distance and in radius substantially, amounting to factors of 1.4–6.7 for this dataset." This large range implies that the ratio that is obtained depends on the specifies of the data for the Cepheid which varies from star to star., This large range implies that the ratio that is obtained depends on the specifics of the data for the Cepheid which varies from star to star. ]xeck I1 NIRSPEC image A and the Subaru IRCS image D.,Keck II NIRSPEC image $A$ and the Subaru IRCS image $B$. These are reproduced in Fig. 3..," These are reproduced in Fig. \ref{ao_core}," where we have marked (wo features that seem to be present in both images., where we have marked two features that seem to be present in both images. Most of the other apparent features in one or the other of the images are likely cue to speckle noise., Most of the other apparent features in one or the other of the images are likely due to speckle noise. The strongest of the “real” [features (aside from the stellar object to the east). labeled α in Fig. 3..," The strongest of the “real” features (aside from the stellar object to the east), labeled $a$ in Fig. \ref{ao_core}," lies within the error bars of the position of the radio core ancl is plausibly to be identified with (he nuclear region of 2294., lies within the error bars of the position of the radio core and is plausibly to be identified with the nuclear region of 294. The position of object « falls near a local minimun in (he //-band image of Qui, The position of object $a$ falls near a local minimum in the $H$ -band image of \citet{qui01} (see Fig. rrenbachetal.(2001) (see Fie., \ref{aoimagefig}$ $D$; this weakness may indicate that the nucleus is strongly obscured at shorter wavelengths. LD: hisiwealnessmagyindicatethalthe raysourceinaC 2294isahighlyobscuredquasarwithaluminosilyo[7 10 erg s—1., Such obscuration would be consistent with the conclusion of \citet{fab03} that the central hard X-ray source in 294 is a highly obscured quasar with a luminosity of $\sim10^{45}$ erg ${-1}$. Ifthe radio nucleus lies within the diffuse nebulosity. what is the nature of stellar object to the east?," If the radio nucleus lies within the diffuse nebulosity, what is the nature of stellar object to the east?" The density of star-like objects of similar or greater brightness at A in the field of 2294 is on the order of 10 per square arcinin. so il would be quite unusual for (here {ο be an unrelated object within," The density of star-like objects of similar or greater brightness at $K$ in the field of 294 is on the order of 10 per square arcmin, so it would be quite unusual for there to be an unrelated object within" hours.,hours. " With both feedback schemes, the accuracy of energy conservation arises because at each simulation step the entire system is integrated."," With both feedback schemes, the accuracy of energy conservation arises because at each simulation step the entire system is integrated." " Therefore, all particles are aware of the hydrodynamical state of their neighbours."," Therefore, all particles are aware of the hydrodynamical state of their neighbours." We will develop this argument in more detail in Sec. 3.., We will develop this argument in more detail in Sec. \ref{sec:individual}. " Here, we focus on how and why there is agreement between the two schemes."," Here, we focus on how and why there is agreement between the two schemes." It is somehow expected that both methods give the same results., It is somehow expected that both methods give the same results. " Indeed, Sedov's initial conditions are the total energy of the explosion and the medium density."," Indeed, Sedov's initial conditions are the total energy of the explosion and the medium density." The only requirement is that a large amount of energy is instantaneously injected in a small but its form is not specified (Landau&Lifshitz1959)., The only requirement is that a large amount of energy is instantaneously injected in a small but its form is not specified \citep{Landau1959}. ". One can input either all thermal, all kinetic or a combination of both forms and obtain the same similarity solution at any given time."," One can input either all thermal, all kinetic or a combination of both forms and obtain the same similarity solution at any given time." " Since the hydrodynamics conservation laws are used to derive the solution, a property of the similarity solution is that the fractions of thermal and kinetic energies of the blast are constant in time."," Since the hydrodynamics conservation laws are used to derive the solution, a property of the similarity solution is that the fractions of thermal and kinetic energies of the blast are constant in time." " However, in the numerical integration, a finite time is required to convert one form of energy to the other and reach the energy budget given by the analytic solution (see illustration in Fig. 4))."," However, in the numerical integration, a finite time is required to convert one form of energy to the other and reach the energy budget given by the analytic solution (see illustration in Fig. \ref{fig:concordratio}) )." As long as momentum can be converted into thermal energy by physical processes like e.g. the numerical integration of the conservation laws should reach the similarity solution., As long as momentum can be converted into thermal energy by physical processes like e.g. the numerical integration of the conservation laws should reach the similarity solution. We show in Fig., We show in Fig. 3 the time evolution of the energy conservation relative error (given by Eq. 3)), \ref{fig:concordenergy} the time evolution of the energy conservation relative error (given by Eq. \ref{eq:energyconservation}) ) " for all test simulations, where solid and dashed lines refer to the thermal and kinetic energy injection methods, respectively."," for all test simulations, where solid and dashed lines refer to the thermal and kinetic energy injection methods, respectively." Lines of the same colour are for simulations with the same numerical parameters., Lines of the same colour are for simulations with the same numerical parameters. Energy injection happens at time t=0., Energy injection happens at time $t=0$. We first concentrate on the reference simulation (black lines)., We first concentrate on the reference simulation (black lines). " We show in the plot that the violation of energy conservation happens in the early stage of the explosion (tx 1072), when the energy contrast is the largest."," We show in the plot that the violation of energy conservation happens in the early stage of the explosion $t\le10^{-2}$ ), when the energy contrast is the largest." " In the thermal case (solid line), there is initially a jump of ~0.15% around t=10~°."," In the thermal case (solid line), there is initially a jump of $\sim0.15$ around $t=10^{-5}$." " The conversion of energy into momentum happens very quickly, and after t=4x107 the evolution follows the kinetic case with an offset slowly decreasing."," The conversion of energy into momentum happens very quickly, and after $t=4\times10^{-4}$ the evolution follows the kinetic case with an offset slowly decreasing." " At later times, both curves flatten to roughly 0.8%."," At later times, both curves flatten to roughly $0.8$." ". 'The same behaviour can be seen in the energy variation tests (blue and green lines), where the input energy is decreased by a factor of 10 and 100, respectively."," The same behaviour can be seen in the energy variation tests (blue and green lines), where the input energy is decreased by a factor of 10 and 100, respectively." Decreasing the input energy slows the blast evolution and gives the time offset seen the plot., Decreasing the input energy slows the blast evolution and gives the time offset seen the plot. " With constant o, varying the input energy gives similar relative errors, providing an estimate that is independent of the energy value."," With constant $\alpha$, varying the input energy gives similar relative errors, providing an estimate that is independent of the energy value." " Moreover, energy conservation is achieved at a comparable level for both thermal and kinetic feedback."," Moreover, energy conservation is achieved at a comparable level for both thermal and kinetic feedback." b)).. with @ and b respectively equal to about 0.2 and 0.8 (Llansen&Staclel2006:: see also Luclowetal.2011. for an alternative expression). although with a substantial scatter this time.,"(r)=a , with $a$ and $b$ respectively equal to about $-0.2$ and $0.8$ \citealt{HS06}; see also \citealt{Ludea11} for an alternative expression), although with a substantial scatter this time." The origin of all these trends is certainly related with the way dark matter clusters., The origin of all these trends is certainly related with the way dark matter clusters. In hierarchical cosmologies. haloes erow through continuous mergers with notably dilleren dynamic effects according to the relative mass of the captured and capturing objects.," In hierarchical cosmologies, haloes grow through continuous mergers with notably different dynamic effects according to the relative mass of the captured and capturing objects." For this reason. it is usually. distinguished between major mergers. with a dramatic effect each. and minor mergers. contributing together with the capture of diluse matter (if anv) to the so-called accretion. responsible of just a smooth secular evolution of the system.," For this reason, it is usually distinguished between major mergers, with a dramatic effect each, and minor mergers, contributing together with the capture of diffuse matter (if any) to the so-called accretion, responsible of just a smooth secular evolution of the system." Some authors have attempted to explain the tvpical halo density profile as the result of repeated major (or intermediate) mergers (Sver&WΜπο1998:Salvador-Soléetal. 2003).," Some authors have attempted to explain the typical halo density profile as the result of repeated major (or intermediate) mergers \citep{SW98,SSM98,Suea00,Dea03}." . Others have concentrated instead in the eleets of pure accretion (PA) (Avila-Reeseetal.1998:Nusser&Shethal.2000:Manriquect2003:Ascasibaret2004:Salvador-Solé 2007).," Others have concentrated instead in the effects of pure accretion (PA) \citep{ARea98,NS99,DPea00,metal03,As04,Sea07}." . Both extreme scenarios have also been investigated regarding the possible origin of the pseudo phase-space density and. velocity anisotropy profiles (Llansen&Moore2006)., Both extreme scenarios have also been investigated regarding the possible origin of the pseudo phase-space density and velocity anisotropy profiles \citep{HM06}. . The PA scenario has received much support from the results by Wang&White(2009). showing that all tvpical halo trends are aroad set in the first generation haloes formed by monolithie collapse (ie. no major merger: only accretion of dilluse matter in warm dark matter cosmologies., The PA scenario has received much support from the results by \citet{WW09} showing that all typical halo trends are already set in the first generation haloes formed by monolithic collapse (i.e. no major merger; only accretion of diffuse matter) in warm dark matter cosmologies. Regarding the shape. CDM haloes are found to be triaxial ellipsoids. with a trend. towards prolate rather than oblate shapes (e.g. Frenketal1988:Dujinski&Culberg1991:Warrenal.1992:ColeLacey1996:Springel2004:Allgoodetal.2006:Llavashi2007:MaccióctStadel2009:Vera-Ciro 20112).," Regarding the shape, CDM haloes are found to be triaxial ellipsoids, with a trend towards prolate rather than oblate shapes (e.g. \citealt{Fea88,dc91,Wa92,CL96,Sp04,All06,Ha07,Macea07,St09,VCea11}) )." Inside cach individual object. the typical minor to major axial ratio takes a roughly uniform vaue of about 0.6. with a slight trend to an outward-decreasing triaxiality (Erenketal1988:Bulock202:Jing&Suto2002:Springelal.2004:IxasunEvrarcl2005:BailinSteinmetz 2011).," Inside each individual object, the typical minor to major axial ratio takes a roughly uniform value of about $0.6$, with a slight trend to an outward-decreasing triaxiality \citep{Fea88,Bull02,JS02,Sp04,KE05,bs05,All06,Ha07,Be07,St09,VCea11}." . The main axis is preferentially aligned. at all scales. alorig with the filament. [eeing the halo (e.g. Lemson&Ixaullmann1999:Basilakosοἱ 20113).," The main axis is preferentially aligned, at all scales, along with the filament feeding the halo (e.g. \citealt{LK99,BPYGT06,Patea06,Macea07,Ragea10,VCea11}) )." This indicates that the memory of the preferred. direction of major mergers and accretion is not erased during virialisation (Vera-Ciroctal.2011) or. equivalently. that the shape of virialisecl haloes depends on tja of their seeds.," This indicates that the memory of the preferred direction of major mergers and accretion is not erased during virialisation \citep{VCea11} or, equivalently, that the shape of virialised haloes depends on that of their seeds." Moreover. as haloes are not supported by rotation but by the local anisotropic veocity tensor. the fact that their triaxial shape is related to the shape of protohaloes automatically implies that their kinematies must also be related to it.," Moreover, as haloes are not supported by rotation but by the local anisotropic velocity tensor, the fact that their triaxial shape is related to the shape of protohaloes automatically implies that their kinematics must also be related to it." The seeds of haloes are believed to be peaks (secondary maxima) in the primordial random Caussian density field filtered at the scale of the halo., The seeds of haloes are believed to be peaks (secondary maxima) in the primordial random Gaussian density field filtered at the scale of the halo. Ehe isodensity contours in the immediate vicinity of peaks are triaxial (Doroshkevich1970). and rather prolate with a trend to become more spherical for very high peaks (Bardeenctal.1986: hereafter DDINS)., The isodensity contours in the immediate vicinity of peaks are triaxial \citep{Dor70} and rather prolate with a trend to become more spherical for very high peaks \citealt{BBKS}; hereafter BBKS). As the monolithic collapse of non-spherical systems is highly non-radial (Zeldovich.1970).. giving rise to filaments and riaxial νακο objects.," As well-known, the monolithic collapse of non-spherical systems is highly non-radial \citep{Z70}, giving rise to filaments and triaxial virialised objects." Thus. it is natural to believe that the shape of peaks is somehow translated into that of haloes. in agreement with the above mentioned alignments.," Thus, it is natural to believe that the shape of peaks is somehow translated into that of haloes, in agreement with the above mentioned alignments." A few authors (Leeetal.2005:Rossi2011). have tried to make the ink between the shape of haloes and that of peaks through the modelling of ellipsoidal collapse.," A few authors \citep{Lee05,RST11} have tried to make the link between the shape of haloes and that of peaks through the modelling of ellipsoidal collapse." Unfortunately. these models do not account for the highly non-linear effects of shell-crossing during virialisation. which play a crucial role in setting the inal properties of virialised haloes.," Unfortunately, these models do not account for the highly non-linear effects of shell-crossing during virialisation, which play a crucial role in setting the final properties of virialised haloes." On the other hand. there is in the literature no attempt to relate the kinematics of haloes with the shape of their seeds.," On the other hand, there is in the literature no attempt to relate the kinematics of haloes with the shape of their seeds." In à recent. paper. Salvador-Soléetal... (2012: hereafter SV'AIS) have shown that the kinematics of virialised haloes in (bottom-up) hierarchical cosmologies with dissipationless collisionless dark matter depends on their triaxial shape. contrarilv o their spherically averaged density. profile which does not.," In a recent paper, \citeauthor{Sea12} \citeyear{Sea12}; hereafter SVMS) have shown that the kinematics of virialised haloes in (bottom-up) hierarchical cosmologies with dissipationless collisionless dark matter depends on their triaxial shape, contrarily to their spherically averaged density profile which does not." This allowed ολο to infer. under the assumption of PA. the vpical spherically averaged densitv. profile for haloes from that of peaks in the primordial density field. determined by the »ower-speetrum of density perturbations.," This allowed SVMS to infer, under the assumption of PA, the typical spherically averaged density profile for haloes from that of peaks in the primordial density field, determined by the power-spectrum of density perturbations." Furthermore. SVMS showed that the density profile for haloes having undergone major mergers is indistinguishae from that of haloes &rown by PA. so the model actually holds for all haloes regardless of heir individual aggregation hisOLN.," Furthermore, SVMS showed that the density profile for haloes having undergone major mergers is indistinguishable from that of haloes grown by PA, so the model actually holds for all haloes regardless of their individual aggregation history." In the present. paper. we extend the SVAIS model to the kinematics and triaxial shape of virialisecl objects.," In the present paper, we extend the SVMS model to the kinematics and triaxial shape of virialised objects." Under he PA assumption and neelecting any possible rotation tically induced. by surrounding matter. we derive the halo shape. velocity anisotropy profile and oeudo phase-space density profile from the triaxial shape of peaks. taking into account the ‘all virialisation process.," Under the PA assumption and neglecting any possible rotation tidally induced by surrounding matter, we derive the halo shape, velocity anisotropy profile and pseudo phase-space density profile from the triaxial shape of peaks, taking into account the full virialisation process." We first assume the simple case of PA and then study the foresccable cllects of major mergers., We first assume the simple case of PA and then study the foreseeable effects of major mergers. This allows us to establish the ink between those twpical halo properties and the power-spectrum of density. perturbations., This allows us to establish the link between those typical halo properties and the power-spectrum of density perturbations. The heoretical predictions obtainec when this formalism is applied to CDM. haloes are in good. agreement with the results of numerical simulations., The theoretical predictions obtained when this formalism is applied to CDM haloes are in good agreement with the results of numerical simulations. The paper is organised as follows., The paper is organised as follows. In Section ??.. we derive some general relations valid for triaxial svstems. regardless of whether they are in equilibrium or not.," In Section \ref{axratio}, we derive some general relations valid for triaxial systems, regardless of whether they are in equilibrium or not." Assuming PA. these relations are used. in Section ??.. to make the link between the triaxial shape of a virialised object formed by PA and thatof its seed.," Assuming PA, these relations are used, in Section \ref{eccentricity}, to make the link between the triaxial shape of a virialised object formed by PA and thatof its seed." The tvpical velocity anisotropy and. velocity dispersion profiles for virialised objects are derived in Section ?? from their triaxial shape., The typical velocity anisotropy and velocity dispersion profiles for virialised objects are derived in Section \ref{anisotropy} from their triaxial shape. In Section ??.. we apply the model to CDM," In Section \ref{haloes}, , we apply the model to CDM" hiehly relativisüce [low is really the most plausible explanation of the CXO quasar jel observations. aud to look [or possibilities of discriminating between (his aud other models (e.g..Aharonian2002:Dermer&Atovan2002;StawarzOstrowski2002).,"highly relativistic flow is really the most plausible explanation of the CXO quasar jet observations, and to look for possibilities of discriminating between this and other models \citep[e.g.,][]{aha02,der02,sta02}." . Analysis of the morphology of the emitting regions constitutes an interesting approach to this problem., Analysis of the morphology of the emitting regions constitutes an interesting approach to this problem. The most apparent characteristic of quasar jets is their knotty morphology with high knot-to-interknot brightness contrast. but also with distinct (in some cases) inter-knot diffuse enussion.," The most apparent characteristic of quasar jets is their knotty morphology with high knot-to-interknot brightness contrast, but also with distinct (in some cases) inter-knot diffuse emission." In addition. knot profiles seem to be lvequencs-ixdependent. and knot extents are similar when observed al radio. optical ancl X-ray. photon energies.," In addition, knot profiles seem to be frequency-independent, and knot extents are similar when observed at radio, optical and X-ray photon energies." Detailed observations of the 3C 273 jet (Jesteretal.2001) reveal also that spectral changes along the flow are not correlated. with brightness changes this may be a general characteristic of these objects., Detailed observations of the 3C 273 jet \citep{jes01} reveal also that spectral changes along the flow are not correlated with brightness changes — this may be a general characteristic of these objects. Finally. in some cases spatial olfsets between the maxima of the N-ray. and radio emission within the knot regions were noted (e.g..PINS1127-145.Siemiginowskaetal.2002).," Finally, in some cases spatial offsets between the maxima of the X-ray and radio emission within the knot regions were noted \citep[e.g., PKS 1127-145,][]{sie02}." . It is nol clear whether all of these features can be explained in a Iramework of models involving extended shock waves within continuous jet flow., It is not clear whether all of these features can be explained in a framework of models involving extended shock waves within continuous jet flow. In fact. we argue that the morphological characteristics cannot be explained in this wav. and that substantial modifications of the standard picture are required.," In fact, we argue that the morphological characteristics cannot be explained in this way, and that substantial modifications of the standard picture are required." Such modifications are especially needed if (he X-ray emission of quasar Jets is due to the EIC process., Such modifications are especially needed if the X-ray emission of quasar jets is due to the EIC process. We propose that at least some aspects of the IIST and CXO observations can be understood in terms of intermittent (modulated) jet aclivitv., We propose that at least some aspects of the HST and CXO observations can be understood in terms of intermittent (modulated) jet activity. In this context. we comment on both the external-Compton scenario of quasar jet X-ray emission. and on a model of boundary laver acceleration andresulting high-energv raciation (Stawarz&Ostrowski2002).," In this context, we comment on both the external-Compton scenario of quasar jet X-ray emission, and on a model of boundary layer acceleration andresulting high-energy radiation \citep{sta02}." . In particular. in 2 we emphasize the problems with modeling X-ray knots of quasar jets as stationary regions of particle acceleration.," In particular, in 2 we emphasize the problems with modeling X-ray knots of quasar jets as stationary regions of particle acceleration." In 3 we consider the possibility (hat (he knots are moving sources of non-thermal radiation. propose a possible connection of this scenario to models of intermittent jet activity. and discuss the particle acceleration processes possibly involved in such a scenario.," In 3 we consider the possibility that the knots are moving sources of non-thermal radiation, propose a possible connection of this scenario to models of intermittent jet activity, and discuss the particle acceleration processes possibly involved in such a scenario." The discussion ancl final conclusions are presented in 4 and 5. respectively.," The discussion and final conclusions are presented in 4 and 5, respectively." In the most common version of the EIC model. in which the knots are identified with strong stationary shocks through which the jet matter flows continuously. none of the morphological features mentioned in the introduction are straightlorwarcdly expected.," In the most common version of the EIC model, in which the knots are identified with strong stationary shocks through which the jet matter flows continuously, none of the morphological features mentioned in the introduction are straightforwardly expected." The knots appear to be localized along the jet. vet stationary shocks are likely to be highly oblique (with respect to the jet axis) and significantly elongated in the flow direction. if the jel is confined by external pressure (Sanders1933:Ixomissarov&Falle 1997)..," The knots appear to be localized along the jet, yet stationary shocks are likely to be highly oblique (with respect to the jet axis) and significantly elongated in the flow direction, if the jet is confined by external pressure \citep{san83,kom97}. ." Large-scale, Large-scale galaxies and smaller than ratios measured for typical type 2 AGNs (usually 0.1. c.g. Robinson ct al. 1987)),"galaxies and smaller than ratios measured for typical type 2 AGNs (usually $>$ 0.1, e.g. Robinson et al. \citeyear{rob87}) )" The emission. lines are narrower in the tidal tail and nuc2 than at the quasar nucleus., The emission lines are narrower in the tidal tail and $nuc2$ than at the quasar nucleus. FWAOLI] = 3302-10 km and EWIINIGLT2)z 140 km for nuc2: ENILMOLLI] = 310430 Km Land ΜΕ 140 kim + for the tidal tail., FWHM[OIII] = $\pm$ 10 km $^{-1}$ and $\beta$ $\leq$ 140 km $^{-1}$ for $nuc2$; FWHM[OIII] = $\pm$ 30 km $^{-1}$ and $\beta$ $\le$ 140 km $^{-1}$ for the tidal tail. The quasar nucleus shows FEWIIM = 400440 Καὶ 1 and 3804-20 for ΟΠΗ) and 12 respectively., The quasar nucleus shows FWHM = $\pm$ 40 km $^{-1}$ and $\pm$ 20 for [OIII] and $\beta$ respectively. Thus. SDSS J0025-10 is undergoing a merger process with a companion star forming galaxy.," Thus, SDSS J0025-10 is undergoing a merger process with a companion star forming galaxy." We propose that both the companion nucleus and the northern tidal tail are photoionized by voung stars which have probably formed as a consequence of the interaction process., We propose that both the companion nucleus and the northern tidal tail are photoionized by young stars which have probably formed as a consequence of the interaction process. ΑΠΟ] is probably a companion star forming object., $knot1$ is probably a companion star forming object. We find no clear evidence [or a quasar extended ionized nebula along PA 0 or PA 60 at surface brightness levels Z3023.2.10. P erg tem? arcsecE , We find no clear evidence for a quasar extended ionized nebula along PA 0 or PA 60 at surface brightness levels $\ga$ $\sigma$ $\times$ $^{-18}$ erg $^{-1}$ $^{-2}$ $^{-2}$. The VET-FOIBS2 broad and narrow band images are shown in Fig., The VLT-FORS2 broad and narrow band images are shown in Fig. 6., 6. Xn extended diffuse structure is detected towards the N-W. whose morphology appears more clearly defined in the broad. band image ancl is reminiscent of a tidal tail.," An extended diffuse structure is detected towards the N-W, whose morphology appears more clearly defined in the broad band image and is reminiscent of a tidal tail." A compact knot is also detected to the IE. which appears relatively stronger in the narrow band image.," A compact knot is also detected to the E, which appears relatively stronger in the narrow band image." Vhis suggests that it is a strong lino emitter at the same z as the quasar., This suggests that it is a strong line emitter at the same $z$ as the quasar. The PA 116 slit crosses both the tidal tail ancl the knot., The PA 116 slit crosses both the tidal tail and the knot. The OL 2D spectrum (Fig., The $\beta$ -[OIII] 2D spectrum (Fig. 7) shows that the compact knot emits strong lines and. very faint continuum. as expected from the images.," 7) shows that the compact knot emits strong lines and very faint continuum, as expected from the images." Low surface brightness lines are also detected between the quasar and the knot. possibly emitted by an EEL associated with the quasar.," Low surface brightness lines are also detected between the quasar and the knot, possibly emitted by an EELR associated with the quasar." The structure reminiscent of a tidal tail mentioned above emits only faint. dilluse continuum.," The structure reminiscent of a tidal tail mentioned above emits only faint, diffuse continuum." The nuclear line ratios are shown in Table 2., The nuclear line ratios are shown in Table 2. The reddening derived. from the Balmer lines is most. likely wrong. since the galaxy continuum is strong and 1 and LH (not so much 112. which has larger equivalent width) are likely to be strongly. absorbed.," The reddening derived from the Balmer lines is most likely wrong, since the galaxy continuum is strong and $\gamma$ and $\delta$ (not so much $\beta$, which has larger equivalent width) are likely to be strongly absorbed." Given the large uncertainties due to this effect. we will ignore nuclear dust reddening in the diagnostic diagram in this case.," Given the large uncertainties due to this effect, we will ignore nuclear dust reddening in the diagnostic diagram in this case." The knot is dominated by line emission and is not alleetec by this problem: Ly /1E72-0.4643:0.03 is consistent with the case B recombination value 0.47 (Osterbrock 1989))., The knot is dominated by line emission and is not affected by this problem: $\gamma$ $\beta$ $\pm$ 0.03 is consistent with the case B recombination value 0.47 (Osterbrock \citeyear{ost89}) ). It is therefore not reddened., It is therefore not reddened. Three apertures were used to extract. LD spectra from dilferent spatial regions along the slit (Fig., Three apertures were used to extract 1D spectra from different spatial regions along the slit (Fig. 7. top): the knot. the quasar and the intermediate region between them.," 7, top): the knot, the quasar and the intermediate region between them." The location of the individual spectra are shown in the diagnostic diagram., The location of the individual spectra are shown in the diagnostic diagram. While the nuclear spectrum. lies very far [from the LU galaxies and is consistent with the AGN models (also Hell is strong. 1115502050.00: Table 2). the knot overlaps with the LLL galaxy region.," While the nuclear spectrum lies very far from the HII galaxies and is consistent with the AGN models (also HeII is strong, $\beta$ $\pm$ 0.06; Table 2), the knot overlaps with the HII galaxy region." For the intermediate region. lower limits are shown. due to the non detection of 1123.," For the intermediate region, lower limits are shown, due to the non detection of $\beta$." Ehe location overlaps with the LILLE galaxy region as well., The location overlaps with the HII galaxy region as well. The lines emitted. by the knot. are. split. into. two kinematics components (see Fig., The lines emitted by the knot are split into two kinematics components (see Fig. Y. top).," 7, top)." The dominant component is very narrow (EWIIM. <120 km s |) and shows very low /113—3.6-E0.3., The dominant component is very narrow (FWHM $\la$ 120 km $^{-1}$ ) and shows very low $\beta$ $\pm$ 0.3. μονο properties and its location on the LIL regionὃν area in the diagnostico diagramso sugeest that the knot is a star forming object where the gas is photoionized by voung stars., These properties and its location on the HII region area in the diagnostic diagrams suggest that the knot is a star forming object where the gas is photoionized by young stars. Lt is redshiftecl by -260+70, It is redshifted by $\pm$ 70 this model is captured by equation 7. (Section 2.1.1)).,this model is captured by equation \ref{eqn:mass2mag} (Section \ref{sec:eqns}) ). For convenience. we invert this equation to obtain where {f(2) is defined by equation 2..," For convenience, we invert this equation to obtain where $H(z)$ is defined by equation \ref{eqn:Hz}." Equation 13 can be used to take à quasar with observed bolometric luminosity Lo at redshift z and predict its halo virial mass. assuming values for parameters 5 (the relationship between virial and circular velocities) and 5 (the Eddington luminosity fraction of the quasar).," Equation \ref{eqn:mag2mass} can be used to take a quasar with observed bolometric luminosity $L_Q$ at redshift $z$ and predict its halo virial mass, assuming values for parameters $\gamma$ (the relationship between virial and circular velocities) and $\eta$ (the Eddington luminosity fraction of the quasar)." Equation 13. is plotted in figure 10.., Equation \ref{eqn:mag2mass} is plotted in figure \ref{fig:evolution}. From this figure alone the quasar host virial mass (either. individual or averaged: over a group) for a given quasar Luminosity and redshift may be simply. reacl oll (solid lines)., From this figure alone the quasar host virial mass (either individual or averaged over a group) for a given quasar luminosity and redshift may be simply read off (solid lines). We emphasise. We discuss the uncertainty on such masses below.," We emphasise, We discuss the uncertainty on such masses below." Also over-plottecl in figure 10. are the corresponding mean space densities of quasar hosts. (dashed lines). calculated. from the quasar luminosity (Section 2.2)). and the black hole mass at fixed. luminosity (horizontal dotted lines). as given by equation 6..," Also over-plotted in figure \ref{fig:evolution} are the corresponding mean space densities of quasar hosts (dashed lines), calculated from the quasar luminosity (Section \ref{sec:selection}) ), and the black hole mass at fixed luminosity (horizontal dotted lines), as given by equation \ref{eqn:LQ}." The spacing of density contours relative to halo mass ughliehts a main result. of this work. which is that the distribution. of the masses of dark matter halos hosting quasars narrows with decreasing redshift.," The spacing of density contours relative to halo mass highlights a main result of this work, which is that the distribution of the masses of dark matter halos hosting quasars narrows with decreasing redshift." This leads to xhaviour such as luminosity dependent. clustering at. high redshift but not at low (see Section. 3.8)). and. luminosity dependent quasar Lifetimes at. low redshift but. not. high (κος Section 3.4)).," This leads to behaviour such as luminosity dependent clustering at high redshift but not at low (see Section \ref{sec:lumclustering}) ), and luminosity dependent quasar lifetimes at low redshift but not high (see Section \ref{sec:lifetimes}) )." Also. as discussed. Section 3.5... the urnover of density contours at zX2 relative to black hole mass demonstrates downsizing in the black hole population.," Also, as discussed Section \ref{sec:BHMF}, the turnover of density contours at $z \simlt 2$ relative to black hole mass demonstrates downsizing in the black hole population." At higher redshifts. rare massive black holes show no downsizing trend. whereas the more common L quasars are predicted to be upsizing. especially at redshifts greater than 2o.," At higher redshifts, rare massive black holes show no downsizing trend, whereas the more common $L^*$ quasars are predicted to be upsizing, especially at redshifts greater than $z \sim 4$." 3elore applving our model (particularly equation. 13)) to an observation or set of observations Ἡ djs prudent to understand the limits to which dark matter halo mass can be inferred given both the built in theoretical and observational uncertainties., Before applying our model (particularly equation \ref{eqn:mag2mass}) ) to an observation or set of observations it is prudent to understand the limits to which dark matter halo mass can be inferred given both the built in theoretical and observational uncertainties. Observational error is drawn from local measurements and has been propagated through cach equation appropriately., Observational error is drawn from local measurements and has been propagated through each equation appropriately. Near the characteristic luminosity οἱ the quasar population.; Log1012517h-;L.. the mass error has magnitude 0.32 dex in log units.," Near the characteristic luminosity of the quasar population, $L_Q/\eta\sim 10^{12}h_{70}^{-1}L_\odot$, the mass error has magnitude $0.32$ dex in log units." One magnitude brighter or fainter than this increases the error to 0.34 dex. whereas two magnitudes translates to an error of 0.39 dex.," One magnitude brighter or fainter than this increases the error to $0.34$ dex, whereas two magnitudes translates to an error of $0.39$ dex." While somewhat large at the extremes. this uncertainty is still sullicientlv manageable that tight clustering constraints," While somewhat large at the extremes, this uncertainty is still sufficiently manageable that tight clustering constraints" We calibrated the photometry relative to 2MASS.,We calibrated the photometry relative to 2MASS. However. there was uot a sufficient nuuber of nusaturated stars in the field of to do this iu one step.," However, there was not a sufficient number of unsaturated stars in the field of to do this in one step." We therefore used other fields observed ou the same uight over a range of ailnuiasses. uerallv below 1.2.," We therefore used other fields observed on the same night over a range of airmasses, generally below $1.2$." Using only stars that were still in he linear reginae of the detector and were not crowded (16 stars in cach field over 5 fields). we used aperture photometry im with a large aperture of 179 radius and a sky auuulus from 275 to 3δ.," Using only stars that were still in the linear regime of the detector and were not crowded (1–6 stars in each field over 5 fields), we used aperture photometry in with a large aperture of $1\farcs9$ radius and a sky annulus from $2\farcs5$ to $3\farcs8$." We corrected to airinass of 1.0 using approximate airmass cocfitcicuts for he site (0.10. 0.03. and 0.07 + for J. Jf. and AS respectively) aud determined the zero-poiuts for he night.," We corrected to airmass of 1.0 using approximate airmass coefficients for the site (0.10, 0.03, and 0.07 $^{-1}$ for $J$, $H$, and $K_s$ respectively) and determined the zero-points for the night." " The final photometry for Hs J=18.590.02. fF=18.35+0.06. and A,=15.398+ 0.06. where the errors are statistical onlv."," The final photometry for is $J=18.59\pm0.02$, $H=18.37\pm0.06$, and $K_s=18.38\pm0.06$ , where the errors are statistical only." " We estimate that the uncertainties in the photometric zero points were at nost 0.03 mae for A, aud 11. aud 0.02 for J."," We estimate that the uncertainties in the photometric zero points were at most 0.03 mag for $K_s$ and $H$, and 0.02 for $J$." Spectra of the optical counterpart to wwere taken on the nieht of 1999 July 15 using FORSI at the Very Large Telescope., Spectra of the optical counterpart to were taken on the night of 1999 July 15 using FORS1 at the Very Large Telescope. The setup was tle same as that usedby ?. for a spectroscopic study of the faint neutron star. RN 3751 (Cain 300V with R300. AA//pix dispersion: wwide loue-sht. //pix spatial scale).," The setup was the same as that usedby \citet{2001A&A...378..986V} for a spectroscopic study of the faint neutron star, RX $-$ 3754 (Grism 300V with $R\approx$ 300, /pix dispersion; wide long-slit, /pix spatial scale)." The reduction followed that described by those authors., The reduction followed that described by those authors. Briefly. two 15-nuuute spectra were taken. covering the range of 3600 to aat a resolution of ~12À.. with the slit position angle thosen such that both the counterpart aud star 1 of ? wereσ," Briefly, two 45-minute spectra were taken, covering the range of 3600 to at a resolution of $\sim\!13$, with the slit position angle chosen such that both the counterpart and star 1 of \cite{1993ApJ...411L..83B} were." "ον The reductiou involved bias subtraction. sky subtraction.οςδι, aud optimal extraction (7) of the spectra of the counterpart using the spatial profile of star 1."," The reduction involved bias subtraction, sky subtraction, and optimal extraction \citep{1986PASP...98..609H} of the spectra of the counterpart using the spatial profile of star 1." Flux calibration was doue in two steps., Flux calibration was done in two steps. " First. we calibrated the fluxes of star 1 using a shorter. 5-uinute spectrum taken through a wide slit (with he instrumental response doeterimüned from two fiux standards: see ὃν, especially their E11)."," First, we calibrated the fluxes of star 1 using a shorter, 5-minute spectrum taken through a wide slit (with the instrumental response determined from two flux standards; see \citealt{2001A&A...378..986V}, especially their 4.4)." Next. we estimated the slit losses by fitting a quadratic fiction to he ratio of the narrow-slit to wide-slit spectra of star 1. and used this to calibrate the fluxes of the counterpart.," Next, we estimated the slit losses by fitting a quadratic function to the ratio of the narrow-slit to wide-slit spectra of star 1, and used this to calibrate the fluxes of the counterpart." Overall. we believe our relative fluxes should be accurate o about between 1500 audAA.," Overall, we believe our relative fluxes should be accurate to about between 4500 and." . Shortward ofAA.. the calibration is more uncertain. since it is less clear whether our slit losses are corrected well: the ratio of the narrow- to wide-slit spectra of star 1 shows systematic. ~1056 deviations. likely because the wide-slit spectra were taken at high ainmass.," Shortward of, the calibration is more uncertain, since it is less clear whether our slit losses are corrected well: the ratio of the narrow- to wide-slit spectra of star 1 shows systematic, $\sim\!10$ deviations, likely because the wide-slit spectra were taken at high airmass." The absolute flux calibration is also less certain. since there was some οταν at the start of the nieht.," The absolute flux calibration is also less certain, since there was some cirrus at the start of the night." We find that we have to scale the fluxes up by to match theHST photometry in 82.1., We find that we have to scale the fluxes up by to match the photometry in 2.4. Furthermore. some regions of the spectrm are contaminated by atimospheric absorption aud high backeround we have simply excluded these areas from consideration.," Furthermore, some regions of the spectrum are contaminated by atmospheric absorption and high background – we have simply excluded these areas from consideration." — We analysed several observations of wwith theHST. both imaging (WFPC2 and ACS) and spectroscopy (ACS).," We analysed several observations of with the, both imaging (WFPC2 and ACS) and spectroscopy (ACS)." The Advanced Camera for Surveys (ACS) observations consisted originally of five visits. oue in the NUV and optical using the IHieli-resolution Camera (IRC) and the reniünder in the FUV. using the Solar-blind Chaunel (SBC) detector.," The Advanced Camera for Surveys (ACS) observations consisted originally of five visits, one in the NUV and optical using the High-resolution Camera (HRC) and the remainder in the FUV, using the Solar-blind Channel (SBC) detector." We retrieved WEPC2 obscrvatious of the field of19... taken in the two wide-band filters PSSSW and FalWW (roushly V aud I baud) ou 1996-05-19.," We retrieved WFPC2 observations of the field of, taken in the two wide-band filters F555W and F814W (roughly V and I band) on 1996-05-19." There were four exposures of 1LOss each. for a total of ss taken through each filter.," There were four exposures of s each, for a total of s taken through each filter." " The source was located on the PC chip of the rav in every case. with a pixel scale of 0.0155"" /pix."," The source was located on the PC chip of the array in every case, with a pixel scale of $\arcsec$ /pix." Photometry was performed using IISTphot (?).. a software package optimized to WEPC2 photometry bv profile fitting.," Photometry was performed using HSTphot \citep{2000PASP..112.1383D}, a software package optimized to WFPC2 photometry by profile fitting." It efiicicutly rejects bad data (hot pixels aud cosmic rav hits) and fits stellar profiles from libraries of pre-built PSF images (originally created using TiuvTia)., It efficiently rejects bad data (hot pixels and cosmic ray hits) and fits stellar profiles from libraries of pre-built PSF images (originally created using TinyTim). For the source. we obtained (Vega-maguitudes) Επ=20.899(10) and mpgsipw=19.116(8).," For the source, we obtained (Vega-magnitudes) $m_{\rm F555W}=20.899(10)$ and $m_{\rm F814W}=19.416(8)$." Since the observations were taken carly in the WEPC? lifetime. the charec transter efficiency. (CTE) corrections are very sanall.," Since the observations were taken early in the WFPC2 lifetime, the charge transfer efficiency (CTE) corrections are very small." huaeiug observations are required by the prism spectroscopy. as a wav to set the waveleugth scale for cach extracted spectrum.," Imaging observations are required by the prism spectroscopy, as a way to set the wavelength scale for each extracted spectrum." These images are useful. iu their own right. for accurate broad-band photometry.," These images are useful, in their own right, for accurate broad-band photometry." From our observations. we have three bauds. E555W. F330W and FLLOLP. cach with a detection of the suvsteii.," From our observations, we have three bands, F555W, F330W and F140LP, each with a detection of the system." One exposure was acquired in cach single orbit. at the start of cach orbit for the NUV. aud the end for the FUV.," One exposure was acquired in each single orbit, at the start of each orbit for the NUV and the end for the FUV." We performed aperture photometry on these. with an aperture size set to contain about of the flux. which maximizes the signal-to-noise.," We performed aperture photometry on these, with an aperture size set to contain about of the flux, which maximizes the signal-to-noise." The correction to total flux was done using the encircled energy. tables in the (sce also ?)). aud converted to flux using the information supplied iu the nuage headers.," The correction to total flux was done using the encircled energy tables in the (see also \citealt{2005PASP..117.1049S}) ), and converted to flux using the information supplied in the image headers." These are based ou the latest calibration at the time of download (Jauuary 2010)., These are based on the latest calibration at the time of download (January 2010). Figure 3. shows the fields centered on Hn the three broad-band filters., Figure \ref{imaging} shows the fields centered on in the three broad-band filters. For F555W aud F110LP. iiultiple images could be used to effectively remove cosmic ravs aud detector blenishes.," For F555W and F140LP, multiple images could be used to effectively remove cosmic rays and detector blemishes." We oulv had one P330W image to work with. however. so such rejection was not possible.," We only had one F330W image to work with, however, so such rejection was not possible." No CR is seen in or around the photometry aperture., No CR is seen in or around the photometry aperture. The CTE correction for the flux in E555W is very simall because the source is comparatively bright iu thatter®., The CTE correction for the flux in F555W is very small because the source is comparatively bright in that. . Ou the other haud. the E330. fux does have a substantial correction of the order .," On the other hand, the F330W flux does have a substantial correction of the order ." . In this case. the flux is already relatively uncertain (see Table 3). aud the CTE effect also mereases the muicertaiuty.," In this case, the flux is already relatively uncertain (see Table 3), and the CTE effect also increases the uncertainty." a simple cliscontinnitw. but rather with several locations of large electric currents.,"a simple discontinuity, but rather with several locations of large electric currents." It is important to note Chat (he velocities in the upper part of the jet ἐς>1.5 Mm) are directed upward during the entire evolution., It is important to note that the velocities in the upper part of the jet $z > 1.5$ Mm) are directed upward during the entire evolution. No downflows are found in (he jet al anv point in time. in contrast to the simulated spicules of twpe1. in which both up and downllows are found.," No downflows are found in the jet at any point in time, in contrast to the simulated spicules of type, in which both up and downflows are found." The rapid [facing of the jet at the end of its evolution is described in detail in section ??.., The rapid fading of the jet at the end of its evolution is described in detail in section \ref{sec:fading}. A movie of the jet evolution is provided as on-line material accompanying this paper., A movie of the jet evolution is provided as on-line material accompanying this paper. A detailed description of the setup and evolution of the flux emergence in this simulation have been given in detail by Martinez-Svkoraetal.(2008.," A detailed description of the setup and evolution of the flux emergence in this simulation have been given in detail by \citet{paper1,Martinez-Sykora:2009rw}." 2009b).. Martinez-Svkora(2000b) «demonstrated (hat [Iux emergence causes the magnetic field to expand into the corona. and that this expansion produces discontinuities in the coronal field.," \citet{Martinez-Sykora:2009rw} demonstrated that flux emergence causes the magnetic field to expand into the corona, and that this expansion produces discontinuities in the coronal field." We believe that (his also applies to the regions of large magnetic field gradient obtained in (he present paper., We believe that this also applies to the regions of large magnetic field gradient obtained in the present paper. These discontinuities are the source of the Joule heating which produces the hot loops. ancl iive (he indirect consequence of producing the jet upllow. as described below.," These discontinuities are the source of the Joule heating which produces the hot loops, and have the indirect consequence of producing the jet upflow, as described below." We have located emergence events in individual eranules at the photosphere that are ikelv precursors of the jet described in the other sections., We have located emergence events in individual granules at the photosphere that are likely precursors of the jet described in the other sections. The sequence of images shown in Fig., The sequence of images shown in Fig. d shows one such event., \ref{fig:emerg3d} shows one such event. In (he six panels comprising the ligure we illustrate the emergence and gradual blending of a set of field. lines (green. lines) with a set of field ines representing the pre-existing Ποια in the vieinity of the jet (blue lines)., In the six panels comprising the figure we illustrate the emergence and gradual blending of a set of field lines (green lines) with a set of field lines representing the pre-existing field in the vicinity of the jet (blue lines). Also shown is the velocity field in the photosphere. ie. at height 2=0 Mm. and the logarithin of ihe temperature in an 2— plane placed al y=6 Mm (this is the same plane used to describe (he jet in Fig. 5)).," Also shown is the velocity field in the photosphere, i.e. at height $z=0$ Mm, and the logarithm of the temperature in an $x-z$ plane placed at $y=6$ Mm (this is the same plane used to describe the jet in Fig. \ref{fig:forc}) )." In the upper left panel. at /=850 s. the emerging field within a granule (see the horizontal component in the photosphere of the green lines) shows one footpoint connected to the convection zone. while the other footpoint is linked somewhere below the photosphere to field lines that expancl into the chromosphere. forming loops that are oriented al an angle to the pre-existing field.," In the upper left panel, at $t=850$ s, the emerging field within a granule (see the horizontal component in the photosphere of the green lines) shows one footpoint connected to the convection zone, while the other footpoint is linked somewhere below the photosphere to field lines that expand into the chromosphere, forming loops that are oriented at an angle to the pre-existing field." In the top center panel. at /=1050 s. these field lines are seen to connect to newly emerged horizontal field oriented in the y-direction with [footpoints near the pre-existing field [oot points.," In the top center panel, at $t=1050$ s, these field lines are seen to connect to newly emerged horizontal field oriented in the $y$ -direction with footpoints near the pre-existing field foot points." As the emereing field continues to rise into the chromosphere. shown in the top right and bottom left panels at /=1200 s and /=1300 5 respectively. the strong hairpin curve in (he emereine field is seen to become shallower as the field straightens ancl the field lines beein to blend with the pre-existing field," As the emerging field continues to rise into the chromosphere, shown in the top right and bottom left panels at $t=1200$ s and $t=1300$ s respectively, the strong hairpin curve in the emerging field is seen to become shallower as the field straightens and the field lines begin to blend with the pre-existing field" and where pp is (he maximun momentum in (he Fermi distribution ancl is related to the proper particle densitv V/V bv If we define the Fermi velocity ej by [add ep are independent of particle properties.,and where $p_{F}$ is the maximum momentum in the Fermi distribution and is related to the proper particle density $N/V$ by If we define the Fermi velocity $v_F$ by $t$ and $v_F$ are independent of particle properties. substituting the above expressions for p aud e into Eqs. (12)), Substituting the above expressions for $p$ and $\epsilon$ into Eqs. \ref{dudr}) ) " and (13)) one obtains: and These equations are to be integrated from the values vu=0.//p alr=O lor=ry, where /,=0 (which makes p= 0). aud «=wy."," and \ref{dpdr}) ) one obtains: and These equations are to be integrated from the values $u=0, t=t_0$ at $r=0$ to $r=r_b$ where $t_b = 0$ (which makes $p=0$ ), and $u = u_b$." 50 lar. (he equations are written in relativistic units. Le. such that e=1.G1.," So far, the equations are written in relativistic units, i.e., such that $c = 1, G=1$." This determines the unit of time and the unit of mass in terms of still arbitrary unit of length., This determines the unit of time and the unit of mass in terms of still arbitrary unit of length. jets in powerful radio sources clisplay approximately evlindrical geometry. and therefore it is thought that thev must be confined.,"jets in powerful radio sources display approximately cylindrical geometry, and therefore it is thought that they must be confined." The nature of their confinement is unknown. but it has been shown that the low-densitv and high-pressure nonthermal medium of the radio lobe can be an efficient confinement agent (Begelman&Ciolli1989).," The nature of their confinement is unknown, but it has been shown that the low-density and high-pressure nonthermal medium of the radio lobe can be an efficient confinement agent \citep{beg89}." . If we are not seeing the shape of the shocks themselves. could the emissivitv patterns give rise to the knot morphology?," If we are not seeing the shape of the shocks themselves, could the emissivity patterns give rise to the knot morphology?" It seenis unlikely. since the cooling time of low-enerev electrons responsible for up-scattering CAMB photons to the observed. X-ray energies is extremely long when compared with the lifetime of electrons emitüing svuchrotron optical photons in an equiparütion magnetic field.," It seems unlikely, since the cooling time of low-energy electrons responsible for up-scattering CMB photons to the observed X-ray energies is extremely long when compared with the lifetime of electrons emitting synchrotron optical photons in an equipartition magnetic field." In addition. the EIC emission is not. very. sensitive to the magnetic field structure or slow adiabatie losses within the uniform. well-collimatecl flow.," In addition, the EIC emission is not very sensitive to the magnetic field structure or slow adiabatic losses within the uniform, well-collimated flow." Therefore. in the case of the EIC model and a continuous jet wil knot regions marking the positions of the stationary (e.g.. reconlinement) shocks. one should rather expect extended. X-rav. knot emission. with approximately constant [flux along the jet Gl the jet bulk velocity is roughly constant. on the large scales). and with knot profiles reflecting directly the laree differences in radiative and acliabatic cooling times of electrons radiating in radio. optical and. X-ravs.," Therefore, in the case of the EIC model and a continuous jet with knot regions marking the positions of the stationary (e.g., reconfinement) shocks, one should rather expect extended X-ray knot emission, with approximately constant flux along the jet (if the jet bulk velocity is roughly constant on the large scales), and with knot profiles reflecting directly the large differences in radiative and adiabatic cooling times of electrons radiating in radio, optical and X-rays." This is in disagreement wilh observations. and hence modifications to the EIC! model are required.," This is in disagreement with observations, and hence modifications to the EIC model are required." One possibility is to assume an inhomogeneous structure of the emission regions. consisting of a number of small. [zn-from-equipartition and adiabatically expanding clumps of radiating plasma (Tavecchioetal.2003).," One possibility is to assume an inhomogeneous structure of the emission regions, consisting of a number of small, far-from-equipartition and adiabatically expanding clumps of radiating plasma \citep{tav03}." . The EIC model was claimed to be strongly supported by energetic arguments 2001)., The EIC model was claimed to be strongly supported by energetic arguments \citep{ghi01}. . Let us briefly re-discuss this issue in the context of (he clumping scenario., Let us briefly re-discuss this issue in the context of the clumping scenario. " If the jet is composed of a magnetic field of unknown intensity. 2 (measured in the comoving [rame?)). protons. and radiating electrons. one can find a value of the magnetic field that minimizes (he total kinetic power of the emission regions lor a given observed svnchrotron Iuninosity. Loy. observed volume of the emitting plasma V. ratio of proton-to-electron energy densities jjΞuw,1/ui. spectral energy distribution of the radiating ultrarelativistic electrons. bulk Lorentz [actor D. ancl jet inclination 0."," If the jet is composed of a magnetic field of unknown intensity $B$ (measured in the comoving ), protons, and radiating electrons, one can find a value of the magnetic field that minimizes the total kinetic power of the emission regions for a given observed synchrotron luminosity $L_{\rm syn}$, observed volume of the emitting plasma $V$, ratio of proton-to-electron energy densities $\eta \equiv u'_{\rm p}/u'_{\rm e}$, spectral energy distribution of the radiating ultrarelativistic electrons, bulk Lorentz factor $\Gamma$, and jet inclination $\theta$." This is because the total jet power is Ly. where the Povuting. flux is. Lyx>B-. the bulk kinetic. power carried. by the radiating electrons is Lexui. and the bulk kinetic power due to the protons is Lyxur.," This is because the total jet power is $L_{\rm tot} = L_{\rm B} + L_{\rm e} + L_{\rm p}$ , where the Poynting flux is $L_{\rm B} \propto B^2$, the bulk kinetic power carried by the radiating electrons is $L_{\rm e} \propto u'_{\rm e}$, and the bulk kinetic power due to the protons is $L_{\rm p} \propto u'_{\rm p}$." As the electron energy density. for. a given- total synchrotron IuminosityB isB vlxB> 7. one has," As the electron energy density for a given total synchrotron luminosity is $u'_{\rm e} \propto B^{-2}$ , one has" Gravitational radiatiou appears to be a major channel in the emissious roni the torus iu long bursts. along with cinissions iu ucutrinos aud winds comune off the torus.,"Gravitational radiation appears to be a major channel in the emissions from the torus in long bursts, along with emissions in neutrinos and winds coming off the torus." Calculations iu the suspeucded-accretion state indicate a jet luminosity in gravitational waves of about ouc-third the net Iunuinositv of he black hole? This amounts to a fluence Ey about 14 of the mass-cherey of the central black hole.," Calculations in the suspended-accretion state indicate a net luminosity in gravitational waves of about one-third the net luminosity of the black \cite{mvp01d} This amounts to a fluence $E_{gw}$ about $1\%$ of the mass-energy of the central black hole." The frequency fy ta these enmissious at twice the Iseplerian frequency of the torus. as it develops a quadrupole moment iu its nass distribution. is expected to be about 1-2kIIz for a black hole mass of about 10A/..," The frequency $f_{gw}$ in these emissions at twice the Keplerian frequency of the torus, as it develops a quadrupole moment in its mass distribution, is expected to be about 1-2kHz for a black hole mass of about $10M_\odot$." This range overlaps with the design bandwidth of 0.1-1.5XIIz of the upconmiug Laser Tuterferometric Gravitational Wave Observatories LIGO/VIRGO., This range overlaps with the design bandwidth of 0.1-1.5kHz of the upcoming Laser Interferometric Gravitational Wave Observatories LIGO/VIRGO. " This raises an unanticipated prospect: calorimetric evidence for Kerr black holes from the emission iu C»eravitational waves from the torus! Iudeed. consicer the product a=27E,f£, Which expresses a nieasure for the ratio of rotational cherey to the linear size of the inner cneine."," This raises an unanticipated prospect: calorimetric evidence for Kerr black holes from the emission in gravitational waves from the \cite{mvp01e} Indeed, consider the product $\alpha=2\pi E_{gw}f_{gw}$, which expresses a measure for the ratio of rotational energy to the linear size of the inner engine." It appears that à from black svstenis may reach values in excess of those attainable by rapidly rotating neutron stars., It appears that $\alpha$ from black hole-torus systems may reach values in excess of those attainable by rapidly rotating neutron stars. " A LICO/VIRGO detection of a large a. therefore. individually Or as an average over a saniple of detections. would be evidence for the Kerr relationship £,,;AL/3 between the rotational cucrev [νε aud the mass AL of a rapidly rotating black hole."," A LIGO/VIRGO detection of a large $\alpha$, therefore, individually or as an average over a sample of detections, would be evidence for the Kerr relationship $E_{rot}\sim M/3$ between the rotational energy $E_{rot}$ and the mass $M$ of a rapidly rotating black hole." The proposed association of gamuna-ray bursts to black hole-torus systeuis will be reviewed in 822. and prospects for GRDs as potential LIGO/VIRGO sources is outlines in 8323.," The proposed association of gamma-ray bursts to black hole-torus systems will be reviewed in 2, and prospects for GRBs as potential LIGO/VIRGO sources is outlines in 3." We close with a comment on the potential for calorunetric evidence of I&err black holes in CRBs., We close with a comment on the potential for calorimetric evidence of Kerr black holes in GRBs. A black hole-torus svstem is of compact dimension. consistent with the short time-variability iu the CRB lieht-curves aud the proposed CRB-SNT association.," A black hole-torus system is of compact dimension, consistent with the short time-variability in the GRB light-curves and the proposed GRB-SXT association." The mass iu the surrounding torus or disk will be lnited. iu both the hyperuovae and binary black hole-ueutron star coalescence scenario.," The mass in the surrounding torus or disk will be limited, in both the hypernovae and binary black hole-neutron star coalescence scenario." This introduces relatively short time-scales of accretion. leaving a central Werr black hole as the major enerey reservoir.," This introduces relatively short time-scales of accretion, leaving a central Kerr black hole as the major energy reservoir." This poses two questions: what accounts for the duration in long GRBs aud how can the rotational energy of the black hole create barvou poor jets?, This poses two questions: what accounts for the duration in long GRBs and how can the rotational energy of the black hole create baryon poor jets? A black hole-torus svstem may form from binary black hole-neutrou star coalescence., A black hole-torus system may form from binary black hole-neutron star coalescence. Tere. the neutron star eradually approaches the black hole by augular womentum loss iu gravitational radiation.," Here, the neutron star gradually approaches the black hole by angular momentum loss in gravitational radiation." The neutron star will then be subject to tidal interactions. which max lead to break-up outside the inner most stable circular," The neutron star will then be subject to tidal interactions, which may lead to break-up outside the inner most stable circular" proposed here.,proposed here. The empirical model is based on probability istributions. and no specific physical assumptions are made in writing down the probability distributions.," The empirical model is based on probability distributions, and no specific physical assumptions are made in writing down the probability distributions." GET provides a physical basis for a probability distribution mt. according to I5dwards Stappers (2004).. reflects the distribution of points seen in Figure 1..," GFR provides a physical basis for a probability distribution that, according to Edwards Stappers \shortcite{ES04}, reflects the distribution of points seen in Figure \ref{figES}." Hlowever. this is not the interpretation that we suggest.," However, this is not the interpretation that we suggest." Our interpretation is based on the polarizations of the two orthogonal modes nearly canceling: provided the two modes have nearly equal intensities their sum is weakly polarized. with a wide spread in polarization.," Our interpretation is based on the polarizations of the two orthogonal modes nearly canceling: provided the two modes have nearly equal intensities their sum is weakly polarized, with a wide spread in polarization." With our assumption that the OPMs are polarized. i£ the intensities are markedly. different (in a given. pulse) then the polarization is necessarily close to that of the mode with the higher intensity.," With our assumption that the OPMs are polarized, if the intensities are markedly different (in a given pulse) then the polarization is necessarily close to that of the mode with the higher intensity." An implication of the interpretation we propose is that the points around the annulus must be weakly. polarized., An implication of the interpretation we propose is that the points around the annulus must be weakly polarized. Phere is no such implication with the GER. interpretation., There is no such implication with the GFR interpretation. There is à major cdillieulty in understanding how radiation can be produced in two modes with nearly equal intensities and significantly dillerent ray. paths., There is a major difficulty in understanding how radiation can be produced in two modes with nearly equal intensities and significantly different ray paths. llow the radiation becomes separated into two natural modes is poorly understood., How the radiation becomes separated into two natural modes is poorly understood. Most. radio emission mechanisms favor radiation into a single natural mocoe., Most radio emission mechanisms favor radiation into a single natural mode. For example. any maser process that causes one mode o grow faster than the other leads. after many. growth ines. to the faster growing mode completely dominating.," For example, any maser process that causes one mode to grow faster than the other leads, after many growth times, to the faster growing mode completely dominating." In principle. this need not be the case: if the erowth rate is arger than the rate of generalized. Faraday rotation. and if the maser is intrinsically polarized. with a polarization dilferent. from that of either natural mode in the medium. hen the growing radiation can be an intrinsic mixture of he two natural modes (Alelrose&Judge2004).," In principle, this need not be the case: if the growth rate is larger than the rate of generalized Faraday rotation, and if the maser is intrinsically polarized with a polarization different from that of either natural mode in the medium, then the growing radiation can be an intrinsic mixture of the two natural modes \cite{MJ04}." . Although he conditions required for this to apply seem. implausible. he alternatives scem even less plausible.," Although the conditions required for this to apply seem implausible, the alternatives seem even less plausible." “Phe alternative is that the emission. mechanism results in a single mocoe. and that the separation into two moces occurs somewhere along the propagation path.," The alternative is that the emission mechanism results in a single mode, and that the separation into two modes occurs somewhere along the propagation path." Although mode coupling does occur due to inhomogeneitv. it is usually a weak. elfect. whereas the interpretation of OPMs requires comparable intensities in the two modes.," Although mode coupling does occur due to inhomogeneity, it is usually a weak effect, whereas the interpretation of OPMs requires comparable intensities in the two modes." This is especially the case for the interpretation of the broad. spread. in. polarization shown in Figure 1:: our modeling suggests that this implies that {ο is strongly correlated with ἐν., This is especially the case for the interpretation of the broad spread in polarization shown in Figure \ref{figES}: our modeling suggests that this implies that $I_2$ is strongly correlated with $I_1$. Ellective mode mixing could occur due to reflection of waves olf a sharp bouncdarv. which would need to be near the source region to be ellective. (," Effective mode mixing could occur due to reflection of waves off a sharp boundary, which would need to be near the source region to be effective. (" Far from the source the refractive indices are very close to unity. precluding significantly: dillerent. ray paths for the two modes. as seems to be essential for the interpretation of OPMs.),"Far from the source the refractive indices are very close to unity, precluding significantly different ray paths for the two modes, as seems to be essential for the interpretation of OPMs.)" However. there is no model which incorporates reflection olf sharp boundaries.," However, there is no model which incorporates reflection off sharp boundaries." Moreover. near the source one of the modes should have wave properties close to the vacuum. referred to as the X mode by Arons Barnard (1986).. and this neither reflects olf sharp graclients nor otherwise couples to the other mode.," Moreover, near the source one of the modes should have wave properties close to the vacuum, referred to as the X mode by Arons Barnard \shortcite{AB86}, and this neither reflects off sharp gradients nor otherwise couples to the other mode." In. brief. it is very clillicult to account for. pulsar radiation that is an approximately equal mixture of two natural mocdes. despite the overwhelming observational evidence that the radiation is such à mixture.," In brief, it is very difficult to account for pulsar radiation that is an approximately equal mixture of two natural modes, despite the overwhelming observational evidence that the radiation is such a mixture." Hopefully. further use of empirical models will lead to information on the polarizations of the OPAIs that will help constrain the mechanism that leads to the separation into two modes.," Hopefully, further use of empirical models will lead to information on the polarizations of the OPMs that will help constrain the mechanism that leads to the separation into two modes." The observed. polarization is clearly elliptical in some cases. implving that the natural modes of the pulsar plasma are elliptical at the point where the radiation. effectively escapes the magnetosphere.," The observed polarization is clearly elliptical in some cases, implying that the natural modes of the pulsar plasma are elliptical at the point where the radiation effectively escapes the magnetosphere." As the radiation in a given mode wopagates through. the medium. its polarization adjusts continuously so that it remains that of the natural mode at every point along the rav. path. (," As the radiation in a given mode propagates through the medium, its polarization adjusts continuously so that it remains that of the natural mode at every point along the ray path. (" A small leakage into he other mode occurs. implving some mode coupling.),"A small leakage into the other mode occurs, implying some mode coupling.)" This »utative point is referred to as the polarization limiting region. which may be defined as the region bevond which the mecium becomes ineffective in changing the polarization of he radiation propagating through it.," This putative point is referred to as the polarization limiting region, which may be defined as the region beyond which the medium becomes ineffective in changing the polarization of the radiation propagating through it." Polarization limiting is most likely to occur near the evelotron resonance where he polarization of the natural modes is changingoὃν fastest as à function of distance along the ray path (Melrose&Luo 2004)., Polarization limiting is most likely to occur near the cyclotron resonance where the polarization of the natural modes is changing fastest as a function of distance along the ray path \cite{ML04}. . Thus the empirical moceling of the polarization oovides information on the polarization limiting region. and on how it varies statistically from pulse to pulse.," Thus the empirical modeling of the polarization provides information on the polarization limiting region, and on how it varies statistically from pulse to pulse." Such information should help to identify the location of the xobawization limiting region., Such information should help to identify the location of the polarization limiting region. In this paper we present an empirical model that. is useful in simulating data on the Stokes parameters. for observations of single pulses at à given. pulsar phase., In this paper we present an empirical model that is useful in simulating data on the Stokes parameters for observations of single pulses at a given pulsar phase. The observed: polarization changes from. pulse to. pulse. and the polarization in any given. pulse can be quite dilferent from the (mean) polarization found by summing over a laree number of pulses.," The observed polarization changes from pulse to pulse, and the polarization in any given pulse can be quite different from the (mean) polarization found by summing over a large number of pulses." The underlving model for the interpretation of the observed polarization is in terms of two OPAls: the observed radiation is assumed to be a mixture of the two (completely. polarized) ΟΔΙΕ. with intensities dy. D. that are partially but not completely. correlated.," The underlying model for the interpretation of the observed polarization is in terms of two OPMs: the observed radiation is assumed to be a mixture of the two (completely polarized) OPMs, with intensities $I_1$, $I_2$, that are partially but not completely correlated." " We model this by assuming that the intensity for mode 1 has og-normal statistics. with the mean intensity set to unity without loss of eenerality and the variance in the natural log set to A,=0.8 based on observation. (Cairns.JohnstonDas 2004)."," We model this by assuming that the intensity for mode 1 has log-normal statistics, with the mean intensity set to unity without loss of generality and the variance in the natural log set to $\Delta_1=0.8$ based on observation, \cite{cjd04}." . The ratio. &. of the intensities in niocle 1 and 2 is assumed to have a gaussian distribution with a mean Ay and à variance Aes.," The ratio, $k$, of the intensities in mode 1 and 2 is assumed to have a gaussian distribution with a mean $\Iot$ and a variance $\dfIt$." Tho results of the simulations are sensitive o this correlation. and the choice of these parameters are severely constrained by the data. with Ay near but not equal o unity and As small but nonzero. T'Fable 1.," The results of the simulations are sensitive to this correlation, and the choice of these parameters are severely constrained by the data, with $\Iot$ near but not equal to unity and $\dfIt$ small but nonzero, Table 1." In the empirical model presented here. we assume that he polarization of cach OVAL is determined by a probability," In the empirical model presented here, we assume that the polarization of each OPM is determined by a probability" which means that the 3-D velocity s)ectruni duces. ds 3.L. which is verv close to the 3-D deusitv spectral index.,"which means that the 3-D velocity spectrum index is $-3.4$, which is very close to the 3-D density spectral index." The transition poiut between deusitv aud velocity doninated reguues is equal to the velocity dispersion on the scale of the whole SAIC (~ 1 kpc). which is ~ 22 (Stamimurovic et al.," The transition point between density and velocity dominated regimes is equal to the velocity dispersion on the scale of the whole SMC $\sim$ 4 kpc), which is $\sim$ 22 (Stanimirovic et al.," iu prepara1011)., in preparation). As the spatial power spectnwn shows the inportauce of structure on various spatial scales. its power-law behavior sugeests the hierarchica stycture organization iu the ISAL. without preferred spatial scales.," As the spatial power spectrum shows the importance of structure on various spatial scales, its power-law behavior suggests the hierarchical structure organization in the ISM, without preferred spatial scales." This phenomenon is usually ascribed to the iuerstelay turbulence (Scalo1987:Ehucercen 2000).," This phenomenon is usually ascribed to the interstellar turbulence \citep{Scalo87,Elmegreen00}." . ITowever. without velocity iuformation one can always wonder whetrer we deal with a static structure or a real turbilence.," However, without velocity information one can always wonder whether we deal with a static structure or a real turbulence." Iudeed. a distribution of sizes of sand eraius on a beach also follows a power-law. but no one would call his “turbulence”.," Indeed, a distribution of sizes of sand grains on a beach also follows a power-law, but no one would call this “turbulence”." Tιο velocity information changes the Xeture dramatically., The velocity information changes the picture dramatically. Heuce. the extreme importance of the techniques which relate the observed 2-D power spectrum with the uiderlving 3-D statistics of both density aud velocity.," Hence, the extreme importance of the techniques which relate the observed 2-D power spectrum with the underlying 3-D statistics of both density and velocity." " Were. we have tested the theoretical predictions for such a technique (Lazarian&Pogosvan 2000).. and as a result prover. for the first time, the presence of an active turbulence i1i the SAIC."," Here, we have tested the theoretical predictions for such a technique \citep{Lazarian99}, and as a result proved, for the first time, the presence of an active turbulence in the SMC." " Iu view of theoretical results in Lazari&Pososvau(2000) it is now appropriate to reanalvze all the earlier data,", In view of theoretical results in \citet{Lazarian99} it is now appropriate to reanalyze all the earlier data. Tjese. data were obtained without uch conuceru about the thickuess of velocity slices., These data were obtained without much concern about the thickness of velocity slices. " Therefore the observe variations of the power iudex can be due to transitions from “thin” to “thick” and to ""verv thick” slices.", Therefore the observed variations of the power index can be due to transitions from “thin” to “thick” and to “very thick” slices. " Iu the case of (οσο (1993) data additional colplicatiois are related to a divergent liue of sight SCOTTY,", In the case of Green's (1993) data additional complications are related to a divergent line of sight geometry. A more detailed discussioi of the available data will be eiven esewhere., A more detailed discussion of the available data will be given elsewhere. We note that although the descripJon in terms of power svectra 19 COMMNOIL im hvadrodyiuudes auk the MIID theory it has certain liuitations. as discussed in Lazarian (1999).," We note that although the description in terms of power spectra is common in hydrodynamics and the MHD theory, it has certain limitations, as discussed in Lazarian (1999)." For example. the power svectra analysis does uot 1iclude information about the phase disributiou. dealing only with the modulus of the Fovier transforni. nor dt contains information about the structure comecivitv (Scalo LOST).," For example, the power spectrum analysis does not include information about the phase distribution, dealing only with the modulus of the Fourier transform, nor it contains information about the structure connectivity (Scalo 1987)." Other mehods heuce. should be used as complementary statistical descriptors.," Other methods hence, should be used as complementary statistical descriptors." Power spectrum as it is cau provide s with a1i iuportaut insight of what sind of turbuleuce we deal with. c.g. distinguish the turbulence originating from shock waves from the hydrodvuamic turbulence.," Power spectrum as it is can provide us with an important insight of what kind of turbulence we deal with, e.g. distinguish the turbulence originating from shock waves from the hydrodynamic turbulence." The atcClupts to test Lazarian Pogosvan (2000) theory were made recently in Elucercen et al. (, The attempts to test Lazarian Pogosyan (2000) theory were made recently in Elmegreen et al. ( 2000) using the TT observations of the LMC.,2000) using the HI observations of the LMC. Iu aerecment with theoretica predictions. the steepening of Προςτα was observed for high sxitial frequencies.," In agreement with theoretical predictions, the steepening of spectrum was observed for high spatial frequencies." The puzzling thine discovered by Ehueercen et al. (, The puzzling thing discovered by Elmegreen et al. ( 2000) was the fattening of the spectra for velocitv-iutegrated intensity. which was iuterpreed as an effect of the finite LAIC cisk thickness.,"2000) was the flattening of the spectra for velocity-integrated intensity, which was interpreted as an effect of the finite LMC disk thickness." This is an iuterestingC» explanation which eutails that the LMC spectra at he scales larger than 100 pe becomes essentialv two dimensional, This is an interesting explanation which entails that the LMC spectrum at the scales larger than 100 pc becomes essentially two dimensional. Our study has not noticed à svstenatic change of the velocity integrated power spectiu nat large syatial scales., Our study has not noticed a systematic change of the velocity integrated power spectrum at large spatial scales. This may reflect the fact that the SAIC. uulike the LAIC. is esseutially a 3-D eutitv.," This may reflect the fact that the SMC, unlike the LMC, is essentially a 3-D entity." Another approach in relating the 2-D with the 3- statistics in the case of he SAIC was presented iu Colnun (2000)., Another approach in relating the 2-D with the 3-D statistics in the case of the SMC was presented in Goldman (2000). " There it is assunued that the density fluctuations are a ""passive scalar. being driven by the velocity fluctuations. and heice having the same powVOL specruni."," There it is assumed that the density fluctuations are a “passive scalar”, being driven by the velocity fluctuations, and hence having the same power spectrum." " If we accept that f1ο intensity fluctuations are due to the density fluctuations. then the corresponding specval index q of iuteusitv fiuctuatious ina 2-D slice c“ALL then be related to the 3-D desity spectrum 1idex n as which for the SAIC data produces 9)zδν, "," If we accept that the intensity fluctuations are due to the density fluctuations, then the corresponding spectral index $q$ of intensity fluctuations in a 2-D slice can then be related to the 3-D density spectrum index $n$ as which for the SMC data produces $n\approx -4$." "Lowey""OY. we note tjit. the data used in (οσα (20VO) are not in the real space 6eg:) for which his treatinent would be correct. but are in the velocity space Geye)."," However, we note that the data used in Goldman (2000) are not in the real space $xyz$ ) for which his treatment would be correct, but are in the velocity space $xyv$ )." In this situation the Lazariui&Pogosvau(2000) treatment is appropriate and it provides a different result. αλλο]. velocity index ®3.1 and density index =23:3.," In this situation the \citet{Lazarian99} treatment is appropriate and it provides a different result, namely, velocity index $\approx -3.4$ and density index $\approx -3.3$." Eq. (2)), Eq. \ref{q}) ) also predicts that the differeuce in the power slo)o between thiu aud tick slices is equal to 1., also predicts that the difference in the power slope between thin and thick slices is equal to $1$. This is inconsistent with Fie., This is inconsistent with Fig. l., 1. We also note that for t16 Ixoliiogorov spectrui the predictions in Lazariui&Pogosvan(20) {SCC Table 1) coincide with » «aleulated usine Eq. 2j).," We also note that for the Kolmogorov spectrum the predictions in \citet{Lazarian99} (see Table 1) coincide with $n$ calculated using Eq. \ref{q}) )," 1ut this correspondence is accideutal., but this correspondence is accidental. Au interesting applicatin of the power spectrum of III opacity fluctuations was made by Deshpande(2000).. oei order to explain the lono-staidiuns puzzle of the tiuv-scale structure in III (Ileiles1997).," An interesting application of the power spectrum of HI opacity fluctuations was made by \citet{Deshpande00a}, in order to explain the long-standing puzzle of the tiny-scale structure in HI \citep{Heiles97}." . Assunuis a sinele power spectrum of the opacity fiucuations. with a skype of 2.75 over the range of ~ 0.02 pe to L pc. Deshpaxde obtained opacities οςunsisteut with the observatknis of small-scale IIT structure in Deshpandeetal.(200n..," Assuming a single power spectrum of the opacity fluctuations, with a slope of 2.75 over the range of $\sim$ 0.02 pc to $\sim$ 4 pc, \citet{Deshpande00a} obtained opacities consistent with the observations of small-scale HI structure in \citet{Deshpande00b}." This is very cacouraging and τοςnos reduterpretation of previous observations of the siaLscale structure 1la similar way., This is very encouraging and requires re-interpretation of previous observations of the small-scale structure in a similar way. A prelinnary nvestieaion of the sinall-scale structure found so far by Teiles(2000) suggested though a more colples strucure function. wi ha significant cha120 of slope for scales sainaller tran 0.01 pe.," A preliminary investigation of the small-scale structure found so far by \citet{Heiles00} suggested though a more complex structure function, with a significant change of slope for scales smaller than 0.01 pc." What can drive the turbuence in the SAIC?, What can drive the turbulence in the SMC? The natiral asstuuption would be that it is due to the μπας of he ISAL produced by a arec 11uber of expanding shells foind in the SAIC., The natural assumption would be that it is due to the stirring of the ISM produced by a large number of expanding shells found in the SMC. The shell sizes range frou 30 pe to ~ 2k XC., The shell sizes range from $\sim$ 30 pc to $\sim$ 2 kpc. Ileuce. one scenario could 1ος that the largest shells drive the turbulent cascade cowi to smallest. observed scaes.," Hence, one scenario could be that the largest shells drive the turbulent cascade down to smallest observed scales." " Ilowewver. processes like sliJl fragimentation aud/or slrell propagation frou the smaler scales (hbottom-mp scheue, see Scalo 1987). may play significant role too."," However, processes like shell fragmentation and/or shell propagation from the smaller scales (bottom-up scheme, see Scalo 1987), may play significant role too." The mai- problem in pinning down the exact mechanisius is that. so far. we have not observed changes iu the power spectrum. at auv scale up to the ecutive size of the SAIC. whic[um would be indicative of cuerev injection.," The main problem in pinning down the exact mechanisms is that, so far, we have not observed changes in the power spectrum, at any scale up to the entire size of the SMC, which would be indicative of energy injection." Au alternatiw« explanation was sugeestedOO in Coldiman(2000).. where‘by the huge scale turbulence is induced by instabilities 1- the large-scale flows during the last SAIC)LMC encounter.," An alternative explanation was suggested in \citet{Goldman00}, whereby the large scale turbulence is induced by instabilities in the large-scale flows during the last SMC–LMC encounter." Future comparison with simulations of differeut types of turbulent cascades are essential to resolve this question., Future comparison with simulations of different types of turbulent cascades are essential to resolve this question. We lave successfully tested predictions of the Lazariau study on the change of slope of," We have successfully tested predictions of the \citet{Lazarian99} study on the change of slope of" from the source.,from the source. On the other hand. we may be observing (wo completely independent [Fe 11] peaks in the and.VLT data. rather than the same near-stationary feature.," On the other hand, we may be observing two completely independent [Fe ] peaks in the and data, rather than the same near-stationary feature." The leature mav have [aded. to be replaced by a new peak in the.VLT observations.," The feature may have faded, to be replaced by a new peak in the observations." " The cooling time. from 20.000 IX to 7.000 Ix for dense (10—10"" *). post-shock gas will be of the order of weeks or even days (Smith2003).. so morphological changes are certainly. possible."," The cooling time, from 20,000 K to 7,000 K for dense $10^{5}-10^{6}$ $^{-3}$ ), post-shock gas will be of the order of weeks or even days \citep{smi03}, so morphological changes are certainly possible." This might explain the apparent “upwind” movement of (his feature., This might explain the apparent “upwind” movement of this feature. A number of groups have attempted to the emission-line region at the base of ihe 113 outflow., A number of groups have attempted to the emission-line region at the base of the 13 outflow. Davisetal.(2002) used a Fabry-Perot (FP) etalon to “boost” the line/continuum ratio in their data., \citet{dav02} used a Fabry-Perot (FP) etalon to “boost” the line/continuum ratio in their data. " The Il; emission at (he jet base is certainlv. evident in their image. although the poor spatial resolution of their observations (71"")) somewhat limits their ability to extract spatial information."," The $_2$ emission at the jet base is certainly evident in their image, although the poor spatial resolution of their observations $\sim$ ) somewhat limits their ability to extract spatial information." They do collapse their image along an axis perpendicular to the jet and attempt to subtract the continuum emission from the resulting profile (their Figure 4)., They do collapse their image along an axis perpendicular to the jet and attempt to subtract the continuum emission from the resulting profile (their Figure 4). " Thev identily a “peak” and à ""plateau along the jet axis which max correspond to II» components 2 and 3 in theVLT data.", They identify a “peak” and a “plateau” along the jet axis which may correspond to $_2$ components 2 and 3 in the data. We list theoffsets of these features in Table 2.. Noriega-, We list theoffsets of these features in Table \ref{table2}. Crespoelal.(2002) used theAST to obtain high-spatial resolution near-IR images of the 77-11 outflow., \citet{nor02} used the to obtain high-spatial resolution near-IR images of the 7-11 outflow. They. present a continiuni-subtracted Ils image of 113 (their Figure 3)., They present a continuum-subtracted $_2$ image of 13 (their Figure 3). " IIowever. residual artifacts left over from the continuum subtraction. in the bright core but also in a ring of radius 71"".. make identifving features within oof 113 more-or-less impossible."," However, residual artifacts left over from the continuum subtraction, in the bright core but also in a ring of radius $\sim$, make identifying features within of 13 more-or-less impossible." " However. they do detect and resolve the I5 emission in the flow at offsets of 221""."," However, they do detect and resolve the $_2$ emission in the flow at offsets of $>$." Within oof 113 the II» appears to comprise at least (wo knots superimposed on to a patch of moderately extended emission. suggesting a broad opening angle for the IH» flow.," Within of 13 the $_2$ appears to comprise at least two knots superimposed on to a patch of moderately extended emission, suggesting a broad opening angle for the $_2$ flow." Component 2inthe data (the HVC in the observations) may therefore constitutesknots: we give a combined offset for these two features (measured along the slit axis) in Table 2. [or reference.," Component 2 in the data (the HVC in the observations) may therefore constitutes; we give a combined offset for these two features (measured along the slit axis) in Table \ref{table2} for reference." Overall. the results from these (wo imaging survevs can only be used to confirm the presence of emission features.," Overall, the results from these two imaging surveys can only be used to confirm the presence of emission features." Uncertainües in the continuum subtraction limit their usefulness when measuring PMs., Uncertainties in the continuum subtraction limit their usefulness when measuring PMs. Notably. the compact LYC evident in both theSubaru audVLT spectroscopy was not extracted from the FP orLST images.," Notably, the compact LVC evident in both the and spectroscopy was not extracted from the FP or images." Clearly. follow-up observations wilh theCO svstem are needed to better constrain (he PM measurements discussed above. particularly for the [Fe Π peak and the II? components further downwind.," Clearly, follow-up observations with the system are needed to better constrain the PM measurements discussed above, particularly for the [Fe ] peak and the $_2$ components further downwind." Confirmation of the “stationary” [Fe n] peak would add credence to the collimation-shock interpretation., Confirmation of the “stationary” [Fe ] peak would add credence to the collimation-shock interpretation. If we also ultimatelv find that the IIs peaks do, If we also ultimately find that the $_2$ peaks do timescales if the parallel and perpendicular extent of the NRFs is approximately 125 to 1.,timescales if the parallel and perpendicular extent of the NRFs is approximately 125 to 1. " This length-scale is similar to the observed length to width ratio in multiple filamentary structures (?),, implying that diffusion along the length of the filamentary arcs acts on a similar time frame to diffusion across the much smaller NRF width."," This length-scale is similar to the observed length to width ratio in multiple filamentary structures \citep{2004ApJS..155..421Y}, implying that diffusion along the length of the filamentary arcs acts on a similar time frame to diffusion across the much smaller NRF width." " Since the calculation of magnetic field order stands as a lower limit in this calculation, it is feasible that perpendicular diffusion is in fact entirely irrelevant in the population of NRF structures."," Since the calculation of magnetic field order stands as a lower limit in this calculation, it is feasible that perpendicular diffusion is in fact entirely irrelevant in the population of NRF structures." The overall normalization of the diffusion constant depends sensitively on the length scale of the turbulent disturbances in the magnetic medium (?) and is highly uncertain., The overall normalization of the diffusion constant depends sensitively on the length scale of the turbulent disturbances in the magnetic medium \citep{1966ApJ...146..480J} and is highly uncertain. " While simulations are able to constrain the mean galactic diffusion constant through observations of cosmic ray primary-to-secondary ratios at the solar position these simulations do not constrain local diffusion (e.gconstants,?),, especially in magnetically unique regions such as NRFs."," While simulations are able to constrain the mean galactic diffusion constant through observations of cosmic ray primary-to-secondary ratios at the solar position \citep[e.g][]{1998ApJ...509..212S}, these simulations do not constrain local diffusion constants, especially in magnetically unique regions such as NRFs." " 'The synchrotron energy loss time of an electron is given by: Due to the difficulties of calculating the diffusion constant within a partially ordered magnetic field, we choose a parallel diffusion constant such that electrons remain within the NRF for a length of time given by: where 7 is the ratio of the diffusion timescale for 8 GeV electrons compared to their synchrotron energy loss time."," The synchrotron energy loss time of an electron is given by: Due to the difficulties of calculating the diffusion constant within a partially ordered magnetic field, we choose a parallel diffusion constant such that electrons remain within the NRF for a length of time given by: where $\tau$ is the ratio of the diffusion timescale for 8 GeV electrons compared to their synchrotron energy loss time." " For example, in the case 7 = 1.0, 8 GeV electrons diffuse out of the NRF on a timescale equal to their synchrotron energy loss time."," For example, in the case $\tau$ = 1.0, 8 GeV electrons diffuse out of the NRF on a timescale equal to their synchrotron energy loss time." " Thus the 7 parameter can also be seen as an indicator of the average synchrotron exhaustion, or the average time that an electron generated by dark matter annihilation has propagated through the NRF before producing the synchrotron emission presently observed."," Thus the $\tau$ parameter can also be seen as an indicator of the average synchrotron exhaustion, or the average time that an electron generated by dark matter annihilation has propagated through the NRF before producing the synchrotron emission presently observed." The additional factor of E~°-** accounts for the energy dependence of the diffusion constant calculated by ?.., The additional factor of $^{-0.33}$ accounts for the energy dependence of the diffusion constant calculated by \citet{1941DoSSR..30..301K}. We note that the synchrotron softening ofan electron spectrum for a given value of 7 is independent of the magnetic field strength., We note that the synchrotron softening ofan electron spectrum for a given value of $\tau$ is independent of the magnetic field strength. In Fig., In Fig. " 2 (right), we show the spectrum of electrons from dark matter annihilations after accounting for synchrotron energy losses for 7 — 1.0."," \ref{fig:leptonflux} (right), we show the spectrum of electrons from dark matter annihilations after accounting for synchrotron energy losses for $\tau$ = 1.0." We are now prepared to calculate the synchrotron spectrum resulting from dark matter annihilations taking place within a NRF., We are now prepared to calculate the synchrotron spectrum resulting from dark matter annihilations taking place within a NRF. " In Fig. 3,,"," In Fig. \ref{fig:synchrotron_spectrum}," " we plot the synchrotron spectrumfrom dark matter annihilations for magnetic field strengths of 50 µία, 100 wG, and 200uG and for values 7T —0.1, 1.0 and 2.0."," we plot the synchrotron spectrumfrom dark matter annihilations for magnetic field strengths of 50 $\mu$ G, 100 $\mu$ G, and $\mu$ G and for values $\tau$ =0.1, 1.0 and 2.0." " In each case, we predict a peak in synchrotron energy at ~1-10 GHz followed by a suppression of the synchrotron emissivity at higher frequencies."," In each case, we predict a peak in synchrotron energy at $\sim$ 1-10 GHz followed by a suppression of the synchrotron emissivity at higher frequencies." " In the following section, we will compare this prediction to the synchrotron spectrum observed from specific NRFs."," In the following section, we will compare this prediction to the synchrotron spectrum observed from specific NRFs." " In astrophysical interpretations of NRF observations, variations in the electron injection spectrum can be invoked to effectively explain the different spectral features in each NRF, since the peak of the synchrotron emission spectrum depends on the square of the electron energy."," In astrophysical interpretations of NRF observations, variations in the electron injection spectrum can be invoked to effectively explain the different spectral features in each NRF, since the peak of the synchrotron emission spectrum depends on the square of the electron energy." " However, in the case of dark matter annihilations, the injected electron spectrum must be uniform in each filament."," However, in the case of dark matter annihilations, the injected electron spectrum must be uniform in each filament." Variations in the observed synchrotron spectra may still originate from differences in either the magnetic field strength or diffusion timescales of each NRF., Variations in the observed synchrotron spectra may still originate from differences in either the magnetic field strength or diffusion timescales of each NRF. " These effects are relatively weak, however, and would be unable to explain extreme variations in the spectral turnover of different NRFs."," These effects are relatively weak, however, and would be unable to explain extreme variations in the spectral turnover of different NRFs." Thus a population survey ofthe synchrotron spectra in NRFs remains a powerful diagnostic for testing the dark matter interpretation., Thus a population survey ofthe synchrotron spectra in NRFs remains a powerful diagnostic for testing the dark matter interpretation. " In Table 1,, we have compiled the observed synchrotron spectra of the most thoroughly studied NRFs."," In Table \ref{tab:spectra}, we have compiled the observed synchrotron spectra of the most thoroughly studied NRFs." " We find the population to be relatively homogeneous, with a hard spectrum below ~5 GHz that quickly turns over at higher frequencies."," We find the population to be relatively homogeneous, with a hard spectrum below $\sim$ 5 GHz that quickly turns over at higher frequencies." " The variation in the spectral turnover from the hardest NRF (G0.2-0.0, Radio Arc) to the softest Northern Thread) is approximately an order of (G0.08+0.15,magnitude."," The variation in the spectral turnover from the hardest NRF (G0.2-0.0, Radio Arc) to the softest (G0.08+0.15, Northern Thread) is approximately an order of magnitude." " In order to test whether magnetic field and diffusion timescale variations can explain these spectral and intensity variations within the highly constrained framework of a uniformelectron injection spectrum, we consider four NRFs with particularly well measured spectra and intensities: G0.2-0.0 (theRadioArc, ?),, G0.16-0.14 (theArcFilament, ?), G0.08--0.15 (the and G359.1-0.2 (theSnake, ?).. "," In order to test whether magnetic field and diffusion timescale variations can explain these spectral and intensity variations within the highly constrained framework of a uniformelectron injection spectrum, we consider four NRFs with particularly well measured spectra and intensities: G0.2-0.0 \citep[the Radio Arc,][]{reich2003}, , G0.16-0.14 \citep[the Arc Filament,][]{1992PASJ...44..367S}, , G0.08+0.15 \citep[the Northern Thread,][]{1999ApJ...526..727L} and G359.1-0.2 \citep[the Snake,][]{1995ApJ...448..164G}. ." "Data were extracted using the Dexter package (?),, and"," Data were extracted using the Dexter package \citep{2001ASPC..238..321D}, , and" The phase referenced VLBA map of YZ CAG is shown in Fie. 2..,The phase referenced VLBA map of YZ CMi is shown in Fig. \ref{fig:cntr}. Evidence for spatial resolution was found iu his map., Evidence for spatial resolution was found in this map. Further evidence for extended cmission cau ve most clearly ποσα by examine fringe amplitude versus vascline leneth obtained using the VLA-VLBA baselines (sce Fig. 3..," Further evidence for extended emission can be most clearly seen by examing fringe amplitude versus baseline length obtained using the VLA-VLBA baselines (see Fig. \ref{fig:uvplots}," left plot)., left plot). We obtained this plot bv first coherently averaging the data ou cach baseline-scan (75 winutes) in order to increase the signal to noise ratio sienificautly above unitv., We obtained this plot by first coherently averaging the data on each baseline-scan (75 minutes) in order to increase the signal to noise ratio significantly above unity. We then binned the amplitude over baseline leneth finding the mean amplitude iu cach iu bv iucohercut averaging., We then binned the amplitude over baseline length finding the mean amplitude in each bin by incoherent averaging. The error bars onthis average were determined from the internal scatter of the data., The error bars on this average were determined from the internal scatter of the data. The fall off noticeable in Fig., The fall off noticeable in Fig. 5. left plot clearly indicates a resolved source., \ref{fig:uvplots} left plot clearly indicates a resolved source. What is more. the phase values on VLBI baselines to the phased VLA over the whole observation show no significaut variation from zero.," What is more, the phase values on VLBI baselines to the phased VLA over the whole observation show no significant variation from zero." There is therefore no evidence for auvthing other than a sinele ceutro-svuuuetric component., There is therefore no evidence for anything other than a single centro-symmetric component. We searched also for other evidence for nou-syiunnetrical structure looking at closure phases. but the SNR of these were too low.," We searched also for other evidence for non-symmetrical structure looking at closure phases, but the SNR of these were too low." Given the close to quadratic fall off of the füiuge auplitude with 0—distauce shown in Fig., Given the close to quadratic fall off of the fringe amplitude with -distance shown in Fig. 3 left plot it is napossible to distinguish between gaussian. sphere. disk or rue like models (Pearson 1995)).," \ref{fig:uvplots} left plot it is impossible to distinguish between gaussian, sphere, disk or ring like models \cite{Pearson}) )." We therefore fitted one-component gaussian models to the YZ CAL data., We therefore fitted one-component gaussian models to the YZ CMi data. The uwmumerical values for the fits are summarized iu Table 1.., The numerical values for the fits are summarized in Table \ref{tab:sum}. The dimensions of sphere. disk aud ring which would show simular fits are expected to be respectively 1.5. 1.6 and 1.1 times the gaussian EWIIP values (Pearson 1995).," The dimensions of sphere, disk and ring which would show similar fits are expected to be respectively 1.8, 1.6 and 1.1 times the gaussian FWHP values (Pearson 1995)." Two wavs of fitting were followed: fitting in AIPS using the task UVFIT aud our own model fitting to the data., Two ways of fitting were followed: fitting in AIPS using the task UVFIT and our own model fitting to the data. The first fitted au elliptical gaussian aud obtained for the whole data set a major axis of FWIIP of 1.1 40.3 Duas and a nuünor axis of 0.5 +£0.25 mas (lo errors)., The first fitted an elliptical gaussian and obtained for the whole data set a major axis of FWHP of 1.4 $\pm$ 0.3 mas and a minor axis of 0.5 $\pm$ 0.25 mas $\sigma$ errors). There is therefore no strong evidence for ellipticitv. aud our subsequent fittine of the data outside of AIPS asstned only a circular gaussian.," There is therefore no strong evidence for ellipticity, and our subsequent fitting of the data outside of AIPS assumed only a circular gaussian." With such a model it was possible to fit most of the data within 1 7., With such a model it was possible to fit most of the data within 1 $\sigma$. The best fitting FWHP size of he corona was found to be 0.98 40.2 mas. which corresponds to 1.7 +0.3 stellar diameters.," The best fitting FWHP size of the corona was found to be 0.98 $\pm$ 0.2 mas, which corresponds to 1.7 $\pm$ 0.3 stellar diameters." Since the second. VLBI scan corresponds precisely to oue of the two strong flares (sce Fie. 1..," Since the second VLBI scan corresponds precisely to one of the two strong flares (see Fig. \ref{fig:light97}," left plot). it was interesting to study it more closely.," left plot), it was interesting to study it more closely." Fig., Fig. 3 απο plot) shows the amplitude versus distance., \ref{fig:uvplots} (right plot) shows the amplitude versus -distance. Of Ls sca we selected. the subscan on the target with the highest fiux density value aud coherently averaged the data over it (3 nüuutes). obtaiulug one poi xr VLA-VLBA vascline.," Of this scan we selected the subscan on the target with the highest flux density value and coherently averaged the data over it (3 minutes), obtaining one point per VLA-VLBA baseline." The solid line corresponds to the same gaussian model fitted to the whole data set (see Fie. 3..," The solid line corresponds to the same gaussian model fitted to the whole data set (see Fig. \ref{fig:uvplots}," loft ot) except for the total flux deusitv which was increased to 5.1 uty., left plot) except for the total flux density which was increased to 5.1 mJy. We fud that this scaled model fits the data within the errors and therefore there is no evidence for a chanee iu source size during the flare., We find that this scaled model fits the data within the errors and therefore there is no evidence for a change in source size during the flare. Independent gaussian fits to he data are also consistent with this conclusion (see Table 1)., Independent gaussian fits to the data are also consistent with this conclusion (see Table \ref{tab:sum}) ). We should add tha the contribution of the proper notion aud of the changing parallax of the star curing he ten hours of observation is -0.32 mas aud -0.16 mas in a and à. respectively:," We should add that the contribution of the proper motion and of the changing parallax of the star during the ten hours of observation is -0.32 mas and -0.16 mas in $\alpha$ and $\delta$, respectively." These values are small enough that hey do not eive a significant contribution on the spatial extent., These values are small enough that they do not give a significant contribution on the spatial extent. Au image of AD Leo is shown in Fie. 2.., An image of AD Leo is shown in Fig. \ref{fig:cntr}. It appears slightly elongated., It appears slightly elongated. This nuage is probably affected by the stars ligh proper motion (Table 1)). since the extension is exactly along the expected direction: the star," This image is probably affected by the star's high proper motion (Table \ref{tab:sum}) ), since the extension is exactly along the expected direction: the star" represents (he size of the source.to make this scenario work.,"represents the size of the source,to make this scenario work." Such transverse velocities have been proposed for NGC 4151 bv Iraemeretal.(20060)., Such transverse velocities have been proposed for NGC 4151 by \citet{kraemer06}. The third possibility is that the last components are present the whole time. but in 2001. when the flux is low. there was no light from accretion disk behind them for them to absorb.," The third possibility is that the fast components are present the whole time, but in 2001, when the flux is low, there was no light from accretion disk behind them for them to absorb." In 2006. the source [αν is much brighter. whether intrinsic source output change or flux change due to variable covering factor by thick gas. which could result. [rom a flare on the disc that illuminates the fast components Irom behind. and which subsequently they. absorb along the line of sight.," In 2006, the source flux is much brighter, whether intrinsic source output change or flux change due to variable covering factor by thick gas, which could result from a flare on the disc that illuminates the fast components from behind, and which subsequently they absorb along the line of sight." With the current spectra. one cannot rule out any of these scenarios.," With the current spectra, one cannot rule out any of these scenarios." With better S/N spectra. one might be able to confirm (or rule out) changes in the (photo-ionization state if the fast component is detected (or not detected) in low ionization species during the low flix state.," With better S/N spectra, one might be able to confirm (or rule out) changes in the (photo-)ionization state if the fast component is detected (or not detected) in low ionization species during the low flux state." Il one would detect a change in the covering fraction in (he narrow absorption lines. which we are not able to detect here. that would be evidence for transverse velocities (Ixraemeretal.2006).," If one would detect a change in the covering fraction in the narrow absorption lines, which we are not able to detect here, that would be evidence for transverse velocities \citep{kraemer06}." . The possibility. of flaring on the disc is most difficult to test. as the angular resolution required for detecting sources on sub-disc scales is currently prohibitive.," The possibility of flaring on the disc is most difficult to test, as the angular resolution required for detecting sources on sub-disc scales is currently prohibitive." We have analvzed the kinematic and thermal structure of the ionized outflow in3516., We have analyzed the kinematic and thermal structure of the ionized outflow in. . We [ind absorption troughs in dozens of charge states Chat extend [rom zero to almost 5000L., We find absorption troughs in dozens of charge states that extend from zero to almost 5000. . We model the outflow with four absorption svstems., We model the outflow with four absorption systems. The first ancl second components are outflowing al 350 and 1500|. and span a considerable range of ionization from at least Fe! to 237) [20.5 10^{10} \rm{g cm^{-3}}$ ) quickly attains an isothermal configuration after birth." " At outer quickly of the crust. the temperature follows an approximate regionsrelation. TG) ‘Ye where 7; is the of the isothermal inner crust and is the temperatureabove which the crust. is py,isothermal."," At outer regions of the crust, the temperature follows an approximate relation, ) = , where $T_{i}$ is the temperature of the isothermal inner crust and $\rho_{b}$ is the density above which the crust is practically isothermal." " As densitythe star cools. larger fraction of the practicallycrust starts becoming isothermal. with p, being approximately eiven by. The relations 4. and 5 above have been obtained bv fitting to the racial profiles publish by Cucmuncdsson. Pethicktemperature (1983)."," As the star cools, larger fraction of the crust starts becoming isothermal, with $\rho_{b}$ being approximately given by, = The relations \ref{temp} and \ref{rho} above have been obtained by fitting to the radial temperature profiles published by Gudmundsson, Pethick Epstein (1983)." " For. the time evolution of 2; we use theEpstein. results of Urpin van Riper (1993) for the case of standard. cooling (the crusta temperature Z5, in their notation corresponds to 7; above).", For the time evolution of $T_i$ we use the results of Urpin van Riper (1993) for the case of standard cooling (the crustal temperature $T_m$ in their notation corresponds to $T_i$ above). A third. parameter that should be considered in conductivity is the impurity. concentration., A third parameter that should be considered in determining conductivity is the impurity concentration. Thedetermining elfect. of impurities on the conductivity is usually parametrisecl by a quantity €. defined as 6)=nZZy. where D ds the total ion density. 2; is LY.the densityo of / with charge Z;. and Z is the ionic chargeimpurity in the specieslattice (Yakovlev Urpin 1980).," The effect of impurities on the conductivity is usually parametrised by a quantity $Q$, defined as $Q = \frac{1}{n} \sum_{i}{{n_{i}}(Z - Z_{i})^2}$, where $n$ is the total ion density, $n_i$ is the density of impurity species $i$ with charge $Z_i$, and $Z$ is the ionic charge in the pure lattice (Yakovlev Urpin 1980)." In the literature @Q is pureassumed to lie in the range 0.0 - 0.1., In the literature $Q$ is assumed to lie in the range 0.0 - 0.1. But statistical indicate that the magnetic field of isolated. pulsarsanalyses do not significant decay. during the radio pulsar life time undergo(Bhattacharya 1992. Hartman 1997. WKembhavi 1997).," But statistical analyses indicate that the magnetic field of isolated pulsars do not undergo significant decay during the radio pulsar life time (Bhattacharya 1992, Hartman 1997, Mukherjee Kembhavi 1997)." Ht has been shown (Ixonar 1997)Mukhoerjee that to be consistent with this impurity values in excess of 0.01 are not allowed in the crustal moclel., It has been shown (Konar 1997) that to be consistent with this impurity values in excess of 0.01 are not allowed in the crustal model. ‘Lo solve (2)) we assume the multipole racial profile used. by equationDhattacharya Datta (1996. sec also Ixonar. Bhattacharva 1997).," To solve equation \ref{e_radial}) ) we assume the multipole radial profile used by Bhattacharya Datta (1996, see also Konar Bhattacharya 1997)." This contains the and he width of the current profile as input parametersdepth and we vary them to check the configurationsensitivity of the result to hese., This profile contains the depth and the width of the current configuration as input parameters and we vary them to check the sensitivity of the result to these. We solve equation (2)) numerically using the Crank-icholson method of , We solve equation \ref{e_radial}) ) numerically using the Crank-Nicholson method of differencing. We have moclificc the numerical code developed: by dillerencing.IXonar. (1997). and. used. by lxonar Bhattacharva (1997) to compute the evolution of magnetic fields satisfving the appropriate rotunclary multipolarConditions given by equation. (3))., We have modified the numerical code developed by Konar (1997) and used by Konar Bhattacharya (1997) to compute the evolution of multipolar magnetic fields satisfying the appropriate boundary conditions given by equation \ref{e_bc}) ). In figures and. 2]] we plot the evolution of the various multipole 1] of the field. assuming the same initial components for all. with magnetictime due to pure in isolated. stre," In figures \ref{f_fig1a}] ] and \ref{f_fig1b}] ] we plot the evolution of the various multipole components of the magnetic field, assuming the same initial strength for all, with time due to pure diffusion in an isolated neutron star." ngth evident the diffusionthat anexcept for neutronhigh star.multipoleLtis orders from(42° 25) the figuresreduction in the field very is very similar to that of the dipole component., It is evident from the figures that except for very high multipole orders $l\gsim 25$ ) the reduction in the field strength is very similar to that of the dipole component. For a strengthmultipole of order / there would be 2 reversals across the stellar surface., For a multipole of order $l$ there would be $2^{l}$ reversals across the stellar surface. For typical spin-periods the size of the polar bounded the base of the open field lines is ~0.01% of capthe total surfaceby area., For typical spin-periods the size of the polar cap bounded by the base of the open field lines is $\sim 0.01\%$ of the total surface area. nask munmediatelv north of the S Phune).,mask immediately north of the S Plume). Pattersou Thuan(1992) studied UCC optic7636 using optical aud 21-1 imaging. and found short al tidal tails extending ~ inorth and south of the dwarf. aud evidence for rai. wressure stripping of its neutral lvdrogen eas.," Patterson Thuan (1992) studied UGC 7636 using optical and 21-cm imaging, and found short optical tidal tails extending $\sim$ north and south of the dwarf, and evidence for ram pressure stripping of its neutral hydrogen gas." The inear. low smface brightuess S Plume is aligned with he relatively high surface brightuess tails ideutified by Patterson Thuan. aud is likely au extension of the southern tidal tail to larger radius.," The linear, low surface brightness S Plume is aligned with the relatively high surface brightness tails identified by Patterson Thuan, and is likely an extension of the southern tidal tail to larger radius." The narrowness ofthe pune argues. however. that this interaction is not the sale that eave rise to the πιο broader. more exteuded NW and SE Shells.," The narrowness of the plume argues, however, that this interaction is not the same that gave rise to the much broader, more extended NW and SE Shells." The interleaved structure of those shells. roughly along the imajor axis of the ΑΠΟ. is verv reminiscent of simulations of the accretion and subsequent disruption of sinall satellite galaxies around larger ellipticals (Quinn 1981. Heruquist Quinn 1988. 1989).," The interleaved structure of those shells, roughly along the major axis of the M49, is very reminiscent of simulations of the accretion and subsequent disruption of small satellite galaxies around larger ellipticals (Quinn 1984, Hernquist Quinn 1988, 1989)." While major mergers can also leave behind shell-like structures IIleruquist Sperecl 1992). these are ecucrally not so aligued. aud interleaved the wav the shells in MI9 are.," While major mergers can also leave behind shell-like structures Hernquist Spergel 1992), these are generally not so aligned and interleaved the way the shells in M49 are." These shells are also extremely sharp: a radial cut along the NW Shell (Region 1) shows a sudden 2 over E eekpe). while the SE Shell (Regiou 3) shows a steep ddrop over ((3.8 kpe). while the innermost shell (Reeiou 2) has a much more diffuse decline iu radial intensity.," These shells are also extremely sharp: a radial cut along the NW Shell (Region 1) shows a sudden 2 drop over (2.7 kpc), while the SE Shell (Region 3) shows a steep 1.5 drop over (3.8 kpc), while the innermost shell (Region 2) has a much more diffuse decline in radial intensity." The fact that the sharpness of the shell is correlated with its distance from the ceuter of ALL9 is consistent with an accretion origin. where the inner shells have experienced several dynamical crossings. resulting in heightened orbital mixing and diffusion of the shell’s sharpness.," The fact that the sharpness of the shell is correlated with its distance from the center of M49 is consistent with an accretion origin, where the inner shells have experienced several dynamical crossings, resulting in heightened orbital mixing and diffusion of the shell's sharpness." The sharpness of the outer shell argues that it has Όσοι relatively unperturbed divine its lifetime: we return to this implication im &11., The sharpness of the outer shell argues that it has been relatively unperturbed during its lifetime; we return to this implication in 4. The second galaxy we study is M87. the eiaut elliptical at the heart of the Virgo Cluster.," The second galaxy we study is M87, the giant elliptical at the heart of the Virgo Cluster." Its fal mask includes all of the small ealaxies nearby Gaotably NCC 1078. 1176) and several diffraction spikes aud saturation bleeds from bright stars.," Its final mask includes all of the small galaxies nearby (notably NGC 4478, 4476) and several diffraction spikes and saturation bleeds from bright stars." " Our fit uses a fixed center (at à —12:30:19.1. à= |12:23:28.2Tope, J2000). aud extends outward to yj~ to’(180 where the surfacebrightuess dropsbelow jy29 our le photometric limit."," Our fit uses a fixed center (at $\alpha=$ 12:30:49.4, $\delta=$ +12:23:28.2 J2000), and extends outward to $\rsma \sim 40\arcmin\ $ (180 kpc), where the surface brightness drops below $=29$, our $\sigma$ photometric limit." For display purposes. our subtracted images show residuals rol an extended fit which coutinues iuto this sky level. mt our quantitative discussion and profile fittine are restricted to the part of the profile with js29.," For display purposes, our subtracted images show residuals from an extended fit which continues into this sky level, but our quantitative discussion and profile fitting are restricted to the part of the profile with $<29$." Figure 2 shows M8T's surface briglhtuess profile aud other best Bt isophote parameters., Figure \ref{allfits} shows M87's surface brightness profile and other best fit isophote parameters. Also plotted in Figure 2— with our ellipticity aud »osition angle profiles are results from similar previous studies of MIST., Also plotted in Figure \ref{allfits} with our ellipticity and position angle profiles are results from similar previous studies of M87. Jedrzejewski (1987) published surface photometry of M87 in both Band B. while Caon (1990) studied AIS? usine a combination of D-baud CCD imaging and wide-field Schinidt photographic ates.," Jedrzejewski (1987) published surface photometry of M87 in both B and R, while Caon (1990) studied M87 using a combination of B-band CCD imaging and wide-field Schmidt photographic plates." IK09 also combine them own observations with surface photometry published iu the literature to construct a composite surface brightuess profile of AIST in the V-baud., K09 also combine their own observations with surface photometry published in the literature to construct a composite surface brightness profile of M87 in the V-band. While our data exteud to somewhat arecr seni-nmajor axis. there is. for the amost part. eood agreement in the geometric iophlotal parameters in regions of overlap.," While our data extend to somewhat larger semi-major axis, there is, for the most part, good agreement in the geometric isophotal parameters in regions of overlap." At huge radius (Ri>5.5. or Hoc15) there is some divergence in the ellipticity. but this is in regions of very low surface brightuess G37. Sanding ybeduetocontam ination fromgalacticeirrustotheso ," At large radius $R^{1\over 4}> 5.5$, or $R>15$ ) there is some divergence in the ellipticity, but this is in regions of very low surface brightness $>$ 27.5) and may be due to contamination from galactic cirrus to the southeast of M87 (see discussion below)." The isophotal fits to Sérrsic and 2dV profiles ave shown in Figure 2 and Table 2..with, The isophotal fits to Sérrsic and 2dV profiles are shown in Figure \ref{allfits} and Table \ref{sbfits}. For the Sévrsic fit. our extracted paralcters agree well those determined by 109.," For the Sérrsic fit, our extracted parameters agree well with those determined by K09." We note that 2dV is a somewhat better fit to the profile than the Sévrsic model: however. mich of the discrepancy between the fits comes in the outer regions at very low surface brightness.," We note that 2dV is a somewhat better fit to the profile than the Sérrsic model; however, much of the discrepancy between the fits comes in the outer regions at very low surface brightness." The total huuinositv of MB8T is Ey=land1.2&ΤΟΠ. for the Sérrsic aud 2d¥ fits. respectively. aud in the 20V model the outer componcut accounts for of the total hunuinosity.," The total luminosity of M87 is $L_V = 1.1 {\rm\ and\ } 1.2\times 10^{11} L_\sun$ for the Sérrsic and 2dV fits, respectively, and in the 2dV model the outer component accounts for of the total luminosity." We subtract the smooth isophotal model for M87 frou the original inage aud show the subtracted inmige below the original in Figure 3.., We subtract the smooth isophotal model for M87 from the original image and show the subtracted image below the original in Figure \ref{subtract_m49m87}. A major source of uncertainty n iunuediatelv visible iu this nuage coutaiuination by back-scattered Galactic light from the galactic cimus (Sandage 1976: Witt 2008: Rudick 2010)., A major source of uncertainty is immediately visible in this image – contamination by back-scattered Galactic light from the galactic cirrus (Sandage 1976; Witt 2008; Rudick 2010). Much. of the residual structure seen to the southeast (lower left) of AIST correlates stronglv with far infrared maps of Galactic dust (Schlegel 1095: Aliille-Descheuues Lagache 2005). sugeesting mich of what we are secing ix due to scattering from galactic dust.," Much of the residual structure seen to the southeast (lower left) of M87 correlates strongly with far infrared maps of Galactic dust (Schlegel 1998; Miville-Deschênnes Lagache 2005), suggesting much of what we are seeing is due to scattering from galactic dust." It is particularly troublesome that this ciissiou connects smoothly with the broad excess of light to the southeast of ALSF which Weil (1997) attributect to tidal encounter: this feature mav be nothing more than scattered light from ealactic cirrus., It is particularly troublesome that this emission connects smoothly with the broad excess of light to the southeast of M87 which Weil (1997) attributed to tidal encounter; this feature may be nothing more than scattered light from galactic cirrus. Cavern the likehhood of contamination by dust. we avoid attributingany substructure in this region to true tidal features around ALS itself.," Given the likelihood of contamination by dust, we avoid attributing substructure in this region to true tidal features around M87 itself." We linit our analysis to regions to the northwest of ABST which are larecly free of dust contamination., We limit our analysis to regions to the northwest of M87 which are largely free of dust contamination. Ihehliehted in Figure 39. are several exteuded features surrounding Ms?., Highlighted in Figure \ref{subtract_m49m87} are several extended features surrounding M87. There is a wide pluue extending racially to the north ofM87s center (Region I). aud also wo narrow streams extending to the northwest (Beeious 112 aud These radial streams ave bright enough hat they are easily visible even iu the unsubtracted deep," There is a wide plume extending radially to the north of M87's center (Region 4), and also two narrow streams extending to the northwest (Regions 1+2 and These radial streams are bright enough that they are easily visible even in the unsubtracted deep" differential imaging (SDI) VET camera optimized lor multi-wavelengüli speckle suppression (Billeretal.2006).,differential imaging (SDI) VLT camera optimized for multi-wavelength speckle suppression \citep{biller2006}. . This shows the potential of ADI to achieve high-contrast detection al sub-arcsec separations using a simple. vet ellicient. observing technique with standard instruments.," This shows the potential of ADI to achieve high-contrast detection at sub-arcsec separations using a simple, yet efficient, observing technique with standard instruments." Fig., Fig. 6. illustrates the noise attenuation obtained for Vega (August 26th) using ihe ADI technique., \ref{fig6} illustrates the noise attenuation obtained for Vega (August 26th) using the ADI technique. Mass limits corresponding to these observations. corrected [or the filteruse?.. are estimated using evolutionary models of Daraffeetal.(2003) assuming ages of 350. 45 and 85 Myr [or Vega. IIDI88023 and 11D97324D. respectively (Soneοἱal.2001:Monteset2001).," Mass limits corresponding to these observations, corrected for the filter, are estimated using evolutionary models of \citet{baraffe2003} assuming ages of 350, 45 and 85 Myr for Vega, HD18803 and HD97334B, respectively \citep{song2001,montes2001}." ". Both IID13803 and 1D97324D achieve detection limits of 1-2 Mj, at 37 (60 AU for both targets). while 73 Aljy) is obtained for Vega at 8"" (63 AU)."," Both HD18803 and HD97334B achieve detection limits of 1-2 $_{\rm{Jup}}$ at $^{\prime \prime}$ (60 AU for both targets), while $\sim$ 3 $_{\rm{Jup}}$ is obtained for Vega at $^{\prime \prime}$ (63 AU)." The ADI technique is thus well suited lo survey jovian Companions at intermediate separations (50-300 AU) orbiting voung nearby stars., The ADI technique is thus well suited to survey jovian companions at intermediate separations (50-300 AU) orbiting young nearby stars. In the previous sections it was shown that the ADI technique can achieve high contrast eiven a sufficiently long integration time and good PSF stability., In the previous sections it was shown that the ADI technique can achieve high contrast given a sufficiently long integration time and good PSF stability. " To compare (he performances of ADI and classical observations we analvze the first 38 images of the IID97334D. ADI sequence and (he 38 images of the IIDIJ405. ""classical sequence.", To compare the performances of ADI and classical observations we analyze the first 38 images of the HD97334B ADI sequence and the 38 images of the HD1405 “classical” sequence. For (his analysis. both data seis have been reduced. according to section. ??..," For this analysis, both data sets have been reduced according to section \ref{reduc}." Furthermore. an 8x EWIIM unsharp mask was applied to all images to remove (he low spatial Ireequency (quasi-static noise.," Furthermore, an $8\times 8$ FWHM unsharp mask was applied to all images to remove the low spatial frequency quasi-static noise." Then alxlEWILIM median filter was applied to all images to remove the bad/hot pixels., Then a $1\times 1$ FWHM median filter was applied to all images to remove the bad/hot pixels. These steps are performed here only to bring the classical observations on even ground with ADI in order to study the evolution of the noise al spatial scales that most severely limit point source detections., These steps are performed here only to bring the classical observations on even ground with ADI in order to study the evolution of the noise at spatial scales that most severely limit point source detections. For the 11D97334D sequence. images dillerences were obtained according lo section ??:: these differences were then rotated to align the FOV to that of the first image.," For the HD97334B sequence, images differences were obtained according to section \ref{adialgo}; these differences were then rotated to align the FOV to that of the first image." " An increasing number of images (differences for HD97334B) of both sequences were median combined to study the noise attenuation as a function of the total observing time at 2"". the results are presented in Fig. &.."," An increasing number of images (differences for HD97334B) of both sequences were median combined to study the noise attenuation as a function of the total observing time at $^{\prime \prime}$, the results are presented in Fig. \ref{fig7}." The ADI reduction technique achieves 30 times better speckle noise attenuation compared to classical AO observations in 30 minutes integration time., The ADI reduction technique achieves 30 times better speckle noise attenuation compared to classical AO observations in 30 minutes integration time. This ligure also illustrates the power of ADI imaging in which noise attenuation. and (hus companion S/N. increases nearly as the expected γη while it saturates rapidly [ου normal imaging.," This figure also illustrates the power of ADI imaging in which noise attenuation, and thus companion S/N, increases nearly as the expected $\sqrt{n}$ while it saturates rapidly for normal imaging." during an eucouuter with velocity V.,during an encounter with velocity $V$. " The function p(V) has been determined using the parametrization reported in Table 5 for the values of V. available from our umnuerical investigation aud then fitting these poiuts with a function of the form W/V"".", The function $p(V)$ has been determined using the parametrization reported in Table 5 for the values of $V$ available from our numerical investigation and then fitting these points with a function of the form $K/V^{\beta}$. We obtain20078119) and describe this function in Figure 23., We obtain and describe this function in Figure 23. This quantities our finding that sealaxies in environments characterized by hieh density aud low-velocity dispersion. like compact eroups. will be more Likely to show sigus of past or recent iuteractious iu agreement with the results of a ΠΠΟΙ of investigatious (see e.g. Zepf Whitinore 1995. Alenudes de Oliveira ITickson 199D.," This quantifies our finding that galaxies in environments characterized by high density and low-velocity dispersion, like compact groups, will be more likely to show signs of past or recent interactions in agreement with the results of a number of investigations (see e.g. Zepf Whitmore 1993, Mendes de Oliveira Hickson 1994)." These observational studies argue that the fraction of distorted morphologics in conipact eroups is larger than the fraction observed iu clusters (which have similar uunber densities but üeher velocity dispersions) aud in sample of feld ealaxies (which are likely to suffer low-velocity encounters but ina ow-densitv environment)., These observational studies argue that the fraction of distorted morphologies in compact groups is larger than the fraction observed in clusters (which have similar number densities but higher velocity dispersions) and in sample of field galaxies (which are likely to suffer low-velocity encounters but in a low-density environment). Asstuine that vouus galaxies were located in deuse euviromuenuts aud characterized by ower. previnalized velocity dispersious. our conclusions are consistent with the results of Abraham et al. (," Assuming that young galaxies were located in dense environments and characterized by lower, previrialized velocity dispersions, our conclusions are consistent with the results of Abraham et al. (" 19965) who have shown that the distribution of A for galaxies in he IDF is skewed toward Ligh values compared to that for ealaxies in the AIDS which. in turn. are more asviunnetric hau local field galaxics.,"1996b) who have shown that the distribution of $A$ for galaxies in the HDF is skewed toward high values compared to that for galaxies in the MDS which, in turn, are more asymmetric than local field galaxies." Au additional useful diagnostic is the ratio of the serturber to the primary masses necessary fo produce a eiven value of maxcl., An additional useful diagnostic is the ratio of the perturber to the primary masses necessary to produce a given value of $\max A$. This is casily obtained from the fits discussed in 8123 and is given by 80isotopicinaDLAatlimit z=1.15., \citet{lev06} reported a lower limit } $>$ 80 in a DLA at $=1.15$. " However in this case, the metallicity of the system is [Fe/H]~—1and the role of fast rotators could be minor."," However in this case, the metallicity of the system is $\sim -1$and the role of fast rotators could be minor." The value found by Levshakov et al., The value found by Levshakov et al. cannot be compared to our models in Fig., cannot be compared to our models in Fig. 1 because the chemical evolution of DLAs most probably proceeded in a radically different way than for the galactic halo (see ??)..," \ref{fig1} because the chemical evolution of DLAs most probably proceeded in a radically different way than for the galactic halo \citep[see][]{chiap03,dess07}. ." The impact of fastrotators in DLAs will be the subject of a It is wort, The impact of fastrotators in DLAs will be the subject of a forthcoming paper. "h !1?C/!?Cforthcomingratiospaper.haverecently been measured (?) in globular cluster unevolved stars, in the metallicity range [Fe/H]~—2.0 to ~ —0.8."," It is worth noticing that } ratios have recently been measured \citep{carr05} in globular cluster unevolved stars, in the metallicity range $\sim -2.0$ to $\sim -0.8$ ." A low value, A low value of the coadded spectra (which favours a smaller number of spectra with the largest E(B— V)s).,of the coadded spectra (which favours a smaller number of spectra with the largest $E(B-V)$ s). " We also need to consider the goodness-of-fit of the spectra that will make up the composite spectrum, and so it was necessary to make a cut based upon the Dmax statistic (Section ??))."," We also need to consider the goodness-of-fit of the spectra that will make up the composite spectrum, and so it was necessary to make a cut based upon the $D_{\mathrm{max}}$ statistic (Section \ref{dustquant}) )." " However, it is conceivable that a system with a large SMC-Dmax value, and thus poor SMC fit, will in fact be well characterised by a MW extinction curve."," However, it is conceivable that a system with a large $D_{\mathrm{max}}$ value, and thus poor SMC fit, will in fact be well characterised by a MW extinction curve." We certainly do want to remove such objects which exhibit a MW type dust signature from the composite sample., We certainly do want to remove such objects which exhibit a MW type dust signature from the composite sample. " This Dmax discrepancy (between SMC and MW extinction curves) becomes more significant at higher E(B—V) values, and we can quantify, for a given absorber redshift, the E(B—V)swc value which corresponds to a poor-fit Dmax=0.04."," This $D_{\mathrm{max}}$ discrepancy (between SMC and MW extinction curves) becomes more significant at higher $E(B-V)$ values, and we can quantify, for a given absorber redshift, the $E(B-V)_{\mathrm{SMC}}$ value which corresponds to a poor-fit $D_{\mathrm{max}}=0.04$." We have determined how this E(B—V)swc cutoff varies as a function of redshift and the results are shown in Fig 12., We have determined how this $E(B-V)_{\mathrm{SMC}}$ cutoff varies as a function of redshift and the results are shown in Fig \ref{cap:natdustcomp1}. ". Absorption systems in the shaded region of Fig 12,, are those which satisfy the parameterised condition: where a—38.7, b—4.55, and c—0.04."," Absorption systems in the shaded region of Fig \ref{cap:natdustcomp1}, are those which satisfy the parameterised condition: where $a=38.7$, $b=4.55$, and $c=0.04$." " For such absorbers, the form of the extinction curve, SMC or MW, can be determined via their SMC/MW Dynax statistics."," For such absorbers, the form of the extinction curve, SMC or MW, can be determined via their SMC/MW $D_{\mathrm{max}}$ statistics." " We created a composite spectrum (Fig 13)) from objects satisfying the condition in Equation 10,, by taking the flux value at each wavelength."," We created a composite spectrum (Fig \ref{cap:coaddstrongmg}) ) from objects satisfying the condition in Equation \ref{ebvcond}, by taking the flux value at each wavelength." " Three further composites were created from the fitted extinction curves (SMC, LMC, MW) corresponding to each absorber."," Three further composites were created from the fitted extinction curves (SMC, LMC, MW) corresponding to each absorber." " This allows for the characterisation of the type of dust by investigating whether the stacked spectrum is well fit by the SMC, LMC or MW curves."," This allows for the characterisation of the type of dust by investigating whether the stacked spectrum is well fit by the SMC, LMC or MW curves." " The resulting curves possess E(B—V) values of 0.12, 0.16, and 0.13 for the SMC, LMC and MW respectively."," The resulting curves possess $E(B-V)$ values of 0.12, 0.16, and 0.13 for the SMC, LMC and MW respectively." " As predicted, Fig 13 shows that on average our carefully-selected high E(B—V) absorber subsample exhibits an extinction curve very similar to that of the SMC."," As predicted, Fig \ref{cap:coaddstrongmg} shows that on average our carefully-selected high $E(B-V)$ absorber subsample exhibits an extinction curve very similar to that of the SMC." " We can quantify the significance of the SMC- versus LMC- and MW-type reddening by examining the relative contributions of SMC-, LMC- and MW-type dust to the composite spectrum in the region around the feature (Fig. 13--(bottom-right)))."," We can quantify the significance of the SMC- versus LMC- and MW-type reddening by examining the relative contributions of SMC-, LMC- and MW-type dust to the composite spectrum in the region around the feature (Fig. \ref{cap:coaddstrongmg}- ))." " We obtain an estimate for the ratio of SMC-to-LMC-to-MW type spectra which contribute to our composite, by coadding a number of SMC, LMC, and MW extinction curves and minimising the between the coadd and the composite spectrum (in the range AA))."," We obtain an estimate for the ratio of SMC-to-LMC-to-MW type spectra which contribute to our composite, by coadding a number of SMC, LMC, and MW extinction curves and minimising the between the coadd and the composite spectrum (in the range )." " Formally, we found that a combination of SSMC-, LLMC- and MMW-curves provides the best fit to the composite spectrum in the feature region."," Formally, we found that a combination of SMC-, LMC- and MW-curves provides the best fit to the composite spectrum in the feature region." The best-fitting combination is shown in ÀFig. 13--, The best-fitting combination is shown in Fig. \ref{cap:coaddstrongmg}- different. configurations and that the switching of the magnetosphere between (hese states can result in the observed mode changes and nulls.,different configurations and that the switching of the magnetosphere between these states can result in the observed mode changes and nulls. Timokhin(2010) further notes that each state would have a different spin-down rate., \citet{tim10} further notes that each state would have a different spin-down rate. Timokhin(2007) shows that oscillation modes of high spherical degree and non-vanishing velocities al the surface can alter the local Goldreich-Julian (GJ) charge density 1969)., \citet{tim07} shows that oscillation modes of high spherical degree and non-vanishing velocities at the surface can alter the local Goldreich-Julian (GJ) charge density \citep{gj69}. . The GJ charge density. while not a contributing factor to the spin-down rate in the [orce-[ree model. is then a combination of the charge density clue to rotation and the charee density due to oscillations.," The GJ charge density, while not a contributing factor to the spin-down rate in the force-free model, is then a combination of the charge density due to rotation and the charge density due to oscillations." In (his paper. we assume that. like white dwarf stars. neutron star oscillations can change with both amplitude and spherical degree. therefore allecting the total charge density aud (he magnetospheric configuration.," In this paper, we assume that, like white dwarf stars, neutron star oscillations can change with both amplitude and spherical degree, therefore affecting the total charge density and the magnetospheric configuration." If the charge density is al least partially responsible for the energy loss of the pulsar and/or the change in pulsation mode changes the magnetospheric configuration. we expect to observe a change in spin-down rale.," If the charge density is at least partially responsible for the energy loss of the pulsar and/or the change in pulsation mode changes the magnetospheric configuration, we expect to observe a change in spin-down rate." Under some models we expect for the spin-down rate and the pulse shape to change with both spherical degree and the amplitude of the velocities of the oscillations.Vo.," Under some models we expect for the spin-down rate and the pulse shape to change with both spherical degree and the amplitude of the velocities of the oscillations,." .. Timokhin(2007) caleulates the GJ charge density lor neutron star oscillations assuming the standard pulsar model of a rotating magnetized conducting sphere surrounded by plasma. and explores the excitation of oscillations by neutron star glitches.," \citet{tim07} calculates the GJ charge density for neutron star oscillations assuming the standard pulsar model of a rotating magnetized conducting sphere surrounded by plasma, and explores the excitation of oscillations by neutron star glitches." He shows that oscillation modes of high spherical degree and non-vanishing velocities al the surface can alterthe local GJ charge density (pe;;) where poy~ ο , He shows that oscillation modes of high spherical degree and non-vanishing velocities at the surface can alterthe local GJ charge density $\rho_{GJ}$ ) where $\rho_{GJ} \sim$ $(V_{osc}/c)(B/4\pi{R_{NS}})$. The charge density will affect the accelerating electric field., The charge density will affect the accelerating electric field. For the oscillations to be strong enough to influence the parücle distribution. resulting in effects Chat we can observe. Timokhin(2007) suggests the spherical degree is approximately several hundred. which is in agreement with our independent measurements (Rosen&Clemens2008:RosenDemorest2010).," For the oscillations to be strong enough to influence the particle distribution, resulting in effects that we can observe, \citet{tim07} suggests the spherical degree is approximately several hundred, which is in agreement with our independent measurements \citep{ros08,ros10}." ". Decause more particles leave (he stellar surface when the charge densitwv is greater. we expect the spin-down rate (ο increase with either: 1) increasingἐν, 2) increasing15,4... or 2) increasing andVice."," Because more particles leave the stellar surface when the charge density is greater, we expect the spin-down rate to increase with either: 1) increasing, 2) increasing, or 3) increasing and." Assuming that the current density in the magnetosphere is given by Equation 1 (Lorimer&Ilxramer 2004).. the charge density is directly related to the spin-down rate by:," Assuming that the current density in the magnetosphere is given by Equation \ref{eqn:1} \citep{hbpa}, , the charge density is directly related to the spin-down rate by:" variable in both density ancl mass-transfer rate.,variable in both density and mass-transfer rate. This causes a change in the number of electrons which are available for acceleration in the jet. which alters the synchrotron luminosity.," This causes a change in the number of electrons which are available for acceleration in the jet, which alters the synchrotron luminosity." Radio photometry monitors the change in jet emission following a change in the WolfRavet state and three distinct states of emission in the unresolved: core of the system have been identified (Waltman et 11995): Continuous monitoring determines the radio state of Cve N-3.. and allows detailed. investigation of the jet mechanism and structure during these cillerent states.," Radio photometry monitors the change in jet emission following a change in the Wolf–Rayet state and three distinct states of emission in the unresolved core of the system have been identified (Waltman et 1995): Continuous monitoring determines the radio state of Cyg X-3, and allows detailed investigation of the jet mechanism and structure during these different states." Daily radio monitoring was carried out using the ltvle Telescope in Cambridge and the Green Dank Interferometer (VBI) in West Virginia., Daily radio monitoring was carried out using the Ryle Telescope in Cambridge and the Green Bank Interferometer (GBI) in West Virginia. Phese observatories provided photometry at 2.3 and 8.3 Gllz (CDI) and 15 Cillz (Itvlo)., These observatories provided photometry at 2.3 and 8.3 GHz (GBI) and 15 GHz (Ryle). Identification of a minor Hare in 1996 November triggered a set of interferometric observations using the MEBRLIN array., Identification of a minor flare in 1996 November triggered a set of interferometric observations using the MERLIN array. The ALERLIN observations were scheduled at €-band. (5 CGllz) with 6 epochs of 12 hours in duration cach separated by one week., The MERLIN observations were scheduled at C-band (5 GHz) with 6 epochs of 12 hours in duration each separated by one week. The aim of these observations was to map the emission from a plasmon as it travelled. from the centre of the binary. as observed by Newell (1995).," The aim of these observations was to map the emission from a plasmon as it travelled from the centre of the binary, as observed by Newell (1995)." At a frequency of 5 CGllz a plasmon at 10 kpe. travelling at a speed of 0.35 c in the plane of the sky. would. separate from the core at one ALERLEN beam-ewidth per epoch (50mas).," At a frequency of 5 GHz a plasmon at 10 kpc, travelling at a speed of 0.35 $c$ in the plane of the sky, would separate from the core at one MERLIN beam-width per epoch $(\simeq 50\;{\rm mas})$." This jet velocity. taken from the apparent transverse motion measured by Spencer ct ((1986). represents a. lower-limit to the separation per epoch.," This jet velocity, taken from the apparent transverse motion measured by Spencer et (1986) represents a lower-limit to the separation per epoch." Other measurements have indicated higher velocities of components close to the plane of the sky (0.66 from et (0000) and 2θ.δὸ [rom Mioduszewski et ((2000))., Other measurements have indicated higher velocities of components close to the plane of the sky $\simeq 0.6c$ from et (2000) and $\simeq 0.8c$ from Mioduszewski et (2000)). These larger apparent. velocities would. therefore vield. greater separations per ALERLIN epoch., These larger apparent velocities would therefore yield greater separations per MERLIN epoch. refrvle-phot shows the radio photometry from. the Rvle telescope at 15 CGllz which was used as a trigger for the ALERLIN observations., \\ref{ryle-phot} shows the radio photometry from the Ryle telescope at 15 GHz which was used as a trigger for the MERLIN observations. Cvg A-3 was in quiescence until 50400 when it underwent a mild. quenching perioc (flux around 50 mJ)., Cyg X-3 was in quiescence until 50400 when it underwent a mild quenching period (flux around 50 mJy). Shortly after the quenching. a minor Hare occurred. on ALJD 50407 which signalled the start of a minor Uare period.," Shortly after the quenching, a minor flare occurred on MJD 50407 which signalled the start of a minor flare period." Subsequent minor Lares occurred a random times after this date., Subsequent minor flares occurred at random times after this date. Observations were taken using the standard 5 Cllz AIERLUEN continuum setup., Observations were taken using the standard 5 GHz MERLIN continuum setup. A 15 MlIA bandwidth was usec or observations of the target source Cygnus N-3. a phase calibrator source. 2005|403. a [lux calibrator 3€84. and a »oint source calibrator. either. OQ 208 or 0552|3908.," A 15 MHz bandwidth was used for observations of the target source Cygnus X-3, a phase calibrator source 2005+403, a flux calibrator 3C84, and a point source calibrator, either OQ 208 or 0552+398." To calibrate the flux casily. observation of a point source of known Hux is required.," To calibrate the flux easily, observation of a point source of known flux is required." However. on the longer. ALERLLN xwelines all the point sources are variable in Dux. and al he constant [Iux sources are resolved.," However, on the longer MERLIN baselines all the point sources are variable in flux, and all the constant flux sources are resolved." One has to observe a point source over all baselines and calibrate the Dux scale »v measurements of a source of known [lux using the shor xiselines only., One has to observe a point source over all baselines and calibrate the flux scale by measurements of a source of known flux using the short baselines only. Details of this calibration procedure are given in the MERLLIN user's guide. Phomasson et ((1993) anc Oevley (1998).," Details of this calibration procedure are given in the MERLIN user's guide, Thomasson et (1993) and Ogley (1998)." The source and observational details for all the epochs are given in Table 1.., The source and observational details for all the epochs are given in Table \ref{obs_characteristics}. " The times of the ALERLIN observations are shown in Merlin, pochstogetherwithtylepholometrgatl56 HH zaroundlhesametim", The times of the MERLIN observations are shown in \\ref{Merlin_epochs} together with Ryle photometry at 15 GHz around the same time. oe., The MERLIN observations are indicated by the arrows. Beeause of the variable nature of the source at the time of the MEIRLIN observations. a robust map of the source is almost impossible to obtain.," Because of the variable nature of the source at the time of the MERLIN observations, a robust map of the source is almost impossible to obtain." Variations in observed amplitude can be due to two things: a variable core: or, Variations in observed amplitude can be due to two things: a variable core; or (his energv band is dominated by the Fe-L line complex which is rather sensitive to the temperature. the failure of the LAINB+IAMINE (or PL+IAUNL) model suggests. as we expected. that the thin thermal plasma distributed in the central ~ 1.2 kpe region of M 31 cannot be described by a single temperature.,"this energy band is dominated by the Fe-L line complex which is rather sensitive to the temperature, the failure of the LMXB+1MKL (or PL+1MKL) model suggests, as we expected, that the thin thermal plasma distributed in the central $\sim$ 1.2 kpc region of M 31 cannot be described by a single temperature." To improve the model. we added another MINL component.," To improve the model, we added another MKL component." This model. LMXD--2MNKL model. is essentially the same as that used in Paper 1. except the plasma codes.," This model, LMXB+2MKL model, is essentially the same as that used in Paper 1, except the plasma codes." As presented in Figure {ος and Table 3.. this model has successfully reproduced the 0.67 keV spectra. vielcling (wo temperatures of ~0.6 keV and ~0.3 keV. These results reconfirm the conclusion of Paper 1 that two sub-keV temperatures are needed to reproduce the 0.610 keV ASC. over a 127 radius region around the M 31 nucleus.," As presented in Figure \ref{fig:0.6-7keV}c c and Table \ref{tab:fit}, this model has successfully reproduced the 0.6–7 keV spectra, yielding two temperatures of $\sim 0.6$ keV and $\sim 0.3$ keV. These results reconfirm the conclusion of Paper 1 that two sub-keV temperatures are needed to reproduce the 0.6–10 keV ${\it ASCA}$ over a $\arcmin$ radius region around the M 31 nucleus." Although the temperature of the hotter plasma (~0.6 keV) obtained in this wav is a little lower than that in Paper 1 (0.9 keV). the disagreement can be attributed to the difference of the plasma models.," Although the temperature of the hotter plasma $\sim 0.6$ keV) obtained in this way is a little lower than that in Paper 1 (0.9 keV), the disagreement can be attributed to the difference of the plasma models." Actually. it becomes 0.3 keV (Figure 4dd and Table 3)). in eood agreement will Paper 1. when we restore the RS models (LAINB+2RS model) instead of the MIXL (LAINB+2\INL).," Actually, it becomes 0.8 keV (Figure \ref{fig:0.6-7keV}d d and Table \ref{tab:fit}) ), in good agreement with Paper 1, when we restore the RS models (LMXB+2RS model) instead of the MKL (LMXB+2MKL)." We tentatively identily the present 0.6 keV. component with the 0.9 keV one found with SCA., We tentatively identify the present 0.6 keV component with the 0.9 keV one found with ${\it ASCA}$. Incidentally. the RS model gives a worse 47. due to a residual structure around | keV which probably arises from an insufficient modeling of the Fe-L complex.," Incidentally, the RS model gives a worse $\chi^{2}$, due to a residual structure around 1 keV which probably arises from an insufficient modeling of the Fe-L complex." When the LMXD--2MBKL. model determined in the 0.67 keV band is extrapolated toward lower energies. the model prediction Falls significantly short of the actual data (Figure dcc).," When the LMXB+2MKL model determined in the 0.6–7 keV band is extrapolated toward lower energies, the model prediction falls significantly short of the actual data (Figure \ref{fig:0.6-7keV}c c)." As a result. the LMXND-2MNKL fit actually becomes unacceptable when the 0.10.6 keV band is included.," As a result, the LMXB+2MKL fit actually becomes unacceptable when the 0.4–0.6 keV band is included." " The fit is improved by re-adjusting the model parameters except Ny, and Τον.", The fit is improved by re-adjusting the model parameters except $N_{\rm H}$ and $kT_{\rm BB}$ . Nevertheless. the temperature of the cooler MIXL component becomes lower than that obtained in $ 3.2. and the abundances are (oo low.," Nevertheless, the temperature of the cooler MKL component becomes lower than that obtained in $\S$ 3.2, and the abundances are too low." When the temperature and abundances are [ixed even al 0.25 keV and the 0.1 solar values. respectively. the fit becomes unacceptable (A? == 819/706).," When the temperature and abundances are fixed even at 0.25 keV and the 0.1 solar values, respectively, the fit becomes unacceptable $\chi^{2}$ = 819/706)." " In short. the LMXD--2MEKL modeling does not give a reasonable account of the 0.47 keV spectra,"," In short, the LMXB+2MKL modeling does not give a reasonable account of the 0.4–7 keV spectra." This in turn suggests the presence of a forth. ancl the softest. emission component. which was not detected with SCA (Paper 1). because of the limited soft. X-ray. sensitivilv.," This in turn suggests the presence of a forth, and the softest, emission component, which was not detected with ${\it ASCA}$ (Paper 1), because of the limited soft X-ray sensitivity." The soltest component max be contributed by O-Ix lines appearing in the 0.50.6 keV range., The softest component may be contributed by O-K lines appearing in the 0.5–0.6 keV range. We therefore added one more MIXL component to jointly fit the total-band (0.47 keV) MOS/PN spectra., We therefore added one more MKL component to jointly fit the total-band (0.4–7 keV) MOS/PN spectra. [ere and herealter. weallow the nitrogen abundance (ο vary [reelv.," Here and hereafter, weallow the nitrogen abundance to vary freely," We have presented a homogeneous analvsis of the binary. fraction in MIO as a function ol the radial distance from the cluster centre. from the core region. out to e2rj.,"We have presented a homogeneous analysis of the binary fraction in M10 as a function of the radial distance from the cluster centre, from the core region, out to $\sim 2 r_h$." Within the errors. the derived binary. fraction is consistent with that measured in other GCs. which have typical values of ρουspanning from ~1056 to ~25% (S07: Davis οἱ al.," Within the errors, the derived binary fraction is consistent with that measured in other GCs, which have typical values of $\xi_{TOT}$spanning from $\sim 10\%$ to $\sim 25\%$ (S07; Davis et al." " 2003) but itis significantly smaller (han Chat estimated for the faintest clusters in (he sample of Sollimaetal.(2007).. which reach also binary fractions €:o,~50%."," 2008) but it is significantly smaller than that estimated for the faintest clusters in the sample of \citet{sol07}, which reach also binary fractions $\xi_{TOT}\sim 50\%$." This is in agreement with the quoted anti-correlation between binary fraction aud total Iuminositv (Miloneetal.2008:Sollimaοἱ 2010).," This is in agreement with the quoted anti-correlation between binary fraction and total luminosity \citep{milone08, sol08, sol10}." . Also the binary [raction bevond the hall-mass racdius (~ 154) is consistent with previous estimates in GC's (seeTable1Davisοἱal.2008).," Also the binary fraction beyond the half-mass radius $\sim 1\%$ ) is consistent with previous estimates in GCs \citep[see Table 1][]{davis08}." ". The binary fraction decreases [rom ~6% within r,.. to e15€ bevond the radius."," The binary fraction decreases from $\sim 6\%$ within $r_c$, to $\sim 1\%$ beyond the half-mass radius." An analogous trend was found for the fraction of binaries with q>0.6 and for the binary fraction (Fig. 11)).," An analogous trend was found for the fraction of binaries with $q\ge 0.6$ and for the binary fraction (Fig. \ref{trend}) )," the latter varving from e14% to e1.5% [rom the core to bevond the hall-mass radius., the latter varying from $\sim 14\%$ to $\sim 1.5\%$ from the core to beyond the half-mass radius. Such a radial behavior is in agreement with what has been previously found in the lew other GC's where this kind of investigation has been performed (Rubenstein&Bailvn1997:Bellazzinietal.2002:Zhao2005:SommarivaTable1ofDavisetal... 2003).," Such a radial behavior is in agreement with what has been previously found in the few other GCs where this kind of investigation has been performed \citep[][and references in Table 1 of Davis et al. 2008]{rubai97, bell02, zhao05, somma09}." . IC is also in agreement with the expectations of dynamical models. where the effect is essentially due to the mass-segregation process. which leads (o an increase in the number of binaries in (he cluster cores (e.g..2008:Fregeanοἱal.2009:Ivanova 2011).," It is also in agreement with the expectations of dynamical models, where the effect is essentially due to the mass-segregation process, which leads to an increase in the number of binaries in the cluster cores \citep[e.g.,][]{hurl07, sol08, freg09, ivanova11}." . Indeed. the hall-mass relaxation time of MIO (~0.8Gyr.Harris1996:seealsoGnedinetvanderMarel2005) is just a small fraction (~ 4%) of the cluster age 2010).. so il seems safe to conclude that the svstem has already had time (ο achieve equipartilion.," Indeed, the half-mass relaxation time of M10 \citep[$\sim 0.8$ Gyr, Harris 1996; see also][]{gnedin99,mcLvdM05} is just a small fraction $\sim 4\%$ ) of the cluster age \citep[$t\sim 13$ Gyr;][]{dot10}, so it seems safe to conclude that the system has already had time to achieve equipartition." By comparing the radial variation of the MS stellar mass function derived from the observations. with that obtained in N-body simulations. 010 suggested that either an IMDII or a population of binaries should be present and act as a central enerev source in MIO. supressing (he mass-segregation profile.," By comparing the radial variation of the MS stellar mass function derived from the observations, with that obtained in N-body simulations, B10 suggested that either an IMBH or a population of binaries should be present and act as a central energy source in M10, supressing the mass-segregation profile." hi particular. (the shallow mass-segregation prolile could be modeled without an IMDBII only when the simulations started with a primordial binary [raction of about 3-—5%.," In particular, the shallow mass-segregation profile could be modeled without an IMBH only when the simulations started with a primordial binary fraction of about $3-5\%$." Within this framework. in Figure 11 we compare our derived values of ρου. with those obtained from the dynamical evolution of the primordial binary population in the 21 particle simulation of DIO.," Within this framework, in Figure \ref{trend} we compare our derived values of $\xi_{TOT}$, with those obtained from the dynamical evolution of the primordial binary population in the 32K particle simulation of B10." For a proper comparison we considered a simulation snapshot at ~7 relaxation times. and only those binaries made of two ALS stus and with the primary component in (he mass range 0.44+ 0.56... corresponding to the lower ancl upper cuts of the magnitude range along the MSRL.," For a proper comparison we considered a simulation snapshot at $\sim 7$ relaxation times, and only those binaries made of two MS stars and with the primary component in the mass range $0.44\div 0.56 M_\odot$ , corresponding to the lower and upper cuts of the magnitude range along the MSRL." The resulting binary fractions lor the three considered radial bins are: £y.η)-0.02).(0.032c0.007).(0.026+ 0.006). from the centre to," The resulting binary fractions for the three considered radial bins are: $\xi_{N-body}=(0.070\pm0.02), (0.032\pm 0.007), (0.026\pm 0.006)$ , from the centre to" This expansion is accurate to better than when 1/1.>0.9.,This expansion is accurate to better than when $T/T_c > 0.9$. Numerically. the value of T; can be estimated as follows.," Numerically, the value of $T_c$ can be estimated as follows." The mass of the paneson in the soft wall model is found by solving a particular wave equation whose solutions involve Laguerre polynomials., The mass of the $\rho$ -meson in the soft wall model is found by solving a particular wave equation whose solutions involve Laguerre polynomials. " A boundary condition leads to the relation y,=2c.", A boundary condition leads to the relation $m_{\rho} = 2\sqrt{c}$. " The IHawking-Page analysis of the phase transition in |ls] gives T,=im5/4x192 MeV. A similar analvsis in the hard wall model vields a transition temperature of approximately m,/6.354 |18]..", The Hawking-Page analysis of the phase transition in \cite{softwallD} gives $T_c = m_{\rho}/4 \approx 192$ MeV. A similar analysis in the hard wall model yields a transition temperature of approximately $m_{\rho}/6.354$ \cite{softwallD}. Is a negative shear relaxation (ime unphnvsical?, Is a negative shear relaxation time unphysical? First consider real. positive gq aad complex iw.," First consider real, positive $q$ and complex $\omega$." A shear plane wave propagating in (he z-direction has the form .—t gecl(qi — ο...hye where the frequency. has been decomposed into its real ancl imaginary paris as w=wpcej., A shear plane wave propagating in the $z$ -direction has the form = _0 = _0 where the frequency has been decomposed into its real and imaginary parts as $\omega = \omega_R + i \omega_I$. The real part vanishes and the imaginary part is Vi DRUL τη (Fl) which is definitely negative if 7>0., The real part vanishes and the imaginary part is _I = -Dq^2 ( 1 + D q^2 + ) which is definitely negative if $\tau > 0$. This is the usual situation where the waves falls off exponentially in time., This is the usual situation where the waves falls off exponentially in time. If 7«0 then the first (wo terms of the expansion cannot be trusted for q?>1/7D|.,If $\tau < 0$ then the first two terms of the expansion cannot be trusted for $q^2 > 1/|\tau D|$. But the first two terms of {he expansioncannol be trustecl lor larger values of q even if 7 was positive., But the first two terms of the expansioncannot be trusted for larger values of $q$ even if $\tau$ was positive. Now consider real. positive w and complex q.," Now consider real, positive $\omega$ and complex $q$." The shear dispersion relation ls 30 wan. The↜, The shear dispersion relation is q^2 = ( i + + ). ↜↼∙↜ wavenumber can be decomposed into ils real and imaginary parts as q =dp+iq., The wavenumber can be decomposed into its real and imaginary parts as $q=q_R+iq_I$. The dispersion relation to the required order is determined bv the solution to the following equation: qud - ciu 8))-040) Obviously qq;=w/2D> 0., The dispersion relation to the required order is determined by the solution to the following equation: q_R^2 - q_I^2 - + i ( 2 q_R q_I - ) = 0 Obviously $q_R q_I = \omega/2D > 0$ . The shear wave behliaves as, The shear wave behaves as more massive haloes have a larger probability to merge with other structures.,more massive haloes have a larger probability to merge with other structures. We have used a large set of high-resolution simulated haloes to analvse the statistics of subhaloes in dark matter halocs. and their dependency as a function of the parent halo mass and physical properties of the parent halo.," We have used a large set of high-resolution simulated haloes to analyse the statistics of subhaloes in dark matter haloes, and their dependency as a function of the parent halo mass and physical properties of the parent halo." While some of the results discussed in this study confirm results from previous studies. it is the first time that a systematic analysis of the properties and evolution of dark matter substructures is carried out. using a large simulation set carried out. using the same cosmological parameters and simulation code.," While some of the results discussed in this study confirm results from previous studies, it is the first time that a systematic analysis of the properties and evolution of dark matter substructures is carried out using a large simulation set carried out using the same cosmological parameters and simulation code." Our main results can be summarized as follows: Dark matter substructures mark the sites where luminous satellites are expected. to. be found. so. their evolution and. properties do provide important information on the galaxy. population that forms in hierarchical models.," Our main results can be summarized as follows: Dark matter substructures mark the sites where luminous satellites are expected to be found, so their evolution and properties do provide important information on the galaxy population that forms in hierarchical models." As discussed. in previous studies. however. because of the strong tidal stripping sullerecl by haloes falling onto larger structures. it is not possible to simplv correlate the population of subhalocs identified at a given. cosmic epoch to that of the corresponding galaxies.," As discussed in previous studies, however, because of the strong tidal stripping suffered by haloes falling onto larger structures, it is not possible to simply correlate the population of subhaloes identified at a given cosmic epoch to that of the corresponding galaxies." The galaxy luminosity/stellar mass is expected to be more strongly related to the mass of the substructure at the time ofοί and. depending on the resolution of the simulations. there night be a significant fraction of the galaxy population that cannot be traced with dark matter substructures because hey have been stripped. below the resolution limit of the simulation (the ‘orphan’ galaxies - see for example ?)).," The galaxy luminosity/stellar mass is expected to be more strongly related to the mass of the substructure at the time of and, depending on the resolution of the simulations, there might be a significant fraction of the galaxy population that cannot be traced with dark matter substructures because they have been stripped below the resolution limit of the simulation (the `orphan' galaxies - see for example )." Nevertheless. our results do provide indications about he properties of the galaxy poypopulations Ipredicted. by ucrarchical models.," Nevertheless, our results do provide indications about the properties of the galaxy populations predicted by hierarchical models." Tidal stripping is largely independent of the environmen we have parametrized this as the parent ido mass) while the accretion rates of new subhaloes increases at increasing redshift.," Tidal stripping is largely independent of the environment (we have parametrized this as the parent halo mass), while the accretion rates of new subhaloes increases at increasing redshift." The nearly invariance of he subhalo mass function results from the ance between hese two physical processes., The nearly invariance of the subhalo mass function results from the balance between these two physical processes. " Lf the amount of dark matter substructures is tracing the [fraction of recently infallen galaxies. the fraction of star forming galaxies is expected o increase with increasing redshift. (the ""Dutcher-Oemler? ellect. 2.. 2))."," If the amount of dark matter substructures is tracing the fraction of recently infallen galaxies, the fraction of star forming galaxies is expected to increase with increasing redshift (the `Butcher-Oemler' effect, , )." In addition. our findings suggest that stronger mass segregation should be found with increasing recdshift.," In addition, our findings suggest that stronger mass segregation should be found with increasing redshift." There is a Large halo-to-halo scatter that can be only partially explained by a wide range of physical properties., There is a large halo-to-halo scatter that can be only partially explained by a wide range of physical properties. This is expected to translate into a large scatter in c.g. the fraction of passive galaxies for haloes of the same mass. with more concentrated haloes hosting Larger fraction of redpassive galaxies.," This is expected to translate into a large scatter in e.g. the fraction of passive galaxies for haloes of the same mass, with more concentrated haloes hosting larger fraction of red/passive galaxies." Finally. there is an obvious merger bias that is expected to translate into a dilferent morphological mix for haloes of dilferent mass.," Finally, there is an obvious merger bias that is expected to translate into a different morphological mix for haloes of different mass." In future work. we plan to carry out a more direct comparison with observational data at different cosmic times. bv applying detailed semi-analvtic model to the merger trees extracted from our simulations.," In future work, we plan to carry out a more direct comparison with observational data at different cosmic times, by applying detailed semi-analytic model to the merger trees extracted from our simulations." WD 0806-661 D should have a mass of ~7 Mj.,WD 0806-661 B should have a mass of $\sim7$ $M_{\rm Jup}$. The models that best match the absolute magnitude and age of WD 0s06-661 D have effective. temperatures of ~300. TI. WD 0806-661 D is a strong couteudoer for the faintest known brown dwarf based on the available photometric auc astrometric mcasurements., The models that best match the absolute magnitude and age of WD 0806-661 B have effective temperatures of $\sim300$ K. WD 0806-661 B is a strong contender for the faintest known brown dwarf based on the available photometric and astrometric measurements. With au estimated T;~300 I. it would be significautlv cooler than the latest T chwarf currently known (Zi 54120602010).," With an estimated $T_{\rm eff}\sim300$ K, it would be significantly cooler than the latest T dwarf currently known \citep[$T_{\rm eff} 500." Moreover. its photosphere would be sufficiently cool to harbor water ice clouds. making it a likely prototvpe for the Y dwarf spectral class.," Moreover, its photosphere would be sufficiently cool to harbor water ice clouds, making it a likely prototype for the Y dwarf spectral class." " We also estimate a ο. ~7 Mu, for WD Os06- D from the evolutionary models.", We also estimate a mass of $\sim7$ $M_{\rm Jup}$ for WD 0806-661 B from the evolutionary models. Caven that cloud core fragmentation appears capable of making binary conrpanions near this mass (e.e..Todorovetal.2010).. it seecnas likely that a companion of this kind iu a very lavee orbit (2500 AU) would have formed in this manner.," Given that cloud core fragmentation appears capable of making binary companions near this mass \citep[e.g.,][]{tod10}, it seems likely that a companion of this kind in a very large orbit (2500 AU) would have formed in this manner." However. the mass estimate also falls within the range of masses measured for close-in extrasolar plaucts C5152001).," However, the mass estimate also falls within the range of masses measured for close-in extrasolar planets \citep[$\lesssim15$~$M_{\rm Jup}$." Because the progenitorALi. of the primary was fairly massive (~2 M). its circtuustellar disk at birth could have beeu nassive enough to eive rise to a conipauilon at this mass.," Because the progenitor of the primary was fairly massive $\sim2$ $M_\odot$ ), its circumstellar disk at birth could have been massive enough to give rise to a companion at this mass." Thus. WD 0806-661 D could be a giaut planet that has been dvnauically scattered to a larger orbit.," Thus, WD 0806-661 B could be a giant planet that has been dynamically scattered to a larger orbit." Spectroscopy and multibaud photometry are necessary to verify theo substellar nature of WD üs(06-661 D aud to better estimate its plysical properties., Spectroscopy and multi-band photometry are necessary to verify the substellar nature of WD 0806-661 B and to better estimate its physical properties. If confirmed as the coolest kuown brown dwarf. it will represent a valuable laboratory for studyiug atiuosplieres In a new tempcrature regine. and its colors will help to guide searches for the coldest brown dwarfs with facili&es like the Wide-field. Iufvared. Survey Explorer aud the James Webb Space Telescope.," If confirmed as the coolest known brown dwarf, it will represent a valuable laboratory for studying atmospheres in a new temperature regime, and its colors will help to guide searches for the coldest brown dwarfs with facilities like the Wide-field Infrared Survey Explorer and the James Webb Space Telescope." We thank Robin Ciardullo for advice regarding age estimates for white chwarts. telescope operator Mauricio Martinez at Maecllan for his assistance with the FIRE observations. and Nigel Παπ] for his helpful referee report.," We thank Robin Ciardullo for advice regarding age estimates for white dwarfs, telescope operator Mauricio Martinez at Magellan for his assistance with the FIRE observations, and Nigel Hambly for his helpful referee report." We acknowledge support from eraut AST-0511588 from the National Science. Foundation (x. L.. J. D.) aud the Chris and Warren Helhiuau Fellowship Program (A. D.)," We acknowledge support from grant AST-0544588 from the National Science Foundation (K. L., J. B.) and the Chris and Warren Hellman Fellowship Program (A. B.)." The Center for Exoplanets and IHabitable Worlds i$ supported by the Peuusvlvania State University. the Eberly College of Scicuce. aud the Peuusylvauia Space Crant Consortimu.," The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium." When the neutron star surface temperature Z5:5 there are no values of 0 or P for which NRICS can initiate a cascade in the vacuum gap. (,When the neutron star surface temperature $T_6 \le 5$ there are no values of $\beta_Q$ or $P$ for which NRICS can initiate a cascade in the vacuum gap. ( Only when Z529 are there anv 0o.P values which permit an NIUCS-initiated cascade. and even at these high temperatures the allowed range of o and 2 values is very small and atypical of neutron stars.),"Only when $T_6 \ga 9$ are there any $\beta_Q,P$ values which permit an NRICS-initiated cascade, and even at these high temperatures the allowed range of $\beta_Q$ and $P$ values is very small and atypical of neutron stars.)" Pherefore. no pulsar death boundaries appear for the NRICS process in Fig. S..," Therefore, no pulsar death boundaries appear for the NRICS process in Fig. \ref{deathfig}." lt ds well known that a strong magnetic field increases the binding energy. of individual atom and that of the zero-pressure condensed. nater., It is well known that a strong magnetic field increases the binding energy of individual atom and that of the zero-pressure condensed matter. Very approximately. lor DUuBy sce Eq. (," Very approximately, for $B\gg B_0$ [see Eq. (" "1)]. he former increases as (InD)7 while the latter scales as B""","1)], the former increases as $(\ln B)^2$ while the latter scales as $B^{0.4}$." Phorelore one expects that the outermos laver of a neutron star may be in the condensed state when the magnetic field D js sullicientlv strong and/or the surface temperature 7 is sulficieruly low., Therefore one expects that the outermost layer of a neutron star may be in the condensed state when the magnetic field $B$ is sufficiently strong and/or the surface temperature $T$ is sufficiently low. Exactly under wha conditions this occurs is an important quesion that entails quantitative cdeulations., Exactly under what conditions this occurs is an important question that entails quantitative calculations. In this pader. using our recent results on the cohesive properties of magnetized condensed matter (Medin&Lai2YOGa.b).. we have established quantitatively the parameter regime (in D and T space) for whic1 surface condensation occurs.," In this paper, using our recent results on the cohesive properties of magnetized condensed matter \citep{medin06a,medin06b}, we have established quantitatively the parameter regime (in $B$ and $T$ space) for which surface condensation occurs." Our calculations showed that there are a range ο| neutron star magnetic field strengths and surface temperatures where the condensed surface wi| have an important effect on radiation from these stars., Our calculations showed that there are a range of neutron star magnetic field strengths and surface temperatures where the condensed surface will have an important effect on radiation from these stars. " For example. if the surface composition is Fe. 1ien strong-field neutron stars (D=107? € with moderate (P<10"" ds) surface emp«eHabupes svould have amospheres/vapors that are effectively. transparent to twrmal raciation. so that the emission comes that [rom a bare concdensed surface."," For example, if the surface composition is Fe, then strong-field neutron stars $B\ga10^{13}$ G) with moderate $T\la10^6$ K) surface temperatures should have atmospheres/vapors that are effectively transparent to thermal radiation, so that the emission becomes that from a bare condensed surface." This may explain the nearly blackhock-like raciaion spectrum observed. from he nearby. isolated neutron star AN JIS56.5-3754 (e.g. jurwitzetal.2003:vanAdesberg2005:LIo 20073).," This may explain the nearly blackbody-like radiation spectrum observed from the nearby isolated neutron star RX J1856.5-3754 (e.g., \citealt{burwitz03,vanadelsberg05,ho07}) )." We have also examined he conditions for the formation of a vacuum acceleratior1 exp above the polar cap region of the neutron star., We have also examined the conditions for the formation of a vacuum acceleration gap above the polar cap region of the neutron star. The inner acceeration gap model. first developed by Rucerman&Suherlancl(1975).. has provided a useful ramework to understand numerous observations of radio pulsars.," The inner acceleration gap model, first developed by \citet{ruderman75}, has provided a useful framework to understand numerous observations of radio pulsars." Most notably. the nxxlel naturally explains the phenomenon of criting subpulses observec in many pulsars (e... Backer1976:Deshpande&Rankin1999:Wetevredeetal. 2006)) in terms m ‘the EB circulation of pasma filaments produced by vacuum discharges.," Most notably, the model naturally explains the phenomenon of drifting subpulses observed in many pulsars (e.g., \citealt{backer76,deshpande99,weltevrede06}) ) in terms of the ${\bf E}\times{\bf B}$ circulation of plasma filaments produced by vacuum discharges." ParialN SCEPCOCDOCC gaps have also been studied Ce. Cheng<uderman1980:Cailctal.206)3. 20063).," Partially screened gaps have also been studied (e.g., \citealt{cheng80,gil03,gil06}) )." However. it ias lone been recognized that the original Ruderman Suherlancl model is problematic since the dipole magnetic field inerred. [ron D.P may not be strong enough to inhibit charge emission from the surace.," However, it has long been recognized that the original Ruderman Sutherland model is problematic since the dipole magnetic field inferred from $P,\dot P$ may not be strong enough to inhibit charge emission from the surface." Our caleulations described in this p:iper quantivV the condition for vacuum gap formation (sce Fig. 7))., Our calculations described in this paper quantify the condition for vacuum gap formation (see Fig. \ref{gapfig}) ). While tus condition (ie... 1 is smaller than a critical value which depends on D and composition) may not IC σαisfiecl for most pulsars (unless one invokes surface magnetic fiels much stixNeer han that inferred [rom {2P: see Cil et al.," While this condition (i.e., $T$ is smaller than a critical value which depends on $B$ and composition) may not be satisfied for most pulsars (unless one invokes surface magnetic fields much stronger than that inferred from $P,\dot P$; see Gil et al." 2006 and references therein). it could well be satisfied. [or son| neutron savs.," 2006 and references therein), it could well be satisfied for some neutron stars." In particular. the recently. discovered iigh-D radio piilssus. having dipole surface m:venetic fields in excess o 11027 GG and tem»rature about LO? Ix. (e.g... )). may operate a vacuum gap accelerator.," In particular, the recently discovered high-B radio pulsars, having dipole surface magnetic fields in excess of $10^{14}$ G and temperature about $10^6$ K (e.g., \citealt{kaspi04,mclaugh05}) ), may operate a vacuum gap accelerator." On 11e other hand. while magnetars have similar magnetic field strengths. their surface temperatures are about five times larger than those of high-B radio pulsars. and therefore nlav no have a vacuum eap.," On the other hand, while magnetars have similar magnetic field strengths, their surface temperatures are about five times larger than those of high-B radio pulsars, and therefore may not have a vacuum gap." In this regard. it is interesting to note tha ΗΕ1ος maenctars do not show racio emission (though this may be because the radio pulse is beamed away from us or the cause their magnetosphere plasma moverwhelms the radio pulses). and the two recently detected radio magnetars have rather cilerent racio emission properties (e.g. he spectrum extends to hieh frequency. and. the radiation shows high degrees of linear. polarization) compared. to “normal” radio pulsars.," In this regard, it is interesting to note that most magnetars do not show radio emission (though this may be because the radio pulse is beamed away from us or the because their magnetosphere plasma “overwhelms” the radio pulses), and the two recently detected radio magnetars have rather different radio emission properties (e.g., the spectrum extends to high frequency and the radiation shows high degrees of linear polarization) compared to “normal” radio pulsars." We may therefore speculate that a key cillerence between magnetars ànd high-D radio pulsars is their dillerence in surface temperature., We may therefore speculate that a key difference between magnetars and high-B radio pulsars is their difference in surface temperature. In any case. our gap formation condition (Fig. 7))," In any case, our gap formation condition (Fig. \ref{gapfig}) )" suggests tju the radio emission property of neuron stars may depend not only on the magnetic field and rotation rate. but also on the| surface temperature.," suggests that the radio emission property of neutron stars may depend not only on the magnetic field and rotation rate, but also on the surface temperature." We note that our caleulation of the requirements for vacuum gap formation assumes ideaized conditions., We note that our calculation of the requirements for vacuum gap formation assumes idealized conditions. A real neutron star polar cap may be immersed in a strong radiation field and suller bombardment from high energy particles (e.g. 20072).," A real neutron star polar cap may be immersed in a strong radiation field and suffer bombardment from high energy particles (e.g., \citealt{arons81,beloborodov07}) )." The effective cohesive energy of the surface may. be somewhat smaller than what we used in our paper due to surface defects (Arons 2007. wivate communication).," The effective cohesive energy of the surface may be somewhat smaller than what we used in our paper due to surface defects (Arons 2007, private communication)." Whether the vacuum gap survives in realistic situations is unclear., Whether the vacuum gap survives in realistic situations is unclear. It has been suggested that a partially screened. gap is formed instead. (Ciletal.2003.2006).," It has been suggested that a partially screened gap is formed instead \citep{gil03,gil06}." .. With small modilications e.g. the potential drop given by Eq. (52))," With small modifications [e.g., the potential drop given by Eq. \ref{eq:Phidrop}) )" is reduced]. our discussion of pair cascades in the vacuum gap can be easily generalized to the case of a partially screene gap.," is reduced], our discussion of pair cascades in the vacuum gap can be easily generalized to the case of a partially screened gap." A major part of our paper is devoted to the pair cascade physies in the vacuum gap (Section r 5))., A major part of our paper is devoted to the pair cascade physics in the vacuum gap (Section \ref{sect:death}) ). We find that. pair cascade initiated by curvature radiation can account for most pulsars in the 2? 2 diagram. but significant field line curvature near the stellar surface is needed.," We find that pair cascade initiated by curvature radiation can account for most pulsars in the $P$ $\dot{P}$ diagram, but significant field line curvature near the stellar surface is needed." Although such fiel curvature is possible for some pulsars. it is unlikely to occur for all of them.," Although such field curvature is possible for some pulsars, it is unlikely to occur for all of them." For a pure dipole magnetic field. only about half of all pulsars can be explained by a curvature raciation-initiatcd cascade.," For a pure dipole magnetic field, only about half of all pulsars can be explained by a curvature radiation-initiated cascade." Contrary to previous works (e.g.. Zhangetal. 2000)). we find that inverse Compton scatterings (resonant or not) are not cllicient in producing vacuum breakdown via. pair cascade.," Contrary to previous works (e.g., \citealt{zhang00}) ), we find that inverse Compton scatterings (resonant or not) are not efficient in producing vacuum breakdown via pair cascade." The recent detection of the radio emission [rom two AXIS (Camiloetal.2006. 2007)) is of great interest.," The recent detection of the radio emission from two AXPs \citealt{camilo06,camilo07}) ) is of great interest." The emission appears to be triggered by N-ray outbursts of usually quiescent magnetars., The emission appears to be triggered by X-ray outbursts of usually quiescent magnetars. This may be due to a rearrangement of the surface magnetic field. which made pair cascades. possible.," This may be due to a rearrangement of the surface magnetic field, which made pair cascades possible." We note that the occurrence of pair cascades depends strongly on the, We note that the occurrence of pair cascades depends strongly on the O.218-0.53 M... we lind a radius range οἱ 0.[88-0.635. 2...,"0.248-0.53 $M_\sun$, we find a radius range of 0.488-0.635 $R_\sun$ ." Adopting {ο=0.55+0.07R.. we cau convert surface brightuess to Mq: aud therefore find the corresponding AZ) for our M1.5 dwarl.," Adopting $R_2 = 0.55 \pm 0.07 R_\sun$, we can convert surface brightness to $M_V$ and therefore find the corresponding $M_V$ for our M1.5 dwarf." We corrected for extinction using the infrared dust maps of Schlegeletal.(1998)., We corrected for extinction using the infrared dust maps of \citet{Sch98}. . These maps provide our best estimate for the amount of extinetion due to dust., These maps provide our best estimate for the amount of extinction due to dust. However. the method is uunperfect. as they give the amount of extinction to the edge of the Galaxy rather than to 5DSS1511.," However, the method is imperfect as they give the amount of extinction to the edge of the Galaxy rather than to SDSS1544." Patchiness al scales below their 6-arcmiu resolution would also affect the extinction estimate., Patchiness at scales below their 6-arcmin resolution would also affect the extinction estimate. Coubinit© Our values for ni. AA. aud Ay. we calculate a distauce of 80043180 pc.," Combining our values for $m_V$, $M_V$ , and $A_V$, we calculate a distance of $800 \pm 180$ pc." We may also apply the donor sequence derived by ίσος(2006) to calculate a distance (see. again. Table 2)).," We may also apply the donor sequence derived by \citet{Knigge06} to calculate a distance (see, again, Table \ref{Table 2}) )." Using the Ex iuagnitude from the 2MÀSS survey and the absolute magnitude from μίσοςMD(2006) s empirical douor sequence. we get a distauce of 510 pc.," Using the K magnitude from the 2MASS survey and the absolute magnitude from \citet{Knigge06}' 's empirical donor sequence, we get a distance of 810 pc." We find that SDSS1511 is an eclipsing CV witha period of 6.03 lir. and determiue an ephemeris.," We find that SDSS1544 is an eclipsing CV with a period of 6.03 hr, and determine an ephemeris." The Ha emission velocities show a prouounced rotational disturbance., The $\alpha$ emission velocities show a pronounced rotational disturbance. We also note that the determiued emission velocities are not exactly out of phase with the absorption. which would point to asymainetric disk eimissiou.," We also note that the determined emission velocities are not exactly out of phase with the absorption, which would point to asymmetric disk emission." The decomposed spectrum is fitted best with a M1.» star. which iudicates that the secondary is somewhat evolved.," The decomposed spectrum is fitted best with a M1.5 star, which indicates that the secondary is somewhat evolved." We also calculate the distance to 5DSS1I511 by two different methocs., We also calculate the distance to SDSS1544 by two different methods. Both result in a distance of roughly 800 pc., Both result in a distance of roughly $800$ pc. This work was supported by NSF erants AST-0307113 anc AST-0708810., This work was supported by NSF grants AST-0307413 and AST-0708810. The authors wish to thank the MDM stall for observing support. as well as Joe Patterson for donation of observing time.," The authors wish to thank the MDM staff for observing support, as well as Joe Patterson for donation of observing time." We would also like to thaukan anonymous referee for helpful commentsaud careful readiug oL the manuscript., We would also like to thankan anonymous referee for helpful commentsand careful reading of the manuscript. data from Mouut. Wilson Observatory to find the rotation rate at different latitudes aud noted that the rotation rates for the Doppler patter were some faster than the spectroscopic rate and. niserouslv. sole faster than the simall magnetic features hat are observed to outline their borders.,"data from Mount Wilson Observatory to find the rotation rate at different latitudes and noted that the rotation rates for the Doppler pattern were some faster than the spectroscopic rate and, mysteriously, some faster than the small magnetic features that are observed to outline their borders." Alore recently Beck&Schou(2000) MSCQL a Fourier ransform method to fud tha the larger features do rotate more rapidly flal he “πια: feares and that the low wavenunber components of he Doppler pattern rode more rapidly than he plasina at auv level within the surface shear aver., More recently \citet{BeckSchou00} used a Fourier transform method to find that the larger features do rotate more rapidly than the smaller features and that the low wavenumber components of the Doppler pattern rotate more rapidly than the plasma at any level within the surface shear layer. This led them to suggestOO that supereramules rave wave-like characteristics with a preference ‘or prograde propagalon., This led them to suggest that supergranules have wave-like characteristics with a preference for prograde propagation. Hatawayotal.(2006) showed that this Usuper-cotation oftιο Doypler pattern could be attribited to projecion effects associated with the Doppler signal itself., \citet{Hathaway_etal06} showed that this “super-rotation” of the Doppler pattern could be attributed to projection effects associated with the Doppler signal itself. As the velocity pattern rotates across the fie do [view the observed line-of-sigh component is modulated iu a way frat essentially adds another half wave to the pattern and eives a higher rotation rate that increases proportionally with decreasing wavenumber., As the velocity pattern rotates across the field of view the observed line-of-sight component is modulated in a way that essentially adds another half wave to the pattern and gives a higher rotation rate that increases proportionally with decreasing wavenumber. " T10v took a fixed velocity patern (which had spatial characteristics that nuached the SOIIO/MDI data) ancl rotated it rieilv to show this ""super-rotation” effect.", They took a fixed velocity pattern (which had spatial characteristics that matched the SOHO/MDI data) and rotated it rigidly to show this ``super-rotation'' effect. While lis indicated that he Doppler projection effec should be accounted OL. he fixed pattern couk rot account for all the variatious reported by Beck&Schou(," While this indicated that the Doppler projection effect should be accounted for, the fixed pattern could not account for all the variations reported by \citet{BeckSchou00}." "2000).. Cüzonetal.(2003) used timie-distaice wchoscisinology to find the supergranular flow (rather than direc Doypler measurements) and Sc1011(2003) ""divked-out the linc-of-icht nodulation.", \citet{Gizon_etal03} used time-distance helioseismology to find the supergranular flow (rather than direct Doppler measurements) and \citet{Schou03} “divided-out” the line-of-sight modulation. Both studies found slower rotation rates that mateicc tha of the magnetic features it SUV evideuce for wave-like prograde ux rograde movire compoucuts., Both studies found slower rotation rates that matched that of the magnetic features but saw evidence for wave-like prograde and retrograde moving components. " Meunier&Roucic1’(2001) colmpared rotation rates obtained bv rackiug Doper features. magnetic features. arc divergence features (which were, in turn. derive roni correlation tracking of smaller intensity eatures)."," \citet{MeunierRoudier07} compared rotation rates obtained by tracking Doppler features, magnetic features, and divergence features (which were, in turn, derived from correlation tracking of smaller intensity features)." While they couchided that xojection effects do 1ifiuence the rotation rate determine roni the Doppler features. they fouix that the naegnetic features rotate more slowly than the supergrauu," While they concluded that projection effects do influence the rotation rate determined from the Doppler features, they found that the magnetic features rotate more slowly than the supergranules." Iu this )pper we report OW OUP ajnlvses of ata fixuu the SOIIO/MDI iistriuent [Scherrertal.(1995)]] aud. from si.ated data iu which the superegrauules are siuplv advected by ifferenlal rotation aud meriional flow that virv with laitude aud depth., In this paper we report on our analyses of data from the SOHO/MDI instrument \citet{Scherrer_etal95}] ] and from simulated data in which the supergranules are simply advected by differential rotation and meridional flow that vary with latitude and depth. The siuulated data are esigned to faithftIv nimc tl1ο SOIIO/MDI data he σαne data that was aindvzed in Beck.&Schou(2000) aud Schou{2003) with simple Assyloli aout the αντιunical structure of jo surface shear laver., The simulated data are designed to faithfully mimic the SOHO/MDI data [the same data that was analyzed in \citet{BeckSchou00} and \citet{Schou03}] ] with simple assumptions about the dynamical structure of the surface shear layer. The analyses iuclude reprocdictions of those done in earlier studies., The analyses include reproductions of those done in earlier studies. Througithe sinmlations we can better deteriuine 16 actial ciffercutial rotation ancl meridional flow oxofiles consistent with the Doppler observations (which are subject to le-ofsight projection effects)., Through the simulations we can better determine the actual differential rotation and meridional flow profiles consistent with the Doppler observations (which are subject to line-of-sight projection effects). The full-disk Doppler images frou: SOTO/MDI are obtained at a T-uiuute cadence to resolve the temporal variations associated with the p-mode oscillations., The full-disk Doppler images from SOHO/MDI are obtained at a 1-minute cadence to resolve the temporal variations associated with the p-mode oscillations. We |cf., We [cf. Hathawayctal.(2000) aud Deck&Schou (2000) have temporally filtered the tuages to remove the panuode signal by using a 3i-ninute long tapered Gaussian with a FWIIM of 16 iunutes on sets of 31 images tha were de-rotated to register cach to the central image., \citet{Hathaway_etal00} and \citet{BeckSchou00}] ] have temporally filtered the images to remove the p-mode signal by using a 31-minute long tapered Gaussian with a FWHM of 16 minutes on sets of 31 images that were de-rotated to register each to the central image. These filtered imagesOo were formed at 15-1inute intervals over the 60-day MDI Dynamics Run in |996., These filtered images were formed at 15-minute intervals over the 60-day MDI Dynamics Run in 1996. " This filtering process effectively removes the pauode sigual and leaves behind the Doppler signal from flows with temporal variations longer than about 16 mun1""S", This filtering process effectively removes the p-mode signal and leaves behind the Doppler signal from flows with temporal variations longer than about 16 minutes. Supergranules. with tvpical wavenunibers of Hout 1]0. are verv well resolved in this data (at disk ceuer wavenunboers up te» 1500 are resolved).," Supergranules, with typical wavenumbers of about 110, are very well resolved in this data (at disk center wavenumbers up to 1500 are resolved)." " While orauules are not well resolved. they do iopear in the data as xxel-to-pixel aud inage-to-Huage οίκο, as a convective blue shift (due to the correlation betweeu brightuess au updratts). alb aslsolved sttctives for the largest iienibers."," While granules are not well resolved, they do appear in the data as pixel-to-pixel and image-to-image “noise,” as a convective blue shift (due to the correlation between brightness and updrafts), and as resolved structures for the largest members." These data are prewed for studving the cellular feaures byv first Πο and removing the Doypler signals due to: 1) «observer motion. 2) convoective blue shift. 3) differ‘ential rotation. aud 1) the axisviunetriiieridioual flow.," These data are prepared for studying the cellular features by first measuring and removing the Doppler signals due to: 1) observer motion, 2) convective blue shift, 3) differential rotation, and 4) the axisymmetricmeridional flow." Tιο data are then mapped onto heiograplüe coordinates with equal s]ocius in both oneitudoe aud latitude., The data are then mapped onto heliographic coordinates with equal spacing in both longitude and latitude. This mapping includes accounting for the position angle, This mapping includes accounting for the position angle (Ciranato&Danese1994).. respectively) and on the strength of the ποσοτο. luminosity.,"\citep{granato94}, respectively) and on the strength of the accretion luminosity." We adopted: the absorption and scattering cocllicients given by Laor&Draine(1993) for dust. grains of different dimensions. weighted with the standard AIRN distribution (Mathisetal.1977).," We adopted the absorption and scattering coefficients given by \cite{laor93} for dust grains of different dimensions, weighted with the standard MRN distribution \citep{mathis77}." .. Crains dimensions range from 0.005 to 0.25 for graphite. and 0.025 to 0.25 for silicate.," Grains dimensions range from 0.005 to 0.25 for graphite, and 0.025 to 0.25 for silicate." The dust density within the torus is modeled in. such a wav to allow a gradient along both the radial and. the angular coordinates: with 3 taking the ciserete values 0.0. -0.5 and -1.0. and ~ the values 0.0 and 6.0.," The dust density within the torus is modeled in such a way to allow a gradient along both the radial and the angular coordinates: with $\beta$ taking the discrete values 0.0, -0.5 and -1.0, and $\gamma$ the values 0.0 and 6.0." " When 5z0.0 the dust distribution in no longer a ""Dared disk"" but takes a shape that resembles that of a donut. hence the name “torus”."," When $\gamma \ne 0.0$ the dust distribution in no longer a “flared disk” but takes a shape that resembles that of a donut, hence the name “torus”." " The ""zero value? ais defined by the value of the equatorial optical depth at 9.7 micron. Τατ."," The “zero value” $\alpha$ is defined by the value of the equatorial optical depth at 9.7 micron, ${\rm \tau}_{9.7}$." " One of the novelties of this work is the use of low optical depth tori (76,7« 1).", One of the novelties of this work is the use of low optical depth tori ${\rm \tau}_{9.7} < 1$ ). Even though they are part of model sets present in the literature (e.g. Ciranato&Danese 1994)). they have not been used. to explain the 1t emission of AGN.," Even though they are part of model sets present in the literature (e.g. \citealt{granato94}) ), they have not been used to explain the IR emission of AGN." The implications of this approach are explained in Section 6.., The implications of this approach are explained in Section \ref{discuss}. The global model SEDs are computed at dillerent angles of the line-of-sight with respect to the torus equatorial plane. in order to account for both tvpe-1 and tvpe-2 objects emission. and include three contributions: emission from the AGN (partially extinguished if the torus intercepts the line-ol-ight). thermal and scattering emission bv. dust in cach volume element.," The global model SEDs are computed at different angles of the line-of-sight with respect to the torus equatorial plane, in order to account for both type-1 and type-2 objects emission, and include three contributions: emission from the AGN (partially extinguished if the torus intercepts the line-of-sight), thermal and scattering emission by dust in each volume element." " ‘Torus models with Rosifin of 300 are a priori excluded from the runs. even though they belong to the ""standard? evicl of models. presented. by Fritzetal.(2006).. as they imply tori with physical sizes of several hundred: parsecs. sometimes even Κρο"," Torus models with $\rm R_{out}/R_{in}$ of 300 are a priori excluded from the runs, even though they belong to the “standard” grid of models presented by \cite{fritz06}, as they imply tori with physical sizes of several hundred parsecs, sometimes even kpc." For such a ratio. an AGN of 1075 erg/sec accretion luminosity and an inner radius of 1.3 pe would have an outer radius of ~400 pe.," For such a ratio, an AGN of $^{46}$ erg/sec accretion luminosity and an inner radius of 1.3 pc would have an outer radius of $\sim$ 400 pc." " In the general case. only models with It,/Rin of 30 and 100 are allowed. but models with Itδι of 300 will be revisited in Section in order to address specific cases."," In the general case, only models with $\rm R_{out}/R_{in}$ of 30 and 100 are allowed, but models with $\rm R_{out}/R_{in}$ of 300 will be revisited in Section \ref{sec:mips} in order to address specific cases." The stellar emission will play à minor role in this work. since we are dealing with bright. mainly high redshift’ quasars. for which the galaxy light is not significant.," The stellar emission will play a minor role in this work, since we are dealing with bright, mainly high redshift quasars, for which the galaxy light is not significant." However. for completeness. we add a stellar component modeled. as the sum of spectra of Simple Stellar Population (SSP) models of cilferent age. all assumed with a common (solar) metallicity.," However, for completeness, we add a stellar component modeled as the sum of spectra of Simple Stellar Population (SSP) models of different age, all assumed with a common (solar) metallicity." The set of SSP used for this analysis is built with Padova evolutionary tracks (Bertellictal.L994).. a Salpeter IME with masses in the range 0.15 120 M. and the Jacobyet(1984). library of observed stellar spectra in the optical domain.," The set of SSP used for this analysis is built with Padova evolutionary tracks \citep{bertelli94}, a Salpeter IMF with masses in the range 0.15 – 120 $_\odot$ and the \cite{jacoby84} library of observed stellar spectra in the optical domain." Phe extension to the UV and LH range is obtained bv means of Ixurucz theoretical libraries., The extension to the UV and IR range is obtained by means of Kurucz theoretical libraries. Dust emission from circumstellar envelopes of AGB stars has been added: by AMessanetal.(1998)., Dust emission from circumstellar envelopes of AGB stars has been added by \cite{bressan98}. . For the cold dust component. the major contributor to the emission at wavelengths longer than ~30pni. we use two observational starburst templates. namely MS2 as a representative of a “typical” starburst Ht emission and Arp 220 as representative of a very extinguished starburst.," For the cold dust component, the major contributor to the emission at wavelengths longer than $\sim 30$, we use two observational starburst templates, namely M82 as a representative of a “typical” starburst IR emission and Arp 220 as representative of a very extinguished starburst." A more exhaustive approach would require us to provide a physical model of the starburst component. which however is fav bevond the scope of this work.," A more exhaustive approach would require us to provide a physical model of the starburst component, which however is far beyond the scope of this work." Starburst: templates are used only when there are observed datapoints longwared of 24 restframe. (typically only when 70 and/or 160 data are available). and if à torus mocdel fails to provide an acceptable description of the observational SED.," Starburst templates are used only when there are observed datapoints longward of 24 restframe, (typically only when 70 and/or 160 data are available), and if a torus model fails to provide an acceptable description of the observational SED." This choice is. in fact. arbitrary as nothing forbids the presence of a starburst component fainter than the 70 detection limit.," This choice is, in fact, arbitrary as nothing forbids the presence of a starburst component fainter than the 70 detection limit." The llux at24g. though. is dominated by the torus: the starburst contribution at this wavelength is minimal. as it coincides with the presence of a deep absorption feature in their SEDs (see Section 5.5)). an with no more catapoints recwards of 24 it is simply impossible to constrain that part. of the SED.," The flux at, though, is dominated by the torus: the starburst contribution at this wavelength is minimal, as it coincides with the presence of a deep absorption feature in their SEDs (see Section \ref{sec:mips}) ), an with no more datapoints redwards of 24 it is simply impossible to constrain that part of the SED." Adding a starburst component in order to fit all objects would only increase the degeneracy and uncertainties of our results., Adding a starburst component in order to fit all objects would only increase the degeneracy and uncertainties of our results. Quantities such as the LX Iuminosity (see Sections 4.1 and 5.2)). though. might be seen as lower limits for the objects with no MIPS το and/or 160 detections.," Quantities such as the IR luminosity (see Sections \ref{sec:physics} and \ref{sec:lir}) ), though, might be seen as lower limits for the objects with no MIPS 70 and/or 160 detections." Given the large amount of data available. we developed a fully automatic fitting procedure. where the goodness of the fit is measured in terms of a 47 function: where O; are the observed. values. Ad; the values computed. from the model and a; are the observed: errors of the photometric point.," Given the large amount of data available, we developed a fully automatic fitting procedure, where the goodness of the fit is measured in terms of a $\chi^2$ function: where $O_i$ are the observed values, $M_i$ the values computed from the model and $\sigma_i$ are the observed errors of the photometric point." The expected values from the model are computed by convolving the synthetic [ux with the filters’ response curves. after an opportune normatisation ancl Wecorrection is applied.," The expected values from the model are computed by convolving the synthetic flux with the filters' response curves, after an opportune normalisation and K-correction is applied." The dominant component in the UV. and. NIB. (rest-frame) is the aceretion disk., The dominant component in the UV and NIR (rest-frame) is the accretion disk. For very low redshift objects light from the host galaxy might also be present., For very low redshift objects light from the host galaxy might also be present. Ehe former is clearly distinguishable from a twpical stellar SED. because it is in general bluer. aud Hat over the entire range of overlap.," The former is clearly distinguishable from a typical stellar SED, because it is in general bluer and flat over the entire range of overlap." Hence. if a good Lit is not achieved. stars are removed from the final SED. and a pure AGN component is used at these wavelengths.," Hence, if a good fit is not achieved, stars are removed from the final SED, and a pure AGN component is used at these wavelengths." Since we are dealing with an GN sample (i.e. we expect an AGN component to be present in the observed. SEDs of all the objects). the starburst emission. which dominates over the other components only in the ELI. is included only if there are observed 70 and/or 160 datapoints.," Since we are dealing with an AGN sample (i.e. we expect an AGN component to be present in the observed SEDs of all the objects), the starburst emission, which dominates over the other components only in the FIR, is included only if there are observed 70 and/or 160 datapoints." Examples of fits are shown in Fig. 1:, Examples of fits are shown in Fig. \ref{fig:fits}: on the left. an object whose SED was reproduced by an AGN component only: in the middle a case of an AGN with starburst emission: and in the right an object with all three components (torus. starburst and stars) present.," on the left, an object whose SED was reproduced by an AGN component only; in the middle a case of an AGN with starburst emission; and in the right an object with all three components (torus, starburst and stars) present." Even though the minimum X7 will define the best fit. the associated: probabilities can not be taken at Lace value. as for a number of reasons the derived: reduced vs are overestimated.," Even though the minimum $\chi^2$ will define the best fit, the associated probabilities can not be taken at face value, as for a number of reasons the derived reduced $\chi^2$ s are overestimated." First. of all. in order to compute the model magnitudes. the models are convolved: with the," First of all, in order to compute the model magnitudes, the models are convolved with the" "equation (12)) to equation (27)) occurs at e1.500,44, for q—2.",equation \ref{fast_wind_angular_momentum}) ) to equation \ref{slow_wind_angular_momentum}) ) occurs at $v \sim 1.5 a \Omega_{\rm orb}$ for $q=2$. Tf we asstune that slow winds blow from the primary aud the mass of the secondary docs not chauge (AL=(0. the separation is calculated from Therefore. the critical value of ἐν is about 0.54=0.5(M5/M4) for shrinking/expanucding of the separation.," If we assume that slow winds blow from the primary and the mass of the secondary does not change $\dot M_2=0$ ), the separation is calculated from Therefore, the critical value of $\ell_{\rm w}$ is about $0.5 q = 0.5 (M_2/M_1)$ for shrinking/expanding of the separation." When e~«Qo. the systemic loss of the aneular moment is estimated as 21.7.O.55(efaQuaY?~1.0 from equation (38)).," When $v \sim a \Omega_{\rm orb}$, the systemic loss of the angular momentum is estimated as $\ell_{\rm w} \approx 1.7 - 0.55(v/a \Omega_{\rm orb})^2 \sim 1.0$ from equation \ref{both_wind_angular_momentum}) )." " We therefore have é«zxDAL,AL< 0.", We therefore have $\dot a/a \approx 2 \dot M_1 / M_2 < 0$ . Ouce the binary svstem begius to shrink. its evolution becomes simülar to a conuuon euvelope evolution (seeD-D iu Fig. A1)).," Once the binary system begins to shrink, its evolution becomes similar to a common envelope evolution (see in Fig. \ref{channel}) )." " As the separation shrinks. the orbital velocity of «8,4, iucreases."," As the separation shrinks, the orbital velocity of $a \Omega_{\rm orb}$ increases." If the wind velocity is almost constant. the ratio of οΌρων iu equation (38)) becomes snaller and smaller aud the shrinking is accelerated more aud more.," If the wind velocity is almost constant, the ratio of $v/a \Omega_{\rm orb}$ in equation \ref{both_wind_angular_momentum}) ) becomes smaller and smaller and the shrinking is accelerated more and more." " Thus.the separation is reduced by a factor ofLfLO1/50. i6. 0,730.10007f. for Af;~7AL. aud Mo;~1AL..."," Thus,the separation is reduced by a factor of $1/40-1/50$, i.e., $a_f \sim 30-1000 ~R_\odot$ for $M_{1,i} \sim 7 ~M_\odot$ and $M_{2,i} \sim 1 ~M_\odot$." The orbital period becomes Py~15—3000 d for AAypy~1lM. aud Alyn~LAL. Din Fig. AT)).," The orbital period becomes $P_0 \sim 15-3000$ d for $M_{\rm WD,0} \sim 1 ~M_\odot$ and $M_2 \sim 1 ~M_\odot$ in Fig. \ref{channel}) )." These initial sets of the paralucters are very consistent with the initial conditions of our WD|RG progenitor systems., These initial sets of the parameters are very consistent with the initial conditions of our WD+RG progenitor systems. To summarize. we iust include binaries with the separation of iuto the category ofbinaries. where e is the velocity of slow wind (super wind) at the cud of ACB evolution and &~1.5 is a umumerical factor defined ly Ἠαο. we take the critical wind velocity of shrinking/expanding as at the beegiuniug of super wind phase.," To summarize, we must include binaries with the separation of into the category of, where $v$ is the velocity of slow wind (super wind) at the end of AGB evolution and $\xi \sim 1.5-1.7$ is a numerical factor defined by Here, we take the critical wind velocity of shrinking/expanding as at the beginning of super wind phase." We estimate the SN Ta rate in our Galaxy coming frou our WD|RG/WDMS systems by using equation (1) of Then Tutukov (1981). 1.6.. where Aq. AloeA. Ma. and Mg ie the appropriate ranges of the mass ratio. of the initial separation. and the lower and the upper limits of the primary mass for SN Ia explosions in solar nass uuits. respectively.," We estimate the SN Ia rate in our Galaxy coming from our WD+RG/WD+MS systems by using equation (1) of Iben Tutukov (1984), i.e., where $\Delta q$, $\Delta \log A$, $M_A$, and $M_B$ are the appropriate ranges of the mass ratio, of the initial separation, and the lower and the upper limits of the primary mass for SN Ia explosions in solar mass units, respectively." " The estimated rate of the WD|RG/WDMS systems is close to the observedrate in our Galaxy. v~0,003 yr| (e.g. Cappellaroetal.1997:: sce also Yunsgelsou&Livio1998) ). as will be shown below."," The estimated rate of the WD+RG/WD+MS systems is close to the observedrate in our Galaxy, $\nu \sim 0.003$ $^{-1}$ (e.g., \cite{cap97}; see also \cite{yun98}) ), as will be shown below." For the WD|RG progenitors. we asstuue that the initial region of the separation includes e;~L500—10000RH. as well as o;<1500£e. (see discussions above iu 812).," For the WD+RG progenitors, we assume that the initial region of the separation includes $a_i \sim 1500 - 40000 ~R_\odot$ as well as $a_i \lesssim 1500 ~R_\odot$ (see discussions above in 4.2)." Dividing the initial white dwarf mass ΟΕ iuto four intervals. bo. (8ΟΛΕν O09LOA. L0.L.LAZ... aud l.l1.24M.. we estimate the realization frequencies.," Dividing the initial white dwarf mass of $M_{\rm WD,0}$ into four intervals, i.e., $0.8-0.9 M_\odot$, $0.9-1.0 M_\odot$, $1.0-1.1 M_\odot$, and $1.1-1.2 M_\odot$, we estimate the realization frequencies." The lnass range of ApoO0.7A. is not meluded because uoSN Ta explosions are expected for such low initial mass WDs.," The mass range of $M_{{\rm WD,0}} < 0.7 M_\odot$ is not included because noSN Ia explosions are expected for such low initial mass WDs." " We omit the range of Mywp,g=0.7.OAL. because its realization frequency is too small to coutribute to the SN Ta rate as seen in Figures Al2 and AL3.."," We omit the range of $M_{{\rm WD,0}}=0.7-0.8 M_\odot$ because its realization frequency is too small to contribute to the SN Ia rate as seen in Figures \ref{ztotreg100} and \ref{ztotreg030}." " To estimate the initial separation(or orbital period). logA. aud the initial lower/upper masses. A4 aud Mp. of our WD|RG svstenus, we need to obtain the zero-age main sequence lass of the primary component (M4,;) aud the contraction factor after the first comunon euvelope pliase."," To estimate the initial separation(or orbital period), $\log A$, and the initial lower/upper masses, $M_A$ and $M_B$, of our WD+RG systems, we need to obtain the zero-age main sequence mass of the primary component $M_{1,i}$ ) and the contraction factor after the first common envelope phase." In single star evolutions. 0.7.1.2.M.. white dwarts descend from stars with the zero-age main sequence nass of M;~38M. be. Ma3M. aud Mg~sal...," In single star evolutions, $0.7-1.2 M_\odot$ white dwarfs descend from stars with the zero-age main sequence mass of $M_i \sim 3-8 M_\odot$ , i.e., $M_A \sim 3 M_\odot$ and $M_B \sim 8 M_\odot$." More precisely. using Yuneclson et al," More precisely, using Yungelson et al." "s (1995) equation (11) gives the final core mass (οο WD amass) vs. the zero-agemail sequence mass relation. as dnnuueriealle παπαλος. ino Table AL. where Ahwvp,ao=Meo.","'s (1995) equation (11) gives the final core mass (C+O WD mass) vs. the zero-agemain sequence mass relation, as numerically summarized in Table \ref{tbl_contraction_factor}, , where $M_{\rm WD,0} = M_{\rm C+O}$." " The initial separation should be larger thia in order that the C]O core grows up to Meo= AMwp,o."," The initial separation should be larger than in order that the C+O core grows up to $M_{\rm C+O}= M_{\rm WD,0}$ ." Hero. f(q)=0.5 for q=AAfA;~2.T aud the radius of stars at the AGB phase is eiven by (Ibeon&Tutukoyv 1981))5.," Here $f(q) \approx 0.5$ for $q \equiv M_{1,i}/M_{2,i} \sim 2-7$ and the radius of stars at the AGB phase is given by \cite{ibe84}) )." For example. the initial separation should be larger than e;~1.200R. for Αίνου=LOAL.. as sumunarized in Table AL.," For example, the initial separation should be larger than $a_i \sim 1,200 ~R_\odot$ for $M_{\rm WD,0}=1.0 M_\odot$ as summarized in Table \ref{tbl_contraction_factor}." For the binary of ἁνου=LOAL.. aud Mo;=LAL... the contraction factor is estimated to be 1/37 by assunüug the common envelope cficiency factor of age= 1.," For the binary of $M_{\rm WD,0}=1.0 M_\odot$ and $M_{2,i} = 1 M_\odot$, the contraction factor is estimated to be $1/37$ by assuming the common envelope efficiency factor of $\alpha_{\rm CE}=1$ ." The ranee of the separation after common euvelope evolution becomes ap~321.120BR. (correspouding to Py~15 d) because ofa;1.200.£1.700Ri as παπασος in Table AL.," The range of the separation after common envelope evolution becomes $a_f \sim 32-1,120 ~R_\odot$ (corresponding to $P_0 \sim 15-3,070$ d) because of $a_i \sim 1,200-41,700 ~R_\odot$ as summarized in Table \ref{tbl_contraction_factor}." The orbital period of Py—153.070 d covers the SN Ta region (WD|RC svstem) of Fieure ALL. ," The orbital period of $P_0 \sim 15-3,070$ d covers the SN Ia region (WD+RG system) of Figure \ref{zams10}. ." The binary parameters for other AAyp.y are sumunarized in Table A L. ," The binary parameters for other $M_{\rm WD,0}$ are summarized in Table \ref{tbl_contraction_factor}. ." The regions ofthe orbital period. log Py. also covers the SN Ta region (WD|RG svstem) of Fieure Al2..," The regions of the orbital period, $\log P_0$ , also covers the SN Ia region (WD+RG system) of Figure \ref{ztotreg100}. ." Πω weassume e=10 dans | aud e isa real positive nuuber.," is where $\tilde{t}_j = t_j/ \Delta_m t$ , $\Delta_m t = \gamma \min{ [ \{t_{j+1} - t_j\}]}$ and $\gamma$ is a real positive number." " Because of the normalization bv A,,ft. time tj is expressed in units of the shortest sampling time interval."," Because of the normalization by $\Delta_m t$, time $\tilde{t}_j$ is expressed in units of the shortest sampling time interval." Apart from the substitution of the Fourier matrix Fo with F. the uneven sampling of signals docs not modify the foriualiii introduced in the previous section.," Apart from the substitution of the matrix $\Fb$ with $\Fmatcb$ , the uneven sampling of signals does not modify the formalism introduced in the previous section." Iu particular. the covariance matrixCz defined in Eq. (16))," In particular, the covariance matrix$\Cb_{\zhb}$ defined in Eq. \ref{eq:Ce}) )" becomes The N«AL imatric Z docs not have the properties (8))-(12))., becomes The $N \times M$ $\Fmatcb$ does not have the properties \ref{eq:inverse}) \ref{eq:prop}) ). As consequence. and also iu the case that a is the realization ofa standard white-noise process Cy= FI. matrix Cz.," As consequence, and also in the case that $\xb$ is the realization ofa standard white-noise process $\Cb_{\xb} = \Ib$ , matrix $\Cb_{\zhb}$ ," "The excess m counts seen at the bright cud is due to the saturation of brighter objects (V. <16),",The excess in counts seen at the bright end is due to the saturation of brighter objects $V\lsim16$ ). Using the preliniuary color catalog for point sources the observed color distribution of stars brighter than Vo-21 is compared to model predictions in figure over three ranges of magnitude as indicated in each panel., Using the preliminary color catalog for point sources the observed color distribution of stars brighter than $V=21$ is compared to model predictions in figure over three ranges of magnitude as indicated in each panel. The model computes starcounts in D.V. aud 7 by adopting a series of color-magnitude diagrams appropriate for the disk. thick-disk aud halo of our Galaxy.," The model computes starcounts in $B, V$ and $I$ by adopting a series of color-magnitude diagrams appropriate for the disk, thick-disk and halo of our Galaxy." In order to output predicted counts in the natural passhands of the EIS survey. the ransformation given by equations CLi-(1) have been used to couvert ron the EIS magnitudes to the Jolnsou-Cousinus svstemi in such a wav that the predicted counts are actually evaluated in the EIS passbands aud are convolved using the error nodel given in figure 9..," In order to output predicted counts in the natural passbands of the EIS survey, the transformation given by equations (1)-(4) have been used to convert from the EIS magnitudes to the Johnson-Cousins system in such a way that the predicted counts are actually evaluated in the EIS passbands and are convolved using the error model given in figure \ref{fig:errors}." " As can 0 seen from figure 5.. the uuuber of rec (BW)> 1.2) standard stars defining the color transformation is very «λα, so that one might expect possible discrepaucies )etween the observed aud predicted counts; particularly or redder colors."," As can be seen from figure \ref{fig:color}, the number of red $(B-V)>1.2$ ) standard stars defining the color transformation is very small, so that one might expect possible discrepancies between the observed and predicted counts, particularly for redder colors." " One wav of overcoming this would be ο use svuthetic star colors using the svstenmi response ""uetfious given in paper L Πωπονο, for the purposes of describing the usetuluess of the data. the current calibration is sufficient."," One way of overcoming this would be to use synthetic star colors using the system response functions given in paper I. However, for the purposes of describing the usefulness of the data, the current calibration is sufficient." Considering that none of the nodel xuwanmeters have been adjusted to fit the present data. the good agreement of the model to the observed counts in both (5. V)aud(Vfy) isvemarkable. although sole discrepancies can also be readily seen.," Considering that none of the model parameters have been adjusted to fit the present data, the good agreement of the model to the observed counts in both $(B-V)$ and $(V-I)$ is remarkable, although some discrepancies can also be readily seen." At the brightest magnitude biu one sees a deficit of red objects relative to the model predictions in both (D. V) and (V.P) especially iu the former. which is due to saturation effects," At the brightest magnitude bin one sees a deficit of red objects relative to the model predictions in both $B-V$ ) and $(V-I)$, especially in the former, which is due to saturation effects." Note that objects with saturated pixels have been discarded frou the color catalog., Note that objects with saturated pixels have been discarded from the color catalog. "Observations of GRBOLLOLT show two distinct spectral components 2003): A low energv component. with photon energies 5,x;3 MeV. and a high energv component.z, z3 MeV. The low energy component shows rapid variability. has a characteristic GRB spectrum peaking al £4,~0.5 MeV. and decays over LOO s. The hieh energv component has a very hard spectrum. number of photons per unit photon energy ot. and persists over ~200 s. The dillerent temporal behavior suggests that the two components are produced in different regions of the expanding fireball.","Observations of GRB941017 show two distinct spectral components \citep{Gonzalez}: A low energy component, with photon energies $\varepsilon_\gamma\lsim3$ MeV, and a high energy component, $\varepsilon_\gamma\gsim3$ MeV. The low energy component shows rapid variability, has a characteristic GRB spectrum peaking at $\varepsilon_\gamma\sim0.5$ MeV, and decays over $\sim100$ s. The high energy component has a very hard spectrum, number of photons per unit photon energy $dn_\gamma/d\varepsilon_\gamma\propto\varepsilon_\gamma^{-1}$ , and persists over $\sim200$ s. The different temporal behavior suggests that the two components are produced in different regions of the expanding fireball." The characteristics of the low energy component suggest that it is produced by internal shocks. similar to other GRBs.," The characteristics of the low energy component suggest that it is produced by internal shocks, similar to other GRBs." The temporal behavior of the high energy component suggests Chat it is produced during the (transition to sell-similar expansion (Granot&Guetta2003)., The temporal behavior of the high energy component suggests that it is produced during the transition to self-similar expansion \citep{GnG}. ". The hard. dn./dz,x7,1. spectrum is difficult to account for in models where emission is dominated by shock accelerated electrons (Gonzálezefaf."," The hard, $dn_\gamma/d\varepsilon_\gamma\propto\varepsilon_\gamma^{-1}$, spectrum is difficult to account for in models where emission is dominated by shock accelerated electrons \citep{Gonzalez}." 2003).. This has lead Gonzallez el al., This has lead Gonzállez et al. to suggest that the high energy tail is due to electromagnetic cascades initiated by the interaction of photons with ultra-high enerev shock-acceleratecl protons (Wasinan1995:Vielri1995:Dótcher&Dermer1998:TotaniWaxmanBaheall 2000).," to suggest that the high energy tail is due to electromagnetic cascades initiated by the interaction of photons with ultra-high energy shock-accelerated protons \citep{W95,Vietri,Dermer98,Totani98,WnB00}." . We present here an alternative explanation: Electrons accelerated in the forward shock inverse-Compton scaler optical photons. emitted by the reverse shock electrons. to create the observed spectra.," We present here an alternative explanation: Electrons accelerated in the forward shock inverse-Compton scatter optical photons, emitted by the reverse shock electrons, to create the observed spectra." A Κον point. whieh allows to reproduce the observed. hare spectrum. is the modification of the svuehrotron spectrum by sell-absorption in the reverse shock.," A key point, which allows to reproduce the observed hard spectrum, is the modification of the synchrotron spectrum by self-absorption in the reverse shock." We show that this effect allows to reproduce the observed hard. high energy tail also in (he internal shock phase (see 4)).," We show that this effect allows to reproduce the observed hard, high energy tail also in the internal shock phase (see \ref{sec:numeric}) )." Ilowever. we consider (he latter explanation less likely. due to the weak time dependence of the high energv component.," However, we consider the latter explanation less likely, due to the weak time dependence of the high energy component." Granol&Guetta(2003). have recently considered. inverse-Conmpton enussion [rom reverse shock electrons during the transition to self-similarity. as an explanation to the hieh energev (ail of GRD941017.," \citet{GnG} have recently considered inverse-Compton emission from reverse shock electrons during the transition to self-similarity, as an explanation to the high energy tail of GRB941017." Thev have found (hat in order lor such an explanation to be viable. the Lorentz [actor associated with fireball expansion should be higher. P>107. and the magnetic field in the fireball plasma should be much lower (well below equipartition). compared to values (vpicallv inlerred [rom early afterglow observations (see.]xobavashi&Mészáros 2003).," They have found that in order for such an explanation to be viable, the Lorentz factor associated with fireball expansion should be higher, $\Gamma\gtrsim10^{4}$, and the magnetic field in the fireball plasma should be much lower (well below equipartition), compared to values typically inferred from early afterglow observations \citep[see, e.g.,][]{ZKM03}." . We show here that the high energy (tail may be explained as enussion Irom the forward shock electrons. with fireball plasma parameters which are typical to those inferred [rom GRD observations: Pe107 and magnetic field close to equipartition (within the fireball plasma).," We show here that the high energy tail may be explained as emission from the forward shock electrons, with fireball plasma parameters which are typical to those inferred from GRB observations: $\Gamma\sim10^2$ and magnetic field close to equipartition (within the fireball plasma)." In (his scenario. the inferred density of plasma surrounding the fireball is lower than inferred for most other GRBs (the magnetic field strength in the shock driven by the fireball into the surrounding gas is poorly constrained by current observations).," In this scenario, the inferred density of plasma surrounding the fireball is lower than inferred for most other GRBs (the magnetic field strength in the shock driven by the fireball into the surrounding gas is poorly constrained by current observations)." We consider (he latter scenario more likely. since it requires a modification of the parameters of the environment external to the fireball. rather than mocdifications of the fireball physics.," We consider the latter scenario more likely, since it requires a modification of the parameters of the environment external to the fireball, rather than modifications of the fireball physics." Our analvsis further improves on that of Granot&Guetta.(2003). in including the effects of, Our analysis further improves on that of \citet{GnG} in including the effects of gas.,gas. " Furthermore, near infrared emitting gas observed in this portion of the SNR (see below Fig. 9))"," Furthermore, near infrared emitting gas observed in this portion of the SNR (see below Fig. \ref{ir-radio}) )" " together with abundant neutral gas, correlated both in space and velocity with the optical filaments, indicate the presence of radiative shocks propagating into gas of different densities."," together with abundant neutral gas, correlated both in space and velocity with the optical filaments, indicate the presence of radiative shocks propagating into gas of different densities." The quality of the new 330 MHz image allows us to identify the close radio/optical correspondence in most of the small-scale radio structures observed as extensions from the bright eastern portion of the shell., The quality of the new 330 MHz image allows us to identify the close radio/optical correspondence in most of the small-scale radio structures observed as extensions from the bright eastern portion of the shell. This is in good agreement with the behavior previously noticed by using radio continuum observations at 1420 MHz., This is in good agreement with the behavior previously noticed by \citet{lee08} using radio continuum observations at 1420 MHz. The southern radio ridge is also mimicked by a quite faint optical counterpart., The southern radio ridge is also mimicked by a quite faint optical counterpart. Absorption due to the molecular gas mainly located in the foreground of the SNR is probably responsible for the observed weakness in the optical emission in this part of IC 443., Absorption due to the molecular gas mainly located in the foreground of the SNR is probably responsible for the observed weakness in the optical emission in this part of IC 443. " In the breakout region toward the western side of IC 443 only few local radio enhancements, immersed in faint diffuse radio emission, are observed at the locations of the optical filaments."," In the breakout region toward the western side of IC 443 only few local radio enhancements, immersed in faint diffuse radio emission, are observed at the locations of the optical filaments." "? (HzRG""): (b) blank-field submm survey counts (a fit to the SHADES counts by ?)}: (c} counts from submm imaging surveys of clusters at 2.1 (22).","\citealt{stevens03} (“HzRG”); (b) blank-field submm survey counts (a fit to the SHADES counts by \citealt{coppin06}) ); (c) counts from submm imaging surveys of clusters at $z\sim\rm 1$ \citep{best02, webb05}." The raw number counts have been corrected for effective survey area as a function of limiting flux density., The raw number counts have been corrected for effective survey area as a function of limiting flux density. However. we have not corrected for incompleteness or for flux boosting.," However, we have not corrected for incompleteness or for flux boosting." At the faintest levels. or in noisy regions of the map where sources lie near the flux limit. these effects are significant. but they are difficult to correct in maps of this size and involve assumptions about the number count distribution. uusing the blank-field counts with which we are attempting to compare.," At the faintest levels, or in noisy regions of the map where sources lie near the flux limit, these effects are significant, but they are difficult to correct in maps of this size and involve assumptions about the number count distribution, using the blank-field counts with which we are attempting to compare." Nevertheless. assuming Poisson errors there is a signiticant excess over the blank-field counts.," Nevertheless, assuming Poisson errors there is a significant excess over the blank-field counts." The seven radio galaxy fields and the three z5Q fields each contain a total of |2 850-jm companion sources., The seven radio galaxy fields and the three z5Q fields each contain a total of 12 $\mu$ m companion sources. The z5Q counts (and those of the 2~| clusters) are consistent with the radio galaxy field counts Gwith the caveat that the z5Q sample spans a more limited range in flux density. due to shallower limit and smaller total area): both contain more SMGs than blank fields by a factor 4—5 across a range of 850-j m flux densities. including the 2:6-mJy regime where the effects of flux boosting are minimal and overall sample reliability is excellent.," The z5Q counts (and those of the $z\sim\rm 1$ clusters) are consistent with the radio galaxy field counts (with the caveat that the z5Q sample spans a more limited range in flux density, due to shallower limit and smaller total area); both contain more SMGs than blank fields by a factor 4–5 across a range of $\mu$ m flux densities, including the $\gs$ 6-mJy regime where the effects of flux boosting are minimal and overall sample reliability is excellent." In a blank-field survey of equivalent area and depth to all three of our fields combined. one would expect (based upon model fits tothe SHADES counts from ?)) to detect —3. —2 and | sources brighter than sso = +1. 5.4 and mmy. respectively.," In a blank-field survey of equivalent area and depth to all three of our fields combined, one would expect (based upon model fits tothe SHADES counts from \citealt{coppin06}) ) to detect $\sim$ 3, $\sim$ 2 and $\sim$ 1 sources brighter than $S_{850\rm \mu m}$ = 4.1, 5.4 and mJy, respectively." It is thus likely that some of the 12 750 companion sources are foreground contaminants. as we have seen already in refsec:photoz..," It is thus likely that some of the 12 z5Q companion sources are foreground contaminants, as we have seen already in \\ref{sec:photoz}." Others. as we have also seen. are consistent with SMGs at high redshift. based on their radio/submm and jim/850 jim. flux density ratios.," Others, as we have also seen, are consistent with SMGs at high redshift, based on their radio/submm and $\mu$ $\mu$ m flux density ratios." We conclude that the maps probably contain SMGs genuinely associated with the dark matter haloes inhabited by our target quasars. leading to the statistical overdensities observed.," We conclude that the maps probably contain SMGs genuinely associated with the dark matter haloes inhabited by our target quasars, leading to the statistical overdensities observed." As well as the potential for foreground objects to contaminate the sample directly via their submm emission. we should consider whether the observed excess of SMGs may be due to their gravitational lensing effects (e.g.2).," As well as the potential for foreground objects to contaminate the sample directly via their submm emission, we should consider whether the observed excess of SMGs may be due to their gravitational lensing effects \citep[e.g.][]{chapman02}." Depending on the slope of the luminosity function. ?— estimate that mi of ~6 quasars could be lensed.," Depending on the slope of the luminosity function, \citet{wl02} estimate that $\sim\frac{1}{14}-\frac{1}{3}$ of $z\sim\rm 6$ quasars could be lensed." Targeting two submm-bright quasar hosts may have introduced an additional bias toward lensed fields. while the possibility that the submm-faint host is lensed is enhanced by the presence of a foreground radio galaxy Cand possibly a cluster associated with that radio galaxy).," Targeting two submm-bright quasar hosts may have introduced an additional bias toward lensed fields, while the possibility that the submm-faint host is lensed is enhanced by the presence of a foreground radio galaxy (and possibly a cluster associated with that radio galaxy)." The degree to which number counts are boosted by lensing depends on a competition between (1) the abundance of faint sources available to be boosted by the gravitational magnification and (11) the stretching of area in the source plane., The degree to which number counts are boosted by lensing depends on a competition between (i) the abundance of faint sources available to be boosted by the gravitational magnification and (ii) the stretching of area in the source plane. Since the submm source counts are steep. (I) is a strong effect.," Since the submm source counts are steep, (i) is a strong effect." Deep optical images of 2>5 quasars. including SDSS 1020103348. have failed to reveal any morphological signatures of strong lensing (2)..," Deep optical images of $z>\rm 5$ quasars, including SDSS J1030+0524, have failed to reveal any morphological signatures of strong lensing \citep{fan03}." Neither are line-of-sight galaxies. that could provide magnifications greater than |.l. in evidence (2)..," Neither are line-of-sight galaxies, that could provide magnifications greater than $\sim$ 1.1, in evidence \citep{willott05}." " For now. therefore. we consider the observed overdensity to be due to high-redshift SMGs in the vicinity of the signpost quasars, rather than lensing or unusual foreground activity."," For now, therefore, we consider the observed overdensity to be due to high-redshift SMGs in the vicinity of the signpost quasars, rather than lensing or unusual foreground activity." We can estimate SFRs for SMGs from their 850-;7m flux densities. Sxxajau. assuming that they lie at the redshifts of the quasars.," We can estimate SFRs for SMGs from their $\mu$ m flux densities, $S_{\rm 850\mu m}$ , assuming that they lie at the redshifts of the quasars." " The range of FIR luminosity of a source at the average redshift of the three quasars ἐς= 5.7) 8 Leip = bb |(κουμμνfed) 1011... assuming thermal SEDs with 7;, = KK and 3 = [.5-1.9."," The range of FIR luminosity of a source at the average redshift of the three quasars $z=\rm 5.7$ ) is $L_{\rm FIR}$ = $\rightarrow$ 1.4 $\times(S_{\rm 850\mu m}/{\rm mJy})\times 10^{12}$ $_{\odot}$, assuming thermal SEDs with $T_{\rm d}$ = K and $\beta$ = 1.5–1.9." If. Leu is powered by reprocessed stellar light. this translates into an instantaneous formation rate of massive stars of Wo(Lei10)Τι. MM. 1.," If $L_{\rm FIR}$ is powered by reprocessed stellar light, this translates into an instantaneous formation rate of massive stars of $\Psi\times(L_{\rm FIR}/10^{10} {\rm L}_{\odot}$ $_{\odot}$ $^{-1}$." Here. V depends upon factors such as the stellar mass function and the efficiency with which starlight is reprocessed by dust: we assume V.—1 giving a SFR range of 2140. C9ssouu/mJv) MM. vyri.," Here, $\Psi$ depends upon factors such as the stellar mass function and the efficiency with which starlight is reprocessed by dust; we assume $\Psi\sim\rm 1$ giving a SFR range of $\rightarrow$ 140 $\times (S_{\rm 850\mu m}/{\rm mJy})$ $_{\odot}$ $^{-1}$." Summing up the contributions of the companion SMGs (but not of the quasars. to avoid AGN contamination. even though it is likely that a substantial fraction of their submm luminosity is due to star formation) gives a total SFR per field. averaged over the three maps. of &f. 4000 MM. yyr 1. where [ες represents the fraction of sources at the quasar redshifts.," Summing up the contributions of the companion SMGs (but not of the quasars, to avoid AGN contamination, even though it is likely that a substantial fraction of their submm luminosity is due to star formation) gives a total SFR per field, averaged over the three maps, of $\approx f_{z>\rm 5}\times$ $\rightarrow$ $_{\odot}$ $^{-1}$ , where $f_{z>\rm 5}$ represents the fraction of sources at the quasar redshifts." Thisstar formation is apparently taking place in a region of volume =. MMpce*., Thisstar formation is apparently taking place in a region of volume $\ls$ $^3$. " Adopting a dust opacity #12sjan30cem⋅ 2 1 (see ,? for an explanation). the dust mass corresponding to σύρμα. 1S AL, =OS 61.000 OSssoyaufnel)107 MM... giving a total dust"," Adopting a dust opacity $\kappa_{\rm 125\mu m}=30$ $^2$ $^{-1}$ (see \citealt{priddey03} for an explanation), the dust mass corresponding to $S_{\rm 850\mu m}$ is $M_{\rm d}$ = $\rightarrow$ 1.0 $\times (S_{\rm 850\mu m}/{\rm mJy})\times 10^{8}$ $_{\odot}$ , giving a total dust" methods.,methods. In the first method. we will fit the data while simultaneously estimating the svslelmatic errors in the velocity dispersion and the mass-to-light ratio.," In the first method, we will fit the data while simultaneously estimating the systematic errors in the velocity dispersion and the mass-to-light ratio." " When combined with ihe measurement errors. (hese define new uncertaintv estimates lor the data whieh we will call the ""bad case errors in comparison to (he original uncertainties (the ""good"" case)."," When combined with the measurement errors, these define new uncertainty estimates for the data which we will call the “bad” case errors in comparison to the original uncertainties (the “good” case)." These broadened uncertainties can be representative of either (rue svsteniatic uncertainties. such as the ones we discussed above for the dvnamical measurements. or indicative of inhomogeneities in (he structure or evolution of the galaxies.," These broadened uncertainties can be representative of either true systematic uncertainties, such as the ones we discussed above for the dynamical measurements, or indicative of inhomogeneities in the structure or evolution of the galaxies." In (he second method we will compare these two cases using the approach outlined in Press(1997). to determine (he degree to which the sample homogeneous or heterogeneous., In the second method we will compare these two cases using the approach outlined in \citet{bo97} to determine the degree to which the sample homogeneous or heterogeneous. " In this method. we assume that there are probabilities pe and p, that the galaxies have homogeneous structures or evolutionary histories in (he sense (hat the scatter in (he measurements is simply determined by the “good” measurement errors."," In this method, we assume that there are probabilities $p_\sigma$ and $p_L$ that the galaxies have homogeneous structures or evolutionary histories in the sense that the scatter in the measurements is simply determined by the “good” measurement errors." " There are (hen probabilities 1—p, aud 1—p, that the galaxies are not a homogeneous eroup in either their structure or their evolution. where we characterize (his by assuming that the uncertainties in the velocity dispersion aud (he mass-to-light ratio are significantly broadened to be the ""bad"" measurement errors."," There are then probabilities $1-p_\sigma$ and $1-p_L$ that the galaxies are not a homogeneous group in either their structure or their evolution, where we characterize this by assuming that the uncertainties in the velocity dispersion and the mass-to-light ratio are significantly broadened to be the “bad” measurement errors." In essence. we are determining the relative probabilities of the stated measurement errors and our estimate of the (rue uncertainties from the first method.," In essence, we are determining the relative probabilities of the stated measurement errors and our estimate of the true uncertainties from the first method." Both approaches provide uncertainties on the average properties of the sample that account. for potential inhomogeneities. although the second method is a better formal approach since it can reject individual objects.," Both approaches provide uncertainties on the average properties of the sample that account for potential inhomogeneities, although the second method is a better formal approach since it can reject individual objects." " In the first approach. we will estimate the fractional svstematic errors ες and e, in the velocity dispersion and Iuminosity."," In the first approach, we will estimate the fractional systematic errors $e_\sigma$ and $e_L$ in the velocity dispersion and luminosity." The 47 expressions are modified to use uncertainties OlB ey;—vez;2e20?E and ej;—Veg;2οι Dor. the velocity-. dispersionsfq... and the logarithm.A of the mass-to-light ratios respectively., The $\chi^2$ expressions are modified to use uncertainties of $e_{\sigma i} \rightarrow \sqrt{e_{\sigma i}^2+e_\sigma^2\sigma_i^2}$ and $e_{L i} \rightarrow \sqrt{e_{Li}^2+e_L^2}$ for the velocity dispersions and the logarithm of the mass-to-light ratios respectively. " We assume logarithmic priors lor f. CM,/L)4. and (GLCME)/dz). ancl the theoretical prior defined by Equ. (3))"," We assume logarithmic priors for $f_*$ , $\left({M_{\ast}/ L}\right)_0$, and $\left({d\left(M/L\right)/dz}\right)$, and the theoretical prior defined by Eqn. \ref{eqn:c1}) )" for the concentration e;., for the concentration $c_i$. Note that we are forcing all galaxies to have the same concentration. which should have no significant impact eiven the scales we are studving.," Note that we are forcing all galaxies to have the same concentration, which should have no significant impact given the scales we are studying." " The priors for the svstematic errors. Pleg)αν)ego? and οι)=νο) ez. naturally switch between uniform priors for systematic errors small compared to the mean square measurement errors ((e2,) and (e7,)) and logarithmic priors for large systematic errors."," The priors for the systematic errors, $P(e_\sigma)=1/\sqrt{\langle e_{\sigma i}^2 \rangle + e_\sigma^2\sigma_i^2}$ and $P(e_L)=1/\sqrt{\langle e_{Li}^2\rangle + e_L^2}$ naturally switch between uniform priors for systematic errors small compared to the mean square measurement errors $\langle e_{\sigma i}^2 \rangle$ and $\langle e_{Li}^2 \rangle$ ) and logarithmic priors for large systematic errors." " The resulting probability distiibution for the fractional errors is then where P(Dile;.£) and P(Dj;|e,.€) are the probability distributions modified by the addition of the svstematie errors e, and e;."," The resulting probability distribution for the fractional errors is then where $P\left(D_i|e_\sigma,\mathbf{\xi}\right)$ and $P\left(D_i|e_L,\mathbf{\xi}\right)$ are the probability distributions modified by the addition of the systematic errors $e_\sigma $ and $e_L$ ." " We then use these svstematic error estimates (o define the uncertainties used for the ""bad"" case in our second formalism.", We then use these systematic error estimates to define the uncertainties used for the “bad” case in our second formalism. The second.Press(1997). approach properly weights all combinatoricpossibilities of," The second,\citet{bo97} approach properly weights all combinatoricpossibilities of" are the muubers of single. binary. triple aud quadruple systems: see Patience 1998)). instead of the (bf=ital: also. DAL ouly estimate esf.,"are the numbers of single, binary, triple and quadruple systems; see Patience \cite{patience}) ), instead of the $bf=\frac{B+T+Q}{S+B+T+Q}$ ); also, DM only estimate $csf$." Finally. for each study. T tried to choose a separation range over which the scusitivity is hieh cnough so that all companions cau be found.," Finally, for each study, I tried to choose a separation range over which the sensitivity is high enough so that all companions can be found." These ranges are presented in Appendix A. The intuitive way of comparing all clusters is to select a wide separation range aud to count the ποτ of binaries in this ranee for cach region., These ranges are presented in Appendix A. The intuitive way of comparing all clusters is to select a wide separation range and to count the number of binaries in this range for each region. Due to the differeut distances involved. however. the common separation range is narrow anc leads to simall uuubers of companions.," Due to the different distances involved, however, the common separation range is narrow and leads to small numbers of companions." The statistical sieuificauce of the results is thus quite low., The statistical significance of the results is thus quite low. The most powerful comparison of all clusters ds obtaiue by comparing each to that of the MS in je παλιο separation range: cach SER. however. has becu survevec in different rauges bydifferent studies.," The most powerful comparison of all clusters is obtained by comparing each to that of the MS in the same separation range; each SFR, however, has been surveyed in different ranges by different studies." I calculate ic tota of the SER from all surveys aud. concerunme 1ο MS value. I estimate it in the same separation ranec or each survey (bv inteeration of the analytic perio distribution given by DM) and Laverage these values using je ΠΠΡΟ of targets as a weight.," I calculate the total of the SFR from all surveys and, concerning the MS value, I estimate it in the same separation range for each survey (by integration of the analytic period distribution given by DM) and I average these values using the number of targets as a weight." In reffinal.. esfays is the averaged AIS value to be compares with the esf iu the 1th column.," In \\ref{final}, $csf_{MS}$ is the averaged MS value to be compared with the $csf$ in the 4th column." " 74, is the total uuniber of targets.", $N_{\mathrm{obs}}$ is the total number of targets. Two non critical assmuptions are made: the tota system nass is LAL. and the actual seni major-axis e is linked to the apparent separation p via loge=logp|0.1 (Reipurth —Ziunecker 1993)): reasonable chauges iu these parameters does not chauge the bv more than," Two non critical assumptions are made: the total system mass is $M_\odot$ and the actual semi major-axis $a$ is linked to the apparent separation $\rho$ via $\overline{\log a} = \overline{\log \rho} + 0.1$ (Reipurth Zinnecker \cite{rz}) ); reasonable changes in these parameters does not change the by more than." Also. some corrections have been applied iu some cases (sec refdetails)} το take iufo account poor aud non homogcencous cdvnanc range or selection biases.," Also, some corrections have been applied in some cases (see \\ref{details}) ) to take into account poor and non homogeneous dynamic range or selection biases." Concerning the dynamic range. it has to boe large enough to detect binaries with mass ratio y=0.11. which ds the lower huit of DMUs survey (they cannot observe binaries with q<0.3 for all tarects. but thev estimate a correction down to this liit).," Concerning the dynamic range, it has to be large enough to detect binaries with mass ratio $q=0.1$, which is the lower limit of DM's survey (they cannot observe binaries with $q<0.3$ for all targets, but they estimate a correction down to this limit)." Using Baratte (1998))s 1nass-Iuuünositv relation at MM. it appears that such a mass ratio is equivalent to AA=2.9. Al=3.6 aud AV= L3inmae at this age.," Using Baraffe \cite{isa}) )'s mass-luminosity relation at Myr, it appears that such a mass ratio is equivalent to $\Delta K=2.9$, $\Delta I=3.6$ and $\Delta V=4.3$ mag at this age." " These limits are reached in all pre-main sequence (PAIS) survevs except when a speckle echuique is used (these studies are lamited to absolute magnitude aud not flux ratios. so that some stars were observed with worse sensitivities): in this case. a correction has been applied to take into aACCOMILL the stronely non uniform scusitivitv of the survey,"," These limits are reached in all pre-main sequence (PMS) surveys except when a speckle technique is used (these studies are limited to absolute magnitude and not flux ratios, so that some stars were observed with worse sensitivities); in this case, a correction has been applied to take into account the strongly non uniform sensitivity of the survey." All. companions with qo<0.1 were excluded from the statistics to allow significant comparisons with DM: this has not been done iu the previous studies., All companions with $q<0.1$ were excluded from the statistics to allow significant comparisons with DM; this has not been done in the previous studies. Determining mass ratios from flux ratios is somewhat hazardous for PAIS stars because of possible infrared excesses and differcut ages. but P assmme that this does uot lead to anv systematic bias.," Determining mass ratios from flux ratios is somewhat hazardous for PMS stars because of possible infrared excesses and different ages, but I assume that this does not lead to any systematic bias." In older clusters. as the mass-luninosity relation steepeus with imcreasing finie. the mncompleteness correction becomes maportant. aud cannot be neglected for the ITvades aud the Pleiades.," In older clusters, as the mass-luminosity relation steepens with increasing time, the uncompleteness correction becomes important, and cannot be neglected for the Hyades and the Pleiades." reffual prescuts all the results developed iu this section., \\ref{final} presents all the results developed in this section. For cach SER. I explain what has been done (f auvthine) after ΠΡΙΝ collecting the data from the literature.," For each SFR, I explain what has been done (if anything) after simply collecting the data from the literature." The speckle results of Chez (1993)) does not ποσα any correction. as all stars were observed with a large chough cvnamic range.," The speckle results of Ghez \cite{ghez93}) ) does not need any correction, as all stars were observed with a large enough dynamic range." The linar occultation survey of Sinon (1995)). also reporting results from Richichi (199 D). however. suffers froma poor dvuaiic range. and I applied a correction simular to Cchez (1993)).," The lunar occultation survey of Simon \cite{simon95}) ), also reporting results from Richichi \cite{richichi94}) ), however, suffers from a poor dynamic range, and I applied a correction similar to Ghez \cite{ghez93}) )." This method takes iuto account the fact that all stars were not smveved with the same dynamic range: the targets are binned by relative brightuess of approximately equal magnitude steps. aud the πήρα of detected binaries in each bin is rescaled to the total umuber of targets.," This method takes into account the fact that all stars were not surveyed with the same dynamic range: the targets are binned by relative brightness of approximately equal magnitude steps, and the number of detected binaries in each bin is rescaled to the total number of targets." Tere. it adds ~E companions.," Here, it adds $\sim4$ companions." The final uncertaimtics are estimated from Poisson statistics on the auuber of companions and corrected (this ucthod gives a conservative estimation of the error). auk rot on the final. corrected ummber of companions.," The final uncertainties are estimated from Poisson statistics on the number of companions and corrected (this method gives a conservative estimation of the error), and not on the final, corrected number of companions." Recent JOST aud adaptive optics inages of the binary system UIs Tau have revealed a eicuustellar disk aroun he secondary (Stapelfeldt 1998))., Recent $HST$ and adaptive optics images of the binary system HK Tau have revealed a circumstellar disk around the secondary (Stapelfeldt\cite{hktau}) ). As it is seen on. the star is totally hidden. and we can only see scattere ieht.," As it is seen edge-on, the star is totally hidden, and we can only see scattered light." This explain why AJ?=3.1 unnae while the mass ratio is estimated to be about 4~0.5 from the spectra vpes of both conrponents (Stapelteldt aL)., This explain why $\Delta H=3.1$ mag while the mass ratio is estimated to be about $q\sim0.5$ from the spectral types of both components (Stapelfeldt ). This syste has not been excluded here., This system has not been excluded here. Otherwise. three faint conipaudons had to be excluded. from the Leimert (19933) survey.," Otherwise, three faint companions had to be excluded from the Leinert \cite{leinert}) ) survey." Iu some cases. Leinert (1993)) report the imaecine results from Reipurth Zinnecker (1993)) without further bigh angular resolution observations.," In some cases, Leinert \cite{leinert}) ) report the imaging results from Reipurth Zinnecker \cite{rz}) ) without further high angular resolution observations." New inaees with adaptive optics lave revealed new subarcseconds comipanious to four of thesesvstenis (see Appendix B). which were added im this study.," New images with adaptive optics have revealed new subarcseconds companions to four of thesesystems (see Appendix B), which were added in this study." Both Chez (1993)) and Simon (1995)) results were corrected for incompleteness withthe same method as dn Taurus. leading to an estimation of ~[1 missed conipaiiolis.," Both Ghez \cite{ghez93}) ) and Simon \cite{simon95}) ) results were corrected for incompleteness withthe same method as in Taurus, leading to an estimation of $\sim4$ missed companions." of gamma rays Irom (he uiushocked wind could be: (1) an extremely powerful stellar wind. ie. very low values of the jj parameter: Gi) unconventional. ie. verv low (Ty<107) or very large (Ty> 10°) values of the pulsar wind bulk Lorentz factor.,"of gamma rays from the unshocked wind could be: (i) an extremely powerful stellar wind, i.e. very low values of the $\eta$ parameter; (ii) unconventional, i.e. very low $\Gamma_0 \ll 10^4$ ) or very large $\Gamma_0 \geq 10^6$ ) values of the pulsar wind bulk Lorentz factor." The first condition requires (the pulsar to interact with the stellar disc all over the orbit., The first condition requires the pulsar to interact with the stellar disc all over the orbit. This implies a very specific realization in the sense of orientation of the stellar disc (namely the orbital plane and the disc plane should almost coincide). which contradicts to the current expectations (Melatosetal.1995:Dogomazov2005:Dogovalov2008:Nerschhagel2010).," This implies a very specific realization in the sense of orientation of the stellar disc (namely the orbital plane and the disc plane should almost coincide), which contradicts to the current expectations \citep{melatos95,bogomazov05,bogovalov08,kerschhaggl10}." . ILowever. we should note that one cannot exclude (hat the pulsar wind is strongly anisotropic.," However, we should note that one cannot exclude that the pulsar wind is strongly anisotropic." If so. the eanmma rav signal should be anisotropic as well.," If so, the gamma ray signal should be anisotropic as well." This can be another reason for reduction of ihe gamma rav flux. which unfortunately would make the conclusions concerning the range of parameters D and 7 less robust.," This can be another reason for reduction of the gamma ray flux, which unfortunately would make the conclusions concerning the range of parameters $\Gamma_0$ and $\eta$ less robust." Finally. one should mention that if the pulsar wine is not absolutely cold. electrons in the frame of the wind might have a rather broader distribution.," Finally, one should mention that if the pulsar wind is not absolutely cold, electrons in the frame of the wind might have a rather broader distribution." This would make the gamma ray spectrum less distinct and smoother compared to the ones shown in Figures 2. and 3.., This would make the gamma ray spectrum less distinct and smoother compared to the ones shown in Figures \ref{fig:per} and \ref{fig:before}. Reeardinge VIE energv gamma ravs produced after termination of the wind. (the new optical observations of Negueruelaοἱal.(2011) imply a significant reduction of the flux of IC gumma rays produced by shock-accelerated electrons.," Regarding VHE energy gamma rays produced after termination of the wind, the new optical observations of \citet{negueruela10} imply a significant reduction of the flux of IC gamma rays produced by shock-accelerated electrons." All three main factors related to (1) the larger distance to (he source. (2) the gamma-egammnma attenuation. and (3) the Compton drag of the pulsar wind work in the same (negative) direction reducing (he gamma ray flux by a factor of up to 10.," All three main factors related to (1) the larger distance to the source, (2) the gamma-gamma attenuation, and (3) the Compton drag of the pulsar wind work in the same (negative) direction reducing the gamma ray flux by a factor of up to 10." Given that the previous studies based on the old optical observations already have required a significant fraction of the spin-down Iuminositv 10%)) to be released in TeV gamma ravs. the revised energy requirements become almost unbearable.," Given that the previous studies based on the old optical observations already have required a significant fraction of the spin-down luminosity ) to be released in TeV gamma rays, the revised energy requirements become almost unbearable." A possible solution to the energv budget crisis could be the Doppler boosting of radiation as suggested in Ixhangulvanetal.(2008)., A possible solution to the energy budget crisis could be the Doppler boosting of radiation as suggested in \citet{khangulyan08}. . This important issues will be discussed elsewhere., This important issues will be discussed elsewhere. The work of $.V.Dogovalov have been supported by the Federal Targeted. Program “The Scientific and Peclagogical Personnel of the Innovative Russia’ in 2009-2013 (the state contract N 536 on May 17. 2010).," The work of S.V.Bogovalov have been supported by the Federal Targeted Program ""The Scientific and Pedagogical Personnel of the Innovative Russia"" in 2009-2013 (the state contract N 536 on May 17, 2010)." ALR. acknowledges support by the Spanish Ministerio cle Ciencia e Innovaciónn CMICINN) under grant. FPA2010-22056-C06-02. as well as financial support from MICINN and European Social Funds through a fellowship.," M.R. acknowledges support by the Spanish Ministerio de Ciencia e Innovaciónn (MICINN) under grant FPA2010-22056-C06-02, as well as financial support from MICINN and European Social Funds through a fellowship." of radiative transport: it is by definition part of the calculations.,of radiative transport; it is by definition part of the calculations. Iu fact. as we discussed iu 2. solving the transfer equation in the two normal modes that the mocles evolve adiabatically.," In fact, as we discussed in 2, solving the transfer equation in the two normal modes that the modes evolve adiabatically." What the mocles are called above aud below the resouaut cleusity is irrelevant. given that the transfer eqtatious are written[un lor the normal modes of propagation aud uot lor polarization eigeustates (the so-called extraordinary and. ordinary modes) as we discussed above.," What the modes are called above and below the resonant density is irrelevant, given that the transfer equations are written for the normal modes of propagation and not for polarization eigenstates (the so-called extraordinary and ordinary modes) as we discussed above." Therefore. they criticise incorrectly the previous works for uot iucludiug tliis new pliysical ellect.," Therefore, they criticise incorrectly the previous works for not including this new physical effect." " For the same reasons. it is in [act meaningless to ""include"" or to “neglect” uode conversion (in the terminology of Lai Ho 2002) because neglecting the adiabatic inode evolution does uot describe auy physical situation."," For the same reasons, it is in fact meaningless to “include” or to “neglect” mode conversion (in the terminology of Lai Ho 2002) because neglecting the adiabatic mode evolution does not describe any physical situation." The differeuce in the results between these two cases most likely arises [rou the different uunmerical treatineuts the authors employ. iu each case. both of which are highly inaccurate as discussed in 81.," The difference in the results between these two cases most likely arises from the different numerical treatments the authors employ in each case, both of which are highly inaccurate as discussed in 4." Ho Lai (2002. 82.1) also claim that in the limit of nou-adibaticity. the radiative trausfer formalisin breaks down aud cannot describe the evolution of photons.," Ho Lai (2002, 2.4) also claim that in the limit of non-adibaticity, the radiative transfer formalism breaks down and cannot describe the evolution of photons." This is also incorrect., This is also incorrect. As discussed above. oue simply. needs to solve all four equatious (2)) iu this case rather than the two equations for the diagonal terms of £2;;.," As discussed above, one simply needs to solve all four equations \ref{eq:full}) ) in this case rather than the two equations for the diagonal terms of $R_{ij}$." We emphasize that this case is not relevant for the problem discussed here but iu general cau be easily addressed by keeping the equatious for the off-diagonal lernms., We emphasize that this case is not relevant for the problem discussed here but in general can be easily addressed by keeping the equations for the off-diagonal terms. During the last four vears. the region has oen observed: repeatedly by and.NALALNewlon. including several extensive campaigns focused. on Ser A’ Baganoll 2001. 2003: Coldwurnm 2003: Porquet 2003)).,"During the last four years, the region has been observed repeatedly by and, including several extensive campaigns focused on Sgr $^*$ Baganoff 2001, 2003; Goldwurm 2003; Porquet 2003)." Both observatories have also carried out. wide-angle X-rav. surveys in which sets of overlapping xntings have been used to give coverage of the Galactic ane within 1 of theCentre (Wang. Gotthelf Lang 2002: Warwick 2002: Sakano 20046).," Both observatories have also carried out wide-angle X-ray surveys in which sets of overlapping pointings have been used to give coverage of the Galactic plane within $1^{\circ}$ of the (Wang, Gotthelf Lang 2002; Warwick 2002; Sakano 2004c)." The excellent. imaging capability and high sensitivity. of the wo observatories has allowed: the cliserete X-ray source population in the direction of theCentre to be studied over a range in X-ray luminosity extending from 107 down to 103Lc7., The excellent imaging capability and high sensitivity of the two observatories has allowed the discrete X-ray source population in the direction of the to be studied over a range in X-ray luminosity extending from $10^{38}$ down to $\sim 10^{31}$. " lopThe temporal and spectral ooperties ofContre low-mass ancl high-mass N-rav jxnaries. typically seen in outburst with Lx>107"" are now well established. through the work of numerous missions. past ancl present. including most recentlyTTE."," The temporal and spectral properties of low-mass and high-mass X-ray binaries, typically seen in outburst with $L_{\rm X} > 10^{36}$, are now well established through the work of numerous missions, past and present, including most recently." However. much less is known about sources with. peak luminosities.EN below 10°4n7. since. this MEAis close to the effective detection limit for earlier hard. X-ray imaging missions such as andS.," However, much less is known about sources with peak luminosities below $\sim 10^{35}$, since this is close to the effective detection limit for earlier hard X-ray imaging missions such as and." LX. In essence. the recent surveys of and have provided a new window on faint source populations at the Aluno 2003a. 2003b. 2004b).," In essence, the recent surveys of and have provided a new window on faint source populations at the Muno 2003a, 2003b, 2004b)." The spectra of the X-ray sources in the with Lx29107I. most. of which are low- X-ray binaries (LAINB) containing either a neutron μαar or black hole. are often featureless (Sicloli 1999: uwakano 2002).," The spectra of the X-ray sources in the with $L_{\rm X} > 10^{35}$, most of which are low-mass X-ray binaries (LMXB) containing either a neutron star or black hole, are often featureless (Sidoli 1999; Sakano 2002)." On the other hand. Wang 2002) report that the summed spectrum of the faint sources etected in the wide-angle Survey garows significant 6.7 keV Fe IEx-line emission. implying the xistence of one or more dilferent. populations of sources at lower luminosity.," On the other hand, Wang (2002) report that the summed spectrum of the faint sources detected in the wide-angle Survey shows significant 6.7 keV Fe K-line emission, implying the existence of one or more different populations of sources at lower luminosity." More recently. the ~2000 X-ray sources etected in the very deep: observations of the field around Ser X. have been shown on average to have very hard (photon index E« 1) spectra in addition to strong like anel LI-like Ix-lines from Si. S. Ar. Ca and Fe (Muno 2003a. 2004b).," More recently, the $\sim 2000$ X-ray sources detected in the very deep observations of the field around Sgr $^*$, have been shown on average to have very hard (photon index $\Gamma < 1$ ) spectra in addition to strong He-like and H-like K-lines from Si, S, Ar, Ca and Fe (Muno 2003a, 2004b)." Although resolved. point sources contribute up to 10% of total hard. X-ray emission from theCentre. the bulk of the X-ray Iuminosity of the region must either be truly cliffuse in nature or originate in a very faint population of point sources with very hard. spectra which are more numerous than cataclysmic variables (Muno 2003a. 2004a).," Although resolved point sources contribute up to $\sim 10\%$ of total hard X-ray emission from the, the bulk of the X-ray luminosity of the region must either be truly diffuse in nature or originate in a very faint population of point sources with very hard spectra which are more numerous than cataclysmic variables (Muno 2003a, 2004a)." In the case of the former. it remains unclear," In the case of the former, it remains unclear" at the time and sky position of each target observation.,at the time and sky position of each target observation. The pointing corrections. along with the measurements of the atmospheric opacity at the time of observation. were then included in the data processing using the software CRUSH. version 2.01-4 (Kováees 2008).," The pointing corrections, along with the measurements of the atmospheric opacity at the time of observation, were then included in the data processing using the software CRUSH, version 2.01-4 (Kováccs 2008)." In the final map. the total flux was measured within the 3c contour using the MIRIAD (Sault et al.," In the final map, the total flux was measured within the $\sigma$ contour using the MIRIAD (Sault et al." 1995) software., 1995) software. The absolute flux calibration was based on the scans of the planet Uranus and the planet flux at the observation date from the JPL Horizons model., The absolute flux calibration was based on the scans of the planet Uranus and the planet flux at the observation date from the JPL Horizons model. The total uncertainty in the HR 8799 flux is35%.. a combination of the small (6%)) variation in the Uranus flux measurements and the rms noise level in measured in the final source map.," The total uncertainty in the HR 8799 flux is, a combination of the small ) variation in the Uranus flux measurements and the rms noise level in measured in the final source map." To quantify the location of the emission peak. the distance from the host star position to the brightest part of the disk was measured.," To quantify the location of the emission peak, the distance from the host star position to the brightest part of the disk was measured." Since the photosphere of HR 8799 is not detectable at 350g¢m. it was necessary to identify the location of the central source based on the telescope pointing.," Since the photosphere of HR 8799 is not detectable at $\mu$ m, it was necessary to identify the location of the central source based on the telescope pointing." The bright calibration targets were used to empirically measure the pointing accuracy., The bright calibration targets were used to empirically measure the pointing accuracy. For the pointing test. each calibrator scan was reduced in a manner analogous to the targets - Le. by removing that calibrator scan (and others taken within a few minutes) from the pointing correction caleulation and deriving anew pointing correction from the remaining calibrators and pointing model and then applying the pointing offset to the CRUSH reduction.," For the pointing test, each calibrator scan was reduced in a manner analogous to the targets - i.e. by removing that calibrator scan (and others taken within a few minutes) from the pointing correction calculation and deriving a new pointing correction from the remaining calibrators and pointing model and then applying the pointing offset to the CRUSH reduction." This approach should be conservative in calculating the pointing offset to apply to the calibrator scan since the calibrators for the target are taken at most 30min before/after the targets. while this approach for the calibrators has mainly included calibrators ~60min before/after each calibrator scan treated as a pointing test.," This approach should be conservative in calculating the pointing offset to apply to the calibrator scan since the calibrators for the target are taken at most 30min before/after the targets, while this approach for the calibrators has mainly included calibrators $\sim$ 60min before/after each calibrator scan treated as a pointing test." The absolute value of the pointing error for each calibrator analysed with this procedure was measured from the difference of the position of the calibrator in each map to its known coordinates., The absolute value of the pointing error for each calibrator analysed with this procedure was measured from the difference of the position of the calibrator in each map to its known coordinates. Since we are interested in the central position of the source. we calculated the standard deviation of the mean of the absolute offsets.," Since we are interested in the central position of the source, we calculated the standard deviation of the mean of the absolute offsets." " Based on this empirical test. the position uncertainty is +076,"," Based on this empirical test, the position uncertainty is $\pm$ $\farcs$ 6." Since the position of the emission peak is identified within a fraction of a pixel in. the final map. the source position uncertainty dominates the uncertainty on distance measurements.," Since the position of the emission peak is identified within a fraction of a pixel in the final map, the source position uncertainty dominates the uncertainty on distance measurements." To interpret the debris disk map. the flux and norphology were compared with three numerical models -- a radiative transfer model of à star surrounded by symmetric zones of dust a simulation of massive planets migrating outwards and interacting with planetesimals and dust. and a simulation from the literature. of a low mass planet interacting with planetesimals.," To interpret the debris disk map, the flux and morphology were compared with three numerical models – a radiative transfer model of a star surrounded by symmetric zones of dust, a simulation of massive planets migrating outwards and interacting with planetesimals and dust, and a simulation from the literature of a low mass planet interacting with planetesimals." The Monte Carlo 3D continuum radiative transfer code MCFOST (Pinte et al., The Monte Carlo 3D continuum radiative transfer code MCFOST (Pinte et al. 2006) was used to generate SED models and images at 350jm. In the MCFOST routines. the photons from the central star with properties given in Reidemeister et al. (," 2006) was used to generate SED models and images at $\mu$ m. In the MCFOST routines, the photons from the central star with properties given in Reidemeister et al. (" 2009) were propagated through the disk with a model incorporating a combination of Mie theory scattering. absorption. and re-emission.,"2009) were propagated through the disk with a model incorporating a combination of Mie theory scattering, absorption, and re-emission." The disk parameters used to construct the SED model are given in Table 1., The disk parameters used to construct the SED model are given in Table 1. The disk zones are based on the 3-component model described in Su (2009)., The disk zones are based on the 3-component model described in Su (2009). Minor modifications were included to account for the dynamically cleared chaotic zones around the innermost and outermost planet (Quillen Faber 2006: Moro-Martinn et al., Minor modifications were included to account for the dynamically cleared chaotic zones around the innermost and outermost planet (Quillen Faber 2006; Moro-Martínn et al. 2010; Fabrycky Murray-Clay 2010)., 2010; Fabrycky Murray-Clay 2010). A series of simulated images were generated for a range of outer disk radi and nclinations. and Table 1 shows the values most consistent with the CSO map.," A series of simulated images were generated for a range of outer disk radii and inclinations, and Table 1 shows the values most consistent with the CSO map." The structure in the CSO map was also compared with umerical models performed using an N-body code., The structure in the CSO map was also compared with numerical models performed using an N-body code. Our umerical model included the interaction of planets resembling HR 8799b (6 Μαρ) (Currie et al., Our numerical model included the interaction of planets resembling HR 8799b (6 $_\mathrm{Jup}$ ) (Currie et al. 2011) and HR 8799e (8 Mj) (Currie et al., 2011) and HR 8799c (8 $_\mathrm{Jup}$ ) (Currie et al. 2011) migrating outwards at the same rate through a disk of planetesimals., 2011) migrating outwards at the same rate through a disk of planetesimals. Since there was no significant difference in the results when two planets were included rather than one. the planets more distant planets from the debris disk should have no impact and were not added to the simulation.," Since there was no significant difference in the results when two planets were included rather than one, the planets more distant planets from the debris disk should have no impact and were not added to the simulation." The initial planetesimal belt had a width of 5 AU and an inner radius of 91 AU. and the planets migrated 15 AU to their final orbits.," The initial planetesimal belt had a width of 5 AU and an inner radius of 91 AU, and the planets migrated 15 AU to their final orbits." Once the two planets had reached approximately their present day orbits (Marois et al., Once the two planets had reached approximately their present day orbits (Marois et al. 2008). the orbits were circularised. and the planetesimal disk replaced by a dust disk.," 2008), the orbits were circularised, and the planetesimal disk replaced by a dust disk." The stability of the planetesimals 1n a very similar configuration has already been shown in previous simulations (Moro-Martinn et al., The stability of the planetesimals in a very similar configuration has already been shown in previous simulations (Moro-Martínn et al. 2010)., 2010). The transformatior of planetesimals to dust entailed the introduction of radiatio pressure and Poynting-Robertson drag through the parameter f that quantifies the ratio of radiation to gravitational forces (Burns et al., The transformation of planetesimals to dust entailed the introduction of radiation pressure and Poynting-Robertson drag through the parameter $\beta$ that quantifies the ratio of radiation to gravitational forces (Burns et al. 1979)., 1979). The grains responsible for the 350jmi emission have a size distribution peaked near 350um. so the B value appropriate for the map is 0.0055.," The grains responsible for the $\mu$ m emission have a size distribution peaked near $\mu$ m, so the $\beta$ value appropriate for the map is 0.0055." The model is designed to investigate the inner region of the Kuiper belt and does not include the entire disk structure or all three components of the SED model., The model is designed to investigate the inner region of the Kuiper belt and does not include the entire disk structure or all three components of the SED model. Simulated surface density maps of the inner Kuiper belt were produced at a range of wavelengths., Simulated surface density maps of the inner Kuiper belt were produced at a range of wavelengths. Finally. the CSO map structure was also considered in the context of results of dynamical simulations of a low mass planet interacting with a planetesimal belt (Reche et al.," Finally, the CSO map structure was also considered in the context of results of dynamical simulations of a low mass planet interacting with a planetesimal belt (Reche et al." 2008)., 2008). The CSO map is given in Figure |. and the measured flux for the disk integrated over the 3c contour is 89 + 26 mJy.," The CSO map is given in Figure 1, and the measured flux for the disk integrated over the $\sigma$ contour is 89 $\pm$ 26 mJy." The 350um map of the HR 8799 debris disk reveals emission that is extended compared to the maps of the bright point source calibrators taken on the same night., The $\mu$ m map of the HR 8799 debris disk reveals emission that is extended compared to the maps of the bright point source calibrators taken on the same night. " Only spatially resolved images of dust with small 6 values are capable of distinguishing the location of the dust based on the structure. since the SED solution for the disk radius is degenerate with dust properties such as à,,;,"," Only spatially resolved images of dust with small $\beta$ values are capable of distinguishing the location of the dust based on the structure, since the SED solution for the disk radius is degenerate with dust properties such as $_{min}$." The inner disk is not resolved. but set at 100 AU. based on previous simulations of orbital stability (Moro- et al.," The inner disk is not resolved, but set at 100 AU, based on previous simulations of orbital stability (Moro-Mart\'{i}nn et al." 2010) and the mass of the outermost planet., 2010) and the mass of the outermost planet. ↥⋅↸∖↴∖↴∏↕↑↴∖↴⋜∐⋅↸∖↻↥⋅↸∖↴∖↴↸∖∐↑↕⋅↖⇁⋯∐⋅↸∖∐⋜∏⋝↕↸∖∶↕≧↸∖↸∖↘↽⋯⋜∐⊔∖↑⋜↧↕∙≺∐≝↭∏↸⊳∪∐↴∖↴⊓⋅⋜↧↕↕∐∖≼↧↑∐↸∖↕∐↸⊳∐∐⋜↧↑↕∪∐↑∪∐↸∖↕∐↑∐↸∖↥⋅⋜⋯∶↴⋁↸∖∣⋡∶↕∩↴∶≩↕↴ ⋜⋯≼↧↸⊳∪↕∐⊳↕⋯∐∖≺↧⋀∐∩⋀∐∙∙∖↖⊽,results are presently unreliable: Beekman et (1997) constrained the inclination to lie in the range $i=10^{\circ}-31^{\circ}$ and concluded $M>9~M_{\odot}$. ↸∖⋝↴⊓∖⋜↧↕⋅⊓⊇∪∩↭↸⊳∪∐↸⊳↕∏≼∐∖≼↧∣⋟↓⋅↱⊐↴⋜⋯≼∟∐⊇∙⊇⋀∐⋅↖↖↽↕↑∐⋜↧⋯⋜↧⊼↕⋯⋯⊔⋯⋜↧↴∖∷∖↴↑↕⋯↑↕↴∖↴ ∐∪↑↸⊳∪∐↴∖↴⊓⋅⋜∏↕∐∖≼↧∙≼∶↸∖∐∐∪⋜⋯, Webb et (2000) concluded $i<45^{\circ}$ and $M>2.2~M_{\odot}$ with a maximum mass that is not constrained. ≼↧∐⋜∐⋅↥⋅↕↴∖↴∪∐⋖⊇∩∩∶≩⋟↻↥⋅↸∖↴∖↴↸∖∐↑↑∐↸∖↴∖↴↥⋅∪∐∶↴∙⊾↸∖↴∖↴↑↸∖↖↽↕≼∐∖∐↸⊳↸∖↕≯∪↥⋅⋜↧↕∪↖↖⇁⋯⋜↧↴∖∷∖↴∶↑∐↸∖⋅↖⇁↸⊳∪∐↸⊳↕⋯∐∖∕↓∶≩↴⋜⋯≺↧ ⋀∐↓∙≝⊔⋀∐⋅∙∐∪↖↖↽↸∖↖↽, Gelino and Harrison (2003) present the strongest evidence for a low mass; they conclude $i>43^{\circ}$ and $M<4.92~M_{\odot}$. ↸∖↥⋅∙↕∐⋜↧⋯∪↥⋅↸∖↥⋅↸∖↸⊳↸∖∐↑↕↘⊽↸∖↸⊳↨↘↽∫∖⊽≓↴⋝⋜⋯≼↧↴∖↴↑∏≼↧⋅↖↽↕⊰↸∖⋅↖⇁↕⋯↕≼⇂↴∖↴↸∖↑⋜↧↕∙⊓⊇∩∩⊤⋝↕⋟∪∏∐≼⊔∐⋜↧↑⋅⇁⋀∖⊽∪↸⊳↕↸∖⋜∐⋅↸∖∐∏≻↴∖↴∪↕≼↧⋜↧↕ ⋯∪≼↧∏↕⋜↧↑↕∪∐↕↴∖↴↻↥⋅↸∖↴∖↴↸∖∐↑↕∐↑∐↸∖∐∶↴∙⊾↕↑↸⊳⋃⋅↖⇁↸∖∙∙∙⋅⊲⋜∐∐⇂↸⊳∪↕∐⊳↕∏≼∐∖≼∙⋅⇁⋯↑∐⋜↕↑↻↥⋅↸∖↖⇁↕∪∏↴∖↴↕∐↕≯↥⋅⋜∐⋅↸∖≺⊔⋝⋜↧↴∖↴↸∖≺↧⋜↧↑↑↸∖∐∏≻↑↴∖↴↑∪↸⊳∪∐↴∖↴⊓⋅⋜∏∐↑↕∐∖ ⋯⋜↧↴∖↴↴∖↴∪↕⋟↑∐↸∖↻∏↑⋜↧↑↕↖⇁↸∖↴⋝↕⋜↕↸⊳↨↘↽∐∪," However, in a more recent Keck $K$ -band study Reynolds et (2007) found that “No clear ellipsoidal modulation is present in the light curve...” and concluded, “...that previous infrared-based attempts to constrain the mass of the putative black hole in this system are prone to considerable uncertainty.”" ↕↸∖↕∐↑∐↕↴∖↴↴∖↴⋅↖⇁↴∖↴↑↸∖↕⊔⋜∐⋅↸∖↻↥⋅∪∐↸∖↑∪↸⊳∪∐↴∖↴↕≼∐∖↥⋅⋜∏⋝↕↸∖∏∐↸⊳↸∖↥⋅↑⋜↧↕," Thus, it appears that a far more comprehensive photometric study (cf." ∐↑⋅↖↽∙⋅⊲↽∕∏⋯↴∖↴∙↕↑⋜∏≻↻↸∖⋜∐⋅↴∖↴↑∐⋜↧↑⋜↧↕⋟⋜∐⋅⋯∪↥⋅↸∖ ↸⊳≺≻∐∏∐⋅↸∖∐↸∖∐↴∖↴↕↖⇁↸∖↻∐∪↑∪∐∐∖, Cantrell et 2010) is required in order to obtain a firm mass constraint. ⊓⋅↕↸⊳↴∖↴↑∏≼↧⋅↖↽⋖↸⊳⋟∙≼⊲⋜⋯⊓⋅↸∖∐↸∖↑⋜↕↕∙⊇⊇∩↕∣⋟↕↴∖↴↥⋅↸∖≺∣∏∐⋅↸∖≼↧↕∐∪↥⋅≼∐∖↥⋅↑∪∪↴, There are six systems in Table 2 with black holes of indeterminate mass. ⋝↑⋜↧↕∐⋜↧∱∎∐⋅⋯⋯⋜↧↴∖↴↴∖↴↸⊳∪∐↴∖↴⊓⋅⋜↧↕∐↑∙ ↽∕∏∐∖↥⋅↸∖⋜∐⋅↸∖↴∖↴↕↘↴∖↴⋅↖⇁↴∖↴↑↸∖↕⊔↴∖↴↕∐⊺⋜∏⊓∖⊇↖↖↽↕↑∐↴⋝↕⋜↕↸⊳↨↘↽∐∪↕↸∖↴∖↴∪↕⋡↕∐≺∐∖↑↸∖↥⋅↕⊔∐↓⋜↧↑↸∖↕⊔⋜↧↴∖↴↴∖↴∙⊺∐↸∖↻↥⋅∪↴∖↴⋉∖↸⊳↑↴∖↴↕⋟∪↥⋅⋯↸∖⋜↧↴∖↴↿∐⋅↕∐∶↴∙⊾∪↥⋅∏↴∖↴↸∖↕≯∏∐⋅↖↽ ↸⊳∪∐↴∖↴⊓⋅⋜↕∐∐∐∶↴⋁↑∐↸∖⋯⋜↧↴∖↴↴∖↴↸∖↴∖↴∪↕≯↑↖↖↽∪∪↕≯↑∐∖⋯∙∫⇀⋀∖∐⊲⊸∖⊽≓∶≩⋜⋯≼↧⊸∖⊽⊺⊏⋅∐≺∖∖⋅↱⊐∩≓⊇⊇⊓∙⋜∐⋅↸∖↴⋝↥⋅↕∶↴⋁∐↑∶↖↖⊽∪↥⋅↨↘↽∪∐↑∐↸," The prospects for measuring or usefully constraining the masses of two of them, LMC X-3 and XTE J1859-226, are bright: Work on the former is almost complete Orosz, private communication), and the additional data required to confirm the orbital period and large mass function of the latter are obtainable." ∖↕≯∪↥⋅↕⊔↸∖↥⋅↕↴∖↴⋜↧∐⊔∪↴∖↴↑ ↸⊳∪∐∏≻↕↸∖↑↸∖⋖⋅↧∙≼↙≽≼≓≽↥⋅∪↴∖↴∑∙↻↥⋅↕↖↽⋜↧↑↸∖⋯⊔∐⋯∐↸⊳⋜↧↑↕∪∐⋝∙⋜⋯≼⊔↕∐∖⋜∥∐↕↑↕∪∐⋜↧↕≺↧⋜↧↑⋜↧↥⋅↸∖≺∣∏∐⋅↸∖≼↧↑∪↸⊳∪∐∱∎∐⋅⋯↑↕∐∖∪↥⋅↴⋝↕↑⋜↧⊔⋉∖↥⋅↕∪≼↧⋜⋯≼↧↕⋜∐⋅∶↴∙⊾↸∖ ⋯⋜↧↴∖↴↴∖↴↕⋟∏∐↸⊳↑↕∪∐∪↕≯↑∐↸∖↕⋜↧⇈↸∖," That leaves four systems (GRO J0422+32, GRS 1009–45, Nova Mus 1991 and XTE J1650–500) with black hole masses that are only very weakly constrained: $M>~f(M)~\gtrsim 1-3~M_{\odot}$." ↥⋅⋜∐⋅↸∖∪↴⋝↑⋜↧↕↕⋜∏⋝↕↸∖∙↽∕∏↓⋜↧↑↕↸∖⋜↧↖↽↸∖↴∖↴↕⋟⋯∐⋅↴∖↴⋅↖⇁↴∖↴↑↸∖⋯↴∖↴≺≼∶↕⊰≼≓≽⋅↧∩⊔⊓∶≩⊇∙≼∶↕⊰≋↕∩∩∩↓⋅↱⊐⇠∖⊽∪↖⇁⋜↧⋀∖↕∏↴∖↴↕∩∩↕ ⋜⋯≼↧⊸∖⊽↽∕∏⋮⋅∐⊓⋅↱↗∩⋅↱↗∪↭∖↖↽↕↑∐↴⋝↕⋜↧↸⊳↨↘↽∐∪↸∖⋯⋜↧↴∖↴↴∖↴↸∖↴∖," As indicated above and as Cantrell et (2010) have shown, it will be very challenging to place stronger and reliable constraints on the masses of these black holes." ↴↑∐⋜↧↑⋜⋯∖∪∐↕⋅↖↽↖⇁↸∖↥⋅⋅↖⇁↖↖⇁↸∖⋜∐↘↽↕⋅↖⇁↸⊳∪∐↴∖↴⊓⋅⋜↧↕↕∐∖≼↧∶⋀∐⋅, Data for 32 X-ray transient systems are given in Table 3. ↗⊔∟∐⋝∿↕∶≩⋀∐⋅∙⊀≚↴∖↴ ↕∐≼∐↸⊳⋜↧↑↸∖≺↧⋜∏⋝∪↖⇁↸∖⋜⋯≼↧⋜↧↴∖↴≼⊲⋜⋯⊓⋅↸∖↕↸∖↑⋜↧↕∙⊓⊇∩↕↭∐⋜↧↖↽↸∖↴∖↴∐∪↖↖⇁↕∙↕," These systems lack radial velocity data, and most even lack an optical counterpart." ↑↖↖⇁↕∐↴⋝↸∖↖⇁↸∖↥⋅⋅↖⇁↸⊳∐⋜↧∐↸∖∐∶↴⋁↕∐∶↴⋁↑∪↻↕⋜⋯∖↴∖↴↑↥⋅∪∐∶↴∙⊾↸∖↥⋅⋜⋯≼⊔⋅↸∖∐⋜∏⋝↕↸∖ ↸⊳∪∐↴∖↴⊓⋅⋜∏∐↑↴∖↴∪∐↑∐↸∖↕⊔⋜↧↴∖↴↴∖↴↸∖↴∖↴∪↕⋟↑∐↸∖↴∖↴↸∖↴⋝↕⋜↧↸⊳↨↘↽∐∪↕↸∖↴∖↴∙ ↕≻⋜↧↑⋜↧↕≯∪↥⋅∶≩⊇⊸∖⊽≓↥⋅⋜↧⋅↖↽⊓⋅⋜⋯↴∖↴↕↸∖∐↑↴∖↴⋅↖↽↴∖↴↑↸∖⋯↴∖↴⋜∐⋅↸∖∶↴∙⊾↕↖↽↸∖∐↕∐⊺⋜∏⋝↕↸∖∶≩∙↽∕∏∐∖↴∖↴↸∖↴∖↴⋅↖⇁↴∖↴↑↸∖⋯↴∖↴↕⋯⊳↨↘↽↥⋅⋜∥∐⋜↧↕↖↽↸∖↕∪↸⊳↕↑⋅↖↽≼↧⋜↕↑⋜↧∙⋜⋯≼⊔⊔∪↴∖↴↑↸∖↖↽↸∖∐↕⋜↧↸⊳↨↘↽ ⋜⋯∪↻↑↕↸⊳⋜↕↕↸⊳∪∏∐↑↸∖↥⋅↻⋜∐⋅↑∙⊺↕⋯↴∖↴∙↻↥⋅↸∖↴∖↴↸∖∐↑↕⋅↖↽∙↑↕∐∖↥⋅↸∖⋜∐⋅↸∖∐∪≼↧⋅↖↽∐⋜∐⊔↕↸⊳⋜↧↕↸⊳∪∐↴∖↴⊓⋅⋜↧↕∐↑↴∖↴∪∐↑∐↸∖↕⊔⋜↧↴∖↴↴∖↴↸∖↴∖↴∪↕≯↑∐↸∖∐⋅↸⊳∪∐∏⋯↸⊳↑↻↥⋅↕⋯⋜∐⋅↕↸∖↴∖↴∙ ↖↖⇁↕∐↸⊳∐⋜∐⋅↸∖↴⋝↸∖∐↸∖↖⇁↸∖≺↧↑∪↴⋝↸∖↴⋝↕⋜↕↸⊳↨↘↽∐∪↕↸∖↴∖↴↴⋈∖↸⊳⋜⋯↴∖↴↸∖↑∐↸∖⋅↖↽↴∖↴∐⋜∐⋅↸∖↸⊳↸∖↥⋅↑⋜↧↕∐↸⊳∐⋜∐⋅⋜↧↸⊳↑↸∖↥⋅↕↴∖↴↑↕↸⊳⊸∖⊽≓↥⋅⋜↧⋅↖⇁≻↥⋅∪↻↸∖↥⋅↑↕↸∖↴∖↴↖↖⇁↕↑∐↑↕∐∖⊇∶≩↸∖↴∖↴↑⋜∏⋝∐∖↴∐↸∖≺↧ black holes (MeCliutock Remillard 2006).," Thus, presently, there are no dynamical constraints on the masses of their compact primaries, which are believed to be black holes because they share certain characteristic X-ray properties with the 23 established black holes (McClintock Remillard 2006)." As indicated in Table 3. the primary source of information about these systems is the catalogue of Lin et ((2007) aud references therein.," As indicated in Table 3, the primary source of information about these systems is the catalogue of Liu et (2007) and references therein." For additional information aud references on Waly of these systems. see Table 13 and text iu MeCliutock aud Remillard (2006).," For additional information and references on many of these systems, see Table 4.3 and text in McClintock and Remillard (2006)." lu this section. we use the measurements of the mass functions. as well as anv available coustraints ou the nias ratios aud iuclinations for the black holes in low-mass N-ray binaries shown in Table 2 in order to place quantitative constraints ou the individual black hole masses.," In this section, we use the measurements of the mass functions, as well as any available constraints on the mass ratios and inclinations for the black holes in low-mass X-ray binaries shown in Table 2 in order to place quantitative constraints on the individual black hole masses." " In particular, our aim is to derive the likelihood Pi(data|AZ). which measure the chance of obtaining the particular set of data shown in Table 2 for the -th source if that source had mass A."," In particular, our aim is to derive the likelihood $P_i({\rm data} \vert M)$, which measure the chance of obtaining the particular set of data shown in Table 2 for the $i$ -th source if that source had mass $M$." We divide the sources into three categories based ou the amount aud quality of information regarding their nass ratios and iuclinatious: For six sources. the mass ratios and the inclinations are tightly coustrained. leading to well-determined black hole," We divide the sources into three categories based on the amount and quality of information regarding their mass ratios and inclinations: For six sources, the mass ratios and the inclinations are tightly constrained, leading to well-determined black hole" "which holds. if the distribution [function πι.) is separable in the space and the monientum variables. and if the momentum operator £, is space independent.","which holds, if the distribution function $f({\bf r}, p, t)$ is separable in the space and the momentum variables, and if the momentum operator ${\cal L}_p$ is space independent." It should be noted that equations(5)) and (3)) hold only for momentum changes Ap<

~3 by Guhathakurta. Tyson Majewski (1990) and Steidel Hamilton (1992).," At redshifts of $z\simeq6$ it is now standard practice to select galaxy candidates using the $i-$ drop technique, a straightforward extension of the Lyman-break method pioneered at $z\simeq3$ by Guhathakurta, Tyson Majewski (1990) and Steidel Hamilton (1992)." Within this context. the unique combination of depth and image quality oovided by the Hubble Space Telescope (HST) has arguably made the largest contribution to our understanding of high-redshift galaxies.," Within this context, the unique combination of depth and image quality provided by the Hubble Space Telescope (HST) has arguably made the largest contribution to our understanding of high-redshift galaxies." Analysis of the Hubble deep fields. the GOODS fields. and in particular the Hubble ultra-deep field (HUDF). has led to the identification of hundreds of; drop galaxy candidates at faint (23:0ο 2619) magnitudes (e.g. Bouwens et al.," Analysis of the Hubble deep fields, the GOODS fields, and in particular the Hubble ultra-deep field (HUDF), has led to the identification of hundreds of $i-$ drop galaxy candidates at faint $z_{850}\geq26$ ) magnitudes (e.g. Bouwens et al." 2006: Malhotra et al., 2006; Malhotra et al. 2005: Bunker et al., 2005; Bunker et al. 2004: Dickinson et al., 2004; Dickinson et al. 2004)., 2004). As a consequence. we now have a vastly improved understanding of the galaxies which undoubtedly dominate the star-formation density of the Universe during the epoch immediately following reionisation.," As a consequence, we now have a vastly improved understanding of the galaxies which undoubtedly dominate the star-formation density of the Universe during the epoch immediately following reionisation." However. although HST has greatly advanced our knowledge," However, although HST has greatly advanced our knowledge" effect of primordial binarity depends on the characteristics of those binaries.,effect of primordial binarity depends on the characteristics of those binaries. " The proper way to set up a primordial population is not obvious, especially when considering the very early evolution of a cluster where some studies advocate significant early dynamical processing of the primordial population (e.g.Kroupa1995;Parkeretal.2009), and others argue that the binary population is largely stable by the time gravitational dynamics become the dominant physical process (Moeckel&Bate2010)."," The proper way to set up a primordial population is not obvious, especially when considering the very early evolution of a cluster where some studies advocate significant early dynamical processing of the primordial population \citep[e.g.][]{kroupa95,parker09a}, and others argue that the binary population is largely stable by the time gravitational dynamics become the dominant physical process \citep{moeckel10}." ". A full treatment of this issue is beyond the scope of this paper, but we can draw on previous work to speculate on the likely effects."," A full treatment of this issue is beyond the scope of this paper, but we can draw on previous work to speculate on the likely effects." Kouwenhovenetal.(2010) find that including a primordial binary population can lead to hierarchical systems consisting of a primordial binary and a dynamicall-formed very wide companion., \citet{kouwenhoven10} find that including a primordial binary population can lead to hierarchical systems consisting of a primordial binary and a dynamicall-formed very wide companion. " If the primordial binary is small enough that it can approximately be treated as its center of mass, ie. it is energetically hard by local standards, then we expect that some fraction of the wide systems produced would be members of hierarchical triples (or possibly quadruples)."," If the primordial binary is small enough that it can approximately be treated as its center of mass, i.e. it is energetically hard by local standards, then we expect that some fraction of the wide systems produced would be members of hierarchical triples (or possibly quadruples)." " Interactions between more comparably sized binaries will naturally be more complex; these will be sensitive to the length of time the cluster spends pre-core collapse, since this determines the amount of processing the primordial binaries may undergo."," Interactions between more comparably sized binaries will naturally be more complex; these will be sensitive to the length of time the cluster spends pre-core collapse, since this determines the amount of processing the primordial binaries may undergo." This timescale is highly dependent on the initial density structure, This timescale is highly dependent on the initial density structure "we obtained The line-of-sight effect reduces the observed Doppler velocity Py. às Pons=v;cos€, where 6 is the angle between the direction of the plasma motion and the line of sight.","we obtained The line-of-sight effect reduces the observed Doppler velocity $\tilde{v}_{\mathrm{obs}}$ as $\tilde{v}_{\mathrm{obs}} = \tilde{v}_1 \cos \theta$ , where $\theta$ is the angle between the direction of the plasma motion and the line of sight." " Using Eq. (3)),"," Using Eq. \ref{v-I}) )," the energy flux of compressible mode is estimated as follows: The observed Doppler velocity tor fast sausage mode is cancelled along the line of sight at boundaries of each loop. so we used 7 instead of v from Eq. (3)).," the energy flux of compressible mode is estimated as follows: The observed Doppler velocity for fast sausage mode is cancelled along the line of sight at the boundaries of each loop, so we used $\tilde{I}$ instead of $\tilde{v}$ from Eq. \ref{v-I}) )." The energy flux transported by torsional Alfvénn mode or fast kink mode is represented as The calculated energy flux as a function of position along the slit is shown in Figure 5.., The energy flux transported by torsional Alfvénn mode or fast kink mode is represented as The calculated energy flux as a function of position along the slit is shown in Figure \ref{power}. " Red pluses and blue crosses represent fast sausage mode and fast kink mode, respectively."," Red pluses and blue crosses represent fast sausage mode and fast kink mode, respectively." Green and orange diamonds respectively represent upwardly and downwardly propagating slow mode estimated using intensity amplitude., Green and orange diamonds respectively represent upwardly and downwardly propagating slow mode estimated using intensity amplitude. " As outlined in section 3, we determined propagation direction based on phase delays between intensity and Doppler velocity as follows: upwardly propagating was defined as a phase delay in the range of (5/6yr to π and --π to —(5/6yr. while downwardly propagating was defined as a phase delay in the range of —(1/6yr to (1/6)."," As outlined in section 3, we determined propagation direction based on phase delays between intensity and Doppler velocity as follows: upwardly propagating was defined as a phase delay in the range of $(5/6) \pi$ to $\pi$ and $-\pi$ to $-(5/6)\pi$ , while downwardly propagating was defined as a phase delay in the range of $-(1/6)\pi$ to $(1/6)\pi$." Green and orange triangles respectively represent upwardly and downwardly propagating slow mode estimated using Doppler velocity amplitude., Green and orange triangles respectively represent upwardly and downwardly propagating slow mode estimated using Doppler velocity amplitude. " We assumed py=8.4x10eem"". ος=167kms*' and c4=10x107kms!."," We assumed $\rho_0 = 8.4 \times 10^{-16} \mspace{3mu} \mathrm{g} \mspace{3mu} {\mathrm{cm}}^{-3}$, $c_S = 167 \mspace{3mu} \mathrm{km} \mspace{3mu} {\mathrm{s}}^{-1}$, and $c_A = 1.0 \times 10^3 \mspace{3mu} \mathrm{km} \mspace{3mu} {\mathrm{s}}^{-1}$." If our interpretations in terms of MHD waves are correct. our findings indicate that fast sausage mode waves have a significant proportionof the energy flux needed for coronalheating in active regions (10ereem s). as estimated by Withbroe&Noyes (1977)..," If our interpretations in terms of MHD waves are correct, our findings indicate that fast sausage mode waves have a significant proportionof the energy flux needed for coronalheating in active regions $10^7 \mspace{3mu} \mathrm{erg} \mspace{3mu} {\mathrm{cm}}^{-2} \mspace{3mu} {\mathrm{s}}^{-1}$ ), as estimated by \citet{wit77}. ." We also obtained titje at the 1.5-m telescope at Palomar on the night of 1999. April L. using its IR caiera.,"We also obtained time at the 1.5-m telescope at Palomar on the night of 1999, April 4, using its IR camera." We imaged the 20 brightest sars at Is band as a check of our Gemini data as well as lagi& the list at J yack., We imaged the 20 brightest stars at K band as a check of our Gemini data as well as imaging the list at J band. These data were reduced in a similar fashion to the (ιοί data., These data were reduced in a similar fashion to the Gemini data. The unce1ainties for both data sets were deermined by the standard deviation of the brightness of the staidard star throwhout the night., The uncertainties for both data sets were determined by the standard deviation of the brightness of the standard star throughout the night. A total of 77 stars oit oL the original sauple of 302 were observed either at Palomar or with Cemini o: both., A total of 77 stars out of the original sample of 302 were observed either at Palomar or with Gemini or both. We have restricted our auaysis to the brightest part of the sample in order to have a reliable catalog with a well defined limit., We have restricted our analysis to the brightest part of the sample in order to have a reliable catalog with a well defined limit. Table 1 shows the 28 bright stars with ni«9 in the dark spot. with the original LIRC? Ix magnitude. the Palomar J and Ix inagnitudes (16060 and ]x60) auc the Lick Gemini lx aud L inagnitudes.," Table \ref{tab:stars} shows the 28 bright stars with $m < 9$ in the dark spot, with the original LIRC2 K magnitude, the Palomar J and K magnitudes (J60 and K60) and the Lick Gemini K and L magnitudes." We have used the Lick Ix aud L magnitudes in this paper., We have used the Lick K and L magnitudes in this paper. Having obtained the photometry from the ground lor the bright stars. the ask was to match up the ground. based data to the space based data.," Having obtained the photometry from the ground for the bright stars, the task was to match up the ground based data to the space based data." " Figure 3 shows a projectjon o‘the DIRBE pixels on tlie ""dark spot as well as the stars 1uaged by LIRC2."," Figure \ref{fig:cold-spot-list} shows a projection of the DIRBE pixels on the “dark spot"" as well as the stars imaged by LIRC2." The most obvious cdifIicuty turus out to ye that the DIRBE pixels are uo alie1ο with the EW aud NS axes: therefore. some only. partialy enter the box.," The most obvious difficulty turns out to be that the DIRBE pixels are not aligned with the EW and NS axes; therefore, some only partially enter the box." Also the values within the pixels jeiiselves 'epreseut the average ileusiy seen when the 0.17 SC1iare DIRBE beam is centered witliu the pixe boundary. aud hence are alectec by the pixels arouxl them since the beam does not :ibrupty stop at the edge of the pixel.," Also the values within the pixels themselves represent the average intensity seen when the $0.7^\circ$ square DIRBE beam is centered within the pixel boundary, and hence are affected by the pixels around them since the beam does not abruptly stop at the edge of the pixel." To compute the response ina given pixel Oa given sar. we found the probability tliat he star was inside he DIRBE 0.7© sellawe beam assuming tlat tie beam center was uuiformly distributed inside the yixel. amd tha| the beam orientatOl) Was lllform in augle.," To compute the response in a given pixel to a given star, we found the probability that the star was inside the DIRBE $0.7^\circ$ square beam assuming that the beam center was uniformly distributed inside the pixel, and that the beam orientation was uniform in angle." This is a fair asstinptiou since each jixel was observed huxdreds of times in 1ally different angles during the lifetime of he uuission., This is a fair assumption since each pixel was observed hundreds of times in many different angles during the lifetime of the mission. To be specific. let H(b.0.3) be Liftle star with position given by the unit vector Sis il the square beam when it is cenered at. positiou baid oriented with position angle 0. aud QO if he star is not in the beam.," To be specific, let $H(\hat{b},\theta,\hat{s})$ be 1 if the star with position given by the unit vector $\hat{s}$ is in the square beam when it is centered at position $\hat{b}$ and oriented with position angle $\theta$, and 0 if the star is not in the beam." " Then tje probability of the j star being in data taken in the 7"" pixel is eiven by where f=?). is the angular extent of the i” pixel.", Then the probability of the $j^{th}$ star being in data taken in the $i^{th}$ pixel is given by where $\Omega_i$ is the angular extent of the $i^{th}$ pixel. Then the predicted contribution from bright stars to the intensity in the i/” pixel is given by, Then the predicted contribution from bright stars to the intensity in the $i^{th}$ pixel is given by where Since small bodies resulting from successive collisions are rapidly removed by the eas drag.he collision cascade reduces the surface density of solids.,"where Since small bodies resulting from successive collisions are rapidly removed by the gas drag, collision cascade reduces the surface density of solids." " (INtobavashi&Tanaka2010:Kobavashietal.POLO) where aud hg=lp,""."," \citep{kobayashi10,kobayashi+10} where and $h_0=1.1\rho_{\rm p}^{-2/3}$." " For the derivation. of Equation (18)). we apply the. fragmentation outcome model of Iobavashi&Tanaka(2010): ejecta vielded by a sinele collision between ny aud mo are characterised by their total mass n. and their power-law ass spectimm with an exponcut b below the mass mi=εν|omo)jof(loy, wheree< Lis a coustant."," For the derivation of Equation \ref{eq:dsigma_dt}) ), we apply the fragmentation outcome model of \citet{kobayashi10}; ejecta yielded by a single collision between $m_1$ and $m_2$ are characterised by their total mass $m_{\rm e}$ and their power-law mass spectrum with an exponent $b$ below the mass $m_{\rm L} = \epsilon (m_1+m_2)\phi/(1+\phi)^2$, where$\epsilon < 1$ is a constant." " The X, reduction rate is insensitive to € and b (Nobavashi&Tanaka 2010).", The $\Sigma_{\rm s}$ reduction rate is insensitive to $\epsilon$ and $b$ \citep{kobayashi10}. . We set b=5/3 and e=0.2 in this paper., We set $b = 5/3$ and $\epsilon=0.2$ in this paper. Dividing Equation (16)) bv Equation (18)) aud integrating. we obtain the relation between the Clubrvo mass M aud the surface deusitv X: where Ay is the initial eiibrvo mass.," Dividing Equation \ref{eq:dM_pla}) ) by Equation \ref{eq:dsigma_dt}) ) and integrating, we obtain the relation between the embryo mass $M$ and the surface density $\Sigma_{\rm s}$: where $M_0$ is the initial embryo mass." When an embrvo reaches a final mass ⋀∐∩↕∙∑∖↕⊔⋜↧∙↖↽↴⋈∖≺∐∖↴∖↴↸⊳↥⋅∏⋝↸∖≺↧⋜↧↴∖↴∊↴∑⋀∐∩↕∣∣↼∖∣↖↖⇁↕↑∐⋜↧ We set CN=(kl to derive a final mass.," When an embryo reaches a final mass $M_ {\rm ca}$, We set $C_{\Sigma_{\rm s}} = 0.1$ to derive a final mass." From Eqs. (21)), From Eqs. \ref{eq:mass_sigma}) ) " aud (22)) we obtain a final Clubrvo lass Ποσο, we assume M2My."," and \ref{eq:sigma_limit}) ), we obtain a final embryo mass Here, we assume $M_{\rm ca} \gg M_0$." " For kilnmeter-zed or larger planetesinials. Qh=QuePpt with constants Qu, and Jo."," For kilometer-sized or larger planetesimals, $Q_{\rm D}^* = Q_{\rm 0g} \rho_{\rm p} r^{\beta_{\rm g}}$ with constants $Q_{\rm 0g}$ and $\beta_{\rm g}$." " We apply Qu,=2lergcube? aud je=1.19 for ico (Bonz&Asphaug1999) and 6?c» 6. and Equation (23)) can then be rewritten as Since planetesinals erow before plauctesimals’ fracinentation starts. planctesimal dass 1 is slightly larecr than initial plauctesimal mass ry."," We apply $Q_{\rm 0g} = 2.1 \,{\rm erg\, cm}^3\,{\rm g}^{-2}$ and $\beta_{\rm g} = 1.19$ for ice \citep{benz99} and $\tilde e^2 \gg 6$ , and Equation \ref{eq:Mca_ori}) ) can then be re-written as Since planetesimals grow before planetesimals' fragmentation starts, planetesimal mass $m$ is slightly larger than initial planetesimal mass $m_0$ ." "November 8, 2004, have noticed the presence of unexplained emission features between 3600 and4400A.","November 8, 2004, have noticed the presence of unexplained emission features between 3600 and." ". A more detailed analysis has shown that these emissions where present on all the FORS2 data of that night, i.e. a set of MXU exposures 2700 seconds each, obtained between 00:15 and 07:08 using the 600B grism."," A more detailed analysis has shown that these emissions where present on all the FORS2 data of that night, i.e. a set of MXU exposures 2700 seconds each, obtained between 00:15 and 07:08 using the 600B grism." " As expected, no trace of these features was visible in a similar data set obtained three days later."," As expected, no trace of these features was visible in a similar data set obtained three days later." An example is shown in Fig., An example is shown in Fig. " 22 where, for comparison, an analogous spectrum obtained on November 11 is also plotted."," \ref{fig:thunder} where, for comparison, an analogous spectrum obtained on November 11 is also plotted." " Clearly, the two spectra differ mainly for the presence of two prominent emission bands, peaking at and4278À,, which are identified as Nj first negative bands 1N(0-0) and 1N(0-1) (Chamberlain 1961;; Table 5.4)."," Clearly, the two spectra differ mainly for the presence of two prominent emission bands, peaking at and, which are identified as $_2^+$ first negative bands 1N(0-0) and 1N(0-1) (Chamberlain \cite{chamberlain}; Table 5.4)." " These features, which are normally very weak or even absent in the nightglow (Broadfoot Kendall 1968)) are on the contrary typical of the aurora spectrum (Chamberlain 1961))."," These features, which are normally very weak or even absent in the nightglow (Broadfoot Kendall \cite{broadfoot}) ) are on the contrary typical of the aurora spectrum (Chamberlain \cite{chamberlain}) )." " Besides being an extremely strange phenomenon at the latitudes of Paranal, an aurora would certainly be accompanied by other spectral markers, like for instance a large increase in the emission of the [OI]5577 line, which can reach in fact an intensity of 100 kR during a IBC III aurora (Chamberlain 1961)."," Besides being an extremely strange phenomenon at the latitudes of Paranal, an aurora would certainly be accompanied by other spectral markers, like for instance a large increase in the emission of the [OI]5577 line, which can reach in fact an intensity of 100 kR during a IBC III aurora (Chamberlain \cite{chamberlain}) )." The flux carried by this line in the same spectrum presented in Fig., The flux carried by this line in the same spectrum presented in Fig. " 22 is —183 R, that is slightly below the average level measured for Paranal (230R, see Sec. 6.1.1))."," \ref{fig:thunder} is $\sim$ 183 R, that is slightly below the average level measured for Paranal (230R, see Sec. \ref{sec:oi5577}) )." " This definitely rules out an exceptional auroral event as the responsible for the unusual spectrum observed on November 8, 2004."," This definitely rules out an exceptional auroral event as the responsible for the unusual spectrum observed on November 8, 2004." " A plausible explanation, proposed by Castro Garcia (private communication), is the contamination by the reflection from clouds of a number of lightning strokes."," A plausible explanation, proposed by Castro Garcia (private communication), is the contamination by the reflection from clouds of a number of lightning strokes." " In effects, in the spectral range covered by the FORS2 data (3600-6100A)), the most prominent features in a lightning spectrum are the N5 first negative bands 1N(0-0) and 1N(0-1) (see for instance Wallace 1964))."," In effects, in the spectral range covered by the FORS2 data ), the most prominent features in a lightning spectrum are the $_2^+$ first negative bands 1N(0-0) and 1N(0-1) (see for instance Wallace \cite{wallace}) )." " Additionally, on the night of Nov 8 2004 thick and thin cirrus were reported in the ESO-Paranal night logs, substantiating the hypothesis of scattered light from a rather far thunderstorm."," Additionally, on the night of Nov 8 2004 thick and thin cirrus were reported in the ESO-Paranal night logs, substantiating the hypothesis of scattered light from a rather far thunderstorm." " This kind of events must be indeed very rare, since no other example could be found in the FORS1 spectral data base presented in this paper."," This kind of events must be indeed very rare, since no other example could be found in the FORS1 spectral data base presented in this paper." " For a first exploratory analysis I have computed the linear correlation coefficients in the log F-logF plane between all measured features.. The results are presented in Table 8 and they basically confirm the correlations found by Barbier (1956)), even though new interesting facts do appear."," For a first exploratory analysis I have computed the linear correlation coefficients in the $\log F$ $\log F$ plane between all measured features.. The results are presented in Table \ref{tab:fluxcorr} and they basically confirm the correlations found by Barbier \cite{barbier}) ), even though new interesting facts do appear." " The pioneering optical, eight-color photometric studies by Barbier (1956)) have shown the existence of the so-called groups: the ([OI]5577, O» Herzberg bands, the blue bands, the green continuum and the O5(0-1) band), thegroup (Na I D doublet and the OH bands) and thegroup, which includes only the [OI]6300,6364 doublet)"," The pioneering optical, eight-color photometric studies by Barbier \cite{barbier}) ) have shown the existence of the so-called : the ([OI]5577, $_2$ Herzberg bands, the blue bands, the green continuum and the $_2$ (0-1) band), the (Na I D doublet and the OH bands) and the, which includes only the [OI]6300,6364 doublet)." " So far, the latter appeared to be completely independent from any other component of the airglow (see Chamberlain 1961))."," So far, the latter appeared to be completely independent from any other component of the airglow (see Chamberlain \cite{chamberlain}) )." " Nevertheless, as it is shown in Fig. 23,, ["," Nevertheless, as it is shown in Fig. \ref{fig:oinicorr}, [" OIJ6300 shows a very tight correlation with the N I feature at5200À.,OI]6300 shows a very tight correlation with the N I feature at. ". The linear correlation factor in the log-log plane is r=0.95 and this appears to be one of the strongest correlation between airglow features found in the data set presented here, surpassed only by that shown by the OH bands (see Table 8))."," The linear correlation factor in the log-log plane is $r$ =0.95 and this appears to be one of the strongest correlation between airglow features found in the data set presented here, surpassed only by that shown by the OH bands (see Table \ref{tab:fluxcorr}) )." " To my knowledge, this is the first time this finding is reported; most likely, it escaped the attention of previous investigations simply because the N I feature is rather weak (x30 R) and hence practically impossible to measure with intermediate passband filters."," To my knowledge, this is the first time this finding is reported; most likely, it escaped the attention of previous investigations simply because the N I feature is rather weak $\leq$ 30 R) and hence practically impossible to measure with intermediate passband filters." " Even though a correlation between N I 5200 and [OI]5577 is found (see Fig. 23,"," Even though a correlation between N I 5200 and [OI]5577 is found (see Fig. \ref{fig:oinicorr}," upper panel) this is less marked (r=0.56) and the spread around the best fit relation is much larger (020.29 vs. o=0.11).," upper panel), this is less marked $r$ =0.56) and the spread around the best fit relation is much larger $\sigma$ =0.29 vs. $\sigma$ =0.11)." " Finally, the correlation between [OI]5577 and [OIJ6300 is indeed weak (r=0.29, o=0.39); nevertheless, the data presented here seem to indicate that, on average, the maximum value attained by the red line is related to the flux of the green-line through the simple relation x2xF([OI]5577)."," Finally, the correlation between [OI]5577 and [OI]6300 is indeed weak $r$ =0.29, $\sigma$ =0.39); nevertheless, the data presented here seem to indicate that, on average, the maximum value attained by the red line is related to the flux of the green-line through the simple relation $\leq$ $\times$ F([OI]5577)." " The strongest correlation within the [OI]5577 covariance group is that with the O» band (r=0.85), followed by the blue bands B1 (r=0.61), N (r=0.56), B2 (r=0.55), C3 (r=0.43) and C2 (r=0.41)."," The strongest correlation within the [OI]5577 covariance group is that with the $_2$ band $r$ =0.85), followed by the blue bands B1 $r$ =0.61), N I $r$ =0.56), B2 $r$ =0.55), C3 $r$ =0.43) and C2 $r$ =0.41)." The correlation with the other continuum regions is weaker (r <0.4)., The correlation with the other continuum regions is weaker $r\leq$ 0.4). " As for the Na I D group, besides the very tight"," As for the Na I D group, besides the very tight" , with previous results regarding the morphological evolution in clusters. we have found that the largest llate-type galaxies are found to be large early-types in WINGS clusters. as it is apparent studying the morphologies above the tilted line in Figure 2.,"with previous results regarding the morphological evolution in clusters, we have found that the largest late-type galaxies are found to be large early-types in WINGS clusters, as it is apparent studying the morphologies above the tilted line in Figure \ref{fig:morph}." .The BCGs. instead. have been found to evolve both in mass (a factor of ~2) and size (a factor of ~4). in agreement with other recent theoretical and observational results.," .The BCGs, instead, have been found to evolve both in mass (a factor of $\sim2$ ) and size (a factor of $\sim4$ ), in agreement with other recent theoretical and observational results." Our findings show that the progenitor bias (in age or morphology) plays an important role in the size-growth paradigm. and must be carefully taken into account when comparing local galaxy sizes with those of massive high-z galaxies.," Our findings show that the progenitor bias (in age or morphology) plays an important role in the size-growth paradigm, and must be carefully taken into account when comparing local galaxy sizes with those of massive high-z galaxies." 4-sphere at the enhancoon locus.,4-sphere at the enhançoon locus. We leave it for a future work., We leave it for a future work. Despite this and other obvious differences the essence of the problem concerning spherical symmetry remains., Despite this and other obvious differences the essence of the problem concerning spherical symmetry remains. It is because the enhangoon shell they considered was spherical and supported homogenously a melting .V D6-branes on it., It is because the enhançoon shell they considered was spherical and supported homogenously a melting $N$ D6-branes on it. An inconsistency with field theory is again encountered (and cured by the fuzzy geometry) in their case., An inconsistency with field theory is again encountered (and cured by the fuzzy geometry) in their case. That is because spherically symmetric t Hooft-Polyakov monopoles with multiple magnetic charge do not exist [28].., That is because spherically symmetric t' Hooft-Polyakov monopoles with multiple magnetic charge do not exist \cite{WG}. Needles to say that the same enhangoon-fuzzy mechanism applies for the SO(4+) monopoleonopole and andcures it fromfrc the multichargeicharge disease which could undergoin i the branera picture had the geometry not become fuzzy., Needles to say that the same enhançoon-fuzzy mechanism applies for the $SO(4)$ monopole and cures it from the multicharge disease which could undergo in the brane picture had the geometry not become fuzzy. " In this paper, a Type HA geometric realization of the Yang monopole in six dimensions givenin [1] is revisited and its apparent contradictions are clarified."," In this paper, a Type IIA geometric realization of the Yang monopole in six dimensions given in \cite{BDS2} is revisited and its apparent contradictions are clarified." " In the construction of the magnetic object, it has been used the result of the duality between Type IIA superstring compactified on the K3 surface and heterotic superstring on T!."," In the construction of the magnetic object, it has been used the result of the duality between Type IIA superstring compactified on the K3 surface and heterotic superstring on $T^4$." " The $U(2) gauge symmetry of the Yang monopole is considered as the enhanced gauge symmetry corresponding to shrinking 2-cycles inside the K3 surface, and the Yang monopole comes up by wrapping D-branes on the K3 non-trivial cycles."," The $SU(2)$ gauge symmetry of the Yang monopole is considered as the enhanced gauge symmetry corresponding to shrinking 2-cycles inside the K3 surface, and the Yang monopole comes up by wrapping D-branes on the K3 non-trivial cycles." " In this way, the properties of the Yang monopole are encoded in the K3 surface data."," In this way, the properties of the Yang monopole are encoded in the K3 surface data." " With respect to the charges of the configuration, suggestions and objections that came up during the presentation of [1] have been taking in full consideration."," With respect to the charges of the configuration, suggestions and objections that came up during the presentation of \cite{BDS2} have been taking in full consideration." " In our opinion, the present work brings light to the main objections strengthening and completing the brane picture of the Yang monopole."," In our opinion, the present work brings light to the main objections strengthening and completing the brane picture of the Yang monopole." " Firstly, it was claimed that the number of charges of one D4-brane setup should be four, as accounted for the two ways the brane and the antibrane can wrap a 2-cycle."," Firstly, it was claimed that the number of charges of one D4-brane setup should be four, as accounted for the two ways the brane and the antibrane can wrap a 2-cycle." The answer is given at the end of section ??.., The answer is given at the end of section \ref{sec:TSCYM}. " There it is explained that the four configurations are actually identified in pairs, so it results in just two homotopically different configurations."," There it is explained that the four configurations are actually identified in pairs, so it results in just two homotopically different configurations." " Indeed, as explain in the same section, the $0(4) extended-Yang monopole is the one who carries four charges and a brane picture for it is proposed."," Indeed, as explain in the same section, the $SO(4)$ extended-Yang monopole is the one who carries four charges and a brane picture for it is proposed." The second objection have been taken into analysis in section ??.., The second objection have been taken into analysis in section \ref{sec:MCDEC}. " When more than one D4-brane are added to the model, its interpretation as a Yang monopole gets into trouble since and infinite tower of charges seem to appear."," When more than one D4-brane are added to the model, its interpretation as a Yang monopole gets into trouble since and infinite tower of charges seem to appear." This is what we have called multicharge disease., This is what we have called multicharge disease. " The multi-charge problem of this construction gets satisfactory solved by the dynamics of the enhancoon mechanism which, as explained in section 23, ruins spherical symmetry in the multi-brane setup and then saves the model from"," The multi-charge problem of this construction gets satisfactory solved by the dynamics of the enhançoon mechanism which, as explained in section \ref{sec:MCDEC}, ruins spherical symmetry in the multi-brane setup and then saves the model from" 2000) for dwarfs. we can expect that the stellar halo formed from the wz Cen’s host with Ap ~ 14 mage has the likely peak value of ο) ~ —L2 (or somewhere between —1.5 and O.S4in Fe/L]) in its metallicity distribution for D.V = 0.5.,"2000) for dwarfs, we can expect that the stellar halo formed from the $\omega$ Cen's host with $M_{\rm B}$ $\sim$ $-14$ mag has the likely peak value of [Fe/H] $\sim$ $-1.2$ (or somewhere between $-1.5$ and $-0.84$ in [Fe/H]) in its metallicity distribution for $B-V$ = $0.5$." " Εις we suggest that the Galactic halo stars with ‘esl ~ 2 and L, — 500 and Ly. ~ 300 kpe km s can originate [rom w Cen’s host.", Thus we suggest that the Galactic halo stars with [Fe/H] $\sim$ $-1.2$ and $L_{\rm z}$ $\sim$ $-500$ and $L_{\rm xy}$ $\sim$ 300 kpc km $^{-1}$ can originate from $\omega$ Cen's host. w Cen-like objects have been already discovered. in other and environments: Gl in M31(e.g... Mevlan et al.," $\omega$ Cen-like objects have been already discovered in other galaxies and environments: G1 in M31 (e.g., Meylan et al." 2) sand. very bright GI-like cluster in NGC 1023 mna200)., 2001) and very bright G1-like cluster in NGC 1023 (Larsen 2001). We suggest that if c Cen-like objects in disc ealaxies are formed from ancient nucleated dwarls merging with disces. there should be some correlations between the existence of v Cen-like objects and structural properties of disces. because galaxy interaction/merging can be responsible not only for the formation of thick disces and bars and for the formation of starbursts and AXGNs(ασ. Noguchi 1987).," We suggest that if $\omega$ Cen-like objects in disc galaxies are formed from ancient nucleated dwarfs merging with discs, there should be some correlations between the existence of $\omega$ Cen-like objects and structural properties of discs, because galaxy interaction/merging can be responsible not only for the formation of thick discs and bars and for the formation of starbursts and AGNs (e.g., Noguchi 1987)." For example. it is an interesting observational question whether or not disc galaxies with c Cen-like objects are more likely to have thick clises.," For example, it is an interesting observational question whether or not disc galaxies with $\omega$ Cen-like objects are more likely to have thick discs." WKB acknowledge the financial support of the Australian Research Council throughout the course of this work., KB acknowledge the financial support of the Australian Research Council throughout the course of this work. techniques that provides improvements in image fidelity and sensitivity.,techniques that provides improvements in image fidelity and sensitivity. We note that a similar technique was briefly discussed in ?.. although it was not considered in any detail. nor was 1t compared to the traditional approach to RM synthesis imaging.," We note that a similar technique was briefly discussed in \citet{pen_GMRT-eor_2009}, although it was not considered in any detail, nor was it compared to the traditional approach to RM synthesis imaging." Furthermore. deconvolution was not considered.," Furthermore, deconvolution was not considered." With the advent of RM synthesis the concept of rotation measure. defined to be the amount that. the observed polarization angle changes as a function of frequency. has become somewhat outdated.," With the advent of RM synthesis the concept of rotation measure, defined to be the amount that the observed polarization angle changes as a function of frequency, has become somewhat outdated." With RM synthesis. one does not measure RMs. but instead reconstructs the polarized intensity as a function of Faraday depth.," With RM synthesis, one does not measure RMs, but instead reconstructs the polarized intensity as a function of Faraday depth." In the simplest case. where a single. discrete source of polarized emission is positioned behind a Faraday rotating medium. the RM is equal to the Faraday depth.," In the simplest case, where a single, discrete source of polarized emission is positioned behind a Faraday rotating medium, the RM is equal to the Faraday depth." In all other cases this is not true., In all other cases this is not true. In general. RM cannot be used as a proxy for Faraday depth. and the full distribution of polarized brightness as a function of Faraday depth is the most appropriate quantity to study.," In general, RM cannot be used as a proxy for Faraday depth, and the full distribution of polarized brightness as a function of Faraday depth is the most appropriate quantity to study." Therefore. we avoid use of the term RM to describe this new method. and instead call it Faraday synthesis.," Therefore, we avoid use of the term RM to describe this new method, and instead call it Faraday synthesis." Throughout the remainder of this paper. RM synthesis will refer to the LOS imaging method developed by ?..," Throughout the remainder of this paper, RM synthesis will refer to the LOS imaging method developed by \citet{brentjens_faraday_2005}." The traditional practical approach of first Imaging individual frequencies using 2D aperture synthesis techniques and then reconstructing the LOS brightness distribution on a pixel-by-pixel basis will be referred to as 2+1D imaging. in contrast to Faraday synthesis. which we will often refer to as 3D imagine.," The traditional practical approach of first imaging individual frequencies using 2D aperture synthesis techniques and then reconstructing the LOS brightness distribution on a pixel-by-pixel basis will be referred to as 2+1D imaging, in contrast to Faraday synthesis, which we will often refer to as 3D imaging." In Sec., In Sec. 2. we briefly review the theories of aperture and RM synthesis imaging., \ref{sec:Synthesis-imaging} we briefly review the theories of aperture and RM synthesis imaging. In See., In Sec. 3 we introduce the Faraday synthesis imaging technique.," \ref{sec:Faraday-synthesis} we introduce the Faraday synthesis imaging technique." |n Sec., In Sec. + we describe the proof of concept software that we have implemented. and in Sec.," \ref{sec:Proof-of-concept} we describe the proof of concept software that we have implemented, and in Sec." 5 we compare test results obtained by imaging mock data using both the 3D and 2+1D techniqtes., \ref{sec:Tests} we compare test results obtained by imaging mock data using both the 3D and 2+1D techniques. We conclude in Sec., We conclude in Sec. 6 with a summary and discussion of our results., \ref{sec:Discussions-and-conclusions} with a summary and discussion of our results. In this section. we review the fundamentals of aperture and RM synthesis imaging before showing how they can be performed simultaneously in Faraday synthesis imaging., In this section we review the fundamentals of aperture and RM synthesis imaging before showing how they can be performed simultaneously in Faraday synthesis imaging. Reviews are included here for completeness and to highlight the assumptions that are typically made and the limitations that result., Reviews are included here for completeness and to highlight the assumptions that are typically made and the limitations that result. We can not possibly provide a complete review of the theory of aperture synthesis., We can not possibly provide a complete review of the theory of aperture synthesis. We only wish to review those aspects that are most relevant to the current work., We only wish to review those aspects that are most relevant to the current work. For a comprehensive treatment. the reader is referred to ?..," For a comprehensive treatment, the reader is referred to \citet{2001_thompson_interferometry}." With an interferometer. one measures not the sky brightness directly. but rather a collection of discrete samplings of the aperture plane.," With an interferometer, one measures not the sky brightness directly, but rather a collection of discrete samplings of the aperture plane." These samples are complex quantities. typically referred to as visibilities. denoted as V.," These samples are complex quantities, typically referred to as visibilities, denoted as $V$." The visibilities are the correlated voltage output of pairs of antennas., The visibilities are the correlated voltage output of pairs of antennas. For a narrow-band observation. they are related to the sky brightness distribution. 7. by The coordinates (u.v.) are spatial frequency coordinates. or the distance between pairs of antennas. measured in numbers of wavelengths.," For a narrow-band observation, they are related to the sky brightness distribution, $I$, by The coordinates $(u,v,w)$ are spatial frequency coordinates, or the distance between pairs of antennas, measured in numbers of wavelengths." The coordinate 4 measures the distance in the cardinal North-South direction. while v measures the distance in the East-West direction.," The coordinate $u$ measures the distance in the cardinal North-South direction, while $v$ measures the distance in the East-West direction." The coordinate w points in the direction of the phase reference position on the sky., The coordinate $w$ points in the direction of the phase reference position on the sky. The (50) coordinates are direction cosines relative to the (4.v) coordinates.," The $(l,m)$ coordinates are direction cosines relative to the $(u,v)$ coordinates." The wavelength at which the visibilities are measured is given by 22., The wavelength at which the visibilities are measured is given by $\lambda$. This relationship can be simplified to a two-dimensional (2D) Fourier transformation in two circumstances., This relationship can be simplified to a two-dimensional (2D) Fourier transformation in two circumstances. The first is in the case of an East-West oriented array such as the WSRT., The first is in the case of an East-West oriented array such as the WSRT. In this case. the telescopes move through a plane such that w=0 as the Earth rotates.," In this case, the telescopes move through a plane such that $w=0$ as the Earth rotates." The second case is when only a small patch of the sky is being imaged. such that w(VI-P-nm-1)=0.," The second case is when only a small patch of the sky is being imaged, such that $w\left(\sqrt{1-l^{2}-m^{2}}-1\right)\approx0$." For the time being. we assume that we are looking at a small patch of the sky and henceforth neglect this w-term.," For the time being, we assume that we are looking at a small patch of the sky and henceforth neglect this $w$ -term." A radio telescope is not equally sensitive to the entire sky., A radio telescope is not equally sensitive to the entire sky. The sky brightness distribution is attenuated by the antenna power pattern. A. which is commonly referred to as the primary beam.," The sky brightness distribution is attenuated by the antenna power pattern, $A$, which is commonly referred to as the primary beam." Including this effect. the visibilities are related to the sky brightness distribution via the relationship In reality. as mentioned above. only discrete locations in the aperture planeare sampled.," Including this effect, the visibilities are related to the sky brightness distribution via the relationship In reality, as mentioned above, only discrete locations in the aperture planeare sampled." " The measured visibilities. V. are related to the true visibilities by The sampling function S$ can be represented as where b=5,4+b,$ is the distance between two antennas. known as the baseline length. and the unit vectors X and Y point toward the North and East. respectively."," The measured visibilities, $\widehat{V}$, are related to the true visibilities by The sampling function $S$ can be represented as where $\mathbf{b}=b_{x}\hat{x}+b_{y}\hat{y}$ is the distance between two antennas, known as the baseline length, and the unit vectors $\mathbf{\hat{x}}$ and $\mathbf{\hat{y}}$ point toward the North and East, respectively." The function W allows for the inclusion of weighting factors. e.g. by the inverse of the noise.," The function $W$ allows for the inclusion of weighting factors, e.g. by the inverse of the noise." The / subseript is an index over the list of discrete values of b and 2 for which measurements have been made., The $i$ subscript is an index over the list of discrete values of $\mathbf{b}$ and $\lambda$ for which measurements have been made. To recover the sky brightness distribution from visibility data. one must invert Eqs.," To recover the sky brightness distribution from visibility data, one must invert Eqs." 2. and 3.., \ref{eq:vis_sky_relation_2d} and \ref{eq:true_to_measured_visibility}. . Due to the sampling function and the presence of noise. it is not possible to solve," Due to the sampling function and the presence of noise, it is not possible to solve" of its companion is identical to the value predicted from membership.,of its companion is identical to the value predicted from membership. The justification was a color index supposedly too red to belong to the Hyades but. more importantly. the distance of the common proper motion pair to the center of the cluster.," The justification was a color index supposedly too red to belong to the Hyades but, more importantly, the distance of the common proper motion pair to the center of the cluster." This author concluded that this common proper motion pair is projected on the cluster but only at about a third of the distance to the cluster., This author concluded that this common proper motion pair is projected on the cluster but only at about a third of the distance to the cluster. The comprehensive study of Perrymanetal.(1998) considered the 5.490 Hipparcos Catalog stars corresponding to the field of the Hyades.," The comprehensive study of \cite{per98} considered the 5,490 Hipparcos Catalog stars corresponding to the field of the Hyades." Hipparcos astrometry was combined with radial velocity measurements in order to obtain three-dimensional velocities. which allowed candidate membership selection based on position and kinematic criteria.," Hipparcos astrometry was combined with radial velocity measurements in order to obtain three-dimensional velocities, which allowed candidate membership selection based on position and kinematic criteria." The authors divided the Hyades into four components by using the three-dimesional distance to the cluster center., The authors divided the Hyades into four components by using the three-dimensional distance to the cluster center. The distance of BD+26 730 to the center of the cluster is 29 pe and therefore it was classified as a former member of the Hyades cluster. currently lying beyond the tidal radius (~10 pe).," The distance of $+$ 26 730 to the center of the cluster is 29 pc and therefore it was classified as a former member of the Hyades cluster, currently lying beyond the tidal radius $\sim$ 10 pc)." In contrast. deBruijne(1999) preferred not to include BD+26 730 in their list of Hyades member stars following the conclusions of a study based on the convergent-point method.," In contrast, \cite{deb99} preferred not to include $+$ 26 730 in their list of Hyades member stars following the conclusions of a study based on the convergent-point method." It is also worth mentioning two further pieces of evidence that were not included in the studies mentioned above., It is also worth mentioning two further pieces of evidence that were not included in the studies mentioned above. One is the metal content of BD+26 730., One is the metal content of $+$ 26 730. As discussed in Sect. 2..," As discussed in Sect. \ref{sec:obs}," we have reliably determined the metallicity of this star and obtained a value of [Fe/H]=0.03+ 0.09., we have reliably determined the metallicity of this star and obtained a value of $=0.03\pm0.09$ . This is in reasonably good agreement with the Hyades metallicity of [Fe/H]=0.14+0.05 as determined by Perrymanetal.(1998)., This is in reasonably good agreement with the Hyades metallicity of $=0.14\pm0.05$ as determined by \cite{per98}. . The result is not conclusive. however. because the mean metallicity of field stars is of |Fe/H]=-—0.14+40.19 (Nordstrómm et al.," The result is not conclusive, however, because the mean metallicity of field stars is of $=-0.14\pm0.19$ (Nordströmm et al." 2004)., 2004). The other important point is the detection of lithium in the spectrum of BD+26 730 by BarradoyNavascués&Stauffer(1996).. which clearly favours a relatively young age for this object. and in agreement with the rest of the Hyades members studied.," The other important point is the detection of lithium in the spectrum of $+$ 26 730 by \cite{bar96}, which clearly favours a relatively young age for this object, and in agreement with the rest of the Hyades members studied." It has been often mentioned that there is a spatially unbound group of stars in the solar neighbourhood with the same kinematies as the Hyades open cluster (Eggen et al., It has been often mentioned that there is a spatially unbound group of stars in the solar neighbourhood with the same kinematics as the Hyades open cluster (Eggen et al. 1993b: Perryman et al., 1993b; Perryman et al. 1998)., 1998). This group of stars is called the Hyades stream or Hyades supercluster., This group of stars is called the Hyades stream or Hyades supercluster. Chereuletal.(1999) mapped the density-velocity inhomogeneities of an absolute magnitude limited sample of A-F type dwarfs., \cite{che99} mapped the density-velocity inhomogeneities of an absolute magnitude limited sample of A–F type dwarfs. Three different clumps within the Hyades stream were distinguished. each one of them with characteristic space velocities. which are given in Table 4..," Three different clumps within the Hyades stream were distinguished, each one of them with characteristic space velocities, which are given in Table \ref{tab:vel}." The authors also claimed that the Hyades stream contains probably three groups of 0.5-0.6 Gyr. | Gyr and 1.6-2 Gyr. which are in an advanced stage of dispersion in the same velocity volume.," The authors also claimed that the Hyades stream contains probably three groups of 0.5–0.6 Gyr, 1 Gyr and 1.6–2 Gyr, which are in an advanced stage of dispersion in the same velocity volume." Each stream presents a characteristic age distribution. although the velocity separation does not produce aclear age separation.,"Each stream presents a characteristic age distribution, although the velocity separation does not produce a clear age separation." In Table 4. we provide the radial and space velocities of BD+26 730 and WD0433+270., In Table \ref{tab:vel} we provide the radial and space velocities of $+$ 26 730 and $+$ 270. We also give the kinematic properties of the Hyades open cluster (OCI and of each clump within the stream according to Chereuletal.(1999) (called SCI 1. 2 and 3 by these authors).," We also give the kinematic properties of the Hyades open cluster (OCl) and of each clump within the stream according to \cite{che99} (called SCl 1, 2 and 3 by these authors)." The recent spatial velocities of the Hyades stream calculated by Famaeyetal.(2005) are also listed., The recent spatial velocities of the Hyades stream calculated by \cite{fam05} are also listed. As can be seen. both members of the common proper motion pair have velocities compatible with those of the Hyades open cluster and are somewhat different from the velocities characteristic of the Hyades stream or the clumps within the stream.," As can be seen, both members of the common proper motion pair have velocities compatible with those of the Hyades open cluster and are somewhat different from the velocities characteristic of the Hyades stream or the clumps within the stream." From the kinematic. considerations made here. together with the lithium detection in BD+26 730. we favour the hypothesis that the common proper motion pair studied here is indeed linked with the Hyades cluster evolution-wise.," From the kinematic considerations made here, together with the lithium detection in $+$ 26 730, we favour the hypothesis that the common proper motion pair studied here is indeed linked with the Hyades cluster evolution-wise." It is certainly not a cluster member because of it location beyond the tidal radius of the cluster but it is likely a former member that has escaped., It is certainly not a cluster member because of it location beyond the tidal radius of the cluster but it is likely a former member that has escaped. If this scenario 18 correct. the components of the pair should have the age of the Hyades cluster. which was estimated to be 625+50 Myr by Perrymanetal. (1998).," If this scenario is correct, the components of the pair should have the age of the Hyades cluster, which was estimated to be $625\pm50$ Myr by \cite{per98}." . However. we do not have conclusive evidence supporting this evolutionary link and thereforethe," However, we do not have conclusive evidence supporting this evolutionary link and thereforethe" The mechamisin of formation of massive stars remade one of the open questions in the feld of star formation.,The mechanism of formation of massive stars remains one of the open questions in the field of star formation. It is known that these stars originate inside massive molecular clouds but the sequence of processes that take place during the formation of the star are mostly uukuown., It is known that these stars originate inside massive molecular clouds but the sequence of processes that take place during the formation of the star are mostly unknown. It has been sugeested. for example. that the coalescence of various protostars m the same cloud can lead to the emergence of a μιαςνο star (0.8. Bounell. Bate. Zinnecker 1998).," It has been suggested, for example, that the coalescence of various protostars in the same cloud can lead to the emergence of a massive star (e.g. Bonnell, Bate, Zinnecker 1998)." Massive stars appear in massive stellar associations where cloud Yagnientation seenis to be common., Massive stars appear in massive stellar associations where cloud fragmentation seems to be common. Alternatively. a dnassive star could form bv the collapse of the core of a massive cloud. with associated episodes of mass accretion and ejection. as observed in low-mass stars (c.g. Shu. Adams Lizauo 1987).," Alternatively, a massive star could form by the collapse of the core of a massive cloud, with associated episodes of mass accretion and ejection, as observed in low-mass stars (e.g. Shu, Adams Lizano 1987)." Tn such a case. the effects of jets propagating through the medium that surrounds the protostar should be detectable.," In such a case, the effects of jets propagating through the medium that surrounds the protostar should be detectable." Recently. Garay et al. (," Recently, Garay et al. (" 2003) have detected: a triple radio contimun source associated with the protostar IRAS 1217.,2003) have detected a triple radio continuum source associated with the protostar IRAS $-$ 4247. The radio source presents a linear structure consisting of a thermal core. aud two radio lobes.," The radio source presents a linear structure consisting of a thermal core, and two radio lobes." The southern lobe is clearly non-thermal. indicating the presence of relativistic electrons that produce the observed radiation by svuchrotron mechanism.," The southern lobe is clearly non-thermal, indicating the presence of relativistic electrons that produce the observed radiation by synchrotron mechanism." This non-thermal source has been interpreted by Caray et al. (, This non-thermal source has been interpreted by Garay et al. ( 2003) as the termination poiut of one of the jets ejected by the protostar.,2003) as the termination point of one of the jets ejected by the protostar. There. a stroug shock would accelerate the clectrous up to relativistic energies bv Feri mechanism (e.g. Bell 1978).," There, a strong shock would accelerate the electrons up to relativistic energies by Fermi mechanism (e.g. Bell 1978)." " The observed spectral iudex of a~0.6 (S,x vw) ds in good agreement with what is expected from an uncooled population of relativistic electrons produced by diffusive shock acceleration at a strong relativistic shock (c.g. Protheroe 1999).", The observed spectral index of $\alpha\sim -0.6$ $S_{\nu}\propto\nu^{\alpha}$ ) is in good agreement with what is expected from an uncooled population of relativistic electrons produced by diffusive shock acceleration at a strong non-relativistic shock (e.g. Protheroe 1999). The aneular separation of the nou-thermal source frou the core corresponds to a linear distance of only 0.11 pc. aud then the population of relativistic particles is oeside the molecular cloud.," The angular separation of the non-thermal source from the core corresponds to a linear distance of only 0.14 pc, and then the population of relativistic particles is inside the molecular cloud." Houce. these particles are iu a vich cuviroument. with a high censity of aubicut matter uid photon field from the infrared cussion of the cloud.," Hence, these particles are in a rich environment, with a high density of ambient matter and photon field from the infrared emission of the cloud." Tuverse Compton (IC) aud relativistic Dromisstralilung losses are then unavoidable for these particles., Inverse Compton (IC) and relativistic Bremsstrahlung losses are then unavoidable for these particles. If protons are accelerated at the teriunuation shock along with the electrons. then inelastic pp collisions cau take place. xoduceiueg pious. which will decay πιο eiuiuuia-ravs.4. relativistic olectrou-positron pairs and neutrinos.," If protons are accelerated at the termination shock along with the electrons, then inelastic $pp$ collisions can take place, producing pions, which will decay yielding gamma-rays, relativistic electron-positron pairs and neutrinos." Th5 radiation produced via all these iiechanisuis will be likely steady at scales of vears due to the dviuuical timescales of the processes occuring at the source., The radiation produced via all these mechanisms will be likely steady at scales of years due to the dynamical timescales of the processes occurring at the source. The main goal of the preseut paper is to estimate he ligh-enerey vield of all these interactions. both eptonic aud hadronic. in order to ponder whether eamiunua-rav astronomy can be used to probe the massive star ornation and the outflows it could produce.," The main goal of the present paper is to estimate the high-energy yield of all these interactions, both leptonic and hadronic, in order to ponder whether gamma-ray astronomy can be used to probe the massive star formation and the outflows it could produce." Till now. herimal racio aud X-ray emission lias been associated witli he formation of low-mass stars.," Till now, thermal radio and X-ray emission has been associated with the formation of low-mass stars." Here we will show that hassive protostars can produce a sienificaut amount of radiation iu the ezunia-ray domain. because of the dense aud rich iuiedimiu iu which they are formed.," Here we will show that massive protostars can produce a significant amount of radiation in the gamma-ray domain, because of the dense and rich medium in which they are formed." The structure of the paper is as follows., The structure of the paper is as follows. " Iu the jiext section we provide the basic information about IRAS 1217. the assoclatedradio sources, ancl he ambient mediun."," In the next section we provide the basic information about IRAS $-$ 4247, the associatedradio sources, and the ambient medium." Then. in Section ?? we diseuss he particle acceleration and the different losses for he relativistic particles iu the southern lobe of the radio source.," Then, in Section \ref{loss} we discuss the particle acceleration and the different losses for the relativistic particles in the southern lobe of the radio source." Section ?? deals with the oe@amuna-ray xoducetion., Section \ref{gamma} deals with the gamma-ray production. Our results are there presented iu the form of spectral energy. distributions (SEDs). for different sets of paraueters.," Our results are there presented in the form of spectral energy distributions (SEDs), for different sets of parameters." We close with a brief discussion and a ΜΙΑΝ πι οσο ?7?.., We close with a brief discussion and a summary in Section \ref{disc}. The source IRAS 1217 corresponds to a vounug massive star-forming region. associated with an O-tvpe protostar. located at 2.9 kpe (Carav ot al.," The source IRAS $-$ 4247 corresponds to a young massive star-forming region, associated with an O-type protostar, located at 2.9 kpc (Garay et al." 2003)., 2003). The luminosity of the source is L—62«101L.zm21 eyeo Ἐν peaking at the infrared. which makes of it," The luminosity of the source is $L \sim 6.2\times 10^{4} L_{\odot}\approx 2.4 \times 10^{38}$ erg $^{-1}$ , peaking at the infrared, which makes of it" , This latter case motivates an alternative strateev. which recognises that the mareinal error is dominated uot by the curvature of the likelihood in the parameter directions. but by the curvature along the principal axis of the [Hessian matrix with the smallest cigeuvalic.,"This latter case motivates an alternative strategy, which recognises that the marginal error is dominated not by the curvature of the likelihood in the parameter directions, but by the curvature along the principal axis of the Hessian matrix with the smallest eigenvalue." " Figure 2 shows how various strategies fare with a simultaneous estimation of the amplitude of clustering A aud the redshift distortion parameter 3, ina simulation of the PSCz ealaxy redshift survey."," Figure 2 shows how various strategies fare with a simultaneous estimation of the amplitude of clustering $\Delta$ and the redshift distortion parameter $\beta$, in a simulation of the PSCz galaxy redshift survey." The top left panel shows the likelihood surface for the full set of 508 modes considered for this analysis (102v more are used in the analysis of the real survey)., The top left panel shows the likelihood surface for the full set of 508 modes considered for this analysis (many more are used in the analysis of the real survey). The uodes used. and iudeed the parameters involved. are not uuportant for the arguments here.," The modes used, and indeed the parameters involved, are not important for the arguments here." We see that i6 paralucter estimates are highly correlated., We see that the parameter estimates are highly correlated. The second pancl. top right. shows the sinele-paramcter optimisation of the first part of this paper.," The second panel, top right, shows the single-parameter optimisation of the first part of this paper." The modes are optimised for 2. and only the best 320 modes are used.," The modes are optimised for $\beta$, and only the best 320 modes are used." " We see that the conditional error in the 3 direction is not much worse than the full set. but ιο likelihood declines slowly along the ridge. and the mareinal errors ou both ο) and A have increased substantially,"," We see that the conditional error in the $\beta$ direction is not much worse than the full set, but the likelihood declines slowly along the ridge, and the marginal errors on both $\beta$ and $\Delta$ have increased substantially." Ta the pancl bottom left. the SVD procedure has been applied to the union of modes optimised for 3 and A. keeping the best 320 modes.," In the panel bottom left, the SVD procedure has been applied to the union of modes optimised for $\beta$ and $\Delta$, keeping the best 320 modes." The procedure does reasonably well. but in this case 1ο error along the ridee has increased.," The procedure does reasonably well, but in this case the error along the ridge has increased." The bottom right eraph shows the result of diagonaliziug the Fisher matrix aud optimising for the eieeuvalue along the ridge., The bottom right graph shows the result of diagonalizing the Fisher matrix and optimising for the eigenvalue along the ridge. " We see excclleut behaviour for the best 320 modes, with alinost no loss of information compared with the full set."," We see excellent behaviour for the best 320 modes, with almost no loss of information compared with the full set." This illustrative example shows row data compression nav be achieved with good results bv application of a combination of rigorous optimusation aud a helping of common seuse., This illustrative example shows how data compression may be achieved with good results by application of a combination of rigorous optimisation and a helping of common sense. We have shown that sinele-paraicter estimation by likelibood analysis can be made effiieut in the sense that we can compress the original data set to make parameter estimation tractable. aud it is optimal iu the sense that there is πο loss of information about the parameter we wish to estimate.," We have shown that single-parameter estimation by likelihood analysis can be made efficient in the sense that we can compress the original data set to make parameter estimation tractable, and it is optimal in the sense that there is no loss of information about the parameter we wish to estimate." " Our cigcumodes are ecneralised versions of the signal-to-noise ciecuimocdes., and are optimal for parameters cutering the data covariance matrix in arbitrary wavs."," Our eigenmodes are generalised versions of the signal-to-noise eigenmodes, and are optimal for parameters entering the data covariance matrix in arbitrary ways." As with all parameter estimation. this is a mocdeldependent method in the seuse that we need oulv to know the covariance matrix of the data and the assuuption of Caussianity.," As with all parameter estimation, this is a model-dependent method in the sense that we need only to know the covariance matrix of the data and the assumption of Gaussianity." However we have uot had to introduce auvthing more than the standard assuniptious of Likchhood analysis., However we have not had to introduce anything more than the standard assumptions of likelihood analysis. The dependence on the initial choice of parameter values is minimal. aud can be reduced further by iteration.," The dependence on the initial choice of parameter values is minimal, and can be reduced further by iteration." For mmauv-paraleter estimation. we have shown the effects of two aleoritlinus for optimisation.," For many-parameter estimation, we have shown the effects of two algorithms for optimisation." Optimising separately for several paraüueters by the sinele-paramcter method. and trimming the resulting dataset via an SVD step is successful in recovering the conditional likelihood crrors.," Optimising separately for several parameters by the single-parameter method, and trimming the resulting dataset via an SVD step is successful in recovering the conditional likelihood errors." " For correlated parameter estimates, a promising technique appears to be to diagonalize the Fisher matrix aud optimise for the single parameter along the likchhood ridge."," For correlated parameter estimates, a promising technique appears to be to diagonalize the Fisher matrix and optimise for the single parameter along the likelihood ridge." may occur.,may occur. LE we conservatively estimate that the peak Iuminosity during the peak of the X-ray burst is only 1/10 of the I5ddington luminosity (there is for example a factor of about 6 to 7 between the maximum and. minimum peak burst luminosities in 43U/MXD 1636-53. sec Fujimoto 11988). then the corresponding distance will be reduced by a factor of 3.," If we conservatively estimate that the peak luminosity during the peak of the X-ray burst is only 1/10 of the Eddington luminosity (there is for example a factor of about 6 to 7 between the maximum and minimum peak burst luminosities in 4U/MXB 1636-53, see Fujimoto 1988), then the corresponding distance will be reduced by a factor of 3." Vhis will lower the estimated. distance of the source to about 5 kpe., This will lower the estimated distance of the source to about 5 kpc. The 0.24821-d. period suggests that. the system is a low-mass X-ray binary (see the catalogue of X-ray binaries compiled by van Paradijs 1995)., The 0.24821-d period suggests that the system is a low-mass X-ray binary (see the catalogue of X-ray binaries compiled by van Paradijs 1995). In a low-mass system. the companion star must fill its Roche lobe to allow mass transfer to occur.," In a low-mass system, the companion star must fill its Roche lobe to allow mass transfer to occur." We show in Fie., We show in Fig. 6 the radius £j of the companion stars Roche lobe (Egeleton 1983) as a function of its mass ο lor a circular binary orbit anda 1.4 M. wimary., 6 the radius $R_{\rm h}$ of the companion star's Roche lobe (Eggleton 1983) as a function of its mass $M_2$ for a circular binary orbit anda 1.4 $_\odot$ primary. In the same diagram we also show the radii of stars in the mass range from 0.1 to 1.0 AL. derived. [rom 1ο evolutionary models given in Baralle ((1998). at ages ο. 0.1 and 10 Cyr.," In the same diagram we also show the radii of stars in the mass range from 0.1 to 1.0 $_\odot$ derived from the evolutionary models given in Baraffe (1998), at ages 0, 0.1 and 10 Gyr." " The requirement that the companion stars radius A is approximately equal to its Roche-lobe radius £2), implies Pozi0.74. ancl consequently. restricts the mass of the companion star to be below 0.7. AL. if it is a hyelrogen main-sequence star.", The requirement that the companion star's radius $R_2$ is approximately equal to its Roche-lobe radius $R_{\rm h}$ implies $R_2 \la 0.7 R_\odot$ and consequently restricts the mass of the companion star to be below 0.7 $_\odot$ if it is a hydrogen main-sequence star. Although a cillerent mass limit can be obtained for helium stars. the detection of hydrogen absorption lines ClFomsick 10998a) makes it unlikely that the companion star in RATE J2123. 058 be a helium star.," Although a different mass limit can be obtained for helium stars, the detection of hydrogen absorption lines (Tomsick 1998a) makes it unlikely that the companion star in RXTE $-$ 058 be a helium star." The actual mass is probably slightly lower than 0.7 M... as the star might have evolved olf the main-sequenee.," The actual mass is probably slightly lower than 0.7 $_\odot$, as the star might have evolved off the main-sequence." Moreover. the pre-outburst. X-ray luminosity was weak. indicating that the star uncderfilled: its Roche lobe.," Moreover, the pre-outburst X-ray luminosity was weak, indicating that the star underfilled its Roche lobe." A low-mass companion star. a distance of LO kpc and galactic coordinates of /=46°28/58.4 and 361157.37 imply that RNTE J2123 058 is an old X-ray binary in the galactic halo.," A low-mass companion star, a distance of $\sim 10$ kpc and galactic coordinates of $l = 46^{\circ} 28' 58.4''$ and $b = -36^{\circ} 11' 57.3''$ imply that RXTE $-$ 058 is an old low-mass X-ray binary in the galactic halo." "For a 0.7 M. star with an ageof about LOS10"" vr. the absolute magnitudes in the V. 2 and £ bands are AL).σε6.8. AL,c6.2 and M,zm5.7 (assuming a metal abundance ALY=0.5 and Y = 0.25) (Baralle 11998).","For a 0.7 $_\odot$ star with an ageof about $10^8 - 10^9$ yr, the absolute magnitudes in the $V$, $R$ and $I$ bands are $M_{_V} \approx 6.8$, $M_{_R} \approx 6.2$ and $M_{_I} \approx 5.7$ (assuming a metal abundance ${\rm [M/H]} = -0.5$ and Y = 0.25) (Baraffe 1998)." " Ata distance of 15 kpe. the corresponding apparent magnitudes (neglecting extinction) are nm,zc22.7. m,c22.1 and m,2 21.6."," At a distance of 15 kpc, the corresponding apparent magnitudes (neglecting extinction) are $m_{_V} \approx 22.7$, $m_{_R} \approx 22.1$ and $m_{_I} \approx 21.6$ ." " HE we take a distance of5 kpc. then the apparent magnitudes are ny.2λ 20.3. mi,%19.7 and m,zm 19.2."," If we take a distance of 5 kpc, then the apparent magnitudes are $m_{_V} \approx 20.3$ , $m_{_R} \approx 19.7$ and $m_{_I} \approx 19.2$ ." As RATE 058 is probably a halo source. the extinction," As RXTE $-$ 058 is probably a halo source, the extinction" has been made.,has been made. Our work highlights the importance of the proper consideration of the threshold of detection of [lares against the contemporaneous continuous X-ray emission., Our work highlights the importance of the proper consideration of the threshold of detection of flares against the contemporaneous continuous X-ray emission. In particular we showed that: These findings suggest a model where the steep decay is produced. by some form of activity of the internal engine which would be required to be still alive at. those. times (see however Genet&Cranot.2000. for a complementary view). while [ares could be powered by instabilities allecting the physical source. of energy. which gives origin to the steep decay.," In particular we showed that: These findings suggest a model where the steep decay is produced by some form of activity of the internal engine which would be required to be still alive at those times (see however \citealt{Genet09} for a complementary view), while flares could be powered by instabilities affecting the physical source of energy which gives origin to the steep decay." “Phis would explain the X-ray. flares erratic behaviour., This would explain the X-ray flares erratic behaviour. In this picture. the shallow decay phase would be due to a completely distinct. component of emission. which progressively hides both the steep decay and the X-ray fares as time proceeds.," In this picture, the shallow decay phase would be due to a completely distinct component of emission which progressively hides both the steep decay and the X-ray flares as time proceeds." The (L3x¢2edμι-1 has been analysed in. the context of accretion and magnetar models of GRBs., The $\langle L \rangle\propto t^{-2.7\pm0.1}$ has been analysed in the context of accretion and magnetar models of GRBs. In particular: 1n both scenarios the variability. which. is the main signature of the Daring activity. establishes as à consequence of different kinds of instabilities.," In particular: In both scenarios the variability, which is the main signature of the flaring activity, establishes as a consequence of different kinds of instabilities." In the case of accretion models. thermal. viscous or gravitational instabilities could either lead to disk breakdown or fragmentation.," In the case of accretion models, thermal, viscous or gravitational instabilities could either lead to disk breakdown or fragmentation." Our analysis constrains the mass of the accreting material to scale as mg(l)-xtuu (Iq., Our analysis constrains the mass of the accreting material to scale as $m_{f}(t)\propto t^{-1.7}$ (Eq. 7)., 7). However. the presence of magnetic Ποιος gives rise to MIA instabilities and strongly. moclilies the dynamies of accretion: the accumulation of magnetic Hux curing the accretion can repeatedly stop and. restart the accretion process (Proga&Zhang2006)).," However, the presence of magnetic fields gives rise to MRI instabilities and strongly modifies the dynamics of accretion: the accumulation of magnetic flux during the accretion can repeatedly stop and restart the accretion process \citealt{Proga06}) )." This would account for the erratic [lare emission while explaining the Oase VS. Oseep belation., This would account for the erratic flare emission while explaining the $\alpha_{\rm{flare}}$ vs. $\alpha_{\rm{steep}}$ relation. Alternatively. differentially rotating milliseconcl pulsars provide a viable mechanism where the existence of the eupae VS. Cates relation can be reasonably explained.," Alternatively, differentially rotating millisecond pulsars provide a viable mechanism where the existence of the $\alpha_{\rm{flare}}$ vs. $\alpha_{\rm{steep}}$ relation can be reasonably explained." We note that if the Dare origin is linked. to the magnetic energy. dissipation. the Ilare emission is likely to be polarised (Fanetal.2005)). while a disk fragmentation origin is likely to be accompanied by detectable gravitational wave signal (Piro&Pfhal 2007)).," We note that if the flare origin is linked to the magnetic energy dissipation, the flare emission is likely to be polarised \citealt{Fan05}) ), while a disk fragmentation origin is likely to be accompanied by detectable gravitational wave signal \citealt{Piro07}) )." Both signals will be detectable in the near future., Both signals will be detectable in the near future. Whatever the mechanism. powering the X-ray [lare emission is. it is extremely clillieult to account. for the late-time {{1000 s) flare activity cdisplavecl by some bursts using the (L9.x42 Component: exceptional circumstances leading to the revival of the instabilities would. be needed.," Whatever the mechanism powering the X-ray flare emission is, it is extremely difficult to account for the late-time $t>1000$ s) flare activity displayed by some bursts using the $\langle L \rangle \propto t^{-2.7}$ component: exceptional circumstances leading to the revival of the instabilities would be needed." An interesting possibility is ollerecl by Fig. 7:, An interesting possibility is offered by Fig. \ref{Fig:fluxratio}: while the lower edge of the distribution. of the Hux ratio is probably incomplete. this figure suggests the existence of two populations of X-ray [lares (sce also C10. their figure 13).," while the lower edge of the distribution of the flux ratio is probably incomplete, this figure suggests the existence of two populations of X-ray flares (see also C10, their figure 13)." A first population with flux contrast 5 (whieh is the one responsible for the average are and continuum behaviour of Fig. 6)), A first population with flux contrast $\sim5$ (which is the one responsible for the average flare and continuum behaviour of Fig. \ref{Fig:continuum}) ) ancl a second. population of bright Hares with a typical ZZ£F~100 but extending up to ARR~1000., and a second population of bright flares with a typical $\Delta F/F\sim 100$ but extending up to $\Delta F/F\sim 1000$. Fig., Fig. 6G directly links the X-ray Hares to the unclerlving tux., \ref{Fig:continuum} directly links the X-ray flares to the underlying flux. Lis therefore possible that at [ate times only the small fraction of Lares belonging to the second. population are able to overshine the contemporaneous shallow decay component., It is therefore possible that at late times only the small fraction of flares belonging to the second population are able to overshine the contemporaneous shallow decay component. This would explain why late time Lares are so rare., This would explain why late time flares are so rare. The detailed characterisation of the two [lare populations is beyond the scope of the present work and is left for a future study., The detailed characterisation of the two flare populations is beyond the scope of the present work and is left for a future study. Vhe authors thank the anonvmous referee for constructive criticism., The authors thank the anonymous referee for constructive criticism. RAL RBD and RS thank Chris Lindner. Todd Thompson. Francesco Pasotti for valuable discussions.," RM, RBD and RS thank Chris Lindner, Todd Thompson, Francesco Pasotti for valuable discussions." This work is supported by ASL grant SWIET 1/011/07/0. by the Ministry of University and Research of Italy. (PRIN ΔΙ 2007LNYZXL). by NLAE and bv the Universitv of Milano Aicocca. Ltaly.," This work is supported by ASI grant SWIFT I/011/07/0, by the Ministry of University and Research of Italy (PRIN MIUR 2007TNYZXL), by MAE and by the University of Milano Bicocca, Italy." rajectories. the behaviour of a trajectory before it passed hrough a point was analysed to determine whether it was a first uperossing (a creation event). and. the subsequent »haviour. was analvsed to determine. the form. of∙ creation.,"trajectories, the behaviour of a trajectory before it passed through a point was analysed to determine whether it was a first upcrossing (a creation event), and the subsequent behaviour was analysed to determine the form of creation." . Both the trajectories ancl the simulations were sullicientLy sampled that this numerical problem should not allect the conclusions drawn from this work., Both the trajectories and the simulations were sufficiently sampled that this numerical problem should not affect the conclusions drawn from this work. Definingo the mergerD raction. fueCM.oy). by where zy ds 1e final redshift of the halo and Aly is the final⋅ mass οἱ⋅ the halo. we can write the normalized proportion.az of new halos created by merger as where fü(Aly) isthe average of fuosCAp.2r) over all," Defining the merger fraction, $f_{\rm merg}(M_f,z_f)$, by where $z_f$ is the final redshift of the halo and $M_f$ is the final mass of the halo, we can write the normalized proportion of new halos created by merger as where $\bar{f}_{\rm merg}(M_f)$ is the average of $f_{\rm merg}(M_f,z_f)$ over all" wough the barrier ancl thence. propagate unhindered to 1ο surface. where they are lost from the star. whilst rw remaining rellected fraction will contribute to. the establishment of ‘somewhat-stationary’ waves interior to 1 barrier.,"through the barrier and thence propagate unhindered to the surface, where they are lost from the star, whilst the remaining reflected fraction will contribute to the establishment of `somewhat-stationary' waves interior to the barrier." Within the acliabatic approximation. these waves must decay exponentially in amplitude with time to compensate for the the energy lost through leakage. but will 4.still exhibit a cliserete eigenfrequeney spectrum.," Within the adiabatic approximation, these waves must decay exponentially in amplitude with time to compensate for the the energy lost through leakage, but will still exhibit a discrete eigenfrequency spectrum." Shibahashi Osaki (7). when considering a similar situation [or high-frequeney g2mocdes in evolved earlv-tvpe stars. drew a useful analogy with virtual levels in the potential problem. of quantum mechanics: therefore. it seems appropriate to refer to such partially-trappecl waves as.," Shibahashi Osaki \shortcite{ShiOsa1976}, when considering a similar situation for high-frequency $g$ -modes in evolved early-type stars, drew a useful analogy with virtual levels in the potential problem of quantum mechanics; therefore, it seems appropriate to refer to such partially-trapped waves as." modes. Whether virtual modes can actually be selfexcited in a star depends on the balance between the input of vibrational energy. [rom a suitable driving mechanism. and the loss of vibrational energy. associated with the leakage: non-adiabatie calculations are required to answer such a questions.," Whether virtual modes can actually be self-excited in a star depends on the balance between the input of vibrational energy from a suitable driving mechanism, and the loss of vibrational energy associated with the leakage; non-adiabatic calculations are required to answer such a questions." " The trapping cut-oll frequency ay. which separates the leaking virtual mocles from. the Lully-trappecl ""traditional niodes. is given by the smaller root of the dispersion relation (13)) at the stellar surface. namely where # ds the stellar radius."," The trapping cut-off frequency $\omegat$, which separates the leaking virtual modes from the fully-trapped `traditional' modes, is given by the smaller root of the dispersion relation \ref{eqn:dispersion2}) ) at the stellar surface, namely where $R$ is the stellar radius." " “Phis expression demonstrates the pivotal rólle of the cllective transverse waventunber A, discussed. at the end of the preceding section. in determining the trapping condition at the surface."," This expression demonstrates the pivotal rôlle of the effective transverse wavenumber $\ktr$, discussed at the end of the preceding section, in determining the trapping condition at the surface." " In the non-rotating context. Ay, can be eliminated from this expression through use of equation (14)) to give for O=0."," In the non-rotating context, $\ktr$ can be eliminated from this expression through use of equation \ref{eqn:transverse2}) ) to give for $\Omega = 0$." " When the effects. of rotation are included. the more general expression (12)) for Zi, must be used in evaluating the sign of A using the dispersion relation (13))."," When the effects of rotation are included, the more general expression \ref{eqn:transverse1}) ) for $\ktr$ must be used in evaluating the sign of $k_{r}^{2}$ using the dispersion relation \ref{eqn:dispersion2}) )." However. propagation diagrams may be constructed. and. interpreted in exactly the same manner as the non-rotating case.," However, propagation diagrams may be constructed and interpreted in exactly the same manner as the non-rotating case." " Figure 2. shows the propagation diagram for the TAL: stellar moclel considered. previously. but with rotation included at an angular [requenev Q=80410""rads* which is half of the critical rotation rate for the star. ancl corresponds to a period of 21.7 hours."," Figure \ref{fig:propdiag2} shows the propagation diagram for the $7\,\msun$ stellar model considered previously, but with rotation included at an angular frequency $\Omega = 8.04 \times 10^{-5}\,{\rmn rad\ s^{-1}}$, which is half of the critical rotation rate for the star, and corresponds to a period of 21.7 hours." The effects of the rotation on the squilibrium stellar structure having been neglected., The effects of the rotation on the equilibrium stellar structure having been neglected. " Calculation of the eigenvalue. Ay, in equation (12)). for cach frequency. ordinate value in the (log2:057) plane. was accomplished using Townsend's. (?) implementation of the matrix eigenvalue. method. presented. by Lee Saio (?).."," Calculation of the eigenvalue $\llm$ in equation \ref{eqn:transverse1}) ), for each frequency ordinate value in the $(\log T, \omega^{2})$ plane, was accomplished using Townsend's \shortcite{Tow1997} implementation of the matrix eigenvalue method presented by Lee Saio \shortcite{LeeSai1990}." This method corresponds to the spectral expansion of Ilough functions in à truncated series of associated Legendre polynomials of the same azimuthal order m: 100 expansion terms were used throughout the calculations. a value deemed to provide sullicient accuracy since a similar calculation with 200 terms produced no numerical change in the results.," This method corresponds to the spectral expansion of Hough functions in a truncated series of associated Legendre polynomials of the same azimuthal order $m$; 100 expansion terms were used throughout the calculations, a value deemed to provide sufficient accuracy since a similar calculation with 200 terms produced no numerical change in the results." An azimuthal order n=1 was adopted. so fig.," An azimuthal order $m=-1$ was adopted, so fig." 2. should be taken as appropriate for modes with (m)=(4.1).," \ref{fig:propdiag2} should be taken as appropriate for modes with $(l,m)=(4,-1)$." " Inspection of this figure shows that the trapping cut- is significantly larger (a7zSO«10""rad?s7) than in the non-rotating case."," Inspection of this figure shows that the trapping cut-off is significantly larger $\omegat^{2} \approx 8.0 \times 10^{-9}\,{\rmn rad^{2}\ s^{-2}}$ ) than in the non-rotating case." " This is a direct consequence of the influence of rotation on A: at low frequencies. where ωκBOL 1. and Ay, can assume laree values. as discussed in the preceding section."," This is a direct consequence of the influence of rotation on $\ktr$; at low frequencies where $\omega < 2\Omega$, $\nu > 1$, and $\ktr$ can assume large values, as discussed in the preceding section." The appropriate expression for ay in rotating stars is given by although this should. be regarded: as formal. since it must be remembered that Ap; is itself a function. of w through its dependence on the parameter v.," The appropriate expression for $\omegat$ in rotating stars is given by although this should be regarded as formal, since it must be remembered that $\llm$ is itself a function of $\omega$ through its dependence on the parameter $\nu$ ." However. in the limi zrE2fat the surface). this expression will have solutions corresponding to v3»1. and thus the asymptotic expressions (16..18 ) found. previously may be used in the place of the general expression. (19)) for Ai.," However, in the limit $\Omega^{2} \gg \sound^{2}/r^{2}$(at the surface), this expression will have solutions corresponding to $\nu \gg 1$, and thus the asymptotic expressions \ref{eqn:transverse4}, \ref{eqn:transverse5}) ) found previously may be used in the place of the general expression \ref{eqn:trapping1}) ) for $\ktr$ ." Solving the resulting equations for oi then gives for OFc»ον., Solving the resulting equations for $\omegat$ then gives for $\Omega^{2} \gg \sound^{2}/r^{2}$. " Applying the middle expression to the TAL: model for Q—S0410""radsland efr=9.7610""s Lat the surface. leads to the asymptotic value o7=745510""rad?s7 [or (Fm)=(4.1) modes. which is in reasonably good agreement with the value 100""radps57 shown in ⋠⋅fig."," Applying the middle expression to the $7\,\msun$ model for $\Omega = 8.04 \times 10^{-5}\,{\rmn rad\ s^{-1}}$, and $\sound/r = 9.76 \times 10^{-6}\,{\rmn s^{-1}}$ at the surface, leads to the asymptotic value $\omegat^{2} = 7.85 \times 10^{-9}\,{\rmn rad^{2}\ s^{-2}}$ for $(l,m)=(4,-1)$ modes, which is in reasonably good agreement with the value $\omegat^{2} \approx 8.0 \times 10^{-9} {\rmn rad^{2}\ s^{-2}}$ shown in fig. \ref{fig:propdiag2}." The above expressions. when compared with equation (20)). demonstrate that the elect of rotation is to Increase )0 trapping cut-olf zy for all but the prograce sectoral modes: these latter modes. will exhibit a smaller. cut-oll in rotating stars than in the non-rotating case. due to rely transformation into Ixelvin waves discussed previously.," The above expressions, when compared with equation \ref{eqn:trapping2}) ), demonstrate that the effect of rotation is to increase the trapping cut-off $\omegat$ for all but the prograde sectoral modes; these latter modes will exhibit a smaller cut-off in rotating stars than in the non-rotating case, due to their transformation into Kelvin waves discussed previously." ‘This result is interesting in light of anecdotal observational evidence favouring prograde sectoral modes as the source of »eriodic line-profile variations in rapiclly-rotating early-type stars., This result is interesting in light of anecdotal observational evidence favouring prograde sectoral modes as the source of periodic line-profile variations in rapidly-rotating early-type stars. If such evidence can be substantiated at a quantitative evel. as has been done by Llowarth shortcitellow1998 [or the. rapidlv-rotating pulsators 993521 and 664760. then it can be suggested. that the bias towards. prograde sectoral modes is due to the suppression of other twpes of mode. which will have a large values of a) at rapid rotation rates and therefore preferentially leak from the star without self-excitation.," If such evidence can be substantiated at a quantitative level, as has been done by Howarth \\shortcite{How1998} for the rapidly-rotating pulsators 93521 and 64760, then it can be suggested that the bias towards prograde sectoral modes is due to the suppression of other types of mode, which will have a large values of $\omegat$ at rapid rotation rates and therefore preferentially leak from the star without self-excitation." " In addition to its influence on the trapping cut-olf frequency ay. rotation modifics the cigenfrequencics and eigenfunctions of individual modes through its influence on the positions of trapping boundaries: thiscan be anticipated. [rom the appearance of Àj, in the pulsation equations (3- 4))."," In addition to its influence on the trapping cut-off frequency $\omegat$, rotation modifies the eigenfrequencies and eigenfunctions of individual modes through its influence on the positions of trapping boundaries; thiscan be anticipated from the appearance of $\llm$ in the pulsation equations \ref{eqn:pulsation1}- \ref{eqn:pulsation2}) )." To, To process.,process. Skibo & Ramaty (1993) estimate that the former process dominatesAlthough in the 5-rav band. we restrict. our to the LC mechanism only.," Although Skibo & Ramaty (1993) estimate that the former process dominates in the $\gamma$ -ray band, we restrict our investigation to the IC mechanism only." This is because IC calculationsinvestigation are subject to smaller , This is because IC calculations are subject to smaller uncertainties. But one should note that the total contribution of the ELE ealaxiesuncertainties. to the CRB likely exeeeds the figures obtained in the paper., But one should note that the total contribution of the FIR galaxies to the GRB likely exceeds the figures obtained in the paper. 2., \sk ∋ 2. COSALIC-RAY ELECTRONS IN FIR GALAXIES The dominant of radio emission in galaxies is radiation by cosmiccomponent rav. electrons moving in the magnetic fieldsvnchrotron which fills the interstellar space., COSMIC-RAY ELECTRONS IN FIR GALAXIES \ssk ∋ The dominant component of radio emission in galaxies is synchrotron radiation by cosmic ray electrons moving in the magnetic field which fills the interstellar space. " 1 the electron energy. spectrum has the power law form: ΑΟ)Α.Ο"". using standard formulae (e.g. Itvbicki & Lightman 1979) one can get: where b=D5uG (OB is the strength of field). vo is radiation [requenev in CGllz and we have put p=2.5."," If the electron energy spectrum has the power law form: $N(E) = N_{\circ} E^{-p}$, using standard formulae (e.g. Rybicki & Lightman 1979) one can get: where $b=B/5\mu{\rm G}$ (B is the strength of magnetic field), $\nu_9$ is radiation frequency in GHz and we have put $p=2.5$." magnetic Galaxies with a high star formation rate (starburst galaxies) are bright in the far infrared., Galaxies with a high star formation rate (starburst galaxies) are bright in the far infrared. They are also rich in cosmic ravs. what makes them. bright radio ," They are also rich in cosmic rays, what makes them relatively bright radio sources." The observational correlation between therelatively luminosities in these two sources.domains can be fitted: using the power law approximation (Chi & Wolfendale 1990): where {ιο is a luminosity in t atv = L49ClHIz and Lyin is the luminosity (in solar units) integrated from 40 to μι. Since there is à dependence of P on Lis (Chi & Wolfendale 1990)): 2— Eq.," The observational correlation between the luminosities in these two domains can be fitted using the power law approximation (Chi & Wolfendale 1990): where $P_{1.49}$ is a luminosity in $^{-1}$ at $\nu = 1.49$ GHz and $L_{\rm FIR}$ is the luminosity (in solar units) integrated from 40 to $\mu$ m. Since there is a dependence of $B$ on $L_{\rm FIR}$ (Chi & Wolfendale 1990)): $B \sim L_{\rm FIR}^{0.125}$, Eq." Land 2 could be combined to the relationship between theLY. Lyin and the normalization of cosmic rav giveelectron distribution: These cosmic electrons. the οταν photons via. the LCprocess on the radiationrav field in the producegalaxy., 1 and 2 could be combined to give the relationship between the $L_{\rm FIR}$ and the normalization of cosmic ray electron distribution: These cosmic ray electrons produce the $\gamma$ -ray photons via the ICprocess on the radiation field in the galaxy. " In effect. the most. luminous FIR galaxies of Leu,=LOL. become also strong 5-rav sources with ⋠↔ ⊳⋅ £L23.15⋅107⇁⋆≻↴eres ⊥MeV. Dl5. Iuminositiesat10M"," In effect, the most luminous FIR galaxies of $L_{\rm FIR} =10^{12}\,L_{\odot}$ become also strong $\gamma$ -ray sources with luminosities at $10$ MeV of $L = 3.1\times 10^{38}$ $^{-1}$ $^{-1}$." eVof 3., \sk ∋ 3. THE GCAAIAIA-RAY BACKGROUND The total number of cosmic ray electrons in FIR galaxies within is the over the FIR) function and the lMpc*correspondinggiven bylocal luminosityintegral density at 10MeV. luminosityproduced. via the IC elfect by these electrons £zL4107 Alpe?)., THE GAMMA-RAY BACKGROUND \ssk ∋ The total number of cosmic ray electrons in FIR galaxies within $^3$ is given by the integral over the FIR luminosity function and the corresponding local luminosity density at 10 MeV produced via the IC effect by these electrons ${\cal L} \approx 1.4\times 10^{40}$ $^3)$. One can calculate the of the background (ARB) and GRB produced by the luminosity intensitydensity taking X-rayinto account evolutionary elfects: where denotes the density at encrey £ at recishift > and all other ZGE.z)svmbols have their usual luminos," One can calculate the intensity of the X-ray background (XRB) and GRB produced by the luminosity density taking into account evolutionary effects: where ${\cal L}(E,z)$ denotes the luminosity density at energy $E$ at redshift $z$ and all other symbols have their usual meaning." ity Evolution of the density Z7.2) meaning.results from the dependence of the CMD temperature on luminosityredshift. evolution of the FIR radiation field and the variations of the cosmic electron concentration in La," Evolution of the luminosity density ${\cal L}(E,z)$ results from the dependence of the CMB temperature on redshift, evolution of the FIR radiation field and the variations of the cosmic electron concentration in galaxies." , In Fig. we show the Lor selected: models., 1 we show the predicted background for selected models. galaxies.Crosses Fig.ldenote the background predicted.produced. by backgroundscattering of CMD. only assuming evolufion of cosmic rav electrons., Crosses denote the background produced by scattering of CMB photons only assuming of cosmic ray electrons. At 10MeV. the photonsmoclel produces roughly 0.54. of the observed background., At 10 MeV the model produces roughly 0.5 % of the observed background. However. it is likely," However, it is likely" , The formation of diffuse radio regious (radio halos or relics) detected so far in a limited uumber of clusters of galaxies seems due to large-scale shocks and turbulence associated O gravitational mereers of subclusters aud groups able to provide the necessary iugredieuts. namely. magnetic [ielc aiplification ard particle reacceleration (Tribble 1993: B‘tunelti 2001: FDita. Takizawa. Sarazin 2003).,"The formation of diffuse radio regions (radio halos or relics) detected so far in a limited number of clusters of galaxies seems due to large-scale shocks and turbulence associated to gravitational mergers of subclusters and groups able to provide the necessary ingredients, namely, magnetic field amplification and particle reacceleration (Tribble 1993; Brunetti 2001; Fujita, Takizawa, Sarazin 2003)." " Iu particular. the megaparsec-scale of racdk» halos or relies combined with the relaively short racliaive lifetimes of the electrons (~LO"" ves) steeests au iu-situ elecron reacceleration iucced by very rece itor current mereer events whose link wih diffuse racio eiuilsslon seenus to e evidencec by X-ray observatious (Markeviteh Vikblinin 200:|: Covoni 2001."," In particular, the megaparsec-scale of radio halos or relics combined with the relatively short radiative lifetimes of the electrons $\sim 10^8$ yrs) suggests an in-situ electron reacceleration induced by very recent or current merger events whose link with diffuse radio emission seems to be evidenced by X-ray observations (Markevitch Vikhlinin 2001; Govoni 2004)." " The existence of t]ese ""adio regions could be related to the origin of hard. X-ray {HAR) emisslon", The existence of these radio regions could be related to the origin of hard X-ray (HXR) emission where sinks are iuvoked.,where sinks are invoked. It is normally assmued that auv inatter imside a sink flows dustautaneouslv onto he central protostar., It is normally assumed that any matter inside a sink flows instantaneously onto the central protostar. Tere. we assmue that the mass acereted iuto a sink is deposited on au immer accretion disc (IAD) inside the sink. where it piles up until it vecolcs Lot enough that thermal ionisation couples the natter to the magnetic field.," Here, we assume that the mass accreted into a sink is deposited on an inner accretion disc (IAD) inside the sink, where it piles up until it becomes hot enough that thermal ionisation couples the matter to the magnetic field." At this juncture the MBI is activated. transporting angular momentum outwards. and thereby allowing the matter accumulated in the IAD ο spiral inwards aud outo the central protostar.," At this juncture the MRI is activated, transporting angular momentum outwards, and thereby allowing the matter accumulated in the IAD to spiral inwards and onto the central protostar." IHeuce he sink mass is divided between the central protostar (41) and its TAD (AL.weLAL ): Matter is assuued to flow from the LAD onto the protostar at a rate where the first term on the righthaud side is a low regular accetion rate that obtains at all times. and the second ter is auch higher accretion rate that obtains oulv when MBI acts to transport angular moment in the IAD.," Hence the sink mass is divided between the central protostar $M_\star$ ) and its IAD $M_{_{\rm IAD}}$ ): Matter is assumed to flow from the IAD onto the protostar at a rate where the first term on the righthand side is a low regular accetion rate that obtains at all times, and the second term is a much higher accretion rate that obtains only when MRI acts to transport angular momentum in the IAD." The IAD is presuiied to be a coutinuation of the much more extended accretion dise outside the sink. which is simulated explicitly.," The IAD is presumed to be a continuation of the much more extended accretion disc outside the sink, which is simulated explicitly." " Iu detaileddisc models (2???) the matter in the LAD couples to the maguectic field. due to thermal ionisation. once the temperature reachesa threshold of Dy, K."," In detaileddisc models \citep{Zhu09,Zhu09b,Zhu10,Zhu10b} the matter in the IAD couples to the magnetic field, due to thermal ionisation, once the temperature reachesa threshold of $T_{_{\rm MRI}}\sim 1400\,{\rm K}$ ." Using au a-parameterization (7) for the effective viscosity delivered by the MBI. ? then estimate that theaccretion rate diving au outburst is where μμ Gwlere μι Is the effective Slalsura-Suuvavey parameter (2?) for MBI viscosity).," Using an $\alpha$ -parameterization \citep{Shakura73} for the effective viscosity delivered by the MRI, \cite{Zhu10} then estimate that theaccretion rate during an outburst is where $\alpha_{_{\rm MRI}}$ (where $\alpha_{_{\rm MRI}}$ is the effective Shakura-Sunyayev parameter \citep{Shakura73} for MRI viscosity)." " 2 also find that the duration of au outburst is Ilere is the vate at which matter Hows iuto the siuk and AZ,onto the TAD.", \cite{Zhu10} also find that the duration of an outburst is Here $\dot{M}_{_{\rm IAD}}$ is the rate at which matter flows into the sink and onto the IAD. We assume that the critical temperature for the AIRT to be activated is reached when cnough mass for an IRenabled outburst has been accumulated in the TAD. i.c. Using Eqs.," We assume that the critical temperature for the MRI to be activated is reached when enough mass for an MRI-enabled outburst has been accumulated in the IAD, i.e. Using Eqs." 6 and 7 we obtain We do not mocel iu detail the thermal aud iouisatiou balance in the LAD. since this is not the main concern of this paper.," \ref{eq:mrimdot} and \ref{eq:mridt} we obtain We do not model in detail the thermal and ionisation balance in the IAD, since this is not the main concern of this paper." " Iustead. based ou observations aud models of FU Ozri-tvpe stars (22). we presume that rapid accretion outo the protostar. at a rate given by is initiated as soon as Mj, exceeds Mj: f, Is the time at which this occurs. aud the outburst teriuiinates atf Af "," Instead, based on observations and models of FU Ori-type stars \citep{Hartmann96,Zhu10}, we presume that rapid accretion onto the protostar, at a rate given by is initiated as soon as $M_{_{\rm IAD}}$ exceeds $M_{_{\rm MRI}}$; $t_{_{\rm O}}$ is the time at which this occurs, and the outburst terminates at $t_{_{\rm O}}+\Delta t_{_{\rm MRI}}$." "The time taken to accumulate (or re-accumulate) M, is At~MAUMS ie. This is wich longer than the duration of the outburst (see Eq. 7))."," The time taken to accumulate (or re-accumulate) $M_{_{\rm MRI}}$ is $\Delta t_{_{\rm ACC}} \sim M_{_{\rm MRI}}/\dot{M}_{_{\rm IAD}}$ , i.e. This is much longer than the duration of the outburst (see Eq. \ref{eq:mridt}) )." " With the above formulation the only free parameter jn usps Which controls the strength and duration of the outhirst: increasiug o4, Dies for a lore intenso. shorter outburst."," With the above formulation the only free parameter is $\alpha_{_{\rm MRI}}$, which controls the strength and duration of the outburst; increasing $\alpha_{_{\rm MRI}}$ makes for a more intense, shorter outburst." " The mass delivered im cach outburst. and the duration of the interval between outbursts. are essentially independent of «μι. Which is fortunate. in the seuse that ay), is rather uncertain."," The mass delivered in each outburst, and the duration of the interval between outbursts, are essentially independent of $\alpha_{_{\rm MRI}}$, which is fortunate, in the sense that $\alpha_{_{\rm MRI}}$ is rather uncertain." " Observations aud siuulatious suggest à,20.01to0.1 (2)...", Observations and simulations suggest $\alpha_{_{\rm MRI}}\!=\!0.01\;{\rm to}\;0.4$ \citep{King07}. " We have adopted 20.1. which is cousisteut with observations of FU Ori44, events (7?).."," We have adopted $\alpha_{_{\rm MRI}}\!=\!0.1\,$, which is consistent with observations of FU Ori events \citep{Zhu07}." To evaluate the consequences of episodic accretion for dise fraeiieutation and low-mass star formation we perform radiation hwdrodyvuanic simulations of a collapsing turbulent molecular core. with properties chosen to match the observed properties of prestellar cores (e.g. 2). ," To evaluate the consequences of episodic accretion for disc fragmentation and low-mass star formation, we perform radiation hydrodynamic simulations of a collapsing turbulent molecular core, with properties chosen to match the observed properties of prestellar cores \citep[e.g.][]{Andre00}. ." The initial deusity profile is Tere Poa=38d0Seem7 ds the central deusity. and Rog=5.000AU is the radius of the ceutral region within which the density is approximatcly uuiform.," The initial density profile is Here $\rho_{_{\rm KERNEL}}=3\times 10^{-18}\,{\rm g}\,{\rm cm}^{-3}$ is the central density, and $R_{_{\rm KERNEL}}=5,000\,{\rm AU}$ is the radius of the central region within which the density is approximately uniform." " The outer euvelope of the core extends to Roo=50000AU.so the total core mass is M,= Όντο "," The outer envelope of the core extends to $R_{_{\rm CORE}}=50,000\,{\rm AU}$,so the total core mass is $M_{_{\rm CORE}}=5.4\,{\rm M}_\odot$ ." The eas is initially isothermal at FT=lok. and heuce the initial ratio of thermal to eravitational energy IS μμ=0.2. We impose an initial raudon. divergence-free. turbulent velocity feld. with power spectrum PidkxKktdk. to match the scaling laws observed iu molecular clouds (?).. aud amplitude such that Ον=OIU—03.," The gas is initially isothermal at $T=10\,{\rm K}$, and hence the initial ratio of thermal to gravitational energy is $\alpha_{_{\rm THERM}}=0.3\,.$ We impose an initial random, divergence-free, turbulent velocity field, with power spectrum $P_kdk\propto k^{-4}dk$, to match the scaling laws observed in molecular clouds \citep{Larson81}, and amplitude such that $\alpha_{_{\rm TURB}}\equiv{U_{_{\rm TURB}}}/{|U_{_{\rm GRAV}}|}=0.3\,$." The core is assuned to ulevolve im isolation. 1.0. any interactions with its environment are ignored.," The core is assumed to evolve in isolation, i.e. any interactions with its environment are ignored." This appears to be the case in Ophiuchus. where ?. conclude that individual cores do not have time to interact with one another before evolving iuto protostars.," This appears to be the case in Ophiuchus, where \cite{Andre07} conclude that individual cores do not have time to interact with one another before evolving into protostars." Iu deuser star formation regions interactions between cores Way occur. but oulv very close eucounuters will iuflueuce disc fragmentation in scales less than a few lundred AU.," In denser star formation regions interactions between cores may occur, but only very close encounters will influence disc fragmentation in scales less than a few hundred AU." Such encounters are expected to chhance disc fragmentation (?).., Such encounters are expected to enhance disc fragmentation \citep{Thies10}. . " The molecular cloud core is represented by 109SPIT particles. so cach SPII particle has massm,~DhX 8AL.."," The molecular cloud core is represented by $10^{6}$SPH particles, so each SPH particle has mass$m_{_{\rm SPH}}\simeq 5\times 10^{-6}\,{\rm M}_\odot$ ." " The niuiumui resolvable mass is therefore MuaycmMata,mS0 TALL."," The minimum resolvable mass is therefore $M_{_{\rm MIN}}\simeq {\cal N}_{_{\rm NEIB}}m_{_{\rm SPH}}\simeq 3\times 10^{-4}\,{\rm M}_\odot$ ." " This is much sualler than the thoretical minimum mass for star formation (3410PMo usually refered to as Limit),"," This is much smaller than the thoretical minimum mass for star formation $\sim 3\times 10^{-3}\,{\rm M}_\odot$ ; usually refered to as )," amoug the differeut models that we have computed for this object.,among the different models that we have computed for this object. The dark matter mass fraction for the models computed in this paper amouuts to aboutLOY%.. part could be barvouic (substellar) aud part uon barvonic.," The dark matter mass fraction for the models computed in this paper amounts to about, part could be baryonic (substellar) and part non baryonic." This result iuplies that AM; is smaller than about and that the mass fraction of nou barvonic dark matter mide the Iohuberg radius is also smaller than about10546., This result implies that $M_{sub}$ is smaller than about and that the mass fraction of non baryonic dark matter inside the Holmberg radius is also smaller than about. ". For r= Lash. the p value derived elobular clusters. it follows that for the typical nreeular galaxy Afi,=26.6 aud AL,=13.6 inside Ry."," For $r = 1.85$ , the $r$ value derived globular clusters, it follows that for the typical irregular galaxy $M_{sub} = 26.6$ and $M_{nb} = 13.6$ inside $R_H$." By comparing bursting SFR models with coutinuous SER anocdels of the same age the differences in the final abundance ratios are very snall., By comparing bursting SFR models with continuous SFR models of the same age the differences in the final abundance ratios are very small. Consequently. it can be said that the shape of the SFR doesnot affect the," Consequently, it can be said that the shape of the SFR doesnot affect the" which the derivatives are computed to reduce noise.,which the derivatives are computed to reduce noise. The smallest. resolvable separation between neighbouring spot features appearing in a sineleo line profile is roughlyo 5 pixels (Vig. 3)).," The smallest resolvable separation between neighbouring spot features appearing in a single line profile is roughly 5 pixels (Fig. \ref{fig:minsep}) )," which suggestsὃν that a two-pixel ollsct is optimal in this respect., which suggests that a two-pixel offset is optimal in this respect. We treat the matched filter in the same wav: lere. fi; is the contribution of the gaussian matched filter to the ith pixel of the jth profile in the time-series. which spans the velocity range from v;peo toe; pes: The scale factor Wis then computed from these derivative maps via the optimal scaling:llere στ; is the variance associated with the data point Sj. SO Note that the scale factor. V. is the equivalent width in velocity units of the starspot bump that would be seen in the deconvolved. profile if the spot were observed at. the centre of the stellar cise. and so is expressed in kin 1," We treat the matched filter in the same way: Here $f_{i,j}$ is the contribution of the gaussian matched filter to the $i$ th pixel of the $j$ th profile in the time-series, which spans the velocity range from $v_{i-1/2}$ to $v_{i+1/2}$: The scale factor $\hat{W}$ is then computed from these second-derivative maps via the optimal scaling:Here $\sigma^{2}_{i,j}$ is the variance associated with the data point $s_{i,j}$, so Note that the scale factor $\hat{W}$ is the equivalent width in velocity units of the starspot bump that would be seen in the deconvolved profile if the spot were observed at the centre of the stellar disc, and so is expressed in km $^{-1}$." The optimal fitting procedure determines both. Wo and the associated badness-of-fit statistic [or a given set of matched-filter parameters (oO.IN.€0).," The optimal fitting procedure determines both $\hat{W}$ and the associated badness-of-fit statistic for a given set of matched-filter parameters $(\phi,K,\Omega)$." To identify spot signatures and. measure their parameters. we construct a sequence of maps on a (Có.A) grid. for a range of rotation periods P?=22/0.," To identify spot signatures and measure their parameters, we construct a sequence of maps on a $(\phi,K)$ grid, for a range of rotation periods $P=2\pi/\Omega$." The sequence maps is stacked to form a data cube. We(Oo.N.O) or ΑλίotÓ.IN.)) which is then searched for local maxima in all three dimensions.," The sequence of maps is stacked to form a data cube, $\hat{W}(\phi,K,\Omega)$ or $\Delta\chi^2(\phi,K,\Omega)$ which is then searched for local maxima in all three dimensions." Lnevitably some of the weaker local maxima are noise features. so it is necessary to impose a eutoll on WW. spuriousCor better. on 2) below which candidate spots are rejected as being probable noise features.," Inevitably some of the weaker local maxima are spurious noise features, so it is necessary to impose a cutoff on $\hat{W}$ (or better, on $\Delta\chi^{2}$ ) below which candidate spots are rejected as being probable noise features." An appropriate cutoll is found by computing the (Ó.IN) maps over a range of AV values somewhat greater than the stellar esin7. and tuning the eutolf to reject all features with Aesin/.," An appropriate cutoff is found by computing the $(\phi,K)$ maps over a range of $K$ values somewhat greater than the stellar $v\sin i$, and tuning the cutoff to reject all features with $K > v\sin i$." Note also [rom Fig., Note also from Fig. 2 that σου repeated: phase coverage was obtained on at least 3 of the 4 nights only for features INcentre of the line profile in the phase range [rom 0.1 “rosin)to LL)., \ref{fig:dyndecon96} that good repeated phase coverage was obtained on at least 3 of the 4 nights only for features crossing the centre of the line profile in the phase range from 0.50 to 1.00. The search was therefore restricted to this phase range., The search was therefore restricted to this phase range. This viclded the list of candidate spots in Table 1.., This yielded the list of candidate spots in Table \ref{tab:spotpar}. The parameter values are Listecl together with their formal le errors. derived. using and similarly for ó and. P.," The parameter values are listed together with their formal $1\sigma$ errors, derived using and similarly for $\phi$ and $P$." Phe le errors on the spot velocity amplitude and period are consistent with the values expected. from simple considerations: if the radial velocity of a spot bump can be determined to a precision of order 0.1 pixel (300 nis ly the uncertainty in the time at which it crosses the observer's moeridian is of order 20s.," The $1\sigma$ errors on the spot velocity amplitude and period are consistent with the values expected from simple considerations: if the radial velocity of a spot bump can be determined to a precision of order 0.1 pixel (300 m $^{-1}$ ), the uncertainty in the time at which it crosses the observer's meridian is of order 20s." Over a 6-dav. (12-rotation) baseline. this gives an uncertainty of about 0.00003 day in the period determination.," Over a 6-day (12-rotation) baseline, this gives an uncertainty of about 0.00003 day in the period determination." Determining the racial acceleration and hence A involves measuring the change in spot velocity over the course of roughly. one-sixth of the rotation evele. which again involves velocity and timing measurements that are uncertain at the Ol kms! ancl 20s levels respectively.," Determining the radial acceleration – and hence $K$ – involves measuring the change in spot velocity over the course of roughly one-sixth of the rotation cycle, which again involves velocity and timing measurements that are uncertain at the 0.1 km $^{-1}$ and 20s levels respectively." The resulting uncertainty in A ought therefore to be of order 0.1 to 0.2 kms + for a well- spot., The resulting uncertainty in $K$ ought therefore to be of order 0.1 to 0.2 km $^{-1}$ for a well-observed spot. We explored. the elfects. of possible errors. in the limb-darkening cocllicient by repeating the matcehed-filter analysis using a more solar-like «=0.6 rather than ΕΞ0.77., We explored the effects of possible errors in the limb-darkening coefficient by repeating the matched-filter analysis using a more solar-like $u=0.6$ rather than $u=0.77$. Given that the time-averagecl spectrum is subtraceck prior to deconvolution. the principal elfect of decreasing he limb-darkening coellicient is to decrease the contrast between the strength of a spot signature viewed at the centre of the disc and near the stellar limb.," Given that the time-averaged spectrum is subtracted prior to deconvolution, the principal effect of decreasing the limb-darkening coefficient is to decrease the contrast between the strength of a spot signature viewed at the centre of the disc and near the stellar limb." As expected. we found that the lower value of η vielded a slightlv. poorer fit to the data.," As expected, we found that the lower value of $u$ yielded a slightly poorer fit to the data." The velocity amplitudes and rotations periods of individual spots were found. however. to be nearly identical (to within the 1-0 error limits) for both values of wv.," The velocity amplitudes and rotations periods of individual spots were found, however, to be nearly identical (to within the $\sigma$ error limits) for both values of $u$ ." This confirms that the results are insensitive to any error in the adopted value of the limb-darkening coelIicient., This confirms that the results are insensitive to any error in the adopted value of the limb-darkening coefficient. As was mentioned in Section 3.2 above. the equivalent width of a spot bump is related to the area of the spot.," As was mentioned in Section \ref{sec:matchfilt} above, the equivalent width of a spot bump is related to the area of the spot." "transitions from 211-365 GHz to find = K and log[n((Ha)) = for the emitting material, while Dickel&Goss suggest that the absorption likely (1987)arises from material of density ~ assuming a temperature of 60 K based on the work of Guilloteauetal. (1983).","transitions from 211–365 GHz to find = K and )] = for the emitting material, while \citet{DG87} suggest that the absorption likely arises from material of density $\sim$ assuming a temperature of 60 K based on the work of \citet{GSD83}." . They note that 60 K likely represents an upper limit to the temperature of the absorption region and also test 40 K to demonstrate the temperature dependency of their procedure., They note that 60 K likely represents an upper limit to the temperature of the absorption region and also test 40 K to demonstrate the temperature dependency of their procedure. " 3A and 3B areClass 0 sources separated by 6"" that share a common envelope in a potential protobinary system (Barsonyetal. of which 3B dominates at mm wavelengths (Terebey1998),,&Padgett1997)."," 3A and 3B areClass 0 sources separated by $\arcsec$ that share a common envelope in a potential protobinary system \citep{Bar98}, of which 3B dominates at mm wavelengths \citep{TP97}." ". and observations by Volgenauetal.(2006) indicate a systemic velocity between 3.4-5.8s',, consistent with our observation = 4.8 "," and observations by \citet{Volg06} indicate a systemic velocity between 3.4–5.8, consistent with our observation = 4.8 )." The transition was not detected., The transition was not detected. (Vrgn Maretst)).(2004) employed LVG modeling of several transitions from 141-364 GHz to find = 90 K and n((H2)) = e, \citet{Maret04} employed LVG modeling of several transitions from 141–364 GHz to find = 90 K and ) = . "m?.. Premier examples of embedded, low mass star formation."," Premier examples of embedded, low mass star formation." " Separated by ~ 30"", 4A and B are the brightest of three sources in the IRAS 4 core (Sandelletal.1991) and each have independently been resolved into binary systems (Looney1998;Looneyetal.2000)."," Separated by $\sim$ $\arcsec$, 4A and B are the brightest of three sources in the IRAS 4 core \citep{Sand91} and each have independently been resolved into binary systems \citep{Loon98,Loon00}." ". P Cygni profiles, indicative of infall and characterized by a blueshifted emission component and redshifted absorption, have been detected toward both cores in interferometric observations of 226 GHz) and CS (DiFrancescoetal.2001)."," P Cygni profiles, indicative of infall and characterized by a blueshifted emission component and redshifted absorption, have been detected toward both cores in interferometric observations of, 226 GHz) and CS \citep{DiF01}." ". This (312-211,,profile is eschewed in all but our observations of IRAS 4A, which indicates an absorption component at 7.5 with two emission components at ~ 7.0 being detected in both transitions."," This profile is eschewed in all but our observations of IRAS 4A, which indicates an absorption component at 7.5 with two emission components at $\sim$ 7.0 being detected in both transitions." " The broader, wing component of the emission can be attributed to outflow material."," The broader, wing component of the emission can be attributed to outflow material." " The absorption feature in the spectrum of IRAS 4A has the effect of bisecting the Gaussian profiles of both emission components, eliminating the high velocity component of the profile detected in the transition but without bringing the net J=3 profile below the baseline."," The absorption feature in the spectrum of IRAS 4A has the effect of bisecting the Gaussian profiles of both emission components, eliminating the high velocity component of the profile detected in the transition but without bringing the net $J=3$ profile below the baseline." " Because of the blending in this spectrum, the total integrated emission over the FWZI of the entire line profile for IRAS 4A has been used for our analysis with the integrated intensity from the Gaussian fit to the absorption component added to the total J=3 intensity."," Because of the blending in this spectrum, the total integrated emission over the FWZI of the entire line profile for IRAS 4A has been used for our analysis with the integrated intensity from the Gaussian fit to the absorption component added to the total $J=3$ intensity." " The observations toward IRAS 4B were well fit by single Gaussians between 6.9 and 7.1s, in agreement with the average systemic velocity of 7.0 found for the IRAS 4 group by DiFrancescoetal. (2001)."," The observations toward IRAS 4B were well fit by single Gaussians between 6.9 and 7.1, in agreement with the average systemic velocity of 7.0 found for the IRAS 4 group by \citet{DiF01}." ". However, the emission was anomalously low, resulting in a transition ratio that could not be fit by the LVG model."," However, the emission was anomalously low, resulting in a transition ratio that could not be fit by the LVG model." " Based on the aforementioned detection of absorption toward 4B within the velocity range over which our emission was observed, it is possible that the J—3 emission is being subtracted by an absorption component not visually reflected in our line profile."," Based on the aforementioned detection of absorption toward 4B within the velocity range over which our emission was observed, it is possible that the $J=3$ emission is being subtracted by an absorption component not visually reflected in our line profile." This possibility is discussed in detail in refSourceSize.., This possibility is discussed in detail in \\ref{SourceSize}. " Using LVG modeling of several transitions from 141-364 GHz, Maretetal.(2004) derived the following properties: = 50 K, n((H2)) =από; = 80 K, = cm?."," Using LVG modeling of several transitions from 141–364 GHz, \citet{Maret04} derived the following properties: = 50 K, ) =; = 80 K, ) = ." . BlakeTetal.(1995) analyzed a combinationn((H2)) of (several transitions from 218-365 GHz) and CS line ratios to find = 20-40 K and n((Ha)) = for both core, \citet{Bla95} analyzed a combination of (several transitions from 218–365 GHz) and CS line ratios to find = 20–40 K and ) = for both core (the radius which contains half of the integrated light) is shown in Figure 9..,(the radius which contains half of the integrated light) is shown in Figure \ref{size-dist}. " The median H, was 2.2 ACS pixels. or 3.5 pe. which confirms that our selection procedure did indeed select mostly slightly extended objects."," The median $R_e$ was 2.2 ACS pixels, or 3.5 pc, which confirms that our selection procedure did indeed select mostly slightly extended objects." Fewer than of our candidates were flagged as “possibly stellar byISHAPE., Fewer than of our candidates were flagged as `possibly stellar' by. There is a difference in the size distributions of red and blue clusters., There is a difference in the size distributions of red and blue clusters. " The red clusters. with a median A,=4.1 pe. are slightly larger than the blue clusters. whose meclian size is 3.2 pc."," The red clusters, with a median $R_e=4.1$ pc, are slightly larger than the blue clusters, whose median size is $3.2$ pc." Dynamical studies of star cluster evolution (e.g.Gnedin&Ostriker1997). show that large clusters are more easily destroved. so we expected that the red (older) clusters would be slightly smaller on average than the blue (vounger).," Dynamical studies of star cluster evolution \citep[e.g. ][]{go97} show that large clusters are more easily destroyed, so we expected that the red (older) clusters would be slightly smaller on average than the blue (younger)." However. since the clusters are only mareinally resolved. the difference between (he two groups is not of major sienilicance and could reflect contamination of the red cluster sample by vounger clusters or galaxies.," However, since the clusters are only marginally resolved, the difference between the two groups is not of major significance and could reflect contamination of the red cluster sample by younger clusters or galaxies." " The range of blue cluster candidate sizes is similar to the range found by Larsen(1999) for ‘voune massive clusters’ ancl is also comparable to the median hall-light radius for Milky Wav globular clusters £2,=3.2 pe (larris1996)."," The range of blue cluster candidate sizes is similar to the range found by \citet{lar99} for `young massive clusters' and is also comparable to the median half-light radius for Milky Way globular clusters $R_e=3.2$ pc \citep{h96}." . We have presented (he results [rom an initial search for star clusters in Hubble Space Telescope/Advancecl Camera for Survevs images of the nearby giant spiral MIOL., We have presented the results from an initial search for star clusters in Hubble Space Telescope/Advanced Camera for Surveys images of the nearby giant spiral M101. Defining a reliable sample of cluster candidates in these complex. crowded images proved to be a challenge.," Defining a reliable sample of cluster candidates in these complex, crowded images proved to be a challenge." Our final cluster candidate list contains nearly 3000 objects of which a majority are blue ancl associated with the galaxys spiral arms., Our final cluster candidate list contains nearly 3000 objects of which a majority are blue and associated with the galaxy's spiral arms. " These cluster candidates have color distiibutions similar to candidates ancl confined clusters in other spirals including the Milky Wav. M21. ΔΙΣ, M32. and M51."," These cluster candidates have color distributions similar to candidates and confirmed clusters in other spirals including the Milky Way, M31, M81, M33, and M51." MIOL has fewer bright. red clusters than the earlier-tvpe spiral M81. but many more faint red clusters (asoriginallynotedbyChandaretal.2004).," M101 has fewer bright, red clusters than the earlier-type spiral M81, but many more faint red clusters \citep[as originally noted by][]{cwl04}." . If all of these faint red. clusters were globulars. MIOLI would have a much higher globular cluster specilic frequency aid a much different elobular cluster huminosity function from other ealaxies.," If all of these faint red clusters were globulars, M101 would have a much higher globular cluster specific frequency and a much different globular cluster luminosity function from other galaxies." We suggest that many of the red MIOLI clusters are likely to be recldened voung clusters. which is supported by the consistency of the overall cluster Iuminosity distribution and fiducial cluster densitv. wilh those found in other spirals by Larsen(2002)..," We suggest that many of the red M101 clusters are likely to be reddened young clusters, which is supported by the consistency of the overall cluster luminosity distribution and fiducial cluster density with those found in other spirals by \citet{lar02b}." The spatial distribution of the MIOL clusters shows a relatively flat core ancl a steep drop-oll al larger ealactocentrie distances. suggesting that the clusters are associated with the galaxy disk rather than its halo.," The spatial distribution of the M101 clusters shows a relatively flat core and a steep drop-off at larger galactocentric distances, suggesting that the clusters are associated with the galaxy disk rather than its halo." " The size distributions of the AILOL cluster candidates show them to be slightly resolved. as expected. and are consistent with cluster sizes measured in other galaxies,"," The size distributions of the M101 cluster candidates show them to be slightly resolved, as expected, and are consistent with cluster sizes measured in other galaxies." We conclude for the peniocde spectrum that:,We conclude for the -mode spectrum that: stellar population.,stellar population. Thus. the current observations are consistent with the idea that some cluster Es are the remuauts of cls which have been stripped of their ISM.," Thus, the current observations are consistent with the idea that some cluster dEs are the remnants of dIs which have been stripped of their ISM." Taken at [ace vaue. the derived --1641 stellar population ages iudicate that t1ο last inajor star formation episode in the Virgo «Es occurred 5-7 Gyr ago. or at 2>0.5.," Taken at face value, the derived mean stellar population ages indicate that the last major star formation episode in the Virgo dEs occurred 5-7 Gyr ago, or at $z > 0.5$." However. due to the inherent ambietuties in stellar populatjon --iocdels. it is dillicult to determine exactly |ow loug i las been siuce star formation occurred in hese galaxies.," However, due to the inherent ambiguities in stellar population models, it is difficult to determine exactly how long it has been since star formation occurred in these galaxies." For example. the observed coOrs are LO ly consistent with the tw'O burst moclels ]scussed ayove (extended. starburst ancl siort btrst jut also with a galaxy wuch has hac constant star formation rate which is abruply truncat 3 Gyr ago (2~0.3).," For example, the observed colors are not only consistent with the two burst models discussed above (extended starburst and short burst), but also with a galaxy which has had a constant star formation rate which is abruptly truncated 3 Gyr ago $z \sim 0.3$ )." Unortuuately. Virgo dwars are too distant to produce detailed sar —iation histories as is possible witlin Local CrotL2 (e.g..Skillinaretal.2003).," Unfortunately, the Virgo dwarfs are too distant to produce detailed star formation histories as is possible within the Local Group \citep[e.g.,][]{STCDSGDM03}." . Neoethieless. a oL these iuodels indicate that the Vir (Es have 1X had substantlal star formation activity wiliu the last lew Gyr.," Nonetheless, all of these models indicate that the Virgo dEs have not had substantial star formation activity within the last few Gyr." Furthe nore.je Observer [a /Fe] ratios ale soal Ors ib-solar. indicatiug that the stellar mass of the cluser dEs |as been built gradually. rather than (ough a major burst of star foriαἱlon.," Furthermore, the observed $\alpha$ /Fe] ratios are solar or sub-solar, indicating that the stellar mass of the cluster dEs has been built gradually, rather than through a major burst of star formation." Tlus. not only clo OW Tass €uster galaxies have cliTere:t structural properties than their elaut COins. their stellar populais and star formation jlsto‘ies appear to be substantially cilferent.," Thus, not only do low mass cluster galaxies have different structural properties than their giant cousins, their stellar populations and star formation histories appear to be substantially different." Wule both giant. aud dwarf iptical galaxies appear o have strong environmeutal depeuceices Ol their formation atd evoluti it is likely that low mass cluster galaxies follow cifferent evolutionary paths than their giaut. counte1parts.," While both giant and dwarf elliptical galaxies appear to have strong environmental dependences on their formation and evolution, it is likely that low mass cluster galaxies follow different evolutionary paths than their giant counterparts." For example. iueractions with the cluster potential aid the IC Limay be the key to form:ion of dEs. while galaxy-galaxy interactious may play a major role in he evolution of giaut ellipticals.," For example, interactions with the cluster potential and the ICM may be the key to formation of dEs, while galaxy-galaxy interactions may play a major role in the evolution of giant ellipticals." Since {ie early recognition of similar structural parameters between dE and cl galaxies WKormendy 1985)... it has offen been suggested that dEs cotId simply. be dls stripped of leir gas and eft to fade.," Since the early recognition of similar structural parameters between dE and dI galaxies \citep[e.g.,][]{LF83,K85}, it has often been suggested that dEs could simply be dIs stripped of their gas and left to fade." The exteusive study of the Virgo cluster resiltine in he VCC (c.f.Biteeelietal.1935:Saudage.Biunggeli.&Taminaun1955:BinMOD195T) ¢‘oul1ued the strong overia€» between tiese two populations. but led Biuggeli(1955) to couclucde that the dEs are 1 κ.ied [rom dI due to the apparent lack of a brigh progeiitor dI populatic)l ald to the presence light nuclei in a large fraction of dEs.," The extensive study of the Virgo cluster resulting in the VCC \citep[c.f.,][]{VCC,SBT85,BTS87} confirmed the strong overlap between these two populations, but led \citet{B85} to conclude that the dEs are not formed from dIs due to the apparent lack of a bright progenitor dI population and to the presence of bright nuclei in a large fraction of dEs." While Biuggeli(1955) was carefu to note that his a'2u1s applied ouvy to the brightest dEs. he argued tiat if one could not explain tje entire dE popton with stripIsine then it did not luase sense tolwoke this process since it is luelegaut to explain the well celiied sequence in L. a. TSyace with more thar Ole Plocess.," While \citet{B85} was careful to note that his arguments applied only to the brightest dEs, he argued that if one could not explain the entire dE population with stripping then it did not make sense to invoke this process since it is inelegant to explain the well defined sequence in L, $\alpha$, $\mu$ space with more than one process." Iu vaiZeeetal.(200L).. we proposed iat Virgo dEs a'e formed thr inultigle processes.," In \citet{vSH04}, we proposed that Virgo dEs are formed through multiple processes." First. it is lisely that te most massive galaxi esIear the core of the custer 1ος] wil ha coterie of satellite galaxies. whic L became dE gaaxles.," First, it is likely that the most massive galaxies near the core of the cluster formed with a coterie of satellite galaxies, which soon became dE galaxies." However. we also SLLOW the Vireo cluster is still forming today. aux field galaxies a de[n]‘oups of galaxies are falli o the cluster 1987).," However, we also know that the Virgo cluster is still forming today, and that field galaxies and groups of galaxies are falling into the cluster \citep{TS84,BTS87}." . HE tlie grou into the Vireo cluster were similar to our Local Goup. then they ikely consisted of roughly equ: mbers of dE aud dl," If the groups of galaxies that later fell into the Virgo cluster were similar to our Local Group, then they likely consisted of roughly equal numbers of dE and dI" " Arzmiln(Arf.ΔΙ.Δρ). Where: and In the previous expressions. rj Is the distance between the planets p and p’ and r,, is thedistance between the planet p and star s.","$\Delta t$ $(\Delta t_h, \Delta t_{n1}, \Delta t_{n2}) $, where: and In the previous expressions, ${\bf r}_{pp'}$ is the distance between the planets $p$ and $p'$ and ${\bf r}_{ps}$ is thedistance between the planet $p$ and star $s$." We note that throughout our simulations. the time step size is ~1/800 the binary orbital As in Paper 1. we adopt computational units 11 which the total mass of the binary is M.ΞI. the gravitational constant is G=|. and the radius r=2 in the computational domain corresponds to 5 AU.," We note that throughout our simulations, the time step size is $\sim 1/800$ the binary orbital As in Paper I, we adopt computational units in which the total mass of the binary is $M_*=1$, the gravitational constant is $G=1$, and the radius $r=2$ in the computational domain corresponds to 5 AU." " The unit of time is Q7!=JG.T.fet, where a,=0.4 is the initial semimajor axis of the binary."," The unit of time is $\Omega^{-1}=\sqrt{GM_*/a_b^3}$, where $a_b=0.4$ is the initial semimajor axis of the binary." This corresponds to an initial separation between the two stars of ~1AU. In the simulations presented here. close encounters between two planets can result in a physical collision.," This corresponds to an initial separation between the two stars of $\sim 1\;\text{AU}$ In the simulations presented here, close encounters between two planets can result in a physical collision." " Here. this is supposed to occur whenever the mutual distance dj, between planets p and p' is less than (Αμπρο)+Gn,πρ)! 2 wherep is the mass density which we assume to be the same for each planet and equal to p=3g.cm7*."," Here, this is supposed to occur whenever the mutual distance $d_{pp'}$ between planets $p$ and $p'$ is less than $(3m_p/4\pi\rho)^{1/3}+(3m_p'/4\pi\rho)^{1/3}$ , where $\rho$ is the mass density which we assume to be the same for each planet and equal to $\rho=3\; g.cm^{-3}$." " If a collision is found to occur between the planets p and p'. these are assumed to merge and are subsequently substituted by a single body with mass i),+ ΜΗ."," If a collision is found to occur between the planets $p$ and $p'$, these are assumed to merge and are subsequently substituted by a single body with mass $m_p+m_p'$ ." The position and velocity of the latter are set to the position and velocity of the centre of mass of the planets p and p’., The position and velocity of the latter are set to the position and velocity of the centre of mass of the planets $p$ and $p'$. As in Paper L the dise aspect ratio H/R is assumed to be constant and equal to H/R=0.05.," As in Paper I, the disc aspect ratio $H/R$ is assumed to be constant and equal to $H/R=0.05$." " We use also the ""alpha"" preseription of Shakura Sunyaev (1973) to model the disc anomalous kinematic viscosity v—acy, where c, is the isothermal sound speed and where «=107."," We use also the “alpha” prescription of Shakura Sunyaev (1973) to model the disc anomalous kinematic viscosity $\nu=\alpha c_s H$, where $c_s$ is the isothermal sound speed and where $\alpha=10^{-4}$." The reason for choosing such a low « value is discussed in detail in Paper I. but is essentially because a larger value causes rapid evolution of the binary orbit that would prohibit the long simulations we present In Paper I. we showed that both the disc and binary evolve toward a near-steady state as they interact with each other.," The reason for choosing such a low $\alpha$ value is discussed in detail in Paper I, but is essentially because a larger value causes rapid evolution of the binary orbit that would prohibit the long simulations we present In Paper I, we showed that both the disc and binary evolve toward a near-steady state as they interact with each other." From the time this equilibrium configuration. is reached. the apsidal lines of the dise and binary are aligned.," From the time this equilibrium configuration is reached, the apsidal lines of the disc and binary are aligned." Also. the disc structure and the orbital elements of the binary remain essentially constant.," Also, the disc structure and the orbital elements of the binary remain essentially constant." " For example. we find that the eccentricity of a binary with mass ratio go=O.1 and initial separation a,=O.4 saturates at a value of e;~0.08."," For example, we find that the eccentricity of a binary with mass ratio $q_b=0.1$ and initial separation $a_b=0.4$ saturates at a value of $e_b\sim 0.08$." The simulations presented in paper I of one planet interacting with a eircumbinary dise. were performed using this quasi-equilibrium state as initial conditions for the dise and binary., The simulations presented in paper I of one planet interacting with a circumbinary disc were performed using this quasi-equilibrium state as initial conditions for the disc and binary. " Depending on the model we consider. we adopt here a similar approach when setting up our initial 1) In simulations of pairs of planets embedded in a circumbinary disc. we restart the runs presented in Paper | once the planet is trapped at the cavity edge but with a second planet evolving on a circular orbit with @,=2.5 and ἐν=0.5""."," Depending on the model we consider, we adopt here a similar approach when setting up our initial i) In simulations of pairs of planets embedded in a circumbinary disc, we restart the runs presented in Paper I once the planet is trapped at the cavity edge but with a second planet evolving on a circular orbit with $a_p=2.5$ and $i_p=0.5^\circ$." " The latter is allowed to interact with the dise whose mass Is M,~0.01 and with the other planet and binary.", The latter is allowed to interact with the disc whose mass is $M_d\sim 0.01\; M_\star$ and with the other planet and binary. " ii) In. simulations that evolve five-planet systems in a circumbinary disc; we embed the planets in the disc once the latter and the binary have reached a stationary state. as described in Paper I. We set the innermost planet at αρ1.8 and then calculate the initial location of the others by asssuming that two adjacent bodies p and p’ are separated by ~5μμ. Where R4; is the mutual Hill radius defined by: Each body is assumed to initially evolve on a circular orbit with /,,20.5""."," ii) In simulations that evolve five-planet systems in a circumbinary disc, we embed the planets in the disc once the latter and the binary have reached a stationary state, as described in Paper I. We set the innermost planet at $a_p=1.8$ and then calculate the initial location of the others by asssuming that two adjacent bodies $p$ and $p'$ are separated by $\sim 5 \;R_{mH}$, where $R_{mH}$ is the mutual Hill radius defined by: Each body is assumed to initially evolve on a circular orbit with $i_p=0.5^\circ$." Note that the initial separation between planets we adopt is greater that the eritical value of ~3.46.Αι below which rapid instability occurs for two planets on initially circular orbits (Gladman 1993)., Note that the initial separation between planets we adopt is greater that the critical value of $\sim 3.46\; R_{mH}$ below which rapid instability occurs for two planets on initially circular orbits (Gladman 1993). " In paper I we considered planets with masses 71,7 5. 10 and 20 M."," In paper I we considered planets with masses $m_p$ = 5, 10 and 20 $M_\oplus$." Therefore. we adopt here the same values for the mass ΜΗ of the mnermost planet which is assumed to be trapped at the cavity edge of the disc.," Therefore, we adopt here the same values for the mass $m_i$ of the innermost planet which is assumed to be trapped at the cavity edge of the disc." " For each value of m;. we have performed two or three runs for which zi, was varied between 5€m,<20 Ma."," For each value of $m_i$, we have performed two or three runs for which $m_o$ was varied between $5 \le m_o \le 20 \;M_\oplus$ ." " Table | gives the values of zi. n, and g=mij, for each run."," Table \ref{table1} gives the values of $m_i$ , $m_o$ and $q=m_i/m_o$ for each run." An interesting feature of the results ofthese simulations is that varyingthe value of g can lead to different outcomes., An interesting feature of the results ofthese simulations is that varyingthe value of $q$ can lead to different outcomes. Below. we discuss in detail the different modes of evolution obtained in the simulations. and how they change depending onwhether or not q> l.," Below, we discuss in detail the different modes of evolution obtained in the simulations, and how they change depending onwhether or not $q \ge 1$ ." " ο. x A. on. ci>. By pC. £ (T~108 προLO75-7ον7) (Boliviuger1995) (simetal.1990) «|B]7,(7/10kpc)12bpO fis Ferettietal.(1995). ( ~7.2ane (Lawler&Deunison1982:Tsim1991:Goldshuudt&Rephach1993) Hennessy.Owen.&Eilels(1989). "," $n_{e}$ $\chi$ $\lambda$ $n_{e}$ ${\rm cm^{-3}}$ $B_{\|}$ $\mu$ $L$ ${\rm \sim 10^8}$ ${n_{e}}\sim 10^{-3}\,h_{75}^{1/2}\ {\rm cm^{-3}}$ \citep{hans95} \citep{kk90} $ <|B|>_{icm}$$(\ell /10\ {\rm kpc})^{-1/2}\,h_{75}^{1/2}\ \mu $ $\ell$ \citet{feretti95} $\ell$ $\sim 7.2\,h_{75}^{1/2}\mu$ \citep{ld82, kim91, gr93} \citet{hoe89} " protons as antiprotons.,protons as antiprotons. The same calculation cau be doue for autideuterons., The same calculation can be done for antideuterons. Tere. there is a significant effect since protons. which are the dominant source of musicentifications. can be rejected with modest efficicney by the TOF because their οποιον deposit differs from that of an autideuterou.," Here, there is a significant effect since protons, which are the dominant source of misidentifications, can be rejected with modest efficiency by the TOF because their energy deposit differs from that of an antideuteron." This is sufficient to reach the ~101Lot yate of accidental musidentification per proton. which is required.," This is sufficient to reach the $\sim10^{-12}-10^{-14}$ rate of accidental misidentification per proton, which is required." Other sources of backeround leading to musicdentifications are less iuportaut than those considered here., Other sources of background leading to misidentifications are less important than those considered here. We have probably uuderestimated the true rejection power., We have probably underestimated the true rejection power. Much of the backeround we considered is generated when activation -ravs of higher energy than the ladder transition N-ravs Compton-scatter m a detection cell. leading to a partial energv deposit minickius a ladder transition X-ray.," Much of the background we considered is generated when activation $\gamma$ -rays of higher energy than the ladder transition X-rays Compton-scatter in a detection cell, leading to a partial energy deposit mimicking a ladder transition X-ray." The scattered 2-rav will be absorbed iu another cell allowing a possibility of using other detection cells as part of a veto syste for such eveuts., The scattered $\gamma$ -ray will be absorbed in another cell allowing a possibility of using other detection cells as part of a veto system for such events. Pionic N-ravs are also produced in the nuclear annihilation aud when used iu coimcideuce with ladder X-rays can provide additional discriminatory capability., Pionic X-rays are also produced in the nuclear annihilation and when used in coincidence with ladder X-rays can provide additional discriminatory capability. We have not vet investigated their potential., We have not yet investigated their potential. " We should also note that CAPS has uo problem distineuishing autiprotous from autideuterous because the ladder transition N-ravs are uniquely identified iu the two cases,", We should also note that GAPS has no problem distinguishing antiprotons from antideuterons because the ladder transition X-rays are uniquely identified in the two cases. This scheme is cramatically different than the approach of Wellsetal.(1999)., This scheme is dramatically different than the approach of \citet{wells99}. . It does not require any caloriuetiic signature for identification., It does not require any calorimetric signature for identification. " The fact that the relevant N-rav signature is ""coustrained iu one detection cell provides additional fesibility for rejecting backerouud that necds to be investigated.", The fact that the relevant X-ray signature is “constrained” in one detection cell provides additional flexibility for rejecting background that needs to be investigated. We primarily cuvision GAPS being emploved with high οποιον resolution CZT detectors., We primarily envision GAPS being employed with high energy resolution CZT detectors. However alkali halide sciutillator crystals such as δα) provide a. simpler and cheaper alternative X-ray detector., However alkali halide scintillator crystals such as NaI(Tl) provide a simpler and cheaper alternative X-ray detector. The backerouud rejection capability of NalCIl) is comparable or even somewhat better than CZT., The background rejection capability of NaI(Tl) is comparable or even somewhat better than CZT. The poorer energy resolution is more than offset bv the superior teniporal resolution compared to CZT., The poorer energy resolution is more than offset by the superior temporal resolution compared to CZT. Tf Nal is used the euergy. resolution is «ufficieut so that the autiprotou and autideuteron can be resolved cleanly through the comparison of the highest energv of the 3 ladder N-vavs of interest iu cach case (refor to table 1.. 2)).," If NaI is used the energy resolution is sufficient so that the antiproton and antideuteron can be resolved cleanly through the comparison of the highest energy of the 3 ladder X-rays of interest in each case (refer to table \ref{e_pbar}, \ref{e_dbar}) )." The 2 lowest energv N-aravs frou the autiprotonic and autideuteronic atoms cannot be resolved from cach other i Nal. The preference for CZT is primarily based on the belief (to be studied) that it will be easier to implement the highly seeumeuted readout system aud multi-cell detection ecometiy., The 2 lowest energy X-rays from the antiprotonic and antideuteronic atoms cannot be resolved from each other in NaI. The preference for CZT is primarily based on the belief (to be studied) that it will be easier to implement the highly segmented readout system and multi-cell detection geometry. In addition. the accuracy to which the 3.{ ladder N-ravs cau be measured in CZT provides a very powerful positive confirmation of the presence of antimatter.," In addition, the accuracy to which the 3–4 ladder X-rays can be measured in CZT provides a very powerful positive confirmation of the presence of antimatter." We discuss a few poteutial applications of CAPS based on model calculation of iustruuent performance., We discuss a few potential applications of GAPS based on model calculation of instrument performance. As discussed in refintroybarascasiticity~LOnm 2srGeV tsee1 is required below 1 CeV/n. A imultivear space mission is required to achieve such seusitivities.," As discussed in \\ref{intro_dbar} a sensitivity $\sim 10^{-9}$ $^{-2}$ $^{-1}$ $^{-1}$ $^{-1}$ is required below 1 GeV/n. A multiyear space mission is required to achieve such sensitivities." We have simulated a lüeh inclination N) mission., We have simulated a high inclination $^\circ$ N) mission. The high latitude mission (IILM) is advantageous iu reducing the ecomagnuetic rigidity cutoff., The high latitude mission (HLM) is advantageous in reducing the geomagnetic rigidity cutoff. Asstumineg nitrogen eas and 27 CAPS cells of size !=160 cii surrounded by pixellated CZT detectors. we achieve a peak grasp of 9.0 1u?sr for antideuteriun over an energy band of 0.1 to 0.1 CoV/n with the detector size of £=5 m aud a total mass of less than 10.000 Tbs (table D).," Assuming nitrogen gas and 27 GAPS cells of size $l=160$ cm surrounded by pixellated CZT detectors, we achieve a peak grasp of 9.0 $^2$ sr for antideuterium over an energy band of 0.1 to 0.4 GeV/n with the detector size of $L=5$ m and a total mass of less than 10,000 lbs (table \ref{dbar_mission}) )." This results in the seuzitivitv 10Pm Puy (GeV tsee bin 3 vears. 20 times better than AMIS (table 5)).," This results in the sensitivity $2.6\times10^{-9}$ $^{-2}$ $^{-1}$ $^{-1}$ $^{-1}$ in 3 years, 20 times better than AMS (table \ref{dbar_table}) )." A model calculation of the effective grasp for the proposed experiment is in figure 11.., A model calculation of the effective grasp for the proposed experiment is in figure \ref{dbar_grasp}. In addition to superior scusitivity to AMS. we also note that the cost of a GAPS iustiruuenut with 20 times the seusitivitv of AXIS is about an order of maenitude less.," In addition to superior sensitivity to AMS, we also note that the cost of a GAPS instrument with 20 times the sensitivity of AMS is about an order of magnitude less." " The type of mission described. here could readily be executed as a immodestlv sized NASA ""MIDEN"" class uiissiou.", The type of mission described here could readily be executed as a modestly sized NASA “MIDEX” class mission. The recent BESS ineasurements detected. only a few autiprotons below 200 MeV. with resultant large eror bars.," The recent BESS measurements detected only a few antiprotons below 200 MeV, with resultant large error bars." " To detect a statistically significant nuniber of antiprotous in several low cuerey bauds at E,<0.5 (ον requires a sensitivity of ~10% an2sr 1G06V. duoc |."," To detect a statistically significant number of antiprotons in several low energy bands at $E_{\bar{p}}<0.5$ GeV requires a sensitivity of $\sim 10^{-3}$ $^{-2}$ $^{-1}$ $^{-1}$ $^{-1}$." We simulated a balloou-borne experiment performed at lüeh latitude where the rigidity cutoff is < 0.5 GeV. The detector size is £=2 m and the overall detector column deusity is 9 ecu7., We simulated a balloon-borne experiment performed at high latitude where the rigidity cutoff is $<$ 0.5 GeV. The detector size is $L=2$ m and the overall detector column density is 9 $^{-2}$. It consists of 54«5=125 cubic cells of size /=10 cem., It consists of $5\times5\times5=125$ cubic cells of size $l=40$ cm. The estimated total weight of the detector is less than [000 lbs., The estimated total weight of the detector is less than 4000 lbs. Neon gas is clioseu since 3 ladder X-rays (29.12. 53.60. 115.8 keV) are observable by al 7? thick Nal detector (preferred over CZT ou a balloon experiment because if is cheaper).," Neon gas is chosen since 3 ladder X-rays (29.12, 53.60, 115.8 keV) are observable by a 1 $^{-2}$ thick NaI detector (preferred over CZT on a balloon experiment because it is cheaper)." The effective grasp is 2.1 nig with a bandwidth ~70 MeV for each energv channel., The effective grasp is 2.4 $^2$ sr with a bandwidth $\sim 70$ MeV for each energy channel. " This is | to 8 times larger than the ecolctrical erasp of the AMIS and BESS: experiments respectively,", This is 4 to 8 times larger than the geometrical grasp of the AMS and BESS experiments respectively. Acceptance for cach cnerey channel is LO! wwe sec for 1 day observation time.," Acceptance for each energy channel is $1.4\times10^4$ $^{2}\,$ $\,$ $\,$ sec for 1 day observation time." " In several balloon fights over the 11 wear solar cycle. one could study. the effect of solar modulation or amy excess fron the predicted secondary flux at 5 different energy. bands over E,=120100 MeV. Τὸ inost effective micas of probing exotic sources of antiprotons such as the evaporation of primordial black holes (MacCüibbou&Carr1991:Makietal.1996) or the annihilation of ποπγαμος (Jungman&Wamionkowski1901:Dottiuoctal. 1998).. is to send an iustrunent iuto deep space )vond the heliosphere."," In several balloon flights over the 11 year solar cycle, one could study the effect of solar modulation or any excess from the predicted secondary flux at 5 different energy bands over $E_{\bar{p}}=120-400$ MeV. The most effective means of probing exotic sources of antiprotons such as the evaporation of primordial black holes \citep{macgibbon91, maki96} or the annihilation of neutralinos \citep{jungman94, bottino98}, is to send an instrument into deep space beyond the heliosphere." An iustruneut in deep space is far removed from solar modulation effects and ecomaguetic vieidity cutoff iuhereut in low earth orbit nüssious., An instrument in deep space is far removed from solar modulation effects and geomagnetic rigidity cutoff inherent in low earth orbit missions. " This »onmuits investigation of low energy autiprotous. especially at E,«100 MeV. We have designed a detector with wo enerev channels"," This permits investigation of low energy antiprotons, especially at $E_{\bar{p}}<100$ MeV. We have designed a detector with two energy channels." A measurement in the lower energy wand LO60 MeV. where the flux due to p.p interactions is neeligible. is to obtain a clean signature of the p|Te and tertiary antiprotous or these oein combination with a xossible neutralino signature. aud/or primordial black hole sjenature.," A measurement in the lower energy band $40-60$ MeV, where the flux due to p–p interactions is negligible, is to obtain a clean signature of the p+He and tertiary antiprotons or these in combination with a possible neutralino signature, and/or primordial black hole signature." The second channel at 100 to 120 MeV. anchors he autiproton flux and spectral shape to higher energy observations., The second channel at 100 to 120 MeV anchors the antiproton flux and spectral shape to higher energy observations. The detector is a cubic cell of size £=6 cm comparable with a receuth-proposed BOO detector by Wellsetal. (1999)., The detector is a cubic cell of size $L=6$ cm comparable with a recently-proposed BGO detector by \citet{wells99}. . Areon eas is mandatory from the constraint ou the gas deusity discussed iu retdensity.., Argon gas is mandatory from the constraint on the gas density discussed in \\ref{density}. . All six surfaces of the cube see the whale skv, All six surfaces of the cube see the whole sky Further analytical progress can be made by combining the thin boundary (TB) and the thin tube (TT) approximations.,Further analytical progress can be made by combining the thin boundary (TB) and the thin tube (TT) approximations. This was done extensively byGoossensetal.(1992)., This was done extensively by\citet{goossens92}. ". We perform à asymptotic expansion of the Bessel functions present in the dispersion relation (7)) by considering the long-wavelengthlimit, i... Acad«1, and only keep the lowest order, nonzero term of the expansion."," We perform a asymptotic expansion of the Bessel functions present in the dispersion relation \ref{eq:disperalfven}) ) by considering the long-wavelengthlimit, i.e., $k_z a \ll 1$, and only keep the lowest order, nonzero term of the expansion." " Thus, the dispersion relation (7)) becomes, Now, we write the frequency as @=Wp+ic."," Thus, the dispersion relation \ref{eq:disperalfven}) ) becomes, Now, we write the frequency as $\omega = \omega_{\rm R} + i \omega_{\rm I}$." It follows from the resonant conditions that GA=We Wr., It follows from the resonant conditions that $\omega_{\rm A} = \omega_c = \omega_{\rm R}$ . " The position of the Alfvénn, r4. and slow, r,. resonance points can be computed by equating the real part of the kink mode frequency to the local Alfvénn and slow frequencies, respectively."," The position of the Alfvénn, $r_{\rm A}$, and slow, $r_s$, resonance points can be computed by equating the real part of the kink mode frequency to the local Alfvénn and slow frequencies, respectively." " By this procedure, we obtain for the Alfvénn resonance point, and for the slow resonance point."," By this procedure, we obtain for the Alfvénn resonance point, and for the slow resonance point." " In order to derive equation (10)), wehave used the approximation ως3Xcs. which. is. valid. for> c;3< vy."," In order to derive equation \ref{eq:resSpoint}) ), wehave used the approximation $\omega_c^2 \approx \cs^2 k_z^2$, which is valid for $\cs^2 \ll \va^2$ ." " Note that we need the value of> cog to determine. r4 and r,.", Note that we need the value of $\omega_{\rm R}$ to determine $r_{\rm A}$ and $r_s$ . " Expressions for |O,pg|4 and |0,pol, are obtained from the density profile (eq. [1]."," Expressions for $\left| \pd_r \rho_0 \right|_{\rm A}$ and $\left| \pd_r \rho_0 \right|_s$ are obtained from the density profile (eq. \ref{eq:profile}] ])," " with ag=πίτα-α)/{ and a,=z(r,—e)/I.", with $\alpha_{\rm A} = \pi \left( r_{\rm A} - a \right)/l$ and $\alpha_s = \pi \left( r_s- a \right) / l$. " We insert these expressions in equation (8)) and neglect terms with cx. i.c., low-damping situation."," We insert these expressions in equation \ref{eq:drttap}) ) and neglect terms with $\omega_{\rm I}^2$, i.e., low-damping situation." Then we obtain an expression for the ratio p/w after some algebraic manipulations., Then we obtain an expression for the ratio $\omega_{\rm R}/\omega_{\rm I}$ after some algebraic manipulations. " Since the oscillatory period, P. and the dampingtime, Tp. are related tothe frequency as followsit is then straight-forward to give an expression for rp/P."," Since the oscillatory period, $P$ , and the dampingtime, $\tau_{\rm D}$ , are related tothe frequency as followsit is then straight-forward to give an expression for $\tau_{\rm D} / P$ ," For Avpp29Rey. the single scattering approximation is valid and the light beam reaching the observer is attenuated as €. with 7=Res/Aepy.,"For $\lambda_{eff} \gg R_{CS}$, the single scattering approximation is valid and the light beam reaching the observer is attenuated as $e^{-\tau}$ , with $\tau=R_{CS}/\lambda_{eff}$." This is the case applicable Lor extinction by dust in the interstellar medium., This is the case applicable for extinction by dust in the interstellar medium. For Αι\sigma_a$, in a wavelength dependent manner." In particular. we examine (he cases where the light scattering properties of dust particles in the CS matter are similar to what has been moceled for interstellar dust grains the Milkv-Way (Draine2003) or the LAIC 2001).," In particular, we examine the cases where the light scattering properties of dust particles in the CS matter are similar to what has been modeled for interstellar dust grains the Milky-Way \citep{Draine03} or the LMC \citep{WD01}." ". Table 1. shows the the wavelength dependent. albedo [actor (=o./(o7,+0,)) sud the average of the cosine of the scattering angle for interactions between light ancl dust particles."," Table \ref{tbl-1} shows the the wavelength dependent albedo factor $= \sigma_{s}/(\sigma_{s}+\sigma_{a})$ ) and the average of the cosine of the scattering angle for interactions between light and dust particles." Also tabulatecl is the absorption cross-section divided by dust mass., Also tabulated is the absorption cross-section divided by dust mass. Note that the Milkv-Way parameters correspond (o a dust size distribution matching A4.=3.1 lor dimunine of stars in (he Galaxy., Note that the Milky-Way parameters correspond to a dust size distribution matching $R_V=3.1$ for dimming of stars in the Galaxy. Wang(2005) considered (he impact of circumstellar dust upon the measured value of A. but only the extreme case where all scattered photons may reach the observer.," \citet{lifan05} considered the impact of circumstellar dust upon the measured value of $R_V$, but only the extreme case where all scattered photons may reach the observer." That assumption overlooks an important aspect of the problem: while the bluer photons scalter more. {μον also are more likely to be absorbed.," That assumption overlooks an important aspect of the problem: while the bluer photons scatter more, they also are more likely to be absorbed." This leads (ο a steeper wavelength dependence of the effective extinction law. possibly explaining (he unusual total to selective ex(netion ratios found in studies of SNla.," This leads to a steeper wavelength dependence of the effective extinction law, possibly explaining the unusual total to selective extinction ratios found in studies of SNIa." In order to estimate the net effect of scattering and absorption on the lieht reaching the outer edge of a shell of circumstellar dust around. the SN site. Res. a Monte-Carlo simulation was performed.," In order to estimate the net effect of scattering and absorption on the light reaching the outer edge of a shell of circumstellar dust around the SN site, $R_{CS}$ , a Monte-Carlo simulation was performed." Photons with energies corresponding to the central wavelengths ol the UDVRIJIH photometric svstem were generated ancl subsequently followed as they propagate in the dustv A uniform distribution of scatterers within a sphere of radius Rey is usedin the caleulations., Photons with energies corresponding to the central wavelengths of the $UBVRIJHK$ photometric system were generated and subsequently followed as they propagate in the dusty A uniform distribution of scatterers within a sphere of radius $R_{CS}$ is usedin the calculations. Our treatment is rather insensitiveof the physical size of Rey since what, Our treatment is rather insensitiveof the physical size of $R_{CS}$ since what "too, at lower temperatures KK) given a high pressure (Hellingetal.1996).","too, at lower temperatures K) given a high pressure \citep{hel96}." ". The region of benzene production is at a temperature of a few hundred degrees, and sits just below a region of sufficiently high temperature for PAH formation."," The region of benzene production is at a temperature of a few hundred degrees, and sits just below a region of sufficiently high temperature for PAH formation." " Invoking vertical mixing here could raise benzene and other organics into the higher temperature region, as well as push newly-formed PAHs into the surface layers of the disk, where they are observed."," Invoking vertical mixing here could raise benzene and other organics into the higher temperature region, as well as push newly-formed PAHs into the surface layers of the disk, where they are observed." Mixing timescales at a few AU are fast enough (7625yr;Ilgner&Nelson2006) to dredge material from the midplane to surface layers within the lifetime of a T Tauri disk (7109 yyr).," Mixing timescales at a few AU are fast enough \citep[$\sim$625\,yr;][]{ilg06} to dredge material from the midplane to surface layers within the lifetime of a T Tauri disk $\sim$ $^6$ yr)." " For PAHs to subsist in the solar system, the rate of growth of the PAH must be greater than the rate of photodissociation."," For PAHs to subsist in the solar system, the rate of growth of the PAH must be greater than the rate of photodissociation." " However, once a PAH reaches 30-40 carbon atoms in size, it is effectively safe from photodissociation since at this size the infrared radiative rate of the PAH dominates the photodissociation rate."," However, once a PAH reaches 30-40 carbon atoms in size, it is effectively safe from photodissociation since at this size the infrared radiative rate of the PAH dominates the photodissociation rate." " In the ISM, a benzene molecule is destroyed (by removal of an acetylene molecule) at a rate of 1.5x10 !?ss !, giving a lifetime of around 200 years."," In the ISM, a benzene molecule is destroyed (by removal of an acetylene molecule) at a rate of $\times$ $^{-10}$ $^{-1}$, giving a lifetime of around 200 years." " The growth time (accretion of an acetylene molecule) is given by Tar=(noXcnskosn,)|s (Allainetal.1996).", The growth time (accretion of an acetylene molecule) is given by $\tau_\mathrm{gr} = (n_0 X_\mathrm{C_2H_2} k_\mathrm{C_2H_2})^{-1}~\mathrm{s}$ \citep{all96}. ". Inserting typical values for the abundance of acetylene in the inner part of the disk, Xc,4,=10~"", and the reaction rate for accretion of acetylene, kc,u,—10! 1, gives a necessary density of 1.5x10? ccm? for PAH growth from benzene."," Inserting typical values for the abundance of acetylene in the inner part of the disk, $X_\mathrm{C_2H_2}$ $^{-7}$, and the reaction rate for accretion of acetylene, $k_\mathrm{C_2H_2}$ $^{-11}$ $^{-1}$, gives a necessary density of $\times$ $^8$ $^{-3}$ for PAH growth from benzene." This tallies with the low abundances of benzene in (low density) interstellar cloud models (see Sect. ??)), This tallies with the low abundances of benzene in (low density) interstellar cloud models (see Sect. \ref{sec:diffenvs}) ) and the lack of a detection of benzene in the ISM., and the lack of a detection of benzene in the ISM. " However, these conditions met within the inner regions of a protostellar disk, as has been shown in our chemical model (which also includes destruction of benzene by reactions with ions)."," However, these conditions met within the inner regions of a protostellar disk, as has been shown in our chemical model (which also includes destruction of benzene by reactions with ions)." " In fact, the strength of the UV field drops below the interstellar level for much of the midplane region, and will remain at that level for much of the transition towards a debris disk."," In fact, the strength of the UV field drops below the interstellar level for much of the midplane region, and will remain at that level for much of the transition towards a debris disk." " Assuming a PAH of 40 carbon atoms forms solely through the addition of acetylene to a benzene ring, a PAH could be produced from a benzene molecule on a timescale of approximately fifty years at a density of 101? cem?."," Assuming a PAH of 40 carbon atoms forms solely through the addition of acetylene to a benzene ring, a PAH could be produced from a benzene molecule on a timescale of approximately fifty years at a density of $^{10}$ $^{-3}$." " Even though the actual route to PAH formation is likely to be different, this estimate does give a representative timescale and show that PAH production from benzene could possibly be prolific in this type of environment."," Even though the actual route to PAH formation is likely to be different, this estimate does give a representative timescale and show that PAH production from benzene could possibly be prolific in this type of environment." We will consider the formation of larger aromatics in a future paper., We will consider the formation of larger aromatics in a future paper. " Having ascertained that benzene can survive for an amount of time long enough for PAHs to form from it, the question arises, do PAHs form in similar regions to which benzene forms?"," Having ascertained that benzene can survive for an amount of time long enough for PAHs to form from it, the question arises, do PAHs form in similar regions to which benzene forms?" " The answer to this is unclear, since the supporting observational evidence is sparse."," The answer to this is unclear, since the supporting observational evidence is sparse." " Of the three detections of PAHs in T Tauri-type disks (Geersetal.2006),, all three disks are thought to have inner dust holes (from SED models)."," Of the three detections of PAHs in T Tauri-type disks \citep{gee06}, all three disks are thought to have inner dust holes (from SED models)." Thus it may just be a selection effect that PAH emission is only detected from the upper layers of disks because of the presence of these dust holes: otherwise the continuum emission swamps any possible PAH emission feature originating from deeper in the disk., Thus it may just be a selection effect that PAH emission is only detected from the upper layers of disks because of the presence of these dust holes: otherwise the continuum emission swamps any possible PAH emission feature originating from deeper in the disk. Further observations are necessary to confirm the correlation between the presence of benzene and PAHs., Further observations are necessary to confirm the correlation between the presence of benzene and PAHs. of the components to agree within our measuring uncertainties.,of the components to agree within our measuring uncertainties. Table 9 shows the comparison. where the final column gives the observed velocity cilference in terius of our measuriug uicertainty. which we take as 1.5 |.," Table \ref{table-wide} shows the comparison, where the final column gives the observed velocity difference in terms of our measuring uncertainty, which we take as 1.5 $^{-1}$." Of the two wide systems. GL 169 aud GL £71 are clearly not associated (unless one bas au unseen companion). but our data show ouly a 3o diflereuce between Cl {5 and the CI 22 system.," Of the two wide systems, Gl 469 and Gl 471 are clearly not associated (unless one has an unseen companion), but our data show only a $\sigma$ difference between Gl 48 and the Gl 22 system." Except for GI 110 A/C. where orbital motion might affect the velocity of the brighter star. the remaining candidate binaries have velocity dillerences cousisteut with our ineasuring uncertainties.," Except for Gl 140 A/C, where orbital motion might affect the velocity of the brighter star, the remaining candidate binaries have velocity differences consistent with our measuring uncertainties." The chromospheric age-activity correlation amongst maiu-sequeuce stars has been studied extensively [or solar-type dwarls. where it is usually parameterised iu terms of the t to the halt law (Skumauich1972).. where F(Ca) is the Ca II Ix eimissiou-line flux. 4 is a constant aud / the age.," The chromospheric age-activity correlation amongst main-sequence stars has been studied extensively for solar-type dwarfs, where it is usually parameterised in terms of the `t to the half' law \citep{sk72}, where $F(Ca)$ is the Ca II K emission-line flux, $A$ is a constant and $t$ the age." Based on that calibration aud observations of local G dwarls. several groups lave attempted to reconstruct the recent star formation history iu the disk.," Based on that calibration and observations of local G dwarfs, several groups have attempted to reconstruct the recent star formation history in the disk." In. particular. both Barry(1988). and. claim that the data indicate several significant. bursts of star formation over the last | Gyrs.," In particular, both \citet{barry} and \citet{rp00} claim that the data indicate several significant bursts of star formation over the last 4 Gyrs." Ou the other haud. Soderbun.Duucan.&Jolusou(1991) argue that these ‘bursts’ are the result of a more complicated activity/age relation than that implied by a simple Skumanich type power law.," On the other hand, \citet{sdj91} argue that these `bursts' are the result of a more complicated activity/age relation than that implied by a simple Skumanich type power law." Our goal is to use our observatious of M dwarls in the VC sample to address the local star formation history., Our goal is to use our observations of M dwarfs in the VC sample to address the local star formation history. To that eid. we first investigate tlie range of activity aud the correlation of activity with age for the low-mass M cdwarls.," To that end, we first investigate the range of activity and the correlation of activity with age for the low-mass M dwarfs." In. particular. we do uot require that tle M dwarfs follow the same age-activity relation used for the CC cdwarfs.," In particular, we do not require that the M dwarfs follow the same age-activity relation used for the G dwarfs." The primary indicator of eliroriospherie activity in M. dwarfs is Ha emission., The primary indicator of chromospheric activity in M dwarfs is $\alpha$ emission. Iun. Figure 5 we plot the equivalent width of Ha as a fuuction of TiO» (spectral type/ellective temperature)., In Figure \ref{fig-tio5ha1} we plot the equivalent width of $\alpha$ as a function of TiO5 (spectral type/effective temperature). Figure 6 is an expauded view of the absorption (uegative) equivalent width portion of Figure 5.., Figure \ref{fig-tio5ha2} is an expanded view of the absorption (negative) equivalent width portion of Figure \ref{fig-tio5ha1}. Active stars known to be short-period binaries (Tables 6 and. 7)) are shown as open circles while members of the VC sample are shown as solid triangles., Active stars known to be short-period binaries (Tables \ref{table-sb2} and \ref{table-sb1}) ) are shown as open circles while members of the VC sample are shown as solid triangles. Additional stars from this paper which are uot in the VC sample are shown as open triangles., Additional stars from this paper which are not in the VC sample are shown as open triangles. To aid discussion. we have labelled five groups (A-E).," To aid discussion, we have labelled five groups (A-E)." A: The majority of NE. dwarls show Ha absorption. with larger average absorptiou equivalent widtlis at early spectral types.," The majority of M dwarfs show $\alpha$ absorption, with larger average absorption equivalent widths at early spectral types." Ha absorption does not necessarilyindicate an abseuce oL chromospheric activity. as discussed by Cram&Mullan(1979). aud Cram&Ciampapa(1957 )..," $\alpha$ absorption does not necessarilyindicate an absence of chromospheric activity, as discussed by \citet{cm79} and \citet{cg87}. ." stellar thick disk.,stellar thick disk. Understanding the origin of these relationships will improve our picture of the primordial Milky. Way., Understanding the origin of these relationships will improve our picture of the primordial Milky Way. At the same time. theoretical interest in globular cluster evolution has been motivated by the. discovery hat two-bods relaxation would drive evolution on a time scale that is much less than the age of a typical cluster (Ambartsumian 1938: Spitzer 1940: Chanclrasekhar 1942).," At the same time, theoretical interest in globular cluster evolution has been motivated by the discovery that two-body relaxation would drive evolution on a time scale that is much less than the age of a typical cluster (Ambartsumian 1938; Spitzer 1940; Chandrasekhar 1942)." Subsequent research provided. an understanding of the eravothermal instability (Lvynden-Dell Wood. 1968) and he phenomenon of core collapse (e.g. Cohn 1980)., Subsequent research provided an understanding of the gravothermal instability (Lynden-Bell Wood 1968) and the phenomenon of core collapse (e.g. Cohn 1980). One of he basic conclusions of this work on cluster evolution is hat relaxation inevitably leads to evaporation (c.g. Spitzer 1987)., One of the basic conclusions of this work on cluster evolution is that relaxation inevitably leads to evaporation (e.g. Spitzer 1987). Additional refinements to the picture of relaxation-driven evolution have been required to account for a source of energy which halts core collapse (e.g. Lenon 1961: Lee Ostriker 1987) and to include tidal inlluences which arise on à clusters orbit in a parent galaxy. (Ostriker. Spitzer Chevalier. 1972: Chernoll.. IxXochanek. Shapiro 1986: Weinberg 1994: Cnedin Ostriker 1996: Alurali Weinberg 1996. hereafter Paper D.," Additional refinements to the picture of relaxation-driven evolution have been required to account for a source of energy which halts core collapse (e.g. Henon 1961; Lee Ostriker 1987) and to include tidal influences which arise on a cluster's orbit in a parent galaxy (Ostriker, Spitzer Chevalier 1972; Chernoff, Kochanek Shapiro 1986; Weinberg 1994; Gnedin Ostriker 1996; Murali Weinberg 1996, hereafter Paper I)." Recent work on tidal inlluences has shown that evaporation is accelerated by the interaction ofa cluster with the tidal field. produced by the halo and clisk of the Galaxy (Cinedin Ostriker 1996: Paper D., Recent work on tidal influences has shown that evaporation is accelerated by the interaction of a cluster with the tidal field produced by the halo and disk of the Galaxy (Gnedin Ostriker 1996; Paper I). These studies show that depletion depends strongly on cluster mass and. orbit. in the Galaxy., These studies show that depletion depends strongly on cluster mass and orbit in the Galaxy. This suggests that understanding the initial characteristics of clusters ancl their relationship to other stellar populations in the Galaxy requires a comprehensive description of evolution since the time of formation., This suggests that understanding the initial characteristics of clusters and their relationship to other stellar populations in the Galaxy requires a comprehensive description of evolution since the time of formation. In a related. study which supports this view. Murali Weinberg (1996: hereafter Paper HD). have demonstrated the importance of evolution in shaping the MS elobular cluster population and as a partial cause for the specific frequency conundrum in Fundamental plane ellipticals.," In a related study which supports this view, Murali Weinberg (1996; hereafter Paper II), have demonstrated the importance of evolution in shaping the M87 globular cluster population and as a partial cause for the specific frequency conundrum in fundamental plane ellipticals." Alotivated by. these results in the present work. we investigate the degree to which evolution has shaped. the Milkv Way cluster population.," Motivated by these results in the present work, we investigate the degree to which evolution has shaped the Milky Way cluster population." Our approach is to predict he initial spatial ancl kinematic distributions of the elobular cluster system using the Fokker-PlLanck description of cluster evolution discussed. in Paper Loin combination with the »wametrie statistical framework. emploved. in. Paper LL., Our approach is to predict the initial spatial and kinematic distributions of the globular cluster system using the Fokker-Planck description of cluster evolution discussed in Paper I in combination with the parametric statistical framework employed in Paper II. The predictions describe the initial population of clusters which evolve quasi-statically through relaxation and. tidal icing and indicate changes which dynamical evolution las wrought on the svstem as a whole., The predictions describe the initial population of clusters which evolve quasi-statically through relaxation and tidal heating and indicate changes which dynamical evolution has wrought on the system as a whole. The results also »ovide a basis for understanding the primordial relationship of globular clusters to other stellar populations., The results also provide a basis for understanding the primordial relationship of globular clusters to other stellar populations. We first study the evolutionary behavior of clusters which inhabit the cisk anc halo of the Galaxy., We first study the evolutionary behavior of clusters which inhabit the disk and halo of the Galaxy. The calculations demonstrate the importance of disk heating on cluster evolution and. quantify dependences on important internal and external parameters. including orbit in the Galaxy and cluster concentration.," The calculations demonstrate the importance of disk heating on cluster evolution and quantify dependences on important internal and external parameters, including orbit in the Galaxy and cluster concentration." We also examine the behavior of internal censity profiles and mass spectra in evolving clusters., We also examine the behavior of internal density profiles and mass spectra in evolving clusters. Lavine considered the detailed. physical behavior. we examine properties of the full cluster population.," Having considered the detailed physical behavior, we examine properties of the full cluster population." We first Jaracterize properties of the current cluster population aud ren predict its initial conditions using the data set compiled by Gnedin Ostriker (1996) and the three-space velocities erived by Cudworth. (1993)., We first characterize properties of the current cluster population and then predict its initial conditions using the data set compiled by Gnedin Ostriker (1996) and the three-space velocities derived by Cudworth (1993). The inferences are derived from both spherical and two-component disk|sphere models of the cluster. clistribution., The inferences are derived from both spherical and two-component disk+sphere models of the cluster distribution. While several analyses have garown the cluster system to be approximately spherically istributed (Chernoll Djorgovski 1980: Thomas. 1989). other investigations show two components: a Lattencel. rapidlv rotating high-metallicity component associated with the Galactic disk and a spherically clistributecd low-metallicity Component associated with the Galactic. halo (Zinn 1985: Armanclroll 1950).," While several analyses have shown the cluster system to be approximately spherically distributed (Chernoff Djorgovski 1989; Thomas 1989), other investigations show two components: a flattened, rapidly rotating high-metallicity component associated with the Galactic disk and a spherically distributed low-metallicity component associated with the Galactic halo (Zinn 1985; Armandroff 1989)." Further subdivisions may also exist. (Zinn 1993: Zinn 1996)., Further subdivisions may also exist (Zinn 1993; Zinn 1996). The choice of moclels rellects the gross characteristics of the cluster svstem and allows us to compare the candidate distributions., The choice of models reflects the gross characteristics of the cluster system and allows us to compare the candidate distributions. Phe results predict significant dillerences in the initial ancl present-day cluster populations. indicating the role of evolution in shaping the present-day cluster svstem.," The results predict significant differences in the initial and present-day cluster populations, indicating the role of evolution in shaping the present-day cluster system." Moreover. neither model is completely. successful in describing the cluster population probably due to the combined elfects of evolution and obseuration.," Moreover, neither model is completely successful in describing the cluster population probably due to the combined effects of evolution and obscuration." The plan of the paper is as follows., The plan of the paper is as follows. In refsecunvestigalion.. we summarize the approach ane scenario used throughout the investigation.," In \\ref{sec:investigation}, we summarize the approach and scenario used throughout the investigation." The results are presented in relsce:results— and. include. description. of the physical behavior as a function of orbit. examination of the internal properties of evolving clusters and analysis and. prediction of the initial conditions of the observed. population.," The results are presented in \\ref{sec:results} and include description of the physical behavior as a function of orbit, examination of the internal properties of evolving clusters and analysis and prediction of the initial conditions of the observed population." Finally. refsecidiscussion| discusses the implications of the results.," Finally, \\ref{sec:discussion} discusses the implications of the results." The appendices provide derivations of the models and a discussion of the statistical procedure., The appendices provide derivations of the models and a discussion of the statistical procedure. Our fiducial population consists of clusters which formed in a single episode approximately 11Cwr ago. the lower limit on cluster ages estimated. from. current models. of stellar evolution (Chabover 1995).," Our fiducial population consists of clusters which formed in a single episode approximately $11 \Gyr$ ago, the lower limit on cluster ages estimated from current models of stellar evolution (Chaboyer 1995)." For older ages. the evolution in the properties of the cluster system is greater. than the estimates derived: below.," For older ages, the evolution in the properties of the cluster system is greater than the estimates derived below." Initial clusters are. assigned Wo5 King model profiles., Initial clusters are assigned $W_0=5$ King model profiles. Investigation of concentration dependence in refsec:concentration— shows that evaporation times vary little with Wo., Investigation of concentration dependence in \\ref{sec:concentration} shows that evaporation times vary little with $W_0$. We assume that each cluster has a Salpeter IME m/-7 with i=2.35 and lower mass limit m=0.1M., We assume that each cluster has a Salpeter IMF $m^{-\beta}$ with $\beta=2.35$ and lower mass limit $m_l=0.1 \msun$. For this choice. stellar evolution would dominate for thefirstCivr.. roughly. corresponding to the main sequence lifetime of a 2M. Xestar.. which we choose as the upper mass limit. m4.," For this choice, stellar evolution would dominate for thefirst, roughly corresponding to the main sequence lifetime of a $2 \msun$ A-star, which we choose as the upper mass limit, $m_u$ ." Following the phase of strong stellar evolution. relaxation. external heating and. ultimately. core collapse," Following the phase of strong stellar evolution, relaxation, external heating and, ultimately, core collapse" reffig:modelseds)).,). " As a result of this strong PDR contribution, therefore, these galaxies exhibit a significant excess in flux in the mid-infrared."," As a result of this strong PDR contribution, therefore, these galaxies exhibit a significant excess in flux in the mid-infrared." " We find that they can make a significant contribution in the λ>24um rregime, without adversely affecting the fit of the model at shorter optical to mid-IR wavelengths."," We find that they can make a significant contribution in the $\lambda \ge 24$ regime, without adversely affecting the fit of the model at shorter optical to mid-IR wavelengths." " of the 65 SINGS galaxies discussed in Draine et ((2007) are of this type; these include Mrk33, NGC2798, NGC3049 and Tol89."," of the 65 SINGS galaxies discussed in Draine et (2007) are of this type; these include Mrk33, NGC2798, NGC3049 and Tol89." " We modelled an SED with such an infrared excess, based on the starburst galaxy Mrk33."," We modelled an SED with such an infrared excess, based on the starburst galaxy Mrk33." Our SED is based on the observed mid-IR of Mrk33 from SINGS observations with IRS as well as broadband photometry from Dale et ((2005) to constrain the dust blackbody at longer wavelength., Our SED is based on the observed mid-IR of Mrk33 from SINGS observations with IRS as well as broadband photometry from Dale et (2005) to constrain the dust blackbody at longer wavelength. This SED and the broadband data appear in reffig:modelseds.., This SED and the broadband data appear in \\ref{fig:modelseds}. We substituted this SED for a comparable fraction (16%)) of the dusty late-type galaxies in our model by replacing the Scd galaxies (Table 1)) with this starburst population., We substituted this SED for a comparable fraction ) of the dusty late-type galaxies in our model by replacing the Scd galaxies (Table \ref{t-lf}) ) with this starburst population. This component is shown as the dash-dot line in reffig:24cnts.., This component is shown as the dash-dot line in \\ref{fig:24cnts}. " We find that including these sources in our PLE model yields a significant improvement in the fit to the counts, particularly at the bright end, suggesting that at tthe counts are dominated by sources with warmer dust and higher SFRs - primarily starburst galaxies."," We find that including these sources in our PLE model yields a significant improvement in the fit to the counts, particularly at the bright end, suggesting that at the counts are dominated by sources with warmer dust and higher SFRs – primarily starburst galaxies." " While the bright end of the number counts are extremely well matched, at $2444«0.5 mJy the counts are still underpredicted by a factor of a few."," While the bright end of the number counts are extremely well matched, at $S_{24 \rm{\umu m}}<0.5$ mJy the counts are still underpredicted by a factor of a few." " This suggests that our model is deficient in the number of predicted ssources at high redshift, and comparing the predicted redshift distribution of the model to the observed n(z) (Perez-Gonzalez et al.,"," This suggests that our model is deficient in the number of predicted sources at high redshift, and comparing the predicted redshift distribution of the model to the observed $n(z)$ (Perez-Gonzalez et al.," 2005) confirms that this is the case., 2005) confirms that this is the case. " Babbedge et ((2006) suggest that while the galaxy luminosity functions at IRAC wavelengths show relatively little evolution, there is strong evolution in the LLF, particularly out to z®&1."," Babbedge et (2006) suggest that while the galaxy luminosity functions at IRAC wavelengths show relatively little evolution, there is strong evolution in the LF, particularly out to $z\approx1$." " Including our Mrk33 component brings our model in line with local observations and in doing so enables us to match the bright-flux, low-redshift end of the counts."," Including our Mrk33 component brings our model in line with local observations and in doing so enables us to match the bright-flux, low-redshift end of the counts." " Allowing this warm-dust, high-SFR component to evolve more strongly could make it"," Allowing this warm-dust, high-SFR component to evolve more strongly could make it" Apart from the particular topic of intermittency. his paper is also intended t0 stimulate increst in this general approach.,"Apart from the particular topic of intermittency, this paper is also intended to stimulate interest in this general approach." Many techniques. exist for studying he wave mechanics of clisorcerecl svstenis. such as the renormalization group and path-integral mehods. few of which are used by cosmologists working in tis area.," Many techniques exist for studying the wave mechanics of disordered systems, such as the renormalization group and path-integral methods, few of which are used by cosmologists working in this area." Lt is o be hoped that the introduction of some of these methocls may allow better physical insights into the behaviour of inear structure formation than can be fou using IN-hbodv techniques., It is to be hoped that the introduction of some of these methods may allow better physical insights into the behaviour of non-linear structure formation than can be found using brute-force $N$ -body techniques. (albeit very large) sample depends heavily on the sample itself. and therefore. in view of the detection probability found here. whether + will be or will be not detected depends also of a question ou hick.,"(albeit very large) sample depends heavily on the sample itself, and therefore, in view of the detection probability found here, whether $ r $ will be or will be not detected depends also of a question on luck." Iu addition. the results for many skies preseuted in this section show the consistency of our whole approach to deteriuue r.," In addition, the results for many skies presented in this section show the consistency of our whole approach to determine $ r $." Similar results are valid for the other cosmological parameters., Similar results are valid for the other cosmological parameters. " Tore we consider two extremal cases of bias. modelled as being au duaprecise determination of the foreground residuals R,."," Here we consider two extremal cases of bias, modelled as being an imprecise determination of the foreground residuals $ R_\ell $." We keep fixed the residuals introduced in the noise of the test covariances. while we change the residuals RP?* to soie A; XX.in the the noise. of. the observatious.. that is⋅⋅ in Eq. (9)).," We keep fixed the residuals introduced in the noise of the test covariances, while we change the residuals $ R_\ell^{XX} $ to some $ {R'}_\ell^{XX} $ in the the noise of the observations, that is in Eq. \ref{covres}) )." " Then.↴ we write⋅ = ία | ix) ). X—2T.E.D.(23) where for the numbers 3, we consider the two extremal cases: We cousider a level of of the tov model of foreground residuals displayed in Fig."," Then, we write = (1 + ^X ), X= T, E, B, where for the numbers $ \beta_\ell $ we consider the two extremal cases: We consider a level of of the toy model of foreground residuals displayed in Fig." 2 for the bias effect., \ref{foreres_TE_EE} for the bias effect. In the case we change the overall signi of ni in Eq. (21)).," In the case we change the overall sign of $ \beta_\ell^X $ in Eq. \ref{caso2}) )," we introduce au additional spurious power in the estimation at low f anda depression of the power at high (., we introduce an additional spurious power in the estimation at low $ \ell $ and a depression of the power at high $ \ell $. This would crroucously increase the probability to detect i., This would erroneously increase the probability to detect $r$. The peaks in the cosmological parameters (with the exception of kc) ect shifted mainly due to the bias from the T modes., The peaks in the cosmological parameters (with the exception of $ r $ ) get shifted mainly due to the bias from the $T$ modes. However. they stav within oue or two σ of the WALAP values.," However, they stay within one or two $ \sigma $ of the WMAP values." Iu case we do not add bias in the Fo modes. only is affected significantly by the bias;," In case we do not add bias in the $T$ modes, only $ r $ is affected significantly by the bias." Namely. in case (11) without bias in Z/ imiodes. all cosmological parameters except r peak practically at the same value as in absence of bias.," Namely, in case (ii) without bias in $T$ modes, all cosmological parameters except $ r $ peak practically at the same value as in absence of bias." Ou the contrary. the likelihood distribution for + is determined by the bias ou the B modes aud turus to be similar to the one in Fie.," On the contrary, the likelihood distribution for $ r $ is determined by the bias on the $B$ modes and turns to be similar to the one in Fig." H1 for the bias case (ii)., \ref{probd3} for the bias case (ii). The bias introduced in case Gi) goes in the opposite direction to the theoretical doublewell models where 04 jucreascs with r (see Fig. 1))., The bias introduced in case (ii) goes in the opposite direction to the theoretical double–well models where $ n_s $ increases with $ r $ (see Fig. \ref{banana}) ). " We only present here the bias for the AC DAI, model.", We only present here the bias for the $\Lambda$ $r$ model. The likelihood distributions for the ACDAIrT model includiues bias are similar to those of the ACDAIy model except for r where a lower bound shows up due to the theoretical constraint., The likelihood distributions for the $\Lambda$ $r$ T model including bias are similar to those of the $\Lambda$ $r$ model except for $ r $ where a lower bound shows up due to the theoretical constraint. We only consider here two extreme cases of bias: case (1) where bias is practically hixiuless aud case (d) where it distorts significantly the cosimological parameters. especially ¢ which is not amvimere detected.," We only consider here two extreme cases of bias: case (i) where bias is practically harmless and case (ii) where it distorts significantly the cosmological parameters, especially $ r $ which is not anymore detected." Iu this paper we provide a precise forecast for thePlanck results ou cosimological parameters. in particular for the tensortoscalar ratio r.," In this paper we provide a precise forecast for the results on cosmological parameters, in particular for the tensor–to–scalar ratio $ r $." These new forecasts eo far bevoud the published ones (see ce. PlanckCollaboration(2006).. Colomboetal. (2009)3) and pave the road for a prouisime scicutific exploitation and interpretation of the data (once cleaned from the different astroplivsical foregrounds).," These new forecasts go far beyond the published ones (see e.g. \citet{PlanckBlueBook}, \citet{otros}) ) and pave the road for a promising scientific exploitation and interpretation of the data (once cleaned from the different astrophysical foregrounds)." We appropriately combined the following. as main mgredieuts: the current public available knowledge ofPlanck iustrunmnent scusitivity and a reasonable tov model estimation of the residuals from svstematic errors aud foregrounds: the highly predictive theory setup (Bovanovslkyetal.2009:Destri2008a.b) provided by the Canzbiure-Laudan approach to inflation to produce and analyze the skies GQuock data) which allows a decisive gain iu the plivsical iusight and data analysis: precise AICAIC methods to produce the skies (mock data) aud to analyze thei.," We appropriately combined the following, as main ingredients: the current public available knowledge of instrument sensitivity and a reasonable toy model estimation of the residuals from systematic errors and foregrounds; the highly predictive theory setup \citep{reviu,mcmc1,mcmc2} provided by the Ginzburg-Landau approach to inflation to produce and analyze the skies (mock data) which allows a decisive gain in the physical insight and data analysis; precise MCMC methods to produce the skies (mock data) and to analyze them." This turus iuto an oeuprovenent in the plivsical analysis. in particular for the ratio r.," This turns into an improvement in the physical analysis, in particular for the ratio $ r $." " Tt aust be also stressed that. in the cousidered framework. better measurements for jo, will nuprove the predictions ou r from the Z. TE aud E modes even if a secure detection of B modes will be still lacking."," It must be also stressed that, in the considered framework, better measurements for $ n_s $ will improve the predictions on $ r $ from the $T$, $TE$ and $E$ modes even if a secure detection of $B$ modes will be still lacking." We remark also that the model is falsifiable iu the case of constraints ou ον aud © not compatible with the banana shape of the cousidered framework.,We remark also that the model is falsifiable in the case of constraints on $ n_s $ and $ r $ not compatible with the banana shape of the considered framework. The lower bounds and most probable value inferred from: WALAP for r (6z 0.01) in the considered framework support the search for B mode polarization in {πο data aud the future CMD £2 oricuted polarization missions., The lower bounds and most probable value inferred from WMAP for $ r $ $ r \simeq 0.04 $ ) in the considered framework support the search for $B$ mode polarization in data and the future CMB $B$ oriented polarization missions. The stress-cncrey tensor of the Uuids can be expressed as where V can be interpreted as a generalized) pressure ancl is defined by Let us emphasize that so far we have made no assumption with respect to the space-time geometry so that the above covariant expressions. based only on the exterior calculus. are valid both in (special and general) relativity and in the Newtonian limit.,"The stress-energy tensor of the fluids can be expressed as where $\Psi$ can be interpreted as a generalized pressure and is defined by Let us emphasize that so far we have made no assumption with respect to the space-time geometry so that the above covariant expressions, based only on the exterior calculus, are valid both in (special and general) relativity and in the Newtonian limit." In the following sections we will show how to construct the Lagrangian density A in cach case., In the following sections we will show how to construct the Lagrangian density $\Lambda$ in each case. We consider a uniform mixture with four constituents: neutrons. protons. electrons and. possibly muons.," We consider a uniform mixture with four constituents: neutrons, protons, electrons and possibly muons." Such a composition is expected to be found in the interior of low-mass neutron stars and in the outer core of massive neutron stars at densities above the crust-core transition density foo~ρα and below <2399. where poc2.8.LOM e-em? is the saturation density of infinite symmetric nuclear matter.," Such a composition is expected to be found in the interior of low-mass neutron stars and in the outer core of massive neutron stars at densities above the crust-core transition density $\rho_{\rm cc}\sim \rho_0/2$ and below $\lesssim 2-3 \rho_0$, where $\rho_0 \simeq 2.8\times 10^{14}$ $^{-3}$ is the saturation density of infinite symmetric nuclear matter." Given the current uncertainties on the composition of neutron star core (for a recent review see for instance 2)). it is sometimes assumed for simplicity that this composition remains the same at higher densities.," Given the current uncertainties on the composition of neutron star core (for a recent review see for instance \citealt*{haensel-06}) ), it is sometimes assumed for simplicity that this composition remains the same at higher densities." At densities below ~3po. the nucleons are essentially non-relativistic.," At densities below $\sim 3 \rho_0$, the nucleons are essentially non-relativistic." For instance. the sound velocity for the realistic model ALS|deULN? of ?.. becomes comparable to the speed of light at censities around ~Spo.," For instance, the sound velocity for the realistic model $A18+\delta v+{\rm UIX}^*$ of \citet{akmal-98}, becomes comparable to the speed of light at densities around $\sim 5 \rho_0$." Por this model. such densities are reached in very massive neutron stars with a mass larger than 24...," For this model, such densities are reached in very massive neutron stars with a mass larger than $2 M_\odot$." However the most. precisely measured neutron star masses (in neutron star binaries) lie below 1.5M. (7)., However the most precisely measured neutron star masses (in neutron star binaries) lie below $1.5 M_\odot$ \citep{lattimer-07}. . Besicles as shown by ? (chapter 3. Section 4). the effects of General relativity are negligible at the microscopic scale.," Besides as shown by \citet{glendenning-00} (chapter 3, Section 4), the effects of General relativity are negligible at the microscopic scale." Moreover at the macrocoscopic scale. the (uid velocities are small compared to the speed. of light.," Moreover at the macrocoscopic scale, the fluid velocities are small compared to the speed of light." Indeed the velocity at the equator of the most rapidly spinning neutron stars is only about ~204 of the speed of light (taking 1 ms for the period and 10 km for the radius)., Indeed the velocity at the equator of the most rapidly spinning neutron stars is only about $\sim 20\%$ of the speed of light (taking $1$ ms for the period and $10$ km for the radius). For the purpose of matching the microscopic nuclear model to the macroscopic hyvdrodynamical model. it will therefore be convenient to start with a local analysis considering non-relativistic Uuids in the Newtonian framework.," For the purpose of matching the microscopic nuclear model to the macroscopic hydrodynamical model, it will therefore be convenient to start with a local analysis considering non-relativistic fluids in the Newtonian framework." Such non-relativistic models can be also very useful by themselves for studying qualitatively the dynamics of supertluicl mixtures in neutron stars (2).., Such non-relativistic models can be also very useful by themselves for studying qualitatively the dynamics of superfluid mixtures in neutron stars \citep{andersson-01}. " In order to facilitate the correspondence »etween relativistic and non-relativistic models. we will use the fully 4D covariant formalism developed by οον,"," In order to facilitate the correspondence between relativistic and non-relativistic models, we will use the fully 4D covariant formalism developed by \citet{CCI-04,CCII-05,CCIII-05}." Ne will then show how to construct fully relativistic [uid models in Section 4. (as required for a General Relativistic description of the star)., We will then show how to construct fully relativistic fluid models in Section \ref{sect.rel.hydro} (as required for a General Relativistic description of the star). For simplicity we only consider the possible presence of the magnetic field hy supposing that leptons ancl protons are Cco-moving. as discussed in Section 1..," For simplicity we only consider the possible presence of the magnetic field by supposing that leptons and protons are co-moving, as discussed in Section \ref{sect.intro}." We therefore consider only two independent Iuids: the neutron superlluid and the Iuid of charged particles (protons. electrons and possibly muons).," We therefore consider only two independent fluids: the neutron superfluid and the fluid of charged particles (protons, electrons and possibly muons)." TFhis two-lluicd mocdel includes the limit of non-superlluid neutron star cores since in this case. all the particles are essentially co-moving and can thus be treated as a single uid. (?)..," This two-fluid model includes the limit of non-superfluid neutron star cores since in this case, all the particles are essentially co-moving and can thus be treated as a single fluid \citep{baym-69}." Including the magnetic field is in principle straightforward., Including the magnetic field is in principle straightforward. It has been recently shown that under some circumstances the magnetic field. can even be variationally taken into account in the purely Newtonian context despite the non-Calilean invariance of Alaxwell’s equations (2).., It has been recently shown that under some circumstances the magnetic field can even be variationally taken into account in the purely Newtonian context despite the non-Galilean invariance of Maxwell's equations \citep{carter-06}. " However taking into account the magnetic field as a dynamical field. implies à better understanding of the lepton dynamics as well as the proton superconductivity which is bevond the scope of the present. model,"," However taking into account the magnetic field as a dynamical field, implies a better understanding of the lepton dynamics as well as the proton superconductivity which is beyond the scope of the present model." Let us now briefly review the +cdimensional geometric structure of the Newtonian space-time (see? for a detailed discussion)., Let us now briefly review the 4-dimensional geometric structure of the Newtonian space-time (see \citealt{CCI-04} for a detailed discussion). Newtonian theory postulates the existence of a universal time £. leading to a foliation of the space-time into 3-dimensional hypersurfaces.," Newtonian theory postulates the existence of a universal time $t$, leading to a foliation of the space-time into 3-dimensional hypersurfaces." " Each of these spatial sections are [at and are endowed with the 3-dimoensional Euclidean metric. giving rise to the svimmietric contravariant tensors 7"" and ye by pushforward and by pull-back respectively."," Each of these spatial sections are flat and are endowed with the 3-dimensional Euclidean metric, giving rise to the symmetric contravariant tensors $\eta^{\mu\nu}$ and $\eta_{\mu\nu}$ by pushforward and by pull-back respectively." " Phese tensors are not metric tensors since they are degenerate where /,,ὃν and the “ether” How vector H e. normalized by the condition characterizes a particular Aristotelian [rame corresponding to the usual kind. of 311 space-time decomposition."," These tensors are not metric tensors since they are degenerate where $t_\nu = \partial_\nu t$ and the “ether” flow vector $e^\mu$ , normalized by the condition characterizes a particular Aristotelian frame corresponding to the usual kind of 3+1 space-time decomposition." The particle 4-currents introduced in Section ὸ are given by nf=nul. where ης are the corresponding particle number densities. and the Jevelocities n7 are defined by with eZ being the corresponding push forward of the usual 3-velocities in the given Avistotclianfranc.," The particle 4-currents introduced in Section \ref{sect.variation} are given by $n_{_{\rm X}}^{\, \mu}=n_{_{\rm X}} u_{_{\rm X}}^{\, \mu}$, where $n_{_{\rm X}}$ are the corresponding particle number densities, and the 4-velocities $u_{_{\rm X}}^{\, \mu}$ are defined by with $v_{_{\rm X}}^{\, \mu}$ being the corresponding push forward of the usual 3-velocities in the given Aristotelianframe." IH is easily secu from I5q. (8)), It is easily seen from Eq. \ref{eq.norm_ether}) ) that the 4+-velocitices are normalized as, that the 4-velocities are normalized as wights.,heights. Phe motion within the convectively stable region in all these cases is generated by overshooting plumes from the convectively unstable regions that lic on either side of this aver., The motion within the convectively stable region in all these cases is generated by overshooting plumes from the convectively unstable regions that lie on either side of this layer. As there is no point at which the vertical componen of momentum vanishes in any of these cases there is a route or mixing of passive and. dynamic quantities between the wo convectively unstable regions., As there is no point at which the vertical component of momentum vanishes in any of these cases there is a route for mixing of passive and dynamic quantities between the two convectively unstable regions. Only for a substantia increase in the box height will the vertical component of momentum fall to a very small value at one plane in the ron., Only for a substantial increase in the box height will the vertical component of momentum fall to a very small value at one plane in the box. However. further increase in the box height would. be extremely computationally expensive for this problem arc also unwarranted in the physical context.," However, further increase in the box height would be extremely computationally expensive for this problem and also unwarranted in the physical context." In A-type main sequence stars the separation between the unstable layers does not extend. past a couple of scale heights., In A-type main sequence stars the separation between the unstable layers does not extend past a couple of scale heights. Fherefore. on the basis of the present work we can conclude. that in A-type stars there is a clear connection between the convectively unstable zones that lic immediately. below the stellar photosphere.," Therefore, on the basis of the present work we can conclude that in A-type stars there is a clear connection between the convectively unstable zones that lie immediately below the stellar photosphere." In the context. of A-type stars. the conductivity in the convectively stable laver is not expected to vary greatly from that in the unstable zones and so. in the language of the model. the stiffness is low.," In the context of A-type stars, the conductivity in the convectively stable layer is not expected to vary greatly from that in the unstable zones and so, in the language of the model, the stiffness is low." However. from a mathematical view point it is interesting to give some consideration to what happens if the stiffness of the mic-region is increased.," However, from a mathematical view point it is interesting to give some consideration to what happens if the stiffness of the mid-region is increased." Typical values of the stiffness in the convectively stable laver in previous numerical simulations have reached: 15 (Vobiasefa£ (1998): Tobiasefaf (2001))). a very large value.," Typical values of the stiffness in the convectively stable layer in previous numerical simulations have reached 15 \cite{TBCT1}; ; \cite{TBC2}) ), a very large value." However. here we choose to push up even further to a Ss value of 30: this is certainly greater than that which is encountered. in A-type stars.," However, here we choose to push up even further to a $S_2$ value of 30; this is certainly greater than that which is encountered in A-type stars." Even such a large stiffness parameter only vields a variation of 1.91. pressure scale heights across the stable region., Even such a large stiffness parameter only yields a variation of 1.91 pressure scale heights across the stable region. Pherefore. the analytic arguments hy Latour lead us to expect that. even for such an extreme choice of the stillness parameter. there will," Therefore, the analytic arguments by Latour lead us to expect that, even for such an extreme choice of the stiffness parameter, there will" o fragments condensing out of the cise and being heated by compression.,to fragments condensing out of the disc and being heated by compression. Fig., Fig. " 6(c) shows radial velocity oofiles on the equatorial plane. normalised to the local isothermal souncl speed. e,(rz=0)/atr.0). from Run 7."," 6(c) shows radial velocity profiles on the equatorial plane, normalised to the local isothermal sound speed, $v_r(r,z\!=\!0)/a(r,z\!=\!0)$, from Run 7." The eas in the equatorial plane is close to freefall until it hits the acerction shock at the outer edge of the disc., The gas in the equatorial plane is close to freefall until it hits the accretion shock at the outer edge of the disc. " Because the disc is so extended. the material hitting the accretion shock is not moving very fast: for example. at the outer eclee of the disc it is moving with v,Alach2."," Because the disc is so extended, the material hitting the accretion shock is not moving very fast; for example, at the outer edge of the disc it is moving with $v_r\,<{\rm Mach}\,2$." ‘Thus the eas entering the disc is only heated mildby., Thus the gas entering the disc is only heated mildly. Phe racial velocity of the gas in the dise is small. although there are significant perturbations in the vicinities of fragments.," The radial velocity of the gas in the disc is small, although there are significant perturbations in the vicinities of fragments." Fig 6(d) shows azimuthal velocity. profiles on the equatorial plane. (ro.—0). from ]tun 7.," Fig 6(d) shows azimuthal velocity profiles on the equatorial plane, $v_\phi(r,z\!=\!0)$, from Run 7." Throughout the disc the gas is in approximate centrifugal balance. but because the gravitational field. is dominated by the mass of the disc. rather than the mass of the primary protostar. the profile is significantly Latter than Ixeplerian. ie. Os(dInefdInr)z;0.25. except for where it is perturbed by a forming fragment.," Throughout the disc the gas is in approximate centrifugal balance, but because the gravitational field is dominated by the mass of the disc, rather than the mass of the primary protostar, the profile is significantly flatter than Keplerian, i.e. $0\la (-d\ln v_\phi/d\ln r)\la 0.25$, except for where it is perturbed by a forming fragment." Outside the disc. the infalling matter changes from its initial solid-bocdvy Dun=O)xr to nes=O)xr teas it falls inside Q0.000AL.," Outside the disc, the infalling matter changes from its initial solid-body $\,v_\phi(r,z\!=\!0)\!\propto\! r\,$ to $\,v_\phi(r,z\!=\!0)\!\propto\! r^{-1}$, as it falls inside $\sim 10,000\,{\rm AU}$." Fig., Fig. 6(0) shows radial profiles of the disc aspect ratio. z(r)/r. from Run 7.," 6(e) shows radial profiles of the disc aspect ratio, $\,{\bar z}(r)/r$, from Run 7." The aspect ratio is almost constant at a value z(r)/r.0.6 within the inner disc (« 200AU). and it falls off sliehtly at larger radii where it is strongly perturbed by spiral armis. and ragmoents.," The aspect ratio is almost constant at a value $\,{\bar z}(r)/r\sim 0.6$ within the inner disc $r<200{\rm AU}$ ), and it falls off slightly at larger radii, where it is strongly perturbed by spiral arms and fragments." Again it is neither Hat nor Haring: theiso-density surfaces are approximately conical., Again it is neither flat nor flaring; theiso-density surfaces are approximately conical. " Since the micplanc density follows 1.5(Ααραμα)2.0 and the scale-reight varies as 2Xr. the surface-density of the cise follows )5-(dinX/dinr) 1.0. and the disc mass follows )5S(dlnM,edinr)L0."," Since the midplane density follows $1.5\la (-d\ln \rho/d\ln r)\la 2.0$ and the scale-height varies as ${\bar z}\propto r$, the surface-density of the disc follows $0.5\la (-d\ln \Sigma/d\ln r)\la 1.0$ , and the disc mass follows $0.5\la (d\ln M_{_{\rm DISC}}/d\ln r)\la 1.0$." " Phe azimuthal velocity should approximate to i,~(CALui)r7. hence 0dineαμι). 0.25. as indeed it does (see Fig."," The azimuthal velocity should approximate to $v_\phi\sim\left(GM_{_{\rm DISC}}(r)/r\right)^{1/2}$, hence $0\la (-d\ln v_\phi/d\ln r)\la 0.25$ , as indeed it does (see Fig." 6(d)). moculo the Iuctuations due to forming fragments.," 6(d)), modulo the fluctuations due to forming fragments." Fig., Fig. " 4 shows the growth of the primary orotostar. AZ (/). and the growth of the disc. Ad), (7). inRun"," 4 shows the growth of the primary protostar, $M_\star(t)$ , and the growth of the disc, $M_{_{\rm D}}(t)$ , inRun" ..: The symbiotic stars are a collection of objects which exhibit the characteristic opticalinfrared absorption bands of a cool giant upon which are superimposed. emission lines whose origin requires conditions tvpical of a much hotter object., The symbiotic stars are a collection of objects which exhibit the characteristic optical–infrared absorption bands of a cool giant upon which are superimposed emission lines whose origin requires conditions typical of a much hotter object. Multi-frequeney observations have led to the universal acceptance that they are binary svstenis. typically containing a post-asvmptotic giant branch star or main-sequence dwarf accreting matter from. a late-twpe giant. or supergiant.," Multi-frequency observations have led to the universal acceptance that they are binary systems, typically containing a post-asymptotic giant branch star or main-sequence dwarf accreting matter from a late-type giant or supergiant." Radio emission from svmbiotic stars is. dominated ov [ree-[ree radiation [rom gas ionised by the hotter of he binary companions., Radio emission from symbiotic stars is dominated by free-free radiation from gas ionised by the hotter of the binary companions. Seaquist. Tavlor Button (1984. jereafter STB) and Scaquist et ((1990. 1993) investigated he radio properties of ~100 symbioties. finding cillerences oetween the ionised regions around. D-type systems (those containing Miras. where the It emission is predominantIv rom dust) and S-type systems (containing first-ascent giants where the Lt emission is predominantly. photospheric).," Seaquist, Taylor Button (1984, hereafter STB) and Seaquist et (1990, 1993) investigated the radio properties of $\sim 100$ symbiotics, finding differences between the ionised regions around D-type systems (those containing Miras, where the IR emission is predominantly from dust) and S-type systems (containing first-ascent giants where the IR emission is predominantly photospheric)." " The SEDs of D-type systems turn over from. partially optically hick (aLo where P5x 7"") to optically thin emission (α 0.1) at centimetre wavelengths. whereas the SEDs of S-type systems remain optically thick throughout the racio regime."," The SEDs of D-type systems turn over from partially optically thick $\alpha \sim 1$, where $F_{\nu} \propto \nu^{\alpha}$ ) to optically thin emission $\alpha \sim -0.1$ ) at centimetre wavelengths, whereas the SEDs of S-type systems remain optically thick throughout the radio regime." The frequency of the turnover to optically thin free-free emission. £A. is of particular interest: in the SLB model. £jx (where a is. the binary. separation). and the optically. thin portion of the free-free spectrum is very [lat (a~ 0): in the colliding winds model οςxa.17. and the spectral index never Hattens (a~10.5. even for vz fA).," The frequency of the turnover to optically thin free-free emission, $\nu_{\rm t}$, is of particular interest: in the STB model, $\nu_{\rm t} \propto a^{-0.7}$ (where $a$ is the binary separation) and the optically thin portion of the free-free spectrum is very flat $\alpha \sim 0$ ); in the colliding winds model, $\nu_{\rm t} \propto a^{-1.5}$, and the spectral index never flattens $\alpha \sim +0.5$, even for $\nu > \nu_{\rm t}$ )." Alm/sub-nim observations have determined the spectral urnovers in several D-type systems (Ivison. Llughes Bode 1992: Seaquist lavlor 1992: Ivison et 11995).," Mm/sub-mm observations have determined the spectral turnovers in several D-type systems (Ivison, Hughes Bode 1992; Seaquist Taylor 1992; Ivison et 1995)." Until recently. 10wever. the limited sensitivity of bolometer detectors had ündered attempts to pin down the turnover frequency in quiescent S-type systems.," Until recently, however, the limited sensitivity of bolometer detectors had hindered attempts to pin down the turnover frequency in quiescent S-type systems." These are thought to be fainter. wobably because of a feedback. between the lower mass-oss rate of their earlier-tvpe. giant (compared: with D-vpe giants) and the consequent low accretion rate onto he ionising companion star.," These are thought to be fainter, probably because of a feedback between the lower mass-loss rate of their earlier-type giant (compared with D-type giants) and the consequent low accretion rate onto the ionising companion star." The result is a lower gas density and a lower flux of ionising radiation. which both ead to a lower emission measure.," The result is a lower gas density and a lower flux of ionising radiation, which both lead to a lower emission measure." Brighter S-type systems AAG Peg. PU Vul) are often recovering from. nova- outbursts making them unsuitable representives of the normally quiescent population.," Brighter S-type systems AG Peg, PU Vul) are often recovering from nova-type outbursts making them unsuitable representives of the normally quiescent population." This situation is unfortunate because the SLB model, This situation is unfortunate because the STB model astReid2006)). (INirkpatzrick20051... (Baszi2007). p," \citealt{1995AJ....110.1838R, 2006AJ....132.2360H}) \citep{2005ARA&A..43..195K}. \citep{2006AJ....132..663B, 2007ApJ...668..492A}." " = OT, | = very widest pairs (p 2 1"", « z 10100 AU)."," $\rho$ $\lesssim$ $\farcs$ $a$ $\lesssim$ very widest pairs $\rho$ $\gtrsim$ $\arcsec$, $a$ $\gtrsim$ 10–100 AU)." The short perios of the former are useful for Keplerian lass Lueasurenients ando radius queasurenients (6.8. Stassunοἳal. 2006)). both required to test low-niass stellar structure models (e.g... Chabrieretal. 20093).," The short periods of the former are useful for Keplerian mass measurements and radius measurements (e.g., \citealt{2006Natur.440..311S}) ), both required to test low-mass stellar structure models (e.g., \citealt{2009AIPC.1094..102C}) )." For those systems with independent age determinations (cluster iienibers. companions to age-dated stars}. these lüeasurenients also serve to test evolutionary theory (ZapateroOsorioetal.2001:Dupuy2009)..," For those systems with independent age determinations (cluster members, companions to age-dated stars), these measurements also serve to test evolutionary theory \citep{2004ApJ...615..958Z, 2009ApJ...692..729D}." " The identification aud study of tight VEM multiples is challenged. however. bv the need for adaptive optics-chhanced audor space-based high-resolution ασιο, and in a few Cases large-aperture lieh resolution spectroscopic monitoring(Reidetal.2002:Dazi&Rein-ers2006:Jocrgens&Müller 2007).."," The identification and study of tight VLM multiples is challenged, however, by the need for adaptive optics-enhanced and/or space-based high-resolution imaging, and in a few cases large-aperture high resolution spectroscopic monitoring \citep{2002AJ....124..519R, 2006AJ....132..663B, 2007ApJ...666L.113J}." Tn contrast. wide VLM multiples have prolibitively oue orbits for lass ieasurements. but detailed investigations of their coeval components can be made.," In contrast, wide VLM multiples have prohibitively long orbits for mass measurements, but detailed investigations of their coeval components can be made." These systems facilitate comparative analyses of low-cluperature atmospheres auc magnetic eniüssion iu the absence of age and composition dependencies (6.8. Durgasser&[ονα2006:AfcEhwainBuregasscr2006:Martinetal.relativelyIKasper 200891).," These systems facilitate comparative analyses of low-temperature atmospheres and magnetic emission in the absence of age and composition dependencies (e.g., \citealt{2006AJ....131.1007B, 2006AJ....132.2074M, 2006A&A...456..253M, 2009ApJ...695..788K}) )." Wide VLM pairs are also rare. with svsteis wider hana z 20 AU coluprisiug <2%22% ofall VEMmultiples in thefield (Allen2007:Caballero 2007a)). although a cowsvstenas exceeding 1000 separation have Όσοι identified (e.g.. Caballero2007b:AU‘ofArtigauetal.2007: 2009)).," Wide VLM pairs are also relatively rare, with systems wider than $a$ $\gtrsim$ 20 AU comprising $\lesssim$ ofall VLMmultiples in thefield \citealt{2007ApJ...668..492A,2007ApJ...667..520C}) ), although a fewsystems exceeding 1000 AU separation have been identified (e.g., \citealt{2007A&A...462L..61C, 2007ApJ...659L..49A, 2009ApJ...698..405R}) )." The rarity wide VLMlbinarics, The rarity of wide VLM binaries would also be consisent witLa low rate of dE creation in the present epoch aud a laree population of dEs formed from stἼρρθς cls.,would also be consistent with a low rate of dE creation in the present epoch and a large population of dEs formed from stripped dIs. Arguments agaiust conversion rom dls to dEs by ram pressure stripping have also been inacle on theoretical [n]0'ouuds., Arguments against conversion from dIs to dEs by ram pressure stripping have also been made on theoretical grounds. Ferguson&BinMODooel](1991) revisit this question aud offer a rough calculaion of the tiMe scae [or rau pressure stripping aud note that it is uureasonably long for distauces grealer han 300 kpe from MS (which: excludes only the very core of the Virgo cluster., \citet{FB94} revisit this question and offer a rough calculation of the time scale for ram pressure stripping and note that it is unreasonably long for distances greater than 300 kpc from M87 (which excludes only the very core of the Virgo cluster). " They conclide tha “stripphg was proyably not the domirali gas-reimova inechanism"" in the Virgo cluster.", They conclude that “stripping was probably not the dominant gas-removal mechanism” in the Virgo cluster. However. they 1ote that a nore realistic treatment of the ISM iu a cl might vie dseuilicantlv sl[9]‘ter gas removal times.," However, they note that a more realistic treatment of the ISM in a dI might yield significantly shorter gas removal times." Tle empirical counter example to tlis theoretical calculalon COLves in the form of HI observatiois of the spiral ealaxy NGC 1522 1).., The empirical counter example to this theoretical calculation comes in the form of HI observations of the spiral galaxy NGC 4522 \citep{KvGV04}. They show this 0.5 * ealaxy to be uude'eolug significar| stripping at a projected distance of 800 kpe from M 8T., They show this 0.5 $^{\star}$ galaxy to be undergoing significant stripping at a projected distance of $\sim$ 800 kpc from M 87. T1e stripping of the HI is complete to significantly hieler llbass su‘face deusities than seen in most «warf galaxies. and tlus auy gas rich dwarf in this envirounent is likely to be stripped.," The stripping of the HI is complete to significantly higher mass surface densities than seen in most dwarf galaxies, and thus any gas rich dwarf in this environment is likely to be stripped." Biπα (1985) argument concerning the lack of a progenitor population lor 1ucleatec cLEs renals as a possibe constraint on the uunber of Virgo dEs which are created as a restlt of hlripping of au infalliug dl. Uufortunately. without a couseusus view on the formation of the 1uclei of nuLcealed dEs (see.e.g..Oh&Lin2000:Biiggeli.Barazza.Jerjen2000).. it is ciffietlt to judge he streneth o Ais coustraint.," Binggeli's \markcite{B85} (1985) argument concerning the lack of a progenitor population for nucleated dEs remains as a possible constraint on the number of Virgo dEs which are created as a result of stripping of an infalling dI. Unfortunately, without a consensus view on the formation of the nuclei of nucleated dEs \citep[see, e.g.,][]{OL00, BBJ00}, it is difficult to judge the strength of this constraint." Tje fact 1iat the mtcleated CEs are more strongly cluserec than tje nou-nucleaed dEs (e.g..Biuggelieta.LOST) may be an indication that they are part of an populaion of galaxies ormed as saellites o ‘the original cluster galaxies.," The fact that the nucleated dEs are more strongly clustered than the non-nucleated dEs \citep[e.g.,][]{BTS87} may be an indication that they are part of an population of galaxies formed as satellites of the original cluster galaxies." Based oi specilic gloular cluster frequencies. Mileretal.(1998) sropose that the non-nucleated dEs are thre inore lisely dEs ο form as a resilt «of strippiig.," Based on specific globular cluster frequencies, \citet{MLFSW98} propose that the non-nucleated dEs are the more likely dEs to form as a result of stripping." However. in this regard. note that 3 of the 5 ealanies I he vanZeeetal.(2001). siiple with strong; rotationa support (v/o > 1) are nucleated dEs.," However, in this regard, note that 3 of the 5 galaxies in the \citet{vSH04} sample with strong rotational support $\sigma$ $>$ 1) are nucleated dEs." Altenatively. i is possible tha nucleated cEs could be fo1ued from dis with large central starbusts (Davies&Phillipps1955).," Alternatively, it is possible that nucleated dEs could be formed from dIs with large central starbursts \citep{DP88}." . Ftuther sttdy of their stelar populations aud structure are eeclec| to understaL Cally tle origin of he nuclei aud tjus to deermine if stripped dls cau evolve Into1ucleated dwarl ellipticals., Further study of their stellar populations and structure are needed to understand fully the origin of the nuclei and thus to determine if stripped dIs can evolve into nucleated dwarf ellipticals. yinally. a possible conce‘nh for dl to dE evolution {1rough rau pressure stripplug is a possible isparity i baryon-to-dark 1latter ratios in tlese low mass galaxies.," Finally, a possible concern for dI to dE evolution through ram pressure stripping is a possible disparity in baryon-to-dark matter ratios in these low mass galaxies." While the characteristics of he d:wk iiatter halos of the Local Group dSpli galaxies are ¢uwrentlv a matter of debae (cL.al.2002:StoelirePalinaet 2003).. it aypears tha dSpli hay lave ower dark matter-to-Iuminosity ratios thau similar luminosity dwarf irregular galaxies (e.g..Mateo1998).," While the characteristics of the dark matter halos of the Local Group dSph galaxies are currently a matter of debate \citep[cf.,][]{KWEGF02, PPAO02, SWTS02, PMSPOL03}, it appears that dSph may have lower dark matter-to-luminosity ratios than similar luminosity dwarf irregular galaxies \citep[e.g.,][]{M98}." .. However. such results shoud be viewed with some caution since dark halter 1alos are rjeasured in different. ways lor rotatLl& and non-rotatiug systems (Maeo1993).," However, such results should be viewed with some caution since dark matter halos are measured in different ways for rotating and non-rotating systems \citep{M98}." . Thus. at this time. possible discrepancies in the masses of dark matter halos aud baryou-to-dark halter ‘atios of non-rotatiug Virgo dEs are not sullicieily robust to exclude ram pressire stripping as a viable evolutionary pathway from dl to dE. Further. as shown in Figure L. the rotating Virgo dEs lave maximum rotation velocities comparable ο similar luminosity dls. suggestiug that at least," Thus, at this time, possible discrepancies in the masses of dark matter halos and baryon-to-dark matter ratios of non-rotating Virgo dEs are not sufficiently robust to exclude ram pressure stripping as a viable evolutionary pathway from dI to dE. Further, as shown in Figure \ref{fig:rot}, , the rotating Virgo dEs have maximum rotation velocities comparable to similar luminosity dIs, suggesting that at least" iowever. be some changes to merger rates because. lower mass galaxies have longer civnamical friction timescales.,"however, be some changes to merger rates because lower mass galaxies have longer dynamical friction timescales." We jan to investigate the importance of this elfect in future work., We plan to investigate the importance of this effect in future work. The correction to galaxy masses needed to make he simulated mass function agree with the observations is shown in the bottom panel of Figure 1.., The correction to galaxy masses needed to make the simulated mass function agree with the observations is shown in the bottom panel of Figure \ref{fig:mf}. In the galaxy. mass range that we consider. 210734.cMaa6oLOCAL. at ο=O. the correction is well approximated by a constant [actor of 2.75 (dotted line).," In the galaxy mass range that we consider, $2\times10^{10}\Msun < \mgal < 6\times10^{11}\Msun$ at $z=0$, the correction is well approximated by a constant factor of $2.75$ (dotted line)." Fhus we expect that a physical or numerical fix to the mass cliscrepaney would have only modest impact on the merger rates at à given mass ratio., Thus we expect that a physical or numerical fix to the mass discrepancy would have only modest impact on the merger rates at a given mass ratio. Llowever. the correction becomes more significant at. low masses (a factor of 18 for the lowest mass bin). which suggests that we may significantly overestimate the number of mergers when one parent has a mass less than 10!AL..," However, the correction becomes more significant at low masses (a factor of 18 for the lowest mass bin), which suggests that we may significantly overestimate the number of mergers when one parent has a mass less than $10^{10}\Msun$." We will use the galaxy masses from the simulations in our discussion. but when connecting to observations we note that to get the correct number density of galaxies these masses should be divided roughly by a factor of 2.75.," We will use the galaxy masses from the simulations in our discussion, but when connecting to observations we note that to get the correct number density of galaxies these masses should be divided roughly by a factor of 2.75." An alternative way to make the connection to observed galaxy populations is to match the cumulative space density above mass thresholds in our simulation to the cumulative space density computed from the observed galaxy Luminosity function (7). assuming that luminosity is a monotonic function of mass.," An alternative way to make the connection to observed galaxy populations is to match the cumulative space density above mass thresholds in our simulation to the cumulative space density computed from the observed galaxy luminosity function \citep{blan:03}, assuming that luminosity is a monotonic function of mass." The luminosities implied by this number density matching procedure are given in Table 1.., The luminosities implied by this number density matching procedure are given in Table \ref{tab:prop}. Figure 2. illustrates the merger history of three simulated &ealaxies. selected to show a range of behaviors.," Figure \ref{fig:nar} illustrates the merger history of three simulated galaxies, selected to show a range of behaviors." In the left panels. lines show the barvonic masses (stars plus cold. eas) of each galaxys progenitors as a function of lookback time.," In the left panels, lines show the baryonic masses (stars plus cold gas) of each galaxy's progenitors as a function of lookback time." In the second column. green points mark particles that are members of the galaxy at 2=0. anc blue points mark stars in other galaxies.," In the second column, green points mark particles that are members of the galaxy at $z=0$, and blue points mark stars in other galaxies." Rec points mark the surrounding gas particles. most of which are at. high temperature.," Red points mark the surrounding gas particles, most of which are at high temperature." The remaining panels show the positions of these particles at 2=0.5. 1. and 2. in regions of constant comoving size.," The remaining panels show the positions of these particles at $z=0.5$, 1, and 2, in regions of constant comoving size." Green points always represent particles that will be in the ealaxy at z—0., Green points always represent particles that will be in the galaxy at $z=0$. The topmost galaxy has three clearly identifiable progenitors at =0.5., The topmost galaxy has three clearly identifiable progenitors at $z=0.5$. It experiences two major mergers (roughly 1:3) in the final Giver. and it still has a bimoclal appearance at =0.," It experiences two major mergers (roughly 1:3) in the final Gyr, and it still has a bimodal appearance at $z=0$." In fact. SIXID splits the svstem into two components at z—0. but they are a single component at an earlier output and are therefore counted as a single ealaxy.," In fact, SKID splits the system into two components at $z=0$, but they are a single component at an earlier output and are therefore counted as a single galaxy." Phe galaxy in the micelle panels undergoes its last major merger at z1.2. and thereafter it grows by smooth accretion. doubling its mass by z=0.," The galaxy in the middle panels undergoes its last major merger at $z\sim 1.2$, and thereafter it grows by smooth accretion, doubling its mass by $z=0$." The morphological vpe recipe that we adopt in refsee:btd (similar to that in semi-analvtic models) assigns he post-merger accretion to a disk component and therefore assigns this galaxw a bulge-to-total mass ratio of ~0.5.," The morphological type recipe that we adopt in \\ref{sec:btd} (similar to that in semi-analytic models) assigns the post-merger accretion to a disk component and therefore assigns this galaxy a bulge-to-total mass ratio of $\sim 0.5$." Llowever.if some mechanism suppresses hot gas acerction at ate times (2277). then the bulge fraction would be higher (seo refsee:btd for further discussion).," However,if some mechanism suppresses hot gas accretion at late times \citep{binn:04,kkdw:03,db:04,keres:05}, then the bulge fraction would be higher (see \\ref{sec:btd} for further discussion)." Phe galaxy in the bottom xuiel experiences many mergers. but all of them are minor: our morphological type recipe would therefore identify this as a cdisk-dominated system.," The galaxy in the bottom panel experiences many mergers, but all of them are minor; our morphological type recipe would therefore identify this as a disk-dominated system." In quantitative terms. we would like to know the funetion V. where," In quantitative terms, we would like to know the function $\Psi$ where" "In this appendix we present additional material, which may be useful.","In this appendix we present additional material, which may be useful." " In particular, we show the list of all the sources in the sampled field, from the SIMBAD Astronomical Database (Table A1)) the integrated intensity map of the C!8O(1- 0) emission from our FCRAO observations (Fig. A1));"," In particular, we show the list of all the sources in the sampled field, from the SIMBAD Astronomical Database (Table \ref{SIMBAD}) ); the integrated intensity map of the $^{18}$ O(1-0) emission from our FCRAO observations (Fig. \ref{integr_tot2}) );" the channel map of our FCRAO '?CO(1-0) data (Fig. A2));, the channel map of our FCRAO $^{13}$ CO(1-0) data (Fig. \ref{13cototcanali}) ); " and finally the overlay between the '3CO(1-0) clumps and the APEX continuum clumps with the Spitzer emission at 3.6, 8 and 24 um (Fig. A3))."," and finally the overlay between the $^{13}$ CO(1-0) clumps and the APEX continuum clumps with the Spitzer emission at 3.6, 8 and 24 $\mu$ m (Fig. \ref{CO-apex-spitzer}) )." ihe fermion sphere in which it is embedded.,the fermion sphere in which it is embedded. This is the case for all the models we have caleulatec., This is the case for all the models we have calculated. " For each choice of the barvonic mass of the gas M. we obtained the radius 72, of the eas component (the radius al which (he gas pressure vanishes). the surface gravitational acceleration g. and the redshift at the gas surface 2."," For each choice of the baryonic mass of the gas $M^g$, we obtained the radius $R_g$ of the gas component (the radius at which the gas pressure vanishes), the surface gravitational acceleration $g$, and the redshift at the gas surface $z$." The redshift 2G) at radius r is defined as For g. we rewrite equations (6)) and (26)) in the following form. which defines the effective gravitational acceleration.," The redshift $z(r)$ at radius $r$ is defined as For $g$, we rewrite equations \ref{eq:dpdr}) ) and \ref{eq:dpdx}) ) in the following form, which defines the effective gravitational acceleration." At the surface of the accretecl gas. particles are nonrelativistic. thus p/p?<1.," At the surface of the accreted gas, particles are nonrelativistic, thus $p^g/\rho^g \ll 1$." The quantity X in equation (18)) is the surface mass density which is defined by dX(r)ονη., The quantity $\Sigma$ in equation \ref{eq:geff}) ) is the surface mass density which is defined by $d\Sigma(r)=\rho^g(r)\sqrt{A(r)}dr$. We also calculated an effective accretion efficienev jj=μμ)Λο. which measures the fraction of the rest mass energy of accreting matter (hat is released. when gas accretes on the ferniüon-fermion star.," We also calculated an effective accretion efficiency $\eta\equiv L_{\rm acc}/\dot Mc^2$, which measures the fraction of the rest mass energy of accreting matter that is released when gas accretes on the fermion-fermion star." This is obtained in terms of the gravitational mass of the star as follows: We show in Appendix A that 7 is given very simply in terms of the redshift at the surface of the gas sphere., This is obtained in terms of the gravitational mass of the star as follows: We show in Appendix A that $\eta$ is given very simply in terms of the redshift at the surface of the gas sphere. The relation we derive is a relativistic generalization for a (wvo-fIuid system ol a Newtonian result obtained bv Rosenbluth et al. (, The relation we derive is a relativistic generalization for a two-fluid system of a Newtonian result obtained by Rosenbluth et al. ( 1973).,1973). Figure 2 shows (he results of the caleulations., Figure 2 shows the results of the calculations. The four panels show the variations of the radius of (he gas sphere. the exavitational acceleration al its surface. the redshilt. aud the aceretion efficiency. as functions of the gas barvonic mass.," The four panels show the variations of the radius of the gas sphere, the gravitational acceleration at its surface, the redshift, and the accretion efficiency, as functions of the gas baryonic mass." With increasing gas mass. the radius of the gas sphere decreases. (he gravitational acceleration increases. ancl the reclshilt and accretion efficiency. increase.," With increasing gas mass, the radius of the gas sphere decreases, the gravitational acceleration increases, and the redshift and accretion efficiency increase." The wigele in the curves at small masses corresponds {ο a switch between (wo solution branches., The wiggle in the curves at small masses corresponds to a switch between two solution branches. Note that the maximum mass in (his sequence of models is O.782AL.: bevond this mass. the object collapses to a black hole.," Note that the maximum mass in this sequence of models is $0.782M_\odot$; beyond this mass, the object collapses to a black hole." Boson stars are macroscopic quanti states resulting [from (he sell-eravitational equilibrium of boson fiekls (see the reviews by Jetzer 1992: Lee 1992: Liddle Madsen 1992: Mielke, Boson stars are macroscopic quantum states resulting from the self-gravitational equilibrium of boson fields (see the reviews by Jetzer 1992; Lee 1992; Liddle Madsen 1992; Mielke reproducing a set of observed. datapoints.,reproducing a set of observed datapoints. Llere we are focusing on the properties of the AGN emission. and we will hence not ace this issue with respect to the stellar component (bot1 stars and cust heated by star formation)," Here we are focusing on the properties of the AGN emission, and we will hence not face this issue with respect to the stellar component (both stars and dust heated by star formation)." We will exploit the fact that the AIR domain is strongly dominated by ACN in our sample objects., We will exploit the fact that the MIR domain is strongly dominated by AGN in our sample objects. With respect to this approaci the degeneracy problem translates into the [act that there are more AC models. with cdilferent parameters. tha vield equally good or acceptable in terms of X7 values. Lits. so that the properties of the dusty torus can not be uneculvocally assessed.," With respect to this approach, the degeneracy problem translates into the fact that there are more AGN models, with different parameters, that yield equally good –or acceptable in terms of $\chi^2$ values– fits, so that the properties of the dusty torus can not be unequivocally assessed." To properly deal with this issue. we keep trace of he exploration. of the models parameter space. and we analyse the 30 best model fits for cach object of the sample.," To properly deal with this issue, we keep trace of the exploration of the model's parameter space, and we analyse the 30 best model fits for each object of the sample." For most of the objects. even when only the first wo solutions are considered the discrepancies. measured as Aparam/paramn(Q) where peremí(0) is the value of a given xwameter corresponding to the best fit model. are larger han50%.," For most of the objects, even when only the first two solutions are considered the discrepancies, measured as $\Delta param/param(0)$ where $param(0)$ is the value of a given parameter corresponding to the best fit model, are larger than." . In order to understand this behaviour one has o take into account the influence of cach of the model xwameters to the global model SEDs as well as the fac that not all parameters are independent., In order to understand this behaviour one has to take into account the influence of each of the model parameters to the global model SEDs as well as the fact that not all parameters are independent. In fact. most of them are correlated in some wav.," In fact, most of them are correlated in some way." For instance. the LoS and covering actor are tightly related: if the covering [actor is small. Los can vary ina larger interval: however as the covering factor increases. the LoS is restricted in those angles that permit direct. view of the central source. especially in the case of ugh optical depths.," For instance, the LoS and covering factor are tightly related: if the covering factor is small, LoS can vary in a larger interval; however as the covering factor increases, the LoS is restricted in those angles that permit direct view of the central source, especially in the case of high optical depths." In fact. the parameters that are best constrained: are Lace and therefore Ray (from equation 3)) and. Lin. despite he lack of points longward A= 24," In fact, the parameters that are best constrained are $\rm L_{acc}$ and therefore $\rm R_{in}$ (from equation \ref{eqn:rin}) ) and $\rm L_{IR}$ , despite the lack of points longward $\rm \lambda$ = 24." yim., Fig. .. Fig. 13. shows row the fraction of objects with stanclare deviation of the uminositv over the best fit luminosity. e(L)/L(0). ofx (plain lines). (dashed. lines). anc (dotted ines). varies as a function of the first à solutions (n ranges rom 2 to 30).," \ref{fig:Lstats} shows how the fraction of objects with standard deviation of the luminosity over the best fit luminosity, $\sigma$ (L)/L(0), of $\le$ (plain lines), $\le$ (dashed lines), and $\le$ (dotted lines), varies as a function of the first $n$ solutions $n$ ranges from 2 to 30)." Laceis shown in black while Lin is represented in red., $\rm L_{acc}$is shown in black while $\rm L_{IR}$ is represented in red. one-third of the quiet exposure time. including it increases (he signal-to-noise of the summed quiet spectrum.,"one-third of the quiet exposure time, including it increases the signal-to-noise of the summed quiet spectrum." We used the ΗΑΕ package STSDAS (version 3.3.1. 2005 March 31) to split the timetag event lists into the «quiet ancl Marine (me intervals ancl then (o extract. spectra for these intervals.," We used the IRAF package STSDAS (version 3.3.1, 2005 March 31) to split the timetag event lists into the quiet and flaring time intervals and then to extract spectra for these intervals." To split the event lists. we used the task inttag! (version 1.1. 2000 January 26).," To split the event lists, we used the task 'inttag' (version 1.1, 2000 January 26)." To ex(ract the spectra. we used the task calstis. (version 2.18. 2005 February 15) with the best calibration reference files available on 2005 Julv 10.," To extract the spectra, we used the task 'calstis' (version 2.18, 2005 February 15) with the best calibration reference files available on 2005 July 10." The calibration process removed radial velocity shifts caused by orbital motion of the spacecraft around the Earth and the Earth around the Sun., The calibration process removed radial velocity shifts caused by orbital motion of the spacecraft around the Earth and the Earth around the Sun. Ilence. every. extracted spectrum is in (the same) heliocentric reference frame.," Hence, every extracted spectrum is in (the same) heliocentric reference frame." Table 2 provides the UT and Julian Date (JD) at the start of each exposure., Table 2 provides the UT and Julian Date (JD) at the start of each exposure. YZ CMi has a measured rotation velocity ο sin 7 = 6.5 kin ! (Dellosse et al., YZ CMi has a measured rotation velocity $v$ sin $i$ = 6.5 km $^{-1}$ (Delfosse et al. 1998)., 1998). With a nominal radius of 0.2 Εμ. this corresponds (to a minimum period of 1.6 davs. considerably longer than the total (consecutive) elapsed time of the HIST exposures (~ 0.4 days).," With a nominal radius of 0.2 $_{sun}$, this corresponds to a minimum period of 1.6 days, considerably longer than the total (consecutive) elapsed time of the HST exposures $\sim$ 0.4 days)." The individual exposures comprise < of the minimum period. indicating negligible change in the location of a given active region cluring a single exposure.," The individual exposures comprise $<$ of the minimum period, indicating negligible change in the location of a given active region during a single exposure." We do not see strong evidence for smooth (non-flaring) variability within a given orbit as was found by Robinson et al. (, We do not see strong evidence for smooth (non-flaring) variability within a given orbit as was found by Robinson et al. ( 1999) in their near-ultraviolet photometric observations of YZ CALi using LIST with the High Speed Photometer instrument.,1999) in their near-ultraviolet photometric observations of YZ CMi using HST with the High Speed Photometer instrument. Our analvsis of the STIS spectrosopic data is not presently suitable for comparison with their Hare frequency analvsis. but it would be interesting to reanalvze the NLAMA (imetag data in sum over shorter time intervals to more rigorouslv identifv individual flares.," Our analysis of the STIS spectrosopic data is not presently suitable for comparison with their flare frequency analysis, but it would be interesting to reanalyze the MAMA timetag data in sum over shorter time intervals to more rigorously identify individual flares." However. this is bevond the scope of the present paper.," However, this is beyond the scope of the present paper." Figure 1 ancl Table 1 show that YZ CAH was in an obvious flaring state for approximately of the total 224 minutes of exposure time comprising the six separate exposures., Figure 1 and Table 1 show that YZ CMi was in an obvious flaring state for approximately of the total 224 minutes of exposure time comprising the six separate exposures. The flux emitted in the near-ultraviolet bandpass sampled here (2300-3050A)) is approximately 12 x10.P eres ! 7 during quiet periods., The flux emitted in the near-ultraviolet bandpass sampled here ) is approximately 4.2 $\times 10^{-12}$ ergs $^{-1}$ $^{-2}$ during quiet periods. Using a distance of 6 parsecs for YZ CMI. (he quiescent energy emitted from the visible hemisphere during the 224 minutes of exposure was ~L2xLO? eres. while the energy emitted by flares was ~1xLO eres. giving a total energy in this bandpass of ~1.3x10 eres.," Using a distance of 6 parsecs for YZ CMi, the quiescent energy emitted from the visible hemisphere during the 224 minutes of exposure was $\sim 1.2 \times 10^{32}$ ergs, while the energy emitted by flares was $\sim 1 \times 10^{31}$ ergs, giving a total energy in this bandpass of $\sim 1.3 \times 10^{32}$ ergs." The flare energv comprises ~ of the total., The flare energy comprises $\sim$ of the total. Figure 2 illustrates the spectrum summnmed over all quiet intervals., Figure 2 illustrates the spectrum summed over all quiet intervals. The line identifications were made using (he Chianti database (Dere et al., The line identifications were made using the Chianti database (Dere et al. 1997. Landi οἱ al.," 1997, Landi et al." 2006)., 2006). Clearly most of {he emission lines in the near-UV come from Fe IH. with the notable addition of the Mg II h," Clearly most of the emission lines in the near-UV come from Fe II, with the notable addition of the Mg II h" It is also worth noting that the obvious strong variation of bisector shape is in apparent contradiction to the finding of ? who found that the BIS loses its diagnostic power for extremely low vsini.,It is also worth noting that the obvious strong variation of bisector shape is in apparent contradiction to the finding of \citet{saar+donahue1997} who found that the BIS loses its diagnostic power for extremely low $v\sin i$. " Their model results were confirmed recently by ?,, who found that a lless than the spectrograph resolution (which is certainly the case for EK Eri) should yield a constant bisector shape."," Their model results were confirmed recently by \citet{desort+2007}, who found that a less than the spectrograph resolution (which is certainly the case for EK Eri) should yield a constant bisector shape." " This was confirmed by ? and ? who found negligible BIS-RV correlations for the slow (vsini«1 kms~!)) rotators andHya,, respectively."," This was confirmed by \citet{bonfils+2007} and \citet{huelamo+2008} who found negligible BIS-RV correlations for the slow $v\sin i < 1$ ) rotators and, respectively." This is in contrast to our findings as evident from Fig. 10.., This is in contrast to our findings as evident from Fig. \ref{fig:bis}. " Presently, we can offer no explanation of this."," Presently, we can offer no explanation of this." Two other aspects are worth pointing out., Two other aspects are worth pointing out. " First, while ? find the BIS-RV slope to be negative in all their simulations, we are clearly seeing mostly positive slopes, although with at least one period of negative slope as well."," First, while \citet{desort+2007} find the BIS-RV slope to be negative in all their simulations, we are clearly seeing mostly positive slopes, although with at least one period of negative slope as well." These authors however presented only a few models and only for main sequence stars., These authors however presented only a few models and only for main sequence stars. " Secondly, while ? find a clear loop pattern in the plot of RV versus H+K emission, which they interpret in terms of rotational modulation, our results are less clear, mostly due to the incomplete phase coverage."," Secondly, while \citet{bonfils+2007} find a clear loop pattern in the plot of RV versus H+K emission, which they interpret in terms of rotational modulation, our results are less clear, mostly due to the incomplete phase coverage." " However, from the time evolution of the Ryx--RV and BIS-RV relations as depicted in Figs."," However, from the time evolution of the –RV and BIS–RV relations as depicted in Figs." " 9 and 10 we can see that there appears to be different segments of similar loop patterns for different observing seasons, which could mean that these segments of the loops are not associated with the same spot regions."," \ref{fig:rhk} and \ref{fig:bis} we can see that there appears to be different segments of similar loop patterns for different observing seasons, which could mean that these segments of the loops are not associated with the same spot regions." " Indeed, if the star is viewed equator-on, then one spot or spot group is not enough to produce a sinusoidal light curve, much less the radial velocity and activity variations."," Indeed, if the star is viewed equator-on, then one spot or spot group is not enough to produce a sinusoidal light curve, much less the radial velocity and activity variations." " One possible conceptual model of EK Eri is that of an oblique rotator seen close to i=90°, with the magnetic axis of a dipolar field tilted with respect to the rotation axis."," One possible conceptual model of EK Eri is that of an oblique rotator seen close to $i=90^\circ$, with the magnetic axis of a dipolar field tilted with respect to the rotation axis." " This assumes that we approximate the star as a single dipole, which we believe is a reasonable approximation, taking into account also the results of ?.."," This assumes that we approximate the star as a single dipole, which we believe is a reasonable approximation, taking into account also the results of \citet{auriere+2008}." " Assuming that the magnetic poles are associated with the spots, we propose a model of EK Eri involving two large spots or spot-covered areas, located 180° opposite each other."," Assuming that the magnetic poles are associated with the spots, we propose a model of EK Eri involving two large spots or spot-covered areas, located $^\circ$ opposite each other." " Although ? observed no sign changes in the average longitudinal field over the photometric phase 0.21«ϕ<0.83, which would correspond to the hypothetical two spots gradually rotating into (respectively, out of) view, we note that their observations were performed during a period where EK Eri seemed to be undergoing another cycle change similar to the one of 1987-1992."," Although \citet{auriere+2008} observed no sign changes in the average longitudinal field over the photometric phase $0.21 < \phi < 0.83$, which would correspond to the hypothetical two spots gradually rotating into (respectively, out of) view, we note that their observations were performed during a period where EK Eri seemed to be undergoing another cycle change similar to the one of 1987–1992." " During these periods the light amplitude is low, indicating that spots are small and possibly dominated by dynamo-related activity rather than by the large scale dipole field."," During these periods the light amplitude is low, indicating that spots are small and possibly dominated by dynamo-related activity rather than by the large scale dipole field." " In this scenario, the light curve minima correspond to a spot facing the observer, which happens twice per rotation."," In this scenario, the light curve minima correspond to a spot facing the observer, which happens twice per rotation." " Hence, the rotation period P, of the star is not equal to Pphot, but rather twice that."," Hence, the rotation period $P_\mathrm{rot}$ of the star is not equal to $P_\mathrm{phot}$ but rather twice that." This would mean that the true latitude-averaged rotation period of EK Eri is Βιο=617.6 d. The possibility of Βιοι being two or even three times the photometric period was also mentioned by ? but not investigated further., This would mean that the true latitude-averaged rotation period of EK Eri is $P_\mathrm{rot}=617.6$ d. The possibility of $P_\mathrm{rot}$ being two or even three times the photometric period was also mentioned by \citet{auriere+2008} but not investigated further. " Such a relationship has been observed for the Sun (e.g.,?) where the rotation of active regions across the solar disk gives rise to a 13- period, i.e., half the solar rotation period."," Such a relationship has been observed for the Sun \citep[e.g.,][]{durrant+schroter1983} where the rotation of active regions across the solar disk gives rise to a 13-day period, i.e., half the solar rotation period." The phenomenon of Prot=2Povs has also been suggested for Procyon (?).., The phenomenon of $P_\mathrm{rot} = 2P_\mathrm{obs}$ has also been suggested for Procyon \citep{arentoft+2008}. " Note that the period 2Pos, would not show up in the period analysis unless the spots were of uneven size and stable over several rotations, which is clearly not the case."," Note that the period $2P_\mathrm{obs}$ would not show up in the period analysis unless the spots were of uneven size and stable over several rotations, which is clearly not the case." " Although simple, this would explain the differences seen in the Ruk--RV loop patterns which seem to change direction for every second loop, while also qualitatively explaining the appearance of the light curve."," Although simple, this would explain the differences seen in the –RV loop patterns which seem to change direction for every second loop, while also qualitatively explaining the appearance of the light curve." " Of course, we are assuming that the field is poloidal, that the spots are associated with the large scale field,and that the star is seen equator-on."," Of course, we are assuming that the field is poloidal, that the spots are associated with the large scale field,and that the star is seen equator-on." We have however not been able to produce a spot model that, We have however not been able to produce a spot model that For comparison. we derive the bestfit data using all of the 8.0 4050 data from? and fud ms;(Complete)=2.173logeP|15.058 with a standard deviation of 0.602.,"For comparison, we derive the best–fit data using all of the $8.0$ $\mu m$ data from \cite{Ngeow2008} and find $m_{8.0\mu m}(\mbox{Complete}) = -2.473\log P + 15.058$ with a standard deviation of $0.602$." The relatious given iu ? are deteriuued usine an iterative fitting method where a bestfit relation is determined aud then any Cepheids with a brightuess that is more than 30 different are removed aud a new PL relation is computed and the process repeats until the PL velation couverges., The relations given in \cite{Ngeow2008} are determined using an iterative fitting method where a best–fit relation is determined and then any Cepheids with a brightness that is more than $3\sigma$ different are removed and a new PL relation is computed and the process repeats until the PL relation converges. Here. we compute the PL relation using all of the data without the iterative approach. The liner relations are shown in Figure 9..," Here, we compute the PL relation using all of the data without the iterative approach, The linear relations are shown in Figure \ref{f4a}." Although we are oulv able to confideutlv state that Ll of the Cepheids, Although we are only able to confidently state that 44 of the Cepheids Within this resonance condition. we mav replace the time. integral. involving. cos-(ο4/jl: where Af=[>fi.,"Within this resonance condition, we may replace the time integral involving $\cos [\kappa(R)\,(t_2-t')]$: where $\Delta t\equiv t_2-t_1$." A similar simplification occurs for the sine integral. Only these factors have resonant denominators.," A similar simplification occurs for the sine integral, Only these factors have resonant denominators." Integrating Eqs. (68- 71)), Integrating Eqs. \ref{eq:delta-p-varphi2}- \ref{eq:delta-varphi2}) ) gives no change in the angular momentun. for the radial displacement. for the radial momentum. and for the Iongitucde. We are now ready to compute the torque exerted on the disk.," gives no change in the angular momentum, for the radial displacement, for the radial momentum, and for the longitude, We are now ready to compute the torque exerted on the disk." Since the torque on the unperturbed disk: vanishes. we may compute the oS average torque on the first-order perturbecl disk.," Since the torque on the unperturbed disk vanishes, we may compute the $\phi_2^{(0)}$ -averaged torque on the first-order perturbed disk." Recalling that only the m component. of the perturbation gives an angle-averagecl torque on the m component of the perturbation. we find Using Eqs. (76- 79)).," Recalling that only the $-m$ component of the perturbation gives an angle-averaged torque on the $m$ component of the perturbation, we find Using Eqs. \ref{eq:int-pp}- \ref{eq:int-p}) )," we may evaluate this as: The quantity in braces [] looks complicated. but if we substitute &(4?)2νέουςους (ef," we may evaluate this as: The quantity in braces $\{\}$ looks complicated, but if we substitute $\kappa(R)=\sqrt{C_{020}C_{002}}$ (c.f." I5. 37)), Eq. \ref{eq:kappaR}) ) " it simplifies to where the interaction amplitude is We note that while &' is formally evaluated at time |=fo. its time dependence is xοUCOu and hence its. modulus [S5""nid(0| is constant."," it simplifies to where the interaction amplitude is We note that while ${\cal S}^{(m)}$ is formally evaluated at time $t=t_2$, its time dependence is $\propto \rme^{-\rmi m\Omega_{\rm s}t}$ and hence its modulus $|{\cal S}^{(m)}(t)|$ is constant." " We can also relate S!nd lo Sno. since ""nnad—HU and since the sign of the resonant term. ο"," We can also relate ${\cal S}^{(m)}$ to ${\cal S}^{(-m)}$: since $H_1^{(-m)}=H_1^{(m)\ast}$, and since the sign of the resonant term [c.f." ", Eq. (73))]", Eq. \ref{eq:D}) )] changes when we switch from nodo nm. We can then write thefofad torque arising from both the mn ancl m resonant terms as 27—1777|157: Since DG?) Hips sign between the 25» and m resonances. Equation (86)) has now separated into two pieces.," changes when we switch from $m$ to $-m$ , We can then write the torque arising from both the $m$ and $-m$ resonant terms as $T=T^{(m)}+T^{(-m)}$: Since $D(R)$ flips sign between the $m$ and $-m$ resonances, Equation \ref{eq:T-total}) ) has now separated into two pieces." " There is an. Zi-dependent. prefactor that contains the form of the resonance. and the factor S'""nid that encodes. information on the normalization of the resonance and does not vary significantly across its width."," There is an $R$ -dependent prefactor that contains the form of the resonance, and the factor ${\cal S}^{(m)}$ that encodes information on the normalization of the resonance and does not vary significantly across its width." " ""The first piece can be simplified by noting thatit is dominated. by regions with μμ) 10 MeV).", Data from PSTAR are applicable to antiprotons in the so-called Bethe-Bloch regime $E_{p} >$ 10 MeV). For aud.. we used a wellknown scaling law (Leo&Iaase1991).," For and, we used a well-known scaling law \citep{leo90}." ". At low cucrey (QE, 10 MeV). there are several iunor effects that can cause rauges for antiprotons to deviate from the proton data."," At low energy $E_{\bar{p}}<$ 10 MeV), there are several minor effects that can cause ranges for antiprotons to deviate from the proton data." The difference in the sigu of charge affects the stopping power below 1 MeV. (Darkasetal. 1963)., The difference in the sign of charge affects the stopping power below 1 MeV \citep{barkas63}. . The stopping power for autiprotous becomes roughly twice as large as protous at the Bloch peal ] MeV) (Adamoetal.1993)., The stopping power for antiprotons becomes roughly twice as large as protons at the Bloch peak $\sim$ 1 MeV) \citep{adamo93}. ". The estimated deviation iu range is about for E,= 10 MeV. Multiple-scatteriug by atomic clectrous modifies the direction of incident particles (sieiificant at E,< I1 MeV).", The estimated deviation in range is about for $E_{\bar{p}}=$ 10 MeV. Multiple-scattering by atomic electrons modifies the direction of incident particles (significant at $E_{\bar{p}}<$ 1 MeV). Hence. effective range will be shorter than the mean range assuniue a straight line projectile.," Hence, effective range will be shorter than the mean range assuming a straight line projectile." Due to its heavy mass compared to an electron. the estimated error is less than fora 10 MeV autiprotou (Berecrctal.1999).," Due to its heavy mass compared to an electron, the estimated error is less than for a 10 MeV antiproton \citep{pstar}." . The statistical distribution iu range. so-called range strageline. must be taken iuto account.," The statistical distribution in range, so-called range straggling, must be taken into account." " A parameter &=Α/Τ, Where A: the mean cucrey loss and 1,4: the maxuma cucrey trauster in a single collision. is wach Luwger than 1 for the typical detector configuration."," A parameter $\kappa=\bar\Delta / W_{max}$, where $\bar\Delta$: the mean energy loss and $W_{max}$: the maximum energy transfer in a single collision, is much larger than 1 for the typical detector configuration." This iuplies that the range |is well described by a Craussian distribution iu the thick “tressabsorber approximation (Leo&Taase1991)., This implies that the range straggling is well described by a Gaussian distribution in the thick absorber approximation \citep{leo90}. where s ds the distance over which a particle propagates iu a material with density p., where $x$ is the distance over which a particle propagates in a material with density $\rho$ . For a material with thickness 1 geni7 and 50 MeV autiprotous. the estimated error is less than," For a material with thickness 1 $^{-2}$ and 50 MeV antiprotons, the estimated error is less than." Cross sectious for direct annihilation of antiprotous have recently been studied., Cross sections for direct annihilation of antiprotons have recently been studied. " The lowest energy οριο! was done at E,=20 MeV by the OBELIX collaboration (Bertinetal.1996).", The lowest energy experiment was done at $E_{\bar{p}}=1-20$ MeV by the OBELIX collaboration \citep{obelix96}. . Another experiment by Drückneretal.(1990) provided data at £j=20200 MeV. Although a l/c law is valid at high energies. this is modified by Coulomb attractionbetween the autiparticle aud the nucleus at low cucrev.," Another experiment by \citet{bruckner90} provided data at $E_{\bar{p}}=20-200$ MeV. Although a $1/v$ law is valid at high energies, this is modified by Coulomb attractionbetween the antiparticle and the nucleus at low energy." A ecucral form for the aunihilation cross section is (I&urki-Suonio&Silwola2000).. where eas the velocity of au incident particle in the center of lass frame.," A general form for the annihilation cross section is \citep{kurki-suonio00}, where $v^*$ is the velocity of an incident particle in the center of mass frame." We ft the above formula to the experimental data. obtaining a=12.7 mb.," We fit the above formula to the experimental data, obtaining $\sigma_0=12.7$ mb." "leratedThe probability of direct aunihilation when X is dece from By=Ey to E, Is given by. Since the stopping power is almost incepeudent of the material type. 7,,; 1s duscusitive to the atomic umber Z."," The probability of direct annihilation when $\bar{X}$ is decelerated from $E_{\bar{X}}=E_0$ to $E_1$ is given by, Since the stopping power is almost independent of the material type, $\tau_{ann}$ is insensitive to the atomic number $Z$." Loss of autiparticles by direct aunihilatiou is b.—1054 im the typical configuration of GAPS., Loss of antiparticles by direct annihilation is $5-10$ in the typical configuration of GAPS. The efficiency of particle detection depends on the orientation of the detector aud particles with respect to the ecomaeguetic field., The efficiency of particle detection depends on the orientation of the detector and particles with respect to the geomagnetic field. The mnünumuun rieicdity at some ecomaenetic latitude ο aud ecocentiic radius 7 is eiven by. where jy. is the Earth's dipole moment aud yr)./R5G0 GV (Zombeck1982:Donatoetal.," The minimum rigidity at some geomagnetic latitude $\varrho$ and geocentric radius $R$ is given by, where $\mu_{\oplus}$ is the Earth's dipole moment and $\mu_{\oplus}/R_{\oplus}^2 = 60$ GV \citep{zombeck82,donato00}." 2000).. 0 is the angle between the direction of arrival of the and the tangent to the circle of latitude., $\theta$ is the angle between the direction of arrival of the particle and the tangent to the circle of latitude. For a giventhe particleorbit. we computed είLy.Qaer) as a fraction of observation time in which a particle of kinetic energy. less than Ex can reach the detector within itsviewing anele Ὁ ," For a given orbit, we computed $\epsilon_{rig} (E_{\bar{X}}, \Omega_{det})$ as a fraction of the observation time in which a particle of kinetic energy less than $E_{\bar{X}}$ can reach the detector within itsviewing angle $\Omega_{det}$ ." "For instance. asstuning the detector sees the cutire sly. frig(Ep=1GeVyn)0.2 ou the ISS orbit (52° N). while it is increased to 0.1 at. TO"" N where a high latitude space nussion is possible."," For instance, assuming the detector sees the entire sky, $\epsilon_{rig}(E_{\bar{D}}=1\mbox{ GeV/n}) = 0.2$ on the ISS orbit $52^\circ$ N), while it is increased to 0.4 at $70^\circ$ N where a high latitude space mission is possible." different in early phase of galaxy evolution (Todini&Ferrara2001:Salvaterra 2004).,"different in early phase of galaxy evolution \citep{todini01,nozawa03,maiolino04,schneider04}." . Moreover. the effects of interstellar processing of dust grains. especially accretion of heavy elements onto dust grains. coagulation. and shattering. depend on metallicity Cor dust bundance).," Moreover, the effects of interstellar processing of dust grains, especially accretion of heavy elements onto dust grains, coagulation, and shattering, depend on metallicity (or dust abundance)." Thus. it is probable that the grain properties evolve as galaxies evolve.," Thus, it is probable that the grain properties evolve as galaxies evolve." Although it is difficult to obtain the rest-frame FIR data of distant galaxies in an early phase of galaxy evolution. there are nearby possible “templates” of primeval galaxies. blue compact dwarf galaxies (BCDs).," Although it is difficult to obtain the rest-frame FIR data of distant galaxies in an early phase of galaxy evolution, there are nearby possible “templates” of primeval galaxies, blue compact dwarf galaxies (BCDs)." Indeed. BCDs have on-going star formation in metal-poor and gas-rich. environments (Sargent&Searle1970:vanZee.Skillman.&Salzer 1998).. which could be similar to those in high-redshift star-forming galaxies.," Indeed, BCDs have on-going star formation in metal-poor and gas-rich environments \citep{sargent70,vanzee98}, which could be similar to those in high-redshift star-forming galaxies." Moreover. BCDs harbour an appreciable amount of dust (e.g.Thuan.Sauvage.&Madden1999) and can be used to investigate the dust properties in chemically unevolved galaxies (Takeuchietal.2005).," Moreover, BCDs harbour an appreciable amount of dust \citep[e.g.][]{thuan99} and can be used to investigate the dust properties in chemically unevolved galaxies \citep{takeuchi05}." . It is possible to investigate the metallicity dependence of dust properties by sampling BCDs with a variety of metallicity., It is possible to investigate the metallicity dependence of dust properties by sampling BCDs with a variety of metallicity. Recently Engelbrachtetal.(2008) have examined the metallicity dependence of dust emission in various wavelengths by using data., Recently \citet{engelbracht08} have examined the metallicity dependence of dust emission in various wavelengths by using data. " In FIR. they have used Multiband Imaging Photometer for (MIPS) 70 jim and 160 jim bands, and have shown that there is a correlation between dust temperature derived from these two bands and metallicity."," In FIR, they have used Multiband Imaging Photometer for (MIPS) 70 $\mu$ m and 160 $\mu$ m bands, and have shown that there is a correlation between dust temperature derived from these two bands and metallicity." This indicates the importance of studies on dust emission in a wide metallicity range., This indicates the importance of studies on dust emission in a wide metallicity range. The satellite (Murakamietal.2007). provides us with a good opportunity to study FIR colour-colour relations. since Far-Infrared Surveyor (FIS) on has four bands in FIR (65 jim. 90 pim. 140 jim. and. 160 πι) (Murakamietal.etal. 2007).," The satellite \citep{murakami07} provides us with a good opportunity to study FIR colour–colour relations, since Far-Infrared Surveyor (FIS) on has four bands in FIR (65 $\mu$ m, 90 $\mu$ m, 140 $\mu$ m, and 160 $\mu$ m) \citep{murakami07,kawada07}." . Indeed. seven of the eight BCDs in Hirashita(2008.hereafterHOS) are detected at 65 am. 90 jim. and 140 jim. This indicates that it is possible to study the FIR colour-colour relation of BCDs by using data.," Indeed, seven of the eight BCDs in \citet[hereafter H08]{hirashita08} are detected at 65 $\mu$ m, 90 $\mu$ m, and 140 $\mu$ m. This indicates that it is possible to study the FIR colour–colour relation of BCDs by using data." In this paper. we add four more BCDs available in the archive and examine the FIR colourcolour relation of BCDs.," In this paper, we add four more BCDs available in the archive and examine the FIR colour–colour relation of BCDs." Then. we extract information on what determines or regulates the FIR emission in metal-poor environments with the aid of theoretical models for dust emission.," Then, we extract information on what determines or regulates the FIR emission in metal-poor environments with the aid of theoretical models for dust emission." This paper is organized as follows., This paper is organized as follows. First. in Section ??.. we describe the models of dust emission with a simple radiative transfer recipe.," First, in Section \ref{sec:model}, we describe the models of dust emission with a simple radiative transfer recipe." Then. in Section ??.. we explain the data analysis of the BCD sample observed byAKAR/.," Then, in Section \ref{sec:data}, we explain the data analysis of the BCD sample observed by." . In Section ??.. we overview the results of the model caleulations in comparison with the observational data.," In Section \ref{sec:result}, we overview the results of the model calculations in comparison with the observational data." In Section ??.. we discuss our results. focusing on the relation between FIR colour and dust content.," In Section \ref{sec:discussion}, we discuss our results, focusing on the relation between FIR colour and dust content." Finally. the conclusion is presented in Section ??..," Finally, the conclusion is presented in Section \ref{sec:conclusion}." We adopt the theoretical framework of Draine&Li(2001) to calculate the SED of dust emission in FIR.," We adopt the theoretical framework of \citet{draine01} to calculate the SED of dust emission in FIR." The framework has already been described in Hirashita.Hibi.&Shibai HHS07).. but we modify it to treat BCDs in this paper.," The framework has already been described in \citet*[hereafter HHS07]{hirashita07}, but we modify it to treat BCDs in this paper." Moreover. we newly include the effect of radiative transfer in a similar way to Gallianoetal. (2003).," Moreover, we newly include the effect of radiative transfer in a similar way to \citet{galliano03}." . We overview our framework. focusing on the change from HHS07.," We overview our framework, focusing on the change from HHS07." The stellar SEDs of BCDs are generally harder than those of spiral galaxies (Boselli.Gavazzi.&S, The stellar SEDs of BCDs are generally harder than those of spiral galaxies \citep*{boselli03}. anvito2003).. Maddenetal.(2006) also show a hard stellar radiation field from the observation of mid-infrared emission lines in low-metallicity star-forming galaxies., \citet{madden06} also show a hard stellar radiation field from the observation of mid-infrared emission lines in low-metallicity star-forming galaxies. " Thus. we change the SED of ISRF. and adopt the following fitting formula according to the averaged SED of the BCD sample in Bosellietal.(2003): where AU is the ISRF intensity whose normalization is determined so that the intensity at wavelength A=0.2sam (almost the centre of the UV range: Buat&Xu1996)) is equal to the solar neighborhood ISRF estimated by Mathis.Mezger.&Pana-gia(1983) πλ is expressed in units of erg > 4). Aju is the wavelength in units of jim. 2(2) is the Planck function. (71.75)=(1000.4000WK). and (M4.105.2.90. Lot), "," Thus, we change the SED of ISRF, and adopt the following fitting formula according to the averaged SED of the BCD sample in \citet{boselli03}: where $J_\lambda^{(0)}$ is the ISRF intensity whose normalization is determined so that the intensity at wavelength $\lambda =0.2~\mu$ m (almost the centre of the UV range; \citealt{buat96}) ) is equal to the solar neighborhood ISRF estimated by \citet*{mathis83} $4\pi\lambda J_\lambda^{(0)}$ is expressed in units of erg $^{-2}$ $^{-1}$ ), $\lambda_{\mu\mathrm{m}}$ is the wavelength in units of $\mu$ m, $B_\lambda (T)$ is the Planck function, $(T_1,\, T_2)=(1000,\, 4000~\mathrm{K})$, and $(W_1,\, W_2)=(1.61\times 10^{-15},\, 2.90\times 10^{-14})$ ." In this paper. we newly include the effect of dust extinction on the ISRF.," In this paper, we newly include the effect of dust extinction on the ISRF." We simply assume that the ISRF intensity. /\. at optical depth τν is where \ is the scaling factor of the ISRF relative to JU and is assumed to be independent of wavelength.," We simply assume that the ISRF intensity, $J_\lambda$, at optical depth $\tau_\lambda$ is where $\chi$ is the scaling factor of the ISRF relative to $J_\lambda^{(0)}$ and is assumed to be independent of wavelength." " For the wavelength dependence of 74. we assume the Milky Way extinction curve taken from Cardelli,Clayton.&Mathis(1989) with ιν=3.1."," For the wavelength dependence of $\tau_\lambda$, we assume the Milky Way extinction curve taken from \citet*{cardelli89} with $R_V=3.1$." Thus. the extinction at any wavelength A. ον (in units of magnitude). can be determined if we set a value of ἐν. (extinction at V. band).," Thus, the extinction at any wavelength $\lambda$, $A_\lambda$ (in units of magnitude), can be determined if we set a value of $A_V$ (extinction at $V$ band)." The optical depth can be related with the extinction as τν=Ap/ 1.086., The optical depth can be related with the extinction as $\tau_\lambda =A_V/1.086$ . The following results does not change drastically if we assume an extinction curve appropriate for the Large Magellanic Clouds (LMC) or the Small Magellanic Cloud (SMC). since the detailed shape of UV—optical SED is not important in this paper.," The following results does not change drastically if we assume an extinction curve appropriate for the Large Magellanic Clouds (LMC) or the Small Magellanic Cloud (SMC), since the detailed shape of UV–optical SED is not important in this paper." Strictly speaking. we treat scattering as effective absorption. and this treatment would overestimate the absorbed energy.," Strictly speaking, we treat scattering as effective absorption, and this treatment would overestimate the absorbed energy." Thus. we interpret Ly: given here as effective absorption optical depth. so that the total energy absorbed by dust in our formulation is equal to the energy that would be absorbed if scattering were properly treated.," Thus, we interpret $A_V$ given here as effective absorption optical depth, so that the total energy absorbed by dust in our formulation is equal to the energy that would be absorbed if scattering were properly treated." Gallianoetal.(2003) also adopted a similar treatment. which is valid if dust is distributed in a thin shell surrounding the stars.," \citet{galliano03} also adopted a similar treatment, which is valid if dust is distributed in a thin shell surrounding the stars." Such a “screen” geometry enhances the effect of dust extinction G.e.. radiative transfer) in comparison with a mixed geometry between stars and dust.," Such a “screen” geometry enhances the effect of dust extinction (i.e., radiative transfer) in comparison with a mixed geometry between stars and dust." Thus. our models are suitable to examine the extent to which the radiative transfer effects could affect the FIR SEDs.," Thus, our models are suitable to examine the extent to which the radiative transfer effects could affect the FIR SEDs." We consider silicate and graphite grains in this paper., We consider silicate and graphite grains in this paper. Since we are interested in the wavelength range appropriate for the ΕΙΡ bands (A~ 50—180 sem: Section 3.1). we neglect polycyclic," Since we are interested in the wavelength range appropriate for the FIS bands $\lambda\sim 50$ –180 $\mu$ m; Section \ref{subsec:analysis}) ), we neglect polycyclic" dex and « 0.1 dex about the best fit lines of the Amati and Ghirlanda relations respectively.,dex and $<$ 0.1 dex about the best fit lines of the Amati and Ghirlanda relations respectively. " Interestingly, Epint is highly correlated with both Eis. Ey in G04a sample."," Interestingly, $\epi$ is highly correlated with both $\eiso$ $\eg$ in G04a sample." " However, the hope for the existence of a significant difference between the correlation coefficients of the two relations vanishes when it is found that the Amati and Ghirlanda relations,relations, have correlation coefficients that are within the 1c uncertainties of each other."," However, the hope for the existence of a significant difference between the correlation coefficients of the two relations vanishes when it is found that the Amati and Ghirlanda relations, have correlation coefficients that are within the $1\sigma$ uncertainties of each other." The uncertainties in the correlation coefficients were determined via the bootstrap method by generating a large enough number of synthetic data sets., The uncertainties in the correlation coefficients were determined via the bootstrap method by generating a large enough number of synthetic data sets. " The resulting Kendall rank correlation coefficients were Tx,a=0.65+0.16(3.50) τκ.αΞ-0.85+0.08(4.60) for the Amati Ghirlanda relations respectively."," The resulting Kendall rank correlation coefficients were $\tau_{K,A}=0.65\pm 0.16 ~(3.5\sigma)$ $\tau_{K,G}=0.85\pm 0.08 ~(4.6\sigma)$ for the Amati Ghirlanda relations respectively." " Moreover, thescatter of the Amati relation reduces to σα=0.14 when fit to the same sample of 16 LGRBs, which is comparable to the og=0.08 for the Ghirlanda relation."," Moreover, thescatter of the Amati relation reduces to $\sigma_{A}=0.14$ when fit to the same sample of 16 LGRBs, which is comparable to the $\sigma_{G}=0.08$ for the Ghirlanda relation." " The apparent correlation difference between the two relations diminishes yet further when considering thewhole sample of GRBs given in G04a, for which TK,4=0.74-£0.08(5.20) tk,g=0.80+0.07 (5.60)."," The apparent correlation difference between the two relations diminishes yet further when considering thewhole sample of GRBs given in G04a, for which $\tau_{K,A}=0.74\pm 0.08 ~(5.2\sigma)$ $\tau_{K,G}=0.80\pm 0.07 ~(5.6\sigma)$ ." Both relations have the same scatter (σ= 0.15) about their best linear fits., Both relations have the same scatter $\sigma=0.15$ ) about their best linear fits. " GRB 970508 was excluded from the above analysis because of its uncertain Ey,obs in G04a ranging from 145 KeV to >800 KeV, The small size of the G04a sample with firmly reported O;et itself raises questions about the correlation improvement of the Ghirlanda relation."," GRB 970508 was excluded from the above analysis because of its uncertain $\epo$ in G04a ranging from 145 KeV to $>$ 800 KeV, The small size of the G04a sample with firmly reported $\theta_{jet}$ itself raises questions about the correlation improvement of the Ghirlanda relation." " Furthermore, were the cited correlation improvements to have a physical origin, they should manifest themselves more strongly in larger samples of GRBs."," Furthermore, were the cited correlation improvements to have a physical origin, they should manifest themselves more strongly in larger samples of GRBs." " Unfortunately, a significantly larger sample is not yet available."," Unfortunately, a significantly larger sample is not yet available." " A recent update of the Amati, Ghirlanda Liang-Zhang relations have been given by GOT, extending the number of GRBs with firmly measured spectral data from 16 in G04a to 24 in G07."," A recent update of the Amati, Ghirlanda Liang-Zhang relations have been given by G07, extending the number of GRBs with firmly measured spectral data from 16 in G04a to 24 in G07." " Reanalyzing the sample of LGRBs given in G07, we confirm the correlations and scatters found therein: σα=0.20, og=0.09, σιΖ=0.10 for the Amati, Ghirlanda Liang-Zhang respectively."," Reanalyzing the sample of LGRBs given in G07, we confirm the correlations and scatters found therein: $\sigma_{A}=0.20$, $\sigma_{G}=0.09$, $\sigma_{LZ}=0.10$ for the Amati, Ghirlanda Liang-Zhang respectively." " However, considering the same sample of bursts (i.e. only those with firmly measured spectral data, including θει) for all three relations, the scatter of Amati relation becomes comparable to the two others (cA= 0.14)."," However, considering the same sample of bursts (i.e. only those with firmly measured spectral data, including $\theta_{jet}$ ) for all three relations, the scatter of Amati relation becomes comparable to the two others $\sigma_{A}=0.14$ )." " Also, the correlation coefficient improvement observed in 16 GRBs of G04a sample deteriorates substantially: T&,A=0.76+0.09(5.2σ) Tk,a=0.82+0.06(5.60)."," Also, the correlation coefficient improvement observed in 16 GRBs of G04a sample deteriorates substantially: $\tau_{K,A}=0.76\pm 0.09 ~(5.2\sigma)$ $\tau_{K,G}=0.82\pm 0.06 ~(5.6\sigma)$." " Including GRB 070125, GRB 071010B GRB 050904, recently found outliers to the Ghirlanda relation at >30 level (Urata et al."," Including GRB 070125, GRB 071010B GRB 050904, recently found outliers to the Ghirlanda relation at $>3\sigma$ level (Urata et al." 2009; Sugita et al., 2009; Sugita et al. 2009; Bellm et al., 2009; Bellm et al. " 2008), makes the Ghirlanda relation comparable to the Amati relation and results in TK,A=0.76+0.08(5.50) TK,G=0.73+0.07(5.40) with oa= 0.16, σα= 0.22."," 2008), makes the Ghirlanda relation comparable to the Amati relation and results in $\tau_{K,A}=0.76\pm 0.08 ~(5.5\sigma)$ $\tau_{K,G}=0.73\pm 0.07 ~(5.4\sigma)$ with $\sigma_{A}=0.16$ , $\sigma_{G}=0.22$ ." It is important to mention that we did not include any of the G07 bursts with uncertain spectral parameters (such, It is important to mention that we did not include any of the G07 bursts with uncertain spectral parameters (such (26)) and. (27)) and are independent of yin the Hill approximation.,\ref{origa}) ) and \ref{orig}) ) and are independent of $\mu$ in the Hill approximation. Vhis result also holds in an obvious extension to three dimensions., This result also holds in an obvious extension to three dimensions. The rescaled circumplanctary disc equations are then very similar to the circumstellar cise equations previously analysed or close binary stars with order unity mass ratio., The rescaled circumplanetary disc equations are then very similar to the circumstellar disc equations previously analysed for close binary stars with order unity mass ratio. One dillerence is the form of the potential. which has a singlenonaxisymmetric azimuthal number m=2 in the Hill approximation.," One difference is the form of the potential, which has a singlenonaxisymmetric azimuthal number $m=2$ in the Hill approximation." However. this is the dominant tidal term in close binaries.," However, this is the dominant tidal term in close binaries." Consider a disc in binary that orbits star 1 and is tically perturbed by star 2., Consider a disc in binary that orbits star 1 and is tidally perturbed by star 2. At a small distance rtet from star T. the potential terms due o the star 1 and the m=2 tidal component due to star 2 is given bv O=GALLfr3M»cos(20)1/(487).," At a small distance $r \ll a$ from star 1, the potential terms due to the star 1 and the $m=2$ tidal component due to star 2 is given by $\phi = -G M_1/r -3 G M_2 \, \cos(2\theta) \, r^2/(4a^3)$." This potential is similar (within a factor of 2) to the rescaled. potential of equation (21)) with €/—la=1. and masses Ad)=M»1/2.," This potential is similar (within a factor of 2) to the rescaled potential of equation \ref{phi}) ) with $G=1, a=1$, and masses $M_1 = M_2= 1/2$." In particular. the ratio of the m=2 tidal to central potentials is the same for both cases.," In particular, the ratio of the $m=2$ tidal to central potentials is the same for both cases." Therefore. the disc How equations or à planet in the Hill approximation are similar to those for a binary star system with unity mass ratio. for a given value of {ἐν and a.," Therefore, the disc flow equations for a planet in the Hill approximation are similar to those for a binary star system with unity mass ratio, for a given value of $H/r$ and $\alpha$." tesonances occur in the dise where the forcing frequency. matches a natural frequency. in the disc., Resonances occur in the disc where the forcing frequency matches a natural frequency in the disc. Angular momentum can oe transferred to the star from the dise by the tidal torques that are exerted at the Lindblad: resonances within the disc (Cioldreich&‘Tremaine1979)., Angular momentum can be transferred to the star from the disc by the tidal torques that are exerted at the Lindblad resonances within the disc \citep{goldreich79}. .. At such resonances. rotationally mocified pressure waves are launched.," At such resonances, rotationally modified pressure waves are launched." Torques are exerted on he disc at radii where the waves damp., Torques are exerted on the disc at radii where the waves damp. Resonance torques could play a role in truncating the disc., Resonance torques could play a role in truncating the disc. In this section we consider whether circular. eccentric. or vertical resonances could lie within the disc.," In this section we consider whether circular, eccentric, or vertical resonances could lie within the disc." We only consider nearly circular orbits in this analysis., We only consider nearly circular orbits in this analysis. We find this approximation holds well out to the radius where orbits begin to cross (Section 3.4))., We find this approximation holds well out to the radius where orbits begin to cross (Section \ref{cross}) ). Since we expect he disc to be truncated inside or at this radius. we should find all of the resonances present in the disc in this approximation.," Since we expect the disc to be truncated inside or at this radius, we should find all of the resonances present in the disc in this approximation." Llowever. for a disc as warm as suggested during the T Tauri accretion phase. {ένο0.3 (equation (4))). some gas might extend bevond the orbit crossing radius and olf-resonant forcing could play a role.," However, for a disc as warm as suggested during the T Tauri accretion phase, $H/r \sim 0.3$ (equation \ref{Hr}) )), some gas might extend beyond the orbit crossing radius and off-resonant forcing could play a role." Ofl-resonant forcing is possible because for m of order unity. the resonance width scales as (fr?rg.," Off-resonant forcing is possible because for $m$ of order unity, the resonance width scales as $(H/r)^{2/3}\, r_{\rm H}$." With such a laree width. the resonance could overlap with the disc. even though the cxact resonance location does not lie within the main body of the disc. as has been investigated in the binary star case by Savonije.Papaloizou&Lin(1994).," With such a large width, the resonance could overlap with the disc, even though the exact resonance location does not lie within the main body of the disc, as has been investigated in the binary star case by \cite*{savonije94}." . We apply the angular velocity of the disc in the Lill approximation given in equation (24)) to the Lindblad resonance condition Goldreich&‘Tremaine(1979)., We apply the angular velocity of the disc in the Hill approximation given in equation \ref{angvel}) ) to the Lindblad resonance condition \cite{goldreich79}. . The circular Lindblad resonances then occur where In the Hill approximation we have only the m=2 term of the potential., The circular Lindblad resonances then occur where In the Hill approximation we have only the $m=2$ term of the potential. We find that the only positions inside the orbit crossing radius is for the m=1 term which is at 2=0., We find that the only positions inside the orbit crossing radius is for the $m=1$ term which is at $R=0$. For a cold disc. the resonance width is very small and the tidal forcing is very weak near the dise center.," For a cold disc, the resonance width is very small and the tidal forcing is very weak near the disc center." For a warm disc. stronger resonant excitation is possible.," For a warm disc, stronger resonant excitation is possible." At higher order in (6077. other mevalucs are present (equation 25)).," At higher order in $\mu^{1/3}$, other $m$ -values are present (equation \ref{phiex}) )." However. these higher order resonances also fail to lie inside the orbit crossing radius.," However, these higher order resonances also fail to lie inside the orbit crossing radius." " Ifthe orbit of the planet is slightly eccentric with eccentricity e. the tidal forcing can be decomposed into a series or rigidly rotating potentials at various frequencies (£3, for integer £6 (Goldreich&Tremaine1979)."," If the orbit of the planet is slightly eccentric with eccentricity $e$, the tidal forcing can be decomposed into a series or rigidly rotating potentials at various frequencies $\ell \, \Omega_{\rm p}$ for integer $\ell$ \citep{goldreich79}." . The eccentric Lindblad resonances then occur where For m=2. the lowest order resonance that lies within the orbit crossing radius has (=7.," The eccentric Lindblad resonances then occur where For $m=2$, the lowest order resonance that lies within the orbit crossing radius has $\ell =7$." The resonant torque scales as cll2i|. where m is. the azimuthal. wavenumber ofB the tidal. potential.," The resonant torque scales as $e^{2 |l-m|}$, where $m$ is the azimuthal wavenumber of the tidal potential." . 4Consequently. the torque would scale as Ie. whichH suggests that the torque would be quite weak for modest. eccentricities.," Consequently, the torque would scale as $e^{10}$, which suggests that the torque would be quite weak for modest eccentricities." For such a resonance to be able to overcome the ellects of disc turbulent viscosity and truncate the disc. we roughly require aE(refH)7ct (sec.Artvmowiez&Lubow1994).," For such a resonance to be able to overcome the effects of disc turbulent viscosity and truncate the disc, we roughly require $\alpha \la (r/H)^2 \,e^{10}$ \citep[see,][]{artymowicz94}." . Consequently. the disc viscosity would need to be very small.," Consequently, the disc viscosity would need to be very small." There is also a set of resonances associated with the vertical disc motions., There is also a set of resonances associated with the vertical disc motions. For each m. the vertical disc resonance Lies closer to the planet than the corresponding horizontal (coplanar) Lindblad resonance. although the torque it produces is a factor of (Hr) smaller than the corresponding horizontal resonance.," For each $m$ , the vertical disc resonance lies closer to the planet than the corresponding horizontal (coplanar) Lindblad resonance, although the torque it produces is a factor of $(H/r)^2$ smaller than the corresponding horizontal resonance." The vertical resonance generates horizontally propagating waves, The vertical resonance generates horizontally propagating waves JO137--3309 was used to fix the absolute amplitude scale and to correct for the bandpass.,J0137+3309 was used to fix the absolute amplitude scale and to correct for the bandpass. Table 1 contains a summary of the observing details., Table 1 contains a summary of the observing details. The data reduction was carried out within the Common Astronomical Software Applications (CASA) package. version 3.0.2.," The data reduction was carried out within the ommon stronomical oftware pplications (CASA) package, version 3.0.2." At each frequency. the data [rom each configuration were first independently calibrated and then combined into a single UV data set.," At each frequency, the data from each configuration were first independently calibrated and then combined into a single UV data set." The imaging process was performed by setting the Briges robust parameter equal to 0. a compromise between uniform weighting of the baseline for highest angular resolution and natural weighting for highest sensitivity.," The imaging process was performed by setting the Briggs robust parameter equal to 0, a compromise between uniform weighting of the baseline for highest angular resolution and natural weighting for highest sensitivity." We also used a multi-seale CLEANing algorithm. intended for high resolution image but sensitive to extended structures (Broganetal.2006).. resulting in a single image with a rms noise ol 0.07 mJxvbeam! and a synthetic beam of 37009 for the 5 GIIz observations. and a rms noise of 0.5 mJvbeam| ancl a svnthetic beam of 18755x 18766 for the 1.4 Gllz observations.," We also used a multi-scale CLEANing algorithm, intended for high resolution image but sensitive to extended structures \citep{Brogan_06}, resulting in a single image with a rms noise of 0.07 ${\rm mJy \,beam^{-1}}$ and a synthetic beam of $ \times $ 09 for the 5 GHz observations, and a rms noise of 0.5 ${\rm mJy \, beam^{-1}}$ and a synthetic beam of $ \times$ 6 for the 1.4 GHz observations." Inlrared imaging of the field including G79.29+0.46 was performed at 3.6. 4.5. 5.8. and 8.0 jam with the InfraRed Array Camera (HAC) (Fazioetal.2004). on the Spitzer Space Telescope (Wernerοἱal.2004).," Infrared imaging of the field including G79.29+0.46 was performed at 3.6, 4.5, 5.8, and 8.0 $\mu$ m with the InfraRed Array Camera (IRAC) \citep{fazio04} on the Spitzer Space Telescope \citep{werner04}." .. AIL available data lor G79.29+0.46 from the crvogenic Spitzer mission archive were used. including AORIDs 6050560. 17330688. 217106560. and 27107534.," All available data for G79.29+0.46 from the cryogenic Spitzer mission archive were used, including AORIDs 6050560, 17330688, 27106560, and 27107584." " The observations used the 12 and 30 second IIDI. modes. which obtain integrations with frame limes of 0.6 12 seconds and 1.2 30» seconds. respectively,"," The observations used the 12 and 30 second HDR modes, which obtain integrations with frame times of 0.6 12 seconds and 1.2 30 seconds, respectively." The Basic Calibrated Data (BCD) were retrieved Irom the archive (pipeline version $13.18). and," The Basic Calibrated Data (BCD) were retrieved from the archive (pipeline version S18.18), and" as oxygen and carbon it is possible (although unlikely) that important amounts are tied up in dust and therefore not observable.,as oxygen and carbon it is possible (although unlikely) that important amounts are tied up in dust and therefore not observable. But still important conclusions can be drawn from Fig.22., But still important conclusions can be drawn from 2. " First of all, the observed points appear to lie between the curves for Z=0.02 and 0.008, i.e. there is a general agreement between the predicted and observed abundances."," First of all, the observed points appear to lie between the curves for Z=0.02 and 0.008, i.e. there is a general agreement between the predicted and observed abundances." Four PNe seem to be in the range of PNe with initial mass greater thanSMMo., Four PNe seem to be in the range of PNe with initial mass greater than. ". Three of them are bipolar nebulae: 66302, 66537 and He2-111."," Three of them are bipolar nebulae: 6302, 6537 and He2-111." They appear to have passed the stage of hot-bottom burning., They appear to have passed the stage of hot-bottom burning. " The fourth PN, M1-42, is difficult to compare with the theoretical curves because the high abundances indicate that it may have a high value of Z, and perhaps a high initial helium abundance since it lies much closer to the galactic center than the other PNe."," The fourth PN, M1-42, is difficult to compare with the theoretical curves because the high abundances indicate that it may have a high value of Z, and perhaps a high initial helium abundance since it lies much closer to the galactic center than the other PNe." " Three other bipolar PNe, 22440, Hb5 and Hul-2 appear to have a slightly lower initial mass, between and5MMo,, a value of Z=0.008 or somewhat higher, and have also have undergone hot-bottom burning, which destroys carbon to produce nitrogen and possibly some oxygen as well."," Three other bipolar PNe, 2440, Hb5 and Hu1-2 appear to have a slightly lower initial mass, between and, a value of Z=0.008 or somewhat higher, and have also have undergone hot-bottom burning, which destroys carbon to produce nitrogen and possibly some oxygen as well." The elliptical nebula 55315 is also in this category., The elliptical nebula 5315 is also in this category. " The three elliptical PNe 66153, 66886 and 22392 have rather high N/O ratios indicating initial masses slightly above4MMo."," The three elliptical PNe 6153, 6886 and 2392 have rather high N/O ratios indicating initial masses slightly above." . They have different He/H ratios however which could indicate that they are stars of different initial helium abundances., They have different He/H ratios however which could indicate that they are stars of different initial helium abundances. " All the other PNe are very close to the Z=0.008 curve for stars between initial masses of and4MMog,, and are all elliptical PNe."," All the other PNe are very close to the Z=0.008 curve for stars between initial masses of and, and are all elliptical PNe." " The only exception is the bipolar PN 66445, whose N/O ratio indicate that it is in this initial mass range but it has a much higher He/H ratio and therefore difficult to understand."," The only exception is the bipolar PN 6445, whose N/O ratio indicate that it is in this initial mass range but it has a much higher He/H ratio and therefore difficult to understand." The large majority of the nebulae can be interpreted with central star masses which agree with the helium and nitrogen abundances predicted by Karakas., The large majority of the nebulae can be interpreted with central star masses which agree with the helium and nitrogen abundances predicted by Karakas. The question now arises whether the observed carbon abundances fit into this picture., The question now arises whether the observed carbon abundances fit into this picture. Carbon abundances are somewhat more uncertain than nitrogen abundances because all the observable ions are in the ultraviolet which makes them much more dependent on correct extinction and electron temperature determination., Carbon abundances are somewhat more uncertain than nitrogen abundances because all the observable ions are in the ultraviolet which makes them much more dependent on correct extinction and electron temperature determination. We lack four determinations of carbon in these nebulae because of the very large extinction in the ultraviolet spectrum of these nebulae which made it impossible to measure the carbon lines., We lack four determinations of carbon in these nebulae because of the very large extinction in the ultraviolet spectrum of these nebulae which made it impossible to measure the carbon lines. In Fig.33 the N/O ratio has been plotted against the C/O ratio for those PNe with carbon abundances., In 3 the N/O ratio has been plotted against the C/O ratio for those PNe with carbon abundances. " The predicted values of these ratios (Karakas (2003))) as a function of stellar mass for initial values of Z=0.004, 0.008 and 0.02 are shown as points connected by dashed lines."," The predicted values of these ratios (Karakas \cite{karakas}) ) as a function of stellar mass for initial values of $=$ 0.004, 0.008 and 0.02 are shown as points connected by dashed lines." It may be seen that a very similar picture emerges as that drawn from the N/O vs He/H plot., It may be seen that a very similar picture emerges as that drawn from the N/O vs He/H plot. " The only three PNe which are close to the and lines are again the bipolar nebulae 66302, 66537 and He2-111."," The only three PNe which are close to the and lines are again the bipolar nebulae 6302, 6537 and He2-111." M1-42 now is separated from this group and is in the neighborhood of the two other bipolar PNe Hul-2 and 22440., M1-42 now is separated from this group and is in the neighborhood of the two other bipolar PNe Hu1-2 and 2440. In Hb5 the extinction is too high for the carbon lines to be measured., In Hb5 the extinction is too high for the carbon lines to be measured. " The last bipolar nebula, 66445 is again at a position of lower initial mass."," The last bipolar nebula, 6445 is again at a position of lower initial mass." " Again 55315 and 66153 are at a position predicted for a mass ofMMo,, as are 22392 and 66886."," Again 5315 and 6153 are at a position predicted for a mass of, as are 2392 and 6886." " The low helium abundance of these two PNe placed them in a more anomalous position in 22, but both the N/O and C/O ratios indicate that they are evolved from stars of initial mass somewhat more than4ΜΜς."," The low helium abundance of these two PNe placed them in a more anomalous position in 2, but both the N/O and C/O ratios indicate that they are evolved from stars of initial mass somewhat more than." . 66741 has about this mass as well., 6741 has about this mass as well. Ieiacdes as clusters having tighter MS. thereby imposing us more severe constraints on the theoretical predictions.,"Pleiades as clusters having tighter MS, thereby imposing us more severe constraints on the theoretical predictions." Perryman et al. (, Perryman et al. ( 1998) first. used. Hipparcos data to investigate the distance. structure. membership. dynamics and age of the Hyades.,"1998) first used Hipparcos data to investigate the distance, structure, membership, dynamics and age of the Hyades." In. Paper Lowe adopted: Evades parallaxes as improved by Alacsen et al. (, In Paper I we adopted Hyades parallaxes as improved by Madsen et al. ( 2000) according to their kinematical method.,2000) according to their kinematical method. In the present paper we used the latest values given. by Madsen et al. (, In the present paper we used the latest values given by Madsen et al. ( 2002): however the dilferences in the Llvacdes CAL diagram appear to be negligible.,2002); however the differences in the Hyades CM diagram appear to be negligible. Regarcing the Pleiades. Madsen. ct al. (," Regarding the Pleiades, Madsen et al. (" 2002) already observed that the kinematics does not improve the Llippareos parallaxes.,2002) already observed that the kinematics does not improve the Hipparcos parallaxes. The reddening of the Lvacles is generally assumed to be negligible (see e.g. Perryman et al., The reddening of the Hyades is generally assumed to be negligible (see e.g. Perryman et al. 1998)., 1998). As well known. the interstellar medium inside the Pleiades is not homogeneous. thus the cluster is alfected by a dillerential reddening (van Leeuwen 1983. Breeer 1986. Llansen-Ruuz van Leeuwen 1997) which produces a ALS slightly. scattered.," As well known, the interstellar medium inside the Pleiades is not homogeneous, thus the cluster is affected by a differential reddening (van Leeuwen 1983, Breger 1986, Hansen-Ruiz van Leeuwen 1997) which produces a MS slightly scattered." As a. Birst approximation we adopted the commonly accepted average value )z0.04 mag (Robichon ct al., As a first approximation we adopted the commonly accepted average value $\approx$ 0.04 mag (Robichon et al. 1999a. Mermilliod et al.," 1999a, Mermilliod et al." 1997. van Leeuwen 1999a.Pinsonneault et al.," 1997, van Leeuwen 1999a,Pinsonneault et al." 1998. Loktin. Matkin Gerasimenko 1994 cte.).," 1998, Loktin, Matkin Gerasimenko 1994 etc.)." " By adopting the above quoted values of the reddening and the distance moduli we have drown the (My). (B-V),, CAL diagrams for the two clusters shown in Fig.l: their relative location indicates that the Pleiades stars. should have lower metallicity and/or larger helium content."," By adopting the above quoted values of the reddening and the distance moduli we have drown the $_{\mathrm o}$, $_{\mathrm o}$ CM diagrams for the two clusters shown in Fig.1; their relative location indicates that the Pleiades stars should have lower metallicity and/or larger helium content." Phe aim of this work is to check if suitable theoretical models are able to reproduce the LHipparcos CAL diagram for stars of cillerent metallicities., The aim of this work is to check if suitable theoretical models are able to reproduce the Hipparcos CM diagram for stars of different metallicities. " We are mainly interested in the region not allected by external convection. that. is a region in which the [it does not depend on the free ""mixing length"" parameter."," We are mainly interested in the region not affected by external convection, that is a region in which the fit does not depend on the free “mixing length” parameter." As already. discussed in Paper 1. theoretical temperatures are indeed. independent. of the clliciency of the external convection only for stars hotter han B-¥~O-4 (where the convection. vanishes) or cooler han B-V~L.2 (where the convection becomes adiabatic)," As already discussed in Paper I, theoretical temperatures are indeed independent of the efficiency of the external convection only for stars hotter than $\sim$ 0.4 (where the convection vanishes) or cooler than $\sim$ 1.2 (where the convection becomes adiabatic)." As in Paper L we assume for the HLyvades stars Z=0.024 (sce c.g. Peorrvman ct al.," As in Paper I, we assume for the Hyades stars Z=0.024 (see e.g. Perryman et al." 1998) together with Y-0.278. as given by extrapolation of the linear relation between Y and Z. connecting metal poor Pop.," 1998) together with Y=0.278, as given by extrapolation of the linear relation between Y and Z, connecting metal poor Pop." ll sts (Z=10.1 Y=0.23) to he original composition of the Sun given by standard solar models (S8M) Z=0.02 Y=0.27 (see e.g. Pagel Portinari 1998. Castellani. DeelInnocenti Marconi 1999).,"II stars $={10}^{-4}$ $=0.23$ ) to the original composition of the Sun given by standard solar models (SSM) $=0.02$ $=0.27$ (see e.g. Pagel Portinari 1998, Castellani, Degl'Innocenti Marconi 1999)." As for the Pleiacles. recent estimates (Thevenin. 1998. Friel Joesgaard. 1990. Cirenon. 1999). eive -0.19 X Le1I] Es 0.03.," As for the Pleiades, recent estimates (Thevenin 1998, Friel Boesgaard 1990, Grenon 1999), give -0.19 $\la$ [Fe/H] $\la$ 0.03." It should be noted that Fe/1I]—0 does not necessarily correspond to the solar metallicity because the Fe/LH] value also depends on the helium content., It should be noted that [Fe/H]=0 does not necessarily correspond to the solar metallicity because the [Fe/H] value also depends on the helium content. Again according to SSM. the present metallicity and helium abundance at the solar surface. after cdillusion processes. are estimated: to o 2221001: 0.018. 0.24. reproducing the observational value: (Z/X).0.0230 (see e.g. DBahcall. Pinsonneault Basu 2001. Brun. TFurck-Chiezze Zahn 1999. Ciacio. Degl'Innocenti Ricci 1997. DeelInnocenti et al.," Again according to SSM, the present metallicity and helium abundance at the solar surface, after diffusion processes, are estimated to be $\approx$ $\div$ 0.018 $\approx$ 0.24, reproducing the observational value: $_{\odot} \sim 0.0230$ (see e.g. Bahcall, Pinsonneault Basu 2001, Brun, Turck-Chièzze Zahn 1999, Ciacio, Degl'Innocenti Ricci 1997, Degl'Innocenti et al." 1997)., 1997). Thus a star with present surface abundance of Zzz0.02 Yx0.27 shows a value of Fe/L of about 0.06., Thus a star with present surface abundance of $\approx$ 0.02 $\approx$ 0.27 shows a value of [Fe/H] of about 0.06. As discussed rclow we will adopt the value Z=0.012 for the cluster fit. which is within the observed range of metallicities.," As discussed below we will adopt the value Z=0.012 for the cluster fit, which is within the observed range of metallicities." Stellar models were computed. with a version of the FRANEC. evolutionary code (Chielli Stranicro 1989: Ciacio et al., Stellar models were computed with a version of the FRANEC evolutionary code (Chieffi Straniero 1989; Ciacio et al. 1997). improved so as to account for the most recent input physics (Cassisi et al.," 1997), improved so as to account for the most recent input physics (Cassisi et al." 1998). adopting OPAL EOS (Rogers ct al.," 1998), adopting OPAL EOS (Rogers et al." 1996) ancl using the Castelli (1999. C07) model atmospheres to derive stellar magnitudes in the selected photometric bands (see also Castelli 1998. Castelli. Gratton Ixurucz 1997).," 1996) and using the Castelli (1999, C97) model atmospheres to derive stellar magnitudes in the selected photometric bands (see also Castelli 1998, Castelli, Gratton Kurucz 1997)." As well known. a decrease of metallicity or an increase of helium shifts the MS toward higher temperatures.," As well known, a decrease of metallicity or an increase of helium shifts the MS toward higher temperatures." Thus to fi observational data one could tune these two values to within reasonable ranges., Thus to fit observational data one could tune these two values to within reasonable ranges. IH£ one fixes the metallicity at Z=0.015. to fit observations one would. need a helium abundance of Y50.30. a value which appears slightly too large.," If one fixes the metallicity at Z=0.015, to fit observations one would need a helium abundance of $\approx$ 0.30, a value which appears slightly too large." Figure 2 shows our preferred fit for the two clusters. as obtained. for a Pleiades metallicity of Z-0.012. well within the range of metallicity estimates. with a helium content of Y=0.27.," Figure 2 shows our preferred fit for the two clusters, as obtained for a Pleiades metallicity of Z=0.012, well within the range of metallicity estimates, with a helium content of Y=0.27." One inds that theoretical results nicely reproduce observations in all regions excepting the lower end of the Eyades AES: this oblem has already been analyzed in MPaper E and it will be not discussed here., One finds that theoretical results nicely reproduce observations in all regions excepting the lower end of the Hyades MS; this problem has already been analyzed in Paper I and it will be not discussed here. Interestingly enough. one finds that the »»rtion. o£ the MS. allected by external convection can be satisfactorlv fitted with the same value of the mixing length xwcameter (az1.9).," Interestingly enough, one finds that the portion of the MS affected by external convection can be satisfactorly fitted with the same value of the mixing length parameter $\alpha$ =1.9)." We conclude that the adopted stellar models seem to be able to account for the location of Ε burning structures even with cdillerent metallicitios. and that there is no evidence against the adopted: evolutionary scenario.," We conclude that the adopted stellar models seem to be able to account for the location of H burning structures even with different metallicities, and that there is no evidence against the adopted evolutionary scenario." Ehe estimated, The estimated (3) Compute the timing residuals via I5q. (30)),(3) Compute the timing residuals via Eq. \ref{diag1}) . ] is then trivial to add: deterministic processes. like cquacratic spin-downs. to the simulated timing-residuals.," It is then trivial to add deterministic processes, like quadratic spin-downs, to the simulated timing-residuals." We test our algorithm bv generating mock timine-resicuals for a number of milliseeoncl pulsars which are. positioned randomly in the sky., We test our algorithm by generating mock timing-residuals for a number of millisecond pulsars which are positioned randomly in the sky. We found it convenient to parametrise the GWD spectrum by ch, We found it convenient to parametrise the GWB spectrum by [cf. Eq. (6))],Eq. \ref{eq:spectraldensity}) )] Our mock timine-residualsὃν are a singleo realisation of GWD for some values of ef and 5 and the pulsar timing noise., Our mock timing-residuals are a single realisation of GWB for some values of $A$ and $\gamma$ and the pulsar timing noise. Ranclom quacdratic-spin-down terms are added., Random quadratic-spin-down terms are added. We then perform several separate investigations as Our algorithm is tested on several datasets in the following The mock datasets were generated with parameters resembling an experiment of 20 pulsars. with observations approximately every 5 weeks for 5 vears.," We then perform several separate investigations as Our algorithm is tested on several datasets in the following The mock datasets were generated with parameters resembling an experiment of $20$ pulsars, with observations approximately every $5$ weeks for $5$ years." The pulsar timing noise was set toan optimistic level of 100 ns cach (rms timing resicluals)., The pulsar timing noise was set to an optimistic level of $100$ ns each (rms timing residuals). In all cases the level of GWB has been set to Lv? with s=7/3.," In all cases the level of GWB has been set to $A=10^{-15} \hbox{yr}^{1/2}$ , with $\gamma=7/3$." This level of GWB is an order of magnitude smaller than the most recent upper limits of this tvpe(?).., This level of GWB is an order of magnitude smaller than the most recent upper limits of this \citep{Jenet-2006}. We then analyze this mock data using the MCMC method., We then analyze this mock data using the MCMC method. In Figs 2- 4. we see examples of the joint 24 ~ probability cistribution. obtained by these analyses.," In Figs \ref{fig:mcmc-white}- \ref{fig:mcmc-power} we see examples of the joint $A$ $\gamma$ probability distribution, obtained by these analyses." For cach dataset we also calculate the maximum likelihood value of all parameters using a conjugate directions search., For each dataset we also calculate the maximum likelihood value of all parameters using a conjugate directions search. The algorithm gives results consistent with the input parameters (ie. they recover the amplitude and the slope of the CWD within measurement errors).," The algorithm gives results consistent with the input parameters (i.e., they recover the amplitude and the slope of the GWB within measurement errors)." This was observed in all our tests., This was observed in all our tests. For al datasets we also calculated the Fisher information matrix. a matrix consisting of second-order derivatives to all parameters. at the maximum likelihood points.," For all datasets we also calculated the Fisher information matrix, a matrix consisting of second-order derivatives to all parameters, at the maximum likelihood points." We can use this matrix to approximate the posterior by à multi dimensional Gaussian. since for some particular models. this approximation is quite good.," We can use this matrix to approximate the posterior by a multi dimensional Gaussian, since for some particular models this approximation is quite good." “Phe Fisher information matrix can be calculated. in a fraction of the time needed to perform a full. ΙΟΧΙΟ analysis., The Fisher information matrix can be calculated in a fraction of the time needed to perform a full MCMC analysis. For all datasets we have plotted the loa contour of the multi dimensional Gaussian approximation., For all datasets we have plotted the $1\sigma$ contour of the multi dimensional Gaussian approximation. As an extra test. we have also used datasets &enerated » the popular pulsar timing package tempo2 (?) with a suitable GAVB simulation plug-in (Llobbs et abl.," As an extra test, we have also used datasets generated by the popular pulsar timing package tempo2 \citep{Hobbs06} with a suitable GWB simulation plug-in (Hobbs et al.," in reparation)., in preparation). We were able to generate datasets with exactly he same parameters as with our own algorithm. provided hat the timing noise was white.," We were able to generate datasets with exactly the same parameters as with our own algorithm, provided that the timing noise was white." We have confirmed. that hose datasets vield similar results when analysed with our algorithm., We have confirmed that those datasets yield similar results when analysed with our algorithm. An important point is that that the spectral form of he timing noise has a large impact on the cetectability of the GWD., An important point is that that the spectral form of the timing noise has a large impact on the detectability of the GWB. For a red. Lorentzian pulsar timing noise there is [ar greater degeneracy between. the spectral slope and amplitude in the timing residual data for the GWD than [or white pulsar timing noise. and thus the overall signal-to-noise ratio is significantly. reduced by the red component of the timing noise.," For a red Lorentzian pulsar timing noise there is far greater degeneracy between the spectral slope and amplitude in the timing residual data for the GWB than for white pulsar timing noise, and thus the overall signal-to-noise ratio is significantly reduced by the red component of the timing noise." ‘To estimate the robustness of our. algorithm.in] we also perform a maximum: likelihood search on many (a) We generate a multitude of mock timing-residual," To estimate the robustness of our algorithm, we also perform a maximum likelihood search on many (a) We generate a multitude of mock timing-residual" The three-dimnieusional motions of stars aud galaxies xovide valuable information on the local Universe. ranging from planetary companions of nearby stars to he orbital properties of ucarby galaxies aud Calactic satellites (2)..,"The three-dimensional motions of stars and galaxies provide valuable information on the local Universe, ranging from planetary companions of nearby stars to the orbital properties of nearby galaxies and Galactic satellites \citep{Unwin:2007wj}." However. because measuremenuts of proper notion must be done with respect to cosmic standards of rest. such as background galaxies aud quasistellar objects. they depend sensitively ou the nunber aud mature of background objects in the target field.," However, because measurements of proper motion must be done with respect to cosmic standards of rest, such as background galaxies and quasi-stellar objects, they depend sensitively on the number and nature of background objects in the target field." To obtain iieasuremoents of required precision. long baselines and repeat iieasurenieutfs are necessary. ranging frou several vears for space-based telescopes to teus of vears for ground-based telescopes.," To obtain measurements of required precision, long baselines and repeat measurements are necessary, ranging from several years for space-based telescopes to tens of years for ground-based telescopes." Nonetheless. despite thei low luminosities. large distances. and simall augular separations. about a dozen nearby galaxies now have measured proper motions (?)..," Nonetheless, despite their low luminosities, large distances, and small angular separations, about a dozen nearby galaxies now have measured proper motions \citep{Piatek_Fornax}." Among the nearest of these galaxies are the dwarf spheroidals. which have observed huuinosities that vary auvwhere frou ai thousand to a million times the luninositv of the Sun.," Among the nearest of these galaxies are the dwarf spheroidals, which have observed luminosities that vary anywhere from a thousand to a million times the luminosity of the Sun." " These galaxies are supported primarily by them velocity dispersion and have high inass-to-Helit ratios z100 ALL/ L.. (22???ον,"," These galaxies are supported primarily by their velocity dispersion and have high mass-to-light ratios $\simgt 100$ $_\odot/$ $_\odot$ \citep{Mateo1998,Lokas2005,Gilmore2007,StrigariRedefining, SimonGeha,Walkeretal2007}." Proper motions have heen measured for several Mülkv Way dSphs (777).. with errors ~10 iuilliareseconds per century. corresponding to transverse velocity errors —100 kins|! for typical dSpli distances.," Proper motions have been measured for several Milky Way dSphs \citep{Piatek_UrsaMinor,Piatek_Sculptor,Piatek_Fornax}, with errors $\sim 10$ milli-arcseconds per century, corresponding to transverse velocity errors $\sim 100$ km $^{-1}$ for typical dSph distances." In coutrast. their volocities in the direction of the observer are now known {ος llus |.," In contrast, their velocities in the direction of the observer are now known to $\simlt 1$ km $^{-1}$." Iu this paper. we introduce au alternative technique for determining the proper motions of Milkv Wax dSplis.," In this paper, we introduce an alternative technique for determining the proper motions of Milky Way dSphs." " Specifically, we utilize present samples of stellar πιοofsight velocities. together with the effect known as “perspective rotation."" im which the tangential motion of the ealaxy contributes to the measured line-of-sight velocity at large augular separations from the ceuter of the galaxw."," Specifically, we utilize present samples of stellar line-of-sight velocities together with the effect known as “perspective rotation,"" in which the tangential motion of the galaxy contributes to the measured line-of-sight velocity at large angular separations from the center of the galaxy." Perspective rotation has been detected iu Galactic globular clusters (7).. aud has been used to measure the distance to the Large Magellanic Cloud and the mass of MD (2.," Perspective rotation has been detected in Galactic globular clusters \citep{Merritt1997}, and has been used to measure the distance to the Large Magellanic Cloud \citep{Gould2000} and the mass of M31 \citep{vanderMarel:2007yw}." Here we show that. using perspective rotation. proper motions of several dSpls cau be determined to a precision rivaling the best existing eround aud space-based measurcmcuts.," Here we show that, using perspective rotation, proper motions of several dSphs can be determined to a precision rivaling the best existing ground and space-based measurements." Additionally. the fist proper motion mcasurcuents will be possible for several dSpls that are difficult to access via traditional micthocds.," Additionally, the first proper motion measurements will be possible for several dSphs that are difficult to access via traditional methods." Perspective rotation is simple to understand if we consider the dSphs as exteuded objects., Perspective rotation is simple to understand if we consider the dSphs as extended objects. Because of theirclose proximity and spatial extent. tle line-of-sight velocities of the stars vary as a function of projected radial separation. R. frou the center of the galaxy.," Because of theirclose proximity and spatial extent, the line-of-sight velocities of the stars vary as a function of projected radial separation, $R$, from the center of the galaxy." As R increases. the line-of-sight velocities receive increasinely larger contributions from the tanecutial motion of the object im space.," As $R$ increases, the line-of-sight velocities receive increasingly larger contributions from the tangential motion of the object in space." The net result of this racially varving hue-ofsight velocity is known as perspective rotation (?).., The net result of this radially varying line-of-sight velocity is known as perspective rotation \citep{Feast1961}. An object that is not rotating intrinsically acquires a velocity eracdicut that is proportional to the projected distance from the ceuter of the galaxy., An object that is not rotating intrinsically acquires a velocity gradient that is proportional to the projected distance from the center of the galaxy. To describe the effect of perspective rotation. we define a cartesian coordinate svsteni in which the z-axis poiuts in the direction of the observer from the ceuter of the ealaxy. the w-axis points in the direction of decreasing right ascension. and the y-axis points iu the direction of increasing declination.," To describe the effect of perspective rotation, we define a cartesian coordinate system in which the $z$ -axis points in the direction of the observer from the center of the galaxy, the $x$ -axis points in the direction of decreasing right ascension, and the $y$ -axis points in the direction of increasing declination." The angle o is measured counter-clockwise froin the positive .c-axis. and pis the angular separation from the ceuter of the galaxy.," The angle $\phi$ is measured counter-clockwise from the positive $x$ -axis, and $\rho$ is the angular separation from the center of the galaxy." The lue-ofsight velocity is then For all of the dSphs that we consider. it is appropriate to use the simall angle approximation. snp~RD. where R=/2|oF. and D is the distance to the dSph.," The line-of-sight velocity is then For all of the dSphs that we consider, it is appropriate to use the small angle approximation, $\sin \rho \simeq R/D$, where $R = \sqrt{x^2 + y^2}$, and $D$ is the distance to the dSph." Then using ysino=g/R. equation 1 can be written as Cus=letD|tyyfDes.," Then using $\sin \phi = y/R$, equation \ref{eq:vlos} can be written as $\vlos = v_x x/D + v_y y/D - v_z$." In the lit that sinpI. the Ἠπιο-οsight velocity is constant across the dSphs aud we recover in this limut that ej.= e-.," In the limit that $\sin \rho \ll 1$, the line-of-sight velocity is constant across the dSphs and we recover in this limit that $\vlos = -v_z$ ." " It is evident from equation 1 that the transverse velocities c, aud vy have the maximal contributions for galaxies that are the appropriate combination of the most nearby and the most spatially extended.", It is evident from equation \ref{eq:vlos} that the transverse velocities $v_x$ and $v_y$ have the maximal contributions for galaxies that are the appropriate combination of the most nearby and the most spatially extended. "by Sterken(2005).. quadratic fitting is often eschewed im heht-curve analysis on the grounds that it is unable to adequately model asvunuetiic light Πα,","by \citet{Ste2005}, quadratic fitting is often eschewed in light-curve analysis on the grounds that it is unable to adequately model asymmetric light minima." However. if the shape of the lizht curve docs not vary from cvcle to evele. then this bias is irrelevant: it matters not that ooccurs slightly before or after the precise time of muni. as long as the lead or lag remains invariant.," However, if the shape of the light curve does not vary from cycle to cycle, then this bias is irrelevant: it matters not that occurs slightly before or after the precise time of minimum, as long as the lead or lag remains invariant." Nevertheless. to explore anv bias introduced by the use of quadratic fitting. we have repeated our analysis using cubic fitting to measure the yvalucs.," Nevertheless, to explore any bias introduced by the use of quadratic fitting, we have repeated our analysis using cubic fitting to measure the values." Three salient points stand out from this analysis: (d) the vvalues of the cubicMH fits are not siguificautly πα than those of the quadratic fits (cf., Three salient points stand out from this re-analysis: (i) the values of the cubic fits are not significantly smaller than those of the quadratic fits (cf. Tab. 1)): MINIS G, Tab. \ref{tab:minima}) ); ( i) there's no evidence for a systematic lag or lead the quadratic and cubic nüniue: (ui) there anu obvious difference between the widths of the PDFs. which are à factor ~2 broader in the cubic cases than iu the quadratic oues.,"ii) there's no evidence for a systematic lag or lead between the quadratic and cubic minima; (iii) there an obvious difference between the widths of the PDFs, which are a factor $\sim 2$ broader in the cubic cases than in the quadratic ones." Thus. we conclude that quadratic iniu fitting docs not introduce auy appreciable bias. and moreover is the more robust approach.," Thus, we conclude that quadratic minimum fitting does not introduce any appreciable bias, and moreover is the more robust approach." The Ποπποιος star ΠΟ 37776 was found bx Alkulisekctal.(2008) to exhibit) a progressive leugthenine iu its 105387 rotation period. with a characteristic spiu-down tie nj—P/P=0.25\Ivr.," The Helium-strong star HD 37776 was found by \citet{Mik2008} to exhibit a progressive lengthening in its $1\fd5387$ rotation period, with a characteristic spin-down time $\tspin \equiv P/\dot{P} = 0.25\,{\rm Myr}$." Foro tthe absence of photomoetric data in the 19808 ancl 1990s nieans that we cannot cupirically differentiate between steady spin-down and a sequence of abrupt brakine episodes., For the absence of photometric data in the 1980s and 1990s means that we cannot empirically differentiate between steady spin-down and a sequence of abrupt braking episodes. However. the steady scenario ix lent strong support by mmaenetohydrodvnamucal (MITD) simulations of angular ποιοτα loss in magnetically chaunelled ine-driven winds (ud-Doulaetal.2009).. which indicate that the lenethenine of rotation periods should be a smooth process.," However, the steady scenario is lent strong support by magnetohydrodynamical (MHD) simulations of angular momentum loss in magnetically channelled line-driven winds \citep{udD2009}, which indicate that the lengthening of rotation periods should be a smooth process." Therefore. the use of a quadratic ephemeris (cf.," Therefore, the use of a quadratic ephemeris (cf." equ. 5)), eqn. \ref{eqn:ephem}) ) " appears justified. aud we derive a characteristic spin-down tine Tin=I.31"")anjMTbe"," appears justified, and we derive a characteristic spin-down time $\tspin = 1.34^{+0.10}_{-0.09}\,{\rm Myr}$." This value coimcides very well with the £u= predicted specifically for ον ud-Doulaetal.(2009).. from their MIID-calibrated scaling law for spin-cown times. (," This value coincides very well with the $\tspin = 1.4\,{\rm Myr}$ predicted specifically for by \citet{udD2009}, from their MHD-calibrated scaling law for spin-down times. (" Such a close agreement is partly fortuitous. given the uncertainties in stellar aud wind parameters).,"Such a close agreement is partly fortuitous, given the uncertainties in stellar and wind parameters)." Assuming that hhas remained coustaut over ther. ‘lifepintime of M star iuples that it can be nuo older than 1.16rotatingSMS (otherwise. it would at some stage have been faster than the critical rate Par~015).," Assuming that has remained constant over the lifetime of the star implies that it can be no older than $1.16^{+0.09}_{-0.08}\,{\rm Myr}$ (otherwise, it would at some stage have been rotating faster than the critical rate $P_{\rm crit} \sim 0\fd5$ )." This upper limit ou the age fits within the lower portion of the 0.5.8Myr age range estimated for the σ Oxionis cluster (Caballero2007.audreferencestherein)..," This upper limit on the age fits within the lower portion of the $0.5-8\,{\rm Myr}$ age range estimated for the $\sigma$ Orionis cluster \citep[][and references therein]{Cab2007}." lu suunuuw. then. we couclude that the observations are consistent with uundersoiug rotational braking due to its magnetized line-dziven wind.," In summary, then, we conclude that the observations are consistent with undergoing rotational braking due to its magnetized line-driven wind." This result is significant: although maguetic rotational braking is inferred from population studies of low-mass stars (6.8.Donati&Laudstreot2009).. direct nieasurement of spin-down in an iudividual (uou-degenerate) object is noteworthy. aud has been achieved so far for only handful of magnetic B and A stars (seeMikuláseketal.2009).," This result is significant: although magnetic rotational braking is inferred from population studies of low-mass stars \citep[e.g.,][]{DonLan2009}, direct measurement of spin-down in an individual (non-degenerate) object is noteworthy, and has been achieved so far for only handful of magnetic B and A stars \citep[see][]{Mik2009}." RUDT. DIC and SPO acknowledge support from NASA exaut NNGUOS5SCC36C. We thauk the referee. Prof. Johu Laudstrect. for lis thoughtful consideration of the paper.," RHDT, DHC and SPO acknowledge support from NASA grant NNG05GC36G. We thank the referee, Prof. John Landstreet, for his thoughtful consideration of the paper." This research has made use of NASA's Astroplysics Data System Bibliographic Services., This research has made use of NASA's Astrophysics Data System Bibliographic Services. holds even when the cooling rate is enhanced in the mnocoel as discussed in (ii).,holds even when the cooling rate is enhanced in the model as discussed in (ii). The primary limitation of current. cosmological SPL simulations is the relatively poor resolution attainable even with the largest computers., The primary limitation of current cosmological SPH simulations is the relatively poor resolution attainable even with the largest computers. ὃν comparing our SPL or mmodels to the full semi-analvtic mocel (FSA). we eain some idea of how important these resolution ellects are in practice.," By comparing our SPH or models to the full semi-analytic model (FSA), we gain some idea of how important these resolution effects are in practice." Furthermore. since the nunocdel includes prescriptions for star. formation and feedback that are not modelled at all in the SPL simulations we have considered. we can also assess how important these processes are in determining the properties of hot ane cold eas in the mocderately large galaxies that form in our SPI simulations.," Furthermore, since the model includes prescriptions for star formation and feedback that are not modelled at all in the SPH simulations we have considered, we can also assess how important these processes are in determining the properties of hot and cold gas in the moderately large galaxies that form in our SPH simulations." The total amount of gas that can cool in an SPI simulation is determined bv the resolution limit., The total amount of gas that can cool in an SPH simulation is determined by the resolution limit. On the other hand. because of its intrinsically high resolution. the semi-analvtic model traces the evolution of gas even in small halos which the SPIE simulation assigns to the uncollapsed phase.," On the other hand, because of its intrinsically high resolution, the semi-analytic model traces the evolution of gas even in small halos which the SPH simulation assigns to the uncollapsed phase." As a result. not only is the fraction of halo gas (hot and cold) larger in the mmocel than in the SPILL simulation. but its cold gas mass function extends to smaller masses that can be resolved in the SPI simulation.," As a result, not only is the fraction of halo gas (hot and cold) larger in the model than in the SPH simulation, but its cold gas mass function extends to smaller masses that can be resolved in the SPH simulation." Phe FSA cold gas mass function has a much sharper cut-oll at the massive end than either the oor SPLE models., The FSA cold gas mass function has a much sharper cut-off at the massive end than either the or SPH models. In summary. our comparisons demonstrate a higher level of consistenev than was perhaps expected between the results. of ΙΙ simulations and the more icealized semi-analvtic models.," In summary, our comparisons demonstrate a higher level of consistency than was perhaps expected between the results of SPH simulations and the more idealized semi-analytic models." X particularly. uncertain component of the semi-analvtic treatment ds the assumption that gas cools from a quasi-equilibrium state established. when the gas is shock-heatec to the virial temperature. of halo during collapse., A particularly uncertain component of the semi-analytic treatment is the assumption that gas cools from a quasi-equilibrium state established when the gas is shock-heated to the virial temperature of a halo during collapse. Our comparisons do not test. this assumption cirectlv. only its net elfect on. the amount of gas that cools.," Our comparisons do not test this assumption directly, only its net effect on the amount of gas that cools." Globallv.. this turns out to. be very similar to the SPL result.," Globally, this turns out to be very similar to the SPH result." However. the semi-analvtic model tends to produce somewhat less cool gas in massive halos than the SPILL simulation. particularly in the CDM cosmology.," However, the semi-analytic model tends to produce somewhat less cool gas in massive halos than the SPH simulation, particularly in the $\Lambda$ CDM cosmology." We stress that due to the limited: resolution of our SPIEL simulations. our conclusions are restricted to massive. galaxies.. with. barvonic. mass of⋅ z107NM...," We stress that due to the limited resolution of our SPH simulations, our conclusions are restricted to massive galaxies, with baryonic mass of $\gsim 10^{11}M_{\odot}$." Lt will be important to check whether our results still hold in higher resolution simulations., It will be important to check whether our results still hold in higher resolution simulations. In this paper we have focussed. on statistical properties of the galaxy population., In this paper we have focussed on statistical properties of the galaxy population. Agreement at this level does not necessarily imply agreement on the properties of galaxies on a case-by-case basis., Agreement at this level does not necessarily imply agreement on the properties of galaxies on a case-by-case basis. We intend to examine this question in future work., We intend to examine this question in future work. Our present results. however. provide useful support for the reliability of current techniques for modelling galaxy formation in a cosmological Context.," Our present results, however, provide useful support for the reliability of current techniques for modelling galaxy formation in a cosmological context." AJB and CSE acknowledge receipt of à PPARC Studentship and Senior Fellowship respectively., AJB and CSF acknowledge receipt of a PPARC Studentship and Senior Fellowship respectively. CSE also acknowledges receipt of a Leverhulme Research Fellowship., CSF also acknowledges receipt of a Leverhulme Research Fellowship. This work was supported in part by a PPARC rolling grant and by the European Community's Ελα Network for Galaxy Formation and Evolution., This work was supported in part by a PPARC rolling grant and by the European Community's TMR Network for Galaxy Formation and Evolution. We acknowledge the Virgo Consortium for making available the simulations used in this study and our colleagues. Shaun Cole and Cedric Lacey. for allowing us to use results from the Durham semi-analvtic ealaxy formation model.," We acknowledge the Virgo Consortium for making available the simulations used in this study and our colleagues, Shaun Cole and Cedric Lacey, for allowing us to use results from the Durham semi-analytic galaxy formation model." We are. grateful Shaun Cole and David Weinberg for many stimulating discussions. aud to James Binney whose incisive questions encouraged: us to pursue this project.," We are grateful to Shaun Cole and David Weinberg for many stimulating discussions, and to James Binney whose incisive questions encouraged us to pursue this project." Phese simulations were carried. out on the T3D at the Edinburgh Parallel. Computing Centre οςο), These simulations were carried out on the T3D at the Edinburgh Parallel Computing Centre (EPCC). AMeger et al. (,Breger et al. ( 2005).,2005). Phis led to 80 amplitude and SO phase (epoch) values., This led to 80 amplitude and 80 phase (epoch) values. These were used to prewhiten the data for all the frequencies outside the chosen frequency range. Lc. fewer than SO frequencies were used. (," These were used to prewhiten the data for all the frequencies outside the chosen frequency range, i.e., fewer than 80 frequencies were used. (" b) The data were divided. into time bins covering »proximately one week.,b) The data were divided into time bins covering approximately one week. The actual time covered in each bin depended on the coverage and the number of measurements available so that in some cases slightly longer time bins were chosen. (, The actual time covered in each bin depended on the coverage and the number of measurements available so that in some cases slightly longer time bins were chosen. ( c) To improve the signal/noise ratio it is useful lo nalvze the e and y data together.,c) To improve the signal/noise ratio it is useful to analyze the $v$ and $y$ data together. “Phe pulsations of the star are. however. wavelength dependent.," The pulsations of the star are, however, wavelength dependent." The prewhitencc frequencies. were treated correctly. since the prewhitening was performed with separate solutions for the two passbancds.," The prewhitened frequencies were treated correctly, since the prewhitening was performed with separate solutions for the two passbands." This only leaves potential problems for the moce(s) inside the chosen frequeney region of interest., This only leaves potential problems for the mode(s) inside the chosen frequency region of interest. They were solved in the following manner: The larger pulsation amplitudes in the (0 passband were corrected for by. scaling the magnitudes by an experimentally determined. factor of 0.70 and increasing the weight in all the caleulations by 1/0.70., They were solved in the following manner: The larger pulsation amplitudes in the $v$ passband were corrected for by scaling the magnitudes by an experimentally determined factor of 0.70 and increasing the weight in all the calculations by 1/0.70. The phase lags between the two passbands: were taken into account bv computing for each time bin the deviations in phase from an overall average for the passband. (, The phase lags between the two passbands were taken into account by computing for each time bin the deviations in phase from an overall average for the passband. ( d) We then adopted the best value ofa single frequency inside the frequency. region of interest. and. computed. the amplitude changes and. phase shifts for cach time bin.,d) We then adopted the best value of a single frequency inside the frequency region of interest and computed the amplitude changes and phase shifts for each time bin. The results were examined for consistency between the separate vears and the relationship between the measured amplitude and phase changes (e.g... see the comparison shown in Fig.," The results were examined for consistency between the separate years and the relationship between the measured amplitude and phase changes (e.g., see the comparison shown in Fig." 1). (, 1). ( ο) A two-frequeney model to give the lowest residuals in magnitudes was determined from Fourier analyses of the observed. light curves. and. multifrequeney. fits. [from PEHRIODO4 (Lenz Breger 2005).,e) A two-frequency model to give the lowest residuals in magnitudes was determined from Fourier analyses of the observed light curves and multifrequency fits from PERIOD04 (Lenz Breger 2005). Phe result was check by a Fourier analysis of the observed. amplitude variations. (, The result was checked by a Fourier analysis of the observed amplitude variations. ( £) Phe two-frequeney mocel was used to replace the observed. magnitudes by predictions for the same times of measurement.,f) The two-frequency model was used to replace the observed magnitudes by predictions for the same times of measurement. We used the method outlined: previously. in (d) to compute the sinele-frequcney amplitude changes an phase shifts for each time bin (this time. however. for the predicted. tvo-[requeney. data).," We used the method outlined previously in (d) to compute the single-frequency amplitude changes and phase shifts for each time bin (this time, however, for the predicted two-frequency data)." These were then compare with the values derived from the actual observations and are shown as dotted lines in Figs., These were then compared with the values derived from the actual observations and are shown as dotted lines in Figs. 1 to 4., 1 to 4. We have subcdivided the available data from 2002 .— 2004 and. applied the method. deseribed in the previous section., We have subdivided the available data from 2002 – 2004 and applied the method described in the previous section. The best single frequency. was found to be 12.15412 evele d+., The best single frequency was found to be 12.15412 cycle $^{-1}$. ig., Fig. P shows the variations in amplitude and phase for the three vears., 1 shows the variations in amplitude and phase for the three years. In this figure. the uncertainties were calculated by using the standard: relations lor calculating amplitude and. phasing uncertainties (Breger et al.," In this figure, the uncertainties were calculated by using the standard relations for calculating amplitude and phasing uncertainties (Breger et al." 1999b) together with error propogation Formulae to account for the measurements in two cdilferent. passbands., 1999b) together with error propogation formulae to account for the measurements in two different passbands. The variations are similar in all three vears with a beat period of dd. Another important result is that the phase changes are coupled to the amplitude changes., The variations are similar in all three years with a beat period of d. Another important result is that the phase changes are coupled to the amplitude changes. In particular. minimum. amplitude occurs at the time of ‘average’ phase and the time of most rapid. phase change.," In particular, minimum amplitude occurs at the time of 'average' phase and the time of most rapid phase change." This suggests beating hy two separate close frequencies., This suggests beating by two separate close frequencies. Ehe visual result is confirmed. by a two-frequeney model with the optimum parameters of [requenev. amplitude ancl phase determined by PERIODOA.," The visual result is confirmed by a two-frequency model with the optimum parameters of frequency, amplitude and phase determined by PERIOD04." Xn excellent agreement is obtained for both the amplitude and. phase changes with the two-f[requeney model., An excellent agreement is obtained for both the amplitude and phase changes with the two-frequency model. Lowe extend the analysis to include the 1995 data. we also find an excellent agreement between the predicted. anc observed amplitudes and phases of the earlier measurements.," If we extend the analysis to include the 1995 data, we also find an excellent agreement between the predicted and observed amplitudes and phases of the earlier measurements." We conclude that the amplitude ancl phase variations of the 12.15 evele d+ frequency can be explained by. the beating of two close frequencies., We conclude that the amplitude and phase variations of the 12.15 cycle $^{-1}$ frequency can be explained by the beating of two close frequencies. This frequency also shows considerable amplitude variations [rom 2 to 6 mmag as well as phase changes., This frequency also shows considerable amplitude variations from 2 to 6 mmag as well as phase changes. These variations take place from vear to vear as well as within a single observing season., These variations take place from year to year as well as within a single observing season. This is shown in Fig., This is shown in Fig. 2., 2. We notice that the situation is quite similar to that of the 12.15 evele d+ frequeney. except that the Blazhko period is longer by about a month.," We notice that the situation is quite similar to that of the 12.15 cycle $^{-1}$ frequency, except that the Blazhko period is longer by about a month." Again. the signature of beating is evident: minimum. amplitude occurs at the time of ‘average’ phase and the time of rapid. phase change.," Again, the signature of beating is evident: minimum amplitude occurs at the time of 'average' phase and the time of rapid phase change." The fit of the two-frequency. model is quite good. but two items need to be discussed: the amplitude may not be constant from vear to vear and one point fits poorly: this point at LJD 245 2800 has by far the smallest. number of measurements because they were obtained at the end of the observing season.," The fit of the two-frequency model is quite good, but two items need to be discussed: the amplitude may not be constant from year to year and one point fits poorly: this point at HJD 245 2809 has by far the smallest number of measurements because they were obtained at the end of the observing season." Consequently. the error. bars are larger. but the point still deviates by more than 2 standard deviations.," Consequently, the error bars are larger, but the point still deviates by more than 2 standard deviations." The amplitude increases from 2002 to 2004., The amplitude increases from 2002 to 2004. This is also seen in a dillerent wav: after prewhitening two frequencies (23.4034 ancl 23.3973 evele 1) with constant amplitucles. 16 Fourier analysis reveals a third. frequeney. with a small mplitude (Table 1).," This is also seen in a different way: after prewhitening two frequencies (23.4034 and 23.3973 cycle $^{-1}$ ) with constant amplitudes, the Fourier analysis reveals a third frequency with a small amplitude (Table 1)." Phe Fourier analysis shows two possible values for this third. frequency: 23.3915 and 23.3942. evele τν, The Fourier analysis shows two possible values for this third frequency: 23.3915 and 23.3942 cycle $^{-1}$. Phe first value forms an almost equidistant triplet with 10 previously found doublet. while the other value shows a distance ratio in frequency. spacing.," The first value forms an almost equidistant triplet with the previously found doublet, while the other value shows a 2:1 distance ratio in frequency spacing." At this stage. we are not able to judge whether or not this triple frequency SpLIting has a physical meaning. but note that it does not correspond to the effects of annual aliasing. which leads to a smaller splitting of 0.0027 evele c1.," At this stage, we are not able to judge whether or not this triple frequency splitting has a physical meaning, but note that it does not correspond to the effects of annual aliasing, which leads to a smaller splitting of 0.0027 cycle $^{-1}$." Furthermore. rotational splittingLI can also be ruled out since it is a factor of 100 larger (7 0.53 evele +).," Furthermore, rotational splitting can also be ruled out since it is a factor of 100 larger $\sim$ 0.53 cycle $^{-1}$ )." ‘Trial caleulations with PERLODO show that the value of 23.3942. evcle d (rather than 23.3915 evele 1) leads to lower residuals in every one of the vears with observations and is subsequently. adopted., Trial calculations with PERIOD04 show that the value of 23.3942 cycle $^{-1}$ (rather than 23.3915 cycle $^{-1}$ ) leads to lower residuals in every one of the years with observations and is subsequently adopted. The third. frequency provides an exeellent. fit. but we cannot clisprove the possibility that it is just an artefact of true amplitude variability of one of the two modes involved," The third frequency provides an excellent fit, but we cannot disprove the possibility that it is just an artefact of true amplitude variability of one of the two modes involved" ROSAT has identified a mall eroup of hot aud radio-quiet isolated neutron stars (INSs. see reviews by Motchi 2001.. Treves et al.,"ROSAT has identified a small group of hot and radio-quiet isolated neutron stars (INSs, see reviews by Motch \cite{mo2001}, Treves et al." 2001. and IIaberl 2003))., \cite{treves2000} and Haberl \cite{haberl03}) ). None of these objects seenis associated with a SNR aud low iuterstellar absorption towards thei mdicates distances of the order of a few hundred parsecs at most., None of these objects seems associated with a SNR and low interstellar absorption towards them indicates distances of the order of a few hundred parsecs at most. Grating X-ray spectra of the two brightest ucmbers. ((Pacrels et al. 20011) ," Grating X-ray spectra of the two brightest members, (Paerels et al. \cite{paerels2001}) )" and ((Dumwitz ct al 2001, and (Burwitz et al. \cite{bur2001}; Drake ot al. 200151).," Drake et al. \cite{drake02}) )," do πω sienificautly depart from pure dackbody energv distributions., do not significantly depart from pure blackbody energy distributions. Luferred blackbody temperatures range between 50 and 100 eV. Soft X-ray pulsatious with periods around LOss are now detected iu a majority of sources although some period caudidates still require confirmation., Inferred blackbody temperatures range between 50 and 100 eV. Soft X-ray pulsations with periods around s are now detected in a majority of sources although some period candidates still require confirmation. Optical counterparts are very fai objects whose brightuecss secs to be mostly due to thermal cluission from the neutron star surface (see Pavlov ct al., Optical counterparts are very faint objects whose brightness seems to be mostly due to thermal emission from the neutron star surface (see Pavlov et al. 2002 for a recent review)., \cite{pavlov2002} for a recent review). These INSs undergo little. if any. magnetospheric activity and are thus prime targets to measure fundamental paramcters through modeling the neutron star thermal enüssion and to constrain the debated equations of state.," These INSs undergo little, if any, magnetospheric activity and are thus prime targets to measure fundamental parameters through modeling the neutron star thermal emission and to constrain the debated equations of state." The evolutionary status of these objects is stil unclear., The evolutionary status of these objects is still unclear. Sole of the 105 to 10? INSs born iu the Calaxy could have space velocities and rotation periods slow enough to accrete from relatively dense phases of the interstellar amedimn aud be re-heated to temperatures similar to those observed (see c.g. Blacs Macdau 1993) )., Some of the $^{8}$ to $^{9}$ INSs born in the Galaxy could have space velocities and rotation periods slow enough to accrete from relatively dense phases of the interstellar medium and be re-heated to temperatures similar to those observed (see e.g. Blaes Madau \cite{bm93}) ). The fraction of old INSs detectable in N-rayv is of the order of several percents but stronely depends on the assned velocity distribution (ALadau Blaes 1991))., The fraction of old INSs detectable in X-ray is of the order of several percents but strongly depends on the assumed velocity distribution (Madau Blaes \cite{madau94}) ). This hypothesis currently faces two main difficulties., This hypothesis currently faces two main difficulties. First. the space density of hot radio-quiet INSs is much lower than predicted by the accretion models (Treves et al. 2001)).," First, the space density of hot radio-quiet INSs is much lower than predicted by the accretion models (Treves et al. \cite{treves2000}) )." Second. the rotation periods. although. relatively long for neutron star standards. are still too. short to allow accretion to take place iu average interstellar medi conditions unless the magnetic fields of INSs have sjeuificautlv decreased by about two orders of magnitudes over their life time (sec c.g. Wang 1997)).," Second, the rotation periods, although relatively long for neutron star standards, are still too short to allow accretion to take place in average interstellar medium conditions unless the magnetic fields of INSs have significantly decreased by about two orders of magnitudes over their life time (see e.g. Wang \cite{wang97}) )." Alternatively. these INSs could. be vouug cooling objects.," Alternatively, these INSs could be young cooling objects." Loug rotation periods are observed im few radio pulsars as well as in ANPs showing that uuder certain circtuustances (efficicut braking or bith with a low aneular momentum). relatively vouus ueutron stars can rotate slowly.," Long rotation periods are observed in few radio pulsars as well as in AXPs showing that under certain circumstances (efficient braking or birth with a low angular momentum), relatively young neutron stars can rotate slowly." Optical observations can efficicutly help to discriminate between the two hvpotheses. re-leating o accretioun. from the imsterstellay medium or relatively voung cooling objects.," Optical observations can efficiently help to discriminate between the two hypotheses, re-heating by accretion from the insterstellar medium or relatively young cooling objects." For some of the objects. proper notions can be ieasured which. assuuüug Bouceli-Ilovle accretiou. may rule out the accretiug scenario.," For some of the objects, proper motions can be measured which, assuming Bondi-Hoyle accretion, may rule out the accreting scenario." Additionally. the optical o N-rav flux ratio is sensitive o the chemical composition of the neutron star surface (Pavlov ot al. 1996))," Additionally, the optical to X-ray flux ratio is sensitive to the chemical composition of the neutron star surface (Pavlov et al. \cite{pavlov96}) )" aud nav therefore reveal the xeseuce of newly accreted material from the interstellar Ποπ or from a fossil disc., and may therefore reveal the presence of newly accreted material from the interstellar medium or from a fossil disc. Iu both the optical iux N-vav band. lis the second xiehtest INS among those discovered with ROSAT.," In both the optical and X-ray band, is the second brightest INS among those discovered with ROSAT." This object exhibits pulsations at a period o 8.3988 (Taber et al. 1997)), This object exhibits pulsations at a period of s (Haberl et al. \cite{haberl97}) ) with |P| < 3.6 1? (kaplan et. al. 20023)., with $|\dot{\rm P}|$ $<$ 3.6 $^{-13}$ $^{-1}$ (Kaplan et al. \cite{kaplan02}) ). The X-rav spectrum is blackbodv-like with kKT~86 eV (as given by the ROSAT data)., The X-ray spectrum is blackbody-like with $^\infty\simeq 86$ eV (as given by the ROSAT data). ESO-NTT aud I&eck observations have led to the optica identification of wwith a faint stellar-like object (Moteli Taber] 1998: I&ullarui van I&erkwijk 1998)5Woe report here on new lurclass telescope iux ESO-VLT observations of wwhich reveal its proper motion. show its blue UV continui and provide coustraiuts on the nature of its thermal eaission.," ESO-NTT and Keck observations have led to the optical identification of with a faint stellar-like object (Motch Haberl \cite{mh98}; Kulkarni van Kerkwijk \cite{KvK98}) ).We report here on new 4m-class telescope and ESO-VLT observations of which reveal its proper motion, show its blue UV continuum and provide constraints on the nature of its thermal emission." While this paper was in the referecing process we became aware of a preprint bv Iaplan ct al.(2003)) reporting ou IST obscrvatious of wwhich confirm the steep optical to UV. energy distribution of the star)., While this paper was in the refereeing process we became aware of a preprint by Kaplan et \cite{kaplan03}) ) reporting on HST observations of which confirm the steep optical to UV energy distribution of the star). "As the analysed flare is right on the Eastern limb and close to the solar equator, a(e) and b(e) correspond to the source sizes parallel (width) and perpendicular (vertical extent) to the solar surface.","As the analysed flare is right on the Eastern limb and close to the solar equator, $a(\epsilon)$ and $b(\epsilon)$ correspond to the source sizes parallel (width) and perpendicular (vertical extent) to the solar surface." The results of the X-ray visibility forward fit parameters are summarised in Figure 4.., The results of the X-ray visibility forward fit parameters are summarised in Figure \ref{fig:vis_fits_jan06}. They again show the trend seen in the images (Figure 2)) of decreasing height and source size with energy., They again show the trend seen in the images (Figure \ref{fig:images_jan06}) ) of decreasing height and source size with energy. " We can also see that the source becomes more elliptical at higher energies, starting with e~0.5 for 18-22 keV but increasing to e~0.85 for 75-250 keV. The circular Gaussian source fitted to the northern footpoint also shows the general trend of decreasing source height and FWHM at higher energies but with considerably larger errors due to this source being weaker."," We can also see that the source becomes more elliptical at higher energies, starting with $e\sim0.5$ for 18-22 keV but increasing to $e\sim 0.85$ for 75-250 keV. The circular Gaussian source fitted to the northern footpoint also shows the general trend of decreasing source height and FWHM at higher energies but with considerably larger errors due to this source being weaker." " Let us consider the evolution of the electron flux spectrum in the chromosphere F(E,s) along magnetic field lines s using purely collisional transport and ignoring collective effects and effects connected with the magnetic mirroring (?).."," Let us consider the evolution of the electron flux spectrum in the chromosphere $F(E,s)$ along magnetic field lines $s$ using purely collisional transport and ignoring collective effects and effects connected with the magnetic mirroring \citep{brown2002}. ." " In this approximation the electron flux spectrum can be written (?) where Fo(£) is the injected spectrum of energetic electrons, taken to be a powerlaw of Fo(E)«E-? and where K=2re?InA, InA is the Coulomb logarithm, e is the electron charge."," In this approximation the electron flux spectrum can be written \citep{brown1971} where $F_0(E)$ is the injected spectrum of energetic electrons, taken to be a powerlaw of $F_0(E)\propto E^{-\delta}$ and where $K=2\pi e^2 \ln\Lambda$, $\ln\Lambda$ is the Coulomb logarithm, $e$ is the electron charge." The chromosphere below the transition region can be conveniently assumed to be neutral (???) therefore InA=Aeg— ??)..," The chromosphere below the transition region can be conveniently assumed to be neutral \citep{brown1973,kontar2002,2009ApJ...705.1584S} therefore $\ln\Lambda = \ln\Lambda _{eH} = 7$ \citep[e.g.][]{brown1973,emslie1978}." " The X-ray flux spectrum emitted by7 the(e.g. energetic electrons in a magnetic flux tube ofcross-sectional area A and observed at 1AU is given as where c(E,c) is the isotropic bremsstrahlung R is the Sun-Earth distance, A is the cross-sectional area of the loop."," The X-ray flux spectrum emitted by the energetic electrons in a magnetic flux tube ofcross-sectional area $A$ and observed at 1AU is given as where $\sigma (E,\epsilon)$ is the isotropic bremsstrahlung cross-section, $R$ is the Sun-Earth distance, $A$ is the cross-sectional area of the loop." " The X-ray flux spectrum expressed by Equation (9)) has a maximum or equivalently dI(e,s)/ds=0 for every energy ε because of the growing density along electron path and simultaneously decreasing electron flux due to collisions (??).."," The X-ray flux spectrum expressed by Equation \ref{eq:sol_I}) ) has a maximum or equivalently $d I(\epsilon,s)/ds=0$ for every energy $\epsilon$ because of the growing density along electron path and simultaneously decreasing electron flux due to collisions \citep{brown2002,aschwanden2002}." " Assuming a hydrostatic density profile of where is the radial distance from the Sun centre, the photosphericr density no=1.16x10!” cm? [fixed value and ro is the reference height, we can find these two (?)],free parameters Δρ and r=ro by forward fittingthe measured radial distance of maxima (Figure 5,, bottom"," Assuming a hydrostatic density profile of where $r$ is the radial distance from the Sun centre, the photospheric density $n_0=1.16\times 10^{17}$ $^{-3}$ [fixed value \citep{vernazza1981}] ], and $r_0$ is the reference height, we can find these two free parameters $h_0$ and $r=r_0$ by forward fittingthe measured radial distance of maxima (Figure \ref{fig:spectr}, , bottom" breakout with exactly the same A. that apply inside (he star.,"breakout with exactly the same $k$ , $m$ that apply inside the star." The characteristic position Ris again the position which evolves according to the Lorentz [actor T: £2~|—1/2T7., The characteristic position $R$ is again the position which evolves according to the Lorentz factor $\Gamma$: $\dot{R}\simeq 1-1/2\Gamma^2$. since (he hyvdrodyvnamic equations still hold as well. Eqs. 9.. 1H.. 15..," Since the hydrodynamic equations still hold as well, Eqs. \ref{chi}, \ref{g_general}, \ref{f_general}," 16 must remain valid when />0., \ref{h_general} must remain valid when $t>0$. To find the complete solution alter breakout we need to specily the boundary conditions., To find the complete solution after breakout we need to specify the boundary conditions. We proceed by looking at the behavior of the similarity variables X. gy. f. h.," We proceed by looking at the behavior of the similarity variables $\chi$, $g$, $f$, $h$ ." The relevant range in X depends on A. and while the relation between. R and Τ is the same before and alter breakout. 2 alter breakout is not the position of the shock front.," The relevant range in $\chi$ depends on $R$, and while the relation between $R$ and $\Gamma$ is the same before and after breakout, $R$ after breakout is not the position of the shock front." Instead. the front. has infinite Lorentz [actor ancl 2 lags further and further behind the shock with increasing (ime.," Instead, the front has infinite Lorentz factor and $R$ lags further and further behind the shock with increasing time." A nice physical interpretation exists for R after breakout., A nice physical interpretation exists for $R$ after breakout. 2 (racks the position corresponding to a fluid element which has expanded by a [factor of order unity. so Z2 marks (he transition in position between fIuid elements which have expanded and accelerated signilicantlv since being shocked and fluid elements whose size and speed have remained roughly constant.," $R$ tracks the position corresponding to a fluid element which has expanded by a factor of order unity, so $R$ marks the transition in position between fluid elements which have expanded and accelerated significantly since being shocked and fluid elements whose size and speed have remained roughly constant." since it takes longerfor fluid elements with smaller Lorentz [actors to expand anclaccelerate significantly. 2 moves backward relative to the leadingedge of the flow at 7=/.," Since it takes longerfor fluid elements with smaller Lorentz factors to expand andaccelerate significantly, $R$ moves backward relative to the leadingedge of the flow at $x=t$." Because & becomes positive after breakout. the range of possible .e in the solution outside thestar is xxd.," Because $R$ becomes positive after breakout, the range of possible $x$ in the solution outside thestar is $x\leq t$." Then 4—0 at the [ront r=/. and the relevant range in X in the solution outside is 0c. spacetimes following Noether svnunetry approach without ganee term for the matter cdomunated universe., In a recent work Roshan and Shojai \cite{fat} studied Palatini $f(R)$ cosmology in flat FRW spacetimes following Noether symmetry approach without gauge term for the matter dominated universe. They found out the form of ΓΕ) as power-law aud exact solutious for cosmic scale factor., They found out the form of $f(R)$ as power-law and exact solutions for cosmic scale factor. Di this study. we have eeucralized : ∙∙ s ↑↕∐∖∐⋅↥⋅↸∖↴∖↴∏↕↑↸⊳∪∐↴∖↴↕≼↸∖↥⋅⋯∶↴∙⊾⋀∖≼∣⊱⋜∏∏∐⋅∪⋜↧↸⊳∐↖↖↽↕↑↕∐∐↑∐↸∖↴∖↴↸⊳∪⋉∖ ∙∙ ∪↕⋟↑∐↸∖↕⋟⋜↧↕⋜↧↑↕∐↕⋅↗↳⊽∪⊽∩∩⊾↥, In this study we have generalized their result considering NGS approach within the scope of the Palatini $f(R)$ gravity. ⋅⋜↧↖↽↕↑⋅↖↽∙o This palpaper is organizedot ‘as follows., This paper is organized as follows. In the followinez section. the Palatini formalisni is briefly reviewed.," In the following section, the Palatini formalism is briefly reviewed." Iu section 3.. we diseuss the Nocther svuuaetry approach with/without a eauge term for the Palatini fi?) eravitv.," In section \ref{ngs}, we discuss the Noether symmetry approach with/without a gauge term for the Palatini $f(R)$ gravity." Iu section Lb. we search the cosmological solutions by using the obtained forms of f(2).," In section \ref{solution}, we search the cosmological solutions by using the obtained forms of $f(R)$." Finally. Section ⋅≼⋅5.. -we couclude with a. brief summary.," Finally, in Section \ref{conc}, we conclude with a brief summary." "A= 20 Iu four dimensions. the action of the Palatini f(R) eravity theory with matter is writtenas Tere FOR) is a differentiable fuuction of the Ricci scalarbu RAL=€ubORAE).Vabtl). RolAut|T) isix the RicciBucer t tensorof, curvaturealy torsonless4 connectionab D independent ofin ⋅⋝ MMCgap AL L,,IDEA is the matter Laeraneian and (0 represcuts. thefin matter fields."," In four dimensions, the action of the Palatini $f(\mathcal{R})$ gravity theory with matter is writtenas Here $f(\mathcal{R})$ is a differentiable function of the Ricci scalar $\mathcal{R} = g^{a b}\mathcal{R}_{a b}(\Gamma)$, $\mathcal{R}_{a b}(\Gamma)$ is the Ricci tensor of any independent torsionless connection $\Gamma$ independent of $g_{ab}$ and $L_{m}$ is the matter Lagrangian and $\psi$ represents collectively the matter fields." " The matter ]Lagrangian takes is chosen as Ly,=pmod7 for matter dominated cosmoloev."," The matter Lagrangian is chosen as $L_{m} = -\rho_{m0} a^{-3}$ for matter dominated cosmology." In general there are two approach im order to derive the dvnamical field equatious of inotiou in f(R) exavitv., In general there are two approach in order to derive the dynamical field equations of motion in $f(R)$ gravity. The first one is Palatini approach (Flanagan2001:Olino2005b:Fayctal.2007:Daojiuet in which the metric and connection are considere as judependent quantities. and the action is varie with respect to both of them.," The first one is Palatini approach \cite{pala,olmo05b,fay07,bao07} in which the metric and connection are considered as independent quantities, and the action is varied with respect to both of them." " The second approach is the metre formalism iu which action is varie akvi2lO3psffect to ietric tensor,", The second approach is the metric formalism in which action is varied with respect to metric tensor. The field equations in the metric formalism are fourth-order cdiffereutia equations. while for Palatiui formalisi they are secoud-order.," The field equations in the metric formalism are fourth-order differential equations, while for Palatini formalism they are second-order." If FCR) is linear in R. the two approaches leac to the same equation.," If $f(R)$ is linear in $R$ , the two approaches lead to the same equation." In this study we will use the Palatini forxinaliu., In this study we will use the Palatini formalism. Variation of the action (1)) with respect to metric tensor viclds followingS field equations| (Braxctal.2008) aud the variation of the action (1)) with respect to the connection gives where fg=dfTR aud ων is the usual stresscenergy tensor of the matter.," Variation of the action \ref{action}) ) with respect to metric tensor yields following field equations \cite{Brax08} and the variation of the action \ref{action}) ) with respect to the connection gives where $f_{\mathcal{R}} = df/d \mathcal{R}$ and $T_{a b}$ is the usual stress-energy tensor of the matter." Also. the trace of Eq. (2)) is ⊺↕∐∖," Also, the trace of Eq. \ref{f-eq1}) )" ∙⊺⊽⋖↗↗∎∖↗⋟∶↴∙⊾↥⋅⋜↧↖↽↕↑⋅↖↽↑∐↸∖∪↥⋅⋅↖⇁↕∐↕⋟⋜↧↕⋜↧↑↕∐↕↕⋟∪↥⋅⋯⋜↧∐∖↴⋯↕↴∖↴ equivalent to £pp=3/2 a Brans-Dicke (BD) theory., is The $f(\mathcal{R})$ gravity theory in Palatini formalism is equivalent to $\omega_{BD} = -3/2$ a Brans-Dicke (BD) theory. Tn order to coustruct a canonically effective poiut-like Lagrangian.. we have to use the dynamical. equivalence: between Palatini Επ) formalism aud the BD theory of gravity (Sotiiou2006:Capozzi," In order to construct a canonically effective point-like Lagrangian, we have to use the dynamical equivalence between Palatini $f\mathcal({R})$ formalism and the BD theory of gravity \cite{st06,cap11}." lloetal.2011).. Therctorcf the action (1)) can be written as follows where o=fg. Uto)—ωχ)Ενω). R=vto) and Π is a curvature scalar coustructed frou the Levi-Civita connection of metric tensor.," Therefore the action \ref{action}) ) can be written as follows where $\phi=f_{\mathcal{R}}$, $U(\phi)=\phi \chi(\phi) - f(\chi(\phi))$, $\mathcal{R}=\chi(\phi)$ and $R$ is a curvature scalar constructed from the Levi-Civita connection of metric tensor." We note that this is the action of the BD theory with the BD parameter “BD=3/2., We note that this is the action of the BD theory with the BD parameter $\omega_{BD} = -3/2$. It was also shown that iu the metric formalisin the f(R) eravity is equivalent to the BD theory with epp=0 (SotizionzudFaraoni 2010)., It was also shown that in the metric formalism the $f(R)$ gravity is equivalent to the BD theory with $\omega_{BD} = 0$ \cite{fr}. . Tn this studs. we consider a matter-doniünated model in a spatially flat FRW universe with signature Εν1.," In this study, we consider a matter-dominated model in a spatially flat FRW universe with signature $+,+,+,-$ )." " Using the action (5)) with thescalar forERW: inetric- ⋅⋅the inform R=⋅ 6(fa⋅⋅≻⋅≻|àTscali £,, =3 page7.a⋅⋅ point-like Laerangian ⋝⋅ ‘and such a form (Roshan. aucShojai2008)∖collectivelyfab "," Using the action \ref{action-1}) ) with thescalar curvature for FRW metric in the form $R= 6\left( \ddot{a}/a + \dot{a}^2 / a^2 \right)$ and taking $L_m = -\rho_{m0} a^{-3}$ , a point-like Lagrangian takes such a form \cite{fat} " characterized by a relatively younger stellar population.,characterized by a relatively younger stellar population. This effect may result both as a consequence of the cluster environment. which excises star formation in infalling galaxies. and/or due to an earlier formation epoch of galaxies residing in the cluster center ?)..," This effect may result both as a consequence of the cluster environment, which excises star formation in infalling galaxies, and/or due to an earlier formation epoch of galaxies residing in the cluster center \citep[e.g., ][]{2001ApJ...547..609E}." In general. the presence of a gradient in the galaxy colors is naturally predicted by semi-analytical models of galaxy formation (em 2). ," In general, the presence of a gradient in the galaxy colors is naturally predicted by semi–analytical models of galaxy formation \citep[e.g., ][]{2001MNRAS.323..999D}. ." In Figure 9 we show the radial variation of the DV. color or all galaxies found in our set of simulated clusters., In Figure \ref{fi:colrad} we show the radial variation of the $B-V$ color for all galaxies found in our set of simulated clusters. Consistent with observational results. the mean galaxy colors become bluer as We move towards the outer cluster regions.," Consistent with observational results, the mean galaxy colors become bluer as we move towards the outer cluster regions." Quite remarkably. his effect extends well beyond the virial radius. thus implying hat galaxies feel the cluster environment already at fairly large distances.," Quite remarkably, this effect extends well beyond the virial radius, thus implying that galaxies feel the cluster environment already at fairly large distances." While the trend exists for both a Salpeter and a top— IMF. the latter generally predicts much redder colors. consistent with the CMR results shown in Fig. 2..," While the trend exists for both a Salpeter and a top--heavy IMF, the latter generally predicts much redder colors, consistent with the CMR results shown in Fig. \ref{fi:cmr_z0}." Our results for he Salpeter IMF are consistent with those reported by ?. for the ow-redshift bin (0.180 (x«« 1)."," When $0.01\la a \la0.1$, $\omega_{\rm i}\approx\omega_{\rm m}\approx\omega_{\rm s}\approx0$ $\chi_{\rm i}\approx\chi_{\rm m}\approx\chi_{\rm s}\approx1$ ) but $\omega_*>0$ $\chi_*<1$ )." " In this case, we have Thus, we find Φις)«1/2; we expect a reduction of T; relative to that without scattering."," In this case, we have Thus, we find $\Phi_{\rm i(3)}<1/2$; we expect a reduction of $T_{\rm i}$ relative to that without scattering." " When 0.1Sa 1-10 wi£4wm©0 (χιF2Xm& 1) and ws&wx>0 (XsLun,©Xx« 1)."," When $0.1\la a \la1$ --10 , $\omega_{\rm i}\approx\omega_{\rm m}\approx0$ $\chi_{\rm i}\approx\chi_{\rm m}\approx1$ ) and $\omega_{\rm s}\approx\omega_*>0$ $\chi_{\rm s}\approx\chi_*<1$ )." " In this case, we have When 1-10Sa 10-100um,, wi&0 (xi&1) and Wm&%WsP3>0 (XmF2Xs&Xx< 1)."," In this case, we have When $10\la a \la10$ –100, $\omega_{\rm i}\approx0$ $\chi_{\rm i}\approx1$ ) and $\omega_{\rm m}\approx\omega_{\rm s}\approx\omega_*>0$ $\chi_{\rm m}\approx\chi_{\rm s}\approx\chi_*<1$ )." " Then, we have When aZ 10-100um,, the opacity becomes almost grey, thus, the three-layer model is no longer valid."," Then, we have When $a\ga10$ –100, the opacity becomes almost grey, thus, the three-layer model is no longer valid." We should choose the two-layer model in this case., We should choose the two-layer model in this case. Figure 6 shows the scattering reduction factor ®;(3) given by equations (32-34) as a function of the albedo for the stellar radiation.," Figure 6 shows the scattering reduction factor $\Phi_{\rm i,(3)}$ given by equations (32–34) as a function of the albedo for the stellar radiation." " We find that the factor decreases from equation (32) to (34), in other words, as a function of the grain size."," We find that the factor decreases from equation (32) to (34), in other words, as a function of the grain size." " The factor Φις gives the reduction of the interior temperature, Ti, in the three-layer model by isotropic scattering relative to that in the two-layer model without scattering."," The factor $\Phi_{\rm i,(3)}^{1/4}$ gives the reduction of the interior temperature, $T_{\rm i}$, in the three-layer model by isotropic scattering relative to that in the two-layer model without scattering." " For typical grain sizes found in protoplanetary discs of 0.1--10um,, equation (33) would give a good approximation for the reduction factor."," For typical grain sizes found in protoplanetary discs of 0.1–10, equation (33) would give a good approximation for the reduction factor." " If ω.z1, equations (32) and (33) are reduced to ©x.=ν]-ω.."," If $\omega_*\approx1$, equations (32) and (33) are reduced to $\approx\chi_*=\sqrt{1-\omega_*}$." " In this case, we expect the reduction factor of Ti to be g(1—ως)1/5 which is found in Figure 7 later."," In this case, we expect the reduction factor of $T_{\rm i}$ to be $\approx(1-\omega_*)^{1/8}$ which is found in Figure 7 later." Figure 7 shows the temperature of the interior as a function of the grain size., Figure 7 shows the temperature of the interior as a function of the grain size. " The numerical solutions presented in section 2 are shown by symbols: circles for the no scattering case, triangles for the wo=0.9 case, and squares for the wo=0.99 case."," The numerical solutions presented in section 2 are shown by symbols: circles for the no scattering case, triangles for the $\omega_0=0.9$ case, and squares for the $\omega_0=0.99$ case." The analytic models are shown by the solid lines., The analytic models are shown by the solid lines. " In analytic models, we always assume the optically thick interior."," In analytic models, we always assume the optically thick interior." Most of the numerical solutions shown in Figure 7 are really optically thick., Most of the numerical solutions shown in Figure 7 are really optically thick. " However, when the grain"," However, when the grain" "than 2x10. 24,4) we assumed tha the core retained no angular momentn at all. and tjerefore the specific angular 1noijentuin in the convection zone is given by Jay=Shotfi{μοι Wher 1,nv is the current mass of te convection zone.","than $2 \times 10^{-5} J_{tot}$ ) we assumed that the core retained no angular momentum at all, and therefore the specific angular momentum in the convection zone is given by $J_M = J_{tot}/M_{env}$ , where $M_{env}$ is the current mass of the convection zone." " As he star loses mass. the a1OUL of tot: ar nomentitio at each timeStep is sim)M7 Joi—Jot,oldJaglenvjJAAL."," As the star loses mass, the amount of total angular momentum at each timestep is simply $J_{tot}=J_{tot,old} - J_M(env) \Delta M$." The toal augular 1i of the star at the tip of ie giant breveh is the sn of the losses at each tijestep., The total angular momentum of the star at the tip of the giant branch is the sum of the losses at each timestep. The final case. case D. is the sitiplest in white1 to calculate the amoun of angular mone1 left at the tip of the giat brauch.," The final case, case D, is the simplest in which to calculate the amount of angular momentum left at the tip of the giant branch." In this case. e core of the star (as cleined iu case B rete its malin sequence augul:UW nomentuu. aud the evelope has constant specific angular 1ometLOL," In this case, the core of the star (as defined in case B) retains its main sequence angular momentum, and the envelope has constant specific angular momentum." 1 The value of Ja; is set at the beeinuing of the calcuation to be equation to JenaeMese. where quautities are evaluated at the poitt of maxint1 convection zone depth. aud is not allowe chauge throughout the subsequent evolutiou.," The value of $J_M$ is set at the beginning of the calculation to be equation to $J_{env}/M_{env}$, where both quantities are evaluated at the point of maximum convection zone depth, and is not allowed to change throughout the subsequent evolution." In tis case. the total amount of augular 1onmet lost over the entire giant brauch evolution is jo;=JayMy.," In this case, the total amount of angular momentum lost over the entire giant branch evolution is $\Delta J_{tot} = J_M \Delta M_{tot}$." Figure 1l shows the angular momentsur evolution of a star [rom the main sequence to the iorizoutal branch. demonstrating the effecs of the chaeine stricture on tje rotation rate cX the star.," Figure 1 shows the angular momentum evolution of a star from the main sequence to the horizontal branch, demonstrating the effects of the changing structure on the rotation rate of the star." Iu each paiel. we show the angular velocity profie as afinction of iis in the star.," In each panel, we show the angular velocity profile as a function of radius in the star." We iave also marker the positions of the ceuer of the hydrogen buruiug she e radius at whicl he hydrogen couent is N Lass. aud he base of te surface couvectiou zoue.," We have also marked the positions of the center of the hydrogen burning shell, the radius at which the hydrogen content is by mass, and the base of the surface convection zone." The star show. rere has a lass of 0.5 AL. anc we assude LO lass loss or aiυπ nmiomentum1 loss alonο the [n]ejant branch. ai no interna transport of angular mojentum.," The star shown here has a mass of 0.8 $M_{\sun}$ and we assume no mass loss or angular momentum loss along the giant branch, and no internal transport of angular momentum." All angual luoinenttun evolution is caused by the chaiging stricture of the star., All angular momentum evolution is caused by the changing structure of the star. Tie first. pauel sLOWS à 5 alia he mai sequence urnolf. wich we have assumed is rotating as a soid body (w = coustaut) witl radius.," The first panel shows a star at the main sequence turnoff, which we have assumed is rotating as a solid body $\omega$ = constant) with radius." The seconc »anel shows the rotation profie of the star at the )osition ou the giant braich where t1e convectior zone reaches its Wanitaui cleοἱ in mass., The second panel shows the rotation profile of the star at the position on the giant branch where the convection zone reaches its maximum depth in mass. The prcile at ἰie tip of the giant. brachi is shown iu the ird panel. anc the final parel gives he rolatloi€al profil eon{le zero age horizouta braucl.," The profile at the tip of the giant branch is shown in the third panel, and the final panel gives the rotational profile on the zero age horizontal branch." The rlace rotational veloci lesaud ages cof the star are elyen in each parel., The surface rotational velocities and ages of the star are given in each panel. As tle star evolves along the stDelaut aich aud up tle glaut brauch to tle position of e tuaNitwtl1 convectio1 zone depth. the core ας)Mracts. he cojvective envelope deepeus. ald the rlace expaxls.," As the star evolves along the subgiant branch and up the giant branch to the position of the maximum convection zone depth, the core contracts, the convective envelope deepens, and the surface expands." The aigular monaieltin wlich is fouid in the coivectiou zoue is recdistrited according to the rotation law for convectio1 reeions (ii thus case assuned to be solid body. alid Ie core of the star spit sup as It COLtracts.," The angular momentum which is found in the convection zone is redistributed according to the rotation law for convection regions (in this case assumed to be solid body), and the core of the star spins up as it contracts." This trei COLLes for the rest of the giaut bauch evolution. up to the ti) of tlie glant yancl.," This trend continues for the rest of the giant branch evolution, up to the tip of the giant branch." As the cofe contracts. continues to spin up. while inaterial at the base o “the convectio1 ZOLLe [alls into tie hydrogen |oirning shell. aud the strlace continues to expand.," As the core contracts, it continues to spin up, while material at the base of the convection zone falls into the hydrogen burning shell, and the surface continues to expand." Al the tip of tle glal| branch. tle surface of 1ο star is rotating LOO lues slower than it was on tle nail sequence.," At the tip of the giant branch, the surface of the star is rotating 100 times slower than it was on the main sequence." Diring the heliuim flash. wheithe star moves [rom the tip," During the helium flash, whenthe star moves from the tip" "show the distribution in 6, and in ϐ,, of stars in the solar neighbourhood. taken from the phase-mixed. model.","show the distribution in $\theta_r$ and in $\theta_\phi$ of stars in the solar neighbourhood, taken from the phase-mixed model." " The narrow distribution in &,, rellects the fact that the stars are taken from a very narrow range in ©. and that there is à close relationship between © and 8,.."," The narrow distribution in $\theta_\phi$ reflects the fact that the stars are taken from a very narrow range in $\phi$, and that there is a close relationship between $\phi$ and $\theta_\phi$." The average value of 6 (approximated using eq. 4)), The average value of $\delta$ (approximated using eq. \ref{eq:delta}) ) for stars in the survey volume is 0.16., for stars in the survey volume is $\sim0.16$. " The relative density of stars in @, is at à maximuni around O (ie. apocentre) and a minimum. around (pericentre).", The relative density of stars in $\theta_r$ is at a maximum around $0$ (i.e. apocentre) and a minimum around $\pm\pi$ (pericentre). The stars at. apocentre have guiding. radii smaller than their current radius. and those at. pericentre have guiding radii larger than their current radius.," The stars at apocentre have guiding radii smaller than their current radius, and those at pericentre have guiding radii larger than their current radius." " The excess of stars at apocentre is due to the facet. that the density. of stars. and their velocity. dispersion. decreases with increasing radius. so more stars visit. the Solar neighbourhood from. guiding radii smaller than Zi, than from guiding radii larger than ο."," The excess of stars at apocentre is due to the fact that the density of stars, and their velocity dispersion, decreases with increasing radius, so more stars visit the Solar neighbourhood from guiding radii smaller than $R_0$ than from guiding radii larger than $R_0$." " Since stars at apocentre are lageing circular rotation. while those at pericentre are leading it. this non-uniformity in the 8, distribution is directly related to asymmetric drift. ane the skew distribution in ο seen in Figure 3 (e.g.?2).."," Since stars at apocentre are lagging circular rotation, while those at pericentre are leading it, this non-uniformity in the $\theta_r$ distribution is directly related to asymmetric drift, and the skew distribution in $v_y$ seen in Figure \ref{fig:UVhist} \citep[e.g.][]{GDII}." " Phis behaviour is cilferent from that suggested by SLO who incorrectly claimed that one should expect low relative density of stars around both 6,=+r and 6,=0.", This behaviour is different from that suggested by S10 who incorrectly claimed that one should expect low relative density of stars around both $\theta_r=\pm\pi$ and $\theta_r=0$. " 1n Figure 5.r L show density contours for the values of 0, and &,, taken from the phase-mixecl model.", In Figure \ref{fig:mod_0_cont} I show density contours for the values of $\theta_r$ and $\theta_\phi$ taken from the phase-mixed model. " There is a clear relationship between the two values. with ϐ,,0 for 9,>0. and &,,=0 for €,« 0."," There is a clear relationship between the two values, with $\theta_\phi\gtrsim0$ for $\theta_r>0$, and $\theta_\phi\lesssim0$ for $\theta_r<0$ ." " Phere are extrema in £,, at 0,— ctzj2. and 6,zz0 for 6,20 tr."," There are extrema in $\theta_\phi$ at $\theta_r=\pm\pi/2$ , and $\theta_\phi\approx0$ for $\theta_r=0$ $\pm\pi$." " This is again due to the fact | am selecting stars from a very. narrow range in ó. and. because of the relationship between @, and ϐ,, for a given orbit at a given point illustrated in Figures 1. and 2.."," This is again due to the fact I am selecting stars from a very narrow range in $\phi$, and because of the relationship between $\theta_r$ and $\theta_\phi$ for a given orbit at a given point illustrated in Figures \ref{fig:scheme} and \ref{fig:UVaxes}." ] now compare the phase-mixed model analysed in Section ?? to the stars in the Solar neighbourhood observed by the GCS., I now compare the phase-mixed model analysed in Section \ref{sec:smooth} to the stars in the Solar neighbourhood observed by the GCS. The GCS cata are taken from the table produced by ?.. and | follow 810 in restricting the analysis to stars that have full GD phase-space coordinates quoted. are at distances 200pe from the Sun. and are not. directly associated with the IIvades cluster.," The GCS data are taken from the table produced by \cite{GCS09}, and I follow S10 in restricting the analysis to stars that have full 6D phase-space coordinates quoted, are at distances $\leq200\pc$ from the Sun, and are not directly associated with the Hyades cluster." Ehe. distributions in angle space that | find ave very. similar to those found. by 510. and the small dillerences are due to the different choices of Galactic potential and the use of torus-fitting as opposed to integrating orbits in the plane.," The distributions in angle space that I find are very similar to those found by S10, and the small differences are due to the different choices of Galactic potential and the use of torus-fitting as opposed to integrating orbits in the plane." " In Figure 6. L plot the distributions in 6,|n,, of the GCS stars (solid line) and those taken from the phase-mixed model (dotted line) for a series of integers n.", In Figure \ref{fig:meat} I plot the distributions in $\theta_r+n\theta_\phi$ of the GCS stars (solid line) and those taken from the phase-mixed model (dotted line) for a series of integers $n$. Naively one would simply expect an OLIt to produce a peak for some value of n0. and an ILI. to produce a peak for some value of à«0 (with the perturber being [n|-fold symmetric).," Naively one would simply expect an OLR to produce a peak for some value of $n>0$, and an ILR to produce a peak for some value of $n<0$ (with the perturber being $|n|$ -fold symmetric)." " The relationship between 6, and ϐ,, due to selection ellects produces a peak around 0 in plots with à?«0 and around cx ornc0.", The relationship between $\theta_r$ and $\theta_\phi$ due to selection effects produces a peak around $0$ in plots with $n<0$ and around $\pm\pi$ for $n>0$. " There are two main features in the angle distribution ol the GCS data (besides those clue to selection ellects). one peak that lies at 6,—1.5. and one that lies at 6,~2.2."," There are two main features in the angle distribution of the GCS data (besides those due to selection effects), one peak that lies at $\theta_r\sim-1.5$, and one that lies at $\theta_r\sim2.2$." " lt is also noticeable that the peak at 0 which appears in the model data for η«0 is ollset to slightly lower values in the GCS data this can be associated with the small peak in the 6, distribution at θεQ.4.", It is also noticeable that the peak at $0$ which appears in the model data for $n<0$ is offset to slightly lower values in the GCS data – this can be associated with the small peak in the $\theta_r$ distribution at $\theta_r\sim-0.4$. Figure 7 shows the distribution of stars taken [from the GCS data in the c.c0-plane (assuming the Solar velocity relative to the local stanclarel of rest given in eq. 5))," Figure \ref{fig:UV_GCS} shows the distribution of stars taken from the GCS data in the $v_x,v_y$ -plane (assuming the Solar velocity relative to the local standard of rest given in eq. \ref{eq:vsol}) )" " overlaid on the lines of constant 6, and of constant &,, (at the Sun's position) as shown in Figure 2..", overlaid on the lines of constant $\theta_r$ and of constant $\theta_\phi$ (at the Sun's position) as shown in Figure \ref{fig:UVaxes}. " This makes it easy to see which of the familiar features in the oe,-plane correspond to which peaks in Figure 6.."," This makes it easy to see which of the familiar features in the $v_x,v_y$ -plane correspond to which peaks in Figure \ref{fig:meat}." " The peak at 8,~—1.5 is associated. with the Livacdes moving group. the peak at 9,~2.2 is associated with the Sirius moving group and the peak at 8,~09 is associated with the Pleiades moving eroup."," The peak at $\theta_r\sim-1.5$ is associated with the Hyades moving group, the peak at $\theta_r\sim2.2$ is associated with the Sirius moving group and the peak at $\theta_r\sim-0.4$ is associated with the Pleiades moving group." " The peak at 8,~1.5 clearly appears in all the plots shown in Figure 6.. shifted to higher values for a«0 and to lower values for pnz0."," The peak at $\theta_r\sim-1.5$ clearly appears in all the plots shown in Figure \ref{fig:meat}, shifted to higher values for $n<0$ and to lower values for $n>0$." This peak is made up of almost the same set of stars in cach plot., This peak is made up of almost the same set of stars in each plot. It is this feature that SLO identified as the signature of an ELT., It is this feature that S10 identified as the signature of an ILR. " LH is clear from Figure that these data are consistent with the stars that make up the peak at 6,~—1.5 being associated with any value of η between 4 and 4 (including non-integer values. and indeed for |n]z4 though these are not shown as selection ellects Create ever greater distortions)."," It is clear from Figure \ref{fig:meat} that these data are consistent with the stars that make up the peak at $\theta_r\sim-1.5$ being associated with any value of $n$ between $-4$ and $4$ (including non-integer values, and indeed for $|n|>4$ though these are not shown as selection effects create ever greater distortions)." While S10 shows plots that are almost identical to the centre and bottom-left panels of Figure 6. (his fig., While S10 shows plots that are almost identical to the centre and bottom-left panels of Figure \ref{fig:meat} (his fig. 4 upper panel and Πο., 4 upper panel and fig. " 7 top panel. respectively). the peaks in these plots are misidentilied as being primarily due to selection cllects that SLO incorrectly claimed should result in high relative densities around 6,=4E» "," 7 top panel, respectively), the peaks in these plots are misidentified as being primarily due to selection effects that S10 incorrectly claimed should result in high relative densities around $\theta_r=\pm\pi/2$ ." "The peak at 6,~2.2 becomes a more clearly defined (ancl higher) peak for àz0 (shifted to higher values). and nearly disappears for p<<0."," The peak at $\theta_r\sim2.2$ becomes a more clearly defined (and higher) peak for $n>0$ (shifted to higher values), and nearly disappears for $n<0$." " Lt is also noticeable that the feature around 6,—1.5 becomes more sharply pealect for n«ο.", It is also noticeable that the feature around $\theta_r\sim-1.5$ becomes more sharply peaked for $n<0$. " Phis would seem to imply that the peak at 06,~2.2 is associated with an OLR. and the peak at 0,~1.5 is associated with an ILIt. but this is not necessarily the— case. both because of the selection. cllects discussed: previously. and. because of the other condition on resonant stars (eq. 2.."," This would seem to imply that the peak at $\theta_r\sim2.2$ is associated with an OLR, and the peak at $\theta_r\sim-1.5$ is associated with an ILR, but this is not necessarily the case, both because of the selection effects discussed previously, and because of the other condition on resonant stars (eq. \ref{eq:res_om}," see Section 6))., see Section \ref{sec:resmod}) ). " In Figure S. E show a contour plot of the density in the 0,. 6,, plane of the selected stars from the CCS catalogue."," In Figure \ref{fig:contGCS} I show a contour plot of the density in the $\theta_r$, $\theta_\phi$ plane of the selected stars from the GCS catalogue." The plots in Figure ο are found from the distribution in angle space plotted. in Figure S. by. marginalising it over straight lines. the eradient of which are determined by η.," The plots in Figure \ref{fig:meat} are found from the distribution in angle space plotted in Figure \ref{fig:contGCS} by marginalising it over straight lines, the gradient of which are determined by $n$." 1n Figure S.. lines corresponding to a few cdillerent. values of η are plotted. centred on the main overdensities. to guide the eve.," In Figure \ref{fig:contGCS}, , lines corresponding to a few different values of $n$ are plotted, centred on the main overdensities, to guide the eye." " The distribution in the 6,.6,, plane seen in Figure & showsthe samestrong selection ellects in @ illustrated bv the phase-müxed model."," The distribution in the $\theta_r,\theta_\phi$ plane seen in Figure \ref{fig:contGCS} showsthe samestrong selection effects in $\bolth$ illustrated by the phase-mixed model." " These selection. effects. have a verv strong effect. on the overdensitics associated: with the Pleiades and Sirius moving groups. which drives them. towards the observed: correlation between 9, and 6,, in the (wo clifferent cases."," These selection effects have a very strong effect on the overdensities associated with the Pleiades and Sirius moving groups, which drives them towards the observed correlation between $\theta_r$ and $\theta_\phi$ in the two different cases." " Phe Lyvades overdensity (around 4,= 1.5) isa less straightforward case.", The Hyades overdensity (around $\theta_r=-1.5$ )is a less straightforward case. " Lt is approximately triangular in the 6,.6,, plane. and lies either side of the expected. minimum in 6, at 6,=—z/2 (this minimum is"," It is approximately triangular in the $\theta_r,\theta_\phi$ plane, and lies either side of the expected minimum in $\theta_\phi$ at $\theta_r=-\pi/2$ (this minimum is" Under these conditions. the detection problem consists iu deciding whether a ds a pure noise à (hvpothesis fy) or it contains also the contribution of a source s (hivpothesis 111).,"Under these conditions, the detection problem consists in deciding whether $\xb$ is a pure noise $\nb$ (hypothesis $H_0$ ) or it contains also the contribution of a source $\ssb$ (hypothesis $H_1$ )." " Iu other words. the source detection problem is equivalent to a decision problem where two hvpothleses hold: Under Hy the probability density fiction of a is even by pla|Hy) whereas under Hy, by μίασέ)."," In other words, the source detection problem is equivalent to a decision problem where two hypotheses hold: Under $\Hc_0$ the probability density function of $\xb$ is given by $p(\xb| \Hc_0)$ whereas under $\Hc_1$ by $p(\xb| \Hc_1)$." At this point. it is necessary to fix the criterion to 1se for the detection.," At this point, it is necessary to fix the criterion to use for the detection." Clearly. one caunot hoe to find all the sources present in a given signal.," Clearly, one cannot hope to find all the sources present in a given signal." Hence. sole choices are liCCCSSIaV.," Hence, some choices are necessary." For example. oue could decide that the unou-detection or the nüsideutilcatioun of a bright source could be more important than that of a fainter one. or vice versa.," For example, one could decide that the non-detection or the misidentification of a bright source could be more important than that of a fainter one, or vice versa." A very conuuon and effective criterion is theNevinau-Pearson criterion that cousists iu the maximization of the Py uuder the constraint that the Pry (ic. the probability of a false detection) does not exceed a fixed value a.," A very common and effective criterion is theNeyman-Pearson criterion that consists in the maximization of the $\PD$ under the constraint that the $\PFA$ (i.e., the probability of a false detection) does not exceed a fixed value $\alpha$." The Neyaiuau-Pearsou theorem (e...seeKay1998). is a powerful tool that allows to design a decision process that pursues this aiu: The test of the ratio is called the(LRT).," The Neyman-Pearson theorem \citep[e.g., see ][]{kay98} is a powerful tool that allows to design a decision process that pursues this aim: The test of the ratio is called the(LRT)." Au important example of application of LRT is when noise rds Gaussian with correlation fuuction C., An important example of application of LRT is when noise $\nb$ is Gaussian with correlation function $\Cb$. Actually. in CMD οςreriments this condition is satisiied only for observations at Heh Galactic latitudes where the CMD Cluission aud he imstrunental noise are bv far +1ο coma contributors.," Actually, in CMB experiments this condition is satisfied only for observations at high Galactic latitudes where the CMB emission and the instrumental noise are by far the dominant contributors." At lower latitudes. it is often usted to hold locally.," At lower latitudes, it is often assumed to hold locally." For example. the contribution to a of components that in small patch of sky. preseuts linear spatial trends ire ofen approxinated wihn stationary Gaussian processes with a steep spoectruni (eg. Lif noises}.," For example, the contribution to $\xb$ of components that in small patch of sky presents linear spatial trends are often approximated with stationary Gaussian processes with a steep spectrum (e.g. $1/f$ noises)." Du amy case. even if the Caussianity couditiou was unrealistic. it is offen made anyway since it allows an analytical treatineut of the problem of interest aud the results can be used as a benchinarl iu the analysis of more couples scenarios.," In any case, even if the Gaussianity condition was unrealistic, it is often made anyway since it allows an analytical treatment of the problem of interest and the results can be used as a benchmark in the analysis of more complex scenarios." With Gaussian m. it is with The LRT is given bx Hence. it results that Hy has to be chosen when for the statistic Z(2) (called detector) it is with 5 such as Le. Here. Qtr)=1Por) with PCr) the standard κfunction. ο is the corresponding inverse fiction.," With Gaussian $\nb$ , it is with The LRT is given by Hence, it results that $\Hc_1$ has to be chosen when for the statistic $T(\xb)$ (called ) it is with $\gamma$ such as i.e., Here, $Q(x) = 1 - \Phi(x)$ with $\Phi(x)$ the standard Gaussian, $Q^{-1}(.)$ is the corresponding inverse function." Equation is due to the fact that F(a) is a Caussian random variable with variance: 87C.1Is and expected values equal to zero under Hy aud s7C1 ⋅⊱↨∏∐≼∐∖↥⋅⋤∟∠⊥∙⊟≻↥⋅↑∐↸∖↴∖↴⋜∐, Equation is due to the fact that $T(\xb)$ is a Gaussian random variable with variance $\ssb^T \Cb^{-1} \ssb$ and expected values equal to zero under $\Hc_0$ and $\ssb^T \Cb^{-1} \ssb$ under $\Hc_1$. ⊔↸∖↥⋅↸∖⋜↧↴∖↴∪∐↕↑↕↴∖↴ ; ⋅⋅ (9) be written iu the form Tiw)=atu> u-C Froui this equation appears that u cui be thought asa liucar filter of igual a. that is called filter (ATF).," For the same reason it is Equation can be written in the form with From this equation appears that $\ub$ can be thought as a linear filter of signal $\xb$ , that is called (MF)." There are some inportautpoiuts to stress with reeard the MIF when used in practical aplicatious., There are some importantpoints to stress with regard the MF when used in practical aplications. They are:, They are: S3 and ~70 kin during ο.,S3 and $\sim$ 70 km during S4. The ratio of 0.1.10.0 keV fiux in the blackbody component compared to the powerlaw is for all the spectra except $3. where is it94.," The ratio of 0.1–10.0 keV flux in the blackbody component compared to the powerlaw is for all the spectra except S3, where is it." The effects of significa absorption are clearly secu in the $3 spectrum as a change in spectral shape aud lucreased curvature in the 123 keV range (see Fie. 3))., The effects of significant absorption are clearly seen in the S3 spectrum as a change in spectral shape and increased curvature in the 1–3 keV range (see Fig. \ref{fig:spectra}) ). This iniplies au absorption of Z1077 atom 7., This implies an absorption of $\approxgt$$10^{22}$ atom $^{-2}$. However. substantial flux remains S05 keV. which should be absorbed with such a high absorption.," However, substantial flux remains $\approxlt$ 0.5 keV, which should be absorbed with such a high absorption." There are a number of possible explanations for such behavior: (1) the presence of separate “scattered” and “absorbed” spectral componcnts. (2) partial covering of the emittiug region(s). and (3) absorption by partially ionized material such that the low Z materials responsible for the majority of the absorption 0.5 keV are significantly ionized. while the higher Z elements are not.," There are a number of possible explanations for such behavior: (1) the presence of separate “scattered” and “absorbed” spectral components, (2) partial covering of the emitting region(s), and (3) absorption by partially ionized material such that the low $Z$ materials responsible for the majority of the absorption $\approxlt$ 0.5 keV are significantly ionized, while the higher $Z$ elements are not." Possibilities (1) and (2) cannot be spectrally distinguished. and are referred to as “partial covering. although this should be taken to," Possibilities (1) and (2) cannot be spectrally distinguished and are referred to as “partial covering”, although this should be taken to" errors in background subtraction.,errors in background subtraction. Ilowever. we note (hat a similar cliflerence in Call Ix strength is seen between (he spectra of NGC 6441 ancl its M 31 counterparts by (2004).. on the basis of different datasets.," However, we note that a similar difference in CaII HK strength is seen between the spectra of NGC 6441 and its M 31 counterparts by \cite{be04}, on the basis of different datasets." We compared Call IN strengths measured in the Hectospec spectra with those measured in spectra obtained with IXeck/LBIS by comm.) and found them to be consistent with each other. after accounting Lor the different instrumental resolutions.," We compared CaII HK strengths measured in the Hectospec spectra with those measured in spectra obtained with Keck/LRIS by \citep{st10} and found them to be consistent with each other, after accounting for the different instrumental resolutions." Therefore. we conclude that the Hectospec spectra are [ree of important svstematic effects due to background subtraction.," Therefore, we conclude that the Hectospec spectra are free of important systematic effects due to background subtraction." Regarding (he MW data. the similarity in the strengths of the residuals in the Ca II and Ix. lines in the ratio spectra ol Figure 15. suggests that there indeed may be a background subtraction problem with the spectra of these (vo metal-rich NW. GCs. but that cannot be the whole storv. as the size of the sky-sublraction error required to explain the data is too lareeand even in that case. it cannot explain differences in the Ca II and Ix lines.," Regarding the MW data, the similarity in the strengths of the residuals in the Ca H and K lines in the ratio spectra of Figure \ref{ratio_6528} suggests that there indeed may be a background subtraction problem with the spectra of these two metal-rich MW GCs, but that cannot be the whole story, as the size of the sky-subtraction error required to explain the data is too large—and even in that case, it cannot explain differences in the Ca H and K lines." Independent data would help solving this puzzle., Independent data would help solving this puzzle. " To summarize. we are not entirelv convinced that. NGC 6528 and 6553 indeed cliffer from their M 31 counterparts in terms of their carbon ancl nitrogen relative abundances. in spite of the fact that CN bands seem to be weaker in their spectra than in M 31 metal-rich GCs,"," To summarize, we are not entirely convinced that NGC 6528 and 6553 indeed differ from their M 31 counterparts in terms of their carbon and nitrogen relative abundances, in spite of the fact that CN bands seem to be weaker in their spectra than in M 31 metal-rich GCs." It is possible that the differences are partly due to skv-subtraction uncertainties. but (his requires errors (hat seem unreasonably high.," It is possible that the differences are partly due to sky-subtraction uncertainties, but this requires errors that seem unreasonably high." The best way (o approach this problem is (hrough a study of CN strengths in statistically significant samples of resolved stars in those two bulge Milky Wav GCs., The best way to approach this problem is through a study of CN strengths in statistically significant samples of resolved stars in those two bulge Milky Way GCs. Martell&Smith(2009). have recently collected mecdium-resolution spectra of roughly a dozen individual stus in NGC 6528 and found a few of them to be CN-strong., \cite{ms09} have recently collected medium-resolution spectra of roughly a dozen individual stars in NGC 6528 and found a few of them to be CN-strong. " Whether that would translate into a CN-strong integrated spectrum or not. is a question that can only be answered on the basis of spectra of a much larger saanple of GC members,"," Whether that would translate into a CN-strong integrated spectrum or not, is a question that can only be answered on the basis of spectra of a much larger sample of GC members." such a picture of the eddies as separate fluid. elements is appropriate.,such a picture of the eddies as separate fluid elements is appropriate. Elastic scattering is in fact counter to the standard assumption in mixing-length theory that eddies deposit their entire angular momentum and entropy into the ambient fluid with each scattering., Elastic scattering is in fact counter to the standard assumption in mixing-length theory that eddies deposit their entire angular momentum and entropy into the ambient fluid with each scattering. This result also assumes an isotropic scattering whereas rotation clearly breaks this symmetry., This result also assumes an isotropic scattering whereas rotation clearly breaks this symmetry. In the anisotropic case Kumaretal.(1995) find that in principle angular momentum can be transferred outward by convection. an idea we consider in more detail in the next section.," In the anisotropic case \citet{kum95} find that in principle angular momentum can be transferred outward by convection, an idea we consider in more detail in the next section." In Figure 7. we plot the evolution of the WD spin during the simmering stage assuming solid body rotation within the convective zone., In Figure \ref{fig:shear_solid} we plot the evolution of the WD spin during the simmering stage assuming solid body rotation within the convective zone. The initial spin is taken to be uniform with ο20.67s! line)., The initial spin is taken to be uniform with $\Omega=0.67\ {\rm s^{-1}}$ ). The overall trend is spitdown from heating and expansion., The overall trend is spin-down from heating and expansion. Uniform rotation in the convective zone leads to shear at its top with a discontinuouan velocity of AV—I0?10*ems! at late times., Uniform rotation in the convective zone leads to shear at its top with a discontinuous velocity of $\Delta V\sim10^5-10^6\ {\rm cm\ s^{-1}}$ at late times. The other rotation law that we consider is motivated by numerical simulations and observations of the Sun., The other rotation law that we consider is motivated by numerical simulations and observations of the Sun. In theoretical and numerical studies where Ro=l. a generic feature is that angular momentum ts transported outward away from the poles and towards the equator (Gilman1979;Miesch2000:Brun&Toomre2002:Browningetal. 2004).," In theoretical and numerical studies where $Ro\lesssim1$, a generic feature is that angular momentum is transported outward away from the poles and towards the equator \citep{gil79,mie00,bru02,bro04}." . This appears to be controlled by the largest scale eddies that are most influenced by rotation (Browningetal.2004)., This appears to be controlled by the largest scale eddies that are most influenced by rotation \citep{bro04}. . Such features are qualitatively consistent with helioseismic measurements that map the outer convective region of the Sun (Thompsonetal.2003.andreferencestherein)..., Such features are qualitatively consistent with helioseismic measurements that map the outer convective region of the Sun \citep[][and references therein]{tho03}. The main disparity 1s that theory and numerics generally result in a more Taylor-Proudman like spin profile whereas the Sun's velocity contours are more radial., The main disparity is that theory and numerics generally result in a more Taylor-Proudman like spin profile whereas the Sun's velocity contours are more radial. This may be due to the tachocline (Mieschetal.2006).. which ts present in cases with surface convection.," This may be due to the tachocline \citep{mie06}, which is present in cases with surface convection." The study of core convection in rotating A-stars by Browningetal.(2004).. which also finds a Taylor-Proudman spin profile. may be the most relevant comparison to the WD case.," The study of core convection in rotating A-stars by \citet{bro04}, which also finds a Taylor-Proudman spin profile, may be the most relevant comparison to the WD case." " To mimic the general features of the spin profiles described above we consider the following rotation law. 0) = JQ. where ©, is the spin at the WD's center.) 1s the fractional change in spin across the convective zone. and ϐ is the latitude measured from the pole."," To mimic the general features of the spin profiles described above we consider the following rotation law, ) = _c, where $\Omega_c$ is the spin at the WD's center, $\beta$ is the fractional change in spin across the convective zone, and $\theta$ is the latitude measured from the pole." For caleulational purposes. we choose Jj=0.4.," For calculational purposes, we choose $\beta=0.4$." This is in reasonable agreement with the results of Browningetal.(2004) and solar observations (Thompsonetal.2003).. which both have a similar value of Ro~0.1 in comparison to our case here.," This is in reasonable agreement with the results of \citet{bro04} and solar observations \citep{tho03}, which both have a similar value of $Ro\sim0.1$ in comparison to our case here." In Figure 8 we plot the spin profile along the equator using equation (64)) as the rotation law within the convection., In Figure \ref{fig:shear_incr} we plot the spin profile along the equator using equation \ref{eq:rotationlaw}) ) as the rotation law within the convection. The outward transport of angular momentum is much more prominent in comparison to the uniform rotation case considered earlier., The outward transport of angular momentum is much more prominent in comparison to the uniform rotation case considered earlier. Since the rotation is eylindrical. at higher latitudes the shear is significantly smaller.," Since the rotation is cylindrical, at higher latitudes the shear is significantly smaller." The typical velocity jump at the equator is AV—10610ems. which may be comparable to the speeds of the burning fluid elements that will be buoyantly rising through the WD once explosive carbon ignition occurs.," The typical velocity jump at the equator is $\Delta V\sim10^6-10^7\ {\rm cm\ s^{-1}}$, which may be comparable to the speeds of the burning fluid elements that will be buoyantly rising through the WD once explosive carbon ignition occurs." This could in principle shear out the burning. enhancing it because of the increased surface area.," This could in principle shear out the burning, enhancing it because of the increased surface area." The shear present at the convective/non-convective boundary represents free energy that has been made available, The shear present at the convective/non-convective boundary represents free energy that has been made available "To isolate regions with fixed aco and ógapn, we separate each galaxy into several zones.","To isolate regions with fixed $\alpha_{\rm CO}$ and $\delta_{\rm GDR}$, we separate each galaxy into several zones." " We treat the ""inner"" part of M 31 separately from the 10 kpc ring and further divide the ring into a ""north"" and ""south"" part."," We treat the ""inner"" part of M 31 separately from the 10 kpc ring and further divide the ring into a ""north"" and ""south"" part." We exclude 60? around the minor axis (in the plane of the galaxy) of M 31 (see 84.3))., We exclude $60\arcdeg$ around the minor axis (in the plane of the galaxy) of M 31 (see \ref{sec:diffuse_hi}) ). " We break M 33 into an ""inner"" zone where rg«2 kpc and an ""outer"" zone where 2 kpc 0.09 AU? for d = 27 pc.," Assuming a temperature $<$ 84 K, the total effective particle cross-section is $> 0.09$ $^{2}$ for d = 27 pc." Following argunieuts euploved for Vega aud the other main sequence debris disk archetypes discovered by IRAS (Dackniuu aud Paresce 1993). we assume the IR excess cluission around WD 105 aud WD 150706 is from graius orbiting. aud iu thermal equilibrium with radiation frou. the ceutral stars.," Following arguments employed for Vega and the other main sequence debris disk archetypes discovered by IRAS (Backman and Paresce 1993), we assume the IR excess emission around HD 105 and HD 150706 is from grains orbiting, and in thermal equilibrium with radiation from, the central stars." Model πιο and outer radii for disks containing the cold material around ΠΟ 105 aud IID 150706 can be calculated with assmuptions regarding eraiu composition. size distributions. aud spatial distiibutious.," Model inner and outer radii for disks containing the cold material around HD 105 and HD 150706 can be calculated with assumptions regarding grain composition, size distributions, and spatial distributions." The lack of distinct 10imeralogical features in the observed IRS spectra (πλος would constrain the dust properties) means there can be no unique model but rather a rauge of models that satisfv the observations., The lack of distinct mineralogical features in the observed IRS spectra (which would constrain the dust properties) means there can be no unique model but rather a range of models that satisfy the observations. For ΠΟ 150706 the suele data point for the IR excess translates iuto a Dit that the material ust lie farther from the star than ~ 11 AU if it isin the form of “blackbody” erains leger than the longest waveleneth of significant emission.," For HD 150706 the single data point for the IR excess translates into a limit that the material must lie farther from the star than $\sim$ 11 AU if it is in the form of “blackbody"" grains larger than the longest wavelength of significant emission." Sunaller graius would satisfy the same temperature constraint at larger distances from the star., Smaller grains would satisfy the same temperature constraint at larger distances from the star. " The material around WD 105 is consistent with being distributed i a narrow rine with inner edee Ryy at 12+ 6 AU and an outer edee at Rorr-Riy < E AU if ""blackbods grains are assed."," The material around HD 105 is consistent with being distributed in a narrow ring with inner edge $_{IN}$ at 42 $\pm$ 6 AU and an outer edge at $_{OUT}$ - $_{IN}$ $<$ 4 AU if “blackbody"" grains are assumed." " The ranges result from photometric wucertainty and are incdependeut of the assumed erain surface deusity radial power law exponent within the rauge Str)~rl22901,"," The ranges result from photometric uncertainty and are independent of the assumed grain surface density radial power law exponent within the range $\Sigma (r) \sim r^{[-2.0,0]}$." Tf material in the inner “hole” is assumed to have coustaut surface density with radius (as would be produced through the PovutiugRobertson (P.B) effect). the surface density in the zoue at r « Rx is less than 3«10? of the model surface deusity at r o> Ryy.," If material in the inner “hole"" is assumed to have constant surface density with radius (as would be produced through the Poynting–Robertson (P–R) effect), the surface density in the zone at r $<$ $_{IN}$ is less than $3 \times 10^{-2}$ of the model surface density at r $>$ $_{IN}$." Another family of models containing imtermecdiate-sized (eravbodyv) egraius with emissiity falling as 1/À bevond A= f0ja possesses inner edees Ryy ranging from about 50 to 70 AU and outer edges Bor ranging from 250 to 1500 AU depending ou the assumed radial power law exponeut of the surface density distribution., Another family of models containing intermediate-sized (graybody) grains with emissivity falling as $1/\lambda$ beyond $\lambda = 40 \mu$ m possesses inner edges $_{IN}$ ranging from about 50 to 70 AU and outer edges $_{OUT}$ ranging from 250 to 1500 AU depending on the assumed radial power law exponent of the surface density distribution. Given the above results for WD 105 aud IID 150706 frou sinple models with strong (but reasonable) assuniptious about the grain properties of the observed disks. we now explore ranges of disk models that are cousisteut with the data following Wolf Ilillenbraud (2003).," Given the above results for HD 105 and HD 150706 from simple models with strong (but reasonable) assumptions about the grain properties of the observed disks, we now explore ranges of disk models that are consistent with the data following Wolf Hillenbrand (2003)." For erain conrposifions we assunied “astronomical” silicate plus eraphite iu the ISM ratio and surface density distribution Xr)x(19.," For grain compositions we assumed “astronomical"" silicate plus graphite in the ISM ratio and surface density distribution $\Sigma(r) \propto r^0$." The amass of the disk was adjusted to match the peak flux in the infrared excess., The mass of the disk was adjusted to match the peak flux in the infrared excess. " Parameters such as erain size distribution v(a)~a"" powerlaw exponeut. ninimuimiu/naximuin eran size. and the inner/outer οσο of the disk. were varied to find the range of values consistent with the observed spectral energy. distribution of IID 105."," Parameters such as grain size distribution $n(a) \sim a^{-p}$ power–law exponent, minimum/maximum grain size, and the inner/outer edge of the disk, were varied to find the range of values consistent with the observed spectral energy distribution of HD 105." The models were relatively insensitive to the radial density distribution exponent., The models were relatively insensitive to the radial density distribution exponent. The wavelength at which the dust re-cuussion spectrum beeins to depart sienificantly from the stellar plotosphere was used to fud the smallest erain size and smallest inner disk radius cousistent with the data., The wavelength at which the dust re-emission spectrum begins to depart significantly from the stellar photosphere was used to find the smallest grain size and smallest inner disk radius consistent with the data. Tjose Two parameters are degenerate resulting iu single erai Lsizes m the range 0.3. 5. and & nu requiring inner gap sizes of 1000. 120. and 12 AU respectively.," These two parameters are degenerate resulting in single grain sizes in the range 0.3, 5, and 8 $\mu$ m requiring inner gap sizes of 1000, 120, and 42 AU respectively." Adoptinga minimi erain size of 5 jan and allowing for a grain size distribution up to 100 or 1000 pou produced lower 47 fits aud decreased the required inner radius from 120 to 15 AU (32 AU for ayy ~ 5 jan or larger)., Adoptinga minimum grain size of 5 $\mu$ m and allowing for a grain size distribution up to 100 or 1000 $\mu$ m produced lower $\chi^2$ fits and decreased the required inner radius from 120 to 45 AU (32 AU for $_{MIN}$ $\sim$ 8 $\mu$ m or larger). The upper grain size. if one exists. and the outer radius are not well constrained iu the absence of sub- mecasurcuicuts.," The upper grain size, if one exists, and the outer radius are not well constrained in the absence of sub-millimeter measurements." The mass m grains <1 mun for the above models is between «10.5 aud 1410.* ML..., The mass in grains $<$ 1 mm for the above models is between $\times10^{-8}$ and $\times10^{-7}$ $_\odot$ . For, For the cartesian box geometries (2222222). usually used in turbulence studies (because they allow much higher resolutions than more complicated geometries).,"the cartesian box geometries \citep{biskamp96,biskamp99,dastgeer00,dastgeer03,cho04,shaikh05,cho09} usually used in turbulence studies (because they allow much higher resolutions than more complicated geometries)." The studies in box geometries in particular all found spectra that are similar to the classical 5/3 Kolmogorov spectrum. as well as changes in slope that were interpreted as a dissipative cutoff.," The studies in box geometries in particular all found spectra that are similar to the classical 5/3 Kolmogorov spectrum, as well as changes in slope that were interpreted as a dissipative cutoff." Results in two and three dimensions were also found to be broadly similar., Results in two and three dimensions were also found to be broadly similar. The turbulent Hall cascade has been found to reach a stable equilibrium on a timescale of -0.3—0.5 (?2).. efficiently transferring energy from large to small scales.," The turbulent Hall cascade has been found to reach a stable equilibrium on a timescale of $t'\sim0.3-0.5$ \citep{cho04,cho09}, efficiently transferring energy from large to small scales." Our recent work (??) has highlighted a limitation of previous box simulations. in that they all employed hyperdiffusivity. replacing the Ohmic term by (V7)’B. where 7 is typically 2 or 3.," Our recent work \citep{wareing09a,wareing09b} has highlighted a limitation of previous box simulations, in that they all employed hyperdiffusivity, replacing the Ohmic term by $(\nabla^2)^\eta{\bf B}$, where $\eta$ is typically 2 or 3." As we noted. this masks the equivalence of the terms in the governing equation.," As we noted, this masks the equivalence of the terms in the governing equation." Both contain the same number of derivatives so it is conceivable that the nonlinear term will always dominate. even on arbitrarily short lengthscales.," Both contain the same number of derivatives so it is conceivable that the nonlinear term will always dominate, even on arbitrarily short lengthscales." As demonstrated by 9?.. one obtains a dissipative cutoff only if one assumes that the cascade tis local in Fourier space.," As demonstrated by \cite{hollerbach02}, one obtains a dissipative cutoff only if one assumes that the cascade is local in Fourier space." The argument is as follows: the ratio of the Hall term to the Ohmic term is given by the field strength Bo. independent of any lengthscales.," The argument is as follows: the ratio of the Hall term to the Ohmic term is given by the field strength $B_0$, independent of any lengthscales." Implicitly a dependence on lengthscales may still exist: if the coupling is purely local in Fourier space. then the relevant field strength1s only the fieldw," Implicitly a dependence on lengthscales may still exist: if the coupling is purely local in Fourier space, then the relevant field strengthis only the field." "avenumber, For sufficiently large &. this local field is then reduced sufficiently for the Ohmic term to dominate the Hall term. resulting in a dissipative cutoff at that κ."," For sufficiently large $k$, this local field is then reduced sufficiently for the Ohmic term to dominate the Hall term, resulting in a dissipative cutoff at that $k$." It is clear however how crucially this argument depends on the coupling being purely local in Fourier space: if this 15 not the case. then the same global Bo applies to all lengthscales. and the Hall term always dominates the Ohmie term.," It is clear however how crucially this argument depends on the coupling being purely local in Fourier space; if this is not the case, then the same global $B_0$ applies to all lengthscales, and the Hall term always dominates the Ohmic term." Our 3D simulations (?) reach a stable equilibrium by £~0.2 and produce a smooth energy spectrum extending over the whole range of Fourier space., Our 3D simulations \citep{wareing09b} reach a stable equilibrium by $t'\sim0.2$ and produce a smooth energy spectrum extending over the whole range of Fourier space. " For large Bo. this tends towards the E,AxKk scaling suggested by Goldreich and Reisenegger."," For large $B_0$, this tends towards the $E_k \propto k^{-2}$ scaling suggested by Goldreich and Reisenegger." We found no evidence. in either 2D or 3D. of a dissipative cutoff. implying that the Hall term is able to dominate on all scales and that the coupling is nonlocal in Fourier space.," We found no evidence, in either 2D or 3D, of a dissipative cutoff, implying that the Hall term is able to dominate on all scales and that the coupling is nonlocal in Fourier space." Additional evidence of the nonlocal nature of the Hall cascade comes from the strong anisotropy in the presence of a uniform field found by ourselves and others (22):: if the coupling were purely local in Fourier space. then including a uniform field would have no effect at all on small scales. in contrast to what is observed.," Additional evidence of the nonlocal nature of the Hall cascade comes from the strong anisotropy in the presence of a uniform field found by ourselves and others \citep{cho04,cho09}; if the coupling were purely local in Fourier space, then including a uniform field would have no effect at all on small scales, in contrast to what is observed." In a very different approach. ? (henceforth referred to as R&GG) performed a linear stability analysis of Eq. (1)).," In a very different approach, \cite{rheinhardt02} (henceforth referred to as G) performed a linear stability analysis of Eq. \ref{eq:A}) )," and showed that for a particular choice of background field. growing eigenmodes exist at small wavenumbers 0«ky.ky<5.," and showed that for a particular choice of background field, growing eigenmodes exist at small wavenumbers $0 < k_x, k_y < 5$." They conjectured that the transfer of magnetic energy from a background (large-scale) field to small-scale modes may therefore proceed in a non-local way in phase space. resulting in a Hall instability.," They conjectured that the transfer of magnetic energy from a background (large-scale) field to small-scale modes may therefore proceed in a non-local way in phase space, resulting in a Hall instability." This instability could be identified on the basis of its energy spectrum that does not decline monotonically (e.g. as in a turbulence spectrum) but instead exhibits an increasingly large peak at some large k. corresponding to a transfer of energy directly from the largest scale to this small-scale peak.," This instability could be identified on the basis of its energy spectrum that does not decline monotonically (e.g. as in a turbulence spectrum) but instead exhibits an increasingly large peak at some large $k$ , corresponding to a transfer of energy directly from the largest scale to this small-scale peak." Iu the modern theory of cosniüc evolution. strucures orm hierarchically through accretion aud merecrs White Rees 1975: White Freuk 1991: Iauftiiai 1993: Coe 2000: Bower 2006).," In the modern theory of cosmic evolution, structures form hierarchically through accretion and mergers White Rees 1978; White Frenk 1991; Kauffmann 1993; Cole 2000; Bower 2006)." A geejoric eature of this hisorv. then. is the presence of a ueh-redshift populatioi of eravitationallv-bound. strucures hat were much less massive than preseut-day galaxies.," A generic feature of this history, then, is the presence of a high-redshift population of gravitationally-bound structures that were much less massive than present-day galaxies." At virial temperatures below LO! IK. atomic transitions of lvdrogen aud helium are not excited. and the eas inst radiate energy via iiolectior transition lines or dust enission.," At virial temperatures below $^{4}$ K, atomic transitions of hydrogen and helium are not excited, and the gas must radiate energy via molecular transition lines or dust emission." Although some IL. left over from recombination was able to cool t1ο earliest structures Abel 2002: Dronuu 2002: Stacy 2010: Turk 20093. he resulting 11.2-13.6 eV background emission youn these objects Taian 1997.2000: Ciardi 200: Sokasian 200: O'Shea Norman 2007) quickly dissociated the alreacvo low abundance of these munordial molecules (Calli Palla 19985).," Although some $_2$ left over from recombination was able to cool the earliest structures Abel 2002; Bromm 2002; Stacy 2010; Turk 2009), the resulting 11.2-13.6 eV background emission from these objects Haiman 1997,2000; Ciardi 2000; Sokasian 2004; O'Shea Norman 2007) quickly dissociated the already low abundance of these primordial molecules (Galli Palla 1998)." Th fact. even if some sinall fraction of molecules survived. it is uulikelv o have had a large effect on he structure of these low-nass objects Whalen 2008a: Alun 2009).," In fact, even if some small fraction of molecules survived, it is unlikely to have had a large effect on the structure of these low-mass objects Whalen 2008a; Ahn 2009)." The result of this ineficiceut cooling then. was a large »»pulatiou of primordial. atonic “uninihalos” that were unable to orm stars until triggeredao by some exterior influence.," The result of this inefficient cooling then, was a large population of primordial, atomic “minihalos"" that were unable to form stars until triggered by some exterior influence." A prime candidate for inducing star formation iu these objec sis galaxy outflows. powered by core-collapse superiovae aud winds frou uiassive stars.," A prime candidate for inducing star formation in these objects is galaxy outflows, powered by core-collapse supernovae and winds from massive stars." Such outflows have been ound originating from a varicty of galaxies. from dwarfs to inassive starmusts. over a wide range of redshifts Lehnert Heckman 1996: Frans 1997: Pettini 1998: Martin 1999: Teckiman 2000: Veilleux 2005: Rupke 2005: Chung 2H1).," Such outflows have been found originating from a variety of galaxies, from dwarfs to massive starbursts, over a wide range of redshifts Lehnert Heckman 1996; Franx 1997; Pettini 1998; Martin 1999; Heckman 2000; Veilleux 2005; Rupke 2005; Chung 2011)." Furtherinore. theoretical studies have argued that many of these early ealaxies represent the tail cud of a laree population of low-mass starbursts that aceired hefore reionizatkn (Seannapieco. Ferrera. Alaau 2002: Thacker. οιULUapleco. Davis 2002).," Furthermore, theoretical studies have argued that many of these early galaxies represent the tail end of a large population of low-mass starbursts that occurred before reionization (Scannapieco, Ferrera, Madau 2002; Thacker, Scannapieco, Davis 2002)." While ionizing photous generated by these carly galaxies would have lead to the pletoionization of huge regious of soie. these photous are also casily trapped behind outflows as they sweep 1ip intergalactic eas (Fujita 2003).," While ionizing photons generated by these early galaxies would have lead to the photoionization of large regions of space, these photons are also easily trapped behind outflows as they sweep up intergalactic gas (Fujita 2003)." This sieoosts that many regious iu the intergalactic medi Way ave be impacted by outflows before they were ionized., This suggests that many regions in the intergalactic medium may have be impacted by outflows before they were ionized. Iu the first two papers in this series (Cray Seaunapieco 2010. hereafter Paper I Grav Scaunapieco 2Ml. hereafter Paper ID) we carried out high-resolution. three-dinieusional adaptive mesh refinement sinulatiois of the interaction between a typical primordial minuihalo and high redshift ealaxv outflow. capturing all the Huportant physical processes in detail.," In the first two papers in this series (Gray Scannapieco 2010, hereafter Paper I; Gray Scannapieco 2011, hereafter Paper II) we carried out high-resolution, three-dimensional adaptive mesh refinement simulations of the interaction between a typical primordial minihalo and high redshift galaxy outflow, capturing all the important physical processes in detail." In Paper I we ooked at the influence of a ll-spoecies primordial nou-quilibrimu chemical network witji asoclated cooling terms. and showed that much of the minihalo barvouic latter is removed from the dark imatter halo and compressed iuto several dense chunps embedded in a ribbou of gas.," In Paper I we looked at the influence of a 14-species primordial non-equilibrium chemical network with associated cooling terms, and showed that much of the minihalo baryonic matter is removed from the dark matter halo and compressed into several dense clumps embedded in a ribbon of gas." The iuclusiou of a dissociating UV. backeround. while altering the final molecular abundances. had no effect on the Ἡial distribution.," The inclusion of a dissociating UV background, while altering the final molecular abundances, had no effect on the final distribution." In Paper [EH we extended this study by including the effects of metallne cooling aud urbulence., In Paper II we extended this study by including the effects of metal-line cooling and turbulence. Turbulence had the primarv ctfect of mixing netals iuto the primordial cloud from the outflow. which curiched the ↽⋅≻ ↸⊳↕∪∏≼↧↑∪∑≈⊥∩−∑↔↖↖⇁hile metals provided another source of cooliis. we found that they did rot have a sienificant iupact on the final structure of the cloud.," Turbulence had the primary effect of mixing metals into the primordial cloud from the outflow, which enriched the cloud to Z $\approx$ $^{-2}$ $_{\odot}.$ While metals provided another source of cooling, we found that they did not have a significant impact on the final structure of the cloud," data alone (n particular. (he observed. value of the svnchrotron sell-absorption frequency) and ecuipartition.,"data alone (in particular, the observed value of the synchrotron self-absorption frequency) and equipartition." The fact that these two independent methods to determine the enerev clensiGes in magnetic fields aud relativistic electrons give (he same value lends support to the Compton cooling scenario., The fact that these two independent methods to determine the energy densities in magnetic fields and relativistic electrons give the same value lends support to the Compton cooling scenario. This is futher strengthened by the determination of the shock velocity. for which both methods give approximately (he same value.," This is further strengthened by the determination of the shock velocity, for which both methods give approximately the same value." Internally produced svinclirotron photons are unlikely to contribute to the cooling as can be seen [rom the lollowing argument., Internally produced synchrotron photons are unlikely to contribute to the cooling as can be seen from the following argument. " When cooling is important and p22.0. (he energy density of svnchrotron photons is UC,pheUbstvaο(Olen)ο...fente? "," When cooling is important and $p\approx 2.0$, the energy density of synchrotron photons is $U_{\rm ph}\sim U_{\rm B}(v_{\rm sh}/c)(\epsilon_{\rm rel}/\epsilon_{\rm B})^{1/2}$." The condition corresponcdine5Lo equation (8)) then becomes eM5/03)>4r(oa/0)Ceraeps).," The condition correspondingto equation \ref{eq:1.8}) ) then becomes $\epsilon_{\rm rel} (\dot{M}_{-5}/v_{\rm w,3})>4.7 (v_{\rm sh}/c)^{-4/3}(\epsilon_{\rm rel}/\epsilon_{\rm B})^{1/3}$." μυ... necessary lor Compton scattering to dominate svuchrotron radiation. (his requires an even higher mass loss rate than the svnchrotron cooling scenario.," Since $\epsilon_{\rm rel}/\epsilon_{\rm B} > 1$ is necessary for Compton scattering to dominate synchrotron radiation, this requires an even higher mass loss rate than the synchrotron cooling scenario." The estimates above show that Compton cooling can provide a natural scenario for SN 2002ap., The estimates above show that Compton cooling can provide a natural scenario for SN 2002ap. A more detailed model fit to the observations is therefore warranted., A more detailed model fit to the observations is therefore warranted. We have for (his purpose used the numerical model in Fransson&Djórnsson(1998).. which solves the raciative transfer equation for the svnchrotron radiation. including sell-absorption. together with the kinetic equation for the electron distribution. including svuchrotron. Compton and Coulomb losses.," We have for this purpose used the numerical model in \citet{FB98}, which solves the radiative transfer equation for the synchrotron radiation, including self-absorption, together with the kinetic equation for the electron distribution, including synchrotron, Compton and Coulomb losses." The latter is unimportant for SN 2002ap., The latter is unimportant for SN 2002ap. As discussed above. we assume that a constant fraction. ey. of the thermal energy behind the shock goes into magnetic fields and a fraction. ej4. into relativistic electrons.," As discussed above, we assume that a constant fraction, $\epsilon_{\rm B}$, of the thermal energy behind the shock goes into magnetic fields and a fraction, $\epsilon_{\rm rel}$, into relativistic electrons." The other important input parameters are p. Mf. and η. the ejecta density power law index (specibving the shock velocity. see above).," The other important input parameters are $p$, $\Mdot/v_{\rm w}$, and $n$, the ejecta density power law index (specifying the shock velocity, see above)." Finally. the bolometric luminosity. Lj. determines (he Compton cooling.," Finally, the bolometric luminosity, $L_{\rm bol}$, determines the Compton cooling." " For Li, we use the bolometric light curve determined by Mazzalietal.(2002).. Yoshiietal. (2003)... and Pandevοἱal.(2003)."," For $L_{\rm bol}$ we use the bolometric light curve determined by \citet{Maz02}, \citet{YO03}, and \cite{P03}." ". Because Iree-Iree absorption is unimportant in (he cases we consider. and the svnchrotron sell-absorption is determined by D. 44 and H only. Mn always enters in the combination epMfns and enll/ty. reducing the nmunber of free parameters by one. but also preventinge us from determininge M//(,.W separately."," Because free-free absorption is unimportant in the cases we consider, and the synchrotron self-absorption is determined by $B$, $n_{\rm rel}$ and $R$ only, $\Mdot/v_{\rm w}$ always enters in the combination $\epsilon_{\rm B}\Mdot/v_{\rm w}$ and $\epsilon_{\rm rel} \Mdot/v_{\rm w}$, reducing the number of free parameters by one, but also preventing us from determining $\Mdot/v_{\rm w}$ separately." Using (his model. we havevaried (he parameters to eive a best fit of the radio lieht curves together with the NMM flux at 6 davs. taken [rom Sutaria. (2003).," Using this model, we havevaried the parameters to give a best fit of the radio light curves together with the XMM flux at 6 days, taken from \citet{SCB03}." . In Figure 1. we show the resulting light curves and in Figure 2. the full spectrum al 6 davs. together with the VLA and XMM observations.," In Figure \ref{fig1} we show the resulting light curves and in Figure \ref{fig2} the full spectrum at 6 days, together with the VLA and XMM observations." In this figure we have also added (he huminosity [rom (the supernova photosphere., In this figure we have also added the luminosity from the supernova photosphere. The latter can on day 6 be well approximated as a black-body with temperature of ~5000 Ix. and. a total luminosity of 1.6x107ergs! (Pandevetal. 2003).., The latter can on day 6 be well approximated as a black-body with temperature of $\sim 5000$ K and a total luminosity of $1.6\EE{42}\ergs$ \citep{P03}. . As input electron spectrum we use p= 2.1. and," As input electron spectrum we use $p=2.1$ , and" electron beam on atmospheric heating and the statistical equilibrium of HI. but not Ale.,"electron beam on atmospheric heating and the statistical equilibrium of H, but not Mg." The RII code that we use to generate spectra from the Allred et al., The RH code that we use to generate spectra from the Allred et al. flare model includes a standard implementation of partial redistribution., flare model includes a standard implementation of partial redistribution. " A ""cohereney fraction” (see Uitenbroek 2001. eqn."," A “coherency fraction” (see Uitenbroek 2001, eqn." 13) mixes coherent scattering aid complete redistribution in proportion to the depopulation rate (due to radiation and inelastic collisions) ancl elastic collision rate. respectively.," 13) mixes coherent scattering and complete redistribution in proportion to the depopulation rate (due to radiation and inelastic collisions) and elastic collision rate, respectively." Typically. elastic collisions are due (ο van der Waals and Stark broadening.," Typically, elastic collisions are due to van der Waals and Stark broadening." However. the RII code does not include the contribution to the elastic collision rate due to interactions with the electron beam.," However, the RH code does not include the contribution to the elastic collision rate due to interactions with the electron beam." We speculate that the inclusion of (he beam collisions would enhance the collisional rates. increasing the redistribution of line core photons into the wings and possibly producing the far wing lime emission seen in the data.," We speculate that the inclusion of the beam collisions would enhance the collisional rates, increasing the redistribution of line core photons into the wings and possibly producing the far wing line emission seen in the data." We plan to investigate (his possibility in our next generation of flare models., We plan to investigate this possibility in our next generation of flare models. We analyzed six orbils of IST/STIS near-ultraviolet spectroscopic data on YZ CM ancl found that the star was flaring approximately of the time., We analyzed six orbits of HST/STIS near-ultraviolet spectroscopic data on YZ CMi and found that the star was flaring approximately of the time. The flares contributed ~ ol the energv observed in the near-ultraviolet 300-3050A)) during the 224 total minutes of exposure (ime., The flares contributed $\sim$ of the energy observed in the near-ultraviolet ) during the 224 total minutes of exposure time. Ten flaring and eight «quiet intervals were identified. and (wo of the flares (F2. F9) were large enough to divide into sub-intervals to study the time evolution of the rear-ullvaviolet emission during those flares.," Ten flaring and eight quiet intervals were identified, and two of the flares (F2, F9) were large enough to divide into sub-intervals to study the time evolution of the near-ultraviolet emission during those flares." The Mg II k emission line was examined in detail and found (ο change significantly between different flares. showing blue enhancements in some flares. red enhancements in others. and svimetrie enhancements in the wings or core in still others.," The Mg II k emission line was examined in detail and found to change significantly between different flares, showing blue enhancements in some flares, red enhancements in others, and symmetric enhancements in the wings or core in still others." This indicates that. Me II emitting material mar experience outward or inward directed velocities (1.e. evaporation or condensation) depending on the individual Lave reading., This indicates that Mg II emitting material may experience outward or inward directed velocities (i.e. evaporation or condensation) depending on the individual flare heating. The strongest Fe II line (UV1) showed similar behavior to the Meg II k line., The strongest Fe II line (UV1) showed similar behavior to the Mg II k line. Further. flare FO showed a remarkable line broadening. which fit a Gaussian profile corresponding to a velocity FWILM of ~ 250 km !.," Further, flare F9 showed a remarkable line broadening, which fit a Gaussian profile corresponding to a velocity FWHM of $\sim$ 250 km $^{-1}$." This velocity is highly supersonic. and if the broadening is interpreted as due to either svmmetric mass motions. or turbulence. implies a kinetic energv during the flare that vastly exceeds the racdiated enerey (bv several orders of magnitude).," This velocity is highly supersonic, and if the broadening is interpreted as due to either symmetric mass motions, or turbulence, implies a kinetic energy during the flare that vastly exceeds the radiated energy (by several orders of magnitude)." Overlapping emission due to explosive microflares. as has been suggested {ο explain the broad. components observed in optically (hin transition region emission lines. does not appear to be a physically plausible explanation for the emission from the Me II lines which are formed in a dense. optically thick regime.," Overlapping emission due to explosive microflares, as has been suggested to explain the broad components observed in optically thin transition region emission lines, does not appear to be a physically plausible explanation for the emission from the Mg II lines which are formed in a dense, optically thick regime." The data were compared to Mg 1I k line profiles generated using the preflare and E10 flare models of Allred et al. (, The data were compared to Mg II k line profiles generated using the preflare and F10 flare models of Allred et al. ( 2006) together with the RII code of Uitenbroek (2001).,2006) together with the RH code of Uitenbroek (2001). The, The "these figures, the conclusions remain same for other values of Qo.","these figures, the conclusions remain same for other values of $\Omega_{m0}$." " With future data, one can probe the background expansion at higher redshifts thereby probing the higher derivatives of the scale factor."," With future data, one can probe the background expansion at higher redshifts thereby probing the higher derivatives of the scale factor." Hence Statefinder Hierarchy wil be quite useful to distinguish various dark energy models., Hence Statefinder Hierarchy will be quite useful to distinguish various dark energy models. We further study the w'—w phase plane for different thawing dark energy models., We further study the $w^{\prime}-w$ phase plane for different thawing dark energy models. Here ‘prime’ denotes the differentiation with respect to loga., Here `prime' denotes the differentiation with respect to $\log a$. " As discussed in the previous section, for smaller values of A;, all the thawing models behave similar to the cosmological constant."," As discussed in the previous section, for smaller values of $\lambda_{i}$, all the thawing models behave similar to the cosmological constant." " So to study the w'—w phase plane, we assume A;—1 for which the thawing models behave significantly different from cosmological constant."," So to study the $w^{\prime}-w$ phase plane, we assume $\lambda_{i} =1$ for which the thawing models behave significantly different from cosmological constant." Linder and Caldwell have previously showed that the thawing models are constrained to lie between (1+w)€w'3(14- region in w'—w phase plane., Linder and Caldwell have previously showed that the thawing models are constrained to lie between $(1+w) \leq w^{\prime} \leq 3(1+w)$ region in $w^{\prime}-w$ phase plane. In Fig., In Fig. 5 and Fig., 5 and Fig. " 6, we show different thawing models in the w’—w phase plane at different redshifts and compare them with the constraint proposed by Linder and Caldwell CCaldwell Linder (2005)) (LC)."," 6, we show different thawing models in the $w^{\prime}-w$ phase plane at different redshifts and compare them with the constraint proposed by Linder and Caldwell Caldwell Linder (2005)) (LC)." " It can be seen that for higher redshifts, all the thawing models are inside the LC bound."," It can be seen that for higher redshifts, all the thawing models are inside the LC bound." This is obvious as all the thawing models behave very close to cosmological constant for larger redshifts and hence satisfy the LC bound., This is obvious as all the thawing models behave very close to cosmological constant for larger redshifts and hence satisfy the LC bound. " But at the present epoch (z=0), for smaller values of Qmo0, thawing models with certain potentials ( as shown in Figure 5) are outside the LC bound."," But at the present epoch (z=0), for smaller values of $\Omega_{m0}$, thawing models with certain potentials ( as shown in Figure 5) are outside the LC bound." " But as one increases the value of Qmo (see Figure 6), they tend to satisfy the LC bound."," But as one increases the value of $\Omega_{m0}$ (see Figure 6), they tend to satisfy the LC bound." " Hence thawing models which deviate significantly from the ACDM behaviour at smaller redshift tend to satisfy the LC bound for higher values of Qmo whereas for lower values of (πιο, some of the potentials do not satisfy the LC bound."," Hence thawing models which deviate significantly from the $\Lambda$ CDM behaviour at smaller redshift tend to satisfy the LC bound for higher values of $\Omega_{m0}$ whereas for lower values of $\Omega_{m0}$, some of the potentials do not satisfy the LC bound." " In this section, we constrain the parameters in the thawing scalar field models with the assumption of a flat Universe by using the latest observational data including the Type-1a Supernovae Union2 compilation AAmanullah et al. ("," In this section, we constrain the parameters in the thawing scalar field models with the assumption of a flat Universe by using the latest observational data including the Type-1a Supernovae Union2 compilation Amanullah et al. (" "2010)), the BAO EEisenstein et al. (","2010)), the BAO Eisenstein et al. (" 2005)) measurement from the SDSS PPercival et al.,2005)) measurement from the SDSS Percival et al. PPercival et al. (, Percival et al. ( "2010)), the CMBR measurement given by WMAP?7 KKomatsu et al. (","2010)), the CMBR measurement given by WMAP7 Komatsu et al. (" "2011)) observations, the H(z) data from HST key Project FFreedman et al. (","2011)) observations, the H(z) data from HST key Project Freedman et al. (" 2001)) and a simulated dataset HHolsclaw et al. (,2001)) and a simulated dataset Holsclaw et al. ( 2010)) based on the upcoming JDEM SN-survey containing around 2300 Supernovae.,2010)) based on the upcoming JDEM SN-survey containing around 2300 Type-1a Supernovae. "Because there are relatively few objects with such unusual features, it is entirely plausible that the properties of all these objects can be explained in a similar way e.g. with a specific viewing angle of the torus that maximises the observed emission area of the torus whilst still obscuring the central engine, consistent with the scheme described by Murayama&Taniguchi (1998),, Nagaoetal.(2001) and Nagaoetal.(2000).","Because there are relatively few objects with such unusual features, it is entirely plausible that the properties of all these objects can be explained in a similar way e.g. with a specific viewing angle of the torus that maximises the observed emission area of the torus whilst still obscuring the central engine, consistent with the scheme described by \citet{murayama2}, , \citet{nagao1} and \citet{nagao2}." ". Q1131+16 has a remarkable spectrum which displays a multitude of FHILs of relatively high equivalent width, as well as the more common emission lines expected of an AGN spectrum."," Q1131+16 has a remarkable spectrum which displays a multitude of FHILs of relatively high equivalent width, as well as the more common emission lines expected of an AGN spectrum." " An in-depth study of the spectrum of Q1131+16 has revealed: Based on the high densities and relatively quiescent kinematics implied by our observations, it is likely that the FHILs in Q1131+16 are emitted by the torus wall, with the inner wall on the far side of the torus viewed directly by the observer, but the quasar itself remaining hidden."," An in-depth study of the spectrum of Q1131+16 has revealed: Based on the high densities and relatively quiescent kinematics implied by our observations, it is likely that the FHILs in Q1131+16 are emitted by the torus wall, with the inner wall on the far side of the torus viewed directly by the observer, but the quasar itself remaining hidden." This geometry is also consistent with the relatively small radial distance found for the FHIL region., This geometry is also consistent with the relatively small radial distance found for the FHIL region. These results demonstrate the potential of the FHILs for probing the circum-nuclear obscuring regions in AGN., These results demonstrate the potential of the FHILs for probing the circum-nuclear obscuring regions in AGN. M.R. acknowledges support in the form of an STFC PhD studentship., M.R. acknowledges support in the form of an STFC PhD studentship. C.R.A. ackowledges financial support from STFC PDRA (ST/G001758/1)., C.R.A. ackowledges financial support from STFC PDRA (ST/G001758/1). The authors acknowledge Jose Antonio Acosta Pulido for his valuable help with the LIRIS data reduction., The authors acknowledge Jose Antonio Acosta Pulido for his valuable help with the LIRIS data reduction. We would like to thank the referee for useful comments and suggestions., We would like to thank the referee for useful comments and suggestions. " The authors acknowledge the data analysis facilities provided by the Starlink Project, which is run by CCLRC on behalf of PPARC."," The authors acknowledge the data analysis facilities provided by the Starlink Project, which is run by CCLRC on behalf of PPARC." The William Herschel Telescope and its service programme are operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofissica de Canarias., The William Herschel Telescope and its service programme are operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofíssica de Canarias. " This work is based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministérrioda"," This work is based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministérrioda" an accretion disk.,an accretion disk. Moreover. a significant part of the disk surface is not obscured from the central X-ray source so that the irracliatively induced temperature inversion can occur.," Moreover, a significant part of the disk surface is not obscured from the central X-ray source so that the irradiatively induced temperature inversion can occur." lt is interesting to note that the 1999. July (Fig. 1..," It is interesting to note that the 1999 July (Fig. \ref{fig:Halpha-fits}," phase 0.88) observation. which was the first spectrum to show double-peaked. lines. was taken in the evele after an orbit during which ασια not have a post-periastron X-ray Πάγο only a handful of orbits observed by NPE had. not shown such a [lare before then.," phase 0.88) observation, which was the first spectrum to show double-peaked lines, was taken in the cycle after an orbit during which did not have a post-periastron X-ray flare; only a handful of orbits observed by XTE had not shown such a flare before then." Lt is possible that this has some bearing on the visibility of the optical lines from the aceretion disk. for instance if the absence of an X-ray outburst means that matter which usually obscures the clisk was more transparent than usual.," It is possible that this has some bearing on the visibility of the optical lines from the accretion disk, for instance if the absence of an X-ray outburst means that matter which usually obscures the disk was more transparent than usual." Alternatively. the aceretion rates during this observational epoch were low enough to allow a mature Ixeplerian disk to develop within an orbital evele.," Alternatively, the accretion rates during this observational epoch were low enough to allow a mature Keplerian disk to develop within an orbital cycle." The couble-peakecl lines seen in 2000 May (Fig. 1..," The double-peaked lines seen in 2000 May (Fig. \ref{fig:Halpha-fits}," phase 0.62) did not occur after such an anomalous orbit., phase 0.62) did not occur after such an anomalous orbit. Llowever. by that stage the X-ray [lux observed by hhad begun to drop (see Sec 3.2.. Fig. 2)).," However, by that stage the X-ray flux observed by had begun to drop (see Sec \ref{sec:Secular-variation}, Fig. \ref{fig:eqw}) )," which might also imply that veiling material was thinner., which might also imply that veiling material was thinner. lt is possible that. instead. of being an intrinsically double-peakec line. the profile observed. on 2000. May. 16 is actually [lat-topped.," It is possible that, instead of being an intrinsically double-peaked line, the profile observed on 2000 May 16 is actually flat-topped." Such lines have seen in several black hole candidates. such as GX 4 (Smithetal.1999:Soriaetal.1999). and GRO 40 (Soriaοἱal.2000)... where they are interpreted as arising in a horizontal wind launched from a disk (Murray&Chiang1997).," Such lines have seen in several black hole candidates, such as GX $-$ 4 \cite{sfl99,swj99} and GRO $-$ 40 \cite{swh00}, where they are interpreted as arising in a horizontal wind launched from a disk \cite{mc97}." . Possibly the line in aarises in a similar fashion: however. this requires the emission site to change from a spherical outllow (phases «0.5: Fig. 1))," Possibly the line in arises in a similar fashion; however, this requires the emission site to change from a spherical outflow (phases $< 0.5$; Fig. \ref{fig:Halpha-fits}) )" to a horizontal wind (phase 0.6) to a disk (phase 0:55)A, to a horizontal wind (phase 0.6) to a disk (phase 0.88). The interpretation of the line as a barely-resolved: double. peak has at least the virtue of being a simpler explanation., The interpretation of the line as a barely-resolved double peak has at least the virtue of being a simpler explanation. Assuming the double-peaked lines arise in an accretion disk. then the separation rellects the velocity at the outer edge of the emission region of the accretion disk. (Smak 1981).," Assuming the double-peaked lines arise in an accretion disk, then the separation reflects the velocity at the outer edge of the emission region of the accretion disk \cite{sma81}." . The separation of the peaks was very cdillerent on the two occasions the cdouble-peakect profile was observed iin 1999 July. iin 2000 May). which suggests that the accretion disk had a very different size.," The separation of the peaks was very different on the two occasions the double-peaked profile was observed in 1999 July, in 2000 May), which suggests that the accretion disk had a very different size." This could be due to the dillerent phase of 16 observation. implying the disk is shrinking as periastron pproaches.," This could be due to the different phase of the observation, implying the disk is shrinking as periastron approaches." Figure 6 shows a comparison between the bservecl peak separations and a model where the size of 1e disk is truncated. by the size of the Roche lobe in an eccentric orbit., Figure \ref{fig:disksize} shows a comparison between the observed peak separations and a model where the size of the disk is truncated by the size of the Roche lobe in an eccentric orbit. This represents the largest possible size for 1e aceretion disk. and hence afewer limit to the separation [the two peaks.," This represents the largest possible size for the accretion disk, and hence a limit to the separation of the two peaks." The fact that the observed. velocities are bove this limit implies that either the disk has not reached 10 truncation radius. or that the emission region for Ho iis not at the outer edge of the disk.," The fact that the observed velocities are above this limit implies that either the disk has not reached the truncation radius, or that the emission region for $\alpha$ is not at the outer edge of the disk." The former would imply mt. after the disk is disrupted at periastron. it has not had ime to grow to the truncation radius before the Roche lobe »eeins to Contract again (Fig. 6)).," The former would imply that, after the disk is disrupted at periastron, it has not had time to grow to the truncation radius before the Roche lobe begins to contract again (Fig. \ref{fig:disksize}) )," which would imply that 10 viscous timescale for the growth of the disk is longer aan the dynamical timescale. which is 8 d for half an orbit.," which would imply that the viscous timescale for the growth of the disk is longer than the dynamical timescale, which is 8 d for half an orbit." Alternatively. the change in peak separation could. be 10 result of a secular variation in the size of the emitting region: or the temperature of the disk could be varving. so wt the location of the Lla eemission site is changing.," Alternatively, the change in peak separation could be the result of a secular variation in the size of the emitting region; or the temperature of the disk could be varying, so that the location of the $\alpha$ emission site is changing." In lis case. the smaller peak separation implies a hotter disk. with the emission site having moved towards the outside of 1e disk.," In this case, the smaller peak separation implies a hotter disk, with the emission site having moved towards the outside of the disk." Other explanations for the double-peaked: profiles are »xossible which do not require the presence of an accretion isk., Other explanations for the double-peaked profiles are possible which do not require the presence of an accretion disk. They could. for instance. arise in a bipolar jet. since a relativistic jet has been inferred. (rom high-resolution racio maps of the source (Fenderetal. 1998)..," They could, for instance, arise in a bipolar jet, since a relativistic jet has been inferred from high-resolution radio maps of the source \cite{fst+98}. ." However. in SS 433. which has a jet with velocity ~099. the separation of he components is hundreds of angstroms (Alareon1984).. compared to the sseen in our spectra.," However, in SS 433, which has a jet with velocity $\sim 0.3c$, the separation of the components is hundreds of ngstroms \cite{mar84}, compared to the seen in our spectra." Such a small separation could only be oduced: by a relativistic jet if the jet was almost in the xane of the sky. (in which case the transverse Doppler shift would cause both. components to be redshifted)., Such a small separation could only be produced by a relativistic jet if the jet was almost in the plane of the sky (in which case the transverse Doppler shift would cause both components to be redshifted). Thus any jet would need to be non-relativistic to produce the observed. ines., Thus any jet would need to be non-relativistic to produce the observed lines. Variable double-peaked lines have also been seen. in infrared. spectra of (νο X-3 (Fenderetal.1999)... where hey were interpreted as arising in a cisk-like wind outside he binary orbit.," Variable double-peaked lines have also been seen in infrared spectra of Cyg X-3 \cite{fhp99}, where they were interpreted as arising in a disk-like wind outside the binary orbit." Such a cisk-winel requires a large angular momentum. whichwould be unlikely in a svstem like," Such a disk-wind requires a large angular momentum, whichwould be unlikely in a system like" 8M. (Evansctal.1987).. (Nelemaus2009)... (Nelemanus&Tout2005)..," $8 \mathrm{M_{\odot}}$ \citep[GWs,][]{peters63:GW_radiation_Keplerian_orbit,paczynski67:GW_close_binaries}. \citep{evans87:WD_binaries_as_GW_sources}, \citep{nelemans09:binaries_review}. \citep{nelemans05:common_envelope_in_WD_binaries}." WDs whose combined mass is above the Chandrasekhar limit. the mereer might trigger a thermonuclear runaway and lead to a Type Ia supernova (SN) explosion (hen&Tutukov1981:Webbin198 LD)..," WDs whose combined mass is above the Chandrasekhar limit, the merger might trigger a thermonuclear runaway and lead to a Type Ia supernova (SN) explosion \citep{iben84:typeIsn,webbink84:DDWD_Ia_progenitors}." This possibility. often referred to as the double degenerate WD (DDWD) SN Ia progenitor scenario. is the only theoretical model that naturally explains the absence of IT iu the nebular spectra of Type Ia SN (seeLeonard2007.audrefereucestherein).. and it has motivated a number of searches for suitable candidate systems.," This possibility, often referred to as the double degenerate WD (DDWD) SN Ia progenitor scenario, is the only theoretical model that naturally explains the absence of H in the nebular spectra of Type Ia SN \citep[see][and references therein]{Leonard07:H_nebular_Ia_spectra}, and it has motivated a number of searches for suitable candidate systems." The most comprehensive of these searches. the SPY survey (Napiwotzkictal.2001).. exanuned the spectra of ~1000 WDs to look for radial velocity (RV) shifts in the characteristic absorption lines.," The most comprehensive of these searches, the SPY survey \citep{napiwotzki01:SPY_survey}, examined the spectra of $\sim1000$ WDs to look for radial velocity (RV) shifts in the characteristic absorption lines." The total uuuber of detached DDWDs fouud to date by SPY aud other surveys is around LOO (Napiwotzkictal. 2001).. but the periods and mass estimates have only »een published for 21 systems (Nelemansetal.2005).," The total number of detached DDWDs found to date by SPY and other surveys is around 100 \citep{napiwotzki04:SPY_04}, , but the periods and mass estimates have only been published for 24 systems \citep{nelemans05:SPY_IV}." . So far. noue of these svstenmis clearly fulfills the requisites o he a SN Ia progenitor.," So far, none of these systems clearly fulfills the requisites to be a SN Ia progenitor." Iu this paper aud in a companion publication (Mullallyal. 2009).. we present the first results fromSWARMS.. he Sloan White dwArf Radial velocity data Miniug Survey.," In this paper and in a companion publication \citep{mullally09:DDWDs}, we present the first results from, the Sloan White dwArf Radial velocity data Mining Survey." The aim of lis to mine the WD catalog iu the spectroscopic data vase of the Sloan Digital Sky Survey (SDSS.Yorkotal.2000) in search of CWDBs.," The aim of is to mine the WD catalog in the spectroscopic data base of the Sloan Digital Sky Survey \citep[SDSS,][]{york00:SDSS_Technical} in search of CWDBs." Our ultimate goal is to fíud he DDWD progenitors of Type Ia SNe. or at least put constraints ou the rate of DD iuersers in the Galactic disk that can be compared with measurements of the οσα] Type Ia SN rate.," Our ultimate goal is to find the DDWD progenitors of Type Ia SNe, or at least put constraints on the rate of DD mergers in the Galactic disk that can be compared with measurements of the local Type Ia SN rate." This will allow us to assess the viabilitv of the DDWD progenitor scenario for SN Ta. This paper is organized as follows., This will allow us to assess the viability of the DDWD progenitor scenario for SN Ia. This paper is organized as follows. Our data iinine strategv is briefle described aud compared to the SPY survev in Section 2.. using as an example the CWDD ((heuceforth. 5128)). the. fist. object discoveredby.," Our data mining strategy is briefly described and compared to the SPY survey in Section \ref{sec:Strategy}, using as an example the CWDB (henceforth, ), the first object discoveredby ." SWARAIS.. Iu Section 3.. we present the follow-up observations of," In Section \ref{sec:Followup}, , we present the follow-up observations of" Dwiuf galaxies in he Local Group (LC) clearly obev a nkxphologv-deusitv relation.,Dwarf galaxies in the Local Group (LG) clearly obey a morphology-density relation. Close to the Milkv Way aud ΑΟ we fud earVAINoe dwarf ealaxies. αλλο] fait (Mp> LL) low surfi«Ὁ brnightuess dwarf spheroidals (dSphs} and more luminous Mp= 17). higher surface byiehtuess dwart ellipticas («Es).," Close to the Milky Way and M31 we find early-type dwarf galaxies, namely faint $M_B > -14$ ) low surface brightness dwarf spheroidals (dSphs) and more luminous $M_B > -17$ ), higher surface brightness dwarf ellipticals (dEs)." All these galaxies are ucarlv devoid of gas. contaiu ¢lark iater and mainly old stars οι ALC SUDppOred by ve‘locity dispersion (Fergusou Bineech 1991. hereafter FEBOL: Mateo 1998. hereafter Mads: Crebel 1999. hereafter C99: Va1 deu Bergh 1999).," All these galaxies are nearly devoid of gas, contain dark matter and mainly old stars and are supported by velocity dispersion (Ferguson Binggeli 1994, hereafter FB94; Mateo 1998, hereafter Ma98; Grebel 1999, hereafter Gr99; Van den Bergh 1999)." Adoπο them Draco aid Ursa Minor have the highest dark. latter densities ever neasured (Lake 1990)., Among them Draco and Ursa Minor have the highest dark matter densities ever measured (Lake 1990). Ou the «mtskirts of the LG we find similarly faint (Mp> -Is) uid dark matter domiuaed duit nreeular galaxies (dvrs) that are gas rich. star-forming svstenis with like gnenatics (Ma98.. Vau den Dereh 1999. C99).," On the outskirts of the LG we find similarly faint $M_B>$ -18) and dark matter dominated dwarf irregular galaxies (dIrrs), that are gas rich, star-forming systems with disk-like kinematics (Ma98, Van den Bergh 1999, Gr99)." Drevious attempts o explain the origin of dSphlis in the LG iive relied. on eas dyvuziuical processes to remove the eas in divs., Previous attempts to explain the origin of dSphs in the LG have relied on gas dynamical processes to remove the gas in dIrrs. " Gas stripping iav result either because of the Messuro exored wean external hot gaseous medi111 in the halo of the Misv Wav (""rn pressure) (Eiuasto ot al", Gas stripping may result either because of the pressure exerted by an external hot gaseous medium in the halo of the Milky Way (“ram pressure”) (Einasto et al. 1971) or jcause of internal strong supernovae wis (Dekel Silk |986)., 1974) or because of internal strong supernovae winds (Dekel Silk 1986). However. ram pressure wolld require an external gas density that is several orders of maeutude hieher than recently iuferred for the Malsv Way (Murali 2000) aid siupernovae winds cannot explain the «sisting morphlologv-deusitv relation.," However, ram pressure would require an external gas density that is several orders of magnitude higher than recently inferred for the Milky Way (Murali 2000) and supernovae winds cannot explain the existing morphology-density relation." Moreover. such dissiative mechanisms would remove the gas but world uot directly alter the structure and kinematics of the pre-existing stellar component.," Moreover, such dissipative mechanisms would remove the gas but would not directly alter the structure and kinematics of the pre-existing stellar component." However. the light follows an exponential profile iu both dSphs aud dias (Faber Liu 1983: bwin Uatzclimitrion 1995: Ma98) aud a positive correlation between surface brightuess aud huninosity is shown by both types of dwufs (FB91). sugecsting an evolutionary link between them.," However, the light follows an exponential profile in both dSphs and dIrrs (Faber Lin 1983; Irwin Hatzdimitriou 1995; Ma98) and a positive correlation between surface brightness and luminosity is shown by both types of dwarfs (FB94), suggesting an evolutionary link between them." Is there a mechanisimi that cau transform dwiuf galaxies between iuorphological classes or must we accept the idea that dSphs are fundamentally ciffercut from cars?, Is there a mechanism that can transform dwarf galaxies between morphological classes or must we accept the idea that dSphs are fundamentally different from dIrrs? Within rich galaxy clusters. fas fly-by encounters with the larges ealaxies can transforqu a disk system into a spheroical or SO ealaxv in jist SL Cr (Moore et al.," Within rich galaxy clusters, fast fly-by encounters with the largest galaxies can transform a disk system into a spheroidal or S0 galaxy in just 3-4 Gyr (Moore et al." 1996. 1998).," 1996, 1998)." " If the halos of bright galaxies were scaled down versions of ealaxy chsters then this ""galaxy harassment” would be equallv iuportant within them.", If the halos of bright galaxies were scaled down versions of galaxy clusters then this “galaxy harassment” would be equally important within them. Ilowever. whereas rich clusters οςmitain over thirty large (L..) porturbing galaxies. the Micy Wav and AI31 have onlv a cotple of satellites sufiicicutly massive to harass the other dwarf galaxies (Moore e al.," However, whereas rich clusters contain over thirty large $L_*$ ) perturbing galaxies, the Milky Way and M31 have only a couple of satellites sufficiently massive to harass the other dwarf galaxies (Moore et al." 1999: πηρα ct al., 1999; Klypin et al. 1999) As a result. the rate for eective satellite-satellite flv-bv encounters is less than onc an every 10 Cr (the LAIC and the SAIC being a notabe exception).," 1999) As a result, the rate for effective satellite-satellite fly-by encounters is less than one in every 10 Gyr (the LMC and the SMC being a notable exception)." Thus. we are left only with the repeated acion of tidal forces from the primary galaxy as an evolutiowary driver.," Thus, we are left only with the repeated action of tidal forces from the primary galaxy as an evolutionary driver." These operate on the orbital timescale. which is of order of {ανν in both clusters aud ealactic halos.," These operate on the orbital timescale, which is of order of 3-4 Gyr in both clusters and galactic halos." However. even the relatively low age of large. virialized clusters. ealaxies have typically approached the cluster center ouly ouce by the present time. while dSphlis satellites have had," However, given the relatively low age of large, virialized clusters, galaxies have typically approached the cluster center only once by the present time, while dSphs satellites have had" isorder as the luminosity released in the accretion disk.,is as the luminosity released in the accretion disk. More precisely the data we have used suggest ο2L4;4; at high luminosities aud Lj>Leigh at intermediate and low huuimnosities., More precisely the data we have used suggest $L_{jet} \simeq L_{disk}$ at high luminosities and $L_{jet} > L_{disk}$ at intermediate and low luminosities. Asstuning that y=10. as estimated above and that the accretion takes place with the standard radiative effiieucy €20.1. the near equality of Γι aud L5: then requires Pra=Pace.," Assuming that $\eta = 10^{-1}$ as estimated above and that the accretion takes place with the standard radiative efficiency $\epsilon\simeq 0.1$, the near equality of $L_{jet}$ and $L_{disk}$ then requires $P_{\rm jet}=P_{\rm acc}$." Ou the other haud. a dominance of Lj over ων at lower Iuninosities could be attributed to a lower value of ε«0.1 which may be expected if the accretion rate is largely sub-Eddineton.," On the other hand, a dominance of $L_{jet}$ over $L_{disk}$ at lower luminosities could be attributed to a lower value of $\epsilon << 0.1$ which may be expected if the accretion rate is largely sub-Eddington." In the latter case the rauge in lununosities spanned by Fie., In the latter case the range in luminosities spanned by Fig. 2 should be mainly a rauge in accretion rates rather than a range in black hole masses., 2 should be mainly a range in accretion rates rather than a range in black hole masses. For iustauce the mininuun jet powers oftInce of the BL Lacs in Fig 2 are around 1011 ere/s which suggests requiring amass of 10* for critical accretion rate;, For instance the minimum jet powers of three of the BL Lacs in Fig 2 are around $10^{44}$ erg/s which suggests $P_{jet}\simeq 10^{45}$ requiring a mass of $10^7$ for critical accretion rate. Siuce the disk luuinosity is less than 107. if the acerction rate is Eddiugtou the iuplied mass is again ↽⋅109 AL...," Since the disk luminosity is less than $10^{42}$, if the accretion rate is Eddington the implied mass is again $10^9$ $M_{\odot}$." Although very common in the radio baud. before the launch of theChandra satellite iu 1999 only a παπαμα of extragalactic kpe scale jets were known to cuit X-ravs.," Although very common in the radio band, before the launch of the satellite in 1999 only a handful of extragalactic kpc scale jets were known to emit X-rays." Among them the bright aud promincut jets in 30273. M87. Con A. studied withEINSTEIN audROSAT.," Among them the bright and prominent jets in 3C273, M87, Cen A, studied with and." With the superior scusitivityv auc. especially. spatial resolution of umucrous jets have been detected. trigecring a new intense theoretical and observational work.," With the superior sensitivity and, especially, spatial resolution of numerous jets have been detected, triggering a new intense theoretical and observational work." Even in the source selected for the first lieht. the distant (2= 0.6) quasar PISS 0637-752. a pronunent jet has been discovered (Chartas et al.," Even in the source selected for the first light, the distant $z=0.6$ ) quasar PKS 0637-752, a prominent jet has been discovered (Chartas et al." 2000)., 2000). Soon after the iscovery of the N-rav jet in PISS 0637-0752 other jets have been detected both in radio galaxies aud in quasars., Soon after the discovery of the X-ray jet in PKS 0637-0752 other jets have been detected both in radio galaxies and in quasars. A recent census (see e.g. the WEB site maimtened by D. IEuris)) reported 25 jets detected in X-rays., A recent census (see e.g. the WEB site maintened by D. ) reported 25 jets detected in X-rays. Differeut classes of ACUNS are represeuted in the sample: the most miamerous eroup is that of radio-galaxies (both FRI and ΕΠΟ. but a large fraction is colmposed by powerful radio-loud QSOs.," Different classes of AGNs are represented in the sample: the most numerous group is that of radio-galaxies (both FRI and FRII), but a large fraction is composed by powerful radio-loud QSOs." Most of the jets have also an optical counterpart. usually detected byLEST.," Most of the jets have also an optical counterpart, usually detected by." The first problem posed by observations is tle identification of the emission mechanisi respousible for the production of X-rays., The first problem posed by observations is the identification of the emission mechanism responsible for the production of X-rays. Since these jets are known to enit in radio. the first candidate mechanism is svuchrotron emission.," Since these jets are known to emit in radio, the first candidate mechanism is synchrotron emission." Iu some cases (n particular for jets in radio-galaxies) this interpretation is consistent with the data. but in other several cases (especially iu quasars) it fails to explain the observational evidence.," In some cases (in particular for jets in radio-galaxies) this interpretation is consistent with the data, but in other several cases (especially in quasars) it fails to explain the observational evidence." This is the case of the first jet discovered, This is the case of the first jet discovered To illusirate the significance of (his. if one assumes (hat gas pressure is zero (rather (han considering the limiting case when gas pressure tends (o zero). the infinite family of possible solutions results in wind mass loss rates (hat may. vary [rom any. value arbitrarily close to zero up to the wind mass loss rate of the solution which contains the critical point.,"To illustrate the significance of this, if one assumes that gas pressure is zero (rather than considering the limiting case when gas pressure tends to zero), the infinite family of possible solutions results in wind mass loss rates that may vary from any value arbitrarily close to zero up to the wind mass loss rate of the solution which contains the critical point." Therefore. the fact that the wind mass loss rate in a supersonic Ine-driven wind arrives al the maxinunm possible value (that of the critical point solution) is a gas pressure effect7.," Therefore, the fact that the wind mass loss rate in a supersonic line-driven wind arrives at the maximum possible value (that of the critical point solution) is a gas pressure effect." ", This means that although theeract value of the gas pressure may not significantly affect the actual value of the wind mass loss rate of a steady wind. the existence of gas pressure causes (he wind mass loss rate to have a unique value that. corresponds (to the critical point type wind solution."," This means that although the value of the gas pressure may not significantly affect the actual value of the wind mass loss rate of a steady wind, the existence of gas pressure causes the wind mass loss rate to have a unique value that corresponds to the critical point type wind solution." Thus. without gas pressure effects. the wind mass loss rate would not be uniquely determined. possibly having arbitrarily low values. which in (urn could have important ellects on the evolution of astrophysical svstenmis where line-driven winds are present.," Thus, without gas pressure effects, the wind mass loss rate would not be uniquely determined, possibly having arbitrarily low values, which in turn could have important effects on the evolution of astrophysical systems where line-driven winds are present." A second motive lor considering gas pressure effects is that [or cases where a steady disk wind solution is not possible (when assuming gas pressure to be zero). inclusion ol gas pressure effects may allow a uniquely. well-determined solution.," A second motive for considering gas pressure effects is that for cases where a steady line-driven disk wind solution is not possible (when assuming gas pressure to be zero), inclusion of gas pressure effects may allow a uniquely well-determined solution." " An example of this is the ""5 model” of Paper I. If one assumes gas pressure to be zero for the S model. then the corresponding nozzle function is monotonically decreasing. and thus the critical point is al infinity,"," An example of this is the “S model” of Paper I. If one assumes gas pressure to be zero for the S model, then the corresponding nozzle function is monotonically decreasing, and thus the critical point is at infinity." Since information. in principle. cannot travel an infinite distance in a finite lime. a steady. physical solution is not realizable for the zero gas pressure case.," Since information, in principle, cannot travel an infinite distance in a finite time, a steady physical solution is not realizable for the zero gas pressure case." ILowever. when eas pressure effects are included. the corresponding small corrections to the nozzle function produce a minimum in the nozzle function ab a finite distance (Paper D).," However, when gas pressure effects are included, the corresponding small corrections to the nozzle function produce a minimum in the nozzle function at a finite distance (Paper I)." Thus. once gas pressure effects are considered. (he critical point is no longer at infinity. but rather at a finite well-defined distance. allowing for a unique physical solution to be found.," Thus, once gas pressure effects are considered, the critical point is no longer at infinity, but rather at a finite well-defined distance, allowing for a unique physical solution to be found." The fact that the inclusion of gas pressure effects may lead a system [rom not presenting the existence of a steady. solution to presenting the existence of a steady solution. is a an obvious and more than sufficient motivation to include gas pressure effects.," The fact that the inclusion of gas pressure effects may lead a system from not presenting the existence of a steady solution to presenting the existence of a steady solution, is a an obvious and more than sufficient motivation to include gas pressure effects." Thircl. since evidence in favor and against the existence of steady line-clriven disk wind solutions comes Irom numerically intensive 2.5D disk wind models which include gas pressure. Tam unavoidably led to include gas pressure.," Third, since evidence in favor and against the existence of steady line-driven disk wind solutions comes from numerically intensive 2.5D disk wind models which include gas pressure, I am unavoidably led to include gas pressure." If 1 do not include gas pressure. lor example. I leave open Che possibility that some subtle gas pressure effect at (he wind base could generate strong fluctuations down stream causing apparent “intrinsic unsteacdiness.," If I do not include gas pressure, for example, I leave open the possibility that some subtle gas pressure effect at the wind base could generate strong fluctuations down stream causing apparent “intrinsic unsteadiness.”" The remnant formed ino the coalescence of linary neutron stars is likely to be differcutially rotating (sec. e.g.àY the dynamical simulatious of Rasio Shapiro 1992. 199. 1999: Shibata Urvu 2000. 2002: Faber. Rasio Manor 2001: Occhilin. Rosswoe Thiclemann. 2002: Shibata. Taniguchi ανα 2003: Faber. Crandclémiment Rasio 2003: see also the review of Bamuearte and Shapiro 2003).,"The remnant formed in the coalescence of binary neutron stars is likely to be differentially rotating (see, e.g., the dynamical simulations of Rasio Shapiro 1992, 1994, 1999; Shibata Uryū 2000, 2002; Faber, Rasio Manor 2001; Oechlin, Rosswog Thielemann, 2002; Shibata, Taniguchi Uryū 2003; Faber, Grandclémment Rasio 2003; see also the review of Baumgarte and Shapiro 2003)." It is likely that differential rotation will plav au iuportaut role in the dvuazuucal stability. of these remnants. since it can be very effective in iucreasing the thei maxim allowed mass (Daunsarte. Shapiro Shibata 2000. hereafter BSS: Lytord. Daunugare Shapiro 2003. hereafter LBS).," It is likely that differential rotation will play an important role in the dynamical stability of these remnants, since it can be very effective in increasing the their maximum allowed mass (Baumgarte, Shapiro Shibata 2000, hereafter BSS; Lyford, Baumgarte Shapiro 2003, hereafter LBS)." Most neutron stars in binudes have individual eravitational imasses close to l.lM. (colupare Table 2. below)., Most neutron stars in binaries have individual gravitational masses close to 1.4$M_{\odot}$ (compare Table \ref{Table2} below). FurtlOCYliolc. nost recent realistic nuclear equations of state predict a maxiuun allowed mass for nonrotatiue neutron stars 1 the range of about 1.7 2.3Mi M. (compare Tade 1 below).," Furthermore, most recent realistic nuclear equations of state predict a maximum allowed mass for nonrotating neutron stars in the range of about 1.7 – 2.3 $M_{\odot}$ (compare Table \ref{Table1} below)." Taken together. these facts ποσα fo suggest that the coalescence of binary neutron stars would leac to prompt collapse to a black hole.," Taken together, these facts seem to suggest that the coalescence of binary neutron stars would lead to prompt collapse to a black hole." " However, rotation. aud especially differential rotation. call increase the τοατα allowed wasssiguificantly."," However, rotation, and especially differential rotation, can increase the maximum allowed mass." . The maxima allowed mass of rotating stars is lunited by the spin rate at which the fluid at the οςator moves on a eeodesie (the I&epler Iuuit): amy further specd-up would lead to mass shedding., The maximum allowed mass of rotating stars is limited by the spin rate at which the fluid at the equator moves on a geodesic (the Kepler limit); any further speed-up would lead to mass shedding. " Uniform rotatiol ca therefore merease the maxima allowed mass by about 20 at most for very stiff equations of state (Cook. Shapiro Teukolsky, 1992. 199la. 199Ib. hereafter CSTI. CST2 and CST3 respectively: see also Table 1. below). which is not sufficient to stabilize reiinauts of binary neutron star coalescence."," Uniform rotation can therefore increase the maximum allowed mass by about 20 at most for very stiff equations of state (Cook, Shapiro Teukolsky, 1992, 1994a, 1994b, hereafter CST1, CST2 and CST3 respectively; see also Table \ref{Table1} below), which is not sufficient to stabilize remnants of binary neutron star coalescence." Uniformly rotating neutron stars with rest lnassces exceeding the παπα allowed rest mass for non-rotating stars (for tle same equation of state) are referred. to as neutron stars., Uniformly rotating neutron stars with rest masses exceeding the maximum allowed rest mass for non-rotating stars (for the same equation of state) are referred to as neutron stars. Differential votation. however. is much more effective ii increasing the maxima allowed mass.," rotation, however, is much more effective in increasing the maximum allowed mass." " Unlike a uuiformly rotating star. the rotation rate at the core of a differentially rotating star is not restricted to the aN rotation rate at the equator. so that the core cau be supported by rapid rotation without the equator having to exceed the Repler Πιτ,"," Unlike a uniformly rotating star, the rotation rate at the core of a differentially rotating star is not restricted to the maximum rotation rate at the equator, so that the core can be supported by rapid rotation without the equator having to exceed the Kepler limit." This effect was demonstrated in Newtouian eravitation bv Ostriker. Bocdenheincr Lvudeu-Bell (1966) for white dwarfs. aud in general relativity by BSS for »=L polvtropes.," This effect was demonstrated in Newtonian gravitation by Ostriker, Bodenheimer Lynden-Bell (1966) for white dwarfs, and in general relativity by BSS for $n=1$ polytropes." BSS also showed by wav of illustration that stars with about iore mass than the maxinuun allowed mass of the corresonding nonrotatiuge star can be dynamically stable against both radial aud nonaxisviunetrie modes., BSS also showed by way of illustration that stars with about more mass than the maximum allowed mass of the corresonding nonrotating star can be dynamically stable against both radial and nonaxisymmetric modes. BSS rofer to differentially rotating equilibrium coufiguratious with rest masses exceeding the maximum rest mass of a uniformly rotating star as neutron stars., BSS refer to differentially rotating equilibrium configurations with rest masses exceeding the maximum rest mass of a uniformly rotating star as neutron stars. LBS eeucralized the equilibrimm results of BSS to other polvtropic indices in the range 0.5-5»x 2.9. aud found that the largest relative increases in the mania," LBS generalized the equilibrium results of BSS to other polytropic indices in the range $0.5 \leq n \leq 2.9$ , and found that the largest relative increases in the maximum" which included numerous improvements over their previous work. such as a better (treatment of radiative transler in optically thin regions of the disk and elimination of the spurious numerical heating in the inner disk regions where Boss (2007) found fragments to form.,"which included numerous improvements over their previous work, such as a better treatment of radiative transfer in optically thin regions of the disk and elimination of the spurious numerical heating in the inner disk regions where Boss (2007) found fragments to form." Cai et al. (, Cai et al. ( 2010) suggested that the main difference might be artilicially [ast cooling in the Boss nodels as a result of the thermal bath boundary conditions used in Boss models. which could 100 be duplicated with the Cai et al. (,"2010) suggested that the main difference might be artificially fast cooling in the Boss models as a result of the thermal bath boundary conditions used in Boss models, which could not be duplicated with the Cai et al. (" 2010) code because of numerical stability problenis.,2010) code because of numerical stability problems. Analvtical test cases have been advanced as one means for testing radiative transfer in the numerical codes (e.g.. Dolev et al.," Analytical test cases have been advanced as one means for testing radiative transfer in the numerical codes (e.g., Boley et al." 2006)., 2006). Boss (2009) derived two new analvtical radiative transfer solutions and showed that Boss code does an excellent job of handling the radiative boundary. conditions of a disk immersed in a thermal bath: the Boss code relaxes to the analviical solutions for both a spherically svinnetric cloud and an axisvanmnietric disk., Boss (2009) derived two new analytical radiative transfer solutions and showed that Boss code does an excellent job of handling the radiative boundary conditions of a disk immersed in a thermal bath; the Boss code relaxes to the analytical solutions for both a spherically symmetric cloud and an axisymmetric disk. Recently. Boss (2010) published models showing that disk instability is considerably less robust inside 20 AU in disks with half the mass of previous models (e.g.. Boss 2007). but still possible.," Recently, Boss (2010) published models showing that disk instability is considerably less robust inside 20 AU in disks with half the mass of previous models (e.g., Boss 2007), but still possible." Inutsuka. Machida. Matsumoto (2010) found in their magnetohydrodyvnamic collapse calculations that the massive disks that formed were subject to gravitational instability and fragment formation. even inside 20 AU.," Inutsuka, Machida, Matsumoto (2010) found in their magnetohydrodynamic collapse calculations that the massive disks that formed were subject to gravitational instability and fragment formation, even inside 20 AU." Arguments against inner disk fragmentation are often based on simple cooling time estimates (e... Cai et al.," Arguments against inner disk fragmentation are often based on simple cooling time estimates (e.g., Cai et al." 2010)., 2010). IIowever. Meru Date (2010. 2011) have emphasized (hat many previous numerical calculations with [fixed cooling times are likely (o have reached incorrect results. in part as a result of insullicient spatial resolution.," However, Meru Bate (2010, 2011) have emphasized that many previous numerical calculations with fixed cooling times are likely to have reached incorrect results, in part as a result of insufficient spatial resolution." Meru Date (2010. 2011) presented numerous disk instability models (hat underwent fragmentation inside 20 AU for a variety of initial conditions.," Meru Bate (2010, 2011) presented numerous disk instability models that underwent fragmentation inside 20 AU for a variety of initial conditions." While the debate over inner disk [fragmentation is likely to continue. the present models should be considerably less controversial. given their restriction to fragmentation at distances greater than 20 AU.," While the debate over inner disk fragmentation is likely to continue, the present models should be considerably less controversial, given their restriction to fragmentation at distances greater than 20 AU." Table 1 lists the initial conditions chosen for the five disk models presented here., Table 1 lists the initial conditions chosen for the five disk models presented here. " Models 2.0. 1.5. 1.0. 0.5. and 0.1 depict disks around protostars with masses of M,=2.0. 1.5. 1.0. 0.5. and 0.1. M... representing future À3. ADS. G2. early M. ancl late M dwarls. respectively. depending on (heir subsequent accretion of mass."," Models 2.0, 1.5, 1.0, 0.5, and 0.1 depict disks around protostars with masses of $M_s = 2.0$, 1.5, 1.0, 0.5, and 0.1 $M_\odot$, representing future A3, A5, G2, early M, and late M dwarfs, respectively, depending on their subsequent accretion of mass." The disk envelopes are taken (o have temperatures (7.) between 50 Ix and 30 Ix. in all cases hotter than the disks themselves. which beein their evolutions uniformly isothermal at (he initial temperatures (7;) shown in Table 1.," The disk envelopes are taken to have temperatures $T_{e}$ ) between 50 K and 30 K, in all cases hotter than the disks themselves, which begin their evolutions uniformly isothermal at the initial temperatures $T_i$ ) shown in Table 1." The critical density for differentiating between (he disk and the disk envelope is taken to be 1013 ο for models 2.0. 1.5. 1.0. and 0.5. and 10.!! ο ? for model 0.1. which effectively determines the onset of the envelope thermal bath.," The critical density for differentiating between the disk and the disk envelope is taken to be $10^{-13}$ g $^{-3}$ for models 2.0, 1.5, 1.0, and 0.5, and $10^{-14}$ g $^{-3}$ for model 0.1, which effectively determines the onset of the envelope thermal bath." Variations in these parameters have been tested by Boss (2007) and found to have relatively minor effects., Variations in these parameters have been tested by Boss (2007) and found to have relatively minor effects. "where the first term on the right side is the accretion rate of that element, and the second term is the rate of gravitational settling (where we use a positive velocity to represent elements diffusing downward).","where the first term on the right side is the accretion rate of that element, and the second term is the rate of gravitational settling (where we use a positive velocity to represent elements diffusing downward)." " Assuming that τ,M,v are constant, the solution of this equation is where the first term on the right side is the starting value of the element abundance at the beginning of the accretion phase."," Assuming that $\tau, \dot{M}, v$ are constant, the solution of this equation is where the first term on the right side is the starting value of the element abundance at the beginning of the accretion phase." Some conclusions can be drawn immediately from this simple equation., Some conclusions can be drawn immediately from this simple equation. " If the accretion rate is constant for some multiple of the diffusion timescale (~5 for practical purposes, given the typical uncertainties in observed elemental abundances), the abundance will approach an asymptotic (“steady state”) value (we omit the index cvz from X for simplicity) of and for the ratio of elements 1 and 2, we obtain where in r(el2)the last M(eI2)step, we replaced the accretion rate by the element abundances in the accreted matter."," If the accretion rate is constant for some multiple of the diffusion timescale $\approx 5$ for practical purposes, given the typical uncertainties in observed elemental abundances), the abundance will approach an asymptotic (“steady state”) value (we omit the index $\mathrm{cvz}$ from $X$ for simplicity) of and for the ratio of elements 1 and 2, we obtain where in the last step, we replaced the accretion rate by the element abundances in the accreted matter." " If the diffusion times are less than a few years, we can reasonably assume that this steady state has been reached."," If the diffusion times are less than a few years, we can reasonably assume that this steady state has been reached." " Since we can calculate the timescales from the parameters of the star, we can thus determine the abundances in the accreted matter from the observed abundances in the star."," Since we can calculate the timescales from the parameters of the star, we can thus determine the abundances in the accreted matter from the observed abundances in the star." " Even more simply, since the timescales for the commonly observed elements of Ca, Mg, and Fe are often within a factor of two, we can assume the observed abundances (which are rarely more accurate than a factor of 2) to be a first approximation to the accreted abundances."," Even more simply, since the timescales for the commonly observed elements of Ca, Mg, and Fe are often within a factor of two, we can assume the observed abundances (which are rarely more accurate than a factor of 2) to be a first approximation to the accreted abundances." " However, all of these conclusions depend critically on the assumption that the steady state is reached, and are therefore valid only in the case of short diffusion timescales."," However, all of these conclusions depend critically on the assumption that the steady state is reached, and are therefore valid only in the case of short diffusion timescales." " It is instructive to consider by a simple example, the consequences of being unable to assume steady state (i.e., in all cases where the timescales exceed a few years)."," It is instructive to consider by a simple example, the consequences of being unable to assume steady state (i.e., in all cases where the timescales exceed a few years)." " For this exercise, we studied the abundances of two elements, where the diffusion timescales differed by a factor of two."," For this exercise, we studied the abundances of two elements, where the diffusion timescales differed by a factor of two." We started with zero abundance and switched accretion on for 10 times the shorter timescale., We started with zero abundance and switched accretion on for 10 times the shorter timescale. Then accretion is switched off again., Then accretion is switched off again. We were able to distinguish three phases (see Fig. 1)), We were able to distinguish three phases (see Fig. \ref{fig1}) ) " The third phase would also describe a different scenario, where accretion occurs at a high rate in a short time, such as the accretion of an entire asteroid at once."," The third phase would also describe a different scenario, where accretion occurs at a high rate in a short time, such as the accretion of an entire asteroid at once." The abundances would reflect exactly the accreted abundances during this time and start the exponential decay from there., The abundances would reflect exactly the accreted abundances during this time and start the exponential decay from there. In such a case we would be unable able to determine the composition of the accreted matter., In such a case we would be unable able to determine the composition of the accreted matter. We note that the above example is not extreme., We note that the above example is not extreme. " In particular, when including light or very heavy elements in the comparison the factor between timescales can be «4."," In particular, when including light or very heavy elements in the comparison the factor between timescales can be $\approx 4$." And we also do not need to consider the extreme case of totally switching accretion on and off., And we also do not need to consider the extreme case of totally switching accretion on and off. " Even a change in the accretion rate, for example by a factor of 100 leads to an intermediate change in the abundance ratio of a factor >10, before the asymptotic ratio of 2 is reached again."," Even a change in the accretion rate, for example by a factor of 100 leads to an intermediate change in the abundance ratio of a factor $>10$, before the asymptotic ratio of 2 is reached again." The conclusion of this simple exercise is that it is only possible to infer abundances of the accreted matterreached., The conclusion of this simple exercise is that it is only possible to infer abundances of the accreted matter. For diffusion timescales longer than a few decades at most this can never be assumed., For diffusion timescales longer than a few decades at most this can never be assumed. Equating the observed atmospheric abundance ratios to those of the accreted matter can in such cases be incorrect by orders of magnitude., Equating the observed atmospheric abundance ratios to those of the accreted matter can in such cases be incorrect by orders of magnitude. " We apply the general results to two specific objects with circumstellar material and atmospheric metal traces, which have been discussed in numerous recent studies: 229-38 and 3362."," We apply the general results to two specific objects with circumstellar material and atmospheric metal traces, which have been discussed in numerous recent studies: 29-38 and 362." specily the associated FITS files within tle sequence file database (See Fig. 10)).,specify the associated FITS files within the sequence file database (See Fig. \ref{SQLCoadd}) ). The full set of file splits then comprises the input to MapRecduce., The full set of file splits then comprises the input to MapReduce. The consequence of usiug SQL to determine the relevant FITS files and seudiug only. those FITS files to MapReduce is that this method does not suffer from false positives as described above., The consequence of using SQL to determine the relevant FITS files and sending only those FITS files to MapReduce is that this method does not suffer from false positives as described above. Thus. the mappers waste uo time cousideriug (and discarding) irrevelant FITS files since every FITS file received by a mapper is guaranteed to contribute to the final coadd.," Thus, the mappers waste no time considering (and discarding) irrevelant FITS files since every FITS file received by a mapper is guaranteed to contribute to the final coadd." The iuteutiou is clearly to reduce the mapper running time as a result., The intention is clearly to reduce the mapper running time as a result. Table 2. shows the number of FITS files read. as input to MapRecuce for each of the six experimental methods., Table \ref{numFitsProcessed} shows the number of FITS files read as input to MapReduce for each of the six experimental methods. Note that prelilteriug is üunperlect. it suffers from [alse positives aud accepts FITS files which are ultimately irrelevant to the coadcdition task.," Note that prefiltering is imperfect, it suffers from false positives and accepts FITS files which are ultimately irrelevant to the coaddition task." However. the SQL methods ouly process tle relevant files.," However, the SQL methods only process the relevant files." While the present inodels are extremely useful for explaiuiug the phenomenon of trausieut,While the present models are extremely useful for explaining the phenomenon of transient 2008).,. . In these svstems with multiple planets. there are several additional avenues which mav lead (o catastrophic impacts of residual embryos onto their envelopes.," In these systems with multiple planets, there are several additional avenues which may lead to catastrophic impacts of residual embryos onto their envelopes." For example: A3) Regardless of the low formation and survival probability of the first-generation planets (Ida&Lin2008b).. their birth leads to gap formation which provide a secondary. pressure maxinmnmn in the gas disk outside their orbits (Lin&Papaloizou 20003..," For example: A3) Regardless of the low formation and survival probability of the first-generation planets \citep{Ida2008b}, their birth leads to gap formation which provide a secondary pressure maximum in the gas disk outside their orbits \citep{Lin1979, Lin1993, Bryden2000a}." This induced disk structure also sets up a barrier against the orbital decay of grains and embryos., This induced disk structure also sets up a barrier against the orbital decay of grains and embryos. The accumulation of heavy elements beyond (he outer edge of the gap promotes the formation of more-distant second-generation cores on time scales much shorter than that required Lor (hem to assemble in isolation (Drydenοἱal.2000).., The accumulation of heavy elements beyond the outer edge of the gap promotes the formation of more-distant second-generation cores on time scales much shorter than that required for them to assemble in isolation \citep{Bryden2000b}. . In (his sequential formation scenario. the second-generation gas giants. rapid mass increase. during (heir advanced growth phase. also introduces non-adiabatie changes in the systems. gravitational potential which have a tendency to destabilize the orbits of the nearby residual embryos.," In this sequential formation scenario, the second-generation gas giants' rapid mass increase, during their advanced growth phase, also introduces non-adiabatic changes in the systems' gravitational potential which have a tendency to destabilize the orbits of the nearby residual embryos." At) After the eas depletion. planets’ orbits continue to evolve due to their scattering of residual planetesimals.," A4) After the gas depletion, planets' orbits continue to evolve due to their scattering of residual planetesimals." I multiple planets’ orbits have spread out. Lom a more compact configuration. orbital instabilities aud scattering amongst giant planets may also lead to late accretion of planetesimals by. gas eiants (Tsiganisοἱal.2005).," If multiple planets' orbits have spread out from a more compact configuration, orbital instabilities and scattering amongst giant planets may also lead to late accretion of planetesimals by gas giants \citep{Tsiganis2005}." . The main focus of this paper is {ο examine the structure. adjustment of gas giants envelopes after major merger events rather (han a statistical study on the coalescence probability., The main focus of this paper is to examine the structure adjustment of gas giants' envelopes after major merger events rather than a statistical study on the coalescence probability. We do not consider collisions in which the intruding embryos pass through the envelope οἱ gas giants without losing a significant fraction of their heavy. elemental masses., We do not consider collisions in which the intruding embryos pass through the envelope of gas giants without losing a significant fraction of their heavy elemental masses. " For merger models. we choose representative rather (han a realistic distribution of models to illustrate (he possibility and character (rather than probability) of (wo sets of outcomes. (he intiruding embryos either disintegrate in the eas giants. envelope or impact onto their 60105,"," For merger models, we choose representative rather than a realistic distribution of models to illustrate the possibility and character (rather than probability) of two sets of outcomes, the intruding embryos either disintegrate in the gas giants' envelope or impact onto their cores." For simplicity. we consider mostly head-on collisions.," For simplicity, we consider mostly head-on collisions." Bupacting planetesimals much smaller than the giant. planet would likely sulfer ablative disintegration during (heir passage (hroueh the gaseous envelope., Impacting planetesimals much smaller than the giant planet would likely suffer ablative disintegration during their passage through the gaseous envelope. On the other haad sufficiently massive impactors may penetrate deep and reach the core., On the other hand sufficiently massive impactors may penetrate deep and reach the core. A projectile's disintegration becomes likely when it collides with an air-nass comparable to ils own Uxorveansky&Zahnle2005)., A projectile's disintegration becomes likely when it collides with an air-mass comparable to its own \citep{Korycansky2005}. ". For head-on collisions. (he distance traveled in a gas giants envelope belore disinteeration is approximately where p, and p, are the average density of the embryo and gas giant. and FH, is the radius of the embryo."," For head-on collisions, the distance traveled in a gas giant's envelope before disintegration is approximately $D \sim (\rho_e/\rho_g) R_e$ where $\rho_e$ and $\rho_g$ are the average density of the embryo and gas giant, and $R_e$ is the radius of the embryo." " Reaching the center of a planet (D= H,) requires a sullicientlv large", Reaching the center of a planet $D\gtrsim R_p$ ) requires a sufficiently large to supernova light curves than the n~1 cm-? case.,to supernova light curves than the $n\sim 1$ $^{-3}$ case. " 'The predicted rate of decline is slower than a Type Ia supernova post maximum (i.e., zz2.5—3 mag in ~100 d)."," The predicted rate of decline is slower than a Type Ia supernova post maximum (i.e., $\approx 2.5-3$ mag in $\sim 100$ d)." " It is, however, faster than a typical Type IIP supernova light curve, which exhibits a plateau for ~100 d. Color evolution can in principle also be used to distinguish off-axis afterglows from other transients."," It is, however, faster than a typical Type IIP supernova light curve, which exhibits a plateau for $\sim 100$ d. Color evolution can in principle also be used to distinguish off-axis afterglows from other transients." " Since the afterglow is synchrotron emission the optical waveband is generally above the characteristic(and frequency, Vm), it has a power-law spectrum with a fixed slope F,οςv@-?)/2 and hence a constant red color g—r»0.2 mag for p=2.5."," Since the afterglow is synchrotron emission (and the optical waveband is generally above the characteristic frequency, $\nu_m$ ), it has a power-law spectrum with a fixed slope $F_{\nu}\propto\nu^{(1-p)/2}$ and hence a constant red color $g-r\sim 0.2$ mag for $p=2.5$." " By comparison, Figure 9 shows that the color of a shock break-out and rising ΠΡ SNe increases by a magnitude from blue to red in just à few days."," By comparison, Figure \ref{fig:compare} shows that the color of a shock break-out and rising IIP SNe increases by a magnitude from blue to red in just a few days." " Although the colors of a rising SN Ia are similar to the afterglow emission, events observed near their peak case in which a background Type Ia supernova light curve(the could be mistaken for a low density afterglow) are much redder."," Although the colors of a rising SN Ia are similar to the afterglow emission, events observed near their peak (the case in which a background Type Ia supernova light curve could be mistaken for a low density afterglow) are much redder." " Finally, both radio and optical counterparts will satisfy Virtue #44, although at low frequency and low signal-to-noise ratio, EVLA/ASKAP positions will typically be =few arcsec, as opposed to sub-arcsecond in the optical band."," Finally, both radio and optical counterparts will satisfy Virtue 4, although at low frequency and low signal-to-noise ratio, EVLA/ASKAP positions will typically be $\gtrsim {\rm few}$ arcsec, as opposed to sub-arcsecond in the optical band." " At a typical distance of 200 Mpc this should not be an impediment for a host galaxy association (1""e0.8 kpc), but it will not allow a robust study of the sub-galactic environment, and hence an association with specific stellar populations (c.f., Fongetal. 2010))."," At a typical distance of 200 Mpc this should not be an impediment for a host galaxy association $1''\approx 0.8$ kpc), but it will not allow a robust study of the sub-galactic environment, and hence an association with specific stellar populations (c.f., \citealt{Fong+10}) )." It may also impede the rejection of AGN., It may also impede the rejection of AGN. We therefore conclude that optical and radio afterglows do not satisfy all of the required cardinal Virtues for an EM counterpart., We therefore conclude that optical and radio afterglows do not satisfy all of the required cardinal Virtues for an EM counterpart. " The fraction of detectable off-axis optical afterglows is ~0.1, and possibly even lower depending on the range of energy and circumburst density for typical NS-NS/NS-BH mergers."," The fraction of detectable off-axis optical afterglows is $\sim 0.1$, and possibly even lower depending on the range of energy and circumburst density for typical NS-NS/NS-BH mergers." The fraction of detectable radio afterglows may be close to zero due to the limited range of E—n phase-space accessible with existing and planned radio telescopes., The fraction of detectable radio afterglows may be close to zero due to the limited range of $E-n$ phase-space accessible with existing and planned radio telescopes. If the majority of NS-NS/NS-BH mergers occur in low density environments (n<107? cm?) or produce low energy jets (EX107? then optical afterglows are no longer effective counterparts.," If the majority of NS-NS/NS-BH mergers occur in low density environments $n \lesssim 10^{-3}$ $^{-3}$ ) or produce low energy jets $E\lesssim 10^{49}$ erg), then optical afterglows are no longer effective counterparts." "erg), This is also true if most NS-NS mergers are not accompanied by SGRBs.", This is also true if most NS-NS mergers are not accompanied by SGRBs. In these, In these have undergone a significant merger over the last ten gigayears.,have undergone a significant merger over the last ten gigayears. " A merger with mass ratio 3:1 or less is considered a major merger in the model, causing the destruction of the stellar and gas discs and the transfer of this material to the bulge of the descendant."," A merger with mass ratio 3:1 or less is considered a major merger in the model, causing the destruction of the stellar and gas discs and the transfer of this material to the bulge of the descendant." We see from Fig., We see from Fig. " 11 that not only major mergers cause the sudden drop in M,oiq.", \ref{fig:lowZ_specgals} that not only major mergers cause the sudden drop in $M_{\textnormal{cold}}$. Gas-rich minor mergers are also effective at inducing starbursts and the rapid growth of the central SMBH through ‘quasar mode’ accretion., Gas-rich minor mergers are also effective at inducing starbursts and the rapid growth of the central SMBH through `quasar mode' accretion. " During such events, a black hole can grow by swallowing both cold gas and the smaller black hole of its companion."," During such events, a black hole can grow by swallowing both cold gas and the smaller black hole of its companion." " 92 per cent of the galaxies in the low-Z sub-sample have present-day black holes with masses greater than 10°°M.q, that were formed through this process."," 92 per cent of the galaxies in the $Z$ sub-sample have present-day black holes with masses greater than $10^{8.0} \textnormal{M}_{\textnormal{\astrosun}}$, that were formed through this process." " The remaining 8 per cent have either grown their black holes gradually through radio-mode accretion, or do not contain a central SMBH."," The remaining 8 per cent have either grown their black holes gradually through radio-mode accretion, or do not contain a central SMBH." " We note that although large black holes are a feature of almost all the galaxies in the low-Z sub-sample, they do not the low metallicities seen in these galaxies at z=0."," We note that although large black holes are a feature of almost all the galaxies in the $Z$ sub-sample, they do not the low metallicities seen in these galaxies at $z=0$." " These are instead caused by a cessation in star formation due to the sudden drop in cold gas mass below Maa, followed by accretion of metal-poor gas."," These are instead caused by a cessation in star formation due to the sudden drop in cold gas mass below $M_{\textnormal{crit}}$, followed by accretion of metal-poor gas." " This galactic accretion is limited to a low rate by the suppression of cooling from radio mode AGN feedback, allowing it to continue for an extended amount of time without re-igniting star formation."," This galactic accretion is limited to a low rate by the suppression of cooling from radio mode AGN feedback, allowing it to continue for an extended amount of time without re-igniting star formation." The three galaxies in Fig., The three galaxies in Fig. 11 therefore show that of the gas phase due to metal-poor infall of gas in the absence of star formation is the main process producing the low-Z sub-sample., \ref{fig:lowZ_specgals} therefore show that of the gas phase due to metal-poor infall of gas in the absence of star formation is the main process producing the $Z$ sub-sample. " This is an effect that is not seen in hydrodynamic simulations of galaxy evolution such as those carried out by Finlator&Davé(2008) and Davé,Oppenheimer&Finlator (2011)..", This is an effect that is not seen in hydrodynamic simulations of galaxy evolution such as those carried out by \citet{FD08} and \citet{D11a}. " In those models, galaxies quickly fall back into an equilibrium between their infall, outflow and star formation rates after a perturbative event, whereby Monten=M.+ Moutfiow-"," In those models, galaxies quickly fall back into an equilibrium between their infall, outflow and star formation rates after a perturbative event, whereby $\dot{M}_{\textnormal{infall}} = \dot{M}_{*} + \dot{M}_{\textnormal{outflow}}$ ." " Instead, the inclusion of AGN feedback in our model enables galaxies to slowly accrete metal-poor gas for a number of gigayears without forming stars."," Instead, the inclusion of AGN feedback in our model enables galaxies to slowly accrete metal-poor gas for a number of gigayears without forming stars." We note that it remains to be seen whether the fraction of massive galaxies in the models with very, We note that it remains to be seen whether the fraction of massive galaxies in the models with very estimate that the completeness limits of our observations are 1805: y in 00024416 and 200;Jy in I-03.,estimate that the completeness limits of our observations are $\mu$ Jy in 0024+16 and $\mu$ Jy in $-$ 03. The archival mid-infrared data for the central region of 1—03 (Program #883). were obtained from theSpitzer archive.," The archival mid-infrared data for the central region of $-$ 03 (Program 83), were obtained from the archive." The observations were taken on 2004 September 23. centered on 110.8. —03 000557 (J2000).," The observations were taken on 2004 September 23, centered on 10.8, $-$ 57 (J2000)." We use the post-basic-calibrated data. and subject it to the same extraction criteria as described in 822.1.," We use the post–basic-calibrated data, and subject it to the same extraction criteria as described in 2.1." These data are slightly shallower than our mosaic. and we take this into account in our subsequent analysis.," These data are slightly shallower than our mosaic, and we take this into account in our subsequent analysis." We use existing deep optical and near-infrared imaging to obtain colors for the 24j/m sources in these regions., We use existing deep optical and near-infrared imaging to obtain colors for the $\mu$ m sources in these regions. For both clusters we use Subaru SuprimeCam B- and R- observations taken for the PISCES survey (Kodama et 22005)., For both clusters we use Subaru SuprimeCam $B$ - and $R$ -band observations taken for the PISCES survey (Kodama et 2005). The Cl00024+16 field was observed on 2002 September 6 under good conditions., The 0024+16 field was observed on 2002 September 6 under good conditions. " The seeing was 0.7-1” for the R- and ~ 1—1.3"" for the B-band. with exposure times of 5.280ss and 3.600 respectively. reaching a depth of R~27 (we use Vega-based ssmagnitudes throughout)."," The seeing was $\sim0.7$ $1''$ for the $R$ - and $\sim1$ $1.3''$ for the $B$ -band, with exposure times of s and s respectively, reaching a depth of $R\sim27$ (we use Vega-based magnitudes throughout)." The observations and data reduction technique are described in Kodama et ((2004)., The observations and data reduction technique are described in Kodama et (2004). " 1-03 was observed on 2001 January 21-22. again in good conditions with 1.0” seeing in the B-band and 0.8"" in the R-band."," $-$ 03 was observed on 2001 January 21–22, again in good conditions with $''$ seeing in the $B$ -band and $''$ in the $R$ -band." Total exposure times were 7200ss in B and 4800ss in R. again yielding photometry for objects as faint as R~21.," Total exposure times were s in $B$ and s in $R$, again yielding photometry for objects as faint as $R\sim 27$." Panoramic near-infrared K-band imaging of both clusters is also available with WIRC (Wilson et 22003) on the Palomar Hale 5.1-m telescope., Panoramic near-infrared $K$ -band imaging of both clusters is also available with WIRC (Wilson et 2003) on the Palomar Hale 5.1-m telescope. These data comprise a 3« mosaic of WIRC pointings. providing a contiguous observed are of 26«26’ centered on each cluster.," These data comprise a $3\times3$ mosaic of WIRC pointings, providing a contiguous observed are of $26'\times26'$ centered on each cluster." Full details of the observations and data reduction are published elsewhere 0002416: Smith et 22005: 00451—03: Smith et 22006. in prep).," Full details of the observations and data reduction are published elsewhere 0024+16: Smith et 2005; $-$ 03: Smith et 2006, in prep)." " Point sources in the final reduced mosaics have a full width half maximum of 0.9"" and 1.0” in C100024+16 and 1-03 respectively.", Point sources in the final reduced mosaics have a full width half maximum of $0.9''$ and $1.0''$ in 0024+16 and $-$ 03 respectively. The data reach a 5-0 point sources detection threshold of K219.5 and K=20.0 in C100024+16 and 1—03 respectively., The data reach a $\sigma$ point sources detection threshold of $K=19.5$ and $K=20.0$ in 0024+16 and $-$ 03 respectively. The nominal 24;j/m coverage of the two clusters is ~0.21 ddegrees~., The nominal $\mu$ m coverage of the two clusters is $\sim$ $^2$. In the case of 1-03. the archival GTO data contribute an extra ~29 aaremin-.," In the case of $-$ 03, the archival GTO data contribute an extra $\sim$ $^2$." When the optical and near-infrared coverage is taken into account. the total coincident coverage of 24;im. B-. R-. K- is ddegrees and ddegrees~ in C100024+416 and 1-03 respectively.," When the optical and near-infrared coverage is taken into account, the total coincident coverage of $\mu$ m, $B$ -, $R$ -, $K$ -bands is $^2$ and $^2$ in 0024+16 and $-$ 03 respectively." We detect objects and extract photometry from the optical frames by running in two-frame mode such that detections were made in the R-band image and measurements made at identical pixel locations in R and B (the frames were previously aligned to good accuracy)., We detect objects and extract photometry from the optical frames by running in two-frame mode such that detections were made in the $R$ -band image and measurements made at identical pixel locations in $R$ and $B$ (the frames were previously aligned to good accuracy). " We catalog all sources with 3 contiguous pixels (the pixel scale is 0.204"") at least 2-7 above the background. and lay down 2” diameter apertures to measure colors in the BRK-band frames."," We catalog all sources with 3 contiguous pixels (the pixel scale is $0.204''$ ) at least $\sigma$ above the background, and lay down $''$ diameter apertures to measure colors in the $BRK$ -band frames." " The MIPS observations of our two clusters yield 986 sources in the (10002416 field and 1071 in 1-03. both with 24;rm flux densities above $3,,4,7 2005/Jy (unless otherwise stated. quoted fluxes are always the corrected 16"" aperture values)."," The MIPS observations of our two clusters yield 986 sources in the 0024+16 field and 1071 in $-$ 03, both with $\mu$ m flux densities above $S_{\rm 24\mu m}>200\mu$ Jy (unless otherwise stated, quoted fluxes are always the corrected $''$ aperture values)." In the case of 00451—03 the count includes sources in the archival region 1n the core., In the case of $-$ 03 the count includes sources in the archival region in the core. We assess the false detection rate by running our algorithm on the inverse of the data. and detect ~20 sources in each frame. all with fluxes in the range 200-3304 y. representing ~2% of the detected sample.," We assess the false detection rate by running our algorithm on the inverse of the data, and detect $\sim 20$ sources in each frame, all with fluxes in the range $\mu$ Jy, representing $\sim$ of the detected sample." Our analysis requires matched optical R<24 identifications and so we expect the false rate will be much less thanI%., Our analysis requires matched optical $R<24$ identifications and so we expect the false rate will be much less than. . As we demonstrate below. the achieved source surface density is below | object per 40 beams. the classical definition of a confused map (Hogg 2001). and so our maps are not expected to be confused at this depth.," As we demonstrate below, the achieved source surface density is below 1 object per 40 beams, the classical definition of a confused map (Hogg 2001), and so our maps are not expected to be confused at this depth." We next use the deep optical and near-infrared imaging of these fields to investigate the photometric properties of mid-infrared sources., We next use the deep optical and near-infrared imaging of these fields to investigate the photometric properties of mid-infrared sources. The influence of false detections described above is minimised in. the main part of our analysis. since we require the mid-infrared sources to have optical and near-infrared counterparts.," The influence of false detections described above is minimised in the main part of our analysis, since we require the mid-infrared sources to have optical and near-infrared counterparts." Positional matching of multi-wavelength data sets has been along standing problem in astronomy. and can be particularly troublesome when there is a large disparity in the resolution and sampling in two datasets.," Positional matching of multi-wavelength data sets has been a long standing problem in astronomy, and can be particularly troublesome when there is a large disparity in the resolution and sampling in two datasets." We find that a simple nearest-neighbor match is not adequate to pair mid-infrared sources with optical counterparts — the method can fail to match complicated interacting systems for example., We find that a simple nearest-neighbor match is not adequate to pair mid-infrared sources with optical counterparts – the method can fail to match complicated interacting systems for example. " Instead. we apply the technique of de Ruiter, Arp Willis (1977) who use a Bayesian estimator for the probability. p(id|7). that a nearby source Is a true match and not à chance unrelated object."," Instead, we apply the technique of de Ruiter, Arp Willis (1977) who use a Bayesian estimator for the probability, $p({\rm id}\mid r)$ , that a nearby source is a true match and not a chance unrelated object." In Appendix A. we briefly outline the key elements of the method. but refer the reader to de Ruiter. Arp Willis (1977) for a thorough derivation.," In Appendix A, we briefly outline the key elements of the method, but refer the reader to de Ruiter, Arp Willis (1977) for a thorough derivation." The result of our matching analysis 18 a list of probable optical counterparts for the 24j/m sources in our catalogs., The result of our matching analysis is a list of probable optical counterparts for the $\mu$ m sources in our catalogs. We identify 611 and 650 counterparts to 347m sources which are brighter than R=24 and jy in 00024416 and 1-03 respectively., We identify 611 and 650 counterparts to $\mu$ m sources which are brighter than $R=24$ and $\mu$ Jy in $+$ 16 and $-$ 03 respectively. In 1-03 this includes sources in the archival region., In $-$ 03 this includes sources in the archival region. In Figure | we plot the (8—R) versus R color-magnitude diagram for each cluster. comparing the distribution of colors for the mid-infrared sources and their apparent magnitudes with the optical population in these regions.," In Figure 1 we plot the $(B-R)$ versus $R$ color-magnitude diagram for each cluster, comparing the distribution of colors for the mid-infrared sources and their apparent magnitudes with the optical population in these regions." The first thing to note is the broad similarity in the distributions on the color-magnitude plane of the 24/:m sources in the two fields., The first thing to note is the broad similarity in the distributions on the color-magnitude plane of the $\mu$ m sources in the two fields. Looking at the color distributions in more detail. the median (B—R) color of mid-infrared sources at R<22 is 1.75 and 1.80 for C000244-16 and 00451—03 respectively.," Looking at the color distributions in more detail, the median $(B-R)$ color of mid-infrared sources at $R<22$ is 1.75 and 1.80 for 0024+16 and $-$ 03 respectively." The 24-jmm counterparts exhibit a broad peak in (8—R) color. which lies between the peaks of red and blue galaxies (Fig.," The $\mu$ m counterparts exhibit a broad peak in $(B-R)$ color, which lies between the peaks of red and blue galaxies (Fig." 1)., 1). This association of 24j/m sources with galaxies having transition colors is intriguing., This association of $\mu$ m sources with galaxies having transition colors is intriguing. It may simply reflect the fact that these galaxies are dustier examples of the general blue star-forming field population. where dust reddening produces somewhat redder colors.," It may simply reflect the fact that these galaxies are dustier examples of the general blue star-forming field population, where dust reddening produces somewhat redder colors." Or it may be evidence that some of these galaxies are part of an evolutionary sequence connecting the blue star-forming population. and the passive types inhabiting the red-sequence.," Or it may be evidence that some of these galaxies are part of an evolutionary sequence connecting the blue star-forming population, and the passive types inhabiting the red-sequence." In Figure 2 we plot the (R— versus (B—R) colors of the mid-infrared sources in. CI0002416.K) and 00451—03 compared to the optically-selected populations in the two fields., In Figure 2 we plot the $(R-K)$ versus $(B-R)$ colors of the mid-infrared sources in 0024+16 and $-$ 03 compared to the optically-selected populations in the two fields. We also indicate the expected colors of cluster members with a range of spectral types (King Ellis 1985)., We also indicate the expected colors of cluster members with a range of spectral types (King Ellis 1985). These model colors provide a rough guide to the relative level of current to past star-formation in the galaxies and the reader should note that the influence of dust extinction will move galaxies parallel to this sequence. further complicating anyinterpretation of the star-formation histories of these galaxies.," These model colors provide a rough guide to the relative level of current to past star-formation in the galaxies and the reader should note that the influence of dust extinction will move galaxies parallel to this sequence, further complicating anyinterpretation of the star-formation histories of these galaxies." Looking at the panel for 0002416 in Figure 2. we see a clear ridge of 24-;m sources with colors comparable to," Looking at the panel for 0024+16 in Figure 2, we see a clear ridge of $\mu$ m sources with colors comparable to" have resulted in the production of an observed stellar system containing one or more merger products.,have resulted in the production of an observed stellar system containing one or more merger products. These steps are:, These steps are: rivariate distribution of (2.Z) is visually indistinguishable rom those of. c.g.Balletal. and Collister&Lahay(2004).,"bivariate distribution of $(\zhat,Z)$ is visually indistinguishable from those of, e.g.,\citeauthor{Ball08} and \cite{Collister04}." . We determine estimator bias by binning the predictions as a function of Z. then in cach bin computing 2Z. with = being a trimmed mean.," We determine estimator bias by binning the predictions $\zhat$ as a function of $Z$, then in each bin computing $\bar \zhat - Z$, with $\bar \zhat$ being a trimmed mean." See the top left panel of Fie. 2.., See the top left panel of Fig. \ref{fig:bias}. Ht is readily apparent that there is a downward slope in the bias (νο. redshifts are overestimated at low Z. and unclerestimated at high Z).," It is readily apparent that there is a downward slope in the bias (i.e., redshifts are overestimated at low $Z$, and underestimated at high $Z$ )." This is not caused by model bias (a bias that one would mitigate by adding complexity to the model. e.e.. changing from linear to quadratic regression). but rather bybias. in which measurement error (Le. uncertainty in the predictor. in this case the dillusion coordinates) reduces the slope of the regression line (see Fig. 3u," This is not caused by model bias (a bias that one would mitigate by adding complexity to the model, e.g., changing from linear to quadratic regression), but rather by, in which measurement error (i.e., uncertainty in the predictor, in this case the diffusion coordinates) reduces the slope of the regression line (see Fig. \ref{fig:atten};" see also. e.g.. Carrolletal. 2006)).," see also, e.g., \citealt{Carroll06}) )." To demonstrate that our data are allected by attenuation bias. we perform. a simple experiment.," To demonstrate that our data are affected by attenuation bias, we perform a simple experiment." First. we take the AISG: training set fluxes and resample them according to the prescription given. in Appendix. D...," First, we take the MSG training set fluxes and resample them according to the prescription given in Appendix \ref{sect:sample}." Fhis increases all measurement errors. (, This increases all measurement errors. ( To see this intuitively. imagine sampling random. variables YoονΑς1). ie. each value of Nis sampled: from a Gaussian. distribution with mean O and variance. 1.,"To see this intuitively, imagine sampling random variables $X \sim N(0,1)$, i.e., each value of $X$ is sampled from a Gaussian distribution with mean 0 and variance 1." Then resample from the observed. values VW: YcNGNXLI).," Then resample from the observed values $X$: $Y \sim N(X,1)$." The standard. deviation of the resulting sample is now V2. i.c. the error has been artificially increased. by resampling.)," The standard deviation of the resulting sample is now $\sqrt{2}$, i.e., the error has been artificially increased by resampling.)" Then we resample luxes for 1.000 randomly selected. validation set objects.," Then we resample fluxes for 1,000 randomly selected validation set objects." By doing cach resampling (training set ancl validation set) 25 imes. we build up a set of 625 predictions of Z for cach of he 1.000 selected objects.," By doing each resampling (training set and validation set) 25 times, we build up a set of 625 predictions of $\zhat$ for each of the 1,000 selected objects." Following the same prescription as above. we estimate the bias: the top panel of Fig.," Following the same prescription as above, we estimate the bias; the top panel of Fig." 4 shows row for the MS dataset. increasing the measurement error via resampling leads to a steepening of the bias slope. ic. he elfect of attenuation bias is magnilied.," \ref{fig:comp_bias} shows how for the MSG dataset, increasing the measurement error via resampling leads to a steepening of the bias slope, i.e., the effect of attenuation bias is magnified." There exist methods. for. correcting the bias. in incar regression cocllicient. estimation caused. by additive. jeteroscedastic (Le. non-constant) measurement errors of known magnitude that are based. on theSIMEX. or simulation-extrapolation. algorithm. (Cook&Stefan-ski 1904: see. e.g. Carrolletal.2006— and. references therein).," There exist methods for correcting the bias in linear regression coefficient estimation caused by additive, heteroscedastic (i.e., non-constant) measurement errors of known magnitude that are based on the, or simulation-extrapolation, algorithm \citealt{Cook94}; see, e.g., \citealt{Carroll06} and references therein)." Indeed. one of the advantages to our. approach is that the non-linearity is in the reparametrization. not the fitted: model.," Indeed, one of the advantages to our approach is that the non-linearity is in the reparametrization, not the fitted model." Hence. available methocs for correcting for measurement error could be utilized.," Hence, available methods for correcting for measurement error could be utilized." We are currently exploring the implementation of SIMEX-based methods in a computationally efficient. manner. and. we will present. our results in a future publication.," We are currently exploring the implementation of -based methods in a computationally efficient manner, and we will present our results in a future publication." While attenuation bias is caused. bv measurement error. its magnitude is allected by the distribution of the predictors. Le. the design.," While attenuation bias is caused by measurement error, its magnitude is affected by the distribution of the predictors, i.e., the design." Expressions relating the design to the bias magnitude are highly problem dependent., Expressions relating the design to the bias magnitude are highly problem dependent. " In the simplest. one-dimensional example of attenuation bias. the predictors are assumed. to be normally XoON.στ): and the elect on the slope 2, is to reduce its value: τι Αι. where A=a7:flat;|στ] and m, "," In the simplest, one-dimensional example of attenuation bias, the predictors are assumed to be normally $X \sim N(\mu_x,\sigma_x^2)$ –and the effect on the slope $\beta_1$ is to reduce its value: $\hat{\beta_1} \rightarrow \lambda \beta_1$ where $\lambda = \sigma_x^2/(\sigma_x^2 + \sigma_u^2)$ and $\sigma_u$ " cinission is a redshifted [OT] A3727 line of a starburst enütter at redshift 2=0.315. because he redshifted and |OTH) A5007 eolussious should then]© Visible iu the red part of the spectrum (respectively at A6539 and AGT36 Aj). and we can similarly exclude |MIgII] A2798 aat +=0.79.,"emission is a redshifted [OII] $\lambda 3727$ line of a starburst emitter at redshift $z= 0.345$, because the redshifted $\beta$ and [OIII] $\lambda 5007$ emissions should then be visible in the red part of the spectrum (respectively at $\lambda 6539$ and $\lambda 6736$ ), and we can similarly exclude [MgII] $\lambda 2798$ at $z=0.79$." In addition. the observed line is broad. auc asvaunnetric.," In addition, the observed line is broad and asymmetric." This olject is μίαmost likely a Lye cunitter at =3.12: sec also et (2000). where snmailar findings are discussed for cuussion line objects in Virgo.," This object is most likely a $\alpha$ emitter at $z=3.12$; see also Kudritzki et (2000), where similar findings are discussed for emission line objects in Virgo." The ID spectrmm of the second (weaker) enission. labeled ΤΟ. is ceutred at ASN0G.2A.," The 1D spectrum of the second (weaker) emission, labeled IG2B, is centred at $\lambda 5006.2$." Suiuuilur considerations to those for ΤΟΣΑ sugecst that this is also a Lvo emitter. at redshift +3.11.," Similar considerations to those for IG2A suggest that this is also a $\alpha$ emitter, at redshift $z = 3.11$." For ICH. again there are no additional lines iu the optical. excluding redshifted [OITI| A5007A.. |OII| A38727A.. and [MellI| A2798 aus identification for the observed emission at A5O28.5À.," For IG1, again there are no additional lines in the optical, excluding redshifted [OIII] $\lambda 5007$, [OII] $\lambda 3727$, and [MgII] $\lambda 2798$ as identification for the observed emission at $\lambda 5028.5$." . This. and the fact that the observed line is broad aud asviunuetric. arene that we are seciug a να line.," This, and the fact that the observed line is broad and asymmetric, argue that we are seeing a $\alpha$ line." The near-infrared part of the spectrum shows an additional weal cluission liue at À9191.0À., The near-infrared part of the spectrum shows an additional weak emission line at $\lambda 9191.0$. . Both observed Tues cau be explained the emission line object is à Lye emitter at redshift +Lyn1u3.126. in which case the second Ime is frou red-shifted. fluorescent ΕΟΠ UV. eunission at Az2220 ((Sigut Pradhan 1998).," Both observed lines can be explained if the emission line object is a $\alpha$ emitter at redshift $z=3.126$, in which case the second line is from red-shifted, $\alpha$ fluorescent FeII UV emission at $\lambda \simeq 2220$ (Sigut Pradhan 1998)." The other strong ines the- expected at longer waveleneths frou fluorescent Fell arc not detected in our spectrum., The other strong lines then expected at longer wavelengths from fluorescent FeII are not detected in our spectrum. They would fall in the regio- of strong ΟΠ sky emission., They would fall in the region of strong OH sky emission. The main conclusion of the preseut work is that there is no population of PNe at 10 Mpe associated with the intraeroup HII cloud iu the Leo group. because (i) the bright edee of luninesity function (LE) for the ciission line objects in this field is z1.2 maenitude faimter than the bright cut-off ofPNLE for the main elliptical galaxies in Leo: (ii) the LF of the emission line caucdidates in the field agrees with the LF for Lya enütters at 2= 3.1: aud," The main conclusion of the present work is that there is no population of PNe at 10 Mpc associated with the intragroup HI cloud in the Leo group, because (i) the bright edge of luminosity function (LF) for the emission line objects in this field is $\simeq 1.2$ magnitude fainter than the bright cut-off ofPNLF for the main elliptical galaxies in Leo; (ii) the LF of the emission line candidates in the field agrees with the LF for $\alpha$ emitters at $z = 3.1$ ; and" "some neutron star systems. could definitely lie. outside this so called “X-ray burster box"".","some neutron star systems, could definitely lie outside this so called “X-ray burster box”." " Therefore unless a very high luminosity hard tail is found. the fact that a source lies outside the ""X-ray burster box"" is not a definite proof for a black hole binary (Di Salvo et al."," Therefore unless a very high luminosity hard tail is found, the fact that a source lies outside the “X-ray burster box” is not a definite proof for a black hole binary (Di Salvo et al." 2001)., 2001). " In addition. the spectral parameters we obtain from our spectral fits in all ""states"" are radically different from those usually observed in black hole binaries (e.g. MeClintock Remillard 2004). even in their quiescent states (e.g. Kong et al."," In addition, the spectral parameters we obtain from our spectral fits in all “states” are radically different from those usually observed in black hole binaries (e.g. McClintock Remillard 2004), even in their quiescent states (e.g. Kong et al." 2002)., 2002). This is particularly true for the parameters of the cut-off energy. or equivalently the electron temperature which are in agreement with those presented by Barret (2000) in the case of neutron star As already pointed out in another system (4U 2206454 Torrejónn et al.," This is particularly true for the parameters of the cut-off energy, or equivalently the electron temperature which are in agreement with those presented by Barret (2000) in the case of neutron star As already pointed out in another system (4U 2206+54 Torrejónn et al." 2004). we note that during the “Faint” state the black body temperature is high. while the source luminosity is not very high (although higher than in 3Η 22064054," 2004), we note that during the “Faint” state the black body temperature is high, while the source luminosity is not very high (although higher than in 4U 2206+054)." Following the procedure presented by Torrejónn et al. (, Following the procedure presented by Torrejónn et al. ( 2004). we can estimate the radius of the black body emitter following Ru=3x10xdiVFCORνοκ Gn't Zand et al.,"2004), we can estimate the radius of the black body emitter following $R_{bb}=3\times 10^4 \times{\mathrm{d_{kpc}}}\sqrt{f^{\mathrm{bol}}/(1+y)}/{\mathrm{kT_{bb}}}$ (in't Zand et al." " 1999), where y is the Compton parameter v«kT,r-. f the “bolometric” flux and kT), the black body temperature."," 1999), where y is the Compton parameter $y\propto\mathrm{kT_{e}\tau^2}$, $f^{bol}$ the “bolometric” flux and $_{\mathrm{bb}}$ the black body temperature." Using the values found in our study (expanding the flux to the 0.1-200 keV range following in’t Zand et al., Using the values found in our study (expanding the flux to the 0.1-200 keV range following in't Zand et al. " 1999). we obtain Rpp=0.999Xd),,. km."," 1999), we obtain $_{bb}$ $\times \mathrm{d_{kpc}}$ km." We remark here a factor of 2 discrepancy between Torrejónn et al. (, We remark here a factor of 2 discrepancy between Torrejónn et al. ( 2004) and in't Zand et al. (,2004) and in't Zand et al. ( 1999). the values given in the former are the diameter of the black body emitter. but this does not change their conclusions.,"1999), the values given in the former are the diameter of the black body emitter, but this does not change their conclusions." This value implies that even at a very far distance (e.g. 20 kpc. therefore outside of our Galaxy. which appears rather unlikely). the black body radius is consistent with the radius of a neutron star.," This value implies that even at a very far distance (e.g. 20 kpc, therefore outside of our Galaxy, which appears rather unlikely), the black body radius is consistent with the radius of a neutron star." The absorption column density (Ny=~ 3-10x107 em) of derived from the spectral fits to the data is much higher than the Galactic absorption towards the source (1.26x107. em Dickey Lockman. 1990).," The absorption column density $N_{\mathrm H}$ $\sim3$ $10 \times 10^{22}$ $^{-2}$ ) of derived from the spectral fits to the data is much higher than the Galactic absorption towards the source $\times10^{22}$ $^{-2}$ Dickey Lockman, 1990)." This favours an absorption intrinsic to the object. and therefore the presence of absorbing material in the vicinity of the compact object.," This favours an absorption intrinsic to the object, and therefore the presence of absorbing material in the vicinity of the compact object." The variations of the absorption (Fig., The variations of the absorption (Fig. + and Table 7)) also point toward an absorption intrinsic to the source., \ref{fig:contour} and Table \ref{tab:RXTE}) ) also point toward an absorption intrinsic to the source. This is in fact similar to what is observed in IGR J16320-4751 (Rodriguez et al., This is in fact similar to what is observed in IGR J16320-4751 (Rodriguez et al. 2003b). or 4U 1700-37 (Boroson et al.," 2003b), or 4U $-$ 37 (Boroson et al." 2003). in which the absorption is seen to vary by a factor of about 2 in the former source (a most likely High Mass X-ray Binary HMXB: Rodriguez et al.," 2003), in which the absorption is seen to vary by a factor of about 2 in the former source (a most likely High Mass X-ray Binary HMXB; Rodriguez et al." 2003b) and 10 in the latter (a dynamically confirmed HMXB)., 2003b) and 10 in the latter (a dynamically confirmed HMXB). The presence of absorbing material is consistent with the detection of a (cold) tron line., The presence of absorbing material is consistent with the detection of a (cold) iron line. It is interesting to note that although when comparing Obs., It is interesting to note that although when comparing Obs. I. 2 and 3. the iron line fluxes are all comparable within the uncertainties (Table 8)). while Ny varies significantly. the line flux is much stronger in Obs.," 1, 2 and 3, the iron line fluxes are all comparable within the uncertainties (Table \ref{tab:line}) ), while $N_{\mathrm H}$ varies significantly, the line flux is much stronger in Obs." 3 high (interval 2). than in Obs.," 3 high (interval 2), than in Obs." 3 low (interval 1). re. it is stronger here when Ny is higher.," 3 low (interval 1), i.e. it is stronger here when $N_{\mathrm H}$ is higher." In addition. there seems to be a tight correlation between the 1-200 keV (unabs.)," In addition, there seems to be a tight correlation between the 1-200 keV (unabs.)" " flux of and the flux of the line although the case of the ""Faint state does not obey this relation. and the parameters of the line are poorly constrained in the “Bright” state."," flux of and the flux of the line although the case of the “Faint” state does not obey this relation, and the parameters of the line are poorly constrained in the “Bright” state." This relation. and the relative constancy of the line energy in most of the cases suggest that the line 1s produced through fluorescence in a cold medium as in e.g. Vela X-1 (Ohashi et al.," This relation, and the relative constancy of the line energy in most of the cases suggest that the line is produced through fluorescence in a cold medium as in e.g. Vela X-1 (Ohashi et al." 1984)., 1984). In addition. the intensity of the iron line during the observations is comparable to the intensity observed in the HMXB GX 301-2 at a similar flux (Saraswat et al.," In addition, the intensity of the iron line during the observations is comparable to the intensity observed in the HMXB GX $-$ 2 at a similar flux (Saraswat et al." 1996)., 1996). In the latter system the line width (measured with ASCA) was consistent with the instrumental spectral resolution. which seems to be the case in IGR J19140+0951. although the energy resolution of both RXTE/PCA and /NTEGRAL/JEM-X is very poor in comparison to that of ASCA/SIS.," In the latter system the line width (measured with ) was consistent with the instrumental spectral resolution, which seems to be the case in IGR J19140+0951, although the energy resolution of both /PCA and /JEM-X is very poor in comparison to that of /SIS." These similarities between different systems would tend to indicate is an HMXB. rather than a system containing a low-mass secondary star (LMXB).," These similarities between different systems would tend to indicate is an HMXB, rather than a system containing a low-mass secondary star (LMXB)." Finally we observe that the hardest spectra (ie. those for which the electron temperature or the cut-off energy is the highest) are observed at higher lummosities. which again is very similar to the HMXB 4U 2206454 (Masetti et al.," Finally we observe that the hardest spectra (i.e. those for which the electron temperature or the cut-off energy is the highest) are observed at higher luminosities, which again is very similar to the HMXB 4U 2206+54 (Masetti et al." 2004). and rather contrary to what observed in the case of LMXB (Barret Independently. the temporal variability on timescale ~1000 s is very similar to the HMXBs 4U 22064054 (Nereguela Reig 2001). 28 O114+65 (Yamauchi et al.," 2004), and rather contrary to what observed in the case of LMXB (Barret Independently, the temporal variability on timescale $\sim$ 1000 s is very similar to the HMXBs 4U 2206+054 (Nereguela Reig 2001), 2S 0114+65 (Yamauchi et al." 1990). and Vela X-1 (Kreykenbohm et al.," 1990), and Vela X-1 (Kreykenbohm et al." 1999)., 1999). In these systems. this variability is commonly interpreted as due to random inhomogeneities in the accretion flow (e.g. Masetti et al.," In these systems, this variability is commonly interpreted as due to random inhomogeneities in the accretion flow (e.g. Masetti et al." 2004 and references therein)., 2004 and references therein). The level of variability from 0.06 Hz on is compatible with what was found in 4U 1700-37 (Boroson et al., The level of variability from 0.06 Hz on is compatible with what was found in 4U 1700-37 (Boroson et al. 2003) or 4U 2206-54 (Nereguela Reig 2001). re. the variability is compatible with purely Poisson noise.," 2003) or 4U 2206+54 (Nereguela Reig 2001), i.e. the variability is compatible with purely Poisson noise." In the former source significant. aperiodic variability is detected only below 0.01 Hz. although a 13 mHz QPO is detected at a fractional amplitude 4.0 (Boroson et al.," In the former source significant aperiodic variability is detected only below 0.01 Hz, although a 13 mHz QPO is detected at a fractional amplitude 4.0 (Boroson et al." 2003)., 2003). As discussed in Sec., As discussed in Sec. 3.1. if such a feature was present in IGR 19140-0951. it should have been detected at least in Obs.," 3.1, if such a feature was present in IGR J19140+0951, it should have been detected at least in Obs." 3., 3. In 4U 2206-54. on the other hand. significant aperiodic variability is seen below ~0.06 Hz.," In 4U 2206+54, on the other hand, significant aperiodic variability is seen below $\sim 0.06$ Hz." However. no QPOs are detected in this system.," However, no QPOs are detected in this system." Again the similarity of the behaviour of with that of confirmed HMXB. would tend to argue in favour of a high mass secondary star in and therefore X-ray lummosity due to wind accretion onto the compact The hypothesis of being à HMXB is again in good agreement with the relatively large value of the orbital period of 13.55 days (Corbet et al.," Again the similarity of the behaviour of with that of confirmed HMXB, would tend to argue in favour of a high mass secondary star in and therefore X-ray luminosity due to wind accretion onto the compact The hypothesis of being a HMXB is again in good agreement with the relatively large value of the orbital period of 13.55 days (Corbet et al." 2004). since HMXBs have usually higher orbital period than LMXBs.," 2004), since HMXBs have usually higher orbital period than LMXBs." Note that this is not a definite proof since some LMXB can have large orbital period as e.g. GRS 1915+105 and GRO J1744-28 with ~33 days and ~12 days. respectively.," Note that this is not a definite proof since some LMXB can have large orbital period as e.g. GRS 1915+105 and GRO J1744-28 with $\sim 33$ days and $\sim 12$ days, respectively." The fact that the modulation ts sinusoidal (Corbet et al., The fact that the modulation is sinusoidal (Corbet et al. 2004) would tend to indicate a high inclination system (1.8. the orbital plane almost parallel to the line of sight) rather than variations of the X-ray, 2004) would tend to indicate a high inclination system (i.e. the orbital plane almost parallel to the line of sight) rather than variations of the X-ray the observations.,the observations. We present our resulis in 46., We present our results in 4–6. A discussion follows in 7. and the conclusions in 8.," A discussion follows in 7, and the conclusions in 8." We assume throughout a cosmology where Jf) = 71 km ! |. Qj = 0.24. and O4 = 0.76.," We assume throughout a cosmology where $H_0$ = 71 km $^{-1}$ $^{-1}$, $\Omega_M$ = 0.24, and $\Omega_{\Lambda}$ = 0.76." The Large Area Sky Survey (LASS) detected 842 hard. N-rav (0.8 — 20 keV) sources over the entire sky (?).., The Large Area Sky Survey (LASS) detected 842 hard X-ray (0.8 $-$ 20 keV) sources over the entire sky \citep{Wood84}. To date. 29 BL Lacertae objects have been identified in the LASS catalog (2).. one of which (2201+044) is now known to be a Sevlert 1 galaxy. (2)..," To date, 29 BL Lacertae objects have been identified in the LASS catalog \citep{LaurentMuehleisen93}, one of which (2201+044) is now known to be a Seyfert 1 galaxy \citep{Veron-Cetty93}." Note that 22012-044 is part of our sample., Note that 2201+044 is part of our sample. The RGB sample of BL Lacs was generated Irom a cross-correlation of the ROSAT All-Sky Survey (RASS) and a reanalysis of the 1987 Green Dank 6-em radio survey (??)..," The RGB sample of BL Lacs was generated from a cross-correlation of the $ROSAT$ All-Sky Survey (RASS) and a reanalysis of the 1987 Green Bank 6-cm radio survey \citep{Gregory96,LaurentMuehleisen97}." VLA observations of the BL Lae sample have been presented by ? and ?.., VLA observations of the BL Lac sample have been presented by \citet{LaurentMuehleisen93} and \citet{Kollgaard96}. Ilere we present VLBI polarization results lor nine BL Lacs. along with eight BL Lacs belonging to the RGB sample.," Here we present VLBI polarization results for nine BL Lacs, along with eight BL Lacs belonging to the RGB sample." In all. there ave 13 HIIDLs. 4 LBLs and 1 Sevfert-1 galaxy.," In all, there are 13 HBLs, 4 LBLs and 1 Seyfert-1 galaxy." Of the 4 LDLs. 1147+245 also belongs to the 1-Jv sample.," Of the 4 LBLs, 1147+245 also belongs to the 1-Jy sample." The BL Lac sample is presented in Table 1.. which has the following columns: Cols. (," The BL Lac sample is presented in Table \ref{sampleBL}, which has the following columns: Cols. (" 1) (2) LAU and other names. (3) DL Lac classification based on the SED peak frequency and/or the log (f/./f.) evilerion (see cf.& 1). (4) sample membership. with II denoting sources belonging to the sample. Roto the RGB sample. and J to the 1-Jy sample. (5) membership of other “heritage” X-ray samples: RX =ROSAT All-skv Survey. LE. 2E ES =HEinslein. second Image Proportional Counter (IPC) N-rav Survey. and “Slew” Survey. respectively. (6) redshift. (7) projected linear scale corresponding lo an angular scale of 1 mas. (8) — (10) the epochs for which results are presented here. aud (11) (12) the references for the redshifts and BL Lac classification. respectively.,"1) (2) IAU and other names, (3) BL Lac classification based on the SED peak frequency and/or the log $f_x/f_r$ ) criterion (see $cf.~\S$ 1), (4) sample membership, with H denoting sources belonging to the sample, R to the RGB sample, and J to the 1-Jy sample, (5) membership of other “heritage” X-ray samples: RX = All-sky Survey, 1E, 2E ES =, second Image Proportional Counter (IPC) X-ray Survey, and “Slew” Survey, respectively, (6) redshift, (7) projected linear scale corresponding to an angular scale of 1 mas, (8) $-$ (10) the epochs for which results are presented here, and (11) (12) the references for the redshifts and BL Lac classification, respectively." The polarization observations were made at 5 GlIz wilh (1) a global VLBI array on February 23. 1993 (1993.15) and Gi} on July 13. 1995 (1995.53) and June 23. 1998 (1998.49) with the 10-element Very. Large Baseline Array(VLDA)!.," The polarization observations were made at 5 GHz with (i) a global VLBI array on February 23, 1993 (1993.15) and (ii) on July 13, 1995 (1995.53) and June 28, 1998 (1998.49) with the 10-element Very Large Baseline Array." . In all cases. each source was observed for a total of roughly 1.3 to 2.8 hours. in 1226 scans distributed throughout the time the source was observable with all or nearly all of the antennas in the VLB arravs.," In all cases, each source was observed for a total of roughly 1.3 to 2.8 hours, in 12–26 scans distributed throughout the time the source was observable with all or nearly all of the antennas in the VLB arrays." Two intermediate, Two intermediate ]t is now evident that early-tvpe galaxies are far from being the simple. (violently) relaxed. isothermal. purely stellar systems anticipated by the traditional picture developed by Hubble.,"It is now evident that early-type galaxies are far from being the simple, (violently) relaxed, isothermal, purely stellar systems anticipated by the traditional picture developed by Hubble." They. are often found. to contain a complex interstellar medium. (ISM). stellar clises and/or cusps and other discrete. dvnamical. components (c.g. ce Zeeuw οἱ al.," They are often found to contain a complex interstellar medium (ISM), stellar discs and/or cusps and other discrete dynamical components (e.g. de Zeeuw et al." 2002)., 2002). Lt now seems hiehly plausible that much of this complexity originates in mergers or other interactions between these galaxies and their environments., It now seems highly plausible that much of this complexity originates in mergers or other interactions between these galaxies and their environments. In addition. the statistical frequency of active galactie nuclei (hereafter AGNs) in the form of quasars and radio galaxies (which are generally associated with elliptical galaxies) at. medium to high redshift has led to the realization that the majority of nearby. elliptical galaxies may well harbor a central massive Mack hole (e.&.. Chokshi Turner 1992).," In addition, the statistical frequency of active galactic nuclei (hereafter AGNs) in the form of quasars and radio galaxies (which are generally associated with elliptical galaxies) at medium to high redshift has led to the realization that the majority of nearby elliptical galaxies may well harbor a central massive black hole (e.g., Chokshi Turner 1992)." Indeed. recent. stellar. kinematic studies using spectroscopy. have provided evidence or the presence of black holes in tens of earlv-tvpe galaxies (l'oerrarese Merritt 2000: Goebhbardt et 22000).," Indeed, recent stellar kinematic studies using spectroscopy have provided evidence for the presence of black holes in tens of early-type galaxies (Ferrarese Merritt 2000; Gebhardt et 2000)." They. reveal the o)esence of a correlation between black hole mass and xulge velocity dispersion. which suggests à causal connection »etween the formation history of the black hole and that of he host galaxy.," They reveal the presence of a correlation between black hole mass and bulge velocity dispersion, which suggests a causal connection between the formation history of the black hole and that of the host galaxy." One long-standing problem associated with the growth of black holes is the fucling mechanism., One long-standing problem associated with the growth of black holes is the fueling mechanism. It has remained eenerallv unclear how to transfer significant amounts of mass [rom the central kiloparsec of galaxy into its inner regions (at, It has remained generally unclear how to transfer significant amounts of mass from the central kiloparsec of galaxy into its inner regions (at with the relativistic electron population in the emission region.,with the relativistic electron population in the emission region. As a consequence of this parametrization. (he magnetic field will οταν chanee throughout the evolution of the blob as particles are being injected aud subsequently cool along the jet.," As a consequence of this parametrization, the magnetic field will gradually change throughout the evolution of the blob as particles are being injected and subsequently cool along the jet." " The blob moves with relativistic speed e/c=dp\/l—1/T? along the jet which is directed at an angle 6,,, (with ft=cos 8,,,) with respect to the line of sight.", The blob moves with relativistic speed $v / c = \beta_{\Gamma} = \sqrt{1 - 1 / \Gamma^2}$ along the jet which is directed at an angle $\theta_{\rm obs}$ (with $\mu \equiv \cos\theta_{\rm obs}$ ) with respect to the line of sight. The Doppler boosting of emission from the co-moving to the observer's frame is determined bythe Doppler factor D=[V(1—μὴb ," The Doppler boosting of emission from the co-moving to the observer's frame is determined bythe Doppler factor $D = \left[ \Gamma \, (1 - \beta\mu) \right]^{-1}$." As the emission region moves outward along the jet. particles are continuously injected according to Eq. 1..," As the emission region moves outward along the jet, particles are continuously injected according to Eq. \ref{Qe}," are cooling. primarily due to radiative losses. and may leak out of the svslem.," are cooling, primarily due to radiative losses, and may leak out of the system." We paramelrize particle escape through an energv-independent escape lime scale lose=pfigf/e with jg>1.," We parametrize particle escape through an energy-independent escape time scale $t_{\rm esc} = \eta \, R_b / c$ with $\eta \ge 1$." This parametrization of particle escape can also be used to include acdiabatic losses. which are not explicitly taken into account in our simulations.," This parametrization of particle escape can also be used to include adiabatic losses, which are not explicitly taken into account in our simulations." hadiation mechanisms imcluded in our simulations are svnchrotron emission. Compton upscattering of svuchrotron photons (SSC = Svnchrotron Self Compton scattering). ancl Compton upscattering ol external photons (EC — External Compton scattering). including photons coming directly from the disk as well as re-processed photons from the broad line region.," Radiation mechanisms included in our simulations are synchrotron emission, Compton upscattering of synchrotron photons (SSC = Synchrotron Self Compton scattering), and Compton upscattering of external photons (EC = External Compton scattering), including photons coming directly from the disk as well as re-processed photons from the broad line region." " The broad line region is modelled as a spherical shell between rppri,=0.2 pe and rperou=0.25 pe (we note. however. that the details of the radial distribution of the DLR. material do not play an important role as long as ρω—FLS MBean). and a radial Thomson depth τειL.BLR which is considered a free parameter."," The broad line region is modelled as a spherical shell between $r_{\rm BLR, in} = 0.2$ pc and $r_{\rm BLR, out} = 0.25$ pc (we note, however, that the details of the radial distribution of the BLR material do not play an important role as long as $r_{\rm BLR, out} - r_{\rm BLR, in} \lesssim r_{\rm BLR, in}$ ), and a radial Thomson depth $\tau_{\rm T, BLR}$ which is considered a free parameter." +> absorption and the correspondingg pair production rates are taken into account sell-consistentilv. using the general solution for the pair production rate of Bottcher&Schlickeiser(1997).," $\gamma\gamma$ absorption and the corresponding pair production rates are taken into account self-consistently, using the general solution for the pair production rate of \cite{bs97}." . However. in all simulations presented in this paper. the 55 opacity is «I out to at least several tens of GeV so that 5 absorption aud pair production do not play an important role.," However, in all simulations presented in this paper, the $\gamma\gamma$ opacity is $\ll 1$ out to at least several tens of GeV so that $\gamma\gamma$ absorption and pair production do not play an important role." " Motivated by the ~10 hr minimun) variability (ime scale observed in W Comae (Iagliaferriοἱal.2000).. we choose Hy=LOM em. and P—D=10. which implies 6,),.=5.74""."," Motivated by the $\sim 10$ hr minimum variability time scale observed in W Comae \citep{tagliaferri00}, we choose $R_b = 10^{16}$ cm, and $\Gamma = D = 10$, which implies $\theta_{\rm obs} = 5.74^o$." Based on an equipartition parameter ej1l. we expect (vpical magnetic field values of order D1 G (Dótteher.Mukherjee.&Reimer2002).. which implies a svuchrotron cooling time scale (in the observer's frame) of electrons emitting sviclirotron radiation at an observed energy E.=1Ey keV of For N-rav photon energies. (his is shorter than thedvnamical (ime scale A25/(D c). in agreement with the approximately svnunetric shape of the X-ray light curves generally observed both in W Comae (Inglialerrietal.2000) and BL Lacertae (Ravasioetal. 2002)..," Based on an equipartition parameter $\epsilon_B \sim 1$, we expect typical magnetic field values of order $B \sim 1$ G \citep{bmr02}, which implies a synchrotron cooling time scale (in the observer's frame) of electrons emitting synchrotron radiation at an observed energy $E_{\rm sy} = 1 \, E_{\rm keV}$ keV of For X-ray photon energies, this is shorter than thedynamical time scale $R_B / (D \, c)$ , in agreement with the approximately symmetric shape of the X-ray light curves generally observed both in W Comae \citep{tagliaferri00} and BL Lacertae \citep{ravasio02}. ." significant and these cases could not reliably be separated from core-jet type sources without visual analysis.,significant and these cases could not reliably be separated from core–jet type sources without visual analysis. Galaxies for which there are three FIRST matches within 30 aresec are accepted if any of the following three conditions are satistied: (i) the nearest match is within 3 aresee: (i) any of the three pairs of sources satisfies the criteria to be accepted as a FIRST double source: (ii) the flux-weighted mean position of all three sources is within 3 aresec of the optical galaxy position. with the angle subtended by the outer two sources relative to the middle one larger than 135 degrees Ge.," Galaxies for which there are three FIRST matches within 30 arcsec are accepted if any of the following three conditions are satisfied: (i) the nearest match is within 3 arcsec; (ii) any of the three pairs of sources satisfies the criteria to be accepted as a FIRST double source; (iii) the flux-weighted mean position of all three sources is within 3 arcsec of the optical galaxy position, with the angle subtended by the outer two sources relative to the middle one larger than 135 degrees (ie." the source looks like a straighttish) triple source)., the source looks like a straight(ish) triple source). Figure 7 shows the results of this selection., Figure \ref{firsttriples} shows the results of this selection. Automated classification of more than three sources cannot be carried out in an efficient and reliable way., Automated classification of more than three sources cannot be carried out in an efficient and reliable way. For galaxies with four or more matches. the nearest three matches are analysed using the criteria for three-source matches to test whether they may be classitied as triples. doubles or singles.," For galaxies with four or more matches, the nearest three matches are analysed using the criteria for three-source matches to test whether they may be classified as triples, doubles or singles." All galaxies not accepted in this way are sent for visual analysis (ta total of 23 optical galaxies or 0.01% of the SDSS sample)., All galaxies not accepted in this way are sent for visual analysis (a total of 23 optical galaxies or $\sim 0.01$ of the SDSS sample). The final list of matches was examined to ensure that two different SDSS galaxies were not associated with the same NVSS source., The final list of matches was examined to ensure that two different SDSS galaxies were not associated with the same NVSS source. This occurred on 24 occasions and these cases were all examined visually., This occurred on 24 occasions and these cases were all examined visually. In two cases. two SDSS galaxies were associated with the same NVSS source and there was no FIRST counterpart.," In two cases, two SDSS galaxies were associated with the same NVSS source and there was no FIRST counterpart." In a further I4 cases. two SDSS galaxies were associated with the same NVSS source which had a single FIRST counterpart which lay close enough to both galaxies.," In a further 14 cases, two SDSS galaxies were associated with the same NVSS source which had a single FIRST counterpart which lay close enough to both galaxies." For these 16 objects. the nearer galaxy was accepted as the true match and the other galaxy was removed from the radio source catalogue.," For these 16 objects, the nearer galaxy was accepted as the true match and the other galaxy was removed from the radio source catalogue." There were a further 8 cases Where it was found that two galaxies matched the same NVSS source but had distinct FIRST counterparts., There were a further 8 cases where it was found that two galaxies matched the same NVSS source but had distinct FIRST counterparts. In other words. both galaxies were genuine radio sources. but at the lower resolution of NVSS they had been convolved together.," In other words, both galaxies were genuine radio sources, but at the lower resolution of NVSS they had been convolved together." In these cases the flux density of the NVSS source was divided between the two galaxies according to the ratio of their integrated FIRST flux densities., In these cases the flux density of the NVSS source was divided between the two galaxies according to the ratio of their integrated FIRST flux densities. If the galaxies still remained above the S5mmJy flux density limit. they were retained in the radio source catalogue.," If the galaxies still remained above the mJy flux density limit, they were retained in the radio source catalogue." The results of the cross-matching procedure are provided in Table I.., The results of the cross-matching procedure are provided in Table \ref{makecat}. This table gives the number of SDSS galaxies accepted as radio sources compared to the number of cases accepted from the same number of random positions. for each different radio source type.," This table gives the number of SDSS galaxies accepted as radio sources compared to the number of cases accepted from the same number of random positions, for each different radio source type." It therefore provides a direct measure of the reliability of each of the criteria defined above., It therefore provides a direct measure of the reliability of each of the criteria defined above. Overall. assuming visual analysis to be reliable. only 30.1 false identifications are expected amongst the tinal sample of 2712 radio sources.," Overall, assuming visual analysis to be reliable, only 30.1 false identifications are expected amongst the final sample of 2712 radio sources." This corresponds to an overall reliability of98., This corresponds to an overall reliability of. 94c.. The most unreliable part of the sample selection is for NVSS sources without a FIRST counterpart., The most unreliable part of the sample selection is for NVSS sources without a FIRST counterpart. Of these. will be false identifications.," Of these, will be false identifications." This is unavoidable., This is unavoidable. If sources with no FIRST counterpart are excluded. this reduces the completeness and strongly biases the derived radio source sample by removing of the more extended sources.," If sources with no FIRST counterpart are excluded, this reduces the completeness and strongly biases the derived radio source sample by removing of the more extended sources." The completeness of the sample is more difficult to estim:ασ than the reliability. since the true number of matches expected is unknown.," The completeness of the sample is more difficult to estimate than the reliability, since the true number of matches expected is unknown." However. various estimates can be made.," However, various estimates can be made." For galaxies with multiple NVSS components. a comparison of the number of candidate NVSS doubles in the SDSS and random samples with the numbers accepted suggests that the completeness is close to90%.," For galaxies with multiple NVSS components, a comparison of the number of candidate NVSS doubles in the SDSS and random samples with the numbers accepted suggests that the completeness is close to." . For the single NVSS component sources. Figure 3 shows that there were 2973 SDSS galaxies with an NVSS source within [5 arcsec. compared to only 311 random galaxies.," For the single NVSS component sources, Figure \ref{nvssoffs} shows that there were 2973 SDSS galaxies with an NVSS source within 15 arcsec, compared to only 311 random galaxies." Assuming that this excess is entirely due to genuine sources and that all true matches lie within 15 arcsec. 2662 genuine single-component NVSS sources are expected.," Assuming that this excess is entirely due to genuine sources and that all true matches lie within 15 arcsec, 2662 genuine single–component NVSS sources are expected." Table |. indicates hat 2543 single component sources were actually found by he adopted selection. procedures. of which about 30 will be ulse detections.," Table \ref{makecat} indicates that 2543 single component sources were actually found by the adopted selection procedures, of which about 30 will be false detections." An estimate of the completeness is then 2 IN, An estimate of the completeness is then $=$. otethallhisvalucisconservativebeeauscafractionoftl ," Note that this value is conservative because a fraction of the excess matches are likely to be associated with companion galaxies, and so 2662 is an overestimate of the true number of expected matches." The val," Therefore, the overall completeness of the sample likely exceeds." ues quoted for completeness and reliability are or all types of radio source., The values quoted for completeness and reliability are for all types of radio source. There will be a small (but unavoidable) bias against extended sources: the completeness for he single-component FIRST sources approaches1006€... while hat of multi-NVSS-component sources is around90%.," There will be a small (but unavoidable) bias against extended sources: the completeness for the single–component FIRST sources approaches, while that of multi–NVSS–component sources is around." . Note that completeness estimates from previous cross—correlations with the FIRST catalogue have not taken into account the sources missed because sources with radio—optical offsets greater than 3 arcsec are excluded (~3% of our final source catalogue) as are sources hat are completely resolved out by FIRST (5%))., Note that completeness estimates from previous cross–correlations with the FIRST catalogue have not taken into account the sources missed because sources with radio–optical offsets greater than 3 arcsec are excluded $\sim 3$ of our final source catalogue) as are sources that are completely resolved out by FIRST ). These samples will also miss a fraction of the extended NVSS sources (656) and the multi-component FIRST sources })., These samples will also miss a fraction of the extended NVSS sources ) and the multi–component FIRST sources ). These omissions iive a severe effect on the completeness of any radio sample derived for the SDSS spectroscopic sample using the FIRST survey alone., These omissions have a severe effect on the completeness of any radio sample derived for the SDSS spectroscopic sample using the FIRST survey alone. The radio luminosities of many sources would also be underestimated using FIRST alone: the distribution of FIRST to NVSS flux density ratios for the final sample of sources is plotted in Figure 8.. and shows a long tail to low values.," The radio luminosities of many sources would also be underestimated using FIRST alone: the distribution of FIRST to NVSS flux density ratios for the final sample of sources is plotted in Figure \ref{fluxrat}, and shows a long tail to low values." Note. however. that," Note, however, that" (Chandrasekhar1970:FriedmanLOTS:Friedinan1999:Andersson&Ixokkotas2001:2003:Stergioulas2003) Ibis (IIesselsetαἱ.2006).. (Jones2001a.b:Navvar&Owen2006:ChatterjeeDandyopadhyay.2006.2007a).. (Ilaenseletal.2000.2001.2002:Navvar&Owen2006:Andersson2007).. (Madsen.1992.200," \citep{Chan,Fri1,Fri2,Fri3,Fri98,Lin98,And98,And99,Kok,And01,Ster} \citep{Cha2,Cha}. \citep{Hes}. \citep{Jon1,Jon2,Lin02,Han3,Dal,Dra,Nar,DR1,DR2}. \citep{Han1,Han2,Han3,Nar,And06}. \citep{Mad92,Mad00,Don1,Don2}," 0:Dongetal.20072.b).. (Dragoοἱal..2005;Panetal.200," \citep{Dra,Pan} \citep{Schm,Alf,Alf3,Bas,Bas2}." 0:Dongetal.20072.b).. (Dragoοἱal..2005;Panetal.2006," \citep{Dra,Pan} \citep{Schm,Alf,Alf3,Bas,Bas2}." 0:Dongetal.20072.b).. (Dragoοἱal..2005;Panetal.2006)," \citep{Dra,Pan} \citep{Schm,Alf,Alf3,Bas,Bas2}." "(1907). we model the Vsgusdei, colours expected for the evolving. galaxy models. considered. in RLWO2.","(1997), we model the $V_{STIS}-I_{814}$ colours expected for the evolving galaxy models considered in RLK02." Ehe I2 and SO mocels diller in the initial starburst duration. but both evolve passively at 2<2.," The E and S0 models differ in the initial starburst duration, but both evolve passively at $z<2$." The spiral and. Ler models have ος decreasing approximately exponentially and include. cust., The spiral and Irr models have SFRs decreasing approximately exponentially and include dust. We also model a non-evolving 50 Myr age pure starburst. with and without dust.," We also model a non-evolving 50 Myr age pure starburst, with and without dust." Figure 8 shows these models together with the whole-galaxy colours of S4 and SLO. and also the colour of the companion ealaxy to S4. measured. in a 0.5 arcsec radius aperture as Vfg=0.93x0.05.," Figure 8 shows these models together with the whole-galaxy colours of S4 and S10, and also the colour of the companion galaxy to S4, measured in a 0.5 arcsec radius aperture as $V-I=0.93\pm 0.05$." S4 has the red colour of a passive ealaxy with no indication of ongoing star-Formation. while its cisk-tvpe companion and SLO are both much bluer and consistent. with evolving spirals.," S4 has the red colour of a passive galaxy with no indication of ongoing star-formation, while its disk-type companion and S10 are both much bluer and consistent with evolving spirals." Using cgeomap. the STIS images could. be rebinned to the pixel grid. of the WEPC2 cata.," Using `geomap', the STIS images could be rebinned to the pixel grid of the WFPC2 data." " Colour profiles were then extracted. by using ""ISophote! to measure STIS fluxes on the isophotes already fitted to the £ images. and are shown on Figure 7."," Colour profiles were then extracted, by using `isophote' to measure STIS fluxes on the isophotes already fitted to the $I$ images, and are shown on Figure 7." SIO is significantly non-uniform in colour. with a relatively red. centre. V.1lcL2. which is closer to a massive than a spiral model.," S10 is significantly non-uniform in colour, with a relatively red centre, $V-I\simeq 1.2$, which is closer to a passive than a spiral model." At r-0.38 aresec there is à sudden transition to much bluer colours of V.lc04 A9. consistent with an evolving spiral or a mocdoeratelvy reddened οV)20.5 mag) starburst.," At $r>0.38$ arcsec there is a sudden transition to much bluer colours of $V-I\simeq 0.7$ --0.9, consistent with an evolving spiral or a moderately reddened $E(B-V)\simeq 0.5$ mag) starburst." This suggests hat the galaxy. was initially a normal star-lorming spiral. with à nucleus containing older stellar population in its nucleus.," This suggests that the galaxy was initially a normal star-forming spiral, with a nucleus containing older stellar population in its nucleus." This appears to have been greathy disrupted »v an interaction. triggering extensive. starbursting with," This appears to have been greatly disrupted by an interaction, triggering extensive starbursting with" set of conputer siulations was performed byALacdoxrcvkFreeda1(1995) to test for possible svsteinatic effects on the detection of the RGB tip.,set of computer simulations was performed by\citet{1995AJ....109.1645M} to test for possible systematic effects on the detection of the RGB tip. The authors fou xltat a reasonable lower limit to he uuuber of sIW within 1 magnitude from the ip is 50., The authors found that a reasonable lower limit to the number of stars within 1 magnitude from the tip is 50. Beow this level. strong biases cau affect he deternuned uaenitude of the tip.," Below this level, strong biases can affect the determined magnitude of the tip." Note that iu he suaXe of DaCosta&Anuaudroff(1990). the ΠΙΟ of stars within 1 magnitude from the tip Is never larger tiani 20. and can be as low as 2.," Note that in the sample of \citet{1990AJ....100..162D} the number of stars within 1 magnitude from the tip is never larger than 20, and can be as low as 2." A sieificant jmaprovement on this situation was oresened by Bellazzinictal.(2001).., A significant improvement on this situation was presented by \citet{2001ApJ...556..635B}. Iu thei work. he authors derive a new calibration of the naeniude of the tip iu the form AL;TROD.11|FeI|O.IS|Fe/I] 3.66.," In their work, the authors derive a new calibration of the magnitude of the tip in the form $M_I^{TRGB}=0.14\rm{[Fe/H]}^2 + 0.48\rm{[Fe/H]} -3.66$ ." The result is used ol an extensive sample of stars observed iu different bands including the near-IR aud esen edin Ferraroetal.(1999.200ο," The result is based on an extensive sample of stars observed in different bands including the near-IR and presented in \citet{1999AJ....118.1738F,2000AJ....119.1282F}." Although used oon a larger sample of stars han the one esened in Leeetal.(1993).. this calibration «tll dIOS not meet the completeness criteria estalished bv Madore&Freecana1(1995)..," Although based on a larger sample of stars than the one presented in \citet{1993ApJ...417..553L}, this calibration still does not meet the completeness criteria established by \citet{1995AJ....109.1645M}." Iu πουn. both this calibration a the oue bv Leectal.(1993) require a knowledee of the neallicity of the underlving popuation. either weasuyed independently or deduced frou the color of he RGB. iteratiug through measurements of he distance aud the metallicity.," In addition, both this calibration and the one by \citet{1993ApJ...417..553L} require a knowledge of the metallicity of the underlying population, either measured independently or deduced from the color of the RGB, iterating through measurements of the distance and the metallicity." The ouly calibration based on ai suffiicicut iiber of stars is derived for 2 Centauri by Bellazziuietal.(2001).., The only calibration based on a sufficient number of stars is derived for $\omega$ Centauri by \citet{2001ApJ...556..635B}. According to this caibration. he absolute ταστὰude of the RGB tip is ALPRCR=LOL#OA2 ata unctallicity of [Fe/II]~—1.7.," According to this calibration, the absolute magnitude of the RGB tip is $M_I^{TRGB}=-4.04 \pm 0.12$ at a metallicity of ${\rm [Fe/H]} \sim -1.7$." This value is tied o the distance of the eclipsing ary OQLEGC l? iu w Centauri (Thompsonetal.2001 ).. al it’s completely iudepoeudeut TOM auv other opical RR. Lyrae clistances.," This value is tied to the distance of the eclipsing binary OGLEGC 17 in $\omega$ Centauri \citep{2001AJ....121.3089T}, and it's completely independent from any other optical RR Lyrae distances." A yossible source Of1ncertaimtfv associated wih this calibration is the wite and complex colorfmetallicity distriion observed in aw Centauri. mt several studies have shown that the doninaut population is rather metal-poor. and that the peak of the allicity distribuion is at [Fe/I]—LZ (Pauci1Oetal.2000:Suntzeff&[raft1996)..," A possible source of uncertainty associated with this calibration is the wide and complex color/metallicity distribution observed in $\omega$ Centauri, but several studies have shown that the dominant population is rather metal-poor, and that the peak of the metallicity distribution is at ${\rm [Fe/H]} \sim -1.7$ \citep{2000ApJ...534L..83P,1996AJ....111.1913S}." his work. woe will adopt the value μα...=1.014E 0.12.," In this work, we will adopt the value $M_I^{TRGB}=-4.04 \pm 0.12$ ." We note that this assttion is the YCSOSOlL behind our choice of the selection. criteria NO Lave» adopted to define the ROB sample. as cau be verified in Fieure 9..," We note that this assumption is the reason behind our choice of the selection criteria we have adopted to define the RGB sample, as can be verified in Figure \ref{omegacen.ps}." The left panel of Figure 9 shows the CAID of NCC 300. Field 2.," The left panel of Figure \ref{omegacen.ps} shows the CMD of NGC 300, Field 2." Oulv 20 6ft the stars are plotted. for easier reading.," Only 20 of the stars are plotted, for easier reading." The right panel shows the CMD of 2 Centauri ποια Roseubergetal.(2000a.b)..," The right panel shows the CMD of $\omega$ Centauri from \citet{2000A&AS..145..451R,2000A&AS..144....5R}." Horizoutal aud vortica lues show the position of the RGB tip as imeasured in NCC 300., Horizontal and vertical lines show the position of the RGB tip as measured in NGC 300. It is evident that it is possible to define in NGC 300 à sample of RGD stars tiat perfectly overlaps with the RGD of w Centarrl., It is evident that it is possible to define in NGC 300 a sample of RGB stars that perfectly overlaps with the RGB of $\omega$ Centauri. Assmune £(BWV)=0.096+0.008 (Cücreuotal.2005).. we derived distauce moduli both with t16 ED and ML inethods. and for the 6 ACS Fields.," Assuming $E(B-V)=0.096 \pm 0.008$ \citep{2005ApJ...628..695G}, we derived distance moduli both with the ED and ML methods, and for the 6 ACS Fields." The results are presented in Table 2., The results are presented in Table \ref{tab3}. To estimate the OYYOYS attached to. these linslnaenfss Wwe sexuwate the errors connected to the detection of the tip aud the photometric calibration(¢nternad error) aud the errors due to the extinction correcjon aud the calibration of the absolute ταστὰude of the tipπας error).," To estimate the errors attached to these measurements, we separate the errors connected to the detection of the tip and the photometric calibration error) and the errors due to the extinction correction and the calibration of the absolute magnitude of the tip error)." The errors due to the detection of the tip lave alread* been discussed carlicy in this Seclon., The errors due to the detection of the tip have already been discussed earlier in this Section. The CLTOYS conneced with the couversion TOM ACS photometric system aud BVI system call be quautified iu 0.02 mae (Simlaotal.2015)., The errors connected with the conversion from ACS photometric system and BVI system can be quantified in 0.02 mag \citep{2005astro.ph..7614S}. The error attached to the ECVY) nieasuremeut provicle«d by Caerenetal.(2005). is 0.006 mae. NIC1 accounts for a total of 0.01 mag attached to AY.," The error attached to the $E(B-V)$ measurement provided by \citet{2005ApJ...628..695G} is 0.006 mag, which accounts for a total of 0.01 mag attached to $A_I$." Fually. the error iu the absolute calibration is 0.12 nae (Bellazzinietal.2001).. aud it’s basically determined by the unucertaiutv in fre distauce to w Contau (Thompsonetal.2007V.," Finally, the error in the absolute calibration is 0.12 mag \citep{2001ApJ...556..635B}, and it's basically determined by the uncertainty in the distance to $\omega$ Centauri \citep{2001AJ....121.3089T}." " The total aluout ofinfernal errors attached to the ciffereut cistaὉ moduli computed for the six Ficlds are reportsc im columns 3 aud 5 of Tale 2.. for ED aud ME methods, respectively,"," The total amount of errors attached to the different distance moduli computed for the six Fields are reported in columns 3 and 5 of Table \ref{tab3}, , for ED and ML methods, respectively." To derive our final distance modi. we computed a weielied iue of the measurements in the six," To derive our final distance moduli, we computed a weighted mean of the measurements in the six" . o>i. where we have dropped constant nuuerical factors of order unity.,", >1, where we have dropped constant numerical factors of order unity." With these expressions one finds ," With these expressions one finds, meaning that viscous disk is optically thick only when ." "When the condition (A9)} is violated disk becomes optically thin aud we find Y(aya) cT, DIL"," When the condition \ref{eq:tau_1_omega}) ) is violated disk becomes optically thin and we find _f, T_f, , <1." Derivation of equations CÀ3))-CÀI9)) assiues that it is the internal viscous dissipation in the disk that sects its uudplanue temperature., Derivation of equations \ref{eq:Sig_eq_thick}) \ref{eq:tau_eq_thin}) ) assumes that it is the internal viscous dissipation in the disk that sets its midplane temperature. However. analogous to the case studied in 83.9. one can consider a possibility that the disk. teiiperature is set by external radiatiou at the level of Z=Tj even when its angular momentum transport has non-egravitational nature.," However, analogous to the case studied in \ref{subsect:irrad} one can consider a possibility that the disk temperature is set by external irradiation at the level of $T=T_0$ even when its angular momentum transport has non-gravitational nature." From equation CÀ6)) we find that an optically thick self-Iniuiuous viscous disk changes to au externally irraciated disk at a radius wherea, From equation \ref{eq:T_eq_thick}) ) we find that an optically thick self-luminous viscous disk changes to an externally irradiated disk at a radius where. na Analogously. equation (AL7)) predicts that an optically thin trausition from a selÉluuinous to an externally iradiated disk occurs at the point where," Analogously, equation \ref{eq:T_eq_thin}) ) predicts that an optically thin transition from a self-luminous to an externally irradiated disk occurs at the point where" Within cach region we searched. for radio sources up to a peak Hux density z 5 times the rms value of the region.,Within each region we searched for radio sources up to a peak flux density $\geq$ 5 times the rms value of the region. ‘The sources were extracted using the task (Search And Destrov) which attempts to find all the sources whose peaks are brighter than a given level., The sources were extracted using the task (Search And Destroy) which attempts to find all the sources whose peaks are brighter than a given level. For each selected source the Hux. the position and the size are estimated. using a least square Gaussian fit.," For each selected source the flux, the position and the size are estimated using a least square Gaussian fit." However. for faint sources a Ciaussian fit may be unreliable (see Condon 1997. for an extensive," However, for faint sources a Gaussian fit may be unreliable (see Condon 1997, for an extensive" angular momentum is then caleulated as being: where A. is the mass of the core.,angular momentum is then calculated as being: where $M_{c}$ is the mass of the core. " The rotational parameter 3,;.] calculated in the (hree-climensional space. is usually defined as being: Where Lyng. and E,, we the cores gravitational energy and kinetic energy stored in rotational motions. respectively,"," The rotational parameter $\beta_{rot}$, calculated in the three-dimensional space, is usually defined as being: where $E_{grav}$ and $E_{rot}$ are the core's gravitational energy and kinetic energy stored in rotational motions, respectively." " The latter is given by its basic definition: where V. is the volume of the core. and c is the local angular velocity given bv: The gravitational energy Ej, Οἱ the cores is observationally approximated by —qGB. where M, is the mass of the core and q is a positive number which accounts for the core morphology and inner mass distribution."," The latter is given by its basic definition: where $V_{c}$ is the volume of the core, and ${\bf \omega}$ is the local angular velocity given by: The gravitational energy $E_{grav}$ of the cores is observationally approximated by $E_{grav}=-q G M_{c}^{2}/R_{c}$ , where $M_{c}$ is the mass of the core and $q$ is a positive number which accounts for the core morphology and inner mass distribution." " However. as 2,4 is intended (o represent a volume integrated estimate of the balance between centrifugal lorces and effective gravitational forees taking into account that dense cores in molecular clouds are not isolated objects. and in order not (o make anv assumption on the values of q in the 3D estimate. il is more adequate. from a theoretical point of view. to replace E, bv the quantity W whichis slightly different than E, (e.g.. Dib et al."," However, as $\beta_{rot}$ is intended to represent a volume integrated estimate of the balance between centrifugal forces and effective gravitational forces taking into account that dense cores in molecular clouds are not isolated objects, and in order not to make any assumption on the values of $q$ in the 3D estimate, it is more adequate, from a theoretical point of view, to replace $E_{grav}$ by the quantity $W$ whichis slightly different than $E_{grav}$ (e.g., Dib et al." 2007a) and which is given by: where © is the gravitational potential., 2007a) and which is given by: where $\phi$ is the gravitational potential. " Note thal WW is not exactly equal to the volume gravitational energy. £,,4,. because the true gravitational potential is a result of the distribution ol matter inside the core and outside of it (e.g.. (he parent cloud)."," Note that $W$ is not exactly equal to the volume gravitational energy, $E_{grav}$, because the true gravitational potential is a result of the distribution of matter inside the core and outside of it (e.g., the parent cloud)." ILowever. as already shown in Dib et al. (," However, as already shown in Dib et al. (" "2007a). the essential part of the gravitational acceleration in the core is due to (he mass contained inside thecore and in general Wo £Z,,,.","2007a), the essential part of the gravitational acceleration in the core is due to the mass contained inside thecore and in general $W \approx E_{grav}$ ." " Thus. our definition of 5,5; is:"," Thus, our definition of $\beta_{rot}$ is:" "Looney, Tobin Kwon 2007; Tobin et al.","Looney, Tobin Kwon 2007; Tobin et al." " 2007; Ybarra Lada 2009) Channel 2 recovers the strongest jet emission, since its bandpass (4 to 5um)) includes three relatively bright pure rotational H2 emission lines, 0-0 S(9) 4.69, 0-0 S(10) 4.41 and 0-0 S(11)4.18,m;; the jet is well detected in Channel 3 as well, where another couple of H» lines are found (0-0 S(6) 6.11 and 0-0 S(7) 5.51ym)) (see De Buizer Vacca 2010)."," 2007; Ybarra Lada 2009) Channel 2 recovers the strongest jet emission, since its bandpass (4 to ) includes three relatively bright pure rotational $_2$ emission lines, 0-0 S(9) 4.69, 0-0 S(10) 4.41 and 0-0 S(11); the jet is well detected in Channel 3 as well, where another couple of $_2$ lines are found (0-0 S(6) 6.11 and 0-0 S(7) ) (see De Buizer Vacca 2010)." " In Figure 2, we show the iimage of the region around the source of HH 34, rotated so that the outflow axis is parallel to the ordinate."," In Figure 2, we show the image of the region around the source of HH 34, rotated so that the outflow axis is parallel to the ordinate." This image shows a surprising symmetry between the southern jet in optical and the northern counterjet., This image shows a surprising symmetry between the southern jet (detected in optical images) and the northern counterjet. " (detectedWe have defined a 7 images)pixel (4"".2) wide, recangular box aligned with the HH 34 axis, within which we subtract the background emission as a linear interpolation between the pixels immediately(defined outside of the long edges of the box)."," We have defined a 7 pixel $4''.2$ ) wide, recangular box aligned with the HH 34 axis, within which we subtract the background emission (defined as a linear interpolation between the pixels immediately outside of the long edges of the box)." " The result of this background emission subtraction is shown on the right hand side of Figure 2, in which the knot structure along the HH 34 jet and counterjet is seen more clearly."," The result of this background emission subtraction is shown on the right hand side of Figure 2, in which the knot structure along the HH 34 jet and counterjet is seen more clearly." " We have carried out paraboloidal fits to the emission peaks of the knots along the outflow axis, determining the positions of the peaks with an error of z0.2 pix. —0"".12."," We have carried out paraboloidal fits to the emission peaks of the knots along the outflow axis, determining the positions of the peaks with an error of $\approx 0.2$ pix. $= 0''.12$." " Through this procedure, we obtain the positions and of the 7 knots along the jet and the counterjet x;(respectively)."," Through this procedure, we obtain the positions $x_j$ and $x_{cj}$ of the 7 knots along the jet and the counterjet (respectively)." "3ο] The position of the source is not so well determined, because the image of the source is partially saturated, and has a complex point spread function."," The position of the source is not so well determined, because the image of the source is partially saturated, and has a complex point spread function." " Because of this, we have estimated the position of the source as the average of the coordinates of the seven knots along the jet and the counterjet."," Because of this, we have estimated the position of the source as the average of the coordinates of the seven knots along the jet and the counterjet." À paraboloidal fit to the emission of the region around the source actually results in a similar position (with offsets of ~0.2 pix along and z1 pix across the jet axis with respect to the average position of the ensemble of knots)., A paraboloidal fit to the emission of the region around the source actually results in a similar position (with offsets of $\approx 0.2$ pix along and $\approx 1$ pix across the jet axis with respect to the average position of the ensemble of knots). " In Figure 3, we plot the positions x; of the consecutive knots along the counterjet as a function of the positions of the corresponding knots along the jet."," In Figure 3, we plot the positions $x_{cj}$ of the consecutive knots along the counterjet as a function of the positions $x_j$ of the corresponding knots along the jet." This figure x;shows the remarkable symmetry (with respect to the position of the source) of the knots along the jet and the counterjet., This figure shows the remarkable symmetry (with respect to the position of the source) of the knots along the jet and the counterjet. " In Figure 3, we also plot the offsets Ax=— (between the positions of the corresponding jet/counterjet|x;πο] knot pairs) as a function of r;."," In Figure 3, we also plot the offsets $\Delta x=|x_j-x_{cj}|$ (between the positions of the corresponding jet/counterjet knot pairs) as a function of $x_j$." " The first three knots have monotonically growing offsets, with Ax=0"".11—0"".44 (ranging from ~1—4 times the measurement error, see above)."," The first three knots have monotonically growing offsets, with $\Delta x = 0''.11\to 0''.44$ (ranging from $\sim 1\to 4$ times the measurement error, see above)." " The four knots further away from the source generally have larger offsets, with a top value Az—1"".57 for the 6th knot out from the source."," The four knots further away from the source generally have larger offsets, with a top value $\Delta x=1''.57$ for the 6th knot out from the source." " The resulting Ax vs. dependence therefore has low offsets close to the source, x;and increasingly large (and"," The resulting $\Delta x$ vs. $x_j$ dependence therefore has low offsets close to the source, and increasingly large (and" times the stellar mass resolution).,times the stellar mass resolution). Lhe profiles do not show any variation if we change the threshold. stellar mass [or selecting galaxies., The profiles do not show any variation if we change the threshold stellar mass for selecting galaxies. The current choice of stellar mass is an optimization between resolution elements and statistics., The current choice of stellar mass is an optimization between resolution elements and statistics. Phe profiles are normalized to the mean number density of the corresponding species (satellite AGNdark matter/ satellite ealaxies) within fous (e.g...2)..," The profiles are normalized to the mean number density of the corresponding species (satellite AGN/dark matter/ satellite galaxies) within $R_{200}$ \citep[e.g.,][]{n&k05}." We also fit NEW. profile (2). to the AGN. radial distribution., We also fit NFW profile \citep{nfw97} to the AGN radial distribution. We fit the profiles for different concentration parameters ancl caleulate the corresponding P values., We fit the profiles for different concentration parameters and calculate the corresponding P values. At all redshifts our data strongly clisfavors the null hypothesis and the NEW profile is ruled out at 30., At all redshifts our data strongly disfavors the null hypothesis and the NFW profile is ruled out at $3\sigma$. We note that the AGN are more centrally concentrated than dark matter and galaxics., We note that the AGN are more centrally concentrated than dark matter and galaxies. The reason that we see an enhanced. population of AGN at the center of the halo compared to galaxies is because of the merging process of black holes., The reason that we see an enhanced population of AGN at the center of the halo compared to galaxies is because of the merging process of black holes. When two ealaxies merge there exists a time lag between merging ealaxies and the merging of AGN that reside in them., When two galaxies merge there exists a time lag between merging galaxies and the merging of AGN that reside in them. This time lag is due to the time it takes for the satellite AGN to fall in to the halo center where it can merge with the central AGN., This time lag is due to the time it takes for the satellite AGN to fall in to the halo center where it can merge with the central AGN. After the two galaxies merge the time that it takes for the AGN to merge can then be further allected by the eas content of these ealaxies., After the two galaxies merge the time that it takes for the AGN to merge can then be further affected by the gas content of these galaxies. ? measure the racial profile of radio sources in clusters and show that it is consistent with an NEW profile with a concentration of 25., \citet{l&m07} measure the radial profile of radio sources in clusters and show that it is consistent with an NFW profile with a concentration of $25$. 2 study the racial distribution of N-rav. selected AGN) in. clusters and find that AGN with N-ray luminosities above 1077 ergs/s show stronger central concentration than cluster host galaxies., \citet{martinietal07} study the radial distribution of X-ray selected AGN in clusters and find that AGN with X-ray luminosities above $10^{42}$ ergs/s show stronger central concentration than cluster host galaxies. However. a bigger sample with Lyz107 ergs/s (closer to our sample of ACN) does not show any stronger evidence of central concentration: dillerent. from what we observe in simulation.," However, a bigger sample with ${\rm L_{X}} \geq 10^{41}$ ergs/s (closer to our sample of AGN) does not show any stronger evidence of central concentration; different from what we observe in simulation." In lll we show the relation between stellar mass anc AGN luminosity at z=1.0., In 11 we show the relation between stellar mass and AGN luminosity at $z=1.0$. The stellar mass is computed. within a spherical region of radius 90 kpe surrounding the black hole., The stellar mass is computed within a spherical region of radius $30$ kpc surrounding the black hole. We selected. dillerent. spatial scales to compute the stellar mass., We selected different spatial scales to compute the stellar mass. Phe values converge between radii of 25 kpe to 30 kpe ancl hence we chose 30 kpe to be the relevant radius for computing the stellar mass content in AGN host galaxies., The values converge between radii of $25$ kpc to $30$ kpc and hence we chose $30$ kpc to be the relevant radius for computing the stellar mass content in AGN host galaxies. The black points represent central. AGN ancl the red open circles show the satellite distribution., The black points represent central AGN and the red open circles show the satellite distribution. In the case of central ACIN the stellar mass for more luminous AGN is generally higher., In the case of central AGN the stellar mass for more luminous AGN is generally higher. AGN will have higher Luminosity when the accretion rate is high. which is more likely when the gas density is high.," AGN will have higher luminosity when the accretion rate is high, which is more likely when the gas density is high." Also when the gas density is high the cooling rate will be higher and hence there will be more stars., Also when the gas density is high the cooling rate will be higher and hence there will be more stars. So in general higher density will correspond to high accretion rates of GN and higher stellar mass., So in general higher density will correspond to high accretion rates of AGN and higher stellar mass. For satellite AGN this trend is very weak., For satellite AGN this trend is very weak. But even for satellite AGN if we consider a luminosity selected sample we will svstematicallv choose AGN with higher stellar mass., But even for satellite AGN if we consider a luminosity selected sample we will systematically choose AGN with higher stellar mass. Also in 33 we see that ACN with higher stellar mass content tend to reside in the central regions of the halos., Also in 3 we see that AGN with higher stellar mass content tend to reside in the central regions of the halos. This can potentially increase the higher concentration of AGN seen in, This can potentially increase the higher concentration of AGN seen in (SD) phases (Sterkenetal.1997).. might be very small for D416.,"(SD) phases \cite{ste97}, might be very small for B416." They might well have been overlooked. in the past. since little or any photometric data. beside those in this work. exist for the star.," They might well have been overlooked in the past, since little or any photometric data, beside those in this work, exist for the star." It may well also be that the 0.17 maenituce cdillerence in Clear that we measured. between 1987 and 1997 is indicative of a small scale SD phase of D416. as expected in low Luminosity LBVs.," It may well also be that the 0.17 magnitude difference in Clear that we measured between 1987 and 1997 is indicative of a small scale SD phase of B416, as expected in low luminosity LBVs." On the other hand. this difference in magnitude can be just a fraction of a Larger amplitude SD phase. that might have occured between those two vears or even before 1987.," On the other hand, this difference in magnitude can be just a fraction of a larger amplitude SD phase, that might have occured between those two years or even before 1987." We therefore believe that it is suitable to classify DAI6 as a true LBY, We therefore believe that it is suitable to classify B416 as a true LBV. In the previous section we argued that according to our observations and the available archived data. it is very likely hat B416 is a relatively faint LBV with a mass of the order of 20M; (Llumphrevsand.Davidson1994).," In the previous section we argued that according to our observations and the available archived data, it is very likely that B416 is a relatively faint LBV with a mass of the order of $_{\sun}$ \cite{hum94}." . From here it is à straightforward. step to describe the small. amplitude ight variations that we observe as the microvariations of his LBY star., From here it is a straightforward step to describe the small amplitude light variations that we observe as the microvariations of this LBV star. Phe period 7S8 day is well within the range of quasi-periods measured in known LBs (see Brevsacher 997 and Lamers et al., The period $\sim$ 8 day is well within the range of quasi-periods measured in known LBVs (see Breysacher 1997 and Lamers et al. 1998)., 1998). These microvariations. also observed in à Cveni type supergiants. are mainly irregular or quasi-periodic (Lamersetal.1998). and are attributed to »ulsational instabilities of the LBV (or blue supergiant) cue o the increase of Luminosity up to and. near the Eddington uminositv.," These microvariations, also observed in $\alpha$ Cygni type supergiants, are mainly irregular or quasi-periodic \cite{lam98} and are attributed to pulsational instabilities of the LBV (or blue supergiant) due to the increase of luminosity up to and near the Eddington luminosity." “Phe observed microvariations in DA416 increase in amplitude with decreasing wavelength., The observed microvariations in B416 increase in amplitude with decreasing wavelength. This behaviour is observed in LDVs in quiescence. since during that stage of he SD phase the star is more compact and hot. giving it a Xue colour (Lamersetal.1998).," This behaviour is observed in LBVs in quiescence, since during that stage of the SD phase the star is more compact and hot, giving it a blue colour \cite{lam98}." . Periodic microvariations were recently reported. in the LBV LID 5980. (Breysacher 1997).., Periodic microvariations were recently reported in the LBV HD 5980 \cite{bre97}. This detection was based on observations that were carried out during one observational season (between 1995 and. 1996)., This detection was based on observations that were carried out during one observational season (between 1995 and 1996). Our data indicate. periodic microvariations of D416. which are coherent and stable over a whole decade.," Our data indicate periodic microvariations of B416, which are coherent and stable over a whole decade." We conclude that D416 is an LBY of the rather fainter class It 71., We conclude that B416 is an LBV of the rather fainter sub-class R 71. Ht should therefore be added to the list of 32 known LDVs (Dohannan1997). as the fifth known LDV in AI33 and could be placed near I. 71 on the LER diagram.," It should therefore be added to the list of 32 known LBVs \cite{boh97} as the fifth known LBV in M33 and could be placed near R 71 on the HR diagram." The detected periodic light variation is evidence for periodic and stable microvariations found for the first time in an LDV., The detected periodic light variation is evidence for periodic and stable microvariations found for the first time in an LBV. A continued. photometric followup of this Interesting star is required. in order to look for the anticipated SD phase and to keep an eve on the clock of the microvariations., A continued photometric followup of this interesting star is required in order to look for the anticipated SD phase and to keep an eye on the clock of the microvariations. A dense spectroscopic monitoring Is also required in order to correlate the spectra with the microvariations. while high resolution spectroscopy might detect the LBV circumstellar nebula. which is expected. around LBVs due to a large amount of mass loss (HumphreysancDavidson1994).," A dense spectroscopic monitoring is also required in order to correlate the spectra with the microvariations, while high resolution spectroscopy might detect the LBV circumstellar nebula, which is expected around LBVs due to a large amount of mass loss \cite{hum94}." . We would like to thank Noah Broseh who helped. in the coordination of the initial 1986/87. Wise Observatory photometric survey of luminous stars in M33. ancl Anna LUcller who participated in it and performed. most of its ata reduction.," We would like to thank Noah Brosch who helped in the coordination of the initial 1986/87 Wise Observatory photometric survey of luminous stars in M33, and Anna Heller who participated in it and performed most of its data reduction." We acknowledge the assistance of Gaghik ‘Tovmassian and Camron Hastings in obtaining some of rw APO spectra., We acknowledge the assistance of Gaghik Tovmassian and Camron Hastings in obtaining some of the APO spectra. We also thank Shai WKaspi anc Liliana Formigeini for their assistance in the photometric ancl spectroscopic reduction procedures., We also thank Shai Kaspi and Liliana Formiggini for their assistance in the photometric and spectroscopic reduction procedures. We are grateful to WO stall members Ezra Alashal. που Loinger. Sami )on-Giügi and John Dan for their crucial contribution to us project.," We are grateful to WO staff members Ezra Mashal, Friedel Loinger, Sami Ben-Gigi and John Dan for their crucial contribution to this project." This research has made use of the SIMDBAD database. operated at CDS. France.," This research has made use of the SIMBAD database, operated at CDS, France." Astronomy at the WO is supported. by erants from the Israel Science Foundation., Astronomy at the WO is supported by grants from the Israel Science Foundation. We would like to thank the referee for his useful comments., We would like to thank the referee for his useful comments. AA)) spectra.,) spectra. The spectra presented here are the IUE newly extracted spectra (INES) that were taken from the INES access catalogue publicly available on the WWW at http://ines.vilspa.esa.es/mes/. This site contains also an important documentation including the quality flag deseription., The spectra presented here are the IUE newly extracted spectra (INES) that were taken from the INES access catalogue publicly available on the WWW at: http://ines.vilspa.esa.es/ines/. This site contains also an important documentation including the quality flag description. The INES flux extraction algorithm. (Rodrígguez-Pascual et al. 1998)), The INES flux extraction algorithm guez-Pascual et al. \cite{RSW98}) ) was built to correct some problems found in the spectra of the IUE final archive (IUEFA) reduced with the NEWSIPS software., was built to correct some problems found in the spectra of the IUE final archive (IUEFA) reduced with the NEWSIPS software. The comparison of IUE flux extraction by INES and NEWSIPS shows that the INES spectra are generally more reliable than the NEWSIPS spectra in difficult conditions (Schartel Skillen 1998)., The comparison of IUE flux extraction by INES and NEWSIPS shows that the INES spectra are generally more reliable than the NEWSIPS spectra in difficult conditions (Schartel Skillen \cite{SS98}) ). " The ultraviolet (UV) continuum light curves (see Table 2)) were extracted from eight ccontinuum bands centered atΑΑ.,AA..AA.. AA.. ΑΑ., AA.. aand ((see Fig. 5)."," The ultraviolet (UV) continuum light curves (see Table \ref{tabirouv}) ) were extracted from eight continuum bands centered at, and (see Fig. \ref{iue}) )." We considered only the wavelength bins with a quality flag of zero., We considered only the wavelength bins with a quality flag of zero. The spectra having no such bin in a continuum band are therefore not included in the corresponding light curve (e.g. SWPOI365LL)., The spectra having no such bin in a continuum band are therefore not included in the corresponding light curve (e.g. SWP01365LL). " The flux density F, and its uncertainty AΕν in a bband were defined as where F,, and AF), are respectively the INES flux density and its uncertainty at the frequency v;. and .e is a correction factor."," The flux density $F_{\nu}$ and its uncertainty $\Delta\,F_{\nu}$ in a band were defined as where $F_{\nu_i}$ and $\Delta\,F_{\nu_i}$ are respectively the INES flux density and its uncertainty at the frequency $\nu_i$, and $x$ is a correction factor." " The factor .c is introduced to ensure that the average uncertainty E,A corresponds to the experimental value derived from all pairs of observations taken within one day."," The factor $x$ is introduced to ensure that the average uncertainty $\overline{\Delta\,F_{\nu}}$ corresponds to the experimental value derived from all pairs of observations taken within one day." The obtained values of .c reported in Table 4+ are not simply equal to one. because the bins used to calculate the fluxes are not independent from each other due to the oversampling of the IUE spectra.," The obtained values of $x$ reported in Table \ref{tabxiue} are not simply equal to one, because the bins used to calculate the fluxes are not independent from each other due to the oversampling of the IUE spectra." However. by calculating .« for a single INES bin. we obtain on average over the eight values given in Table 4 a value of + 00.36. which shows that the INES uncertainties for a single bin are in good agreement with the experimental values derived from consecutive spectra.," However, by calculating $x$ for a single INES bin, we obtain on average over the eight values given in Table \ref{tabxiue} a value of $\pm$ 0.36, which shows that the INES uncertainties for a single bin are in good agreement with the experimental values derived from consecutive spectra." Our estimation of the uncertainties gives average relative values.," Our estimation of the uncertainties gives average relative values," Thus far we have characterized the effects of oscillations in terms of the unperturbed core parameters.,Thus far we have characterized the effects of oscillations in terms of the unperturbed core parameters. " However, large-amplitude pulsations can dramatically alter the observed appearance of a core, with important consequences for the interpretation of starless core statistics."," However, large-amplitude pulsations can dramatically alter the observed appearance of a core, with important consequences for the interpretation of starless core statistics." " In Keto&Field (2005),, Ketoetal. (2006),, and Brodericketal.(2007) we showed how pulsations alter the molecular line profiles and widths."," In \citet{KetoField2005}, \citet{Keto2006}, and \citet{Broderick2007} we showed how pulsations alter the molecular line profiles and widths." " Here we how pulsations the apparent core column density exploreprofiles, X(R)."," Here we explore how pulsations modify the apparent core column density profiles, $\Sigma(R)$." " In this modifysection we study the of 21). finding that generally these are substantiallyrange asymmetric,perturbed frequently devolving into structures, and are biased towards azimuthally-manyaveraged peakedprofiles that are best fit with super-critical static isothermal "," In this section we study the range of perturbed $\Sigma(R)$, finding that generally these are substantially asymmetric, frequently devolving into many peaked structures, and are biased towards azimuthally-averaged profiles that are best fit with super-critical static isothermal configurations." "That is, stable, starless cores will typically configurations.appear to be strongly pulsatingasymmetric and super-critical if fit with a static BE model."," That is, stable, pulsating starless cores will typically appear to be strongly asymmetric and super-critical if fit with a static BE model." " To ascertain the typical observational consequences of the oscillating cores, we generate an ensemble of pulsating cores."," To ascertain the typical observational consequences of the oscillating cores, we generate an ensemble of pulsating cores." " We do this for each of the energy spectra described in Section 2.3 by setting the density to where the po(r) is the unperturbed density, o,;(r)Yr,(£) are the eigenfunctions and the 4,;,, are randomly densitydetermined perturbationphases, corresponding to a random realization of the oscillations."," We do this for each of the energy spectra described in Section \ref{sec:TOES} by setting the density to where the $\rho_0(\bmath{r})$ is the unperturbed density, $\rho_{nl}(r) Y_{lm}(\bmath{\hat{r}})$ are the density perturbation eigenfunctions and the $\Phi_{nlm}$ are randomly determined phases, corresponding to a random realization of the particular oscillations." " realization for which p(r) vanishes particularanywhere is discarded, Anythough this has little effect the statistical since the distribution of the various uponobservables is nearly quantitiesidentical for the accepted and discarded cores."," Any realization for which $\rho(\bmath{r})$ vanishes anywhere is discarded, though this has little effect upon the statistical quantities since the distribution of the various observables is nearly identical for the accepted and discarded cores." " We do not vary the E,;,,, nor do we consider different for underlyingconcreteness a stable equilibriumconfiguration, near configurations,critical, with choosing¢=14."," We do not vary the $E_{nlm}$, nor do we consider different underlying equilibrium configurations, choosing for concreteness a stable configuration, near critical, with $\zeta=14$." " Since we vary only the phases, ®,;,, we are not producing a complete ensemble; such an ensemble would necessarily have variations in the amplitudes of the oscillations, the total"," Since we vary only the phases, $\Phi_{nlm}$, we are not producing a complete ensemble; such an ensemble would necessarily have variations in the amplitudes of the oscillations, the total" Dokkum et 11998b).,Dokkum et 1998b). Hence for each galaxy we approximate the evolution of the complex population by that of a single age population formed at £2f... with For f.~1. the stellar population is dominated by a burst at the end of the star formation history. and for f.~0 the population is dominated by a burst at the start of the star formation history.," Hence for each galaxy we approximate the evolution of the complex population by that of a single age population formed at $t=t_*$, with For $\fstar\approx 1$, the stellar population is dominated by a burst at the end of the star formation history, and for $\fstar \approx 0$ the population is dominated by a burst at the start of the star formation history." If the star formation rate is approximately constant from f=Kya to f£—Γκορ. then f.~0.5.," If the star formation rate is approximately constant from $t=\tstart$ to $t=\tstop$, then $\fstar \approx 0.5$." We tested the accuracy of our approach by calculating the luminosity and color evolution of galaxies with complex star formation histories (e.g.. an exponentially declining star formation rate followed by a star burst). and comparing the results to predictions from single burst models with the same values of f..," We tested the accuracy of our approach by calculating the luminosity and color evolution of galaxies with complex star formation histories (e.g., an exponentially declining star formation rate followed by a star burst), and comparing the results to predictions from single burst models with the same values of $f_*$ ." After transformation to early-type galaxy (Le. »1.5 GGyr after star formation has ceased) our approximation of luminosity and color evolution ts accurate to a few percent.," After transformation to early-type galaxy (i.e., $>1.5$ Gyr after star formation has ceased) our approximation of luminosity and color evolution is accurate to a few percent." Three possible star formation histories of early-type galaxies are shown in reffstar.plot.., Three possible star formation histories of early-type galaxies are shown in \\ref{fstar.plot}. The model with £.=0.7 has a star burst at the end of its star formation history. and may be appropriate for spiral galaxies falling into clusters. or mergers.," The model with $f_*=0.7$ has a star burst at the end of its star formation history, and may be appropriate for spiral galaxies falling into clusters, or mergers." Although these histories are quite complex. >1.5 GGyr after star formation has ceased their evolution is similar to that of single age stellar populations formed at£=ffCIfan. ," Although these histories are quite complex, $\gtrsim 1.5$ Gyr after star formation has ceased their evolution is similar to that of single age stellar populations formed at $t_* = \fstar \tstop + (1-\fstar) \tstart$. }}" Our parameterization allows straightforward computation of luminosities and. colors of galaxies. because the luminosity evolution of a single age stellar population can be approximated by a power law (e.g.. Tinsley 1980. Worthey 1994).," Our parameterization allows straightforward computation of luminosities and colors of galaxies, because the luminosity evolution of a single age stellar population can be approximated by a power law (e.g., Tinsley 1980, Worthey 1994)." Therefore. to good approximation. The coefficient «+ depends on the passband. the IMF. and the metallicity.," Therefore, to good approximation, The coefficient $\kappa$ depends on the passband, the IMF, and the metallicity." In this paper we will limit the discussion to rest frame B band luminosities. and rest frame U—B colors.," In this paper we will limit the discussion to rest frame $B$ band luminosities, and rest frame $U-B$ colors." Our results can easily be expressed in other (rest frame) bands., Our results can easily be expressed in other (rest frame) bands. " The Worthey (1994) models give #,20.91 and κ—1.07 for solar metallicity and a Salpeter (1955) IMF.", The Worthey (1994) models give $\kappa_B = 0.91$ and $\kappa_U=1.07$ for solar metallicity and a Salpeter (1955) IMF. The color evolution can be approximated by Expressed in magnitudes. color and luminosity evolution are related through in these models.," The color evolution can be approximated by Expressed in magnitudes, color and luminosity evolution are related through in these models." The evolution of the mean color and scatter in the color will therefore be similar to the scaled evolution of the mean M/L ratio and its scatter., The evolution of the mean color and scatter in the color will therefore be similar to the scaled evolution of the mean $M/L$ ratio and its scatter. In the following. we use Monte-Carlo simulations to calculate model predictions for given values of Top. f.. and faa," In the following, we use Monte-Carlo simulations to calculate model predictions for given values of $\taustop$, $\fstar$, and $\tstart$." This approach has the advantage that the mean and scatter in colors and luminosities at a given time can be computed using the same methods as for the observations., This approach has the advantage that the mean and scatter in colors and luminosities at a given time can be computed using the same methods as for the observations. In the simulations. all galaxies start out as star forming objects at f— fag ," In the simulations, all galaxies start out as star forming objects at $t=\tstart$ ." Each galaxy is assigned a value for fyp. the time when star formation ceases.," Each galaxy is assigned a value for $\tstop$, the time when star formation ceases." " Thedistribution of A, is given by reffirst.eq.. with boundary condition 0«f,<0.9fo. with fo the present age of the Universe."," Thedistribution of $\tstop$ is given by \\ref{first.eq}, with boundary condition $0<\tstop<0.9 \t0$, with $\t0$ the present age of the Universe." At each timestep ¢. objects which satisfy the condition {ορ+0.1%441.," We consider a typical case with $\mu_c > \mu_e > 1$." " I£ M ts the relative macro-amplification factor between images | and 2. we have Using these expressions with A=My, and ji=qi. in Eqs."," If $M$ is the relative macro-amplification factor between images 1 and 2, we have Using these expressions with $A = M \mu_c$ and $\mu = \mu_c$ in Eqs." " 4 and 5. we find With jj.>fled. Fay>0 and Fay,>0."," 4 and 5, we find With $\mu_c > \mu_e > 1$ $ F_M > 0$ and $F_{M\mu}> 0$." " As expected. Py contains the emission profile £, unaffected by microlensing. Fay, contains the continuum. and both F3; and Fs, contain a part of the micro-amplified emission profile E,."," As expected, $F_M$ contains the emission profile $E_b$ unaffected by microlensing, $F_{M\mu}$ contains the continuum, and both $F_M$ and $F_{M\mu}$ contain a part of the micro-amplified emission profile $E_a$." " Up to a sealing factor. the micro-amplified profile E, is given by Fa,—Fe."," Up to a scaling factor, the micro-amplified profile $E_a$ is given by $F_{M\mu} - F_c$." ‘ To effectively compute Eqs., To effectively compute Eqs. 4 and 5 and to determine the profile of Fij4. we need to know M (or ji).," 4 and 5 and to determine the profile of $F_{M\mu}$, we need to know $M\,$ (or $\mu_c$ )." Practically. we consider M as a free parameter in Eq.," Practically, we consider $M$ as a free parameter in Eq." " 5 and. by varying it. we adopt the value of M closest to A such that Fa,(M)ΣΕ at all wavelengths (Eq."," 5 and, by varying it, we adopt the value of $M$ closest to $A$ such that $F_{M\mu}(M) \geq F_c$ at all wavelengths (Eq." 7)., 7). This ts equivalent to adopt a value of i. as close as possible to 1. thus ensuring that the macro- and micro-amplifications are best separated (see also Sluse et al. 2007)).," This is equivalent to adopt a value of $\mu_c$ as close as possible to 1, thus ensuring that the macro- and micro-amplifications are best separated (see also Sluse et al. \cite{slu07}) )." Unless M= A. this method provides a reasonably accurate estimate of M. and then of µ..," Unless $M \simeq A$ , this method provides a reasonably accurate estimate of $M$ , and then of $\mu_c$ ." Indeed. denoting the free parameter M' and using expressions À.1 and A.2 in Eq.," Indeed, denoting the free parameter $M'$ and using expressions A.1 and A.2 in Eq." " 5. we write such that Fi4,CM')>Εν is satisfied when with If E,= Oand Ejz0 at some wavelengths. then pinin=1 and M=M'."," 5, we write such that $F_{M\mu}(M') \geq F_c$ is satisfied when with If $E_a=0$ and $E_b \ne 0$ at some wavelengths, then $\mu_{\rm min} =1$ and $M = M'$." This means that M can be derived empirically when at least a portion of the observed emission line profile Εν is not micro-amplified., This means that $M$ can be derived empirically when at least a portion of the observed emission line profile $F_e$ is not micro-amplified. In fact this is formally always true., In fact this is formally always true. " Indeed. i£ 454,#1. the whole profile would be micro-amplified by μήν 1.8. macro-amplified by Mgr; instead of M. which ts inconsistent with an optimal separation of macro- andlensing."," Indeed, if $\mu_{\rm min} \neq 1$, the whole profile would be micro-amplified by $\mu_{\rm min}$ i.e. macro-amplified by $M\mu_{\rm min}$ instead of $M$, which is inconsistent with an optimal separation of macro- and." . It should nevertheless be kept in mind that ifthe emission line is amplified just like the continuum.microlensing cannot be distinguished from macrolensing.," It should nevertheless be kept in mind that ifthe emission line is amplified just like the continuum,microlensing cannot be distinguished from macrolensing." " Fortunately. it is realistic to assume that a portion -even a verysmall one- ofthe observedemission line profile Εν, is not micro-amplified"," Fortunately, it is realistic to assume that a portion –even a verysmall one– ofthe observedemission line profile $F_e$ is not micro-amplified" So keep themission withthe 159 M$ MIDEX budget. (cheap) Sun- svuchronous Polar,"If we assume planets down to Uranus/Neptune mass, we expect to find roughly 21,000 planetary transits with periods roughly up-to 30 days." orbitsuch thoseofIRAS. COROT? and wwould have(wo viewports (hesame focal plane.However. significant," The brightest subset of 10,000 planets will have 3-color photometry at the 2 mmag level, and these are the systems that can most likely be classified photometrically as transiting planets." witha photometric mission. sothat wedo notrequire," We compared our mission with the, and missions to arrive at a reasonable cost estimate." the exquisite basic angle stability. as requiredby LEAVIT ssastrometric cousins.," Our cost model takes into account the overall weight, launch costs, mirror size, number of CCDs, electronics, instrument weight, bus mass, attitude control and science operations." The mirror is rectangular andmeas," We define scaling relations that result in good estimates for the, and budgets." ures 12x55 cm witha local lengthof5 meters., This model results in a total cost for the mission of 159 (FY2005). play (6.8. tha develops a tail containing a small number «ft large prooplancts.," \citep[e.g.][]{S72,G78,WS89,KI96} that develops a tail containing a small number of large protoplanets." It is however not always clear what fraction of the tota llass participates i us runaway erowtli aud what xotoplanet size cdistribiion such ταmaway erowtli en«Ss rlse fo (Lee2000:Malvslikiu&Coocuan 2001).," It is however not always clear what fraction of the total mass participates in this runaway growth and what protoplanet size distribution such runaway growth gives rise to \citep{MHL00,MG01}." . lutjs paper we address both of these questious., In this paper we address both of these questions. Iu the folkwine SCC‘tions. we discuss runaway erowth in the couext of the kauoer belt. which is an ideal laboratory ο test our results. since it is a remnant of the primordial Solar svstem. wwere planet formation never reached completion.," In the following sections, we discuss runaway growth in the context of the Kuiper belt, which is an ideal laboratory to test our results, since it is a remnant of the primordial Solar system, where planet formation never reached completion." The results however. also apply to runaway erowth during planet formation am erowtli iu debris disk. as long as gas pavs no significant role in the accretion and damping of the velocity dispersion.," The results however, also apply to runaway growth during planet formation and growth in debris disk, as long as gas plays no significant role in the accretion and damping of the velocity dispersion." The Kuiper belt consists of a cisk of icy bodies ocated at the outskirts of our planctary svsteni. just besmad the orbit of Neptune and contaius soue of the least pixπο bodies in our system.," The Kuiper belt consists of a disk of icy bodies located at the outskirts of our planetary system, just beyond the orbit of Neptune and contains some of the least processed bodies in our Solar system." Moivated bv tlic discovery of the first Ikuiper Dolbelt veraοἱject (Jewitt&Lint!993) after Pluto aud Charon. se erou5 conducted large scale surveys to characterize the [xaiper belt.," Motivated by the discovery of the first Kuiper belt object \citep{JL93} after Pluto and Charon, several groups conducted large scale surveys to characterize the Kuiper belt." These efforts led to the discovery of iore than 1200 objects in the luper belt to dato., These efforts led to the discovery of more than 1200 objects in the Kuiper belt to date. The Isuiper belt size distribution contaims manv important clues concerning the formation, The Kuiper belt size distribution contains many important clues concerning the formation version of the method of fitting with a Gaussian fiction that has been couvolved with a 106 kin tophat function that was eimploved in Dixonetal.(2001). and later papers (nethod #2).,"version of the method of fitting with a Gaussian function that has been convolved with a 106 km $^{-1}$ tophat function that was employed in \citet{dixon_etal_01} and later papers (method $\#2$ )." The modification is to add a second tophat-convolyed Caussian to model the second order aairglow feature that appears at 1031 in the daytime data., The modification is to add a second tophat-convolved Gaussian to model the second order airglow feature that appears at 1031 in the daytime data. See Figure 2 for the fitting results., See Figure \ref{fig:vansplot} for the fitting results. Both methods cleanly separate the 11032 ffeature from the davtime 1031 ffeature., Both methods cleanly separate the 1032 feature from the daytime 1031 feature. Table 2) preseuts the intensity micasurements., Table \ref{table:intensityresults} presents the intensity measurements. We average the measurements. vielding an observed intensity in the 11032 πιο of 23104630 LU.," We average the measurements, yielding an observed intensity in the 1032 line of $2340 \pm 630$ LU." To place the 11032 intensity alone our off-cloud sight line iuto contest. we compare it with 11032 Hutensitics measured for other high-latitude lines of seht.," To place the 1032 intensity along our off-cloud sight line into context, we compare it with 1032 intensities measured for other high-latitude lines of sight." Using archival ddata. Dixonctal.(2006) and Dison&Saukrit(2008) have searched for diffuse pphotous along roughly 2300 lines of sight.," Using archival data, \citet{dixon_etal_06} and \citet{dixon_sankrit_08} have searched for diffuse photons along roughly 300 lines of sight." Here we consider the 51 sight lines iu their sample (plus E12102) with Calactie latitudes of [b]220° and orbital-night exposure times exceeding 18 κου., Here we consider the 54 sight lines in their sample (plus E12402) with Galactic latitudes of $|b| > 20\degr$ and orbital-night exposure times exceeding 18 ksec. This sample is complete in the seuse that any ciission brighter thau 2000 LU would have been detected im au 18 ksec night-time exposure., This sample is complete in the sense that any emission brighter than 2000 LU would have been detected in an 18 ksec night-time exposure. Within this sample. 63% have statisticallv-sienificaut (1.0.. > 20) iuteusities of 1032 pphotous. the ereatest of which is 5500 LU.," Within this sample, $\%$ have statistically-significant (i.e., $> 2\sigma$ ) intensities of 1032 photons, the greatest of which is 5500 LU." " If uull detections are treated as having zero fiux aud a 10 error. then the median and mean intensities in the 1032 line are 2100 aud 15800 LU. respectively, while the standard deviation about the mean is 1620 LU."," If null detections are treated as having zero flux and a 1 $\sigma$ error, then the median and mean intensities in the 1032 line are 2100 and 1800 LU, respectively, while the standard deviation about the mean is 1620 LU." Our cloud sight line. with an observed 1032 Hutensity of 2310+630 LU. lies within oue sigma of the mean. so it is not at all unusual.," Our off-cloud sight line, with an observed 1032 intensity of $2340\pm 630$ LU, lies within one sigma of the mean, so it is not at all unusual." Our measurements of the weaker LLO38 ‘feature were not as sound as our measurements of the stronger 1032 ‘feature., Our measurements of the weaker 1038 feature were not as sound as our measurements of the stronger 1032 feature. " The 1038 ‘feature sits to the right of the 1057 line and to the left of the aairelow feature. making it mipossible to determine the vackeround coutimmiun accurately,"," The 1038 feature sits to the right of the 1037 line and to the left of the airglow feature, making it impossible to determine the background continuum accurately." For this reason. we resent neither | night nor uielt-only 1005 nnieasurements.," For this reason, we present neither $+$ night nor night-only 1038 measurements." We do. however. present nieasuremoenuts from our search for a second 11032 feature.," We do, however, present measurements from our search for a second 1032 feature." This search was motivated by the observation of a weak intermediate velocity (τον=112 kan sec3) 'eature in the LAB survey of galacticL., This search was motivated by the observation of a weak intermediate velocity $V_{LSR} = -112$ km $^{-1}$ ) feature in the LAB survey of galactic. If infalline eas at this LSR velocity was accompanied byVL. then the strouecr line in its doublet would appear at a wavelenetli of 1031.10. Hn our heliocentric restframe spectra.," If infalling gas at this LSR velocity was accompanied by, then the stronger line in its doublet would appear at a wavelength of 1031.49 in our heliocentric restframe spectra." We searched for such a feature ina 0.36 wwide window (corresponding to the width of the LWRS aperture) in the mielt-ouly data., We searched for such a feature in a 0.36 wide window (corresponding to the width of the LWRS aperture) in the night-only data. We did not search for the feature iu the dav|might data. because it would have overlapped with the second order ffeature.," We did not search for the feature in the day+night data, because it would have overlapped with the second order feature." Using method #1. we found a statistically insiguificant excess intensity of 210 + 180 LU.," Using method $\#1$, we found a statistically insignificant excess intensity of 210 $\pm$ 480 LU." We exmuumed the on-cloud data. as well.," We examined the on-cloud data, as well." These spectra were of very poor quality. because of the short observation time (51LL seconds of day|aight data. including 2056 seconds of night-oulv data.)," These spectra were of very poor quality, because of the short observation time (5144 seconds of $+$ night data, including 2056 seconds of night-only data.)" Neither ucthod #1 nor method #2 could fud cussion features around 1032 or 1038Α., Neither method $\#1$ nor method $\#2$ could find emission features around 1032 or 1038. . We were able to use method #1 to detexiuiue and subtract the continui aud then neasure the residual intensity within the waveleneth ranee where the 1032 ‘feature was expected to be fouud. based on the location of the 1032 feature in the offcloud spectra taken from the | nieht data.," We were able to use method $\#1$ to determine and subtract the continuum and then measure the residual intensity within the wavelength range where the 1032 feature was expected to be found, based on the location of the 1032 feature in the off-cloud spectra taken from the $+$ night data." This method vielded a measured intensity of -213 + 1601 LU. where the uegative sigu indicates that this regiou of the spectrum has fewer counts than the fitted coutiuuuu.," This method yielded a measured intensity of -243 $\pm$ 1604 LU, where the negative sign indicates that this region of the spectrum has fewer counts than the fitted continuum." " Method #2 yielded 3 σ upper linits of 3090 aud 2060 LU from the |night and night-ounlv data. respectively,"," Method $\#2$ yielded 3 $\sigma$ upper limits of 3090 and 2060 LU from the $+$ night and night-only data, respectively." Iu both cases. the uncertainties are too huge to constrain our conceptions of the iuterstellar πουπια.," In both cases, the uncertainties are too large to constrain our conceptions of the interstellar medium." Iu order to deteriunue the velocities using method #1. the helioceutric spectra were refit using a Caussian for the feature in question aud a low-order polynomial for the contimuu.," In order to determine the velocities using method $\#1$, the heliocentric spectra were refit using a Gaussian for the feature in question and a low-order polynomial for the continuum." Method: #2 also vielded velocity estimates., Method $\#2$ also yielded velocity estimates. Iu both cases. the reference frames of the analyzed spectra were heliospheric.," In both cases, the reference frames of the analyzed spectra were heliospheric." The resulting velocities have been converted to the LSR reference frame by the addition of 16.73 kau +. (, The resulting velocities have been converted to the LSR reference frame by the addition of 16.73 km $^{-1}$. ( See Table 3 for the mcasurement results.),See Table \ref{table:velocityresults} for the measurement results.) The wavelength scale is accurate to 10 km 1 (Sheltonctal.2001)., The wavelength scale is accurate to $\sim10$ km $^{-1}$ \citep{shelton_etal_01}. . For optically thin plasmas. the 1038 Tine is half as strong as the 1032 line.," For optically thin plasmas, the 1038 line is half as strong as the 1032 line." Asstuning this ratio. the doublet intensity becomes 3500£910 LU (Table 1)).," Assuming this ratio, the doublet intensity becomes $3500 \pm 940$ LU (Table \ref{table:allintensities}) )." The observed imtensitv is due to photous enütted iu the halo but attenuated by, The observed intensity is due to photons emitted in the halo but attenuated by this strange velocity feature that comprises Slit 4 Ixnots 1-3 will be presented.,this strange velocity feature that comprises Slit 4 Knots 1-3 will be presented. New kinematical information has been obtained for three separate features of the 5g Carinae nebulosity., New kinematical information has been obtained for three separate features of the $\eta$ Carinae nebulosity. " “Phe implications for the ""outer shellof knots. the ""spike, and the care. will now be discussed along with consideration of the mechanisms that cause the ionization of the high-speed. ejecta."," The implications for the `outer shell'of knots, the `spike' and the `arc' will now be discussed along with consideration of the mechanisms that cause the ionization of the high-speed ejecta." " Wo the knots in the outer ""shell in Figs.", If the knots in the outer `shell' in Figs. " 1 35 form part of a coherent feature then it is firstly. notable that its centroid is olfset by z 12"" to the NE ol η Carinae.", 1 2 form part of a coherent feature then it is firstly notable that its centroid is offset by $\approx$ $^{\prime\prime}$ to the NE of $\eta$ Carinae. In any case a simple interpretation of this whole feature as a racially expanding irregular shell is apparently contracicted by the kinematical observations shown in Figs., In any case a simple interpretation of this whole feature as a radially expanding irregular shell is apparently contradicted by the kinematical observations shown in Figs. 3(8)-(c)., 3(a)-(c). This contradiction is epitomised by the profiles in the py array along Slits 1. 2 3 in Figs.," This contradiction is epitomised by the profiles in the pv array along Slits 1, 2 3 in Figs." 3(3).(b) (ο) respectively. which pass over what could be the edge of the outer ‘shell’.," 3(a),(b) (c) respectively, which pass over what could be the edge of the outer `shell'." 1n these arrays. certainly detected: velocity. features. which are bright in the Hu] lines. extend. all the way out to x 1P00kms * (ος.," In these arrays, certainly detected velocity features, which are bright in the [N ] lines, extend all the way out to $\approx$ $-$ 1200 $\kms$ (eg." see Slit 2 Woot 5) from the systemic racial velocity., see Slit 2 Knot 5) from the systemic radial velocity. Single profiles at the systemic radial velocity c 10 kn1513 would be expected. to characterise he edge of a simple. racially expanding shell.," Single profiles at the systemic radial velocity $\approx$ $-$ 10 $\kms$ ) would be expected to characterise the edge of a simple, radially expanding shell." Even more extreme bright knots are suggested out το. 1450km s (cg., Even more extreme bright knots are suggested out to $-$ 1450 $\kms$ (eg. sce Slit 3 Woot 6 and Sli 2 [xnot 10)., see Slit 3 Knot 6 and Slit 2 Knot 10). The complex profiles in the pv array in Fig., The complex profiles in the pv array in Fig. 3(a) from he knots along the north eastern edee of the outer shell. covered by Slit 1. exhibit approaching. radial velocities out oz 200 kms| [rom an extended region. as well as a component at the systemic radial velocity.," 3(a) from the knots along the north eastern edge of the outer shell, covered by Slit 1, exhibit approaching, radial velocities out to $\approx$ $-$ 200 $\kms$ from an extended region, as well as a component at the systemic radial velocity." " However. the knots in the north western quadrant. of the outer ‘shell’. covered also by Slit 1. emit the i] line [rom a region 1"" across whose profiles have EFWLIIMs of & 80 kms.1 but are displaced to radial velocities of zz: |250 kms with respect to the systemic radial velocity."," However, the knots in the north western quadrant of the outer `shell', covered also by Slit 1, emit the ] line from a region $^{\prime\prime}$ across whose profiles have FWHMs of $\approx$ 80 $\kms$ but are displaced to radial velocities of $\approx$ +250 $\kms$ with respect to the systemic radial velocity." Note that the nearby ‘lobe’ of the inner shell (identified in Fig., Note that the nearby `lobe' of the inner shell (identified in Fig. " 1) and the southern part of this shell (S Ridge in Walborn et al 1978) was shown in Paper 1 t0 emit. red-shifted line profiles out to 1400 Kms.* with respect to the systemic radial velocity (sce Slits 127N and 4.8 12""8 in lig."," 1) and the southern part of this shell (S Ridge in Walborn et al 1978) was shown in Paper 1 to emit red-shifted line profiles out to +400 $\kms$ with respect to the systemic radial velocity (see Slits $^{\prime\prime}$ N and 4, 8 $^{\prime\prime}$ S in fig." 5 of Paper 1)., 5 of Paper 1). Some of the present (ancl previous - see Papers 22 3) kinematical observations are then consistent with the “polar blowout’ model of Lester et al (1991) (and. its precursor. model in Paper 1 - see fig.," Some of the present (and previous - see Papers 1, 2 3) kinematical observations are then consistent with the `polar blowout' model of Hester et al (1991) (and its precursor model in Paper 1 - see fig." S(b))., 8(b)). What is loosely described as the outer ‘shell’ of knots in Fig., What is loosely described as the outer `shell' of knots in Fig. Lis composed nearly exclusively of ionized material owing towards the observer even around its perimeter., 1 is composed nearly exclusively of ionized material flowing towards the observer even around its perimeter. " “Phese knots (and the ""jet — see Paper 3) must all then be a consequence of an approaching outflow on the nearside ofthe bi-polar axis of the clusty Lomunculus reflection nebula (Paper 2).", These knots (and the `jet' – see Paper 3) must all then be a consequence of an approaching outflow on the nearside of the bi-polar axis of the dusty Homunculus reflection nebula (Paper 2). The SE lobe of the HLomunculus is approaching ancl the NW receding from the observer along a common axis tilted at 33 to the plane of the sky., The SE lobe of the Homunculus is approaching and the NW receding from the observer along a common axis tilted at $^{\circ}$ to the plane of the sky. Within he polar blowout’ model the inner shell’ and ‘lobe’ in Fig., Within the `polar blowout' model the `inner shell' and `lobe' in Fig. 1 are then on the far side of the Lomunculus and [owing away rom the observer., 1 are then on the far side of the Homunculus and flowing away from the observer. " The ""spike! and ‘are’ in Fig.", The `spike' and `arc' in Fig. 1 are similarly Uowing owards the observer but are elongated. well bevond the SE end. of the bi-polar axis of the Homunculus., 1 are similarly flowing towards the observer but are elongated well beyond the SE end of the bi-polar axis of the Homunculus. " They. would clearly have to have an extreme configuration to make them xwt of a simple ""polar. blowout from the centre of the llomunculus but are. likely to be closelv. related to. this eruptive event.", They would clearly have to have an extreme configuration to make them part of a simple `polar blowout' from the centre of the Homunculus but are likely to be closely related to this eruptive event. Of particular interest are the line profiles over the “spike” intercepted by Slit 2 in Fig., Of particular interest are the line profiles over the `spike' intercepted by Slit 2 in Fig. 1., 1. These are characterised in the py array in Fig., These are characterised in the pv array in Fig. 3(b) by a bright Nu] emission feature. z 1 Á across that has a EWLIIM of only 60 kms1 but displaced from the systemic radial velocity by = 650 kms1 (Slit 2. Ixnot 4 in Table 1 and Fig.," 3(b) by a bright ] emission feature, $\approx$ 1 $^{\prime\prime}$ across that has a FWHM of only 60 $\kms$ but displaced from the systemic radial velocity by $\approx$ $-$ 650 $\kms$ (Slit 2, Knot 4 in Table 1 and Fig." 3(b))., 3(b)). A faint velocity component, A faint velocity component however. a fainter “halo” of X-ray emission. with a radius of ~1507.. is indeed seen surrounding thePWN.,"however, a fainter “halo” of X-ray emission, with a radius of $\sim$, is indeed seen surrounding the." . Both and argue that most of this halo X-ray emission is not from the outer shock. but is rather due to dust scattering.," Both and argue that most of this halo X-ray emission is not from the outer shock, but is rather due to dust scattering." However. a relatively weak. limb-brightened X-ray component. is also seen on the eastern side. which has been interpreted as non-thermal emission associated with the supernova shock(77).," However, a relatively weak, limb-brightened X-ray component is also seen on the eastern side, which has been interpreted as non-thermal emission associated with the supernova shock." With the goal. of identibving any radio emission associated with this non-thermal X-ray. emission [from the Forward: shock. we obtained. sensitive new observations of aancd its surroundings.," With the goal of identifying any radio emission associated with this non-thermal X-ray emission from the forward shock, we obtained sensitive new observations of and its surroundings." We observed iin the 1.4 CGllz band on 2008 March 17. using the C array configuration of the National Radio Astronomy (NRAO) VLA. with a total time of 6 hours.," We observed in the 1.4 GHz band on 2008 March 17, using the C array configuration of the National Radio Astronomy (NRAO) VLA, with a total time of 6 hours." In this array configuration. the VLA is sensitive to structures up to iin size. so the structure of the putative raclio-shell around sshould be well-sampled.," In this array configuration, the VLA is sensitive to structures up to in size, so the structure of the putative radio-shell around should be well-sampled." La order to maximise the field-ol-view. coverage and dynamic range. we observed in spectral line mode. using spaced. centre frequencies. of 1.4649 and 1.3851 Giz in the two intermecdiate-frequency (IF) channels.," In order to maximise the field-of-view, coverage and dynamic range, we observed in spectral line mode using spaced centre frequencies of 1.4649 and 1.3851 GHz in the two intermediate-frequency (IF) channels." " We. phase-referenced: our observations. to the compact. source. PALIN 1085. whose. position is accurate to better than1"". therefore our astromietric uncertainty is dominated by contributions from noise and errors in. phase-referencing."," We phase-referenced our observations to the compact source PMN $-$ 1035, whose position is accurate to better than, therefore our astrometric uncertainty is dominated by contributions from noise and errors in phase-referencing." We estimate our astrometric uncertainty at <47)., We estimate our astrometric uncertainty at $<4$. Our flux density scale was set. from observations of 3C 48 and 3€ 286., Our flux density scale was set from observations of 3C 48 and 3C 286. The data reduction was carried. out using standard: procedures from NIUXOs ALPS software package., The data reduction was carried out using standard procedures from NRAO's AIPS software package. Our final images were made [rom self-calibrated Visibility data. using CLEAN deconvolution with multiple non-coplanar facets.," Our final images were made from self-calibrated visibility data, using CLEAN deconvolution with multiple non-coplanar facets." Since our two IE. [frequencies dilfer by ~6'%.. sources with dillerent. spectral. indices could: show noticeable cillerences in relative brightness between the two Is.," Since our two IF frequencies differ by $\sim$, sources with different spectral indices could show noticeable differences in relative brightness between the two IFs." " In particular. in we found that the spectral index. a (where the flux density S at frequeney vis x 9""). of the DPWN is quite uniform over the nebula. with a value of UUο."," In particular, in we found that the spectral index, $\alpha$ (where the flux density $S$ at frequency $\nu$ is $\propto \nu^\alpha$ ), of the PWN is quite uniform over the nebula, with a value of $+0.08^{+0.06}_{-0.09}$." In contrast to a PAWN. a supernova shell would be expected to have a notably steeper spectrum. with a typical value of OS~ O4," In contrast to a PWN, a supernova shell would be expected to have a notably steeper spectrum, with a typical value of $-0.8 \sim -0.4$." In order that such spectral-inces dilferences not. limit the dynamic range in the deconvolved image. we chose to image and deconvolve our two Lks separately.," In order that such spectral-index differences not limit the dynamic range in the deconvolved image, we chose to image and deconvolve our two IFs separately." We then averaged the resulting. two images to obtain our final. combined image.," We then averaged the resulting two images to obtain our final, combined image." The final image should correctly represent the brightness at the mean frequency of 1.43 Cllz regardless of the spectral index., The final image should correctly represent the brightness at the mean frequency of 1.43 GHz regardless of the spectral index. Separate imaging of the two Les cid in fact. produce a slightly. higher dynamic range than did combining the two Les before the Fourier transform stage., Separate imaging of the two IFs did in fact produce a slightly higher dynamic range than did combining the two IFs before the Fourier transform stage. We also discuss 327 MllIz images of this region resulting from earlier. VLA observations of a large segment. of the Galactic plane., We also discuss 327 MHz images of this region resulting from earlier VLA observations of a large segment of the Galactic plane. These 327-MllIz observations were taken as part of an elfort to survey the inner Galactic plane at low radio frequencies. and are described in??.," These 327-MHz observations were taken as part of an effort to survey the inner Galactic plane at low radio frequencies, and are described in." ". Phe FWILAL resolution is85"".", The FWHM resolution is. .. A lower-resolution image mace from these data. which covers the part of the plane relevant. to this paper. is reproduced in?.," A lower-resolution image made from these data, which covers the part of the plane relevant to this paper, is reproduced in." . Finally we also discuss a N-rav image of aand dts environs. produced. by combining a total of 7520 ksec of observations in the energy range 0.2 to LOkeV.," Finally we also discuss a X-ray image of and its environs, produced by combining a total of $\sim$ 520 ksec of observations in the energy range 0.2 to 10." . The X-ray data are described in ?7?., The X-ray data are described in . . We show the wicde-Licld racdio-image of the rregion in the top part of Fig. l.., We show the wide-field radio-image of the region in the top part of Fig. \ref{fwide}. This image represents only part of the imaged area. chosen to show the sources of interest.," This image represents only part of the imaged area, chosen to show the sources of interest." We further chose the range of grevscale in order to show the weaker sources. with the result that the stronger ones such as itself are saturated.," We further chose the range of greyscale in order to show the weaker sources, with the result that the stronger ones such as itself are saturated." Clearly. visible in this image is the [eature called the 7northern knot. —2' tto the north of the centre o£a.," Clearly visible in this image is the feature called the “northern knot”, $\sim$ to the north of the centre of." This image is corrected for the response of the primary beam (which has a EWIIM of aat LAS Cllz)., This image is corrected for the response of the primary beam (which has a FWHM of at 1.43 GHz). As a consequence the rms. background level increases with distance [rom the pointing centre., As a consequence the rms background level increases with distance from the pointing centre. Near0.9.. the rms background. brightness was ~260pdx ," Near, the rms background brightness was $\sim260\,\mu$ ." This is the deepest. radio image so [ar obtained of aand its surroundings., This is the deepest radio image so far obtained of and its surroundings. The bottom part of Fig., The bottom part of Fig. 1. shows the X-ray image for the same field., \ref{fwide} shows the X-ray image for the same field. In addition to tthere are a number of other sources visible., In addition to there are a number of other sources visible. “Phe brightest isQSO J1832-105. with a 143-Cllz flux density of 1.07 Jy.," The brightest isQSO J1832-105, with a 1.43-GHz flux density of 1.07 Jy." Two other resolved sources are visible at approximately RA = IS! 3322. == LO’ 2270 and RA = Is? 32/4. == 10 2283.," Two other resolved sources are visible at approximately RA = $18^{\rm h}$ 2, = $-10$ 0 and RA = $18^{\rm h}$ 4, = $-10$ 3." We call these sources aand0.59. as they are likely both Galactic. and we will cliscuss them below.," We call these sources and, as they are likely both Galactic, and we will discuss them below." Phere are also a number of weaker unresolved sources visible. which are likely extragalactic and which we do not discuss further.," There are also a number of weaker unresolved sources visible, which are likely extragalactic and which we do not discuss further." Also present in the full image ancl included. in the deconvolution and. sel(-calibration. was the supernova remnant Wes 69. which is to the northwest of 0.," Also present in the full image and included in the deconvolution and self-calibration was the supernova remnant Kes 69, which is to the northwest of." 9.. We choose to exclude Kes 69 from the portion of the image displaved in Fig. L..," We choose to exclude Kes 69 from the portion of the image displayed in Fig. \ref{fwide}," as it is bevond the point of the primary beam. and the image details are not reliable.," as it is beyond the point of the primary beam, and the image details are not reliable." 60).. Some artifacts are visible in the western and northwester parts of the image. due to J1832-105 and Wes 69.," Some artifacts are visible in the western and northwester parts of the image, due to J1832-105 and Kes 69." In Fig., In Fig. 2. we show a detail of the radio image showing the PPNN., \ref{fg21only} we show a detail of the radio image showing the . The image corresponds well.albeitat lower resolution. to the one of ?..," The image corresponds well,albeitat lower resolution, to the one of ." Besides the optical depth and the Einstein crossing time. a third quantity was proposed by Paezyrísski (1986) as relevant for the study of the microlensing experiments.,"Besides the optical depth and the Einstein crossing time, a third quantity was proposed by Paczyńsski (1986) as relevant for the study of the microlensing experiments." This quantity is the microlensing event rate I. which provides the rate at which the lenses enter the microlensing tube.," This quantity is the microlensing event rate $\Gamma$, which provides the rate at which the lenses enter the microlensing tube." While the optical depth does not depend on the mass function. the event rate does. and consequently useful information about the different populations responsible for the micronlensing envents can be obtained by studying it.," While the optical depth does not depend on the mass function, the event rate does, and consequently useful information about the different populations responsible for the micronlensing envents can be obtained by studying it." In Fig., In Fig. 5 we display with solid lines the normalized distributions of the microlensing event rate as a function of the event duration for the different populations of the canonical thick disk (left panels). the metal-weak thick disk (central panels) and the halo (right panels).," 5 we display with solid lines the normalized distributions of the microlensing event rate as a function of the event duration for the different populations of the canonical thick disk (left panels), the metal-weak thick disk (central panels) and the halo (right panels)." We also show the results obtained by the MACHO team with a dashed, We also show the results obtained by the MACHO team with a dashed relative abundances with respect to the solar value (Grevesse&Sauval 1998).,relative abundances with respect to the solar value \citep{grevesse1998}. ". For Ti, Cr, Fe and Ni most absorption lines with considerable strength are present and these elements are most important for the overall metallicity of the star."," For Ti, Cr, Fe and Ni most absorption lines with considerable strength are present and these elements are most important for the overall metallicity of the star." " Apart from Mn and for star I, abundances of all elements we computed are consistent,§ within their error-bars, with the input values."," Apart from Mn and S for star I, abundances of all elements we computed are consistent, within their error-bars, with the input values." " The mean difference in normalised flux between the input and fitted spectrum is -0.004 (input — fitted spectrum) for both stars with a standard deviation of 0.013 and 0.010 for star I and II, respectively."," The mean difference in normalised flux between the input and fitted spectrum is -0.004 (input – fitted spectrum) for both stars with a standard deviation of 0.013 and 0.010 for star I and II, respectively." " 'These test spectra are also suitable to investigate the influence of an offset in effective temperature, surface gravity and rotational velocity."," These test spectra are also suitable to investigate the influence of an offset in effective temperature, surface gravity and rotational velocity." " Therefore, we computed Emicro and abundances with a temperature of + 100 K, leaving the surface gravity and rotational velocity at the correct value."," Therefore, we computed $\xi_{micro}$ and abundances with a temperature of $\pm$ 100 K, leaving the surface gravity and rotational velocity at the correct value." Similar tests are performed for an increase / decrease of 0.1 in surface gravity and 5 ! in rotational velocity., Similar tests are performed for an increase / decrease of 0.1 in surface gravity and 5 $^{-1}$ in rotational velocity. The computed Emicro for the different tests are given in Table 5.., The computed $\xi_{micro}$ for the different tests are given in Table \ref{vmicro}. The changes in micro due to changes in stellar parameters are of the order of the error found for Emicro when we use the correct stellar parameters., The changes in $\xi_{micro}$ due to changes in stellar parameters are of the order of the error found for $\xi_{micro}$ when we use the correct stellar parameters. Only for a decrease in vsin? the value for Emicro decreases by about twice the error., Only for a decrease in $v \sin i$ the value for $\xi_{micro}$ decreases by about twice the error. " In order to test the influence of an offset in Emicro, the abundances are recomputed with Emicro + 2 ss!."," In order to test the influence of an offset in $\xi_{micro}$, the abundances are recomputed with $\xi_{micro}$ $\pm$ 2 $^{-1}$." The resulting abundances are shown in Fig. 3.., The resulting abundances are shown in Fig. \ref{starres}. " When comparing the results of the tests described above, it becomes clear that the scatter of the computed abundance values around the input abundance of the synthetic test spectra is dominated by scatter inherent to the method (see top panels of Fig. 3))."," When comparing the results of the tests described above, it becomes clear that the scatter of the computed abundance values around the input abundance of the synthetic test spectra is dominated by scatter inherent to the method (see top panels of Fig. \ref{starres}) )." The standard deviations of all computed abundances with respect to the input abundances are 0.17 dex and 0.12 dex for star I, The standard deviations of all computed abundances with respect to the input abundances are 0.17 dex and 0.12 dex for star I εrese total coitributious aud the stellar mass at presenut-dav in halos o τὰ given nmiass Is essentially the coutributiou arising from star formation since τ~1.,these total contributions and the stellar mass at present-day in halos of a given mass is essentially the contribution arising from star formation since $z\sim1$. Finally. the bottom panels of Figure 6 contrast the individal contributions to the stellar mass asseniblv in the SAAIs (solid lines) and ZCZOT. (dashed. lines). showing the relative. contributions to the final central ooOalaxyv roni niereers of snaller ceutral galaxies (thick lues) aid satellite 1nergers (thin lines).," Finally, the bottom panels of Figure \ref{fig:Fig9MillHOD} contrast the individual contributions to the stellar mass assembly in the SAMs (solid lines) and ZCZ07 (dashed lines), showing the relative contributions to the final central galaxy from mergers of smaller central galaxies (thick lines) and satellite mergers (thin lines)." The individual Contribitions from these mocels are strikinely different., The individual contributions from these models are strikingly different. Tn ZCZV. the main ierecr contribution fo present-αν cenral galaxies comes from mergers of the sinaller central progenitor galaxies. while in the SAMs a larecr contribution comes from satellite ealaxies.," In ZCZ07, the main merger contribution to present-day central galaxies comes from mergers of the smaller central progenitor galaxies, while in the SAMs a larger contribution comes from satellite galaxies." As iientioned already in 833.3. the contribution from sualler ceutral progenitor galaxies in the AIPA model is particularly minor. while it is somewhat larger in the Durham model.," As mentioned already in 3.3, the contribution from smaller central progenitor galaxies in the MPA model is particularly minor, while it is somewhat larger in the Durham model." The implications of these differences are discussed further below., The implications of these differences are discussed further below. Iu this section we use the SAM catalogs to test the validity of soe of the assuiiptious adopted in the ZCZüT method., In this section we use the SAM catalogs to test the validity of some of the assumptions adopted in the ZCZ07 method. We note that these tests can be done despite the, We note that these tests can be done despite the Centaur phase for 200 Myr. which was obtained by measuring the total time each HIHQ Centaur resided in this phase and dividing by the total simulation time or lifetime of the particle.,"Centaur phase for 200 Myr, which was obtained by measuring the total time each HIHQ Centaur resided in this phase and dividing by the total simulation time or lifetime of the particle." This typical residence time is consistent with that found by Gladman et al. (, This typical residence time is consistent with that found by Gladman et al. ( 2009) for the evolution of 2008 KV42$Q372.,2009) for the evolution of 2008 KV42. In Fig., In Fig. 2. we chose these longer-lived cases for illustrative purpose only., \ref{evo} we chose these longer-lived cases for illustrative purpose only. A natural question to ask is what are the long-term inclination and perihelion distributions of these objects., A natural question to ask is what are the long-term inclination and perihelion distributions of these objects. We have computed these distributions by recording the inclination and. perihelion distance of each object in the HIHQ Centaur state at each output interval in our simulations., We have computed these distributions by recording the inclination and perihelion distance of each object in the HIHQ Centaur state at each output interval in our simulations. The steady-state inclination and perihelion distributions are depicted in Fig. 3.., The steady-state inclination and perihelion distributions are depicted in Fig. \ref{iqdist}. The distributions are normalised such that the sum of the bins is unity., The distributions are normalised such that the sum of the bins is unity. " The median inclination is 104.6"" and the median q is 22 AU.", The median inclination is $^\circ$ and the median $q$ is 22 AU. As can be seen the majority of objects should have their perihelion near Uranus., As can be seen the majority of objects should have their perihelion near Uranus. Approximately of objects have ὁο1007.110]. exactly where 2008 KV42 was found.," Approximately of objects have $i \in [100^\circ,110^\circ]$, exactly where 2008 KV42 was found." The other two objects. 2010 WG9 and 2002 XU93. are in the first bin.," The other two objects, 2010 WG9 and 2002 XU93, are in the first bin." In fact. all three objects are found in the region where the model predicts most objects should Now that we have shown the mechanism behind the production of HIHQ Centaurs from the Oort cloud. and what the expected perihelion and inclination distribution of these objects are. we proceed to estimate how many HIHQ Centaurs there could be.," In fact, all three objects are found in the region where the model predicts most objects should Now that we have shown the mechanism behind the production of HIHQ Centaurs from the Oort cloud, and what the expected perihelion and inclination distribution of these objects are, we proceed to estimate how many HIHQ Centaurs there could be." We can use the dynamies of the Oort cloud to estimate how many HIHQ Centaurs we would expect., We can use the dynamics of the Oort cloud to estimate how many HIHQ Centaurs we would expect. Brasser (2008) suggested that the Oort cloud formed in two stages: the first state would occur while the Sun was in its birth cluster. at the time just after the formation of Jupiter and Saturn. when the gas from the primordial solar nebula was still present.," Brasser (2008) suggested that the Oort cloud formed in two stages: the first state would occur while the Sun was in its birth cluster, at the time just after the formation of Jupiter and Saturn, when the gas from the primordial solar nebula was still present." The second stage would occur some 600 Myr later. at the time of a dynamical instability of the giant planets. which is thought to have coincided with the Late Heavy Bombardment of the terrestrial planets (Tsiganis et al..," The second stage would occur some 600 Myr later, at the time of a dynamical instability of the giant planets, which is thought to have coincided with the Late Heavy Bombardment of the terrestrial planets (Tsiganis et al.," 2005: Gomes et al..," 2005; Gomes et al.," 2005)., 2005). Thus the Oort cloud is a mixture of bodies from two sources and as we demonstrated above. the HIHQ Centaurs can originate from both the inner and classical cloud.," Thus the Oort cloud is a mixture of bodies from two sources and as we demonstrated above, the HIHQ Centaurs can originate from both the inner and classical cloud." This means we cannot isolate one source over the other., This means we cannot isolate one source over the other. Unfortunately we have very little information about the size distribution and total mass of the planetesimals that formed the first stage of the Oort cloud. apart from the fact that the total mass seattered by Jupiter and Saturn may have been much more than during the second stage (e.g. Thommes et al..," Unfortunately we have very little information about the size distribution and total mass of the planetesimals that formed the first stage of the Oort cloud, apart from the fact that the total mass scattered by Jupiter and Saturn may have been much more than during the second stage (e.g. Thommes et al.," 2003: Levison et al..," 2003; Levison et al.," 2010)., 2010). However. we know much more about the size distribution and total mass during the second stage.," However, we know much more about the size distribution and total mass during the second stage." Thus we shall focus on the second stage Morbidelli et al. (, Thus we shall focus on the second stage Morbidelli et al. ( 2009) claim that there were approximately 10 objects in the trans-Neptunian dise at the time of the LHB with //.«S. assuming all these objects had an albedo of4.,"2009) claim that there were approximately $10^8$ objects in the trans-Neptunian disc at the time of the LHB with $H<8$, assuming all these objects had an albedo of." 5%.. Taking a efficiency for Oort cloud formation in the current Galactic environment (Dones et αἱ..," Taking a efficiency for Oort cloud formation in the current Galactic environment (Dones et al.," ". 2004: Kaib Quinn. 2008) implies there are at least 3-10"" Oort cloud objects with Lf<8. and therefore we expect at least 30 HIHQ objects of the same An alternative estimate is obtained as follows. but this is only applicable to the inner Oort cloud and/or if the inner cloud is the dominant source of HIHQ Centaurs."," 2004; Kaib Quinn, 2008) implies there are at least $3 \times 10^6$ Oort cloud objects with $H<8$, and therefore we expect at least 30 HIHQ objects of the same An alternative estimate is obtained as follows, but this is only applicable to the inner Oort cloud and/or if the inner cloud is the dominant source of HIHQ Centaurs." Schwamb et al. (, Schwamb et al. ( 2010) argue hat there are between 11 to 1577. Sedna-like objects in the inner Oort cloud with semi-major axes @«3000 AU or objects whose size distribution follows the cold and hot yopulation KBOs respectively (Fraser et al..,"2010) argue that there are between $^{+423}_{-71}$ to $^{+1949}_{-400}$ Sedna-like objects in the inner Oort cloud with semi-major axes $a < 3\,000$ AU for objects whose size distribution follows the cold and hot population KBOs respectively (Fraser et al.," . 2010), 2010). The error values correspond to contidence levels., The error values correspond to confidence levels. The latter value could be problematic because the low formation efficiency of Brasser et al. (, The latter value could be problematic because the low formation efficiency of Brasser et al. ( 2011) would suggest there were more than 30000 Sedna-sized bodies in the disc. and thus its total mass should have been several jiundred Earth masses.,"2011) would suggest there were more than $30\,000$ Sedna-sized bodies in the disc, and thus its total mass should have been several hundred Earth masses." Nevertheless. we shall use this estimate in our derivation below.," Nevertheless, we shall use this estimate in our derivation below." We take the cumulative slope in absolute magnitude of KBOs from Fraser et al. (, We take the cumulative slope in absolute magnitude of KBOs from Fraser et al. ( 2010). which is à.=0.82 for the cold KBOs and à.=0.35 for the hot KBOs. and assume that the size distribution of bright KBOs applies to objects with the same size as the HIHQ Centaurs.,"2010), which is $\alpha=0.82$ for the cold KBOs and $\alpha=0.35$ for the hot KBOs, and assume that the size distribution of bright KBOs applies to objects with the same size as the HIHQ Centaurs." The absolute magnitude of Sedna is 1.6 (Brown et al..," The absolute magnitude of Sedna is 1.6 (Brown et al.," 2004) and thus the number of objects in the inner Oort cloud with //«8 ranges from 1.1a10° ifa—0.35 to 2.0-10° ifa=0.82., 2004) and thus the number of objects in the inner Oort cloud with $H<8$ ranges from $1.1^{+5.0}_{-0.7} \times 10^5$ if $\alpha = 0.35$ to $2.0^{+9.0}_{-1.5} \times 10^7$ if $\alpha = 0.82$. With a production probability of LO”. he nominal number of HIHQ Centaurs with //.κ5 is expected o range from | to 200.," With a production probability of $10^{-5}$, the nominal number of HIHQ Centaurs with $H<8$ is expected to range from 1 to 200." The former value is too low since more objects have already been found and the sample is far from being observationally complete., The former value is too low since more objects have already been found and the sample is far from being observationally complete. The highest value is also problematic or reasons discussed earlier: too much mass had to exist in the orimordial dise and be deposited in the inner Oort cloud., The highest value is also problematic for reasons discussed earlier: too much mass had to exist in the primordial disc and be deposited in the inner Oort cloud. Thus. we believe that the current number of HIHQ Centaurs is probably in between these two extremes.," Thus, we believe that the current number of HIHQ Centaurs is probably in between these two extremes." In any case the direct link between he HIHQ Centaurs and the Oort cloud could be used to constrain Oort cloud formation models and possibly infer the mass and size of the primordial solar nebula once more HIHQ Centaur objects are discovered., In any case the direct link between the HIHQ Centaurs and the Oort cloud could be used to constrain Oort cloud formation models and possibly infer the mass and size of the primordial solar nebula once more HIHQ Centaur objects are discovered. and so the confusion noise increases.,and so the confusion noise increases. " As £i, increases above fe. the less strongly magnilied images at racli larger than £k contribute a steadily increasing fraction of the detected [ux clensity: therefore. the contribution of the strongly masenified images at radii near Op is steadily diluted. and so the confusion noise tends gradually to its unlensed. value."," As $\theta_{\rm b}$ increases above $\theta_{\rm E}$, the less strongly magnified images at radii larger than $\theta_{\rm E}$ contribute a steadily increasing fraction of the detected flux density; therefore, the contribution of the strongly magnified images at radii near $\theta_{\rm E}$ is steadily diluted, and so the confusion noise tends gradually to its unlensed value." The confusion noise expected. in each observing band and model of galaxy. evolution. is shown in Table14. and 44., The confusion noise expected in each observing band and model of galaxy evolution is shown in 1 and 4. The results for beam-widths of 1 and aaremin are presented in 11. while in Fig.44 the results in à l-arcmin beam are compared with earlier. estimates.," The results for beam-widths of 1 and arcmin are presented in 1, while in 4 the results in a 1-arcmin beam are compared with earlier estimates." The estimates of unlensed confusion noise are significantly larger than those of Helou Beichman (1990) and Fischer Lange (1093). but are more similar to those of Franceschini οἱ al. (," The estimates of unlensed confusion noise are significantly larger than those of Helou Beichman (1990) and Fischer Lange (1993), but are more similar to those of Franceschini et al. (" 1991).,1991). They are in good agreement with observationally-based. estimates (DIS)., They are in good agreement with observationally-based estimates (BIS). Confusion noise is expected to dominate the SZ signal at a wavelength of p/m and to be very significant at wavelengths of jin and mmm., Confusion noise is expected to dominate the SZ signal at a wavelength of $\mu$ m and to be very significant at wavelengths of $\mu$ m and mm. In a l-arcmin beam the lensed confusion noise is always predicte to be at least 20 per cent of the SZ signal in all three mocels., In a 1-arcmin beam the lensed confusion noise is always predicted to be at least 20 per cent of the SZ signal in all three models. Only at à wavelength of 2mm is the SZ signal expectec to be much larger than the confusion noise., Only at a wavelength of mm is the SZ signal expected to be much larger than the confusion noise. These results suggest both that the kinematic SZ elfect would be cillieul to detect. and that the thermal SZ elfect would be dillicul to measure accurately. in an observation of a single cluster. unless the population of distant cust. star-forming galaxies is very sparse or evolves very weakly.," These results suggest both that the kinematic SZ effect would be difficult to detect, and that the thermal SZ effect would be difficult to measure accurately, in an observation of a single cluster, unless the population of distant dusty star-forming galaxies is very sparse or evolves very weakly." In the light of recen observations (SLB) either of these scenarios appears very unlikely., In the light of recent observations (SIB) either of these scenarios appears very unlikely. The kev parameter that determines the οσοι of eravitational lensing on the confusion noise in an observation is the Einstein radius of the lensing cluster 8e. which in urn depends on the redshift σος velocity dispersion σν and internal structure of the cluster.," The key parameter that determines the effects of gravitational lensing on the confusion noise in an observation is the Einstein radius of the lensing cluster $\theta_{\rm E}$, which in turn depends on the redshift $z_{\rm c}$, velocity dispersion $\sigma_{\rm V}$ and internal structure of the cluster." H£ the cluster is assumed to »' an isothermal sphere. and λές.2.) is the angular diameter istance between a redshift z and a source at redshift 2... wn ÓpxDlse.nv (Paper 1).," If the cluster is assumed to be an isothermal sphere, and $D(z,z_{\rm s})$ is the angular diameter distance between a redshift $z$ and a source at redshift $z_{\rm s}$, then $\theta_{\rm E} \propto D(z_{\rm c},z_{\rm s}) \sigma_{\rm V}^2$ (Paper 1)." Note that because ος is vpically much larger than unity for faint submillimetre-wave sources. increasing 2. does not significantly reduce 1e surface density of background. sources. and so the only significant elect. of changing 2. on the expected. confusion due to lensed images is introduced through the resulting change in 0c.," Note that because $z_{\rm s}$ is typically much larger than unity for faint submillimetre-wave sources, increasing $z_{\rm c}$ does not significantly reduce the surface density of background sources, and so the only significant effect of changing $z_{\rm c}$ on the expected confusion due to lensed images is introduced through the resulting change in $\theta_{\rm E}$." The dependence of the SZ signal from an unresolved cluster on σν and τς was discussed by De Luca. Deéssert Puget (1995). using models of cluster evolution [rom Waiser (1986) and Bartlett Silk (1994). and found to take the form⋅ (1|2lo10/5DO.s.)7.," The dependence of the SZ signal from an unresolved cluster on $\sigma_{\rm V}$ and $z_{\rm c}$ was discussed by De Luca, Déssert Puget (1995), using models of cluster evolution from Kaiser (1986) and Bartlett Silk (1994), and found to take the form $(1+z_{\rm c}) \sigma_{\rm V}^{10/3} / D(0, z_{\rm c})^2$." A beam correction. can be added to calculate the SZ signal expected. from. clusters that are resolved in smaller observing beams., A beam correction can be added to calculate the SZ signal expected from clusters that are resolved in smaller observing beams. The expected. dependence of both the confusion noise and the SZ signal at a wavelength. of yam for clusters with 0.05<2.€ Land kkmss+xe< 2000kkmss is shown in 55(a) 5(b) for model Ll., The expected dependence of both the confusion noise and the SZ signal at a wavelength of $\mu$ m for clusters with $0.05 \le z_{\rm c} \le 1$ and $^{-1} \le \sigma_{\rm v} \le 2000$ $^{-1}$ is shown in 5(a) 5(b) for model I1. The results are normalised to match the predictions for the model lensing cluster in the previous sections. which had ου = 0.171 and ay=1360kkmss 4.," The results are normalised to match the predictions for the model lensing cluster in the previous sections, which had $z_{\rm c}$ = 0.171 and $\sigma_{\rm V}=1360$ $^{-1}$." The confusion noise is expected to be smaller and larger by a factor of a few in mocels 1 and 12 respectively., The confusion noise is expected to be smaller and larger by a factor of a few in models H and I2 respectively. Confusion noise is expected to be less significant as compared. with the SZ signal in observations of more massive and more distant clusters that are mace in larger beams. as shown by the signal-to-noise ratios in Figs 5(c) 5(d).," Confusion noise is expected to be less significant as compared with the SZ signal in observations of more massive and more distant clusters that are made in larger beams, as shown by the signal-to-noise ratios in Figs 5(c) 5(d)." Three erouncd-based detections of the millimetre-wave SZ clleet have been published: for Abell 2163 at a wavelength of mnun in a L4-arcemin-wide beam (Wilbanks ct al., Three ground-based detections of the millimetre-wave SZ effect have been published; for Abell 2163 at a wavelength of mm in a 1.4-arcmin-wide beam (Wilbanks et al. 1994). and for Abell 2744 ancl S1077 at wavelengths of 2 and mmm in 46- and 44-arcsec-wide beams respectively," 1994), and for Abell 2744 and S1077 at wavelengths of 2 and mm in 46- and 44-arcsec-wide beams respectively" "due to the turbulence continue to have au impact ou the migration of 30 |, protoplaucts.",due to the turbulence continue to have an impact on the migration of 30 $_{\oplus}$ protoplanets. The eccentricity evolution is slow in the right panel of figure 10.., The eccentricity evolution is shown in the right panel of figure \ref{fig10}. " The values obtained are simular to those for the LOAD), planets. indicating little erowth of the eccentricity because the damping induced by the underlving type 1 resonant disk interaction."," The values obtained are similar to those for the 10 $_{\oplus}$ planets, indicating little growth of the eccentricity because the damping induced by the underlying type I resonant disk interaction." We Low exaniue the torques experienced by the protoplaucts during the simulations in more detail., We now examine the torques experienced by the protoplanets during the simulations in more detail. Iu view of the large uunber of planets cousidered. we restrict our discussion to a few specific examples which are illustrative of the range of behaviour observed iu the simulations as a whole.," In view of the large number of planets considered, we restrict our discussion to a few specific examples which are illustrative of the range of behaviour observed in the simulations as a whole." We also discuss the iuplications for type I migration of low mass planets inturbulent disks., We also discuss the implications for type I migration of low mass planets inturbulent disks. Fiewre 11 shows four cxaiples of the time evolution of he torque per unit mass experienced by the planets iu he simulations., Figure \ref{fig11} shows four examples of the time evolution of the torque per unit mass experienced by the planets in the simulations. The torque per unit mass is defined by equation (9)). aud is prescuted iu the units described iu section L.," The torque per unit mass is defined by equation \ref{torque}) ), and is presented in the units described in section \ref{units}." " Moviug from left to right aud from top to tton. the pauels show results roni simulations with: (yp= 0. ry 2.6): (iy;= 1. ry;= 2.1 (ny;=5. ry= 25) ny;=10. ry;= 2.6). where the radii, ey; refor o the initial orbital radii of the planets"," Moving from left to right and from top to bottom, the panels show results from simulations with: $m_{pi}=0$ , $r_{pi}=2.6$ ); $m_{pi}=1$ , $r_{pi}=2.4$ ); $m_{pi}=3$, $r_{pi}=2.8$ ); $m_{pi}=10$, $r_{pi}=2.6$ ), where the radii, $r_{pi}$, refer to the initial orbital radii of the planets." In each panel. he torque on the planet due to the inner disk is shown by he black (blue) line. that due to he outer disk is show- x the light exev (ereen) liue. aux the dark erev (red) ine represents the total torque.," In each panel, the torque on the planet due to the inner disk is shown by the black (blue) line, that due to the outer disk is shown by the light grey (green) line, and the dark grey (red) line represents the total torque." In all cases the torque is a highly variable quantity. as discussed previously i- NP2001.," In all cases the torque is a highly variable quantity, as discussed previously in NP2004." Ou the same scale. the type I torque due to a- equivalent. laminar:diskHis: ~41.5«+10.m (5).," On the same scale, the type I torque due to an equivalent laminardiskis $\simeq 1.5 \times 10^{-6} \left(\frac{m_{pi}}{M_{\oplus}}\right)$ ." Thisol value, This value however. point out that bin 3 is the bin with the highest mean I5dcdington ratio.,"however, point out that bin 3 is the bin with the highest mean Eddington ratio." As seen in Table 6.. the quasars in bin 3 are also seen to be the least variable. with the Lowest value for V(Nr=100).," As seen in Table \ref{mbhlumplfittab}, the quasars in bin 3 are also seen to be the least variable, with the lowest value for $V(\Delta{\tau}=100)$." To interpret. our. hypothesised relationship between optical variability ancl the Eddington ratio. we use the theoretical relationship between the luminosity of a quasar and its accretion rate: where g is à measure of the radiative ellicieney. of the quasar and is dependent on the specific physical parameters used to model the black hole (see.e.g..Ixrolik.1998.forde-tailedcaleulations)..," To interpret our hypothesised relationship between optical variability and the Eddington ratio, we use the theoretical relationship between the luminosity of a quasar and its accretion rate: where $\eta$ is a measure of the radiative efficiency of the quasar and is dependent on the specific physical parameters used to model the black hole \citep[see, e.g.,][for detailed calculations]{krolikbook}." The two canonical values correspond to the Schwarzschilel black hole. which has y=0.06. and the νους black hole. which has η=0.42.," The two canonical values correspond to the Schwarzschild black hole, which has $\eta \approx 0.06$, and the Kerr black hole, which has $\eta = 0.42$." Given our lack of knowledge about the physical parameters of the supermassive black holes that power quasars. the gencral practice is to adopt a value that lies between these two extremes. Le. 90.1.," Given our lack of knowledge about the physical parameters of the supermassive black holes that power quasars, the general practice is to adopt a value that lies between these two extremes, i.e., $\eta \sim 0.1$." ὃν combining Equations 4. and 5.. we have the simple model in which the optical luminosity is related. to. the accretjon rate CAL). the radiative efficiency. (η) ancl the fraction of the bolometric luminosity that is emitted in the optical (2): In light of Equation 6.. changes in the optical Iuminosity of a quasar can be driven either by a change in e. 4. or AL.," By combining Equations \ref{optbolratio} and \ref{radeff}, we have the simple model in which the optical luminosity is related to the accretion rate $\dot M$ ), the radiative efficiency $\eta$ ) and the fraction of the bolometric luminosity that is emitted in the optical $\varepsilon$ ): In light of Equation \ref{simplemodel}, changes in the optical luminosity of a quasar can be driven either by a change in $\epsilon$, $\eta$, or $\dot M$." A varving value of e would require radical changes of a quasars spectral shape across multiple wavelength regimes., A varying value of $\varepsilon$ would require radical changes of a quasar's spectral shape across multiple wavelength regimes. A varving 4 would require the nature of an individual black hole to change with time., A varying $\eta$ would require the nature of an individual black hole to change with time. On the rest-frame time-scales of our observations. it is unlikely that either of these two would be comparable to variations in the aceretion [low. which should. naturally occur due to the dynamics of the entire accretion process.," On the rest-frame time-scales of our observations, it is unlikely that either of these two would be comparable to variations in the accretion flow, which should naturally occur due to the dynamics of the entire accretion process." Η we assume that variations in the optical luminosity. of the quasar are tied to variations in the accretion rate. this can be interpreted as a link between the optical variability of à quasar and its ‘age’.," If we assume that variations in the optical luminosity of the quasar are tied to variations in the accretion rate, this can be interpreted as a link between the optical variability of a quasar and its `age'." " In the cocoon model (see.e.g..Llaas2004:Llopkinsetal. 2005). quasars become observable in the optical at high aceretion rate (after feedback ""blows away enshrouding gas ancl dust). and fade away when the accretion rate drops."," In the cocoon model \citep[see, e.g.,][]{haas04, hopkins05}, quasars become observable in the optical at high accretion rate (after feedback `blows away' enshrouding gas and dust), and fade away when the accretion rate drops." The IExldington ratio. therefore. could be construed as a proxy for the age of the quasar. or more precisely. the time since the quasar became observable in the optical portion of the spectrum.," The Eddington ratio, therefore, could be construed as a proxy for the age of the quasar, or more precisely, the time since the quasar became observable in the optical portion of the spectrum." Martini&Schneider(2003) describe one possible test for measuring quasar lifetimes in mocels such as this. emploving large. multi-epoch surveys.," \citet{martini03} describe one possible test for measuring quasar lifetimes in models such as this, employing large, multi-epoch surveys." At constant black hole mass. optical luminosity could oovide a measure of the gas that is available for accretion onto the black hole.," At constant black hole mass, optical luminosity could provide a measure of the gas that is available for accretion onto the black hole." Pherefore. we might expect that vounger quasars are more luminous because they have a greater uel supply.," Therefore, we might expect that younger quasars are more luminous because they have a greater fuel supply." Similarly. when comparing two quasars with he same optical luminosity. the quasar with the larger Mack hole mass would be olderits lower Eddington ratio is indicative of it having burned through much of its once-arecr fuel supply.," Similarly, when comparing two quasars with the same optical luminosity, the quasar with the larger black hole mass would be older–its lower Eddington ratio is indicative of it having burned through much of its once-larger fuel supply." " Thus. when comparing populations of quasars (as in our bins in. Lop), and Alea). the greater variability seen in the lower Luminosity. objects would. be a consequence of a dwindling fuel supply."," Thus, when comparing populations of quasars (as in our bins in $L_{opt}$ and $M_{BH}$ ), the greater variability seen in the lower luminosity objects would be a consequence of a dwindling fuel supply." As less eas is avallable. the rate at which the gas is supplied to the lack hole varies more. much like the Uickering of a cing ire.," As less gas is available, the rate at which the gas is supplied to the black hole varies more, much like the flickering of a dying fire." Either way. the possibility that variability is tied to he Eddington ratio. which is in essence a measure of the cllicicney of a quasar. is an intriguing one.," Either way, the possibility that variability is tied to the Eddington ratio, which is in essence a measure of the efficiency of a quasar, is an intriguing one." Both panels of Figure 10. appear to demonstrate that jack hole mass is related. to variability. at larger time ags., Both panels of Figure \ref{Fig3.5} appear to demonstrate that black hole mass is related to variability at larger time lags. This is also seen in Table 6.. which shows that the veh black hole mass bins not only have smaller values of V(Az=100). but also larger power law slopes. indicating hat the cilferences in. variability will be more prominent at longer time lags.," This is also seen in Table \ref{mbhlumplfittab}, which shows that the high black hole mass bins not only have smaller values of $V(\Delta{\tau}=100)$, but also larger power law slopes, indicating that the differences in variability will be more prominent at longer time lags." This agrees with Wold.Brotherton.& who saw little correlation between variability ancl black hole. mass for a sample of observations with time separations less than 100 days. but a clear correlation between the two for Ar greater than 100 days.," This agrees with \citet{wold07}, who saw little correlation between variability and black hole mass for a sample of observations with time separations less than 100 days, but a clear correlation between the two for $\Delta{\tau}$ greater than 100 days." This apparent increase in the elfect of back hole mass on longer time-scale variability clearly indicates the need for longer observed time baselines., This apparent increase in the effect of back hole mass on longer time-scale variability clearly indicates the need for longer observed time baselines. The results presented herein only use data from the completed SDSS-L survey., The results presented herein only use data from the completed SDSS-I survey. The ongoing SDSS-LL will ultimately. adel another three vears to this baseline. for an average increase in the maximum rest-framoe Ar of roughly one vear for cach quasar.," The ongoing SDSS-II will ultimately add another three years to this baseline, for an average increase in the maximum rest-frame $\Delta{\tau}$ of roughly one year for each quasar." The analysis in this paper focused on the € sample. which consists only of quasars with z21.69. as € is blueward of the SDSS spectral response at lower recdshifts.," The analysis in this paper focused on the C sample, which consists only of quasars with $z > 1.69$ , as C is blueward of the SDSS spectral response at lower redshifts." The remaining. lower redshift quasars can be analysed in a similar manner. however. by utilising other emission lines. such as Mg or Ll.," The remaining, lower redshift quasars can be analysed in a similar manner, however, by utilising other emission lines, such as Mg or $_{\beta}$." Not only would this analysis nearly triple the number of quasars studied. but it would also extend the redshift’ baseline of our sample. thereby allowing us to test the hypothesisecl relationship between optical variability and accretion rate at other cosmic epochs.," Not only would this analysis nearly triple the number of quasars studied, but it would also extend the redshift baseline of our sample, thereby allowing us to test the hypothesised relationship between optical variability and accretion rate at other cosmic epochs." In this paper. we have studied the ensemble variability properties of almost 5.000 spectroscopically identified quasars from the Sloan Digital Sky Survey Equatorial Stripe.," In this paper, we have studied the ensemble variability properties of almost 8,000 spectroscopically identified quasars from the Sloan Digital Sky Survey Equatorial Stripe." These objects have been observed an average of over en times each., These objects have been observed an average of over ten times each. By using their € line dispersions ane nearby continuum luminosities. we have estimated black role masses for approximately 2.500 of these quasars.," By using their C line dispersions and nearby continuum luminosities, we have estimated black hole masses for approximately 2,500 of these quasars." We mve binned these quasars in luminosity and black hole mass ancl examined the variability properties of the quasars in each bin., We have binned these quasars in luminosity and black hole mass and examined the variability properties of the quasars in each bin. We have been able to: (1) Hteproduce the wellknown anticorrelation between luminosity and variability. and (2) Detect a correlation between variability ancl black hole mass.," We have been able to: (1) Reproduce the well-known anticorrelation between luminosity and variability, and (2) Detect a correlation between variability and black hole mass." ὃν combining (1) ancl (2). it appears that. variability is inversely related to the Eddington ratio in quasars.," By combining (1) and (2), it appears that variability is inversely related to the Eddington ratio in quasars." Εις points to variability being related to the quasar’s accretion elliciency., This points to variability being related to the quasar's accretion efficiency. Given that the relation with black hole mass is more evident at longer time lags. we believe future stuclies involving longer time baselines will shed more light on this new result.," Given that the relation with black hole mass is more evident at longer time lags, we believe future studies involving longer time baselines will shed more light on this new result." DB. €. W. and I. J. B. would. like toacknowledge support from. Microsoft. Research. the University of Hlinois. and NASA through grants. NNOGOGCGIII56 and ND," B. C. W. and R. J. B. would like toacknowledge support from Microsoft Research, the University of Illinois, and NASA through grants NNG06GH156 and NB" DB. €. W. and I. J. B. would. like toacknowledge support from. Microsoft. Research. the University of Hlinois. and NASA through grants. NNOGOGCGIII56 and ND.," B. C. W. and R. J. B. would like toacknowledge support from Microsoft Research, the University of Illinois, and NASA through grants NNG06GH156 and NB" Funding lor the Sloan Digital Sky Survey (SDSS) has been provided by the Alfred PL Sloan Foundation. the Participating Institutions. the National Aeronautics and Space Administration. the National Science Foundation. the U.S. Department of Energy. the Japanese \lonbukagakusho. and the Max. Planck Society.,"Funding for the Sloan Digital Sky Survey (SDSS) 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 ishttp://www., The SDSS Web site is. sdss.org/. The SDSS is managed. by the Astrophysical Research Consortium (ARC) for the Participating Institutions., The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. " The ""articipating Institutions are Phe University of Chicago. Fermilab. the Institute for Acwanced Study. the Japan -articipation Group. The Johns Llopkins University. the korean Scientist Croup. Los Alamos National Laboratory. he Alax-Planck-Llustitute for Astronomy (AIPLA). the Max-tanck-lnstitute for Astrophysics (ΛΗΛ). New Mexico State University. University of Pittsburgh. University. of Portsmouth. Princeton University. the United States Naval Observatory, and the University of Washington."," The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Korean Scientist Group, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington." Substituting the phase matrix from the Eq. (1))-(4)), where Substituting the phase matrix from the Eq. \ref{eq:Pcore}) \ref{eq:P2}) ) " we obtain where Joc) is the mean intensity and J,0”) is the second moment Thefirst term in Eq. (149) ", we obtain where $J_0^0(\nu')$ is the mean intensity and $J_0^2(\nu')$ is the second moment Thefirst term in Eq. \ref{eq:xiI}) ) deseribes isotropic scattering and depends only on the mean intensity., describes isotropic scattering and depends only on the mean intensity. The second term represents coherent scattering and depends on the magnetic field., The second term represents coherent scattering and depends on the magnetic field. It's value is negligible in comparison with the first term. because the anisotropy of the radiation field is usually very small.," It's value is negligible in comparison with the first term, because the anisotropy of the radiation field is usually very small." Therefore. Stokes { is mainly determined by the mean intensity.," Therefore, Stokes $I$ is mainly determined by the mean intensity." In contrast. the polarization part of the line source function (see Eq. (15)))," In contrast, the polarization part of the line source function (see Eq. \ref{eq:xiQ}) ))" does not contain contributions from isotropic scattering and linearly depends on Js., does not contain contributions from isotropic scattering and linearly depends on $J_0^2$. Due to the Wy factor this part is also subject to the Hanle effect., Due to the $W_{\rm H}$ factor this part is also subject to the Hanle effect. Therefore. the Q//-signal is proportional to the anisotropy of the radiation field which is given by (seeTrujilloBueno2001:Holzreuteretal.2005) ByD definition. the anisotropy. describes the excess of the radiation incident from the radial directions (close to vertical) in comparison with the radiation incident. from the side (horizontal direction).," Therefore, the $Q/I$ -signal is proportional to the anisotropy of the radiation field which is given by \citep[see][]{trujillo2001, holzreuteretal2005} By definition, the anisotropy describes the excess of the radiation incident from the radial directions (close to vertical) in comparison with the radiation incident from the side (horizontal direction)." For solving the statistical. equilibrium. and the radiative transfer equations for the CN violet system lines we employ the numerical NLTE code (hereafter RH-code) written. by Uitenbroek(2001) and based on the multilevel accelerated lambda iterations (MALI) method (cf.Rybicki&Hummer1991]. 1992)..," For solving the statistical equilibrium and the radiative transfer equations for the CN violet system lines we employ the numerical NLTE code (hereafter RH-code) written by \citet{uitenbroek2001} and based on the multilevel accelerated lambda iterations (MALI) method \citep[cf.][]{rybickihummer1991, rybickihummer1992}. ." Contributions from other lines were considered, Contributions from other lines were considered grains (e.g. a crystal lattice compared to amorphous ice).,grains (e.g. a crystal lattice compared to amorphous ice). Of course the EXAFS peak may represent a different mineral than ice., Of course the EXAFS peak may represent a different mineral than ice. The EXAFS will also contain instrumental features present., The EXAFS will also contain instrumental features present. Since the thickness of the instrumental ice layer is constant with time. as checked by regular calibrations. and the X-lobservations were performed in the same time frame as the lobservations. the spectra of both sources will be similarly affected by the instrumental ice layer.," Since the thickness of the instrumental ice layer is constant with time, as checked by regular calibrations, and the observations were performed in the same time frame as the observations, the spectra of both sources will be similarly affected by the instrumental ice layer." Assuming that the amplitude of both and EXAFS peaks scale in the same way with the amount of oxygen. this means that a maximum of of the EXAFS 7?=2.1 peak may be instrumental.," Assuming that the amplitude of both and EXAFS peaks scale in the same way with the amount of oxygen, this means that a maximum of of the EXAFS $R=2.4$ peak may be instrumental." " If we assume the total instrumental EXAFS feature R=1.9 peak to be due to an Oxygen column density of Ne=2«θα7. the interstellar component of the EXAFS. a minimum of of its total peak. would amount to 1.5 times the instrumental Oxygen which is ο=ὃν104""cm 2."," If we assume the total instrumental EXAFS feature $R=1.9$ peak to be due to an Oxygen column density of $N_O= 2 \times 10^{17} {\rm cm}^{-2}$, the interstellar component of the EXAFS, a minimum of of its total peak, would amount to 1.5 times the instrumental Oxygen which is $N_O= 3 \times 10^{17} \: {\rm cm}^{-2}$ ." Since the total interstellar Oxygen column density towards is about No=10«103cm2 (2). this means that the intensity of the EXAFS spectral features hints that at least of the interstellar Oxygen in the galactic plane towards is bound in solids. if we assume that the peak intensity in the EXAFS Fourier plot behaves as it would do if it would represent ice.," Since the total interstellar Oxygen column density towards is about $N_O= 10 \times 10^{17} \: {\rm cm}^{-2}$ \citep{deVries03}, this means that the intensity of the EXAFS spectral features hints that at least of the interstellar Oxygen in the galactic plane towards is bound in solids, if we assume that the peak intensity in the EXAFS Fourier plot behaves as it would do if it would represent ice." If the total EXAFS signal in can be attributed to interstellar origin. this would present an upper limit of bound in solids.," If the total EXAFS signal in can be attributed to interstellar origin, this would present an upper limit of bound in solids." This part for solids is only a very approximate number given instrumental uncertainties and other systematics and should only be seen as an indication., This part for solids is only a very approximate number given instrumental uncertainties and other systematics and should only be seen as an indication. However. such a number does not appear entirely unrealistic.," However, such a number does not appear entirely unrealistic." A major part of the Oxygen will be in atomic form (given the visibility of the narrow Is-2p line) and not be part of solids., A major part of the Oxygen will be in atomic form (given the visibility of the narrow 1s-2p line) and not be part of solids. If other atoms than oxygen are responsible for the photo-electron back scatter. as can be the case in other solids than ice. these atoms can have higher cross-sections for the back scatter process.," If other atoms than oxygen are responsible for the photo-electron back scatter, as can be the case in other solids than ice, these atoms can have higher cross-sections for the back scatter process." In such cases the estimate for the amount of oxygen bound in solids will be correspondingly lower., In such cases the estimate for the amount of oxygen bound in solids will be correspondingly lower. The EXAFS peak does fit remarkably well with amorphous ice., The EXAFS peak does fit remarkably well with amorphous ice. Problem however is that the extinction towards iis likely caused by diffuse dust clouds in the general interstellar medium., Problem however is that the extinction towards is likely caused by diffuse dust clouds in the general interstellar medium. Although water-ice is present in. the cores of dense molecular clouds. it is hardly found in diffuse clouds (see e.g. ?)).," Although water-ice is present in the cores of dense molecular clouds, it is hardly found in diffuse clouds (see e.g. \cite{Draine05}) )." Other. more robust minerals containing Oxygen. like silicates. are thought to form dust particles in diffuse clouds.," Other, more robust minerals containing Oxygen, like silicates, are thought to form dust particles in diffuse clouds." Although water-ice. given the position found for our peak in the EXAFS plot. does fit. we need data on other minerals to see if water-ice remains the only candidate.," Although water-ice, given the position found for our peak in the EXAFS plot, does fit, we need data on other minerals to see if water-ice remains the only candidate." Especially around the Oxygen edge however. such data are scarce.," Especially around the Oxygen edge however, such data are scarce." In the X-ray spectrum ofX-1.. the Oxygen-K edge was searched for the existence of EXAFS. which indicate the presence of solids in the absorbing medium.," In the X-ray spectrum of, the Oxygen-K edge was searched for the existence of EXAFS, which indicate the presence of solids in the absorbing medium." A clear signal was found., A clear signal was found. Comparing with spectra of it is found that instrumental effects may account for of the signal., Comparing with spectra of it is found that instrumental effects may account for of the signal. Assuming that EXAFS signals scale with that of water-ice we find roughly of the absorbing oxygen Is bound in solid material., Assuming that EXAFS signals scale with that of water-ice we find roughly of the absorbing oxygen is bound in solid material. Although amorphous water-1ce does fit the EXAFS peaks found. this material is an unlikely candidate given the diffuse character of the absorbing medium.," Although amorphous water-ice does fit the EXAFS peaks found, this material is an unlikely candidate given the diffuse character of the absorbing medium." The data presented here can help solving the character of interstellar dust grains when appropriate laboratory data on various. plausible materials become available., The data presented here can help solving the character of interstellar dust grains when appropriate laboratory data on various plausible materials become available. "revised models which address these issues should not only reproduce the ""red and dead"" nature of ellipticals today but also of their immediate progenitors — which may occur naturally if the progenitors have masses greater than some critical mass (see Cooray Milosavljevié 2005).",revised models which address these issues should not only reproduce the “red and dead” nature of ellipticals today but also of their immediate progenitors – which may occur naturally if the progenitors have masses greater than some critical mass (see Cooray Milosavljević 2005). The main uncertainty in the observed merger fraction is the possibility that the Northern NDWFS field. which contains over the sample. is special in its frequency of tidally disturbed objects.," The main uncertainty in the observed merger fraction is the possibility that the Northern NDWFS field, which contains over the sample, is special in its frequency of tidally disturbed objects." This seems unlikely given its area of ~400 MMpc? at <=0.1. but the issue of field-to-field variations in the merger fraction will only be settled conclusively when independent fields of similar size are studied in the same way.," This seems unlikely given its area of $\sim 400$ $^2$ at $z=0.1$, but the issue of field-to-field variations in the merger fraction will only be settled conclusively when independent fields of similar size are studied in the same way." The main uncertainty in the merger and mass aceretion rate 15 the timescale of the mergers., The main uncertainty in the merger and mass accretion rate is the timescale of the mergers. Although our estimates broadly agree with other studies (see. e.g.. Lin et 22004. and references therein). this may simply reflect the fact that similar assumptions lead to similar results.," Although our estimates broadly agree with other studies (see, e.g., Lin et 2004, and references therein), this may simply reflect the fact that similar assumptions lead to similar results." Modeling of red. gas-poor mergers has not been done in a systematic way using modern techniques. and it will be interesting to see what the timescales are for the initial coalescence and the subsequent surface brightness evolution of tidal debris.," Modeling of red, gas-poor mergers has not been done in a systematic way using modern techniques, and it will be interesting to see what the timescales are for the initial coalescence and the subsequent surface brightness evolution of tidal debris." Specifically. modeling of the 19 merging systems and 44 remnants presented here would provide much better constraints on the merger rate and mass accretion rate. particularly when more complete redshift information is available.," Specifically, modeling of the 19 merging systems and 44 remnants presented here would provide much better constraints on the merger rate and mass accretion rate, particularly when more complete redshift information is available." More detailed observational studies of the mergers and their remnants may help answer the question the mergers are red. te. what made the progenitors lose their gas?," More detailed observational studies of the mergers and their remnants may help answer the question the mergers are red, i.e., what made the progenitors lose their gas?" If active nuclei prevent the cooling of gas above some critical mass at early times they may play the same role during mergers. and it will be interesting to compare the degree of nuclear activity in undisturbed galaxies. ongoing mergers. and remnants.," If active nuclei prevent the cooling of gas above some critical mass at early times they may play the same role during mergers, and it will be interesting to compare the degree of nuclear activity in undisturbed galaxies, ongoing mergers, and remnants." Also. sensitive diagnostics of young populations (e.g.. Hà line strengths and ultra-violet photometry) can provide better constraints on the star formation histories of the mergers and remnants.," Also, sensitive diagnostics of young populations (e.g., $\delta$ line strengths and ultra-violet photometry) can provide better constraints on the star formation histories of the mergers and remnants." Finally. studies with higher spatial resolution can provide information on the detailed isophotal shapes (boxy or disky) of the remnants and their progenitors. and on possible correlations between large scale smooth distortions and the sharp ripples and shells that have been reported in z~0 ellipticals (see Hernquist Spergel 1995).," Finally, studies with higher spatial resolution can provide information on the detailed isophotal shapes (boxy or disky) of the remnants and their progenitors, and on possible correlations between large scale smooth distortions and the sharp ripples and shells that have been reported in $z\approx 0$ ellipticals (see Hernquist Spergel 1995)." Our study focuses on events that we can see today. and it will be very interesting to push the analysis to higher redshifts.," Our study focuses on events that we can see today, and it will be very interesting to push the analysis to higher redshifts." Although the most recent generation of mergers could be largely “dry”. previous generations likely involved. blue galaxies and/or were accompanied by strong star formation (see. e.g.. 1988).," Although the most recent generation of mergers could be largely “dry”, previous generations likely involved blue galaxies and/or were accompanied by strong star formation (see, e.g., 1988)." Unfortunately it will be difficult to identify the broad red tidal features that we see here at significantly higher redshift due to the (1-2) cosmological surface brightness dimming., Unfortunately it will be difficult to identify the broad red tidal features that we see here at significantly higher redshift due to the $(1+z)^4$ cosmological surface brightness dimming. The limiting depth of the MUSYC and NDWFS images is ~29 ((1o. AB).," The limiting depth of the MUSYC and NDWFS images is $\sim 29$ $1\sigma$, AB)." An equivalent survey at 2| should cover an area of >I square degree and reach levels of ~31.5 aat >=| and ~33.5 aat z22., An equivalent survey at $z\geq 1$ should cover an area of $\gtrsim 1$ square degree and reach levels of $\sim 31.5$ at $z=1$ and $\sim 33.5$ at $z=2$. Even when (unfavorable) K-corrections are ignored these requirements are well beyond the capabilities of current ground- or space-based telescopes., Even when (unfavorable) $K$ -corrections are ignored these requirements are well beyond the capabilities of current ground- or space-based telescopes. A more viable technique is to focus on the fraction of red galaxies in pairs., A more viable technique is to focus on the fraction of red galaxies in pairs. Although pair statistics require large corrections due to the short timescale of the mergers. pairs are easily detectable out to high redshift with the Hubble Space Telescope (see 1999).," Although pair statistics require large corrections due to the short timescale of the mergers, pairs are easily detectable out to high redshift with the Hubble Space Telescope (see 1999)." Based on the work presented here the mergerfraction among galaxies on the red sequence should be (0.06£0.02)«(14-2) for separations <20 kkpe and luminosity ratios >0.3., Based on the work presented here the mergerfraction among galaxies on the red sequence should be $(0.06 \pm 0.02) \times (1+z)^m$ for separations $<20$ kpc and luminosity ratios $\geq 0.3$ . follow their equilibrium values.,follow their equilibrium values. We do not attain quenched abundances for No and NI; even al the 1000 bar lower boundary of our atmosphere. but we show in subsequent sections (hat {his does not have a strong elfect on our results.," We do not attain quenched abundances for $_2$ and $_3$ even at the 1000 bar lower boundary of our atmosphere, but we show in subsequent sections that this does not have a strong effect on our results." As an upper boundary. condition we set a zero flux lid at 1 prbar with no flow allowed into or out of the top of the atmosphere., As an upper boundary condition we set a zero flux lid at 1 $\mu$ bar with no flow allowed into or out of the top of the atmosphere. From theoretical calculations. GJ 1214b is thought to be potentially undergoing atmospheric mass loss at a rate of ~9x105 &e/s (?).. however this rate is unconstrained by observations and we therefore choose to ignore the effects οἱ mass loss in our photochemical calculations.," From theoretical calculations, GJ 1214b is thought to be potentially undergoing atmospheric mass loss at a rate of $\sim 9 \times 10^8$ g/s \citep{cha09}, however this rate is unconstrained by observations and we therefore choose to ignore the effects of mass loss in our photochemical calculations." To caleulate photolvsis rates it is necessary to know the amount of stellar UV flix that is absorbed bv (he planets atmosphere., To calculate photolysis rates it is necessary to know the amount of stellar UV flux that is absorbed by the planet's atmosphere. However. (he UV spectrum of GJ 1214 has not been measured.," However, the UV spectrum of GJ 1214 has not been measured." Generally. M-stars such as GJ 1214 tend to be relatively more active than earlv-0tvpe stus. with stellar activity. decreasing as a function of stellar age.," Generally, M-stars such as GJ 1214 tend to be relatively more active than early-type stars, with stellar activity decreasing as a function of stellar age." In theory. we can place GJ 1214 on a stellar type vs. age diagram (suchasrom?) (o determine its expected level of UV flux.," In theory, we can place GJ 1214 on a stellar type vs. age diagram \citep[such as from][]{sel07} to determine its expected level of UV flux." However. given the large uncertainty in the star's age ?).. the constraints that we can place on its UV [lux are essentially meaningless.," However, given the large uncertainty in the star's age \citep[6 $\pm ^4 _3$ Gyr;][]{cha09}, the constraints that we can place on its UV flux are essentially meaningless." For this reason. we choose to include UV flux as an additional parameter in our grid of photochemical models.," For this reason, we choose to include UV flux as an additional parameter in our grid of photochemical models." We choose stellar spectra that represent (vo bounding cases of a low and high UV flix as shown in Figure L.., We choose stellar spectra that represent two bounding cases of a low and high UV flux as shown in Figure \ref{f1}. It is our assumption that the actual UV spectrum lor GJ 1214 falls somewhere in between these (wo extremes., It is our assumption that the actual UV spectrum for GJ 1214 falls somewhere in between these two extremes. For our low UV case. we emplov a stellar model with the same 7;jj and θες as GJ 1214. which we caleulate by interpolating between bracketing models by ?..," For our low UV case, we employ a stellar model with the same $T_{eff}$ and $g_{surf}$ as GJ 1214, which we calculate by interpolating between bracketing models by \citet{hau99}." The stellar model does not include sources of UV emission due to stellar activitv. so it produces a spectrum that crops off precipitously in the UV following the stellar blackbods. whieh is almost certainly an underestimate for the actual UV. [hix from GJ 1214.," The stellar model does not include sources of UV emission due to stellar activity, so it produces a spectrum that drops off precipitously in the UV following the stellar blackbody, which is almost certainly an underestimate for the actual UV flux from GJ 1214." For our high UV case. we take (he observed time-averaged spectrum of the active MA.5V. flare star AD Leo from?) (T;jj=3400 IN). which is one of the most active known Me-stars.," For our high UV case, we take the observed time-averaged spectrum of the active M4.5V flare star AD Leo from \citet{seg05} $T_{eff} = 3400$ K), which is one of the most active known M-stars." The incident stellar spectrum is then calculated at (he orbital distance of GJ 1214b. from 100 to 1000 nm. and (his flux is used for calculating photoclissociation rates for the 33 photolvsis reactions included in (he photochemical kinetics code.," The incident stellar spectrum is then calculated at the orbital distance of GJ 1214b, from 100 to 1000 nm, and this flux is used for calculating photodissociation rates for the 33 photolysis reactions included in the photochemical kinetics code." Usine the chemical abundances profiles (hat we obtain from (he photochemical mocleling. we calculate transmission spectra using the model outlined in ? [or super-Earth exoplanets.," Using the chemical abundances profiles that we obtain from the photochemical modeling, we calculate transmission spectra using the model outlined in \citet{mil09} for super-Earth exoplanets." We calculate absorption of stellar light along chords through the planets upper atinosphere and then integrate to determine the total absorption over the entire projected. annulus of the planets atmosphere in transit., We calculate absorption of stellar light along chords through the planet's upper atmosphere and then integrate to determine the total absorption over the entire projected annulus of the planet's atmosphere in transit. This results in a waveleng(h-clepencent transmission, This results in a wavelength-dependent transmission detector. the number of systems with eccentricities above 0.01 les between and4%.,"detector, the number of systems with eccentricities above 0.01 lies between and." . The eccentricity of NS-NS systems are larger than those of binaries containing BHs., The eccentricity of NS-NS systems are larger than those of binaries containing BHs. Given a much larger expected detection rate for ET. this means that there should be a significant number of NS-NS binaries with detectable eccentricities.," Given a much larger expected detection rate for ET, this means that there should be a significant number of NS-NS binaries with detectable eccentricities." Finally. in the case of DECIGO a fraction of between," Finally, in the case of DECIGO a fraction of between" this implies £(BV)=0.740-4. where the error is derived from the apparent spread in CD.V) in the figure.,"this implies $E(B-V)=0.7\pm0.4$, where the error is derived from the apparent spread in $E(B-V)$ in the figure." This supports the extinction determination of Llowarth (1983)., This supports the extinction determination of Howarth (1983). A similar method may be cmiplovecl using the dilfuse interstellar bands (DIBs) to measure extinction., A similar method may be employed using the diffuse interstellar bands (DIBs) to measure extinction. LHerbig (1975) provides plots of E(D1) versus EW for a number of dilfuse bands., Herbig (1975) provides plots of $E(B-V)$ versus EW for a number of diffuse bands. Phese plots show loss intrinsic scatter than the Na relations of Hobbs (1974) and should therefore give a better measure of E(D/—V)., These plots show less intrinsic scatter than the Na relations of Hobbs (1974) and should therefore give a better measure of $E(B-V)$. In addition they extend to higher (I1j values (~ 2.0) than the Llobbs (1974) sodium data. and so better cover the range of interest here.," In addition they extend to higher $E(B-V)$ values $\sim2.0$ ) than the Hobbs (1974) sodium data, and so better cover the range of interest here." We measure the lines in two CCD spectra taken during the previously described JINT observing run. and a total of eight spectra obtained on 1993 December 5 and 7 from the 1.5m telescope at. Mount. Palomar using the [/s.75 Cassegrain echelle spectrograph in regular erating mode (AleCarthy 1988).," We measure the lines in two CCD spectra taken during the previously described JKT observing run, and a total of eight spectra obtained on 1993 December 5 and 7 from the 1.5m telescope at Mount Palomar using the f/8.75 Cassegrain echelle spectrograph in regular grating mode (McCarthy 1988)." The DIBs measured were those centred at 5780. 5797. 6269 and 6613 (we do not employ the strong 4430 DIB as Herbig shows that it is only poorly correlated: with E(D. V).," The DIBs measured were those centred at 5780, 5797, 6269 and 6613 (we do not employ the strong 4430 DIB as Herbig shows that it is only poorly correlated with $E(B-V)$ )." The mean equivalent widths in cach band are 480. 160. 110 anc 250mA respectively. corresponding to £(BV) values of 0.8. 0.4. 0.5 and 0.9.," The mean equivalent widths in each band are 480, 160, 110 and 250 respectively, corresponding to $E(B-V)$ values of 0.8, 0.4, 0.5 and 0.9." The mean £(2BV) , The mean $E(B-V)$ fraction of sources are represented by Daring objects.,fraction of sources are represented by flaring objects. The analysis of the optical images of the Ες hosted by galaxies pointed out the presence of companion galaxies in the target environment. supporting the idea that voung radio sources reside in groups.," The analysis of the optical images of the HFPs hosted by galaxies pointed out the presence of companion galaxies in the target environment, supporting the idea that young radio sources reside in groups." The parent galaxy is usually the brightest. elliptical at the eroup centre with the exception of two sources., The parent galaxy is usually the brightest elliptical at the group centre with the exception of two sources. In. JOSO4|5431 the galaxy hosting the HPP is at the periphery of the group. and it seems interacting with a close elliptical.," In J0804+5431 the galaxy hosting the HFP is at the periphery of the group, and it seems interacting with a close elliptical." A surprising result is represented. by the LEP J1109P3831 that is hosted in a spiral that seems to be interacting with a close elliptical., A surprising result is represented by the HFP J1109+3831 that is hosted in a spiral that seems to be interacting with a close elliptical. The fact that voung radio sources reside in groups support the idea that the interactions occurring between the galaxies are at the origin of the radio We thank S. Bardelli for his help on the analysis of the optical spectra., The fact that young radio sources reside in groups support the idea that the interactions occurring between the galaxies are at the origin of the radio We thank S. Bardelli for his help on the analysis of the optical spectra. The VLA and the VLBA are operated. by the US National Radio Astronomy Observatory which is a facility of the National Science Foundation operated: under Cooperative agreement by Associated Universities. Inc. This work has made use of the NASA/IPAC Extragalactic Database NED which is operated by the JPL. Californian Institute of Technology. under contract with the National Acronautics and Space Administration.," The VLA and the VLBA are operated by the US National Radio Astronomy Observatory which is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This work has made use of the NASA/IPAC Extragalactic Database NED which is operated by the JPL, Californian Institute of Technology, under contract with the National Aeronautics and Space Administration." Funding for the SDSS and SDSS-LL has been provided by the Alfred P. Sloan Foundation. the participating Institutions. the National Science. Foundation. the U.S. Department of Energy. the National Aeronautics ancl Space Aclniinistration. the Japanese Monbukagakusho. the Max Planck Society. and the Llieher Education Funding Council for England.," 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 Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England." Phe SDSS was managed by the Astrophysical Rescarch Consortium for the Participating Institutions., The SDSS was managed by the Astrophysical Research Consortium for the Participating Institutions. "The zodi-subtracted DIRBE intensity in the 7"" pixel. DZ;. should be the sum of the cataloged stars. B;: the faint stars. Fi. assumed constant for all pixels in the qi region: and the CIRD. C which is isotropic. ie. The cataloged star contribution was computed using the “smearing” described in (2000) and Wright(2001).. where OQ, is the solid angle of the DIRBE beam. 5; is the flux of the j star and pj; is the probability of the j star affecting the 7” pixel under the assumptionsthat over the many observations in which the DIRBE beam was centered in the /"""" pixel. the beam center was uniformly distributed within the pixel aud the beam orientation is uniformly distributed in position angle.","The zodi-subtracted DIRBE intensity in the $i^{th}$ pixel, $DZ_i$, should be the sum of the cataloged stars, $B_i$; the faint stars, $F_q$, assumed constant for all pixels in the $q^{th}$ region; and the CIRB, C ,which is isotropic, i.e. The cataloged star contribution was computed using the “smearing” described in \citet{gor00} and \citet{elw01}, where $\Omega_b$ is the solid angle of the DIRBE beam, $S_j$ is the flux of the $j^{th}$ star and $p_{ij}$ is the probability of the $j^{th}$ star affecting the $i^{th}$ pixel under the assumptionsthat over the many observations in which the DIRBE beam was centered in the $i^{th}$ pixel, the beam center was uniformly distributed within the pixel and the beam orientation is uniformly distributed in position angle." " Due to the random distribution of the orientation of tlie square 0.77x0.1 beam. the probablility as a function of the angular distance. r((0.0).(0,.0,)]. between the beam center (0.0) and a particular star al (αν. ὃν) is where / is (he width of the beam (0.7 deg) ancl. Then. to account for the random position of the beam center within the pixel. this probability must be averaged over the area of (he pixel bv integrating P(r) over the solid angle of the pixel aud dividing by the pixel solid angle. Q;. so that Uneerlainties in D; were calculated as in Wright (2001)::"," Due to the random distribution of the orientation of the square $0.7^\circ \times 0.7^\circ$ beam, the probablility as a function of the angular distance, $\alpha, \delta), (\alpha_\star, \delta_\star$ )], between the beam center $\alpha, \delta$ ) and a particular star at $\alpha_\star, \delta_\star$ ) is where $l$ is the width of the beam (0.7 deg) and, Then, to account for the random position of the beam center within the pixel, this probability must be averaged over the area of the pixel by integrating P(r) over the solid angle of the pixel and dividing by the pixel solid angle, $\Omega_i$ , so that Uncertainties in $B_i$ were calculated as in \citet{elw01}: :" sull. both and LGRBs are accompanied by a rare (vpe of SNe. suggesting a strong connection between the two phenomena.,"Still, both and LGRBs are accompanied by a rare type of SNe, suggesting a strong connection between the two phenomena." Moreover. late observations of accompanied S5Ne suggest (hal their progenitors harbor central engines elal.2006a).," Moreover, late observations of accompanied SNe suggest that their progenitors harbor central engines \citep{Li99,Soderberg06}." . The two concepts can be reconciled if /-GRBs’ jets simply fail to breakout [rom (heir progenitors., The two concepts can be reconciled if ' jets simply fail to breakout from their progenitors. A “failed jet clissipates all its energy into the surrounding cocoon and drives its expansion.," A ""failed jet"" dissipates all its energy into the surrounding cocoon and drives its expansion." As the cocoon reaches the edge of the star its forward shock may become mildly or even ultra relativistic emitting the observed 5-ravs when it breaks out., As the cocoon reaches the edge of the star its forward shock may become mildly or even ultra relativistic emitting the observed $\gamma$ -rays when it breaks out. This idea that arise from shock breakouts is not new., This idea that arise from shock breakouts is not new. It was suggested shortly following the observations of GRBOS80425/SN1998bw (Ixulkarnietal.1998:MacFadyen.Woosley.&lleger2001:Tan.Matzuer.&Mcelxee. 2001).," It was suggested shortly following the observations of GRB980425/SN1998bw \citep{Kulkarni98,MacFdyen01,Tan01}." . It drew much more attention following the observation of additional with similar properties and especially with the observation of a thermal component in the spectrum of 060218 (Campanaοἱal.2006:Wangelal.2007:Waxnman.Mészáros.&Campana 2007).," It drew much more attention following the observation of additional with similar properties and especially with the observation of a thermal component in the spectrum of 060218 \citep{Campana06,Wang07,Waxman07}." . Yet. it was hard to explain how shock breakout releases enough energy in the form of 5-ravs. Ixatz.," Yet, it was hard to explain how shock breakout releases enough energy in the form of $\gamma$ -rays." Dudnik.&Waxman(2010) realized that the deviation of the breakout radiation from thermal equilibrium provides a natural explanation to the observed 5-raxs., \cite{Katz10} realized that the deviation of the breakout radiation from thermal equilibrium provides a natural explanation to the observed $\gamma$ -rays. More recently. Nakar&Sari(2011). calculated the emission from mildly ancl ultra-relativistic shock breakouts. including the post breakout dvnanmiucs and gas-radiation coupling.," More recently, \cite{Nakar11} calculated the emission from mildly and ultra-relativistic shock breakouts, including the post breakout dynamics and gas-radiation coupling." Thev find (that the total energy. spectral peak. and duration of all can be well explained by relativistic shock breakouts.," They find that the total energy, spectral peak and duration of all can be well explained by relativistic shock breakouts." Moreover. they lind that such breakouts must satisfy a specilic relation between the observed total energy. spectral peak aud duration. aud that all satislv this relation.," Moreover, they find that such breakouts must satisfy a specific relation between the observed total energy, spectral peak and duration, and that all satisfy this relation." These results lend a strong support to the idea that are relativistic shock breakouts., These results lend a strong support to the idea that are relativistic shock breakouts. From a historical point of view Chis understanding closes (he loop with Colgate's (1968) original idea. Chat preceded the detection of GRBs. (hat à SN shock breakout will produce a GRD.," From a historical point of view this understanding closes the loop with Colgate's (1968) original idea, that preceded the detection of GRBs, that a SN shock breakout will produce a GRB." In a relativistic shock breakout the burst duration is set by the properties of the shock and the envelope at the edge of the star and not by the activity tme of the engine., In a relativistic shock breakout the burst duration is set by the properties of the shock and the envelope at the edge of the star and not by the activity time of the engine. Therefore. {he engine may operate for only a short time. and still eenerate a very long burst like (hat ol 060218 anc 100316D. Thus. both longer and shorter duration may be generated by this mechanism.," Therefore, the engine may operate for only a short time, and still generate a very long burst like that of 060218 and 100316D. Thus, both longer and shorter duration may be generated by this mechanism." The activity of the central engine. within the Collapsar model. is independent of the breakout time of the jet.," The activity of the central engine, within the Collapsar model, is independent of the breakout time of the jet." This implies (hat the duration of the majority of bursts should be comparable to. or longer than. their jet breakout Gime and that lor Too EGGyr. in agreement with previous studies.,"I to $_2$ in merger remnants and ellipticals, particularly for ages $>1$ Gyr, in agreement with previous studies." We wish to thank an anonvmous referee for several very constructive and. helpful. comments., We wish to thank an anonymous referee for several very constructive and helpful comments. MILI. acknowledges support from NASA LPSA grant NIGA-98-03-L'TS.A-039., AMH acknowledges support from NASA LTSA grant NRA-98-03-LTSA-039. ‘This research has mace use of the Extragalactic Database (NED). which is operated by the Jet. Propulsion Laboratory. Caltech. uncer contract with the National Acronautics and Space Administration.," This research has made use of the Extragalactic Database ), which is operated by the Jet Propulsion Laboratory, Caltech, under contract with the National Aeronautics and Space Administration." We then repeated the microlensing fits of table 2. including a sinusoidal modulation with three additional reo parameters: period. phase and amplitude of the nodulation (Gdentical for both colors).,"We then repeated the microlensing fits of table 2, including a sinusoidal modulation with three additional free parameters: period, phase and amplitude of the modulation (identical for both colors)." Results of the fit are given in table 1.., Results of the fit are given in table \ref{tabresidus}. The fits give almost ideutica results Or uy.fy.At and bleudiug factors as jose 1n table 2 (respectively 0.12. 2568..," The fits give almost identical results for $u_0, t_0, \Delta t$ and blending factors as those in table 2 (respectively 0.42, 2568.," 123., 123. aud 0.71)., and 0.74). Of course. the nodulation can affect either the amplified component. or he blended companion.," Of course, the modulation can affect either the amplified component, or the blended companion." The results of ie fits favor the first possibility. though only at the 2.50 level.," The results of the fits favor the first possibility, though only at the $2.5\sigma$ level." We expect hat the data reported by the MACIIO. collaboration CAlcock et al.," We expect that the data reported by the MACHO collaboration (Alcock et al.," " 19975) have enough statistical power to discriminate between these two οκμμΊος,", 1997b) have enough statistical power to discriminate between these two possibilities. " We remark ∐⋜↧↑↑∐↸∖∖−∪↕↑↕∐∖∐↑↴∖↴↕↕⊔⊳↕∏≼∐∐∶↴⋁⋜↧∐↓∪≼⊔∏⋜↧⊓∪∐↑↸∖↥⋅⋯⋜∐⋅↸∖""M ⋅⋅⋅ ⋅ ↴∖↴⋜↧↑↕↴∖↴↕≯⋯⊳↑∪↥⋅⋅↖↽∙↕∐≼∐⋯↕∐∶↴∙⊾⋜↧↸⊳↸⊳⋯⋅⋜↧↑↸∖⋯∪≼∐∖"," We remark that the $\chi^2$ of the fits including a modulation term are satisfactory, indicating accurate modeling of errors." ↕∐∶↴∙⊾∪↕≯↸∖↥⋅↥⋅∪↥⋅↴∖↴∙ Figure 6 illustrates the position of the candidate reconstructed star iu the color-magnitude diagram of the surrounding region (star marker) as well as that of the two components of the bleud (circles).," Figure \ref{hrcand_1} illustrates the position of the candidate reconstructed star in the color-magnitude diagram of the surrounding region (star marker), as well as that of the two components of the blend (circles)." They all lie ou the main sequeuce., They all lie on the main sequence. The optical depth is the iustautaucous probability that a eiven source star be maenif&ed by more than a factor of 1.31., The optical depth is the instantaneous probability that a given source star be magnified by more than a factor of 1.34. It can be estimated as where e(Af) is the detection cficiency οἴνοι in table 2. T1] year aud Noi.=5.43105 stars;," It can be estimated as where $\epsilon(\Delta t)$ is the detection efficiency given in table \ref{eff}, $T_{\rm obs} = 1$ year and $N_{\rm obs}=5.3\,10^6$ stars." With the characteristics of the single event described above. this vields (fi with blending): ie. about of the optical depth predicted bv a “standard” isothermal aud isotropic spherical halo fully conrprised of compact objects (cf section 5).," With the characteristics of the single event described above, this yields (fit with blending): i.e. about of the optical depth predicted by a “standard” isothermal and isotropic spherical halo fully comprised of compact objects (cf section 5)." It isconsistent with that measured toward the Laree Alagellanic Cloud Alcocketal.1997¢.. see also Ansari et al.," It isconsistent with that measured toward the Large Magellanic Cloud \cite{Macho2yr}, see also Ansari et al." 199G6a)., 1996a). Asstuuing a standard halo model with a mass raction f composed of dark compact objects having a sinele mass AM. a likelihood analysis allows us to estimate the most probable mass of the deflector generating the observed event.," Assuming a standard halo model with a mass fraction $f$ composed of dark compact objects having a single mass $M$, a likelihood analysis allows us to estimate the most probable mass of the deflector generating the observed event." The likelihood is the product of the Poisson probability of detecting Nit events when expecting fNap. bw the probability of observing the time-scales GNE1MILLAE).," The likelihood is the product of the Poisson probability of detecting $N_{\rm evt}$ events when expecting $f\,N_M$, by the probability of observing the time-scales $(\Delta t_1,..\,, \Delta t_{\rm evt})$." We calculate likechhood contours in the (loe(oAL).£) plane usingo a Bavesian method with a uniform ↻↥⋅↕∪↥⋅↻↥⋅∪↴⋝⋜∏⋝∐↕↑∙↖↽≺∐∖∐↴∖↴↕↑⋅↖↽↕∐⋅↗↳⊽⋜⋯≼↧↕∐↕∪∶↴∙⊾∐∫⋝≺↕∙↸∖∙↸∖≺∣∏⋜↧↕ ↻↥⋅≺⋔⋜∏⋝∐↕↑∙↖↽↻↸∖↥⋅≺∐∖⋯≼∐∖∪↕≯⋯⋜↧," We calculate likelihood contours in the $(\log(M),f)$ plane using a Bayesian method with a uniform prior probability density in $f$ and in $\log(M)$ (i.e. equal probability per decade of mass)." ↴∖∷∖↴⋝∙↽∕∏∐∖⋅↖⇁⋜∐⋅↸∖↴∖↴∐∪↖↖↽∐↕∐∱↕∶↴⋁↿∐⋅↸∖ f, They are shown in figure \ref{lkl}. . ↴∖∷∖↴⋝∙↽∕∏∐∖⋅↖⇁⋜∐⋅↸∖↴∖↴∐∪↖↖↽∐↕∐∱↕∶↴⋁↿∐⋅↸∖ fa, They are shown in figure \ref{lkl}. . ↴∖∷∖↴⋝∙↽∕∏∐∖⋅↖⇁⋜∐⋅↸∖↴∖↴∐∪↖↖↽∐↕∐∱↕∶↴⋁↿∐⋅↸∖ fae, They are shown in figure \ref{lkl}. . lower than that of cosmological GRBs aud suggest that these originate from low metallicity donors of somewhat less nass than that of N33 N-7.,lower than that of cosmological GRBs and suggest that these originate from low metallicity donors of somewhat less mass than that of M33 X-7. Our suggestion that NTE J1550-56 should have the angular iionieutuni eucrey iu its explosion.E which is as large as that of cosmological CRBs. should soon be tested by the measureimoeut of the Ikerr parameter.," Our suggestion that XTE J1550-564 should have the angular momentum energy in its explosion, which is as large as that of cosmological GRBs, should soon be tested by the measurement of the Kerr parameter." " We would Like to thauk Jeff MeClintock for maux useful discussions,", We would like to thank Jeff McClintock for many useful discussions. C.E.D. was supported bv the US Department of Energy. under Crant No. DE-FC2-SSER0388., G.E.B. was supported by the US Department of Energy under Grant No. DE-FG02-88ER40388. CL.ILL. was supported by Grant No., C.H.L. was supported by Grant No. ROL-2005-000-1033LO (2005) from the Basie Research Program of the Ίνοτοα Science Eneinecring Fouudation., R01-2005-000-10334-0 (2005) from the Basic Research Program of the Korea Science Engineering Foundation. snowing the νο parameters we can make quantitative estimates of energv., Knowing the Kerr parameters we can make quantitative estimates of energy. The amount of energy poured iuto he accretiou disk of the black hole. aud. therefore. also pressure is almost untathomable..," The amount of energy poured into the accretion disk of the black hole, and, therefore, also pressure is almost unfathomable.," the 5«LOM eres bene 500 nues the energy of a stroug supernova explosion. the latter being spread over a auch larger volune than that of the accretion disk.," the $5\times10^{53}$ ergs being $500$ times the energy of a strong supernova explosion, the latter being spread over a much larger volume than that of the accretion disk." Near the horizon of the black hole. the physical situation might become quite complicated 1986).," Near the horizon of the black hole, the physical situation might become quite complicated \citep{Tho86}." . Field-line recoustruction mieht be common aud lead to serious breakdowns iu the freezing of the field to the asina: aud the field ou the black hole sometimes wieght become so strong as to push its back off the black hole aud iuto he disk (Ravleigh-Tavlor Iustabilitv) concentrating the energy even more., Field-line reconstruction might be common and lead to serious breakdowns in the freezing of the field to the plasma; and the field on the black hole sometimes might become so strong as to push its back off the black hole and into the disk (Rayleigh-Taylor Instability) concentrating the energy even more. " During the instability the magnetic field ines will be distributed randomly in ""elobs. the large ones having eaten the simall ones."," During the instability the magnetic field lines will be distributed randomly in “globs"", the large ones having eaten the small ones." It secs reasonable that the Dlaudford-Zuajek mechanisin is disnantled., It seems reasonable that the Blandford-Znajek mechanism is dismantled. Later. however. conservation laws demaud that the augular 1101200tuiuà rot used up in the GRB aud livyperuova explosion be reconstituted im the herr parameter of the black hole.," Later, however, conservation laws demand that the angular momentum not used up in the GRB and hypernova explosion be reconstituted in the Kerr parameter of the black hole." temperature. zonal (east-west) and meridional (north-south) wind velocity.,"temperature, zonal (east-west) and meridional (north-south) wind velocity." Throughout this analysis. we use the model atmosphere obtained after 1450 planetary days of integration.," Throughout this analysis, we use the model atmosphere obtained after 1450 planetary days of integration." The corresponding atmospheric structure and wind pattern are deseribed in detail in Rauscher Menou (2010)., The corresponding atmospheric structure and wind pattern are described in detail in Rauscher Menou (2010). The model extends vertically from 1 mbar at the top to 220 bar at the bottom., The model extends vertically from 1 mbar at the top to 220 bar at the bottom. Temperatures are typically around 1800 K in much of the deep atmosphere. while they vary noticeably between day and night near the model top. with lows of about 500 K and highs of about 1500 K. From the pressure and temperature. we infer local gas densities using the ideal gas law. p2pmigp/KT. with mean molecular weight j/=2.3321).," Temperatures are typically around 1800 K in much of the deep atmosphere, while they vary noticeably between day and night near the model top, with lows of about 500 K and highs of about 1500 K. From the pressure and temperature, we infer local gas densities using the ideal gas law, $\rho=\mu m_{\rm H}\,p/kT$, with mean molecular weight $\mu=2.33 m_p$." 4 Densities in the atmosphere range from about 107 g em? at the model bottom to ~1077—10 & em at the top.," Densities in the atmosphere range from about $10^{-3}$ g $^{-3}$ at the model bottom to $\sim 10^{-8}-10^{-7}$ g $^{-3}$ at the top." High in the atmosphere (say. at nanobar levels). UV photo-tonization is important in determining the atmospheric ionization level (e.g.. Murray-Clay et al.," High in the atmosphere (say, at nanobar levels), UV photo-ionization is important in determining the atmospheric ionization level (e.g., Murray-Clay et al." " 2009). but in the relatively dense levels modeled here. thermal ionization is expected to dominate the ionization At the temperatures of interest in our model atmosphere. the main source of free electrons is provided by thermal ionization of alkali metals with low first-ionization potentials: Na. Al. and K. Under these conditions. the mean ton mass is on the order of m;2:30m, (see e.g. Draine et al."," 2009), but in the relatively dense levels modeled here, thermal ionization is expected to dominate the ionization At the temperatures of interest in our model atmosphere, the main source of free electrons is provided by thermal ionization of alkali metals with low first-ionization potentials: Na, Al, and K. Under these conditions, the mean ion mass is on the order of $m_i\approx 30 m_p$ (see e.g. Draine et al." 1983)., 1983). " For simplicity. we choose to approximate Saha's equation for ionization balance with a formulation that only accounts for theionization of potassium (Balbus Hawley 2000). where n, and n, are the number densities of electrons and of neutrals. respectively (in em™). ag is the potassium abundance. and 7 is the temperature in K. Equation (1)) is a valid approximation only as long the resulting 1onization fraction. x,. remains much smaller than the abundance of potassium. ag."," For simplicity, we choose to approximate Saha's equation for ionization balance with a formulation that only accounts for theionization of potassium (Balbus Hawley 2000), where $n_e$ and $n_n$ are the number densities of electrons and of neutrals, respectively (in $^{-3}$ ), $a_K$ is the potassium abundance, and $T$ is the temperature in K. Equation \ref{eq:xe}) ) is a valid approximation only as long the resulting ionization fraction, $x_e$, remains much smaller than the abundance of potassium, $a_K$." " We have verified that this condition is reasonably well satisfied for the atmospheric conditions of interest here. with x, reaching at most ~107 in a few localized regions and taking much smaller values (Qv,~ 1077-1077) in the rest of the atmosphere."," We have verified that this condition is reasonably well satisfied for the atmospheric conditions of interest here, with $x_e$ reaching at most $\sim 10^{-9}$ in a few localized regions and taking much smaller values $x_e \sim 10^{-10}$ $10^{-14}$ ) in the rest of the atmosphere." Throughout our analysis. we assume a near solar abundance of potassium. ay=1077.," Throughout our analysis, we assume a near solar abundance of potassium, $a_K = 10^{-7}$." " This is not a critical model assumption given the much more important. exponential dependence of v, with temperature."," This is not a critical model assumption given the much more important, exponential dependence of $x_e$ with temperature." We also estimate that. even at 7~1800 K. the free electron contribution from sodium. which is ~17 times more abundant than potassium at solar composition. approaches only marginally that of potassium.," We also estimate that, even at $T \simeq 1800$ K, the free electron contribution from sodium, which is $\sim 17$ times more abundant than potassium at solar composition, approaches only marginally that of potassium." While a more complete Saha equation solution would be a clear improvement upon the very simple approach adopted here. it would not qualitatively alter our main conclusions about the role of magnetic drag.," While a more complete Saha equation solution would be a clear improvement upon the very simple approach adopted here, it would not qualitatively alter our main conclusions about the role of magnetic drag." " We assume conditions of gas neutrality. Le. 72,=2;. where n; Is the tonic number density."," We assume conditions of gas neutrality, i.e. $n_e=n_i$, where $n_i$ is the ionic number density." " The coupling between charged (i.e) and neutral particles depends on their rate of collisions. (ov),.. for which we adopt the expressions from Draine et al. ("," The coupling between charged $(i,e)$ and neutral particles depends on their rate of collisions, $\left<\sigma {\rm v}\right>_{i,e}$, for which we adopt the expressions from Draine et al. (" "1983) The electrical conductivity. o,. and the corresponding resistivity. jj. are respectively given by Cu an","1983) The electrical conductivity, $\sigma_e$, and the corresponding resistivity, $\eta$, are respectively given by _e =." dy Before proceeding with a calculation of induced currents. we need to evaluate the relative importance of various non-ideal MHD effects.," Before proceeding with a calculation of induced currents, we need to evaluate the relative importance of various non-ideal MHD effects." We begin by considering the full induction equation + where the last three terms are the ohmic. Hall and ambipolar diffusion terms. respectively.," We begin by considering the full induction equation +, where the last three terms are the ohmic, Hall and ambipolar diffusion terms, respectively." In. the above equation. the current density )..(5)v is the velocity of the neutrals. p; is the ton mass density and ~ 15 the drag coefficient. which is given by Q2.," In the above equation, the current density, ${\bf v}$ is the velocity of the neutrals, $\rho_i$ is the ion mass density and $\gamma$ is the drag coefficient, which is given by =." We estimate the relative importance of the three non-ideal MHD terms by selecting relevant velocity and length scales for the atmospheric flow., We estimate the relative importance of the three non-ideal MHD terms by selecting relevant velocity and length scales for the atmospheric flow. " For a representative induction velocity. we take the sound speed c,. since It is representative of the wind speeds achieved in the modeled transonic flow."," For a representative induction velocity, we take the sound speed $c_s$ , since it is representative of the wind speeds achieved in the modeled transonic flow." " Following Rauscher Menou (2009). we use the adiabatic value e,=“(CAT/um). with an adiabatic index T=1.47."," Following Rauscher Menou (2009), we use the adiabatic value $c_s=\sqrt(\Gamma kT/\mu m_p)$, with an adiabatic index $\Gamma=1.47$." " For now. we adopt a pressure scale height. H,,. as a representative length scale for our comparison of the non-ideal MHD terms. even though we argue below that using the resistive scale height may be a more appropriate choice."," For now, we adopt a pressure scale height, $H_p$, as a representative length scale for our comparison of the non-ideal MHD terms, even though we argue below that using the resistive scale height may be a more appropriate choice." With these choices. the magnetic Reynolds number can be evaluated as = =7 where A!=R/j3.78«107 erg/g/K is the effective gas constant and g29.42 m/s? is the gravitational acceleration of the planet.," With these choices, the magnetic Reynolds number can be evaluated as R_m H_p= , where $R'=R/\mu=3.78\times 10^7$ erg/g/K is the effective gas constant and $g=9.42$ $^2$ is the gravitational acceleration of the planet." We evaluate the relative magnitude of the Ohmic(Ohm). Hall (Hall) and Ambipolar diffusion (Amb) terms with respect," We evaluate the relative magnitude of the Ohmic(Ohm), Hall (Hall) and Ambipolar diffusion (Amb) terms with respect" 339-4 after the recovery of the jet at the end of the 1999-2000 outburst does have an unusually optically thin spectrum.,339-4 after the recovery of the jet at the end of the 1999–2000 outburst does have an unusually optically thin spectrum. The single best example of jet reactivation in the hard intermediate state appears to be the 2003 outburst of XTE 11720-318 (see Fig |)., The single best example of jet reactivation in the hard intermediate state appears to be the 2003 outburst of XTE J1720-318 (see Fig 1). In this outburst the peak radio flux appears to oceur at a hardness ratio of (OL1$, we apply reflective boundary conditions (cf." Silverman 1986: Raden 1996). replacing the Gaussian kernel with: which also ensures the correct normalization. n“Lef(qilq=1.," Silverman 1986; Ryden 1996), replacing the Gaussian kernel with: which also ensures the correct normalization, $\int_{0}^{1} \hat{f}(q) {\rm d}q =1$." In Figure 5 we present the projected axial ratio distributions for the different membership groups (circles). as indicated in the different panels. with their Poisson le error bars. while the solid lines shows the kernel estimate f for the appropriate width. /.," In Figure 5 we present the projected axial ratio distributions for the different membership groups (circles), as indicated in the different panels, with their Poisson $\sigma$ error bars, while the solid lines shows the kernel estimate $\hat{f}$ for the appropriate width, $h$." In order to find the intrinsic axial ratio distribution assuming that groups are either oblate or prolate spheroids. we use an inversion method. described. below.," In order to find the intrinsic axial ratio distribution assuming that groups are either oblate or prolate spheroids, we use an inversion method, described below." Although there is no physical justification for the restriction to oblate or prolate spheroids. it greathy simplifies the inversion problem.," Although there is no physical justification for the restriction to oblate or prolate spheroids, it greatly simplifies the inversion problem." Furthermore. if groups are a mixture of the two spheroidal populations or they have triaxial configurations then there is no unique inversion (Plionis. Barrow Frenk 1991).," Furthermore, if groups are a mixture of the two spheroidal populations or they have triaxial configurations then there is no unique inversion (Plionis, Barrow Frenk 1991)." The relation. between the apparent anc intrinsic axial ratios. is described by à set of integral equations first investigated by Hubble. (1926).," The relation between the apparent and intrinsic axial ratios, is described by a set of integral equations first investigated by Hubble (1926)." These are based on the assumptions that the orientations are random with respect to the line of sight. and that the intrinsic shapes can be approximated by either oblate or prolate spheroids.," These are based on the assumptions that the orientations are random with respect to the line of sight, and that the intrinsic shapes can be approximated by either oblate or prolate spheroids." Writing the intrinsic axial ratios as 2 and the estimated distribution function as Nf3) for oblate spheroids. and ..3) for prolate spheroids then the corresponding distribution of apparent axial ratios is given for the oblate case by: and for the prolate case by: Inverting equations τὸ). and (ος). gives us the distribution of real axial ratios as a function of the measured cistribution: and with flo)=0.," Writing the intrinsic axial ratios as $\beta$ and the estimated distribution function as $\hat N_o(\beta)$ for oblate spheroids, and $\hat N_p(\beta)$ for prolate spheroids then the corresponding distribution of apparent axial ratios is given for the oblate case by: and for the prolate case by: Inverting equations \ref{eq:apaobl}) ) and \ref{eq:apaprol}) ) gives us the distribution of real axial ratios as a function of the measured distribution: and with $\hat{f}(0)=0$." In order for Nu7) and Nf1} to be physically meaningful they should be positive for all 7s. Following Raden (1996). we numerically integrate eq.(9)) ancl eq.(10)) allowing Αν) anc N63) to take any value.," In order for $\hat{N}_{p}(\beta)$ and $\hat{N}_{o}(\beta)$ to be physically meaningful they should be positive for all $\beta$ 's. Following Ryden (1996), we numerically integrate \ref{eq:oblate}) ) and \ref{eq:prolate}) ) allowing $\hat{N}_{p}(\beta)$ and $\hat{N}_{o}(\beta)$ to take any value." we can safely state that. for the considered phases of each cycle. the shock wave will produce intensity emissions of similar strength.,"we can safely state that, for the considered phases of each cycle, the shock wave will produce intensity emissions of similar strength." In contrast. the u. q. and v Stokes parameters can strongly vary from one cycle to another.," In contrast, the u, q, and v Stokes parameters can strongly vary from one cycle to another." Both symmetries and amplitudes of q. u. and v signatures are found to be altered in many cases. inducing a change in the linear polarization angle.," Both symmetries and amplitudes of q, u, and v signatures are found to be altered in many cases, inducing a change in the linear polarization angle." Interestingly. the linear. polarization rate seems to be roughly conserved through cycles.," Interestingly, the linear polarization rate seems to be roughly conserved through cycles." This allows us to stress the non-repeatability of the polarizing processes in action., This allows us to stress the non-repeatability of the polarizing processes in action. Indeed. we know already that each cycle of the luminosity. variation of omicron Ceti is not an exact copy of the previous ones," Indeed, we know already that each cycle of the luminosity variation of omicron Ceti is not an exact copy of the previous ones" While the accelerating expansion implies only that TE1/3. combinations of CAIB data. SNla data. and arge-scale-structure data suggestthat « is most likely in he rango Ll \theta$." " IE) is à compensated filter function. then M, can be expressed in terms of the tangential component of the observable shear. 5. where the function € is related to C by In this paper we use the /21 radial filter function from. the family given in Schneider ct al. ("," If $U(\vartheta)$ is a compensated filter function, then $M_{\rm{ap}}$ can be expressed in terms of the tangential component of the observable shear, $\gamma_{\rm{t}}$ , where the function $Q$ is related to $U$ by In this paper we use the $l = 1$ radial filter function from the family given in Schneider et al. (" 1998): where vw= 8/0.,1998): where $x=\vartheta / \theta$ . Taking the expectation value over, Taking the expectation value over work. and using the recently released WFC3 observations of this region.,"work, and using the recently released WFC3 observations of this region." By searching for objects with Ho excess emission. we have already found tantalizing evidence of multiple star formation episodes (De Marchi et al.," By searching for objects with $\alpha$ excess emission, we have already found tantalizing evidence of multiple star formation episodes (De Marchi et al.," in. preparation). like in 33603.," in preparation), like in 3603." Furthermore. two distinct populations with ages of ~| and ~I5 MMyr are present in the populatior of the star cluster 3346 in the Small Magellanic Clouc (De Marchi et abl.," Furthermore, two distinct populations with ages of $\sim 1$ and $\sim 15$ Myr are present in the population of the star cluster 346 in the Small Magellanic Cloud (De Marchi et al.," in. preparation)., in preparation). Given the different environmental conditions and chemical compositions of the three clusters (Z.. for 33603. —1/3Z.. for 30 Dor anc 1/10Z.. for 3346; see HAOS. Andersen et al.," Given the different environmental conditions and chemical compositions of the three clusters $Z_\odot$ for 3603, $\sim 1/3~Z_\odot$ for 30 Dor and $\sim 1/10~Z_\odot$ for 346; see HA08, Andersen et al." 2009 and Hennekemper et al., 2009 and Hennekemper et al. 2008. respectively). this similarity supports the hypothesis that continuing star formation coulc be the preferential channel for the formation of stars Ἡ starburst clusters.," 2008, respectively), this similarity supports the hypothesis that continuing star formation could be the preferential channel for the formation of stars in starburst clusters." According to Vinkóetal.(2009).. the young cluster 996 in NGC 2403 is known to positively exhibit a young population (10—16 MMyr) together with a relatively old one (32— I00MMvr) thus suggesting multiple star formation events in a range of ages at least 4 times wider than in 33603.," According to \cite{vin09}, the young cluster 96 in NGC 2403 is known to positively exhibit a young population $10-16$ Myr) together with a relatively old one $32-100$ Myr) thus suggesting multiple star formation events in a range of ages at least 4 times wider than in 3603." A spread in the MS turn-off has been reported for clusters of intermediate age in the LMC and has been interpreted as an age spread of ~300 MMyr (seeMiloneetal. 2009)., A spread in the MS turn-off has been reported for clusters of intermediate age in the LMC and has been interpreted as an age spread of $\sim 300$ Myr \citep[see][]{mil09}. . Moreover. the discovery of multiple stellar populations along the MSand red giant branch of a large number of Galactic globular clusters (Piotto2008;Leeetal.2009) requires two or more bursts m the star formation history of these objects. separated by at a least few 107 yyr (seeCarrettaetal.2010.andreferencestherein)..," Moreover, the discovery of multiple stellar populations along the MSand red giant branch of a large number of Galactic globular clusters \citep[][]{pio08,lee09} requires two or more bursts in the star formation history of these objects, separated by at a least few $10^7$ yr \citep[see][and references therein]{car10}." Therefore. it appears that multiple generations of stars spread over a wide range of ages are present in star clusters.," Therefore, it appears that multiple generations of stars spread over a wide range of ages are present in star clusters." A detailed investigation will be necessary in order to understand what is at the origin of the observed age spread and. for example. what tis the influence of the environment and chemical/physical state (metallicity. turbulence. density. mass. etc.)," A detailed investigation will be necessary in order to understand what is at the origin of the observed age spread and, for example, what is the influence of the environment and chemical/physical state (metallicity, turbulence, density, mass, etc.)" of the parent molecular cloud on the formation of stars in clusters., of the parent molecular cloud on the formation of stars in clusters. Establishing whether age spreads like those seen in 33603 are common in. starburst clusters will have profound implications for theories of star cluster formation. for the meaning and determination of the IMF and finally for the general assumption that clusters are simple stellar populations.," Establishing whether age spreads like those seen in 3603 are common in starburst clusters will have profound implications for theories of star cluster formation, for the meaning and determination of the IMF and finally for the general assumption that clusters are simple stellar populations." We are indebted to an anonymous referee for valuable comments and suggestions that have helped us to improve the presentation of our work., We are indebted to an anonymous referee for valuable comments and suggestions that have helped us to improve the presentation of our work. We thank Vera Kozhurina-Platais for providing FORTRAN codes for WFC3 geometric distortion corrections and Max Mutchler for producing the drizzled images shown in Figure 1. and 7.., We thank Vera Kozhurina-Platais for providing FORTRAN codes for WFC3 geometric distortion corrections and Max Mutchler for producing the drizzled images shown in Figure \ref{fig_ha} and \ref{fig_ks}. This paper is based on Early Release Science observations made by the WFC3 Scientific Oversight Committee., This paper is based on Early Release Science observations made by the WFC3 Scientific Oversight Committee. We are grateful to the Director of the Space Telescope Science Institute. for awarding Director's. Discretionary time for this program., We are grateful to the Director of the Space Telescope Science Institute for awarding Director's Discretionary time for this program. Finally. we are deeply indebted to the brave astronauts of STS-125 for rejuvenating HST. (WFC3)..," Finally, we are deeply indebted to the brave astronauts of STS-125 for rejuvenating HST. ." lillecl toward us (Beipurth.Raga.&Heathcote1992).,tilted toward us \citep{Reipurth1992}. . The svstemic velocity in this svsteni is assumed to be 8.904014 L5R. as before.," The systemic velocity in this system is assumed to be $\pm$ 0.14 LSR, as before." Throughout this paper. (he velocity is relative (ο (his svstemic value.," Throughout this paper, the velocity is relative to this systemic value." As shown in Figure Gaa. the continuum emission associated with the VLÀ | source is now resolved into a disk-like structure perpendicular to the jet axis. will a Gaussian deconvolved (FWIIM) size of ~ 076x073 (~ 240x120 AU) and a P.A. of7.," As shown in Figure \ref{fig:cont}a a, the continuum emission associated with the VLA 1 source is now resolved into a disk-like structure perpendicular to the jet axis, with a Gaussian deconvolved (FWHM) size of $\sim$ $\times$ $\sim$ $\times$ 120 AU) and a P.A. of." 67... As found in PaperII. {his emission has a total flux of ~ 285440 mJv and it is the thermal emission mainly from a dusty disk. with the inner part of which already seen with a deconvolved size of ~ (60 AU) at 7 mm (Rodriguezοἱal.2008).," As found in \citet{Lee2010HH111}, , this emission has a total flux of $\sim$ $\pm$ 40 mJy and it is the thermal emission mainly from a dusty disk, with the inner part of which already seen with a deconvolved size of $\sim$ (60 AU) at 7 mm \citep{Rodriguez2008}." . Note that the emission seems to show a little Laint protrusion (o the east along the jet axis., Note that the emission seems to show a little faint protrusion to the east along the jet axis. This faint protrusion seems {ο be seen in 3.6 cm and 7 mm as well. and it may (race either the material along the jet axis or a disk around a companion in a close binary svstem as suggested in Rodriguezetal.(2008).," This faint protrusion seems to be seen in 3.6 cm and 7 mm as well, and it may trace either the material along the jet axis or a disk around a companion in a close binary system as suggested in \citet{Rodriguez2008}." . In addition. a [aint protrusion is also seen extending to the southeast from (he southern part of the cisk.," In addition, a faint protrusion is also seen extending to the southeast from the southern part of the disk." As in Paper IL. faint emission is also detected around the VLA 2 source (~ 4 σ detection with le=0.9 !)). probably tracing a disk around it.," As in \citet{Lee2010HH111}, , faint emission is also detected around the VLA 2 source $\sim$ 4 $\sigma$ detection with $\sigma=0.9$ ), probably tracing a disk around it." Moreover. (wo more faint emission peaks DCN and DC'S are seen at in the north and in the south respectively near the equatorial plane (PA. ~ 77)). probably tracing the density enhancementthere.," Moreover, two more faint emission peaks DCN and DCS are seen at in the north and in the south respectively near the equatorial plane (P.A. $\sim$ ), probably tracing the density enhancementthere." Previously in the observations (PaperL).. a flattened envelope is seen perpendicular to the jet axis. extending to ~ 7200 AU (189) out from the VLA 1 source.," Previously in the observations \citep{Lee2010HH111}, a flattened envelope is seen perpendicular to the jet axis, extending to $\sim$ 7200 AU ) out from the VLA 1 source." I is rotating. with the blueshifted emission in the north and the redshifted emission in the south.," It is rotating, with the blueshifted emission in the north and the redshifted emission in the south." " The outer part (242000— 7200 AU. or ~ 18"")) seems to have a rotation that has constant specific angular momentum with c~3.904.!+. while the inner part (~ 60—2000 AU. or ~ 5"")) seems to have a Keplerian rotation with e,L.75d""|. where d is the radial distance [rom the source in the unit of arcesecond."," The outer part $\sim$ $-$ 7200 AU, or $\sim$ ) seems to have a rotation that has constant specific angular momentum with $v_\phi\sim 3.90 d^{-1}$, while the inner part $\sim$ $-$ 2000 AU, or $\sim$ ) seems to have a Keplerian rotation with $v_\phi \sim 1.75 d^{-0.5}$, where $d$ is the radial distance from the source in the unit of arcsecond." "Outflow is also seenin O., with the blueshifted emission extending to the west and the redshifted emission extending to the east.","Outflow is also seenin , with the blueshifted emission extending to the west and the redshifted emission extending to the east." Crattonuet Piotto (Carrettaetal.2009a.1)) (Grattonetal.2001)) (Deuisenkov&199533). Carrettaetal.2009¢)) w for extensive references). aud the recently scrutinized NCC 6656 (AL 22. Miuiuoetal.20093). Terzan 5 (Ferraroctal. 2009)). aud possibly AL 51 (Sarajedini&Lavden1995:Bellazzinietal.92008: Bos. aud references therein).,"\citealt{gra04} \citealt{pio09}) \citealt{car09a,car09b}) \citealt{gra01}) \citealt{den89,lan93}) \citealt{car09c}) $\omega$ \citealt{fre75,but78,nor95} for extensive references), and the recently scrutinized NGC 6656 (M 22, \citealt{mar09}) ), Terzan 5 \citealt{fer09}) ), and possibly M 54 \citealt{sar95,bel08}: B08, and references therein)." The most striking signal of the carly pollution is the Na-O auticorrelation., The most striking signal of the early pollution is the Na-O anticorrelation. While its shape may differ from cluster to cluster. its widespread existence led us to associate it to the same definition of CC (Carrettactal. 2009d0)).," While its shape may differ from cluster to cluster, its widespread existence led us to associate it to the same definition of GC \citealt{car09d}) )." We need an adequate sapling of the Na- anticorrelation to shed light on the complex scene of the initial cluster evolution. likely occuiug in the core of eiauts clouds/associatious or even in the core of dwarf ealaxies (Bekkictal.2007:Boker 20091).," We need an adequate sampling of the Na-O anticorrelation to shed light on the complex scene of the initial cluster evolution, likely occurring in the core of giants clouds/associations or even in the core of dwarf galaxies \citealt{bek07,bok09}) )." Combining information coming from the cliemiustry au he color-imagnidude diagrams (anticorrelationus between elements. inferred THe cnuhancement. multiple/coniplex hall sequences and subgiaut branches. horizouta xenches. see Bragaglia2010 for a recent review). we nav be able to put together several pieces of the mizzle and reach a iore in-depth wnderstanding of star formation in dense environments.," Combining information coming from the chemistry and the color-magnidude diagrams (anticorrelations between elements, inferred He enhancement, multiple/complex main sequences and subgiant branches, horizontal branches, see \citealt{bra10} for a recent review), we may be able to put together several pieces of the puzzle and reach a more in-depth understanding of star formation in dense environments." This will offer a cireunstautiated answer to fundamental questions sucli as how the CCs formed iud whether they were able to mild at least part of their metaρα, This will offer a circumstantiated answer to fundamental questions such as how the GCs formed and whether they were able to build at least part of their metals. Tn this coutext. M 51 (NGC 6715) appears as a kev object.," In this context, M 54 (NGC 6715) appears as a key object." It is an old. metal-poor (e.g... Lavden&Saraje-dini 1998)). massive GC inuuersed in the nucleus of the Sagittarius dwarf spheroidal (Ser dSph) galaxy. prescutly disrupting within our Galaxy (Ibataetal.1991... Bos. and references therein).," It is an old, metal-poor (e.g., \citealt{lay98}) ), massive GC immersed in the nucleus of the Sagittarius dwarf spheroidal (Sgr dSph) galaxy, presently disrupting within our Galaxy \citealt{iba94}, B08, and references therein)." " ALS tis the most massive of the four GCs associated to the Ser dSpl. aud it has a very extended horizoutal branch GIB) with a population of ""blue hook” stars. found only in a few of the most massive GCs (Rosenbergetal. 2001))."," M54 is the most massive of the four GCs associated to the Sgr dSph, and it has a very extended horizontal branch (HB) with a population of “blue hook"" stars, found only in a few of the most massive GCs \citealt{ros04}) )." Therefore. it is af the same time the nearest fide extragalactic cluster aud the second most massive GC in the Milky," Therefore, it is at the same time the nearest extragalactic cluster and the second most massive GC in the Milky" numbers are most likely allected. by the cluster structure and dynamical evolution in wavs that are currently not well understood.,numbers are most likely affected by the cluster structure and dynamical evolution in ways that are currently not well understood. We therefore use the simulations to find the position of blue stragelers in the colour-magnitude diagrams and hence locate possible blue stragelers in the real clusters., We therefore use the simulations to find the position of blue stragglers in the colour-magnitude diagrams and hence locate possible blue stragglers in the real clusters. ‘To add the observed errors to the simulations we have modelled the observed error. distribution. and. found. the model that makes the colour spread in the observed. and simulated CALDs the same for I8z «20.," To add the observed errors to the simulations we have modelled the observed error distribution, and found the model that makes the colour spread in the observed and simulated CMDs the same for $\le$ $<$ 20." From each simulation we find the expected. number of stars in each. cluster., From each simulation we find the expected number of stars in each cluster. The simulation is normalised to the data using the number of observed. ancl sipulated: stars with 17«V«19., The simulation is normalised to the data using the number of observed and simulated stars with $<$ $<$ 19. This magnitude range avoids background contamination and also the bright star region where the blue strageler [raction is somewhat uncertain., This magnitude range avoids background contamination and also the bright star region where the blue straggler fraction is somewhat uncertain. First we find the metallicity that best. ceseribes the cluster CMDs., First we find the metallicity that best describes the cluster CMDs. . As can be seen from the isochrones in Figure 3.. for ΝΤ the isochrone shape depends only on metallicity ancl not on age.," As can be seen from the isochrones in Figure \ref{fig:VIcolmag}, for $>$ 19 the isochrone shape depends only on metallicity and not on age." Also. the reddening vector is virtually parallel to the main sequence in this region and so reddening also does not significantly allect the fit.," Also, the reddening vector is virtually parallel to the main sequence in this region and so reddening also does not significantly affect the fit." We have checked whether the background LALC field population could be inlluencing our metallicity determination using the colour-magnituce diagram in Figures 3 S of Hunter et shorteitellunt97.., We have checked whether the background LMC field population could be influencing our metallicity determination using the colour-magnitude diagram in Figures 3 8 of Hunter et \\shortcite{Hunt97}. These show that there is very little dillerence between the pre ancl post background subtraction colour-magnituce ciagrams at all magnitudes. and for stars brighter than Vez21 there is no cdillerence.," These show that there is very little difference between the pre and post background subtraction colour-magnitude diagrams at all magnitudes, and for stars brighter than $\approx$ 21 there is no difference." Figure 1 shows the observed. and simulated CAIDs of NGCTISIS and ας1505., Figure \ref{fig:metsim} shows the observed and simulated CMDs of NGC1818 and NGC1805. In Νις1505 there is à small colour shift between the chips (see Section 2)). and so we just. compare the simulations to the colour-magnitude diagram from the PC chip. which contains most of the bright cluster stars.," In NGC1805 there is a small colour shift between the chips (see Section \ref{sec:data}) ), and so we just compare the simulations to the colour-magnitude diagram from the PC chip, which contains most of the bright cluster stars." The points are the observed data and the σον scale is the simulation., The points are the observed data and the grey scale is the simulation. Phe grey scale gives the expected. number of stars in a box of width (V-I) 0.01. mags and. height (V) 0.1 mags., The grey scale gives the expected number of stars in a box of width (V-I) 0.01 mags and height (V) 0.1 mags. The simulation has age 25 Myr. metallicity Z=0.02 and the data have been de-reddened assuming I5(D-V)=0.075.," The simulation has age 25 Myr, metallicity Z=0.02 and the data have been de-reddened assuming E(B-V)=0.075." For ease of comparison the Be stars have been removed from the real data in Figure 11., For ease of comparison the Be stars have been removed from the real data in Figure \ref{fig:metsim}. .DBoth of the clusters are described well bv the simulation lor 19., .Both of the clusters are described well by the simulation for $>$ 19. The solar metallicity that we find here is higher than ve Fe/H]e-0.4 that is expected for the LMC clusters (sce discussion in section. 1))., The solar metallicity that we find here is higher than the $\approx$ -0.4 that is expected for the LMC clusters (see discussion in section \ref{sec:intro}) ). Ht could. be the case that jese clusters are more metal-rich than the surrounding population as there are no metallicity measurements. for stars in NOGC'J1SQ05 and only a couple of stars measured with veh resolution in NGCISIS., It could be the case that these clusters are more metal-rich than the surrounding population as there are no metallicity measurements for stars in NGC1805 and only a couple of stars measured with high resolution in NGC1818. Some of the dillerence could rowever be due to a systematic error in the calibration of LIST. magnitudes to Johnson-Cousins which. as noted in subsection 2.1. could be as high as 0.04 in V-L. Next we fix the simulation metallicity at Z=0.02 and consider the age of each cluster.," Some of the difference could however be due to a systematic error in the calibration of HST magnitudes to Johnson-Cousins which, as noted in subsection \ref{subsec:WFPC2red} could be as high as 0.04 in V-I. Next we fix the simulation metallicity at Z=0.02 and consider the age of each cluster." The age allects the appearance of the CMD at bright mags (V«I18)., The age affects the appearance of the CMD at bright mags $<$ 18). We have compared each cluster to 10. 25 and 40 Myr old simulations. and. also to combined simulations of two ages. 225 Myr and 25&440 Myr.," We have compared each cluster to 10, 25 and 40 Myr old simulations, and also to combined simulations of two ages, 25 Myr and 40 Myr." Ehe latter are used to provide constraints on any age spread in the clusters., The latter are used to provide constraints on any age spread in the clusters. The isochrones in Figure 3 illustrate that the red supergiant positions in the CALD are mostly allected by age., The isochrones in Figure \ref{fig:VIcolmag} illustrate that the red supergiant positions in the CMD are mostly affected by age. The observed red supergiant numbers and magnitudes rule out the LO Myr old. simulation., The observed red supergiant numbers and magnitudes rule out the 10 Myr old simulation. Unfortunately. as can also be seen from Figure 3.. the exposure time for the FSIJW. observations was long enough to saturate these stars and so the red supergiant positions do not allow us to distinguish between the 25 and 40 Myr old simulations.," Unfortunately, as can also be seen from Figure \ref{fig:VIcolmag}, the exposure time for the F814W observations was long enough to saturate these stars and so the red supergiant positions do not allow us to distinguish between the 25 and 40 Myr old simulations." Most. of the red supergiants are not saturated in the V. vs. VLE, Most of the red supergiants are not saturated in the V vs V-H "In our SN database, 2908 (14%)) of the supernovae are observed post r-band peak while 1489 (796)) are observedpre r-band peak.","In our SN database, 2908 ) of the supernovae are observed post $r$ -band peak while 1489 ) are observedpre $r$ -band peak." " See Figure and Table [1] for the results for the 600 SNe in the sample[2 with peaks (i.e., the regression spline maximum is not at an end point)."," See Figure \ref{fig:dfilt} and Table \ref{tab:dfilt} for the results for the 600 SNe in the sample with peaks (i.e., the regression spline maximum is not at an end point)." " The z-axis of Figure shows At=t,—to, while the second and third columns of Table[ll show the estimated mean and standard deviation for At. ("," The $x$ -axis of Figure \ref{fig:dfilt} shows $\Delta t = \hto - t_o$, while the second and third columns of Table \ref{tab:dfilt} show the estimated mean and standard deviation for $\Delta t$ . (" The fourth column indicates the estimated correlation between At and redshift z.),The fourth column indicates the estimated correlation between $\Delta t$ and redshift $z$ .) " We find that using the time of the r-band peak flux as our estimator t, is the proper choice: it is nearly unbiased[5] and it Table],has the minimum variance.", We find that using the time of the $r$ -band peak flux as our estimator $\hto$ is the proper choice: it is nearly unbiased and it has the minimum variance. " In Figure and we characterize t5, the r-band max estimator of to, given 1,000 examples each of different SN types, each observed in the r band."," In Figure \ref{fig:dsne} and Table \ref{tab:dsne}, we characterize $\hto$, the -band max estimator of $t_0$, given 1,000 examples each of different SN types, each observed in the $r$ band." " The conclusion that we draw is that if we corrected {ο using host z estimates, the effect on other SN types would be minimal, judging by the standard deviations shown in Table "," The conclusion that we draw is that if we corrected $\hto$ using host $z$ estimates, the effect on other SN types would be minimal, judging by the standard deviations shown in Table \ref{tab:dsne}. ." Simulated SNe light curveswithout a peak in the B.r-band are treated differently from those with peaks., Simulated SNe light curveswithout a peak in the -band are treated differently from those with peaks. To estimate, To estimate lt has long been known (c.g. Visvanathan anc Sandage 1977) that the more luminous early-twpe (elliptical. and SO) galaxies tend το have receler colours.,It has long been known (e.g. Visvanathan and Sandage 1977) that the more luminous early-type (elliptical and S0) galaxies tend to have redder colours. Expressed in magnitudes. the colour-magnituce relation (CALR) is approximately linear.," Expressed in magnitudes, the colour-magnitude relation (CMR) is approximately linear." Phe form of the CMI is most readily observed in a rich galaxy cluster. which provides a very wide luminosity range of I/8S0s at a single redshift.," The form of the CMR is most readily observed in a rich galaxy cluster, which provides a very wide luminosity range of E/S0s at a single redshift." The CMBI provides significant information about galaxy evolution., The CMR provides significant information about galaxy evolution. Firstly. from the tightness (scatter <0.05 mag) of the €MB for the E/SO0s in the Coma ancl Virgo clusters. Bower. Lucey and Ellis (1992) concluded that these galaxies had formed at z>2.," Firstly, from the tightness (scatter $<0.05$ mag) of the CMR for the E/S0s in the Coma and Virgo clusters, Bower, Lucey and Ellis (1992) concluded that these galaxies had formed at $z>2$." secondly. the slope of the CMB appeared to derive primarily from a correlation of metallicity with galaxy mass (e.g. Ixocama and Aromoto LOOT: Vazdekis et al.," Secondly, the slope of the CMR appeared to derive primarily from a correlation of metallicity with galaxy mass (e.g. Kodama and Aromoto 1997; Vazdekis et al." 2001)., 2001). Higher metallicity results in redder colours for eiven age., Higher metallicity results in redder colours for a given age. Phe observed. trend would reflect the greater ability of more massive ο/SOs to retain metal-enriched. σας during their formative starbursts., The observed trend would reflect the greater ability of more massive E/S0s to retain metal-enriched gas during their formative starbursts. An increase in stellar age with galaxy mass may play a secondary role., An increase in stellar age with galaxy mass may play a secondary role. Acree sequence’ of 2/80 ealaxies is seen in rich clusters out to at least 2=127. with little or no change in the CMB slope (Blakeslee et al.," A `red sequence' of E/S0 galaxies is seen in rich clusters out to at least $z=1.27$, with little or no change in the CMR slope (Blakeslee et al." 2003: Mei et al., 2003; Mei et al. 2006. 2009).," 2006, 2009)." Ehe red sequence appears to have first formed at z~2 (Labbe et al., The red sequence appears to have first formed at $z\sim 2$ (Labbé et al. asvmametric. suggesting that both intrinsic/environmoental ancl relativistic elfects are important.,"asymmetric, suggesting that both intrinsic/environmental and relativistic effects are important." The 3CRR sample is a complete unbiased. sample of sources selected at a low radio frequency., The 3CRR sample is a complete unbiased sample of sources selected at a low radio frequency. Lt is orientation-independent since the Dux densities of the sources in the sample are generally clominatecl by the dilfuse emission of the racio lobes., It is orientation-independent since the flux densities of the sources in the sample are generally dominated by the diffuse emission of the radio lobes. The presence of jets or probable jets has been found in virtually all 32 quasars in the sample aim in of the radio galaxies., The presence of jets or probable jets has been found in virtually all 32 quasars in the sample and in of the radio galaxies. Therefore. the uncertainties are associated with the presence or otherwise of jets in the remaining of the complete sample and these are no likely to be large.," Therefore, the uncertainties are associated with the presence or otherwise of jets in the remaining of the complete sample and these are not likely to be large." Let us consider first the reliability of using the ‘probable’ jets in the analysis., Let us consider first the reliability of using the `probable' jets in the analysis. The sample was divide into two subsamples. the first containing all sources with probable jets. and the second the remaining S4 sources with clinite Jets.," The sample was divided into two subsamples, the first containing all sources with probable jets, and the second the remaining 84 sources with definite jets." The statistics of probable jets shows that 16/22 TOY) are LEBILE sources while 6 )) are ERI sources., The statistics of probable jets shows that 16/22 ) are +FRII sources while 6 ) are $-$ FRII sources. Lor the second sample. 51/81 (0) and 30/81 (38%))are ΕΠΙ and ΕΠΗ sources respectively.," For the second sample, 51/81 ) and 30/81 )are +FRII and $-$ FRII sources respectively." We conclude that no bias is introduced. by including the probable jets in the analvsis., We conclude that no bias is introduced by including the probable jets in the analysis. According to the relativistic beaming model for the radio jets. there is a strong selection effect. favouring the detection of jets in FRI sources which are oriented close to the line of sight.," According to the relativistic beaming model for the radio jets, there is a strong selection effect favouring the detection of jets in FRII sources which are oriented close to the line of sight." Within the context. of orientation-based unified schemes. it is therefore natural that. the. sources without detectable jets should. be radio galaxies in which the axis of ejection lies close to the plane of the sky.," Within the context of orientation-based unified schemes, it is therefore natural that the sources without detectable jets should be radio galaxies in which the axis of ejection lies close to the plane of the sky." " For these ""missing! sources. the fractional separation dillerence should. be predominantly due το intrinsic/environmoental asvmmetries and the distributions of the space. velocities of lobes e; and. e should. be symmetric about wy=0."," For these `missing' sources, the fractional separation difference should be predominantly due to intrinsic/environmental asymmetries and the distributions of the space velocities of lobes $v_{\rm j}$ and $v_{\rm cj}$ should be symmetric about $x_{\rm l} = 0$." Therefore. jet orientation selection elfect. would not change the symmetry of the observed distributions of cj. but would slightly decrease the asymmetry. parameter.," Therefore, jet orientation selection effect would not change the symmetry of the observed distributions of $x_{\rm l}$, but would slightly decrease the asymmetry parameter." In the worst case. the 20 sources for which the jet side has not been determined would be clistributec exactly svmmetricallv and so we would expect 14.5 more FRI and 14.5 more | FRILL sources. reducing the estimate of 2 from the value 2=0.3 found in Section 6.1 to 0.47.," In the worst case, the 29 sources for which the jet side has not been determined would be distributed exactly symmetrically and so we would expect 14.5 more $-$ FRII and 14.5 more $+$ FRII sources, reducing the estimate of $\varepsilon$ from the value $\varepsilon = -0.3$ found in Section 6.1 to $-0.47$." The sample of 103 sources was derived from a literature search of all available radio maps and it is important to compare the statistics with samples which have been observed with more uniform criteria of sensitivity and angular resolution., The sample of 103 sources was derived from a literature search of all available radio maps and it is important to compare the statistics with samples which have been observed with more uniform criteria of sensitivity and angular resolution. Ligh-resolution observations of a sample of 50 3CTU ETE radio galaxies with z«0.3 are presented by Larceastle (1998). representing the combined samples of Black (1992). Leahy (1997) and. Hardcastle (1997).," High-resolution observations of a sample of 50 3CR FRII radio galaxies with $z < 0.3$ are presented by Hardcastle (1998), representing the combined samples of Black (1992), Leahy (1997) and Hardcastle (1997)." 34 of the 50 ETUL radio galaxies belong to the BCR complete sample., 34 of the 50 FRII radio galaxies belong to the 3CRR complete sample. Of these 34 radio galaxies. only 6 (or 184)) did not possess jets or probable jets. à somewhat greater success rate than for our sample. as expected.," Of these 34 radio galaxies, only 6 (or ) did not possess jets or probable jets, a somewhat greater success rate than for our sample, as expected." For 12 radio galaxies. depolarisation asvmametries have been used to determine the jet-side where no radio jet has been detected.," For 12 radio galaxies, depolarisation asymmetries have been used to determine the jet-side where no radio jet has been detected." Since no jet was detected. the axes of these sources are. Likely to lie close to the. plane of the sky and intrinsic/environmental asvmmetries are likely to be important.," Since no jet was detected, the axes of these sources are likely to lie close to the plane of the sky and intrinsic/environmental asymmetries are likely to be important." These may also be more important than the Laine-Garrington cllect in causing the observed depolarisations (Pecleltw L989a and. AleCarthy 1991)., These may also be more important than the Laing-Garrington effect in causing the observed depolarisations (Pedelty 1989a and McCarthy 1991). Taking the jet-side to be the less depolarized. side may change the true sign of wy from. positive to negative or vice versa with equal probability. as the orientation of the jet axes are assumed to be isotropic.," Taking the jet-side to be the less depolarized side may change the true sign of $x_{\rm l}$ from positive to negative or vice versa with equal probability, as the orientation of the jet axes are assumed to be isotropic." This selection elfect is not likely to influence strongly the observed. distribution of wy and the asvinmetry parameter because it concerns only 12 sources., This selection effect is not likely to influence strongly the observed distribution of $x_{\rm l}$ and the asymmetry parameter because it concerns only 12 sources. We have repeated the complete analysis excluding these 12 radio galaxies and found that their exclusion mates no difference to our conclusions., We have repeated the complete analysis excluding these 12 radio galaxies and found that their exclusion makes no difference to our conclusions. Scheuer (1995) noted a number of other ellects which could bias the analysis of the jet-sicle of the ΕΠΗ sources., Scheuer (1995) noted a number of other effects which could bias the analysis of the jet-side of the FRII sources. For example. misalignmoent of the jets. intrinsic one-sidecdness of the radio jets. and misalignment and distortion of the radio lobes. can all complicate the analysis.," For example, misalignment of the jets, intrinsic one-sidedness of the radio jets, and misalignment and distortion of the radio lobes, can all complicate the analysis." These could. all be modelled (see for example Best. 1995). but the ellects were found to be quite small in that analysis.," These could all be modelled (see for example Best 1995), but the effects were found to be quite small in that analysis." A plot of radio luminosity against fractional separation dilference is presented in Fig. 6.., A plot of radio luminosity against fractional separation difference is presented in Fig. \ref{fig-6}. Phe diagram is V-shaped with a tendency for the spread. in fractional separation difference to increase with increasing luminosity up to Dumor?Wiz.1., The diagram is V-shaped with a tendency for the spread in fractional separation difference to increase with increasing luminosity up to $P_{178} \approx 10^{29}{\rm W} {\rm Hz}^{-1}$. Intrinsic/environmental.MN. asvmnmetries. are necessary to account for negative values of wry and there is à trend for this asvmnmetryv to increase with luminosity. or with redshift since. in the present [lux density. limited sample. radio Luminosity ancl redshift are correlated.," Intrinsic/environmental asymmetries are necessary to account for negative values of $x_{\rm l}$ and there is a trend for this asymmetry to increase with luminosity, or with redshift since, in the present flux density limited sample, radio luminosity and redshift are correlated." A possible explanation for this increase is that high redshift (22 0.5) EHIL radio galaxies are associated with the brightest galaxies in rich. clusters. while their low redshift counterparts tend. to lie in isolated. environments or in small eroups (billy Prestage 1987. Hill Lilly 1991. Best 1998).," A possible explanation for this increase is that high redshift $z>0.5$ ) FRII radio galaxies are associated with the brightest galaxies in rich clusters, while their low redshift counterparts tend to lie in isolated environments or in small groups (Lilly Prestage 1987, Hill Lilly 1991, Best 1998)." Gradients in the intergalactic eas density should be present in these rich clusters on the scale of the overall structure of the radio sources. which might lead to asvmmetric environments on large scales.," Gradients in the intergalactic gas density should be present in these rich clusters on the scale of the overall structure of the radio sources, which might lead to asymmetric environments on large scales." Furthermore. Best (1996. 1997) present evidence that the interstellar medium in the vicinity of ὃς radio galaxies at z~1 must contain clumpy cold gas to account for the pronounced alignment elfect. clisplaved by these. galaxies. which is not observed. at small. redshifts.," Furthermore, Best (1996, 1997) present evidence that the interstellar medium in the vicinity of 3CR radio galaxies at $z \sim 1$ must contain clumpy cold gas to account for the pronounced alignment effect displayed by these galaxies, which is not observed at small redshifts." Both intrinsic/cnvironmental ancl relativistic ellects contribute to positive values of ur. ancl there is considerable spread: of these values at. high luminosities.," Both intrinsic/environmental and relativistic effects contribute to positive values of $x_{\rm l}$ , and there is considerable spread of these values at high luminosities." " The luminositwfractiona separation dillerence correlation for high luminosity quasars Liss>107""Wz+ "," The luminosity–fractional separation difference correlation for high luminosity quasars $P_{178} > 10^{29}\,{\rm W}{\rm Hz}^{-1}$ " is robust enough to resemble the persistence and uniformity OF PerfMeuse OVEL a variety of star forming svstenis with cdilferent local conditions. and whether it can allow [or different slopes seen e.g. in observations of dwarf galaxies under physical. conditions similar to those found. in these πμο...,"is robust enough to resemble the persistence and uniformity of $n_{\rm gas}/n_{\rm dense}$ over a variety of star forming systems with different local conditions, and whether it can allow for different slopes seen e.g. in observations of dwarf galaxies under physical conditions similar to those found in these systems." A geometrical explanation to Eq. (3)), A geometrical explanation to Eq. \ref{densdens}) ) has an additional tantalizing potential consequence., has an additional tantalizing potential consequence. Equation (2)) implies that the star formation rate surface censity scales [linearly with the very dense gas. or. equivalently. that at those high densities the star formation timescale is roughly constant and independent of Xa With Τομις~ Const.," Equation \ref{SFRvsDense}) ) implies that the star formation rate surface density scales linearly with the very dense gas, or, equivalently, that at those high densities the star formation timescale is roughly constant and independent of $\Sigma_{\rm den,gas}$: with $\tau_{\rm SF, dense}\sim {\rm const}$ ." " Llowever. in this case Mapox nd if XuoxSay, due to geometry. then MspoxMES."," However, in this case $\dot{\Sigma}_{\rm SF} \propto \Sigma_{\rm den, gas}$ and if $\Sigma_{\rm gas} \propto \Sigma_{\rm den,gas}^n$ due to geometry, then $\dot{\Sigma}_{\rm SF}\propto \Sigma_{\rm gas}^n$." " The observationallv motivated: assumption of a star formation timescale independent of “ayo, at high densities. in combination with a topologicallv-driven scaling between dense and total gas. can thus provide a geometrical interpretation of the star formation law itself."," The observationally motivated assumption of a star formation timescale independent of $\Sigma_{\rm den}$ at high densities, in combination with a topologically-driven scaling between dense and total gas, can thus provide a geometrical interpretation of the star formation law itself." This paper is structured as follows., This paper is structured as follows. Our formulation and our algorithms for the reproduction of multifractal three-dimensional geometries are discussed. in Section ??.., Our formulation and our algorithms for the reproduction of multifractal three-dimensional geometries are discussed in Section \ref{form}. Our results are presented in Section ??.., Our results are presented in Section \ref{theres}. We discuss our findings in Section ??.. and we summarize our conclusions in Section 22," We discuss our findings in Section \ref{disc}, and we summarize our conclusions in Section \ref{sum}." 1n order to investigate how the mean surface density of very dense gas correlates with the surface density of the total gas in dillerent multifraetal ISM topologies. we need to generate a multifractal structure. ancl perform appropriate “observations” of its total and dense “eas” surface densities.," In order to investigate how the mean surface density of very dense gas correlates with the surface density of the total gas in different multifractal ISM topologies, we need to generate a multifractal structure, and perform appropriate “observations” of its total and dense “gas” surface densities." In this section. we describe these procedures.," In this section, we describe these procedures." To generate a multi-fractal. we adapt the algorithm of Boreani ct al. (," To generate a multi-fractal, we adapt the algorithm of Borgani et al. (" 1993). which is à moclification of the 7 model (Frisch et al.,"1993), which is a modification of the $\beta$ model (Frisch et al." LOTS) and the ranclom-.) mocdel (Benzi ct al., 1978) and the $\beta$ model (Benzi et al. 1984) of Cully developed. turbulence., 1984) of fully developed turbulence. We start with a parent three-dimensional cube of side L. which we divide into 2? equal-volume subcubes. cach of which inherits some fraction. f; of the parent-cube mass. where jm]p...28.," We start with a parent three-dimensional cube of side $L$, which we divide into $2^3$ equal-volume subcubes, each of which inherits some fraction $f_i$ of the parent-cube mass, where $i=1,..,8$." Mass conservation implies that »-fi=1.," Mass conservation implies that $\sum _{i=1}^{8} f_i = 1$." We repeat the fragmentation (where cach subcube now becomes a parent-cube) Jf times., We repeat the fragmentation (where each subcube now becomes a parent-cube) $H$ times. The fraction. of the total mass contained in each final cube of volume £L5/258 depends on its fragmentation history., The fraction of the total mass contained in each final cube of volume $L^3/2^{3H}$ depends on its fragmentation history. The properties of the final structure depend. on the choice of £;., The properties of the final structure depend on the choice of $f_i$. Wall f; are non-zero and equal. then the result is à homogeneous structure.," If all $f_i$ are non-zero and equal, then the result is a homogeneous structure." If some of the f; are zero and all of the non-vanishing f; are equal. then the result. is à monolractal structure. with a fractal dimension uniquely set by the choice of £;.," If some of the $f_i$ are zero and all of the non-vanishing $f_i$ are equal, then the result is a monofractal structure, with a fractal dimension uniquely set by the choice of $f_i$." Wo thenon-vanishing f; are not equal. then a multi-fractal structure results.," If thenon-vanishing $f_i$ are not equal, then a multi-fractal structure results." To obtain a pattern-[ree structure that still retains the scaling properties of a fractal (self-similarity) or a multifractal (self-allinitv). the pattern of f; is not kept constant in all iterations: cach f; value is assigned to a random subeube 7 in cach iteration.," To obtain a pattern-free structure that still retains the scaling properties of a fractal (self-similarity) or a multifractal (self-affinity), the pattern of $f_i$ is not kept constant in all iterations: each $f_i$ value is assigned to a random subcube $i$ in each iteration." Each multifractal cube is taken to represent one LSAL topology., Each multifractal cube is taken to represent one ISM topology. We investigate how the total gas surface density correlates with the dense gas surface censity in cillerent parts of this object in the following wav: once a multifractal cube is constructed according to the algorithm above. a ol-sight is selected. parallel to one side of the cube.," We investigate how the total gas surface density correlates with the dense gas surface density in different parts of this object in the following way: once a multifractal cube is constructed according to the algorithm above, a line-of-sight is selected, parallel to one side of the cube." " The face of the cube which is perpendicular to that line is then split into 228E square patches (each side of the face is split into 2"" ""segments).", The face of the cube which is perpendicular to that line is then split into $2^{2(H-3)}$ square patches (each side of the face is split into $2^{H-3}$ segments). " For each of these patches. an ""observation is mace of its total surface density. by summing up all of the mass within the volume defined by the pateh and extending along the line of sight. ancl dividing by the surface. area of the patch."," For each of these patches, an “observation” is made of its total surface density, by summing up all of the mass within the volume defined by the patch and extending along the line of sight, and dividing by the surface area of the patch." " Similarly. the ""dense gas” surface density is calculated by summing up all of the mass within regions of local volume density above the “dense gas” threshold within the same volume. and dividing by the surface area of the patch."," Similarly, the “dense gas” surface density is calculated by summing up all of the mass within regions of local volume density above the “dense gas” threshold within the same volume, and dividing by the surface area of the patch." ‘To test the robustness of our results against variations of the detailed. properties of the multifractal cube. we have repeated our measurements for seven distinct. multifractals.," To test the robustness of our results against variations of the detailed properties of the multifractal cube, we have repeated our measurements for seven distinct multifractals." The properties of these. multifractals. Cf; ancl number. of refinement levels. 77) ave given in Table 1..," The properties of these multifractals $f_i$ and number of refinement levels, $H$ ) are given in Table \ref{thetable}." The first questions we seek to answer are whether the scaling between the very dense gas and total eas in à multifractal medium resembles that of Eq. 03)):, The first questions we seek to answer are whether the scaling between the very dense gas and total gas in a multifractal medium resembles that of Eq. \ref{densdens}) ); and whether such a scaling is robust enough against. variations in the detailed properties of the multifractal (parameterized in our model by the values of the f; ancl ££) so that such a scaling can be viewed as an intrinsic property of multifractal geometries. rather than as a result. of fine-tuning of the multifractal model.," and whether such a scaling is robust enough against variations in the detailed properties of the multifractal (parameterized in our model by the values of the $f_i$ and $H$ ) so that such a scaling can be viewed as an intrinsic property of multifractal geometries, rather than as a result of fine-tuning of the multifractal model." We address these questions in Fig. 1..," We address these questions in Fig. \ref{fig1}," which shows the surface density of dense gas. Mass in this case defined as gas with local volume density at least 3/5107 times the mean volume density. as a function of the surface density of total gas Xa. for three dillerent. multifractals. (X. B. and C.," which shows the surface density of dense gas, $\Sigma_{\rm den,gas}$, in this case defined as gas with local volume density at least $3\times 10^3$ times the mean volume density, as a function of the surface density of total gas $\Sigma_{\rm gas}$, for three different multifractals (A, B, and C)." Each datapoint corresponds to a dilferent. patch within the multifractal cube., Each datapoint corresponds to a different patch within the multifractal cube. " The three fractals depicted in this figure have different mass fractions. {εν however they all have ""wide"" global PDEs (see upper panel of Fig."," The three fractals depicted in this figure have different mass fractions, $f_i$ , however they all have “wide” global PDFs (see upper panel of Fig." 3. and discussion below)., \ref{fig4} and discussion below). In all cases. the scaling between un. and Milena 19 Clearly nonlinear (significantly deviates fromthe," In all cases, the scaling between $\Sigma_{\rm gas}$ and $\Sigma_{\rm den,gas}$ is clearly nonlinear (significantly deviates fromthe" hot-spot flix by a factor of ο7. where ↕⊳∖⊽⊔∐↲∪↕↽≻∐≺∢≀↧↴↥≼⇂≼↲↕↽≻⊔↥≀↧↴⊳∖⊽⊳∖⇁∪≺∢↕≀↧↴∥↲≼⇂∖∖↽↕⊔↥⊔∐↲∐∪∐−⊔∐↲↕⋅∐↓≀↧↴↥≼↲↥≼↲≺∢∏⋅∪∐⊳∖⊽↕∐⊔∐↲≀↧↴≺∢≺∢↕⋅,"hot-spot flux by a factor of $\e^{-\tau}$, where is the optical depth associated with the non-thermal electrons in the accretion flow." ≼↲∐∪∐∐∪∖∖↽⋅↴∏∐⊳∖⊽ is shown by the magenta lines in Fig. 3.., This is shown by the magenta lines in Fig. \ref{fig:drs}. While we should also include the thermal electron component. al 7mnm waveleneth the non-thermal electrons appear to dominate the opacity.," While we should also include the thermal electron component, at $7\,\mm$ wavelength the non-thermal electrons appear to dominate the opacity." The free parameter dr is associated with the finite extent of the hot spot., The free parameter $\delta r$ is associated with the finite extent of the hot spot. That is. it is possible for the spot to be visible even if the hot-spot center is inside of (he accretion-Llow photosphere.," That is, it is possible for the spot to be visible even if the hot-spot center is inside of the accretion-flow photosphere." It is lor this reason that the centroid variability is more similar to (he idealized Newlouian value for high-Iuminositv spots than for low-Iuminositv. spots., It is for this reason that the centroid variability is more similar to the idealized Newtonian value for high-luminosity spots than for low-luminosity spots. Selling or using the hot-spot photosphere radius alone gives the dotted magenta line. which muclerestimates the centroid variability considerably at small radii for large (brisht) hot spots.," Setting $\delta r$ using the hot-spot photosphere radius alone gives the dotted magenta line, which underestimates the centroid variability considerably at small radii for large (bright) hot spots." This is due to the failure of the idealized Newtonian ealeulation to account [or the strong lensing of large spots in small orbits (with rjjc r)., This is due to the failure of the idealized Newtonian calculation to account for the strong lensing of large spots in small orbits (with $r_{\rm spot}\simeq r$ ). However. simply emploving a larger or larger ad the largest disk/hot-spot Hlux ratio we consider) results in a substantially improved fit.," However, simply employing a larger $\delta r$ larger at the largest disk/hot-spot flux ratio we consider) results in a substantially improved fit." Possible reasons for position wander include intrinsic variations m the position of the emitiing plasma(e.g... variations in (he accretion flow or perhaps in a jet) or extrinsic processes such as refractive interstellar scattering.," Possible reasons for position wander include intrinsic variations in the position of the emitting plasma, variations in the accretion flow or perhaps in a jet) or extrinsic processes such as refractive interstellar scattering." iis observed to be diffractivelv scattered to a size of G4.~0.5(A/0.7cim)? mas. where A is the observing wavelength.," is observed to be diffractively scattered to a size of $\theta_{sc} \sim 0.5 (\lambda/0.7~{\rm cm})^2$ mas, where $\lambda$ is the observing wavelength." Flux density. [Inetuations are modest and decrease in strength with increasing wavelength: thus strong refractive scintillations are not indicated al. 1991)., Flux density fluctuations are modest and decrease in strength with increasing wavelength; thus strong refractive scintillations are not indicated \citep{Gwinn:1991}. ". Any relractive position wander should be «&8, and should occur on time scales 0.D/v. where D is (he distance and v is (he transverse velocity of the scattering ""screen"" relative to the observer (Romani.Narav"," Any refractive position wander should be $\ll \theta_{sc}$ and should occur on time scales $>\theta_{sc}D/v$, where $D$ is the distance and $v$ is the transverse velocity of the scattering “screen” relative to the observer \citep{Romani:1986}." an&Blancllorcdl1936).. For DzzRy228 kpe 1993) and v~100|. characteristic of material in the inner ~100 pe of the Galaxy where large scattering sizes are observed. the refractive time scale is >107 hours.," For $D\approx\Ro\approx8$ kpc \citep{Reid:1993} and $v\sim100$, characteristic of material in the inner $\sim100$ pc of the Galaxy where large scattering sizes are observed, the refractive time scale is $>10^3$ hours." Thus. we would not expect a significant contribution to the short-term wander of [from refractive scattering.," Thus, we would not expect a significant contribution to the short-term wander of from refractive scattering." " For comparison. Gwinnοἱal.(1955), using VLBI observations ol the Ser D2(N) mmnmasers near the Galactic center. [imd a wander limit of «18µας over Limescales of months for maser spots. which are diffractivelv scattered to a comparable size (at 22 GIIz) as ((at 43 Gllz)."," For comparison, \citet{Gwinn:1988}, using VLBI observations of the Sgr B2(N) masers near the Galactic center, find a wander limit of $<18~\muas$ over timescales of months for maser spots, which are diffractively scattered to a comparable size (at 22 GHz) as (at 43 GHz)." " OF course. our results provide an observation limit to any refractive position wander,"," Of course, our results provide an observation limit to any refractive position wander." The atlas is available in table form via the Internet.,The atlas is available in table form via the Internet. The spectra of Vega were recorded in 2006 during observing runs at the Bolwunsan Observatory the aid of DOES. the fiber-Ied echelle spectrograph (Ixim et al..," The spectra of Vega were recorded in 2006 during observing runs at the Bohyunsan Observatory the aid of BOES, the fiber-fed echelle spectrograph (Kim et al.," 2007) attached to the T.8an telescope., 2007) attached to the 1.8-m telescope. The spectrograph has 3 observational modes with three levels of resolving power: 30.000. 45.000 and 90.000.," The spectrograph has 3 observational modes with three levels of resolving power: 30,000, 45,000 and 90,000." The spectrograph has a CCD camera equipped with a 4096x2048 pixels matrix (pixel size 15j/mx15;0n) which allows us to cover in a sinele exposure the wavelength range 73700 e 10000 ddivided into 75-33 spectral orders without anv gaps up to ~9500 A., The spectrograph has a CCD camera equipped with a $\times$ 2048 pixels matrix (pixel size $\mu$ $\times$ $\mu$ m) which allows us to cover in a single exposure the wavelength range $\sim$ 3700 – $\sim$ 10000 divided into 75-83 spectral orders without any gaps up to $\sim$ 9500. . Our spectra were recorded in the highest resolving power mode (R = 90.000) corresponding to the full width al (he half maximum of the instrumental profile ~2.5 pixels.," Our spectra were recorded in the highest resolving power mode (R = 90,000) corresponding to the full width at the half maximum of the instrumental profile $\sim$ 2.5 pixels." The collected. spectra were reduced using standard software packages IRAE. (Τον. 1993) and DECI (Galazutdinov. 1992).," The collected spectra were reduced using standard software packages IRAF (Tody, 1993) and DECH (Galazutdinov, 1992)." The latter was used for final stages of processing: removal of telluric lines. merging of spectra. wavelength scale correction. continuum normalization. measurements of equivalent widths. ete.," The latter was used for final stages of processing: removal of telluric lines, merging of spectra, wavelength scale correction, continuum normalization, measurements of equivalent widths, etc." IRAF was used lor bias/background subtraction and one-dimensional spectra extraction., IRAF was used for bias/background subtraction and one-dimensional spectra extraction. Inter-order stray light in DOES spectra is less (han 2 percent of the intensities of the neighboring order (Ixim et al..," Inter-order stray light in BOES spectra is less than 2 percent of the intensities of the neighboring order (Kim et al.," 2007)., 2007). However. the IRAF task APALL (we used it for the extraction of one-dimensional spectra from echelle images) does not provides anv control of background subtraction equality. therefore we used (he APSCATTER task for careful background subtraction.," However, the IRAF task APALL (we used it for the extraction of one-dimensional spectra from echelle images) does not provides any control of background subtraction quality, therefore we used the APSCATTER task for careful background subtraction." Traces of cosmic ray hits were removed during a stage of combining of individual spectra using an algoritha, Traces of cosmic ray hits were removed during a stage of combining of individual spectra using an algorithm Traces of cosmic ray hits were removed during a stage of combining of individual spectra using an algorithan, Traces of cosmic ray hits were removed during a stage of combining of individual spectra using an algorithm There is a remarkable decrease of Ad=200»67pc. AM=0.10»0.03.M. if our compressible QSAA is substituted. for ΑΛ. i.c. more physical input is used in the frame of a one-dimensional model in space.,"There is a remarkable decrease of $\Delta d=200\rightarrow 67\mbox{pc}$ , $\Delta {\cal M}=0.10\rightarrow 0.03{\cal M}_\odot$ if our compressible QSAA is substituted for UAA, i.e. more physical input is used in the frame of a one-dimensional model in space." Since (10)) was derived. from the dynamic. equation (3)). the mass determination is more accurate from this while the distance is more uncertain.," Since \ref{107a}) ) was derived from the dynamic equation \ref{1.100}) ), the mass determination is more accurate from this while the distance is more uncertain." This is rellected in the shape of the curves in Fig. 3((, This is reflected in the shape of the curves in Fig. \ref{fig3}( ( a).,a). Phe large formal error of d originates [rom the non-separabilitv of errors in 0.8.by.Oba/OLOPho/OU and aUm(s).," The large formal error of $d$ originates from the non-separability of errors in $\vartheta,{\dot\vartheta},{\ddot\vartheta},h_0, \partial h_0/\partial t,\partial^2 h_0/\partial t^2$ and $a^{\rm (dyn)}(r,t)$." A first attempt to derive d. and ME of an RR star from the over-simplified version (1)) of (3)) was described bv Bareza(2003)., A first attempt to derive $d$ and ${\cal M}$ of an RR star from the over-simplified version \ref{1.102}) ) of \ref{1.100}) ) was described by \citet{barc1}. . The present results for the distance and mass of SU Dra only slightly from the previous d=(647+16)pe. M=MMο.”(0.664.03)!..," The present results for the distance and mass of SU Dra differ only slightly from the previous $d=(647\pm 16)\mbox{pc}$, ${\cal M}=(0.66\pm .03){\cal M}_\odot$." The most. probable reason of the very good is the existence of the phase island. with the good. QSAA at qos0.93. just when the atmosphere is at a stancdstill: consequentIvy. (1)) is à good approximation because of ezz0.," The most probable reason of the very good coincidence is the existence of the phase island with the good QSAA at $\varphi\approx 0.93$, just when the atmosphere is at a standstill; consequently, \ref{1.102}) ) is a good approximation because of $v\approx 0$." The values d=640 pc. M=0.47.ME. given by Liu& are very close to the present ones.," The values $d=640$ pc, ${\cal M}=0.47{\cal M}_\odot$ given by \citet{liuj1} are very close to the present ones." However. some caution is appropriate because of the underestimated uncertainties in their derivation.," However, some caution is appropriate because of the underestimated uncertainties in their derivation." Fheir A4 originates [rom using (1)). Le. €=0. the UAX corresponding to line 3 in ‘Table b," Their ${\cal M}$ originates from using \ref{1.102}) ), i.e. $C=0$, the UAA corresponding to line 3 in Table \ref{tab2}." ecause of the uncertain value of ος Nd£dm20.6 is well nOpossible.," Furthermore, because of the uncertain value of $v_\gamma$, $\Delta d/d \la 0.6$ is well possible." In BW method. the propagation of the error Ar.= ean be estimated from (2)) as follows.," In the BW method, the propagation of the error $\Delta v_\gamma=1\:\mbox{kms}^{-1}$ can be estimated from \ref{2.202}) ) as follows." " Typical radius changes of an RR star are fsHu10"" km within P/2zlav.", Typical radius changes of an RR star are $R_{\rm max}-R_{\rm min} \approx 5\times 10^5$ km within $P/2\approx\mbox{half day}$. The error of the radius change is Aανοspall95«10 km. bec ac(Busμι ὃν ," The error of the radius change is $\Delta R \approx \Delta v_\gamma P/2 \approx 5\times 10^4$ km, i.e. $\Delta R/(R_{\rm max}-R_{\rm min}) \approx 0.1$." d=(RinRainEARShuesuuu). the Final error will be Adfd0.1.," By $d=(R_{\rm max}-R_{\rm min} \pm \Delta R) /(\vartheta_{\rm max}-\vartheta_{\rm min})$, the final error will be $\Delta d/d\approx 0.1$." This considerably exceeds the error originating from the projection factor (e.g. Liu&Janes 1990)) converting the observed. radial velocity to. pulsation velocity., This considerably exceeds the error originating from the projection factor (e.g. \citealt{liuj1}) ) converting the observed radial velocity to pulsation velocity. Furthermore. by (2)) and (1) ) the error Adjdzz0.1 propagates to an error AM/M=0.2," Furthermore, by \ref{2.202}) ) and \ref{1.102}) ), the error $\Delta d/d\approx 0.1$ propagates to an error $\Delta {\cal M}/{\cal M} \approx 0.2$." The lower limit of the magnitude averaged visual absolute brightness is Myo>[0.48 mag if d<124 pc. while Ady=|0.26.τίOL mag belong to the improbable values d=S00and900 pc. respectively.," The lower limit of the magnitude averaged visual absolute brightness is $M_V > +0.48$ mag if $d < 724$ pc, while $M_V=+0.26,+0.01$ mag belong to the improbable values $d=800\:\mbox{and}\:900$ pc, respectively." Observed coloursand magnitucles of a spherically pulsating star have been compared with those of static Ixurucz model atmospheres to determine fundamental. paranietors of the star in the frame of the QSAA., Observed coloursand magnitudes of a spherically pulsating star have been compared with those of static Kurucz model atmospheres to determine fundamental parameters of the star in the frame of the QSAA. Photometric and hivedrodynamic conditions have been formulated. for. the validity QSAA in spherically pulsating stars., Photometric and hydrodynamic conditions have been formulated for the validity QSAA in spherically pulsating stars. of Encrev under DOE Nuclear Theory Craut DE-EC2-95ER1093L.,of Energy under DOE Nuclear Theory Grant DE-FG02-95ER40934. where and where the modified IIubble paramcter H is specified as before byEq. (11)).,where and where the modified Hubble parameter ${\cal H}$ is specified as before byEq. \ref{newHub}) ). To conrpare our predictions with the maeuituce residuals measured by Toury ct al. (, To compare our predictions with the magnitude residuals measured by Tonry et al. ( "2003) for 92 SNIa at 2> 0.1. we write Αι=5b(gyyg)5log|le(l| :)DgaC)]. where :. y aud óg are read from cols 7. 8 and 9 of Table 15 in that paper [y=log(d,IT,)].","2003) for 92 SNIa at $z>0.1$ , we write $\Delta m(z)=5(y\pm\delta y)-5\log [c(1+z)\Dfid(z)]$ , where $z$, $y$ and $\delta y$ are read from columns 7, 8 and 9 of Table 15 in that paper $y=\log (\dL\Ho)$ ]." To incorporate the new aud invaluable survey of 23 SNIa at 5—1 compiled by Ricss et al. (, To incorporate the new and invaluable survey of 23 SNIa at $z\sim1$ compiled by Riess et al. ( "2006). we note that 4=log(d,I7,)i(ii,C)where pi, is read frou column 3 of that paper aud C is a constant whose value is fixed by requiring that both samples eive consistentvalues of οfor SNI9OTE at 2=1.755. nuplviug that C=15.825.","2006), we note that $y=\log (\dL\Ho)=\smallfrac{1}{5}(\muo-{\cal C})$where $\muo$ is read from column 3 of that paper and ${\cal C}$ is a constant whose value is fixed by requiring that both samples give consistentvalues of $\dL$for SN1997ff at $z=1.755$ , implying that ${\cal C}=15.825$ ." The solar atinosphere introduces several complications to (he above gravitational deflection scenario.,The solar atmosphere introduces several complications to the above gravitational deflection scenario. They are due to the [acts that it consists partly of a free-electron gas and Chat il is turbulent First. a ree electron eas responds to the (time) variable electric field of a passing electromagnetic wave ancl. for low enough frequencies. will absorb it.," They are due to the facts that it consists partly of a free-electron gas and that it is turbulent First, a free electron gas responds to the (time) variable electric field of a passing electromagnetic wave and, for low enough frequencies, will absorb it." The plasma frequency. al which the refractive index of the plasma turns imaginary and hence absorptive. is proportional to (he square-root of the electron density (e.g. RubickiandLightman (1979))) and (therefore as we go progressively lower into the solar almosphere. progressively higher frequencies of radio waves will not be able to propagate.," The plasma frequency, at which the refractive index of the plasma turns imaginary and hence absorptive, is proportional to the square-root of the electron density (e.g. \citet{rub79}) ) and therefore as we go progressively lower into the solar atmosphere, progressively higher frequencies of radio waves will not be able to propagate." " lessetal.(1999) have shown that the electron density at the Solar photosphere is of the order (1—5)x105 emo3Ὁ,", \citet{and97} have shown that the electron density at the Solar photosphere is of the order $(1-5)\times 10^8$ $^{-3}$. So. even for a quiet Sun. no radiation below a few hundred MIEz can propagate through the solar atinosphere.," So, even for a quiet Sun, no radiation below a few hundred MHz can propagate through the solar atmosphere." second. (he density gradient in (he solar atmosphere aud hence the electron. density influences the propagation of radio waves through the medium.," Second, the density gradient in the solar atmosphere and hence the electron density influences the propagation of radio waves through the medium." Even for those Irequencies which can propagate through it. the anisotropy of (he solar atmosphere will cause refractive bending of the propagating ravs.," Even for those frequencies which can propagate through it, the anisotropy of the solar atmosphere will cause refractive bending of the propagating rays." Since (he densitv decreases outwards. this will cause a divergence in the propagating ravs.," Since the density decreases outwards, this will cause a divergence in the propagating rays." Hlence. the location of the focus for a given impact parameter will be shifted (o lurger distances than expected if the Sun did not have an almosphere.," Hence, the location of the focus for a given impact parameter will be shifted to larger distances than expected if the Sun did not have an atmosphere." Any experiment involving propagation of an electromagnetic waves near the Sun laces a great challenge to overcome the refraction in the immediate solar vicinity due to various sources., Any experiment involving propagation of an electromagnetic waves near the Sun faces a great challenge to overcome the refraction in the immediate solar vicinity due to various sources. The solar plasma is the main source of noise in an observations near the limb of the sun., The solar plasma is the main source of noise in an observations near the limb of the Sun. " In general. one can express the total deflection angle £45, as follows: where 65; is the dominant plasma contribution. and €; contains all non-dispersive sources of"," In general, one can express the total deflection angle $\theta_{\tt tot}$ as follows: where $\theta_{\tt pl}$ is the dominant plasma contribution, and $\theta_{\tt n}$ contains all non-dispersive sources of" The infrared. colours of discs around. voung stars. provide a prime diagnostic tool for analvsing the evolution of circumstellar disces.,The infrared colours of discs around young stars provide a prime diagnostic tool for analysing the evolution of circumstellar discs. Just as the distribution of stars on a Ilertzsprung Russell diagram contains information about the relative duration of various stellar evolutionary stages. so infrared two colour diagrams have played. a similar role in the case of disce studies.," Just as the distribution of stars on a Hertzsprung Russell diagram contains information about the relative duration of various stellar evolutionary stages, so infrared two colour diagrams have played a similar role in the case of disc studies." In. particular. IxXeonson Hartmann (1995) drew attention. in the case of voung stars in the ‘Taurus star forming region. to à pronounced eap in this diagram. intermediate between the colours of optically thick discs and those of stellar. photospheres.," In particular, Kenyon Hartmann (1995) drew attention, in the case of young stars in the Taurus star forming region, to a pronounced gap in this diagram, intermediate between the colours of optically thick discs and those of stellar photospheres." This suggested that voung stars undergo arapid transition between disc possessing and ciscloss status. which is a small fraction (around 104) of their previous lifetimes as cise bearing sources.," This suggested that young stars undergo a transition between disc possessing and discless status, which is a small fraction (around $10 \%$ ) of their previous lifetimes as disc bearing sources." Such “two timescale’ behaviour has provided. a strong constraint on viable models of disc clearing. requiring scenarios. such as photoevaporation (Clarke et al 2001. Alexander et al 2006. Ercolano et al 2008. Ercolano. Clarke Drake 2009. Gorti Hollenbach 2009. Owen et al 2010) or possibly planet formation (Armitage Ilansen 1999) where there is à finalvapid clearing phase.," Such `two timescale' behaviour has provided a strong constraint on viable models of disc clearing, requiring scenarios, such as photoevaporation (Clarke et al 2001, Alexander et al 2006, Ercolano et al 2008, Ercolano, Clarke Drake 2009, Gorti Hollenbach 2009, Owen et al 2010) or possibly planet formation (Armitage Hansen 1999) where there is a final clearing phase." Discriminating between these two scenarios may become possible in the future when cise statistics in clusters of cillerent metallicities start becoming available (Eircolano Clarke 2010. Yasui et al 2009).," Discriminating between these two scenarios may become possible in the future when disc statistics in clusters of different metallicities start becoming available (Ercolano Clarke 2010, Yasui et al 2009)." In recent. vears. data acquired. with the Spitzer Space ‘Telescope has permitted collation of infrared. colours. for stars in a range of star forming regions (Allen ct al 2007: Evans et al 2009: Gutermuth et al 2009: Ixoenig ct al," In recent years, data acquired with the Spitzer Space Telescope has permitted collation of infrared colours for stars in a range of star forming regions (Allen et al 2007; Evans et al 2009; Gutermuth et al 2009; Koenig et al" disk are then dependent as well ou the accuracy of svuthetic stellar spectra. which are not well-coustraimed by observations at these waveleugths.,"disk are then dependent as well on the accuracy of synthetic stellar spectra, which are not well-constrained by observations at these wavelengths." Iu this case. it is not possible to improve the detection limits. aud. in the case ofSpitzer. detectious are limited to 250% of the photospheric flux (Beichmanetal.2005).," In this case, it is not possible to improve the detection limits, and, in the case of, detections are limited to $> 50$ of the photospheric flux \citep{bei05}." . As the ε Eri SED shows. the excess ftux over the photosphere is larger by a factor of Lat 850 ccompared with 70μπα. aud this contrast becomes much ereater for cooler dust.," As the $\epsilon$ Eri SED shows, the excess flux over the photosphere is larger by a factor of 4 at 850 compared with 70, and this contrast becomes much greater for cooler dust." Note that for the very. bright AO star Vega at only 8 pc. the photosphere is ouly 5 ius.," Note that for the very bright A0 star Vega at only 8 pc, the photosphere is only 5 mJy." Therefore. assuming SCUBA-2 calibration to104.. the largest photospherie error in the survey at 850 wwill be £0.5 mJ. so the calibration error will be less than the confusion But fluctuations of 0.7 ud rls.," Therefore, assuming SCUBA-2 calibration to, the largest photospheric error in the survey at 850 will be $\pm 0.5$ mJy, so the calibration error will be less than the confusion limit fluctuations of 0.7 mJy rms." ↕≧⋜↧↸⊳↨↘↽∶↴∙⊾↥⋅∪∏∐≼↧↸⊳∪∐↕⋟∏↴∖↴↕∪∐↕↴∖↴↑∐↸∖⋜∏⋝↴∖↴∪↕∏↑↸∖∏∏↘∐∐∐↑↕≯∪↥⋅, Background confusion is the absolute flux limit for any disk survey. ⋜⋯⋅↖⇁ ⋝↸∖⋜∐⊔↓⋜↧↑⊤∩∕∣⋯ ((the best waveleneth for debris detection). but the photometric techuique actually nuits this to z 2indy (Beichman etal.2005)and often oulv 5 1nJy is reached )ecause of Galactic foregrounds.," For, the confusion limit is 0.7 mJy $^{-1}$ at 70 (the best wavelength for debris detection), but the photometric technique actually limits this to $\approx 2$ mJy \citep{bei05} and often only 5 mJy is reached because of Galactic foregrounds." For 5 Jy at 70 pan erain clussivity of ο =0.7.the SUNS survey is intrinsicallgwore scusitive to dust cooler than 30 IK. For ar-IR limits of 2 nidy. sinele temperature disks would be detectable down to 26 Is aud for a range of Jj of 1.0 to V0. the luüt lies between 26-13 Ix. The bbemn ofSpitzer at T0 aand the bright and complex cirus backeround are further liniting factors to the far-IR scusitivity.," For 5 mJy at 70 and grain emissivity of $\beta = 0.7$, the SUNS survey is more sensitive to dust cooler than 30 K. For far-IR limits of 2 mJy, single temperature disks would be detectable down to 26 K and for a range of $\beta$ of 1.0 to 0.0, the limit lies between 26-43 K. The beam of at 70 and the bright and complex cirrus background are further limiting factors to the far-IR sensitivity." With SCUDBA-2. we lose less than of stars (i.c.. those too far south) and importantly. with absolutely no additional bias due the cirrus backeround. which is uot a factor in submillimeter observations.," With SCUBA-2, we lose less than of stars (i.e., those too far south) and importantly, with absolutely no additional bias due the cirrus background, which is not a factor in submillimeter observations." Subiuillimeter single dish observations of debris disks are constrained by relatively poor resolution compared to optical observations., Submillimeter single dish observations of debris disks are constrained by relatively poor resolution compared to optical observations. " The beamsize of the SUNSS observations will be15"".. the JCAMT’s resolution at 850jou."," The beamsize of the SUNSS observations will be, the JCMT's resolution at 850." However. the poteutial does exist to follow-up detections with 150 oobservations with a substantially better resolution ofτ," However, the potential does exist to follow-up detections with 450 observations with a substantially better resolution of." "ήν, Even out to a distance of approximately 30 pe. we welt expect significant exteuded emission based ou the areest examples with ~300 AU radii νο, aacross) (Sheretotal.2001). and κο accurate photometry requires fully-saupled maps to the same nuiting sensitivity."," Even out to a distance of approximately 30 pc, we might expect significant extended emission based on the largest examples with $\sim 300$ AU radii (i.e., across) \citep{she04}, and so accurate photometry requires fully-sampled maps to the same limiting sensitivity." Existing survevs are lanited by the sparse pixel spaciug of current instrumentation (6.8.Wyattctal.2003).," Existing surveys are limited by the sparse pixel spacing of current instrumentation \citep[e.g.,][]{wdg03}." SCUBA-2’s Nyquist sampling will vc a valuable new feature. which is miportanut if we are )okiug for relatively cool exteuded dust around nearby stars.," SCUBA-2's Nyquist sampling will be a valuable new feature, which is important if we are looking for relatively cool extended dust around nearby stars." Qur detections of new debris disks will provide some clear possible followup observatious., Our detections of new debris disks will provide some clear possible followup observations. Fille iu the SED iib thereby refining dust teniperatures and spectral indices can be carried out in the short subiillieter aud far-IR. and this prospect is nuineut through the current AIART all-sky survey and targeted observations with theObservatory using its photometric instruments SPIRE (theSpectralandPhotometricingREceiver.Griffetal.2006) and PACS (thePho-al.2006).," Filling in the SED and thereby refining dust temperatures and spectral indices can be carried out in the short submillimeter and far-IR, and this prospect is imminent through the current AKARI all-sky survey and targeted observations with the using its photometric instruments SPIRE \citep[the Spectral and Photometric Imaging REceiver,][]{gri06} and PACS \citep[the Photodetector Array Camera and Spectrometer,][]{pog06}." . While the SUNS survey dataset will have a παοτι flux sensitivity. the mass sensitivity of the survey is a function of three factors: the distauce of the target. d. the teiiperature(s) of the material in the disks. {μι aud the opacity of the disks. Εν.," While the SUNS survey dataset will have a uniform flux sensitivity, the mass sensitivity of the survey is a function of three factors: the distance of the target, $d$, the temperature(s) of the material in the disks, $T_d$, and the opacity of the disks, $\kappa_\nu$." At subiillimeter waveleusths. in the Ravleigh-Jeaus limit. the mass of the disk becomes a luear function of the temperature in the disk.," At submillimeter wavelengths, in the Rayleigh-Jeans limit, the mass of the disk becomes a linear function of the temperature in the disk." This makes the mass relatively straight-forward to estimate ifthe temperature can be constrained., This makes the mass relatively straight-forward to estimate if the temperature can be constrained. " The opacity in the disk is wavelenetl dependent (kK,~~A 13 and difficult to mieasure observationallv. but the tvpical value adopted for debris disks at 850 iis LT cn? t,o based on a modified blackbody with >=1 (Deutetal.2000:Pol"," The opacity in the disk is wavelength dependent $\kappa_\nu \propto \lambda^{-1}$ ) and difficult to measure observationally, but the typical value adopted for debris disks at 850 is 1.7 $^2$ $^{-1}$, based on a modified blackbody with $\beta = 1$ \citep{den00,pol94}." lackctL991).. Figure 5. shows the mass sensitivity. of the SUNS survey as a function of teniperature for circumstellar dust emission at several kev clistauces i our survey., Figure \ref{mass_sensitivity} shows the mass sensitivity of the SUNS survey as a function of temperature for circumstellar dust emission at several key distances in our survey. The mass of the closest kuown debris disk. e Evidani. aud the lass Corresponding to teu times that of the I&uiper Belt are also indicated.," The mass of the closest known debris disk, $\epsilon$ Eridani, and the mass corresponding to ten times that of the Kuiper Belt are also indicated." This mass seusitivitv is for unresolved sources., This mass sensitivity is for unresolved sources. For resolved sources. our nass sensitivity will be lower.," For resolved sources, our mass sensitivity will be lower." For new disks. we wout iuuuediatelv be able to constrain the disk temperature. unless measurements (even resulting in nou-doetectious) have been iade in the nuid-IR or far-IR (e.g. through Spitzer. ISO or IRAS).," For new disks, we won't immediately be able to constrain the disk temperature, unless measurements (even resulting in non-detections) have been made in the mid-IR or far-IR (e.g., through Spitzer, ISO or IRAS)." For some cold disks (50 IK). additional 150," For some cold disks $< 50$ K), additional 450" P aud the outer arni(egspg c93.120kins Vy.,") and the outer arm $v_{LSR} \sim -93, -120$ )." For the observatious reported here σος=ene|16©., For the observations reported here $v_{LSR} = v_{hel} + 16$. The sight line is also im a direction where the warp of the outer galaxy extends to large Calactic latitudes., The sight line is also in a direction where the warp of the outer galaxy extends to large Galactic latitudes. The interstellar spectrin of ITIS21|613 is dominated by lines of IT» aud jiu the FUSE bandpass., The interstellar spectrum of H1821+643 is dominated by lines of $_2$ and in the FUSE bandpass. Also preseut areCISLLPu ‘and .," Also present are, and ." Strong aac lines were also detected in spectra obtained while the satellite was in the cartl’s shadow. where the terrestrial day glow enuission lines iu these species are absent.," Strong and lines were also detected in spectra obtained while the satellite was in the earth's shadow, where the terrestrial day glow emission lines in these species are absent." The 1030—10104. rreeion of the spectymu clisplaving LL11032.1035. 10060 aud several IT» lines is shown in Figure 1.," The $1030-1040$ region of the spectrum displaying 1032,1038, 1036 and several $_2$ lines is shown in Figure 1." The lines are strong aud lave ueceative velocity wines extending out to as incl as ~170 for ]:uullli5., The lines are strong and have negative velocity wings extending out to as much as $\sim -170$ for 1145. These negative velocity components are formed above the outer arm. and are also seen in aud linesσα in CUIRS data (Savage.Sembach&Lu1995).," These negative velocity components are formed above the outer arm, and are also seen in and lines in GHRS data \citep{savage95}." . The Il; lines are local aud are not seen at large negative volocities., The $_2$ lines are local and are not seen at large negative velocities. It is interesting to compare the strengths of the LL11018.1066 lines to those in the multiplet at5.," It is interesting to compare the strengths of the 1048,1066 lines to those in the multiplet at." Iu a fully neutral medium. these lues should have simular equivalent widths since they have uearly simular values of P=log(C4A)|logCfA) where A= cosmic abundance. ie. P5859.0," In a fully neutral medium, these lines should have similar equivalent widths since they have nearly similar values of $P \equiv {\rm log}(A) + {\rm log}(f\lambda)$ where $A =$ cosmic abundance, i.e., $P \sim 8.5-9.0$." However. the lues are noticeably weaker than the stronglv saturated lines in the spectra of IT182116123.," However, the lines are noticeably weaker than the strongly saturated lines in the spectra of H1821+643." Sofia have pointed out that in diffuse clouds i unlikely to be depleted onto dust erains.," \citet{sofia98} have pointed out that in diffuse clouds is unlikely to be depleted onto dust grains." Nevertheless. hey argue that in regions that are partially ionized by EUV radiation. nay appear to be deficicut relative to (for yy because it has a substantially larger ionization cross section and thus wieht be more ionized.," Nevertheless, they argue that in regions that are partially ionized by EUV radiation, may appear to be deficient relative to (or ) because it has a substantially larger ionization cross section and thus might be more ionized." Note that iis ouly clearly detected in the intermediate aru., Note that is only clearly detected in the intermediate arm. It is not detected in the Perseus or outer arms. probably because the Ar is more highly ionized at ereater distances from the Galactic plane.," It is not detected in the Perseus or outer arms, probably because the Ar is more highly ionized at greater distances from the Galactic plane." The aabsorption at |120 to 150 lis associated with the outer armi aud distaut warp of our Galaxy., The absorption at $-120$ to $-150$ is associated with the outer arm and distant warp of our Galaxy. If we assume that the halo corotates with the nuuderlving disk. the implied Calactocentric distance of the absorbing gas is ~2550 kpe. and the distance above he plane is ~1020 kpe.," If we assume that the halo corotates with the underlying disk, the implied Galactocentric distance of the absorbing gas is $\sim 25-50$ kpc, and the distance above the plane is $\sim 10-20$ kpc." " Indepeucent evidence for the existence of aabsorptiou iu the outer halo of our galaxy is supplied by heabsence of aabsorptiou at velocities exceeding —£0 iin the FUSE spectrum of K1-16. which is oulv 85"" away youn T1821)613 on the sky. aud is at a distance of 1.6 spe (Ixuketal.2000).."," Independent evidence for the existence of absorption in the outer halo of our galaxy is supplied by the of absorption at velocities exceeding $-70$ in the FUSE spectrum of K1-16, which is only $85''$ away from H1821+643 on the sky, and is at a distance of 1.6 kpc \citep{kruk00}. ." Consequently. the high negative-velocity aabsorptiou seen in W821)618 must be formed in the Galactic halo bevoud IN1-16.," Consequently, the high negative-velocity absorption seen in H1821+643 must be formed in the Galactic halo beyond K1-16." " A high nesative-velocitv 215 1} component of lunll031.03 is coincident with a low velocity IL, line frou the (ο.0)P(3) rotational level at.", A high negative-velocity $-215$ ) component of 1031.93 is coincident with a low velocity $_2$ line from the $(6-0) P(3)$ rotational level at. We have modeled the /=3 II lines iu the spectrin. and Sud a good ft for a total colunun deusitv of NOT?) ~2«JUOD 7 aud a cloud excitation teniperature of Thy~500 Ik. Based ou this model. the expected 75 absorption at ccannot account for the depth or width of the observed line. indicating significant absorption bv lamll032 at 215 ," We have modeled the $J=3$ $_2$ lines in the spectrum, and find a good fit for a total column density of $_2$ ) $\sim 2 \times 10^{15}$ $^{-2}$ and a cloud excitation temperature of $T_{ex} \sim 500$ K. Based on this model, the expected $H_2$ absorption at cannot account for the depth or width of the observed line, indicating significant absorption by 1032 at $-215$ ." This coufirms the tentative identification of this component iu the lamlil5l9 line made with GIIRS/IIST bv Savage.Seubach&Lu (1995)., This confirms the tentative identification of this component in the 1549 line made with GHRS/HST by \citet{savage95}. . This detection is quite interesting. since the line velocity correspouds to the limiting velocity of epsp~—190520]ans ffor Millke Way eas assuniiue corotation aud a flat rotation curve for the outer galaxy.," This detection is quite interesting, since the line velocity corresponds to the limiting velocity of $v_{LSR}\sim-190\pm20$ for Milky Way gas assuming corotation and a flat rotation curve for the outer galaxy." Collisional ionization sccius the most Likely source of Houization iu this component., Collisional ionization seems the most likely source of ionization in this component. Photoionization would require a very hard radiation field (EZ>111 eV) to ionize tto. and the large photoionization parameter. (. requires a very low value of ay aud an extremely long pathlength. |—Nypfngp>100 kpc. to produce the absorption (see Sembachetal. C2000))).," Photoionization would require a very hard radiation field $E>114$ eV) to ionize to, and the large photoionization parameter, $U$, requires a very low value of $n_H$ and an extremely long pathlength, $l=N_H/n_H>100$ kpc, to produce the absorption (see \citet{sembach00}) )." Tripp.Eu&Savage(1998). have detected stroug (AW>200 3) Lye towards T1821|618 at redshifts of 0.1213. 0.1176. 0.1699. 0.2132 and 0.2219.," \citet{tripp98} have detected strong $_\lambda > 200$ ) $\alpha$ towards H1821+643 at redshifts of 0.1213, 0.1476, 0.1699, 0.2132 and 0.2249." Savage.Sembach&Lu(1995) also reported interveniug Lye absorption at +=0.0215IL., \citet{savage95} also reported intervening $\alpha$ absorption at $z=0.02454$. We have detected absorption froufour of these absorbers in the FUSE spectrum. aud the cobluun densities are reported in Table 1.," We have detected absorption fromfour of these absorbers in the FUSE spectrum, and the column densities are reported in Table 1." The Exauan series lines detected with FUSE in these systems provide important coustraiuts on yy since the stronger lines in the UST baudpass are saturated., The Lyman series lines detected with FUSE in these systems provide important constraints on ) since the stronger lines in the HST bandpass are saturated. The reader is also referred to Shulletal.(2000)for discussion of intervening Ly} absorbers., The reader is also referred to \citet{shull00} for discussion of intervening $\beta$ absorbers. Oue iust be awareof the potential for ejected material from the QSO to masquerade as intervening gas. as shown for aabsorptiou line svstenis by Richardsetal. (1999)..," One must be awareof the potential for ejected material from the QSO to masquerade as intervening gas, as shown for absorption line systems by \citet{richards99}. ." We, We (Type ID) supernova. has a shock speed of 170 kin/sec and a thickness no greater than ~LOY em (Blair οἱ al.,"(Type II) supernova, has a shock speed of 170 km/sec and a thickness no greater than $\sim 10^{15}$ cm (Blair et al." 1999). consistent with models 200-0.1 and 400-0.1.," 1999), consistent with models 200-0.1 and 400-0.1." WH is a e2xLOEvi-old remnant of a Type II supernova. where the shock Ironts are colliding with giant molecular cloud (GMC) gas with a density greater (han LO’ cm* (Reach. Rho. Jarrett 2005).," W44 is a $\sim 2 \times 10^4$ -yr-old remnant of a Type II supernova, where the shock fronts are colliding with giant molecular cloud (GMC) gas with a density greater than $10^3$ $^{-3}$ (Reach, Rho, Jarrett 2005)." The shock front has slowed down to 20-10 km/sec and has thickened as a result of the GMC interaction. but is no thicker than ~104 em.," The shock front has slowed down to 20-70 km/sec and has thickened as a result of the GMC interaction, but is no thicker than $\sim 10^{17}$ cm." " For a nearly isothermal shock. the post-shock density n, for propagation in a stationary medium of density ry, ls n;/nj,=οςο). where ος is the shock speed and ον, is the sound speed in the medium (e.g.. Spitzer 1963)."," For a nearly isothermal shock, the post-shock density $n_s$ for propagation in a stationary medium of density $n_m$ is $n_s/n_m = (v_s/c_m)^2$, where $v_s$ is the shock speed and $c_m$ is the sound speed in the medium (e.g., Spitzer 1968)." " For the present models. ος=40 km/sec. c,,=0.2 km/sec. and μι=10? oE. leading to n.Ax10"" em7."," For the present models, $v_s = 40$ km/sec, $c_m = 0.2$ km/sec, and $n_m = 10^2$ $^{-3}$, leading to $n_s = 4 \times 10^6$ $^{-3}$." This is the same shock density as used in model 400-0.1., This is the same shock density as used in model 400-0.1. Evidently. then. models 200-0.1 and 400-0.1 do appear to be reasonable models of evolved Type II supernova remnants similar to the Cvenus Loop and W44. which have expanded. (ο sizes of 10 pc or more after LO! vr of evolution.," Evidently, then, models 200-0.1 and 400-0.1 do appear to be reasonable models of evolved Type II supernova remnants similar to the Cygnus Loop and W44, which have expanded to sizes of 10 pc or more after $\sim 10^4$ yr of evolution." Trigo-Rodríeguez et al. (, Trigo-Rodrígguez et al. ( 2009) suggest that DDc3xI07 is required for an ACB star source of the SLRIs.,2009) suggest that $D \sim 3 \times 10^{-3}$ is required for an AGB star source of the SLRIs. Only models 200-0.1 and 400-0.1 produced D values at least this large., Only models 200-0.1 and 400-0.1 produced $D$ values at least this large. Note that dilution caused bv snowplowing does not need to be invoked here because planetary nebulae speeds are already in the proper range of 20 to 30 km/sec., Note that dilution caused by snowplowing does not need to be invoked here because planetary nebulae speeds are already in the proper range of 20 to 30 km/sec. However. the thickness of the planetary nebula Abell 39 is estimated to be ~3xLO! em (Jacoby. Ferland. ουρία 2001) and for planetary nebula DEP-1 to be ~5xLOM em (Pierce οἱ al.," However, the thickness of the planetary nebula Abell 39 is estimated to be $\sim 3 \times 10^{17}$ cm (Jacoby, Ferland, Korista 2001) and for planetary nebula PFP-1 to be $\sim 5 \times 10^{17}$ cm (Pierce et al." 2004)., 2004). These thicknesses are even greater (han those in (he models with 10 times the standard shock thickness (Table 1). and so are incapable of producing the desired dilution factor.," These thicknesses are even greater than those in the models with 10 times the standard shock thickness (Table 1), and so are incapable of producing the desired dilution factor." Planetary nebulae appear to be too thick to achieve the injection efficiencies needed to explain the solar svstems SLRIs., Planetary nebulae appear to be too thick to achieve the injection efficiencies needed to explain the solar system's SLRIs. The D values in Table 1 are based on injection purely in the gas phase. i.e.. assuming that the SLEIs are either in the gas phase or are locked up in grains small enough to remain lied to the gas.," The $D$ values in Table 1 are based on injection purely in the gas phase, i.e., assuming that the SLRIs are either in the gas phase or are locked up in grains small enough to remain tied to the gas." As noted bv Foster Boss (1997). large dust grains can shoot through the gas of a stalled shock [ront as à result of their momentum. thereby increasing (he SLRI injection ellieieney. as studied by Ouellette οἱ al. (," As noted by Foster Boss (1997), large dust grains can shoot through the gas of a stalled shock front as a result of their momentum, thereby increasing the SLRI injection efficiency, as studied by Ouellette et al. (" 2010).,2010). Hence the D values in Table 1 should be considered as lower bounds., Hence the $D$ values in Table 1 should be considered as lower bounds. and 119990504.,and 19990504. We find SNRs which are typically 1-σ below that reported in B07., We find SNRs which are typically $\sigma$ below that reported in B07. The revised and B07 SNRs are given in Table 2.., The revised and B07 SNRs are given in Table \ref{tab:ListOfFields}. " We note that an independent pipeline written in ParselTongue (Kettenisetal.2006),, a Python interface to AIPS, and run on three of these four sources confirms the lower SNR values found here (Bell2011): 19920826 (SNR=6.0), 19970528 (SNR=4.4), and 19990504 (SNR=4.0)."," We note that an independent pipeline written in ParselTongue \citep{kett06}, a Python interface to AIPS, and run on three of these four sources confirms the lower SNR values found here \citep{bell11}: 19920826 (SNR=6.0), 19970528 (SNR=4.4), and 19990504 (SNR=4.0)." The lowering of SNR (from between 7 and 8 to between 5 and has a pernicious effect when the number of independent6) beams which were search is included., The lowering of SNR (from between 7 and 8 to between 5 and 6) has a pernicious effect when the number of independent beams which were search is included. In refsec:NumberIndependentBeams we estimate this number to be nz&9x107., In \\ref{sec:NumberIndependentBeams} we estimate this number to be $n\approx 9\times 10^7$. In refsec:A we derive the probability density function for the highest m values of n Gaussian random, In \\ref{sec:A} we derive the probability density function for the highest $m$ values of $n$ Gaussian random. numbers®.. In Figure 4. we plot the density function for the highest value (m— and the fourth highest value (m— 4)., In Figure \ref{fig:PdistPoints} we plot the density function for the highest value $m=1$ ) and the fourth highest value $m=4$ ). " As can be seen from1) this Figure 4,, if the SNRs reported here are accepted then the global case for the remaining B07 transients is entirely weakened."," As can be seen from this Figure \ref{fig:PdistPoints}, if the SNRs reported here are accepted then the global case for the remaining B07 transients is entirely weakened." " If, on the other hand, the SNRs reported in B07 are accepted then the four transients reported in B07 do argue for a new class of radio transients."," If, on the other hand, the SNRs reported in B07 are accepted then the four transients reported in B07 do argue for a new class of radio transients." The above approach of using a fixed threshold for all epochs does not result in optimal detection., The above approach of using a fixed threshold for all epochs does not result in optimal detection. " In particular, the threshold for a low resolution survey is lower than that for a higher resolution survey (since the latter has a correspondingly larger number of synthesized "," In particular, the threshold for a low resolution survey is lower than that for a higher resolution survey (since the latter has a correspondingly larger number of synthesized beams)." B07 addressed this problem by requiring that the beams).probability of a false detection (PFD) in an individual epoch was constant and less than N where N is the total number of images., B07 addressed this problem by requiring that the probability of a false detection (PFD) in an individual epoch was constant and less than $N$ where $N$ is the total number of images. " With this approach, the expectation number of false detections is 1 for the entire survey."," With this approach, the expectation number of false detections is 1 for the entire survey." Applying the B07 method we find the following PFDs: 119920826 (log(PFD)=—5.02); 119970205 119970528 (—2.77); 119990504 (—4.61)., Applying the B07 method we find the following PFDs: 19920826 $-5.02$ ); 19970205 $-2.74$ ); 19970528 $-2.77$ ); 19990504 $-4.61$ ). With (—2.74);this more refined approach only 119920826 and 19990504 survive., With this more refined approach only 19920826 and 19990504 survive. " However, for reasons discussed in refsec:RT19990504 we have misgivings about 11990504."," However, for reasons discussed in \\ref{sec:RT19990504} we have misgivings about 1990504." An entirely different (and in some ways orthogonal to the above SNR based approach) is to look at the angular distribution of the transient sources with respect to the primaryaxis!?., An entirely different (and in some ways orthogonal to the above SNR based approach) is to look at the angular distribution of the transient sources with respect to the primary. . Basic interferometry theory informs us that the dirty image is simply the Fourier transform of the visibility data., Basic interferometry theory informs us that the dirty image is simply the Fourier transform of the visibility data. As such the radiometric noise in the dirty image should be independent of the angular offset from the phase center., As such the radiometric noise in the dirty image should be independent of the angular offset from the phase center. " In contrast, the point source sensitivity decreases as one goes away from the pointing center and this is governed by the primary beam response that the spectral resolution of the survey is high (assumingenough that the delay beam is larger than the primary beam)."," In contrast, the point source sensitivity decreases as one goes away from the pointing center and this is governed by the primary beam response (assuming that the spectral resolution of the survey is high enough that the delay beam is larger than the primary beam)." " Thus, once the minimum SNR for detection is fixed, cosmic sources should be concentrated towards the pointing direction whereas noise spikes (masquerading as threshold point sources) should be uniformly distributed."," Thus, once the minimum SNR for detection is fixed, cosmic sources should be concentrated towards the pointing direction whereas noise spikes (masquerading as threshold point sources) should be uniformly distributed." In refsec:PrimaryBeam we derive the expected distribution of cosmic sources as a function of the angular offset., In \\ref{sec:PrimaryBeam} we derive the expected distribution of cosmic sources as a function of the angular offset. " In Figure 5 we plot the expected cumulative distribution and also the angular offset of the four sources which are not artifacts but whose SNR seems to be under dispute, namely 119920826 refsec:RT19920826)), 119970205 refsec:RT19970205)), 119970528 refsec:RT19970528)) and 119990504 "," In Figure \ref{fig:PrimaryBeamPoints} we plot the expected cumulative distribution and also the angular offset of the four sources which are not artifacts but whose SNR seems to be under dispute, namely 19920826 \\ref{sec:RT19920826}) ), 19970205 \\ref{sec:RT19970205}) ), 19970528 \\ref{sec:RT19970528}) ) and 19990504 \\ref{sec:RT19990504}) )." From this Figure one can see that only 119920826 refsec:RT19990504)).lies in the expected region whereas the remaining three are collectively improbable., From this Figure one can see that only 19920826 lies in the expected region whereas the remaining three are collectively improbable. " In summary, two different statistical tests, one based on SNR and the other making use of the spatial signature provided by the primary beam, suggest that of the remaining four sources detected at threshold, only one, namely, 119920826 is a good detection."," In summary, two different statistical tests, one based on SNR and the other making use of the spatial signature provided by the primary beam, suggest that of the remaining four sources detected at threshold, only one, namely, 19920826 is a good detection." " Thus a simple interpretation of our re-analysis is that the rate of B07 transients is considerably lower than that reported by BO7, perhaps an order of magnitude smaller."," Thus a simple interpretation of our re-analysis is that the rate of B07 transients is considerably lower than that reported by B07, perhaps an order of magnitude smaller." "To explore this issue. we measured «vc,2 and «op for simulations with dillerent. ericl resolutions and also [or a set of simulations done with a cdillerent code.","To explore this issue, we measured $$ and $<\rho>$ for simulations with different grid resolutions and also for a set of simulations done with a different code." As a worst case scenario for a cdilfusive grid code we took the beam scheme (Sanders anc Prendergast. 1974). which was used extensively in the earliest galactic disk simulations (Lluntley 1978. Sanders Tubbs 1980. Duval Athanassoula 1983 )," As a worst case scenario for a diffusive grid code we took the beam scheme (Sanders and Prendergast 1974) which was used extensively in the earliest galactic disk simulations (Huntley 1978, Sanders Tubbs 1980, Duval Athanassoula 1983 )." Like BCR. the beam scheme is a gas-kinetie hverocode. i.c. Dluxes are computed. by taking moments of a velocity distribution function. f.," Like BGK, the beam scheme is a gas-kinetic hydrocode, i.e. fluxes are computed by taking moments of a velocity distribution function, $f$." Both schemes arbitrarily choose fo at the beginning of cach updating time-step but. the beam scheme evolves it through the collisionless Boltzmann equation whereas the BCU scheme solves for the time evolution of f throughout an updating time-step using the Xil equation which is a model of the collisional Boltzmann equation., Both schemes arbitrarily choose $f$ at the beginning of each updating time-step but the beam scheme evolves it through the collisionless Boltzmann equation whereas the BGK scheme solves for the time evolution of $f$ throughout an updating time-step using the BGK equation which is a model of the collisional Boltzmann equation. By assuming instantaneous relaxation of f to a Maxwellian velocity distribution at the beginning of the updating time-step. the beam. scheme endows the gas with a mean collision time equivalent to the updating time-ste," By assuming instantaneous relaxation of $f$ to a Maxwellian velocity distribution at the beginning of the updating time-step, the beam scheme endows the gas with a mean collision time equivalent to the updating time-step." ln the BOW scheme. on the other hand. collisions are active throughout the updating time-step and for hyedrocdsynamical applications the BOW scheme demands that the collision time be much smaller than the updating time-step.," In the BGK scheme, on the other hand, collisions are active throughout the updating time-step and for hydrodynamical applications the BGK scheme demands that the collision time be much smaller than the updating time-step." Since dissipation parameters are proportional to the collision time. T. e.g. the dynamical viscosity y=7 p. we easily see that an overestimation of the collision time will lead to a very cilfusive scheme.," Since dissipation parameters are proportional to the collision time, $\tau$, e.g. the dynamical viscosity $\eta = \tau$ p, we easily see that an overestimation of the collision time will lead to a very diffusive scheme." Indeed. fig.," Indeed, fig." " 19. illustrates that is about an order of magnitude larger with the beam scheme than it is with BOI and that the effect is worse in the center of the disk where a plot of

$ is about an order of magnitude larger with the beam scheme than it is with BGK and that the effect is worse in the center of the disk where a plot of $<\rho>$ shows that simulations with different disk fractions are indistinguishable. Figure 19. also shows that even with a BOIS simulation on a 101 101 erie one still does better than beam by about a factor of 5 in the radial inflow velocities in the inner regions of the disk., Figure \ref{difffd_codes_res} also shows that even with a BGK simulation on a 101 $\times$ 101 grid one still does better than beam by about a factor of 5 in the radial inflow velocities in the inner regions of the disk. A look at the morphology. of the disk for simulations performed. with the beam. scheme. (figure 17)) confirms that the inner region of the disk computed with beam is essentially insensitive to disk fraction.," A look at the morphology of the disk for simulations performed with the beam scheme, (figure \ref{morph_beam}) ) confirms that the inner region of the disk computed with beam is essentially insensitive to disk fraction." The morphological changes that accompany a change in clisk fraction (Fig. 8)), The morphological changes that accompany a change in disk fraction (Fig. \ref{morph_diskfrac}) ) are absent., are absent. Interestingly however. figures 19. and 17. show that even with this incredibly dilfusive scheme. one can still distinguish between simulations run with different clisk fractions in the outer regions of the disk where a spiral perturbation is present.," Interestingly however, figures \ref{difffd_codes_res} and \ref{morph_beam} show that even with this incredibly diffusive scheme, one can still distinguish between simulations run with different disk fractions in the outer regions of the disk where a spiral perturbation is present." In order to quantify what has been described in Sections 3 and + we perform an overall comparison. between he observed and simulated kinematics., In order to quantify what has been described in Sections \ref{Parameters} and \ref{massinflow} we perform an overall comparison between the observed and simulated kinematics. Me use two approaches., We use two approaches. First we perform a global least squares analysis (figure 20)) taking into account the location amplitudes of individual wigeles., First we perform a global least squares analysis (figure \ref{chi}) ) taking into account the location amplitudes of individual wiggles. Secondly. we compute the average wigele amplitude (figure 21)). neglecting information about he wigele positions.," Secondly, we compute the average wiggle amplitude (figure \ref{wiggle_amplitude}) ), neglecting information about the wiggle positions." The comparison was performed. on a reduced data set with the very inner disk region removed., The comparison was performed on a reduced data set with the very inner disk region removed. Furthermore. à treatment has been applied to the observed kinematics in order to exclude shocks that are missing from simulations.," Furthermore, a treatment has been applied to the observed kinematics in order to exclude shocks that are missing from simulations." EFhese shocks probably originate from. eravitational elfects (see Ixranz 2002. 84.5.1).," These shocks probably originate from non-gravitational effects (see Kranz 2002, 4.3.2.1)." Figure 20. corresponds to figure 9 in Paper L (except that it uses the reduced: data set described. above) and measures the match in both wigele position and amplitude between the observations anc simulations., Figure \ref{chi} corresponds to figure 9 in Paper I (except that it uses the reduced data set described above) and measures the match in both wiggle position and amplitude between the observations and simulations. Our BCilx simulations with fiducial values for the grid resolution. gas sound speed. ancl pattern speed are plotted with asterices.," Our BGK simulations with fiducial values for the grid resolution, gas sound speed, and pattern speed are plotted with asterices." As argued in Paper La maximal disk mass fraction can be ruled out for NGC 4254 on the basis of this plot.," As argued in Paper I, a maximal disk mass fraction can be ruled out for NGC 4254 on the basis of this plot." Now we can look at how strongly the locations of the points in figure 20 depend on the chosen parameters for the simulations.," Now we can look at how strongly the locations of the points in figure \ref{chi} depend on the chosen parameters for the simulations." Craclually increasing the gas sound speed (temperature) to an unphysical 30. (90.000 Ih) smoothes out the wigeles in the simulations., Gradually increasing the gas sound speed (temperature) to an unphysical 30 (90.000 K) smoothes out the wiggles in the simulations. As a result. a higher gas sound speed cancels out any change in the disk mass fraction (diamonds). so that for c;=30 the simulated gas velocity field is almost independent of fa.," As a result, a higher gas sound speed cancels out any change in the disk mass fraction (diamonds), so that for $c_{\rm s} = 30$ the simulated gas velocity field is almost independent of $f_{\rm d}$." Mowever. for smaller variations (45-10 )) of the gas sound speed relative to our fiducial value of 10. he ellect on the least squares analysis is weak.," However, for smaller variations $\pm$ ) of the gas sound speed relative to our fiducial value of 10 , the effect on the least squares analysis is weak." As for the ellect of the grid resolution. we studied it for the case of fi= per cent (triangles in figure 20)).," As for the effect of the grid resolution, we studied it for the case of $f_{\rm d} = 60$ per cent (triangles in figure \ref{chi}) )." Ehe features resulting rom the simulation on the 100 100 erid are smoother with respect to the fiducial mocdel. thus vielding a slightly worse agreement with the observed kinematies.," The features resulting from the simulation on the 100 $\times$ 100 grid are smoother with respect to the fiducial model, thus yielding a slightly worse agreement with the observed kinematics." On the other mance. the high resolution simulation (400 400 ericl) viclels an even worse agreement with the observations.," On the other hand, the high resolution simulation (400 $\times$ 400 grid) yields an even worse agreement with the observations." This canx understood. by studying figures 7. and 9 which show, This canbe understood by studying figures \ref{shock_az_res} and \ref{denscuts_all} which show "analysis of the HCN 3-2 profiles of 28 high-mass star-forming regions, many of which are also observed in our sample (see ??)).","analysis of the HCN 3-2 profiles of 28 high-mass star-forming regions, many of which are also observed in our sample (see \ref{s:comparison}) )." " Blue excess tends to be somewhat larger for low mass star forming regions observed in 33-2 (Ez0.30; Evans 2003), although Mardones et al. ("," Blue excess tends to be somewhat larger for low mass star forming regions observed in 3-2 $E \approx 0.30$; Evans 2003), although Mardones et al. (" "1997) found a smaller blue excess for a sample of 47 low mass star forming regions, observed in H3CO and CS.","1997) found a smaller blue excess for a sample of $47$ low mass star forming regions, observed in $_2$ CO and CS." " Not all surveys demonstrate a blue excess (e.g. Mardones 2003), although smaller blue excesses may be explained by differences in the optical depth between tracers (Evans 2003, Wu et al."," Not all surveys demonstrate a blue excess (e.g. Mardones 2003), although smaller blue excesses may be explained by differences in the optical depth between tracers (Evans 2003, Wu et al." 2010)., 2010). Sample selection may also bias the blue excess., Sample selection may also bias the blue excess. " However, for a sample of high-mass star forming regions, Wu et al. ("," However, for a sample of high-mass star forming regions, Wu et al. (" 2010) find that asymmetries in HCN 3-2 are often not reflected in the CS 2-1 profiles.,2010) find that asymmetries in HCN 3-2 are often not reflected in the CS 2-1 profiles. Those authors conclude that CS 2-1 is not sufficiently optically thick to trace the inner regions of the clump where inflow occurs., Those authors conclude that CS 2-1 is not sufficiently optically thick to trace the inner regions of the clump where inflow occurs. " A nearly equal number of red (5 of 27) and blue (6 of 27) asymmetries, as we find with the óv parameter (see Table 1), is consistent with a uniform distribution where blue, red and symmetric profiles are all equally likely."," A nearly equal number of red (5 of 27) and blue (6 of 27) asymmetries, as we find with the $\delta v$ parameter (see Table 1), is consistent with a uniform distribution where blue, red and symmetric profiles are all equally likely." A Monte Carlo simulation that picks 27 points from this uniform distribution will reproduce the dv result for ~90% of 10000 trials., A Monte Carlo simulation that picks 27 points from this uniform distribution will reproduce the $\delta v$ result for $\sim$ of 10000 trials. " Even for the visual classification, which has a more pronounced excess of blue profiles (9 of 27) compared to red (4 of 27), the probability that our results could be obtained from a uniform distribution of line profiles is still ~50%.."," Even for the visual classification, which has a more pronounced excess of blue profiles (9 of 27) compared to red (4 of 27), the probability that our results could be obtained from a uniform distribution of line profiles is still $\sim$." " Quantitative measures of the asymmetry agree on the general shape of the line profile, but those results are not always significant, even for"," Quantitative measures of the asymmetry agree on the general shape of the line profile, but those results are not always significant, even for" "value, we may be justified in looking for such variation.","value, we may be justified in looking for such variation." The resulting amplitude of the relative variation is plotted against radius in Figure 4., The resulting amplitude of the relative variation is plotted against radius in Figure 4. The dips in the curves occur near the depths at which the correlation coefficient changes sign (see Figure 3)., The dips in the curves occur near the depths at which the correlation coefficient changes sign (see Figure 3). At these depths the amplitude might be expected to be small., At these depths the amplitude might be expected to be small. " Beneath the convection zone the rise in amplitude with depth might be merely a reflection of the increasing errors in the inferred angular velocity, and is therefore not to be trusted; this is suggested partly by the low correlation coefficients evident in Figure 3."," Beneath the convection zone the rise in amplitude with depth might be merely a reflection of the increasing errors in the inferred angular velocity, and is therefore not to be trusted; this is suggested partly by the low correlation coefficients evident in Figure 3." We conclude this discussion by once again comparing inferences from GONG and MDI., We conclude this discussion by once again comparing inferences from GONG and MDI. Figure 5 depicts the correlation coefficients between the 10.7 cm radio flux and the spherically averaged rotational kinetic energy and angular momentum obtained from the two data sets., Figure 5 depicts the correlation coefficients between the 10.7 cm radio flux and the spherically averaged rotational kinetic energy and angular momentum obtained from the two data sets. It is evident that there is very little difference between the coefficients for rotational kinetic energy and angular momentum., It is evident that there is very little difference between the coefficients for rotational kinetic energy and angular momentum. " There is some discrepancy between the inferences from GONG and MDI in the lower part of the convection zone, a discrepancy similar to one that has been found also in other works (e.g., Schou et al."," There is some discrepancy between the inferences from GONG and MDI in the lower part of the convection zone, a discrepancy similar to one that has been found also in other works (e.g., Schou et al." 2002)., 2002). The reason for that discrepancy is not fully understood., The reason for that discrepancy is not fully understood. " Nevertheless, it does not affect the principal conclusions of this paper."," Nevertheless, it does not affect the principal conclusions of this paper." Howe et al. (, Howe et al. ( 2000b) and Komm et al. (,2000b) and Komm et al. ( 2003) have reported a 1.3-year periodicity in the temporal variation of the angular,2003) have reported a 1.3-year periodicity in the temporal variation of the angular Mo&White(1996) and ours. which is presumably due to the more realistic plivsics used in our model.,"\cite{mo96a} and ours, which is presumably due to the more realistic physics used in our model." Seni-anualvtic models can predict the evolution of i: it will be interesting to see how depenudoeut this statistic is to the details of the galaxy. formation model., Semi-analytic models can predict the evolution of $r_\ast$; it will be interesting to see how dependent this statistic is to the details of the galaxy formation model. We discuss a way to ect a handle on (kc observationally iu Section 1.., We discuss a way to get a handle on $r_\ast$ observationally in Section \ref{observables}. After ealaxies form. they fall iuto poteutial wells under the influence of gravity.," After galaxies form, they fall into potential wells under the influence of gravity." " Because the acceleration on galaxies is the same as that on the dark matter. this gravitational evolution after formation will tend to bring both the bias 5, aud the correlation cocficicnt à, closer to munity. as described by and Tegiiark&Peebles(1998).."," Because the acceleration on galaxies is the same as that on the dark matter, this gravitational evolution after formation will tend to bring both the bias $b_g$ and the correlation coefficient $r_g$ closer to unity, as described by \cite{fry96a} and \cite{tegmark98a}." The evolution of the bias. then. is determined by the properties of forming galaxies (outlined in the previous section) and low those properties evolve after formation.," The evolution of the bias, then, is determined by the properties of forming galaxies (outlined in the previous section) and how those properties evolve after formation." Here we Investigate this process and show that the linear approximations of Fry(1996) aud describe this evolution well. even in the nonlinear regime.," Here we investigate this process and show that the linear approximations of \cite{fry96a} and \cite{tegmark98a} describe this evolution well, even in the nonlinear regime." Fiv(1996) aud Teemark&Peebles(1998) rely ou the continuity equation to study the evolution of the density field of galaxies formed at a given epoch., \cite{fry96a} and \cite{tegmark98a} rely on the continuity equation to study the evolution of the density field of galaxies formed at a given epoch. In this subsection. subscript ο will refer to this coeval set of galaxies.," In this subsection, subscript $c$ will refer to this coeval set of galaxies." Both galaxies and mass satisfy the same equation. which is to first order assundue that ealaxies are ucither created nor destroved.," Both galaxies and mass satisfy the same equation, which is to first order assuming that galaxies are neither created nor destroyed." Since we are dealing with a coeval set of ealaxies. they caumnot be created by definition.," Since we are dealing with a coeval set of galaxies, they cannot be created by definition." Although it is possible to disrupt or merge galaxies in deuse regions (lkravtsov&EKlvpiu 1998)). we are following the stellar mass density in this paper. uot the ealaxyv nuuber deusitv. aud thus do not cousider these effects.," Although it is possible to disrupt or merge galaxies in dense regions \cite{kravtsov98ap}) ), we are following the stellar mass density in this paper, not the galaxy number density, and thus do not consider these effects." Assuniug that there is no velocity bias between the voluue-weiglited velocity fields of mass and of ealaxies Gvhich is borue out by the simmlatious). it follows that à=à.," Assuming that there is no velocity bias between the volume-weighted velocity fields of mass and of galaxies (which is borne out by the simulations), it follows that ${\dot \delta} = {\dot \delta_c}$." " This statement means that ou incarly scaled plots of 6,. against ὃν volume elements are coustrained to evolve along 157 lines."," This statement means that on linearly scaled plots of $\delta_c$ against $\delta$, volume elements are constrained to evolve along $45^\circ$ lines." We test this xedietion on 30 5.+ Mpe top hat scales. which should be close to linear. in Figure 5..," We test this prediction on 30 $h^{-1}$ Mpc top hat scales, which should be close to linear, in Figure \ref{evolve30}." Here we consider a must of galaxies formed at ;=1., Here we consider a burst of galaxies formed at $z=1$. The solid lines are (6.|ój at += 1.2=0.5 and :=0.," The solid lines are $\avg{\delta_c|\delta}$ at $z=1$, $z=0.5$ and $z=0$." The dashed lines are he predictions extrapolated from +=1 ax above. to +=0.5 and 2=0. respectively.," The dashed lines are the predictions extrapolated from $z=1$ as above, to $z=0.5$ and $z=0$, respectively." " Notice use the erowth actor of mass. σί:=0)/o(:1). which on these scales is close to its linear theory value. to determine Ad, and assune that A, is the same."," Notice use the growth factor of mass, $\sigma(z=0)/\sigma(z=1)$, which on these scales is close to its linear theory value, to determine $\Delta\delta$, and assume that $\Delta\delta_c$ is the same." Evideutlv the linear coutinuitv equation works ou these scales., Evidently the linear continuity equation works on these scales. We also est this prediction on the nouliuear scale of 17.1 Mpc in Figure 6.., We also test this prediction on the nonlinear scale of 1 $h^{-1}$ Mpc in Figure \ref{evolve1}. We find that it works extremely well in the range 3«à<100: inhigher aud lower density regions. nonlinear corrections to Equation (5)) are clearly iuportaut.," We find that it works extremely well in the range $3 < \delta < 100$; inhigher and lower density regions, nonlinear corrections to Equation \ref{continuity}) ) are clearly important." Teemark&Peebles(1998) use the contiuuitv equation to make further predictious about the bias properties of coeval galaxies., \cite{tegmark98a} use the continuity equation to make further predictions about the bias properties of coeval galaxies. " Tu particular. given a “bias at bith” of b(2y) aud a ""correlation cocfiicicut at birth” of τον one can express 5,.(:) aud k(:) in terms of the linear erowth factor relative to the epoch of"," In particular, given a “bias at birth” of $b_c(z_0)$ and a “correlation coefficient at birth” of $r_c(z_0)$ , one can express $b_c(z)$ and $r_c(z)$ in terms of the linear growth factor relative to the epoch of" "a photon-noise limited survey. dig,x(1—27)!4. and therefore where d,,,G.B.air.)=dij.RoarOV— a2), ","a photon-noise limited survey, $d_{max} \propto (1-x^{2})^{1/4}$, and therefore where $d_{max}(L,R,a,r,x) = d_{max}(L,R,a,r,0)(1-x^{2})^{1/4}$ ." Here dig(L.Rar.0) is the distance out to which a transit can be detected[or an edge-on (7 = 90°) orbit.," Here $d_{max}(L,R,a,r,0)$ is the distance out to which a transit can be detectedfor an edge-on $i$ = $90^{\rm o}$ ) orbit." We must then integrate over all values of the impact parameter οὐ from 0 to 1. ancl so where. We now determine the dependence of Αρ. the total number of svstems probed. on the remaining parameters L. R. a. aud r.," We must then integrate over all values of the impact parameter $x$ from 0 to 1, and so where, We now determine the dependence of $N_{p}$, the total number of systems probed, on the remaining parameters $L$, $R$, $a$, and $r$." " To do so. we analvze the detection requirement. where AN; is the number of observations of the transit over the length of the survey. 6 is the fractional change in the stars brightness ching the transit. 7 is the fractional error of an individual flux measurement. and A\2,,, is Lhe minimum acceptable difference in V? between a fit Chat assumes a constant [αν and one that takes account of a (transit."," To do so, we analyze the detection requirement, where $N_{t}$ is the number of observations of the transit over the length of the survey, $\delta$ is the fractional change in the star's brightness during the transit, $\sigma$ is the fractional error of an individual flux measurement, and $\Delta \chi_{\rm min}^{2}$ is the minimum acceptable difference in $\chi^{2}$ between a fit that assumes a constant flux and one that takes account of a transit." As we discuss in 3. Nau must be set sufficiently high to avoid spurious detections due to random noise.," As we discuss in \ref{sec:randomnoise},, $\Delta\chi_{\rm min}^{2}$ must be set sufficiently high to avoid spurious detections due to random noise." for E(BV)=0.0 is reasonably close to the dust corrected one of Adelberger&Steidel(2000).,for $E(B-V)=0.0$ is reasonably close to the dust corrected one of \citet{Ade00}. . Adelberger&Steidel(2000). corrected their observed luminosity. function. for dust. by adopting the relation οπου=4.43|1.99.9 (Moeurer.Heckman.&Calzetti1999) for the extinction in magnitudes at 1600A.. where 2 is the UV slope of the spectrum which has a distribution in the range of —3.0]with a peak around 1.5. corresponding to -Aiooo~L4 mag (seeFig.12ofXdelberger—&Steidel2000).," \citet{Ade00} corrected their observed luminosity function for dust by adopting the relation $A_{1600}=4.43 + 1.99\beta$ \citep{Meurer} for the extinction in magnitudes at 1600, where $\beta$ is the UV slope of the spectrum which has a distribution in the range of $[-3, 0]$with a peak around $-1.5$, corresponding to $A_{1600}\sim 1.4$ mag \citep[see Fig. 12 of][]{Ade00}." . This peak value is roughly consistent with the value of 1)=0.15 we adopted here with the Calzettictal.(2000) extinction law ACA). because (2VOACIGOOLL—HL.5n mag.," This peak value is roughly consistent with the value of $E(B-V)=0.15$ we adopted here with the \citet{Calzetti} extinction law $k(\lambda)$, because $E(B-V) k(1600\AA)\sim 1.5$ mag." Fherefore the rough agreement between the simulate uminosity function with £(V)=0.0 for G5 and C6-run and the dust corrected. data points of Acdelbcreer(2000) is encouraging. although not perfect.," Therefore the rough agreement between the simulated luminosity function with $E(B-V)=0.0$ for G5 and G6-run and the dust corrected data points of \citet{Ade00} is encouraging, although not perfect." Also. note that the peaks of the luminosity functions of he GS run with οV)=0.0 are on the brighter side of R=25.5 owing to the lower resolution.," Also, note that the peaks of the luminosity functions of the G5 run with $E(B-V)=0.0$ are on the brighter side of $R=25.5$ owing to the lower resolution." This results in he increase of the number density of the LBGs that satisfy he colour-selection criteria when the resolution is increased rom the G5 to G6 run as described in Section 4.., This results in the increase of the number density of the LBGs that satisfy the colour-selection criteria when the resolution is increased from the G5 to G6 run as described in Section \ref{section:color-color}. Overall. the comparison of the simulated: Iuminosity unctions with the observational results. presented. in Sections 6.1. and 6.1. stresses the importance of having a large simulation box size (2100 Alpe) in order to obtain reasonable agreement at the bright end.," Overall, the comparison of the simulated luminosity functions with the observational results presented in Sections \ref{section:lf_V} and \ref{section:lf_V} stresses the importance of having a large simulation box size $> 100\himpc$ ) in order to obtain reasonable agreement at the bright end." 1n our simulations. only the Ci-series contain a sullicient sample of LBGs brighter than /?225.5 with E(D.V)0.15.," In our simulations, only the G-series contain a sufficient sample of LBGs brighter than $R=25.5$ with $E(B-V)=0.15$." In Figure S.. we show four examples of typical star formation (SE) histories of galaxies in the “GG run with a bin-size of 10. Alves. as derived. [rom the age clistribution of stars founclin each galaxy including all the progenitors that merge prior to z=3.," In Figure \ref{sf_LBG.eps}, we show four examples of typical star formation (SF) histories of galaxies in the `G6' run with a bin-size of 10 Myrs, as derived from the age distribution of stars found in each galaxy including all the progenitors that merge prior to $z=3$." We here chose the G6 run because it gives a reasonable agreement with observations both for the /- band and rest-frame Y-band luminosity functions. and it has higher resolution than the G5 run.," We here chose the G6 run because it gives a reasonable agreement with observations both for the $R$ -band and rest-frame $V$ -band luminosity functions, and it has higher resolution than the G5 run." On the right hand side of cach panel. we indicate for cach galaxy an LD. its stellar mass in units of f1M... its apparent 2 magnitude (for k(BVW)ξ0.19). and its rest-frame V-band maenitucle.," On the right hand side of each panel, we indicate for each galaxy an ID, its stellar mass in units of $\himsun$, its apparent $R$ magnitude (for $E(B-V)=0.15$ ), and its rest-frame $V$ -band magnitude." A notable feature present in all the panels is the numerous spikes of starbursts lving on top of a relatively continuous component., A notable feature present in all the panels is the numerous spikes of starbursts lying on top of a relatively continuous component. The starbursts last. 1020 Alves. but the underlying smooth component shows only moderate variations in its rate when averaged over bins of LOO Alves beginning from high redshift (2~10) to z=3 in these galaxies.," The starbursts last $10-20$ Myrs, but the underlying smooth component shows only moderate variations in its rate when averaged over bins of 100 Myrs beginning from high redshift $z\sim 10$ ) to $z=3$ in these galaxies." " For example. the galaxy shown in the top panel. which is one of the most massive galaxies in the G6 run with a stellar mass of Mau,=L4I0f.!M. and rest-[rame V-band magnitude of 24.4. has continuously formed stars rom >=I0 to 23 at a typical rate of ~40M.vr1"," For example, the galaxy shown in the top panel, which is one of the most massive galaxies in the G6 run with a stellar mass of $\Mstar = 1.4\times 10^{11}\himsun$ and rest-frame V-band magnitude of $-24.4$, has continuously formed stars from $z=10$ to $z=3$ at a typical rate of $\sim 40~\Msun~\yr^{-1}$." In the other panels. we show galaxies of progressively smaller total mass. with correspondinglv lower levels of star ormation.," In the other panels, we show galaxies of progressively smaller total mass, with correspondingly lower levels of star formation." " Note that the galaxy on the bottom has a stellar mass of only Al,=3:LPAAD... vet it still satisfies he colour-colour selection criteria.oR although its luminosity ancl star formation rate are substantially smaller compared with the galaxy shown in the top panel."," Note that the galaxy on the bottom has a stellar mass of only $M_{\star} = 3.2\times 10^{10}\himsun$, yet it still satisfies the colour-colour selection criteria, although its luminosity and star formation rate are substantially smaller compared with the galaxy shown in the top panel." The recent. star ormation near 2=3 has helped to bring the brightness of his relatively small mass galaxy above the limit of /?=25.5., The recent star formation near $z=3$ has helped to bring the brightness of this relatively small mass galaxy above the limit of $R=25.5$. ]nterestinglv. the underlying continuous component of the star formation histories measured here are much smoother than the ones found by Nagamine(2002) when analvsing a Eulerian hyerodvnamic simulation.," Interestingly, the underlying continuous component of the star formation histories measured here are much smoother than the ones found by \citet{Nag02} when analysing a Eulerian hydrodynamic simulation." Their starbursts were more extended on the order of LOO Alves. ancl more sporadic.," Their starbursts were more extended on the order of 100 Myrs, and more sporadic." This dillerence is likely related to the cillerent models used by the codes for the treatment of the phwsies of star formation., This difference is likely related to the different models used by the codes for the treatment of the physics of star formation. In the SPLE methodology. we investigate here. a sub-resolution multiphase model for the ISAL was used which has a self-regulating property: ic. gas i cools smoothly onto the LSAT is also consumed. in a smooth fashion bv star formation. and only gas-rich major mergers can trigger starbursts.," In the SPH methodology we investigate here, a sub-resolution multiphase model for the ISM was used which has a self-regulating property; i.e. gas that cools smoothly onto the ISM is also consumed in a smooth fashion by star formation, and only gas-rich major mergers can trigger starbursts." We have used. state-of-the-art liverodyvnamic simulations of structure formation to study. the properties of LBGs in a AC'DAL universe., We have used state-of-the-art hydrodynamic simulations of structure formation to study the properties of LBGs in a $\Lam$ CDM universe. Our simulations use a new “entropy conserving SPII formulation that minimises svstematic inaccuracies in simulations with cooling. as well as an improved model for the treatment of the multiphase structure of the ISM in the context of star formation ancl [cedback (Springel&LHernquist 2003a)..," Our simulations use a new `entropy conserving' SPH formulation that minimises systematic inaccuracies in simulations with cooling, as well as an improved model for the treatment of the multiphase structure of the ISM in the context of star formation and feedback \citep{SH03a}. ." For the first time. our study. uses a large series of simulations to investigate the properties of LBGs. allowing an exploration. of an unprecedented Iarge dynamic range in both mass ancl spatial scales. while simultaneously. providing reliable estimates of systematic effects due to numerical resolution.," For the first time, our study uses a large series of simulations to investigate the properties of LBGs, allowing an exploration of an unprecedented large dynamic range in both mass and spatial scales, while simultaneously providing reliable estimates of systematic effects due to numerical resolution." "In order to find the number density of potential minima, we have to invert the relations given in Eq. @)),","In order to find the number density of potential minima, we have to invert the relations given in Eq. \ref{eq:newVar}) )," considering that only the diagonal elements of the tensor Z are non-zero after transforming to principal axes., considering that only the diagonal elements of the tensor $\tens{\zeta}$ are non-zero after transforming to principal axes. " After replacing (1,25,£3) by (A9,x,y) and changing the integration boundaries accordingly, we integrate only over X and 5 because the Laplacian of the potential will become crucial in the following discussion, when another constraint on A® will be introduced."," After replacing $(\tilde{\zeta}_1, \tilde{\zeta}_2, \tilde{\zeta}_3)$ by $(\Delta\Phi, \tilde{x}, \tilde{y})$ and changing the integration boundaries accordingly, we integrate only over $\tilde{x}$ and $\tilde{y}$ because the Laplacian of the potential will become crucial in the following discussion, when another constraint on $\Delta\Phi$ will be introduced." We can now rewrite Eq. (8)), We can now rewrite Eq. \ref{eq:minima}) ) " as with the integrals the normalisation constant and the quadrati form Equations (14115) can be integrated analytically, giving identical results."," as with the integrals the normalisation constant and the quadratic form Equations \ref{eq:N1}, \ref{eq:N2}) ) can be integrated analytically, giving identical results." " The final expression for 7(®,A®) is where F and F» are functions depending only on the field's Laplacian, but not on the field itself, We point out that Eqs. (I[8}420))"," The final expression for $\tilde{n}(\Phi,\Delta\Phi)$ is where $F_1$ and $F_2$ are functions depending only on the field's Laplacian, but not on the field itself, We point out that Eqs. \ref{eq:numDensPhiDelPhi}- \ref{eq:numDensPhiDelPhiLast}) )" are valid in this form only for AD>0 and ®«0 because the underlying integrations over X and y were carried out under these restrictions., are valid in this form only for $\Delta\Phi>0$ and $\Phi<0$ because the underlying integrations over $\tilde{x}$ and $\tilde{y}$ were carried out under these restrictions. " Both assumptions are appropriate; the first because of Poisson's equation, and the second because we are only interested in gravitationally bound objects whose potentials must be negative."," Both assumptions are appropriate; the first because of Poisson's equation, and the second because we are only interested in gravitationally bound objects whose potentials must be negative." " For the further evaluation of Eqs. (I8}+20)),"," For the further evaluation of Eqs. \ref{eq:numDensPhiDelPhi}- \ref{eq:numDensPhiDelPhiLast}) )," " we need the first three spectral moments of the potential power spectrum, defined in Eq. ())."," we need the first three spectral moments of the potential power spectrum, defined in Eq. \ref{eq:specMoments}) )." The potential power spectrum Pq(K) is related to the density power spectrum P;(k) through Poisson's equation., The potential power spectrum $P_\Phi(k)$ is related to the density power spectrum $P_\delta(k)$ through Poisson's equation. " The power spectrum, however, only describes the linear evolution of fluctuations for which óS1."," The power spectrum, however, only describes the linear evolution of fluctuations for which $\delta\la 1$." " Thus, we also need an for their non-linear evolution having higher amplitude."," Thus, we also need an for their non-linear evolution having higher amplitude." We shall use the (SCM) to model non-linear effects., We shall use the (SCM) to model non-linear effects. " Along the way, we shall introduce a proper definition of a filtering scale R."," Along the way, we shall introduce a proper definition of a filtering scale $R$." " The gravitational potential is related to the density contrast in comoving coordinates by Poisson's equation in real and Fourier space, respectively."," The gravitational potential is related to the density contrast in comoving coordinates by Poisson's equation in real and Fourier space, respectively." " By the definition of thepower spectrum, where óp denotesdistribution,, and using =(3HjQmo)/(8Ga*), the potential power spectrum is related to the density power spectrum by Since Ps(k)οk for k«kg and Ρο()ek? for ko, where Ko is the comoving wave number of the perturbation mode entering the horizon at matter-radiation equality, we have Po(k)ecK? for k«ko and Po(k)«k! for k>ko."," By the definition of thepower spectrum, where $\delta_\mathrm{D}$ denotes, and using $\rho_\mathrm{b}=(3H_0^2 \Omega_\mathrm{m0})/(8\pi Ga^3)$, the potential power spectrum is related to the density power spectrum by Since $P_\delta(k)\propto k$ for $k\ll k_0$ and $P_\delta(k)\propto k^{-3}$ for $k\gg k_0$ , where $k_0$ is the comoving wave number of the perturbation mode entering the horizon at matter-radiation equality, we have $P_\Phi(k)\propto k^{-3}$ for $k\ll k_0$ and $P_\Phi(k)\propto k^{-7}$ for $k\gg k_0$." " Due to the steepness of the power spectrum, we have to introduce a cut-off wave number kmin when evaluating the spectralmoments, Thus, kmin defines a sharp high-pass filter in k-space."," Due to the steepness of the power spectrum, we have to introduce a cut-off wave number $k_\mathrm{min}$ when evaluating the spectral moments, Thus, $k_\mathrm{min}$ defines a sharp high-pass filter in $k$ -space." It has to be chosen properly to filter out large potential modes and therefore also large-scale potential gradients responsible for peculiar velocities of collapsed structures., It has to be chosen properly to filter out large potential modes and therefore also large-scale potential gradients responsible for peculiar velocities of collapsed structures. " In this way, this filter ensures that the gravitational potential of a structure is defined with respect to the large-scale potential value in its direct vicinity and that the constraint of a vanishing potential gradient is fulfilled for structures of all sizes."," In this way, this filter ensures that the gravitational potential of a structure is defined with respect to the large-scale potential value in its direct vicinity and that the constraint of a vanishing potential gradient is fulfilled for structures of all sizes." " If they moved, they would not be counted when searching for potential minima and the number density derived in that way would be too small."," If they moved, they would not be counted when searching for potential minima and the number density derived in that way would be too small." We will discuss later how to find the proper kmin., We will discuss later how to find the proper $k_\mathrm{min}$ . " The evolution of the density power spectrum between the scale factors a, and a» is parametrised by the D,(a) and the T(k, a),"," The evolution of the density power spectrum between the scale factors $a_1$ and $a_2$ is parametrised by the $D_+(a)$ and the $T(k,a)$ ," motions in the SDSS-DR7 catalog have been corrected for the systematic error noticed by Muun et ((2008).,motions in the SDSS-DR7 catalog have been corrected for the systematic error noticed by Munn et (2008). " Finally. only stars with high quality data iu photometiy (oy7< UL. o; δ.," The variations in the metallicity distribution with different distances to the Galactic plane $|Z|$ ) are shown in Figure 5, where the metallicity peak shiftsfrom $\feh \sim -0.4$ dex for $|Z|<1.5$ , $\feh \sim -0.6$ dex for $1.5 \leq|Z|\le5$ to $\feh \sim -1.3$ dex for $|Z|>8$ ." At 5x|Z|€ s. the star mmnbers between the two components are comparable.," At $5 \leq|Z|\le8$ , the star numbers between the two components are comparable." Note that the result iu, Note that the result in observed Mg I absorption without also dominating the Fe II absorption. their iron gas-phase abundance must be reduced. which we attribute to depletion by dust.,"observed Mg I absorption without also dominating the Fe II absorption, their iron gas-phase abundance must be reduced, which we attribute to depletion by dust." We assume an ISM dust composition [the default Cloudy graphite and silicate. grains with a Mathis.Rumpl.&Nordsieck (1977: hereafter MRN) power-law size distribution]., We assume an ISM dust composition [the default Cloudy graphite and silicate grains with a \citeauthor{MRN77} (1977; hereafter MRN) power-law size distribution]. The dust abundance ts constrained by the measured extinction: Arson—1.0., The dust abundance is constrained by the measured extinction: $A_{2500} \lesssim 1.0$. " Our best-fit value for the typical cloud density is 2,z107 em."," Our best-fit value for the typical cloud density is $n_c\approx 10^{8.5}$ $^{-3}$." This means that the clouds are ~10+ times denser (and have a correspondingly lower ionization parameter) than the surrounding continuous wind., This means that the clouds are $\sim 10^4$ times denser (and have a correspondingly lower ionization parameter) than the surrounding continuous wind. Figure 2 shows the absorptior column densities associated with a string of such clouds as a function of pathlength through the clouds., Figure 2 shows the absorption column densities associated with a string of such clouds as a function of pathlength through the clouds. Our model can account for the observations with cloud densities that range between 10 and 10° em., Our model can account for the observations with cloud densities that range between $10^{7.75}$ and $10^{9}$ $^{-3}$. This leeway reflects the uncertainty in Assoo., This leeway reflects the uncertainty in $A_{2500}$ . " Whereas ἄΚΟΙ employ a extinction of 1.0 magnitude. Asso; could range from ~1.0 dow to 0.2 magnitudes based on a comparison between the spectrum of FBQS 1044 and that of an ""average"" QSO (Weymannetal. 1991)."," Whereas dK01 employ an extinction of 1.0 magnitude, $A_{2500}$ could range from $\sim 1.0$ down to 0.2 magnitudes based on a comparison between the spectrum of FBQS 1044 and that of an “average” QSO \citep{W91}." ". If a population of lower-density clouds were present with a significant fraction of the observed Mg I column. then the dusty clouds would have A»soo> 1. On the other hand. 1Án n,210° em. Assi would drop below 0.25."," If a population of lower-density clouds were present with a significant fraction of the observed Mg I column, then the dusty clouds would have $A_{2500} > 1$ On the other hand, if $n_c \gg 10^{9}$ $^{-3}$, $A_{2500}$ would drop below 0.25." With ης=10 cm we predict Arosa2 0.5 magnitudes. which fits well withiαυ] the inferred range.," With $n_c = 10^{8.5}$ $^{-3}$ we predict $A_{2500} \approx$ 0.5 magnitudes, which fits well within the inferred range." With the extinction already accounted for. the data require the continuous gas component to be effectively dust free.," With the extinction already accounted for, the data require the continuous gas component to be effectively dust free." We tested this hypothesis by including Cloudy’s Orion-type dust (a set of graphite and silicate grains with MRN’s minimum size increased from 0.0025 to 0.03pm. appropriate to a UV-irradiated medium) in the wind. taking into account dust sublimation and sputtering.," We tested this hypothesis by including Cloudy's Orion-type dust (a set of graphite and silicate grains with MRN's minimum size increased from 0.0025 to 0.03, appropriate to a UV-irradiated medium) in the wind, taking into account dust sublimation and sputtering." To include the effects of the latter process. we removed all dust grains whose sputtering time scales (calculated following Tielensetal. 1994)) do not exceed 1000 yr (the approximate time grains spend in the wind if they travel at the observed outflow velocity over a distance of 1 pc).," To include the effects of the latter process, we removed all dust grains whose sputtering time scales (calculated following \citealt{T94}) ) do not exceed 1000 yr (the approximate time grains spend in the wind if they travel at the observed outflow velocity over a distance of $1\ {\rm pc}$ )." Including both of these effects. the predicted dust extinction is over one order of magnitude greater than the maximum value allowed by the observations.," Including both of these effects, the predicted dust extinction is over one order of magnitude greater than the maximum value allowed by the observations." We also considered the effect of changing the scaling of the wind density with radius from nox to nx1777 (as in Blandford&Payne 1982)) and to nXr7.," We also considered the effect of changing the scaling of the wind density with radius from $n \propto r^{-1}$ to $n \propto r^{-3/2}$ (as in \citealt{BP82}) ) and to $n \propto r^{-2}$." These models again overestimate the extinction by about an order of magnitude after dust sublimation and sputtering are taken into account., These models again overestimate the extinction by about an order of magnitude after dust sublimation and sputtering are taken into account. We therefore conclude that. if the gas comprising the shield is associated with a disk outflow. then it must already be dust free when it leaves the disk.," We therefore conclude that, if the gas comprising the shield is associated with a disk outflow, then it must already be dust free when it leaves the disk." Such à situation could arise if the wind originates in a hot disk corona where the matter resides long enough for any dust grains to be destroyed., Such a situation could arise if the wind originates in a hot disk corona where the matter resides long enough for any dust grains to be destroyed. However. to provide the requisite shielding. a dust-free wind requires a higher total gas column than a dusty outflow. so the inferred lack of dust in the wind implies a prohibitively large mass outflow rate — much larger than could be launched by the magnetic field that confines the clouds in our model.," However, to provide the requisite shielding, a dust-free wind requires a higher total gas column than a dusty outflow, so the inferred lack of dust in the wind implies a prohibitively large mass outflow rate — much larger than could be launched by the magnetic field that confines the clouds in our model." Thus. only part of the shield can be outflowing at velocities that are comparable to (or exceed) the observed speeds.," Thus, only part of the shield can be outflowing at velocities that are comparable to (or exceed) the observed speeds." " Perhaps the inner outflow has a lower velocity than we predict. or else some of the shield may not even be outflowing. as in a disk corona or a ""failed"" line-driven wind (see 1»."," Perhaps the inner outflow has a lower velocity than we predict, or else some of the shield may not even be outflowing, as in a disk corona or a “failed” line-driven wind (see \ref{intro}) )." All of these considerations yield our best model. which is compared with the observational results in Table 1.," All of these considerations yield our best model, which is compared with the observational results in Table 1." This model satisfies all the observational constraints and implies that the absorbing gas lies over two orders of magnitude closer to the central source than the earlier estimate., This model satisfies all the observational constraints and implies that the absorbing gas lies over two orders of magnitude closer to the central source than the earlier estimate. The radius where the observed gas leaves the disk surface Is. in general. smaller yet.," The radius where the observed gas leaves the disk surface is, in general, smaller yet." " We can estimate the mass outflow rate associated with the absorbing gas through the relation Maid&AzrfNum,v. where f is the fraction of 4x steradians into which the wind flows. Ny ts the total hydrogen column density of the inferred Mg ΙΙ and Fe Il absorbing region (2:3.9«107? em™). v is the observed outflow speed (~108 em s! ). r (=1.2«10! em) is the inferred distance. and where we assume a vertically and azimuthally continuous wind."," We can estimate the mass outflow rate associated with the absorbing gas through the relation $\dot{M}_{\rm wind} \approx 2 \pi r f N_{\rm H} m_{p} v$ , where $f$ is the fraction of $4 \pi$ steradians into which the wind flows, $N_{\rm H}$ is the total hydrogen column density of the inferred Mg II and Fe II absorbing region $\approx 3.9\times 10^{23}$ $^{-2}$ ), $v$ is the observed outflow speed $\sim 10^{8}$ cm $^{-1}$ ), $r$ $= 1.2 \times 10^{19}$ cm) is the inferred distance, and where we assume a vertically and azimuthally continuous wind." We take f£~0.1 for BALQSO sources (Weymann1997). , We take $f \sim 0.1$ for BALQSO sources \citep{W97}. . For the above values. we find Miu—c8M. yr!.," For the above values, we find $\dot{M}_{\rm wind} \approx 8$ $M_{\odot}$ $^{-1}$." By equating the thermal pressure in the clouds (z2.7x dynes em?) to the confining wind magnetic pressure. BiaSm. we deduce Bying78.2«107G.," By equating the thermal pressure in the clouds $\approx 2.7 \times 10^{-4}$ dynes $^{-2}$ ) to the confining wind magnetic pressure, $B^{2}_{\rm wind}/8 \pi$, we deduce $B_{\rm wind} \approx 8.2 \times 10^{-2}\ {\rm G}$." It is encouraging that. when this value of Bying is used in the n(r)x17! self-similar MHD wind model. it implies a local mass outflow rate that is comparable to the above estimate of Mying. vielding —4Myr!," It is encouraging that, when this value of $B_{\rm wind}$ is used in the $n(r) \propto r^{-1}$ self-similar MHD wind model, it implies a local mass outflow rate that is comparable to the above estimate of $\dot{M}_{\rm wind}$, yielding $\sim 4\ M_{\odot}\ {\rm yr}^{-1}$." " If we instead choose 2,=10? em (so as to satisfy the lower limit on the dust extinction. Azsqq70.25) and require pressure balance. we find Myingz9M.γε."," If we instead choose $n_c = 10^{9}$ $^{-3}$ (so as to satisfy the lower limit on the dust extinction, $A_{2500} = 0.25$ ) and require pressure balance, we find $\dot{M}_{\rm wind} \approx 9\ M_{\odot}\ {\rm yr}^{-1}$." The most robust result of our study is that a shielded. multiphase absorption region reproduces the observations of FBQS 1044 on a conventional BALR scale (~4 pe).," The most robust result of our study is that a shielded, multiphase absorption region reproduces the observations of FBQS 1044 on a conventional BALR scale $\approx 4$ pc)." In addition. when one attributes the Fe II and Mg II absorption to a low-density outflow component and the Mg I absorption to a cospatial high-density outflow component. it is possible to explain the similar kinematic. structure. of the respective spectral features.," In addition, when one attributes the Fe II and Mg II absorption to a low-density outflow component and the Mg I absorption to a cospatial high-density outflow component, it is possible to explain the similar kinematic structure of the respective spectral features." We also find that only a small fraction of the gas along the line of sight can be outfowing at the observed speeds and that only the high-density component of the outflow is dusty., We also find that only a small fraction of the gas along the line of sight can be outflowing at the observed speeds and that only the high-density component of the outflow is dusty. " We derived these results using a “clouds embedded in a continuous MHD disk wind"" model. but our conelusions also apply to other plausible scenarios that include a continuum-shielding gas column and an absorption region that contains distinet low- and high-density components."," We derived these results using a “clouds embedded in a continuous MHD disk wind” model, but our conclusions also apply to other plausible scenarios that include a continuum-shielding gas column and an absorption region that contains distinct low- and high-density components." Our basic conclusions appear to be quite general. although the precise composition of the absorbing gas and its detailed spatial and kinematic properties are not fully constrained by the observations and remain model dependent.," Our basic conclusions appear to be quite general, although the precise composition of the absorbing gas and its detailed spatial and kinematic properties are not fully constrained by the observations and remain model dependent." In addition to explaining the FBQS 1044 observations. this picture may be relevant to the interpretation of absorption features in similar objects where single-phase models imply a large distance.," In addition to explaining the FBQS 1044 observations, this picture may be relevant to the interpretation of absorption features in similar objects where single-phase models imply a large distance." For instance. in the case of the radio-loud galaxy 3C 191. absorber distances of ~28 kpe were inferred by Hamannetal.(2001) using similar arguments to those employed by dKOL.," For instance, in the case of the radio-loud galaxy 3C 191, absorber distances of $\sim 28$ kpc were inferred by \citet{H01} using similar arguments to those employed by dK01." A multiple-phase model could place these absorbers much closer to the central source., A multiple-phase model could place these absorbers much closer to the central source. This interpretation may also be applicable to other AGN observations., This interpretation may also be applicable to other AGN observations. As outlined in l|. several distinct. outflow components have been inferred in various types of AGNs.," As outlined in 1, several distinct outflow components have been inferred in various types of AGNs." There is now growingevidence that these components may not be single-phase., There is now growingevidence that these components may not be single-phase. For the warm-absorber component. which has been inferred to giverise to both X-ray and UV absorption (e.g..Crenshaw1997:Mathuretal.1998;Monier20010. there are indications in at least some sources that the X-ray and UV absorbing components are not identical (e.g.. the Seyfert| galaxy NGC 3783 —,"For the warm-absorber component, which has been inferred to giverise to both X-ray and UV absorption \citep[e.g.,][]{C97,MWE98,MMWE01}, there are indications in at least some sources that the X-ray and UV absorbing components are not identical (e.g., the Seyfert1 galaxy NGC 3783 —" 13200 keV cuerey ranec.,13–200 keV energy range. Standard reduction procedures and sereening criteria have been adopted to produce inearized and equalized event files., Standard reduction procedures and screening criteria have been adopted to produce linearized and equalized event files. Both MECS and PDS data preparation aud linearization was performed using he package under euvironment., Both MECS and PDS data preparation and linearization was performed using the package under environment. The effective exposure time of the observation was 410! s (MECS) and 2.0107 s (PDS)., The effective exposure time of the observation was $\times$ $^4$ s (MECS) and $\times$ $^4$ s (PDS). The observed couutrate or À2319 was 0.908-EO.006. cts/s forthe 2 MECS units and O.58+0.01 cts/s for the PDS instrmucut., The observed countrate for A2319 was $\pm$ 0.006 cts/s forthe 2 MECS units and $\pm$ 0.04 cts/s for the PDS instrument. All spectral fits have been performed using NSPEC Ver., All spectral fits have been performed using XSPEC Ver. 10.00., 10.00. Quoted confidence intervals are 68/4 for L interesting parameter (1.6. AQ= 1). unless otherwise stated.," Quoted confidence intervals are $\%$ for 1 interesting parameter (i.e. $\Delta \chi^2 =1$ ), unless otherwise stated." We have extracted a MECS spectrum from a circular reeion of 16% radius (1.1 Mpc) centered ou the emission ak., We have extracted a MECS spectrum from a circular region of $^{\prime}$ radius (1.4 Mpc) centered on the emission peak. From the ROSAT PSPC radial profile (see E97). we estimate that about 90% of the total cluster emission falls within this radius.," From the ROSAT PSPC radial profile (see F97), we estimate that about $\%$ of the total cluster emission falls within this radius." The backeround subtraction has been serformed using spectra extracted from blauk sky event files in the same region of the detector as the source., The background subtraction has been performed using spectra extracted from blank sky event files in the same region of the detector as the source. " The PDS background-subtracted spectrum bas been produce w plain subtraction of the ""off from the ""on-sourcc spectrum.", The PDS background-subtracted spectrum has been produced by plain subtraction of the “off-” from the “on-source” spectrum. The spectra from the two instruments have con fitted simultaneously. with an optically thin therma clnission model (MERKAL code in the NSPEC package}. absorbed by a galactic line of sight equivalent lydrogecu colunu density. Ny. of «1079 2.," The spectra from the two instruments have been fitted simultaneously, with an optically thin thermal emission model (MEKAL code in the XSPEC package), absorbed by a galactic line of sight equivalent hydrogen column density, $N_H$, of $\times 10^{20}$ $^{-2}$." A ποΊο relative normalization factor among the two iustruimeuts has been added to the spectral fit., A numerical relative normalization factor among the two instruments has been added to the spectral fit. The reason is two-fold: a) the BeppoSAN instirmment response matrices eniplovec in this Letter (September 1997 release) exhibit slight musinatches in the absolute flux calibration: b) the PDS instrument field of view (1.3 degrees FWHAD covers the entire cussion from the cluster. while the MECS spectrin includes cussion out to 1.1 Alpe from the N-ray peak.," The reason is two-fold: a) the BeppoSAX instrument response matrices employed in this Letter (September 1997 release) exhibit slight mismatches in the absolute flux calibration; b) the PDS instrument field of view (1.3 degrees FWHM) covers the entire emission from the cluster, while the MECS spectrum includes emission out to 1.4 Mpc from the X-ray peak." Taking iuto account the mismatch in the absolute fiux calibration. the vignetting of the PDS iustrunueut aix ιο fraction of the emission. falliug outside of the MECS extraction region. we estimate a normalization factor of 1.76.," Taking into account the mismatch in the absolute flux calibration, the vignetting of the PDS instrument and the fraction of the emission falling outside of the MECS extraction region, we estimate a normalization factor of 0.76." In the fitting procedure we allow the normalization value to vary within 15% frou the above value to accouu or the uncertainty in this parameter., In the fitting procedure we allow the normalization value to vary within $\%$ from the above value to account for the uncertainty in this parameter. The NERAL mode is found to fit the data adequately (47.= 183 for 16 of)., The MEKAL model is found to fit the data adequately $\chi^2 =$ 183 for 164 d.o.f.). The best fitting values for the temperature ac he ietal abundance are respectively 9.60.3 keV aac 1254003. where the latter value is expressed iu solar nits.," The best fitting values for the temperature and the metal abundance are respectively $\pm$ 0.3 keV and $\pm$ 0.03, where the latter value is expressed in solar units." The PDS data shows uo evidence of a hard. N-rav sxcess., The PDS data shows no evidence of a hard X-ray excess. However. we cau derive a lower μπιτ to the voluue-weraeed intracluster maguetie field. DB. respousible of the ifuse radio emission located in the central region of the ‘haster.," However, we can derive a lower limit to the volume-averaged intracluster magnetic field, B, responsible of the diffuse radio emission located in the central region of the cluster." " The radio halo spectrum shows au iudex a, ~0.92 i the (105-610) MITZz frequency range and ~2.2 in the ononeauge (610-1100) MIIz: the radio flux is —1 Jy at 610 MITz —F97).", The radio halo spectrum shows an index $\alpha_r$ $\sim$ 0.92 in the (408-610) MHz frequency range and $\sim$ 2.2 in the range (610-1400) MHz; the radio flux is $\sim$ 1 Jy at 610 MHz (F97). From the PDS data we cau place a 90% coufidence o—pper limits of 2.3.10 Ἠ cere ? + and 2.0410. H ere ? + for a power-law spectiuu with cucrey iudex 0.92 aud 2.2. respectively.," From the PDS data we can place a $\%$ confidence upper limits of $\times$ $^{-11}$ erg $^{-2}$ $^{-1}$ and $\times$ $^{-11}$ erg $^{-2}$ $^{-1}$ for a power-law spectrum with energy index 0.92 and 2.2, respectively." " Relating the svuchrotron radio halo fux to the X-ray flux upper limits. assmuine inverse Compton scattering of relativistic electrons with the οὐ] backeround photons. we determine lower linüts of D of 20.0 μα and ~0.035 pC. respectively,"," Relating the synchrotron radio halo flux to the X-ray flux upper limits, assuming inverse Compton scattering of relativistic electrons with the 3K background photons, we determine lower limits of B of $\sim$ 0.04 $\mu$ G and $\sim$ 0.035 $\mu$ G, respectively." The equipartitiou maegucticE feld is estimated to be 0.18. pce (F07)., The equipartition magnetic field is estimated to be 0.48 $\mu$ G (F97). ". We determine also upper lnuits to the energy. density of the euittiug electrous of 1.1410. 12 ere and 9.3410.22 ere cin? for a,=0.92 aud 2.2. respectively. using a size of ~ 0.66 \Ipe in radius for the radio halo."," We determine also upper limits to the energy density of the emitting electrons of $\sim$ $\times 10^{-12}$ erg $^{-3}$ and $\times 10^{-12}$ erg $^{-3}$ for $\alpha_r=0.92$ and 2.2, respectively, using a size of $\sim$ 0.66 Mpc in radius for the radio halo." A proper analysis of extended sources requires that the spectral distortions introduced by the cuerev depeudeut PSF be correctly taken iuto account., A proper analysis of extended sources requires that the spectral distortions introduced by the energy dependent PSF be correctly taken into account. In the case of the MECS instrmucut onboard DeppoSAX the PSF. which is the convolution of the telescope PSF with the detector PSF. is found to vary only wealsly with euergv (D'Acn. De Grandi Moleudi 1998).," In the case of the MECS instrument onboard BeppoSAX the PSF, which is the convolution of the telescope PSF with the detector PSF, is found to vary only weakly with energy (D'Acri, De Grandi Molendi 1998)." This lack of a strone chromatic aberration results frou the fact that the telescope PSF degradation with increasing energv ds approximatively balanced by the improvement of the detector spatial resolution., This lack of a strong chromatic aberration results from the fact that the telescope PSF degradation with increasing energy is approximatively balanced by the improvement of the detector spatial resolution. Though we expect spectral distortions to be small. we have taken them iuto account using theErrAREA program publicly available within the latest release.," Though we expect spectral distortions to be small, we have taken them into account using the program publicly available within the latest release." The program convolves the ROSAT PSPC surtace brightness with an analytic model of the MECS PSF to estimate the spectral distortions., The program convolves the ROSAT PSPC surface brightness with an analytic model of the MECS PSF to estimate the spectral distortions. A more extensive description of the method may be found iu DActi. De Crandi οσοι (1998).," A more extensive description of the method may be found in D'Acri, De Grandi Molendi (1998)." TheErrvares program also Ποιάος corrections for the energy dependet telescope vienetting. which are not discussed in ὉAcri et al. (," The program also includes corrections for the energy dependent telescope vignetting, which are not discussed in D'Acri et al. (" 1998).,1998). The program produces effective area files. which can be used to fit spectra accimniulated. from anuuli or from sectors of annuli.," The program produces effective area files, which can be used to fit spectra accumulated from annuli or from sectors of annuli." " We have accummlated spectra from 6 concentric aunular reeious. with inner aud outer radii of 0-2/, 27-1 |'-6/. 67-8"". 87-12"" and 12’-16""."," We have accumulated spectra from 6 concentric annular regions, with inner and outer radii of $^{\prime}$ $^{\prime}$, $^{\prime}$ $^{\prime}$, $^{\prime}$ $^{\prime}$, $^{\prime}$ $^{\prime}$, $^{\prime}$ $^{\prime}$ and $^{\prime}$ $^{\prime}$." The backeround subtraction has con performed using spectra extracted from blauk skv event files in the same region of the detector as the source., The background subtraction has been performed using spectra extracted from blank sky event files in the same region of the detector as the source. For the 5 innermost annul the euerev range cousidered or spectral fitting was 2-10 keV. while for the outermost aunulus. due to the strong coutzibution of the instrmucutal vackeround iu the 8-10 keV baud. the fit was restricted to he 2-8 keV ranee.," For the 5 innermost annuli the energy range considered for spectral fitting was 2-10 keV, while for the outermost annulus, due to the strong contribution of the instrumental background in the 8-10 keV band, the fit was restricted to the 2-8 keV range." The ROSAT PSPC and HRI images of A2319 (F97) show excess emission. with respect to a racially sviunietric xofile. in the NW and NE direction.," The ROSAT PSPC and HRI images of A2319 (F97) show excess emission, with respect to a radially symmetric profile, in the NW and NE direction." Although the resolution of the MECS image (sce figure 2) is cousiderably iorer than that of the ROSAT images. evidence of the excess is seen also in our data.," Although the resolution of the MECS image (see figure 2) is considerably poorer than that of the ROSAT images, evidence of the excess is seen also in our data." The excess enission imn he NW direction is most likely associated to a subcluster identified from velocity dispersion measureimoeuts (Oceerle et al., The excess emission in the NW direction is most likely associated to a subcluster identified from velocity dispersion measurements (Oegerle et al. 1995). while the structure in the NE direction is coincident with diffuse radio cussion observed at 20 cui (F97).," 1995), while the structure in the NE direction is coincident with diffuse radio emission observed at 20 cm (F97)." " To avoid possible contaminatious to the racially averaged spectra we have excluded data from tle NW aud NE sectors of the third aud fourth απ,", To avoid possible contaminations to the radially averaged spectra we have excluded data from the NW and NE sectors of the third and fourth annuli. Au analysis of the excluded sectors is prescuted in the next subsection., An analysis of the excluded sectors is presented in the next subsection. " We have fitted cach spectrmu with a MERKAL model absorbed bv the galactic Ny of 10°"" cu 7.", We have fitted each spectrum with a MEKAL model absorbed by the galactic $N_H$ of $\times 10^{20}$ $^{-2}$ . In figure l we show the temperature and abundance profiles obtained from the spectral fits., In figure 1 we show the temperature and abundance profiles obtained from the spectral fits. The average temperature and abundance for A2319 are found to be respectively: 9.70.3 keV and 0.3040.03. solar units.," The average temperature and abundance for A2319 are found to be respectively: $\pm$ 0.3 keV and $\pm$ 0.03, solar units." The temperature profile is flat. with no indication of a temperature decline with increasing radius.," The temperature profile is flat, with no indication of a temperature decline with increasing radius." A reduction of the temperature, A reduction of the temperature temperatures.,temperatures. These differences are still modest (with the exception of 1034) because collisional rates are summed over all possible downward transitions. thus averaging the impact of the new rates.," These differences are still modest (with the exception of $10_{29}$ ) because collisional rates are summed over all possible downward transitions, thus averaging the impact of the new rates." Larger differences in the emission line fluxes are however expected as individual state-to-state collisional rates. in particular with ortho-H>. can exceed the scaled He values by more than an order of magnitude.," Larger differences in the emission line fluxes are however expected as individual state-to-state collisional rates, in particular with $_2$, can exceed the scaled He values by more than an order of magnitude." This is demonstrated in Sect., This is demonstrated in Sect. 4., 4. We conclude that using the new HsO-H> collisional rates. non-LTE effects including population inversions will be quenched at lower H» densities. especially in regions where the H» ortho/para ratio ts large.," We conclude that using the new $_2$ $-$ $_2$ collisional rates, non-LTE effects including population inversions will be quenched at lower $_2$ densities, especially in regions where the $_2$ ortho/para ratio is large." In this section we explore. by means of a LVG code. the impact of the new computed collisional coefhcients on the theoretical predictions of water line emission.," In this section we explore, by means of a LVG code, the impact of the new computed collisional coefficients on the theoretical predictions of water line emission." The code is adapted from the one described in Ceccarelli et al. (2002))., The code is adapted from the one described in Ceccarelli et al. \cite{ceccarelli02}) ). It refers to a semi-infinite isodense and isothermal slab (plane-parallel geometry)., It refers to a semi-infinite isodense and isothermal slab (plane-parallel geometry). The code solves self-consistently the statistical level populations and the radiative transfer equations under the approximation of the escape probability. assuming a gradient in the velocity field (Capriotti 1965)).," The code solves self-consistently the statistical level populations and the radiative transfer equations under the approximation of the escape probability, assuming a gradient in the velocity field (Capriotti \cite{capriotti65}) )." We consider the first 45 levels of both ortho- and para-H:O separately., We consider the first 45 levels of both ortho- and $_2$ O separately. The computed line spectrum depends on a few basic parameters: the density of the colliders (H+). the temperature of the emitting gas. the water column density and the maximum gas. velocity.," The computed line spectrum depends on a few basic parameters: the density of the colliders $_2$ ), the temperature of the emitting gas, the water column density and the maximum gas velocity." To have a relatively exhaustive study. we explored a large parameter space.," To have a relatively exhaustive study, we explored a large parameter space." " We varied the H» density between 10 and 1019 cm: the kinetic temperature between 20 and 2000 K: the water column density between 10!"" and 10cm. keeping the velocity equal to | km/s. Note that the velocity only enters in the line opacity. coupled with the H:O column density."," We varied the $_2$ density between $^{4}$ and $^{10}$ $^{-3}$ ; the kinetic temperature between 20 and 2000 K; the water column density between $^{10}$ and $^{15}$ $^{-2}$, keeping the velocity equal to 1 km/s. Note that the velocity only enters in the line opacity, coupled with the $_2$ O column density." In the present study we considered specifically the case of optically thin lines (the low H»O column density case). and the case Where the lines are optically thick (the high H»O column density case).," In the present study we considered specifically the case of optically thin lines (the low $_2$ O column density case), and the case where the lines are optically thick (the high $_2$ O column density case)." In both cases. depending on the gas density. the collisional coefficients may play a major role in the predicted flux.," In both cases, depending on the gas density, the collisional coefficients may play a major role in the predicted flux." " Indeed. even in the case of strongly optically thick lines. the lines could be ""effectively optically thin” if the levels are very sub-thermally populated. as is often the case for water lines."," Indeed, even in the case of strongly optically thick lines, the lines could be “effectively optically thin” if the levels are very sub-thermally populated, as is often the case for water lines." Finally. since the scope of this study 1s to understand the impact of the newly computed collisional coefficients in the line predictions. compared to the old ones. we did not consider the pumping of the levels by infrared and submillimetre radiatiol. Which would unnecessarily complicate the problem.," Finally, since the scope of this study is to understand the impact of the newly computed collisional coefficients in the line predictions, compared to the old ones, we did not consider the pumping of the levels by infrared and submillimetre radiation, which would unnecessarily complicate the problem." We compared the results of the LVG computations with three sets of collisional data: the scaled H»O-He rates of Green et al. (1993)), We compared the results of the LVG computations with three sets of collisional data: the scaled $_2$ O-He rates of Green et al. \cite{green93}) ) between 20 and 2000 K. the H:O-H rates of Phillips et al. (1996))," between 20 and 2000 K, the $_2$ $-$ $_2$ rates of Phillips et al. \cite{phillips96}) )" between 20 and 140 K and the present H:O-H» classical rates beween 20 and 2000 K. The results of this comparison are reported in Fig. 2..," between 20 and 140 K and the present $_2$ $-$ $_2$ classical rates beween 20 and 2000 K. The results of this comparison are reported in Fig. \ref{Figrates2}," where we show the line flux ratios for ortho-H2O at representative densities and temperatures., where we show the line flux ratios for $_2$ O at representative densities and temperatures. Collision rates with ortho-H» only are considered to simplify the interpretation., Collision rates with $_2$ only are considered to simplify the interpretation. The H:O column density ts fixed at I0? em., The $_2$ O column density is fixed at $^{15}$ $^{-2}$. It ean be observed that LVG fluxes based on the classical rates are increased up to a factor of 1O with respect to LVG fluxes based on the scaled H:O—He rates of Green et al. (1993))., It can be observed that LVG fluxes based on the classical rates are increased up to a factor of 10 with respect to LVG fluxes based on the scaled $_2$ $-$ He rates of Green et al. \cite{green93}) ). Ever larger differences were observed at lower temperatures., Even larger differences were observed at lower temperatures. Second. LVG fluxes based on the classical rates are very similar to those based on the rates of Phillips et al. (1996)).," Second, LVG fluxes based on the classical rates are very similar to those based on the rates of Phillips et al. \cite{phillips96}) )," with flux ratios close to ]., with flux ratios close to 1. These findings clearly reflect the differences in collision rates. such as those illustrated in Fig.," These findings clearly reflect the differences in collision rates, such as those illustrated in Fig." 1., 1. They also show that differences in rates are not amplified within the radiative transfer equations., They also show that differences in rates are not amplified within the radiative transfer equations. In particular. it is worth noting that the typical increase of fluxes at 1000 K is less than a factor of 2 at the investigated densities.," In particular, it is worth noting that the typical increase of fluxes at 1000 K is less than a factor of 2 at the investigated densities." Similar results were obtained with para-H». especially above 300 K where differences between para- and ortho-H» rates are minor.," Similar results were obtained with $_2$, especially above 300 K where differences between para- and $_2$ rates are minor." We note. however. that below 100 K. the classical para-H» rates are not necessarily more accurate than the scaled H»O-He rates.," We note, however, that below 100 K, the classical $_2$ rates are not necessarily more accurate than the scaled $_2$ $-$ He rates." Third. we observe that the flux ratios rise steeply with increasing upper energies.," Third, we observe that the flux ratios rise steeply with increasing upper energies." This 1s expected since the critical densities are larger for higher levels and. therefore. the impact of collision rates. i.e. non-LTE effects. becomes more pronounced.," This is expected since the critical densities are larger for higher levels and, therefore, the impact of collision rates, i.e. non-LTE effects, becomes more pronounced." Finally. when the temperature increases. the impact of collision rates is reduced. partly because the low lying levels become thermalized and partly because the differences in rates decrease.," Finally, when the temperature increases, the impact of collision rates is reduced, partly because the low lying levels become thermalized and partly because the differences in rates decrease." It should be noted. however. that at densities higher than 10*em. large flux ratios (~ 10) were still observed at 1000 K for high lying levels.," It should be noted, however, that at densities higher than $^{8}$ $^{-3}$, large flux ratios $\sim$ 10) were still observed at 1000 K for high lying levels." We alsotested the influence of the scaled H»O-He rates employed as substitutes for H» rates in the case of classically-forbidden transitions., We alsotested the influence of the scaled $_2$ $-$ He rates employed as substitutes for $_2$ rates in the case of classically-forbidden transitions. These rates. which generally correspond to AJ>3 and are lower than 1077 em*s7!.were found to," These rates, which generally correspond to $\Delta J>3$ and are lower than $^{-12}$ $^{3}$ $^{-1}$ ,were found to" estimate for theSVOM satellite will be presented in Section 4.5..,estimate for the satellite will be presented in Section \ref{subsec:rate_svom}. " In Figure 5,, blue dash-dotted lines show the redshift distribution of theAdet samples."," In Figure \ref{fig:z_fid_integral}, blue dash-dotted lines show the redshift distribution of the samples." We can expect typically 2.”1 forAdet., We can expect typically $z \sim 1$ for. It is found that the peak of the distribution ofAdet samples is shifted toward lower z from the distribution ofCTAobs samples., It is found that the peak of the distribution of samples is shifted toward lower $z$ from the distribution of samples. " This implies that in contrast toPdet, low-z samples are selected by the C'TA sensitivity."," This implies that in contrast to, $z$ samples are selected by the CTA sensitivity." We found that 90 ofAdet samples have redshifts less than 2.9., We found that 90 of samples have redshifts less than $2.9$. " In Figure 6,, we show the dependence of the GRB detection rate on the typical delay time, Taclay, which is introduced in Section 3.2.."," In Figure \ref{fig:delay-vs-PAdet}, we show the dependence of the GRB detection rate on the typical delay time, $\tau_{\rm delay}$, which is introduced in Section \ref{subsec:detect_conditionCTA}." " The top and the bottom panels represent cases for the prompt emission and theafterglow, respectively."," The top and the bottom panels represent cases for the prompt emission and theafterglow, respectively." " In both panels, the horizontal axis represents Taclay, whereas the vertical axis shows the ratio of the detection rate to that for the fiducial parameter set."," In both panels, the horizontal axis represents $\tau_{\rm delay}$, whereas the vertical axis shows the ratio of the detection rate to that for the fiducial parameter set." " Hence, in both panels, the curves labeled as fiducial have the ratio of 1 if Taclay sec."," Hence, in both panels, the curves labeled as fiducial have the ratio of 1 if $\tau_{\rm delay}=100$ sec." " First, let us consider the prompt emission (the top panel ofFigure 6))."," First, let us consider the prompt emission (the top panel ofFigure \ref{fig:delay-vs-PAdet}))." The red solid curve represents the fiducial case except for Taclay- , The red solid curve represents the fiducial case except for $\tau_{\rm delay}$ . "If Taclay=60 sec for LSTs, the detection rate is enhanced by a factor of1.3."," If $\tau_{\rm delay}=60$ sec for LSTs, the detection rate is enhanced by a factor of$1.3$." The light- dashed curve shows the result for the case where the extra component with Rextra=0.1 is added to a spectrum of the prompt emission in all GRB samples., The light-blue dashed curve shows the result for the case where the extra component with $R_{\rm extra}=0.1$ is added to a spectrum of the prompt emission in all GRB samples. " In this case, independently of Taclay, the detection rate is doubled compared to our fiducial case (Rextra= 0)."," In this case, independently of $\tau_{\rm delay}$, the detection rate is doubled compared to our fiducial case $R_{\rm extra}=0$ )." " In addition, to see the influence of the dispersion of Taciay distribution we draw the magenta dotted curve for the extreme case of no dispersion, i.e., Taclay= for all events."," In addition, to see the influence of the dispersion of $T_{\rm delay}$ distribution we draw the magenta dotted curve for the extreme case of no dispersion, i.e., $T_{\rm delay}=\tau_{\rm delay}$ for all events." " At 90 sec where it is comparable to the peak of the Τοο duration distribution ofCTAobs GRBs, the two lines cross each other."," At $\tau_{\rm delay} = 90$ sec where it is comparable to the peak of the $T_{90}$ duration distribution of GRBs, the two lines cross each other." " If Talay290 sec, the dispersion makes the events with Taeclay smaller than the central value Taclay, which enhances the detection rate."," If $\tau_{\rm delay} \gtrsim 90$ sec, the dispersion makes the events with $T_{\rm delay}$ smaller than the central value $\tau_{\rm delay}$, which enhances the detection rate." " On the other hand, if TaclayS90 sec, the dispersion makes the events with Taelay larger than the central value Taclay, which reduces the detection rate."," On the other hand, if $\tau_{\rm delay} \lesssim 90$ sec, the dispersion makes the events with $T_{\rm delay}$ larger than the central value $\tau_{\rm delay}$, which reduces the detection rate." " Next, let us consider the afterglow (the bottom panelof Figure 6))."," Next, let us consider the afterglow (the bottom panelof Figure \ref{fig:delay-vs-PAdet}) )." " As the red solid curve in the top panel, the blue solid curve is for the fiducial case except for Taelay."," As the red solid curve in the top panel, the blue solid curve is for the fiducial case except for $\tau_{\rm delay}$." " This curve is for the afterglow temporal index p; of —1.5, while the brown dot-dashed and the pink dashed curves are for pe=—1.3 and —1.8, respectively."," This curve is for the afterglow temporal index $p_t$ of $-1.5$, while the brown dot-dashed and the pink dashed curves are for $p_t=-1.3$ and $-1.8$, respectively." " These suggest that for the afterglow detection, the important factor is not Tactay but others such as the well-localized alert rate and the low-energy sensitivity."," These suggest that for the afterglow detection, the important factor is not $T_{\rm delay}$ but others such as the well-localized alert rate and the low-energy sensitivity." The detection rate of theprompt emission is more sensitive to Tac than that of the afterglow as shown in Figure 6.., The detection rate of theprompt emission is more sensitive to $\tau_{\rm delay}$ than that of the afterglow as shown in Figure \ref{fig:delay-vs-PAdet}. This simply comes from the fact that Taciay affects the number ofPobs bursts that satisfy Taclay«Too., This simply comes from the fact that $T_{\rm delay}$ affects the number of bursts that satisfy $T_{\rm delay} 1$, the circular velocity increases from a value of zero at the center of the disks, until it attain a maximum at a critical radius and then decreases to a finite value at the edge of the disk." Also we can see that the value of the critical radius decreases as the value of m increases., Also we can see that the value of the critical radius decreases as the value of $m$ increases. We presented an infinite family of axially svnimetric thin disks of finite radius obtained by means of a particularization of the IIunter method., We presented an infinite family of axially symmetric thin disks of finite radius obtained by means of a particularization of the Hunter method. The disk models so obtained are generalizations of the well known Ixalnajs disk. which corresponds to the first member of the family.," The disk models so obtained are generalizations of the well known Kalnajs disk, which corresponds to the first member of the family." The particularization of the Llunter model was obtained by requiring that the surface density was a monotonically decreasing function of the radius. with a maximum at the center of the disk and vanishing at the edge. in such a wav that the mass clistribution of the higher members of the family were more concentrated at the center.," The particularization of the Hunter model was obtained by requiring that the surface density was a monotonically decreasing function of the radius, with a maximum at the center of the disk and vanishing at the edge, in such a way that the mass distribution of the higher members of the family were more concentrated at the center." We also analyzed the rotation curves of the mocels ancl we find for the first member of the family. the Ixalnajs disk. a circular velocity. proportional to the radius. representing thus a uniformly rotating disk. whereas lor the other members of the family the circular velocity increases from a value of zero at the center of the disks until reach a maximum ata critical radius and then decreases to a finite value at the edge of the disk.," We also analyzed the rotation curves of the models and we find for the first member of the family, the Kalnajs disk, a circular velocity proportional to the radius, representing thus a uniformly rotating disk, whereas for the other members of the family the circular velocity increases from a value of zero at the center of the disks until reach a maximum at a critical radius and then decreases to a finite value at the edge of the disk." Also we find that the value of the critical radius decreases as the value of m increases., Also we find that the value of the critical radius decreases as the value of $m$ increases. We believe that the obtained. thin disk models have some remarkable properties and so they can be considered as appropriated realistic Hat galaxy models. in particular if the superposition of these thin disks with appropriated halo distributions (Binney&Tremaine (1987))) is considered.," We believe that the obtained thin disk models have some remarkable properties and so they can be considered as appropriated realistic flat galaxy models, in particular if the superposition of these thin disks with appropriated halo distributions \cite{BT}) ) is considered." We are now considering some research in this direction., We are now considering some research in this direction. We are now also working in the non axially svmmetric generalization of the here presented. disks models ancl also in the obtention of the relativistic generalization of them for the axiallv symmetric case., We are now also working in the non axially symmetric generalization of the here presented disks models and also in the obtention of the relativistic generalization of them for the axially symmetric case. The authors want to thank the financial support from COLCIHENCLAS. Colombia.," The authors want to thank the financial support from COLCIENCIAS, Colombia." size of the reference region shrinks.,size of the reference region shrinks. For the lowest mass halos the reduction is a factor of 2 to 3 in AV? from the full halo to its innermost (corresponding to a region about 50h !kpc in radius surrounding the galaxy)., For the lowest mass halos the reduction is a factor of 2 to 3 in $\Delta V^2$ from the full halo to its innermost (corresponding to a region about $50 h^{-1}$ kpc in radius surrounding the galaxy). Reductions are by somewhat smaller factors for more massive halos., Reductions are by somewhat smaller factors for more massive halos. " Nevertheless, quite substantial motions are detected even for the smallest regions, so a significant fraction of the core motion is typically relative to the immediately surrounding halo."," Nevertheless, quite substantial motions are detected even for the smallest regions, so a significant fraction of the core motion is typically relative to the immediately surrounding halo." A similar conclusion can be drawn from the upper left panel of Fig., A similar conclusion can be drawn from the upper left panel of Fig. " 2 which shows that the tail of large measured motions shrinks when the effective size of the ""core"" is increased.", 2 which shows that the tail of large measured motions shrinks when the effective size of the “core” is increased. So far we have addressed non-equilibrium excitations of the inner regions of galaxy and cluster halos by looking directly for the position and velocity asymmetries which they may produce., So far we have addressed non-equilibrium excitations of the inner regions of galaxy and cluster halos by looking directly for the position and velocity asymmetries which they may produce. " In this subsection, we approach the issue from a different angle by studying the rate at which material is added to the core regions by the merger/accretion events which typically drive such excitations."," In this subsection, we approach the issue from a different angle by studying the rate at which material is added to the core regions by the merger/accretion events which typically drive such excitations." In galaxies this process is related to the build up of the stellar halo through accretion and disruption events like that currently involving the Sagittarius dwarf galaxy (Ibata et al., In galaxies this process is related to the build up of the stellar halo through accretion and disruption events like that currently involving the Sagittarius dwarf galaxy (Ibata et al. 2001)., 2001). In rich clusters it is related to the formation of the central galaxy by cannibalism of other cluster members (Ostriker Tremaine 1975; White 1976; Dubinski 1998)., In rich clusters it is related to the formation of the central galaxy by cannibalism of other cluster members (Ostriker Tremaine 1975; White 1976; Dubinski 1998). " Using a set of high resolution resimulations of the assembly of cluster halos, Gao et al. ("," Using a set of high resolution resimulations of the assembly of cluster halos, Gao et al. (" 2004b) addressed the latter problem by analysing the rate at which material is added to the innermost region where the visible galaxy lies.,2004b) addressed the latter problem by analysing the rate at which material is added to the innermost region where the visible galaxy lies. " Their most striking finding was that while the total mass of the inner 10A! kpc has evolved little since redshift z~6, much of the material in the current core has been added recently from previously distinct objects."," Their most striking finding was that while the total mass of the inner $10h^{-1}$ kpc has evolved little since redshift $z\sim 6$, much of the material in the current core has been added recently from previously distinct objects." Here we carry out a similar study of the assembly of the inner cores of our Millennium Simulation halos., Here we carry out a similar study of the assembly of the inner cores of our Millennium Simulation halos. Following the approach of Gao et al. (, Following the approach of Gao et al. ( "2004b), we find the fraction of the material in the core of each z—0 halo","2004b), we find the fraction of the material in the core of each $z=0$ halo" , "(2006) provide a recent and accurate approximation for the inelastic cross-section: σεν)=(81.5|Lask0.25L2)&d(EE)! nib. where Ly,=1.22 GeV is the threshold cucrey of production of zÜ-inesous. aud L—lu(E,/1TeV).","(2006) provide a recent and accurate approximation for the inelastic cross-section: $\sigma_{\rm inel}(E_p)=(34.3+1.88\,L+0.25\,L^2)\times\left[1-\left(E_{\rm th}/E_p\right)^{4}\right]^2$ mb, where $E_{\rm th}=1.22$ GeV is the threshold energy of production of $\pi^0_{}$ -mesons, and $L=\ln(E_p/1\,{\rm TeV})$." Tn Fig., In Fig. 2 we show the hadronic ganuua-ray huuinositv eenerated along the jet Guteerated along :) for differcut ϱ directious., \ref{L_o} we show the hadronic gamma-ray luminosity generated along the jet (integrated along $z$ ) for different $\theta$ directions. The beaming factor is defined by the ratio L(0)/L(0=0) for chereies ercater than LO GeV. where the aneular dependence of the emereius flux is almost enerev iudepenudoeut.," The beaming factor is defined by the ratio $L(\theta)/L(\theta=0)$ for energies greater than 10 GeV, where the angular dependence of the emerging flux is almost energy independent." The expressious given by Ikoluer et al. (, The expressions given by Kelner et al. ( 2006) are used to compute the leptonic energy distribution ofe injected along the jet by the charged pion decays.,2006) are used to compute the leptonic energy distribution of $e^\pm$ injected along the jet by the charged pion decays. " The resulting injection rate (leptons per units of cucrey. volume. aud time} cau be expressed iu terms of the variable (6—E/E), asfracder."," The resulting injection rate (leptons per units of energy, volume, and time) can be expressed in terms of the variable $x=E_{e^\pm}/E_p$ as." " Tere. Fite.Efe) is the spectimm of electrons from the w>pr, decay, aad it is ceseribedk by where aud £=In(£,,/1TeV)."," Here, $F_{e}(x,\,E_{e}/x)$ is the spectrum of electrons from the $\pi\to\mu\,\nu_\mu$ decay, and it is described by , where and $L=\ln(E_p/1\,{\rm TeV})$." For the injected proton flux (see Section 3). we obtain (οτνὃνυπο. leptons bao lqqy 7 at the base of the jet. in the observers reference. frame or Model D (an order of magnitude higher for Model A).," For the injected proton flux (see Section 3), we obtain $q_e(E_e)\sim 3\times 10^{27} (E_e/{\rm eV})^{-1.92}$ leptons $^{-1}$ $^{-1}$ $^{-3}$, at the base of the jet, in the observer's reference frame for Model B (an order of magnitude higher for Model A)." Ouce produced. we assiunue that he linear momenta of he leptons loses its angular dependence. erasec by the vaudom nature of the naenetic field.," Once produced, we assume that the linear momentum of the leptons loses its angular dependence, erased by the random nature of the magnetic field." Iu. the calculations. we integrate the 0 dependence of the differential rate of xoduetion of 6 and treat the population as isotropic in the jet reference frame.," In the calculations, we integrate the $\theta$ dependence of the differential rate of production of $e^\pm$ and treat the population as isotropic in the jet reference frame." " The leptous injected aloug the jot suffer from radiative cooling due to svuchrotron ac OG Xocesses, as well as adiabatic expiusiou losses."," The leptons injected along the jet suffer from radiative cooling due to synchrotron and IC processes, as well as adiabatic expansion losses." The evolution of the particle cucrey distribution is studied by dividing the jet iuto slices of suitable size iu order to consider the physical conditions as homogeneous within cach of them., The evolution of the particle energy distribution is studied by dividing the jet into slices of suitable size in order to consider the physical conditions as homogeneous within each of them. Afterward. to obtain the distribution evolution with :. we solve the continuity differential equation.," Afterward, to obtain the distribution evolution with $z$, we solve the continuity differential equation." Note that differcut evolved populations suu up at cach height. since injection occurs all along thejet.," Note that different evolved populations sum up at each height, since injection occurs all along thejet." The expressions uscd are given in Bordas et al. (, The expressions used are given in Bordas et al. ( 2007).,2007). km s! and A=(0010 degrees.,km $^{-1}$ and $\lambda=100_{-9}^{+28}$ degrees. Third. we checked for any correlations between the RM signal and the strength of Ca II H and K emission. or the shape parameters of the instrumental line spread function.," Third, we checked for any correlations between the RM signal and the strength of Ca II H and K emission, or the shape parameters of the instrumental line spread function." Significant correlations would have raised suspicion of systematic errors. but none were found.," Significant correlations would have raised suspicion of systematic errors, but none were found." In addition. if the 29.2 day periodicity detected by B10 ts indeed the rotation period. then a powerful test for spin-orbit misalignment ts available.," In addition, if the 29.2 day periodicity detected by B10 is indeed the rotation period, then a powerful test for spin-orbit misalignment is available." " If the system were well-aligned we would have A20 and {,5907.", If the system were well-aligned we would have $\lambda = 0$ and $i_\star \approx 90^\circ$. This would imply where we have used A.=0.752 R.. and P.=29.2 days (B10).," This would imply where we have used $R_\star = 0.752$ $R_\odot$ and $P_{\rm rot} = 29.2$ days (B10)." When refitting the data with these constraints. the minimum 4 rises from 111.9 to 164.3 (Ay?= 52.4). with 114 degrees of freedom.," When refitting the data with these constraints, the minimum $\chi^2$ rises from 111.9 to 164.3 $\Delta\chi^2 = 52.4$ ), with 114 degrees of freedom." " Thus the well-aligned model is ruled out with 7.20 confidence: either A is large. or else /, must be far from 90° to be compatible with the low amplitude of the RM signal."," Thus the well-aligned model is ruled out with $\sigma$ confidence: either $\lambda$ is large, or else $i_\star$ must be far from $90^\circ$ to be compatible with the low amplitude of the RM signal." The best-fitting well-aligned model is illustrated with a gray dashed curve in Figure 3., The best-fitting well-aligned model is illustrated with a gray dashed curve in Figure 3. " HAT-P-11b is the first ""hot Neptune"" for which the RM effect has been measured.", HAT-P-11b is the first “hot Neptune” for which the RM effect has been measured. Our results suggest that tilted orbits are common for hot Neptunes. just as has been found for hot Jupiters.," Our results suggest that tilted orbits are common for hot Neptunes, just as has been found for hot Jupiters." The same migration mechanisms that are invoked to explain the larger planets with tilted orbits—gravitational scattering by planets. or the three-body Kozai effect—may also have operated in this case.," The same migration mechanisms that are invoked to explain the larger planets with tilted orbits—gravitational scattering by planets, or the three-body Kozai effect—may also have operated in this case." It should be noted that the spin-orbit results are not the only evidence for a perturbative origin for many close-in planets., It should be noted that the spin-orbit results are not the only evidence for a perturbative origin for many close-in planets. " Further evidence comes from their occasionally high orbital eccentricities. the clustering of their orbital distances near the value expected from tidal cireularization, and their tendency to lack companions with periods between 10-100 days (Matsumura et al."," Further evidence comes from their occasionally high orbital eccentricities, the clustering of their orbital distances near the value expected from tidal circularization, and their tendency to lack companions with periods between 10–100 days (Matsumura et al." 2010)., 2010). Since HAT-P-1I1b is the lowest-mass planet yet probed by RM measurements. and it is misaligned. our findings are at odds with the hypothesis that misalignments occur mainly for the most massive planets (Johnson et al.," Since HAT-P-11b is the lowest-mass planet yet probed by RM measurements, and it is misaligned, our findings are at odds with the hypothesis that misalignments occur mainly for the most massive planets (Johnson et al." 2009)., 2009). They do. however. support the correlation between large obliquity and orbital eccentricity (Johnson et al.," They do, however, support the correlation between large obliquity and orbital eccentricity (Johnson et al." 2009. Hébbrard et al.," 2009, Hébbrard et al." 2010). as the orbit of HAT-P-IIb has à significant eccentricity.," 2010), as the orbit of HAT-P-11b has a significant eccentricity." Another emerging trend is that misalignments occur mainly for stars with high effective temperatures or large masses (Taj>6250 K or M.L1.2 M.)., Another emerging trend is that misalignments occur mainly for stars with high effective temperatures or large masses $T_{\rm eff}>6250$ K or $M_\star \gsim 1.2~M_\odot$ ). Winn et al. (, Winn et al. ( 2010) speculated that this is due to tidal interactions: cool stars realign with the orbits. but hot stars cannot realign because tidal dissipation is weaker in their thinner outer convection zones.,"2010) speculated that this is due to tidal interactions: cool stars realign with the orbits, but hot stars cannot realign because tidal dissipation is weaker in their thinner outer convection zones." The HAT-P-11 system is an important test case because the star is cool and low-mass. and yet tidal interactions are weak due to the planet's relatively small size and long period.," The HAT-P-11 system is an important test case because the star is cool and low-mass, and yet tidal interactions are weak due to the planet's relatively small size and long period." If stellar temperature or mass are the determinants then one would expect HAT-P-11 to be well-aligned like other cool stars., If stellar temperature or mass are the determinants then one would expect HAT-P-11 to be well-aligned like other cool stars. But if tides are the underlying factor. then HAT-P-11 would be misaligned. as we have observed.," But if tides are the underlying factor, then HAT-P-11 would be misaligned, as we have observed." Specifically. with reference to Eqn. (," Specifically, with reference to Eqn. (" 2) of Winn et al. (,2) of Winn et al. ( 2010). HAT-P-I] experiences even weaker tides than WASP-8. a cool star already known to have a high Thus. HAT-P-11 is a telling exception to the rule that hot stars have high obliquities: it implicates tidal evolution as the reason for low obliquities among cool stars with more massive planets in tighter orbits.,"2010), HAT-P-11 experiences even weaker tides than WASP-8, a cool star already known to have a high Thus, HAT-P-11 is a telling exception to the rule that hot stars have high obliquities: it implicates tidal evolution as the reason for low obliquities among cool stars with more massive planets in tighter orbits." By good fortune. HAT-P-11 is in the field of view of theKepler spacecraft (Borucki et al.," By good fortune, HAT-P-11 is in the field of view of the spacecraft (Borucki et al." 2010)., 2010). The precise photometric time series will allow the candidate 29.2-day rotation period to be checked., The precise photometric time series will allow the candidate 29.2-day rotation period to be checked. Asteroseismological studies may reveal the stellar mean density. age. inclination. and other parameters (Christensen-Dalsgaard et al.," Asteroseismological studies may reveal the stellar mean density, age, inclination, and other parameters (Christensen-Dalsgaard et al." 2010)., 2010). Furthermore we predict thatKepler will see a pattern of anomalies in the transit light curves that will betray the system's spin-orbit misalignment., Furthermore we predict that will see a pattern of anomalies in the transit light curves that will betray the system's spin-orbit misalignment. " As usual for a spotted star. there will be a ""bump"" or ""rebrightening"" in the transit light curve whenever the planet oecults a starspot (see. e.g.. Rabus et al."," As usual for a spotted star, there will be a “bump” or “rebrightening” in the transit light curve whenever the planet occults a starspot (see, e.g., Rabus et al." 2009)., 2009). For a well-aligned star. the bumps recur in successive transits for as long as the spot is on the visible hemisphere.," For a well-aligned star, the bumps recur in successive transits for as long as the spot is on the visible hemisphere." There is a steady advance in phase of the bumps due to the star's rotation between transits., There is a steady advance in phase of the bumps due to the star's rotation between transits. However. for a star like HAT-P-11 with A=907. the events willnor recur in this manner. because the star’s rotation moves the spot away from the transit chord.," However, for a star like HAT-P-11 with $\lambda\approx 90^\circ$, the events will recur in this manner, because the star's rotation moves the spot away from the transit chord." A spot must complete a full rotation before returning to the transit chord. and even then. the planet will miss it unless it has also completed an integral number of orbits.," A spot must complete a full rotation before returning to the transit chord, and even then, the planet will miss it unless it has also completed an integral number of orbits." For HAT-P-1I. it happens that Pro/Pan~6.," For HAT-P-11, it happens that $P_{\rm rot}/P_{\rm orb} \approx 6$." If the star were well-aligned and had one spot initially on. the transit chord. then we would typically see an alternation between 2-3 light curves with bumps. and 2-3 without bumps (when the spot is on the far side).," If the star were well-aligned and had one spot initially on the transit chord, then we would typically see an alternation between 2–3 light curves with bumps, and 2–3 without bumps (when the spot is on the far side)." But because of the misalignment. spot anomalies will only recur every 29.2 days. after the star has rotated once and the planet has completed 6 orbits.," But because of the misalignment, spot anomalies will only recur every 29.2 days, after the star has rotated once and the planet has completed 6 orbits." Complications may arise due to differential rotation. as well as the multiplicity and evolution of spot patterns.," Complications may arise due to differential rotation, as well as the multiplicity and evolution of spot patterns." Nevertheless. this phenomenon should allow for an independent test of spin-orbit misalignment for P-11 as well as other spotted stars.," Nevertheless, this phenomenon should allow for an independent test of spin-orbit misalignment for HAT-P-11 as well as other spotted stars." We thank Norio Narita and Teruyuki Hirano for sharing their results prior to publication. and Dan Fabrycky and Scott Gaudi for helpful discussions.," We thank Norio Narita and Teruyuki Hirano for sharing their results prior to publication, and Dan Fabrycky and Scott Gaudi for helpful discussions." We acknowledge the support from the MIT Class of 1942. NASA grants NNXO9AD36G and NNXOSAF23G. and NSF grant AST-0702843.," We acknowledge the support from the MIT Class of 1942, NASA grants NNX09AD36G and NNX08AF23G, and NSF grant AST-0702843." The data presented herein were obtained at the W. M. Keck Observatory. which is operated as a scientific partnership among the California Institute of Technology. the University of California. and NASA. and was made possible by the generous financial support of the W. M. Keck Foundation.," The data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and NASA, and was made possible by the generous financial support of the W. M. Keck Foundation." We extend special thanks to those of Hawaiian ancestry on whose sacred mountain of Mauna Kea we are privileged to be, We extend special thanks to those of Hawaiian ancestry on whose sacred mountain of Mauna Kea we are privileged to be "For our final sample of LEGO candidates. we calculate the star formation rate (SFR) as derived from Kennicutt (1983) by: where the Ha luminosity. Ljp,. is obtained with the conversion between Lyo and Ho luminosities of Brocklehurst (1971) of Ίνα) = 8.7. L(Ho).","For our final sample of LEGO candidates, we calculate the star formation rate (SFR) as derived from Kennicutt (1983) by: where the $\alpha$ luminosity, $L_{\mathrm{H}\alpha}$, is obtained with the conversion between $\alpha$ and $\alpha$ luminosities of Brocklehurst (1971) of $\alpha$ ) = $8.7 \times$ $\alpha$ )." The SFR values of the LEGO candidates can be found in Table 3.., The SFR values of the LEGO candidates can be found in Table \ref{photometry}. . The mean SFR. as derived from the Lya-emission for all candidates is 1.5 ../vr.," The mean SFR, as derived from the $\alpha$ -emission for all candidates is $1.8$ $_{\odot}/\mrm{yr}$." " The total SFR is 13 Μ.νι. yielding a star formation rate density pagg of 0.013 M,/vr/Mpc."," The total SFR is $43$ $_{\odot}/\mrm{yr}$, yielding a star formation rate density $\rho_{\mrm{SFR}}$ of $0.013$ $_{\odot}/\mrm{yr}/\mrm{Mpc}^3$." This value is in very good agreement with other results for high redshift galaxies at this redshift of e.g. Madau et al. (, This value is in very good agreement with other results for high redshift galaxies at this redshift of e.g. Madau et al. ( 1996: 0.016 ../vr Alpe). Steidel et al. (,"1996; 0.016 $_{\odot}/\mrm{yr}/\mrm{Mpc}^3$ ), Steidel et al. (" "1999: 0.05 , /vr/Mpc) and Cowie Hu (1998; 0.01 ../sz/Mpc?).",1999; 0.05 $_{\odot}/\mrm{yr}/\mrm{Mpc}^3$ ) and Cowie Hu (1998; 0.01 $_{\odot}/\mrm{yr}/\mrm{Mpc}^3$ ). The results fromSteidel et al. (, The results fromSteidel et al. ( 1999) has been obtained from integrating the extrapolated,1999) has been obtained from integrating the extrapolated using the correction. formulae of Andy. and the UV measurements were also corrected for the reduction in hroughput due to the build-up of contaminants on the UV ilters in between the regular decontaminations.,using the correction formulae of Andy and the UV measurements were also corrected for the reduction in throughput due to the build-up of contaminants on the UV filters in between the regular decontaminations. For CVI. we also calculated the STALAG nllτους magnitude and the (noz; ἐς). colour.," For CV1, we also calculated the STMAG $nUV_{255}$ magnitude and the $nUV_{255}-U_{336}$ ) colour." The results or CVI quoted in what follows include a correction for he red leak of the UV. filters., The results for CV1 quoted in what follows include a correction for the red leak of the UV filters. This was estimated: usingSYNPIHOT.. which is part of the package inIRAF.. combine with the newer filter-throughput data in7°.," This was estimated using, which is part of the package in, combined with the newer filter-throughput data in." Por the purposes of comparison with catalogued values we caleulated the Johnson (C.Vy colours for the CV using he transformation in equation S and the zeropoints in Table 7 of Woltzmanοἱal.(1995)., For the purposes of comparison with catalogued values we calculated the Johnson $(U-V)_{0}$ colours for the CV using the transformation in equation 8 and the zeropoints in Table 7 of \citet{holtz95}. Our X-rav dataset. consists of 16 ks of archival ACIS-S data. obtained from the (see ‘Table 1)).," Our X-ray dataset consists of 16 ks of archival ACIS-S data, obtained from the (see Table \ref{table:obs}) )." The central region of the cluster where CVI resides appears on the back-illuminatecdl S3 chip of he ACES detector. close to the aimpoint of the telescope.," The central region of the cluster where CV1 resides appears on the back-illuminated S3 chip of the ACIS detector, close to the aimpoint of the telescope." Beginning with the level-l pipeline-processed. event. lists. he data were reduced. with the software to apply he latest calibration.," Beginning with the level-1 pipeline-processed event lists, the data were reduced with the software to apply the latest calibration." The data were filtered on the energy range for which the ACIS detector is calibrated. 0.3.10 keV. Dad. pixels ancl times of high. background: were. removed using the pipeline-produced. badpixel file ancl good-time intervals (CCELI).," The data were filtered on the energy range for which the ACIS detector is calibrated, 0.3–10 keV. Bad pixels and times of high background were removed using the pipeline-produced badpixel file and good-time intervals (GTI)." " Source-detection was carried out with the algorithm. which correlates the data with a ""Mexican hat wavelet function."," Source-detection was carried out with the algorithm, which correlates the data with a `Mexican hat' wavelet function." " A source appearing at a=1sb36*""24.71.8 =23754/35"" is consistent with M22 CV1: this position corresponds to a6 racial ollset of ~0.7” from the position (see Section. ?2)). which is within the uncertainties of the (—0.57)) and. (0.67) coordinates."," A source appearing at $\alpha= 18^{\mathrm{h}}36^{\mathrm{m}}24^{\mathrm{s}}\!.71$ , $\delta= -23\degr54\arcmin35\arcsec\!.6$ is consistent with M22 CV1: this position corresponds to a radial offset of $\sim$ from the position (see Section \ref{sec:hstdata}) ), which is within the uncertainties of the $\mathbf{\sim 0.5}$ ) and $\mathbf{0.6}$ ) coordinates." We extracted. the source spectrum. with the L1--contributed seript for point sources.PSENTRACT.," We extracted the source spectrum with the -contributed script for point sources,." . The detector response and elfective-area files were extracted with the ancl tools and binned on the same energy grid., The detector response and effective-area files were extracted with the and tools and binned on the same energy grid. | background. spectrum was extracted [rom source-[ree regions neighbouring the object., A background spectrum was extracted from source-free regions neighbouring the object. The same instrument response files were usec for the background. as for the source., The same instrument response files were used for the background as for the source. The source spectrum was grouped to include at least twenty net counts per bin., The source spectrum was grouped to include at least twenty net counts per bin. Fitting of the source aud background spectra was performed in version The optical spectroscopic observations of AIS were taken during 1991 July and August with the 4.2-m William Lersehel Telescope (WIEE) on La Palma. using both the red ancl blue arms of the Intermediate dispersion Spectrograph and lmaginge System (ISIS).," Fitting of the source and background spectra was performed in version The optical spectroscopic observations of M5 were taken during 1991 July and August with the 4.2-m William Herschel Telescope (WHT) on La Palma, using both the red and blue arms of the Intermediate dispersion Spectrograph and Imaging System (ISIS)." The R3IGR. grating was used with the red arm and the R300D grating with the blue arm. producing a resolution of 3.3A.," The R316R grating was used with the red arm and the R300B grating with the blue arm, producing a resolution of 3.3." . The secing during the spectroscopic observations varied [rom 0.7 to 1.3 aresec., The seeing during the spectroscopic observations varied from 0.7 to 1.3 arcsec. The finding chart for the CY appears in Fig. 4.., The finding chart for the CV appears in Fig. \ref{fig:m5find}. We used. two sets of imaging data., We used two sets of imaging data. The first consists of H-band. images obtained. from the ING. The, The first consists of -band images obtained from the ING The "he GCs start out as part of a ""hot. pressure-supported component of the spiral haloes and. so »vhave clilfercntLy rom the disc stars during the merger.","the GCs start out as part of a “hot”, pressure-supported component of the spiral haloes and so behave differently from the disc stars during the merger." The AIDE of the 1alo clusters thus does not change markedly during merging. whereas that of the halo can be dramatically changed owing o the addition of large numbers of stripped dise stars.," The MDF of the halo clusters thus does not change markedly during merging, whereas that of the halo can be dramatically changed owing to the addition of large numbers of stripped disc stars." In he product elliptical. we therefore end up with metal-poor clusters embedded in à moderately metal-rich and. massive 1alo.," In the product elliptical, we therefore end up with metal-poor clusters embedded in a moderately metal-rich and massive halo." This dynamically constructed difference in MDEs would not be changed if we were to include gas and merger-induced ormation of metal-rich GC's. since numerical simulations iive already demonstrated. that these would mostly be ocated in the central region of he merger remnant and rerefore would. not. contribute to the AIDF of GCs in 1ο outer halo region (Bekki ct al.," This dynamically constructed difference in MDFs would not be changed if we were to include gas and merger-induced formation of metal-rich GCs, since numerical simulations have already demonstrated that these would mostly be located in the central region of the merger remnant and therefore would not contribute to the MDF of GCs in the outer halo region (Bekki et al." 2002)., 2002). In addition. the “bulge” GCs which were already oesent in the progenitor spirals (such as are present in boti the Milky Way and be131) are more concenrated to their parent ealaxy Centers and would stay in the inner regions along with the bulge gaars.," In addition, the “bulge” GCs which were already present in the progenitor spirals (such as are present in both the Milky Way and M31) are more concentrated to their parent galaxy centers and would stay in the inner regions along with the bulge stars." The significan illerence in NDs between the halo gaars and the GC's hat we note in the Ml simulation has been actually observec for M31I. (Durrell ct al., The significant difference in MDFs between the halo stars and the GCs that we note in the M1 simulation has been actually observed for M31 (Durrell et al. 2001) and NOC 5128 (UIP. LOL. LIEIO2). both of which have larec central spheroidal components.," 2001) and NGC 5128 (HHP, HH01, HH02), both of which have large central spheroidal components." A mean ollset in integrated color (and by hypothesis metallicity) between GCs and field stars is also classically observed in many giant ellipticals (e.g. Llarris 1991. Broclie Lluchra 1991).," A mean offset in integrated color (and by hypothesis metallicity) between GCs and field stars is also classically observed in many giant ellipticals (e.g. Harris 1991, Brodie Huchra 1991)." It has frequently been sugeested that the redder. more metal-rich clusters are similar to the bulk of the Licle halo ancl bulge stars. while the bluer. more metal-poor ones have earlier ane different origins. such as within spiral haloes or ο ealaxies (c.g. Larsen et al.," It has frequently been suggested that the redder, more metal-rich clusters are similar to the bulk of the field halo and bulge stars, while the bluer, more metal-poor ones have earlier and different origins, such as within spiral haloes or dwarf galaxies (e.g. Larsen et al." 2001: Forbes. Brodie. Crillmair 1997: Geisler. Lee. Wim 906: Cotte. Marzke. Wes 1998).," 2001; Forbes, Brodie, Grillmair 1997; Geisler, Lee, Kim 1996; Côtté,, Marzke, West 1998)." The Milkv Was. an She-type spira with only a small bulge. is not observed to have such a. dillerence between halo stars and clusters.," The Milky Way, an Sbc-type spiral with only a small bulge, is not observed to have such a difference between halo stars and clusters." We therefore suggest tha the observed. dillerence in MDEs between stellar haloes zu GCs in elliptical galaxies or earlv-twpe spirals with big bulges is consistent with the view that their large spheroida components were formed by past major merger events., We therefore suggest that the observed difference in MDFs between stellar haloes and GCs in elliptical galaxies or early-type spirals with big bulges is consistent with the view that their large spheroidal components were formed by past major merger events. We discuss this point further in EJ., We discuss this point further in 4. Although the models ΑΔΗ ALLO resemble each other in their dvnanics of stellar halo formation and the peak value of the AIDFs of the resulting stellar haloes. the shapes of the MDE's depend on the progenitor disc metallicity gradient. bulge-to-disc-ratio. and the mass fraction and the MDESs of the initial haloes.," Although the models M1 – M10 resemble each other in their dynamics of stellar halo formation and the peak value of the MDFs of the resulting stellar haloes, the shapes of the MDFs depend on the progenitor disc metallicity gradient, bulge-to-disc-ratio, and the mass fraction and the MDFs of the initial haloes." In Fig., In Fig. " 12. we illustrate these elfects: (i) The MDE's show a larger fraction of metal-rich 0.4 < m/H] <0) halo stars in the model with the larger bulge-to-clise-ratio (M2. AL,= 0.6)."," 12, we illustrate these effects: (i) The MDFs show a larger fraction of metal-rich $-0.4$ $\le$ [m/H] $\le$ 0) halo stars in the model with the larger bulge-to-disc-ratio (M2, $M_b =0.6$ )." This is because more of the metal-rich bulge stars can be more efficiently stripped into the stellar halo owing to its larger extension of the bulge in the model with the larger bulge-to-disc-ratio., This is because more of the metal-rich bulge stars can be more efficiently stripped into the stellar halo owing to its larger extension of the bulge in the model with the larger bulge-to-disc-ratio. The MDE, The MDF The large cllective area. very high timeresolution and excellent. telemetry of theRossi Nray. Timing. Explorer (RATE) have made possible the discovery of Quasi Periodic Oscillations (QPOs) in the range 10019200Lf: from a variety of accreting. collapsed objects. weakly magnetic neutron stars (see van der klis 1998 for a review) and. more surprisingly. in black hole candidates (DIICS. Morgan 1997: Remillard 1997).,"The large effective area, very high time–resolution and excellent telemetry of the X–ray Timing Explorer (RXTE) have made possible the discovery of Quasi Periodic Oscillations (QPOs) in the range $\sim 100-1200\; Hz$ from a variety of accreting collapsed objects, weakly magnetic neutron stars (see van der klis 1998 for a review) and, more surprisingly, in black hole candidates (BHCs, Morgan 1997; Remillard 1997)." Ht has been recently suggested (Cuietal.1998). that these QPOs in BIICSs arise through LenseThirring (LT. 1918) precession of matter from the accretion cisks.," It has been recently suggested \cite{czc} that these QPOs in BHCs arise through Lense–Thirring (LT, 1918) precession of matter from the accretion disks." Since motion of a point mass in a Ixerr metric allows an exact treatment. and a detailed comparison of Ixeplerian and LenseThirring frequencies has not been explicitly. carried out in the literature up to now. it seems worthwhile to derive these quantities for an arbitrary black hole mass and specific angular momentum.," Since motion of a point mass in a Kerr metric allows an exact treatment, and a detailed comparison of Keplerian and Lense–Thirring frequencies has not been explicitly carried out in the literature up to now, it seems worthwhile to derive these quantities for an arbitrary black hole mass and specific angular momentum." This allows us to clarify the meaning of the precession frequency. about which some confusion seems to be present in the literature.," This allows us to clarify the meaning of the precession frequency, about which some confusion seems to be present in the literature." “Phis is the aim of thisLeffer., This is the aim of this. In the last section we shall also discuss the problems which are raised by this computation. regarding the interpretation of Cui C1998).," In the last section we shall also discuss the problems which are raised by this computation, regarding the interpretation of Cui (1998)." 1n what follows we will consider a test particle of unit. miss in motion inside a Werr spacetime., In what follows we will consider a test particle of unit mass in motion inside a Kerr spacetime. The metric. in. Bover-Lindquist coordinates (Dover&Lindquist1967). and in units GC=¢= Lis where AI and e are. respectively. the mass and the specilic angular momentum of the black bole.," The metric, in Boyer-Lindquist coordinates \cite{bl} and in units $G=c=1$ is where $M$ and $a$ are, respectively, the mass and the specific angular momentum of the black hole." As Carter. (1905) first. demonstrated. the equation of motion can be separated. and the resulting equations become: with The dot denotes differentiation with respect to the," As Carter \shortcite{car} first demonstrated, the equation of motion can be separated, and the resulting equations become: with The dot denotes differentiation with respect to the" "half-mass diameter of the MW disks at z=3 of about 1"".",half-mass diameter of the MW disks at $z=3$ of about $1''$. No MW progenitor will hence be resolved., No MW progenitor will hence be resolved. " However, in the case of CO(1-0) at z=3 imaged with SKA-HF, the resolution becomes as good as 0.03”, such that a typical MW progenitor will be resolved in roughly 100 pixels (depending on inclination and evolution scenario)."," However, in the case of CO(1–0) at $z=3$ imaged with SKA-HF, the resolution becomes as good as $0.03''$, such that a typical MW progenitor will be resolved in roughly 100 pixels (depending on inclination and evolution scenario)." " The associated order-of-magnitude loss in surface brightness sensitivity implies that many more sources will be picked up in core-only observations, where half of SKA's collecting area is sacrificed to the benefit of having all antennas within a core of 0.5km radius."," The associated order-of-magnitude loss in surface brightness sensitivity implies that many more sources will be picked up in core-only observations, where half of SKA's collecting area is sacrificed to the benefit of having all antennas within a core of $0.5\rm~km$ radius." " In this case the resolution drops to 5.2"" and none of the MW at z=3 will be resolved in CO(1-0).", In this case the resolution drops to $5.2''$ and none of the MW at $z=3$ will be resolved in CO(1–0). In this paper we therefore assume that only the core of SKA-HF is used., In this paper we therefore assume that only the core of SKA-HF is used. " Given these assumptions, none of the MW progenitors at z=3 will be resolved in or CO emission."," Given these assumptions, none of the MW progenitors at $z=3$ will be resolved in or CO emission." " However, other galaxies z=3, larger than the MW progenitors, may still be resolved."," However, other galaxies $z=3$, larger than the MW progenitors, may still be resolved." " In this case, the sensitivity will be reduced relative to the point-source sensitivity of eq. (??))."," In this case, the sensitivity will be reduced relative to the point-source sensitivity of eq. \ref{eq_sigma}) )." " In fact, if every pixel has an RMS noise level o defined by eq. (??)),"," In fact, if every pixel has an RMS noise level $\sigma$ defined by eq. \ref{eq_sigma}) )," then a source extended over m>1 pixels will be subjected to a Jy-noise to σ’=σYm., then a source extended over $m>1$ pixels will be subjected to a Jy-noise equal to $\sigma'=\sigma\sqrt{m}$. " Since real sources are not homogeneous, but equalrather exponentially fading disks, the definition of m is not obvious."," Since real sources are not homogeneous, but rather exponentially fading disks, the definition of $m$ is not obvious." " Here we adopt the approximation =O»»(8) where setα is the half-mass diameter, measured along the major axis, of angular(for line) or (for CO lines), and i is the galaxy inclination defined as the smaller angle between the line-of-sight and the galaxy’s rotational axis."," Here we adopt the approximation =, where $\alpha$ is the angular half-mass diameter, measured along the major axis, of (for line) or (for CO lines), and $i$ is the galaxy inclination defined as the smaller angle between the line-of-sight and the galaxy's rotational axis." Our choice of the the half-mass diameter rather than a larger diameter usingcontaining more of the gas mass relies on the assumption that the central concentration of gas can be exploited in clever algorithms for source extraction., Our choice of using the the half-mass diameter rather than a larger diameter containing more of the gas mass relies on the assumption that the central concentration of gas can be exploited in clever algorithms for source extraction. ALMA’s and SKA’s limitations regarding the spectral resolution and the instantaneous bandwidth can be safely ignored within a limited to the detection of extra-galactic emission studylines in a narrow pureredshift range around z=3 (Sections ?? and ??))., ALMA's and SKA's limitations regarding the spectral resolution and the instantaneous bandwidth can be safely ignored within a study limited to the pure detection of extra-galactic emission lines in a narrow redshift range around $z=3$ (Sections \ref{section_detections_mw} and \ref{section_detections_general}) ). " For typical observing times (At>> 1/Av), the spectral resolution Av is mostly limited by the correlator performance."," For typical observing times $\Delta t\gg1/\Delta\nu$ ), the spectral resolution $\Delta\nu$ is mostly limited by the correlator performance." Both ALMA and SKA will be fitted with correlators allowing the selection of (frequency-dependent) spectral resolutions with an equivalent Doppler velocity far below 1kms~!.," Both ALMA and SKA will be fitted with correlators allowing the selection of (frequency-dependent) spectral resolutions with an equivalent Doppler velocity far below $1\rm\,km\,s^{-1}$." Thus the chosen velocity channels of 75kms! (see Section ??)) never conflict with the spectral resolution limit.," Thus the chosen velocity channels of $75\rm\,km\,s^{-1}$ (see Section \ref{subsection_performace}) ) never conflict with the spectral resolution limit." " As for the instantaneous spectral bandwidth (BW), ALMA (BWx 8GHz) and SKA (BW value with ο=1.1.5.3. and 6.," To see the effect of the width of the distribution, we vary the $\beta$ value with $\beta=1, 1.5, 3, $ and $6$." The larger the ;2 value is. the narrower the distribution is. as seen in Figure 1.," The larger the $\beta$ value is, the narrower the distribution is, as seen in Figure 1." The corresponding median redshiltsfor the four distributions are lined&LAST. 0.99. 0.62 and 0.55 for 9=1.1.5.3. ancl 6. respectively.," The corresponding median redshiftsfor the four distributions are $z_{med}\approx 1.87$, $0.99$, $0.62$ and $0.55$ for $\beta=1, 1.5, 3, $ and $6$, respectively." " In Figure: ο2. we show the results of.. 05,,,,."," In Figure 2, we show the results of $\sigma^2_{0corr}$." For the intrinsic: alignment.: we take sf=0.57.- the value from SDSS. in eq. (," For the intrinsic alignment, we take $A=0.57$, the value from SDSS, in eq. (" 4) (e.g.. Hlevinans οἱ al.,"4) (e.g., Heymans et al." 2006)., 2006). The solid. dotted. dashed. aud dash-dotted lines correspond to 9=6.3.1.5 and 1. respectively.," The solid, dotted, dashed, and dash-dotted lines correspond to $\beta=6, 3, 1.5$ and $1$ , respectively." " For comparison. we also plot ση, (dash-dot-dot-dotted line).κ with. o=0.4 and n,=30.arcmin>."," For comparison, we also plot $\sigma^2_{0ran}$ (dash-dot-dot-dotted line) with $\sigma_{\epsilon}=0.4$ and $n_g=30\hbox{ arcmin}^{-2}$." " We- see that the result with ο=6 and z,,4~0.55 is an order of magnitude larger than that with j—] and z,,;L&T. demonstrating clearly the sensitive dependence of 05,,, on the redshift distribution of background galaxies."," We see that the result with $\beta=6$ and $z_{med}\sim 0.55$ is an order of magnitude larger than that with $\beta=1$ and $z_{med}\sim 1.87$, demonstrating clearly the sensitive dependence of $\sigma_{0corr}$ on the redshift distribution of background galaxies." Therefore lor tomographic analvses of weak lensing effects with source galaxies distributed in narrow redshift bins. the effects of intrinsic alignments can be significant.," Therefore for tomographic analyses of weak lensing effects with source galaxies distributed in narrow redshift bins, the effects of intrinsic alignments can be significant." " The angular dependence of ση. is shallower than 05,,,. and the ratio. ΟἱB σηL7/ Increases. with. the increase. ofB smoothing. scales."," The angular dependence of $\sigma^2_{0corr}$ is shallower than $\sigma^2_{0ran}$, and the ratio of $\sigma^2_{0corr}/\sigma^2_{0ran}$ increases with the increase of smoothing scales." " In Table 1. we list 65,,,/05,,, lor various cases."," In Table 1, we list $\sigma^2_{0corr}/\sigma^2_{0ran}$ for various cases." With the upper limit 1=1.29 from SDSS. the ratio can reach as high as about σοιση~20% lor 3=6 αἱ θε=2arcmin.," With the upper limit $A=1.29$ from SDSS, the ratio can reach as high as about $\sigma^2_{0corr}/\sigma^2_{0ran}\sim 20\%$ for $\beta=6$ at $\theta_G=2 \hbox{ arcmin}$." " Notice that o5, and o7.,,.. depend differently on the distribution of source galaxies.", Notice that $\sigma^2_{0ran}$ and $\sigma^2_{0corr}$ depend differently on the distribution of source galaxies. " While 05, depends mainly on the form of the redshift distribution. 95,%n, "," While $\sigma^2_{0corr}$ depends mainly on the form of the redshift distribution, $\sigma^2_{0ran}\propto n_g^{-1}$." "Thus for surveys with higher surface number density of source galaxies than what we consider here. the ratio One)Taran CU increase considerably,"," Thus for surveys with higher surface number density of source galaxies than what we consider here, the ratio $\sigma^2_{0corr}/\sigma^2_{0ran}$ can increase considerably." Results expected for some surveys are presented in Table 2., Results expected for some surveys are presented in Table 2. The survey parameters for COSMOS are taken [rom Massey. et al. (, The survey parameters for COSMOS are taken from Massey et al. ( 2007).,2007). For SNAP. we adopt the parameters used in Semboloni et al. (," For SNAP, we adopt the parameters used in Semboloni et al. (" 2007).,2007). For deep survevs with large nj. Lomographic analyses with source galaxies distributed in narrow redshift ranges become possible.," For deep surveys with large $n_g$, tomographic analyses with source galaxies distributed in narrow redshift ranges become possible." For example. with total ng~100arcmin7 as expected from surveys similar to SNAP. the background galaxies can be divided into three bins each with ny~30arcmin7.," For example, with total $n_g\sim 100\hbox { arcmin}^{-2}$ as expected from surveys similar to SNAP, the background galaxies can be divided into three bins each with $n_g\sim 30\hbox { arcmin}^{-2}$." The effect of intrinsic alignments can be significantly stronger within each bin than that in total., The effect of intrinsic alignments can be significantly stronger within each bin than that in total. " If we regard the narrow redshift distribution with ο=6 as one of the bins. il is seen from Table 1 that the respective values of 65,,,/05,,,, lor θε=1and2arcmin are about 5% and 1056 with A= 0.57. in comparison with 3.3% and 5% expected for the fullsample of galaxies [rom SNAP as seen in Table 2."," If we regard the narrow redshift distribution with $\beta=6$ as one of the bins, it is seen from Table 1 that the respective values of $\sigma^2_{0corr}/\sigma^2_{0ran}$ for $\theta_G=1 \hbox{ and } 2\hbox{ arcmin}$ are about $5\%$ and $10\%$ with $A=0.57$ , in comparison with $3.3\%$ and $5\%$ expected for the fullsample of galaxies from SNAP as seen in Table 2." In next section. we show that (he number of false peaks in lensing &-maps is very sensitive," In next section, we show that the number of false peaks in lensing $\kappa$ -maps is very sensitive" AII0l is a nearby [ace-0n spiral ealaxy al an estimated distance of 77.2 Alpe.,M101 is a nearby face-on spiral galaxy at an estimated distance of $\sim$ 7.2 Mpc. It is an ideal galaxy for the observation of X-ray binaries. supernova/lvpernova remnants (Snowdenelal... 2001).. and diffuse emission (IXuntzetal...2002).," It is an ideal galaxy for the observation of X-ray binaries, supernova/hypernova remnants \citep{S01}, and diffuse emission \citep{K02}." . We have therefore observed MIOI wilh AACIS [or 93.2 ksec diuing 2000 March 2627., We have therefore observed M101 with ACIS for 98.2 ksec during 2000 March 26–27. The details of the observation. data reduction. source search. the catalog of 110 sources detected on the $3 chip aud their collective properties are described in Penceetal.(2001).," The details of the observation, data reduction, source search, the catalog of 110 sources detected on the S3 chip and their collective properties are described in \cite{P01}." . Here we concentrate on the 6 brightest sources. listed in Table 1.," Here we concentrate on the 6 brightest sources, listed in Table 1." We adopt the source number in Penceetal.(2001) as their names throughout (his paper., We adopt the source number in \citet{P01} as their names throughout this paper. Penceοἱal.(2001) arene on statistical grounds that about of the 110 sources detected on the 53 chip are intrinsic {ο MIOI., \cite{P01} argue on statistical grounds that about of the 110 sources detected on the S3 chip are intrinsic to M101. " Therefore. we will assume that the majority of the six sources in question. if not all. are located in ALLOL,."," Therefore, we will assume that the majority of the six sources in question, if not all, are located in M101." One of the sources. P098. is an order of magnitude brighter (as seen with ACIS-S) than the others aud has other peculiar properties: this object will be the focus of this paper.," One of the sources, P098, is an order of magnitude brighter (as seen with ACIS-S) than the others and has other peculiar properties; this object will be the focus of this paper." llowever. we will first discuss the other 5 svstems listed in Table 1: with observed luminosities in excess of 10N !.," However, we will first discuss the other 5 systems listed in Table 1 with observed luminosities in excess of $^{38}$ $^{-1}$." The inferred bolometric Iuminosities are higher. almost certainly exceeding the Edclington limit for à 1.4 M. object.," The inferred bolometric luminosities are higher, almost certainly exceeding the Eddington limit for a 1.4 $_\odot$ object." These 5 svstems (three of which have been discussed in Snowdenetal.2001. as likely binaries. rather (han hypernova remnants) are therefore black-hole candidates (BIICS). even though (μον do not qualify as ULXs using the threshold of 10 !," These 5 systems (three of which have been discussed in \citealt{S01} as likely binaries, rather than hypernova remnants) are therefore black-hole candidates (BHCs), even though they do not qualify as ULXs using the threshold of $^{39}$ $^{-1}$." We have attempted a simple continuum spectral fit to the five DIICs. using power-law. bremsstrahlung. blackbody and disk blackbody (diskBB. as implemented in NSPEC) models.," We have attempted a simple continuum spectral fit to the five BHCs, using power-law, bremsstrahlung, blackbody and disk blackbody (diskBB, as implemented in XSPEC) models." The spectrum of P104 is best fit with a power-law model. while the diskDD model works best for the others.," The spectrum of P104 is best fit with a power-law model, while the diskBB model works best for the others." The best-fit models do not resemble (vpical spectra of Galactic X-ray pulsars (flat. power-law) or of bright neutron star LAINBs (Comptonized spectra which can be approximated as a 5 keV bremsstrallune: Whiteοἱal. 1995))., The best-fit models do not resemble typical spectra of Galactic X-ray pulsars (flat power-law) or of bright neutron star LMXBs (Comptonized spectra which can be approximated as a 5 keV bremsstrahlung; \citealt{WNP95}) ). We have also examined the timing properties of these sources: their light curves in 5000s bins are shown in Fig., We have also examined the timing properties of these sources: their light curves in 5000 s bins are shown in Fig. 1., 1. Of the five. P104. the power-law source. is highlv variable on a relatively short. limescale (e.g.. note the factor of ~2 drop im count rate in one 53000 s bin near the end of the observation).," Of the five, P104, the power-law source, is highly variable on a relatively short timescale (e.g., note the factor of $\sim$ 2 drop in count rate in one 5000 s bin near the end of the observation)." This is also one of the hypernova candidates of Wane(1999).. since il is coincidentwilh a optically detected supernova remnant MESS (Matonick&Fesen1997).. but the observed variability. excludes (he hypernova interpretation ($nowdenetal. 2001)..," This is also one of the hypernova candidates of \citet{W99a}, since it is coincidentwith a optically detected supernova remnant MF83 \citep{M97}, but the observed variability excludes the hypernova interpretation \citep{S01}. ." The power-law, The power-law have maximum growth rates in the small wavenumboers (see Fie.,have maximum growth rates in the small wavenumbers (see Fig. 3 and 4)., 3 and 4). In summary. as shown in the figures. the evroviscosity cllect ancl pitch angles cause a powerful. instability.," In summary, as shown in the figures, the gyroviscosity effect and pitch angles cause a powerful instability." This σονTOoviscousτο instability has a very laree gowth rates with 0.525-3 for the dillerent piteh angles., This gyroviscous instability has a very large gowth rates with $0.5\Omega-3\Omega$ for the different pitch angles. The gvroviscosity instability may be candidate for amplifving very small seed fields., The gyroviscosity instability may be candidate for amplifying very small seed fields. Pherefore. this instability may apply to protogalaxies. low-density accretion Lows and the intracluster medium of ealaxy clusters which the magnetic fields are sullicientlv small so that dilute plasma conclition is satisfied.," Therefore, this instability may apply to protogalaxies, low-density accretion flows and the intracluster medium of galaxy clusters which the magnetic fields are sufficiently small so that dilute plasma condition is satisfied." The last but not in the least the dependence of the erowth rates on the piteh angle forces us into à qualititive discussion., The last but not in the least the dependence of the growth rates on the pitch angle forces us into a qualititive discussion. We assumed helical magnetic field geometry., We assumed helical magnetic field geometry. EDB απ generates no current. unless we consider an orbit-averaged E;DB wherein the Larmor radii of electrons and ions are dillerent added to this current ancl viscous [lows generates a net current.," $\mathbf{E}\times\mathbf{B}$ drift generates no current, unless we consider an orbit-averaged $\mathbf{E}\times\mathbf{B}$ wherein the Larmor radii of electrons and ions are different added to this current and viscous flows generates a net current." Dep«ding on the pitch angles of current density and the magneAic field vectors the plasma is either pinched or diluted localv by the Lorentz force. J.D.," Depending on the pitch angles of current density and the magnetic field vectors the plasma is either pinched or diluted locally by the Lorentz force, $\mathbf{J}\times\mathbf{B}$." It the pitch angle of the curren density vector is smaller than the magnetic field pitch angl the Lorentz force will dilute otherwise pinch the plasma loc‘ally., If the pitch angle of the current density vector is smaller than the magnetic field pitch angle the Lorentz force will dilute otherwise pinch the plasma locally. Ht appears that when the relative pitch angles of J aux DB makes the growth rate of the unstable mode higher for all pitch angles range. “the currents caused by ELI effects becomes in phase with the current of the ideal-MIID ALR1 eigenmiocle” (Ferraro. 2007).," It appears that when the relative pitch angles of $\mathbf{J}$ and $\mathbf{B}$ makes the growth rate of the unstable mode higher for all pitch angles range, ""the currents caused by FLR effects becomes in phase with the current of the ideal-MHD MRI eigenmode"" (Ferraro, 2007)." We would like to thank the referee for her/his constructive criticism and. careful reading the manuscript., We would like to thank the referee for her/his constructive criticism and careful reading the manuscript. We dedicate this work completed in the International Year of Astronomy (IYA) to the honourable memory of Galileo Galilei who had been recognized. long since as the founder of the modern science., We dedicate this work completed in the International Year of Astronomy (IYA) to the honourable memory of Galileo Galilei who had been recognized long since as the founder of the modern science. This work is supported. by the [ee University Science and Technology. Center (EBILLEEAD and one of the authors (ED) appreciate the support of the Scientific, This work is supported by the Ege University Science and Technology Center (EBİLLTEM) and one of the authors (ED) appreciate the support of the Scientific which is explicitly not ruled out by ?.,which is explicitly not ruled out by . . If so. this implies au interesting coufiguration in which the orbit of the AS 205 binarycopluner with the AS 205N disk.," If so, this implies an interesting configuration in which the orbit of the AS 205 binary with the AS 205N disk." Nou-coplanarity has been observed as a ecucral property of binarics with disks. although there is probably some aliguimient for disks around stars with separations between AAT (2).," Non-coplanarity has been observed as a general property of binaries with disks, although there is probably some alignment for disks around stars with separations between AU ." SCrAisa 1.3” binary., S CrA is a $1.3\arcsec$ binary. Our spectro-astrometry is of the northeru component. the primary at ucar-infrared wavelengths. but the secoudary in the visible.," Our spectro-astrometry is of the northern component, the primary at near-infrared wavelengths, but the secondary in the visible." There is. to our knowledge. no other measurements of the disk geometry of this source in the literature.," There is, to our knowledge, no other measurements of the disk geometry of this source in the literature." " OW Tau has an optical jet with a P.À.—155° and inclination of 11°?j.. qualitatively consistent with the CO spectro-astrometry,"," CW Tau has an optical jet with a $=155\degr$ and inclination of $41\degr$, qualitatively consistent with the CO spectro-astrometry." This is a 2” binary. with the south-eastern component deine an InfraRed Companion (IRC)(7).," This is a $2\arcsec$ binary, with the south-eastern component being an InfraRed Companion (IRC)." Qur spectro-astrometry is of the secondary (at EI-band) southern component - this is the brighter. bv about 0.7 magnitudes. coupoucut iu the N-baud.," Our spectro-astrometry is of the secondary (at K-band) southern component - this is the brighter, by about 0.7 magnitudes, component in the M-band." The secondary disk las PLA. of τας determined using I-baud polarization(?)., The secondary disk has P.A. of as determined using K-band polarization. . The secondary is itself a possible close. equal brightuess. binary with separation 5.6nunas audΕΔΑ). based on speckle imaging.," The secondary is itself a possible close, equal brightness, binary with separation mas and, based on speckle imaging." " The presence of a close biuary may explain the need for two wind compoucnts compoucuts iu our spectro-astrometry, separated by about Laas+ at the time of observation."," The presence of a close binary may explain the need for two wind components components in our spectro-astrometry, separated by about $\rm km\,s^{-1}$ at the time of observation." It should be noted that a mate with a binary is not unambienous. auc other models of extended emission aloug a are also possible.," It should be noted that a match with a binary is not unambiguous, and other models of extended emission along a are also possible." " yeported a binary companion. using spectro-astrometry of Πα. with a separation of >0711 andP.A.=278""."," reported a binary companion, using spectro-astrometry of $\alpha$, with a separation of $>0\farcs14$ and." . We do not detect a companion at {ιτ juu at this PA. and separation with au upper Init of the flux ratio of 6.," We do not detect a companion at $4.7\,\mu$ m at this P.A. and separation with an upper limit of the flux ratio of 6." Speckle tnaging at K-band also does not detect the companion(27)., Speckle imaging at K-band also does not detect the companion. . It is possible that the companion is sienificautly, It is possible that the companion is significantly possible to accurately fit the ccounts across the full range of flux; this would be in line with the approach taken in previous analyses such as that of Babbedge et ((2006) and Rowan-Robinson (2001; 2009).,possible to accurately fit the counts across the full range of flux; this would be in line with the approach taken in previous analyses such as that of Babbedge et (2006) and Rowan-Robinson (2001; 2009). " However, we explore here the alternative possibility that the counts can be matched by exploiting the negative k—correction, combinedwiththemoderatePL Ewhichwassuccessf ulatIRAC wavelengths, insteadof invokingmuchstrongerevolution."," However, we explore here the alternative possibility that the counts can be matched by exploiting the negative $k$ -correction, combined with the moderate PLE which was successful at IRAC wavelengths, instead of invoking much stronger evolution." " 'This is motivated initially by the finding that the shape of the predicted source counts for the normal spirals matches well the shape of the data, showing an upturn around 0.5-1.0 mJy where the counts briefly increase at a super-Euclidean rate reffig:24cnts))."," This is motivated initially by the finding that the shape of the predicted source counts for the normal spirals matches well the shape of the data, showing an upturn around 0.5–1.0 mJy where the counts briefly increase at a super-Euclidean rate \\ref{fig:24cnts}) )." " The Mrk33 model, although matching the bright end normalisation well, has a much flatter shape with no increase at the faint end."," The Mrk33 model, although matching the bright end normalisation well, has a much flatter shape with no increase at the faint end." " 'The faint-end increase in the spiral model arises from a strong negative k-correction, whereas in the Mrk33 SED the k-correction is positive."," The faint-end increase in the spiral model arises from a strong negative $k$ -correction, whereas in the Mrk33 SED the $k$ -correction is positive." " As the SEDs are redshifted, the PAH region moves into the bband."," As the SEDs are redshifted, the PAH region moves into the band." " As this happens, the cool-dust spiral model becomes brighter (giving a negative k-correction) but the Mrk33 model, which has a warm dust component, becomes fainter overall. ("," As this happens, the cool-dust spiral model becomes brighter (giving a negative $k$ -correction) but the Mrk33 model, which has a warm dust component, becomes fainter overall. (" See reffig:modelseds)).,See \\ref{fig:modelseds}) ). " Therefore, where we previously used the Mrk33 component, we now use instead a population with the same z=0 LF as the Mrk33 population (i.e. the same K—[24] colour), providing the good fit to the bright end counts, but with the k+e evolution of our normal spiral galaxies."," Therefore, where we previously used the Mrk33 component, we now use instead a population with the same $z=0$ LF as the Mrk33 population (i.e. the same $K-[24]$ colour), providing the good fit to the bright end counts, but with the $k+e$ evolution of our normal spiral galaxies." We find this gives a good fit to the data across the full flux range reffig:24cnts))., We find this gives a good fit to the data across the full flux range \\ref{fig:24cnts}) ). We are essentially using a hypothetical SED which has the same shape as the rest of our spiral galaxies but a redder K—[24] colour and a greater total IR luminosity., We are essentially using a hypothetical SED which has the same shape as the rest of our spiral galaxies but a redder $K-[24]$ colour and a greater total IR luminosity. " Using the appropriate bright end normalisation, then, PLE yields a good fit across 3 decades of fflux."," Using the appropriate bright end normalisation, then, PLE yields a good fit across 3 decades of flux." " Since there is a decoupling of the stellar and dust emissions, this arbitrary normalisation is not unphysical, however unlike our initial inclusion of the Mrk33 component it is not observationally motivated."," Since there is a decoupling of the stellar and dust emissions, this arbitrary normalisation is not unphysical, however unlike our initial inclusion of the Mrk33 component it is not observationally motivated." We conclude that the bband is the first regime where our simple bimodal PLE model begins to break down., We conclude that the band is the first regime where our simple bimodal PLE model begins to break down. " Even with the Mrk33 galaxies included, the model does not have the sufficient ingredients to match the faint-flux, high-redshift counts."," Even with the Mrk33 galaxies included, the model does not have the sufficient ingredients to match the faint-flux, high-redshift counts." " However, we have shown that these data can be well matched if one component of our spiral galaxies is altered to be much redder in K—[24], although the data can alternatively be matched by allowing for much stronger evolution, above the level found in our PLE model."," However, we have shown that these data can be well matched if one component of our spiral galaxies is altered to be much redder in $K-[24]$, although the data can alternatively be matched by allowing for much stronger evolution, above the level found in our PLE model." In we show number counts in 6 wavebands in the far-IR and sub-mm regimes., In \\ref{fig:fircnts} we show number counts in 6 wavebands in the far-IR and sub-mm regimes. Counts at, Counts at In Fig.,In Fig. 3 the time at which the fastest growing mode switches from non-resonant to resonant is identified by the intersection between the dashed line and the solid (By=1OuG) or the dot-dashed (By Ιμά) one depending on the magnetic field strength., \ref{fig:maxgrowth} the time at which the fastest growing mode switches from non-resonant to resonant is identified by the intersection between the dashed line and the solid $B_0=10 \mu G$ ) or the dot-dashed $B_0=1 \mu G$ ) one depending on the magnetic field strength. The dominant wave mode progressively moves to larger wavelengths., The dominant wave mode progressively moves to larger wavelengths. The implications of this peculiar trend are expected to be profound on the determination of the diffusion coefficient: we recall that the standard Bohm diffusion is the limit obtained for resonant interactions of particles and waves when dB(k)=By for any value of Κ., The implications of this peculiar trend are expected to be profound on the determination of the diffusion coefficient: we recall that the standard Bohm diffusion is the limit obtained for resonant interactions of particles and waves when $\delta B(k)=B_0$ for any value of $k$. " For non-resonant modes, the diffusion properties need to be recalculated from first principles."," For non-resonant modes, the diffusion properties need to be recalculated from first principles." " On one hand, since the most unstable modes have &>>Ε/Γ. most particles do not resonate with these modes and the typical deflection suffered by a single particle within a spatial scale ~1/K is very small."," On one hand, since the most unstable modes have $k\gg 1/r_{L,0}$, most particles do not resonate with these modes and the typical deflection suffered by a single particle within a spatial scale $\sim 1/k$ is very small." " On the other hand the number of scattering events is very large, therefore a substantial reduction of the diffusion coefficient can still be expected (see ? and ?))."," On the other hand the number of scattering events is very large, therefore a substantial reduction of the diffusion coefficient can still be expected (see \cite{reville08} and \cite{zira08b}) )." " We investigated the excitation of streaming instability induced by accelerated particles in the vicinity of a non-relativistic shock wave, typical of supernova shells expanding in the interstellar medium."," We investigated the excitation of streaming instability induced by accelerated particles in the vicinity of a non-relativistic shock wave, typical of supernova shells expanding in the interstellar medium." " The calculation is based on kinetic theory, hence we do not require the MHD approximation to hold for the background plasma."," The calculation is based on kinetic theory, hence we do not require the MHD approximation to hold for the background plasma." " We find that the dispersion relation of the waves leads to the appearance of two modes, a resonant and a non-resonant one."," We find that the dispersion relation of the waves leads to the appearance of two modes, a resonant and a non-resonant one." " The former is the well known unstable mode, discussed by ? and ?., based on a resonant interaction between waves and particles."," The former is the well known unstable mode, discussed by \cite{zweib79} and \cite{achter83}, based on a resonant interaction between waves and particles." " The latter is similar to that discussed by ?,, who however based his analysis on a set of assumptions that called for further investigation: the calculation of ? is based on the assumption that the background plasma can be treated in the MHD regime. and makes specific prescriptions on the return current which compensates the cosmic ray current upstream of the shock."," The latter is similar to that discussed by \cite{bell04}, who however based his analysis on a set of assumptions that called for further investigation: the calculation of \cite{bell04} is based on the assumption that the background plasma can be treated in the MHD regime, and makes specific prescriptions on the return current which compensates the cosmic ray current upstream of the shock." " Moreover, the whole calculation is carried out in the frame of the upstream plasma, where in principle there 1s no stationary solution of the problem."," Moreover, the whole calculation is carried out in the frame of the upstream plasma, where in principle there is no stationary solution of the problem." " Our kinetic calculations are carried out for two models of the compensating current: in the first model, the return current is established through à population of cold electrons, at rest in the shock frame, which exactly compensate the positive charge of cosmic ray protons."," Our kinetic calculations are carried out for two models of the compensating current: in the first model, the return current is established through a population of cold electrons, at rest in the shock frame, which exactly compensate the positive charge of cosmic ray protons." " In the second model, the return current is due to a slight drift between ions and electrons in the background plasma upstream of the shock."," In the second model, the return current is due to a slight drift between ions and electrons in the background plasma upstream of the shock." We have demonstrated that the dispersion relation of the waves is the same in the two cases. to order O(Neg/n;Y.," We have demonstrated that the dispersion relation of the waves is the same in the two cases, to order ${\cal O}\left(N_{CR}/n_i\right)^2$." " The resonant and the non-resonant mode are found at the same time, with growth rates which"," The resonant and the non-resonant mode are found at the same time, with growth rates which" curve.,curve. The standard Hubble curve is a theoretical quantity computed assuming all eravitatiug uatter is homogeneously distributed: whereas. observational data is taken iu the real inhomogeueous Universe.," The standard Hubble curve is a theoretical quantity computed assuming all gravitating matter is homogeneously distributed; whereas, observational data is taken in the real inhomogeneous Universe." In an inhomogeneous universe an observing light beam is leused by inhomogeneities ocated external to. but uear the light beam. aud defocused (relative to the standard Hubble curve) yy the less than average matter density within the beam.," In an inhomogeneous universe an observing light beam is lensed by inhomogeneities located external to, but near the light beam, and defocused (relative to the standard Hubble curve) by the less than average matter density within the beam." The simplest way to take into account hese effects is to correct all beams for tle missing homogeneous matter but correct for lensing only when uecessary., The simplest way to take into account these effects is to correct all beams for the missing homogeneous matter but correct for lensing only when necessary. This procedure requires the introduction of oue additional parameter. a filliu yarameter p.Oxpb2 defined by the fraction of inhomogeneous matter py/py=vir+1)/6€1 excluded from observing beams (7=0 is the standard. fillel beam FLRW case and v=2 is the empty beam case).," This procedure requires the introduction of one additional parameter, a filling parameter $\nu, \ 0\le\nu\le2$ defined by the fraction of inhomogeneous matter $\rho_I/\rho_0 \equiv\nu(\nu+1)/6 \le 1$ excluded from observing beams $\nu=0$ is the standard filled beam FLRW case and $\nu=2$ is the empty beam case)." When observing high z objects (2~1) the reader cau think of the j»arameter vas representiug matter that exists in galaxies but not iu the intergalactic meclitun., When observing high $z$ objects $z\sim 1$ ) the reader can think of the parameter $\nu$ as representing matter that exists in galaxies but not in the intergalactic medium. To iud the theoretical Hubble curve for observations in such a universe oue must solve the geometrical optics equation [see Iantowski (1998)]] given as equation (9)) in the next section., To find the theoretical Hubble curve for observations in such a universe one must solve the geometrical optics equation [see \cite{KR98}] ] given as equation \ref{Area}) ) in the next section. This equation is actually equivalent to the Lame’ equation for general FLRW but as pointed out by reduces to the associated Legendre equation (2)) lor the special case cousidered here. Ou—].," This equation is actually equivalent to the $^{\prime}$ equation for general FLRW but as pointed out by \cite{KKT} reduces to the associated Legendre equation \ref{Legendre}) ) for the special case considered here, $\OO=1$." In 'e[sec-Iumkdist. we solve this equation usiug appropriate boundary coucditious and give the Hubble curve in terms of associated Legeudre functions (eq.[27]]) as well as in terms of hypergeometric 'unctious (ea.[10]])., In \\ref{sec-lumdist} we solve this equation using appropriate boundary conditions and give the Hubble curve in terms of associated Legendre functions \ref{Pans}] ]) as well as in terms of hypergeometric functions \ref{2F1ans}] ]). " In 'e[sec-fit/— we fit this uew Hubble curve to data for 60 superuovae (SNe) from the Supernova Cosmological Project (SCP) ancl from the Cala/n/Tololo Supernova Survey (CTSS) in an attempt o determine the mass parameter £2,, aud the filline parameter ».", In \\ref{sec-fit} we fit this new Hubble curve to data for 60 supernovae (SNe) from the Supernova Cosmological Project (SCP) and from the $^{\prime}$ n/Tololo Supernova Survey (CTSS) in an attempt to determine the mass parameter $\OM$ and the filling parameter $\nu$. Iu 'efsec-counclusions we give some concluding remarks., In \\ref{sec-conclusions} we give some concluding remarks. For models being discussecl here (aud for most cosmological 1nodels). angular or apparent size distance is related to luminosity distance by De(s)=Di(z)/(1z.," For models being discussed here (and for most cosmological models), angular or apparent size distance is related to luminosity distance by $D_<(z)=D_{\ell}(z)/(1+z)^2$." We choose to eive luminosity distauces in this paper., We choose to give luminosity distances in this paper. " The D,(z) which accounts for a partially depleted mass density in the observing beam but neglects leusiug; by external masses is fouud by integratiug the second order differential equation For tlie cross sectional area ασ) of au observing beau [rom source (2= 21) to", The $D_{\ell}(z)$ which accounts for a partially depleted mass density in the observing beam but neglects lensing by external masses is found by integrating the second order differential equation for the cross sectional area $A(z)$ of an observing beam from source $z=z_s$ ) to opPhe energetic ⋠↽X-ray binary. C.venus N-323 has been studied. in. great detail a.since its. discovery. in. 1967 NEED(Ciacconi. ct 11967).,The energetic X-ray binary Cygnus X-3 has been studied in great detail since its discovery in 1967 (Giacconi et 1967). u Ht is. an active. source with. measurements in. the ⋅⋠ ⋠⋅⋅⋅ ↽⋅⊽ ↓⋯⊔∪⋡⊳∖⊔∣⋡−⊔↓⊔↓⊳↓⊔⇂↓⋜⊔∢⋅∠⇂⊳⇀∖−↓⋜↧∙∖⋜⋃∐⇂⋏∙≟⋜⋯↓⊔↓⋜⊢↓⋜↧∙∖⊳∖⋜↧∐∪⇂∖∖⋎↓⋯∼↓↥uu ⋅⋠ indicate. a highly. ⊽⊽⋅⋠variable source.," It is an active source with measurements in the radio, sub-mm, infrared, X-ray and gamma-rays all of which indicate a highly variable source." . Following∖. infrared.⊀⋅∙∙ spectroscopic. measurements.. (van Ixerkwi]k et al., Following infrared spectroscopic measurements (van Kerkwijk et al. 1992: Fender. Hanson Pooley 1999). the accepted morphology of Cve X-3 is a compact object in orbit around a Woll-Ravet⇁⋅ star of⋅ the WN4-5⇁⇁ type.," 1992; Fender, Hanson Pooley 1999), the accepted morphology of Cyg X-3 is a compact object in orbit around a Wolf-Rayet star of the WN4-5 type." " A measured .. . . ⋅ . ⋅ ""∣↾∖⊔⊳∪∪∩⋜∐↓∪∪⊰⋅↓⋅∪⊔↓↥∐⋅≼∙∪↓⋅⋖⋅⋡⇀⋡∖∪⊔⋖⊾⋖∩⋡∖⋖⊾↓⋅∖⇁⋖⊾⋡∖ à- very compact system (< 10naa1t.)within which. 5Yeher a large degree of ονinteraction. takes place."," A measured infrared and X-ray orbital period for the binary of 4.8 hr indicates a very compact system $(\leq 10\;{\rm R_{\odot}})$ within which a large degree of interaction takes place." sThe proximity.. of a compact object. to a star with. a strong wind.: provides. both accretion. onto the compact object.. but also à medium.. of ⋅∙⊀varving optical. depth through. which Ds.jets. formed⋅∙ fron⋅∙ accreted. material.n must travel.," The proximity of a compact object to a star with a strong wind provides both accretion onto the compact object, but also a medium of varying optical depth through which jets, formed from accreted material, must travel." uM Any. emissions froma the jets: cannot be observed directly. until. the wind. becomes optically. thin to the radiation in the jets., Any emission from the jets cannot be observed directly until the wind becomes optically thin to the radiation in the jets. This creates a tinie-lag between radiation at dilferent. frequencies in the jet (tvpicalls. racio. ancl sub-mam emission)D. and between jet. and central infraredun and X-ray.. emission., This creates a time-lag between radiation at different frequencies in the jet (typically radio and sub-mm emission) and between jet and central infrared and X-ray emission. D. ↻⊔⋖⋅⋯⊔⊔⊳∖≺⊾∣⇂↥⋖⋅∠⊔∐≺⊾↓⋅⋖⋅⊔↥↓⋅⋯⊔⋜∐↓∪⊔↓⋅≺⊾⋏∙≟↓⊔↓⋖⋅⊳∖↿∪∙∙ .. . 1nvestigate. clilferenu WOPCLreles: of: the system., One can use the different radiation regimes to investigate different properties of the system. For example. he low-frequeney∙ racliationME at radio. and sub-mam frequencies∙⋠ comes [rom svnchrotron emitting electrons in the jets. and his has been. used by Ogles. et ((in. prep.)," For example, the low-frequency radiation at radio and sub-mm frequencies comes from synchrotron emitting electrons in the jets, and this has been used by Ogley et (in prep.)" " to obtain pt ⋜↧↓↕⇂⇂≻≻⋖⋅↓⋅−↓↕↓↥↓↕⇂∣∪⇂↥∢⊾⊔↓⋜↧⋃⊔⋖⊾↿⊀⊔⇍∐∢⊾↓∠⇂∐↕∣⇂↥⋖⊾⊲∢⊾⇂⊳∖∪⇂∎⇉∩∪"" J 1 ( ] ↓⊔⇂↓⋅⋜⊔⋅∢⊾∠⇂⋜⋯∠⇂⇀∖−↓⋅⋜↧∙∖⇁∪↓⋅∣⋡∐⋜↧↓↓≻∢⊾", to obtain an upper-limit to the magnetic field in the jets of 260 $\mu$ T (2.60 G) at 100 $\rm R_{\sun}$ from the core. ↓⋅↓⋯⇂⇂∪↓⋅↿∐⋖⋅∣⋡↓⊔⋜⊔⋅∙∖⇁∪⇂⊥↖∖↓⊔⋅ | \ μιfrequencies.it mthe?D. emission changesl from[⋅ fsvnchrotron indicatesoq. ∪↿↓↕∢⋅↓⋅⊔⋯↓∐⋅∢⊾⋖⋅−∐⋅∢⊾⋖⋅⊳∖∖⋎↓↕⊲⊔∼⇂↥⊔∪∖∖⊽≼∼∪⊔↓∢⊾⊳∖⇂⋅↓⋅∪⊔↓↿↓↥⋖⋅∖∖⋰↓⊔∠⇂⊲↓⊔⇂↓↥∢⊾ system and not the jets.," As one observes higher frequencies, the emission changes from synchrotron to thermal free-free, which now comes from the wind in the system and not the jets." An example of the wind emission observed by theZ5ONN satellite is ...given in. Ogley. Bell Burnell Lender' (2001). ancl a complete spectrum showing: the dillerent emissionT. mechanisms. from∙ radio. to infrared⊲∙ is ≜⊲given in OelOgley ct Li(fin 1prep.)," An example of the wind emission observed by the satellite is given in Ogley, Bell Burnell Fender (2001), and a complete spectrum showing the different emission mechanisms from radio to infrared is given in Ogley et (in prep.)" Do 66., 6. " ""However. |a thoroughlD investigation.Doro Pmusing a single radiation.. regime. can also provide a great deal of information."," However, a thorough investigation using a single radiation regime can also provide a great deal of information." The accretion process is not. constant. but is probably," The accretion process is not constant, but is probably" a significant supersonic component to the z>3H distribution; ~ of the distribution has >1.,a significant supersonic component to the $z > 3H$ distribution; $\sim$ of the distribution has $|v|/\cs > 1$. " The distribution peaks for Hydro-LA are lower,|v|/c, which is not surprising since there is less kinetic energy in this run."," The distribution peaks for Hydro-LA are lower, which is not surprising since there is less kinetic energy in this run." " However, despite an order of magnitude difference in the saturated kinetic energies, the peak velocity for z>3H is only a factor of 2.5 lower in Hydro-LA than in Hydro-HA."," However, despite an order of magnitude difference in the saturated kinetic energies, the peak velocity for $z > 3H$ is only a factor of 2.5 lower in Hydro-LA than in Hydro-HA." " The mid-plane velocities are significantly lower in Hydro-LA than in Hydro-HA, however."," The mid-plane velocities are significantly lower in Hydro-LA than in Hydro-HA, however." " These results suggest that even when forced with a lower amplitude, the turbulent velocities can steepen significantly in the lower density regions away from the mid-plane."," These results suggest that even when forced with a lower amplitude, the turbulent velocities can steepen significantly in the lower density regions away from the mid-plane." " Taken together, the characteristic velocities in the forced hydro runs are not very different than those in the MRI cases."," Taken together, the characteristic velocities in the forced hydro runs are not very different than those in the MRI cases." This paper represents a step toward making a direct connection between the simulated properties of turbulent protoplanetary disks and actual observations of these systems., This paper represents a step toward making a direct connection between the simulated properties of turbulent protoplanetary disks and actual observations of these systems. " To this end, we have presented a series of calculations with varying physics from which we extracted the turbulent velocity distribution."," To this end, we have presented a series of calculations with varying physics from which we extracted the turbulent velocity distribution." " The simulations do not explicitly predict actual observables, as that would require the inclusion of radiation physics in one form or another."," The simulations do not explicitly predict actual observables, as that would require the inclusion of radiation physics in one form or another." " However, our results do have several implications for the nature of disk turbulence in"," However, our results do have several implications for the nature of disk turbulence in" We next discuss different. accretion scenarios.,We next discuss different accretion scenarios. [CLO X-1 has been coufiiiied as à WR|BIT binary. hence we first discuss wiud aud disce accretion onto a DIT.," IC10 X-1 has been confirmed as a WR+BH binary, hence we first discuss wind and disc accretion onto a BH." NCC300 X-1 has an unknown accretor. and may contain a neutron star: therefore. we also discuss wind aud disc accretion onto a NS.," NGC300 X-1 has an unknown accretor, and may contain a neutron star; therefore, we also discuss wind and disc accretion onto a NS." " Since the emission from Boudi-IHoxle accreting neutron stars appears to originate on or near the surface of the neutron star. it is unclear what ταν emiüsson could be expected frou, Dondi-Itoyxle accretion outo a black hole."," Since the emission from Bondi-Hoyle accreting neutron stars appears to originate on or near the surface of the neutron star, it is unclear what X-ray emission could be expected from Bondi-Hoyle accretion onto a black hole." Tucdeed. there are no known black hole Be NBs. alu all known black hole supergiaut NBs exhibit accretion discs.," Indeed, there are no known black hole Be XBs, and all known black hole supergiant XBs exhibit accretion discs." Furthermore. the modcelne of Doudi-Hovle accretion onto black holes requires relativistic. tliace-cimensioua naguctolydrodvuamical modeling (see.e.g.7.andret-erences within).," Furthermore, the modeling of Bondi-Hoyle accretion onto black holes requires relativistic, three-dimensional magnetohydrodynamical modeling \citep[see. e.g.][ and references within]{font99}." These models have not vet produce unanuibieuous predictions for the variability or ciission nechanisins expected from such svstemes., These models have not yet produced unambiguous predictions for the variability or emission mechanisms expected from such systems. Hence. there are 10 observational or theoretical constraints ou the spectra shape or variability exhibited bv TAINBs powered by Donucdi-Hovle accretion outo a DIT.," Hence, there are no observational or theoretical constraints on the spectral shape or variability exhibited by HMXBs powered by Bondi-Hoyle accretion onto a BH." The short orbital periods (4230 hr) aud high X-ray i1unuinosities of NCC300 N-1 and ICLO N-1 reseiible those of disc-accretiug SC IININDs (2): we therefore consider hei likely disc-accretors also., The short orbital periods $\sim$ 30 hr) and high X-ray luminosities of NGC300 X-1 and IC10 X-1 resemble those of disc-accreting SG HMXBs \citep{kap04}; we therefore consider them likely disc-accretors also. 7? calculated the rauge of orbital periods that permit Roche lobe overflow for 1610 X-1., \citet{prest07} calculated the range of orbital periods that permit Roche lobe overflow for IC10 X-1. They obtained periods of ~2.53 hr. and rejected disc accretion for 10160 N-1 (this also applies to NCCS300 X-1. as it las a similar orbital period to 1010 X-1).," They obtained periods of $\sim$ 2.5–3 hr, and rejected disc accretion for IC10 X-1 (this also applies to NGC300 X-1, as it has a similar orbital period to IC10 X-1)." However. it is cutively possible for the winds of the WoltRavet stars to power disc accretion.," However, it is entirely possible for the winds of the Wolf-Rayet stars to power disc accretion." The three known black hole TAINBs Cveuus N-1. LAICN-1 aud LAIC X-23 are all disc-accreting. with orbital periods of 5.60 d. 1.22 d anc L.FO respectively (seec.g.2.andreferenceswithin)...," The three known black hole HMXBs Cygnus X-1, LMCX-1 and LMC X-3 are all disc-accreting, with orbital periods of 5.60 d, 4.22 d and 1.70 d respectively \citep[see e.g.][and references within]{lvv95}." Of these. oulv LAIC X-3 is thought to be Roche lobe filling.," Of these, only LMC X-3 is thought to be Roche lobe filling." NCC300 N-l aud IC10 X-1 have shorter orbital periods than auv of these systems. so disc accretion onto a BIT in these svstenis is cutirely plausible.," NGC300 X-1 and IC10 X-1 have shorter orbital periods than any of these systems, so disc accretion onto a BH in these systems is entirely plausible." As discussed in Sect., As discussed in Sect. 3. our spectral modeling of NGC200. N-1 allows us to rule out Boucdi-Tovle (iud) accretion onto a NS. as power law spectral fits with DP < Las vield q2/dof >5 for all observations.," 3, our spectral modeling of NGC300 X-1 allows us to rule out Bondi-Hoyle (wind) accretion onto a NS, as power law spectral fits with $\Gamma$ $\le$ 1.8 yield $\chi^2$ /dof $>$ 5 for all observations." However. the Cluission and variability of NGC300 N-1 are in keeping with a disce-fed NS NB.," However, the emission and variability of NGC300 X-1 are in keeping with a disc-fed NS XB." The donor star may be the WR star. in which case. the dise would likely be winel-fecl.," The donor star may be the WR star, in which case, the disc would likely be wind-fed." " Alternatively, δις200 X-1 could be a bright NS LAINB which is merely coiucidenut with the WR."," Alternatively, NGC300 X-1 could be a bright NS LMXB which is merely coincident with the WR." We prefer disc accretion scenarios for 1010 X-1 and NGC300 N-1. although there is no independent evidence for a disc. such as radio jets.," We prefer disc accretion scenarios for IC10 X-1 and NGC300 X-1, although there is no independent evidence for a disc, such as radio jets." All known BIT NBs are disc accreting. vet the properties exhibited by IC10 X-1 and NGC300 N-1 are as vet unrecognised.," All known BH XBs are disc accreting, yet the properties exhibited by IC10 X-1 and NGC300 X-1 are as yet unrecognised." Their observed chussion spectra inost closely resemble the very high (steep power law. SPL) state (??)..," Their observed emission spectra most closely resemble the very high (steep power law, SPL) state \citep{vdk95, mr03}." Tlowever. the PDS of sources in the SPL state are characterised by broken power luvs. where 5 changes from 0 at low frequeucies to ~Lat high frequencies: offen quasi-periodic oscillations (QPOs) are observed {?)..," However, the PDS of sources in the SPL state are characterised by broken power laws, where $\gamma$ changes from $\sim$ 0 at low frequencies to $\sim$ 1 at high frequencies; often quasi-periodic oscillations (QPOs) are observed \citep{mr03}." We uote that Cre X-3. the other WR|co candidate. exhibits similar timing behaviour to NOG(C300 X-1 and 1010 X-1.," We note that Cyg X-3, the other WR+co candidate, exhibits similar timing behaviour to NGC300 X-1 and IC10 X-1." " Some beleve that scattering iu the wind suppresses ligh frequency variability (seee.g.?).. possibly masking aPDS. Ποσο, one might svouder if NGC300 N-1 Gu Observation 1) or ICLO N-1 are diseuisiug SPL states."," Some believe that scattering in the wind suppresses high frequency variability \citep[see e.g.][]{kit92}, possibly masking a. Hence, one might wonder if NGC300 X-1 (in Observation 1) or IC10 X-1 are disguising SPL states." However. the ruis;," However, the r.m.s." variability of NCCS00 ΝΤ was already. ta Observation 1. while the raus.," variability of NGC300 X-1 was already in Observation 1, while the r.m.s." variability of ICLO N-1 was18%., variability of IC10 X-1 was. .. Hence they are already cousiderablv more variable than DII LAINBs in the very high state (?).. making this hypothesis uulikelv.," Hence they are already considerably more variable than BH LMXBs in the very high state \citep{vdk95}, making this hypothesis unlikely." Iustead. we believe that the observed behaviour mavhe due to the status of the corona.," Instead, we believe that the observed behaviour maybe due to the status of the corona." In NS LAINBs. the selradiation of the disc is more efficient than iu BIT LAUXD«. hence NS LMXDs lave hot. stable discs. while all DII LAINBs are transient (2):: they spend the majority oftheir time ina quicscent state. with outbursts eenerallv lasting a few mouths (seee.g.2)..," In NS LMXBs, the self-irradiation of the disc is more efficient than in BH LMXBs, hence NS LMXBs have hot, stable discs, while all BH LMXBs are transient \citep{kk97}; they spend the majority of their time in a quiescent state, with outbursts generally lasting a few months \citep[see e.g.][]{mr03}." During the rise of the outburst. a DII LAND will go from a low accretion rate. hard sta5 with associated radio jets. to a high accretion rate. soft state with no jets (seee.g.?.andreferenceswithiu)..," During the rise of the outburst, a BH LMXB will go from a low accretion rate, hard state with associated radio jets, to a high accretion rate, soft state with no jets \citep[see e.g.][ and references within]{hb05}." It is therefore possible that the source of the hard. nou-thermal cussion. aud also of the jets in DIT LAINBs (6.8. the corona) is ejected duriug this transition: iudecd 7?~ witucss a large radio flare that coimcided with a had soft transition iu CN f.," It is therefore possible that the source of the hard, non-thermal emission, and also of the jets in BH LMXBs (e.g. the corona) is ejected during this transition; indeed \citet{gal04} witness a large radio flare that coincided with a hard to soft transition in GX $-$ 4." By coutrast. the three known Calactic BI IINEND«s are all persisteuthy bright.," By contrast, the three known Galactic BH HMXBs are all persistently bright." The WAINB accretion dises are expected to be sinall. and hence will be more easily. kept rot at the outer edge. making them stable.," The HMXB accretion discs are expected to be small, and hence will be more easily kept hot at the outer edge, making them stable." Therefore. the behaviour of IC10 N-1 aud NCGC300 X-1 nav be explained by stable dise accretion.," Therefore, the behaviour of IC10 X-1 and NGC300 X-1 may be explained by stable disc accretion." A sinall fraction ofthe 10? PADSyr towind froma WR companion caving the vicinity of the L1 poiut could provide enough nass. with sufficicut angular momentum. to sustain au accretion disc that is persistently iu the high state.," A small fraction of the $\sim 10^{-5}-10^{-4}$ $_{\odot}$ $^{-1}$ wind from a WR companion leaving the vicinity of the L1 point could provide enough mass, with sufficient angular momentum, to sustain an accretion disc that is persistently in the high state." Iu this case. the corona could be retained. aud the cussion would heu be dominated by a non-thermal compoucut due to iuverse-C'onmiptonisation of cool pliotous ou hot electrons. as seen din NS NBs at high accretion rate.," In this case, the corona could be retained, and the emission would then be dominated by a non-thermal component due to inverse-Comptonisation of cool photons on hot electrons, as seen in NS XBs at high accretion rate." Observations ofthe Galactic BIT IENEXDs support this hvpothesis., Observations of the Galactic BH HMXBs support this hypothesis. LMC. ΝΤ has never been observed in the lowανα state (seee.g.27)..," LMC X-1 has never been observed in the low/hard state \citep[see e.g.][]{wilms01,yao05}." 7. report “high state” (4.6. power x £6. 1) PDS frou: RNTE observations of LAIC X-1. while ? find its enission spectrum to be dominated by a power law with photon index z3. with a 0.51.1 keV blackbody component.," \citet{now01} report “high state” (i.e. power $\propto$ $\nu^{-1}$ ) PDS from RXTE observations of LMC X-1, while \citet{wilms01} find its emission spectrum to be dominated by a power law with photon index $\ga$ 3, with a 0.8–1.1 keV blackbody component." This cussion spectruni ds reluarkably simular to our best fit models for NCUC300 X-1 in Obs., This emission spectrum is remarkably similar to our best fit models for NGC300 X-1 in Obs. 1. aud to ICLO N-I.," 1 , and to IC10 X-1." Iu contrast. (νο X-! aud," In contrast, Cyg X-1 and" In the simulation. the initial conditions are given for these scalar Binctions: We note here that these initial [unetionsας.οντοςὦ and ev satisfy the homogeneous boundary. conditions [ον each mode 5»>0.,"In the simulation, the initial conditions are given for these scalar functions: We note here that these initial functions$u, v, w, \phi$, and $\psi$ satisfy the homogeneous boundary conditions for each mode $ n \ge 0$." Specifically. for the mode. i.e. when n=0). forthe modes. i.e. when 11400$ MHz (red points) in the $P(1400)-L_{X}$ plane together with the observed correlation of halos at 1400 MHz (black points, taken from Brunetti et al." 2009; see Tab., 2009; see Tab. 1 and references therein)., 1 and references therein). " In this case, to compare model expectations and present observations, we follow C09 (Sect.3) and derive the theoretical distribution of radio halos by considering the combination of the NVSS-XBACSs (Giovannini et al."," In this case, to compare model expectations and present observations, we follow C09 (Sect.3) and derive the theoretical distribution of radio halos by considering the combination of the NVSS-XBACs (Giovannini et al." " 1999) (radio-X-ray) selection criteria and sky coverage (at z=0.044— 0.2), and the X-ray luminosity range and sky coverage of the GMRT radio halo survey (Venturi et al."," 1999) (radio-X-ray) selection criteria and sky coverage (at $z=0.044-0.2$ ), and the X-ray luminosity range and sky coverage of the GMRT radio halo survey (Venturi et al." " 2007, 2008) (at z=0.2- 0.32)*."," 2007, 2008) (at $z=0.2-0.32$ ." ". The observed and theoretical distributions show a good agreement, although data points present a slightly larger scatter than expectations which can be easily interpreted as due to variations of magnetic field in clusters with the same X-ray luminosity (see Sect."," The observed and theoretical distributions show a good agreement, although data points present a slightly larger scatter than expectations which can be easily interpreted as due to variations of magnetic field in clusters with the same X-ray luminosity (see Sect." 2)., 2). " In Fig. 3,,panel,"," In Fig. \ref{Fig.LrLx_1p4}," " the same observed distribution of radio halos at 1.4 GHz (black points) is compared with that of “simulated” halos with v,>1400 MHz (red points) detectable by a LOFAR survey at 120 MHz with é F=0.25 mJy/beam.", the same observed distribution of radio halos at 1.4 GHz (black points) is compared with that of “simulated” halos with $\nu_s>1400$ MHz (red points) detectable by a LOFAR survey at 120 MHz with $\xi$ F=0.25 mJy/beam. " As expected, radio halos with v,>1.4 GHz follow a trend consistent with presently observed halos, while their larger number simply reflects the large sensitivity of LOFAR surveys with respect to present surveys."," As expected, radio halos with $\nu_s\geq1.4$ GHz follow a trend consistent with presently observed halos, while their larger number simply reflects the large sensitivity of LOFAR surveys with respect to present surveys." " The steepening of the correlation is independent of the adopted values of model parameters, at least by considering sets of parameters in the region (Β.η». b, πι) that reproduce both the observed slope of the P(1.4)—M, correlation (ay=2.9+ 0.4) and the observed fraction of galaxy clusters with radio halos."," The steepening of the correlation is independent of the adopted values of model parameters, at least by considering sets of parameters in the region $B_{}$, $b$, $\eta_t$ ) that reproduce both the observed slope of the $P(1.4)-M_v$ correlation $\alpha_M=2.9\pm0.4$ ) and the observed fraction of galaxy clusters with radio halos." C06 and C09 already discussed the dependence of expectations on model parameters., C06 and C09 already discussed the dependence of expectations on model parameters. " They showed that the expected number of radio halos decreases only by a factor of ~2—2.5, from super-linear (b> 1) to sub-linear (b< 1) magnetic scaling (see also Fig."," They showed that the expected number of radio halos decreases only by a factor of $\sim 2-2.5$, from super-linear $b>1$ ) to sub-linear $b<1$ ) magnetic scaling (see also Fig." 4 in Cassano et al., 4 in Cassano et al. 2006b)., 2006b). " For a fixed value of b largervalues of Bey; produce P(1.4)cM$"" correlations with slightly flatter slopes (see Tab.3 in C06).", For a fixed value of $b$ largervalues of $B_{}$ produce $P(1.4)\propto M_v^{\alpha_M}$ correlations with slightly flatter slopes (see Tab.3 in C06). " For example, in the case b=1.5 the allowed values of B range from Bey,~ 1.94G to «2.8 4G, and correspondingly it is «y=3.3 and 2.5, respectively, still consistent with the observed one."," For example, in the case $b=1.5$ the allowed values of $B$ range from $B_{}\simeq1.9\, \mu$ G to $\simeq2.8\, \mu$ G, and correspondingly it is $\alpha_M=3.3$ and $2.5$, respectively, still consistent with the observed one." " The steepening of the correlation is due to the glow up of new radio halos at low frequency, thus another point is whether the fraction of halos with smaller v; (ultra steep spectrum halos) changes from super-linear to sub-linear cases."," The steepening of the correlation is due to the glow up of new radio halos at low frequency, thus another point is whether the fraction of halos with smaller $\nu_s$ (ultra steep spectrum halos) changes from super-linear to sub-linear cases." " To investigate this effect, in Fig."," To investigate this effect, in Fig." " 5 we report the percentage of radio halos with 1205σ maser emission., \ref{Fig:rms} shows $\Delta$ as a function of the maser flux in each of the channels with $>5\sigma$ maser emission. " We find that for all of the maser features, with one exception, A stays approximately constant within a factor of ~3 up to a maser flux of ~50 Jy beam""! after which it increases with Ac(Flux)9?."," We find that for all of the maser features, with one exception, $\Delta$ stays approximately constant within a factor of $\sim3$ up to a maser flux of $\sim50$ Jy $^{-1}$ after which it increases with $\Delta\propto({\rm Flux})^{0.9}$." " During the first epoch, only the maser feature at γιοι=5.4 did not follow this relation and already deviated from the expected rms noise level when its flux became >20 Jy beam!."," During the first epoch, only the maser feature at $V_{\rm LSR}=5.4$ did not follow this relation and already deviated from the expected rms noise level when its flux became $>20$ Jy $^{-1}$." " As this did not occur during the last epoch, this is possibly due to weak narrowband interference."," As this did not occur during the last epoch, this is possibly due to weak narrowband interference." " Since the noise characteristic is similar for both polarizations and all epochs, the rms error increase is unlikely to be due to receiver saturation and would be unable to cause a systematic shift between RCP and LCP."," Since the noise characteristic is similar for both polarizations and all epochs, the rms error increase is unlikely to be due to receiver saturation and would be unable to cause a systematic shift between RCP and LCP." " However, the analysis does imply"," However, the analysis does imply" Alanv of the salient features. of our nearest neighbour ealaxies. the Alagcllanie Cloucls. have been well determined.,"Many of the salient features of our nearest neighbour galaxies, the Magellanic Clouds, have been well determined." Their proximity also allows us to further develop standard cancle techniques for distance determination (e.g. Di JZenedetto 1997: Sasselov et al.," Their proximity also allows us to further develop standard candle techniques for distance determination (e.g., Di Benedetto 1997; Sasselov et al." 1997. but see Udalski ct al.," 1997, but see Udalski et al." 19958)., 1998). Alan classes of objects in our own galaxy have been identified in the Clouds. (see. e.g. Ixeller Bessell 1998: Alantegazza Antonello 19908: Santengelo 1998) and their presence has allowed. us a close view of some of the shorter time scale astrophysical events. such as supernova 19872.," Many classes of objects in our own galaxy have been identified in the Clouds (see, e.g., Keller Bessell 1998; Mantegazza Antonello 1998; Santengelo 1998) and their presence has allowed us a close view of some of the shorter time scale astrophysical events, such as supernova 1987a." llowever. it remains that of the Clouds is not extensively explored.," However, it remains that of the Clouds is not extensively explored." In. particular. only 65 proven or probable planetary nebulae (PN) candidates are known in the area of the Small Magellanic Cloud (SAIC) that is studied. here. (previous catalogues are contained. in ο Azzopardi (1993). hereafter referred to as NLA93. and in Sanculeak. MacConnell and Davis Phillip (1978). hereafter referred to as SMPTS).," In particular, only 65 proven or probable planetary nebulae (PN) candidates are known in the area of the Small Magellanic Cloud (SMC) that is studied here (previous catalogues are contained in Meyssonnier Azzopardi (1993), hereafter referred to as MA93, and in Sanduleak, MacConnell and Davis Phillip (1978), hereafter referred to as SMP78)." Many. fainter PN were found by Jacoby (1980) and Morgan Good (1985)., Many fainter PN were found by Jacoby (1980) and Morgan Good (1985). Llowever. these objects are bevond the detection limits of the current work.," However, these objects are beyond the detection limits of the current work." tt djs the aim of this work to provide à more spatially complete catalogue of the bright PN and emission-line object content of the SAIC., It is the aim of this work to provide a more spatially complete catalogue of the bright PN and emission-line object content of the SMC. We aso describe a new method. of sclocting candidate objects which is highly suited to studies of the Alagellanic Clouds., We also describe a new method of selecting candidate objects which is highly suited to studies of the Magellanic Clouds. Cataloguing any class ο [Galactic astronomical object requires a large solid angle of sky to be observed., Cataloguing any class of Galactic astronomical object requires a large solid angle of sky to be observed. In the case of the SAIC. however. the enire galaxy subtends only ~10 square degrees on the sky.," In the case of the SMC, however, the entire galaxy subtends only $\sim 10$ square degrees on the sky." Thus. the entire SMC can be observed. in different: [recuesicy bands with [few exposures of an extremely wide field elescope or camera. allowing Us tO survey more complet«lv the population of specific classes of objects than by carrying out surveys in the Galaxy.," Thus, the entire SMC can be observed in different frequency bands with few exposures of an extremely wide field telescope or camera, allowing us to survey more completely the population of specific classes of objects than by carrying out surveys in the Galaxy." Estimates of the population in the Magellanic Clouds may herefore provide further insieht into the true population in he Galaxy., Estimates of the population in the Magellanic Clouds may therefore provide further insight into the true population in the Galaxy. Wide field telescopes hase had [limited use in the recent ost., Wide field telescopes have had limited use in the recent past. However. the potential of automated. patrol telescopes with a wide field format is niw starting to be realized. (see. eg..," However, the potential of automated patrol telescopes with a wide field format is now starting to be realized (see, eg.," Carter et al., Carter et al. 1992). especially when used. to observe ransicnt ancl oscillatory sources.," 1992), especially when used to observe transient and oscillatory sources." For the present work. we je used images of the SAC taken with a Nikon survey camera with an approximate 3 degree field.," For the present work, we have used images of the SMC taken with a Nikon survey camera with an approximate $\times$ 7 degree field." Searching for PN candidates in the Cloucts is facilitated »v their strong emission in he Ha and. Ori] bands., Searching for PN candidates in the Clouds is facilitated by their strong emission in the $\alpha$ and ] bands. The gascous ejecta is abundant in both hydrogen. and. oxygen and the remnant star is hot enough to doubly ionize oxvgen with its UV continuum raciaion., The gaseous ejecta is abundant in both hydrogen and oxygen and the remnant star is hot enough to doubly ionize oxygen with its UV continuum radiation. Thus. Hla anc Oi] band images can be used to find P: candidates in the SAIC.," Thus, $\alpha$ and ] band images can be used to find PN candidates in the SMC." side of (7)) drops below unity. around every point ii CA) there is an essentially spherically svininetric patch (8) where the expausion is “weakly accelerated (ie. 1$ $\sigma$ ) than the mean redshift." A further interesting feature of the spectrum is that he Le| oN u] emission blend shows tentative evidence or à broad base of rest-frame width 11.50023-2200. km ου see Figures 4 6).," A further interesting feature of the spectrum is that the $\alpha$$+$ [N ] emission blend shows tentative evidence for a broad base of rest-frame width $\pm$ 2200 km $^{-1}$ (FWHM, see Figures 4 6)." This is consistent with he presence of a scattered (Antonucci&Miller1985). or directly. observed. broad-line region. (BLIU) component.," This is consistent with the presence of a scattered \citep{am}, , or directly observed, broad-line region (BLR) component." Spectropolarimetry observations will be required to confirm. he scattered. BLE. possibility., Spectropolarimetry observations will be required to confirm the scattered BLR possibility. In order to further understand the nature of this object we mace spectroscopic observations of QI131|16 at near-LR wavelengths., In order to further understand the nature of this object we made spectroscopic observations of Q1131+16 at near-IR wavelengths. Phe observed wavelength range (1.4 to 2.45) was selected in order to simultaneously detect both Pao and Pas., The observed wavelength range (1.4 to $\mu$ m) was selected in order to simultaneously detect both $\alpha$ and $\beta$. The Ix-band. NUR spectrum of 01191|16 taken using LIRIS is presented in Figure 7., The K-band NIR spectrum of Q1131+16 taken using LIRIS is presented in Figure 7. Due to its relatively low S/N. this spectrum does not show the abundance of emission lines seen at optical wavelengths.," Due to its relatively low S/N, this spectrum does not show the abundance of emission lines seen at optical wavelengths." Although weak narrow Dao and emission lines are detected. there is no sign of any. broad. Pao and Da: components. implying the BL is enshrouded. by dust.," Although weak narrow $\alpha$ and $\beta$ emission lines are detected, there is no sign of any broad $\alpha$ and $\beta$ components, implying the BLR is enshrouded by dust." A single Gaussian fit to the Paa line shows that it is unresolved. within the uncertainties for the resolution of our observations. and its recdshift (z=0.1731440.00011) is consistent with those of the optical emission lines.," A single Gaussian fit to the $\alpha$ line shows that it is unresolved within the uncertainties for the resolution of our observations, and its redshift $\pm$ 0.00011) is consistent with those of the optical emission lines." Any quasar nucleus component present in this system must be highly extinguished: the relatively τος near-LHi colours of this source measured by 2ALASS do notappearto be due to a moderately extinguished quasar component that becomes visible at the longer near-LHi wavelengths., Any quasar nucleus component present in this system must be highly extinguished; the relatively red near-IR colours of this source measured by 2MASS do notappearto be due to a moderately extinguished quasar component that becomes visible at the longer near-IR wavelengths. " Pherefore this object cannot truly be described as a ""red quasar’.", Therefore this object cannot truly be described as a $\lq$ red quasar'. The emission lines in the spectrum. ofQUIS)|16. were initially fitted with single Ciaussian. profiles. but such fits did not provide an entirely adequate fit to the wings of," The emission lines in the spectrum ofQ1131+16 were initially fitted with single Gaussian profiles, but such fits did not provide an entirely adequate fit to the wings of" "llowever. it should be noted that some investigators set (he permanent change ternis. AD, and AY, to zero.","However, it should be noted that some investigators set the permanent change terms, $\Delta \dot{\nu_p}$ and $\Delta \ddot{\nu_p}$ to zero." " We have allowed Av, to take non-zero values. but keep Ay, as zero."," We have allowed $\Delta \dot{\nu_p}$ to take non-zero values, but keep $\Delta \ddot{\nu_p}$ as zero." Both of these terms affect only the longest time-scales. where both timing noise and the occurrence of (he subsequent elitehes make definitive separation impossible.," Both of these terms affect only the longest time-scales, where both timing noise and the occurrence of the subsequent glitches make definitive separation impossible." The data presented here were recorded between MJD 51505 and 51650., The data presented here were recorded between MJD 51505 and 51650. The arrival time data have been transformed to the Solar System barvcentre using standard techniques., The arrival time data have been transformed to the Solar System barycentre using standard techniques. The position and proper motion of the Vela pulsar was defined by data from the Radio VLBI position of Legge(2001).., The position and proper motion of the Vela pulsar was defined by data from the Radio VLBI position of \citet{legge_private}. The recorded TOAs from all [requencies ancl both svstems were fitted in the program7?., The recorded TOAs from all frequencies and both systems were fitted in the program. . The results of this fit are given in Table I., The results of this fit are given in Table 1. Figure la shows the residuals [rom (he pre-jump fit for data taken on 2000 January 16 (AIJD 51559) with the full polarisation svstem., Figure 1a shows the residuals from the pre-jump fit for data taken on 2000 January 16 (MJD 51559) with the full polarisation system. Shortly alter 07:34 UT. the residuals diverge rom (he fit. indicating a sudden decrease in pulse period.," Shortly after 07:34 UT, the residuals diverge from the fit, indicating a sudden decrease in pulse period." Figure Ib shows an hour of data starting al MJD 51559.3., Figure 1b shows an hour of data starting at MJD 51559.3. Individual data points represent ten second averages constructed rom (he single pulse data., Individual data points represent ten second averages constructed from the single pulse data. The period jump occurs on a verv short timescale. without warning.," The period jump occurs on a very short timescale, without warning." The observations are consistent with an instantaneous change in period: modeling iis shown that a spin-up timescale of forty seconds would produce a three sigma sienal., The observations are consistent with an instantaneous change in period; modeling has shown that a spin-up timescale of forty seconds would produce a three sigma signal. The separation into four time-scales is clear., The separation into four time-scales is clear. The longer three clecay terms are simular to (hose previously reported (Alparetal.1993:Flanagan1990).. and are in an approximately equal ratio of 5.9:5.7.," The longer three decay terms are similar to those previously reported \citep{alpar_1993,flanagan}, and are in an approximately equal ratio of 5.9:5.7." These have been associated with the vortex creep models by and others., These have been associated with the vortex creep models by \citet{alpar_1993} and others. The fast decay (mescale. not. previously observed (or observable) is shown separated Irom the other effects in figure 2.," The fast decay timescale, not previously observed (or observable) is shown separated from the other effects in figure 2." We have subtracted the terms found by in the 2 minute data from the single pulse data folded for 10 seconds., We have subtracted the terms found by in the 2 minute data from the single pulse data folded for 10 seconds. In this plot a gradual spin-up (as opposed to instantaneous) would be a negative excursion around the projected time of the glitch. as we'd have overestimated the phase in the model.," In this plot a gradual spin-up (as opposed to instantaneous) would be a negative excursion around the projected time of the glitch, as we'd have overestimated the phase in the model." We see a positive excursion. followed by a rapid decay.," We see a positive excursion, followed by a rapid decay." A positive excursion could be produced by the pulsar slowing down just before the glitch or. more likely. if the estimate of the elitch epoch was too early because (here was an extra component not resolvable in (he 2 minute data.," A positive excursion could be produced by the pulsar slowing down just before the glitch or, more likely, if the estimate of the glitch epoch was too early because there was an extra component not resolvable in the 2 minute data." Once the original fit was removed this would give a linear rise with the gradient Av found in the 2 minutes data. followed by. a decay.," Once the original fit was removed this would give a linear rise with the gradient $\Delta \nu$ found in the 2 minutes data, followed by a decay." We have fitted this rise (AvA/) followed bv a forth exponential decay term to give the (true gliteh epoch aud the fastest decay. term., We have fitted this rise $\Delta \nu \Delta t$ ) followed by a forth exponential decay term to give the true glitch epoch and the fastest decay term. diffusion to the resulting equations to model dissipative and resistive processes across discontinuities. and this introcluces additional free parameters which control dissipative processes.,"diffusion to the resulting equations to model dissipative and resistive processes across discontinuities, and this introduces additional free parameters which control dissipative processes." In addition. the local conservation. for example third Newton law. is satisfied to the truncation error only.," In addition, the local conservation, for example third Newton law, is satisfied to the truncation error only." This is a potential source of error for the problems with interacting strong shock waves. since the truncation error across a shock wave is always of order of unity.," This is a potential source of error for the problems with interacting strong shock waves, since the truncation error across a shock wave is always of order of unity." Nevertheless. GPALLLD appears to be a viable. albeit noticeably more complex. alternative for ΟΛΗΙΟ. at least for subsonic and. weakly supersonic Lows.," Nevertheless, GPMHD appears to be a viable, albeit noticeably more complex, alternative for SPMHD, at least for subsonic and weakly supersonic flows." Alternatively. one may attempt to utilise a Godunov approach.," Alternatively, one may attempt to utilise a Godunov approach." Lt has been shown that most of. if not all. SPL limitation can be removed by solving a hvedrodynamic Riemann problem between each pair of interacting particles to obtain pressure forces. instead of computing separately pressure forces and artificial viscosity terms (727).," It has been shown that most of, if not all, SPH limitation can be removed by solving a hydrodynamic Riemann problem between each pair of interacting particles to obtain pressure forces, instead of computing separately pressure forces and artificial viscosity terms \citep{2002JCoPh.179..238I, 2003MNRAS.340...73C, 2010MNRAS.403.1165C}." In such Godunoy SPILL (GSP) formulations. the necessary mixing and clissipation is ineluclecl into underlving Ricmann problem which described the physics of the interaction.," In such Godunov SPH (GSPH) formulations, the necessary mixing and dissipation is included into underlying Riemann problem which described the physics of the interaction." Borrowing these ideas. it is therefore conceivable that Codunov-like meshless ALD formulation will eliminate the problems that plague SPMIID formulation. thereby. permitting formulation of consistent Lagrangian meshless MIID scheme.," Borrowing these ideas, it is therefore conceivable that Godunov-like meshless MHD formulation will eliminate the problems that plague SPMHD formulation, thereby permitting formulation of consistent Lagrangian meshless MHD scheme." In this paper we formulate a weighted. particle MIID scheme., In this paper we formulate a weighted particle MHD scheme. Our scheme is based. on a meshless discretisation of the conservation law equations. which was pioneered by 2.. and in Section ?? we present a heuristic derivation of the meshless conservative equations.," Our scheme is based on a meshless discretisation of the conservation law equations, which was pioneered by \cite{VILA:1999}, and in Section \ref{sect:methods} we present a heuristic derivation of the meshless conservative equations." We give the implementation details of our scheme in Section ??.., We give the implementation details of our scheme in Section \ref{sect:Implementation}. In Section ?? we present applications to the equation of ideal hydrodynamics. and in Section ?? we show how our scheme can be applied to theequations of ideal MILD.," In Section \ref{sect:ideal_hd} we present applications to the equation of ideal hydrodynamics, and in Section \ref{sect:ideal_mhd} we show how our scheme can be applied to theequations of ideal MHD." In Section ?? we validate our meshless MIID scheme on several test problems. and finally. we present our conclusions in Section ?77..," In Section \ref{sect:results} we validate our meshless MHD scheme on several test problems, and finally, we present our conclusions in Section \ref{sect:discussion}." In what follows. we present a heuristic derivation of meshless cliscretisation of a scalar conservation law.," In what follows, we present a heuristic derivation of meshless discretisation of a scalar conservation law." The readers interested in a rigorous mathematical formulation supplemented with convergence theorems are referred to the original papers by ? and ?7?..," The readers interested in a rigorous mathematical formulation supplemented with convergence theorems are referred to the original papers by \cite{VILA:1999} and \cite{1404789, 1404790}." Following these works. a weak solution to a scalar conservation law is defined by lere. (x.f) is à scalar field. S(x./) is its source. F(n.x./) is its flux in a frame moving with velocity a(x./). and the integral is carried out over all space-time domain of a problem at hand.," Following these works, a weak solution to a scalar conservation law is defined by Here, $u(\bfx,t)$ is a scalar field, $S(\bfx, t)$ is its source, ${\bf F}(u,\bfx,t)$ is its flux in a frame moving with velocity ${\bf a}(\bfx, t)$, and the integral is carried out over all space-time domain of a problem at hand." Ehe function qo=q(x./£) is an arbitrary cillerentiahble function in space and time. à=ὃνΟἱ|abr’).V is an advective derivative. anc a(x./) is an arbitrary smooth velocity field which will describe motion of particles.," The function $\varphi\equiv\varphi(\bfx,t)$ is an arbitrary differentiable function in space and time, $\dot\varphi = \partial\varphi/\partial t + {\bf a}(x,t)\cdot\nabla\varphi$ is an advective derivative, and ${\bf a}(\bfx, t)$ is an arbitrary smooth velocity field which will describe motion of particles." This integral is ciseretisecl on a set of particles with coordinates x; with the help ofa partition of unity where. w(x)+=»W(x xj;.h(x)) is an estimate of the particle number density and the sum is carried out over all particles. h(x) is a smoothing length. and M(x.P) is à smoothing with a compact support of size : in what follows we assume that the kernel is normalised to unity.," This integral is discretised on a set of particles with coordinates $\bfx_i$ with the help of a partition of unity where, $w(\bfx)^{-1} = \sum_j W(\bfx-\bfx_j,h(\bfx))$ is an estimate of the particle number density and the sum is carried out over all particles, $h(\bfx)$ is a smoothing length, and $W(\bfx, h)$ is a smoothing with a compact support of size $h$; in what follows we assume that the kernel is normalised to unity." Inserting |=»(κ) into an integral of an arbitrary function. we obtain where Vi2fci(x)dx is the elective volume of a particle 7. and in the third term we use first-order Taylor expansion of f(x).," Inserting $1 = \sum_i\psi_i(\bfx)$ into an integral of an arbitrary function, we obtain where $V_i = \int \psi_i(\bfx)\,d\bfx$ is the effective volume of a particle $i$, and in the third term we use first-order Taylor expansion of $f(\bfx)$." In principle. a higher order discretisation is also possible. but for the purpose of this work such an one-point quadrature is sullicient: in fact. on a regular distribution of particles this cliscretisation is second order accurate (c.f. regularitv)).," In principle, a higher order discretisation is also possible, but for the purpose of this work such an one-point quadrature is sufficient; in fact, on a regular distribution of particles this discretisation is second order accurate (c.f. \\ref{sect:regularity}) )." Application of this discretisation to gives Llere. the Einstein summation is assumed over Greek indexes. which refer to the components of à vector.," Application of this discretisation to gives Here, the Einstein summation is assumed over Greek indexes, which refer to the components of a vector." Also. the gradient ofa function s at Zparticle location. (Vs)?i is replaced by its cliserete version (D y2);. and this. for example. can be computed," Also, the gradient of a function $\varphi$ at $i$ -particle location, $(\nabla\varphi)^\alpha_i$ is replaced by its discrete version $(D^\alpha\varphi)_i$ , and this, for example, can be computed" with isotopic ratios raneie from λος Meroe = 1001010 to 76:12:12.,with isotopic ratios ranging from $^{24}$ $^{25}$ $^{26}$ Mg = 100:0:0 to 76:12:12. " The isotopic ratios were determined by 4? fits. bv computing 47 = S(O; S;,)/02. where O; and S; represents the observed and svuthetic spectrum. respectively, aud 6 = !."," The isotopic ratios were determined by $\chi^2$ fits, by computing $\chi^2$ = $\Sigma$ $O_i - S_i$ $\sigma^2$, where $O_i$ and $S_i$ represents the observed and synthetic spectrum, respectively, and $\sigma$ = $^{-1}$." Examples of the \? fits are shown in Figs., Examples of the $\chi^2$ fits are shown in Figs. 2 and 3 for the three recomended Mell features., 2 and 3 for the three recommended MgH features. The resulting Ae isotope ratios are prescuted in Tab., The resulting Mg isotope ratios are presented in Tab. 2., 2. Iu this table are also given the standard deviation from the three different ALell features. which for ?Mg and ??Mg have a typical value of c = and respectively. corresponding to standard errors of and," In this table are also given the standard deviation from the three different MgH features, which for $^{25}$ Mg and $^{26}$ Mg have a typical value of $\sigma$ = and , respectively, corresponding to standard errors of and." As discussed below. tle tue eor for Meg is actually somewhat ialler than for 'Meg.," As discussed below, the true error for $^{26}$ Mg is actually somewhat smaller than for $^{25}$ Mg." " Due to the larger isotopic separation of the ?ONTeTT lines. the determination of ?""Mg/?! Meg is more reliable than Z Mg/2!Mg,"," Due to the larger isotopic separation of the $^{26}$ MgH lines, the determination of $^{26}$ $^{24}$ Mg is more reliable than $^{25}$ $^{24}$ Mg." The clemental abundances of C. δν O. Na. Mg aud A] were obtained by spectral svuthesis. takiug into account blends by atomic. Co aud CN lines. aud the abundances of Si. Ca. Ti; Ni and Zr were obtained frou equivalent widths.," The elemental abundances of C, N, O, Na, Mg and Al were obtained by spectral synthesis, taking into account blends by atomic, $_2$ and CN lines, and the abundances of Si, Ca, Ti, Ni and Zr were obtained from equivalent widths." Carbon abundances were obtained from €» lines around 563 111 aud checked using CTL lines around 130 nu (Plez et al., Carbon abundances were obtained from $_2$ lines around 563 nm and checked using CH lines around 430 nm (Plez et al. 2008. see also Plez Cohen 2005).," 2008, see also Plez Cohen 2005)." Nitrogen abundances were obtained using CN lues around 630-637 ni aud 669-671 nu., Nitrogen abundances were obtained using CN lines around 630-637 nm and 669-671 nm. The CN-vich stars have N abundances ~3 times higher than the CN-weak stars. but the difference may be higher because TiO blends preveut a precise determination of N abtucdeances in the CN-weak stars.," The CN-rich stars have N abundances $\sim$ 3 times higher than the CN-weak stars, but the difference may be higher because TiO blends prevent a precise determination of N abundances in the CN-weak stars." The elemental abundance ratios are eiven iu Tabs., The elemental abundance ratios are given in Tabs. 2 aud 3., 2 and 3. The iron abundances. abundance ratios. and the C|N and C|N1O |[C.N.O/Fo]abuudauce stums. are shown in Fig.," The iron abundances, [C,N,O/Fe] abundance ratios, and the C+N and C+N+O abundance sums, are shown in Fig." Las a function of effective temperature., 4 as a function of effective temperature. " A similar plot for the isotopic τς MgAte, 2729 PINT ratios and the elemental abundance ratios [Na.Mg. is presented in Fig."," A similar plot for the isotopic $^{24,25,26}$ Mg/Mg, $^{25,26}$ $^{24}$ Mg ratios and the elemental abundance ratios [Na,Mg,Al/Fe] is presented in Fig." 5. aud the [Si.CaTi.Ni.Zi.La/Fe| Al/Fe]|ratios are shown iu Fig.," 5, and the [Si,Ca,Ti,Ni,Zr,La/Fe] ratios are shown in Fig." 6., 6. Iu these aud subsequeut figures CNoweak and CN-rich giauts are represented by open and filled circles. respectively.," In these and subsequent figures CN-weak and CN-rich giants are represented by open and filled circles, respectively." The CN status of our sample stars have beeu obtained from Smith Norris (1982) and Lee (2005). except for star M71 1. for which no previous information on its CN bands is available iu the literature.," The CN status of our sample stars have been obtained from Smith Norris (1982) and Lee (2005), except for star M71 I, for which no previous information on its CN bands is available in the literature." Since this star shows stroug CN bands in our HIRES spectruii. we have also iuclided it as a CN-stroug star.," Since this star shows strong CN bands in our HIRES spectrum, we have also included it as a CN-strong star." Ax discussed below. some abundance ratios show trends withT4.," As discussed below, some abundance ratios show trends with." .. The cocficients of the fits for the weak stars are given in Tab., The coefficients of the fits for the CN-weak stars are given in Tab. |., 4. The Me isotopic ratios and the elemental abundances of O. Na. Me aud Al for the CN-weak stars secu to show some treud with effective tempcrature. probably due to NLTE aud 3D effects (Asplind 2005: Collet et al.," The Mg isotopic ratios and the elemental abundances of O, Na, Mg and Al for the CN-weak stars seem to show some trend with effective temperature, probably due to NLTE and 3D effects (Asplund 2005; Collet et al." 2007)., 2007). " After correcting for trends withTag. the scatter in |O.Na.Mg.Al/Fo] for the CN-weak stars is only 0.015. 0.039. 0.018 and 0.021 dex. respectively,"," After correcting for trends with, the scatter in [O,Na,Mg,Al/Fe] for the CN-weak stars is only 0.018, 0.039, 0.018 and 0.021 dex, respectively." The CN-rich stars depart from the behavior of the CNoweak stars. showing larger 79Meg/Mg ratios. larger Na and Al elemental abundances. aud lower O aud Mg elemental imuidaces.," The CN-rich stars depart from the behavior of the CN-weak stars, showing larger $^{25,26}$ Mg/Mg ratios, larger Na and Al elemental abundances, and lower O and Mg elemental abundances." In Figs., In Figs. " 7-1l ave shown the 7!/Mg/Meg. . ο ND, ο Ae and ο Meg. ratios as a function of Mg.Al/Fo]."," 7-11 are shown the $^{24}$ Mg/Mg, $^{25}$ Mg/Mg, $^{25}$ $^{24}$ Mg, $^{26}$ Mg/Mg and $^{26}$ $^{24}$ Mg ratios as a function of [O,Na,Mg,Al/Fe]." Iu. these plots the trend with effective|JO.Na. temperature (Figs., In these plots the trend with effective temperature (Figs. 1-5. Tab.," 4-5, Tab." 1) las been corrected in. the [O.Na.Mg.Al/Fe| ratios. to prevent spurious trends;," 4) has been corrected in the [O,Na,Mg,Al/Fe] ratios, to prevent spurious trends." The ο[ο Λίο isotopic ratios show a larger spread than 7?9Mpe/Mg due to the spread in ?UNDe/Ae (CN-rich giuuts show lower ?/Mg/Meg. than CN-weak eiautz).," The $^{25,26}$ $^{24}$ Mg isotopic ratios show a larger spread than $^{25,26}$ Mg/Mg due to the spread in $^{24}$ Mg/Mg (CN-rich giants show lower $^{24}$ Mg/Mg than CN-weak giants)." In Fig., In Fig. 7 we show that ?!Mg in CN-vich stars is anticorrelated with Na and probably also with Al., 7 we show that $^{24}$ Mg in CN-rich stars is anticorrelated with Na and probably also with Al. " The 2°\To Ale ratios are less reliable than the ??""Me/Mg ratios.", The $^{25}$ Mg/Mg ratios are less reliable than the $^{26}$ Mg/Mg ratios. " Although Table 2 sugeest higher uncertaiuties for ?O0NTe than for ?""Mg. with standard errors of aud1.054.. respectively. the star-to-tar scatter for the CN- stars actually shows that the errors for 7Mg aud 20NTe are audSUC respectively. i; in both cases somewhat lower than the errors estimated frou: Table 2."," Although Table 2 suggest higher uncertainties for $^{26}$ Mg than for $^{25}$ Mg, with standard errors of and, respectively, the star-to-star scatter for the CN-weak stars actually shows that the errors for $^{25}$ Mg and $^{26}$ Mg are and, respectively, i.e., in both cases somewhat lower than the errors estimated from Table 2." " The higher error bar (0.9% )) for TUM Is expected due to the smaller isotopic shift of the Z""MgIE lines.", The higher error bar $\pm$ ) for $^{25}$ Mg is expected due to the smaller isotopic shift of the $^{25}$ MgH lines. Heuce. Ae does not show clear trends besides the fact that A fe is cuhanced in CN-vich eiauts (Figs.," Hence, $^{25}$ Mg does not show clear trends besides the fact that $^{25}$ Mg is enhanced in CN-rich giants (Figs." 8-9)., 8-9). The CN-weak stars do not show any correlation between 7°\Le and the elemental abuudauces of Na. O. Me and Al (Fies.," The CN-weak stars do not show any correlation between $^{26}$ Mg and the elemental abundances of Na, O, Mg and Al (Figs." 10-11). but the CN-rich giants slow strong. weak aud no correlations between 79M and the clemeutal abinidauces of Na aud Al. O. aud Mg. respectively.," 10-11), but the CN-rich giants show strong, weak and no correlations between $^{26}$ Mg and the elemental abundances of Na and Al, O, and Mg, respectively." Fie., Fig. 12 shows the correlations between the clementa abundances of O. Na. Mg and Al which have been corrected for trends with (Fies.," 12 shows the correlations between the elemental abundances of O, Na, Mg and Al, which have been corrected for trends with (Figs." 1-5. Tab.," 4-5, Tab." [). ane therefore any remaining trend or scatter should be real.," 4), and therefore any remaining trend or scatter should be real." " Interestingly, even though the CN-weak stars show ouly stall scatter in their abundauces ratios (0.020.0 dex). and seem to be roughly constant between the nucertaitics. there is a lint of a correlation between Na aud Al"," Interestingly, even though the CN-weak stars show only small scatter in their abundances ratios (0.02–0.04 dex), and seem to be roughly constant between the uncertainties, there is a hint of a correlation between Na and Al." Ou the other haud. Al and Me. anc O and Na. secu to be auti-correlated. although the evidence is weaker for the O:Na auti-correlation.," On the other hand, Al and Mg, and O and Na, seem to be anti-correlated, although the evidence is weaker for the O:Na anti-correlation." The CN-strong stars show strong correlation aud auti-correlation between Na aud Al. aud O aud Na. respectively.," The CN-strong stars show strong correlation and anti-correlation between Na and Al, and O and Na, respectively." As can be seen in Fig., As can be seen in Fig. L the C|N abundance sum is larger in CN-aich than in CN-wealk AIT] giants.," 4, the C+N abundance sum is larger in CN-rich than in CN-weak M71 giants." This is mainly due to the large N enhancement of the CN-vich eqauts. which have N abundances ~0.5 dex higher than the CN-weak eiauts.," This is mainly due to the large N enhancement of the CN-rich giants, which have N abundances $\sim$ 0.5 dex higher than the CN-weak giants." Neck low resolution spectra of CNweak and CN-strong main sequence stars in MT show that CN-stroug dwarfs are also enhanced iu uitroeecere when compared to CN-aweak dwarfs (Briley Cole 2001)., Keck low resolution spectra of CN-weak and CN-strong main sequence stars in M71 show that CN-strong dwarfs are also enhanced in nitrogen when compared to CN-weak dwarfs (Briley Cohen 2001). The C]N1O abundance sum is constant within 0.1 dex (Fig., The C+N+O abundance sum is constant within 0.1 dex (Fig. tj. in agreement with other high resolution analysis of GC elauts in the literature. which fud οΝΟ coustant within 0.3 dex for NGC 6712 ΤΟΠ = -].0. Yong ct al.," 4), in agreement with other high resolution analysis of GC giants in the literature, which find C+N+O constant within 0.3 dex for NGC 6712 ([Fe/H] = -1.0, Yong et al." 2008). MI ([Foe/H]| = -1.1. Sunith et al.," 2008), M4 ([Fe/H] = -1.1, Smith et al." 2005) and MI3 ΤΟΠ = -1.5. Cohen Moléuudez 2005).," 2005) and M13 ([Fe/H] = -1.5, Cohen Melénndez 2005)." Recently. Yonget al (," Recently, Yonget al. (" 2009) have found a larec CIN|O spread of 0.57 dex for NGC 1851 giants (|Fo/1I] = -1.2).,2009) have found a large C+N+O spread of 0.57 dex for NGC 1851 giants ([Fe/H] = -1.2). This spread exceeds their estimated uucertaiuty (0.11 dex). and is much lareer than that observed iu other GCs. where no significant spread is found.," This spread exceeds their estimated uncertainty (0.14 dex), and is much larger than that observed in other GCs, where no significant spread is found." Young et al. (, Yong et al. ( 2009) interpret the huge spread in CIN|O as,2009) interpret the large spread in C+N+O as of J1539+0239 in the Galactic halo (upper panel) and a for a magnification of the Galactic disk region of the trajectory (lower panel).,of J1539+0239 in the Galactic halo (upper panel) and a for a magnification of the Galactic disk region of the trajectory (lower panel). " Hence, in order to keep the trajectory of J1539+0239 bound to the Galaxy, the dark matter halo mass needs to be adjusted."," Hence, in order to keep the trajectory of J1539+0239 bound to the Galaxy, the dark matter halo mass needs to be adjusted." We carried out numerical experiments increasing the halo density by a constant factor., We carried out numerical experiments increasing the halo density by a constant factor. " Finally we found a bound trajectory for a minimum mass of Mi""=1.7x1012msun.", Finally we found a bound trajectory for a minimum mass of $M_{\rm halo}^{\rm new}=1.7\times10^{12}$. ". The last pericenter passage occured at a distance of ~7.7 kkpc and the apocenter distance of the star's trajectory is located far out in the halo, at ~250 kkpc in this case."," The last pericenter passage occured at a distance of $\sim$ kpc and the apocenter distance of the star's trajectory is located far out in the halo, at $\sim$ kpc in this case." If we take into account the full velocity distribution (see Fig. 4)), If we take into account the full velocity distribution (see Fig. \ref{fig:veldistrib_J1539}) ) " of the star we even can derive solutions for the extrema, which correspond to the absolute errors, giving msun.."," of the star we even can derive solutions for the extrema, which correspond to the absolute errors, giving $M_{\rm halo}\sim1.7_{-1.1}^{+2.3}\times10^{12}$ ." as the center of the tadpole orbits around. L4. point.,as the center of the tadpole orbits around $L_4$ point. " At a specific moment /. the osculating orbits of planets Lead to one value of an""(£D)."," At a specific moment $t$, the osculating orbits of planets lead to one value of $a_0^{\rm min}(t)$." At next moment //. the planets have evolved to new osculating orbits.," At next moment $t^\prime$, the planets have evolved to new osculating orbits." We restart the above-mentioned calculations with planets on the new osculating orbits. but the fictitious Trojans still on the same initial orbits as before.," We restart the above-mentioned calculations with planets on the new osculating orbits, but the fictitious Trojans still on the same initial orbits as before." A new value of the central semimajor axis auliillb(E) Tis obtained., A new value of the central semimajor axis $a_0^{\rm min}(t^\prime)$ is obtained. . In such a wav. we finally⋅ get two series. of semimajor axes. one is for Neptune osculating orbit and the other for the corresponding Trojan sat the resonance center.," In such a way, we finally get two series of semimajor axes, one is for Neptune's osculating orbit and the other for the corresponding Trojan at the resonance center." We show the time variations of them in 11., We show the time variations of them in 1. " Applving an FET to the time series of the central ag"" in the upper panel. we get the power spectrum in the lower panel of 11."," Applying an FFT to the time series of the central $a_0^{\rm min}$ in the upper panel, we get the power spectrum in the lower panel of 1." " The frequencies of the peaks tell us the mechanism causing the variation of aj"".", The frequencies of the peaks tell us the mechanism causing the variation of $a_0^{\rm min}$. The highest [our peaks are at. ft=00781.0.0273.0.162 and [i=0.00549 (2zx/vr) ," The highest four peaks are at $f^1=0.0781, f^2=0.0273, f^3=0.162$ and $f^4=0.00549\,\,(2\pi/{\rm yr})$ ." "Denotingf? the meanf motion (orbital frequeney) of planets by fs.fü ancl fx. a simple calculation reveals that ft=fsfs.f?τοff=2f and ""n—f>fs. that is. these frequencies are either the svnocic Irequencies (f? Ὦ or the harmonies (f°) of orbital frequencies in the outer solar svstem."," Denoting the mean motion (orbital frequency) of planets by $f_5, f_6, f_7$ and $f_8$, a simple calculation reveals that $f^1=f_5-f_8, f^2=f_6-f_8, f^3=2f_5$ and $f^4=f_7-f_8$, that is, these frequencies are either the synodic frequencies $f^{1,2,4}$ ) or the harmonics $f^3$ ) of orbital frequencies in the outer solar system." This fact demonstrates again that the asvmametrical shift” in the semimajor axis of the center of the tadpole orbits is only due to the initial orbital configurations of planets., This fact demonstrates again that the asymmetrical “shift” in the semimajor axis of the center of the tadpole orbits is only due to the initial orbital configurations of planets. Because of its largest mass. Jupiter plays the most distinct role in causing this variation.," Because of its largest mass, Jupiter plays the most distinct role in causing this variation." Me present our investigations on the dynamics of the inclined “Trojans in this part., We present our investigations on the dynamics of the inclined Trojans in this part. As mentioned above. the value of the libration center σι changes only slightly with inclination. and therefore we may fix its value at 607 for Ly and 607 for £z; when we study the dependence of stability on the orbital inclination.," As mentioned above, the value of the libration center $\sigma_c$ changes only slightly with inclination, and therefore we may fix its value at $60^\circ$ for $L_4$ and $-60^\circ$ for $L_5$ when we study the dependence of stability on the orbital inclination." Aclopting the spectral number as an indicator of the reeularity of orbits. we construct dynamical maps using 5757 orbits starting [rom a LOL.57 grid on the (a0.75) plane and integrated for MMwvr.," Adopting the spectral number as an indicator of the regularity of orbits, we construct dynamical maps using 5757 orbits starting from a $101\times57$ grid on the $(a_0,i_0)$ plane and integrated for Myr." The power spectrum. of coser [or each orbit is calculated and the number of peaks. which are over one percent of the highest peak. is defined as the SN.," The power spectrum of $\cos\sigma$ for each orbit is calculated and the number of peaks, which are over one percent of the highest peak, is defined as the SN." To limit the number into a manageable range. an SN is forced to be 100 i£ it was originally larger than that.," To limit the number into a manageable range, an SN is forced to be 100 if it was originally larger than that." We also exclude orbits that escape from the 1:1 resonance region., We also exclude orbits that escape from the 1:1 resonance region. A simple criterion is applied: if the averaged value of the semimajor axis e of a test. particle does not satisfy 20.0XUσας AU. it is regarded. as escaped from the resonance. and an SN of 110 is assigned to the orbit.," A simple criterion is applied: if the averaged value of the semimajor axis $a$ of a test particle does not satisfy $29.9\,{\rm AU}<\bar{a}<30.5\,{\rm AU}$ , it is regarded as escaped from the resonance, and an SN of 110 is assigned to the orbit." " We show the dynamical maps in Fig.22 for Lj, and in Fig.33 lor Ls.", We show the dynamical maps in 2 for $L_4$ and in 3 for $L_5$. Because all orbits with inclination higher than 61 can not survive in the Trojan-like orbit. we show in Figs.22 and 3 only for orbits with zo)€07.63.757].," Because all orbits with inclination higher than $61^\circ$ can not survive in the Trojan-like orbit, we show in 2 and 3 only for orbits with $i_0\in [0^\circ, 63.75^\circ]$." The colour in the dynamical map indicates the SN., The colour in the dynamical map indicates the SN. In the ereen region where SN is relatively small. the motion is dominated by a few dominating frequencies and. thus itis more regular: but in the blue and red region.the spectrum of cos is characterized by strong noise and thus the motion is chaotic: the white color with SN=110 indicates escaped orbits.," In the green region where SN is relatively small, the motion is dominated by a few dominating frequencies and thus it is more regular; but in the blue and red region,the spectrum of $\cos\sigma$ is characterized by strong noise and thus the motion is chaotic; the white color with ${\rm SN}=110$ indicates escaped orbits." boundary. conditions is just one of the obstacles in this modelling technique.,boundary conditions is just one of the obstacles in this modelling technique. llere we also take a simplified approach to consider the local reconnection process. aiming to model the effect of reconnection on the field topology in a three-dimensional magnetic separator configuration.," Here we also take a simplified approach to consider the local reconnection process, aiming to model the effect of reconnection on the field topology in a three-dimensional magnetic separator configuration." As discussed in Section 1. such configurations are thought to be likely sites for current sheet formation ancl associated reconnection in the solar atmosphere.," As discussed in Section 1, such configurations are thought to be likely sites for current sheet formation and associated reconnection in the solar atmosphere." To construct our model we (ake advantage of a generic feature of reconnection. namely. the presence of an electric field with a component parallel to the magnetic field in a localised region.," To construct our model we take advantage of a generic feature of reconnection, namely, the presence of an electric field with a component parallel to the magnetic field in a localised region." Such an electric field will. [rom Faradays law. generate a magnetic fIux ring around it.," Such an electric field will, from Faraday's law, generate a magnetic flux ring around it." The flux ring will grow in strength until the reconnection ceases., The flux ring will grow in strength until the reconnection ceases. This situation is illustrated in Figure 2 and can be hither motivated by considering the equation for the evolution of magnetic helicitv., This situation is illustrated in Figure \ref{fig:addstwist} and can be further motivated by considering the equation for the evolution of magnetic helicity. Expressing the electric field. Ei. as (where A is the vector potential for D. lime). we have that the helicity density evolves as In general three-dimensional situations the condition for magnetic reconnection to occur is the existence of isolated regions αἱ which EBz0.," Expressing the electric field, $\mathbf{E}$, as (where $\mathbf{A}$ is the vector potential for $\mathbf{B}$, ), we have that the helicity density evolves as In general three-dimensional situations the condition for magnetic reconnection to occur is the existence of isolated regions at which ${\bf E}\cdot {\bf B} \neq 0$." Such regions act as source terms for magnetic helicity (see the right-hand side of Equation 1)) thus imparting a localised twist (to the eonfiguration al à reconnection site., Such regions act as source terms for magnetic helicity (see the right-hand side of Equation \ref{eq:helicityevolution}) ) thus imparting a localised twist to the configuration at a reconnection site. We mav investigate the effect (hal reconnection has on a certain magnetic field topology bv determining the effect of additional localised (wist within the configuration., We may investigate the effect that reconnection has on a certain magnetic field topology by determining the effect of additional localised twist within the configuration. Adding any new field component in a manner consistent wilh Maxwell's equations provides a basis [or realistic field modifications., Adding any new field component in a manner consistent with Maxwell's equations provides a basis for realistic field modifications. Although the question of which states could be accessed in a ονπας evolution is outwith the scope of the model. comparison of results with large-scale," Although the question of which states could be accessed in a dynamic evolution is outwith the scope of the model, comparison of results with large-scale" Qualitatively it may be predicted that the mid-infrared emission from very small grains is relatively suppressed if the grain growth in clouds is activated.,Qualitatively it may be predicted that the mid-infrared emission from very small grains is relatively suppressed if the grain growth in clouds is activated. However. it is hard to quantitatively predict the galaxy-scale observational features caused by the grain growth in clouds because it is difficult to selectively see the clouds. where grain growth is occurring.," However, it is hard to quantitatively predict the galaxy-scale observational features caused by the grain growth in clouds because it is difficult to selectively see the clouds, where grain growth is occurring." Since observations of galactic spectral energy distribution inevitably include the emission from diffuse medium. other mechanisms modifying the grain size distribution such as shattering and coagulation are also reflected in the observed emission from grains.," Since observations of galactic spectral energy distribution inevitably include the emission from diffuse medium, other mechanisms modifying the grain size distribution such as shattering and coagulation are also reflected in the observed emission from grains." Indeed. Gallianoetal.(2005) show that the grain size distribution is biased toward smaller grains in some dwarf galaxies. which may be interpreted as the efficient grain processing in diffuse medium.," Indeed, \citet{galliano05} show that the grain size distribution is biased toward smaller grains in some dwarf galaxies, which may be interpreted as the efficient grain processing in diffuse medium." " Such a variety will be investigated in the future with a consistent treatment of a nonlinear combination between the small grain production by shattering and sputtering and the grain growth by accretion and coagulation,", Such a variety will be investigated in the future with a consistent treatment of a nonlinear combination between the small grain production by shattering and sputtering and the grain growth by accretion and coagulation. We have formulated and investigated the grain growth rate by accretion in interstellar clouds., We have formulated and investigated the grain growth rate by accretion in interstellar clouds. The formalism is applicable to any grain size distribution., The formalism is applicable to any grain size distribution. We have found that the grain size distribution is really fundamental in regulating the grain growth rate., We have found that the grain size distribution is really fundamental in regulating the grain growth rate. We have also implemented the formulation of grain growth in individual clouds into the chemical evolution models of entire galaxies., We have also implemented the formulation of grain growth in individual clouds into the chemical evolution models of entire galaxies. We have found that the metallicity level where the grain growth in clouds becomes dominant strongly depends on the grain size distribution., We have found that the metallicity level where the grain growth in clouds becomes dominant strongly depends on the grain size distribution. If the significant fraction of the grains have radii Z0.01pum or the grain size distribution is described as power law with r=3.5. the large grain abundance at the sub-solar metallicity level is naturally explained by the grain growth in clouds because the surface-to-volume ratio of the grains is large enough.," If the significant fraction of the grains have radii $\la 0.01~\micron$ or the grain size distribution is described as power law with $r\ga 3.5$, the large grain abundance at the sub-solar metallicity level is naturally explained by the grain growth in clouds because the surface-to-volume ratio of the grains is large enough." The grain growth should be efficient in galaxies whose metallicity is above Z.. estimated in Section 5.2.., The grain growth should be efficient in galaxies whose metallicity is above $Z_\mathrm{cr}$ estimated in Section \ref{subsec:Zcr}. Our formulation for the grain growth is applicable to any grain size distribution and is implemented straightforwardly into any framework of chemical enrichment models., Our formulation for the grain growth is applicable to any grain size distribution and is implemented straightforwardly into any framework of chemical enrichment models. We are grateful to the referee. A. P. Jones. for useful comments. which improved the discussion in this paper very much.," We are grateful to the referee, A. P. Jones, for useful comments, which improved the discussion in this paper very much." We thank A. K. Inoue for helpful discussions on dust evolution in galaxies., We thank A. K. Inoue for helpful discussions on dust evolution in galaxies. H.H. is supported by NSC grant 99-2][2-M-001-006-MY3., H.H. is supported by NSC grant 99-2112-M-001-006-MY3. pholoclissociated IENCO molecule towards a sample of galaxies (Martínetal.2003) showed the non-detection of IINCO in 882. at a very low abundance limit.,"photodissociated HNCO molecule towards a sample of galaxies \citep{Martin08} showed the non-detection of HNCO in 82, at a very low abundance limit." This low IINCO abundance supports the scenario that the PDR. chemistry dominates (he molecular composition of the ISM in (his galaxy., This low HNCO abundance supports the scenario that the PDR chemistry dominates the molecular composition of the ISM in this galaxy. However. from the INCO measured abundance in 2253. 1 would be placed in an intermediate stage of evolution where photodissociation should be starting to plav a significant role in driving a UV-dominated chemistry which has nol been vet identified towards this galaxy.," However, from the HNCO measured abundance in 253, it would be placed in an intermediate stage of evolution where photodissociation should be starting to play a significant role in driving a UV-dominated chemistry which has not been yet identified towards this galaxy." The presence of a significant PDR component in 2253 claimed from the IINCO abundance is also inferred [rom the similar intensity of the atomic fine structure line intensities Irom PDR. tracers like CIL and OL 1996). observed in both S82 and 2253.," The presence of a significant PDR component in 253 claimed from the HNCO abundance is also inferred from the similar intensity of the atomic fine structure line intensities from PDR tracers like CII and OI \citep{Carral94,Lord96} observed in both 82 and 253." In this paper we present the first detection of PDR molecular tracers anc and confirm the detection IICO (tentativelvdetectedbySage&Ziurys1995) in the central region of 2253 which allows the evaluation of the influence of the photoclissociation radiation in the nuclear ISM of this SB &alaxy.," In this paper we present the first detection of PDR molecular tracers $^+$ and $^+$, and confirm the detection HCO \citep[tentatively detected by][]{Sage95} in the central region of 253 which allows the evaluation of the influence of the photodissociation radiation in the nuclear ISM of this SB galaxy." The results presented here support the scenario of the presence of a significant PDR component and clearly show the potential of molecular complexity in estimating (he contribution of the different heating mechanisms of ihe ISM in the nuclei of galaxies., The results presented here support the scenario of the presence of a significant PDR component and clearly show the potential of molecular complexity in estimating the contribution of the different heating mechanisms of the ISM in the nuclei of galaxies. The observations presented in this paper were carried out at the IRAM 30mm and JCAIT telescopes on Pico Veleta. Spain. and \lamna hea. USA. respectively.," The observations presented in this paper were carried out at the IRAM m and JCMT telescopes on Pico Veleta, Spain, and Mauna Kea, USA, respectively." The IRAAI mam observations were performed in svannmetrical wobbler switched mode, The IRAM m observations were performed in symmetrical wobbler switched mode It is interesting {ο note that the result on the restriction of the form lor 5(0) coincides almost with the possible forms that can occur in potential scattering. see [AlN]..,"It is interesting to note that the result on the restriction of the form for $S(0)$ coincides almost with the possible forms that can occur in potential scattering, see \cite{AK}." " More precisely. only the case S(O)=(1"",) cannot occur."," More precisely, only the case $S(0)=\left(\begin{smallmatrix} 1 & 0 \\ 0 & -1 \end{smallmatrix}\right)$ cannot occur." Itis found that det(5(0))——]i dH does not admit a resonance al energv zero., Itis found that $\det\big(S(0)\big)=-1$ if $H$ does not admit a resonance at energy zero. This is referred (to as the generic case (g.c.)., This is referred to as the generic case (g.c.). In this case we thus have wy=—4., In this case we thus have $w_1=-\frac{1}{2}$. The so-called exceptional case (e.c.), The so-called exceptional case (e.c.) corresponds to det(5(0))=| and occurs when such a zero energy resonance exists., corresponds to $\det\big(S(0)\big)=1$ and occurs when such a zero energy resonance exists. " Thus. taking into account that D4—D,=I one obtains from In particular. the correction term —7 corresponds to wy."," Thus, taking into account that $\Gamma_3 = \Gamma_4=1$ one obtains from In particular, the correction term $-\nu$ corresponds to $w_1$." This result is in accordance with the literature Sal., This result is in accordance with the literature . "redshifted IL, |[N 11] emission bleud.",redshifted $_\alpha$ +[N ] emission blend. A broad IL; emission liuc. as well as |O 1) ABOUT. narrow forbidden lines aud possibly a broad Te ADSTS enüssion are also detected.," A broad $_\beta$ emission line, as well as [O ] $\lambda$ 5007 narrow forbidden lines and possibly a broad He $\lambda$ 5875 emission are also detected." All of these features have a redshift + = ΙΞΕΟ 01., All of these features have a redshift $z$ = $\pm$ 0.001. " The presence of these cuiissious muplv that this source is a Type 1 Sevfert galaxy according to. ο,οι, the classification of Osterbrock (1989)."," The presence of these emissions imply that this source is a Type 1 Seyfert galaxy according to, e.g., the classification of Osterbrock (1989)." Assuming the cosimology described above. this redshift micas ao hunduositv distance of 112. Alpe for 2E 1553.71153 and ταν huuiuosities of 4100 ere st aud <1 — CresDULCES lin the 0.12 keV and 20100 keV bands. respecively.," Assuming the cosmology described above, this redshift means a luminosity distance of 412 Mpc for 2E 1853.7+1534 and X-ray luminosities of $\times$ $^{43}$ erg $^{-1}$ and $\times$ $^{44}$ erg $^{-1}$ in the 0.1–2 keV and 20–100 keV bands, respectively." Analogously. this distance implies au absolute optical B-baud maeuitude Mp~ 35 mag.," Analogously, this distance implies an absolute optical $B$ -band magnitude $_B \sim$ $-$ 23.5 mag." This is. strictly speaking. an actual lower init to the DB-baud huuimostyv of 2E 1553.7|1531. as no absorption internal to the AGN host HHgalaxy was considered.," This is, strictly speaking, an actual lower limit to the $B$ -band luminosity of 2E 1853.7+1534, as no absorption internal to the AGN host galaxy was considered." However. substantial intrinsic reddeuiug is not expected im Sevtert 1 ealaxies. so we can confidently cousider this value for Mg as close to the real one.," However, substantial intrinsic reddening is not expected in Seyfert 1 galaxies, so we can confidently consider this value for $_B$ as close to the real one." All of these luninosity estimates place 2E 1853.7|1531 at the bright end of the Sevfert 1 ealaxies distribution (Perola et al., All of these luminosity estimates place 2E 1853.7+1534 at the bright end of the Seyfert 1 galaxies distribution (Perola et al. 2002)., 2002). Next. following IKaspi et al. (," Next, following Kaspi et al. (" 2000) and Wu et al. (,2000) and Wu et al. ( 2001). we cau compute an estimate of the mass of the central black hole in this active galaxy.,"2004), we can compute an estimate of the mass of the central black hole in this active galaxy." This cau be achieved using (1) the fux of the IL; cussion Gu Table 2). corrected considering a foreground Calactie color excess ΓΡ. V)-091 (Schlegel et al.," This can be achieved using (i) the flux of the $_\beta$ emission (in Table 2), corrected considering a foreground Galactic color excess $E(B-V)$ = 0.94 (Schlegel et al." 1998) aud Gi) a broad-line region gas velocity epum~ (v{3/2 )\epwiap ~ 1200 lius 1 Gvhere erway ~ 1800 lan | is the velocity measured from the ENIIML of the IL; emission line).," 1998) and (ii) a broad-line region gas velocity $v_{\rm BLR} \sim$ $\sqrt{3}$ $\cdot$$v_{\rm FWHM}$ $\sim$ 4200 km $^{-1}$ (where $v_{\rm FWHM}$ $\sim$ 4800 km $^{-1}$ is the velocity measured from the FWHM of the $_\beta$ emission line)." From Eq. (, From Eq. ( 2) of Wu et al. (,2) of Wu et al. ( 2001) we find that the BLR size is Ropec SL light-davs.,"2004) we find that the BLR size is $R_{\rm BLR} \sim$ 54 light-days." Furthermore. using Eq. (," Furthermore, using Eq. (" 5) of Kaspi ct al. (,5) of Kaspi et al. ( 2000). the AGN black. hole mass in 2E 1853.7|153 bis Mpo LES 109 AL...,"2000), the AGN black hole mass in 2E 1853.7+1534 is $M_{\rm BH} \sim$ $\times$ $^{8}$ $M_\odot$." Again. this is a lower luüt (but likely close to the real value for the reasous explained above) as no absorption intrinsic to the AGN was accountedt for.," Again, this is a lower limit (but likely close to the real value for the reasons explained above) as no absorption intrinsic to the AGN was accounted for." Analogously to the Case of the LEDA 170191 (Sect., Analogously to the case of the LEDA 170194 (Sect. 1.1). the spectrmm of the putative counterpart to ICR JL9L73|1152 (Fig.," 4.1), the spectrum of the putative counterpart to IGR J19473+4452 (Fig." " 2. lower left) shows several narrow cinission lines. which we identified as [O nu] A3727. Πο. |O mj AAL958.5007. IL,.. [N uf AGSS3. and [S. 11J AAGTIG.6731."," 2, lower left) shows several narrow emission lines, which we identified as [O ] $\lambda$ 3727, $_\beta$, [O ] $\lambda\lambda$ 4958,5007, $_\alpha$, [N ] $\lambda$ 6583, and [S ] $\lambda\lambda$ 6716,6731." All of these eiiissiou features lic at a redshif 2 = (0.0532350.001. consistent with Sazonov et al. (," All of these emission features lie at a redshift $z$ = $\pm$ 0.001, consistent with Sazonov et al. (" 2005).,2005). Iu this case also. the exclusive presence of narrow enission lines iu the spectra of he optical counterpar to ICR J19173|L152 poiuts to the fact that they originate within a Narrow-Line Reeion of an ACN.," In this case also, the exclusive presence of narrow emission lines in the spectrum of the optical counterpart to IGR J19473+4452 points to the fact that they originate within a Narrow-Line Region of an AGN." A coufirmation of this comes by examine the diagnostic line ratios of Ilo et al. (, A confirmation of this comes by examining the diagnostic line ratios of Ho et al. ( 1993. 1997).,"1993, 1997)." " These. [N ΠΠ, = 0.210.083. [S ΠΠ, = 0.3040.06 and. [O m/s; = 11.22.39. place TOR J19173|1152 amone Sevfert 2 ACGNs."," These, [N $_\alpha$ = $\pm$ 0.03, [S $_\alpha$ = $\pm$ 0.06 and [O $_\beta$ = $\pm$ 2.3, place IGR J19473+4452 among Seyfert 2 AGNs." To compute the internal reddening of this galaxy. we again use the procedure described iu Sect.," To compute the internal reddening of this galaxy, we again use the procedure described in Sect." 3.1., 3.1. We find that the ΕΠ.) flux ratio. once corrected for the Calactic absorption £(BVP) = 020 1nae (according to Schlegel et al.," We find that the $_\alpha$ $_\beta$ flux ratio, once corrected for the Galactic absorption $E(B-V)$ = 0.20 mag (according to Schlegel et al." 1998). is 1.59: this indicates a rest-frame internal color excess E(BWy) = 0.18 mae for IGR JL9173|£152.," 1998), is 4.59; this indicates a rest-frame internal color excess $E(B-V)$ = 0.48 mag for IGR J19473+4452." We uote that the total reddening estimate along the Lue of sight corresponds. using the empirical formmla of Predehl Schinitt (1995). to a neutral hydrogen column density ΑΠm [x lo?! 2. that is ~30 times less than the Ny ucasure obtained by Sazonov ct al. (," We note that the total reddening estimate along the line of sight corresponds, using the empirical formula of Predehl Schmitt (1995), to a neutral hydrogen column density $N_{\rm H} \approx$ $\times$ $^{21}$ $^{-2}$, that is $\sim$ 30 times less than the $N_{\rm H}$ measure obtained by Sazonov et al. (" 2005) from N-ray data.,2005) from X-ray data. The measured redshift iuplies a luuinesitv distance o this source of 251 Mpc. aud thus Nav. buninosities of 4107 ere 1 aud 1.9<101! erg tin i the 0.5.8 τον and 1760 keV bands. respectively.," The measured redshift implies a luminosity distance to this source of 254 Mpc, and thus X-ray luminosities of $\times$ $^{43}$ erg $^{-1}$ and $\times$ $^{44}$ erg $^{-1}$ in the 0.5–8 keV and 17–60 keV bands, respectively." Using he B-haud optical maenitucde of his object. the abovedistance poiuts o an absolute B inaguitude Mg~ — 223.1 mag.," Using the $B$ -band optical magnitude of this object, the abovedistance points to an absolute $B$ magnitude $_B \sim$ $-$ 23.4 mag." These values place this source in the bright side of the Type 2 Sevtert galaxies luminosity distribution (Risaliti 2002: Sazonov Revuivtsey 2001)., These values place this source in the bright side of the Type 2 Seyfert galaxies luminosity distribution (Risaliti 2002; Sazonov Revnivtsev 2004). Tn the same wav as performed for ICR 1610. we can determine the Compton resnüue for ICR J191731L152.," In the same way as performed for IGR $-$ 1610, we can determine the Compton regime for IGR J19473+4452." Usine the X-ray spectral information of Sazonov et al. (, Using the X-ray spectral information of Sazonov et al. ( 2005). we obtain a 210 keV flux of LOS Pere 2s +.,"2005), we obtain a 2–10 keV flux of $\times$ $^{-12}$ erg $^{-2}$ $^{-1}$." This implies au Norav/[O ttlsouz ratio of ~30. indicating that this source is well iu the Compton-thiu regüuune for Sevfert 2 ealaxies (Bassani ct al.," This implies an X-ray/[O $_{\rm 5007}$ ratio of $\sim$ 30, indicating that this source is well in the Compton-thin regime for Seyfert 2 galaxies (Bassani et al." 1999)., 1999). For IGR 319173|1152 we can calculate. after having taken iuto account the Galactic and intrinsic absorptions. the SER aud inetallicitv of this ealaxy.," For IGR J19473+4452 we can calculate, after having taken into account the Galactic and intrinsic absorptions, the SFR and metallicity of this galaxy." " Again following ]xenuicutt (1998). we determiue a SER of 2.10.2 AL. from the reddenime-corrected IL, lhunuinositv of (2.614018) ϱ ere sf."," Again following Kennicutt (1998), we determine a SFR of $\pm$ 0.2 $M_\odot$ $^{-1}$ from the reddening-corrected $_\alpha$ luminosity of $\pm$ $\times$ $^{41}$ erg $^{-1}$." " The method (again im I&eunicutt L998) which imstead uses the extiuction-corrected [O 1| huninosity: (5.341.3) «107 ere s+. gives a SRE of 743 A d. which is larger than. but still coniedsten with (at the coufideuce level) that derived using the IL, eunissionu line fiux."," The method (again in Kennicutt 1998) which instead uses the extinction-corrected [O ] luminosity, $\pm$ $\times$ $^{42}$ erg $^{-1}$, gives a SRF of $\pm$ 3 $M_\odot$ $^{-1}$, which is larger than, but still consistent with (at the confidence level) that derived using the $_\alpha$ emission line flux." Aloreover. the detection of |O tm). |O rij aud IL; also allows us to infer the gaseous oxvgeon abundance of this ealaxv.," Moreover, the detection of [O ], [O ] and $_\beta$ also allows us to infer the gaseous oxygen abundance of this galaxy." Iu this occurrence also. the application of the Ixobuluicky et al," In this occurrence also, the application of the Kobulnicky et al." s (1999) method προς a basically solar oxveen abundance.,'s (1999) method implies a basically solar oxygen abundance. " Similar results are obtained using the [N /IL, flux ratio method Usewley Dopita 2002),", Similar results are obtained using the [N $_\alpha$ flux ratio method (Kewley Dopita 2002). Suniumeg up all the knowledge available in the literature. αἲ present (November 2005) 16 unkuown or uewly-discovered sources were ideutified byw meaus of optical spectroscopy.," Summing up all the knowledge available in the literature, at present (November 2005) 16 unknown or newly-discovered sources were identified by means of optical spectroscopy." These are 2 LALINBs (Paper E Roclots et al., These are 2 LMXBs (Paper I; Roelofs et al. 2001). 7 TIAINBs (this work: Reig et al.," 2004), 7 HMXBs (this work; Reig et al." 2005: Ialperun, 2005; Halpern of 197is therefore. highly unusual.,of is therefore highly unusual. The clear trend seen over timescales of davs and weeks suggests that this is a relatively slow process., The clear trend seen over timescales of days and weeks suggests that this is a relatively slow process. Distinguishing between the possibilities as to whether this is related. to changes in the magnetic field structure. or to precessional ellects. or to the fact that the PA swing is not rellecting the geometry of the svstem after. all anc that. propagation ellects in the magnetosphere or non-cipolar field components are involved. is cillieult.," Distinguishing between the possibilities as to whether this is related to changes in the magnetic field structure, or to precessional effects, or to the fact that the PA swing is not reflecting the geometry of the system after all and that propagation effects in the magnetosphere or non-dipolar field components are involved, is difficult." However. there are a number of observed. properties which indeed. suggest the existence of severe propagation cllects in the magnetosphere: (a) we see distinct. polarization modes which change with racio frequeney and time: (b) we see a laree variety of PA values in the LP region: (ο) we have indications of a conversion of linear into circular power for certain pulse longitude ranges (d) we see interesting wiggles in the PA slopes which are hard to explain by a any geometrical model and (ο) even the changing Ilux density spectrum of the individual ALP and LP components could be due to propagation elfects.," However, there are a number of observed properties which indeed suggest the existence of severe propagation effects in the magnetosphere: (a) we see distinct polarization modes which change with radio frequency and time; (b) we see a large variety of PA values in the IP region; (c) we have indications of a conversion of linear into circular power for certain pulse longitude ranges (d) we see interesting wiggles in the PA slopes which are hard to explain by a any geometrical model and (e) even the changing flux density spectrum of the individual MP and IP components could be due to propagation effects." Endeed. the magnetosphere is much Larger than that of a tvpical racio pulsar. and the range of inferred magnetic field. strengths encountered [rom the surface (D.=2.610 Gauss) to the lisht-cvlinder (2=14 Gauss) is certainly. enormous. covering 13 orders of magnitude and hence giving scope for a large variety of effects.," Indeed, the magnetosphere is much larger than that of a typical radio pulsar, and the range of inferred magnetic field strengths encountered from the surface $B=2.6\times10^{14}$ Gauss) to the light-cylinder $B=14$ Gauss) is certainly enormous, covering 13 orders of magnitude and hence giving scope for a large variety of effects." Despite the likelihood. of magnetospherie propagation ellects. it is tempting to associate the deviations from an like swing (and the inability to find a single set of rotating-vector-niodel parameters that connects both the ALP and LP with a satisfactory fit) with deviations from a cdipolar field structure.," Despite the likelihood of magnetospheric propagation effects, it is tempting to associate the deviations from an S-like swing (and the inability to find a single set of rotating-vector-model parameters that connects both the MP and IP with a satisfactory fit) with deviations from a dipolar field structure." We also note that the separation of the IP from he ALP is quite dilferent from the 180 deg expected in a wo-pole model. and that the emission properties of the LP are rather different from. those of the ALP. supporting the interpretation of detecting signatures of non-dipolar field ines.," We also note that the separation of the IP from the MP is quite different from the 180 deg expected in a two-pole model, and that the emission properties of the IP are rather different from those of the MP, supporting the interpretation of detecting signatures of non-dipolar field lines." Indeed. within the magnetar model a dipolar field structure is not necessarily expected.," Indeed, within the magnetar model a dipolar field structure is not necessarily expected." Similar. arguments iive been put forward to explain some of the polarization and. profile properties of milliseconcl pulsars (c.g. Nilouris et al., Similar arguments have been put forward to explain some of the polarization and profile properties of millisecond pulsars (e.g. Xilouris et al. where the evolutionary history of the sources may dead to non-dipolar and sun-spot-like field structures (Ruderman 1991)., \nocite{xkj+98} where the evolutionary history of the sources may lead to non-dipolar and sun-spot-like field structures (Ruderman \nocite{rud91}. . Llowever. depending on the emission wight and hence the physical separation from the field's multipole components. their actual impact in the emission region mav actually be low. although they may allect the asma Low from the surface and hence the observed. racio o»operties.," However, depending on the emission height and hence the physical separation from the field's multipole components, their actual impact in the emission region may actually be low, although they may affect the plasma flow from the surface and hence the observed radio properties." The relative shallowness of the PA swing under he AIP with a slope of only degfdeg is not uncommon for pulsars whereas the PA evolution with epoch certainly is., The relative shallowness of the PA swing under the MP with a slope of only 1 deg/deg is not uncommon for pulsars whereas the PA evolution with epoch certainly is. [H0 ds interesting to compare the properties of with those of voung pulsars. as the characteristic age of 197is less than 10.000 vears.," It is interesting to compare the properties of with those of young pulsars, as the characteristic age of is less than 10,000 years." Johnston Weisberg studied 14 voung pulsars with characteristic ages less than 75 kyr and found. that generally pulse profiles are simple ancl consist of either one or two prominent components whereas the linearly. polarized fraction is nearly always in excess of 70 per cent., Johnston Weisberg \nocite{jw06} studied 14 young pulsars with characteristic ages less than 75 kyr and found that generally pulse profiles are simple and consist of either one or two prominent components whereas the linearly polarized fraction is nearly always in excess of 70 per cent. The latter characteristic is certainly true for but the profile is clearly anything but simple. nor does the trailing component dominate. as Welsberg Johnston (2006) also find. on average. for voung pulsars.," The latter characteristic is certainly true for but the profile is clearly anything but simple, nor does the trailing component dominate, as Weisberg Johnston (2006) also find, on average, for young pulsars." The flat. PA curve could be both explained either by an aligned configuration in which the spin-axis is aligned with the magnetic field axis. or by a very wide cone which is cut [ar away from the magnetic pole.," The flat PA curve could be both explained either by an aligned configuration in which the spin-axis is aligned with the magnetic field axis, or by a very wide cone which is cut far away from the magnetic pole." The solution for the RVAL fits to the ALP presented in Section 3.5. corresponds to an extremely wide cone grazed at the outside for the AIP (a=44°. —39). with a beam radius inferred from the ALP pulse width of about p44. (," The solution for the RVM fits to the MP presented in Section \ref{sec:rvm} corresponds to an extremely wide cone grazed at the outside for the MP $\alpha=44^\circ$, $\beta=39^\circ$ ), with a beam radius inferred from the MP pulse width of about $\rho\sim 44^\circ$. (" Note that both the AIP and LP are not centred. on the steepest graclient of the fitted RWAL curves.),Note that both the MP and IP are not centred on the steepest gradient of the fitted RVM curves.) In contrast. the inferred. beam radius for the IP is much smaller. p8.," In contrast, the inferred beam radius for the IP is much smaller, $\rho\sim8^\circ$." However. there are some hints of a correlation in strength between the LP and trailing ALP components. so that one could consider both emission features as part of another wide cone.," However, there are some hints of a correlation in strength between the IP and trailing MP components, so that one could consider both emission features as part of another wide cone." In comparison. the radio beam of normal radio pulsars appears to scale with xL1/V/P. whieh would imply a beam radius for of less than 3 deg when measured at a intensity level (Lorimer Ixramer 2005).," In comparison, the radio beam of normal radio pulsars appears to scale with $\propto 1/\sqrt{P}$, which would imply a beam radius for of less than 3 deg when measured at a intensity level (Lorimer Kramer 2005)." Alternatively. with an aligned. configuration. the observer's line-o[-sight may hardly ever leave the emission. cone. also creating a wide pulse width.," Alternatively, with an aligned configuration, the observer's line-of-sight may hardly ever leave the emission cone, also creating a wide pulse width." In any case. if we interprete the RWAL fits &cometricallv. then we have to conclude that we observe two emissions cones. that are centred on dilferent. independent magnetic poles separated. by LOO degrees in. neutron-star longitude.," In any case, if we interprete the RVM fits geometrically, then we have to conclude that we observe two emissions cones, that are centred on different independent magnetic poles separated by 109 degrees in neutron-star longitude." We can interprete that either as an olfset dipole or evidence of a non-dipolar field configuration., We can interprete that either as an offset dipole or evidence of a non-dipolar field configuration. " Phe viewing geometry and the rather different emission properties of the various pulse Components are certainly consistent with this view,", The viewing geometry and the rather different emission properties of the various pulse components are certainly consistent with this view. lt is intriguing that shows variations in its spin-down (Camilo et al., It is intriguing that shows variations in its spin-down (Camilo et al. 2006b). which could be related to changes in the torque and hence the magnetic field structure near the light-evlinder.," 2006b), which could be related to changes in the torque and hence the magnetic field structure near the light-cylinder." LP these torque. changes are related. to the magnetic field. structure changing near the lieht-evlineder. it may also show changes in the emission region.," If these torque changes are related to the magnetic field structure changing near the light-cylinder, it may also show changes in the emission region." In the magnetar model (Duncan Thompson one expects that changes in the magnetic Held may trigger energetic outbursts., In the magnetar model (Duncan Thompson \nocite{dt92a} one expects that changes in the magnetic field may trigger energetic outbursts. This seems to be inconsistent with the observation that no X-ray. variation was seen in recen monitoring observations (Camilo et al., This seems to be inconsistent with the observation that no X-ray variation was seen in recent monitoring observations (Camilo et al. 2006b)., 2006b). " Llowever. Aoloborodov ""Fhompson propose that a plasma corona forms around the neutron star. as à result. of occasional starquakes that twist. the external. magnetic Ποια of the star and. induce. electric currents in the closed. magnetosphere."," However, Beloborodov Thompson \nocite{bt06} propose that a plasma corona forms around the neutron star, as a result of occasional starquakes that twist the external magnetic field of the star and induce electric currents in the closed magnetosphere." 1 such. ellect is present. one could speculate as to whether a combination of twisted fieldlines and changing plasma corona is responsible [or the observed. emission. properties.," If such effect is present, one could speculate as to whether a combination of twisted fieldlines and changing plasma corona is responsible for the observed emission properties." Continuing studies of simultaneous. multi-frequeney data. oller a chance. to indeed. separate changing geometrical/ield-configuration ellects from. propagation ellects., Continuing studies of simultaneous multi-frequency data offer a chance to indeed separate changing geometrical/field-configuration effects from propagation effects. Further such studies are in progress and will be presented. elsewhere., Further such studies are in progress and will be presented elsewhere. the general quantum numbers associated with the molecular group svmmetey EP (Bunker&Jensen1998). (NIL; belongs to D3u((M)) and total angular momentum J. we have used both ‘normal mode? ancl ‘local mode” quantum numbers when labelling the energy levels.,"the general quantum numbers associated with the molecular group symmetry $\Gamma$ \citep{TheBook} $_3$ belongs to (M)) and total angular momentum $J$, we have used both `normal mode' and `local mode' quantum numbers when labelling the energy levels." Our labelling scheme is discussed below., Our labelling scheme is discussed below. The structure of the Transition file is simpler., The structure of the Transition file is simpler. It contains three columns: two give the reference numbers of the upper andl lower states as they appear in the Enerey file ancl third contains the Einstein A cocllicicnt 13 for the transition (sec ‘Table 2))., It contains three columns: two give the reference numbers of the upper and lower states as they appear in the Energy file and third contains the Einstein A coefficient $^{-1}$ ) for the transition (see Table \ref{t:Transit-file}) ). The entries in the Transition files are sorted according to the frequency. and we have split them into 120 small files in order to reduce the amount of data that needs to be handled when examining a specific [frequency region.," The entries in the Transition files are sorted according to the frequency, and we have split them into 120 small files in order to reduce the amount of data that needs to be handled when examining a specific frequency region." In the actual PROVE calculations we emploved οσα mode! basis functions in the FBR representation as explained in detail in Yurchenkoetal.(2009)..., In the actual TROVE calculations we employed `local mode' basis functions in the FBR representation as explained in detail in \citet{NH3-T300K-paper}. This allowed us to label the energy levels and hence to assign transitions based on the particular basis set making the largest contribution within the appropriate eigenfunction., This allowed us to label the energy levels and hence to assign transitions based on the particular basis set making the largest contribution within the appropriate eigenfunction. Our local mode quantum numbers include Ead.Tua. Duns ΠενΓονονπιmq.no.," Our local mode quantum numbers include $\Gamma_{\rm rot}, K, \tau_{\rm rot}$, $\Gamma_{\rm vib}$, $n_1, n_2, n_3, n_4, n_5, n_6$." Here A. ds the projection of total angular momentum onto the molecular svmaimetry axis: nj.mo.nma are stretching local mocde quantum numbers (Mills&Itobiette1985). which correlate with the normal mode notation as mi|monma—£y£e nma and ns are deformational bending quanta: ni is the inversion quantuni number equivalent to 2609.|Tins. where (s is the normal mode quantum number and. zy=606;mod2 is the inversion parity (Yurchenkoetal.2005)..," Here $K$ is the projection of total angular momentum onto the molecular symmetry axis; $n_1,\ n_2,\ n_3$ are stretching local mode quantum numbers \citep{mr85} which correlate with the normal mode notation as $n_1 + n_2 + n_3 = \nu_1 + \nu_3$; $n_4$ and $n_5$ are deformational bending quanta; $n_6$ is the inversion quantum number equivalent to $2 v_2 + \tau_{\rm inv}$, where $v_2$ is the normal mode quantum number and $\tau_{\rm inv} = n_6 \ mod \ 2$ is the inversion parity \citep{MolPhysPaper}." . Finally. Py. and Εναν are the rotational ancl vibrational svmmetries in Da3u((M).," Finally, $\Gamma_{\rm rot}$ and $\Gamma_{\rm vib}$ are the rotational and vibrational symmetries in (M)." Apart from the ‘local mode assignment that is generated by PROVE. we also provide the standard normal mode quantum numbers ey.09.e.AN according with the Herzberg convention (Herzberg 1945)..," Apart from the `local mode' assignment that is generated by TROVE, we also provide the standard normal mode quantum numbers $v_1, v_2, v_3^{l_3}, v_4^{l_4}$, according with the Herzberg convention \citep{Herzberg_45}. ." " e, and vc» are the symmetric stretch and symmetric bend. respectively. whilst ος and ey are the asvmametrie stretch and asymmetric bend respectively."," $v_1$ and $v_2$ are the symmetric stretch and symmetric bend, respectively, whilst $v_3$ and $v_4$ are the asymmetric stretch and asymmetric bend respectively." " Ehe additional quantum numbers /; and £j, are necessary to resolve the degeneraey of the e; and ey vibrational states. respectively."," The additional quantum numbers $l_3$ and $l_4$ are necessary to resolve the degeneracy of the $v_3$ and $v_4$ vibrational states, respectively." " The selection rules which determine the allowed electric dipole transitions of NI; anre AJ—JoJ EEGqp. :1) with. svmmetry selection. rules. As,€»HAs. and Lo""oeE. −∕∕"," The selection rules which determine the allowed electric dipole transitions of $^{14}$ are $\Delta J = J\p-J\pp = 0, \pm 1$ $J\pp+J\p \ge 1$ ) with symmetry selection rules, $A_2\p \leftrightarrow A_2\pp$, and $ E\p \leftrightarrow E\pp$." "⇁We used the nuclear spin. statistical weight [actor gu. = 12 and 6 for the ASes and ££sE"" transitions. respectively."," We used the nuclear spin statistical weight factor $g_{\rm ns}$ = 12 and 6 for the $A_2\p \leftrightarrow A_2\pp$ and $ E\p \leftrightarrow E\pp$ transitions, respectively." The A) and AT levels are characterized by gus=0. that is. the corresponding transitions do not exist.," The $A_1\p$ and $A_1\pp$ levels are characterized by $g_{\rm ns} = 0$, that is, the corresponding transitions do not exist." lt should be noted that our assignments do not always agree with the experimental ones for the following reasons: (i) ambiguous definition of the quantum numbers (apart from J and D). which depend on the basis functions used: (ii) strong interactions between ro-vibrational states of close-Iving levels: ancl (iii) mapping between the normal ancl local mocde labels is not always straightforward.," It should be noted that our assignments do not always agree with the experimental ones for the following reasons: (i) ambiguous definition of the quantum numbers (apart from $J$ and $\Gamma$ ), which depend on the basis functions used; (ii) strong interactions between ro-vibrational states of close-lying levels; and (iii) mapping between the normal and local mode labels is not always straightforward." The last of these means that it is sometimes dillicult to distinguish between the svmmetric and asvmimoetric stretch quantum numbers ej ancl ey., The last of these means that it is sometimes difficult to distinguish between the symmetric and asymmetric stretch quantum numbers $v_1$ and $v_3$. Absorption and emission intensity simulations are temperature-dependent., Absorption and emission intensity simulations are temperature-dependent. Specifically. temperature appears in the Boltzmann factorsexp(EZET). where & is the Boltzmann constant.," Specifically, temperature appears in the Boltzmann factors $\exp(-E/ kT)$, where $k$ is the Boltzmann constant." Line lists. in contrast. do not specify a temperature. since the Einstein coefficients for the transitions are independent of temperature.," Line lists, in contrast, do not specify a temperature, since the Einstein coefficients for the transitions are independent of temperature." We thereforeneed to explain why we refer to BYTe as a hot list., We thereforeneed to explain why we refer to BYTe as a `hot' list. Phe reason is that DYIe is able to describe the absorption/emission processes in, The reason is that BYTe is able to describe the absorption/emission processes in relation. cuabling more precise estimates of oy.,"relation, enabling more precise estimates of $\sigma_8$." It may be that other cluster scaliugs cau be effectively combined to reduce the error on additional cosiiological parametor estimates., It may be that other cluster scalings can be effectively combined to reduce the error on additional cosmological parameter estimates. JALC. acknowledgcs support of this work bv a National Science Foundation Cradnuate Research Fellowship., J.M.C. acknowledges support of this work by a National Science Foundation Graduate Research Fellowship. The work of L.A.NL was carried out at the Jet Propulsion Laboratory. California Lhustitute of Technology. with the support of NASA ATEPOS-0169.," The work of L.A.M. was carried out at the Jet Propulsion Laboratory, California Institute of Technology, with the support of NASA ATFP08-0169." D.N. would like to thaul the Radcliffe Institute for Advanced Study and the Ceuter for Astrophysics (CEA) for providing an intellectually stimulating atimosphere that enabled this work., P.N. would like to thank the Radcliffe Institute for Advanced Study and the Center for Astrophysics (CfA) for providing an intellectually stimulating atmosphere that enabled this work. The (SKA) is the next generation radio telescope facility for the 21st century.,The (SKA) is the next generation radio telescope facility for the 21st century. Although it is still in the design stage and unlikely to be fully operational before 2020. various pathfinder experiments will enter scientific service around 2010: one of these pathtinders will probably form the nucleus of the eventual SKA and over the next decade grow in sensitivity from «1 to 1060 per cent SKA.," Although it is still in the design stage and unlikely to be fully operational before 2020, various pathfinder experiments will enter scientific service around 2010; one of these pathfinders will probably form the nucleus of the eventual SKA and over the next decade grow in sensitivity from $<1$ to 100 per cent SKA." The scientific goals of the SKA have been deseribed at length elsewhere (see e.g. Carilli Rawlings 2004). but it is now clear that à new generation of more sophisticated science simulations is needed to optimise the design of the new telescopes and their observing programmes for the efficient realisation of these goals.," The scientific goals of the SKA have been described at length elsewhere (see e.g. Carilli Rawlings 2004), but it is now clear that a new generation of more sophisticated science simulations is needed to optimise the design of the new telescopes and their observing programmes for the efficient realisation of these goals." With this in mind. we present here a new semi-empirical simulation of the extragalactic radio continuum sky.," With this in mind, we present here a new semi-empirical simulation of the extragalactic radio continuum sky." The simulation is part of a suite of simulations developed under the European SKA Design Study (SKADS) initiative and referred to collectively as(, The simulation is part of a suite of simulations developed under the European SKA Design Study (SKADS) initiative and referred to collectively as. 5°). Πες one oftwo simulations aimed at simulating the extragalactic continuum and line-emitting radio sky. which together offer distinet vet complementary approaches to modelling the radio sky.," It is one of two simulations aimed at simulating the extragalactic continuum and line-emitting radio sky, which together offer distinct yet complementary approaches to modelling the radio sky." The first approach. used by the simulations described in this paper. may be best described as ‘semi-empirical’. in the sense that the simulated sources are generated by sampling the observed tor extrapolated) radio continuum luminosity functions.," The first approach, used by the simulations described in this paper, may be best described as `semi-empirical', in the sense that the simulated sources are generated by sampling the observed (or extrapolated) radio continuum luminosity functions." The second, The second In (his contribution we have discussed several issues that affect many voung scientists entering the field.,In this contribution we have discussed several issues that affect many young scientists entering the field. can be efficiently accessed [rom local disks.,can be efficiently accessed from local disks. Clearly. this approach generates a variable nunber of mapper objects depeucdiug ou the structure of the input sequence file.," Clearly, this approach generates a variable number of mapper objects depending on the structure of the input sequence file." In the case of uustructured sequence files. the FITS files relevant to a giveu query are scattered. throughout the sequeuce file database whereas in the case of structured sequence files. the relevant FITS files are more tightly packed.," In the case of unstructured sequence files, the FITS files relevant to a given query are scattered throughout the sequence file database whereas in the case of structured sequence files, the relevant FITS files are more tightly packed." Thus. greater data locality is achieved in the assiguiment of FITS files to iuappers in the structured. case aid fewer mapper objects are required.," Thus, greater data locality is achieved in the assignment of FITS files to mappers in the structured case and fewer mapper objects are required." To complete our understaucdiug ol the differeuce in ruuniug times we must further consider the maxiuum number of mapper objects that the cluster cau sustain simultaneously., To complete our understanding of the difference in running times we must further consider the maximum number of mapper objects that the cluster can sustain simultaneously. Since a mapper represents a conceptual unit of computation. it corresponds to — or directly relies upon — a processor core in order to operate.," Since a mapper represents a conceptual unit of computation, it corresponds to — or directly relies upon — a processor core in order to operate." Therefore. the number of simultaueously sustainable mapper objects for a Hadoop job is limited by he number of cores available ou the entire cluster?.," Therefore, the number of simultaneously sustainable mapper objects for a Hadoop job is limited by the number of cores available on the entire cluster." . In our case. this value is about 800.," In our case, this value is about 800." " We can low see one [fuudamental problem with the unstructured case: not all of the 1711 mappers could ""un slinultaneously: some could uot begin processing until after others had completed their own oocessing.", We can now see one fundamental problem with the unstructured case: not all of the 1714 mappers could run simultaneously; some could not begin processing until after others had completed their own processing. This limitation was uot true in tlie case of structured sequence files where only 338 slots were required aud they could all run simultaneously., This limitation was not true in the case of structured sequence files where only 338 slots were required and they could all run simultaneously. However. oue might actually predict superior yerformance from the uustructured case for the simple [act that it beuelits [rom 800x. parallelism while the structured case ouly benefits from 338s parallelisin.," However, one might actually predict superior performance from the unstructured case for the simple fact that it benefits from 800x parallelism while the structured case only benefits from 338x parallelism." We theorize that the explanation lor why such behavior was not observed lies tn the nonneelieible startup cost of launchiug a mapper object. there is a genuine beuelit in reusing mappers aud there must be some tipping polut in this tradeoll where the beuelit of additional parallelisin is outweighed by the cost of creating mappers for brief computational ueeds.," We theorize that the explanation for why such behavior was not observed lies in the nonnegligible startup cost of launching a mapper object, there is a genuine benefit in reusing mappers and there must be some tipping point in this tradeoff where the benefit of additional parallelism is outweighed by the cost of creating mappers for brief computational needs." This work presented our implemeutation aud evaluation ofimage coacddition within the MapRecduce cdata-processiug framework using Hadoop., This work presented our implementation and evaluation of image coaddition within the MapReduce data-processing framework using Hadoop. We investigated five possible methods of implementation with the latter methocs desigued to improve upon the earlier inetlods., We investigated five possible methods of implementation with the latter methods designed to improve upon the earlier methods. Our first του of experiments processed a dataset containiug 100.000 individual FITS files.," Our first round of experiments processed a dataset containing 100,000 individual FITS files." Despite the use of a prefilteriug mechanism to decrease the iuput size. this method vielded poor performance due to the job initialization costs.," Despite the use of a prefiltering mechanism to decrease the input size, this method yielded poor performance due to the job initialization costs." To decrease the initialization time we must process a dataset consistiug of fewer actual files. but obviously without altering the underlyiug data.," To decrease the initialization time we must process a dataset consisting of fewer actual files, but obviously without altering the underlying data." This eoal is achieved through the use of sequence files which group iudividual files together., This goal is achieved through the use of sequence files which group individual files together. Sequence files are olfered through the Hadoop API [or precisely this purpose., Sequence files are offered through the Hadoop API for precisely this purpose. Our nest rouud of experiments considered sequence files which were grouped in au uustructured manner aud which therelore could uot be preliltered., Our next round of experiments considered sequence files which were grouped in an unstructured manner and which therefore could not be prefiltered. Despite this weakuess relative to the first, Despite this weakness relative to the first resistivity near the mid-pluie is huge enough to cause some damping of AIRT turbulence but not sufficiently aree to completely quench the turbuleuce. resulti in episodic bursts of mid-plane turbulence resenibli he coustaut resistivity ruus of Simonetal.(2011).,"resistivity near the mid-plane is large enough to cause some damping of MRI turbulence but not sufficiently large to completely quench the turbulence, resulting in episodic bursts of mid-plane turbulence resembling the constant resistivity runs of \cite{simon11}." . This dramatic variability results from the compctition )etween Olunic damping of MRI turbulence and t shearing of residual racial field iuto toroidal field sufficient streneth to reactivate the turbulence., This dramatic variability results from the competition between Ohmic damping of MRI turbulence and the shearing of residual radial field into toroidal field of sufficient strength to reactivate the turbulence. Finally. he third shearing box is ceutered on Ry5OAU aud las sustained turbulence throughout the domain as the resistivity is uot large enough to camp out the MBI.," Finally, the third shearing box is centered on $R_0 = 50 {\rm AU}$ and has sustained turbulence throughout the domain as the resistivity is not large enough to damp out the MRI." Thus. we have three ditfereut plivsical regimes for MRI-driven turbulence: one that rescuables the classic lavered accretion model (Caunmue1996).. one that is relatively close to ideal MIID. and one intermediate regine that leads to large amplitude variability iu turbulence levels.," Thus, we have three different physical regimes for MRI-driven turbulence: one that resembles the classic layered accretion model \citep{gammie96}, one that is relatively close to ideal MHD, and one intermediate regime that leads to large amplitude variability in turbulence levels." We should note that the radial locations of these regimes are subject to some uncertainty eiven the particular disk model that we have adopted., We should note that the radial locations of these regimes are subject to some uncertainty given the particular disk model that we have adopted. " If we adopted another model, such as a coustaut à disk model for example. then we may find the radial locatious of our three regimes would be different."," If we adopted another model, such as a constant $\alpha$ disk model for example, then we may find the radial locations of our three regimes would be different." " Finally, as oue of our goals in this work ids to explore how sensitive our derived turbulent velocity distributious are to the underlying mechauisi for eenecratiue turbulence. wei have also run forced turbulence lyvdrodvuamic sheave boxes."," Finally, as one of our goals in this work is to explore how sensitive our derived turbulent velocity distributions are to the underlying mechanism for generating turbulence, we have also run forced turbulence hydrodynamic shearing boxes." " These ruus are also isothermal. vertically stratified with an initially exponential deusitv profile (Equation 1)). aud have the same values for p,. ος, aud Q."," These runs are also isothermal, vertically stratified with an initially exponential density profile (Equation \ref{density_init}) ), and have the same values for $\rho_o$, $\cs$, and $\Omega$." " In these cases. we do not evolve the induction equation (B.— 0). aud we instead add a force to the 1nomenutuim equation. where KR.ἐπL,. ky= kk Sa/L.. and Ais the amplitude of the forcing."," In these cases, we do not evolve the induction equation ${\bmath B} = 0$ ), and we instead add a force to the momentum equation, where $k_x = 4\pi/L_x$, $k_y = 8\pi/L_y$, $k_z = 8\pi/L_z$ , and $A$ is the amplitude of the forcing." " πμ.Thisforcing is oulv applied. for κΠΠ, ", Thisforcing is only applied for $|z| \le 2 H$. "We have produced two of these calculations. oue with 4210? aud oue with --10 3, "," We have produced two of these calculations, one with $A = 10^{-3}$ and one with $A = 10^{-4}$ ." These calculations were performed at a resolution of 36 zones per JF and at a comain size of HT.«SIT.51., These calculations were performed at a resolution of 36 zones per $H$ and at a domain size of $4H\times8H\times8H$. Evolving the MIID simulations becomes difficult if there are magnetized regions of very low deusitv. where a laree Alfvén speed results in a small timestep.," Evolving the MHD simulations becomes difficult if there are magnetized regions of very low density, where a large $\alf$ speed results in a small timestep." Moreover. errors in enerev make it hard to evolve regious of very stroug field relative to eas pressure without cucounterine munerical problems.," Moreover, errors in energy make it hard to evolve regions of very strong field relative to gas pressure without encountering numerical problems." To avoid these problems. we apply a density floor at a level of 10.| of the initial mid-plane density throughout the physical domain in our MIID simulations.," To avoid these problems, we apply a density floor at a level of $10^{-4}$ of the initial mid-plane density throughout the physical domain in our MHD simulations." " We also iuchide a deusitv floor iui our hivdro simulations, which we set to 10."," We also include a density floor in our hydro simulations, which we set to $10^{-8}$." The hvdrodyiiuuic floor can be much lower since there is uo Alfvén speed restriction on the timestep., The hydrodynamic floor can be much lower since there is no $\alf$ speed restriction on the timestep. Table 1. sunuuarizes the runs. along with some basic properties of the turbulence that they generate.," Table \ref{tbl:sims} summarizes the runs, along with some basic properties of the turbulence that they generate." " The ideal MIID runs are labelled with ""Ideal as a prefix and then the οιαντ domain size in units of 11."," The ideal MHD runs are labelled with “Ideal"" as a prefix and then the $x,y,z$ domain size in units of $H$." The resistive ruus have the prefix “Resistive” appended witli the domain's racial location dn our model disk.," The resistive runs have the prefix “Resistive"" appended with the domain's radial location in our model disk." Finally. the forced hydrodvuamiic rus are prefixed with “Uydro™. and suffixed with ILA (for high-amplitude: A=10. 7) or LA (for low-amplitude: A=10 +}.," Finally, the forced hydrodynamic runs are prefixed with “Hydro"", and suffixed with HA (for high-amplitude; $A = 10^{-3}$ ) or LA (for low-amplitude; $A = 10^{-4}$ )." lu this work. we do not consider any radiative transfer effects or an chussion inodel," In this work, we do not consider any radiative transfer effects or an emission model." hDustead. we determine how the deusitv-cweiehted turbulent velocity distribution depends on location within a protoplanetary disk and on the plwsics that we include.," Instead, we determine how the density-weighted turbulent velocity distribution depends on location within a protoplanetary disk and on the physics that we include." Although not equivalent to an observed turbulent line profile. the velocity distribution gives us the probability of observing Cluission at a particular velocity shift along the liue of sight.," Although not equivalent to an observed turbulent line profile, the velocity distribution gives us the probability of observing emission at a particular velocity shift along the line of sight." The line-ofsieht (los) turbulent velocity of a patch of disk will depend on the inclination angle of the disk /. and the azimuthalangle o around the disk ceuter (see Figure 1)). where (604 05.02) is the turbuleut velocity field iu," The line-of-sight $los$ ) turbulent velocity of a patch of disk will depend on the inclination angle of the disk $i$, and the azimuthalangle $\phi$ around the disk center (see Figure \ref{diagram}) ), where $v_r, v_{\phi}, v_z$ ) is the turbulent velocity field in" is 725 corresponding to 276 significance.,is 725 corresponding to $27\sigma$ significance. We show the exponential cutoff power-law model together with the data in Figure 2., We show the exponential cutoff power-law model together with the data in Figure 2. The 0.520 GeV photon flux of Terzau 5isQLIZL1)s10? photons 2 +. corresponding to (6.82.0)«10.th orescm 7s1.," The 0.5–20 GeV photon flux of Terzan 5 is $(3.4\pm1.1)\times 10^{-8}$ photons $^{-2}$ $^{-1}$ , corresponding to $(6.8\pm2.0)\times 10^{-11}$ ergs $^{-2}$ $^{-1}$." To compare with the reported 0.1.10 Ge fux of £7 Tuc (Abdo et al., To compare with the reported 0.1–10 GeV flux of 47 Tuc (Abdo et al. " 20092). the 0.110 CteV fiux of Terzau 5 is about 2«10.* photons em7s +. corresponding to 1.2«1019 ores cm7 sf,"," 2009a), the 0.1–10 GeV flux of Terzan 5 is about $2\times 10^{-7}$ photons $^{-2}$ $^{-1}$, corresponding to $1.2\times10^{-10}$ ergs $^{-2}$ $^{-1}$." The photou flux of Terzau 5 is slightly below the upper limit of 2.6«10.* photons ? + provided by EGRET (Michelsou et al., The photon flux of Terzan 5 is slightly below the upper limit of $2.6\times 10^{-7}$ photons $^{-2}$ $^{-1}$ provided by EGRET (Michelson et al. 1991)., 1994). Using LLAT data. we detect eanuna-rav emission from Terzau 5 for thefirst tin1ο," Using LAT data, we detect gamma-ray emission from Terzan 5 for the time." ", The eamuna-ravs οuitted from GCs are eecnerallv asstmed to associate with MSPs in clusters.", The gamma-rays emitted from GCs are generally assumed to associate with MSPs in clusters. The origin of theSC ΠΟ ΓΗ be either pulsed curvature radiation arising near the polar cap and/or iu outer maguctospleric gaps (e.g. Zhaug Cheng 2003: ILuding. Usov Mushlinov 2005: Veuter De Jager 2008). or inverse Compton scattering plotous between the relativistic electrous/positrous iu the pulsu winds and the backeround soft photous (e.g. Bednarek Sitirek 2007).," The origin of these gamma-rays could be either pulsed curvature radiation arising near the polar cap and/or in outer magnetospheric gaps (e.g. Zhang Cheng 2003; Harding, Usov Muslimov 2005; Venter De Jager 2008), or inverse Compton scattering photons between the relativistic electrons/positrons in the pulsar winds and the background soft photons (e.g. Bednarek Sitarek 2007)." Let us first assume that these eanunise-ravs have the magnetospheric origin., Let us first assume that these gamma-rays have the magnetospheric origin. It is useful to compare Terzan 5 with I7 Tuc. which is the first globular cluster detecte with eammatavs (Abdo et al.," It is useful to compare Terzan 5 with 47 Tuc, which is the first globular cluster detected with gamma-rays (Abdo et al." 2009a)., 2009a). The logarithin of central hpuuinositv density aud core radius for Terzan 5 and LF Tuc are 5.06 Lope? and Lal L.pe7. anc O.5lpe and 0.52pe respectively (Tarvis 1996: version of 2003 February).," The logarithm of central luminosity density and core radius for Terzan 5 and 47 Tuc are 5.06 $L_{\odot}pc^{-3}$ and 4.81 $L_{\odot}pc^{-3}$, and $pc$ and $pc$ respectively (Harris 1996; version of 2003 February)." " However the two body eucouuter rate and immetalliitv. of Terzau 5r, are higher than those of LF Tuc.", However the two body encounter rate and metallicity of Terzan 5 are higher than those of 47 Tuc. Since these two quantities favor the formation of MSPs (e.g. Ivanova 2006.2008: IIui et al.," Since these two quantities favor the formation of MSPs (e.g. Ivanova 2006,2008; Hui et al." 2010). 1 is expected that Terzan 5 can house more MSPs thau lr Tuc.," 2010), it is expected that Terzan 5 can house more MSPs than 47 Tuc." Tf we assume that the mean spin-down power (Loy) of MSPs and the conversion efficiency of power are the same for Terzan 5 aud £7? Tuc. the ratio of umauber of MSP«s between these two clusters is simply eiwen by NrfNtie©(LeperfLopuo)~25 (assuniug the distance to 17 Tuc and Terzan 5 is £ kpe and 10 Ipc. respectively).," If we assume that the mean spin-down power $L_{sd}$ ) of MSPs and the conversion efficiency of power are the same for Terzan 5 and 47 Tuc, the ratio of number of MSPs between these two clusters is simply given by $N_{Ter}/N_{Tuc} \sim (L_{\gamma Ter}/L_{\gamma Tuc})\sim 25$ (assuming the distance to 47 Tuc and Terzan 5 is 4 kpc and 10 kpc, respectively)." This predicted ratio is substantially higher than the current observed uuuber of MSPs for Terzan 5 and LF Tuc. which are 33 and 23 respectively.," This predicted ratio is substantially higher than the current observed number of MSPs for Terzan 5 and 47 Tuc, which are 33 and 23 respectively." It is difücult to nuaegme that Terzan 5 really has 25 times more MSPs than [7 Tuc., It is difficult to imagine that Terzan 5 really has 25 times more MSPs than 47 Tuc. Perhaps the mean properties of AISPs between these clusters are not the sale., Perhaps the mean properties of MSPs between these clusters are not the same. Iu fact. our spectral fits indicate that both of the photon index aud cut-off cherey of Terzan 5 are larger than those of [7 Tuc.," In fact, our spectral fits indicate that both of the photon index and cut-off energy of Terzan 5 are larger than those of 47 Tuc." It has been sugeested that the ealmua-rav efficiency is L.xLy (e.g. Thompson 2005)., It has been suggested that the gamma-ray efficiency is $L_{\gamma} \propto L_{sd}^{1/2}$ (e.g. Thompson 2005). " If the mean spin-down power of MSPs in Terzau 5 is actually higher than that of 17 Tuc. NrNT, will be reduced."," If the mean spin-down power of MSPs in Terzan 5 is actually higher than that of 47 Tuc, $N_{Ter}/N_{Tuc}$ will be reduced." Currently hhas detected £6 eauuna-rav pulsars aud their spectral cut-off energies CZ.) have obtained (Abdo et al., Currently has detected 46 gamma-ray pulsars and their spectral cut-off energies $E_c$ ) have obtained (Abdo et al. 2009€)., 2009c). Using the published data. we fud that E.xLo with a correlation coefficieut about 0.51.," Using the published data, we find that $E_c \propto L_{sd}^{1/4}$ with a correlation coefficient about 0.51." This also suggests that he mean spin-down power of AISPs iu Terzan 5 is larger hau that of 1? Tuc., This also suggests that the mean spin-down power of MSPs in Terzan 5 is larger than that of 47 Tuc. " If this is true the uuuber ratio cau reduce to Np/Np,~25(2.5GeΔΟΕ)11.", If this is true the number ratio can reduce to $N_{Ter}/N_{Tuc} \sim 25 (2.5 GeV/3.8 GeV)^2 \sim 11$ . Wowever. it is still iucousisteut withV/A the observed iunber.," However, it is still inconsistent with the observed number." Another possible factor to reduce this ratio is he distance to the cluster., Another possible factor to reduce this ratio is the distance to the cluster. There are several estimates of the distance of Terzan 5. which are between 5.510.3 spe (Cohn et al.," There are several estimates of the distance of Terzan 5, which are between 5.5–10.3 kpc (Cohn et al." 2002: Ortolani et al., 2002; Ortolani et al. 2007)., 2007). If Terzau 5 ijs located at the lower cud of the estimate. the ratio will become ~L ," If Terzan 5 is located at the lower end of the estimate, the ratio will become $\sim 4$." It is therefore likely that the distance o Terzau 5 is less than 10 kpec., It is therefore likely that the distance to Terzan 5 is less than 10 kpc. Ou the otherhand. if the eamuna-ravs result roni inverse Compton scattering between relativistic clectrous/positrous aud the backerouud soft photons. it is nof surprised that (τοντι)10 (assuniüug a distance of 6 kpe) even though NTNr.~d.," On the otherhand, if the gamma-rays result from inverse Compton scattering between relativistic electrons/positrons and the background soft photons, it is not surprised that $(L_{\gamma Ter}/L_{\gamma Tuc})\sim 10$ (assuming a distance of $\sim 6$ kpc) even though $N_{Ter}/N_{Tuc} \sim 1$." It is because the backeround soft photon iuteusitv from the Galactic plane at the position of Terzau 5 is roughly 10 times of that of [7 Tuc (Strong Moskaleuko. 1998)., It is because the background soft photon intensity from the Galactic plane at the position of Terzan 5 is roughly 10 times of that of 47 Tuc (Strong Moskalenko 1998). Although curreut ddata cannot cüffereutiate these two models. the curvature radiation mechanisi aud the inverse Compton scattering miechanisgu have very different predictions m higher energy ranec.," Although current data cannot differentiate these two models, the curvature radiation mechanism and the inverse Compton scattering mechanism have very different predictions in higher energy range." The curvature radiation moechauisui from pulsar magnetosphere can only produce very few photons with energv higher than 10 CeV (e.g. Chene. Πο and Ruderman 1986).," The curvature radiation mechanism from pulsar magnetosphere can only produce very few photons with energy higher than 10 GeV (e.g. Cheng, Ho and Ruderman 1986)." " On the other haud. if E. corresponds to the peak of the inverse Compton scattering with either relic photous (or IR photous frou the Galactic plane). then there should be two (or ono) more peaks correspond to IR photons and star lights (or star Lehlts) respectively,"," On the other hand, if $E_c$ corresponds to the peak of the inverse Compton scattering with either relic photons (or IR photons from the Galactic plane), then there should be two (or one) more peaks correspond to IR photons and star lights (or star lights) respectively." Therefore the Προςται can be extended to 100 GeV Cee. Bednarek Sitarek 2007: Chene et al., Therefore the spectrum can be extended to 100 GeV (e.g. Bednarek Sitarek 2007; Cheng et al. 2010). which may be detected by MACIC aud/or ILE.S.S. In particular. the background soft photous of Terzan 5 is so high that the possibility of detecting photous with energv 2 10 GeV is very likely.," 2010), which may be detected by MAGIC and/or H.E.S.S. In particular, the background soft photons of Terzan 5 is so high that the possibility of detecting photons with energy $>$ 10 GeV is very likely." Because of this. we attempted to search for amy 710 GeV photons from Terzan 5.," Because of this, we attempted to search for any $> 10$ GeV photons from Terzan 5." By using the LAT databetween 10 aud 20 GeV. a maxima likelihood analysis vields a TS value of L1. corresponding to a detection sienificance of 3.70.," By using the LAT databetween 10 and 20 GeV, a maximum likelihood analysis yields a TS value of 14, corresponding to a detection significance of $3.7\sigma$ ." Visual inspection of the 10.20 GeV, Visual inspection of the 10–20 GeV " (6))2(7)) 09V. (2))2(3)). D/DI=O/O0l+Va-N Rel). £ A. A. M.L? A=(ω--Veh)few. A=aInPi(cos0). M=infsind. L?=(1+1)+(1—m7)/sin?0. (er21fr>>1). w=(Vi2ος)&. Viecος Vi. c; Vis laa (47.7) Viem/¥p. Vi;+c, Ἐν—c Ibb). laa. r/ry—12.0 Ibb) .Nr/rg=2.0 r/ry—1=0. Αρτ0.5. laa {Γόνοςrp=1T. 26;). c "," \ref{equ:cont}) \ref{equ:mome}) $\delta\vct{V}$ \ref{equ:conw}) \ref{equ:momw}) $D/Dt=\partial/\partial t+\vct{V_w}\cdot\vct{\nabla}$ $\vct{\delta V}=\vct{\xi}(r)P_l^m(\cos\theta)\exp(ikr+im\varphi-i\omega t)$ $\vct{\xi}$ $K$ $A$ $M$$L^2$ $K=(\omega-V_wk)/\cs$ $A=\frac{d}{d\theta}\ln P_l^m(\cos\theta)$ $M=m/\sin\theta$ $L^2=l(l+1)+(1-m^2)/\sin^2\theta$ $kr\gg1$$Kr\gg1$ $\omega=(V_w\pm\cs)\,k$ $V_w\pm\cs$ $V_w$ $\cs$ $\Varm$ \ref{fig:patt}a $\varphi,\,r$ $\Varm/V_p$ $V_w+\cs$ $V_w-\cs$ \ref{fig:patt}b \ref{fig:patt}a $r/r_p-1=2.0$ \ref{fig:patt}b $\Delta r/r_p=2.0$ $r/r_p-1=0$ $\Delta r/r_p=0.5$ \ref{fig:patt}a $r_{\rm over}/r_p=1.7$ $2\cs$ $\cs$ " a companion earlier than mid-L. However. they suggested that a definitive test would be provided by IR spectroscopy to directly determine an accurate spectral type for the brown dwarf.,"a companion earlier than mid-L. However, they suggested that a definitive test would be provided by IR spectroscopy to directly determine an accurate spectral type for the brown dwarf." In this paper we present a near-IR spectrum of 00137-, In this paper we present a near-IR spectrum of 0137-349. In Section 2 we discuss the observations and data reduction. in Section 3 we present our analysis of these data. and in Section 4 we discuss the results and comment on the spectral type of 00137-349B.," In Section 2 we discuss the observations and data reduction, in Section 3 we present our analysis of these data, and in Section 4 we discuss the results and comment on the spectral type of 0137-349B." We were awarded Directors Discretionary Time at the 8m Gemini South telescope in November 2005. to obtain a near-IR spectrum of 00137-349 with the Gemini Near-IR Spectrometer (GNIRS. ?)) in programme GS-2005B-DD-9.," We were awarded Director's Discretionary Time at the 8m Gemini South telescope in November 2005, to obtain a near-IR spectrum of 0137-349 with the Gemini Near-IR Spectrometer (GNIRS, \citealt{gnirs}) ) in programme GS-2005B-DD-9." " We selected the cross-dispersed mode. using the short camera. the 32 lines/mm grating centred at 1.65//m. and the 0.3"" (2 pixels) slit. which gives a resolution /?=1700."," We selected the cross-dispersed mode, using the short camera, the 32 lines/mm grating centred at $1.65\um$, and the $0.3''$ (2 pixels) slit, which gives a resolution $R=1700$." In this observing mode. the entire near-IR region from =Q0.9jm to =2.5jm is covered in a single observation with excellent transmission across almost the whole wavelength range.," In this observing mode, the entire near-IR region from $\approx0.9\um$ to $\approx2.5\um$ is covered in a single observation with excellent transmission across almost the whole wavelength range." There is no inter-order contamination as in long slit mode over a single atmospheric window. and this mode is much more efficient than executing separate // and ἐν band observations.," There is no inter-order contamination as in long slit mode over a single atmospheric window, and this mode is much more efficient than executing separate $H$ and $K$ band observations." The observations were conducted in service mode on the night of 2005 November 22nd., The observations were conducted in service mode on the night of 2005 November 22nd. " Our observing condition requirements were met: 70'A -ile image quality (seeing «0.6"" at J and 50A -ile cloud cover t(i.e.. photometric)."," Our observing condition requirements were met: $70\%$ -ile image quality (seeing $<0.6''$ at $J$ ) and $50\%$ -ile cloud cover (i.e., photometric)." The observations were obtained at a mean airmass of 1.12., The observations were obtained at a mean airmass of 1.12. " We took 20. 1208s exposures. using two ""nod"" positions along the 6” long slit giving a total exposure time of 40 minutes."," We took $20 \times 120$ s exposures, using two “nod” positions along the $6''$ long slit giving a total exposure time of 40 minutes." This did not cause any problems of order overlap during the data reduction. since the target is a point source and the seeing was good.," This did not cause any problems of order overlap during the data reduction, since the target is a point source and the seeing was good." With overheads for detector readout etc..," With overheads for detector readout etc.," the observations lasted for =55 minutes. covering =47%& of the binary orbit.," the observations lasted for $\approx55$ minutes, covering $\approx47\%$ of the binary orbit." An VV telluric standard was also observed 110538) both before and after the target. at a similar airmass.," An V telluric standard was also observed 10538) both before and after the target, at a similar airmass." The data were initially reduced using the GNIRS sub-package of the Gemini IRAF package., The data were initially reduced using the GNIRS sub-package of the Gemini IRAF package. Briefly. a correction was first applied to the raw science. standard star and are lamp spectral images for the s-distortion in the orders.," Briefly, a correction was first applied to the raw science, standard star and arc lamp spectral images for the s-distortion in the orders." The data were then flat-fielded. taking care to flat-field each order with the corresponding correctly exposed flat.," The data were then flat-fielded, taking care to flat-field each order with the corresponding correctly exposed flat." Subsequently. difference pairs were assembled from the science and standard star images and any signiticant remaining sky background removed by subtracting linear functions. fitted in the spatial direction. from the data.," Subsequently, difference pairs were assembled from the science and standard star images and any significant remaining sky background removed by subtracting linear functions, fitted in the spatial direction, from the data." The spectral orders of the white dwarfs and the standard stars were then extracted and assigned the wavelength solution derived from the relevant are spectrum., The spectral orders of the white dwarfs and the standard stars were then extracted and assigned the wavelength solution derived from the relevant arc spectrum. Unfortunately. the GNIRS IRAF routines proved inadequate or removing the telluric features from the target spectra and oroviding an approximate flux calibration.," Unfortunately, the GNIRS IRAF routines proved inadequate for removing the telluric features from the target spectra and providing an approximate flux calibration." Instead. at this stage we utilised standard techniques offered by software routines in the STARLINK packages KAPPA and FIGARO.," Instead, at this stage we utilised standard techniques offered by software routines in the STARLINK packages KAPPA and FIGARO." Any features intrinsic o the energy distribution of the standard star were identified by reference to a near-IR spectral atlas of fundamental MK standards (e.g. 2: ?: 2)) and were removed by linearly interpolating over hem.," Any features intrinsic to the energy distribution of the standard star were identified by reference to a near-IR spectral atlas of fundamental MK standards (e.g., \citealt{mkcal}; \citealt{mkcal2}; \citealt{mkcal3}) ) and were removed by linearly interpolating over them." The spectrum of the white dwarf was then co-aligned with he spectrum of the standard star by cross-correlating the telluric features present in the data., The spectrum of the white dwarf was then co-aligned with the spectrum of the standard star by cross-correlating the telluric features present in the data. The science spectral orders were then divided by the corresponding standard star spectral orders and multiplied by a blackbody with the standard star's 7:4. taking into account the differences in exposure times.," The science spectral orders were then divided by the corresponding standard star spectral orders and multiplied by a blackbody with the standard star's $T_{\rm eff}$, taking into account the differences in exposure times." We found that the flux levels of the three brightest spectral orders (number 3. covering =1.055m to x2.5jm. number + covering zc].4jim to zcL.sym. and number 5 covering =1.25m to =1.35pm) were well matched to each other.," We found that the flux levels of the three brightest spectral orders (number 3, covering $\approx1.95\um$ to $\approx2.5\um$, number 4 covering $\approx1.4\um$ to $\approx1.8\um$, and number 5 covering $\approx1.2\um$ to $\approx1.35\um$ ) were well matched to each other." However. it was necessary to scale these fluxes by a single. constant normalisation factor to obtain the best possible agreement between the spectral data and the /. // and A photometric fluxes derived from the 2MASS AII Sky Data Release Point Source Catalogue magnitudes (?) where zero magnitude fluxes were taken from ?..," However, it was necessary to scale these fluxes by a single, constant normalisation factor to obtain the best possible agreement between the spectral data and the $J$, $H$ and $K_{\rm S}$ photometric fluxes derived from the 2MASS All Sky Data Release Point Source Catalogue magnitudes \citep{2MASS} where zero magnitude fluxes were taken from \citet{zombeck}. ." The reduced GNIRS spectrum and 2MASS fluxes are shown in Figure |., The reduced GNIRS spectrum and 2MASS fluxes are shown in Figure 1. We have analysed the GNIRS near-IR spectrum of 00137-349 following the method of ?.., We have analysed the GNIRS near-IR spectrum of 0137-349 following the method of \citet{dobbie05}. We calculated a pure-hydrogen synthetic white dwarf spectrum for the temperature Ky and surface gravity (log g=0.08) determined by ?..," We calculated a pure-hydrogen synthetic white dwarf spectrum for the temperature $T_{\rm eff}=16,500 \pm 500$ K) and surface gravity (log $g = 7.49 \pm 0.08$ ) determined by \citet{maxted06}." We used recent versions of the parallel. hydrostatic. non-local thermodynamic equilibrium (non- atmosphere and spectral synthesis codes TLUSTY (V200: ? and SYNSPEC (48: ftpitlusty.gsfe.nasa.gov/synsplib/synspec).," We used recent versions of the plane-parallel, hydrostatic, non-local thermodynamic equilibrium (non-LTE) atmosphere and spectral synthesis codes TLUSTY (V200; \citealt{hl95} and SYNSPEC (v48; ftp:/tlusty.gsfc.nasa.gov/synsplib/synspec)." The synthetic spectral fluxes have been normalised to the white dwarf's V magnitude (15.33+0.02)., The synthetic spectral fluxes have been normalised to the white dwarf's $V$ magnitude $15.33 \pm 0.02$ ). The synthetic white dwarf spectrum is shown over-plotted the GNIRS data in Figure |., The synthetic white dwarf spectrum is shown over-plotted the GNIRS data in Figure 1. Examination of Figure | reveals a clear difference in the overall shape and level of the synthetic white dwarf spectrum and the observed data in the ἐν band (below e1.955/my., Examination of Figure 1 reveals a clear difference in the overall shape and level of the synthetic white dwarf spectrum and the observed data in the $K$ band (below $\approx1.95\um$ ). " In contrast. we do not readily observe any spectral features typical of the energy distributions ofL or T dwarfs. e.g. Na I absorption at 2.20//m. CH, or CO at 1.677 and 2.3j/m respectively and H2O centred on 1.15. 1.4 and 1.9//m."," In contrast, we do not readily observe any spectral features typical of the energy distributions of L or T dwarfs, e.g. Na I absorption at $\um$, $_{4}$ or CO at $\mu$ and $\um$ respectively and $_{2}$ O centred on 1.15, 1.4 and $\um$." We estimate the signal-to-noise ratio at 2.2jm=12., We estimate the signal-to-noise ratio at $2.2\um\approx12$. To test whether the flux excess in the A' band is due to the brown dwarf companion. and to constrain its spectral type. we have added empirical models for substellar objects to the white dwarf synthetic spectrum and compared these composites to the near-IR spectrum (Figure |).," To test whether the flux excess in the $K$ band is due to the brown dwarf companion, and to constrain its spectral type, we have added empirical models for substellar objects to the white dwarf synthetic spectrum and compared these composites to the near-IR spectrum (Figure 1)." The empirical models have been constructed using the near-IR spectra of L and T dwarfs presented by ?.., The empirical models have been constructed using the near-IR spectra of L and T dwarfs presented by \citet{mclean03}. In brief. the data have been obtained with the NIRSPEC instrument on the Keck Telescope. cover the range 0.05j/im2.31jm with a resolution of A/3Àez2000 and have been flux calibrated— using JJ. I and dvs photometric fluxes derived from the 2MASS magnitudes as described by ?..," In brief, the data have been obtained with the NIRSPEC instrument on the Keck Telescope, cover the range $0.95\um -2.31\um$ with a resolution of $\lambda/\delta\lambda\approx2000$ and have been flux calibrated using $J$, $H$ and $K_{\rm S}$ photometric fluxes derived from the 2MASS magnitudes as described by \citet{mclean01}." " To extend these data out to 2. Επι. our effective red limit. we have appended to them sections of UKIRT CGS4 spectra of late-type dwarfs obtained by ? and ον,"," To extend these data out to $2.4\mu$ m, our effective red limit, we have appended to them sections of UKIRT CGS4 spectra of late-type dwarfs obtained by \citet{leggett01} and \citet{geballe02}." " The fluxes of the empirical models have been scaled to a level appropriate to à location at d=lOpe using the 2MASS J magnitude of each late-type object and the polynomial tits of ?. to the A, versus spectral type for LO-TS field dwarfs/brown dwarfs.", The fluxes of the empirical models have been scaled to a level appropriate to a location at d=10pc using the 2MASS $J$ magnitude of each late-type object and the polynomial fits of \citet{tinney03} to the $M_{\rm J}$ versus spectral type for L0-T8 field dwarfs/brown dwarfs. Subsequently. these fluxes have been re-calibrated to be consistent with the distance of 00137-349. as derived from its measured V magnitude. effective temperature and theoretical AA and radius.," Subsequently, these fluxes have been re-calibrated to be consistent with the distance of 0137-349, as derived from its measured $V$ magnitude, effective temperature and theoretical $M_{\rm V}$ and radius." In Figure | we compare the observed GNIRS near-IR spectrum of 00137-349 to a range of these empirical composite white dwarf | brown dwarf models | LO. L6. L8 and TS).," In Figure 1 we compare the observed GNIRS near-IR spectrum of 0137-349 to a range of these empirical composite white dwarf $+$ brown dwarf models $+$ L0, L6, L8 and T5)." We find the best match to the data is provided by a white dwarf. | L8 composite model., We find the best match to the data is provided by a white dwarf $+$ L8 composite model. " The lack of an obvious CO edge at 2.3,m supports this conclusion.", The lack of an obvious CO edge at $2.3\um$ supports this conclusion. We can estimate the temperature ofthe brown dwarf from its, We can estimate the temperature ofthe brown dwarf from its VS38 Mon (Soker Tvlenda 2003: Tvlenda Soker 2006) and V1309 Sco (Evlenda et al.,V838 Mon (Soker Tylenda 2003; Tylenda Soker 2006) and V1309 Sco (Tylenda et al. 2011). or an evolved star in an unstable phase of evolution that loses a huge amount of mass. as in the model for the Creat Eruption of η Car (Ixashi Soker 2010).," 2011), or an evolved star in an unstable phase of evolution that loses a huge amount of mass, as in the model for the Great Eruption of $\eta$ Car (Kashi Soker 2010)." The average total gravitational power is the average accretion rate times the potential well of the accreting star 1n the binary model discussed. here. acereteck mass is likelv to form an accretion disk or an accretion belt.," The average total gravitational power is the average accretion rate times the potential well of the accreting star In the binary model discussed here, accreted mass is likely to form an accretion disk or an accretion belt." The accretion time must be longer than the viscosity time scale for the accreted mass to lose its angular momentum., The accretion time must be longer than the viscosity time scale for the accreted mass to lose its angular momentum. According to Dubus et al. (, According to Dubus et al. ( "2001) the viscous timescale is where £ is the viscosity of the disk. 44 is the thickness of the disk. €; is the sound speed ance, is the Ixeplerian velocity.","2001) the viscous timescale is where $\nu$ is the viscosity of the disk, $H$ is the thickness of the disk, $C_s$ is the sound speed and $v_\phi$ is the Keplerian velocity." " We scale. AL, and. 2, in equation. (2)) according to the parameters of VS38 Alon (CEvlenda 2005).", We scale $M_a$ and $R_a$ in equation \ref{eq:tvisc1}) ) according to the parameters of V838 Mon (Tylenda 2005). For these parameters the viscous to Weplerian times ratio is ἐςεν& 160., For these parameters the viscous to Keplerian times ratio is $\chi \equiv t_{\rm{visc}}/t_K \simeq 160$ . The acereted mass is determined by the details of the binary interaction process. ane dilfers from object to object.," The accreted mass is determined by the details of the binary interaction process, and differs from object to object." We scale it by AL= Ad., We scale it by $M_{\rm{acc}} = \eta_a M_a$ . Based on the modeled systems (Vs3s Mon. V. 1309 Sco. 5g Car) this mass fraction is 7αι with a large variation.," Based on the modeled systems (V838 Mon, V 1309 Sco, $\eta$ Car) this mass fraction is $\eta_a \lesssim 0.1$ with a large variation." Phe value of a.Ὁ0.1 can be understood. as follows., The value of $\eta_a \lesssim 0.1$ can be understood as follows. " Lf the AIS (or slightly oll-MS) star collides with a star and tidally clisrupts it. as in the model or VS38 Mon (Soker Tvlenda 2003: Tvlenda Soker 2006). the destructed star is likely to be of much lower mass han the aceretor AMSALO.3AL,."," If the MS (or slightly off-MS) star collides with a star and tidally disrupts it, as in the model for V838 Mon (Soker Tylenda 2003; Tylenda Soker 2006), the destructed star is likely to be of much lower mass than the accretor $M_{\rm{acc}} \lesssim M_b \lesssim 0.3 M_a$." Another possibility is that an evolved star loses a huge amount of mass., Another possibility is that an evolved star loses a huge amount of mass. In that case it is possible that the accretor will gain only a small raction of the ejected mass. as in the scenario for the Creat Eruption of η Carinae (Ixashi Soker 2010).," In that case it is possible that the accretor will gain only a small fraction of the ejected mass, as in the scenario for the Great Eruption of $\eta$ Carinae (Kashi Soker 2010)." " Here again we expect AM0.1A4,.", Here again we expect $M_{\rm{acc}} \lesssim 0.1 M_a$. The viscous time scale gives an upper limit on the accretion rate The maximum gravitational power is thereforewhere we replaced the parameters of the viscous time, The viscous time scale gives an upper limit on the accretion rate The maximum gravitational power is thereforewhere we replaced the parameters of the viscous time calculated using the software. package (Taylor&Weisberg1980). and an ephemeris obtained at Joclrel Bank Observatory (Llobbs2002).,calculated using the software package \cite{tay89} and an ephemeris obtained at Jodrell Bank Observatory \cite{hobbs2002}. . Data were folded to create mean pulse profiles., Data were folded to create mean pulse profiles. The up-to-date ephemeris allowec alignment of the profiles acquired on dillerent dates ancl a different frequencies., The up-to-date ephemeris allowed alignment of the profiles acquired on different dates and at different frequencies. The 430-MlI4 average profiles for the ALJD 51188 and 51189 observations are presented in Lies., The 430-MHz average profiles for the MJD 51188 and 51189 observations are presented in Figs. and 3.., \ref{fig:0950.51188} and \ref{fig:0950.51189}. Note that the two profiles are distinctly dilferent in overall form. but that the low-level features are seen at jus he same —.307 longitude before the main pulse (ALP) peak (sce Figs.," Note that the two profiles are distinctly different in overall form, but that the low-level features are seen at just the same $-30^\circ$ longitude before the main pulse (MP) peak (see Figs." 2. 4))., \ref{fig:0950.51188.2} \ref{fig:0950.51189.2}) ). Moreover. a similar pair of features is seen in the MJD 51182 data (not shown).," Moreover, a similar pair of features is seen in the MJD 51182 data (not shown)." In Fig., In Fig. 5. we present a corresponding 1475-MllIz profile or the ALJD 52189 observation. where again a low-level eature is seen at some 30° (see Fig. 6)).," \ref{fig:0950.52189} we present a corresponding 1475-MHz profile for the MJD 52189 observation, where again a low-level feature is seen at some $-30^\circ$ (see Fig. \ref{fig:0950.52189.2}) )." At 430 MIIZ he feature consists of two clips in the profile intensity with wll widths of some 2 and their centers separated by some T., At 430 MHz the feature consists of two dips in the profile intensity with half widths of some $\deg$ and their centers separated by some $7^\circ$. The total width of the feature at 480 MlIZ is 117., The total width of the feature at 430 MHz is $11^\circ$. At 1475 Mllzin both this observation anc another (not shown) on MJD 52187.the feature appears as a single peaks with a width of 37., At 1475 MHz—in both this observation and another (not shown) on MJD 52187—the feature appears as a single peak with a width of $3^\circ$. Several published observations also appear to record the BOO501OS “notches”., Several published observations also appear to record the B0950+08 “notches”. Γον are very clear in the 430-MIIz ime-alignecl profile of Llankins Rankin (2003). but cannot o» discerned in the lower quality observations at. various other frequencies.," They are very clear in the 430-MHz time-aligned profile of Hankins Rankin (2003), but cannot be discerned in the lower quality observations at various other frequencies." Moreover. the “notches” can probably be seen in the polarimetric observations of both Gould Lyne 998) ancl Weishere ((1998).," Moreover, the “notches” can probably be seen in the polarimetric observations of both Gould Lyne (1998) and Weisberg (1998)." Phe former very high quality profiles seem to show vais of features at the correct phase at 408. 610 ancl 925 AMllIz. and in the latter we appear to see apair of features at 14815 Mllz.," The former very high quality profiles seem to show pairs of features at the correct phase at 408, 610 and 925 MHz, and in the latter we appear to see a of features at 1418 MHz." This latter observation (see their Fig., This latter observation (see their Fig. 5) is especially interesting because the features appear to involve the linear polarization also. which is only in the region on the far leading edge of the profile.," 5) is especially interesting because the features appear to involve the linear polarization also, which is only in the region on the far leading edge of the profile." ]t must be said that the features in. D0950|OS. are rather weak. at best reducing the intensity at their centers by a few percent.," It must be said that the features in B0950+08 are rather weak, at best reducing the intensity at their centers by a few percent." Ht might even be regarded. as surprising that such features would be found in a star which is wel known for its sporaclic emission (It may not be known. for instance. whether the pulsar ever nulls. because the range of intensities exhibited by its pulses is so large.)," It might even be regarded as surprising that such features would be found in a star which is well known for its sporadic emission (It may not be known, for instance, whether the pulsar ever nulls, because the range of intensities exhibited by its pulses is so large.)" In this context. it is interesting that Nowakowski ((2003) have shown that this pulsar's profile is comprise of different intensity. fractions which have quite dilleren partial-average profile forms.," In this context, it is interesting that Nowakowski (2003) have shown that this pulsar's profile is comprised of different intensity fractions which have quite different partial-average profile forms." These stuclies indicate that the ALD has three main “components”: the trailing one which is usually strongest. the middle one whieh varies in relative intensity. and a leading one which can only be discerned in certain populations of weak pulses.," These studies indicate that the MP has three main “components”: the trailing one which is usually strongest, the middle one which varies in relative intensity, and a leading one which can only be discerned in certain populations of weak pulses." " It woulcl therefore appear that the distinct. 430-MlIZ. profiles seen. above represent distinct. profile. ""modes? in this star.", It would therefore appear that the distinct 430-MHz profiles seen above represent distinct profile “modes” in this star. Finally. the above study finds that the “notches” are seen only in the very weakest populations of pulses. which nonetheless contribute," Finally, the above study finds that the “notches” are seen only in the very weakest populations of pulses, which nonetheless contribute" is about equally. efficient in suppressing star formation in central galaxies as thermal ones.,is about equally efficient in suppressing star formation in central galaxies as thermal ones. In the left-hancl panel of Figure 6.. we show the gas fraction ab z=0 within a given radius as a function of distance rom the cluster centre.," In the left-hand panel of Figure \ref{g676_fb}, we show the gas fraction at $z=0$ within a given radius as a function of distance from the cluster centre." The radius has been normalized to ooo and the gas fraction is in units of the universal barvon raction adopted in our simulation (i.c. ολου= 0.13)., The radius has been normalized to $R_{\rm 200}$ and the gas fraction is in units of the universal baryon fraction adopted in our simulation (i.e. $\Omega_b/\Omega_0=0.13$ ). The Mack line is for the run without AGN feedback. the blue ine is for thermal bubbles. while the green (a=2.4) and red (a= 2.1) ines show the case of CR bubbles.," The black line is for the run without AGN feedback, the blue line is for thermal bubbles, while the green $\alpha=2.4$ ) and red $\alpha=2.1$ ) lines show the case of CR bubbles." As a generic eature of AG| feedback. it can be seen that the gas fraction is significantly reduced in the central cluster region. while it is increased in the cluster outskirts.," As a generic feature of AGN feedback, it can be seen that the gas fraction is significantly reduced in the central cluster region, while it is increased in the cluster outskirts." As expected. the central gas fraction is most suppressed in the simulation where the CR bubbles have a shallow momentum spectrum.," As expected, the central gas fraction is most suppressed in the simulation where the CR bubbles have a shallow momentum spectrum." On the other hand. the case with a=2.4 leads to a somewhat higher eas fraction with respect to the simulation with purely hermal bubbles. due to the combined ellects of stronger Coulomb cooling and higher gas compressibility.," On the other hand, the case with $\alpha=2.4$ leads to a somewhat higher gas fraction with respect to the simulation with purely thermal bubbles, due to the combined effects of stronger Coulomb cooling and higher gas compressibility." In the right-hand. panel of Figure 6.. we show the total xwvon fraction (solid lines). and the stellar fraction (dashed ines) as a function of radius. using the same colour-coding.," In the right-hand panel of Figure \ref{g676_fb}, we show the total baryon fraction (solid lines), and the stellar fraction (dashed lines) as a function of radius, using the same colour-coding." The amount of stars that. form in the central regions is significantIy reduced by the presence of a supermassive DII. rut it is not allectecd by the nature of the bubbles. as discussed above.," The amount of stars that form in the central regions is significantly reduced by the presence of a supermassive BH, but it is not affected by the nature of the bubbles, as discussed above." Phe total amount of stars crops from a high value in excess of 30% reached in the simulation without AGN heating to a much more realistic value of ~10! which is consistent with observational findings (?)..," The total amount of stars drops from a high value in excess of $\sim 30\%$ reached in the simulation without AGN heating to a much more realistic value of $\sim 10\%$, which is consistent with observational findings \citep{Lin2003}." This also endows the central galaxy with a much redder colour. as observed.," This also endows the central galaxy with a much redder colour, as observed." Due to the reduction of the central stellar fraction the total barvon fraction is lowered in the central regions as well., Due to the reduction of the central stellar fraction the total baryon fraction is lowered in the central regions as well. Only at radii comparable to the turnaround radius. at ~30Pegg. it reaches the universal value in all runs performed.," Only at radii comparable to the turnaround radius, at $\sim 3 \times R_{\rm 200}$, it reaches the universal value in all runs performed." Given that CRs provide a significant pressure support in the central cluster regions it is interesting to examine how they alfect the amplitude of the thermal Sunvacy-Zelcovich, Given that CRs provide a significant pressure support in the central cluster regions it is interesting to examine how they affect the amplitude of the thermal Sunyaev-Zel'dovich. nligure 7.," In Figure \ref{g676_Y}, we plot the ratio of the $y$ parameter between the runs with and without AGN feedback at $z=0$ ." weplol," The left-hand panel illustrates the case where bubbles are purely thermal, while the central $\alpha=2.4$ ) and right-hand panels $\alpha=2.1$ ) refer to the runs with CR bubbles." lherat, The $y$ parameter is essentially determined by the line-of-sight integral of the thermal pressure. ioof," Since AGN-driven bubbles modify the thermal pressure distribution within the cluster, we observe variations of the estimated $y$ parameter." lheC'o," More specifically, the $y$ parameter is significantly reduced in the central cluster regions for all three runs with AGN feedback." mplon," As a side effect of solving the overcooling problem, the self-regulated AGN feedback results in a lower central density that is in better agreement with the density profiles derived from X-ray measurements." merein," In the cluster outskirts, however, the thermal pressure is somewhat increased in the runs with AGN feedback." "g,last"," This implies that the gas pressure distribution is somewhat “puffed up” in the cluster outskirts, which compensates for central gas depletion." acti," Given that the thermal energy of the cluster is roughly constant and independent of the presence or absence of AGN heating, the area integrated $y$ parameter turns out to be quite robust and is not changed much." vit, It is primarily a measure of the cluster's gravitational potential. y nPher," Still, this balance is not perfect as can be deduced by calculating the total $y$ parameter $Y$ within $R_{\rm vir}$." unswithande⋅∖↓≻⊔↓≼↧⇂of," In the case of thermal bubbles, we find that the integrated $y$ parameter is increased by $\sim 10\%$, while in the case of CR bubbles with spectral index of $2.4$ this number is somewhat smaller, being of order $7\%$." the pit cluste," Interestingly, in the case of CR bubbles with a flatter spectral slope the total $y$ parameter is instead lowered by $\sim 7\%$, as a result of a substantial reduction of the thermal pressure in the innermost regions." rOCiC πι., These results indicate that the integrated Comptonization is sensitive at a level of $\sim 10\%$ to the nature of AGN-driven bubbles and to the adopted feedback efficiency. ntsPHclsd handpa," This suggests that the presence of AGN feedback contributes to the scatter in the scaling relation between the cluster mass and $Y$, and the magnitude of this effect depends on the detailed physics of the AGN feedback." nct ill , Further studies are needed to characterize the functional form of the scatter and to quantify a possible mass dependence of this effect. In this study , It is clear that the intended use of $Y$ -measurements for high precision cosmology with galaxy clusters will require an accurate understanding of the detailed physical properties of AGN-inflated bubbles. we have investigated a mocel for self-regulated DIL Feedback with non-thermal relativistic particles in ACGN- bubbles., In this study we have investigated a model for self-regulated BH feedback with non-thermal relativistic particles in AGN-inflated bubbles. To describe the cosmic rav. particles. we rave adopted the formalism developed by ο) and ?) for the reatment ofCh protons. and combined it with prescriptions or BIL growth and feedback. outlined in 2). and ?)..," To describe the cosmic ray particles, we have adopted the formalism developed by \citet{Ensslin2007} and \citet{Jubelgas2007} for the treatment of CR protons, and combined it with prescriptions for BH growth and feedback, outlined in \citet{Springel2005b} and \citet{Sijacki2007}." This allowed: us to study the influence of Cl bubbles on their vost clusters in self-consistent cosmological simulations of galaxy cluster formation. and in particular. to compare with he case where the bubbles are filled with purely thermal eas.," This allowed us to study the influence of CR bubbles on their host clusters in self-consistent cosmological simulations of galaxy cluster formation, and in particular, to compare with the case where the bubbles are filled with purely thermal gas." Our methods also allowed us to gain some insight on how strongly the bubble morphologies and their propagation through the cluster atmosphere are allectecd by a clusters dvnamical state and the gaseous bulk motions in the IC'M., Our methods also allowed us to gain some insight on how strongly the bubble morphologies and their propagation through the cluster atmosphere are affected by a cluster's dynamical state and the gaseous bulk motions in the ICM. We have found that simulations with CR bubbles much more faithfully resemble observational. findings compared with the results for thermal bubbles., We have found that simulations with CR bubbles much more faithfully resemble observational findings compared with the results for thermal bubbles. This is mostly driven by the softer equation of state of gas that is supported by non-thermal pressure. ancl by the longer dissipation timescale of the CR component relative to thermal cooling.," This is mostly driven by the softer equation of state of gas that is supported by non-thermal pressure, and by the longer dissipation timescale of the CR component relative to thermal cooling." As a result. CR. bubbles can rise to the cluster outskirts and even leak into the surrounding intergalactic medium.," As a result, CR bubbles can rise to the cluster outskirts and even leak into the surrounding intergalactic medium." Still. their pressure. support. becomes gradually less. important as they move away from cluster central regions.," Still, their pressure support becomes gradually less important as they move away from cluster central regions." We have also found that the bubble morphologies in forming clusters are rather complex. especially during major merger events. where bubbles can become significantly perturbed from their initially spherical shape and are displaced. from their initial injection axis.," We have also found that the bubble morphologies in forming clusters are rather complex, especially during major merger events, where bubbles can become significantly perturbed from their initially spherical shape and are displaced from their initial injection axis." Fhis implies that based on the spatial position of bubbles alone it is not readily. possible to infer whether the AGN jet has changed its orientation. between two successive outbursts or whether bulk motions in the ICM have displaced buovantIs rising bubbles., This implies that based on the spatial position of bubbles alone it is not readily possible to infer whether the AGN jet has changed its orientation between two successive outbursts or whether bulk motions in the ICM have displaced buoyantly rising bubbles. " Interestingly, we have found in our cosmological simulations that neither the BILARs nor the SElts are very sensitive to the nature of the bubble feedback."," Interestingly, we have found in our cosmological simulations that neither the BHARs nor the SFRs are very sensitive to the nature of the bubble feedback." Llowever. the temperature distribution in the ICM is allectecd noticeably. given that CRO bubbles. provide non-thermal pressure support in central cluster regions.," However, the temperature distribution in the ICM is affected noticeably, given that CR bubbles provide non-thermal pressure support in central cluster regions." Above all. this changes the galaxy cluster temperature profiles which decline. towards the innermost regions. being in much better agreement with the observed temperature profiles of cool core clusters.," Above all, this changes the galaxy cluster temperature profiles which decline towards the innermost regions, being in much better agreement with the observed temperature profiles of cool core clusters." Correspondinglv. the thermal pressure distribution is altered as well by Cl bubbles. with a reduction. of the thermal pressure in the centre and an increase in the outskirts.," Correspondingly, the thermal pressure distribution is altered as well by CR bubbles, with a reduction of the thermal pressure in the centre and an increase in the outskirts." This redistribution of the thermal pressure can mocifv the integrated: Compton-y parameter at a level of ~104. an cHeet that we expect to contribute to the scatter in the relationship between cluster mass and Y.," This redistribution of the thermal pressure can modify the integrated $y$ parameter at a level of $\sim 10\%$, an effect that we expect to contribute to the scatter in the relationship between cluster mass and $Y$ ." We have evaluated bow many significant bubble outburst the central DIEI in our cluster is undergoing during the time interval from z—2 to z—0. when the DIT is in the low accretion. ‘racio-moce regime.," We have evaluated how many significant bubble outburst the central BH in our cluster is undergoing during the time interval from $z=2$ to $z=0$, when the BH is in the low accretion, `radio-mode' regime." Dased on this we obtain an average duty evcle of —107ves.," Based on this we obtain an average duty cycle of $\sim 10^8\,{\rm yrs}$." We note however that sudden inflows of gas towards the central DI triggered by vparamelerbelarit al iC⋅UN qub1 halz=corres to Che major merger host can c more frequent bubble events than the average value during a limited period.," We note however that sudden inflows of gas towards the central BH triggered by merging activity – especially at $z=0.6$, which corresponds to the last major merger of the host cluster – can cause much more frequent bubble events than the average value during a limited period." There is hence considerable variability in the duty evele related to the merger history of the host halo. an issue we plan to investigate in more detail in a forthcoming stucly.," There is hence considerable variability in the duty cycle related to the merger history of the host halo, an issue we plan to investigate in more detail in a forthcoming study." In our simulations. the sizes of the bubbles are not determined. by caleulating the jet physics fromfirst principles. given that we cannot resolve the initial stage of jet formation and bubble inflation by a jet even in the mostadvaneed state-of-art. cosmological simulations.," In our simulations, the sizes of the bubbles are not determined by calculating the jet physics fromfirst principles, given that we cannot resolve the initial stage of jet formation and bubble inflation by a jet even in the mostadvanced state-of-art cosmological simulations." Instead. we rely on simple physical parameterizations and observational," Instead, we rely on simple physical parameterizations and observational" p.,$\nu$. Values of v=3545Give during both the main SE episode anc the starburst of model & improve only mildly he agreement with observations.," Values of $\nu = 35-45\rm\, Gyr^{-1}$ during both the main SF episode and the starburst of model g improve only mildly the agreement with observations." A significant increase in he predicted. value for «Alg/fec] (0. 0.363 dex) is attained when 7=55Cyr (model «)).," A significant increase in the predicted value for $[_V]$ (i.e. 0.363 dex) is attained when $\nu = 55\rm\, Gyr^{-1}$ (model )." In this case. we oediet the ratio Z2. to be ~0.5. therefore it. can be regarded as a moclel similar tog.. but with a more intense SELL during he second. burst.," In this case, we predict the ratio $R_*$ to be $\sim 0.5$, therefore it can be regarded as a model similar to, but with a more intense SFH during the second burst." The problem is that. however. the colours start. to deviate from the observed. relations (U-V—1.67.. V-Ix—3.48 or My=22.2 mag) and the Fe abundance becomes quite ügh («FefHV]= 0.700).," The problem is that, however, the colours start to deviate from the observed relations (U-V=1.67, V-K=3.48 for $M_V = -22.2$ mag) and the Fe abundance becomes quite high $[_V]=0.700$ )." We also tried. another exercise. namely we abandoned our self-consistent evaluation of the time at. which the ealactic wind occurs. based on a detailed. treatment of the SN remnant evolution. and fixed it a priori.," We also tried another exercise, namely we abandoned our self-consistent evaluation of the time at which the galactic wind occurs, based on a detailed treatment of the SN remnant evolution, and fixed it a priori." Here. we present the results for model g. with ρω=0.25 Gyr.," Here we present the results for model g, with $t_{gw}=0.25$ Gyr." In this case. although the predicted abundance ratios (nzimely xΑΙPev]=0433. «FefH7]= 0.414) are fairly consistent with observations. the colours become too blue.," In this case, although the predicted abundance ratios (namely $[_V]=0.433$, $[_V]=0.414$ ) are fairly consistent with observations, the colours become too blue." " In fact. we predict U-V—1.22 and. V-Ix22.83 for a total V magnitude A,=21.0 mag."," In fact, we predict U-V=1.22 and V-K=2.83 for a total V magnitude $M_V = -21.0$ mag." This ack hoc model can be seen as a possible way to extend model to Case 2., This ad hoc model can be seen as a possible way to extend model to Case 2. " In fact. owing to the adopted sell-consistent treatment for the development of the galactic wind. mocel cannot reach A,~ 1."," In fact, owing to the adopted self-consistent treatment for the development of the galactic wind, model cannot reach $R_* \sim 1$ ." " Here. instead. we reduce the SE timescale during the initial burst. (Le. £44) by a factor of 4: therefore we have 2,~1."," Here, instead, we reduce the SF timescale during the initial burst (i.e. $t_{gw}$ ) by a factor of $\sim 4$; therefore we have $R_* \sim 1$." Concerning Case 3. we start by increasing the SE elliciencv during the second. burst.," Concerning Case 3, we start by increasing the SF efficiency during the second burst." " For instance see the model (Le. model with v=20Cyr|. which eads to 2,~ 2). which improves the agreement. between he predictions regarding the chemical properties. although he colours are still bluer than the fiducial case."," For instance see the model (i.e. model with $\nu =20 Gyr^{-1}$, which leads to $R_* \sim 2$ ), which improves the agreement between the predictions regarding the chemical properties, although the colours are still bluer than the fiducial case." Finally. we »esent modelc. an illustrative case for a LOYAL. galaxy in which we vary the parameters in order to have a mild and prolonged. SE before the onset of the merger-induced »urst (occurring at 2 Gaver)," Finally, we present model, an illustrative case for a $10^{12}M_{\odot}$ galaxy in which we vary the parameters in order to have a mild and prolonged SF before the onset of the merger-induced burst (occurring at 2 Gyr)." This corresponds to the region of xwameter space in which 7 varies in the interval 0.5. 10] Cyr and vyx20€vr (during the first burst).," This corresponds to the region of parameter space in which $\tau$ varies in the interval [0.5, 10] Gyr and $\nu \le 20 \rm \, Gyr^{-1}$ (during the first burst)." In particular. we chose 7r—3 Gyr. vy222vr band p2110Cr.+ during he burst.," In particular, we chose $\tau=3$ Gyr, $\nu = 2.2 \rm\, Gyr^{-1}$ and $\nu = 110 \rm\, Gyr^{-1}$ during the burst." A wind developes only after the starburst., A wind developes only after the starburst. The model exhibits “<_V]=0.416$, U-V=1.48 and V-K=3.25 (for a $M_V = -21.8$ mag), values which are pretty close to Paper I's best model results." Nevertheless. he SE produces a very high. Fe enrichment in the bulk of he stars (_V]=0.839$ ) which is not observed." In the hypothesis that this kind of ealactie model can be zirlv represented by a SSP (but see Pipino. Matteucci Chiappini 2005. in preparation). this would. translate into he Lick index «fe>=4.5 (once Worthev's 1904 simple stellar populations are adopted. see Paper 1).," In the hypothesis that this kind of galactic model can be fairly represented by a SSP (but see Pipino, Matteucci Chiappini 2005, in preparation), this would translate into the Lick index $=4.5$ (once Worthey's 1994 simple stellar populations are adopted, see Paper I)." The clleet of moving the epoch of the mergers to fiuzm 5 Gyr is to worsen the results. since the colours become progressively bluer (c.g. V - IX —3.13 for Ady=22.1 mag)," The effect of moving the epoch of the mergers to $t_{acc}\ge$ 5 Gyr is to worsen the results, since the colours become progressively bluer (e.g. V - K =3.13 for $M_V = -22.1$ mag)." " Given its Z2,~2 and the behaviour of its SELL. to some extent. this is a complementary result of what Matteucci Pipino (2005) have shown for Poplll stars in cllipticals (see also Gibson 1996 [or a more extended: discussion on the bimodal SE. in ellipticals) by changing the IMEat early epochs."," Given its $R_* \sim 2$ and the behaviour of its SFH, to some extent, this is a complementary result of what Matteucci Pipino (2005) have shown for PopIII stars in ellipticals (see also Gibson 1996 for a more extended discussion on the bimodal SF in ellipticals) by changing the IMFat early epochs." In any case. even a short. pre-enrichment of the bulk of the stellar populations.," In any case, even a short pre-enrichment of the bulk of the stellar populations," models. including the spectra displaved in Fies.,"models, including the spectra displayed in Figs." 2. and 3.., \ref{fig2} and \ref{fig3}. Since the residual Ποιά scales with the size of the cloud (in parallel clouds of constant densitv). an increase in ;dl produces a decrease in the emitted integrated intensity. when the main pumping mechanism is radiative.," Since the residual field scales with the size of the cloud (in parallel clouds of constant density), an increase in $A_V$ produces a decrease in the emitted integrated intensity, when the main pumping mechanism is radiative." We also note that in the RCM. depending on the formation model. I5 formation pumping produces an IR. excess of about 20—40 with respect to the pumped. IR background.," We also note that in the RCM, depending on the formation model, $_2$ formation pumping produces an IR excess of about $20 - 40$ with respect to the pumped IR background." To highlight spectral features arising [rom specific Ho formation pumping profiles we show in Fig., To highlight spectral features arising from specific $_2$ formation pumping profiles we show in Fig. " 4 the residual spectra computed for the RCM alter subtraction of the ""background"" UV pumpingcontribution. i.e. (he spectrum arising in model (07) (right bottom panel of Fig. 2))."," \ref{fig4} the residual spectra computed for the RCM after subtraction of the “background"" UV pumpingcontribution, i.e. the spectrum arising in model $(vi)$ (right bottom panel of Fig. \ref{fig2}) )." " Since radiative (transfer couples different parts of the cloud. residual spectra may provide an indication of the formation pumping effect. but in general they cannot be considered as an ""exacti"" measure of the formation pumping contribution to line excitation."," Since radiative transfer couples different parts of the cloud, residual spectra may provide an indication of the formation pumping effect, but in general they cannot be considered as an “exact"" measure of the formation pumping contribution to line excitation." The most intense residual emission limes produced by the formation pumping are reported [or each model in Table 3., The most intense residual emission lines produced by the formation pumping are reported for each model in Table 3. Model (0) shares some features with model (777) only., Model $(i)$ shares some features with model $(iii)$ only. All the other formation punping present several common features., All the other formation pumping present several common features. Our proposed formation puniping model produces spectra where the highest vibrational level is ο=4. with no lines [rom high rotational states in the 4—5 jan region.," Our proposed formation pumping model produces spectra where the highest vibrational level is $v = 4$, with no lines from high rotational states in the $4 - 5$ $\mu$ m region." In model (77) (Black&Dalgarno1976).. high rotational evels are pumped. as expected. with the highest being -16 (at an intensity level of Lx10 eres Fem 7 ! yan +).," In model $(ii)$ \citep{BD76}, high rotational levels are pumped, as expected, with the highest being $J = 16$ (at an intensity level of $1 \times 10^{-4}$ ergs $^{-1}$ $^{-2}$ $^{-1}$ $\mu$ $^{-1}$ )." Although presenting the highest integrated intensities. nodels (77) (Black&Dalgarno1976). and (777) (Draine&DBertoldi1996). do not show very prominent spectral features. because of the wide dispersion of the internal energy over a arge number of vibrational states.," Although presenting the highest integrated intensities, models $(ii)$ \citep{BD76} and $(iii)$ \citep{DB96} do not show very prominent spectral features, because of the wide dispersion of the internal energy over a large number of vibrational states." Models (/0) and (e) (Takahashi&Uehara2001). show igh rotational states. as well as a combination of moderately high ο and JJ. such as the (ir.J)=(3.9) state.," Models $(iv)$ and $(v)$ \citep{TU01} show high rotational states, as well as a combination of moderately high $v$ and $J$ , such as the $(v,J) = (3,9)$ state." These models provide quite different spectral patterns. with the former showing brighter lines. while (he latter exhibits a richer spectrum.," These models provide quite different spectral patterns, with the former showing brighter lines, while the latter exhibits a richer spectrum." The most intense transition or model (7) is (4—2) O(3). whereas the (1—0) S(7) line is strongest for all other models.," The most intense transition for model $(i)$ is $(4-2)$ O(3), whereas the $(1-0)$ S(7) line is strongest for all other models." In Table 3. we present emission lines computed for model (07).," In Table 3, we present emission lines computed for model $(vi)$." Since. in Chis model. formation punping is suppressed. spectral features arise from radiative and collisional pumping close to the edge of the cloud.," Since, in this model, formation pumping is suppressed, spectral features arise from radiative and collisional pumping close to the edge of the cloud." Transitions involving low rotational states (7<5) show a svstematic mixing of internal ancl environmental pumping mechanisms., Transitions involving low rotational states $(J \le 5)$ show a systematic mixing of internal and environmental pumping mechanisms. As a consequence. our formation punping model. which predicts little rotational excitation. appears to produce an emission spectrum contaminated by external factors.," As a consequence, our formation pumping model, which predicts little rotational excitation, appears to produce an emission spectrum contaminated by external factors." This contamination does not occur [or cases where the emission is dominated by transitions from high rotational states. such as the (1—0) 50) line in the Black&Dalgarno(1976) model.," This contamination does not occur for cases where the emission is dominated by transitions from high rotational states, such as the $(1-0)$ S(7) line in the \citet{BD76} model." In Figs., In Figs. 5 and 6.. we show the volume emissivities of the (4—2) O(3) and (1—0) S(7) lines as functions of the optical thickness within the cloud.," \ref{fig5} and \ref{fig6}, , we show the volume emissivities of the $(4-2)$ O(3) and $(1-0)$ S(7) lines as functions of the optical thickness within the cloud." The (4—2) O(3) transition has been computed for models (/) and (0/) in the translucent. ancl dense cloud regimes. while,"The $(4-2)$ O(3) transition has been computed for models $(i)$ and $(vi)$ in the translucent and dense cloud regimes, while" "where pjsyp and p, are the density of the ISM and stellar wind. respectively; v; is the velocity of the star with respect to the ISM. and v, is the stellar wind velocity.","where $\rho_{\rm ISM}$ and $\rho_{\rm w}$ are the density of the ISM and stellar wind, respectively; $v_*$ is the velocity of the star with respect to the ISM, and $v_{\rm w}$ is the stellar wind velocity." Assuming spherical mass loss from the star. = [Anz(0) and rearranging the resulting equation yields the well known solution: −," Assuming spherical mass loss from the star, = / 4 r^2, and rearranging the resulting equation yields the well known solution: =." Making the additional assumption of momentum conservation and assuming that the material mixes and cools instantaneously (so that the dense shell has negligible thickness. re. the thin-shell approximation). ? derived an analytic expression for the shape of the bow shock: R(9)) =3 where 4 is the polar angle measured from the axis of symmetry.," Making the additional assumption of momentum conservation and assuming that the material mixes and cools instantaneously (so that the dense shell has negligible thickness, i.e. the thin-shell approximation), \cite{Wil96} derived an analytic expression for the shape of the bow shock: ) =, where $\theta$ is the polar angle measured from the axis of symmetry." Utilising the above analytic models and current estimates of Betelgeuse's wind properties and distance (see Table. 1)).," Utilising the above analytic models and current estimates of Betelgeuse's wind properties and distance (see Table. \ref{tab: bet}) )," " derived a space velocity of v, = 40 ny ?qmss with respect to the local ISM.", \cite{Ueta08} derived a space velocity of $v_*$ = 40 $_{\rm H}^{-1/2}$ $^{-1}$ with respect to the local ISM. Estimates of the ISM density. ng. range from 0.3 em? for a flow emanating from the Orion Nebula Complex (ONC) (2). to 1.5 - 1.9 em™ if the origin of the flow is the Orion OB | association (??)..," Estimates of the ISM density, $_{\rm H}$, range from 0.3 $^{-3}$ for a flow emanating from the Orion Nebula Complex (ONC) \citep{Fri90} to 1.5 - 1.9 $^{-3}$ if the origin of the flow is the Orion OB 1 association \citep{Ueta08,Ueta09}." Given this range of ISM densities. Betelgeuse’s space velocity with respect to the ambient medium is therefore likely to be between 73 ss! and 28 ss!," Given this range of ISM densities, Betelgeuse's space velocity with respect to the ambient medium is therefore likely to be between 73 $^{-1}$ and 28 $^{-1}$." If we assume strong shock conditions. the post-shock temperature corresponding to these stellar velocities. is at least 100000 K. To date. the bow shock has only been detected in the far-infrared. where the bulk of the emission ts probably caused by dust grains with an uncertain contribution from oxygen and carbon fine-structure lines.," If we assume strong shock conditions, the post-shock temperature corresponding to these stellar velocities, is at least 000 K. To date, the bow shock has only been detected in the far-infrared, where the bulk of the emission is probably caused by dust grains with an uncertain contribution from oxygen and carbon fine-structure lines." There are several multi-dimensional hydrodynamic models of wind-ISM interactions with relevant parameters for Betelgeuse., There are several multi-dimensional hydrodynamic models of wind-ISM interactions with relevant parameters for Betelgeuse. For example. ? have investigated the interaction of the ISM with a wind ejected from a stationary star evolving from the main sequence to the RSG and then Wolf-Rayet (WR) phase.," For example, \cite{Gar96} have investigated the interaction of the ISM with a wind ejected from a stationary star evolving from the main sequence to the RSG and then Wolf-Rayet (WR) phase." They found that the RSG wind had a significant effect on the subsequent WR phase., They found that the RSG wind had a significant effect on the subsequent WR phase. The same conclusion was reached by ? who studied the circumstellar medium (CSM) resulting from a moving star in 2D. As expected. in this case à bow shock are was formed rather than a spherical shell.," The same conclusion was reached by \cite{Bri95} who studied the circumstellar medium (CSM) resulting from a moving star in 2D. As expected, in this case a bow shock arc was formed rather than a spherical shell." The implications of an RSG phase for the WR progenitors of gamma-ray bursts was also discussed in a similar investigation by 2., The implications of an RSG phase for the WR progenitors of gamma-ray bursts was also discussed in a similar investigation by \cite{Van06}. .? and ? calculated a series of 3D and 2D hydrodynamic models. respectively. of the interaction of a stellar wind from an asymptotic giant branch (AGB) star with the ISM and the subsequent structure formed during the planetary nebula phase.," \cite{War07a} and \cite{Vil03} calculated a series of 3D and 2D hydrodynamic models, respectively, of the interaction of a stellar wind from an asymptotic giant branch (AGB) star with the ISM and the subsequent structure formed during the planetary nebula phase." Other models of the CSM around fast-moving AGB stars include 3D and axisymmetric models of Mira’s bow shock (??.respectively)...," Other models of the CSM around fast-moving AGB stars include 3D and axisymmetric models of Mira's bow shock \citep[][respectively]{Rag08,Esq10}." More recently. ? have modelled Betelgeuse’s bow shock with 2D high-resolution simulations that include a simple dust tracking scheme.," More recently, \cite{Van11} have modelled Betelgeuse's bow shock with 2D high-resolution simulations that include a simple dust tracking scheme." They show that the flow for grains of various sizes differed and can have important consequences for interpreting infrared observations of bow shocks., They show that the flow for grains of various sizes differed and can have important consequences for interpreting infrared observations of bow shocks. We build on the work above by including a realistic treatment of the thermal physics and chemistry in 3D models and consider à broader range of parameters., We build on the work above by including a realistic treatment of the thermal physics and chemistry in 3D models and consider a broader range of parameters. The numerical method and model parameters are described in Sect. 2.., The numerical method and model parameters are described in Sect. \ref{sec: method}. In Sect. 3.. ," In Sect. \ref{sec: adiab}," we present an adiabatic model that serves as a code test and a point of reference for the simulations that include radiative cooling., we present an adiabatic model that serves as a code test and a point of reference for the simulations that include radiative cooling. The flow characteristics. morphology. and shell properties of the latter are described in Sect. 4..," The flow characteristics, morphology, and shell properties of the latter are described in Sect. \ref{sec: cool}." Finally. the implications of this work. particularly with regard to Betelgeuse’s bow shock morphology. shell mass and age are discussed in Sect. 5..," Finally, the implications of this work, particularly with regard to Betelgeuse's bow shock morphology, shell mass and age are discussed in Sect. \ref{sec: disc}." Smoothed particle hydrodynamics (SPH) is a Lagrangian method in which particles behave like discrete fluid elements., Smoothed particle hydrodynamics (SPH) is a Lagrangian method in which particles behave like discrete fluid elements. However. each of their fluid properties. e.g. density. temperature. or velocity. is the result of mutually overlapping summations and interpolations of the same properties of," However, each of their fluid properties, e.g. density, temperature, or velocity, is the result of mutually overlapping summations and interpolations of the same properties of" The recent observation of high lincar polarization during the prompt -rav cussion of GRB 021206 (Coburn Boges 2003) suggests that CRBs be driven by lughly magnetized. rapidly rotating compact objects;,"The recent observation of high linear polarization during the prompt $\gamma$ -ray emission of GRB 021206 (Coburn Boggs 2003) suggests that GRBs be driven by highly magnetized, rapidly rotating compact objects." Two popular scenarios for their birth are the merger of a colmpact binary or the collapse of a massive star (for a recent review see Mésszárros 2002)., Two popular scenarios for their birth are the merger of a compact binary or the collapse of a massive star (for a recent review see Mésszárros 2002). Tn both scenarios. a rapidly rotating black hole surrounded by au accretion disk seenis to be a comunuon reninaut (Naravan. Paczvisski Piran 1992: Woosley 1993: Mésszirros Rees 19972: Paczvüsski 1998).," In both scenarios, a rapidly rotating black hole surrounded by an accretion disk seems to be a common remnant (Narayan, Paczyńsski Piran 1992; Woosley 1993; Mésszárros Rees 1997a; Paczyńsski 1998)." Iowever. a uillisecond maguctar has also been argued as an alternative imteresting product (Usov 1992: Duncan Thompson 1992: Kluzuniax πάσα 1998: Dai Lu 1998: Spruit 1999: Ruderman. Tao IKlIuzuniak 2000: Wheeler et al.," However, a millisecond magnetar has also been argued as an alternative interesting product (Usov 1992; Duncan Thompson 1992; Kluźnniak Ruderman 1998; Dai Lu 1998; Spruit 1999; Ruderman, Tao Kluźnniak 2000; Wheeler et al." 2000)., 2000). To explain the complex temporal feature. the burst itself. iun some of these energy models. is understood to arise from a series of explosive reconnection events in a rising. amplified magnetic field because of the Parker instability.," To explain the complex temporal feature, the burst itself, in some of these energy models, is understood to arise from a series of explosive reconnection events in a rising, amplified magnetic field because of the Parker instability." This in fact dissipates the differeutiallv rotational euergv aud magnetic enerev of the newborn uaenetar or accretion disk., This in fact dissipates the differentially rotational energy and magnetic energy of the newborn magnetar or accretion disk. After the CRB. the remaining object is reasonably asstumed to be a millisecond magnetar or a rapidly rotating dack hole surrounded by an accretion disk.," After the GRB, the remaining object is reasonably assumed to be a millisecond magnetar or a rapidly rotating black hole surrounded by an accretion disk." For the latter object. the magnetic field in the disk could have becu wuplified initially bv differential rotation to a magnetar strength of ~10 C. and particularly. within the yamework of the collapsar/lypernova model. such a field could be kept. due to longevity (with davs or lounger) of he disk maintained by fallback of the ejecta.," For the latter object, the magnetic field in the disk could have been amplified initially by differential rotation to a magnetar-like strength of $\sim 10^{15}$ G, and particularly, within the framework of the collapsar/hypernova model, such a field could be kept, due to longevity (with days or longer) of the disk maintained by fallback of the ejecta." During the afterglow. the object at the center will directly lose its rotational euerev by the magnetic dipole radiatiou or the Dlaudford-Zuajek moechauisuai.," During the afterglow, the object at the center will directly lose its rotational energy by the magnetic dipole radiation or the Blandford-Znajek mechanism." Au enerev outflow driven maguetically iucludes. three components: low-frequency clectromaguctic waves. a relativistic wiud. and a toroidal magnetic field associated with the wind.," An energy outflow driven magnetically includes three components: low-frequency electromagnetic waves, a relativistic wind, and a toroidal magnetic field associated with the wind." The wind cnereyv flux is unlikely to be barvou-donmünated. because the initial explosion should lave left a clean passage with very few barvou contanunation for a subsequent outflow.," The wind energy flux is unlikely to be baryon-dominated, because the initial explosion should have left a clean passage with very few baryon contamination for a subsequent outflow." The interaction of this outflow with au outward-expaucding fireball implies a coutiuuous injection of the stellar rotational cucrey iuto the fireball., The interaction of this outflow with an outward-expanding fireball implies a continuous injection of the stellar rotational energy into the fireball. Dai Lu (19985. 2000). Zhang Mésszárros (2001) and Chane. Lee Vi (2002) discussed the evolution of a relativistic fireball by assunmiue a pure clectromagnueticavave encrev outflow. while Rees A\eésszarros (1998). Savi Aésszarros (2000). Zhang Alésszárros (2002). and Caanot. Nalar Piran (2003) took into account ai variable anc barvon-donuuated imjectiou.," Dai Lu (1998, 2000), Zhang Mésszárros (2001) and Chang, Lee Yi (2002) discussed the evolution of a relativistic fireball by assuming a pure electromagnetic-wave energy outflow, while Rees Mésszárros (1998), Sari Mésszárros (2000), Zhang Mésszárros (2002), and Granot, Nakar Piran (2003) took into account a variable and baryon-dominated injection." ILowewer. based ou the successful models of the wellobserved. Crab Nebula (Rees Camu 1971: Ἱνοιπο Coroniti 1981: Desehuau Li 1992: Chevalier 2000). a realistic. coutiuuous outflow during the afterelow is expected to be ultra-relativistie aud dominated bv the eucrev flux of electron-positron pairs.," However, based on the successful models of the well-observed Crab Nebula (Rees Gunn 1974; Kennel Coroniti 1984; Begelman Li 1992; Chevalier 2000), a realistic, continuous outflow during the afterglow is expected to be ultra-relativistic and dominated by the energy flux of electron-positron pairs." As in the Crab Nebula. even if au outflow from the pulsar is Povutine-flux-domunated at mall radii. the fluctuating component of the maenetic field iu this outflow cau be dissipated by magnetic reconnection aud used to accelerate the outflow. which is eveutually dominated by the enerev flux of ee pairs within a larger radius ~1057 om (Coroniti 1990: Michel 1991: INirk Skjoraasan 2003).," As in the Crab Nebula, even if an outflow from the pulsar is Poynting-flux-dominated at small radii, the fluctuating component of the magnetic field in this outflow can be dissipated by magnetic reconnection and used to accelerate the outflow, which is eventually dominated by the energy flux of $^+$ $^-$ pairs within a larger radius $\sim 10^{17}$ cm (Coroniti 1990; Michel 1994; Kirk raasan 2003)." In. the case of au afterelow. therefore. it is natural to expect that the central object still produces au ultra-relativistic e! -pair wind. whose interaction with the fireball leads to a relativistic wind bubble.," In the case of an afterglow, therefore, it is natural to expect that the central object still produces an ultra-relativistic $^+$ $^-$ -pair wind, whose interaction with the fireball leads to a relativistic wind bubble." This can be regarded asNebula., This can be regarded as. Iu this paper. we explore the dvuaimics of such a wiud bubble aud its cimission signatures.," In this paper, we explore the dynamics of such a wind bubble and its emission signatures." Iu 82 we preseut expressions of the luminosity of a relativistic wiud frou a highly magnetized. rapidly rotating object.," In 2 we present expressions of the luminosity of a relativistic wind from a highly magnetized, rapidly rotating object." Iu 3 and 1 we discuss evolution of the wind bubble aud, In 3 and 4 we discuss evolution of the wind bubble and retsec:shocks.,. . A composite N-rav/optical/radio image is shown iu refiie:compositel.., A composite X-ray/optical/radio image is shown in \\ref{fig:composite1}. . The 0.3.2.0 keV. tage is shown iu red. radio eniission at [5 CIIz from the VLA is displaved as blue. aud optical r-bind eniüssion from the Sloan Digital Sky Survey. (SDSS: Abazajian et 22009) is shown as ercen.," The $0.3 - 2.0$ keV image is shown in red, radio emission at 4.8 GHz from the VLA is displayed as blue, and optical r-band emission from the Sloan Digital Sky Survey (SDSS; Abazajian et 2009) is shown as green." The AGN is visible in the N-rav. radio. and optical. aud the radio lobes fill the cavities in the N-vay cussion.," The AGN is visible in the X-ray, radio, and optical, and the radio lobes fill the cavities in the X-ray emission." This includes the uer cavities ax well as an outer cavity bounded by a narrow oop to the NW and the outer cavity to the S/SE., This includes the inner cavities as well as an outer cavity bounded by a narrow loop to the NW and the outer cavity to the S/SE. Iu addition. the radio cussion is breaking through the rortherm bubble riu to the north.," In addition, the radio emission is breaking through the northern bubble rim to the north." The X-rav fihuneut extending from the northern bubble rim towards the AGN was found to be associated with fa emission iu Blanton et ((2001)., The X-ray filament extending from the northern bubble rim towards the AGN was found to be associated with $H\alpha$ emission in Blanton et (2001). In refüe:sdsscont.. we show SDSS r-baud contours superposed on ao |image in the 0.3—10.0 seV xyauee that has been simoothed with a 175 radius Gaussian.," In \\ref{fig:sdsscont}, we show SDSS r-band contours superposed on a image in the $0.3 - 10.0$ keV range that has been smoothed with a $1\farcs5$ radius Gaussian." The ceutral cD ealaxy is oriented in the NE-SW direction in the optical., The central cD galaxy is oriented in the NE-SW direction in the optical. The inner bubbles secu in the X-ray euission are withiu the cD galaxy., The inner bubbles seen in the X-ray emission are within the cD galaxy. Iu order to better reveal features in the N-rav. image. we created residual iniages using two differeut techniques.," In order to better reveal features in the X-ray image, we created residual images using two different techniques." Iu the first. we used the method of uusharpauaskiug. and iu the second. we subtracted a 2D beta model frou the N-vav inage.," In the first, we used the method of unsharp-masking, and in the second, we subtracted a 2D beta model from the X-ray image." We fiud that unsharp-maskine is useful for liehliehtius the structure iu the iuner parts of the cluster. while the model subtraction is better at revealing larger-scale features.," We find that unsharp-masking is useful for highlighting the structure in the inner parts of the cluster, while the model subtraction is better at revealing larger-scale features." We created an wusharp-masked iniage in the 0.3.10.0 keV cnerey range., We created an unsharp-masked image in the $0.3 - 10.0$ keV energy range. Sources were detected in the image using the wavelet detection tool “wavaetect™ in CIAO (Freeman et 22002)., Sources were detected in the image using the wavelet detection tool “wavdetect” in CIAO (Freeman et 2002). Several wavelet scales were used. at 1. 2. L 8. and 16 pixels. where 1 pixel = 07192.," Several wavelet scales were used, at 1, 2, 4, 8, and 16 pixels, where 1 pixel = $0\farcs492$." Sources detected using this method were visually exanuned aud several were rejected as being ον X-ray gas endssion rather than point sources., Sources detected using this method were visually examined and several were rejected as being clumpy X-ray gas emission rather than point sources. A source-free nuage was created by replacing the source pixcl values with the average value found in an aunulus surrouucdiug cach source., A source-free image was created by replacing the source pixel values with the average value found in an annulus surrounding each source. We retained the sources m our uusharp-masked mage while making corrections with a source-free inage., We retained the sources in our unsharp-masked image while making corrections with a source-free image. Sunoothed images. both with aud without sources. were created by smoothing with a 0798 radius Gaussian.," Smoothed images, both with and without sources, were created by smoothing with a $0\farcs98$ radius Gaussian." Another copy of the source-free image was smoothed with a 978 Gaussian., Another copy of the source-free image was smoothed with a $9\farcs8$ Gaussian. " A ος, image was made by combining the source-free iniages sinoothed at the two different scales.", A summed image was made by combining the source-free images smoothed at the two different scales. A difference imuage was mace bv subtracting the 978. Caussian-simootled source-free uuaese from the 0798 Chusuanuesnoothed image that contained sources., A difference image was made by subtracting the $9\farcs8$ Gaussian-smoothed source-free image from the $0\farcs98$ Gaussian-smoothed image that contained sources. Finally. the uusharp-auasked image was created by dividiug fιο difference imuage bv the sunmned image.," Finally, the unsharp-masked image was created by dividing the difference image by the summed image." " In this wav. we retain the sources in the image. smoothed at a scale of 098,"," In this way, we retain the sources in the image, smoothed at a scale of $0\farcs98$." " This iuethiod is simular to that in Fabian ct ((2006). although sources are excluded throughout in their wusharp-masked oeages,"," This method is similar to that in Fabian et (2006), although sources are excluded throughout in their unsharp-masked images." The uushirpauasked image is displaved in Figure 6 with VLA Ls GIIz radio contours superposed., The unsharp-masked image is displayed in Figure \ref{fig:unsharp} with VLA 4.8 GHz radio contours superposed. The mbbles in the X-ray enüssion are more easily seen 1- us image. as are the bright bubble rims. the shock exterior to the bubble rius. aud the second shock or cold front feature to the NE.," The bubbles in the X-ray emission are more easily seen in this image, as are the bright bubble rims, the shock exterior to the bubble rims, and the second shock or cold front feature to the NE." The radio emission fills 1ο -immer bubbles aud the southern lobe turus to fll 1e outer southern bubble., The radio emission fills the inner bubbles and the southern lobe turns to fill the outer southern bubble. The radio lobe to the nor1 ppears to be escaping through a gap in the norther1 »bble riu. and a narrow fibuuent is seen iu the radio 1 is region.," The radio lobe to the north appears to be escaping through a gap in the northern bubble rim, and a narrow filament is seen in the radio in this region." The radio euiüssion also extends bevond the mbble rius to the NW to fll à small bubble bouuded by a narrow X-rav fibuueut., The radio emission also extends beyond the bubble rims to the NW to fill a small bubble bounded by a narrow X-ray filament. To the east. au extension in the radio fills a small depression in the N-rav ou the scale of approximately 10”.," To the east, an extension in the radio fills a small depression in the X-ray on the scale of approximately $10\arcsec$ ." A 2D beta model was used to fit the surface brightucss in both 0.3.90 κο and 0.310.0 keV images using a circular region with radius 5/66., A 2D beta model was used to fit the surface brightness in both $0.3 - 2.0$ keV and $0.3 - 10.0$ keV images using a circular region with radius $5\farcm66$. The images were souree-free. with the surface brightuess at the position of sources approximated from the surface brigltuess iu an aunumlus around cach source. as above.," The images were source-free, with the surface brightness at the position of sources approximated from the surface brightness in an annulus around each source, as above." Corrections were made for exposure. using a merged exposure map.," Corrections were made for exposure, using a merged exposure map." Similar results were obtained for the fits to the images iu both energv binds., Similar results were obtained for the fits to the images in both energy bands. Exrors were computed using Cash statistics., Errors were computed using Cash statistics. For the 0.3.2.0 keV nuage. the ceuter of the large scale chluission was fouud to be only 172 away from the position of the AGN.," For the $0.3 - 2.0$ keV image, the center of the large scale emission was found to be only $1\farcs2$ away from the position of the AGN." The emission was found to be slightly elliptical. with an ellipticity value of 0.18250.00081 (where ellipticitv values range from 0 to 1. with 0 indicatiug circular cinission).," The emission was found to be slightly elliptical, with an ellipticity value of $0.18\pm0.00081$ (where ellipticity values range from 0 to 1, with 0 indicating circular emission)." The position angle for the semi-major axis of the ellipse is 38.2c0.17 mcasured north towards east., The position angle for the semi-major axis of the ellipse is $38.2\pm{0.1}^{\circ}$ measured north towards east. The core radius usiue this model is 25.1+0.060” and the beta index is 9=0.16d0.00021., The core radius using this model is $25.1\pm{0.060}\arcsec$ and the beta index is $\beta = 0.46\pm{0.00021}$. The residual nage after 2D beta model subtraction iu he 0.3.2.0 keV. band in shown iu reffie:beta2d.., The residual image after 2D beta model subtraction in the $0.3 - 2.0$ keV band in shown in \\ref{fig:beta2d}. The image has been smoothed with a 7738 radius Gaussian., The image has been smoothed with a $7\farcs38$ radius Gaussian. The smoothing washes out the details in he very center of the image. but the bright bubble rims are clearly visible.," The smoothing washes out the details in the very center of the image, but the bright bubble rims are clearly visible." A spiral feature is seen. starting in the SW aud extending to the NE.," A spiral feature is seen, starting in the SW and extending to the NE." Similar spiral structures wave been seen in other clusters. with A2029 being a articularly clear example (Clarke et 22001).," Similar spiral structures have been seen in other clusters, with A2029 being a particularly clear example (Clarke et 2004)." Spectral maps were created to examine the distribution of temperature. as well as entropy. pressure. and abundance using the technique described in Raudall et ((2008. 2009b).," Spectral maps were created to examine the distribution of temperature, as well as entropy, pressure, and abundance using the technique described in Randall et (2008, 2009b)." " The temperature maps were created by extracting spectra for the separate Chandra observations and fitting them siauultaneouslv in the 0.6/—7.0 keV range with a single temperature APEC inodel with Ny κο to the Galactie value. of 2.71«10?"" an (Dickey Lockiiau 1990) aud the abundance allowed to vary."," The temperature maps were created by extracting spectra for the separate ${\it Chandra}$ observations and fitting them simultaneously in the $0.6 - 7.0$ keV range with a single temperature APEC model, with $N_H$ set to the Galactic value of $2.71\times10^{20}$ $^{-2}$ (Dickey Lockman 1990) and the abundance allowed to vary." Dackeround spectra were extracted from the blauk sky background observations that were reprojected to match cach data set., Background spectra were extracted from the blank sky background observations that were reprojected to match each data set. Data from both the froutside- aud backside-àluiinated (FI and DI) chips were used. with separate response files aud norlmalizations determined for cach ObsID's data set. with the ΕΤand DI novmalizatious allowed to vary indepeudeutly for cach ObsID.," Data from both the frontside- and backside-illuminated (FI and BI) chips were used, with separate response files and normalizations determined for each ObsID's data set, with the FIand BI normalizations allowed to vary independently for each ObsID." Spectra were extracted witha nüninmun of either 2000 or 10000 Dackerouud-subtracted counts. corresponding to a muni SNR of approximately £5 or 100. respectively. depending ou our analysis goals.," Spectra were extracted witha minimum of either 2000 or 10000 background-subtracted counts, corresponding to a minimum SNR of approximately 45 or 100, respectively, depending on our analysis goals." The radius of the, The radius of the well within the uncertainty of the measurement (eq. [3.1].,well within the uncertainty of the measurement (eq. \ref{eq:SMCvelocity}] ]). " At ziii10 the physical separation aud relative velocity of the Clouds are ly =kpe.. ve, = 1."," At $z_{\rm init}\sim 10$ the physical separation and relative velocity of the Clouds are r_a =, v_a = ." Figure 5 shows the evolution of the pliysical separation of the Clouds in this example and iu a second example (b) that has present velocity vy=--1. also consistent. with the measurement. and initial separation aud relative velocity ry —kpe.. ey =—1.," Figure \ref{figure:5} shows the evolution of the physical separation of the Clouds in this example and in a second example (b) that has present velocity v_b=, also consistent with the measurement, and initial separation and relative velocity r_b =, v_b =." Iu both examples there is a recent close passage. 200 Myr ago at απ separation kpe and relative velocity egg=165 km 5 in (a). and 180 Myr ago at rg=12 kpe and Ung=1TO km Lin (b).," In both examples there is a recent close passage, 200 Myr ago at minimum separation $r_{\rm mn}=14$ kpc and relative velocity $v_{\rm mn}=165$ km $^{-1}$ in (a), and 180 Myr ago at $r_{\rm mn}=12$ kpc and $v_{\rm mn}=170$ km $^{-1}$ in (b)." This is quite similar to the most recent. close passage of the Clouds in the solutions in IxX06b. Figure 13. and Besla (2009). Figure 2.," This is quite similar to the most recent close passage of the Clouds in the solutions in K06b, Figure 13, and Besla (2009), Figure 2." In the LG model the Clouds in example (a) Lave been orbiting each other at separation 50 to το kpe prior to that. while in (b) there is another close approach at redshift z1.," In the LG model the Clouds in example (a) have been orbiting each other at separation 50 to 70 kpc prior to that, while in (b) there is another close approach at redshift $z\sim 1$." The case for the recent close passage seenmis reasonably good., The case for the recent close passage seems reasonably good. What happeued before that is not well constraiued by thedyuamical moclel., What happened before that is not well constrained by thedynamical model. "if the source is located in the Galactic bulge or Magellanic Clouds, which is often the case for the current microlensing surveys.","if the source is located in the Galactic bulge or Magellanic Clouds, which is often the case for the current microlensing surveys." " In these cases, we are able to estimate the physical parameters of the whole microlensing systems."," In these cases, we are able to estimate the physical parameters of the whole microlensing systems." " In this section we consider the astrometric events towards the Galactic bulge, SMC and M31 assuming Do, = 8, 65, and 770 kpc, respectively."," In this section we consider the astrometric events towards the Galactic bulge, SMC and M31 assuming $\Dos$ = 8, 65, and 770 kpc, respectively." " We substitute Do,/Ώος = x into equation (1)), which then becomes Therefore, 0 is smaller for a source located at larger distance and is smaller for larger lens distance given the same source location (see upper panels in Fig. 10))."," We substitute $\Dol / \Dos $ = $x$ into equation \ref{eq.tE}) ), which then becomes Therefore, $\AERR$ is smaller for a source located at larger distance and is smaller for larger lens distance given the same source location (see upper panels in Fig. \ref{fig.thetaE}) )." Equation (18)) also implies that the halo lensing events have larger Einstein radii than self-lensing events for a given lens mass., Equation \ref{eq.thetaE_new}) ) also implies that the halo lensing events have larger Einstein radii than self-lensing events for a given lens mass. " For instance, halo lensing events towards SMC with Do, = 15 kpc and M, =1 Mo will induce an astrometric signal with 0g = 645 μας, which is one order of magnitude larger than for self-lensing events (44 µας at D,,, = 64 kpc)."," For instance, halo lensing events towards SMC with $\Dol$ = 15 kpc and $\ML$ = 1 $M_{\odot}$ will induce an astrometric signal with $\AERR$ = 645 $\mu$ as, which is one order of magnitude larger than for self-lensing events (44 $\mu$ as at $\Dol$ = 64 kpc)." Thus we are able to distinguish halo and self-lensing events by the size of the astrometric ellipse., Thus we are able to distinguish halo and self-lensing events by the size of the astrometric ellipse. " The FS effects play an important role when uo s3yJy and R< 21)in the CDF-S. and found a positive evolution in both luminosity and density. suggesting increasing importance of the LIRG and ULIRG populations at higher redshifts.," For example: \citet{2005ApJ...632..169L} analyzed the evolution of the total and $\mu$ m IR luminosity functions (LFs) at $083\mu$ Jy and $R<24$ ) in the CDF-S, and found a positive evolution in both luminosity and density, suggesting increasing importance of the LIRG and ULIRG populations at higher redshifts." " Pérez-Gonzalezetal(2005) used MIPS 24jm observations of the CDF-S and HDF-N (7 &83,/Jy) to find that that L steadily increases by an order of magnitude to -~2. suggesting that the luminosity evolution i5 stronger than the density evolution."," \citet{2005ApJ...630...82P} used MIPS $\mu$ m observations of the CDF-S and HDF-N $>83\mu$ Jy) to find that that $L^*$ steadily increases by an order of magnitude to $z\sim 2$, suggesting that the luminosity evolution is stronger than the density evolution." The Or; scales as 7*2. from :20 to 0.8., The $\Omega_{TIR}$ scales as $^{4.0\pm 0.2}$ from $z$ =0 to 0.8. " Babbedgeetal.(2006) constructed LFs at 3.6. 4.5. 5.8. 8 and 24jm over 02 using the data from the Spitzer Wide-area Infrared Extragalactic (SWIRE) Survey in a 6.5 deg? (5241,44.> 230Jy)."," \citet{2006MNRAS.370.1159B} constructed LFs at 3.6, 4.5, 5.8, 8 and $\mu$ m over $0230 \mu$ Jy)." They found a clear luminosity evolution m all the bands. but the evolution is more pronounced at longer wavelength: extrapolating from 24;;m. they inferred," They found a clear luminosity evolution in all the bands, but the evolution is more pronounced at longer wavelength; extrapolating from $\mu$ m, they inferred" where ry is the core radius. q is the axis ratio and 5 is the power iudex.,", where $r_0$ is the core radius, $q$ is the axis ratio and $\gamma$ is the power index." For an edge-on galaxy. this model has the form (vhere E is the standard Canunua function): o 2.yr," For an edge-on galaxy, this model has the form (where $\Gamma$ is the standard Gamma function): (R,z) = _0 - 2.5." As its dust lane nearly bisects the major axis of NGC 1565. it is difficult for us to fit all the components of this galaxy (uucleus. bulge. disks aud halo} simultaucously.," As its dust lane nearly bisects the major axis of NGC 4565, it is difficult for us to fit all the components of this galaxy (nucleus, bulge, disks and halo) simultaneously." The primary purpose of the present paper is to search for luminous halos in ecec-on galaxies., The primary purpose of the present paper is to search for luminous halos in edge-on galaxies. ence. we concentrate ouly on the three componcuts whose luminosity distributions affect the halo of this galaxy: thin disk (yia projected major axis). thick disk and halo.," Hence, we concentrate only on the three components whose luminosity distributions affect the halo of this galaxy: thin disk (via projected major axis), thick disk and halo." To avoid the possible effect of uucleus. bulec. dust lane and warps. oulv the z-profiles with δη «Rx were used in the ft.," To avoid the possible effect of nucleus, bulge, dust lane and warps, only the $z$ -profiles with $'$ $\leq R \leq$ $'$ were used in the fit." For R-profiles. we rejected the profiles along the dust lane aud the points within bulec.," For $R$ -profiles, we rejected the profiles along the dust lane and the points within bulge." Though there exists obvious asviunietries between the NW aud SE parts of galaxy. they are treated here the same owing to the fact that large areas in both sides of the galaxy are masked.," Though there exists obvious asymmetries between the NW and SE parts of galaxy, they are treated here the same owing to the fact that large areas in both sides of the galaxy are masked." A egoucral V7D method was used to estimateH the paramcters of. the fits., A general $\chi^{2}$ method was used to estimate the parameters of the fits. d In principle.+ one should use a weighted fitting scheme (cf.," In principle, one should use a weighted fitting scheme (cf." " Shaw Cilinore 1989) of the form: with qr auc µη as observed aud fitted surface brightuesses,", Shaw Gilmore 1989) of the form: = with $\mu_i$ and $\mu_{fit}$ as observed and fitted surface brightnesses. Tn practice. the values assigned to e depeud ou what one is trving to fit.," In practice, the values assigned to $w_i$ depend on what one is trying to fit." Unfortunately. the manner in which we can conipeusate for fainter surface brightuess levels (by using larger sample bius) does not fully compensate for the observational errors iu the outer regions. which are πιο larger than those in the immer regious.," Unfortunately, the manner in which we can compensate for fainter surface brightness levels (by using larger sample bins) does not fully compensate for the observational errors in the outer regions, which are much larger than those in the inner regions." Iu. addition. bv sampling with different bin sizes. we lave more measurements nearest the major axis than we do far away from tle major axis.," In addition, by sampling with different bin sizes, we have more measurements nearest the major axis than we do far away from the major axis." Thus. we have more points in our fit for the inside regions with small uncertaiuties than those for the," Thus, we have more points in our fit for the inside regions with small uncertainties than those for the" xopagate the results to 2=0. or to whichever redshift oue wants.,"propagate the results to $z=0$, or to whichever redshift one wants." Thus. one could easily examine the effects that varving the galaxy. formation criteria would have.," Thus, one could easily examine the effects that varying the galaxy formation criteria would have." " Compared to reruuning the full simulation. it is computationally cheap to determine the properties of à. at cach redshift (given the galaxy. formation nodel} and then to reconstruct the evolution of 5,02) aud r4(:)."," Compared to rerunning the full simulation, it is computationally cheap to determine the properties of $\delta_\ast$ at each redshift (given the galaxy formation model) and then to reconstruct the evolution of $b_g(z)$ and $r_g(z)$." The continuity equation may also prove useful iun comparing observations to models., The continuity equation may also prove useful in comparing observations to models. For instance. arge. deep. angular survevs in iaultiple bauds. such as the SDSS. will permit the cross-correlation of different galaxy types as a function of redshift. using plotometry to estimate both redshift and galaxy type (Connolly.Szalav.&Brunner 1998)).," For instance, large, deep, angular surveys in multiple bands, such as the SDSS, will permit the cross-correlation of different galaxy types as a function of redshift, using photometry to estimate both redshift and galaxy type \cite{connolly98ap}) )." If one properly accounts for the evolution of stellar colors. one will be able to test the hypothesis that two galaxy types both obey the continuity equation.," If one properly accounts for the evolution of stellar colors, one will be able to test the hypothesis that two galaxy types both obey the continuity equation." The seuse and degree of auv discrepancy will shed lisht ou whether oue type of galaxy merees to form another. or whether new ealaxies of a specific type are forming.," The sense and degree of any discrepancy will shed light on whether one type of galaxy merges to form another, or whether new galaxies of a specific type are forming." Estimates of the star formation rate as a function of redshift are now possible (Madauetaf1996))., Estimates of the star formation rate as a function of redshift are now possible \cite{madau96ap}) ). Perhaps the next interesting observational goal is to study the evolution of the clustering of star formation., Perhaps the next interesting observational goal is to study the evolution of the clustering of star formation. The Butcher-Ocuuler effect tells us something about the evolution of star formation in dense regions. but it Is necessary to undoerstaud the corresponding evolution iu the field. as well.," The Butcher-Oemler effect tells us something about the evolution of star formation in dense regions, but it is necessary to understand the corresponding evolution in the field, as well." The correlation of star-forming ealaxies at differcut redshifts with the full galaxy population may be a more scusitive discriminant between galaxy formation models than measures of the clustering of all galaxies., The correlation of star-forming galaxies at different redshifts with the full galaxy population may be a more sensitive discriminant between galaxy formation models than measures of the clustering of all galaxies. " This work was supported in part by the erants NACH5-2759, NAC5-603lL. ASTO93-18185. AST96-16901. and the Princetou University Research Board."," This work was supported in part by the grants NAG5-2759, NAG5-6034, AST93-18185, AST96-16901, and the Princeton University Research Board." NÀS acknowledges the additional support of Research Corporation., MAS acknowledges the additional support of Research Corporation. MT is supported by the IIubble Fellowship TF-0108L.01-96À. from STScL. operated by AURA. Iuc.. under NASA contract NAS5-26555.," MT is supported by the Hubble Fellowship HF-01084.01-96A from STScI, operated by AURA, Inc., under NASA contract NAS5-26555." We would like to thanx James E. Gunn. Clixis Melkee. IKeutaro Naganuue. and David N. Spergel for useful discussions. as well as Stépphane Charlot for kindly providing lis spectral svuthesis results.," We would like to thank James E. Gunn, Chris McKee, Kentaro Nagamine, and David N. Spergel for useful discussions, as well as Stépphane Charlot for kindly providing his spectral synthesis results." The couditious required for galaxy formation in each cell of the sinmlation are: The subscript b refers to the barvonic matter: the subscript d refers to the collisionless dark matter., The conditions required for galaxy formation in each cell of the simulation are: The subscript $b$ refers to the baryonic matter; the subscript $d$ refers to the collisionless dark matter. Iu words. these criteria sav that the overdensity must be reasonably lieh. the mass in the cell must be ereater than the Jeaus mass. the eas ust be cooling faster than the local dvuaimical time. aud the flow must be converging.," In words, these criteria say that the overdensity must be reasonably high, the mass in the cell must be greater than the Jeans mass, the gas must be cooling faster than the local dynamical time, and the flow must be converging." " Asstming that the time scale for collapse is the dynamical time. we transfer mass from the eas to collisionless particles at the rate: where fa=fas, if tagcLOO Myrs and fa=100 Mrs if tay,c100 Myers"," Assuming that the time scale for collapse is the dynamical time, we transfer mass from the gas to collisionless particles at the rate: where $t_\ast=t_{\mathrm{dyn}}$ if $t_{\mathrm{dyn}} > 100$ Myrs and $t_\ast= 100$ Myrs if $t_{\mathrm{dyn}} > 100$ Myrs." 'unction is only measurable at small angles 6<107. whereas ow multipoles ( describe surface [luctuations on. rather arger angular scales.,"function is only measurable at small angles $\theta < 10^\circ$, whereas low multipoles $\ell$ describe surface fluctuations on rather larger angular scales." However. in Section 5 we establish hat the signal in low multipoles is actually generated at ow redshift bv spatial fluctuations on relatively small scales. similar to the spatial scales which produce the signal in «(0).," However, in Section \ref{secpk} we establish that the signal in low multipoles is actually generated at low redshift by spatial fluctuations on relatively small scales, similar to the spatial scales which produce the signal in $w(\theta)$." OL course the comparison is not entirely. straight-onward because the two statistics quantify dilferent operties of the galaxy distribution., Of course the comparison is not entirely straight-forward because the two statistics quantify different properties of the galaxy distribution. The value— of €5 quantifies the amplitude. of. Huctuations on the angular scale corresponding to f£., The value of $C_\ell$ quantifies the amplitude of fluctuations on the angular scale corresponding to $\ell$. The value of (0) is the average of the product. of the galaxy. overdensity at. any point with the overdensity at a point at angular separation 6 w(@) depends on angular fluctuations on all scales., The value of $w(\theta)$ is the average of the product of the galaxy overdensity at any point with the overdensity at a point at angular separation $\theta$ – $w(\theta)$ depends on angular fluctuations on all scales. This is illustrated by the inverse of equation Ότι For example. a density map constructed using just one multipole ( possesses a broad angular correlation function.," This is illustrated by the inverse of equation \ref{eqwtocl}: For example, a density map constructed using just one multipole $\ell$ possesses a broad angular correlation function." The purpose of this Section is to demonstrate that. the observed. radio galaxy C spectrum can be understood. in terms of the current [iducial cosmological model., The purpose of this Section is to demonstrate that the observed radio galaxy $C_\ell$ spectrum can be understood in terms of the current fiducial cosmological model. In Section 6 we utilize this framework to determine the linear bias factor of the radio galaxies. marginalizing over other relevant model parameters.," In Section \ref{secbias} we utilize this framework to determine the linear bias factor of the radio galaxies, marginalizing over other relevant model parameters." The angular5 power spectrum C'; is a projection of the spatial power spectrum of mass fluctuations at. different redshifts. Pik.) where & is a co-moving5 wavenumboer.," The angular power spectrum $C_\ell$ is a projection of the spatial power spectrum of mass fluctuations at different redshifts, $P(k,z)$, where $k$ is a co-moving wavenumber." 4n linear perturbation theory. Duetuations with different &. evolve independently. scaling with redshift according to the growth factor ο).," In linear perturbation theory, fluctuations with different $k$ evolve independently, scaling with redshift according to the growth factor $D(z)$ ." " Under this assumption we can simply scale the present-dav matter power spectrum. {ή} back with redshift: Lor an £3,=1. (24=O universe. D(z2)=(1|5."," Under this assumption we can simply scale the present-day matter power spectrum $P_0(k)$ back with redshift: For an $\Omega_m = 1$, $\Omega_\Lambda = 0$ universe, $D(z) = (1+z)^{-1}$." For general cosmological parameters we can use the approximation of Carroll. Press Turner (1992).," For general cosmological parameters we can use the approximation of Carroll, Press Turner (1992)." Lf linear theory holds then the angular power spectrum C; can be written in terms of the present-cay matter power spectrum Ia) as (see c.g. Huterer. Inox Nichol 2001. Tegmark et al.," If linear theory holds then the angular power spectrum $C_\ell$ can be written in terms of the present-day matter power spectrum $P_0(k)$ as (see e.g. Huterer, Knox Nichol 2001, Tegmark et al." 2002) where the kernel M(I) is given by llere. jj; is à spherical Bessel function and. f(r) is a function which depends on the radial distribution of the SOULCOS a assuming a flat geometry.," 2002) where the kernel $W_\ell(k)$ is given by Here, $j_\ell$ is a spherical Bessel function and $f(x)$ is a function which depends on the radial distribution of the sources as assuming a flat geometry." ας) is the co-moving radial co-ordinate αἲ redshift 2. p(s) is the redshift probability cistribution of the sources (normalized such that {p(s)dz= 1) and b(2) is a linear bias Factor which relates the clustering. of galaxies to clustering of the underlving Hass lor )0 purposes of this analysis we assumed. that the linear bias does not evolve with epoch and may be represented by a constant bias factor b(2)=by.," $x(z)$ is the co-moving radial co-ordinate at redshift $z$, $p(z)$ is the redshift probability distribution of the sources (normalized such that $\int \, p(z) \, dz = 1$ ) and $b(z)$ is a linear bias factor which relates the clustering of galaxies to clustering of the underlying mass: For the purposes of this analysis we assumed that the linear bias does not evolve with epoch and may be represented by a constant bias factor $b(z) = b_0$." A useful approximation for the spherical Bessel function (which gets better as ( gets larger) is £).," A useful approximation for the spherical Bessel function (which gets better as $\ell$ gets larger) is $j_\ell(x) \approx (\pi/2\ell)^{1/2} \, \delta(x - \ell)$ ." In this approximation. Thus as £ is increased. the kernel just translates along the A-axis.," In this approximation, Thus as $\ell$ is increased, the kernel just translates along the $k$ -axis." Combining equations 10 and 19.produces the approximation," Combining equations \ref{eqpktocl} and \ref{eqwlapp} produces the approximation" he results from Eulerian codes.,the results from Eulerian codes. This suggests that the Viscosity prescription in iis not a significant source of error., This suggests that the viscosity prescription in is not a significant source of error. Certainly it is not responsible for Ην inability to model mixing processes., Certainly it is not responsible for SPH's inability to model mixing processes. In this section. we use a 1:2 and LS densitv ratio shearing [uid simulation to test mixing inOSPILIL.," In this section, we use a 1:2 and 1:8 density ratio shearing fluid simulation to test mixing in." We use the naming convention NSPII-INS-N. where X. denotes the variety of SPILL Ix the choice of kernel. and N the neighbour number (see Table 2)).," We use the naming convention XSPH-K-N, where X denotes the variety of SPH, K the choice of kernel, and N the neighbour number (see Table \ref{tab:sims}) )." A Welvin-Lelmboltz instability (IXLII). occurs when two shearing fluids are subjected to an infinitesimal perturbation ab the boundary laver., A Kelvin-Helmholtz instability (KHI) occurs when two shearing fluids are subjected to an infinitesimal perturbation at the boundary layer. Phe result. of the perturbation is a lincarly growing phase in which the lavers start. to interpenctrate each other. progressively developing into a vortex in the non-linear phase that mixes the two Hui lavers.," The result of the perturbation is a linearly growing phase in which the layers start to interpenetrate each other, progressively developing into a vortex in the non-linear phase that mixes the two fluid layers." The erowth-rate of the instability is. in general a complicated function of the shear velocity. μα densities. compressibility. interface thickness. gravity. Viscosity. surface tension. magnetic field strength etc.," The growth-rate of the instability is in general a complicated function of the shear velocity, fluid densities, compressibility, interface thickness, gravity, viscosity, surface tension, magnetic field strength etc." In this test. we are only interested in the behaviour of inviscid. incompressible (i.e. with bulk motions very much less than the sound: speed) perfect. [uids neglecting gravity.," In this test, we are only interested in the behaviour of inviscid, incompressible (i.e. with bulk motions very much less than the sound speed) perfect fluids neglecting gravity." In. this case. the linear growth rate of the WII is (7 2)): where &=2x/A is the wavenumber of the instability. p; and po are the densities of the respective lavers and Ότοο is the relative shear velocity.," In this case, the linear growth rate of the KHI is \bcite{1961hhs..book.....C}) ): where $k=2\pi/\lambda$ is the wavenumber of the instability, $\rho_1$ and $\rho_2$ are the densities of the respective layers and $v=v_1-v_2$ is the relative shear velocity." Phe characteristic growth time for the WIL is then: This is a particularly challenging test for, The characteristic growth time for the KHI is then: This is a particularly challenging test for "to include three types of parameters: (1) color (g-r,r-i) k-corrected with ? code, (2) shape in the i-band and 1), and (3) light concentration in the i-band).","to include three types of parameters: (1) color (g-r,r-i) k-corrected with \cite{Blanton05} code, (2) shape in the i–band and ), and (3) light concentration in the i–band)." For color measurements we use model magnitudes corrected for galactic extinction., For color measurements we use model magnitudes corrected for galactic extinction. " and are the isophotal minor and major axes respectively, and is the DeVaucouleurs fitb/a."," and are the isophotal minor and major axes respectively, and is the DeVaucouleurs fit." ". and are the radii containing and of the petrosian flux, respectively."," and are the radii containing and of the petrosian flux, respectively." Adding more parameters does not significantly change the classification and increases the execution time., Adding more parameters does not significantly change the classification and increases the execution time. " The decision to include the color could be discussed, since, as pointed out in the introduction, it is not clear how an early-type or a late-type galaxy is actually defined."," The decision to include the color could be discussed, since, as pointed out in the introduction, it is not clear how an early-type or a late-type galaxy is actually defined." " Since our approach is to define classes as closely as possible to the definition and then compute to them, it makes sense to include color."," Since our approach is to define classes as closely as possible to the definition and then compute to them, it makes sense to include color." " Indeed, for an elliptical to be elliptical it should be red, otherwise it should be called blue elliptical, and it is an exception to the normal classification."," Indeed, for an elliptical to be elliptical it should be red, otherwise it should be called blue elliptical, and it is an exception to the normal classification." " Eitherway, tests performed reveal that removing the color from the parameter space does not significantly change the classification."," Eitherway, tests performed reveal that removing the color from the parameter space does not significantly change the classification." Fewer than 1096 of the galaxies change their main morphological class., Fewer than $10\%$ of the galaxies change their main morphological class. " In figureD], we show the 4 probabilities as a function of some representative parameters used in the classification."," In figure \ref{fig:param_proba}, we show the 4 probabilities as a function of some representative parameters used in the classification." " We observe some obvious correlations: i.e. the probability of being elliptical increases with concentration, and redder galaxies have higher probabilities of being ellipticals."," We observe some obvious correlations: i.e. the probability of being elliptical increases with concentration, and redder galaxies have higher probabilities of being ellipticals." The correlations are less clear for intermediate classes (SO and Sab)., The correlations are less clear for intermediate classes (S0 and Sab). One important conclusion by looking at these plots is that one single parameter is not enough to select galaxies with high probability of being in a given class., One important conclusion by looking at these plots is that one single parameter is not enough to select galaxies with high probability of being in a given class. " For instance, it is common to use a concentration threshold R90/R50>2.6 (in the r-band) to select elliptical galaxies (e.g. ?2))."," For instance, it is common to use a concentration threshold $R90/R50 > 2.6$ (in the r-band) to select elliptical galaxies (e.g. \citealp{Bell03, Kauffmann03}) )." As shown in the top panel of figure this selection results in a significant fraction of galaxies with low probabilities of being elliptical galaxies (as also shown in ?))., As shown in the top panel of figure \ref{fig:param_proba} this selection results in a significant fraction of galaxies with low probabilities of being elliptical galaxies (as also shown in \citealp{Bernardi10}) ). " As pointed out in section DB], there is a critical point in our approach, since the classified sample contains lots of galaxies fainter than the limiting magnitude of the training sample."," As pointed out in section \ref{sec:method}, there is a critical point in our approach, since the classified sample contains lots of galaxies fainter than the limiting magnitude of the training sample." " Therefore, it is very important to check that these faint galaxies are not systematically misclassified just because they are not represented in the training."," Therefore, it is very important to check that these faint galaxies are not systematically misclassified just because they are not represented in the training." " As a first check, we computed the probability distributions of bright (n,«16) and faint galaxies (m,>16) in figure BJ to check that faint galaxies are systematically classified with lower probabilities."," As a first check, we computed the probability distributions of bright $m_g<16$ ) and faint galaxies $m_g>16$ ) in figure \ref{fig:proba_faint_bright} to check that faint galaxies are systematically classified with lower probabilities." " As shown in ?,, the probability is a kind of measure of how good the classification is and how close a given galaxy is to the corresponding associated class."," As shown in \cite{huertas-company08}, the probability is a kind of measure of how good the classification is and how close a given galaxy is to the corresponding associated class." " Low probabilities in all the classes consequently mean that the galaxy is not close to any of the classes of the training, which would mean that faint galaxies are not properly classified because they are not properly sampled in the training set."," Low probabilities in all the classes consequently mean that the galaxy is not close to any of the classes of the training, which would mean that faint galaxies are not properly classified because they are not properly sampled in the training set." We observe in figure [] that there is no evident difference between both probability distributions., We observe in figure \ref{fig:proba_faint_bright} that there is no evident difference between both probability distributions. " A Kolmogorov-Smirnoff test gives between and probability that the 2 distributions are drawn from the same distribution, so the possibility that the 2 distributions are decoupled is rejected."," A Kolmogorov-Smirnoff test gives between and probability that the 2 distributions are drawn from the same distribution, so the possibility that the 2 distributions are decoupled is rejected." " The probability values seem to be quite independent of the galaxy brightness, at least up to the magnitude limit of the sample."," The probability values seem to be quite independent of the galaxy brightness, at least up to the magnitude limit of the sample." " The algorithm is thus able to find a clear, closest class even for the faintest objects, which supports the robustness of the classification."," The algorithm is thus able to find a clear, closest class even for the faintest objects, which supports the robustness of the classification." " As a second check, we looked at some of the images of the faint end of the sample (Fig. H))."," As a second check, we looked at some of the images of the faint end of the sample (Fig. \ref{fig:gal_examples}) )." We confirm that high-probability values for a given morphological class still correspond to galaxies that closely look like galaxies in this given class independently of the magnitude., We confirm that high-probability values for a given morphological class still correspond to galaxies that closely look like galaxies in this given class independently of the magnitude. It therefore seems that the classification is robust even for the faintest objects in the sample and that no major misclassifications are evident., It therefore seems that the classification is robust even for the faintest objects in the sample and that no major misclassifications are evident. In section] we perform a detailed comparison with a visual classification of faint objects., In section \ref{sec:comp} we perform a detailed comparison with a visual classification of faint objects. Another important point that should be studied is the effect of changes in the training set on the final classification., Another important point that should be studied is the effect of changes in the training set on the final classification. " In fact, a robust classification should not change significantly if some elements are removed from the training sample."," In fact, a robust classification should not change significantly if some elements are removed from the training sample." " On the contrary if removing some elements leads to a completely different classification, it means that the parameter space is not properly sampled and therefore the classification is very unstable."," On the contrary, if removing some elements leads to a completely different classification, it means that the parameter space is not properly sampled and therefore the classification is very unstable." " To check this point, we performed 10 different classifications with slightly different training sets."," To check this point, we performed 10 different classifications with slightly different training sets." The samples were generated by randomly selecting a subset of 500 galaxies from the ? sample., The samples were generated by randomly selecting a subset of 500 galaxies from the \cite{fukugita07} sample. We then compared the different classifications in terms of probability., We then compared the different classifications in terms of probability. These 10 runs on the full data set take only a few minutes on a normal laptop., These 10 runs on the full data set take only a few minutes on a normal laptop. The average scatter over the 10 runs of the probability of being early-type (or type) is 12%.,The average scatter over the 10 runs of the probability of being early-type (or late-type) is $12\%$. " In other words, when one changes the training set, the probability for a given galaxy changes ~12% on average."," In other words, when one changes the training set, the probability for a given galaxy changes $\sim12\%$ on average." This scatter is compatible and even less than the typical scatter found when several people perform visual classifications on the same sample (e.g.??)).," This scatter is compatible and even less than the typical scatter found when several people perform visual classifications on the same sample \citealp{postman05,fukugita07}) )." Another way of assessing the robustness of the classification is by measuring the fraction of objects whose classification is uncertain., Another way of assessing the robustness of the classification is by measuring the fraction of objects whose classification is uncertain. If this fraction appears to be too high it would imply that the algorithm is not working for a large fraction of the sample., If this fraction appears to be too high it would imply that the algorithm is not working for a large fraction of the sample. We define, We define The brightest of five main spiral galaxies that forma the Sculptor group. NGC 300 is a fairly typical late-type galaxy(Tully1988). at a distance of 2.1 AIpe (Freecananetal.1992)..,"The brightest of five main spiral galaxies that form the Sculptor group, NGC 300 is a fairly typical late-type galaxy\citep{1988ngc..book.....T} at a distance of $\sim 2.1$ Mpc \citep{1992ApJ...396...80F}." Most of the measurements of the distance to this ealaxv are based on the luuinosity of its Cepheid variables population., Most of the measurements of the distance to this galaxy are based on the luminosity of its Cepheid variables population. Based ou nearinfrared T-baucl observations of two long-period Cepheid variables. Madoreetal.(1987). reported a distance modulus 0AL)=26.35 £0.25.," Based on near-infrared H-band observations of two long-period Cepheid variables, \citet{1987ApJ...320...26M} reported a distance modulus $(m-M)_0=26.35 \pm 0.25$ ." The distance was slightly revised by Walker(1988) who derived a distance modulus (17AL\y=26.Le 0.2., The distance was slightly revised by \citet{1988PASP..100..949W} who derived a distance modulus $(m-M)_0=26.4 \pm 0.2$ . Additional photometry of the same sample of variables by Freediiaanetal.(1992) resulted in the already quoted distance GiALjy=26.6640.10. subsequenutlv revised to (1)A)=26.63+0.06 in Sakaietal.(2001)..," Additional photometry of the same sample of variables by \citet{1992ApJ...396...80F} resulted in the already quoted distance $(m-M)_0=26.66 \pm 0.10$, subsequently revised to $(m-M)_0=26.63 \pm 0.06$ in \citet{2004ApJ...608...42S}." More receutlv. NGC 300 has been selected as a key farget for the Araucaria P," More recently, NGC 300 has been selected as a key target for the Araucaria ." roject?.. Dietrzvüskietal.(2002). presented anextensivecharacterization of 117 Cepheid variables. most," \citet{2002AJ....123..789P} presented anextensivecharacterization of 117 Cepheid variables, most" have the advantage that even if the peaks mismatch. they ave small in the simulation so they clo not carry as much weight in the caleulation of the 47 deviations.,"have the advantage that even if the peaks mismatch, they are small in the simulation so they do not carry as much weight in the calculation of the $\chi^2$ deviations." Hence these simulations might give better. A7. matches., Hence these simulations might give better $\chi^2$ matches. This. suggests ju the us analvsis favors low fa models., This suggests that the $\chi^2$ analysis favors low $f_{\rm d}$ models. This conclusion is not completely: straightforward: because it is not true i all processes that weaken wigeles improve the 47. fit., This conclusion is not completely straightforward because it is not true that all processes that weaken wiggles improve the $\chi^2$ fit. For example. increasing the sound speed. from 10 to 30 kms for the and. disk fraction. niodels worsens ve A7.," For example, increasing the sound speed from 10 to 30 km/s for the and disk fraction models worsens the $\chi^2$." However the robust trend that emerges from. our nalvsis is that changing the various modeling parameters or the higher fa disks causes larger. variations in the 47 wn Changing the same parameters for the lower fu mocels., However the robust trend that emerges from our analysis is that changing the various modeling parameters for the higher $f_{\rm d}$ disks causes larger variations in the $\chi^2$ than changing the same parameters for the lower $f_{\rm d}$ models. In other words. getting the parameters “right” for the high fa models is more crucial. than getting them “right” for," In other words, getting the parameters “right” for the high $f_{\rm d}$ models is more crucial, than getting them “right” for" ise can be settled by comparing the profiles of deusitv diagnostic lines.,issue can be settled by comparing the profiles of density diagnostic lines. Ouce the photoionization model provides satisfactorv fits to the observed integrated Bue intensities. we calculate he line profiles by assuniue a velocity field aud compare he predicted results with the observed oues.," Once the photoionization model provides satisfactory fits to the observed integrated line intensities, we calculate the line profiles by assuming a velocity field and compare the predicted results with the observed ones." For the conrparison. we used a number of stroug lines from different ionic species. incluing ΠΠ. He1r. [S uj. [N uy. O η. ο uj. [O iu. ane Ne n].," For the comparison, we used a number of strong lines from different ionic species, including H, He, [S ], [N ], [O ], [O ], [O ], and [Ne ]." The observed aud oxedieted. line profiles. are xeseuted bv Fie. , The observed and predicted line profiles are presented by Fig. \ref{ic418_c}. . "δν, ionization lines have eeucrally broader profiles than hieh-ionization lines. which iuplies that the expansion velocity is increasing outwards."," Low-ionization lines have generally broader profiles than high-ionization lines, which implies that the expansion velocity is increasing outwards." To reproduce the observed line profiles. the acceleration is required to increase in the outer regious. as shown in Fie. S.," To reproduce the observed line profiles, the acceleration is required to increase in the outer regions, as shown in Fig. \ref{ic418_c}." For the fitting. no turbulence broadening is weeded.," For the fitting, no turbulence broadening is needed." Figure 8 shows that our model can account for most of these strong lines., Figure \ref{ic418_c} shows that our model can account for most of these strong lines. Figure 9 plots the FWIIAIs of the lines as a function of ionization cucrey. as predicted by our model aux observed by Sharpee et al. (2001)) (," Figure \ref{ip} plots the FWHMs of the lines as a function of ionization energy, as predicted by our model and observed by Sharpee et al. \cite{sharpee04}) ) (" see their Fig.,see their Fig. 7)., 7). Goo agreement between the predictions aud the observations is achieved., Good agreement between the predictions and the observations is achieved. The velocity feld produced is in genera aereenmient with the results of Cesicki et al. (1996)).," The velocity field produced is in general agreement with the results of Gesicki et al. \cite{gesicki96}) )," but has a larger outer velocity., but has a larger outer velocity. (ναι that Cesicki et al. (1996)), Given that Gesicki et al. \cite{gesicki96}) ) did not consider the |O 1| ine. their measure outer velocity is unlikely to be reliable.," did not consider the [O ] line, their measured outer velocity is unlikely to be reliable." The sharply-Increasing velocity in the outer regions is associated with the shock at he ionization frout. which is consistent witE the predictions of hydrodvuamic models (e.g. Perinotto e al. 1998)).," The sharply-increasing velocity in the outer regions is associated with the shock at the ionization front, which is consistent with the predictions of hydrodynamic models (e.g. Perinotto et al. \cite{perinotto98}) )." The [ο A7330 line cau be explained by our model. while the observed [O. uf A3726 line is broader than the predicted one.," The [O ] $\lambda7330$ line can be explained by our model, while the observed [O ] $\lambda3726$ line is broader than the predicted one." This is unlikely to be due to temperature variations since the |[N uj AA5751.6581 doublet lines is reproduced well.," This is unlikely to be due to temperature variations since the [N ] $\lambda\lambda5754,6584$ doublet lines is reproduced well." The discrepancy. therefore. can be attributed to density variatious within the PN.," The discrepancy, therefore, can be attributed to density variations within the PN." The ο 1] A3726 line has a critical density about three times lower than that of the [O uj A7330 line. and thus originates in low-density regions.," The [O ] $\lambda3726$ line has a critical density about three times lower than that of the [O ] $\lambda7330$ line, and thus originates in low-density regions." It follows that the outer regions have a lower density than the imuer regions. in contrast to the results of Ctesicki et al. (1996)).," It follows that the outer regions have a lower density than the inner regions, in contrast to the results of Gesicki et al. \cite{gesicki96}) )." For the |O i] AG300 line. our model reproduces the profile in the high-velocity range well," For the [O ] $\lambda6300$ line, our model reproduces the profile in the high-velocity range well." But iu the low-velocitv range. the observed fux is much higher than predicted.," But in the low-velocity range, the observed flux is much higher than predicted." Morisset Stasinsska (2006a)) also icountered difficulty iu fitting the low-velocity range of the |O 1| AG300. line profile., Morisset Stasińsska \cite{morisset06a}) ) also encountered difficulty in fitting the low-velocity range of the [O ] $\lambda6300$ line profile. A possible explanation is that neutral gas is pleutifully abundant sithiu the ionized regions., A possible explanation is that neutral gas is plentifully abundant within the ionized regions. This conjecture was supported by Williams et al. (200:3)).," This conjecture was supported by Williams et al. \cite{williams03}) )," who compared absorptiou- and enmiüssion-liue spectra of IC. [18 and found evideuce that absorbing eas may be preseut., who compared absorption- and emission-line spectra of IC 418 and found evidence that absorbing gas may be present. " If we cuhauce the |O 1| cmissivity iu the inner regions by a factor of —1.5. an excelleut match between the predicted profile aud observed oue is achieved. asshown the Fie. δ.,"," If we enhance the [O ] emissivity in the inner regions by a factor of $\sim$ 1.5, an excellent match between the predicted profile and observed one is achieved, asshown the Fig. \ref{ic418_c}. ." The ZEUS-MP. evavity solver demands that. when placing a spherical distribution of mass on a Cartesian erid. scrupulous attention be paid to the distribution of nass between the sphere aud the οσο of the conrputational exid.," The ZEUS-MP gravity solver demands that, when placing a spherical distribution of mass on a Cartesian grid, scrupulous attention be paid to the distribution of mass between the sphere and the edge of the computational grid." The corners of the erid are expecially Huportant because any significant mass located there will strouely distort the spherical sviunietzy of tlhe potential., The corners of the grid are especially important because any significant mass located there will strongly distort the spherical symmetry of the potential. To avoid this problem. we surrounded our spheres with a medium Whose density was 1000 times less than that at the sphere’s edee.," To avoid this problem, we surrounded our spheres with a medium whose density was 1000 times less than that at the sphere's edge." This method produced highly spherically svinnetric potentials., This method produced highly spherically symmetric potentials. While this density contrast is ercater than is expected ucar the edges of real molecular cloud cores. tests with lower values showed that all deusity contrasts Z 30 gave similar results.," While this density contrast is greater than is expected near the edges of real molecular cloud cores, tests with lower values showed that all density contrasts $\gtrsim$ 30 gave similar results." Because the multigrid gravitv solver fails to produce accurate results in the region of a sharp density discontinuity. the jump in density at the edge of the sphere was smoothed over several cells using a Gaussian function.," Because the multigrid gravity solver fails to produce accurate results in the region of a sharp density discontinuity, the jump in density at the edge of the sphere was smoothed over several cells using a Gaussian function." We also found that it was helpful to situate the edge of the sphere sleltly away from the erid boundary., We also found that it was helpful to situate the edge of the sphere slightly away from the grid boundary. For a exid with dimensions 7«/<7. the initial diameter of the sphere was no more than 0.97.," For a grid with dimensions $l \times l \times l$, the initial diameter of the sphere was no more than $0.9l$." Tn order to lav down a sneulu deusitv profile ou a Cartesian eril. care must be taken im haudliug the cell containing the singularity.," In order to lay down a singular density profile on a Cartesian grid, care must be taken in handling the cell containing the singularity." Our approach to was to munerically iuteerate equation (7)) to determine the mass that belonged in the ceutral. singularitv-containiug cell. ancl to divide by the cells volume to determine its density.," Our approach to was to numerically integrate equation \ref{eq:sing}) ) to determine the mass that belonged in the central, singularity-containing cell, and to divide by the cell's volume to determine its density." μπα. we elected to treat the low-density outer media iu a inauner similar to that used bv Ες.," Initially, we elected to treat the low-density outer medium in a manner similar to that used by FC93." Iu that method. the outer medi was made isothermal aud its sound speed was set to the value required to produce the desired. truncation pressure at the edge of the sphere.," In that method, the outer medium was made isothermal and its sound speed was set to the value required to produce the desired truncation pressure at the edge of the sphere." Experiments showed that. while this medium remained at a constant pressure for long periods of time during the collapse. it would eventually develop unacceptably large fluctuations.," Experiments showed that, while this medium remained at a constant pressure for long periods of time during the collapse, it would eventually develop unacceptably large fluctuations." À successful treatment of the outer iunediun was developed by following the method of BossaudBlack (1982).. wherein a constaut pressurethe pressure required to truncate the initial coreis maintained ou he surface of the core throughout collapse.," A successful treatment of the outer medium was developed by following the method of \citet{BB}, wherein a constant pressure—the pressure required to truncate the initial core—is maintained on the surface of the core throughout collapse." The boundary condition is strictly outflow. allowing material to leave the core as needed but otherwise conserving the mass initially daced within the boundary.," The boundary condition is strictly outflow, allowing material to leave the core as needed but otherwise conserving the mass initially placed within the boundary." The velocity of material outside the core is zeroed., The velocity of material outside the core is zeroed. The effect is to simulate the collapse of a core which las only a finite reservoir of uass fron which to draw., The effect is to simulate the collapse of a core which has only a finite reservoir of mass from which to draw. This is a likely scenario for he formation of a star du an isolated core. and ds also consistent with observations of clustered star formation in p Oph. which indicate that cach accreting object can access Only a Tite amount of material (Motte.Nori 1998).," This is a likely scenario for the formation of a star in an isolated core, and is also consistent with observations of clustered star formation in $\rho$ Oph, which indicate that each accreting object can access only a finite amount of material \citep{Motte}. ." . Iu accordance with the couveution of Foster&Cheva-ler(1993) we define #=0 to be the moment during the collapse of the nonsingular logatropic sphere at which the density profile becomes siugular., In accordance with the convention of \citet{FC93} we define $t=0$ to be the moment during the collapse of the nonsingular logatropic sphere at which the density profile becomes singular. Thus. adjustments frou the nousiugular to the singular configurations occur at times f.0.," Thus, adjustments from the nonsingular to the singular configurations occur at times $t < 0$." The same convention is applied to the singular logatrope: £=O marks the beeimmine of the singular collapse., The same convention is applied to the singular logatrope: $t=0$ marks the beginning of the singular collapse. However. in order toa. facilitate the plotting of some of the results of the nonsingular collapse ou log-log scales. we define an alternative time scale. T—Ft|tine=0 where fone Is the elapsed time between the begining of he simulation aud the formation of the singularity.," However, in order to facilitate the plotting of some of the results of the nonsingular collapse on log-log scales, we define an alternative time scale, $T=t+t_{\rm sing} \ge 0$ where $t_{\rm sing}$ is the elapsed time between the beginning of the simulation and the formation of the singularity." Thus. T=Oauarks for both the sjugular aud nousiugular cores.," Thus, $T=0$ marks for both the singular and nonsingular cores." " Consequcutly T=f for he sineulay core. since it begius from a singular deusity xofile G.c. fa, = 0 for the sineular core)."," Consequently $T=t$ for the singular core, since it begins from a singular density profile (i.e. $t_{\rm sing}$ = 0 for the singular core)." For the purposes of comparison with observations. we have chosen to scale qmost of our results using fiducial values of the triucation pressure. ZA. aud ceutra enpoerature. {νι," For the purposes of comparison with observations, we have chosen to scale most of our results using fiducial values of the truncation pressure, $P_{s}$, and central temperature, $T_{c}$." " Iu order to facilitate remterpretation of our results for other values of P, aud 7... we have also xovided dimensionless versious of the kev results."," In order to facilitate reinterpretation of our results for other values of $P_{s}$ and $T_{c}$, we have also provided dimensionless versions of the key results." " Iu their dimensionless forms. deusities are expressed iu terms of he initial central deusitv. p, speeds in ters of the initia central sound speed. σι. radii m terms of rg. masses iu erii of the total mass of the core. A44. amd tunes in erms of the mean frec-fall time of the core. te."," In their dimensionless forms, densities are expressed in terms of the initial central density, $\rho_{c}$, speeds in terms of the initial central sound speed, $\sigma_{c}$, radii in terms of $r_{0}$, masses in terms of the total mass of the core, $M_{\rm tot}$, and times in terms of the mean free-fall time of the core, $\bar{t}_{\rm ff}$." " All of our results cau be rescaled to other values of P, aud 1: x recaleulatius cach of these quautitics using the data in Table 1 aud the equations in the Appendix of MP96.", All of our results can be rescaled to other values of $P_{s}$ and $T_{c}$ by recalculating each of these quantities using the data in Table \ref{tab:sumdat} and the equations in the Appendix of MP96. The presence of a singularity in the deusitv profile of uaterial on the erid can lead to two primary problems., The presence of a singularity in the density profile of material on the grid can lead to two primary problems. The first is that infalline material may shock as it encounters he sineularity G.c. the protostellar object)., The first is that infalling material may shock as it encounters the singularity (i.e. the protostellar object). The second is that the everincreasing deusities aud velocities iu the region around the singularity inevitably cause a crippling rend toward tiny uunerical time steps., The second is that the ever-increasing densities and velocities in the region around the singularity inevitably cause a crippling trend toward tiny numerical time steps. Iu order to avoid hese problems. we enmiploved ao “sink cell” approach. nodeled after that of BossaudBlack(1982).," In order to avoid these problems, we employed a “sink cell” approach, modeled after that of \citet{BB}." . The use of a sink cell effectively isolates the singularity aud the details of the flow arouud it from the flow on the rest of the exid., The use of a sink cell effectively isolates the singularity and the details of the flow around it from the flow on the rest of the grid. " Tn our method. the iuuenuunost cube of 342343 cells centered on the singularity were blocked off as a collective ""sink cell’."," In our method, the innermost cube of $3 \times 3 \times 3$ cells centered on the singularity were blocked off as a collective “sink cell”." Within this region. two types of uass are counted.," Within this region, two types of mass are counted." The first is mass which is still ou he computational erid and which therefore undergoes he usual bydrodvuamic aud gravitational interactions., The first is mass which is still on the computational grid and which therefore undergoes the usual hydrodynamic and gravitational interactions. The secoud type of mass within the sink is that which las passed iuto a central point mass: this mass docs not interact Lydrodvuamically with the rest of the eric. but continues to exert its eravitational influence via a poiut uass potential.," The second type of mass within the sink is that which has passed into a central point mass; this mass does not interact hydrodynamically with the rest of the grid, but continues to exert its gravitational influence via a point mass potential." The deusitv of grid material within the sink is set to a spatially uniformi value. which is reset at cach time step to the uum of the densities of the face-sharing neighbour cells (the results are insensitive to the exact density in this region).," The density of grid material within the sink is set to a spatially uniform value, which is reset at each time step to the minimum of the densities of the face-sharing neighbour cells (the results are insensitive to the exact density in this region)." We assume that the mass within the sink can be considered to have coudeused onto the central protostellar object (BossandBlack1982)., We assume that the mass within the sink can be considered to have condensed onto the central protostellar object \citep{BB}. . Thus any mass falling into the sink inexcess of the spatially uniform density therein is subtracted from the erid and added to the central poiut mass at the sink’s centre.," Thus, any mass falling into the sink inexcess of the spatially uniform density therein is subtracted from the grid and added to the central point mass at the sink's centre." Figure 2 shows a schematic diagram of our sis, Figure \ref{fig:sinkgrid} shows a schematic diagram of our sink At low frequencies the velocity ὃς computed with 4C-MELT is iu better agreement with the data than the results published in Paper IT obtained with the C-MLT.,At low frequencies the velocity $v_{\rm s}$ computed with G-MLT is in better agreement with the data than the results published in Paper II obtained with the C-MLT. " At hieh frequencies the differences in 6, obtained with the various turbulent spectra are of similar small maeuituce than the results of Paper which assumed heH 5C-MLT.", At high frequencies the differences in $v_{\rm s}$ obtained with the various turbulent spectra are of similar small magnitude than the results of Paper II which assumed the C-MLT. i Best2ww sporoB between theory aud measurements is obtaiued with the NISS for both convection formulations., Best agreement between theory and measurements is obtained with the NKS for both convection formulations. We consider various solar-type stars with masses between LAL. and 24A. im the vicinity of the main sequence.," We consider various solar-type stars with masses between $1\,M_\odot$ and $2\,M_\odot$ in the vicinity of the main sequence." The model paramcters are listed in Table 2.. which correspond to the models cousidered previously by Samadietal.(20015).," The model parameters are listed in Table \ref{tab:models_param}, which correspond to the models considered previously by \cite*{Samadi00b}." As for the solar models in Section 2 we consider two sets of stellar 1nodols: the first set. computed with the C-MLT. is adopted from Samadictal.(2001b3.," As for the solar models in Section 2 we consider two sets of stellar models: the first set, computed with the C-MLT, is adopted from \cite*{Samadi00b}." . The second. set. computed with C-MLT. assumes the calibrated iixiuig leugth of the solar model discussed in Section 2.," The second set, computed with G-MLT, assumes the calibrated mixing length of the solar model discussed in Section 2." The acoustical cut-off frequencies are very simular between the two scts of models and are displaved in Table 2. for the first set., The acoustical cut-off frequencies are very similar between the two sets of models and are displayed in Table \ref{tab:models_param} for the first set. For all stellay models iu both sets we asiune the NKS aud the calibrated values of ο) and A quoted im (2001b) aud iu Table 1.., For all stellar models in both sets we assume the NKS and the calibrated values of $\beta$ and $\lambda$ quoted in \cite*{Samadi00b} and in Table \ref{tab:adjusted_parameters_G-MLT}. The position in the UR diagram of all stellar models and a qualitative overview of their acoustic power spectra P are depicted in 3..., The position in the HR diagram of all stellar models and a qualitative overview of their acoustic power spectra $P$ are depicted in \ref{fig:pRSEPnkcs_stars2stars_HR}. Detailed results of P are shown in 5., Detailed results of $P$ are shown in \ref{fig:pRSEP_CMLTvsGMLT}. At hieh frequencies the differences iu P hetween models computed with the C-MET aud G-MET increase with increasin effective temperature Tig and luminosity L., At high frequencies the differences in $P$ between models computed with the C-MLT and G-MLT increase with increasing effective temperature $T_{\rm eff}$ and luminosity $L$. As discussed in Woucdels(1996).. the nonlocal formulation (C-MLET) xediets sanaller temperature eracieuts in the upper superadiabatic reeion relative to the C-MLT.," As discussed in \cite*{Houdek96}, the nonlocal formulation (G-MLT) predicts smaller temperature gradients in the upper superadiabatic region relative to the C-MLT." This iius that convection is more efficient im models computed with G-AILT which cads to a different xofile (depth-dependence) of the superadia eniperature eradieut between the C-AILT aud the G-AILT., This means that convection is more efficient in models computed with G-MLT which leads to a different profile (depth-dependence) of the superadiabatic temperature gradient between the C-MLT and the G-MLT. The differences in the superacdiabatic eniperature eradieut vetween the two model sets increase with £ aud Tig., The differences in the superadiabatic temperature gradient between the two model sets increase with $L$ and $T_{\rm eff}$. " These results are illustrated iu 6 which shows the superadiabatic teniperature eradient VoV, versus agreement. ith,. η ine the radius of the star."," These results are illustrated in \ref{fig:cmp_gradT} which shows the superadiabatic temperature gradient $\nabla-\nabla_{ad}$ versus $R_* -r$ , with $R_*$ being the radius of the star." With increasing L or Tig. the ιαππα of Voμμ is shifted more rapidly o deeper lavers or the G-MLT models than for the C- models.," With increasing $L$ or $T_{\rm eff}$, the maximum of $\nabla - \nabla_{ad}$ is shifted more rapidly to deeper layers for the G-MLT models than for the C-MLT models." This leads to progressively larger differences in the convective velocities uw and in the shape of the cieeufuuctious between the two sets of nodols., This leads to progressively larger differences in the convective velocities $w$ and in the shape of the eigenfunctions between the two sets of models. These difference in w (note that P depends crucially ou uw. see rofequiA2)) and in the shape of the eiseufuuctious are particular large in the superficial lavers aud result in a larecr amount of acoustic power injected iuto high frequency modes for mocels computed with the C-MLT.," These differences in $w$ (note that $P$ depends crucially on $w$, see \\ref{eqn:A2}) ) and in the shape of the eigenfunctions are particular large in the superficial layers and result in a larger amount of acoustic power injected into high frequency modes for models computed with the C-MLT." There is au additional age effect: it cau be secu from comparing he results of the models E aud F (sec reffie:pRSEP(ALETο LT)., There is an additional age effect: it can be seen from comparing the results of the models E and F (see \\ref{fig:pRSEP_CMLTvsGMLT}) ). Model Ehasthesam, Model E has the same mass than model F but is older. cimeasstha METthanfortheG ALLTinodels., The increase of the maximum acoustic power with age is found to be larger for models computed with the C-MLT than for the G-MLT models. We compute P for all the kineticturbulent spectra discussed in Section 2.3., We compute $P$ for all the kineticturbulent spectra discussed in Section 2.3. The results are shown in, The results are shown in , solution of Johnson&MelIxee(1971). (see also Tan.Matzner&Melxee2001. and Sari2006)) before the breakout ancl each Πα element continues (o accelerate significantly following the breakout.,solution of \cite{Johnson71} (see also \citealt{Tan01} and \citealt{Pan06}) ) before the breakout and each fluid element continues to accelerate significantly following the breakout. These two differences. together with the usual relativistic effects such as relativistic beaming. govern the observed emission. which as we show here is very different ran in the Newtonian case.," These two differences, together with the usual relativistic effects such as relativistic beaming, govern the observed emission, which as we show here is very different than in the Newtonian case." Yet another difference between Newtonian and relativistic radiation mediated shocks is 1e physical width of the shock., Yet another difference between Newtonian and relativistic radiation mediated shocks is the physical width of the shock. In radiation mediated shocks 7;~~ους. where τι is (he total yplical depth (including pairs aud Ixleim-Nishina effects) seen by a photon going from the V.10ck downstream towards the shock upstream.," In radiation mediated shocks $\tau_s \sim c/v_s$, where $\tau_s$ is the total optical depth (including pairs and Klein-Nishina effects) seen by a photon going from the shock downstream towards the shock upstream." In Newtonian radiation mediated. shocks. where no pairs are produced. (he optical depth of a laver remains similar belore it is shocked and once it becomes the shock (transition laver.," In Newtonian radiation mediated shocks, where no pairs are produced, the optical depth of a layer remains similar before it is shocked and once it becomes the shock transition layer." Therefore. the shock breaks out at the laver in which 7=7. where 7 is the Thompson optical depth to the stellar edgebefore the shock crossing (1.e.. witliout pairs).," Therefore, the shock breaks out at the layer in which $\tau=\tau_s$, where $\tau$ is the Thompson optical depth to the stellar edge the shock crossing (i.e., without pairs)." " However. in relativistic shocks. where pairs are produced and Wlein-Nishina effects may become important. the optical depth of a laver is changed signifieamtlv when it is swept up by the shock and the relation between 7, and 7 is nol trivial anvimore."," However, in relativistic shocks, where pairs are produced and Klein-Nishina effects may become important, the optical depth of a layer is changed significantly when it is swept up by the shock and the relation between $\tau_s$ and $\tau$ is not trivial anymore." In order to find this relation one needs to know the structure of the shock transition laver., In order to find this relation one needs to know the structure of the shock transition layer. The structure of relativistic radiation mediated shocks in different regimes was solved numerically by Dudiikefaf(2010). and Levinson&Bromberg(2008)., The structure of relativistic radiation mediated shocks in different regimes was solved numerically by \cite{Budnik10} and \cite{Levinson08}. . The solution of Budnikefaf(2010).. where a sienilicant number of photons is generated within the shock. is the relevant one to the twpe of shocks we consider here (Dromberg.Mikolitzk," The solution of \cite{Budnik10}, where a significant number of photons is generated within the shock, is the relevant one to the type of shocks we consider here \citep{BrombergLevinson11}." y 2011).. Dudnikefal(2010). also provide an approximate analytic description of the shock structure as function of the optical depth., \cite{Budnik10} also provide an approximate analytic description of the shock structure as function of the optical depth. We derive a more accurate analylic description of the structure of the shock transition laver auc use it to find the value of 7 al the point that the shock breaks oul., We derive a more accurate analytic description of the structure of the shock transition layer and use it to find the value of $\tau$ at the point that the shock breaks out. We find that while production of pairs results in a shock that breaks out of the star at 7«I. the observed emission is always dominated by the laver where 721.," We find that while production of pairs results in a shock that breaks out of the star at $\tau \ll 1$, the observed emission is always dominated by the layer where $\tau \approx 1$." We therefore use (he subscripto. and the terminology shell to denote the 7=1 laver. which is not (he actual laver where the breakout takes place. but is the laver that dominates the observed breakout emission.," We therefore use the subscript $_0$ ' and the terminology shell' to denote the $\tau =1$ layer, which is not the actual layer where the breakout takes place, but is the layer that dominates the observed breakout emission." In this paper we calculate the evolution of the observed huminosityv ancl temperature from explosions in which the shock becomes mildly or ultra relativistic. Le. 59/9>0.5.," In this paper we calculate the evolution of the observed luminosity and temperature from explosions in which the shock becomes mildly or ultra relativistic, i.e., $\g_0 \beta_0 >0.5$." We lollow the light curve as long as the observed. radiation is generated by gas that is moving al relativistic velocities., We follow the light curve as long as the observed radiation is generated by gas that is moving at relativistic velocities. At later times the radiation is determined by Newtonian eas. which light curve was diseussed in Nakar&Sari(2010).," At later times the radiation is determined by Newtonian gas, which light curve was discussed in \cite{Nakar10}." . Our solution is limited to cases where the breakout shell ends its post shock acceleration before it doubles its radius., Our solution is limited to cases where the breakout shell ends its post shock acceleration before it doubles its radius. This limit is translated to a final (post-acceleration) Lorentz [actor of the shell <30., This limit is translated to a final (post-acceleration) Lorentz factor of the shell $\lesssim 30$. We also assume that the opacity of the progenitor wind is negligible and do not affect the breakout emission., We also assume that the opacity of the progenitor wind is negligible and do not affect the breakout emission. Our calculations are applicable to a wide range of energetic and/or, Our calculations are applicable to a wide range of energetic and/or timescales of the physical processes which govern the energy release in the upper atmosphere.,timescales of the physical processes which govern the energy release in the upper atmosphere. " An example of this kind of analysis is shown in the upper panel of Fig. 7,,"," An example of this kind of analysis is shown in the upper panel of Fig. \ref{fig:sunanal}," " which illustrates the behavior of the correlation coefficient r for the V data, obtained on 170 separate nights for three different values of Ar (1, 10 and 30 days)."," which illustrates the behavior of the correlation coefficient $r$ for the $V$ data, obtained on 170 separate nights for three different values of $\Delta \tau$ (1, 10 and 30 days)." " The correlation peak is quite broad and it is centered at τ ~30 days; moreover, the maximum correlation tends to increase slightly for larger averaging windows."," The correlation peak is quite broad and it is centered at $\tau\sim$ 30 days; moreover, the maximum correlation tends to increase slightly for larger averaging windows." " This plot also explains why the average solar flux computed in the 30 days before the night sky observations (empty circles) gives a better correlation than the sun flux measured on the preceding day (filled circles), as already pointed out by several authors (see for example Leinert et al. 1995;;"," This plot also explains why the average solar flux computed in the 30 days before the night sky observations (empty circles) gives a better correlation than the sun flux measured on the preceding day (filled circles), as already pointed out by several authors (see for example Leinert et al. \cite{leinert95};" Mattila et al. 1996))., Mattila et al. \cite{attila}) ). " Finally, Fig."," Finally, Fig." " 7 clearly shows that the correlation drops significantly for τ 240 days, a fact that is common to all UBVRI passbands."," \ref{fig:sunanal} clearly shows that the correlation drops significantly for $\tau>$ 40 days, a fact that is common to all $UBVRI$ passbands." An interesting feature to be noticed in Fig., An interesting feature to be noticed in Fig. " 7 (seen also in the equivalent plots for the other filters), is the presence of spurious correlation peaks at a constant separation of about 27 days from the main peak."," \ref{fig:sunanal} (seen also in the equivalent plots for the other filters), is the presence of spurious correlation peaks at a constant separation of about 27 days from the main peak." " This is due the a periodicity present in the solar flux data (see Fig. 7,,"," This is due the a periodicity present in the solar flux data (see Fig. \ref{fig:sunanal}," " lower panel), which is related to the solar rotation, whose synodic period is ~27.3 days (Howard 1999))."," lower panel), which is related to the solar rotation, whose synodic period is $\sim$ 27.3 days (Howard \cite{howard}) )." " This semi-regular recurrence in the solar data explains, for example, the presence of the two bumps close to t=5 and τό» in Fig. 7.."," This semi-regular recurrence in the solar data explains, for example, the presence of the two bumps close to $\tau$ =5 and $\tau$ =65 in Fig. \ref{fig:sunanal}." " The strongest correlation is shown by the U passband data, which presents a rather marked peak r ~0.6 at tT ~15 days, while r ~0.15 for 1-1 day."," The strongest correlation is shown by the $U$ passband data, which presents a rather marked peak $r\sim$ 0.6 at $\tau\sim$ 15 days, while $r\sim$ 0.15 for $\tau$ =1 day." " For this reason, averaging over the last 30 days gives a strong increase in the correlation, much stronger than in any other passband."," For this reason, averaging over the last 30 days gives a strong increase in the correlation, much stronger than in any other passband." A behaviour similar to that displayed in V is seen also in B (correlation peak r~0.45 for τ~25 days) and J (r~0.30 for t~20 days)., A behaviour similar to that displayed in $V$ is seen also in $B$ (correlation peak $r\sim$ 0.45 for $\tau\sim$ 25 days) and $I$ $r\sim$ 0.30 for $\tau\sim$ 20 days). " Somewhat different is the case of R passband, for which the correlation peak (r~0.45) is attained at τ~2 days, suggesting that the sun-dependent features that contribute to the flux in this filter react rather rapidly to the solar flux fluctuations."," Somewhat different is the case of $R$ passband, for which the correlation peak $r\sim$ 0.45) is attained at $\tau\sim$ 2 days, suggesting that the sun-dependent features that contribute to the flux in this filter react rather rapidly to the solar flux fluctuations." " In general, however, and with the possible exception of the U passband, the correlation peaks are rather broad, indicating that different processes take place with different timescales."," In general, however, and with the possible exception of the $U$ passband, the correlation peaks are rather broad, indicating that different processes take place with different timescales." " The behavior of the U band, where the nightglow emission is dominated by the Herzberg and Chamberlain O2 bands (Broadfoot Kendall 1968)), indicates that the photo-chemical reactions that are responsible for the emission in this region are more sensitive to solar activity."," The behavior of the $U$ band, where the nightglow emission is dominated by the Herzberg and Chamberlain $_2$ bands (Broadfoot Kendall \cite{broadfoot}) ), indicates that the photo-chemical reactions that are responsible for the emission in this region are more sensitive to solar activity." " In the previous work I had attempted to detect night sky brightness seasonal variations but, due to insufficient number of data points, I could not draw any firm conclusion (see Fig."," In the previous work I had attempted to detect night sky brightness seasonal variations but, due to insufficient number of data points, I could not draw any firm conclusion (see Fig." 14 in Paper I)., 14 in Paper I). " Thanks to the much larger sample now available, this analysis becomes feasible and, as a matter of fact, traces of a periodic modulation in the average sky brightness are visible already in Fig. 4.."," Thanks to the much larger sample now available, this analysis becomes feasible and, as a matter of fact, traces of a periodic modulation in the average sky brightness are visible already in Fig. \ref{fig:dark}." They become much clearer when each data point is plotted against the number of days from the beginning of the corresponding year., They become much clearer when each data point is plotted against the number of days from the beginning of the corresponding year. The result is shown in Fig., The result is shown in Fig. " 8 where, besides reporting the single dark time measurements, I have also plotted the monthly averages."," \ref{fig:season} where, besides reporting the single dark time measurements, I have also plotted the monthly averages." The input data have been corrected for differential zodiacal light contribution and the solar flux dependency derived in the previous section has been removed using the parameters presented in Table 4.., The input data have been corrected for differential zodiacal light contribution and the solar flux dependency derived in the previous section has been removed using the parameters presented in Table \ref{tab:sunave}. " This semi-annual oscillation (hereafter SAO) is definitely present in V, R and J, while its presence in B is more questionable (U data were not included since the sample in this passband is too poor for this purpose)."," This semi-annual oscillation (hereafter SAO) is definitely present in $V$, $R$ and $I$ , while its presence in $B$ is more questionable $U$ data were not included since the sample in this passband is too poor for this purpose)." " The modulation amplitude grows at longer wavelengths, shows two maxima around April-May and October, and two minima around July- and December-January."," The modulation amplitude grows at longer wavelengths, shows two maxima around April-May and October, and two minima around July-August and December-January." " In general, the variation is more pronounced in Winter-Spring than in Summer-Fall."," In general, the variation is more pronounced in Winter-Spring than in Summer-Fall." " For example, in / it reaches a peak-to-peak value of about 0.5 mag arcsec?."," For example, in $I$ it reaches a peak-to-peak value of about 0.5 mag $^{-2}$." Another way to study the properties of stellar populations is to consider integrated characteristics such as surface brightuesses aud colors of clifferent regions in the galaxy.,Another way to study the properties of stellar populations is to consider integrated characteristics such as surface brightnesses and colors of different regions in the galaxy. The advantage of this approach is that it iucludes both resolved aucl uuresolved stars., The advantage of this approach is that it includes both resolved and unresolved stars. The disadvantage is that populations with different ages contribute to the integrated light aud assumiptious ou the star formation history ieed to be mace to derive the cistributiou of stellar ages., The disadvantage is that populations with different ages contribute to the integrated light and assumptions on the star formation history need to be made to derive the distribution of stellar ages. Iu Fig., In Fig. 12aa — 13ec we show the V. aud J surface-briglitness aud V—4 color distributious along he major axis (i.e. alone the diagonals of the PC and WE3 frames) of NCC 2366 in a wwide strip centered on the star cluster A (Fig. 8)), \ref{Fig13}a a – \ref{Fig13}c c we show the $V$ and $I$ surface-brightness and $V-I$ color distributions along the major axis (i.e. along the diagonals of the PC and WF3 frames) of NGC 2366 in a wide strip centered on the star cluster A (Fig. \ref{Fig8}) ) taken to be the origin., taken to be the origin. Fig., Fig. 13dd — 13ff show he V aud J surface-brightuess and V.—£ color distributions in a wwide strip perpendicular to the major axis of NGC 2366. with the origin taken to be at the intersection of the strip with the major axis. at the distance of as defined in Fig.," \ref{Fig13}d d – \ref{Fig13}f f show the $V$ and $I$ surface-brightness and $V-I$ color distributions in a wide strip perpendicular to the major axis of NGC 2366, with the origin taken to be at the intersection of the strip with the major axis, at the distance of as defined in Fig." 13aa — 13cc. Surface brightuesses and colors are transformed to the staudard V1 photometric system [following the prescripious by Holtzmanetal.(1995b). aud corrected [or extinction wit Ady = 0.12 mag (Schlegeletal.1998)., \ref{Fig13}a a – \ref{Fig13}c c. Surface brightnesses and colors are transformed to the standard $VI$ photometric system following the prescriptions by \citet{Ho95b} and corrected for extinction with $A_V$ = 0.12 mag \citep{S98}. ". It can be seen that cluster A peaks at a surfaceJ brightness"" (V) r apo16.5 mag >7. or e 5.5-- mae brighter than the surface brightuess in the main body (WE3)."," It can be seen that cluster A peaks at a surface brightness $\mu$ $V$ ) $\sim$ 16.5 mag $^{-2}$, or $\sim$ 5.5 mag brighter than the surface brightness in the main body (WF3)." This peak surface brightuess is a lower limit siuce a few central pixels in te V image of cluster A are saturated., This peak surface brightness is a lower limit since a few central pixels in the $V$ image of cluster A are saturated. " The prolile of the HU region around A is broader in V (Fiο,", The profile of the H region around A is broader in $V$ (Fig. 13aa) than in Z (Fig., \ref{Fig13}a a) than in $I$ (Fig. 1910) because of the larger contribution o ‘the extended ionized gas euissiou in V., \ref{Fig13}b b) because of the larger contribution of the extended ionized gas emission in $V$. Thus. the regiou with blue V—/ color (Fig.," Thus, the region with blue $V-I$ color (Fig." 13cc) is particlarly broad., \ref{Fig13}c c) is particularly broad. The buest color is —1.0 imag., The bluest color is $\sim$ –1.0 mag. Fig., Fig. " I3cc shows that there is a slight increase in the V.—7 color from ~ 0.7 for (region 3-1) to ~ 0.9 for .

0$." The group velocity is then positive (negative) outside (inside) corotation., The group velocity is then positive (negative) outside (inside) corotation. These two boundary conditions vield two algebraic equations for ej and eo (see eq. , These two boundary conditions yield two algebraic equations for $c_1$ and $c_2$ (see eq. [ 24] of IKP93) which can be solved to find these cocllicicnts.,24] of KP93) which can be solved to find these coefficients. " To get better numerical accuracy. we repeat the procedure taking for the starting value of the particular solution £4...) the value of £,,; calculated at r=rci, with the above coellicients e; and eo."," To get better numerical accuracy, we repeat the procedure taking for the starting value of the particular solution $\xi_{mr,p}$ the value of $\xi_{mr}$ calculated at $r=r_{in}$ with the above coefficients $c_1$ and $c_2$." " This leads to £,;;,, converging toward the full solution £,,,."," This leads to $\xi_{mr,p}$ converging toward the full solution $\xi_{mr}$." When recalculating e; and c after one iteration we indeed verily that these two constants are very close to zero., When recalculating $c_1$ and $c_2$ after one iteration we indeed verify that these two constants are very close to zero. " This procedure prevents large cancellation between £,,; and the general solutions of the homogeneous equation."," This procedure prevents large cancellation between $\xi_{mr,p}$ and the general solutions of the homogeneous equation." Note that IXP93 found the WI&D approximation not to be accurate enough. for the boundary conditions. and. they accordingly took into account theamplitude as well as the phase variation of the WIXD solution.," Note that KP93 found the WKB approximation not to be accurate enough for the boundary conditions, and they accordingly took into account theamplitude as well as the phase variation of the WKB solution." We found that we could reproduce their results without having to go bevond the WIXD approximation., We found that we could reproduce their results without having to go beyond the WKB approximation. " Once £,, is known. WYnn and eneg can be calculated from. equations (32)) and. (34)). (/nrmagi, and the torque density ο£e is given by equation (58))."," Once $\xi_{mr}$ is known, $W'_m$ and $v'_{m \varphi}$ can be calculated from equations \ref{Wm2}) ) and \ref{vphim2}) ), $v'_{mr}=im \sigma \xi_{mr}$, and the torque density $dT_m/dA$ is given by equation \ref{torquedens}) )." " To caleulate the total torque Z5, exerted by theplanet on the disc. we integrate eus£e over the dise surface (see eq. 51]."," To calculate the total torque $T_m$ exerted by theplanet on the disc, we integrate $dT_m/dA$ over the disc surface (see eq. \ref{torquer1r2}] ])." " The planet. potential softening length. is set to ry10Ir,", The planet potential softening length is set to $r_0=10^{-4} r_p$. Note that in the presence of a magnetic field the results ae insensitive to the value of ry provided it is small enough. since there is no singularity of the homogeneous equation alr =ry. where the potential is singular.," Note that in the presence of a magnetic field the results are insensitive to the value of $r_0$ provided it is small enough, since there is no singularity of the homogeneous equation at $r=r_p$, where the potential is singular." The Landau parameter is set tos=I0.U., The Landau parameter is set to $\gamma=10^{-6}$. As expected. the total torque does not depend on the value of 2. provided it is small enough.," As expected, the total torque does not depend on the value of $\gamma$ provided it is small enough." " For mx5. we integrate the equation from ri,=0.2ry to riu;=Or, whereas. for mz6. we limit the range of integration [roni r;,=0.5r, to riu=15r."," For $m \le 5$, we integrate the equation from $r_{in}=0.2 r_p$ to $r_{out}=5 r_p$, whereas, for $m \ge 6$, we limit the range of integration from $r_{in}=0.5 r_p$ to $r_{out}=1.5 r_p$." We assume that X. e and 7£D75 vary Like power laws of r.," We assume that $\Sigma$, $c$ and $r^2 \langle B^2 \rangle$ vary like power laws of $r$." " According to equations (22)) and (31)). we then have Xxpn, coxr2 and EBPsxας "," According to equations \ref{bs}) ) and \ref{cd}) ), we then have $\Sigma \propto r^{d_1}$, $c \propto r^{c_1}$ and $r^2 \langle B^2 \rangle \propto r^{b_1}$." "Phen de=dy(dy1) and bo=(b,2)(b,D.", Then $d_2=d_1(d_1-1)$ and $b_2=(b_1-2)(b_1-1)$. " Note that Hr~ef(FO)xi!""7 and PoePewr812;"," Note that $H/r \sim c/ \left( r \Omega \right) \propto r^{c_1+0.5}$ and $\beta \equiv c^2/v_A^2 \propto r^{2c_1+d_1-b_1+2}$." Ne comment that the values of the parameters we chose below may require a departure from Ixeplerian rotation that is second order in {1 to ensure hyvdrostatie equilibrium., We comment that the values of the parameters we chose below may require a departure from Keplerian rotation that is second order in $H/r$ to ensure hydrostatic equilibrium. Fhis is here neglected. as in Ward (1986. 1991).," This is here neglected, as in Ward (1986, 1997)." " Vo simplify the discussion. we define the dimensionless quantities 17,=WY,(ον). d,=Lin{SpryY. and P=P,(X107). where the subscript p indicates that the quantity is taken at r=rj."," To simplify the discussion, we define the dimensionless quantities $\tilde{W}'_m = W'_m/\left( r_p^2 \Omega_p^2 \right)$, $\tilde{T}_m = T_m /\left( \Sigma_p r_p^4 \Omega_p^2 \right)$, $\tilde{T}_{m,D} = 2 \pi (T_m/dA) /\left( \Sigma_p r_p^2 \Omega_p^2 \right)$ and $\tilde{F}_m = F_m /\left( \Sigma_p r_p^4 \Omega_p^2 \right)$, where the subscript $p$ indicates that the quantity is taken at $r=r_p$." " The numerical results presented. in this section correspond. to Ad,/Ad,=1.", The numerical results presented in this section correspond to $M_p/M_\ast=1$. " Since M,/(0707)xAL/AL, (see section 4). then WY,ο and 1,x(AL,/AL,) "," Since $\Psi'_m / ( r_p^2 \Omega_p^2 ) \propto M_p/M_\ast$ (see section \ref{sec:potential}) ), then $\tilde{W}'_m \propto M_p/M_\ast$ and $\tilde{T}_m \propto (M_p/M_\ast)^2$ ." ὃν setting. B=0. we have checked. that we recover the IxXD93 results.," By setting $B=0$, we have checked that we recover the KP93 results." In that case. the corotation torque is non zero if dizx1.5 and corresponds to a discontinuity of the angular momentum flux at i£—ry.," In that case, the corotation torque is non zero if $d_1 \ne -1.5$ and corresponds to a discontinuity of the angular momentum flux at $r=r_p$." In figure 2.. we plot V7. the angular momentuni flux Zr) at radius r and the torque ήν.70) exerted by the planet on the disc between the radii rj and rc for D—0. dy =O. ο(νο)=0.03 (e;= 0) and m=10.," In figure \ref{fig2}, we plot $\tilde{W}'_m$ , the angular momentum flux $\tilde{F}_m(r)$ at radius $r$ and the torque $\tilde{T}_m(r_p,r)$ exerted by the planet on the disc between the radii $r_p$ and $r$ for $B=0$, $d_1=0$ , $c/ \left( r_p \Omega_p \right) = 0.03$ $c_1=0$ ) and $m=10$." For comparison. we also plot the angular momentum (ux corresponding to dj=1.5 in the corotation region.," For comparison, we also plot the angular momentum flux corresponding to $d_1=-1.5$ in the corotation region." The parameters used here are the same as those used by IXP93 in their figures 2. 5 and 6. so that a direct comparison can be made.," The parameters used here are the same as those used by KP93 in their figures 2, 5 and 6, so that a direct comparison can be made." " For d,=0. the dimensionless corotation torque is about 102. whereas the dimensionless total torque Trin.Maa) is about 22. in very good agreement with the results displaved by 99."," For $d_1=0$, the dimensionless corotation torque is about 102, whereas the dimensionless total torque $\tilde{T}_m(r_{in},r_{out})$ is about 22, in very good agreement with the results displayed by KP93." " We first consider the case d;=0. c£ον)=0.03 (e, Q5, 2.1=const1 and m=10."," We first consider the case $d_1=0$, $c/ \left( r_p \Omega_p \right) = 0.03$ $c_1=0$ ), $b_1=2$ , $ \beta = {\rm const} = 1$ and $m=10$." " In figures 3.. 4 and 5. we plot WW. Yin and T, versus radius."," In figures \ref{fig3}, \ref{fig4} and \ref{fig5} we plot $\tilde{W}'_m$, $\tilde{T}_{m,D}$ and $\tilde{T}_m$ versus radius." " Note that the rapid variation of Πο) at r=r, is due to the rapid variation of the potential there. not to a singularity of the homogeneous dilferential equation."," Note that the rapid variation of ${\rm Re}(\tilde{W}'_m)$ at $r=r_p$ is due to the rapid variation of the potential there, not to a singularity of the homogeneous differential equation." " We have matched M7, obtained numerically with the analvtical expression (49)) in order to compute the constants C5.", We have matched $W'_m$ obtained numerically with the analytical expression \ref{Wmm}) ) in order to compute the constants $C_\epsilon$ . We find that Ie(C€*4)20 whereas ος4)« 0., We find that ${\rm Re}(C_{+1})>0$ whereas ${\rm Re}(C_{-1})<0$ . According to equation. (63)). the point.like torque exerted at the outer magnetic resonance is then negative whereas that exerted at the inner magnetic resonance is positive.," According to equation \ref{torqueres}) ), the point–like torque exerted at the outer magnetic resonance is then negative whereas that exerted at the inner magnetic resonance is positive." This is in agreement with the curves shown in figure 4. around resonances., This is in agreement with the curves shown in figure \ref{fig4} around resonances. ligure 5 shows the totaltorque computedusing the numerical form of the torque density., Figure \ref{fig5} shows the totaltorque computedusing the numerical form of the torque density. "As a check. we have also caleulated T, by using the analytical expression (613) for the torque density around the resonances (represented by thedashed lines in","As a check, we have also calculated $\tilde{T}_m$ by using the analytical expression \ref{torquedensM}) ) for the torque density around the resonances (represented by thedashed lines in" "with a maximum-likelihood estimation (MLE), or alternatively with Markov chains Monte Carlo (MCMC), by assuming that the noise follows a XS distribution.","with a maximum-likelihood estimation (MLE), or alternatively with Markov chains Monte Carlo (MCMC), by assuming that the noise follows a $\chi^2_2$ distribution." Results for By and W do not depend significantly on the choice made for B4., Results for $B_\mathrm{g}$ and $W$ do not depend significantly on the choice made for $B_\mathrm{a}$. " Table 3 lists the fitted parameters with statistical formal errors, obtained by inverting the Hessian matrix."," Table \ref{tab:bg} lists the fitted parameters with statistical formal errors, obtained by inverting the Hessian matrix." These errors do not include any systematics and assume the model is correct., These errors do not include any systematics and assume the model is correct. Complementary fits including the p-mode region were performed by modelling their contribution as a Gaussian function., Complementary fits including the p-mode region were performed by modelling their contribution as a Gaussian function. " The results for B, and W have not been modified.", The results for $B_\mathrm{g}$ and $W$ have not been modified. " The p-mode Gaussian profile By is characterised by a height HP""?=0.426+0.016ppm?uHz-!, a width Δρ=390220Hz, and a central frequency vi""=2090+20wHz."," The p-mode Gaussian profile $B_\mathrm{p}$ is characterised by a height $H_\mathrm{p}^\mathrm{(max)}=0.426\pm 0.016\unit{ppm^2\,\mu Hz^{-1}}$, a width $\Delta_\mathrm{p}=390\pm20\muHz$, and a central frequency $\nu_\mathrm{p}^\mathrm{(max)}=2090\pm20\muHz$." " We then redid fits over a frequency range starting at 5, 10, orwHz,, instead ofuHz,, without any impact on the results."," We then redid fits over a frequency range starting at 5, 10, or, instead of, without any impact on the results." We also verified that removing the two bins still contaminated by the strong orbit harmonic does not influence the results., We also verified that removing the two bins still contaminated by the strong orbit harmonic does not influence the results. " AroundµΗ7,, the PSD presents a conspicuous comb structure that is typical of solar-like oscillations."," Around, the PSD presents a conspicuous comb structure that is typical of solar-like oscillations." A zoom on the PSD in the region is plotted in Fig. 8.., A zoom on the PSD in the region is plotted in Fig. \ref{fig:fit}. " The small separation between modes of degrees /=0 and 2 is also easily seen, making the mode identification simple."," The small separation between modes of degrees $l=0$ and 2 is also easily seen, making the mode identification simple." The autocorrelation of the spectrum between 1700 and pprovides first estimates of the large and small separations: Av«98.5Hz and δρ~8Hz., The autocorrelation of the spectrum between 1700 and provides first estimates of the large and small separations: $\Dnu\approx 98.5\muHz$ and $\overline{\delta_{02}}\approx 8\muHz$. These values are recomputed from fitted frequencies in Sect. ??.., These values are recomputed from fitted frequencies in Sect. \ref{ssec:freq}. . We build an écchelle diagram using aas the folding frequency., We build an écchelle diagram using as the folding frequency. This is plotted in Fig. 9.., This is plotted in Fig. \ref{fig:echelle}. This écchelle diagram makes the mode identification even more obvious., This écchelle diagram makes the mode identification even more obvious. " On the right-hand side, the clear single ridge corresponds to /=1 modes, whereas, on the left-hand side, the two ridges are identified as the /=2 and /=0 modes."," On the right-hand side, the clear single ridge corresponds to $l=1$ modes, whereas, on the left-hand side, the two ridges are identified as the $l=2$ and $l=0$ modes." We completely exclude the possibility that the two ridges on the left are |=1 modes split by rotation for the following reasons., We completely exclude the possibility that the two ridges on the left are $l=1$ modes split by rotation for the following reasons. " First, the two ridges show clear asymmetry in their power; second, the rotation needed to generate such high splittings is totally incompatible both with the low-frequency signature (Sect. ??))"," First, the two ridges show clear asymmetry in their power; second, the rotation needed to generate such high splittings is totally incompatible both with the low-frequency signature (Sect. \ref{sec:act}) )" and the spectroscopic observations (Sect. ??))., and the spectroscopic observations (Sect. \ref{ssec:spectro}) ). We are able to identify modes presenting a significant signal-to-noise ratio for about ten consecutive orders., We are able to identify modes presenting a significant signal-to-noise ratio for about ten consecutive orders. " Their characteristics are extracted with classical methods, described in thefollowing section."," Their characteristics are extracted with classical methods, described in thefollowing section." , "parameters: μυ= 0.25. O4,=0.75 and ox=0.5 consistent with the WALAPS data (Dunkleyetal.2009)).","parameters: $\Omega_{\rm m0}=0.25$ , $\Omega_{\Lambda0}=0.75$ and $\sigma_8 =0.8$ consistent with the WMAP5 data \citealt{Dun09}) )." This function. includes. only cistinet haloes that are not parts of larger haloes., This function includes only distinct haloes that are not parts of larger haloes. " We correct E to include subhaloes since they may also host We use the simulation results by Conroy.ctal.(2006). galaxies.""for the number fraction of subhaloes (fou) às à function of maximum circular velocity.", We correct it to include subhaloes since they may also host We use the simulation results by \citet{CWK06} for the number fraction of subhaloes $f_{\rm sub}$ ) as a function of maximum circular velocity. " ὃν relating the maximum circular velocity to the halo virial mass using the scaling given by IxIvpinetal. (2010).. we find :à varving fraction from fau,s0.25 (zz0.15) at AlayLOUMI. (this mass scale corresponds to the Conroyetal.(2006). completeness limit) to s0.08 (z0.08) at Ala103BY. [or 2=0 (2= 1)."," By relating the maximum circular velocity to the halo virial mass using the scaling given by \citet{Kly10}, , we find a varying fraction from $f_{\rm sub} \approx 0.25$ $\approx 0.18$ ) at $\Mvir \la 10^{11} \Msun$ (this mass scale corresponds to the \citet{CWK06} completeness limit) to $\approx 0.08$ $\approx 0.08$ ) at $\Mvir \ga 10^{13} \Msun$ for $z=0$ $z=1$ )." Notice that the mass of a distinct halo refers to the epoch under consideration while that of a subhalo is the mass at the time it accreted onto a larger halo., Notice that the mass of a distinct halo refers to the epoch under consideration while that of a subhalo is the mass at the time it accreted onto a larger halo. The mass of a halo (AM) may be linked to the stellar velocity dispersion (0) of the central galaxy for those haloes that host galaxies., The mass of a halo $\Mvir$ ) may be linked to the stellar velocity dispersion $\sigma$ ) of the central galaxy for those haloes that host galaxies. Lf the halo did not host a galaxy in its centre. the central velocity dispersion. (of clark matter particles) would be entirely due to the dark mass potential.," If the halo did not host a galaxy in its centre, the central velocity dispersion (of dark matter particles) would be entirely due to the dark mass potential." In reality. the central galaxy contributes to the central eravitational potential with the degree. of contribution varving from one system to another.," In reality, the central galaxy contributes to the central gravitational potential with the degree of contribution varying from one system to another." The functional relation OCM 4) will depend not only on the stellar mass distribution of the residing galaxy but also how the dark halo has been mocified due to the barvonic physies of galaxy formation., The functional relation $\sigma$ $\Mvir$ ) will depend not only on the stellar mass distribution of the residing galaxy but also how the dark halo has been modified due to the baryonic physics of galaxy formation. Aloreover. the stellar mass clistribution itself is correlated with My to some degree.," Moreover, the stellar mass distribution itself is correlated with $\Mvir$ to some degree." Thus. we may use the abundance matching relation between AZ and σ to gain new insights into the structure of the barvon-moclified dark halo and the dynamical aspect of galaxy formation and evolution.," Thus, we may use the abundance matching relation between $\Mvir$ and $\sigma$ to gain new insights into the structure of the baryon-modified dark halo and the dynamical aspect of galaxy formation and evolution." Fig., Fig. 3 shows the abundance matching AM-e relation at z= 0., \ref{MvirVz0} shows the abundance matching $\Mvir$ $\sigma$ relation at $z=0$ . " It shows both the relations ignoring intrinsic scatters and those taking into account an intrinsic scatter clistribution of V—log,u(o/kms1j as a function of. Ados.", It shows both the relations ignoring intrinsic scatters and those taking into account an intrinsic scatter distribution of $V\equiv \log_{10}(\sigma/\kms)$ as a function of $\Mvir$. " For the latter case the intrinsic scatter distribution is predicted by a bivariate distribution of σ and A, as a function of Au based on an observed scatter of log)CA.) at fixed. M, and an observed scatter distribution of Y as a function of M,", For the latter case the intrinsic scatter distribution is predicted by a bivariate distribution of $\sigma$ and $\Mstars$ as a function of $\Mvir$ based on an observed scatter of $\log_{10}(\Mstars)$ at fixed $\Mvir$ and an observed scatter distribution of $V$ as a function of $\Mstars$. The reader is referred to Appendix A for a brief description and a following work(in preparation) for further details., The reader is referred to Appendix A for a brief description and a following work (in preparation) for further details. " The abundance matching relationis compared against the measured values of Adv, and oo for. individual galaxies/clusters with z ", The abundance matching relation is compared against the measured values of $\Mvir$ and $\sigma$ for individual galaxies/clusters with $z \la 0.3$. Although there arenumerous galaxies/clusters for which either σ or Ada is reported. only for relatively lew svstems both AZ; ancl σ have been measured reliably so far.," Although there arenumerous galaxies/clusters for which either $\sigma$ or $\Mvir$ is reported, only for relatively few systems both $\Mvir$ and $\sigma$ have been measured reliably so far." First. we consider the best-stucied Alilky Way galaxy. for which recent measurements appear to be reasonably concordant. (IxIvpinetal.2002:Battagliaetal.2005.2006:Nue2008)).7 The data from Xueetal.(20615) are clisplaved in Fig. ," First, we consider the best-studied Milky Way galaxy, for which recent measurements appear to be reasonably concordant \citealt{KZS02,Bat05,Bat06,Xue08}) The data from \citet{Xue08} are displayed in Fig. \ref{MvirVz0}." Second. we display the results for 22 SLACS lensing galaxics at mean redshift of z0.2 by Gavazzictal.(2007).," Second, we display the results for 22 SLACS lensing galaxies at mean redshift of $z \sim 0.2$ by \citet{Gav07}." . Phey combine strong and weak lensing and stellar kinematics to analyse the systems., They combine strong and weak lensing and stellar kinematics to analyse the systems. Phired. we consider the first ever discovered. lens system: QOO57T1561 at z=0.36. which is the best. studied. lens system including a cluster for the lens potential.," Third, we consider the first ever discovered lens system Q0957+561 at $z=0.36$, which is the best studied lens system including a cluster for the lens potential." The velocity clispersion for the central galaxy is reported by Tonry&Franx(1999)., The velocity dispersion for the central galaxy is reported by \citet{TF99}. . The virial mass of the cluster is from Nakajimaetal.(2009) who derive the halo mass through weak lensing and find that their result is consistent with the result by Chartasetal.(2002). through X-ray observations., The virial mass of the cluster is from \citet{Nak09} who derive the halo mass through weak lensing and find that their result is consistent with the result by \citet{Char02} through X-ray observations. Finally. we consider galaxy cluster Abell 611 that has been studied. extensivelyby Newmanctal. througha combination of strong and weak lensing and stellar kinematics.," Finally, we consider galaxy cluster Abell 611 that has been studied extensivelyby \citet{New09} througha combination of strong and weak lensing and stellar kinematics." As shown in Fig., As shown in Fig. 3. these individual nmieasurements are in excellent. agreement with the Mg 7 relation based on the abundance matching of statistical functions., \ref{MvirVz0} these individual measurements are in excellent agreement with the $\Mvir$ $\sigma$ relation based on the abundance matching of statistical functions. This agreement bolsters the validity of the Ανν 6 relation at z= 0., This agreement bolsters the validity of the $\Mvir$ $\sigma$ relation at $z=0$ . Notice that the Adve relation shown in Fig., Notice that the $\Mvir$ $\sigma$ relation shown in Fig. 3. isa, \ref{MvirVz0} is a likelihood Ενω < rate ,with extent likelihood and count rate. "> 0,015classify these sources as 9 were inTable 1.", We classify these sources as class=Bl in Table 1. sources with No., The sources No. 3. 69. 83. δι. 100. 157. 158. 160 aud and count selected as candidate X-ray. binaries.," 3, 69, 83, 84, 100, 157, 158, 160 and 242 were selected as candidate X-ray binaries." In Paper I class Dl No., In Paper I sources with No. 26. 105 and 153 were rejected mainly due to the absence of time variability.," 26, 105 and 153 were rejected mainly due to the absence of time variability." For these sources radio, For these sources radio for ο<1 aud Or 2»1.,for $\beta\ll 1$ and for $\beta \gg 1$. For fast modes. the cut-off due to viscous camping is obtained iu. YLUS: 7/°(B7) or}κ1 andΤΘ) .or the high. 3 plasiua. where 5(6p9V7LZA(jg)2VA))2a," For fast modes, the cut-off due to viscous damping is obtained in YL08: for $\beta\ll 1$ and for the high $\beta$ plasma, where $x_{c}=\left(6\rho\delta V^{2}L/(\eta_{0}V_{\A})\right)^{2/3}$." For fast modes. the cut-off scale of turbulence is given by Iu collisionless plasiua. the turbulence is damped due to the Landau damping.," For fast modes, the cut-off scale of turbulence is given by In collisionless plasma, the turbulence is damped due to the Landau damping." The damping rate due to the Landau damping is given by (see YLOS) The cut-off scale of the turbulence is obtained by equating the damping rate to the cascading rate., The damping rate due to the Landau damping is given by (see YL08) The cut-off scale of the turbulence is obtained by equating the damping rate to the cascading rate. From Equatious (A3)) and (B11)) we obtain 02)( Below we describe the NLT for resonance acceleration of dust eras iu MIID turbulence., From Equations \ref{tcas_fast}) ) and \ref{gamma_ncol}) ) we obtain ) Below we describe the NLT for resonance acceleration of dust grains in MHD turbulence. The QLT assumes that the guiding ceuter of the charged particles is regular motion along the uniform maguetic field and that the evro-orbit is not perturbed., The QLT assumes that the guiding center of the charged particles is regular motion along the uniform magnetic field and that the gyro-orbit is not perturbed. " The Fokker-Plauck diffusion cocficicuts (Jokipit 1966: Sclilickeiser Miller 1998) are given as where up=Dona Kun=hau£+. |Enax|=fuas corresponds to the dissipation⋅⋅. scale. ,R.£+ refer. to the left-. and vielt-ciretlarly Dg/8z.polarized modes. aud o=tanbk,ky."," The Fokker-Planck diffusion coefficients (Jokipii 1966; Schlickeiser Miller 1998) are given as where $u_{B}=B_{0}^{2}/8\pi$, $|{\bf k_{min}}|=k_{\min}=L^{-1}$, $|{\bf k_{max}}|=k_{\max}$ corresponds to the dissipation scale, $\mathcal{R,L}$ refer to the left- and right-circularly polarized modes, and $\phi=\tan^{-1}k_x/k_y$." " Above Fe, is the fuuction forresonance coudition. Vj is the pliase speed and © is Larmor frequency."," Above $R_{n}$ is the function forresonance condition, $V_{ph}$ is the phase speed and $\Omega$ is Larmor frequency." Recently aan wwere detected in LISIN by Boucff (2000).,Recently and were detected in L134N by Roueff (2000). This is the first detection of a doublv-deuterated molecule in a dark interstellar cloud., This is the first detection of a doubly-deuterated molecule in a dark interstellar cloud. " BRoucff derived. fractionation ratios of B(ONILLID)=01 and R(ONIIDo)=0.05. where we define the fractionation ratio. AR. of the deuterated species XIL,;D,; to be MNT,D, j4 2/0€NIL,Dou a) where vis the uuuber density."," Roueff derived fractionation ratios of $R(\damm)=0.1$ and $R(\ddamm)=0.05$, where we define the fractionation ratio, $R$, of the deuterated species $_m$ $_{m'}$ to be $n$ $_m$ $_{m'}$ $n$ $_{m+1}$ $_{m'-1}$ ) where $n$ is the number density." wiwas previously detected at the same position bv Olbere (1985) and Saito (2000). who determined RONIL;D)z0.05.," was previously detected at the same position by Olberg (1985) and Saito (2000), who determined $R(\damm)\approx 0.05$." The first interstellar detection of wwas also made at approximately the same location bv Suvder (1977). who derived R(N»D!)20.15.," The first interstellar detection of was also made at approximately the same location by Snyder (1977), who derived $R(\nndp) = 0.45$." hhas been detected in LISIN by Wootten. Loren. Snell (1982). Coréllin. Langer. Wilson (1982). anc Butuer. Lada. Loren (1995) with values for R(DCO!) in the ranee 0.03.0.07.," has been detected in L134N by Wootten, Loren, Snell (1982), Guéllin, Langer, Wilson (1982), and Butner, Lada, Loren (1995) with values for $R(\dcop)$ in the range 0.03–0.07." More receut observations of aaud aat the same location as the ppeak were carried out by Tine (2000). who obtained fractionation ratios of 0.35 aud 0.15. respectively for these Ίο».," More recent observations of and at the same location as the peak were carried out by Tiné (2000), who obtained fractionation ratios of 0.35 and 0.18 respectively for these ions." Tn addition to the deuterimuu fractionation. it is known that the absolute abundances relative to IT» of aaud NoIE! peak at the same position (Ungerechts. Walusleyv. Winnewisser 1980: Swacde L989: Dickens 2000).," In addition to the deuterium fractionation, it is known that the absolute abundances relative to $_2$ of and $_2$ $^+$ peak at the same position (Ungerechts, Walmsley, Winnewisser 1980; Swade 1989; Dickens 2000)." The only other doubly deuterated molecule observed iu the iuterstellar medium is DoCO. which has been detected in two regions: the πο Orion Compact Ridge source (Turner 1990) and the low-nass protostar IRAS 16293-2122 (Ceccarclli 1998: Loinard 2000).," The only other doubly deuterated molecule observed in the interstellar medium is $_2$ CO, which has been detected in two regions: the well-known Orion Compact Ridge source (Turner 1990) and the low-mass protostar IRAS 16293-2422 (Ceccarelli 1998; Loinard 2000)." "Re] Iu both cases. the large DoCO fractionation Π(Ώυςο)=0.02 and 0.35 respectively is thought to result from erain surface chemistry. since the molecular abundances in these wari regious reflect the evaporation of ice mantles from interstellar dust grains BBrown. Charulev, Millar. 1988). aud the post-cvaporation molecular D/II ratios remain equal to the ratios in the precursor ices for over 105 vears (Rodgers Millar 1996)."," In both cases, the large $_2$ CO fractionation -- $R$ $_2$ $) = 0.02$ and 0.35 respectively – is thought to result from grain surface chemistry, since the molecular abundances in these warm regions reflect the evaporation of ice mantles from interstellar dust grains Brown, Charnley, Millar 1988), and the post-evaporation molecular D/H ratios remain equal to the ratios in the precursor ices for over $10^4$ years (Rodgers Millar 1996)." Deuterated foriiialdelivde forms on grains via additiou of IL aud D atoms to CO (Ticlens 1983: Charuley. Ticleus. Rodgers 1997). aud so large amounts of DCO aud DeCO can be expected if the ooOeas-pliase atomic D/II ratio is large.," Deuterated formaldehyde forms on grains via addition of H and D atoms to CO (Tielens 1983; Charnley, Tielens, Rodgers 1997), and so large amounts of HDCO and $_2$ CO can be expected if the gas-phase atomic D/H ratio is large." aud coal also forii on eraius through D aud II atom additions o atomic N (Brown Millar 1989)., and can also form on grains through D and H atom additions to atomic N (Brown Millar 1989). ITowever. as noted by Roueff (2000). the lack of ongoing star formation. ogether with the low temperature in L131N (Tx9 Ik: Swade 1989: Dickens 2000). sugecsts that uautle removal has not occurred.," However, as noted by Roueff (2000), the lack of ongoing star formation, together with the low temperature in L134N $T\approx 9$ K; Swade 1989; Dickens 2000), suggests that mantle removal has not occurred." Markwick. Milhu. Charuley (2000) have proposed a nouthermal mechanism Or removing eran mantles iu dark clouds involving i0u-jeutral strezüuimg produced iu MIID motions.," Markwick, Millar, Charnley (2000) have proposed a nonthermal mechanism for removing grain mantles in dark clouds involving ion-neutral streaming produced in MHD motions." Towever. his process also acts to remove ID! aud NoD! from the eas (Charnley 1998) aud so this iiechanisii is uulikelyv. to ive occurred at the deuterimm emission peak inL13L£N.," However, this process also acts to remove $\rm H_2D^+$ and $\rm N_2D^+$ from the gas (Charnley 1998) and so this mechanism is unlikely to have occurred at the deuterium emission peak in." . It therefore appears that the aud oobserved in L131N must be created in the eas plase., It therefore appears that the and observed in L134N must be created in the gas phase. Iu this paper. we address the issue of gas phase aniunuonia deuteration.," In this paper, we address the issue of gas phase ammonia deuteration." We first discuss the underlying chenuüstiv which coutrols the deuteriun fractionation aud amunoia abuudances in dark clouds., We first discuss the underlying chemistry which controls the deuterium fractionation and ammonia abundances in dark clouds. We then show how successive deuteron trausfer reactions cau lead to large abundances of imultiplv-deuterated amunonmia., We then show how successive deuteron transfer reactions can lead to large abundances of multiply-deuterated ammonia. We derive analytical expressions for the steady-state D/II ratios iu isotopomiers of anumonia. and compare these theoretical ratios with those observed in LISIN aud with those expected frou erain surface chieiistry.," We derive analytical expressions for the steady-state D/H ratios in isotopomers of ammonia, and compare these theoretical ratios with those observed in L134N and with those expected from grain surface chemistry." A πιάνο of sinely-deuterated molecules have been detected im dark interstellar clouds with large fractionations (AR~0.001 0.1). aud. the theory behind the observed D cuhlaucement is well understood WWatson 1971: Guéllin 1982: Millar. Deunctt. Terbst 1989: Roberts Milla: 2000).," A number of singly-deuterated molecules have been detected in dark interstellar clouds with large fractionations $R\sim0.001$ –0.1), and the theory behind the observed D enhancement is well understood Watson 1974; Guéllin 1982; Millar, Bennett, Herbst 1989; Roberts Millar 2000)." Esseutiallv. sanall zero-point cnerev differeuces eusure that molecular ions become preferentially deuterated via D/II exchange reactions with IID. aud subsequent iou-molecule reactions spread this D-curichiment to neutral species.," Essentially, small zero-point energy differences ensure that molecular ions become preferentially deuterated via D/H exchange reactions with HD, and subsequent ion-molecule reactions spread this D-enrichment to neutral species." At 1011. the most important fractionation process is that of ΠΟ ! :," At K, the most important fractionation process is that of $_2$ $^+$ :" , The break in the star formation rate al 2=30 is artificially sharp due to (he simplicity ol our modeling.,The break in the star formation rate at $z=30$ is artificially sharp due to the simplicity of our modeling. In reality. this is likely to be a smoother transition because the molecular eas will not be dissociated instantaneously. and will not be completely dissociated in more massive halos (Machacek.Bryan&Abel2001).," In reality, this is likely to be a smoother transition because the molecular gas will not be dissociated instantaneously, and will not be completely dissociated in more massive halos \citep*{MacBryAbe01}." . We do believe. however. that this transition will be rapid.," We do believe, however, that this transition will be rapid." " The mean free path of LW photonsal z=30 is Anup~LOAIpe (physical). much larger than the typical separation of 10""AL. halos at this redshilt (~30kpe)."," The mean free path of LW photonsat $z=30$ is $\lambda_{\rm mfp} \sim 10 \;{\rm Mpc}$ (physical), much larger than the typical separation of $10^6 \;\msun$ halos at this redshift $\sim 30 \;{\rm kpc}$ )." Photons travel this mean [ree path in ~101ivr. which is short compared to the Hubble time.," Photons travel this mean free path in $\sim 10^7 \;{\rm yr}$, which is short compared to the Hubble time." For these reasons. a roughly uniform background of LAW photons should be set up very. quickly.," For these reasons, a roughly uniform background of LW photons should be set up very quickly." The nunmber of sources increases exponentially wilh Gime. so (he background radiation level will increase rapidly until it is intense enough to dissociate most of the molecules in the universe.," The number of sources increases exponentially with time, so the background radiation level will increase rapidly until it is intense enough to dissociate most of the molecules in the universe." The timescale lor photodissociation of a molecule is inversely proportional to the intensity of the radiation field in the Lyman-Werner bands. Jj. and also depends on how well the molecule is shielded from the radiation.," The timescale for photodissociation of a molecule is inversely proportional to the intensity of the radiation field in the Lyman-Werner bands, $J_{\rm LW}$, and also depends on how well the molecule is shielded from the radiation." " Oh&IIaiman(2002) give the relationship as where Jo,=Ji/107hergem7s!Iztsrto and. faiaa takes into account the effects ofB IH» sell-shieldingB. and is. given. by fija-=min|1..Vin,E/10!emIDEM7)77] (Dramen DBertoldin 1996)."," \citet{OhHai02} give the relationship as where $J_{21}= J_{\rm LW}/10^{-21} \;{\rm erg\,cm^{-2}\,s^{-1}\,Hz^{-1}\,sr^{-1}}$, and $f_{\rm shield}$ takes into account the effects of ${\rm H}_2$ self-shielding and is given by $f_{\rm shield} = {\rm min}[1, (N_{\rm H_{2}}/10^{14}{\rm cm^{-2}})^{-0.75}]$ (Draine Bertoldi 1996)." Thus. the dissociation time at fixed column density depends only on the backeround raciation intensity. approximately given by assuming 10 LW photons are produced per barvon of star formation (see above).," Thus, the dissociation time at fixed column density depends only on the background radiation intensity, approximately given by assuming $10^4$ LW photons are produced per baryon of star formation (see above)." The constants in (this expression have their usual meaning., The constants in this expression have their usual meaning. The optical depth of the IGM to LW photons is estimated (o be 7j;c2—3 (e.g.Ciardietal.20008;Racotti2001).. reducing the UV flux by about an order of magnitude.," The optical depth of the IGM to LW photons is estimated to be $\tau_{\rm IGM} \simeq 2-3$ \citep[e.g.,][]{CiaFerAbe00,RicGneShu01}, reducing the UV flux by about an order of magnitude." Our formula for Jj neglects the redshifting of photons oul of the LW bands. but photous travel a mean free path in a small fraction of the Hubble time and so should be absorbed long before redshilt effects become Inportant.," Our formula for $J_{\rm LW}$ neglects the redshifting of photons out of the LW bands, but photons travel a mean free path in a small fraction of the Hubble time and so should be absorbed long before redshift effects become important." In Figure 3. we show the dissociation time compared to the IIubble time as a function ol redshift for dillerent neutral hydrogen column densities., In Figure \ref{fig:tdiss} we show the dissociation time compared to the Hubble time as a function of redshift for different neutral hydrogen column densities. We also show the lifetime of a VMS lorcomparison., We also show the lifetime of a VMS forcomparison. We have calculated the curves in Figure 3. for a molecular traction of 107. and with τον=2.," We have calculated the curves in Figure \ref{fig:tdiss} for a molecular fraction of $10^{-3}$, and with $\tau_{\rm IGM} = 2$." " X 10MN, halo at 2=30 would havea hydrogen column density of ~4x10?""em>7 if it were a uniform sphere. and about 10 times larger if il had an isothermal density. distribution (Glover&Drand 2001).."," A $10^6\;\msun$ halo at $z=30$ would havea hydrogen column density of $\sim 4\times10^{20} \;{\rm cm^{-2}}$ if it were a uniform sphere, and about 10 times larger if it had an isothermal density distribution \citep{GloBra01}. ." To relate this to the rarity of the peaks. we again consider 2= 30.," To relate this to the rarity of the peaks, we again consider $z=30$ ." A 3-sigma peak has a mass of only 4x10% M...," A 3-sigma peak has a mass of only $4\times 10^3 \;\msun$ ," number of BSs that migrate into the core due to dynamical friction. Nowe is the number that migrate out of the core via kicks experienced during dynamical encounters. and δν is the number of DSs that have evolved. away from. being brighter and bluer than the MSTO in the cluster CMD cue to stellar evolution.,"number of BSs that migrate into the core due to dynamical friction, $_{out}$ is the number that migrate out of the core via kicks experienced during dynamical encounters, and $_{ev}$ is the number of BSs that have evolved away from being brighter and bluer than the MSTO in the cluster CMD due to stellar evolution." We adopt an average stellar mass of m=0.65A/. and an average BS mass of mes=2mL3M.., We adopt an average stellar mass of $m = 0.65 M_{\odot}$ and an average BS mass of $m_{BS} = 2m = 1.3 M_{\odot}$. Phe mass of a BS can provide a rough guide to its lifetime. although a range of lifetimes are still possible for any given mass.," The mass of a BS can provide a rough guide to its lifetime, although a range of lifetimes are still possible for any given mass." bor instance. Sandquist.Bolte&Lernquist(1997). showed that a 1.5 M. blue strageler will have a lifetime of around 0.78 Gives in unmixed mocels. or 1.57 Cars in completely mixed moclels.," For instance, \citet{sandquist97} showed that a 1.3 $_{\odot}$ blue straggler will have a lifetime of around $0.78$ Gyrs in unmixed models, or $1.57$ Gyrs in completely mixed models." Combined with the results of Sillsetal.(2001).. Lombardiοἱal.(2002) ancl Clebbeek&Pols(2008).. we expect a lifetime in the range 1-5 Civrs fora 1.3 M. BS.," Combined with the results of \citet{sills01}, \citet{lombardi02} and \citet{glebbeek08}, we expect a lifetime in the range 1-5 Gyrs for a 1.3 $_{\odot}$ BS." As a first approximation. we choose a likely value of res=1.5 Cives lor the average BS lifetime (e.g.Sillsetal.2001).," As a first approximation, we choose a likely value of $\tau_{BS} = 1.5$ Gyrs for the average BS lifetime \citep[e.g.][]{sills01}." . The ellects had on our results by changing our assumption for the average BS lifetime will be explored in Section 4. and cliscussecl in Section 5.., The effects had on our results by changing our assumption for the average BS lifetime will be explored in Section \ref{results} and discussed in Section \ref{discussion}. We consider only the last res vears., We consider only the last $\tau_{BS}$ years. This is because we are comparing our model predictions to current observations of BS populations. so that we are only concerned with those BSs formed within the last few Covers.," This is because we are comparing our model predictions to current observations of BS populations, so that we are only concerned with those BSs formed within the last few Gyrs." Any BSs formed before this would have evolved away from being brighter ancl bluer than the MSTO by the current cluster age., Any BSs formed before this would have evolved away from being brighter and bluer than the MSTO by the current cluster age. C'onsequentIvy. we set ρου = Noe in Equation 1..," Consequently, we set $_{BS,0}$ = $_{ev}$ in Equation \ref{eqn:number-bss}." We further assume that all central cluster parameters have not changed in the last Tes vears. including the central velocity clispersion. the central uninositv cdensitv. the core radius and the core binary raction.," We further assume that all central cluster parameters have not changed in the last $\tau_{BS}$ years, including the central velocity dispersion, the central luminosity density, the core radius and the core binary fraction." Lt follows that the rate of BS formation is constant or the time-scale of interest., It follows that the rate of BS formation is constant for the time-scale of interest. Vhis time-scale is comparable o the hall-mass relaxation time but much longer than the central relaxation time for the majority of the clusters in our sample (llarrisctal.1996)., This time-scale is comparable to the half-mass relaxation time but much longer than the central relaxation time for the majority of the clusters in our sample \citep{harris96}. .. This suggests that core xwameters such as the central density and the core radius will tvpicallv change in a time res since the time-scale on which these parameters vary is the central relaxation ime (1]οσσίο&Lut2003)., This suggests that core parameters such as the central density and the core radius will typically change in a time $\tau_{BS}$ since the time-scale on which these parameters vary is the central relaxation time \citep{heggie03}. . Therefore. our. assumption of constant rates and cluster parameters is not strictly correct. iowever ib provides a suitable starting point for our mocel.," Therefore, our assumption of constant rates and cluster parameters is not strictly correct, however it provides a suitable starting point for our model." We will discuss the implications of our assumption of time-independent eluster properties and rates in Section 5.., We will discuss the implications of our assumption of time-independent cluster properties and rates in Section \ref{discussion}. In the following sections. we discuss cach of the remaining terms in Equation 1..," In the following sections, we discuss each of the remaining terms in Equation \ref{eqn:number-bss}." " We can approximate the number of DSs formed in the last Tes vears from collisions during cvnamical encounters as: where Ny,4. Ny2 and No2 are the number. of single-single. sinele-binary ancl binary-binary encounters. respectively."," We can approximate the number of BSs formed in the last $\tau_{BS}$ years from collisions during dynamical encounters as: where $_{1+1}$, $_{1+2}$ and $_{2+2}$ are the number of single-single, single-binary and binary-binary encounters, respectively." Phe terms £j.1. £j2 and [ο2 are the fraction of 111. 112 and 212 encounters. respectively. that will produce a BS in the last Tes vears.," The terms $_{1+1}$, $_{1+2}$ and $_{2+2}$ are the fraction of 1+1, 1+2 and 2+2 encounters, respectively, that will produce a BS in the last $\tau_{BS}$ years." We treat these three variables as [ree parameters since we do not know what fraction of collision. products. will produce BSs (i.e. stars with an appropriate combination of colour and brightness to end up in the BS region of the CMD). nor do we know what fraction of 112 and 212 encounters will result in a stellar collision.," We treat these three variables as free parameters since we do not know what fraction of collision products will produce BSs (i.e. stars with an appropriate combination of colour and brightness to end up in the BS region of the CMD), nor do we know what fraction of 1+2 and 2+2 encounters will result in a stellar collision." Numerical scattering experiments have been performed to study the outcomes of 1|2 and 2| encounters (e.g.Lut&Baheall1983:MeMillan.1986:Freecauctal.2004).. however a Large fraction of the relevant parameter space has vet to be explored.," Numerical scattering experiments have been performed to study the outcomes of 1+2 and 2+2 encounters \citep[e.g.][]{hut83, mcmillan86, fregeau04}, however a large fraction of the relevant parameter space has yet to be explored." " In terms of the core radius ο (in. parsecs). the central number density ry (in 7). the root-mean-square velocity cy (in. km 1 0). the average stellar mass m (in. M.) and the average stellar racius Z2? (in 1t. ). the mean time-scale between single-single collisions in. the. core of a GC is (Leonard.1989):: The additional factor (1-f,) 7 comes from the fact that we are only considering interactions between single stars and the central number density of single stars is given. by Gono. where Εν is the binary fraction in the core (Le. the fraction of objects that are binaries)."," In terms of the core radius $r_c$ (in parsecs), the central number density $n_0$ (in $^{-3}$ ), the root-mean-square velocity $v_{m}$ (in km $^{-1}$ ), the average stellar mass $m$ (in $_{\odot}$ ) and the average stellar radius $R$ (in $_{\odot}$ ), the mean time-scale between single-single collisions in the core of a GC is \citep{leonard89}: The additional factor $_b$ $^{-2}$ comes from the fact that we are only considering interactions between single stars and the central number density of single stars is given by $_b$ $_0$, where $_b$ is the binary fraction in the core (i.e. the fraction of objects that are binaries)." For our chosen mass. we assipie a corresponding average stellar raclius using the relation M/M. = Bl. (ben1991).," For our chosen mass, we assume a corresponding average stellar radius using the relation $_{\odot}$ = $_{\odot}$ \citep{iben91}." . Fhe number of 111 collisions expected to have occurred in the last τος wears is then approximated. by: The rate of collisions between single stars and binaries. as well as between two binary pairs. can be roughly approximated in the same way as for single-single encounters (Leonard1989:Sigurdsson&Phinney1993:Baconetal.1996:Freecauctal. 2004).," The number of 1+1 collisions expected to have occurred in the last $\tau_{BS}$ years is then approximated by: The rate of collisions between single stars and binaries, as well as between two binary pairs, can be roughly approximated in the same way as for single-single encounters \citep{leonard89, sigurdsson93, bacon96, fregeau04}." . We adopt the time-scales derived in Leigh&Sills(2011). for the average times between 112 and 2| encounters., We adopt the time-scales derived in \citet{leigh11b} for the average times between 1+2 and 2+2 encounters. These are: and where e is the average binary semi-major axis in the core in AU ancl we have assumed that the average binary mass is equal to twice the average single star mass., These are: and where $a$ is the average binary semi-major axis in the core in AU and we have assumed that the average binary mass is equal to twice the average single star mass. “Phe numbers of 112 and 2)2 encounters expected. to have occurred in the last τες vears are given by. respectively: and The outeomes of 1/2 and 9139. encounters will ultimately contribute to the evolution of the binary fraction in the core.," The numbers of 1+2 and 2+2 encounters expected to have occurred in the last $\tau_{BS}$ years are given by, respectively: and The outcomes of 1+2 and 2+2 encounters will ultimately contribute to the evolution of the binary fraction in the core." How and with what frequeney binary hardening/softening as well as capture. exchange anc," How and with what frequency binary hardening/softening as well as capture, exchange and" How and with what frequeney binary hardening/softening as well as capture. exchange ancl," How and with what frequency binary hardening/softening as well as capture, exchange and" matrix) of the particles depend not only on the wavelength but also on the altitude.,matrix) of the particles depend not only on the wavelength but also on the altitude. Taking these variations fully into account would require wavelength dependent calculations of the optical properties of 80 different particles (40 layers and two model atmospheres)., Taking these variations fully into account would require wavelength dependent calculations of the optical properties of 80 different particles (40 layers and two model atmospheres). Instead. we define four different particles for each model atmosphere (thus. eight in total). corresponding to four altitude ranges in each model atmosphere.," Instead, we define four different particles for each model atmosphere (thus, eight in total), corresponding to four altitude ranges in each model atmosphere." Within each altitude range. the particle type is the same. only the particles? number density varies between the layers.," Within each altitude range, the particle type is the same, only the particles' number density varies between the layers." Considering the almost total lack of constraints on clouds on exoplanets from current observations and condensation models. this reduction of details seems reasonable for this exploratory study that focuses on the radiative transfer in a given model atmosphere.," Considering the almost total lack of constraints on clouds on exoplanets from current observations and condensation models, this reduction of details seems reasonable for this exploratory study that focuses on the radiative transfer in a given model atmosphere." Our different particle types are based on the changes of particle composition in. the atmosphere., Our different particle types are based on the changes of particle composition in the atmosphere. All. particles produces by are altitude dependent mixtures of various solids., All particles produces by are altitude dependent mixtures of various solids. Figure 2 shows how the composition of the particles varies across the two model atmospheres., Figure \ref{fig.volp} shows how the composition of the particles varies across the two model atmospheres. As can be seen. across large regions of each atmosphere. the particle composition only varies slightly with pressure.," As can be seen, across large regions of each atmosphere, the particle composition only varies slightly with pressure." At a few altitudes. however. the particle composition changes rapidly.," At a few altitudes, however, the particle composition changes rapidly." We choose these altitudes as the boundaries between our particle types., We choose these altitudes as the boundaries between our particle types. Based on these boundaries. the particle types in the two model atmospheres have the same composition but different sizes (see below).," Based on these boundaries, the particle types in the two model atmospheres have the same composition but different sizes (see below)." We distinguish the following four particle types (from the top of the atmosphere to the bottom). named after their mam constituent: a high silicate haze. a low silicate haze. an iron cloud. and an aluminium oxide (Α.Ο9) cloud.," We distinguish the following four particle types (from the top of the atmosphere to the bottom), named after their main constituent: a high silicate haze, a low silicate haze, an iron cloud, and an aluminium oxide $_2$ $_3$ ) cloud." Although particle composition stays roughly constant with altitude across the four regions 1n. each model atmosphere. particle size does not (see Fig. 1)).," Although particle composition stays roughly constant with altitude across the four regions in each model atmosphere, particle size does not (see Fig. \ref{fig.atm}) )." Since particle size 1s very important in determining the scattering properties of particles. assuming an altitude independent particle size across à region might have some consequences for our radiative transfer results.," Since particle size is very important in determining the scattering properties of particles, assuming an altitude independent particle size across a region might have some consequences for our radiative transfer results." Fortunately. the particles that produces tend to be very small. especially in the upper atmosphere (above ~1 mbar) where particle size changes most rapidly.," Fortunately, the particles that produces tend to be very small, especially in the upper atmosphere (above $\sim$ 1 mbar), where particle size changes most rapidly." When particles are much smaller thàn the wavelength. however. their extinction. cross-section scales with the cube of their radius. while its spectral dependence does not change (Haneletal. 2003).," When particles are much smaller than the wavelength, however, their extinction cross-section scales with the cube of their radius, while its spectral dependence does not change \citep{han03}." . Hence. for the lower and upper silicate haze. we take into aecount the altitude dependent particle size in the caleulation of a layer's optical thickness. but leave the spectral dependence unchanged.," Hence, for the lower and upper silicate haze, we take into account the altitude dependent particle size in the calculation of a layer's optical thickness, but leave the spectral dependence unchanged." Lower in the atmosphere. the particles are larger. but their size also changes less with altitude.," Lower in the atmosphere, the particles are larger, but their size also changes less with altitude." Hence. for the atmospheric layers containing the iron and Al»O; clouds. we assume a constant (the mean) particle radius.," Hence, for the atmospheric layers containing the iron and $_2$ $_3$ clouds, we assume a constant (the mean) particle radius." The assumed particle sizes used in the Mie calculations are given in Table |., The assumed particle sizes used in the Mie calculations are given in Table 1. These coincide with the average of the mean particle size over the pressure range considered., These coincide with the average of the mean particle size over the pressure range considered. Table 2 summarises the composition of the dirty particles for each of the particle types., Table 2 summarises the composition of the dirty particles for each of the particle types. Using the model atmospheres produced by as input. we calculate dise-integrated (spatially unresolved) new-infrared flux spectra with a doubling-adding algorithm.," Using the model atmospheres produced by as input, we calculate disc-integrated (spatially unresolved) near-infrared flux spectra with a doubling-adding algorithm." The doubling-adding method is often used in calculations of sunlight that is reflected by and/or transmitted. through planetary atmospheres. see e.g. Hansen&Travis(1974) and deHaanetal(1987).," The doubling-adding method is often used in calculations of sunlight that is reflected by and/or transmitted through planetary atmospheres, see e.g. \citet{han74} and \citet{deh87}." It allows the accurate solving of the equation of radiative transfer along paths in a model atmosphere that consists of a stack of plane-parallel. homogeneous layers containing scattering and/or absorbing gaseous molecules and/or aerosol particles.," It allows the accurate solving of the equation of radiative transfer along paths in a model atmosphere that consists of a stack of plane-parallel, homogeneous layers containing scattering and/or absorbing gaseous molecules and/or aerosol particles." Vertically inhomogeneous model atmospheres are created, Vertically inhomogeneous model atmospheres are created is between £m and £m?|dim (Wvithe. Webster Turner 2000b).,"is between $\langle m \rangle$ and $\langle m \rangle + {\rmn d} \langle m \rangle$ (Wyithe, Webster Turner 2000b)." Peleefore) and. pu(tmnj) were computed: using Lat (puo)X (Mus). and. logarithmie (pire)xd assumptions for the Bayesian prior for galactic transverse velocity (Vus).," $p_{v}(v_{eff}|\langle m \rangle)$ and $p_{m}(\langle m \rangle)$ were computed using flat $p(V_{tran})\propto dV_{tran}$ ), and logarithmic $p(V_{tran})\propto \frac{dV_{tran}}{V_{tran}}$ ) assumptions for the Bayesian prior for galactic transverse velocity $V_{tran}$ )." peteogrlimj) was found to be insensitive to the prior assumed. however pyCGOni) showed. some dependence.," $p_{v}(v_{eff}|\langle m \rangle)$ was found to be insensitive to the prior assumed, however $p_{m}(\langle m \rangle)$ showed some dependence." In the remainder of this paper we use prin)) calculated using the assumption of a logarithmic prior., In the remainder of this paper we use $p_{m}(\langle m \rangle)$ calculated using the assumption of a logarithmic prior. We note that the assumption of the [lat prior raises the average light-curve derivative by a few percent., We note that the assumption of the flat prior raises the average light-curve derivative by a few percent. The functions νοπόνοΕΕ) peGocrrltimi)- pin(ina)) and the LALE statistics presented. in this paper were computed for the following assumptions of smooth matter density. photometric error. ancl direction. of the galactic transverse velocity.," The functions $p_{s}(S|\langle m \rangle,v_{eff})$, $p_{v}(v_{eff}|\langle m \rangle)$, $p_{m}(\langle m \rangle)$ and the HME statistics presented in this paper were computed for the following assumptions of smooth matter density, photometric error, and direction of the galactic transverse velocity." Two models are considered for the distribution. of microlenses. one with no continuously distributed. matter. and one where smooth matter contributes of the surface. mass clensity.," Two models are considered for the distribution of microlenses, one with no continuously distributed matter, and one where smooth matter contributes of the surface mass density." Two orientations were chosen for the transverse velocity with respect to the galaxy. having source trajectories parallel to the DB and D axes.," Two orientations were chosen for the transverse velocity with respect to the galaxy, having source trajectories parallel to the $-$ B and $-$ D axes." " The two orientations bracket the range of possibilities. and because the images arepositioned approximately orthogonally with respect to the galactic centre correspond to shear values of 54.5g<0.5c.5p70 and 54.50$ and $\gamma_{A},\gamma_{B}<0,\gamma_{C},\gamma_{D}>0$ respectively." Photometric error was simulated by perturbing the model light-curve by an amount cistributed randomly from a Gaussian of hallwidth 6., Photometric error was simulated by perturbing the model light-curve by an amount distributed randomly from a Gaussian of halfwidth $\sigma$. The simulations used. two dillerent estimates of the error in the photometric magnitudes., The simulations used two different estimates of the error in the photometric magnitudes. In the first case a small error was assumed. (Sl)., In the first case a small error was assumed (SE). For images A and D. ose =0.01 mae. and for images C and D ay¢=0.02 mae.," For images A and B, $\sigma_{SE}$ =0.01 mag, and for images C and D $\sigma_{SE}$ =0.02 mag." In the second case. a larger error was assumed (LI).," In the second case, a larger error was assumed (LE)." For images A and D. 601E —0.02 mag and for images C and D σι p=0.04 mag.," For images A and B, $\sigma_{LE}$ =0.02 mag and for images C and D $\sigma_{LE}$ =0.04 mag." The random component of observational error quoted in Irwin et al. (, The random component of observational error quoted in Irwin et al. ( 1989) was 0.02 mag.,1989) was 0.02 mag. 3oth the microlensing rate due to à transverse velocity (em., Both the microlensing rate due to a transverse velocity (eg. Witt. WKavser ltefsdal 1903). as well as. the corresponding rate due to proper motions (WWΤα) are not functions of the details of the microlens mass distribution. but rather are only dependent on the mean microlens mass.," Witt, Kayser Refsdal 1993), as well as the corresponding rate due to proper motions (WWT00a) are not functions of the details of the microlens mass distribution, but rather are only dependent on the mean microlens mass." We therefore limit our attention to moclels in which all the microlenses have the same mass since the results obtained will be applicable to other models with different forms for the mass function., We therefore limit our attention to models in which all the microlenses have the same mass since the results obtained will be applicable to other models with different forms for the mass function. Intrinsic variation of the quasar in the 2237|0305 system cannot be clirectly measured. since one cannot be sure how much variation is due to mücrolensing and how much is intrinsic to the source., Intrinsic variation of the quasar in the 2237+0305 system cannot be directly measured since one cannot be sure how much variation is due to microlensing and how much is intrinsic to the source. " The afore-mentioned analyses of microlensing in (02237|0305 to determine ps. pe and pr, have utilised. cilference. light-curves."," The afore-mentioned analyses of microlensing in Q2237+0305 to determine $p_s$, $p_v$ and $p_m$ have utilised difference light-curves." This is practical for (Q2237|0305 since the relative time-delays between images (< 1-day (eg Sehneider et al., This is practical for Q2237+0305 since the relative time-delays between images $<$ 1-day (eg Schneider et al. 1988)) are small compared with typical sampling time-scales (weeks or months)., 1988)) are small compared with typical sampling time-scales (weeks or months). However our current goal is to determine whether a particular observed light-curve. derivative. signals a [forthcoming HIME., However our current goal is to determine whether a particular observed light-curve derivative signals a forthcoming HME. Since an observed. (single image) light-curve. derivative. depends on the super-position of microlensing and. intrinsic source variation. the caleulation of an event trigeer requires the inclusion of a statistical description of the intrinsic source variation.," Since an observed (single image) light-curve derivative depends on the super-position of microlensing and intrinsic source variation, the calculation of an event trigger requires the inclusion of a statistical description of the intrinsic source variation." Giveon et al. (, Giveon et al. ( 1999) analysed. optical variability in the sample of Palomar-Green quasars.,1999) analysed optical variability in the sample of Palomar-Green quasars. They find that over time-scales between LOO and. 1000 clays the sources have a power spectra that is of a power-law form. P;x9! with 102.," They find that over time-scales between 100 and 1000 days the sources have a power spectra that is of a power-law form, $P_{\nu}\propto\nu^{\gamma_I}$ with $\gamma_I\sim-2$." We model intrinsic variability. for. Q2237|0305 using a power-spectrum of power-law form., We model intrinsic variability for Q2237+0305 using a power-spectrum of power-law form. Since. long curation intrinsic variability may have been observed in 2237|0305 (Ostensen et al., Since long duration intrinsic variability may have been observed in Q2237+0305 $\O$ stensen et al. 1995). and our current focus is on the potential for rapid intrinsic variability to cause a false trigger. we caleulate model intrinsic light-curves with power spectra P.x£! over a broad range of time-scales: between 1 and 1000 davs.," 1995), and our current focus is on the potential for rapid intrinsic variability to cause a false trigger, we calculate model intrinsic light-curves with power spectra $P_{\nu}\propto\nu^{\gamma_I}$ over a broad range of time-scales: between 1 and 1000 days." We consider à 2-D. parameter space of intrinsic light-curve variance (97 ) and spectrum index σε. and look for regions of this space whose values. when combined with microlensing models produce variability statistics that are inconsistent with observation.," We consider a 2-D parameter space of intrinsic light-curve variance $\sigma_I^2$ ) and power-spectrum index $\gamma_I$, and look for regions of this space whose values, when combined with microlensing models produce variability statistics that are inconsistent with observation." We first describe a method for computing the likelv-hood (given assumed. values for σι and 5;) for a statistic f defined such that larger values of f imply a large intrinsic contribution to variability., We first describe a method for computing the likely-hood (given assumed values for $\sigma_I$ and $\gamma_I$ ) for a statistic $f$ defined such that larger values of $f$ imply a large intrinsic contribution to variability. The likelv-hood is then compared o the observed. value. f(obs) for that. statistic., The likely-hood is then compared to the observed value $f(obs)$ for that statistic. We place imits on the values for oF and 5; using 4 cillerent. but related light-curve statistics f.," We place limits on the values for $\sigma_I^2$ and $\gamma_I$ using 4 different, but related light-curve statistics $f$." Pairs of single image light-curves can be combined to woduce both difference ancl additive light-eurves., Pairs of single image light-curves can be combined to produce both difference and additive light-curves. . While intrinsic ane microlensed variability cannot be directly distinguished. intrinsic variation is only present in the latter.," While intrinsic and microlensed variability cannot be directly distinguished, intrinsic variation is only present in the latter." In addition. microlensed variability in different images is independent.," In addition, microlensed variability in different images is independent." Variability statistics for cillerence and additive light-curves in the absence of intrinsic source. variability should therefore be identical (on average)., Variability statistics for difference and additive light-curves in the absence of intrinsic source variability should therefore be identical (on average). Thus comparison with the data of variability statistics for these two curves. averaged: over 6 image pairs (only three are independent) provides a means of discrimination between different models for intrinsic source variability.," Thus comparison with the data of variability statistics for these two curves, averaged over 6 image pairs (only three are independent) provides a means of discrimination between different models for intrinsic source variability." The statistic f is calculated: for additive (fi). and difference (fo) light-curves., The statistic $f$ is calculated for additive $f_A$ ) and difference $f_D$ ) light-curves. Light-curves that include both intrinsic and microlensed Huctuation. exhibit. higher variability in the additive light-curve. (fi fo)., Light-curves that include both intrinsic and microlensed fluctuation exhibit higher variability in the additive light-curve $f_A>f_D$ ). By comparing fyp—fiyfp calculated from the monitoring data with values obtained from mock observations. for different assumptions For the rate and amplitude of intrinsic variability (0j. 51). we compute the probability of obtaining the observed fipb(obs) as à function. of σι and τε.," By comparing $f_{A-D}=f_A-f_D$ calculated from the monitoring data with values obtained from mock observations for different assumptions for the rate and amplitude of intrinsic variability $\sigma_I^2$, $\gamma_I$ ), we compute the probability of obtaining the observed $f_{A-D}(obs)$ as a function of $\sigma_I$ and $\gamma_I$ ." Microlensing statistics vary with ellective transverse velocity and sampling rate., Microlensing statistics vary with effective transverse velocity and sampling rate. We have therefore computed. this probability as a function of ellective transverse velocity. using mock data sets computed from light-curves with the observed sampling rate:," We have therefore computed this probability as a function of effective transverse velocity, using mock data sets computed from light-curves with the observed sampling rate:" The pulsational modulation of the radial velocity is very significant (see Fig. 1)),The pulsational modulation of the radial velocity is very significant (see Fig. \ref{fig:pulsmodel}) ) making orbital detection far from straightforward., making orbital detection far from straightforward. Any cycle-to-cycle variability will make that a systematic cleaning of the pulsation from the raw radial velocity data yields a residual., Any cycle-to-cycle variability will make that a systematic cleaning of the pulsation from the raw radial velocity data yields a residual. Moreover. strong atmospheric shocks associated with the TTauri pulsations passing through the line-forming region (e.g.?).. have a strong effect C1 the line-profiles.," Moreover, strong atmospheric shocks associated with the Tauri pulsations passing through the line-forming region \citep[e.g.][]{gillet90}, have a strong effect on the line-profiles." This makes the determination of the stellar radial velocity at those pulsational phases problematic., This makes the determination of the stellar radial velocity at those pulsational phases problematic. In Fig. 2, In Fig. \ref{fig:pulscc} we show a few cross-correlation profiles at different phases in the pulsation cycle., we show a few cross-correlation profiles at different phases in the pulsation cycle. The propagation of the shock is well illustrated and in the case of CCen the non-linear behaviour leads to a very significant drop in velocity of more than 20 kmss! over a small phase interval., The propagation of the shock is well illustrated and in the case of Cen the non-linear behaviour leads to a very significant drop in velocity of more than 20 $^{-1}$ over a small phase interval. The shocks in CCen are so energetic that during these phases. He lines are observed in emission (2).," The shocks in Cen are so energetic that during these phases, He lines are observed in emission \citep{maas02}." . Despite the strong pulsational modulation in. the radial velocity data. variability in the radial velocity is detected with a much longer time scale.," Despite the strong pulsational modulation in the radial velocity data, variability in the radial velocity is detected with a much longer time scale." We interpret this as being due to orbital motion and modelled this with a Keplerian model of a binary star., We interpret this as being due to orbital motion and modelled this with a Keplerian model of a binary star. To obtain the orbital elements. we only retained the high quality data outside the pulsation phases where the strong shock is visible in the cross-correlation profile.," To obtain the orbital elements, we only retained the high quality data outside the pulsation phases where the strong shock is visible in the cross-correlation profile." To do so. we required that in all data used for the orbital detection. the 50-point bisector has a variance of less than | kmss7!.," To do so, we required that in all data used for the orbital detection, the 50-point bisector has a variance of less than 1 $^{-1}$." We performed an iterative process on the raw velocity data in which we cleaned the orbital solution from the raw radial velocity data to obtain a good model of the pulsation cycle itself., We performed an iterative process on the raw velocity data in which we cleaned the orbital solution from the raw radial velocity data to obtain a good model of the pulsation cycle itself. We used PDM (Phase Dispersion Minimalisation method developed by ?)) to quantify the fundamental pulsation period (time between successive deep and shallow photometric minimum) and determined a harmonie fit with one overtone as a model description of the pulsation., We used PDM (Phase Dispersion Minimalisation method developed by \citealt{stellingwerf78}) ) to quantify the fundamental pulsation period (time between successive deep and shallow photometric minimum) and determined a harmonic fit with one overtone as a model description of the pulsation. We then cleaned the raw radial velocity data by the pulsation model and performed the next least-square fit of the orbit., We then cleaned the raw radial velocity data by the pulsation model and performed the next least-square fit of the orbit. We stopped the iteration when the changes in the orbital parameters became less than the error., We stopped the iteration when the changes in the orbital parameters became less than the error. The final result is that we indeed found an orbital solution with a period of 1489 + 4 days., The final result is that we indeed found an orbital solution with a period of 1489 $\pm$ 4 days. The errors given in the table are the formal errors obtained using the covariance matrix (2).., The errors given in the table are the formal errors obtained using the covariance matrix \citep{hadrava04}. The mass function is 0.83 M. and the semi-major axis is aysin; = 24 AU.," The mass function is 0.83 $_{\odot}$ and the semi-major axis is $_{1} \, \sin i$ = 2.4 AU." A first look at the infrared spectra of HHer and CCen shows their striking similarity (see refondereen)). both in the global shape and in the dust emission features.," A first look at the infrared spectra of Her and Cen shows their striking similarity (see \\ref{ondereen}) ), both in the global shape and in the dust emission features." In both spectra there is a lack of a strong 10m amorphous silicate feature. while the 4m amorphous feature is prominent.," In both spectra there is a lack of a strong $\mu$ m amorphous silicate feature, while the $\mu$ m amorphous feature is prominent." HHer and CCen show strong emission features around 11.3 - 16.2 - 19.7 - 23.7 - 28 - 33.6pm, Her and Cen show strong emission features around 11.3 - 16.2 - 19.7 - 23.7 - 28 - $\mu$ m "miss more than of the library-type quasars with 7?<22""! (Wolf1998).",miss more than of the library-type quasars with $R<22^m$ \cite{CW2}. refquasars lists all quasars that have been confirmed spectroscopically by CADIS including two quasars identified by the CFRS in its 3hh-field., \\ref{quasars} lists all quasars that have been confirmed spectroscopically by CADIS including two quasars identified by the CFRS in its h-field. Although. the candidate identification on the hh-field and the hh-field is incomplete. we report the present status of our findings.," Although, the candidate identification on the h-field and the h-field is incomplete, we report the present status of our findings." On the CADIS IGhh-field we found seven quasars brighter than R=22 and three 11 galaxies., On the CADIS h-field we found seven quasars brighter than $R=22$ and three 1 galaxies. These ten AGN are more or less uniformly spread over the field., These ten AGN are more or less uniformly spread over the field. The positions have an accuracy of £0711 in each coordinate. measured relative to secondary standards derived from the POSS-II plates and PPM Bastian1991) stars.," The positions have an accuracy of $\pm$ 1 in each coordinate, measured relative to secondary standards derived from the POSS-II plates and PPM \cite{ppm} stars." In the 3hh-field. spectra of 271 objects with lip2275 were taken as part of the CFRS (Hammeret 1995).," In the h-field, spectra of 271 objects with $17\fm50$ we see that the period of the system should increase during the outburst if the material carries away its specific angular momentum." In Fig., In Fig. 1. we plot AMiypal as a function of the mass ratio. q. for the cilferent outburst. models we consider.," \ref{dadm} we plot $\frac{\Delta P/P}{\Delta m_1/M}$ as a function of the mass ratio, $q$, for the different outburst models we consider." The solid. constant line corresponds to this model where the mass ejected carries away its specific angular momentum., The solid constant line corresponds to this model where the mass ejected carries away its specific angular momentum. " Now we consider the elfect of a fraction of the ejected mass. 1, that may be captured by the companion in the outburst."," Now we consider the effect of a fraction of the ejected mass, $\beta$, that may be captured by the companion in the outburst." " We take NAM,=my and ον[ο=1ΔΙ so that The correspondinge changeὃν to the separation is then (Sharaetal.1986).. where q=M3fAL,."," We take $\Delta M_1=-\Delta m_1$ and $\Delta M_2=\beta \Delta m_1$ so that The corresponding change to the separation is then \citep{shara86}, where $q=M_{2}/M_1$." This reduces to equation (7)) with 2=0., This reduces to equation \ref{over}) ) with $\beta=0$. In the absence of strong magnetic elfects the maximum value of 3 is the fractional area of the companions radius., In the absence of strong magnetic effects the maximum value of $\beta$ is the fractional area of the companion's radius. We can estimate the captured fraction of mass with Because the secondary fills its Roche lobe. we can estimate the stellar radius with 2s=PL. where (Egeleton1983).," We can estimate the captured fraction of mass with Because the secondary fills its Roche lobe, we can estimate the stellar radius with $R_2=R_{\rm L}$, where \citep{eggleton83}." . We compute the period change for this mocel incbuding mass accretion on to the secondary star with. equations. (8)) and (112)., We compute the period change for this model including mass accretion on to the secondary star with equations \ref{dp}) ) and \ref{mass}) ). In Fig., In Fig. ον 1. we plot ARID Aen a Function of the mass ratio for this model (clotted line)., \ref{dadm} we plot $\frac{\Delta P/P}{\Delta m_1/M}$ as a function of the mass ratio for this model (dotted line). Generally. the separation change is not so large as the," Generally, the separation change is not so large as the" of finding by chance an object unrelated to the X-ray source within the uuncertainty region is of the order of ~50% (number of detected sources normalised to the area of the eerror circle).,of finding by chance an object unrelated to the X–ray source within the uncertainty region is of the order of $\sim$ (number of detected sources normalised to the area of the error circle). No further object was detected in the ecircle down to a limiting As magnitude of about 22.5 (S/N~1.5)., No further object was detected in the circle down to a limiting $Ks$ magnitude of about 22.5 $\sim$ 1.5). The colors of the IR source. H—Ks=1.2 and i—Ks>3.5 are at variance with those of field stars which lie far from nearby stars in a color-color diagram.," The colors of the IR source, $H-Ks=1.2$ and $i-Ks>3.5$ are at variance with those of field stars which lie far from nearby stars in a color-color diagram." On the contrary the IR colors are to those of other AXP counterparts., On the contrary the IR colors are to those of other AXP counterparts. As an example. the persistent optical/IR emission of hhas H-Ksz1.) and/—Ks=3.8 colours (Hulleman et al.," As an example, the persistent optical/IR emission of has $H-Ks=1.1$ and $I-Ks=3.8$ colours (Hulleman et al." 2000: Israel et al., 2000: Israel et al. 20026). while the “outbursting” IR emission of hhas H—Ks=1.4 (Wang Chakrabarty 2002: note however that the extinction in the direction of the three objects ts different).," 2003c), while the “outbursting” IR emission of has $H-Ks=1.4$ (Wang Chakrabarty 2002; note however that the extinction in the direction of the three objects is different)." These findings make the association of this object with qquite probable., These findings make the association of this object with quite probable. In order to further test the hypothesis of the AXP nature ofXTEJI810-197.. we studied the IR-to-X-ray spectrum.," In order to further test the hypothesis of the AXP nature of, we studied the IR-to-X–ray spectrum." We retrieved the aarchival data on oobtained on 2003 September 8th and extracted and fitted the EPIC-PN spectrum by adopting power-law plus blackbody spectral model deseribed by GO3., We retrieved the archival data on obtained on 2003 September 8th and extracted and fitted the EPIC–PN spectrum by adopting power-law plus blackbody spectral model described by G03. We plotted the IR/optical through X-ray data of tin 22., We plotted the IR/optical through X–ray data of in 2. A value of Ay=5.9-+-0.3 was used to infer the unabsorbed IR fluxes and their uncertainties (this was derived from the N;; inferred from the sspectra and Ay = Ni / < 10?! cemy: Predehl Schmitt 1995)., A value of $A_V$ $\pm$ 0.3 was used to infer the unabsorbed IR fluxes and their uncertainties (this was derived from the $_H$ inferred from the spectra and $A_V$ = $N_H$ / $\times$ $^{21}$ $^{-2}$ ); Predehl Schmitt 1995). Note that the count rate. and thus flux. of the second ddataset of wwas nearly unchanged with respect to the previous aand oobservations: we are thus justified in combining the IR-to-X—ray measurements plotted in 22 (we assumed that the spectral parameters did not change. as suggested also by the constant pulsed fraction level between the two oobservations).," Note that the count rate, and thus flux, of the second dataset of was nearly unchanged with respect to the previous and observations; we are thus justified in combining the IR-to-X--ray measurements plotted in 2 (we assumed that the spectral parameters did not change, as suggested also by the constant pulsed fraction level between the two observations)." It is evident from 22 that the Fx over Fi ratio is larger than 10? and similar to those of other AXPs (for a comparison see 22 of Israel et al., It is evident from 2 that the $F_{\rm X}$ over $F_{\rm IR}$ ratio is larger than $^3$ and similar to those of other AXPs (for a comparison see 2 of Israel et al. 2003b: AXPs)., 2003b; ). The relatively high pulsed fraction of iis not unusua for AXPs: in fact hhas a higher pulsed fraction and additionally. shows. flux variability both in the X-ray and IR bands (Oosterbroek et al.," The relatively high pulsed fraction of is not unusual for AXPs: in fact has a higher pulsed fraction and additionally, shows flux variability both in the X–ray and IR bands (Oosterbroek et al." 1998. Israel et al.," 1998, Israel et al." 2002)., 2002). All the above findings and similarities with known nembers of the AXP class. clearly indicate that iis an AXP. the one possessing the highest degree of X-ray flux variability seeh so far (a factor of about 100 between quiescent and outburst peak fluxes).," All the above findings and similarities with known members of the AXP class, clearly indicate that is an AXP, the one possessing the highest degree of X–ray flux variability seen so far (a factor of about 100 between quiescent and outburst peak fluxes)." The candidate AXP mmight be anther example of variable/transient AXP (TAXP: Toni et al., The candidate AXP might be another example of variable/transient AXP (TAXP; Torii et al. 1998: Gotthelf Vasisht 1998)., 1998; Gotthelf Vasisht 1998). However. wwas caught i1 a high state only once and no P measurement is available in οἱder to definitively assess the AXP nature of this source.," However, was caught in a high state only once and no Ṗ measurement is available in order to definitively assess the AXP nature of this source." We note that the quiescent aand sspectrum of hhas a kkeV absorbed flux of —3.« 107σον (Israel et al 20)3b). quite similar to that of aas seen by |OSAT in 1993 (—5 . 107erecms! GO3).," We note that the quiescent and spectrum of has a keV absorbed flux of $\sim$ $\times$ $^{-13}\ergscm$ (Israel et al 2003b), quite similar to that of as seen by ROSAT in 1993 $\sim$ $\times$ $^{-13}\ergscm$; G03)." Additionally. as in the case ofXTEJI810—197.. also for nno pulsation: were detected in the quiescent phase (although poor statistics prevented to set any sensitive upper limit: Israel apa inclu," Additionally, as in the case of, also for no pulsations were detected in the quiescent phase (although poor statistics prevented to set any sensitive upper limit; Israel et al." dingposi, 2003d). tignql (2755VLTegghaltssJj of whether or not TH existence. of. at least one TAXPμ clearly points. xul Ruwef’ pApsRuthenumber of hidden members of the AXP class in the Galaxy.," Regardless of whether or not is an AXP, the existence of at least one TAXP clearly points to a larger number of hidden members of the AXP class in the Galaxy." As suggested by GO3. part of them might be the radio-quite X-ray unpulsed Central Compact Objects (CCOs) found in an increasing number of SNRs.," As suggested by G03, part of them might be the radio-quite X–ray unpulsed Central Compact Objects (CCOs) found in an increasing number of SNRs." Other AXPs might spend a large fraction of the time in a quiescent state. and therefore might remain unidentified as AXPs.," Other AXPs might spend a large fraction of the time in a quiescent state, and therefore might remain unidentified as AXPs." There are at least two important new facts that should be taken into account in the comparison with models: (1) the X-ray flux variability of more than two orders of magnitude. and (11) the non-detection of ray pulsations in the quiescent state of dduring a 1996 ROSAT observation.," There are at least two important new facts that should be taken into account in the comparison with models: (i) the X–ray flux variability of more than two orders of magnitude, and (ii) the non-detection of X--ray pulsations in the quiescent state of during a 1996 ROSAT observation." Variations in the persistent X-ray emission are common in neutron stars accreting from a companion (White et al., Variations in the persistent X–ray emission are common in neutron stars accreting from a companion (White et al. 1995)., 1995). " The IR measurements presented in this paper for rrule out any hypothetical main sequence companion star from O to F spectral-types. and are comparable to those set for other. more ""standard"". AXPs (Mereghetti et al."," The IR measurements presented in this paper for rule out any hypothetical main sequence companion star from O to F spectral-types, and are comparable to those set for other, more “standard”, AXPs (Mereghetti et al." 1998: Wilson et al 1999)., 1998; Wilson et al 1999). However. a lighter companion cannot be ruled out (as in the case of all the other AXPs) and would imply an extremely small and virtually undetectable Doppler shift in the pulsations (similar e.g. to the 42 minutes orbital period. binary system hosting the 7s pulsar 11626-67; Chakrabarty 1998).," However, a lighter companion cannot be ruled out (as in the case of all the other AXPs) and would imply an extremely small and virtually undetectable Doppler shift in the pulsations (similar e.g. to the 42 minutes orbital period binary system hosting the 7s pulsar 1626–67; Chakrabarty 1998)." If the two transient objects discovered so far do belong to the, If the two transient objects discovered so far do belong to the (which is within οἱος field-of-view). the irraciance of the tertiary star will be detected by SUSE and must be included in the analysis.,"(which is within SUSI's field-of-view), the irradiance of the tertiary star will be detected by SUSI and must be included in the analysis." The offset of the tertiary fringe packet in delay space. D. was calculated using assuming that the spectroscopic pair's fringe packet. is located. at the phase centre of οοἱ.," The offset of the tertiary fringe packet in delay space, $D$, was calculated using assuming that the spectroscopic pair's fringe packet is located at the phase centre of SUSI." |b] and. a are. the projected baseline length ancl position angle respectively., $|{\bf b}|$ and $\eta$ are the projected baseline length and position angle respectively. lt owas found that only two observations had. an offset within the centre half of the observing scan., It was found that only two observations had an offset within the centre half of the $\mu$ m observing scan. For approximately of the observations.ji. the ollset was sullicientl large. to place the tertiary fringe. packet entirely outside the observing scan.," For approximately of the observations, the offset was sufficiently large to place the tertiary fringe packet entirely outside the observing scan." However. the SUSI data reduction pipeline windows the recorded scan. about. the detected peak fringe location (Ireland2005).," However, the SUSI data reduction pipeline windows the recorded scan about the detected peak fringe location \citep{Ireland05}." . Pherefore. the tertiary fringe packet will not be within the ‘cata window and should not alIect the caleulation of V? if both Phe first condition can easily be satisfied by the removal of all observations with an olfset less than 305m. the outer quarter of a scan (bevoncd the edge of the window unction).," Therefore, the tertiary fringe packet will not be within the `data window' and should not affect the calculation of $V^2$ if both The first condition can easily be satisfied by the removal of all observations with an offset less than $\mu$ m – the outer quarter of a scan (beyond the edge of the window function)." Hence. the two data points that were found within he centre half of the fringe sean were rejected. from. the analysis.," Hence, the two data points that were found within the centre half of the fringe scan were rejected from the analysis." Phe second condition may not be satisfied when the »wimary and secondary fringe packets destructively interfere: aat a minimum in the modulation of V? there is the »xossibilitv of mistakenly measuring the interference pattern of the tertiary., The second condition may not be satisfied when the primary and secondary fringe packets destructively interfere; at a minimum in the modulation of $V^2$ there is the possibility of mistakenly measuring the interference pattern of the tertiary. Assuming the primary ancl secondary. fringe yacket cestructive interference is absolute and the tertiary is completely unresolved. then the expected V?<0.013 will be due to the tertiary alone.," Assuming the primary and secondary fringe packet destructive interference is absolute and the tertiary is completely unresolved, then the expected $V^2 \la 0.013$ will be due to the tertiary alone." As this is below the V? detection imit ofSUSL we can neglect such cases.," As this is below the $V^2$ detection limit of SUSI, we can neglect such cases." Hence all remaining observations of & Sco now satisfy both conditions., Hence all remaining observations of $\sigma$ Sco now satisfy both conditions. Phe SUSL data pipeline will nevertheless be allected by the incoherent lux from the tertiary component., The SUSI data pipeline will nevertheless be affected by the incoherent flux from the tertiary component. The required adjustment o the fitted squared-visibilitv model is given in the next section., The required adjustment to the fitted squared-visibility model is given in the next section. for continually changing the optically (hick cross section. e.g.. bv being injected in a variable number of magnetic loops.,"for continually changing the optically thick cross section, e.g., by being injected in a variable number of magnetic loops." We will thus assume (hat the volume filled by non-thermal electrons is generally time-dependent., We will thus assume that the volume filled by non-thermal electrons is generally time-dependent. The radio spectral index al optically Chick low [frequencies is tvpically +1. while the index on the high-lrequency. optically (hin. side is between —0.5 and —1 (Feldinanοἱal.Jonesetal.1996:Beasley 2002).," The radio spectral index at optically thick low frequencies is typically +1, while the index on the high-frequency optically thin side is between $-$ 0.5 and $-$ 1 \citep{feldman78, morris90, jones96, beasley02}." . The turnover [recency (above which the radiation changes to optically thin) is similar in many reported flares. ρω&10—20 GlIIz although values as low as a few GIIz are possible (Morrisetal.1990).," The turnover frequency (above which the radiation changes to optically thin) is similar in many reported flares, $\nu_{\mathrm{peak}} \approx 10-20$ GHz although values as low as a few GHz are possible \citep{morris90}." . From this (vpical spectral model shape. we can estimate (he unabsorbed luminosity at 5 Gllz to be ~1—10 times higher than measured.," From this typical spectral model shape, we can estimate the unabsorbed luminosity at 5 GHz to be $\sim 1-10$ times higher than measured." The unabsorbed radio flux. fp (taken to be 5 limes the observed. flux in what follows) relates to the gvrosvnchrotron. enussivily η. for which Dulk&Marsh(1982). gave the following approximation for the magnetoionic x-moce: (ünergem *s ! 'sr !).," The unabsorbed radio flux $f_{\mathrm{R}}$ (taken to be 5 times the observed flux in what follows) relates to the gyrosynchrotron emissivity $\eta$, for which \citet{dulk82} gave the following approximation for the magnetoionic x-mode: (in erg $^{-3}$ $^{-1}$ $^{-1}$ $^{-1}$ )." B Gn units of Gauss) is the magnetic field strength (assumed to be constant in the source). and vpL222.8x105 [Iz] is the electron 3gvrolrequency.," $B$ (in units of Gauss) is the magnetic field strength (assumed to be constant in the source), and $\nu_{\mathrm{B}} \approx 2.8\times 10^6B$ [Hz] is the electron gyrofrequency." " We will use 7)=27), for the total emissivity. assuming a similar emissivitv [or the o-mode which is approximately valid under (typical coronal conditions."," We will use $\eta = 2\eta_x$ for the total emissivity, assuming a similar emissivity for the o-mode which is approximately valid under typical coronal conditions." We note that in general the o-mocle emissivitv is smaller (Dulk&\larsh1932): we thus overestimate 7 somewhat. and hence we will underestimate the total energy content in the electrons accordingly.," We note that in general the o-mode emissivity is smaller \citep{dulk82}; we thus overestimate $\eta$ somewhat, and hence we will underestimate the total energy content in the electrons accordingly." Since most of the enission is radiated by electrons with large pitch angles. we set 9=60* in what follows.," Since most of the emission is radiated by electrons with large pitch angles, we set $\theta = 60^{\circ}$ in what follows." This represents an average for a uniform pitch angle distribution with 9 around3 in equation 4.., This represents an average for a uniform pitch angle distribution with $\delta$ around3 in equation \ref{emissivity}. The radio flix then is where V is the source volume. d is (he distance to the source. ancl /(5.0.7) collects various terms [rom equation 4.," The radio flux then is where $V$ is the source volume, $d$ is the distance to the source, and $f(B,\delta,\nu)$ collects various terms from equation \ref{emissivity}." The total mstantaneous kinetic energv in the electron distribution (given in equation 3)) is where 9>2 has been assumed., The total instantaneous kinetic energy in the electron distribution (given in equation \ref{distribution}) ) is where $\delta > 2$ has been assumed. The expression ΝΟ(1) is obtained from equation with the known radio flux. {μ., The expression $N(t)V(t)$ is obtained from equation \ref{luminosity} with the known radio flux $f_{\mathrm{R}}$. We finally need (o specily values for ὁ and D., We finally need to specify values for $\delta$ and $B$ . Our observation is not sullicient to derive these values., Our single-frequency observation is not sufficient to derive these values. However. [rom a large body of," However, from a large body of" outburst. data. (wo fits were made.,"outburst data, two fits were made." The first included data from MJD 52435.5 - 52444.5. the second fit (shown as the solid line in Figure 6)) was performed on data from MJD 52437.6 - 52444.5.," The first included data from MJD 52435.5 - 52444.5, the second fit (shown as the solid line in Figure \ref{fig:rise}) ) was performed on data from MJD 52437.6 - 52444.5." Including the (wo points at MJD 52435.6 and 52436.6 had a significant impact on the gradient of the line., Including the two points at MJD 52435.6 and 52436.6 had a significant impact on the gradient of the line. This was the dominant error in determining the time of the start of the outburst., This was the dominant error in determining the time of the start of the outburst. The J-band outburst began al MJD 52436.78 + 0.58 (Gncluding the error mentioned above) whereas tlie X-ray outburst began at MJD 52441.51 + 0.01., The $J$ -band outburst began at MJD 52436.78 $\pm$ 0.58 (including the error mentioned above) whereas the X-ray outburst began at MJD 52441.51 $\pm$ 0.01. Fitting the X-ray data in log space resulted in an outburst start Gime of MJD 52439.38., Fitting the X-ray data in log space resulted in an outburst start time of MJD 52439.38. Hence. the start of the X-ray outburst was delaved bv ~ 3-5 days will respect to the infrared.," Hence, the start of the X-ray outburst was delayed by $\sim$ 3-5 days with respect to the infrared." Similar delavs have been seen in other SXTs (Oroszetal.1997)., Similar delays have been seen in other SXTs \citep{oro97}. . The slopes of the rise are 91.91 + 0.01 counts/sec/daxy for the X-rays and -0.24 + 0.01 mag/daxy for the J-band., The slopes of the rise are 91.91 $\pm$ 0.01 counts/sec/day for the X-rays and -0.24 $\pm$ 0.01 mag/day for the $J$ -band. Since the IR. began to rise before the ASAI. this suggests that the outburst was triggered in the outer regions of the accretion disk.," Since the IR began to rise before the ASM, this suggests that the outburst was triggered in the outer regions of the accretion disk." Caution must be given. however. as the sensitivity level of the RNTE/ASM is orders of magnitude above the quiescent [Iux level for this source. so fine details of the X-ray light curve in the early stages of the outburst are undetectable.," Caution must be given, however, as the sensitivity level of the RXTE/ASM is orders of magnitude above the quiescent flux level for this source, so fine details of the X-ray light curve in the early stages of the outburst are undetectable." In comparing the J-band light curve to that of the ASAI it is not apparent that there is any noticeable difference in (he peak times., In comparing the $J$ -band light curve to that of the ASM it is not apparent that there is any noticeable difference in the peak times. We determined (he peak time in the J-band light curve by filling Gaussian profiles to the rising parts of the light curve., We determined the peak time in the $J$ -band light curve by fitting Gaussian profiles to the rising parts of the light curve. We fixed the y-anis intercept in the fits to the mean values determined for the rise start times (ard)., We fixed the $y$ -axis intercept in the fits to the mean values determined for the rise start times \\ref{sec:outburst_start}) ). T híésweasaddedasaconstanttotlheGeaussian function, This was added as a constant to the Gaussian function. MerestrietedthefilbelieenM JF. D 52450., We restricted the fit between MJD 52400-52450. hepeal:. amplitudeandGaussianwidthiverevaried," The peak, amplitude and Gaussian width were varied." E hebest [ilgaveapeaktimeof MID B24471. emplibtude = —1.9megandiwidlh = 4.8days.," The best fit gave a peak time of MJD = 52447.1, amplitude = -1.9 mag and width = 4.8 days." Phebes! filGaussianisplolledinFigurell, The best fit Gaussian is plotted in Figure \ref{fig:gauss_rise_fit}. Afitivasno raydalaasthesmallnumberof{daltapointsgavelargeerrors., A fit was not performed on the X-ray data as the small number of datapoints gave large errors. " After the primary X-ray peak. the X-ravs and OIR decline until ~ MJD 52460 when the Jy-band light curve. aud {ο a lesser extent the ρα, experiences a small flare."," After the primary X-ray peak, the X-rays and OIR decline until $\sim$ MJD 52460 when the $K$ -band light curve, and to a lesser extent the $J$ -band, experiences a small flare." Just before (his flare. the source. transitionecl briefly into a steep power-law state and low-Irequency QPOs were observed by Parketal.(2004).," Just before this flare, the source transitioned briefly into a steep power-law state and low-frequency QPOs were observed by \cite{par03}." .. No optical or infrared data were obtained by us during the time of transition., No optical or infrared data were obtained by us during the time of transition. At ~ MJD 52462. the A-band returned to the previous decline rate [rom the primary outburst.," At $\sim$ MJD 52462, the $K$ -band returned to the previous decline rate from the primary outburst." Since the overall decline was not interrupted. we suspect (hat (he small flare emission is due to a mechanism different [rom that of the primary outburst.," Since the overall decline was not interrupted, we suspect that the small flare emission is due to a mechanism different from that of the primary outburst." " At ~ MJD 52484 the J- and A-band f(Iuxes experience a significant rise. which we call the ""secondary maxinunr."," At $\sim$ MJD 52484 the $J$ - and $K$ -band fluxes experience a significant rise, which we call the “secondary maximum”." This rise in flux also appears in the optical bands but is much, This rise in flux also appears in the optical bands but is much is comparatively young.,is comparatively young. Beyond these basic conclusions. an association with a SNR also provides an estimate of a neutron star’s age. distance. and birth-site. from the latter of which its projected space velocity can be estimated.," Beyond these basic conclusions, an association with a SNR also provides an estimate of a neutron star's age, distance, and birth-site, from the latter of which its projected space velocity can be estimated." Associations with SNRs have correspondingly been used to infer a variety of properties for the AXPs and SGRs: it has been concluded from SNR associations that SGRs have extremely high space velocities ()). that AXPs are very young objects ()). that AXPs and SGRs are born in higher density regions than areradio pulsars ()). that the supernova explosions which produce SGRs occur on the edge of their progenitor's wind-bubbles 0). and even that AXPs and SGRs are strange stars (:: )).," Associations with SNRs have correspondingly been used to infer a variety of properties for the AXPs and SGRs: it has been concluded from SNR associations that SGRs have extremely high space velocities \cite{td95}) ), that AXPs are very young objects \cite{vg97}) ), that AXPs and SGRs are born in higher density regions than areradio pulsars \cite{mlrh01}) ), that the supernova explosions which produce SGRs occur on the edge of their progenitor's wind-bubbles \cite{gav01}) ), and even that AXPs and SGRs are strange stars \cite{dd00}; \cite{zxq00}) )." It is clearly of considerable interest to identify new instances of such associations. but at the same tme it is crucial to determine whether previously-claimed associations are genuine.," It is clearly of considerable interest to identify new instances of such associations, but at the same time it is crucial to determine whether previously-claimed associations are genuine." There are many regions of the Galactic Plane where the spatial density of SNRs is high., There are many regions of the Galactic Plane where the spatial density of SNRs is high. The possibility that an AXP/SGR and an adjacent SNR are physically unrelated and merely He along similar Imes-of-sight must. therefore be carefully considered., The possibility that an AXP/SGR and an adjacent SNR are physically unrelated and merely lie along similar lines-of-sight must therefore be carefully considered. Indeed. many associations claimed between SNRs and radio pulsars (:: :: )) have subsequently been shown to be spurious (2: 5 ). and similar caution must be applied to associations between SNRs and AXPs/SGRs.," Indeed, many associations claimed between SNRs and radio pulsars \cite{kw90}; \cite{car93}; \cite{mop93}) ) have subsequently been shown to be spurious \cite{fkw94}; \cite{njk96}; \cite{sgj99}) ), and similar caution must be applied to associations between SNRs and AXPs/SGRs." Associations between SNRs and radio pulsars are usually judged on eriteria such as agreement in ages and distances and whether the transverse velocity implied for the pulsar is reasonable., Associations between SNRs and radio pulsars are usually judged on criteria such as agreement in ages and distances and whether the transverse velocity implied for the pulsar is reasonable. However. these criteria are problematic when applied to cases involving AXPs and SGRs.," However, these criteria are problematic when applied to cases involving AXPs and SGRs." The characteristic age parameter used to estimate the ages of radio pulsars (7=P/2P. where P ts the spin-pertod and P is the period-derivative) is applicable only if neutron star's spin-down is entirely due to magnetic dipole aradiation.," The characteristic age parameter used to estimate the ages of radio pulsars $\tau \equiv P/2\dot{P}$, where $P$ is the spin-period and $\dot{P}$ is the period-derivative) is applicable only if a neutron star's spin-down is entirely due to magnetic dipole radiation." However. in the case of a magnetar there is expected to be a significant additional torque due to a relativistic particle wind ο )).," However, in the case of a magnetar there is expected to be a significant additional torque due to a relativistic particle wind \cite{tb98}; \cite{hck99}) )." Furthermore. some AXPs and SGRs show complicated timing behavior not consistent with any kind of steady spin-down (C: ).," Furthermore, some AXPs and SGRs show complicated timing behavior not consistent with any kind of steady spin-down \cite{wkv+99b}; \cite{kgc+01}) )." Finally. in the specific case of the otherwise convincing association of the AXP ΤΕ 22594586 with the SNR CTB 109 (discussed in Section 4.3)). the age of the SNR is a factor ~20 times smaller than the value of 7=P/2P inferred for the AXP.," Finally, in the specific case of the otherwise convincing association of the AXP 1E 2259+586 with the SNR CTB 109 (discussed in Section \ref{sec_axp_other}) ), the age of the SNR is a factor $\sim$ 20 times smaller than the value of $\tau=P/2\dot{P}$ inferred for the AXP." There thus seems to be neither any evidence nor expectation that the ages of AXPs and SGRs can be usefully estimated from their observed spin parameters., There thus seems to be neither any evidence nor expectation that the ages of AXPs and SGRs can be usefully estimated from their observed spin parameters. Distance estimates for most of the AXPs/SGRs come only from a measurement of the column density of absorbing material along the line-of-sight. and so have large uncertainties »50%.," Distance estimates for most of the AXPs/SGRs come only from a measurement of the column density of absorbing material along the line-of-sight, and so have large uncertainties $>$." . Finally. while transverse velocities inferred for radio pulsars can be compared to the pulsar velocity distribution as determined from proper motion measurements citefgw94)). nothing is known about the range of velocities expected for AXPs and SGRs.," Finally, while transverse velocities inferred for radio pulsars can be compared to the pulsar velocity distribution as determined from proper motion measurements \\cite{fgw94}) ), nothing is known about the range of velocities expected for AXPs and SGRs." Therefore the only criterion we can reliably apply in the case of AXPs and SGRs is positional coincidence — namely. whether the neutron star and SNR are sufficiently close on the sky that it is unlikely that they align by chance citekf93:; )).," Therefore the only criterion we can reliably apply in the case of AXPs and SGRs is positional coincidence — namely, whether the neutron star and SNR are sufficiently close on the sky that it is unlikely that they align by chance \\cite{kf93}; \cite{sbl99}) )." Motivated by these considerations. we here present a study of associations of AXPs and SGRs with SNRs. a brief discussion of which was outlined by Gaensler (2000)).," Motivated by these considerations, we here present a study of associations of AXPs and SGRs with SNRs, a brief discussion of which was outlined by Gaensler \nocite{gae00}) )." In Sections 2. and 3 we describe a search for radio SNRs towards two AXPs. aand 0142461u. 10In Section + we discuss the implications of these observations. review possible SNR associations for all other known AXPs. and use the results to infer some general properties about the AXP population.," In Sections \ref{sec_obs} and \ref{sec_results} we describe a search for radio SNRs towards two AXPs, and u. In Section \ref{sec_axps} we discuss the implications of these observations, review possible SNR associations for all other known AXPs, and use the results to infer some general properties about the AXP population." In Section 5 we consider the case of SGRs in SNRs. similarly derive some overall properties of the SGR population. and discuss the possible relationship between AXPs and SGRs.," In Section \ref{sec_sgrs} we consider the case of SGRs in SNRs, similarly derive some overall properties of the SGR population, and discuss the possible relationship between AXPs and SGRs." The regions surrounding the AXPs aand wwere observed with the Very Large Array (VLA). and are summarized in Table ??..," The regions surrounding the AXPs and were observed with the Very Large Array (VLA), and are summarized in Table \ref{tab_obs}." All observations were centered at 1435 MHz. using three adjacent frequency channels each of width 12.5 MHz.," All observations were centered at 1435 MHz, using three adjacent frequency channels each of width 12.5 MHz." Each field was observed in a 3-point mosaic pattern. both to increase the field-of-view and to maximize sensitivity to extended structure.," Each field was observed in a 3-point mosaic pattern, both to increase the field-of-view and to maximize sensitivity to extended structure." Antenna gains and polarization were calibrated using regular observations of PKS BI827—360 (for J170849-400910) and 3C 468.1 (for 01452611)., Antenna gains and polarization were calibrated using regular observations of PKS B1827–360 (for ) and 3C 468.1 (for u). Amplitudes were calibrated using observations of 3C 286 (for J170849—400910)) and 3C 48 (for 0142+61u). assuming flux densities at 1.4 GHz of 15.0 Jy and 16.1 Jy respectively.," Amplitudes were calibrated using observations of 3C 286 (for ) and 3C 48 (for u), assuming flux densities at 1.4 GHz of 15.0 Jy and 16.1 Jy respectively." Data were analyzed using the ppackage., Data were analyzed using the package. Once visibilities were edited and calibrated. an image corresponding to the combination of all three frequency channels was made using multi-frequency synthesis ().," Once visibilities were edited and calibrated, an image corresponding to the combination of all three frequency channels was made using multi-frequency synthesis \cite{sw94}) )." All three pointings towards each source were then deconvolved simultaneously using the aalgorithm ()., All three pointings towards each source were then deconvolved simultaneously using the algorithm \cite{ssb96}) ). The resulting image was then smoothed with à gaussian restoring beam of dimensions corresponding to the diffraction-limited resolution of the observations., The resulting image was then smoothed with a gaussian restoring beam of dimensions corresponding to the diffraction-limited resolution of the observations. Our VLA data on llacks sensitivity to the largest spatial scales., Our VLA data on lacks sensitivity to the largest spatial scales. To search for such emission. we have also obtained a 1.4-GHz image of the region surrounding mmade as part of the Canadian Galactic Plane Survey (CGPS: )) and archived by the Canadian Astronomy Data Center.," To search for such emission, we have also obtained a 1.4-GHz image of the region surrounding made as part of the Canadian Galactic Plane Survey (CGPS; \cite{eti+98}) ) and archived by the Canadian Astronomy Data Center." This image includes both interferometric and single-dish data. and so has sensitivity to all scales down to the resolution limit of 1 aremin.," This image includes both interferometric and single-dish data, and so has sensitivity to all scales down to the resolution limit of 1 arcmin." A ].4 GHz image of the field surrounding iis shown in Fig ??.., A 1.4 GHz image of the field surrounding is shown in Fig \ref{fig_rxj}. Only the lower-resolution DnC-array data have been used to make this Image. so as to give maximal surface-brightness sensitivity.," Only the lower-resolution DnC-array data have been used to make this image, so as to give maximal surface-brightness sensitivity." It is clear that iis in à complex region., It is clear that is in a complex region. Previously identified sources which can be seen in the image include the SNR G346.6-0.2 (~15’ to the east of the AXP: )). the ultra-compact rregion G346.52+0.08 = IRAS 17052-4001 (4' to the north of the AXP: )). the unresolved radio source G346.472+0.053 (1 to the west: )). and the thermal source IRAS 17056-4004 (4' to the east).," Previously identified sources which can be seen in the image include the SNR G346.6–0.2 $\sim15'$ to the east of the AXP; \cite{dmgw93}) ), the ultra-compact region G346.52+0.08 $=$ IRAS 17052–4001 $4'$ to the north of the AXP; \cite{wbhr98}) ), the unresolved radio source G346.472+0.053 $1'$ to the west; \cite{zhb+90}) ), and the thermal source IRAS 17056–4004 $4'$ to the east)." Two aremin to the east of the AXP can be seen an are of diffuse emission. running from north to south for ~8’ before curving around to the east. eventually fading and merging with SNR G346.6-0.2.," Two arcmin to the east of the AXP can be seen an arc of diffuse emission, running from north to south for $\sim8'$ before curving around to the east, eventually fading and merging with SNR G346.6–0.2." The overall morphology is that of a faint partial shell. with a radius of ~ 6’.," The overall morphology is that of a faint partial shell, with a radius of $\sim6'$ ." We have looked for this source in. various archival data-sets: 1.4 GHz VLA observations of SNR G346.6-0.2 ο). 1.4 GHz observations of SNR G347.3-0.5 using the Australia Telescope Compact," We have looked for this source in various archival data-sets: 1.4 GHz VLA observations of SNR G346.6–0.2 \cite{dmgw93}) ), 1.4 GHz observations of SNR G347.3–0.5 using the Australia Telescope Compact" "by lower-metallicity stellar populations: where ? suggests: fi,.72.","by lower-metallicity stellar populations: where \citet{Martin2005} suggests: $f_{\rm L,\odot}\approx2$." The mass loading factor controls star formation at early times. so a can also be set by requiring a match to the observed global star formation rate.," The mass loading factor controls star formation at early times, so $\sigma_{\rm 0}$ can also be set by requiring a match to the observed global star formation rate." Following we set συ=150 km +.," Following \citet{oppe06,oppe07} we set $\sigma_{\rm 0}=150$ km $^{-1}$." Even for this wind implementation the particles are stochastically selected in the same way as for the energy-driven scenario., Even for this wind implementation the particles are stochastically selected in the same way as for the energy-driven scenario. Finally. we include in our simulations the effect of feedback energy from gas accretion onto super-massive black holes (BHs). following the scheme originally introduced by ?/— (seealso2).," Finally, we include in our simulations the effect of feedback energy from gas accretion onto super-massive black holes (BHs), following the scheme originally introduced by \citet{springetal05} \citep[see also][]{dimatteo05}." In this model. BHs are represented by collisionless sink particles initially seeded in dark matter haloes. which subsequently grow Via gas accretion and through mergers with other BHs during close encounters.," In this model, BHs are represented by collisionless sink particles initially seeded in dark matter haloes, which subsequently grow via gas accretion and through mergers with other BHs during close encounters." Every new dark matter halo. identitied by a run-time friends-of-friends algorithm. above the mass threshold AL... is seeded with a central BH of initial mass 107 AZ.. provided the halo does not contain any BH vet.," Every new dark matter halo, identified by a run-time friends-of-friends algorithm, above the mass threshold $M_{\rm th}=10^{10}$ $M_{\rm \odot}$, is seeded with a central BH of initial mass $10^5$ $M_{\rm \odot}$, provided the halo does not contain any BH yet." " Each BH can then grow by local gas accretion. with a rate given by where Ah, is the accretion rate estimated with the Bondi-Hoyle-Littleton formula (e.g.2) and Alpaa is the Eddington accretion rate."," Each BH can then grow by local gas accretion, with a rate given by where $\dot M_{\rm B}$ is the accretion rate estimated with the Bondi-Hoyle-Littleton formula \citep[e.g.][]{bondi1952} and $\dot M_{\rm Edd}$ is the Eddington accretion rate." We refer to ? for the details of the AGN feedback implementation and to ? for a review of the black holes accretion feedback inthe context of cosmological simulations., We refer to \citet{springetal05} for the details of the AGN feedback implementation and to \citet{booth&schaye09} for a review of the black holes accretion feedback inthe context of cosmological simulations. " An important parameter of the model is the radiative efficiency. εν. which gives the radiated energy L, in units of the energy associated to the accreted mass: Following ? and ?.. we fix «,=0.1 as a reference value. which is typical for a radiatively efficient accretion onto a Schwarzschild BH (2).."," An important parameter of the model is the radiative efficiency, $\epsilon_{\rm r}$, which gives the radiated energy $L_{\rm r}$ in units of the energy associated to the accreted mass: Following \citet{springetal05} and \citet{dunja2010}, we fix $\epsilon_{\rm r}=0.1$ as a reference value, which is typical for a radiatively efficient accretion onto a Schwarzschild BH \citep{shakura1973}." The model then assumes that a fraction οἱ of the radiated energy is thermally coupled to the surrounding gas. so that [Ea=ecMpiac is the rate of the energy released to heat he surrounding gas.," The model then assumes that a fraction $\epsilon_{\rm f}$ of the radiated energy is thermally coupled to the surrounding gas, so that $\dot E_{\rm feed}=\epsilon_{\rm r} \epsilon_{\rm f} \dot M_{\rm BH}c^2$ is the rate of the energy released to heat the surrounding gas." Using ος~0.05. 2 were able to reproduce he observed Alouσ relation between bulge velocity dispersion and mass of the hosted BH (seealso??)..," Using $\epsilon_{\rm f}\sim 0.05$, \citet{dimatteo05} were able to reproduce the observed $M_{\rm BH}-\sigma$ relation between bulge velocity dispersion and mass of the hosted BH \citep[see also][]{sizicki2008,dimatteo08}." Gas particle accretion onto the BH is implemented in a stochastic way. by assigning o each neighbouring gas particle a probability of contributing ο the accretion. which is proportional to the SPH kernel weight computed at the particle position.," Gas particle accretion onto the BH is implemented in a stochastic way, by assigning to each neighbouring gas particle a probability of contributing to the accretion, which is proportional to the SPH kernel weight computed at the particle position." In the scheme described above. his stochastic accretion is used only to increase the dynamic mass of the BHs. while the mass entering in the computation of the accretion rate is followed in a continuous way. by integrating the analytic expression for Mou.," In the scheme described above, this stochastic accretion is used only to increase the dynamic mass of the BHs, while the mass entering in the computation of the accretion rate is followed in a continuous way, by integrating the analytic expression for $\dot M_{\rm BH}$." Once the amount of energy to be thermalized is computed for each BH at a given timestep. this energy is then distributed to the surrounding gas particles using the SPH kernel weighting scheme.," Once the amount of energy to be thermalized is computed for each BH at a given timestep, this energy is then distributed to the surrounding gas particles using the SPH kernel weighting scheme." Our research. group. explored. for the first time this new feedback prescription in relation to the high redshift properties of the intergalactic medium. while ? have studied the impact of this feedback mechanism on the low redshift IGM In Table we summiarize the main parameters of the cosmological simulations performed. including the mass associated to the gas particles and the gravitational softening.," Our research group explored for the first time this new feedback prescription in relation to the high redshift properties of the intergalactic medium, while \citet{tornatore2010} have studied the impact of this feedback mechanism on the low redshift IGM In Table we summarize the main parameters of the cosmological simulations performed, including the mass associated to the gas particles and the gravitational softening." All the simulations start at redshift 5=99 and stop at redshift ;=1.5., All the simulations start at redshift $z=99$ and stop at redshift $z=1.5$. In the following we outline the specitic characteristics of each run: The name of each simulation reflects the choice of the IMF. the box size (eveniftheboxsizeish 1M peforalllhesimulalions. wercportilinorderlobeconsistentwitholherus and the feedback prescription adopted (only in the case of the resolution test run. kr37p400edw500. the number of particles is specified in the name).," In the following we outline the specific characteristics of each run: The name of each simulation reflects the choice of the IMF, the box size \citep[even if the box size is equal to 37.5 $h^{-1}$ Mpc for all the simulations, we report it in order to be consistent with other works, and the feedback prescription adopted (only in the case of the resolution test run, kr37p400edw500, the number of particles is specified in the name)." " In this paper. we label as ""reference runs” the first three of the list above: kr37edw500. kr37mdw and kr37agn."," In this paper, we label as “reference runs” the first three of the list above: kr37edw500, kr37mdw and kr37agn." We use the code (2). to compute a-posteriori the CIV ionization fractions for each gas particle., We use the code \citep{ferland} to compute a-posteriori the CIV ionization fractions for each gas particle. As for the work presented in ?.. we choose the option inCLOUDY. which consists of a UVB made by QSOs and galaxies with a photon escape fraction and which is in agreement with other observational constraints (Bolton et al.," As for the work presented in \citet{tex09}, we choose the option in, which consists of a UVB made by QSOs and galaxies with a photon escape fraction and which is in agreement with other observational constraints (Bolton et al." 2005)., 2005). " In the left panel of Figure we plot the CIV ionization fraction. as a function of the gas overdensity us|1= puu/p.at >=3 for a gas temperature of 1059 K (solid black line) and 10°"" K ¢dot-dashed green line)."," In the left panel of Figure we plot the CIV ionization fraction, as a function of the gas overdensity $\delta_{\rm gas}+1=\rho_{\rm gas}/\bar{\rho}$ , at $z=3$ for a gas temperature of $^{4.6}$ K (solid black line) and $^{5.0}$ K (dot-dashed green line)." In the right panel we plot the same ionization fraction. as a function of the gas," In the right panel we plot the same ionization fraction, as a function of the gas" published by other authors. we have used tables ancl figures showing the times of dipping from the literature.,"published by other authors, we have used tables and figures showing the times of dipping from the literature." In other cases. data was analysed. by ourselves. Le. AIPC: Baluccitisska (1988).£EXOSAT* Balucciisska ancl LHasinger (19002).CUNGUL:work.OSA: Batuccitisska-Church. et al. (," In other cases, data was analysed by ourselves, i.e. MPC: Bałuccińsska (1988),: Bałuccińsska and Hasinger (1992),:,: Ba\l{u}cci\'nsska-Church et al. (" 1995). andASC: Dalucciüsska-Church. et al. (,"1995), and: Bałuccińsska-Church et al. (" LOOT).,1997). The All-Skv. Monitor (ASAI: Levine et al., The All-Sky Monitor (ASM; Levine et al. 1996) on boareTL (Braclt. Rothsechilel Swank 1993) scans the sky in 32 οποιον bands: 3. 5 and 12 keV with —90 s exposure.," 1996) on board (Bradt, Rothschild Swank 1993) scans the sky in 3 energy bands: 3, 5 and 12 keV with $\sim$ 90 s exposure." Any source is scanned 20 times per day., Any source is scanned 20 times per day. We iive extracted data from the archive. in these 3 energy xuids. including data from September 6th. 1996 until the esent (October 1998). Lc. including data labelled as clays 250 - 998 (rom the start of ASAI operation.," We have extracted data from the archive, in these 3 energy bands, including data from September 6th, 1996 until the present (October 1998), i.e. including data labelled as days 250 - 998 from the start of ASM operation." Ehe start time was chosen so as to exclude the period between 1996. Alay o August when wwas in the Soft State: thus all of the results presented relate o the Low State of the source., The start time was chosen so as to exclude the period between 1996 May to August when was in the Soft State; thus all of the results presented relate to the Low State of the source. In all cases of archival data. orbital phases were calculated using the new ephemeris of LaSala et. al. (," In all cases of archival data, orbital phases were calculated using the new ephemeris of LaSala et al. (" 1998).,1998). First. the data were sorted into LOO phasebins. and a count was added to cach bin in which dipping activity was observed.," First, the data were sorted into 100 phasebins, and a count was added to each bin in which dipping activity was observed." In a succession of narrow X-ray dips usually occurs. ancl so we add a single count to a given phasebin when dipping is seen. not a count for cach narrow cip.," In a succession of narrow X-ray dips usually occurs, and so we add a single count to a given phasebin when dipping is seen, not a count for each narrow dip." There would be a strong selection cllect due to the [act that coverage of phases has deliberately concentrated on phases close to zero., There would be a strong selection effect due to the fact that coverage of phases has deliberately concentrated on phases close to zero. To compensate for this. we also made a count of the number of times cach phasebin was observed. and the histogram of dip frequency.versus phase was normalized by dividing the dip count by the phasebin count.," To compensate for this, we also made a count of the number of times each phasebin was observed, and the histogram of dip frequency phase was normalized by dividing the dip count by the phasebin count." A selection ellect may remain. as data not analysed bv ourselves. was selected by the various authors as suitable for publication.," A selection effect may remain, as data not analysed by ourselves, was selected by the various authors as suitable for publication." Finally. to improve statistics. phasebins were grouped together in fives to give 20 bins per orbital evcle. and this is shown in Fig.," Finally, to improve statistics, phasebins were grouped together in fives to give 20 bins per orbital cycle, and this is shown in Fig." 1., 1. ]t can be seen that the distribution peaks at. about phase 0.95 with a full width at half. maximum of 70.25., It can be seen that the distribution peaks at about phase 0.95 with a full width at half maximum of $\sim$ 0.25. This ellect. ie. the peak of the distribution being olfset from. phase zero. could. also be seen in individual datasets: for example. Remillard ancl Canizares (1984) noted that short dips tended to occur before phase zero. whereas one S hr dip was centred on phase zero.," This effect, i.e. the peak of the distribution being offset from phase zero, could also be seen in individual datasets; for example, Remillard and Canizares (1984) noted that short dips tended to occur before phase zero, whereas one 8 hr dip was centred on phase zero." This will be discussed fully after the next section on results [rom theRAPE ASAI., This will be discussed fully after the next section on results from the ASM. Data were extracted. from the ASAI archive and stored. as entries in a file. cach entry corresponding to a single 90 s observation.," Data were extracted from the ASM archive and stored as entries in a file, each entry corresponding to a single 90 s observation." Each entry consisted of the time. and the count rate in each of the 3 standard. bands: 3 keV. 5 keV and 12 keV. From these. hardness ratios were constructed using the ratio of count rates in the bands 3:5 keV. and 3 keV designated WRI. and the ratio of count rates in the bands 12 keV. and 5 keV. designated. HB2.," Each entry consisted of the time, and the count rate in each of the 3 standard bands: 3 keV, 5 keV and 12 keV. From these, hardness ratios were constructed using the ratio of count rates in the bands 5 keV and 3 keV designated HR1, and the ratio of count rates in the bands 12 keV and 5 keV, designated HR2." The lighteurve in the total energy. band of the ASAL. together with LRT and UR2. is shown in Fig.," The lightcurve in the total energy band of the ASM, together with HR1 and HR2, is shown in Fig." 2., 2. X brief. period of enhanced intensity can be seen at ~ clay 920: however. this data is excluded by our procedure of selecting data clip cata using hardness ratios (below).," A brief period of enhanced intensity can be seen at $\sim$ day 920; however, this data is excluded by our procedure of selecting data dip data using hardness ratios (below)." Although the count rate varies between 15 and ~ 140 count +. mostly due to [laving activity. the hardness ratios HIVE and LHIU2 were very stable. with mean values 1.102:0.77 and 1.52-50.35. respectively and were unallected: by flaring.," Although the count rate varies between 15 and $\sim$ 140 count $^{-1}$, mostly due to flaring activity, the hardness ratios HR1 and HR2 were very stable, with mean values $\pm 0.77$ and $\pm 0.35$, respectively and were unaffected by flaring." The points with hardness ratio significantly larger than these means are dip data. for which URL can increase to 40 and LII can increase to 10.," The points with hardness ratio significantly larger than these means are dip data, for which HR1 can increase to 40 and HR2 can increase to 10." Dip events can be seen in the light curve. but are more obvious in HIVE and H2.," Dip events can be seen in the light curve, but are more obvious in HR1 and HR2." Phe data folded on the orbital period are shown in Fig., The data folded on the orbital period are shown in Fig. 3., 3. Phere is a clear anti-correlation between the hardness ratios and the count rate. with a reduction in count rate occuring just before. phase zero. ancl associated hardening of the spectrum showing that it is due to absorption.," There is a clear anti-correlation between the hardness ratios and the count rate, with a reduction in count rate occuring just before phase zero, and associated hardening of the spectrum showing that it is due to absorption." Larger increases of hardness ratio in the lower energy bands would be expected for simple absorption: however. as partial covering takes place. the decrease. in intensity at low energies is reduced by the presence of the uncovered part of the emission.," Larger increases of hardness ratio in the lower energy bands would be expected for simple absorption; however, as partial covering takes place, the decrease in intensity at low energies is reduced by the presence of the uncovered part of the emission." The data can also be plotted as à colour-colour diagram. Le. as LR? against HIUL. and this is shown in Fig.," The data can also be plotted as a colour-colour diagram, i.e. as HR2 against HR1, and this is shown in Fig." 4., 4. We next discuss how spectral simulations were used to elucidate the behaviour seen in Fig., We next discuss how spectral simulations were used to elucidate the behaviour seen in Fig. 4. and how selection of dip data was mace.," 4, and how selection of dip data was made." minutes). while the short horizontal dashes crossing them represent the errors in the timescale estimates.,"minutes), while the short horizontal dashes crossing them represent the errors in the timescale estimates." All detailed results are presented in Table 2.., All detailed results are presented in Table \ref{sf_table}. The values of —uss for individual sessions differ from the average SF values., The values of $t_{\rm RISS}$ for individual sessions differ from the average SF values. This 1s understandable because the RISS saturation. level is determined with lower precision. because it is limited by the maximum time lag of the SF calculated for the given session. and because especially in the September 2002 we saw only 4-5 RISS cycles.," This is understandable because the RISS saturation level is determined with lower precision, because it is limited by the maximum time lag of the SF calculated for the given session, and because especially in the September 2002 we saw only 4-5 RISS cycles." This translates into a large uncertainty of triss., This translates into a large uncertainty of $t_{\rm RISS}$. While for the September 2002 session the values agree with those obtained from the general average SF within error estimates. for the first and longest July 2002 session they do ot.," While for the September 2002 session the values agree with those obtained from the general average SF within error estimates, for the first and longest July 2002 session they do not." This may be because this session may also suffer from the untypical flux variations that were observed (see Figure ] and Section 2.1))., This may be because this session may also suffer from the untypical flux variations that were observed (see Figure 1 and Section \ref{flux}) ). Because the general average structure function of our data is the best representative for our results. we'll be using those values for further calculations: £pjss=42.7 minutes. feiss=305 minutes.," Because the general average structure function of our data is the best representative for our results, we'll be using those values for further calculations: $t_{\rm DISS} = 42.7$ minutes, $t_{\rm RISS} = 305$ minutes." Given these. we can calculate the strength of the scattering parameter 4=Ytriss/fpiss2.67.," Given these, we can calculate the strength of the scattering parameter $u= \sqrt{ t_{\rm RISS}/t_{\rm DISS}} = 2.67$." Also. since in our observations we were unable to obtain the value of the decorrelation bandwidth Bpjss (this value greatly exceeds the total observing bandwidth of PSPM 2. which is 192 MHz) we used the results of our timescale measurements to estimate this value.," Also, since in our observations we were unable to obtain the value of the decorrelation bandwidth $B_{\rm DISS}$ (this value greatly exceeds the total observing bandwidth of PSPM 2, which is 192 MHz) we used the results of our timescale measurements to estimate this value." Using the Stinebring Condon (1990)) formula: we obtained a value of Boiss=853 MHz (over 4 times higher than the observing bandwidth)., Using the Stinebring Condon \cite{stin}) ) formula: we obtained a value of $B_{\rm DISS} = 853$ MHz (over 4 times higher than the observing bandwidth). As we mentioned in the previous section. the structure function analysis allows us to calculate not only the scintillation timescales. but also their respective scintillation indices.," As we mentioned in the previous section, the structure function analysis allows us to calculate not only the scintillation timescales, but also their respective scintillation indices." " For a normalized and white-noise corrected structure function the value of the scintillation index mz=(D,,/2)7. and the fractional error in 1 15 a sum of errors from the fractional errors in D, and im (see KS92)."," For a normalized and white-noise corrected structure function the value of the scintillation index $m=(D_{\rm sat}/2)^{1/2}$, and the fractional error in $m$ is a sum of errors from the fractional errors in $D_{\rm sat}$ and $m$ (see KS92)." Table 2 shows the results for the individual sessions as well as for the general average SF for the modulation indices of both diffractive and refractive scintillations., Table \ref{sf_table} shows the results for the individual sessions as well as for the general average SF for the modulation indices of both diffractive and refractive scintillations. For the diffractive scintillations the average value of piss. obtained from the simple arithmetic average of the individual values agrees with the value obtained from general average structure function. which is equal to mpjss=0.89.," For the diffractive scintillations the average value of $m_{\rm DISS}$, obtained from the simple arithmetic average of the individual values agrees with the value obtained from general average structure function, which is equal to $m_{\rm DISS}=0.89$." " This value differs slightly from the modulation index value obtained directly from flux density measurements (0.96. see Table I). but is very close to the expected value for the observed modulation index (0.889, see section 2.2))."," This value differs slightly from the modulation index value obtained directly from flux density measurements (0.96, see Table 1), but is very close to the expected value for the observed modulation index (0.889, see section \ref{flux_ind}) )." The values of the RISS modulation indices are also presented in Table 2.., The values of the RISS modulation indices are also presented in Table \ref{sf_table}. For individual sessions that allowed for an estimation of piss. they differ slightly from the average values. but still agree within the error estimates.," For individual sessions that allowed for an estimation of $m_{\rm DISS}$, they differ slightly from the average values, but still agree within the error estimates." This is not à surprise. because it is difficult to determine the saturation level properly. especially for the shorter sessions (for the same reasons the timescales differ. see previous section).," This is not a surprise, because it is difficult to determine the saturation level properly, especially for the shorter sessions (for the same reasons the timescales differ, see previous section)." On the other hand. the value of gjss=0.56 obtained for the general average structure function 1s very close to the value of the RISS modulation index obtained from the average flux density variation analysis (0.57: see section 2.3. and Fig. 2)).," On the other hand, the value of $m_{\rm RISS}=0.56$ obtained for the general average structure function is very close to the value of the RISS modulation index obtained from the average flux density variation analysis (0.57; see section \ref{flux_av} and Fig. \ref{flux_long}) )." Again. as In the case of the ISS timescales. we will be using the values obtained for the general average structure function as the final result of our analysis: ztpiss=0.89 and /gjss=0.56.," Again, as in the case of the ISS timescales, we will be using the values obtained for the general average structure function as the final result of our analysis: $m_{\rm DISS}=0.89$ and $m_{\rm RISS}=0.56$." The results obtained. from the analysis of our observations suggest that we definitely see both refractive and diffractive scintillations affecting the measured pulsar flux density., The results obtained from the analysis of our observations suggest that we definitely see both refractive and diffractive scintillations affecting the measured pulsar flux density. We were able to calculate both the timescales and modulation indices for these. and also to estimate the expected decorrelation bandwidth.," We were able to calculate both the timescales and modulation indices for these, and also to estimate the expected decorrelation bandwidth." Our observations were performed at the frequency of 4.8 GHz. for which there is only one observational report to be found in the literature by Malofeev at al. (1996)).," Our observations were performed at the frequency of 4.8 GHz, for which there is only one observational report to be found in the literature by Malofeev at al. \cite{malo}) )." This was quite a short project. because PSR B0329-54 was only observed for 130 minutes at this frequency. which given the values of the scintillation timescales we found makes the results unreliable.," This was quite a short project, because PSR B0329+54 was only observed for 130 minutes at this frequency, which given the values of the scintillation timescales we found makes the results unreliable." On the other hand. adding our results to the scintillation parameters estimates obtained by other authors at lower frequencies allows us to study the frequency dependence of these parameters over a much wider range of frequencies.," On the other hand, adding our results to the scintillation parameters estimates obtained by other authors at lower frequencies allows us to study the frequency dependence of these parameters over a much wider range of frequencies." As we mentioned above. PSR BO329+54 at the observing frequency of 4.8 GHz shows large flux density variations owing to ISS.," As we mentioned above, PSR B0329+54 at the observing frequency of 4.8 GHz shows large flux density variations owing to ISS." For some of the individual 3-minute integrations the flux measurements yielded values as high as 200 mJy. over 10 times higher than the average value.," For some of the individual 3-minute integrations the flux measurements yielded values as high as 200 mJy, over 10 times higher than the average value." Those variations happen at à variety of timescales. ranging from minutes to hours. and up to days (c.f.," Those variations happen at a variety of timescales, ranging from minutes to hours, and up to days (c.f." Fig la)., Fig 1a). " This clearly shows the dangers of estimating pulsar flux densities at high frequencies (especially for low-DM pulsars) from observations that are based on a limited number of separate integrations. which is often the case when one tries. for example. to ascertain the pulsar spectrum,"," This clearly shows the dangers of estimating pulsar flux densities at high frequencies (especially for low-DM pulsars) from observations that are based on a limited number of separate integrations, which is often the case when one tries, for example, to ascertain the pulsar spectrum." The diffractive timescale is longer at high frequency. and may be comparable to the actual integration times used - usually of the order of a few tens of minutes when one tries to measure the flux density of some weaker sources - hence. it may strongly affect the outcome.," The diffractive timescale is longer at high frequency, and may be comparable to the actual integration times used - usually of the order of a few tens of minutes when one tries to measure the flux density of some weaker sources - hence, it may strongly affect the outcome." On the other hand. with refractive. timescales of the order of à few hours. repeating the observations after a day or a few days. with the hope that the ISS will be averaged-out. may not solve the problem.," On the other hand, with refractive timescales of the order of a few hours, repeating the observations after a day or a few days, with the hope that the ISS will be averaged-out, may not solve the problem." One has to approach these cases carefully: luckily. for high-DM pulsars this should be less of a problem. because the transition frequency will be much higher and the modulation caused by RISS should be very low. and one has to worry only about diffractive scintillations when performing flux measurements.," One has to approach these cases carefully; luckily, for high-DM pulsars this should be less of a problem, because the transition frequency will be much higher and the modulation caused by RISS should be very low, and one has to worry only about diffractive scintillations when performing flux measurements." simultaneously observed in both COR1 and COR2 in both the Ahead and Behind spacecraft but only in from the Ahead spacecraft in HI.,simultaneously observed in both COR1 and COR2 in both the Ahead and Behind spacecraft but only in from the Ahead spacecraft in HI. " Each event was observed in either the inner coronagraph (COR1) or outer coronagraph (COR2) simultaneously by both STEREO-A and STEREO-B. From these images, the CME apex was localised via tie-pointing (see Maloneyetal.2009 Figure 1, Inhester (2006)))."," Each event was observed in either the inner coronagraph (COR1) or outer coronagraph (COR2) simultaneously by both STEREO-A and STEREO-B. From these images, the CME apex was localised via tie-pointing (see \citealt{Maloney:2009p6617} Figure 1, \citet{Inhester:2006p2249}) )." The trajectory was then reconstructed by tracking it through a series of images., The trajectory was then reconstructed by tracking it through a series of images. " In all the events presented, the CME was only observed in HI by one spacecraft, so an additional constraint was required to localise the CME apex."," In all the events presented, the CME was only observed in HI by one spacecraft, so an additional constraint was required to localise the CME apex." " We therefore assumed that the CME continued along the same path with respect to solar longitude, as it did in the the COR1/2 field-of-view (i.e. travelled radially; Maloneyetal. 2009))."," We therefore assumed that the CME continued along the same path with respect to solar longitude, as it did in the the COR1/2 field-of-view (i.e. travelled radially; \citealt{Maloney:2009p6617}) )." Figure 2 shows the derived trajectory for the 2008 March 25 event., Figure 2 shows the derived trajectory for the 2008 March 25 event. " Once the 3D trajectories were derived, we calculated the height and then took numerical derivatives with respect to time to obtain the velocity and acceleration."," Once the 3D trajectories were derived, we calculated the height and then took numerical derivatives with respect to time to obtain the velocity and acceleration." mounting evidence of massive haloes of neutral and ionizecl eas surrounding nearby spiral galaxies (e.g.?)..,mounting evidence of massive haloes of neutral and ionized gas surrounding nearby spiral galaxies \citep[e.g.][]{safra08}. Phese thick disks rotate more slowly than the thin disks. ancl show inflow motions., These thick disks rotate more slowly than the thin disks and show inflow motions. ? have shown that these haloes cannot be sustained only by galactic fountains., \citet{frabi08} have shown that these haloes cannot be sustained only by galactic fountains. According to them. the gas from the fountains interacting with a pre-existing hot corona would make it to co-rotate with the disk after avery short time (51 Myr) which is not consistent. with the observations.," According to them, the gas from the fountains interacting with a pre-existing hot corona would make it to co-rotate with the disk after a very short time $\la 1$ Myr) which is not consistent with the observations." This result. led them to conclude that a substantial accretion of low angular momentum material from the intergalactic medium would be required. in order to assure a slower rotating halo., This result led them to conclude that a substantial accretion of low angular momentum material from the intergalactic medium would be required in order to assure a slower rotating halo. 1n the model of 2? the clouds are treated. as bullets moving ballisticallv. and hverodynanmical elfects are absent or only roughly represented.," In the model of \citet{frabi08} the clouds are treated as bullets moving ballistically, and hydrodynamical effects are absent or only roughly represented." In order to investigate the issues above more realistically from an hyedrodynamical point. of view. we have simulated the interaction of the MGEs with infalling gas considering two cillerent models. one in which the eas infall is described. as a continuous drizzle. and another in which a single. denser cloud is assumed to fall toward the active area.," In order to investigate the issues above more realistically from an hydrodynamical point of view, we have simulated the interaction of the MGFs with infalling gas considering two different models, one in which the gas infall is described as a continuous drizzle, and another in which a single, denser cloud is assumed to fall toward the active area." (e.g.ofthis only 0.3 dex scatter strong evidence for a coupled formation and evolution of galaxies aud BUs.,"\citep[e.g.][]{marc03,haer04} only 0.3 dex scatter – strong evidence for a coupled formation and evolution of galaxies and BHs." The source coupling is unclear. but feedback mechanisis have been proposed involving the ceutral potential well depth regulatiug DII accretion. or more violent feedback from active ealactic nuclei (AGN) iuto their host galaxies (e.g.Hopkinsetal.2006:Somerville2008:Menucietal 2008).," The source of this coupling is unclear, but feedback mechanisms have been proposed involving the central potential well depth regulating BH accretion, or more violent feedback from active galactic nuclei (AGN) into their host galaxies \citep[e.g.][]{hopk06c,some08,menc08}." . While these scenarios potentially provide ingredients for acquiius consensus with observations. all such iodels iuclude ad hoc assumptions aud do not work from frst priuciples.," While these scenarios potentially provide ingredients for acquiring consensus with observations, all such models include ad hoc assumptions and do not work from first principles." Empirical constraiuts are urecutly needed to investigate the actual plysical processes involved in the coupled evolution., Empirical constraints are urgently needed to investigate the actual physical processes involved in the coupled evolution. Oue strong constraint is the evolution. of the τω Maz puserelation over time.," One strong constraint is the evolution of the $M_\mathrm{BH}$ $M_\mathrm{*,bulge}$ -relation over time." While| circumstantial evidence grows that the value of Mp M.ples Was larger at earlier cosmic times (Pengetal.2006a.b:WeSab. 2009).. studies are subject to biases (Laueretal.X7) aud better statistics are required to investigate where in AZpg. or when m cosmic time. a turnoff from the local Api M.ue relation occurs.," While circumstantial evidence grows that the value of $M_\mathrm{BH}$ $M_\mathrm{*,bulge}$ was larger at earlier cosmic times \citep{peng06a,peng06b,treu07,woo08,walt04,riec08a,riec08b,riec09}, studies are subject to biases \citep{laue07} and better statistics are required to investigate where in $M_\mathrm{BH}$, or when in cosmic time, a turnoff from the local $M_\mathrm{BH}$ $M_\mathrm{*,bulge}$ -relation occurs." Broad-line AGN and their host galaxies are the only systems at higher redshifts iu which both the mass of the ealaxy or its bulge as well as its central DIT cau be estimated., Broad-line AGN and their host galaxies are the only systems at higher redshifts in which both the mass of the galaxy or its bulge as well as its central BH can be estimated. Tere we set constraints on an evolving Mou M. puaerelation by computing optical color-based stellar masses (from HST/ACS aud UST/NICAIOS) aud," Here we set constraints on an evolving $M_\mathrm{BH}$ $M_\mathrm{*,bulge}$ -relation by computing optical color-based stellar masses (from HST/ACS and HST/NICMOS) and" ,. " For each snapshot we define a 1973).spatial average via, 'The restriction on the radial range of the averaging is designed to ignore the plunging region of the accretion flow (r< 6rj) and any effects related to the outer radial boundary."," For each snapshot we define a density-weighted spatial average via, The restriction on the radial range of the averaging is designed to ignore the plunging region of the accretion flow $r\approxlt 6r_g$ ) and any effects related to the outer radial boundary." " Density weighting is used in the vertical direction to take into account the low density, highly magnetized regions while still allowing the dominant contribution to the integral to come from the denser plane of the disk."," Density weighting is used in the vertical direction to take into account the low density, highly magnetized regions while still allowing the dominant contribution to the integral to come from the denser mid-plane of the disk." A comparison of ay and its dependence on vertical domain is given in Figure 5.., A comparison of $\alpha_{\rm M}$ and its dependence on vertical domain is given in Figure \ref{alphacomp}. " The initial growth phase of the MRI is unaffected by the vertical domain as expected, since all the simulations considered have the same vertical resolution and can thus resolve the same unstable MRI modes."," The initial growth phase of the MRI is unaffected by the vertical domain as expected, since all the simulations considered have the same vertical resolution and can thus resolve the same unstable MRI modes." " Over the course of the simulations, the larger vertical extent simulations have, in general, larger values of ayy."," Over the course of the simulations, the larger vertical extent simulations have, in general, larger values of $\alpha_{\rm M}$." We attribute this effect to stifling of the growth of the magnetized regions in the smaller vertical extent simulation., We attribute this effect to stifling of the growth of the magnetized regions in the smaller vertical extent simulation. " However, the long-term effects of vertical extent are ambiguous."," However, the long-term effects of vertical extent are ambiguous." Whether the simulations converge to the same ay or the apparent convergence is a result of short-term variability is unclear from the current simulations., Whether the simulations converge to the same $\alpha_{\rm M}$ or the apparent convergence is a result of short-term variability is unclear from the current simulations. Longer simulations will need to be carried out to determine the vertical domain size that is needed in order to reliably capture the dynamics of a global disk., Longer simulations will need to be carried out to determine the vertical domain size that is needed in order to reliably capture the dynamics of a global disk. " In the one case of runThin.M-Res.6z, the disk was simulated for 664 ISCO orbits."," In the one case of run, the disk was simulated for 664 ISCO orbits." This simulation allows us to search for long-term trends in the dynamics of the disk., This simulation allows us to search for long-term trends in the dynamics of the disk. As shown in Figure 6 there is a slight downward drift in αν over time., As shown in Figure \ref{longtermalpha} there is a slight downward drift in $\alpha_M$ over time. The same temporal trend is also evident in the flux-stress relationship., The same temporal trend is also evident in the flux-stress relationship. Figure 7 shows the flux-stress relationship averaged in 100 orbit blocks starting at 50 ISCO orbits., Figure \ref{longfvsblocks} shows the flux-stress relationship averaged in 100 orbit blocks starting at 50 ISCO orbits. " During the first 300 orbits, there appears to be a secular drift in the flux-stress relation."," During the first 300 orbits, there appears to be a secular drift in the flux-stress relation." " The linear (high-flux) part of the relation achieves a steady state relatively quickly (only the first time block between 50 and 150 ISCO orbits shows significant differences), but the flat (low-flux) part of the relation continues to fall until it too achieves a steady state at approximately 350 ISCO orbits into the run."," The linear (high-flux) part of the relation achieves a steady state relatively quickly (only the first time block between 50 and 150 ISCO orbits shows significant differences), but the flat (low-flux) part of the relation continues to fall until it too achieves a steady state at approximately 350 ISCO orbits into the run." " Associated with this, the “knee” in the flux-stress relation appears to move to smaller fluxes."," Associated with this, the “knee” in the flux-stress relation appears to move to smaller fluxes." " In essence, this result says that low-flux regions still support (small) stresses at early times but that those stresses decay over a period of several hundred ISCO orbits."," In essence, this result says that low-flux regions still support (small) stresses at early times but that those stresses decay over a period of several hundred ISCO orbits." We ascribe this to stresses associated with a sheared residual of the initial magnetic field configuration which are “mixed away” on a relatively long timescale., We ascribe this to stresses associated with a sheared residual of the initial magnetic field configuration which are “mixed away” on a relatively long timescale. Our initial field configuration threads the midplane with regions of net magnetic flux which alternate with a radial periodicity of 5h., Our initial field configuration threads the midplane with regions of net magnetic flux which alternate with a radial periodicity of $5h$. " Radial Fourier transforms of the mid-plane azimuthally-averaged B, do indeed find a (weak) periodicity corresponding to the initial field even once the turbulence is fully developed.", Radial Fourier transforms of the mid-plane azimuthally-averaged $B_z$ do indeed find a (weak) periodicity corresponding to the initial field even once the turbulence is fully developed. This periodic component grows weaker and is no longer detectable at approximately the same time that the flux-stress curve achieves steady-state., This periodic component grows weaker and is no longer detectable at approximately the same time that the flux-stress curve achieves steady-state. These observations further suggest that residual flux from the initial conditions is responsible for the long term variability., These observations further suggest that residual flux from the initial conditions is responsible for the long term variability. " Assuming that a long-lived residual of the initial magnetic field is the driving mechanism for this phenomenon, we can recover the time required to achieve the steady state from elementary arguments."," Assuming that a long-lived residual of the initial magnetic field is the driving mechanism for this phenomenon, we can recover the time required to achieve the steady state from elementary arguments." The time needed to turbulently diffuse together two patches of oppositely directed flux separated by a radial distance Ar=2.5h is given by where meg is the effective turbulent resistivity., The time needed to turbulently diffuse together two patches of oppositely directed flux separated by a radial distance $\Delta r=2.5h$ is given by where $\eta_{\rm eff}$ is the effective turbulent resistivity. " If we define as the effective turbulent magnetic Prandtl number (i.e. Primerthe ratio of the effective turbulent viscosity to the effective turbulent resistivity), we can write"," If we define $Pr_{\rm m,eff}$ as the effective turbulent magnetic Prandtl number (i.e. the ratio of the effective turbulent viscosity to the effective turbulent resistivity), we can write" of dimensionality reduction.,of dimensionality reduction. " In our case, the simplest way to proceed is the determination of the fraction of the disk covered by magnetic structures, the filling factors."," In our case, the simplest way to proceed is the determination of the fraction of the disk covered by magnetic structures, the filling factors." The algorithm employed to determine the filling factors is described in detail in the next section., The algorithm employed to determine the filling factors is described in detail in the next section. " The coefficients W, L, M, δι. and b» are determined by minimizing a combination of squared errors and weights ?.."," The coefficients $\boldsymbol W$ , $\boldsymbol L$ , $\boldsymbol M$ , $b_1$, and $b_2$ are determined by minimizing a combination of squared errors and weights \cite{MacKay1992}." This process is also known as Bayesian regularization., This process is also known as Bayesian regularization. " In this way, we determine the set of coefficients to produce a network that generalizes properly the relations between the input and the output data."," In this way, we determine the set of coefficients to produce a network that generalizes properly the relations between the input and the output data." The algorithm described above can be applied for nowcast as well as for short-term forecast up to two days., The algorithm described above can be applied for nowcast as well as for short-term forecast up to two days. " Here, we define nowcast as a short-term forecast out to six hours."," Here, we define nowcast as a short-term forecast out to six hours." " Here we employ solar disk magnetograms and continuum images to identify the magnetic active regions and sunspots, respectively."," Here we employ solar disk magnetograms and continuum images to identify the magnetic active regions and sunspots, respectively." An example of such observations is provided in Figures 2aa- which show the observations of the solar disk obtained by HMI instruments on 04-Aug-2011 at 9:00 UT.," An example of such observations is provided in Figures \ref{FigHMI1}a a-b, which show the observations of the solar disk obtained by HMI instruments on 04-Aug-2011 at 9:00 UT." Large magnetic active regions and sunspots are present in the northern hemisphere., Large magnetic active regions and sunspots are present in the northern hemisphere. " The feature extraction procedure consists of the identification of the quiet Sun, magnetic active regions, and sunspots."," The feature extraction procedure consists of the identification of the quiet Sun, magnetic active regions, and sunspots." The method to identify magnetic active regions in the disk magnetograms includes the following steps: (a) identification of the disk pixels; (b) segmentation of the image; (c) labelling; (d) computation of the area of each object identified inthe binaryimage;(e) removal of small area objects., The method to identify magnetic active regions in the disk magnetograms includes the following steps: (a) identification of the disk pixels; (b) segmentation of the image; (c) connected-component labelling; (d) computation of the area of each object identified inthe binaryimage;(e) removal of small area objects. and is related to the luminosity function of clusters.,and is related to the luminosity function of clusters. " The second time scale is defined by the dynamical evolution and, especially, by two-body-relaxation-driven mass loss from clusters."," The second time scale is defined by the dynamical evolution and, especially, by two-body-relaxation-driven mass loss from clusters." " Therefore, it is responsible for the evolution of the cluster mass function."," Therefore, it is responsible for the evolution of the cluster mass function." " Moreover, the nuclear lifetime does not depend on cluster mass, whereas the dynamical lifetime of a cluster is strongly related to its mass."," Moreover, the nuclear lifetime does not depend on cluster mass, whereas the dynamical lifetime of a cluster is strongly related to its mass." These differences cause different schemes in the evolution of the luminosity and mass functions., These differences cause different schemes in the evolution of the luminosity and mass functions. " Whereas the cluster luminosity function evolves in coordination with the evolution of the most massive cluster members, the mass function evolves faster at its low-mass end where the dynamical time is short."," Whereas the cluster luminosity function evolves in coordination with the evolution of the most massive cluster members, the mass function evolves faster at its low-mass end where the dynamical time is short." " Since the cluster luminosity function shows a more complicated evolution pattern, we start our consideration with the CMF."," Since the cluster luminosity function shows a more complicated evolution pattern, we start our consideration with the CMF." In Fig., In Fig. 6 we show mass spectra of three cluster subsamples differing just by the upper limit of ages of the clusters., \ref{fig:fuma} we show mass spectra of three cluster subsamples differing just by the upper limit of ages of the clusters. " The first sample contains the 49 youngest clusters with ages less than t,«8 Myr (logt« 6.9)."," The first sample contains the 49 youngest clusters with ages less than $t_y\approx8$ Myr $\log t\leqslant 6.9$ )." This is the lowest age limit where we have been able to construct a significant mass function., This is the lowest age limit where we have been able to construct a significant mass function. " Hereafter, we call this subset the youngest sample."," Hereafter, we call this subset the youngest sample." The second subsample includes additional moderately young clusters and contains 207 entities (logt< 7.9)., The second subsample includes additional moderately young clusters and contains 207 entities $\log t\leqslant7.9$ ). " Finally, we consider all 440 clusters (logt< 9.5)."," Finally, we consider all 440 clusters $\log t\leqslant9.5$ )." " To improve the stability of the solutions, we made re-binning on the mass scale requiring at least five clusters per bin, but keeping the step of AlogM.=0.15 whenever possible."," To improve the stability of the solutions, we made re-binning on the mass scale requiring at least five clusters per bin, but keeping the step of $\Delta\log M_c=0.15$ whenever possible." All three distributions demonstrate similar general patterns that can be separated into two parts., All three distributions demonstrate similar general patterns that can be separated into two parts. " The more massive part at logM.»M;«3.3 is almost linear on the logarithmic scales logy, and logM. although the slope of the relation depends on the upper age limit."," The more massive part at $\log M_c>\log M^*_c\approx3.3$ is almost linear on the logarithmic scales $\log \eta_t$ and $\log M_c$ although the slope of the relation depends on the upper age limit." " At lower masses, the CPDMF changes into a non-linear pattern."," At lower masses, the CPDMF changes into a non-linear pattern." " After reaching the maximum, the mass function of each sample starts to decrease."," After reaching the maximum, the mass function of each sample starts to decrease." " For the youngest sample, the low mass portion of the CMF is rather flat and the turnover is less significant."," For the youngest sample, the low mass portion of the CMF is rather flat and the turnover is less significant." " For older clusters, the CMF maximum is shifted to lower masses."," For older clusters, the CMF maximum is shifted to lower masses." " Choosing other subsamples of clusters by varying the upper age limit from logt=6.9 to logt=9.5, we found that, at the age limit logt=7.4, the CMF reaches a maximum at logM.~2."," Choosing other subsamples of clusters by varying the upper age limit from $\log t = 6.9$ to $\log t = 9.5$, we found that, at the age limit $\log t = 7.4$, the CMF reaches a maximum at $\log M_c \approx 2$." " If we add older and older clusters, this location does not change anymore, although the value of the CMF-maximum increases."," If we add older and older clusters, this location does not change anymore, although the value of the CMF-maximum increases." " On the abscissa of Fig. 6,,"," On the abscissa of Fig. \ref{fig:fuma}," we observe different mass ranges for the different subsamples., we observe different mass ranges for the different subsamples. The lower mass limit depends significantly on the cluster age., The lower mass limit depends significantly on the cluster age. " The younger the clusters, the higher is the lower mass limit (M?~50Mo at logt«6.9 and Mm~5M. at logt« 9.5)."," The younger the clusters, the higher is the lower mass limit $M_c^{min}\approx 50 M_\odot$ at $\log t\leqslant 6.9$ and $M_c^{min}\simeq 5 M_\odot$ at $\log t\leqslant 9.5$ )." We consider this as a manifestation of mass loss driven by the evolution of star clusters., We consider this as a manifestation of mass loss driven by the evolution of star clusters. " On the other hand, the position of the bin of the highest masses seems to be independent of the sample considered."," On the other hand, the position of the bin of the highest masses seems to be independent of the sample considered." " It varies from sample to sample only randomly, simply due to low number statistics of high-mass clusters."," It varies from sample to sample only randomly, simply due to low number statistics of high-mass clusters." roughly of the more massive earbh-tvpe M dwarf iultiple svstems in the Fischer&Mareyv(1992). study have 100 AU πα < 10! AU.,roughly of the more massive early-type M dwarf multiple systems in the \citet{fis92} study have 10 AU $\lesssim$ $a$ $\lesssim$ $^4$ AU. Siuibule. roushlv of AL dwarf multiple svstemis in the 8 pc sample have separations ereater than 10 AU (Reid&Cüzis1997).," Similarly, roughly of M dwarf multiple systems in the 8 pc sample have separations greater than 10 AU \citep{rei97}." ". Tf lower-auass systems lad ai simular fraction of wide binaries, then roughly 20 pairs with ο»1020 AU from the approximately 300 known L aud T dwarts should have been identified. while there are curreuthy none."," If lower-mass systems had a similar fraction of wide binaries, then roughly 20 pairs with $a > 10-20$ AU from the approximately 300 known L and T dwarfs should have been identified, while there are currently none." The absence of wide systems may contribute to the overall deficiency in multiple systems amouest the T chwarts. as the binary fractions of FOC dwarfs audAL dwarts drop to roughly for separations α<10 AU. within the uncertaintv estimates of our bias-corrected result.," The absence of wide systems may contribute to the overall deficiency in multiple systems amongst the T dwarfs, as the binary fractions of F–G dwarfs andM dwarfs drop to roughly for separations $a < 10$ AU, within the uncertainty estimates of our bias-corrected result." We discuss the apparent limit in the separations of low-mass stars and brown dywarfs further in 67.1., We discuss the apparent limit in the separations of low-mass stars and brown dwarfs further in $\S$ 7.1. Finally. we consider the amass ratio distribution. f(q) a statistic that can coustrain the origin of secoudarics dn a binary population.," Finally, we consider the mass ratio distribution, $f(q)$, a statistic that can constrain the origin of secondaries in a binary population." Iu general. masses are difficult to derive for field brown dwrfs as estimates depend on both temperature and age. aud there are few cnpimial clues curently: known for the latter parameter.," In general, masses are difficult to derive for field brown dwarfs, as estimates depend on both temperature and age, and there are few empirical clues currently known for the latter parameter." In Table 7. we lave estimated masses for 2PATASS 0716]2000AD. DENTS 1159AD. 2MASS 1531 2952AD. aud 2MÁSS 2739AB assuming au age of 1 Gyr. the Ἑyy scale of Durgasseretal.(2002d).. and the theoretical models of Burrowsetal.(1997): for 2ATASS 1116|2230AB. we used asian masses of 0.06 AL. based on the presence of the 6708 Li I line in the combined light spectrum (Kirkpatricketal.1900).," In Table 7, we have estimated masses for 2MASS 0746+2000AB, DENIS $-$ 1159AB, 2MASS $-$ 2952AB, and 2MASS $-$ 2739AB assuming an age of 1 Gyr, the $_{eff}$ scale of \citet{me02}, and the theoretical models of \citet{bur97}; for 2MASS 1146+2230AB, we used maximum masses of 0.06 $_{\sun}$ based on the presence of the 6708 Li I line in the combined light spectrum \citep{kir99}." All other mass estimates are taken from the listed references., All other mass estimates are taken from the listed references. Fortunately. the desired quantity. 4. is not ercatly scusitive to these assumptions.," Fortunately, the desired quantity, $q$, is not greatly sensitive to these assumptions." The two T dwarf binarics identified in our sample have relatively larec mass ratios. ¢ = 0.8 ancl 1.0.," The two T dwarf binaries identified in our sample have relatively large mass ratios, $q$ = 0.8 and 1.0." As discussed in 51.23. we were capable of ideutifving svstcms down to q—0.1. albeit not for very closely. separated systems like 2MASS 2052AD.," As discussed in $\S$ 4.3, we were capable of identifying systems down to $q = 0.4$, albeit not for very closely separated systems like 2MASS $-$ 2952AB." When we place these two svstenis in context with the other low-mass binaries listed in Table T. there appears to be a preference for equal-imass svstenis. the lowest mass ratio svsteni being 0.7.," When we place these two systems in context with the other low-mass binaries listed in Table 7, there appears to be a preference for equal-mass systems, the lowest mass ratio system being 0.7." " This is simular to what has been reported in the 8 pe sample (Reid&CagisΤΟ Τὸ, aud is at odds with the flatter distributions of Duqueunov&Mavor(1991) aud Fischer&Marcy(1992)."," This is similar to what has been reported in the 8 pc sample \citep{rei97}, and is at odds with the flatter distributions of \citet{duq91} and \citet{fis92}." . The two binaries identified in our program form too sanall a sample to examine the mass ratio distribution statistically. so we combined our teu T chwarts with the L dwarf sample of Reidetal. (2001)...," The two binaries identified in our program form too small a sample to examine the mass ratio distribution statistically, so we combined our ten T dwarfs with the L dwarf sample of \citet{rei01a}. ." " Based on their conrpleteness lits. aud using the same mass/fius ratio scaling as described in 81.3. we fud that their sample is coniplete to q20.1 for az0725, or a25 AU assmuing a inean distance of 20 pe."," Based on their completeness limits, and using the same mass/flux ratio scaling as described in $\S$ 4.3, we find that their sample is complete to $q \gtrsim 0.4$ for $a \gtrsim 0{\farcs}25$, or $a \gtrsim 5$ AU assuming a mean distance of 20 pc." This is comparable to our completeness fora21 AU. although the inner separation iuit for our sample is roughly ouc-half that of the L dwarf study.," This is comparable to our completeness for $a \gtrsim 4$ AU, although the inner separation limit for our sample is roughly one-half that of the L dwarf study." Nonetheless because simular iustrunenuts and observing strategies were emploved. combining these wo sanples should not introduce significant biases,"Nonetheless, because similar instruments and observing strategies were employed, combining these two samples should not introduce significant biases." The observed binary fraction for this combined sample is 2012 while the bias-corrected fraction is 9!2%.," The observed binary fraction for this combined sample is $^{+9}_{-5}$, while the bias-corrected fraction is $9^{+9}_{-3}$." " Breaking these systems down by mass ratio. we finc systems with 1.0 O01 pe zm 2<10° AU (DBalicall&Sonierva1981: 1991)..," The deficiency of brown dwarf binaries with $a \gtrsim 10$ AU is reminiscent of the deficiency of stellar binaries with $a$ $\gtrsim$ 0.1 pc $\approx$ $\times$ $^5$ AU \citep{bah81,clo90,was91}. ." While there remains some debate as to whether a sharp break exists in the separation distribution(Retterer&Ising1982:WassermanWeinberg1987. 1990).. it i8 ecuerally believed. that impulsive perturbations bw close stellar encounters or passage through a CALC causes a gradual diffusion of separations aud binding cuereics. ultimately resulting in the dissolutiou of weakly bound svsteiis in a catastrophic encounter," While there remains some debate as to whether a sharp break exists in the separation distribution\citep{ret82,was87,was91,clo90}, , it is generally believed that impulsive perturbations by close stellar encounters or passage through a GMC causes a gradual diffusion of separations and binding energies, ultimately resulting in the dissolution of weakly bound systems in a catastrophic encounter" aas measured with if one assures a poiut-like X-ray source at its center.,as measured with if one assumes a point-like X-ray source at its center. For au extended source. photous [rom near the limb has longer path leugths through the cold outer shell. thus the above shell mass is au overestimate. particularly for a linab-brightened X-ray source.," For an extended source, photons from near the limb has longer path lengths through the cold outer shell, thus the above shell mass is an overestimate, particularly for a limb-brightened X-ray source." The poiut-source meoclel that fits the oobservation overpredicts the bby50%., The point-source model that fits the observation overpredicts the by. . This may be due. in part. to the simplistic treatment of the complex geometry: or the outer shell may have been partially ionized at early stages. allowing low enerey photous to escape aud hence complicating our spectral fits (a similar mechanisin may have allowed the very early detection of V838 Her with citepll92)).," This may be due, in part, to the simplistic treatment of the complex geometry; or the outer shell may have been partially ionized at early stages, allowing low energy photons to escape and hence complicating our spectral fits (a similar mechanism may have allowed the very early detection of V838 Her with \\citep{ll92}) )." Extrapolation of this model back to day 5.7. the epoch of the initial oobservation. implies that the column would have been ~2x10?! 7. too high to allow X-rays escape even allowing for some overprediction.," Extrapolation of this model back to day 5.7, the epoch of the initial observation, implies that the column would have been $\sim 2 \times 10^{24}$ $^{-2}$, too high to allow X-rays escape even allowing for some overprediction." That is. tle ustory is suggestive of au origin in an expanding shell. the ejecta (rom the 1999 nova eruption itself.," That is, the history is suggestive of an origin in an expanding shell, the ejecta from the 1999 nova eruption itself." " The mass in this shell is probably somewhat less than 5x10.? if, as seeius likely. the X-ray. emission is [roi a lIunb-brightened iunuer shell."," The mass in this shell is probably somewhat less than $\times 10^{-5}$ if, as seems likely, the X-ray emission is from a limb-brightened inner shell." This inodel of the istory leads naturally to an internal shock model., This model of the history leads naturally to an internal shock model. An expancing outer shell provides the observedqp with the X-ray. produciug shock residiug iuside.," An expanding outer shell provides the observed, with the X-ray producing shock residing inside." The simplest model. then. cousists of two distinct shells of nova ejecta.," The simplest model, then, consists of two distinct shells of nova ejecta." The initial ejecta provide the absorbing column: a laver of later. aud aster-inoviug. ejecta plough iuto the initial ejecta.," The initial ejecta provide the absorbing column; a layer of later, and faster-moving, ejecta plough into the initial ejecta." The bieh shock temperature of kT~10 keV 'equires a stroug shock with velocity cdillereutial of 73000., The high shock temperature of $\sim$ 10 keV requires a strong shock with velocity differential of $\sim$. . Later observatious show a softer spectrum. in KT as well as inNyy... which suggests that the two sets of ejecta are mereing to form. a single layer.," Later observations show a softer spectrum, in kT as well as in, which suggests that the two sets of ejecta are merging to form a single layer." This is a sceuario first proposed by Friedjuug(1957).. which was motivated by the vast literature c1 the optical spectra of classical uovae in eruption.," This is a scenario first proposed by \citet{f87}, which was motivated by the vast literature on the optical spectra of classical novae in eruption." Quantitative models of optical spectra of classical novae are generally based on a single- optically thick wind approximation (Bath&Shaviv|1976).," Quantitative models of optical spectra of classical novae are generally based on a single-component, optically thick wind approximation \citep{b76}." . However useful this [ουμιαάσμα may be. it is clear (rom the rich taxonomy of optical spectra of novae (summarized most notably by Payne-Caposchkin (1957))) that nova ejecta are far more complex than this.," However useful this formalism may be, it is clear from the rich taxonomy of optical spectra of novae (summarized most notably by \citet{pg57}) ) that nova ejecta are far more complex than this." Several distinct systeis are often recoguized., Several distinct systems are often recognized. In time order. these are called pre-inaxinium. principal. diffuse enhanced. aud Orion components.," In time order, these are called pre-maximum, principal, diffuse enhanced, and Orion components." As the name implies. the pre-inaximum Component is the first t»orption features seen. before the visual ligit curve reaches its maximum: their typical velocities are in the rrange.," As the name implies, the pre-maximum component is the first absorption features seen, before the visual light curve reaches its maximum; their typical velocities are in the range." This component therefore is associated with the initial ejecta from the nova eruption. which presumably carries the pseudo-photosphere with it as it expauds.," This component therefore is associated with the initial ejecta from the nova eruption, which presumably carries the pseudo-photosphere with it as it expands." The principal system follows next. with a higher velocity aud a higher ionization: this is the system that persists decacles after the," The principal system follows next, with a higher velocity and a higher ionization; this is the system that persists decades after the" "Without any ""a priori knowledge about the nature of the modulation. frequency modulation (period. changes over. the Blazhko cycle) and phase modulation can not be distinguished: a detected phase variation indicates period changes. and vice-versa.","Without any “a priori” knowledge about the nature of the modulation, frequency modulation (period changes over the Blazhko cycle) and phase modulation can not be distinguished: a detected phase variation indicates period changes, and vice-versa." From now on we refer to this phenomenon as phase modulation., From now on we refer to this phenomenon as phase modulation. We searched for phase modulation in all of our LLyrae stars in the same way as was described in the case of amplitude modulation., We searched for phase modulation in all of our Lyrae stars in the same way as was described in the case of amplitude modulation. " We calculated the Ayo, values from the phase variation function 04,(/).", We calculated the $\Delta \varphi_1$ values from the phase variation function $\delta\varphi_1(t)$. " We expressed the phase differences relative to the total eyele. that is Xó,2:N,/2x (= 0110/ P."," We expressed the phase differences relative to the total cycle, that is $\Delta \phi_1$ $\Delta \varphi_1/ 2 \pi$ (= $\delta P_0/ P_0$ )." The results can be seen in the Sth column of Table 2.., The results can be seen in the 5th column of Table \ref{Blazhko_stars}. We detected clear phase modulation for all the studied Blazhko RRLLyrae stars., We detected clear phase modulation for all the studied Blazhko Lyrae stars. The hardest task was to find it in the case of CCvg. where the Blazhko cycle is longer than the data set and the phase variation during the observed time span was only 0.0014 (1 min).," The hardest task was to find it in the case of Cyg, where the Blazhko cycle is longer than the data set and the phase variation during the observed time span was only 0.0014 $\approx$ 1 min)." The reality of this smal phase variation was checked and confirmed by the sensitive analytical function method (Kolláthetal...2002)., The reality of this small phase variation was checked and confirmed by the sensitive analytical function method \citep{Kol02}. . We can detec period variations smaller than. mmin for three further stars: V783CCvg 55559631). V349 77176080). anc 11125706.," We can detect period variations smaller than min for three further stars: Cyg 5559631), Cyg 7176080), and 1125706." The other extremity is CCrepresentedvg by LLyr and LLyr itself with their values of 0.0224 (= mmin) and 0.0138 (= mmin).respectively.," The other extremity is represented by Lyr and Lyr itself with their values of 0.0224 (= min) and 0.0138 (= min), respectively." There is no clear indication for anv connections between the strengths of the two tvpe of modulations., There is no clear indication for any connections between the strengths of the two type of modulations. As was shown by Szeidl&Juresik(2009) and Benkóetal. (2009).. phase modulation always causes multiplet structures of higher order than triplets in the Fourier spectrum around the main frequency and its harmonics.," As was shown by \cite{SzJ09} and \cite{Ben09}, phase modulation always causes multiplet structures of higher order than triplets in the Fourier spectrum around the main frequency and its harmonics." These multiplet peaks were most clearly detected for CCyg. LLyr and LLyr. the Blazhko stars with the strongest phase modulation in our sample.," These multiplet peaks were most clearly detected for Cyg, Lyr and Lyr, the Blazhko stars with the strongest phase modulation in our sample." The precise and almost continuous observation of 14 Blazhko RRLLyrae stars measured byKepler convincingly demonstrates that in all Blazhko stars both amplitude and phase variation are present., The precise and almost continuous observation of 14 Blazhko Lyrae stars measured by convincingly demonstrates that in all Blazhko stars both amplitude and phase variation are present. Besides the modulation. components that occur in multiplet structures around the main frequency and its harmonics. we found additional frequencies.," Besides the modulation components that occur in multiplet structures around the main frequency and its harmonics, we found additional frequencies." In the cases of CCyg. V355LLvr and LLyr these frequencies are located around fo/2.5fofThis2.5RRfof... where fi denotes the main pulsation frequency.," In the cases of Cyg, Lyr and Lyr these frequencies are located around $f_0/2, 3f_0/2, 5f_0/2,\dots$, where $f_0$ denotes the main pulsation frequency." very interesting period doubling effect has already been discussed briefly in Kolenbergetal.(20102). for LLyr itself. and a separate paper (Szaboetal.2010) is dedicated to it.," This very interesting period doubling effect has already been discussed briefly in \citet{Kol10} for Lyr itself, and a separate paper \citep{Sza10} is dedicated to it." Here we just remark that the presence of these frequencies in the spectra seems to be variable in time and connected to particular, Here we just remark that the presence of these frequencies in the spectra seems to be variable in time and connected to particular The equation of motion in leapfrog approximation is ) = = .) Li ,The equation of motion in leapfrog approximation is 0 = = ) + + H_o^2 + ). "The expansion time /,4 is computed from the analvtic expression for the (time from αρ=0 do d,yo=(a,+a,4)/2.", The expansion time $t_{n+1/2}$ is computed from the analytic expression for the time from $a_0=0$ to $a_{n+1/2}=(a_n+a_{n+1})/2$. The physical acceleration of particle / produced. by (he gravitational. attraction. of. the other particles. is. σας.4»," The physical acceleration of particle $i$ produced by the gravitational attraction of the other particles is ${\cal G}_{i,k,n}/a_n^2$." " :The physical. acceleration. corresponding to the counter term in (he square brackets may be written as uda where r=er is the physical coordinate and. p, is the cosmic mean mass censily al αμ.", The physical acceleration corresponding to the counter term in the square brackets may be written as _n where $r=ax$ is the physical coordinate and $\rho_n$ is the cosmic mean mass density at $a_n$. The counter term (hus causes the peculiar acceleration {ο vanish when the plwsical acceleration matches (hat of a homogeneous universe., The counter term thus causes the peculiar acceleration to vanish when the physical acceleration matches that of a homogeneous universe. When (he particles are represented as point masses.," When the particles are represented as point masses,." """E In the limiting isothermal sphere model for the mass distribution in MW. ¢=1. when {here is à nearby smaller galaxy. j.the terms for this pair in the sums in equation (À4)) are replaced with"," In the limiting isothermal sphere model for the mass distribution in MW, $i=1$, when there is a nearby smaller galaxy, $j$,the terms for this pair in the sums in equation \ref{eq:pointlike}) ) are replaced with" on [rom AMeGaugh (1996). anc in turn Disney (1976) who conclude that the surface brightness function (SBE) of galaxies the number density of galaxies in intervals of surface. brightness is of similar form to he luminosity function.,"on from McGaugh (1996), and in turn Disney (1976) — who conclude that the surface brightness function (SBF) of galaxies — the number density of galaxies in intervals of surface brightness — is of similar form to the luminosity function." Thus both the LE and SBE are described. by a Wat distribution with a cutoll at. bright absolute magnitudes or high. surface. brightnesses., Thus both the LF and SBF are described by a flat distribution with a cutoff at bright absolute magnitudes or high surface brightnesses. Taking he O'Neil result at face value. this implies a further error in measures of the local luminosity density of 2-3 - Le. the contribution to the Iuminositv- (and hence barvon-) density rom galaxies is uncertain to a factor of —10.," Taking the O'Neil result at face value, this implies a further error in measures of the local luminosity density of 2-3 - i.e. the contribution to the luminosity- (and hence baryon-) density from galaxies is uncertain to a factor of $\sim 10$." However he significance of low surface brightness galaxies depends upon their luminosity range and similarly the completeness of the LE relies on the surface brightness intervals. over which each luminosity bin is valid., However the significance of low surface brightness galaxies depends upon their luminosity range and similarly the completeness of the LF relies on the surface brightness intervals over which each luminosity bin is valid. Both representations are incomplete unless the information is combined., Both representations are incomplete unless the information is combined. This eads us to the conclusion that both the total ας and he manner in which this [lux is distributed must be dealt with simultaneously., This leads us to the conclusion that both the total flux and the manner in which this flux is distributed must be dealt with simultaneously. Several papers have been published which deal with either surface brightness distributions or Bivariate Brightness Distributions (Phillipps Disney 1986. Bovee Phillipps 1994. Minchin 1999. Sodre Lahay 1993. and Petrosian 1998).," Several papers have been published which deal with either surface brightness distributions or Bivariate Brightness Distributions (Phillipps Disney 1986, Boyce Phillipps 1994, Minchin 1999, Sodre Lahav 1993, and Petrosian 1998)." These are either theoretical. limited o cluster environments or have poor statistics due to the scarcity of good redshift data.," These are either theoretical, limited to cluster environments or have poor statistics due to the scarcity of good redshift data." lecentlv. Driver (1999) determined the first. measure of the for Ποιά galaxies using Llubble Deep Field. cata (Williams 1996) and capitalising on photometric redshifts (Fernánndez-Soto. 1998).," Recently, Driver (1999) determined the first measure of the for field galaxies using Hubble Deep Field data (Williams 1996) and capitalising on photometric redshifts (Fernánndez-Soto 1998)." The result. based on a volume limited: sample of 47 galaxies. implied that giant. low surface. brightness ealaxies were rare but that there exists à strong Luminositv-Surface Brightness relationship. similar to that seen in Virgo Aneeeli 1993).," The result, based on a volume limited sample of 47 galaxies, implied that giant low surface brightness galaxies were rare but that there exists a strong Luminosity-Surface Brightness relationship, similar to that seen in Virgo (Binggeli 1993)." Phe sense of the relationship implied that ow surface brightness galaxies are preferentially of lower uminositv (Le. cwarfs)., The sense of the relationship implied that low surface brightness galaxies are preferentially of lower luminosity (i.e. dwarfs). If this is borne out it strongly empers the conclusions of O'Neil Bothun (2000)., If this is borne out it strongly tempers the conclusions of O'Neil Bothun (2000). While he number of low surface brightness galaxies may be Large. heir luminosities are low. so their contribution to the loca uminosity density. is also low. 204 (Driver 1999).," While the number of low surface brightness galaxies may be large, their luminosities are low, so their contribution to the local luminosity density, is also low, $< 20$ (Driver 1999)." This paper attempts to bundle these complex. issues onto a more intuitive. platform by expanding the curren representation of the local galaxy population to allow for: surface brightness detection. cllects. star-galaxy separation issues. surface brightness photometric corrections ane clustering effects.," This paper attempts to bundle these complex issues onto a more intuitive platform by expanding the current representation of the local galaxy population to allow for: surface brightness detection effects, star-galaxy separation issues, surface brightness photometric corrections and clustering effects." This is achieved by expanding the mono-variate luminosity function. into a bivariate brightness distribution (BBD) where the additional cimension is surface brightness., This is achieved by expanding the mono-variate luminosity function into a bivariate brightness distribution (BBD) where the additional dimension is surface brightness. The 2dkFCRS allows us to do this for he first time by having a large enough database to separate ealaxies in both magnitude ancl surface brightness withou laving too many problems with small number statistics., The 2dFGRS allows us to do this for the first time by having a large enough database to separate galaxies in both magnitude and surface brightness without having too many problems with small number statistics. In €2 we discuss the revised methodology for measuring he space density of the local galaxy population. the loca uminosity density anc the contribution towards the barvon density in detail.," In 2 we discuss the revised methodology for measuring the space density of the local galaxy population, the local luminosity density and the contribution towards the baryon density in detail." In 83 we present the current 20ECIUS data (containing 45.000 galaxies or one fifth of the expectec final tally).," In 3 we present the current 2dFGRS data (containing $\sim 45,000$ galaxies or one fifth of the expected final tally)." In £4 we correct for the light lost. under the isophote ancl define our surface brightness measure., In 4 we correct for the light lost under the isophote and define our surface brightness measure. In. 85 we apply the methodology to construct the first statistically significant bivariate brightness distribution for field galaxies., In 5 we apply the methodology to construct the first statistically significant bivariate brightness distribution for field galaxies. The results for the number-density ancl luminositv-densitv are detailed in 86 and 87., The results for the number-density and luminosity-density are detailed in 6 and 7. In 8S. we compare these results to other surveys.," In 8, we compare these results to other surveys." Finally we present our conclusions., Finally we present our conclusions. " Throughout we adopt. 44,=L00kms Mpec. | and a standard. flat cosmology with zero cosmological constant qo=0.5..X0)."," Throughout we adopt $H_{o} = 100$ $^{-1}$ $^{-1}$ and a standard flat cosmology with zero cosmological constant $q_{o}=0.5, \Lambda=0$ )." However we note that the results presented here are only weakly dependent on the cosmology., However we note that the results presented here are only weakly dependent on the cosmology. The luminosity density. 7. is the total amount of ux emitted by all galaxies per Mpc.," The luminosity density, $j$ , is the total amount of flux emitted by all galaxies per $^{3}$." When measured in the UV band it can be converted to a measure of the star-formation rate (see for example Lilly 1996. Macau 1998).," When measured in the UV band it can be converted to a measure of the star-formation rate (see for example Lilly 1996, Madau 1998)." When nmieasured at longer wavelengths it can be combined. with nmiass-to-light. ratios to vield an value for the contribution [rom galaxies towards the local matter density Qu independent of Lf. only weakly cosmology dependent ancl not reliant on any specific theory of structure formation (see for cxample Carlbere 1996: Fukugita. Hogan Peebles 1998).," When measured at longer wavelengths it can be combined with mass-to-light ratios to yield an value for the contribution from galaxies towards the local matter density $\Omega_{M}$ — independent of $H_{o}$, only weakly cosmology dependent and not reliant on any specific theory of structure formation (see for example Carlberg 1996; Fukugita, Hogan Peebles 1998)." The two main caveats are firstly the accuracy of je (he luminosity density measured in the D-band). and secondly the assumption of a ubiquitous mass-to-light ratio.," The two main caveats are firstly the accuracy of $j_{B}$ (the luminosity density measured in the B-band), and secondly the assumption of a ubiquitous mass-to-light ratio." Vhe luminosity density. j. is found by integrating the product of the number density @(L/£.) and the luminosity L with respect to Luminosity.," The luminosity density, $j$, is found by integrating the product of the number density $\Phi(L/L_{*})$ and the luminosity L with respect to luminosity." " ὃν convention. j is typically derived [rom a magnitucde-limited redshift. survey by determining the representative Schechter paremeters for a survey (ee. Efstathiou JOSS) and then integrating the luminosity weighted Schechter function. where O(L/L.)d(L/L.) is the Schechter function (Schechter 1976) given by: and ó,.L,. and a are the three parameters which define the survey (referred. to as the normalisation point. characteristic turn-over. luminosity ancl faint-ene slope parameter respectively)."," By convention, $j$ is typically derived from a magnitude-limited redshift survey by determining the representative Schechter parameters for a survey (e.g. Efstathiou 1988) and then integrating the luminosity weighted Schechter function, where $\Phi(L/L_{*})\,d(L/L_{*})$ is the Schechter function (Schechter 1976) given by: and $\phi_*, L_{*},$ and $\alpha$ are the three parameters which define the survey (referred to as the normalisation point, characteristic turn-over luminosity and faint-end slope parameter respectively)." More simply if a survey is defined by these three parameters it follows that: ‘Table 1 shows values for the luminosity density derived from a number of recent magnitude-Iimited redshift surveys (as indicated)., More simply if a survey is defined by these three parameters it follows that: Table 1 shows values for the luminosity density derived from a number of recent magnitude-limited redshift surveys (as indicated). The variation between the measurements of j from these surveys is ~2 and hence the uncertainty in the galaxy contribution tothe mass budgetis at best equally uncertain., The variation between the measurements of $j$ from these surveys is $\sim 2$ and hence the uncertainty in the galaxy contribution tothe mass budgetis at best equally uncertain. Thiscould be due to a number of factors.," Thiscould be due to a number of factors," mininiinmni occurri during 1998. the |re caustic crossing interpretation is already ruled out at z954.,"minimum occurred during 1998, the $+ve$ caustic crossing interpretation is already ruled out at $>95\%$." The first unambiguous microlensing signal was the rise and fall of image A in 1988 during a period when the other images remained at a consistent level (ie., The first unambiguous microlensing signal was the rise and fall of image A in 1988 during a period when the other images remained at a consistent level (ie. no intrinsic variability)., no intrinsic variability). Some insight is gained through comparison of the shape of this leht-curve peak with the 1999 image C event., Some insight is gained through comparison of the shape of this light-curve peak with the 1999 image C event. The two events are described by very cülferent data sets., The two events are described by very different data sets. While the OGLE data has provided. excellent coverage of the 1999 peak. allowing quantities such as the niaximum derivative ancl peak height to be calculated. the 5 observations of the 19SS peak provide a much crucder record.," While the OGLE data has provided excellent coverage of the 1999 peak, allowing quantities such as the maximum derivative and peak height to be calculated, the 5 observations of the 1988 peak provide a much cruder record." In particular the values of maximum pre-peak derivative. the peak height above the minimum and the difference between the minimum cannot be computed.," In particular the values of maximum pre-peak derivative, the peak height above the minimum and the difference between the minimum cannot be computed." On he other hand. our source size estimation was determined rom the assumption tha the image A peak is à caustic Crossing.," On the other hand, our source size estimation was determined from the assumption that the image A peak is a caustic crossing." Statistical determinations of the event ἵνρο are herefore only meaninefu as a check of the self-consistency of the calculations., Statistical determinations of the event type are therefore only meaningful as a check of the self-consistency of the calculations. In that vein we note that. the one eading derivative that can be measured [rom the data is To5 mags/vear., In that vein we note that the one leading derivative that can be measured from the data is $T\sim5$ mags/year. Calculations in WAVTAOO suggest. that he observations should have been followed. by a Caustic crossing in 2.—3 weeks or a cIsp event in 5 weeks. which lie between and after the two brightest observations respectively.," Calculations in WWTA00 suggest that the observations should have been followed by a caustic crossing in $\sim2-3$ weeks or a cusp event in $\sim5$ weeks, which lie between and after the two brightest observations respectively." Fie., Fig. Y shows light-curves of the two peaks. placed on we sanie time-axis such that. the maxima approximately coincide at /—0.," \ref{peak_compare} shows light-curves of the two peaks, placed on the same time-axis such that the maxima approximately coincide at $t=0$." The image A and C peaks are shown by uick and thin lines respectively., The image A and C peaks are shown by thick and thin lines respectively. T1ο large initial rise of the LOSS event measures the minimum. o the maximum eracient (which is surely significantly larger given the high. second derivative)., The large initial rise of the 1988 event measures the minimum to the maximum gradient (which is surely significantly larger given the high second derivative). Ες sharp rise is no replicated. in the 1999 event which had a maximum clerivative of ~2 magnitudes yer vear., This sharp rise is not replicated in the 1999 event which had a maximum derivative of $\sim2$ magnitudes per year. " Since we have a lower |und for the ΠακΙΙΙ derivative of the 1988 image A even which is consistent with all three types of LIALE. the size o“the observed. derivative cannot be used as a diseriminate (although for a cusp event rere is a chance of AL,5 magnitudes per vear)"," Since we have a lower bound for the maximum derivative of the 1988 image A event which is consistent with all three types of HME, the size of the observed derivative cannot be used as a discriminate (although for a cusp event there is a chance of $\dot{M}_{max}<5$ magnitudes per year)." Llowever. the leading three points also measure a lower limit for the maximum seconel derivative.," However, the leading three points also measure a lower limit for the maximum second derivative." Fig., Fig. " S shows probability Py, forOE tje maximum] valuelue. of second Ldderivative] on uic leacing sides of cusp events. (solid lino) ancl |ee (dashed line) and —ee (dotted line) caustic crossings computed. for image A (no systematic error in source size was assumed): The derivatives were calculat«(d using à sampling rate corresponding to the initial 3 observations of the LOSS peak.", \ref{second_deriv} shows probability $P_{\ddot{M}}$ for the maximum value of second derivative on the leading sides of cusp events (solid line) and $+ve$ (dashed line) and $-ve$ (dotted line) caustic crossings computed for image A (no systematic error in source size was assumed): The derivatives were calculated using a sampling rate corresponding to the initial 3 observations of the 1988 peak. Comparing the image A seconcl-cerivative of Afin;~0.5in magnitudes per vear per dav to 1, Comparing the image A second-derivative of $\ddot{M}_{obs}\sim 0.5$ magnitudes per year per day to Fig. ":""4e. S owe infer that the 1955 peak was probably a. |ee caustic crossing.", \ref{second_deriv} we infer that the 1988 peak was probably a $+ve$ caustic crossing. A second feature to be noted from Fig., A second feature to be noted from Fig. 7 is that the 1999 peak appears to have a much longer curation than the LOSS peak., \ref{peak_compare} is that the 1999 peak appears to have a much longer duration than the 1988 peak. Fig., Fig. 9. shows scatter plots of even height above full-wiclth-at-hall-maximum (Pwhm) vs. fwhi for images A (light dots) and € (dark dots)., \ref{height_v_width} shows scatter plots of event height above full-width-at-half-maximum (fwhm) vs. fwhm for images A (light dots) and C (dark dots). The plot on he lef shows the relationship for caustic crossings while the right-hand plot is for cusp events., The plot on the left shows the relationship for caustic crossings while the right-hand plot is for cusp events. The plots hiehlight the rise-time - peak-height correlation for caustic crossings. and the cloud of points due to smooth light-curve variations (both of which were pointed out by Witt Mao (1994)).," The plots highlight the rise-time - peak-height correlation for caustic crossings, and the cloud of points due to smooth light-curve variations (both of which were pointed out by Witt Mao (1994))." The separation of the points into two categories demonstrates the intuitive notion that cusp events have lonecvy durations than caustic, The separation of the points into two categories demonstrates the intuitive notion that cusp events have longer durations than caustic reference catalogues affect the halo population only at very low redshifts and at low halo masses. much below the ranges of interest here.,"reference catalogues affect the halo population only at very low redshifts and at low halo masses, much below the ranges of interest here." We have also checked that our definition of halo mass based on the number of linked particles instead of a spherical overdensity mass estimate does not affect our result., We have also checked that our definition of halo mass based on the number of linked particles instead of a spherical overdensity mass estimate does not affect our result. As an alternative to the FOF group masses. we used as group masses the mass within the radius that encloses a mean overdensity of 200 times the critical density. or the mass within the radius where the overdensity is that expected for virialization in the generalized top-hat collapse model for our cosmology.," As an alternative to the FOF group masses, we used as group masses the mass within the radius that encloses a mean overdensity of $200$ times the critical density, or the mass within the radius where the overdensity is that expected for virialization in the generalized top-hat collapse model for our cosmology." However. we found that this did not lead to any significant differences in the large-scale clustering properties of haloes as a function of mass.," However, we found that this did not lead to any significant differences in the large-scale clustering properties of haloes as a function of mass." In the Millennium Simulation. the orbits of dark matter subhaloes are followed until tidal truncation and stripping due to encounters with larger objects cause them to fall below the simulation resolution limit (20 particles. equivalent to a mass of ~1.7x10195 ΕΜ...," In the Millennium Simulation, the orbits of dark matter subhaloes are followed until tidal truncation and stripping due to encounters with larger objects cause them to fall below the simulation resolution limit $20$ particles, equivalent to a mass of $\sim 1.7\times 10^{10}\, h^{-1}\, \rm{M}_{\odot}$ )." Galaxies follow the orbits of their host. subhalo until this point. and then their remaining survival time as satellite galaxies is estimated using their current orbit and the dynamica friction formula of ?.. calibrated as in ?..," Galaxies follow the orbits of their host subhalo until this point, and then their remaining survival time as satellite galaxies is estimated using their current orbit and the dynamical friction formula of \citet{binney87}, calibrated as in \citet{delucia07}." At the end of this interval. a satellite galaxy is assumed to merge with the central galaxy of the host dark matter halo. which can either be a subhalo or. more frequently. the main halo ofthe associated FOF group (2).," At the end of this interval, a satellite galaxy is assumed to merge with the central galaxy of the host dark matter halo, which can either be a subhalo or, more frequently, the main halo of the associated FOF group \citep{angulo08b}." In the event of a minor galaxy merger. the cold gas of the satellite galaxy is transferred to the dise component of the central galaxy together with the stars produced in a starburs (as described below): moreover. the bulge of the central galaxy grows by incorporating all the stars of the satellite.," In the event of a minor galaxy merger, the cold gas of the satellite galaxy is transferred to the disc component of the central galaxy together with the stars produced in a starburst (as described below); moreover, the bulge of the central galaxy grows by incorporating all the stars of the satellite." Tf instead a major galaxy merger has occurred. the dises of both progenitors are destroyed and all stars in the merger remnant are gathered into the spheroidal bulge component.," If instead a major galaxy merger has occurred, the discs of both progenitors are destroyed and all stars in the merger remnant are gathered into the spheroidal bulge component." " In the galaxy formation model studied here. the starbursts induced by galaxy mergers are described using the “collisional starburst” prescription introduced by ?:: the fraction epu of cold gas which is converted into stars in the merger remnant is given by: epu=Doualamasa)ne- where Opus,=0.7 and Brun,= 0.56. chosen to provide a good fit to the numerical results of ?.."," In the galaxy formation model studied here, the starbursts induced by galaxy mergers are described using the “collisional starburst” prescription introduced by \citet{somerville01}: the fraction $e_{\rm burst}$ of cold gas which is converted into stars in the merger remnant is given by: $e_{\rm burst}=\beta_{\rm burst}(m_{\rm sat}/m_{\rm central})^{\alpha_{\rm burst}}$, where $\alpha_{\rm burst}=0.7$ and $\beta_{\rm burst}=0.56$ , chosen to provide a good fit to the numerical results of \citet{cox04}." " We define as major merger remnants those galaxies that have. in the immediately preceding simulation output. two progenitors with stellar masses larger than 20% of the stellar component of the descendant (as for the FOF haloes. this imposes a minimum mass ratio HI,MIeenuwal= 14)."," We define as major merger remnants those galaxies that have, in the immediately preceding simulation output, two progenitors with stellar masses larger than $20\%$ of the stellar component of the descendant (as for the FOF haloes, this imposes a minimum mass ratio $m_{\rm sat}:m_{\rm central}=1:4$ )." Note that this definition is close. but not identical. to the distinction between minor/major mergers adopted in the underlying galaxy formation model.," Note that this definition is close, but not identical, to the distinction between minor/major mergers adopted in the underlying galaxy formation model." We use the standard definition of the as the excess probability for finding a pair of objects at a distancer. each in the volume elements dV and dW (e.g..2): where z is the average number density of the set of objects under consideration.," We use the standard definition of the as the excess probability for finding a pair of objects at a distance, each in the volume elements ${\rm d}V_{1}$ and ${\rm d}V_{2}$ \citep[e.g.,][]{peacock99}: where $n$ is the average number density of the set of objects under consideration." The between two classes of objects (e.g. haloes and dark matter) is defined as the square-root of the ratio of the corresponding two-point correlation functions: Since the number density of merging objects at a given snapshot is too low for a statistically significant auto-correlation study (see section 49). we adopt a eross-correlation analysis instead.," The between two classes of objects (e.g., haloes and dark matter) is defined as the square-root of the ratio of the corresponding two-point correlation functions: Since the number density of merging objects at a given snapshot is too low for a statistically significant auto-correlation study (see section \ref{sec:qso_clustering}) ), we adopt a cross-correlation analysis instead." In this case the bias is given by where bppa(r) is the bias (relative to the dark matter) of the population we are using as reference in our cross-correlation analysis. and $7;g(r) is the cross-correlation function between the haloes and the reference population.," In this case the bias is given by where $b_{ R, \,\rm{DM}} (r)$ is the bias (relative to the dark matter) of the population we are using as reference in our cross-correlation analysis, and $\xi_{ H,\,R}(r)$ is the cross-correlation function between the haloes and the reference population." By definition. the bias is a function of scale.," By definition, the bias is a function of scale." However. the seale dependence becomes weak or even vanishes at large scales.," However, the scale dependence becomes weak or even vanishes at large scales." Since we are here interested in the behavior of the merger bias at very large scales. we estimate the bias on these scales by finding the best constant value over the range S«r25fj.!Mpc.," Since we are here interested in the behavior of the merger bias at very large scales, we estimate the bias on these scales by finding the best constant value over the range $5 < r < 25 ~ h^{-1} \, \rm{Mpc}$." This adds robustness to our results by reducing noise from counting statistics., This adds robustness to our results by reducing noise from counting statistics. We can define the merger bias as the excess in the clustering of merger remnants at large scales with respect to the global population of objects selected with similar properties: where 5j;2 is the cross-correlation between merger remnants and the reference sample. and Sy)& is the cross-correlation between the global population and the reference sample.," We can define the merger bias as the excess in the clustering of merger remnants at large scales with respect to the global population of objects selected with similar properties: where $\xi_{M, \, R}$ is the cross-correlation between merger remnants and the reference sample, and $\xi_{H, \, R}$ is the cross-correlation between the global population and the reference sample." We estimate errors for our measurements using the bootstrap method. generating for each sample 30 bootstrapped samples of the same size. drawn at random from the parent sample and allowing for repetitions (the error estimates converge already when using just a few dozen bootstrap samples).," We estimate errors for our measurements using the bootstrap method, generating for each sample $50$ bootstrapped samples of the same size, drawn at random from the parent sample and allowing for repetitions (the error estimates converge already when using just a few dozen bootstrap samples)." For each bootstrap sample. we calculate the correlation functions. the bias and the excess bias.," For each bootstrap sample, we calculate the correlation functions, the bias and the excess bias." The standard deviation among these quantities is then taken as error estimate., The standard deviation among these quantities is then taken as error estimate. Recently. ? pointed out that the variance on the two-point correlation function is overestimated when calculated with bootstrap techniques.," Recently, \citet{norberg08} pointed out that the variance on the two-point correlation function is overestimated when calculated with bootstrap techniques." Keeping this in mind. we deliberately choose the bootstrap method in order to be conservative in our error estimates.," Keeping this in mind, we deliberately choose the bootstrap method in order to be conservative in our error estimates." Another option would have been to estimate errors by subdividing the whole Millennium volume into subvolumes (for example eight octants) and then to calculate the variance of the G(r) measured within individual subvolumes., Another option would have been to estimate errors by subdividing the whole Millennium volume into subvolumes (for example eight octants) and then to calculate the variance of the $\xi(r)$ measured within individual subvolumes. This method becomes inaccurate at large scales (few tens of Mpc) due to the smaller volume probed by each subvolume., This method becomes inaccurate at large scales (few tens of $\rm{Mpc}$ ) due to the smaller volume probed by each subvolume. In our study of the merger bias for haloeswe proceed as follows:, In our study of the merger bias for haloeswe proceed as follows: data clustering in the original parameter space.,data clustering in the original parameter space. As a consequence. they represent a larger part of the variance preseut in the original data set.," As a consequence, they represent a larger part of the variance present in the original data set." " In the sue wav, the most poorly determined modes correspond to a small portion of the variance in the data. describing features that wight not be important in our particular analysis."," In the same way, the most poorly determined modes correspond to a small portion of the variance in the data, describing features that might not be important in our particular analysis." In this context. we must determine the uuuber of PCs that will be used in the reconstruction.," In this context, we must determine the number of PCs that will be used in the reconstruction." Our decision must be balanced between how auch information we are willing to discard aud the amount of uncertainty that will not compromise our results., Our decision must be balanced between how much information we are willing to discard and the amount of uncertainty that will not compromise our results. The constraint on reconstructed with Af modes (where ALxρε and INpec is the total nuuber of PCs). is eiven by a simple error propagation of the uucertaiuties associated with each. PC (7) From this expression. if is clear that adding oue more PC adds also its associated uncertainty.," The constraint on $x$ reconstructed with $M$ modes (where $M\leqslant N_{PC}$ and $N_{PC}$ is the total number of PCs), is given by a simple error propagation of the uncertainties associated with each PC \citep{huterer03} From this expression, it is clear that adding one more PC adds also its associated uncertainty." " At this point. we uote that to calculate Fy, we mst choose ummerical values for cach parameter 2J;."," At this point, we note that to calculate $F_{kl}$ we must choose numerical values for each parameter $\beta_i$." This corresponds to specifying a base 1odel as our starting point., This corresponds to specifying a base model as our starting point. As a consequence. the results provided by PCA are interpreted as deviations from this initial model.," As a consequence, the results provided by PCA are interpreted as deviations from this initial model." The uncertainty derived from fitting the data to this base model should also be added in quadrature to equation (2)). to compute the total uncertainty in the final reconstruction.," The uncertainty derived from fitting the data to this base model should also be added in quadrature to equation \ref{eq:sigma_rec}) ), to compute the total uncertainty in the final reconstruction." The question of how many PCs should be used iu the final reconstruction is far frou simple. aud there is no standard quantitative procedure to determine it.," The question of how many PCs should be used in the final reconstruction is far from simple, and there is no standard quantitative procedure to determine it." In many cases. the decision depends ou the particulary data set analyzed aud our expectation towards them (for a complete review see ?.. chapter 6).," In many cases, the decision depends on the particular data set analyzed and our expectation towards them (for a complete review see \citet{jollife02}, chapter 6)." One practical way of facing the problein is to consider how many coniponenuts are inconsistent with zero m a particular reconstruction., One practical way of facing the problem is to consider how many components are inconsistent with zero in a particular reconstruction. Iu iiost cases. the cocthicicuts a; tend to decrease iu modulus for higher 7. at the same time as the uncertainties associated with them increases.," In most cases, the coefficients $\alpha_i$ tend to decrease in modulus for higher $i$, at the same time as the uncertainties associated with them increases." Iu this context. we can choose the final recoustruction as the one whose coefficients are all inconsistent with zero.," In this context, we can choose the final reconstruction as the one whose coefficients are all inconsistent with zero." The determination of one final recoustiuction is bevoud the scope of this work., The determination of one final reconstruction is beyond the scope of this work. " However. to provide au idea of how much of the initial variance is iucluded in our plots. we shall order them following theirPUOPTBULCO,."," However, to provide an idea of how much of the initial variance is included in our plots, we shall order them following their." The total variance preseut in the data is represeuted well by the sum of all A;. aud a reconstruction with the first AL PCs eucloses a percentage of this value (λε) given by Asa consequence. the question of how mauy PCs turus into a matter of what perceutage of total variance we are willing to cuclose.," The total variance present in the data is represented well by the sum of all $\lambda_i$, and a reconstruction with the first $M$ PCs encloses a percentage of this value $t_M$ ), given by As a consequence, the question of how many PCs turns into a matter of what percentage of total variance we are willing to enclose." " Frou, now ou. we consider the distance modulus. p. provided by type Ia supernova observations as our observed quantity Ge;= 45)."," From now on, we consider the distance modulus, $\mu$, provided by type Ia supernova observations as our observed quantity $x_i=\mu_i$ )." Ina very simple approach. if we consider a fiat. homogeneous aud isotropic Uuiverse. described by," In a very simple approach, if we consider a flat, homogeneous and isotropic Universe, described by" It is generally accepted that large. bright galaxies reside within massive dark matter halos: however. the radial extent of: the halos issystematically not wellcoustrainedlower aud. hence. icither is the total mass uor the masstolight ratio these objects.,"It is generally accepted that large, bright galaxies reside within massive dark matter halos; however, the radial extent of the halos is not well–constrained and, hence, neither is the total mass nor the mass–to–light ratio of these objects." H Galaxyt ealaxyC»tlensing. in[mM. which the Tere of foreeround galaxies weakly distort the shapes of isolated has receutly∎ proven to be a powerful the 2dFalae which the masses and mass to liehtratiosof 2dECHS is ⊯be constrained.," Galaxy–galaxy lensing, in which the halos of foreground galaxies weakly distort the shapes of background galaxies, has recently proven to be a powerful method by which the masses and mass–to–light ratios of galaxies may be constrained." " Galaxy galaxy© lensing;has are- selected )cen detected by a umber of different eroups (sec, e.g. he review bv Brainerd Blaudford 2003 aud references herein) aud. in particular. the Sloan Digital Sky Survey (SDSS) collaboration has obtained measureineuts of the ealaxvgalaxy leusiug shear with extremely high statistical ↴∖↴↕⋮↰∙↜↕∏∏≼⋡⋮↕⋯⋡≼∖≼⊏∖∙⋮↰∙↜∙∙⊟↴∖↴≼⋡↕↓⊏∖↥⋅≼∖↾⋮↕↕∙⋮⋮∩∩"," Galaxy–galaxy lensing has been detected by a number of different groups (see, e.g., the review by Brainerd Blandford 2003 and references therein) and, in particular, the Sloan Digital Sky Survey (SDSS) collaboration has obtained measurements of the galaxy–galaxy lensing shear with extremely high statistical significance (e.g., Fischer et 2000; McKay et 2001)." "∩⋮∃↕≼⋡↕⊆≷↕⋝⇁⊏∖↾⋮↕↕∙⋮⋮∩∩↕≻∙ Using weak lensing measurements of the projected mass correlation fiction. Mckay et (2001). hereafter SDSSOL. found that Age, the mass of lens ealaxics terior to a radius of 260).| kpe. scaled rouelily linearly with the Iuuiuosities of the leus galaxies iu all baudpasses except a."," Using weak lensing measurements of the projected mass correlation function, McKay et (2001), hereafter SDSS01, found that $M_{260}^{\rm lens}$, the mass of lens galaxies interior to a radius of $260 h^{-1}$ kpc, scaled roughly linearly with the luminosities of the lens galaxies in all bandpasses except $u'$." Since the galaxy lensing shear is small 0.5% in the case of the SDSS ealaxics) aud is not without its own sources of error (including the the separation of lenses from sources}. Melxay. et ((2002) performed au independent estimate of the masses of dark matter halos surronudiug SDSS ealaxics using the dvuauics of satellite ealaxies.," Since the galaxy–galaxy lensing shear is small $\ls 0.5$ in the case of the SDSS galaxies) and is not without its own sources of error (including the the separation of lenses from sources), McKay et (2002) performed an independent estimate of the masses of dark matter halos surrounding SDSS galaxies using the dynamics of satellite galaxies." Their sample consisted of 618 host ealaxics and 1225 satellites. which was considerably smaller aud shallower than the sample iu the weak leusing analysis due to the necessity of redshifts for all of the galaxies.," Their sample consisted of 618 host galaxies and 1225 satellites, which was considerably smaller and shallower than the sample in the weak lensing analysis due to the necessity of redshifts for all of the galaxies." Nevertheless. MeIvav et al. (," Nevertheless, McKay et al. (" 2002). hereafter SDSS02. found that‘ their ypedynamical 1analysisB led to trends in the dependencel1 off Aog on the1 host galaxyal --fununosity that1 were reasonably cousisteut with the treuds obtained from their previous weak lensing analysis.,"2002), hereafter SDSS02, found that their dynamical analysis led to trends in the dependence of $M_{260}^{\rm dyn}$ on the host galaxy luminosity that were reasonably consistent with the trends obtained from their previous weak lensing analysis." However. the masstolight ratios found from the dynamical analysis were than⋅ those from the leusiug⋅ analysis ⋅ ∙ (ALls260οosre f£).," However, the mass--to--light ratios found from the dynamical analysis were systematically lower than those from the lensing analysis $M_{260}^{\rm dyn}/L \sim 0.8 M_{260}^{\rm lens}/L$ )." " we perform a. dvnamiucal analysis∙∙ of. tle masses of tof host. galaxies in. the4 LOOk .public dataB release of :ialos PadehifeRedshit Survey.Suevov Ewoaftes m9 aff""DG,ο."," Here we perform a dynamical analysis of the masses of isolated host galaxies in the 100k public data release of the 2dF Galaxy Redshift Survey, hereafter 2dFGRS." ..The TRANuethodvackeround bvgalaxies. Calasa Spectroscopic survey ni which the objects ealaxies iiv in the by band frou the APM galaxy survey a ⋅ al.12199044 11990a.b). -extensions todons theson:(Maddox original et," The 2dFGRS is a spectroscopic survey in which the objects are selected in the $b_J$ band from the APM galaxy survey (Maddox et 1990a,b), and extensions to the original survey." Ultimately.a the survey will∙ PEONide. for| SUDPVOY.~250.000 ealaxies brighter than 5;=19.15 audspectra will cover an area ot: order 2000 square degrees (sec. e... Colless et 220n).," Ultimately, the survey will provide spectra for $\sim 250,000$ galaxies brighter than $b_J = 19.45$ and will cover an area of order 2000 square degrees (see, e.g., Colless et 2001)." Our host . span a recshit. range which∙∙∙∙ is similar to that of the galaxiesSDSS02 galaxies. and our sample ds of a snuar size.," Our host galaxies span a redshift range which is similar to that of the SDSS02 galaxies, and our sample is of a similar size." We select host/satellite combinations aud determine∙ dvuamical. n . the host ealaxies| based upon tie methods outlined in or in order conrpare most casily fo their results., We select host/satellite combinations and determine dynamical masses for the host galaxies based upon the methods outlined in SDSS02 in order to compare most easily to their results. In SDSSU2particular. we toinvestigate the apparent lack of dependence of ALL ou the host DIuninuositv fouud by SDSSO2. aud the somewhat low value of the dynamical masstoliebt ratio iu comparison to the lensing masstolight ratio.," In particular, we investigate the apparent lack of dependence of $M_{260}^{\rm dyn}/L$ on the host luminosity found by SDSS02, and the somewhat low value of the dynamical mass–to–light ratio in comparison to the lensing mass–to–light ratio." " Throughout. we adopt a flat. A dominated uiiverse with paruneters Oy=0.5. Ay0.1, aud My1005 km | M[pe +."," Throughout, we adopt a flat, $\Lambda$ –dominated universe with parameters $\Omega_0 = 0.3$, $\Lambda_0 = 0.7$, and $H_0 = 100h$ km $^{-1}$ Mpc $^{-1}$." " Consistent with this we take the absolute magnitude of an L galaxy in the 5; band to be My,logfh—19.66£0.07 (Norberg et al."," Consistent with this, we take the absolute magnitude of an $L^\ast$ galaxy in the $b_J$ band to be $M_{b_J}^\ast- 5 \log_{10} h = -19.66 \pm 0.07$ (Norberg et al.," 2002)., 2002). Iu order to compare to the results of --SDSS02. we sclect host aud satellite galaxies frou the 2dF survey according," In order to compare to the results of SDSS02, we select host and satellite galaxies from the 2dF survey according" radius. r2—0.5νμμ and CO huuinosity as functions of the kinematic distance for all identified objects.,"radius, $r_{e} = 0.5 \sqrt{\lmax\lmin}$ and CO luminosity as functions of the kinematic distance for all identified objects." " The lower envelope of points corresponds to the minimmun effective size of a cloud. where O, is the solid augle per pixel. D is the distauce to the object in kpe. aud NV), is the minima uuuber of pixels per object."," The lower envelope of points corresponds to the minimum effective size of a cloud, where $\Omega_s$ is the solid angle per pixel, D is the distance to the object in kpc, and $N_p$ is the minimum number of pixels per object." " For this decomposition. V,,=5 so that e!""—0211 pe."," For this decomposition, $N_p=5$ so that $r_{e}^{min}=0.31D$ pc." " Simibuly. the mininw CÓ Iuniunositv is. where IN,=2. is the minim umber of velocity channels. de=0.8L +. is the spectroscopic chauncl width. and T;,21.1 IN is the main beam antenua temperature threshold."," Similarly, the minimum CO luminosity is, where $N_c=2$, is the minimum number of velocity channels, $dv$ =0.81 , is the spectroscopic channel width, and $T_{th}$ =1.4 K is the main beam antenna temperature threshold." LUGD) is shown as the solid line in Figuve 2.., $L_{CO}^{min}(D)$ is shown as the solid line in Figure \ref{complete}. At a distance of 10 kpe. the detection limit is 67 Akins|pe.," At a distance of 10 kpc, the detection limit is 67 $K\;km\;s^{-1}\;pc^2$." While nouDY is the detection limit at a given distance. D. the completeness limit is higher than this value since the noise of the data coutributes to the measured luminosity.," While $L_{CO}^{min}(D)$ is the detection limit at a given distance, D, the completeness limit is higher than this value since the noise of the data contributes to the measured luminosity." The completeness lit. εις is defined iu this study at the 5a confidence as Where and 00.93 IN. is the meciau rus temperature for channels with no emission (ever 1998).," The completeness limit, $L_{CO}^c$ is defined in this study at the $\sigma$ confidence as where and $\sigma$ =0.93 K is the median rms temperature for channels with no emission (Heyer 1998)." At LO kpe. the cloud catalog is complete for CO luminosities > 138 AKin5s.31pet.," At 10 kpc, the cloud catalog is complete for CO luminosities $>$ 138 $K\;km\;s^{-1}\;pc^2$." This completeness Init needs to be considered when calculating power Luv descriptions to the CO huuinosity function in 52.5.1., This completeness limit needs to be considered when calculating power law descriptions to the CO luminosity function in $\S$ 2.5.1. Whenever possible. deseriptious of observable quantities are preseuted with few or no asstuuptions.," Whenever possible, descriptions of observable quantities are presented with few or no assumptions." However. for analyses described i 63.2 and 5L1. it is necessary to derive total gas column deusities and masses.," However, for analyses described in $\S$ 3.2 and $\S$ 4.1, it is necessary to derive total gas column densities and masses." Iu this investigation for which ouly oobservatious are available. οσοι deusities ave derived. using the CO to cconversion factor determined from οταν measurements such that where Woe is the Butegrated intensity in IS kun + for a eiven line of sight (Strong Mattos 1996).," In this investigation for which only observations are available, column densities are derived using the CO to conversion factor determined from $\gamma$ -ray measurements such that where $W_{CO}$ is the integrated intensity in K km $^{-1}$ for a given line of sight (Strong Mattox 1996)." Summing over the projected area of the cloud. this corresponds to a conversion from CO huninosity.Leo. iu AKns.|pe? to the total molecular mass. of the identified object. which includes the factor 1.36 to account for the abundances of heavier clemeuts CHildebranud 1983).," Summing over the projected area of the cloud, this corresponds to a conversion from CO luminosity, in $K\;km\;s^{-1}\;pc^2$ to the total molecular mass, of the identified object, which includes the factor 1.36 to account for the abundances of heavier elements (Hildebrand 1983)." The dimensional justification for a coustant conversion factor is summarized by Dickman. Scliloerb (1986).," The dimensional justification for a constant conversion factor is summarized by Dickman, Schloerb (1986)." The COluminosity is the inteeral of the antenna temperature over all velocities and area of the cloud.," The COluminosity is the integral of the antenna temperature over all velocities and area of the cloud," the excess of Lla--line Duxes of these objects.,the excess of -line fluxes of these objects. A overlap between our list of blue objects and the list of emission-line objects of τῇ shows that both criteria can be used to select LDV candidates., A overlap between our list of blue objects and the list of emission-line objects of\cite{Massey2007_Ha}] ] shows that both criteria can be used to select LBV candidates. Non cross-identilied objects of both lists also deserve a special investigation in order to understand what subclass of emission-line objects is rejected by each method., Non cross-identified objects of both lists also deserve a special investigation in order to understand what subclass of emission-line objects is rejected by each method. We included into our additional list of LBV candidates (Table 2)) only objects with V. 1600. because no red objects were selected in the Vox1500. 16700. magnitude interval. and brighter stars are. definitively foreground objects.," We included into our additional list of LBV candidates (Table \ref{FullListRed}) ) only objects with $V>16$ 0, because no red objects were selected in the $V\approx 15$ 0 magnitude interval, and brighter stars are definitively foreground objects." The fact that two red emission objects (NOOGSG2 and NI41751) are also included in the catalog of Massey etal. 2]].," The fact that two red emission objects (N006862 and N141751) are also included in the catalog of Massey et al. \cite{Massey2007_Ha}] ]," where they are classilicd as hot LBY candidates. corroborates the need for the search for reddened stars.," where they are classified as hot LBV candidates, corroborates the need for the search for reddened stars." We perform spectroscopic observations of blue emission objects with the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences., We perform spectroscopic observations of blue emission objects with the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. We already found τῃ the star N938351 whose spectrum exhibits broad. hvdrogen emissions. anc numerous bell and Foll] emission. features., We already found \cite{NewLBVinM33}] ] the star N93351 whose spectrum exhibits broad hydrogen emissions and numerous FeII and [FeII] emission features. We constructed. the spectral energy distribution for this star in the wavelength interval and showed that this object. like AA. has a strong infrared excess.," We constructed the spectral energy distribution for this star in the wavelength interval and showed that this object, like A, has a strong infrared excess." Ehe results of our analysis Hed us to conclude 2]] that N93351 should. be classified as an LDV-type star., The results of our analysis led us to conclude \cite{NewLBVinM33}] ] that N93351 should be classified as an LBV-type star. We used archive of ΕΝ] and Lla--band CCD images of the AL333 galaxy to perform aperture photometry of all objects from catalog ?]] with V.« I8*5., We used archive of UBVR and -band CCD images of the 33 galaxy to perform aperture photometry of all objects from catalog \cite{Massey2006}] ] with $V <$ . . We sclected LBY candidate, We selected LBV candidate We note that this method is not restricted to the case of the GC.,We note that this method is not restricted to the case of the GC. " It can probably be applied successfully in other cases where one is interested in accurate photometry over a large FOV in AO observations of crowded fields, but has to deal with sparse sampling of the PSF."," It can probably be applied successfully in other cases where one is interested in accurate photometry over a large FOV in AO observations of crowded fields, but has to deal with sparse sampling of the PSF." Deconvolution - at least in the linear case - can be regarded as re-imaging the data with a different set of (virtual) optics., Deconvolution - at least in the linear case - can be regarded as re-imaging the data with a different set of (virtual) optics. " However, the difference from real optics is that the true image has already been made and that the noise is already present in the data, the latter point explaining why deconvolution needs to be applied with some care."," However, the difference from real optics is that the true image has already been made and that the noise is already present in the data, the latter point explaining why deconvolution needs to be applied with some care." " In this section, I discuss whether it is valid to combine deconvolution with PSF fitting techniques and what caveats have to be kept in mind."," In this section, I discuss whether it is valid to combine deconvolution with PSF fitting techniques and what caveats have to be kept in mind." " PSF fitting is supposed to be applied to raw images, i.e., the noise statistics of the pixels should be preserved, which will be used to assign weights to the individual pixels (e.g.,?).."," PSF fitting is supposed to be applied to raw images, i.e., the noise statistics of the pixels should be preserved, which will be used to assign weights to the individual pixels \citep[e.g.,][]{Stetson:1987nx}." " Deconvolution, even if it is linear as in Wiener deconvolution, will violate this assumption to a certain degree because it will lead to covariances between the pixels."," Deconvolution, even if it is linear as in Wiener deconvolution, will violate this assumption to a certain degree because it will lead to covariances between the pixels." " This is illustrated in refFig:artim,, which shows the raw and the deconvolved version of an artificial image of a sky (2.5 counts) containing 1 star (1000 counts): The deconvolved sky shows some “granularity” caused by the covariances between the pixels."," This is illustrated in \\ref{Fig:artim}, which shows the raw and the deconvolved version of an artificial image of a sky $2.5$ counts) containing 1 star (1000 counts): The deconvolved sky shows some “granularity” caused by the covariances between the pixels." " In a Monte Carlo simulation, 100 realizations of this image plus star were created."," In a Monte Carlo simulation, 100 realizations of this image plus star were created." " Subsequently, the position and flux of the star as measured in the raw and deconvolved images were compared."," Subsequently, the position and flux of the star as measured in the raw and deconvolved images were compared." refTab:artstat gives the mean of the recovered position and flux as well as their corresponding standard deviations and the mean of the formal uncertainties estimated byStarFinder., \\ref{Tab:artstat} gives the mean of the recovered position and flux as well as their corresponding standard deviations and the mean of the formal uncertainties estimated by. The result of this simulation shows that the position and flux of the star are reliably recovered from the deconvolved image., The result of this simulation shows that the position and flux of the star are reliably recovered from the deconvolved image. " However, the standard deviation of the measurements for the deconvolved image is somewhat larger than in the raw image (e.g., increase in flux uncertainty from 0.4% in the raw image to 0.7% in the deconvolved image) and the PSF fitting algorithm underestimates the true uncertainties of position and flux by a factor of ~3.3."," However, the standard deviation of the measurements for the deconvolved image is somewhat larger than in the raw image (e.g., increase in flux uncertainty from $0.4\%$ in the raw image to $0.7\%$ in the deconvolved image) and the PSF fitting algorithm underestimates the true uncertainties of position and flux by a factor of $\sim3.3$." " In a second simulation, 100 Monte Carlo simulations were run on the artificial star field used inrefsec:simulation."," In a second simulation, 100 Monte Carlo simulations were run on the artificial star field used in." . The local PSF fitting algorithm was performed on both the raw and the deconvolved images., The local PSF fitting algorithm was performed on both the raw and the deconvolved images. " In the case of the raw images, local PSFs were created by merging locally extracted cores with the wings from the guide star PSFs."," In the case of the raw images, local PSFs were created by merging locally extracted cores with the wings from the guide star PSFs." The guide star PSF was used for the deconvolution., The guide star PSF was used for the deconvolution. Input and recovered positions and fluxes were compared to determine the true standard deviations of these quantities., Input and recovered positions and fluxes were compared to determine the true standard deviations of these quantities. Those were subsequently compared with the formal and PSF uncertainty estimates delivered by the PSF fitting algorithm., Those were subsequently compared with the formal and PSF uncertainty estimates delivered by the PSF fitting algorithm. It can be seen in refFig:simulation that the scatter in the uncertainties is lower when Wiener deconvolution is applied., It can be seen in \\ref{Fig:simulation} that the scatter in the uncertainties is lower when Wiener deconvolution is applied. It can also be clearly seen that the formal uncertainties estimated by the PSF fitting algorithm (green stars) are underestimated in the deconvolved images., It can also be clearly seen that the formal uncertainties estimated by the PSF fitting algorithm (green stars) are underestimated in the deconvolved images. The correct uncertainties can however be reproduced when the formal uncertainties in the deconvolved images are scaled by a factor of ~3 before quadratically combining them with the PSF uncertainties., The correct uncertainties can however be reproduced when the formal uncertainties in the deconvolved images are scaled by a factor of $\sim3$ before quadratically combining them with the PSF uncertainties. We note that the simulations may indicate that the PSF uncertainty is overestimated (at least for the bright stars)., We note that the simulations may indicate that the PSF uncertainty is overestimated (at least for the bright stars). " Since this is less of a problem than under-estimating the uncertainty, I have not investigated this point further for the time being."," Since this is less of a problem than under-estimating the uncertainty, I have not investigated this point further for the time being."