diff --git "a/batch_s000001.csv" "b/batch_s000001.csv" new file mode 100644--- /dev/null +++ "b/batch_s000001.csv" @@ -0,0 +1,10381 @@ +source,target +brielituess being within 1” of oue of the 128 GCs ij 2410 7.,brightness being within $''$ of one of the 428 GCs is $\times$ $^{-5}$. + We present the I magnitude. LK. colours. nüasses ages and |Fe/II| metalicities of the four GCs suspected of hosting new BIICs in Table 2.. along with the two M31 GC BICS already identified: the magnitudes were obtained from he RBC: the masses. ages and mectalicitics were drawn from ? and 7.," We present the I magnitude, I-K colours, masses ages and [Fe/H] metalicities of the four GCs suspected of hosting new BHCs in Table \ref{gcprops}, along with the two M31 GC BHCs already identified; the magnitudes were obtained from the RBC; the masses, ages and metalicities were drawn from \citet{caldwell09} and \citet{caldwell11}." + Comparison with the xoperties of the general GC population presentect we? sneeests that the GCs harboring BITC are nore luassive (brighter). aud redder / more metal rich than the general population.," Comparison with the properties of the general GC population presented by \citet{peacock10} suggests that the GCs harboring BHCs are more massive (brighter), and redder / more metal rich than the general population." + We preseut iu Fie., We present in Fig. + 5 the I vs. LK color magnitude diagram or MOI GCs: points represeu the whole GC xopulation with I aud Is maguitudes. open circles represent GCs in our field with associated X-rav endsson (see Barnard ο al.," \ref{ikcd} the I vs. I-K color magnitude diagram for M31 GCs; points represent the whole GC population with I and K magnitudes, open circles represent GCs in our field with associated X-ray emission (see Barnard et al.," + im prep). and filled’ circles represeut the six M31 GCs harboring DIICs: the mean of the whole CC population is represented by a star. the mean of the non-DIIC: N-ray GCs bv a triangle. aud the mean of the DIIC GCs is represented by a square.," in prep), and filled circles represent the six M31 GCs harboring BHCs; the mean of the whole GC population is represented by a star, the mean of the non-BHC X-ray GCs by a triangle, and the mean of the BHC GCs is represented by a square." + It appears hat the BUC GCs are a rather massive and rec subset of the GCs associated with N-rav sources., It appears that the BHC GCs are a rather massive and red subset of the GCs associated with X-ray sources. + While all of the BIC GCs are 214 times more netal rich than the mean ΑΟ CC metalicity of L.08 fouud by ?.. ancl iore massive thau : he CC population. only Bo 163 is particularly nassive and ictal rich.," While all of the BHC GCs are 2–14 times more metal rich than the mean M31 GC metalicity of $-$ 1.08 found by \citet{caldwell11}, and more massive than of the GC population, only Bo 163 is particularly massive and metal rich." +" Bo 82 is the 1th mos nassive of the 379 CC's analysed by οον, but only he LO2ud most metal rh."," Bo 82 is the 4th most massive of the 379 GCs analysed by \citet{caldwell09,caldwell11}, but only the 102nd most metal rich." + Do TLL is the 139th nost massive. but the LOth richest: indeed. it is supersolar. aud richer than any Galactic GC (?)..," Bo 144 is the 139th most massive, but the 10th richest; indeed, it is supersolar, and richer than any Galactic GC \citep{caldwell11}." + Do 153 is the 87th most massive. but the 36th richest.," Bo 153 is the 87th most massive, but the 36th richest." + Bo 163 is the 20th mos Πιννο aud the 2ist richest., Bo 163 is the 20th most massive and the 21st richest. + Bo 185 is the 53d most massive aud the 75th richest., Bo 185 is the 53rd most massive and the 75th richest. + Ποιος GCs that are either lassive or metal rich are able o produce bright N-rav sources. as well as CC's that are both.," Hence GCs that are either massive or metal rich are able to produce bright X-ray sources, as well as GCs that are both." + Despite carly indications for an absence of stellar mass black hole binarics in elobular clusters. they are becoming increasingly common.," Despite early indications for an absence of stellar mass black hole binaries in globular clusters, they are becoming increasingly common." + Out of the 35 XN-rav sources associated with elobular clusters in the central region of MOI. 5 harbor DIICs.," Out of the 35 X-ray sources associated with globular clusters in the central region of M31, 5 harbor BHCs." + Four of these appear to be persüsteutlv bright. aud are consisteut with the theoretical predictions of ? τον binaries formed bw tidal capture of a main sequence star. or for ultra-compact black hole | white dwarf binaries (?7)..," Four of these appear to be persistently bright, and are consistent with the theoretical predictions of \citet{kalogera04} for binaries formed by tidal capture of a main sequence star, or for ultra-compact black hole + white dwarf binaries \citep{ivanova10}." + However. NB1I63 is a recurring transient. and provides the first test of the theoretical predictions of ? reearding binaries formed by exchanec.," However, XB163 is a recurring transient, and provides the first test of the theoretical predictions of \citet{kalogera04} regarding binaries formed by exchange." + We fud that the GCs that are metal rich or nassive are able to produce bright N-rav sources. in addition to GCs that are both.," We find that the GCs that are metal rich or massive are able to produce bright X-ray sources, in addition to GCs that are both." + We observed 5 outbursts in the Chandra aud NADENewton observations of NB163 over ~ 1000 days: however. the large off-axis angle for NB163 in these observations mcaus that further outbursts nav have been missed.," We observed 5 outbursts in the Chandra and XMM-Newton observations of XB163 over $\sim$ 4000 days; however, the large off-axis angle for XB163 in these observations means that further outbursts may have been missed." + Four of the outbursts occurred over LLOO davs., Four of the outbursts occurred over 1100 days. + Furthermore. 7?— found 3 outbursts within LOO davs in the ROSAT observations.," Furthermore, \citet{trudolyubov04} found 3 outbursts within 400 days in the ROSAT observations." + Such behavior may be cousisteut with a black hole | main sequence star formed by exchange ?.. or due to the complex behaviour of a lack hole | white dwarf binary in a hierarchical riple svsteni. as cuvisioucd by ?..," Such behavior may be consistent with a black hole + main sequence star formed by exchange \citet{kalogera04}, or due to the complex behaviour of a black hole + white dwarf binary in a hierarchical triple system, as envisioned by \citet{ivanova10}." + We shall now discuss alternative explanations or the observed behaviour., We shall now discuss alternative explanations for the observed behaviour. + We shall discuss whether they are colucideut Ανα οσα Cluission frou multiple sources. or neutron star iuaries with beamed eniüssion.," We shall discuss whether they are coincident AGNs, blended emission from multiple sources, or neutron star binaries with beamed emission." + As discussed in the previous section. the xobabilitv of cach source being an ACN that is coincident with one of the GCs iu our field is already simall.," As discussed in the previous section, the probability of each source being an AGN that is coincident with one of the GCs in our field is already small." +" The probability that NBOs2. XDB153. X185 and NBII ave all coincident ACNs within 1"" of a CC is «10 78. since the X- LDhuninosities observed in the NAIVENewton observations used to obtain the spectra were each ower than the peak observed luuinosity iu the Chandra data."," The probability that XB082, XB153, X185 and XB144 are all coincident AGNs within $''$ of a GC is $<$ $^{-20}$, since the X-ray luminosities observed in the XMM-Newton observations used to obtain the spectra were each lower than the peak observed luminosity in the Chandra data." +" We shall now consider he possibility that the DIICs in our field are instead blends of multiple N-rav sources: dl4 dt AD. neutron star binaries accreting at Eddiustou would be required o produce the observed NMBMNE-Newton spectra of NBOS2. ND153 and XD185. aud most would rave to be persistent to account for the Chiudra σμήνος,"," We shall now consider the possibility that the BHCs in our field are instead blends of multiple X-ray sources; 4–14 1.4 $_{\odot}$ neutron star binaries accreting at Eddington would be required to produce the observed XMM-Newton spectra of XB082, XB153 and XB185, and most would have to be persistent to account for the Chandra lightcurves." +" We find that XDOS2 varied by: 107 org Liu 9 days. XB153 varied by 1075 ere s+ in 2 days. and NBISh varied by ~3\10°"" cre 1 OVCT ~ 2 hours."," We find that XB082 varied by $^{38}$ erg $^{-1}$ in 9 days, XB153 varied by $^{38}$ erg $^{-1}$ in 2 days, and XB185 varied by $\sim3\times 10^{37}$ erg $^{-1}$ over $\sim$ 2 hours." + Such variation is more Likely to come from a single source than the concerted variation, Such variation is more likely to come from a single source than the concerted variation +"temporal filtering was required; however, both the MOS and pn data trom the second observation suffered from a large flare at the start of the observation, which rendered the pn data unusable and required the MOS data to be filtered using a count rate threshold of 0.5 counts !.","temporal filtering was required; however, both the MOS and pn data from the second observation suffered from a large flare at the start of the observation, which rendered the pn data unusable and required the MOS data to be filtered using a count rate threshold of 0.5 counts $^{-1}$." +" The resulting clean, merged data had a duration of 9700 s (MOS) and 6314 s (pn)."," The resulting clean, merged data had a duration of 9700 s (MOS) and 6314 s (pn)." +" The data were used primarily in our study of the nucleus and the extended, low surface brightness diffuse emission from the group."," The data were used primarily in our study of the nucleus and the extended, low surface brightness diffuse emission from the group." +" The SHS was detected in these observations, the NHS was not."," The SHS was detected in these observations, the NHS was not." +" The larger PSF (relative to Chandra) provides no additional structural constraints, so we use only the data in our study of the hot spots."," The larger PSF (relative to ) provides no additional structural constraints, so we use only the data in our study of the hot spots." +" We present data from threeSpitzer observations of 3C 33, two data sets taken from the public archive (one IRAC and one MIPS observation, both pointed towards the SHS - program ID 3327), and an additional IRAC observation (program ID 3418) centered on the host galaxy taken by the 3CRR low-z consortium (Birkinshaw 2007. in preparation)."," We present data from three observations of 3C 33, two data sets taken from the public archive (one IRAC and one MIPS observation, both pointed towards the SHS - program ID 3327), and an additional IRAC observation (program ID 3418) centered on the host galaxy taken by the 3CRR low-z consortium (Birkinshaw 2007, in preparation)." +" The IRAC observations were made on July 23. 2004 (3327). and January 6, 2005 (3418). with observations times of 96 and 360 seconds, respectively."," The IRAC observations were made on July 23, 2004 (3327), and January 6, 2005 (3418), with observations times of 96 and 360 seconds, respectively." +" The MIPS (24 jim only) observation was made on December 23, 2004 (3327) with an observation time of 200 seconds."," The MIPS (24 $\mu$ m only) observation was made on December 23, 2004 (3327) with an observation time of 200 seconds." + The images used were produced by the data analysis pipeline version 14.1.0., The images used were produced by the data analysis pipeline version 14.1.0. + The SHS is detected in all four IRAC bands and the MIPS image., The SHS is detected in all four IRAC bands and the MIPS image. +" The NHS is only contained within theSpitzer field of view in the 2005 IRAC observation and the MIPS image, and is detected in all four IRAC bands and the MIPS 24 jim band, although there is some confusion from adjacent stars."," The NHS is only contained within the field of view in the 2005 IRAC observation and the MIPS image, and is detected in all four IRAC bands and the MIPS 24 $\mu$ m band, although there is some confusion from adjacent stars." + We also use archivalHST (WFPC and WEPC?) and VLA data in this paper., We also use archival (WFPC and WFPC2) and VLA data in this paper. +" The SHS was observed for 2400 s with the HS7/WFPC2 instrument in 1995 as part of the HST survey of hot spots (PI: P. Crane) using the F702W filter (pivot wavelength of 6919 A)), and for 1800 s with the HS7/WEPC instrument using the F606W filter (pivot wavelength of 5888 A)) 1992)."," The SHS was observed for 2400 s with the /WFPC2 instrument in 1995 as part of the survey of radio-galaxy hot spots (PI: P. Crane) using the F702W filter (pivot wavelength of 6919 ), and for 1800 s with the /WFPC instrument using the F606W filter (pivot wavelength of 5888 ) \citep{cra92}." +. There have been noHST observations of the NHS., There have been no observations of the NHS. + We obtained the reprocessed data of the SHS from theHST archive and used the IRAFsvaipAiot package to apply photometric calibrations., We obtained the reprocessed data of the SHS from the archive and used the IRAF package to apply photometric calibrations. + The fluxes were reddening-corrected using the dust maps of (1998)., The fluxes were reddening-corrected using the dust maps of \citet{sch98}. +. The correction to the flux densities is ~25% in the visual., The correction to the flux densities is $\sim$ in the visual. + A 1.5-GHz radio map with a resolution of 4.0 arcsec was obtained from the 3CRRAtlas!:: this is the image of (1991)., A 1.5-GHz radio map with a resolution of 4.0 arcsec was obtained from the 3CRR: this is the image of \citet{lp91}. +". At higher frequencies, we used 4.9 and 15-GHz data trom the VLA public archive."," At higher frequencies, we used 4.9 and 15-GHz data from the VLA public archive." + Details of the VLA data used and the maps made from them are given in Table |.., Details of the VLA data used and the maps made from them are given in Table \ref{vla}. + The data were calibrated and reduced in the standard manner using AIPS., The data were calibrated and reduced in the standard manner using AIPS. + Results from analyses of these data have been previously published in Rudnick(1988) and Rudnick&Anderson(1990)., Results from analyses of these data have been previously published in \citet{rud88} and \citet{rud90}. +". Finally, we also examined the Optical Monitor (UVM? filter) data and archivalGALEX images of 3C 33."," Finally, we also examined the Optical Monitor (UVM2 filter) data and archival images of 3C 33." + The hot spots were not detected inany of the UV images., The hot spots were not detected inany of the UV images. + The observation, The observation +"planets within our chosen M,a parameter space and v And has three (Figure 3).","planets within our chosen $M,a$ parameter space and $\upsilon$ And has three (Figure 3)." + 'These data do not support the idea that accreting planets have swept up much of the disc., These data do not support the idea that accreting planets have swept up much of the disc. +" In particular, only one system in Figure 3 (HIP 14810) appears to have a ‘starved’ outer planet and both bodies ending up near the star."," In particular, only one system in Figure 3 (HIP 14810) appears to have a `starved' outer planet and both bodies ending up near the star." +" Also, 5/11 of the systems have outer planets that are more massive than the inner planet, contradictory to the idea of sweeping through already-depleted regions of the disc."," Also, 5/11 of the systems have outer planets that are more massive than the inner planet, contradictory to the idea of sweeping through already-depleted regions of the disc." +" From a theoretical perspective, a further problem with the idea that migration can aid planet-building is that most of the gas accretion occurs in a runaway phase, with a timescale much shorter than typical migration timescales (Pollacketal.1996;Ikoma2000;Bryden 2000)."," From a theoretical perspective, a further problem with the idea that migration can aid planet-building is that most of the gas accretion occurs in a runaway phase, with a timescale much shorter than typical migration timescales \citep{pollack, ikoma00, bryden00}." +. Migration is thus implausible as a mechanism that allows a planet to sweep up its bulk in gas from a large region of the disc., Migration is thus implausible as a mechanism that allows a planet to sweep up its bulk in gas from a large region of the disc. +" However, migration could aid in the growth of the solid planetary core (Hourigan&Ward1984;Riceetal. 2003),, and this could allow the core to reach a critical mass to attract an atmosphere, while there is still sufficient gas in the disc."," However, migration could aid in the growth of the solid planetary core \citep{hourigan,rice03}, and this could allow the core to reach a critical mass to attract an atmosphere, while there is still sufficient gas in the disc." +" While migration is thus still important to planetary evolution, neither theory or observational constraints suggest that it solves the mass’ problem of discs."," While migration is thus still important to planetary evolution, neither theory or observational constraints suggest that it solves the `missing-mass' problem of discs." + Small corrections for opacity are known to be needed when converting millimetre dust emission from T Tauri discs into masses., Small corrections for opacity are known to be needed when converting millimetre dust emission from T Tauri discs into masses. +" Andrews&Williams(2007b) estimate that the ratio of optically thick to optically thin submillimetre emission is typically around 0.3, as more opacity would result in flattening of the spectrum."," \citet{aw07b} estimate that the ratio of optically thick to optically thin submillimetre emission is typically around 0.3, as more opacity would result in flattening of the spectrum." +" However, if the discs have a massive central inner region, on unresolved scales of tens of AU or less, then this could be much more optically thick — contributing significant mass, but little extra millimetre signal."," However, if the discs have a massive central inner region, on unresolved scales of tens of AU or less, then this could be much more optically thick – contributing significant mass, but little extra millimetre signal." +" Zhuetal.(2009);Rice&Armitage(2009) have recently shown that if discsare massive with respect to the star, then transport of angular momentum through disc self-gravity does in fact lead to a pile-up of material at smaller radii."," \citet{zhu09,rice09} have recently shown that if discs massive with respect to the star, then transport of angular momentum through disc self-gravity does in fact lead to a pile-up of material at smaller radii." +" A quasi-steady-state is reached in which ~80 of the disc mass ends up within 10-20 AU of the star, with a drop to lower surface densities in the model outer disc extending to 50 AU."," A quasi-steady-state is reached in which $\sim 80$ of the disc mass ends up within 10-20 AU of the star, with a drop to lower surface densities in the model outer disc extending to 50 AU." +" There is thus a physical basis for the idea of a central mass concentration, at scales relevant to planet formation."," There is thus a physical basis for the idea of a central mass concentration, at scales relevant to planet formation." +" Figure 5 shows representative spectral energy distributions (SED) of the star plus disc system -- generated using the HO-CHUNK: 3D radiation transfer code (Whitneyetal.2003) - for a standard power-law distribution of disc mass (top panel), and a case where more material has been artifically added inside 10 AU to double the total disc material (bottom panel)."," Figure 5 shows representative spectral energy distributions (SED) of the star plus disc system – generated using the HO-CHUNK: 3D radiation transfer code \citep{whitney03} – for a standard power-law distribution of disc mass (top panel), and a case where more material has been artifically added inside 10 AU to double the total disc material (bottom panel)." +" There is very little difference in the SED of the power-law and centrally-enhanced discs, especially in the millimetre regime that is canonically ‘mass tracing’."," There is very little difference in the SED of the power-law and centrally-enhanced discs, especially in the millimetre regime that is canonically `mass tracing'." +" In fact, the centrally condensed disc has a submillimetre flux that is slightly lower than that from the lower-mass, power-law disc."," In fact, the centrally condensed disc has a submillimetre flux that is slightly lower than that from the lower-mass, power-law disc." +" Therefore, if real discs are in fact massive, a central pile-up would be both theoretically predicted (Rice&Armitage2009) and not detected in millimetre images where the inner disc is unresolved."," Therefore, if real discs are in fact massive, a central pile-up would be both theoretically predicted \citep{rice09} and not detected in millimetre images where the inner disc is unresolved." +" This provides a potential solution to the missing mass, at least for discs with moderately high mass estimates already."," This provides a potential solution to the missing mass, at least for discs with moderately high mass estimates already." +The standard ACDAL cosmological model has been very successful in accouuting for observations on scales larger than around a Mpc.,The standard $\Lambda$ CDM cosmological model has been very successful in accounting for observations on scales larger than around a Mpc. + However. it appears that this model faces difficulties on the scales of ealaxies auc dwarf galaxies ((van 2000).," However, it appears that this model faces difficulties on the scales of galaxies and dwarf galaxies \markcite{2000AJ....119.1579V}( 2000)." + One such problem is that CDM. simulations of the local group of galaxies predict an order of magnitude more ciwart galaxy halos with masses ereater than ~10°AL. than there are observed satellites of the Milly Way (ATW) Galaxy aud M21 ((Moore 1999: 1999: 1998).," One such problem is that CDM simulations of the local group of galaxies predict an order of magnitude more dwarf galaxy halos with masses greater than $\sim 10^7\,\msun$ than there are observed satellites of the Milky Way (MW) Galaxy and M31 \markcite{1999ApJ...524L..19M,1999ApJ...522...82K,1998ARA&A..36..435M}( 1999; 1999; 1998)." + These simulations predict that of the virial mass of a galaxy. halo is dnosubstruetmres of nass 2LOM..., These simulations predict that of the virial mass of a galaxy halo is in substructures of mass $\simgt 10^7\msun$. + This over prediction of dwarf halos could be a sign that there is something fundamentally wrong with the CDM model., This over prediction of dwarf halos could be a sign that there is something fundamentally wrong with the CDM model. +" Proposed explanations iuclude wart dark matter (DM) which simoothes out small scale structure in the carly universe {ίοιο,Bode.Ostriker. 2001). unorthodox inflation models which break scale invariance ((Ilxanionukowski Liddle 2000) and seltiuteractiug dark matter which causes substructures to evaporate within larger halos ((Spergel 2000)."," Proposed explanations include warm dark matter (WDM) which smoothes out small scale structure in the early universe \markcite{2001ApJ...556...93B}( (e.g., 2001), unorthodox inflation models which break scale invariance \markcite{2000PRL.Kamionkowski}( (Kamionkowski Liddle 2000) and self-interacting dark matter which causes substructures to evaporate within larger halos \markcite{2000PhRvL..84.3760S}( 2000)." +" Alternatively, CDM could be correct and the sanall Dark Matter (DM) clumps could exist. but not contain stars. so as to escape detection as observable dwarf galaxies."," Alternatively, CDM could be correct and the small Dark Matter (DM) clumps could exist, but not contain stars, so as to escape detection as observable dwarf galaxies." +" This situation can casily. perhaps inevitably, come about through the action of feedback"," This situation can easily, perhaps inevitably, come about through the action of feedback" +"confirmed RR Lyrae stars,30 were RRab stars, 11 were RRc stars, and 8 were RRd's.","confirmed RR Lyrae stars,$30$ were RRab stars, $11$ were RRc stars, and $8$ were RRd's." + The RRd variable stars are discussed separately in section 3.2.., The RRd variable stars are discussed separately in section \ref{sec:rrd}. +" Figures 2--5 show the light curves for the RRab, RRc, and the other variable stars."," Figures \ref{abcurves}- \ref{othercurves} show the light curves for the RRab, RRc, and the other variable stars." +" Table 1 lists the identified variable stars, except for the RRd stars, as well as their classification, period, V and B amplitudes, intensity-weighted V and B mean magnitudes, and magnitude-weighted mean B—V color."," Table \ref{vartable} lists the identified variable stars, except for the RRd stars, as well as their classification, period, $V$ and $B$ amplitudes, intensity-weighted $V$ and $B$ mean magnitudes, and magnitude-weighted mean $B-V$ color." + The intensity-weighted mean magnitudes and the magnitude-weighted mean color were obtained through the fitting of the light curves with template light curves (Layden1998).. (, The intensity-weighted mean magnitudes and the magnitude-weighted mean color were obtained through the fitting of the light curves with template light curves \citep{ly98}. ( +"For the relation between these average quantities and the color of the equivalent static star, the reader is referred to Bono et al.","For the relation between these average quantities and the color of the equivalent static star, the reader is referred to Bono et al." + 1995.), 1995.) + Notes on some of the individual stars are in the following subsections., Notes on some of the individual stars are in the following subsections. + Table 2 contains the photometric data for the variable stars., Table \ref{phottable} contains the photometric data for the variable stars. + We use a naming system that is an extension of the one used in Wesselink (1971).., We use a naming system that is an extension of the one used in \citet{we71}. . +" Walker identified the variable stars found by Wesselink by their number in that paper,"," Walker identified the variable stars found by Wesselink by their number in that paper," +physical) means surface mass density perturbations in the two coupled discs are in-phase.,physical) means surface mass density perturbations in the two coupled discs are in-phase. + Stationary surface mass density perturbations in both clises scale in the forms of -xpreLid in azimuthal angle 6., Stationary surface mass density perturbations in both discs scale in the forms of $\propto\mu e^{-\hbox{i}m\theta}$ in azimuthal angle $\theta$. + For aligned perturbations. we have further taken fox where 5 is a positive/negative constant exponent.," For aligned perturbations, we have further taken $\mu\propto r^{-\varepsilon}$ where $\varepsilon$ is a positive/negative constant exponent." + For example in subsection. 3.1. we have chosen 5;=a1|24 for coplanar perturbations carrying the same radial power-LIaw dependence of the background equilibrium disc svstem.," For example in subsection 3.1, we have chosen $\varepsilon=\alpha=1+2\beta$ for coplanar perturbations carrying the same radial power-law dependence of the background equilibrium disc system." + On the other hand. for ¢ being a complex constant exponent. perturbations would appear in spiral forms. namely. the so-called logarithmic spiral ppxrNPexpi3s)Inr] where We) and Be) are the real and imaginary parts ος.," On the other hand, for $\varepsilon$ being a complex constant exponent, perturbations would appear in spiral forms, namely, the so-called logarithmic spiral $\mu\propto r^{-\Re(\varepsilon)}\exp +[-\hbox{i}\Im(\varepsilon)\ln r]$ where $\Re(\varepsilon)$ and $\Im(\varepsilon)$ are the real and imaginary parts of $\varepsilon$." + To ensure the gravitational potential perturbation arising [ron this perturbed surface mass density as computed by Poisson integral (4)) being finite requires mlsm2 (Qian 1992)., To ensure the gravitational potential perturbation arising from this perturbed surface mass density as computed by Poisson integral \ref{fish}) ) being finite requires $-m+1<\Re(\varepsilon) relation is not well understood., The physical basis for the $K-z$ relation is not well understood. + A ow redshifts. the emission is dominated by the ol stellar population in the host galaxy: at high redshifts. samples rest-[ramoe optical wavelengths. where the star ormation history can have a significant. οσοι.," At low redshifts, the emission is dominated by the old stellar population in the host galaxy; at high redshifts, samples rest-frame optical wavelengths, where the star formation history can have a significant effect." + Non-stellar contamination to the light. in the form of reddened quasar light and/or narrow emission lines. also contributes to the difficulty of interpreting the dyz diagram of radio ealaxies. particularly at high redshifts (223).," Non-stellar contamination to the light, in the form of reddened quasar light and/or narrow emission lines, also contributes to the difficulty of interpreting the $K-z$ diagram of radio galaxies, particularly at high redshifts $z > +3$ )." + Despite these caveats. the ἐνz diagram is still of interest as a tool for recshift estimation.," Despite these caveats, the $K-z$ diagram is still of interest as a tool for redshift estimation." + ltedshift estimates based on the Az diagram have seenerally been obtained. by simple application of the empirical A> relation (e.g. Dunlop Peacock 1990)., Redshift estimates based on the $K-z$ diagram have generally been obtained by simple application of the empirical $K-z$ relation (e.g. Dunlop Peacock 1990). + llowever. the significant amount of scatter around this relation requires the use of à more sophisticated: method one which takes into account all the available information in the clagram. and also which allows us to characterise the uncertainty on the output redshift’ estimates.," However, the significant amount of scatter around this relation requires the use of a more sophisticated method – one which takes into account all the available information in the diagram, and also which allows us to characterise the uncertainty on the output redshift estimates." + With these requirements in mind the following approach is adopted: (i) we use Monte Carlo simulations to generate a statistical universe of svnthetic realisations of the Ας diagram. based on à model of its underlving galaxy distribution. and (ii) we extract individual photometric redshift probability density functions from this simulated. population.," With these requirements in mind the following approach is adopted: (i) we use Monte Carlo simulations to generate a statistical universe of synthetic realisations of the $K-z $ diagram, based on a model of its underlying galaxy distribution, and (ii) we extract individual photometric redshift probability density functions from this simulated population." + The most well defined. A2 diagram [or radio galaxies currently available is the one obtained by Willott et. al. (, The most well defined $K-z$ diagram for radio galaxies currently available is the one obtained by Willott et al. ( +2003) from a combined dataset of the radio galaxies [roni the ὃςπι (Laine. Riley Longair 1983). GCE (Eales οἱ al.,"2003) from a combined dataset of the radio galaxies from the 3CRR (Laing, Riley Longair 1983), 6CE (Eales et al." + 1997: Rawlines. Eales Lacy 2001). 6C (Jarvis et al.," 1997; Rawlings, Eales Lacy 2001), 6C* (Jarvis et al." + 2001a.b) and TORS (Lacy ct al.," 2001a,b) and 7CRS (Lacy et al." + 2000. Willott ct al.," 2000, Willott et al." + 2003) Ilux-lipited. samples., 2003) flux-limited samples. +" LO is based. on a total of 204 racio ealaxies with redshifts ranging from 0.05 to 4.4. and its Az relation is well fitted by a second-order polynomial between dy-magnitude anc log),2 (Willott et al."," It is based on a total of 204 radio galaxies with redshifts ranging from 0.05 to 4.4, and its $K-z$ relation is well fitted by a second-order polynomial between $K$ -magnitude and $\log_{10} z$ (Willott et al." + 2003): The main advantage of using this fv2 diagram is that it has been obtained from completely identified samples with close to complete. or complete redshift) information.," 2003): The main advantage of using this $K-z$ diagram is that it has been obtained from completely identified samples with close to complete, or complete redshift information." + This ensures the absence of significant biases in terms of sources with the weakest lines being missed. because their redshifts are cillicult to obtain., This ensures the absence of significant biases in terms of sources with the weakest lines being missed because their redshifts are difficult to obtain. +" Another advantage is that these samples have been selected at a similar radio-frequency to 6C**, with progressively fainter Dux-density limits."," Another advantage is that these samples have been selected at a similar radio-frequency to 6C**, with progressively fainter flux-density limits." + The brightest sample is 83CRAR selected at MMIETZ. with a flux-density limit of στ> 10.9.J.]v (8124c 12.4]v. assuming a spectral index of 0.8): the faintest sample is TORS selected at MMLbIz. with a Ilux-densitv limit of Sy.)2 0.5.JJv.," The brightest sample is 3CRR selected at MHz, with a flux-density limit of $S_{178} +\geq 10.9$ Jy $S_{151} \geq 12.4$ Jy, assuming a spectral index of 0.8); the faintest sample is 7CRS selected at MHz, with a flux-density limit of $S_{151} \geq 0.5$ Jy." + The intermediate samples are GCE and 6€7 selected. at MAIIz. with llux-density limits of 2.0 which represents the elect of the dressing of the colliding particles hy the gravitational polarization induced around them by their own inlluence.," The diffusion coefficient involved depends on the 1-body distributions themselves, in particular through the factor $\mid \!{\cal{D}}\!\mid^{-2}$ which represents the effect of the dressing of the colliding particles by the gravitational polarization induced around them by their own influence." + Unlike in electrical plasmas. the polarization dressing in sell-gravitational systems does not cause any screening of the interaction. which remains elfective even between distant. particles.," Unlike in electrical plasmas, the polarization dressing in self-gravitational systems does not cause any screening of the interaction, which remains effective even between distant particles." + The mutual distance of such particles is limited only. by the finite size of the system., The mutual distance of such particles is limited only by the finite size of the system. + Were the gravitational inlluence of particles on their surrounding to be neglected. the response matrix 5 (equation. (34))) would. reduce to unity and the coellicients of the corresponding Fokker-Planck kinetic. equation would simply be averages by the distribution functions of functions of velocity. as in equations (52))— (53)).," Were the gravitational influence of particles on their surrounding to be neglected, the response matrix $\varepsilon$ (equation \ref{epsilonalphabeta}) )) would reduce to unity and the coefficients of the corresponding Fokker-Planck kinetic equation would simply be averages by the distribution functions of functions of velocity, as in equations \ref{Asanseffetscoll}) ) – \ref{Bsanseffetscoll}) )." + ]t is apparent from the developments of appendix A. which lead to equation (38)). that the k component in angle Fourier space of the gravitational polarization response given to a particle has frequency w=k-Q.," It is apparent from the developments of appendix \ref{grossesmagouilles}, which lead to equation \ref{LAequation}) ), that the ${\mathbf{k}}$ component in angle Fourier space of the gravitational polarization response given to a particle has frequency $\omega = {\mathbf{k}}\! \cdot \! {\mathbf{\Omega}}$." + This means that the polarization cloud. which accompanies a particle forms a structure in angle space which vary as wo£6: it corotates in angle with that particle., This means that the polarization cloud which accompanies a particle forms a structure in angle space which vary as ${\mathbf{w}} - {\mathbf{\Omega}}t$: it corotates in angle with that particle. +" The presence of the Dirac function 0(k;:€,Κυ£22) in equation (38)) indicates that particles interact. resonantly.", The presence of the Dirac function $\delta({\mathbf{k}}_1\!\cdot {\mathbf{\Omega}}_1 - {\mathbf{k}}_2\!\cdot {\mathbf{\Omega}}_2)$ in equation \ref{LAequation}) ) indicates that particles interact resonantly. + This certainly is an important physical property of remote interactions. for which the components of the angle wave vectors Κι and k» must be small.," This certainly is an important physical property of remote interactions, for which the components of the angle wave vectors ${\mathbf{k}}_1$ and ${\mathbf{k}}_2$ must be small." +" For closer encounters. the modulus of these wave vectors is larger and the resonance condition ky,-Q)=ko:Qe becomes less selective. being more easily. satisficc."," For closer encounters, the modulus of these wave vectors is larger and the resonance condition ${\mathbf{k}}_1\cdot {\mathbf{\Omega}}_1 = {\mathbf{k}}_2\cdot {\mathbf{\Omega}}_2$ becomes less selective, being more easily satisfied." + The correlation function has been calculated on the basis of a linearized theory. which is justified by the weakness of the average interactions in this many-body system.," The correlation function has been calculated on the basis of a linearized theory, which is justified by the weakness of the average interactions in this many-body system." + This means that the trajectories of the particles during the collision are regarded as being the unperturbed trajectories., This means that the trajectories of the particles during the collision are regarded as being the unperturbed trajectories. + Similarly. the gravitational polarization cloud around any one of the colliding particles is caleulated as if the partner in the collision were not present: equation (38)) is still à weak collision approximation.," Similarly, the gravitational polarization cloud around any one of the colliding particles is calculated as if the partner in the collision were not present: equation \ref{LAequation}) ) is still a weak collision approximation." + A cutolf at small impact. parameters is therefore needed to account for the rare strong collisions., A cutoff at small impact parameters is therefore needed to account for the rare strong collisions. + Equation (38)) takes full account of the inhomogeneity of the system. which is embodied. in the dependence of the distribution functions on the actions J's. Lt requires no artificial cutoff at large impact parameters.," Equation \ref{LAequation}) ) takes full account of the inhomogeneity of the system, which is embodied in the dependence of the distribution functions on the actions $\mathbf{J}$ 's. It requires no artificial cutoff at large impact parameters." + The details of the trajectories followed by the particles in the present gravitational potential are also fully accounted for. being implicit in the relations which link the angle anc action variables to the position and momentum ones.," The details of the trajectories followed by the particles in the present gravitational potential are also fully accounted for, being implicit in the relations which link the angle and action variables to the position and momentum ones." + These relations depend on the actual global gravitational potential of the svstem. which slowly evolves in time together with the distribution functions.," These relations depend on the actual global gravitational potential of the system, which slowly evolves in time together with the distribution functions." + The clensity-potential basis functions (C7(r) are choosen at the beginningὃνe of the calculation once and for all. but their angleo Fourier transforms csk(J). which depend on the actual trajectories of the particles. changeD with time because the trajectoryJ ofa particle of given actions slowly evolves with the general potential of the svstem as the relaxation proceeds.," The density-potential basis functions $\psi^{\alpha}({\mathbf{r}})$ are choosen at the beginning of the calculation once and for all, but their angle Fourier transforms $\psi^{\alpha}_{\mathbf{k}}({\mathbf{J}})$, which depend on the actual trajectories of the particles, change with time because the trajectory of a particle of given actions slowly evolves with the general potential of the system as the relaxation proceeds." + As long as it sullers no collision. a given particle keeps its vector J fixed because the actions are acliabatic invariants.," As long as it suffers no collision, a given particle keeps its vector ${\mathbf{J}}$ fixed because the actions are adiabatic invariants." +" Collisions. however. cause a secular evolution of the functions f£""(J). which is exactly what equation (38)) describes."," Collisions, however, cause a secular evolution of the functions $f^a({\mathbf{J}})$, which is exactly what equation \ref{LAequation}) ) describes." + The description of particle motions is mace simple by the use of action and angle variables., The description of particle motions is made simple by the use of action and angle variables. + Their complexity is embocied in the supposedly known relation between position and momentum variables and action and angle variables., Their complexity is embodied in the supposedly known relation between position and momentum variables and action and angle variables. + The usefulness, The usefulness +positions.,positions. + The back-traced initial conditions are listed in the third column of table , The back-traced initial conditions are listed in the third column of table (3). +"Incidentally, these initial conditions are close to a (3).multi-resonant configuration where Saturn Uranus and Uranus Neptune are both in 4:3 MMR’s."," Incidentally, these initial conditions are close to a multi-resonant configuration where Saturn Uranus and Uranus Neptune are both in 4:3 MMR's." + Recall that this initial condition is indeed one of the setups that consistently exhibit scattering., Recall that this initial condition is indeed one of the setups that consistently exhibit scattering. +" However, given the similarities in dynamical evolutions among the successful initial conditions of this family, at this level of accuracy, it is probably safe to say that all four of them are compatible with the classical Nice model results."," However, given the similarities in dynamical evolutions among the successful initial conditions of this family, at this level of accuracy, it is probably safe to say that all four of them are compatible with the classical Nice model results." +" Let us now consider the final family of initial conditions, listed in table where Jupiter and Saturn are initially in a 2:1 MMR."," Let us now consider the final family of initial conditions, listed in table (1), where Jupiter and Saturn are initially in a 2:1 MMR." +" (1),Unlike the scenario of the classical Nice model (Tsiaganis et al.", Unlike the scenario of the classical Nice model (Tsiaganis et al. +" 2005), there are no major resonances to cross for Jupiter and Saturn between the 2:1 and the 5:2 MMR’s."," 2005), there are no major resonances to cross for Jupiter and Saturn between the 2:1 and the 5:2 MMR's." +" Consequently, a different mechanism, involving different resonances, is needed to create the instability."," Consequently, a different mechanism, involving different resonances, is needed to create the instability." + Thommes et al. (, Thommes et al. ( +"2008) considered the dynamical evolution of a system where Jupiter Saturn are in a 2:1 MMR, Saturn Uranus are in a 3:2 MMR, and Uranus Neptune are in a 4:3 MMR.","2008) considered the dynamical evolution of a system where Jupiter Saturn are in a 2:1 MMR, Saturn Uranus are in a 3:2 MMR, and Uranus Neptune are in a 4:3 MMR." +" In such a system, the instability is triggered by Uranus and Neptune crossing a 7:5 MMR."," In such a system, the instability is triggered by Uranus and Neptune crossing a 7:5 MMR." +" Due to a weaker, second-order nature of this resonance, the eccentricity increase is rather small."," Due to a weaker, second-order nature of this resonance, the eccentricity increase is rather small." +" Incidentally in this particular system, this is enough for the ice giants to cross orbits and scatter off of each other, but not off of one of the gasgiants?."," Incidentally in this particular system, this is enough for the ice giants to cross orbits and scatter off of each other, but not off of one of the gas." +. It appears that somewhat larger eccentricities are needed., It appears that somewhat larger eccentricities are needed. +" Testing each initial condition with a large number of numerical simulations, as discussed above, is rather time-consuming."," Testing each initial condition with a large number of numerical simulations, as discussed above, is rather time-consuming." +" Consequently, it is worthwhile to quantify the amplitudes of eccentricity jumps due to various resonance crossings before-hand if possible."," Consequently, it is worthwhile to quantify the amplitudes of eccentricity jumps due to various resonance crossings before-hand if possible." +" For this set of initial conditions, under the assumption of adiabatic migration, the eccentricity jumps are deterministic and can be estimated analytically (Henrard 1982)."," For this set of initial conditions, under the assumption of adiabatic migration, the eccentricity jumps are deterministic and can be estimated analytically (Henrard 1982)." +" Following the treatment of (Peale 1986, see also Murray Dermott we consider the planar internal first-order j:(j—1) 1999),resonant Hamiltonian where is the mean longitude, 7=c is the longitude of perihelion, A=(mmo)/(m+mo)/G(mom)a T=A(1—V1-—e?) are their respective Poincaré conjugate momenta, and the prime designates the outer planet."," Following the treatment of (Peale 1986, see also Murray Dermott 1999), we consider the planar internal first-order $j:(j-1)$ resonant Hamiltonian where $\lambda$ is the mean longitude, $\gamma=\varpi$ is the longitude of perihelion, $\Lambda = (m \ m_{\odot})/(m + m_{\odot})\sqrt{G(m_{\odot}+m)a}$ $\Gamma = \Lambda (1-\sqrt{1-e^2})$ are their respective Poincaré conjugate momenta, and the prime designates the outer planet." +" The secular changes in mean longitude and longitude of perihelion are accounted for by the last four terms, while f(a/a’) arises from the classical expansion of the planetary disturbing potential and is a function of Laplace coefficients and their derivatives."," The secular changes in mean longitude and longitude of perihelion are accounted for by the last four terms, while $f(a/a')$ arises from the classical expansion of the planetary disturbing potential and is a function of Laplace coefficients and their derivatives." +γάμο on observations of the local universe.,based on observations of the local universe. + Differential counts are very sensitive to the exact shape of the PALL eatures. which are crucely modelled here.," Differential counts are very sensitive to the exact shape of the PAH features, which are crudely modelled here." + One could. also imagine that the cliscrepancy is partly due to the grain size distribution/chemical composition evolution with redshift. as the redshift) distribution of ISOCAM ealaxies has a meclian z 0.7.," One could also imagine that the discrepancy is partly due to the grain size distribution/chemical composition evolution with redshift, as the redshift distribution of ISOCAM galaxies has a median $z \approx$ 0.7." + We plan to investigate these issues in more detail but that is bevond the scope of this paper., We plan to investigate these issues in more detail but that is beyond the scope of this paper. + Finally. »eceause of the way interactions are mocoelled. cach carly vpe galaxy undergoes a starburst after its host halo has just. collapsed. and it is not obvious that ISOCAM sources (sce figure 3)) in which the vast majority are LItCis (not ULIRGs). are properly described by such a violent. process.," Finally, because of the way interactions are modelled, each early type galaxy undergoes a starburst after its host halo has just collapsed, and it is not obvious that ISOCAM sources (see figure \ref{figinf}) ) in which the vast majority are LIRGs (not ULIRGs), are properly described by such a violent process." + Dvnamical interactions (which are not mocelec in. detail rere). trigecring multiple milder starbursts. with time delays oetween them. might. provide a more realistic description of hese sources and this is another issue we plan to investigate in the future.," Dynamical interactions (which are not modeled in detail here), triggering multiple milder starbursts, with time delays between them, might provide a more realistic description of these sources and this is another issue we plan to investigate in the future." + Another constraint on our models comes from the recdshift distributions., Another constraint on our models comes from the redshift distributions. + Their shapes seem to quite nicelv match the observations in the L band with a mean redshift’ of the distribution of ~ 0.6. (see top left. panel of figure 5)).," Their shapes seem to quite nicely match the observations in the I band with a mean redshift of the distribution of $\sim$ 0.6, (see top left panel of figure \ref{figred}) )." + In the farHt (GO microns). the agreement with cata eathered in the north ecliptie pole region (NEPR) is also fairly convincing.," In the far–IR (60 microns), the agreement with data gathered in the north ecliptic pole region (NEPR) is also fairly convincing." + As predicted in Silk Devriendt. (2000). inclusion of the cosmological constant. A. has shifted the nearLR ancl GO micron peaks towards higher recshifts aud produced a highrecshift tail in the L band. bringing the models into closer agreement with the data.," As predicted in Silk Devriendt (2000), inclusion of the cosmological constant, $\Lambda$, has shifted the near–IR and 60 micron peaks towards higher redshifts and produced a high–redshift tail in the I band, bringing the models into closer agreement with the data." + Disks and early-types are found in comparable proportion in the I-band. with a slight domination of disks for z>0.3 and up to z—1.5.," Disks and early-types are found in comparable proportion in the I-band, with a slight domination of disks for $z>0.3$ and up to $z=1.5$." + There are at least a couple of reasons for this behaviour., There are at least a couple of reasons for this behaviour. + First. in this redshift range. spheroids are already old. their star formation rates are very low and therefore their I-band luminosity comes from an old and dim stellar population.," First, in this redshift range, spheroids are already old, their star formation rates are very low and therefore their I-band luminosity comes from an old and dim stellar population." + secondly. spheroids in a massive starburst phase at. these redshift’ experience high dust. absorption. which reduces," Secondly, spheroids in a massive starburst phase at these redshift experience high dust absorption, which reduces" +independent. but recent results. (Bullockctal.2001.. Wechlseretal. 2002)) show a correlation between these parameters.,"independent, but recent results \citealt{Bul:01}, , \citealt{We:02}) ) show a correlation between these parameters." + The NEW clensity distribution is then a one-parameter familv. namely the virial mass Ale;," The NFW density distribution is then a one-parameter family, namely the virial mass $M_{vir}$." +" From Wechlseret.al.(2002) we take the relations linking AJ,.;, to the concentration parameter e(=res£r). rs and py. at redshift z=0 and for a Universe with A=0.7 and £3,=0.3. starting with Al,;,=ο Ovhere Aj, is the virial overdensity ancl its valueana, is about 337 at 2=0. py is the critical density of the Universe and rà; is the virial radius): NEW halo has then a central density cusp. with prowox [or r+0. and a prolile/amplitude which is controlled v a free parameter AM,"," From \citet{We:02} we take the relations linking $M_{vir}$ to the concentration parameter $c~(=r_{vir}/r_s)$, $r_s$ and $\rho_s$, at redshift $z=0$ and for a Universe with $\Lambda = 0.7$ and $\Omega_0 = 0.3$, starting with $M_{vir} \equiv \frac {4}{3} \pi \Delta_{vir} \rho_{c} r_{vir}^3$ (where $\Delta_{vir}$ is the virial overdensity and its value is about 337 at $z=0$, $\rho_{c}$ is the critical density of the Universe and $r_{vir}$ is the virial radius): NFW halo has then a central density cusp, with $\rho_{\rm NFW} +\propto r^{-1}$ for $r \rightarrow 0$, and a profile/amplitude which is controlled by a free parameter $M_{vir}$." + Notice that in principle. aciabatic contraction of the »imordial dark matter halo due to barvon infall should be aken into account. but since the ellect is to render the malo evenmore concentrated. aggravating thus the known xoblems of the NEW haloes. we neglect. it.," Notice that in principle, adiabatic contraction of the primordial dark matter halo due to baryon infall should be taken into account, but since the effect is to render the halo evenmore concentrated, aggravating thus the known problems of the NFW haloes, we neglect it." +" We constrain the virial halo mass to be Mz,δ1 AL. in that. for a low luminosity spiral. it must. presumably » substantially lower than that of the Alilky Was and other very luminous galaxies. for which it is safely estimated Als&21095 M. (Chengalur.Salpeter& Terzian 1993.. Wilkinson&Evans 1999))."," We constrain the virial halo mass to be $M_{vir}<8 \times 10^{11}$ $_{\odot}$, in that, for a low luminosity spiral, it must presumably be substantially lower than that of the Milky Way and other very luminous galaxies, for which it is safely estimated: $M_{vir} \simeq 2 \times 10^{12}$ $_{\odot}$ \citealt{C:93}, \citealt{W:99}) )." + This constraint allects only N7339 and ESO 79-C1H. due to the relatively [limited extension of their rotation curves. which prevents to rule out large AC'DAL haloes.," This constraint affects only N7339 and ESO 79-G14, due to the relatively limited extension of their rotation curves, which prevents to rule out large $\Lambda$ CDM haloes." +" ltecent numericalsimulations by Mooreetal.(1998). vielded a more concentrated. density. profile: where p, and ry are the characteristic density ancl the scale racius of the distribution.", Recent numericalsimulations by \citet{Mo:98} yielded a more concentrated density profile: where $\rho_s$ and $r_s$ are the characteristic density and the scale radius of the distribution. + This density cistribution has an even sleeper cusp (ptsXV Laefor r: 0) than the previous one.," This density distribution has an even steeper cusp $\rho_{\rm Moore} +\propto r^{-1.5}$ for $r \rightarrow 0$ ) than the previous one." + Similarly to the NEW halo. we consider this profile as having only one free parameter.," Similarly to the NFW halo, we consider this profile as having only one free parameter." + Following Mooreetal. (1999)... we define exij;ose as being L8 times smaller than exp: it is then derived from Iq. 9..," Following \citet{Mo:99}, we define $c_{\rm Moore}$ as being 1.8 times smaller than $c_{\rm NFW}$; it is then derived from Eq. \ref{cmvir}." + For a given virial radius. the scale radius 7; of the Moore halo will then be 1.8 times larger than its corresponding quantity for the NEW halo.," For a given virial radius, the scale radius $r_s$ of the Moore halo will then be 1.8 times larger than its corresponding quantity for the NFW halo." +" p, can be derived from: Also in this case we constrain the virial halo mass to be lower than 8-104 M.", $\rho_s$ can be derived from: Also in this case we constrain the virial halo mass to be lower than $8 \times 10^{11}$ $_{\odot}$. + Early studies of rotation curves (Bosma1981) noted the fact that the ratio between the surface density and the dark matter surface density is approximately constant in the outer parts of galaxies (but. see. Corbelli&Salucei2000)).," Early studies of rotation curves \citep{Bo:81} + noted the fact that the ratio between the surface density and the dark matter surface density is approximately constant in the outer parts of galaxies (but see \citealt{Cor:00}) )." + This led to the hypothesis that dark matter could in some wav be associated with the disc and cistributed in the same manner: this is what is reasonable to expect in the case of models considering for instance HI» clumps as a component of dark matter (Pfenniger.Combes1994)., This led to the hypothesis that dark matter could in some way be associated with the disc and distributed in the same manner; this is what is reasonable to expect in the case of models considering for instance $_2$ clumps as a component of dark matter \citep*{Pf:94}. +. In this case the scaling factor for the contribution to the rotation curve is a free parameter., In this case the scaling factor for the contribution to the rotation curve is a free parameter. + According to MOND. the law of Mocified Newtonian Dynamics (Ailerom—1983)... there exists ᾱ certain acceleration ay below which Newton's law of gravity is no longer valid ancl the expression for the gravitational acceleration reads: where A(r) account for the stellar and gaseous components and au=12;10cms 7 (Begeman.Brocils&Sanders1991 ).," According to MOND, the law of Modified Newtonian Dynamics \citep{Mi:83}, , there exists a certain acceleration $a_0$ below which Newton's law of gravity is no longer valid and the expression for the gravitational acceleration reads: where $M(r)$ account for the stellar and gaseous components and $a_0=1.2 \times 10^{-8}$ cm $^{-2}$ \citep*{Beg:91}." +". The fits were performed by a X7-mininisation. considering both the rotational velocities and their logarithmic gradients (Vo=at), which bear a crucial information on the matter distribution in a ealaxy (see Persic&Salucci1990))."," The fits were performed by a $\chi^2$ -minimisation, considering both the rotational velocities and their logarithmic gradients $\nabla= \frac {d{\rm log} V(r)}{d{\rm log}r}$ ), which bear a crucial information on the matter distribution in a galaxy (see \citealt{PS:90}) )." +" The total 47 value to be mininiised then is xz,=No,|Ns", The total $\chi^2$ value to be minimised then is $\chi^2_{tot}=\chi^2_{vel}+\chi^2_{\nabla}$. + It is worthwhile to point out that the X7 values should only ος considered as à way to compare the dilferent fits within he same galaxy. rather than a probability indicator. because he choice of the error bars is quite subjective and. we plot wo points per beam. so the points are not independent: the goodness of a particular mass model is also related to the raction of observational points that it hits within 1 σ as well as the ones that it baclly misses.," It is worthwhile to point out that the $\chi^2$ values should only be considered as a way to compare the different fits within the same galaxy, rather than a probability indicator, because the choice of the error bars is quite subjective and we plot two points per beam, so the points are not independent; the goodness of a particular mass model is also related to the fraction of observational points that it hits within 1 $\sigma$ as well as the ones that it badly misses." + μα Figs., In Figs. + 9 to 13 we show. for each galaxy. the results of he fits. the residuals (Vins— τω) of the fits and the 10 obabilitv contours in parameter space.," \ref{116} to \ref{7339} we show, for each galaxy, the results of the fits, the residuals $V_{obs}-V_{model}$ ) of the fits and the 1 $\sigma$ probability contours in parameter space." + The case of NGC 7339 will be discussed in Appendix A. The Burkert prolile so as any cored profile has the vest fits to the rotation curves. with no systematic deviation rom the observed rotation curves seen in all galaxies.," The case of NGC 7339 will be discussed in Appendix A. The Burkert profile – so as any cored profile – has the best fits to the rotation curves, with no systematic deviation from the observed rotation curves seen in all galaxies." + None of our LOO data points (considering the five galaxies ogether) is inconsistent with this model. having a residual weer than 3 σ (where & is the observational error).," None of our $\sim$ 100 data points (considering the five galaxies together) is inconsistent with this model, having a residual larger than 3 $\sigma$ (where $\sigma$ is the observational error)." + The stellar banc mass-to-light ratios. which lie between 0.5 and LS. are consistent with population synthesis mocoels (ce... Dell&deJong 2001)).," The stellar I-band mass-to-light ratios, which lie between 0.5 and 1.8, are consistent with population synthesis models (e.g., \citealt{BdJ:01}) )." + The core radii are in the range (0.7 μεν and the central densities are between (0.4 3) 10?! e em.," The core radii are in the range (0.7 – 2.3) $\times~ r_{opt}$, and the central densities are between (0.4 – 3) $\times$ $^{-24}$ g $^{-3}$." + In Fig., In Fig. + LE we plot the galaxies of our sample in the poMoore plane of Burkert (1995).. slightly adapted to spiral galaxies by Salucci&Burkert (2000): despite à certain scatter. they roughly follow the relation. which certainly has animplication for the nature of dark matter.," \ref{bur} we plot the galaxies of our sample in the $\rho_0~-~r_{core}$ plane of \citet{B:95}, , slightly adapted to spiral galaxies by \citet{SB:00}: : despite a certain scatter, they roughly follow the relation, which certainly has animplication for the nature of dark matter." + The minimum X values for the NEW haloes are significantly higher than for theBurkert haloes., The minimum $\chi^2$ values for the NFW haloes are significantly higher than for theBurkert haloes. + The former fail to reproduce both the velocities and. the shape of the observed. rotation curves., The former fail to reproduce both the velocities and the shape of the observed rotation curves. + Moreover. there is à systematic," Moreover, there is a systematic" +"latter correlation test GL, versus Adio). the result was the same with both Adio values for VY Aqr.","latter correlation test $L_{x}$ versus $M_{WD}$ ), the result was the same with both $M_{WD}$ values for VY Aqr." +" Excluding GW Lib decreased the significance to 91 per cent (L, versus AZo nae)and to 63 per cent CL, versus Adi).", Excluding GW Lib decreased the significance to 91 per cent $L_{x}$ versus $kT_{max}$ )and to 63 per cent $L_{x}$ versus $M_{WD}$ ). + We have analvsed the X-ray spectra of 13 dwarl novae with accurate parallax-based distance estimates. and derived the most accurate shape for the X-ray luminosity function. of DNe in the 210 keV band to date due to accurate distance measurements and due to the fact that we did not use an X-ray selected sample.," We have analysed the X-ray spectra of 13 dwarf novae with accurate parallax-based distance estimates, and derived the most accurate shape for the X-ray luminosity function of DNe in the 2–10 keV band to date due to accurate distance measurements and due to the fact that we did not use an X-ray selected sample." +" The derived X-ray luminosities are. located between ~ LO 107 erg showing. a peak at ~ 10""'E erg +."," The derived X-ray luminosities are located between $\sim$ $^{28}$ $^{32}$ erg $^{-1}$, showing a peak at $\sim$ $^{30}$ erg $^{-1}$." + Thus. we have obtained peal: luminosities which are lower compared to other previous studies of CV. luminosity functions.," Thus, we have obtained peak luminosities which are lower compared to other previous studies of CV luminosity functions." +" The shape of the X-ray luminosity function of the source sample suggests that the two following scenarios are possible: 1) the sample can be described by a power law with a single a slope. but the sample becomes more incomplete below ~ 3. 107""t cre + than it+ is+ above this. limit.. or. 2) the shape of the real X-ray luminosity function of dwarf novae is à broken power law with a break at around. 3 107 org "," The shape of the X-ray luminosity function of the source sample suggests that the two following scenarios are possible: 1) the sample can be described by a power law with a single $\alpha$ slope, but the sample becomes more incomplete below $\sim$ 3 $\times$ $^{30}$ erg $^{-1}$ than it is above this limit, or, 2) the shape of the real X-ray luminosity function of dwarf novae is a broken power law with a break at around 3 $\times$ $^{30}$ erg $^{-1}$." +The integrated. luminosity between 1 107 erg s and the maximum luminosity of the sample. 1.50. 1077 ere lods LAS 107 erg .," The integrated luminosity between 1 $\times$ $^{28}$ erg $^{-1}$ and the maximum luminosity of the sample, 1.50 $\times$ $^{32}$ erg $^{-1}$, is 1.48 $\times$ $^{32}$ erg $^{-1}$." + In order to better constrain the integrated luminosity and. the slope of the N-ray luminosity function. more dwarf novae need to be included in the sample.," In order to better constrain the integrated luminosity and the slope of the X-ray luminosity function, more dwarf novae need to be included in the sample." + Εις. we suggest more future N-rav. imaging observations of dwarf novae in the 210 keV band with accurate distance measurements.," Thus, we suggest more future X-ray imaging observations of dwarf novae in the 2–10 keV band with accurate distance measurements." + The total X-ray emissivity of the sample within a radius of 200 pe is 1.81. 1075 erg LN (210 keV)., The total X-ray emissivity of the sample within a radius of 200 pc is 1.81 $\times$ $^{26}$ erg $^{-1}$ $^{-1}_{\odot}$ (2–10 keV). + This accounts for ~ 16 per cent of the total X-ray. emissivity of CVs as estimated by(2006).. and. ~ 5 per cent of the Galactic Riclge X-ray enmissivitsy.," This accounts for $\sim$ 16 per cent of the total X-ray emissivity of CVs as estimated by, and $\sim$ 5 per cent of the Galactic Ridge X-ray emissivity." + Vhe X-ray luminosities and the inclinations of our sample do not show anti-correlation which has been seen in other previous correlation studies. but a strong correlation is seen between the X-ray luminosities and the orbital periods.," The X-ray luminosities and the inclinations of our sample do not show anti-correlation which has been seen in other previous correlation studies, but a strong correlation is seen between the X-ray luminosities and the orbital periods." + Also. evidence for a correlation between the white dwarf masses and the shock temperatures exists.," Also, evidence for a correlation between the white dwarf masses and the shock temperatures exists." + In the future. larger cbwarl nova samples are needed in order to confirm these results.," In the future, larger dwarf nova samples are needed in order to confirm these results." + This research has made use of cata obtained from. the satellite. a collaborative mission between the space agencies of Japan (JANA) and the USA (NASA).," This research has made use of data obtained from the satellite, a collaborative mission between the space agencies of Japan (JAXA) and the USA (NASA)." + JO acknowledges support from. STEC., JO acknowledges support from STFC. +. Part of this work ds based on observations obtained with XAZAZ-Neiwlon. an ESA science mission with instruments and contributions directly Funded by ESA Member States and the USA (NASA).," Part of this work is based on observations obtained with , an ESA science mission with instruments and contributions directly funded by ESA Member States and the USA (NASA)." + We thank the reviewer M. Hoevnivtsev for his helpful comments on this paper., We thank the reviewer M. Revnivtsev for his helpful comments on this paper. +Iu recent vears. the WWide-Field Camera (WFC) aud theExplorer All-Skyv Monitor AASMD have identified two classes of faint low-1ass N-vav binary (LAINB) that iav be closely related: ow-huuimositv trausicuts and low-huuinosity bursters.,"In recent years, the Wide-Field Camera (WFC) and the All-Sky Monitor ASM) have identified two classes of faint low-mass X-ray binary (LMXB) that may be closely related: low-luminosity transients and low-luminosity bursters." + The low-hnuumositv transients consist of a rather Inhomogeneous eroup of about 15 LAINBs with outbursts hat last from a few davs to several mouths. aud. ect no xighter than a few times 1076st. which corresponds ο an accretion rate of 10 citep|e.g..|[zand(0..," The low-luminosity transients consist of a rather inhomogeneous group of about 15 LMXBs with outbursts that last from a few days to several months, and get no brighter than a few times $10^{36}$, which corresponds to an accretion rate of $10^{-10}$ \\citep[e.g.,][]{zand00}." + This distinguishes the low-huninosity ransicuts frou more casily detected transient LAINBs such as Aql X-1 that usually exhibit outbursts brighter han 1075 and from which faint outbursts are ess conumuon (e.g.Simon2002).," This distinguishes the low-luminosity transients from more easily detected transient LMXBs such as Aql X-1 that usually exhibit outbursts brighter than $10^{37}$, and from which faint outbursts are less common \citep[e.g.,][]{sim02}." +". The faintuess of these outbursts has been attributed to average mass trausfor rates of M<10HALL citepzando0, kingdO.."," The faintness of these outbursts has been attributed to average mass transfer rates of $\dot{M} \lesssim 10^{-11}$ \\citep{zand00, king00}." + The low-luninosity trausieuts have attracted particular attention because they include the our known accreting millisecond X-ray pulsars (Wijuaudsetal.2002:Maiurkwiurdt 2003).," The low-luminosity transients have attracted particular attention because they include the four known accreting millisecond X-ray pulsars \citep{wk98,mar02,gal02,mar03}." +. For this reason. it as been livpothesized that the low average accretion rates allow relatively strong C105 Cass) maenetie fields to oersist on the surfaces of the ucutron stars among these LMXDSs. whereas the surface field is buried im svstemis with Neher accretion rates (Cunuuus. Zweibel Bildsten 2001).," For this reason, it has been hypothesized that the low average accretion rates allow relatively strong $> 10^{8}$ Gauss) magnetic fields to persist on the surfaces of the neutron stars among these LMXBs, whereas the surface field is buried in systems with higher accretion rates (Cumming, Zweibel, Bildsten \nocite{cum01}." +. The low-huuinositv X-rav bursters are sources frou which bright thermomuclear X-ray bursts (sce Lewin. vau Daradijs. Taam 1993 for a lave been observed with the WWEC. and vet there was no evidence for X-ray emission roni persistent accretion at the time of the burst (Cocchietal.2001:Cornelisse 2002a.b).," The low-luminosity X-ray bursters are sources from which bright thermonuclear X-ray bursts (see Lewin, van Paradijs, Taam 1993 for a \nocite{lvt93} have been observed with the WFC, and yet there was no evidence for X-ray emission from persistent accretion at the time of the burst \citep{coc01,cor02a,cor02b}." +. This sample of low- bursters may represent a large population of uidiscovered neutron star X-ray binaries. depending upon iow often these systems produce bursts.," This sample of low-luminosity bursters may represent a large population of undiscovered neutron star X-ray binaries, depending upon how often these systems produce bursts." + The intervals )etwoeen X-ray bursts is a strong function of the accretion rate per unit area onto the neutron star. which determines tow quickly a sufficicut column of material is collected for icliumi burning to become unstable (e.g..Bildsten2000).," The intervals between X-ray bursts is a strong function of the accretion rate per unit area onto the neutron star, which determines how quickly a sufficient column of material is collected for helium burning to become unstable \citep[e.g.,][]{bil00}." +. Since the nuclear energy iu accreted materialis at most of the exavitational cucrey that it emitted during accretion (Lewinetal.1993).. sufficient. nuclear energy to produce an easily-detectable 10°? cre burst is collected iu 5 hows ou the suface of a neutron star producing 10°? oof X-rays through accretion (corresponding tfo an accretion rate of 10tt Ly) while such a burst could uot occur for several vears on a star enüitting persistently at 1072 (104! 1jj ," Since the nuclear energy in accreted material is at most of the gravitational energy that it emitted during accretion \citep{lvt93}, sufficient nuclear energy to produce an easily-detectable $10^{39}$ erg burst is collected in 5 hours on the surface of a neutron star producing $10^{35}$ of X-rays through accretion (corresponding to an accretion rate of $10^{-11}$ ), while such a burst could not occur for several years on a star emitting persistently at $10^{32}$ $10^{-14}$ )." +Unfortuately. thePeppoSAX WEC could only place an upper limit of 1079 oon the huunositv of persisteutly faint bursters close to the Galactic center. so estimates of the frequency of bursts from the low-huunosity bursters are uncertain bv several orders of magnitude.," Unfortunately, the WFC could only place an upper limit of $10^{36}$ on the luminosity of persistently faint bursters close to the Galactic center, so estimates of the frequency of bursts from the low-luminosity bursters are uncertain by several orders of magnitude." + Therefore. the nuuber of low-huninosity bursters can oulv be guessed within a factor of 1000. and it is still possible that παν of them are also faint N-rav trausicuts.," Therefore, the number of low-luminosity bursters can only be guessed within a factor of 1000, and it is still possible that many of them are also faint X-ray transients." +" ds both a faiut transient svsteni aud οΓΕ,", is both a faint transient system and a low-luminosity +The spectrum of the secimentecd powder is in good agreement with the result οἱ the calenlation for a CDE with PE environment (see velο indicatinglhepresenceofaconsiderab(sdmnaet oar Π Πω [romsphericals,"The spectrum of the sedimented powder is in good agreement with the result of the calculation for a CDE with PE environment (see \\ref{f:PE_CDE}) ), indicating the presence of a considerable fraction of grains with shapes far away from spherical symmetry." + Conversely. we find that the mean CDE is a good representation of the shape distribution of a real calcite powder with grain sizes within the Ravleigh limit.," Conversely, we find that the mean CDE is a good representation of the shape distribution of a real calcite powder with grain sizes within the Rayleigh limit." + This justilies the use of (his shape distribution for the comparison with observed. data αἱ large wavelengths., This justifies the use of this shape distribution for the comparison with observed data at large wavelengths. + In the following (see sect.44.1) we wil apply this model to simulate dust spectra at low temperatures., In the following (see 4.1) we will apply this model to simulate dust spectra at low temperatures. + The laboratory spectra presented so far are especially relevant [or a comparison with FUR spectra of cold dust in objects such as the planetary nebula NGC 6302., The laboratory spectra presented so far are especially relevant for a comparison with FIR spectra of cold dust in objects such as the planetary nebula NGC 6302. + Ilence. we shall first give a brief review οἱ some key properties of the dust spectrum of this object.," Hence, we shall first give a brief review of some key properties of the dust spectrum of this object." + 694m and another possible broad band feature in (he range of jum. While the jum feature was attributed to crystalline ice (see also Waters οἱ 11996). the uim feature was suspected to be due to crvstalline forsterite and the question for (he carrier of the jmi band remained open.," Barlow (1997) observed features 65 and $\mu$ m and another possible broad band feature in the range of $\mu$ m. While the $\mu$ m feature was attributed to crystalline ice (see also Waters et 1996), the $\mu$ m feature was suspected to be due to crystalline forsterite and the question for the carrier of the $\mu$ m band remained open." + Molster οἱ ((2001) identified the e-65 mn band as a blend. of diopside and crystalline water ice with enstatite., Molster et (2001) identified the $\sim$ $\mu$ m band as a blend of diopside and crystalline water ice with enstatite. + They also confirmed the reality. of the broad feature around jn and suspected that there should be a verv cold dust component present in the nebula., They also confirmed the reality of the broad feature around $\mu$ m and suspected that there should be a very cold dust component present in the nebula. + Kemper et ((2002a.b) first. assigned and the broad emission band around 90;0n to cold calcite dust.," Kemper et (2002a,b) first assigned and the broad emission band around $\mu$ m to cold calcite dust." + As already mentioned above. the temperature of the carbonate dust was asstumecl to be in the 30-GOIXIX range.," As already mentioned above, the temperature of the carbonate dust was assumed to be in the K range." + A mass [raction ol less than (for calcite as well as for dolomite) has been derived by these autliors., A mass fraction of less than (for calcite as well as for dolomite) has been derived by these authors. + We retrieved an ISO-SWS and an I5O-INS spectrum of NGC 6302 from the ISO archive and reduced it by means of the OLP version 10.0., We retrieved an ISO-SWS and an ISO-LWS spectrum of NGC 6302 from the ISO archive and reduced it by means of the OLP version 10.0. + From (he composite spectrum (ranging from jm). we subtracted a combination of Planck functions for temperatures of 30. 55 and IXIx. The remaining residual dust emission. is shown in for the jan range: the," From the composite spectrum (ranging from $\mu$ m), we subtracted a combination of Planck functions for temperatures of 30, 55 and K. The remaining `residual dust emission' is shown in \\ref{f:resid1} for the $\mu$ m range; the" +These optical path mocdulations can be servo controlled using opto-electronie systems previously developed for such kinds of applications (Delageetal (2000): Olivieretal (2005))).,These optical path modulations can be servo controlled using opto-electronic systems previously developed for such kinds of applications \cite{D}; ; \cite{O2}) ). + Lt allows to monitor. with a manometric accuracy. the lincarity of the optical path variation as a function of time.," It allows to monitor, with a nanometric accuracy, the linearity of the optical path variation as a function of time." +" For cach scan. the olfset (OO,fLyay is set in order to display. the signal. that would be observed at. y positionPI forB a classical spatial hypertelescope."," For each scan, the offset $\frac{(OO_i)_y \cdot y}{f}$ is set in order to display the signal that would be observed at $y$ position for a classical spatial hypertelescope." + To properly operate a temporal hyvpertelescope. the optical path mocdulators are driven by an 8 channel function e&enerator and related. high. voltage electronics (not drawn in the picture).," To properly operate a temporal hypertelescope, the optical path modulators are driven by an 8 channel function generator and related high voltage electronics (not drawn in the picture)." + The output voltage drives the optical path mocdulators with a full span in the range of tens yam and a typical nanometric sensitivity., The output voltage drives the optical path modulators with a full span in the range of tens $\mu m$ and a typical nanometric sensitivity. + Phe electronic gain and the voltage generator slopes allow to set the v7; frequencies at the proper values., The electronic gain and the voltage generator slopes allow to set the $\nu _i$ frequencies at the proper values. + In such a configuration. we can theoretically eet the same imagine properties as for the first. classical design using spatial pupil densification.," In such a configuration, we can theoretically get the same imaging properties as for the first classical design using spatial pupil densification." + Lhe breadboard described in this paper and the related experimental results reported in the next paragraphs aim to demonstrate the validity of this new concept., The breadboard described in this paper and the related experimental results reported in the next paragraphs aim to demonstrate the validity of this new concept. + Our experimental set-up. (see figure 5)) has been designed and implemented thanks to the different skills developed in our team for two decades (Allemanetal.1995: Simohamect&Revnaucd199 llussctal 2001: Perrinctal 2006:: Olivieretal 2007))., Our experimental set-up (see figure \ref{schema_complet}) ) has been designed and implemented thanks to the different skills developed in our team for two decades \citealt{All}; \citealt{S}; \citealt{H}; \citealt{Perrin}; \citealt{O}) ). + Consequently. our ΕΙ) experimental test bench uses optical fibres ancl couplers for the cilferent optical functions to be implemented.," Consequently, our THT experimental test bench uses optical fibres and couplers for the different optical functions to be implemented." + Llowever. we would like to stress that the use of guided. optics components is not mandatorv for the implementation of a THT.," However, we would like to stress that the use of guided optics components is not mandatory for the implementation of a THT." + A ‘lassical design with classical components could be chosen if preferred., A classical design with classical components could be chosen if preferred. + “Phis point will remain a minor one as long as we will focus more on the demonstration of TIET. principle mn on the technological aspects., This point will remain a minor one as long as we will focus more on the demonstration of THT principle than on the technological aspects. + The following items give 1e &eneral framework of our experimental study., The following items give the general framework of our experimental study. + The following sections summarize the “VIP bench structure., The following sections summarize the THT bench structure. + It consists of three main parts (cf Fig.5)): a star simulator. a telescope array and a combining interferometer.," It consists of three main parts (cf \ref{schema_complet}) ): a star simulator, a telescope array and a combining interferometer." + The calibrated: object is the first. subsystem: required. for testing the imaging capability of a ΕΕ., The calibrated object is the first subsystem required for testing the imaging capability of a THT. + For this. first experimental demonstration. the selected astronomical target is a binary star with a convenient angular separation ancl adjustable For this purpose. the object consists of two tips of monomode Panda fibres glued on a V-groove.," For this first experimental demonstration, the selected astronomical target is a binary star with a convenient angular separation and adjustable For this purpose, the object consists of two tips of monomode Panda fibres glued on a V-groove." + These monomode waveguides are fed by two independent Distributed FeedBack lasers (DEB) with the same emitting wavelength. and. act as two incoherent point like sources., These monomode waveguides are fed by two independent Distributed FeedBack lasers (DFB) with the same emitting wavelength and act as two incoherent point like sources. + This way the object is spatially incoherent and the dyvnanics is controlled. by adjusting the laser driving currents., This way the object is spatially incoherent and the dynamics is controlled by adjusting the laser driving currents. + A set of doublets ancl collimating lenses allows to. provide an angular intensity distribution compatible with the spatial frequencies ov sampled by our telescope array., A set of doublets and collimating lenses allows to provide an angular intensity distribution compatible with the spatial frequencies $u$ sampled by our telescope array. + In our experiment the angular separation (5. as seen by the telescope array. is 23.75pad.," In our experiment the angular separation $\theta_{0} $, as seen by the telescope array, is $23.75 \mu rad$." + As our instrument ts designed for a linear input polarization. a polarizing cube is inserted in the doublet spacing in order to select. and fixes a linear vertical input polarization (not drawn on fig 5)).," As our instrument is designed for a linear input polarization, a polarizing cube is inserted in the doublet spacing in order to select and fixes a linear vertical input polarization (not drawn on fig \ref{schema_complet}) )." + The experimental setup can be seen in fig.6.., The experimental setup can be seen in \ref{photo_objet}. + The telescope array arrangement has to be carefully selected. to fit the sampling criteria for a proper image analysis., The telescope array arrangement has to be carefully selected to fit the sampling criteria for a proper image analysis. + As previously demonstrated (Armancletal.2008).. high dynamics imaging capability requires a recluncant array configuration.," As previously demonstrated \citep{A}, high dynamics imaging capability requires a redundant array configuration." + Consequently. our telescope array must periodically sample the spatial frequency domain.," Consequently, our telescope array must periodically sample the spatial frequency domain." + The object dimension and the focal length of the collimator have to be determined by comparing the object spectrum and the spatial frequencies sampled by our instrument., The object dimension and the focal length of the collimator have to be determined by comparing the object spectrum and the spatial frequencies sampled by our instrument. + The intensity ανν) observed in the image plane of the instrument isgiven by :, The intensity $I(At;y)$ observed in the image plane of the instrument isgiven by : +Of the 17 galaxies in the Noo et al. (1995)),Of the 17 galaxies in the Koo et al. \cite{koo95}) ) + sample of ‘dnt blue galaxies. niue have redshifts such that the CO J-2-l aud J=3-2 lines are accessible with the IRAM receivers.," sample of faint blue galaxies, nine have redshifts such that the CO J=2-1 and J=3-2 lines are accessible with the IRAM receivers." + Three of these nine galaxies are somewhat nore extended than the other six aud iudeed appear ion-stellar iu eround-based. optical observations (lXoo et al. 1995))., Three of these nine galaxies are somewhat more extended than the other six and indeed appear non-stellar in ground-based optical observations (Koo et al. \cite{koo95}) ). + We excluded these three. galaxies frou our siuuple on the erounds that they may be somewhat more nassive objects; akin perhaps to small spiral ealaxics.," We excluded these three galaxies from our sample on the grounds that they may be somewhat more massive objects, akin perhaps to small spiral galaxies." + Observations of five of the remaining six galaxies were obtained with the IRAM 30 12 telescope in two separate observing runs in January 1996 aud June 1997., Observations of five of the remaining six galaxies were obtained with the IRAM 30 m telescope in two separate observing runs in January 1996 and June 1997. +" The sixth galaxy. SÀ57-5182. was not observed due to tine constraints,"," The sixth galaxy, SA57-5482, was not observed due to time constraints." +" The halfpower beam width is 17"" at 2uni aud 12"" at 1.3nuu.", The half-power beam width is $^{\prime\prime}$ at 2--mm and $^{\prime\prime}$ at 1.3–mm. + We used the 2 and 1.3nuu SiS receivers to observe both lines simultaneously., We used the 2– and 1.3–mm SiS receivers to observe both lines simultaneously. + The receivers were all used iu single sideband mode. aud the vpieal svstein temperatures were 250-500 [KK for the 2uni receiver and 350-700 Is. for the 1.9nuu receiver. in M scale (or. ou average.S GOO IS ar 1200 I in Tap scale. respectively).," The receivers were all used in single sideband mode, and the typical system temperatures were 250-500 K for the 2--mm receiver and 350-700 K for the 1.3–mm receiver, in $_A^*$ scale (or, on average, 600 K and 1200 K in $_{MB}$ scale, respectively)." + The backeuds were esseutiallv two 1MIIZ-filter-bauks. of 512 channels cach. and in addition au auto-correlator: the spectra have been snoothed to 10 km 1 resolution.," The backends were essentially two 1MHz-filter-banks, of 512 channels each, and in addition an auto-correlator; the spectra have been smoothed to 10 km $^{-1}$ resolution." + The observations were made using a nutatiug secondary with a beam throw of 1.5’. The poiuting was checked every two hours aud the Εμ accuracy was estimated to be 3” rns., The observations were made using a nutating secondary with a beam throw of $^\prime$ The pointing was checked every two hours and the pointing accuracy was estimated to be $^{\prime\prime}$ rms. + The spectra were first iuspected. aud any spectruii showing baseline. curvature or other artifacts was discarded.," The spectra were first inspected, and any spectrum showing baseline curvature or other artifacts was discarded." + The remaining spectra were averaged togetlier. weighted by their rus noise.," The remaining spectra were averaged together, weighted by their rms noise." + A first order bascline was removed from cach average spectrin. and the spectra were smoothed to a resolution of 10 kins |! to produce the final spectra (Fie. 1)).," A first order baseline was removed from each average spectrum, and the spectra were smoothed to a resolution of 10 km $^{-1}$ to produce the final spectra (Fig. \ref{fig-1}) )." + The final temperatures (aud rnis noise in Table 1) have heen converted to the Ta;p teirperature scale Gjape=0.15 at 230 Cz. 0.59 at 150 CGIIz).," The final temperatures (and rms noise in Table 1) have been converted to the $T_{MB}$ temperature scale $\eta_{MB} = 0.45$ at 230 GHz, 0.59 at 150 GHz)." + Upper liuits to the integrated CO intensity were derived using the riis noise measured from the CO spectra aud the velocity widths obtained frou measurements of optical ciission lines (soo et al. 1995))., Upper limits to the integrated CO intensity were derived using the rms noise measured from the CO spectra and the velocity widths obtained from measurements of optical emission lines (Koo et al. \cite{koo95}) ). + We adopt as the 3c upper limit to the CO intensity (Wiklind Combes 199bj). where o is the τις nolse in K measured in our 10 kin | channels AV is the velocity width of the CO line. here taken to be the balfanaxinuun of the optical lines. and IN44 lans Lis the umuber of chaunels in the velocity width.," We adopt as the $\sigma$ upper limit to the CO intensity (Wiklind Combes \cite{wik94b}) ), where $\sigma$ is the rms noise in K measured in our 10 km $^{-1}$ channels, $\Delta V$ is the velocity width of the CO line, here taken to be the full-width half-maximum of the optical lines, and $N_{chan} = \Delta V/10$ km $^{-1}$ is the number of channels in the velocity width." + The CO luminosity for a source at hieli redshift is eiven by where 5 is the area of the main beam iu square areseconds aud Dp=(eTT?\dotEUMLTT24021)| is the huninosity distance in Mpc (Wikliud Combes 1991b))., The CO luminosity for a source at high redshift is given by where $\Omega_B$ is the area of the main beam in square arcseconds and $D_L = (c/H_o q_o^2)[q_o z + (q_o-1)(\sqrt{1+2q_oz}-1)]$ is the luminosity distance in Mpc (Wiklind Combes \cite{wik94b}) ). +" We adopt q,=0.5 aud 7L,=70 kin E E in this paper.", We adopt $q_o=0.5$ and $H_o = 70$ km $^{-1}$ $^{-1}$ in this paper. + Table 1 gives the position. redshift. aud velocity width obtained from the optical cussion lines (Isoo ct al. 1995)).," Table \ref{tbl-1} gives the position, redshift, and velocity width obtained from the optical emission lines (Koo et al. \cite{koo95}) )," + as well as the iuteeration time. the nus noise for cach line. aud the CO integrated intensity and CO luminosity calculated from the CO J=3-2 upper limit.," as well as the integration time, the rms noise for each line, and the CO integrated intensity and CO luminosity calculated from the CO J=3-2 upper limit." + Our upper limits to the CO flux are comparable to the best upper limits in the literature for moderate to high redshift objects., Our upper limits to the CO flux are comparable to the best upper limits in the literature for moderate to high redshift objects. + For example. the detections of CO J=3-2 emission at hieh redshift are 6.7 Jv hans 1 for IRAS F1021111721 (Radford ct al. 1996))," For example, the detections of CO J=3-2 emission at high redshift are 6.7 Jy km $^{-1}$ for IRAS F10214+4724 (Radford et al. \cite{radford}) )" + and 8.1 Jy laus. ! for the Cloverleaf (Barvainis ct al. 1991)).," and 8.1 Jy km $^{-1}$ for the Cloverleaf (Barvainis et al. \cite{barvainis}) )," + while our 30 upper linits rauge from 2 to 8 Jv lau +., while our $\sigma$ upper limits range from 2 to 8 Jy km $^{-1}$. + If ow ealaxies had comparable CO fluxes to IRAS F102111172 lor the Cloverleaf quasar. we would have detected them with our observations.," If our galaxies had comparable CO fluxes to IRAS F10214+4724 or the Cloverleaf quasar, we would have detected them with our observations." + In addition. if we asstme the amplification duc to lensing is a factor of 10 in the two hieh redshift ealaxies. their CO huninosities Lew (converted to our cosinologyv) are 8.9<10? and 1.31019 Wy lan »pe. respectirverv.," In addition, if we assume the amplification due to lensing is a factor of 10 in the two high redshift galaxies, their CO luminosities $L_{CO}$ (converted to our cosmology) are $8.9\times 10^9$ and $1.3\times 10^{10}$ K km $^{-1}$ $^2$, respectively." +. Thus.; we would have detected either of these wo galaxies. uuleused. at a redshift of 2~0.5.," Thus, we would have detected either of these two galaxies, unlensed, at a redshift of $z \sim 0.5$." + Since these faint blue galaxies are thought o be distaut counterparts o UTM galaxies. we should also compare our upper lanits with CO observations of nearby ον ealaxies.," Since these faint blue galaxies are thought to be distant counterparts to HII galaxies, we should also compare our upper limits with CO observations of nearby dwarf galaxies." + The CO J=1-0 luminosities of the starburst ealaxy M82 aud the IIII galaxy. UME18 are both Lew—510 Nus ! pe? (ealeulated from Young et al. 1995:, The CO J=1-0 luminosities of the starburst galaxy M82 and the HII galaxy UM448 are both $L_{CO} \sim 5\times 10^8$ K km $^{-1}$ $^2$ (calculated from Young et al. \cite{young}; + Sage et al. 1992))., Sage et al. \cite{sage}) ). + Unfortunately. our ost upper limits are still a factor of LS larecr than the buuinosities of these nearby dwarf galaxies. aud so we would not have detected AIS2 or UALIS at 2~0.5.," Unfortunately, our best upper limits are still a factor of 4-8 larger than the luminosities of these nearby dwarf galaxies, and so we would not have detected M82 or UM448 at $z\sim 0.5$." +" For galaxies iu the local universe with ucar-solar metallicities and normal rates of star formation (1.6.not starburst galaxies). the mass of molecular hydrogen gas is related to the CO luminosity iu the J=1-0 line by Adj,=LSLeo Gc. Solomon et al. 1987))."," For galaxies in the local universe with near-solar metallicities and normal rates of star formation (i.e.not starburst galaxies), the mass of molecular hydrogen gas is related to the CO luminosity in the J=1-0 line by $M_{H_2} = 4.8 L_{CO}$ $_\odot$ (i.e. Solomon et al. \cite{sol87}) )." + Siuce we have observed the CO J—2-1 aud J=3-2 lines. we lust consider the excitation of the eas in estimating nolecular eas masses.," Since we have observed the CO J=2-1 and J=3-2 lines, we must consider the excitation of the gas in estimating molecular gas masses." + In ealactic nuclei. the three trausitious have," In galactic nuclei, the three transitions have" +is Comparable with the extent of the virialized (relaxed) core of a cluster.,is comparable with the extent of the virialized (relaxed) core of a cluster. + Analyses of x-ray observations and dvnamical calculations on these scales make a variety of equilibrium and svinmeltry assumptions., Analyses of x-ray observations and dynamical calculations on these scales make a variety of equilibrium and symmetry assumptions. + Generally. agreement among (he various mass estimation techniques on this scale is impressive.," Generally, agreement among the various mass estimation techniques on this scale is impressive." + Although there are still puzzles about clusters and their evolution. their central regions are reasonably well-studied over a wide redshift range.," Although there are still puzzles about clusters and their evolution, their central regions are reasonably well-studied over a wide redshift range." + Many fewer observational studies have addressed the infall region thiat marks the transition between the cluster core and the surrounding large-scale structure., Many fewer observational studies have addressed the infall region that marks the transition between the cluster core and the surrounding large-scale structure. + At least in part. this inattention reflects the observational challenges of observing these larger. less dense regions.," At least in part, this inattention reflects the observational challenges of observing these larger, less dense regions." + Now wilh wide-field spectroscopic instruments like the Ilectospec on the MALT (Fabricant et al., Now with wide-field spectroscopic instruments like the Hectospec on the MMT (Fabricant et al. + 1998: Fabricant et al., 1998; Fabricant et al. +" 2005). it is possible to acquire dense samples of these fascinating regions (hat lie between Iso, and Ry... the radius of the shell of material just turning around from the ILIubble flow at redshift z (Gunn Gott 1972: Kaiser 1987; Reeos Geller 1939)."," 2005), it is possible to acquire dense samples of these fascinating regions that lie between $_{200}$ and $_{turn}$, the radius of the shell of material just turning around from the Hubble flow at redshift $z$ (Gunn Gott 1972; Kaiser 1987; Regos Geller 1989)." + The infall region is a route to understanding the growth rate of clusters. their ultimate masses. and the relationship between galaxy and cluster evolution (Dialerio Geller 1997: Ellingson et al.," The infall region is a route to understanding the growth rate of clusters, their ultimate masses, and the relationship between galaxy and cluster evolution (Diaferio Geller 1997; Ellingson et al." + 2001: Busha et al., 2001; Busha et al. + 2005: Rines et al., 2005; Rines et al. + 2005: Tran et al., 2005; Tran et al. + 2005)., 2005). + On the scale of the infall region. there are only two techniques to probe the matter distribution. weak lensing (e.g. Lemze et al.," On the scale of the infall region, there are only two techniques to probe the matter distribution, weak lensing (e.g. Lemze et al." + 2009: Umetsu et al., 2009; Umetsu et al. + 2011) and a kinematic technique called the caustic method (Diaferio Geller 1997: Dialerio 1999: Serra et al., 2011) and a kinematic technique called the caustic method (Diaferio Geller 1997; Diaferio 1999; Serra et al. + 2011)., 2011). + Neither of these methods depends on the dynamical state of the svstem and both apply at all clustrocentric radii (Diaferio. Geller Rines 2005).," Neither of these methods depends on the dynamical state of the system and both apply at all clustrocentric radii (Diaferio, Geller Rines 2005)." + Ol course. for nearly all clusters. we can observe them only in redshift (phase) space.," Of course, for nearly all clusters, we can observe them only in redshift (phase) space." + Kaiser (1987) was the first to understand. how spherical infall appears in redshilt space., Kaiser (1987) was the first to understand how spherical infall appears in redshift space. + In his elegant paper (Ixaiser 1937). he shows (his Figure 5) the now widely recognized pattern that characterizes (he appearance of a cluster in redshift space.," In his elegant paper (Kaiser 1987), he shows (his Figure 5) the now widely recognized trumpet-shaped pattern that characterizes the appearance of a cluster in redshift space." + The central. virialized region appears as an extended finger pointing along the lime-of-sight toward the observer.," The central, virialized region appears as an extended finger pointing along the line-of-sight toward the observer." + This elongation is a simple consequence of the fact that the line-ol-sielt component ol the velocities of galaxies relative to one another within the virialized region are larger than the Lhabble flow across the region., This elongation is a simple consequence of the fact that the line-of-sight component of the velocities of galaxies relative to one another within the virialized region are larger than the Hubble flow across the region. + At the effective outer radius of the cluster. Ry... the infall velocily just cancels the IIubble flow.," At the effective outer radius of the cluster, $_{turn}$, the infall velocity just cancels the Hubble flow." + Thus the shell just turning around appears as a line ab (he cluster mean velocity in redshilt space., Thus the shell just turning around appears as a line at the cluster mean velocity in redshift space. + Infalling shells at radii between δεν anc Rey are successively more and more elongated along the line-of-sight producing the trumpet shape., Infalling shells at radii between $_{turn}$ and $_{200}$ are successively more and more elongated along the line-of-sight producing the trumpet shape. + Ii the simple spherical infall model. the outline of the trumpet is a (rue caustic (a line of infinite density in phase space).," In the simple spherical infall model, the outline of the trumpet is a true caustic (a line of infinite density in phase space)." + At about the same time that Ixaiser wrote his paper. there was an increasing awareness," At about the same time that Kaiser wrote his paper, there was an increasing awareness" +his paper.,this paper. + The fine-structure lines are. however. a valuable ool to infer the physical conditions in such svstenis.," The fine-structure lines are, however, a valuable tool to infer the physical conditions in such systems." + In xwlicular. the knowledge of the ionization. state of. the sVslers couped with the information on the volumentric density alloreed by the fine-structure lines allows one to ace limits οn the distance between the absorber ancl the OSO. giving a clue to infer whether they correspond to intervening couds or to material ejected from the QSO (lurnshek.\Wevmann&Williams1979:Morrisetal.1986:Tripp.Lu&Savage1996:Srianand.Petitjean 2000).," In particular, the knowledge of the ionization state of the systems coupled with the information on the volumentric density afforded by the fine-structure lines allows one to place limits on the distance between the absorber and the QSO, giving a clue to infer whether they correspond to intervening clouds or to material ejected from the QSO \cite{TWW79,Morris,TLS96,SP2000}." +". So lar. all the fine-structure lines observed. belong to cither C"" or C..."," So far, all the fine-structure lines observed belong to either $^0$ or $^+$." + Owing to its low ionization fraction (since its lonization potential is lower than that of. hydrogen). atomic carbon is very seldom detected.," Owing to its low ionization fraction (since its ionization potential is lower than that of hydrogen), atomic carbon is very seldom detected." + The three systems listed in table 2) correspond to all of the presently known svstems. apart from the system observed. towards the BL Lac object 0215|015 (Bladesetal.1982:Blades 1985).," The three systems listed in table \ref{obsdata} correspond to all of the presently known systems, apart from the system observed towards the BL Lac object 0215+015 \cite{Bladesa,Bladesb}." + As we gathered observational data from the literature. we rejected any line falling within the Ly-a forest region of the spectrum.," As we gathered observational data from the literature, we rejected any line falling within the $\alpha$ forest region of the spectrum." + Prochaska (1999) observed. the 1335 fine-structure transition in a LL system at sn.=2.652 towards Q2231-00., Prochaska \shortcite{P99} observed the 1335 fine-structure transition in a LL system at $z_{\rmn{abs}}=2.652$ towards Q2231-00. + Llowever. since this transition falls within the Ly-a forest in this object and therefore may have been subject to significant contamination. his claimed value on the column density N(C 1) should be regarded at most as an upper limit to the true value.," However, since this transition falls within the $\alpha$ forest in this object and therefore may have been subject to significant contamination, his claimed value on the column density $^*$ ) should be regarded at most as an upper limit to the true value." + For the same reason we disregarded the DLA system at zi=3.054 towards QO000-26 observed by Giardino Favata (2000)., For the same reason we disregarded the DLA system at $z_{\rmn{abs}}=3.054$ towards Q0000-26 observed by Giardino Favata \shortcite{GF2000}. +. Although the authors quoted their value for 11) as an upper limit. we argue that in principle significant contamination could also be taking place on the ground fine-structure Line. thereby also allecting 11)) and. driving the ratio NOYN in the opposite sense.," Although the authors quoted their value for $^*$ ) as an upper limit, we argue that in principle significant contamination could also be taking place on the ground fine-structure line, thereby also affecting ) and driving the ratio $N^*/N$ in the opposite sense." + Unfortunately. the ground 1334 line is often heavily saturated: to circunvent this problem there have been many alternative approaches to derive the 11) column density bv other indirect methods.," Unfortunately, the ground 1334 line is often heavily saturated; to circunvent this problem there have been many alternative approaches to derive the ) column density by other indirect methods." + Prochaska (1999). used the ratio of NCCIDD/N(GeO12) in à velocity region where the σοι line was not saturated to derive the corresponding value at the component where the line was detected., Prochaska \shortcite{P99} used the ratio of ) in a velocity region where the ground line was not saturated to derive the corresponding value at the component where the line was detected. +" Outram. Challee Carswell (1999) assumed a carbon abundance relative to iron. Fe} >-0.3 to obtain a tighter lower limit on the 1) column density in a DLA svstem at 2,1,=2.62 towards GD1759τὸ,"," Outram, Chaffee Carswell \shortcite{OCC} assumed a carbon abundance relative to iron $>$ -0.3 to obtain a tighter lower limit on the ) column density in a DLA system at $z_{\rmn{abs}}=2.62$ towards GB1759+75." + In our sample we have included only direct. measurements on the column densities., In our sample we have included only direct measurements on the column densities. + In sections 3.1--3.2. below. we will separately study the DLA and LL systems in our sample.," In sections \ref{section:DLA}- \ref{section:LL} below, we will separately study the DLA and LL systems in our sample." + Again. as a working hypothesis we shall assume the temperature-redshift relation as predicted. by the standard model.," Again, as a working hypothesis we shall assume the temperature-redshift relation as predicted by the standard model." + Ehe. validity of this relation is discussed in section 3.3.., The validity of this relation is discussed in section \ref{section:CMBR}. + DLA svstenis have very high. neutral hydrogen column densities (logN(LLEI) 20.3).," DLA systems have very high neutral hydrogen column densities $\log\rmn{N}(\hbox{H\,{\sc i}})>20.3$ )." + This makes them elfectively shiclelecl from the ionizing radiation. causing their contents o be essentially neutral materia (Viegas 1995)..," This makes them effectively shielded from the ionizing radiation, causing their contents to be essentially neutral material \cite{Viegas95}. ." + We use the fine-structure lines column density. ratios observed in the DLA systems listed in table 2. to set upper imits to their neutral hydrogen volume densities mye ancl to he intensities of the UV. radiation field present., We use the fine-structure lines column density ratios observed in the DLA systems listed in table \ref{obsdata} to set upper limits to their neutral hydrogen volume densities $n_{\rmn{H}^0}$ and to the intensities of the UV radiation field present. + Given the ugh neutral hydrogen. column density. probably all of the ivdrogen ionizing radiation will be absorbed. leaving very ew photons with energies greater than 1 Rwd.," Given the high neutral hydrogen column density, probably all of the hydrogen ionizing radiation will be absorbed, leaving very few photons with energies greater than 1 Ryd." + The spectral shape of the UV radiation field willthen be similar to the one found in our own galaxy. and we therefore assume the," The spectral shape of the UV radiation field willthen be similar to the one found in our own galaxy, and we therefore assume the" +Figures | and 2. reveal a smooth evolution along the sequence ΚΗΙ — MIL — Ba/S. in the sense that the upper boundary of the populated region in the («logP) diagram moves towards longer periods (this ts reflected by the three curved lines which roughly delineate the regions populated by these three classes. their exact definition being given below).,"Figures \ref{Fig:elogP_M} and \ref{Fig:elogP_panels} reveal a smooth evolution along the sequence KIII – MIII – Ba/S, in the sense that the upper boundary of the populated region in the $(e - +\log P)$ diagram moves towards longer periods (this is reflected by the three curved lines which roughly delineate the regions populated by these three classes, their exact definition being given below)." + This is clearly a consequence of the larger radii reached by stars evolving along this sequence., This is clearly a consequence of the larger radii reached by stars evolving along this sequence. + In the case of Ba and Te-poor S giants. 1t is actually their white dwarf (WD) companions which reached very large radii while evolving on the AGB.," In the case of Ba and Tc-poor S giants, it is actually their white dwarf (WD) companions which reached very large radii while evolving on the AGB." + For K giants. the situation is in principle somewhat more complex. since this class mixes stars on the first giant branch and stars in the core He-burning phase.," For K giants, the situation is in principle somewhat more complex, since this class mixes stars on the first giant branch and stars in the core He-burning phase." + stars belonging to the latter category have gone through the RGB tip. where they reached a very large radius (similar to. or even larger than that of M giants).," stars belonging to the latter category have gone through the RGB tip, where they reached a very large radius (similar to, or even larger than that of M giants)." + Therefore. if those low-mass. core-He burning stars were to dominate among K giants. their distribution in the (c.logP) diagram should be characterised by an envelope located at even longer periods than that for M giants.," Therefore, if those low-mass, core-He burning stars were to dominate among K giants, their distribution in the $(e - \log P)$ diagram should be characterised by an envelope located at even longer periods than that for M giants." + Fig., Fig. + shows that this is not the case. because the sample of open- K giants plotted in Fig.," \ref{Fig:elogP_panels} shows that this is not the case, because the sample of open-cluster K giants plotted in Fig." + 2. ts in fact dominated by intermediate-mass stars. as may be judged from the turnoff masses of the corresponding clusters. most of them being larger than 2 citepMermilliod-2007b..," \ref{Fig:elogP_panels} is in fact dominated by intermediate-mass stars, as may be judged from the turnoff masses of the corresponding clusters, most of them being larger than 2 \\citep{Mermilliod-2007b}." + The complication introduced by the mixture of evolutionary states among K giants is thus not a concern., The complication introduced by the mixture of evolutionary states among K giants is thus not a concern. + Equating the stellar radius to the Roche radius results in a threshold period (for given component masses) below which the primary star undergoes RLOF., Equating the stellar radius to the Roche radius results in a threshold period (for given component masses) below which the primary star undergoes RLOF. +" Adopting Paezynisski’s usual expression for the Roche radius Πρ around star | where g=AL,/ALS and A is the orbital separation. one finds that a star of radius 40 R.. fills its Roche lobe in a system of period P=το d. for masses M4=1.3 M. and AL,—0.6M ..."," Adopting Paczyńsski's usual expression for the Roche radius $R_{R,1}$ around star 1 where $q = M_1/M_2$ and $A$ is the orbital separation, one finds that a star of radius 40 $_\odot$ fills its Roche lobe in a system of period $P = 70$ d, for masses $M_1 = 1.3 $ $_\odot$ and $M_2 = +0.6$ $_\odot$." + Although the Roche lobe concept is in principle only applicable to circular orbits. one may formally compute the orbital periods for which the primary star fills its Roche lobe periastron. by replacing A by A(1ο) in the above expression.," Although the Roche lobe concept is in principle only applicable to circular orbits, one may formally compute the orbital periods for which the primary star fills its Roche lobe , by replacing $A$ by $A(1-e)$ in the above expression." + It is quite remarkable that the relationship between P and e so obtained (assuming Ry=36 .) exactly matches the boundary of the region occupied by KIII giants in the (6.logP) diagram. both for cluster and giants (Fig. 2)).," It is quite remarkable that the relationship between $P$ and $e$ so obtained (assuming $R_R = 36$ $_\odot$ ) exactly matches the boundary of the region occupied by KIII giants in the $(e - \log P)$ diagram, both for cluster and giants (Fig. \ref{Fig:elogP_panels}) )." + This excellent match thus clearly suggests that mass transfer at periastron plays a crucial role in shaping the («logP?) diagram (?).., This excellent match thus clearly suggests that mass transfer at periastron plays a crucial role in shaping the $(e - \log P)$ diagram \citep{Soker00}. + It may seem surprising that the “periastron envelope’ LA©) 2 constant. or 1€) = constant] represents a better fit to the data than the ‘circularisation envelope’ [ACLc2) = constant. or P7/7(1.—£7) = constant: see Fig.," It may seem surprising that the 'periastron envelope' $A(1-e)$ = constant, or $P^{2/3}(1-e)$ = constant] represents a better fit to the data than the 'circularisation envelope' $A(1-e^2)$ = constant, or $P^{2/3}(1-e^2)$ = constant; see Fig." +" 6 of Paper II]. resulting from the fact that circularisation keeps the angular momentum per unit reduced mass constant (???).,"," 6 of Paper II], resulting from the fact that circularisation keeps the angular momentum per unit reduced mass constant \citep{Zahn-1977,Hut81,Duquennoy-92}." + Indeed. às the star gets closer to its Roche lobe. it should circularise first and then fill its Roche lobe. and possibly disappear from the sample due to cataclysmic mass transfer.," Indeed, as the star gets closer to its Roche lobe, it should circularise first and then fill its Roche lobe, and possibly disappear from the sample due to cataclysmic mass transfer." + The samples of K-giant binaries clearly favour the periastron envelope over thecircularisation envelope., The samples of K-giant binaries clearly favour the periastron envelope over thecircularisation envelope. + The reason for this may be the following., The reason for this may be the following. + When à system is close to filling its, When a system is close to filling its +"One system, CXGG0095951+0140.8,has Amij.=—-0.014mag (i.e., Ami»=2.10X-0.02mag as obtained from the difference between the magnitudes in the rest-frame R200=832+19.6 M200=9.5(+0.42)xr-band),1013 Mo, z=0.372, and six kpc,spectroscopic members.","One system, $+$ 0140.8,has $\mathrm{\Delta m_i}_{12} = 2.19 \pm 0.014~\mathrm{mag}$ (i.e., $\mathrm{\Delta m}_{12} = 2.10 \pm 0.02~\mathrm{mag}$ as obtained from the difference between the magnitudes in the rest-frame $r$ -band), $R_{200} = 832 \pm 19.6~\mathrm{kpc}$, $M_{200} = 9.5~(\pm 0.42) \times 10^{13}~\mathrm{M}_{\sun}$ , $z = 0.372$, and six spectroscopic members." + It is part of a large-scale structure (see fig., It is part of a large-scale structure (see fig. + 1 in (09 and fig., 1 in G09 and fig. + 3 in Scoville et al., 3 in Scoville et al. + 2007) populated by 28 X-ray emitting groups distributed across the entire 2deg? area of the (corresponding to a cross size of about 25.5Mpc at z= 0.37)., 2007) populated by 28 X-ray emitting groups distributed across the entire $2~\mathrm{deg}^2$ area of the (corresponding to a cross size of about $25.5~\mathrm{Mpc}$ at $z=0.37$ ). +" Furthermore, its dominant galaxy (with rest-frame absolute magnitude M;= —24.87) hosts apoint-likea radio source (see Giodini et al."," Furthermore, its dominant galaxy (with a rest-frame absolute magnitude $M_{i} = -24.87$ ) hosts apoint-like radio source (see Giodini et al." + 2010)., 2010). +" The other fossil group, 0095951+0212.6, has Ami,=2.35+0.014mag (ie., Ami»=2.32+0.02mag in the rest-frame r-band), Haeo=478+54.4kpc, Μου=1.9(£0.41)x10?Mo, z=0.425, and eight spectroscopic members."," The other fossil group, $+$ 0212.6, has $\mathrm{\Delta m_i}_{12} = 2.35 \pm 0.014~\mathrm{mag}$ (i.e., $\mathrm{\Delta m}_{12} = 2.32 \pm 0.02~\mathrm{mag}$ in the rest-frame $r$ -band), $R_{200} = 478 \pm 54.4~\mathrm{kpc}$, $M_{200} = 1.9~(\pm 0.41) \times 10^{13}~\mathrm{M}_{\sun}$, $z = 0.425$, and eight spectroscopic members." + It is isolated and its BCG has M;=—23.87., It is isolated and its BCG has $M_{i} = -23.87$. + Basic properties of the two fossil groups under study are listed in Table 1., Basic properties of the two fossil groups under study are listed in Table 1. +" In addition, we note that they populate the upper half of the distribution of the X-ray selected groups in the (galaxy) stellar mass fraction-group total-mass diagram (G09, their fig."," In addition, we note that they populate the upper half of the distribution of the X-ray selected groups in the (galaxy) stellar mass fraction–group total-mass diagram (G09, their fig." +" 5), where quantities are estimated at 0.7 R2oo."," 5), where quantities are estimated at $0.7 R_{200}$ ." + This is particularly true for 0095951--0212.6., This is particularly true for $+$ 0212.6. +" As from GO095,, the stellar mass", As from the stellar mass +" Zuckermanetal.L972:: Sclilkeetal.1992:: Ilrotaοal.1998.. C. HCNII!. al.2002)). ITCNIT! ΝΠΗΟΞΠΝΟ Herbst.Terzieva.&Talbi2000)) was bv Irvinectal.(1996) in comet 61996 D2 (νακακο),"," \citealt{snyder72, zucker72}; \citealt{black76}) \citealt{schilke92}; \citealt{hirota98}, $^+$ $^+$ \citealt{rodgers01a, charnley02}) $^+$ $_2$ \citealt{herbst00}) was by \cite{irvine96} in comet C/1996 B2 (Hyakutake)." + The measured INCΠο abundance ratio..L. was simular to that iu iuterstellar clouds with ac9 temperatureOT of order 50 Ix. sugecstinge that coluctary TNC may be unprocessed interstellar material incorporated inte the comets nucleus.," The measured HNC/HCN abundance ratio, was similar to that in interstellar clouds with a temperature of order 50 K, suggesting that cometary HNC may be unprocessed interstellar material incorporated into the comet's nucleus." + IHToscever. levinectal.(1996) argued that a nuuber of alternative processes may also explain the observed INC/IICN ratio iu comet IIvakutake. including irradiation of icy matrix containiug IICN. non-equilibrium chemical processes in the solar nebula. gas-phase processes iu the coma itself. infrared relaxation of ICN from excited vibrational levels of the eround electronic state. or photo-dissociation of a heavier pareut molecule.," However, \cite{irvine96} argued that a number of alternative processes may also explain the observed HNC/HCN ratio in comet Hyakutake, including irradiation of icy matrix containing HCN, non-equilibrium chemical processes in the solar nebula, gas-phase processes in the coma itself, infrared relaxation of HCN from excited vibrational levels of the ground electronic state, or photo-dissociation of a heavier parent molecule." + A stroug variation of the IENC/IICN abundauce ratio πι comet C/1995 OL (ILde-Bopp) with heliocentric distance (from at 2.9 AU to πο 1 AU: Biverctal.1997: Lhwineetal. 1998)) questioned he interstellar origin of cometary TNC and sugeestedCoco a production imechanisu du the coma itself as a nore likely explanation., A strong variation of the HNC/HCN abundance ratio in comet C/1995 O1 (Hale-Bopp) with heliocentric distance (from at 2.9 AU to near 1 AU; \citealt{biver97}; \citealt{irvine98}) ) questioned the interstellar origin of cometary HNC and suggested a production mechanism in the coma itself as a more likely explanation. + Rodgers&Charuley(1998) srescuted a comprehensive model of the cometary coma chemistry and suggested that iu very active comets. such as comet ILale-Dopp. the observed variation of he TNC abundance with the helioceutrie distance. as observed with sinele-dish telescopes. cau be explained wojsolerization of IIC'N driven by the iupact of ast hwdroseu atoms produced in photo-dissociatiou of went molecules.," \cite{rodgers98} presented a comprehensive model of the cometary coma chemistry and suggested that in very active comets, such as comet Hale-Bopp, the observed variation of the HNC abundance with the heliocentric distance, as observed with single-dish telescopes, can be explained by isomerization of HCN driven by the impact of fast hydrogen atoms produced in photo-dissociation of parent molecules." + However. their model overproduced he TING abundance at ~3 AU by abot a factor of 2.," However, their model overproduced the HNC abundance at 3 AU by about a factor of 2." + Ina subsequent paper Rodgers&Charuley(2001) showed that the same imechauign cannot reproduce observed IENC'/IICN. abundance ratios iu nmoderatelv active comoets at —1 AU. such as cometC7/1999 ITI (Loo).," In a subsequent paper \cite{rodgers01b} showed that the same mechanism cannot reproduce observed HNC/HCN abundance ratios in moderately active comets at 1 AU, such as cometC/1999 H1 (Lee)." + The applicability of the model to very active comets has also been questioned by interferometric observations of, The applicability of the model to very active comets has also been questioned by interferometric observations of +"Of the 13 departures from tolerable fits to redshifts and distances, eight belong to four misfit galaxies, Cetus, Tucana, DDO 210, and the Sagittarius dwarf irregular.","Of the 13 departures from tolerable fits to redshifts and distances, eight belong to four misfit galaxies, Cetus, Tucana, DDO 210, and the Sagittarius dwarf irregular." +" They have similar discrepancies in redshifts and distances, and they have similar orbits (plotted as the dashed lines in Figs."," They have similar discrepancies in redshifts and distances, and they have similar orbits (plotted as the dashed lines in Figs." +" 3 to 5)) that emanate from SGL~200°, SGB~30°."," \ref{Fig:3} to \ref{Fig:5}) ) that emanate from $SGL\sim 200^\circ$, $SGB\sim 30^\circ$." + It may be significant that this is in the direction of the Local Void (Tully et al., It may be significant that this is in the direction of the Local Void (Tully et al. + 2008)., 2008). +" The common features — low redshifts, large distances, and similar orbits — argue against the idea that measurement errors are to blame, and invites the speculation that they are manifestations of an inadequate external mass model that would have to be particularly serious near these four galaxies."," The common features — low redshifts, large distances, and similar orbits — argue against the idea that measurement errors are to blame, and invites the speculation that they are manifestations of an inadequate external mass model that would have to be particularly serious near these four galaxies." +" If an adjustment of our phenomenological representation of the external mass could reduce the peculiar gravitational acceleration toward MW near the four misfits it would allow larger redshifts at lower present distances, in the direction wanted to improve the fit."," If an adjustment of our phenomenological representation of the external mass could reduce the peculiar gravitational acceleration toward MW near the four misfits it would allow larger redshifts at lower present distances, in the direction wanted to improve the fit." +" A search for a fifth external mass capable of producing this effect has not yielded anything promising, however."," A search for a fifth external mass capable of producing this effect has not yielded anything promising, however." + An explanation of the enigmatic properties of these four misfit galaxies remains an interesting open issue., An explanation of the enigmatic properties of these four misfit galaxies remains an interesting open issue. +(EW) baseline vectors.,(EW) baseline vectors. + Next. we cdeseribe the. estimation of array geometry.," Next, we describe the re-estimation of array geometry." + We begin with a brief description of the mode of observations with MICE., We begin with a brief description of the mode of observations with MRT. + MICE has 32 fixed antennas in the EW arm and 15 movable antenna trollevs in the NS arm., MRT has 32 fixed antennas in the EW arm and 15 movable antenna trolleys in the NS arm. + For measuring visibilities. the 15 NS trollevs are configured by spreading them over S4 m with an inter-trollev spacing of 6 m (to avoid shadowing of one trolley by another).," For measuring visibilities, the 15 NS trolleys are configured by spreading them over 84 m with an inter-trolley spacing of 6 m (to avoid shadowing of one trolley by another)." + MICE measures cdillerent. Fourier components of the. brightness clistribution of the sky in 63 dillerent configurations (referred lo as allocations) to. sample NS baselines every mum. Therefore. ellectively. there are 945 antenna positions (63 allocations * 15 antennas/allocation) in the NS arm and a total of 30.240 (945 * 32) visibilities are used for imagine.," MRT measures different Fourier components of the brightness distribution of the sky in 63 different configurations (referred to as ) to sample NS baselines every m. Therefore, effectively, there are 945 antenna positions (63 allocations * 15 antennas/allocation) in the NS arm and a total of 30,240 (945 * 32) visibilities are used for imaging." + A small error in a measuring scale of relatively shorter leneth is likely to build up systematically while establishing the geometry of longer basclines., A small error in a measuring scale of relatively shorter length is likely to build up systematically while establishing the geometry of longer baselines. + This οσο would. be observed. in the instrumental. phases estimated using different calibrators., This effect would be observed in the instrumental phases estimated using different calibrators. + In. principle. the instrumental phases estimated using two calibrators at dilferent. declinations. for a given baseline. should be the same. allowing for temporal variations in the instrumental gains.," In principle, the instrumental phases estimated using two calibrators at different declinations, for a given baseline, should be the same, allowing for temporal variations in the instrumental gains." + A non-zero cdillerence in these estimates may be due to positional errors of the baseline or positions of calibrators., A non-zero difference in these estimates may be due to positional errors of the baseline or positions of calibrators. + As mentioned earlier. our analysis of positional error in sources and the homography matrix cued to positional errors in. baselines (or antenna positions).," As mentioned earlier, our analysis of positional error in sources and the homography matrix cued to positional errors in baselines (or antenna positions)." + The simple principle of astrometry CEhomsonetal.2001) was used to estimate errors in antenna. positions and is discussed below., The simple principle of astrometry \citep{book:thomson} was used to estimate errors in antenna positions and is discussed below. +" The observed. visibility phase. (5/. in a baseline with components (u,;;.0;05). due to calibrator S, with direction cosines (f°!mS!nF!) is given by: Where.⇁ ορETTui represents (rue instrumental; phases. ὁ;=1.2.....32 represents EW antennas and j=1.2.....045 represents NS antennas."," The observed visibility phase, $\psi_{ij}^{\mathcal{S}^{}_1}$, in a baseline with components $\left(u^{}_{ij}, v^{}_{ij}, w^{}_{ij}\right)$, due to calibrator $S^{}_{1}$ with direction cosines $\left(l^{\mathcal{S}_1},m^{\mathcal{S}_1},n^{\mathcal{S}_1}\right)$, is given by: Where, $\phi_{ij}^{\mbox{\small ins}}$ represents true instrumental phases, $i=1,2,\ldots,32$ represents EW antennas and $j=1,2,\ldots,945$ represents NS antennas." +" For moeridian transit imaging Equation 7 becomes: The instrumental phases; 657.δι estimated. using. the measured geometry are given by: Here. Ae; and Aw;, are errors in the assumed. baseline"," For meridian transit imaging Equation \ref{e:obsphasebasiceqn} becomes: The instrumental phases, $\phi_{ij}^{\mathcal{S}^{}_{1}}$, estimated using the measured geometry are given by: Here, $\Delta v^{}_{ij}$ and $\Delta w^{}_{ij}$ are errors in the assumed baseline" +"center to the current position of the bubble and M(R) ts the total gravitating mass within R. then where we have used AR=34"" (2.6kpe). the projected distance from the cluster center. and M(R)=1.4«10!!M. (Cótté et 22001).","center to the current position of the bubble and $M(R)$ is the total gravitating mass within $R$, then where we have used $R = 34''$ $2.6\,{\rm kpc}$ ), the projected distance from the cluster center, and $M(R) = 1.4\times +10^{11}\,M_{\odot}$ (Côtté et 2001)." + Cy~0.5 is the drag coefficient. for a roughly spherical bubble., $C_{W} \sim 0.5$ is the drag coefficient for a roughly spherical bubble. + Since the actual distance to the cluster center almost certainly exceeds the projected distance. this gives a lower limit for the rise time.," Since the actual distance to the cluster center almost certainly exceeds the projected distance, this gives a lower limit for the rise time." + Furthermore. according to (1). the speed of the bubble. 383kms!. exceeds half of the sound speed and so is overestimated.," Furthermore, according to \ref{eq:risetime}) ), the speed of the bubble, $383\rm\ km\ s^{-1}$, exceeds half of the sound speed and so is overestimated." + Thus its rise time is underestimated. even if the budding bubble les in the plane of the sky.," Thus its rise time is underestimated, even if the budding bubble lies in the plane of the sky." + During its rapid mitial expansion. the boundary of the bubble will generally be stable.," During its rapid initial expansion, the boundary of the bubble will generally be stable." + As a result. the motion of the bubble boundary generally needs to be subsonic before a bubble even starts to form.," As a result, the motion of the bubble boundary generally needs to be subsonic before a bubble even starts to form." + This adds a further delay to μις after the outburst. but before the bubble is formed.," This adds a further delay to $\tau_{\rm bubble}$ after the outburst, but before the bubble is formed." + If we do associate the budding bubble with an energetic nuclear event. then the constraints on its formation timescale make it quite reasonable to associate it with the current outburst (associated with the jet) that commenced about 107 years ago.," If we do associate the budding bubble with an energetic nuclear event, then the constraints on its formation timescale make it quite reasonable to associate it with the current outburst (associated with the jet) that commenced about $10^7$ years ago." + The most striking X-ray features in M87 are the two arms that extend east and southwest from the inner lobe region., The most striking X-ray features in M87 are the two arms that extend east and southwest from the inner lobe region. + These also are seen in the 90 em image (see Fig., These also are seen in the 90 cm image (see Fig. + 11. fora composite X-ray-radio view of M87)., \ref{fig:overlay} for a composite X-ray-radio view of M87). + Previous spectroscopic studies of the arms have utilized the XMM-Newton observations (Belsole et al., Previous spectroscopic studies of the arms have utilized the XMM-Newton observations (Belsole et al. + 2001. Molendi 2002).," 2001, Molendi 2002)." + They find that the arms are cool and portions are poorly fit by single temperature components., They find that the arms are cool and portions are poorly fit by single temperature components. + Our Chandra results agree with these previous analyses. as does the XMM-Newton temperature map (Fig. 6)).," Our Chandra results agree with these previous analyses, as does the XMM-Newton temperature map (Fig. \ref{fig:xmm_tmap}) )." + We find that the arms require at least two components (with variable abundances. VMEKAL or VAPEC) with the low and high temperature components in the range 1-1.5 keV and 2-2.7 keV respectively.," We find that the arms require at least two components (with variable abundances, VMEKAL or VAPEC) with the low and high temperature components in the range 1-1.5 keV and 2-2.7 keV respectively." + Although the two arms are likely related to the same outburst. we discuss each separately.," Although the two arms are likely related to the same outburst, we discuss each separately." + The eastern X-ray and radio arm begins at the eastern edge of the inner radio cocoon. but its appearance is much more amorphous than that of the southwestern arm (see Fig. [.. 3..," The eastern X-ray and radio arm begins at the eastern edge of the inner radio cocoon, but its appearance is much more amorphous than that of the southwestern arm (see Fig. \ref{fig:bl1sum}, \ref{fig:flatbl1_sm2}," + and 4))., and \ref{fig:divking}) ). + At the base of the filament (Fig., At the base of the filament (Fig. +" 1. and 2)) are at least four bubbles with sizes comparable to that of the ""bud"" discussed above and streamers of gas bounding these buoyantly rising bubbles.", \ref{fig:bl1sum} and \ref{fig:adapt}) ) are at least four bubbles with sizes comparable to that of the “bud” discussed above and streamers of gas bounding these buoyantly rising bubbles. + Typical bubble sizes are ~10” (0.8 kpe) in radius and are reminiscent of the “effervescent” heating described by Begelman (2003)., Typical bubble sizes are $\sim10''$ (0.8 kpc) in radius and are reminiscent of the “effervescent” heating described by Begelman (2003). + Fig., Fig. +" 9 shows a projection across one of these “effervescent” bubbles 1.25"" (5.8 kpe) east of the M87 nucleus (labeled ""bubble"" in Fig.", \ref{fig:bubble_proj} shows a projection across one of these “effervescent” bubbles $1.25'$ (5.8 kpc) east of the M87 nucleus (labeled “bubble” in Fig. + lee)., \ref{fig:bl1sum}c c). + The temperature structure (Fig. 6)), The temperature structure (Fig. \ref{fig:xmm_tmap}) ) + of the eastern arm shows X-ray features that are consistent with cool matertal uplifted by a rising torus (Churazov et al., of the eastern arm shows X-ray features that are consistent with cool material uplifted by a rising torus (Churazov et al. + 2001)., 2001). + First. the largest concentration of the coolest gas lies midway along the eastern arm (1/—2 from M87's nucleus).," First, the largest concentration of the coolest gas lies midway along the eastern arm $1'-2'$ from M87's nucleus)." +" Second. the cool gas column in the eastern arm narrows at the edge of the radio torus closest to the M87 nucleus and then broadens within the torus (labeled ""Uplifted Gas"" in Fig."," Second, the cool gas column in the eastern arm narrows at the edge of the radio torus closest to the M87 nucleus and then broadens within the torus (labeled “Uplifted Gas” in Fig." + 4bb). just as one might expect for gas uplifted by a buoyant toroidal plasma bubble (see Fig.," \ref{fig:divking}b b), just as one might expect for gas uplifted by a buoyant toroidal plasma bubble (see Fig." + 11. and Fig., \ref{fig:overlay} and Fig. + 3 and 4 in Churazov et al., 3 and 4 in Churazov et al. + 2001)., 2001). + A projection along the arm. Fig. 10..," A projection along the arm, Fig. \ref{fig:eastern_arm_proj}," + shows a brightening at the radial distance of the 14 kpe ring., shows a brightening at the radial distance of the 14 kpc ring. + A similar brightening occurs at about the same angular distance on the southwestern arm., A similar brightening occurs at about the same angular distance on the southwestern arm. + While the feature in the southwestern arm is partially obscured by the change from the ACIS S3 to S2 chip in the Chandra image. it is clearly seen in both the ROSAT HRI and XMM-Newton images (Fig. 5)).," While the feature in the southwestern arm is partially obscured by the change from the ACIS S3 to S2 chip in the Chandra image, it is clearly seen in both the ROSAT HRI and XMM-Newton images (Fig. \ref{fig:rosat}) )." + [f this brightening ts associated with the passage of the same shock that produced the ring. then this arm (and the southwestern arm as well) must lie close to the plane of the sky.," If this brightening is associated with the passage of the same shock that produced the ring, then this arm (and the southwestern arm as well) must lie close to the plane of the sky." +" If this brightening does arise from the passage of the shock. it is likely that the so called ""radio ear"". the vortex- structure that forms the end of the bright eastern radio filament (see Fig. 11))."," If this brightening does arise from the passage of the shock, it is likely that the so called “radio ear”, the vortex-like structure that forms the end of the bright eastern radio filament (see Fig. \ref{fig:overlay}) )," + falls between the shocks associated with the 14 kpe and 17 kpe rings., falls between the shocks associated with the 14 kpc and 17 kpc rings. + This could alternatively explain the flat. ring-like appearance of this radio feature. since passage of a shock through a bubble of relativistic plasma embedded in a background of cold thermal material will induce strong vorticity in the plasma. turning it into a ring-like structure (Ensslin Bruggen 2002).," This could alternatively explain the flat, ring-like appearance of this radio feature, since passage of a shock through a bubble of relativistic plasma embedded in a background of cold thermal material will induce strong vorticity in the plasma, turning it into a ring-like structure (Ensslin Bruggen 2002)." + Combined with the effect of vorticity creation in buoyantly rising bubbles described by Churazov et al. (, Combined with the effect of vorticity creation in buoyantly rising bubbles described by Churazov et al. ( +2001). this could account for the rather filamentary appearance of this feature.,"2001), this could account for the rather filamentary appearance of this feature." + At the end of the eastern arm (~3! east of the M87 nucleus). the X-ray image (Fig. 4))," At the end of the eastern arm $\sim3'$ east of the M87 nucleus), the X-ray image (Fig. \ref{fig:divking}) )" +" shows an almost circular enhancement (radius of I’ centered at RA=12:31:05.397 DEC=+12:25:10.01) extending to the north (beyond the northern ""ear"" of the radio emitting torus).", shows an almost circular enhancement (radius of $1'$ centered at RA=12:31:05.397 DEC=+12:25:10.01) extending to the north (beyond the northern “ear” of the radio emitting torus). + This circular feature is bounded on three sides by X-ray enhancements (see Fig. 4) , This circular feature is bounded on three sides by X-ray enhancements (see Fig. \ref{fig:divking}) ) +which originate at the eastern arm and it is bounded to the northwest by a pair of radio ares (best seen in the 90 cm image: see Fig. 11)., which originate at the eastern arm and it is bounded to the northwest by a pair of radio arcs (best seen in the 90 cm image; see Fig. \ref{fig:overlay}) ). + The X-ray temperature of this circular region is intermediate in temperature (1.8-1.9 keV) as seen in Fig., The X-ray temperature of this circular region is intermediate in temperature (1.8-1.9 keV) as seen in Fig. + 6 and is comparable to that of the end of southeastern arm (as it swings to the east)., \ref{fig:xmm_tmap} and is comparable to that of the end of southeastern arm (as it swings to the east). + The two enhancements. labeled andE2 in Fig.," The two enhancements, labeled and in Fig." + dec). which bound the circular region. appear similar to the two filaments into which the southwestern arm divides (see below).," \ref{fig:divking}c c), which bound the circular region, appear similar to the two filaments into which the southwestern arm divides (see below)." + We suggest that the outer portions of the eastern arm are similar to the southwestern arm. but seen from a different orientation.," We suggest that the outer portions of the eastern arm are similar to the southwestern arm, but seen from a different orientation." + The southwestern X-ray arm originates (see Fig., The southwestern X-ray arm originates (see Fig. + | and Fig. 2))," \ref{fig:inner_cocoon} + and Fig. \ref{fig:adapt}) )" + as a narrow filament of width approximately 10” (0.8 kpc) at its narrowest when it exits from the bright inner core (at a distance of 50”. 3.9 kpe from the nucleus).," as a narrow filament of width approximately $10''$ (0.8 kpc) at its narrowest when it exits from the bright inner core (at a distance of $50''$, 3.9 kpc from the nucleus)." + The filament extends in an almost straight line to the southwest for ~2’ (9.3 kpe)., The filament extends in an almost straight line to the southwest for $\sim 2'$ (9.3 kpc). + As seen in Fig. 11..," As seen in Fig. \ref{fig:overlay}," + over this distance it appears uncorrelated with the radio filament that extends in approximately the same direction., over this distance it appears uncorrelated with the radio filament that extends in approximately the same direction. + At a distance of about 3.4 (15.8 kpe). the X-ray filament bifurcates (the two sections are labeled and in Fig.," At a distance of about $3.4'$ (15.8 kpc), the X-ray filament bifurcates (the two sections are labeled and in Fig." + 4ec)., \ref{fig:divking}c c). + and the correspondence between the radio plasma and X-ray gas becomes more direct., and the correspondence between the radio plasma and X-ray gas becomes more direct. + The brightest radio emission lies between the two X-ray arms as they both rotate clockwise in the plane of the sky and eventually turn due east., The brightest radio emission lies between the two X-ray arms as they both rotate clockwise in the plane of the sky and eventually turn due east. + Young et al (, Young et al. ( +2002) suggested that the arms are overpressurized.,2002) suggested that the arms are overpressurized. + Assuming the southwestern arm is a cylinder lying in the plane of the sky. we find that the pressure in the arm is roughly twice that of the hotter ambient gas.," Assuming the southwestern arm is a cylinder lying in the plane of the sky, we find that the pressure in the arm is roughly twice that of the hotter ambient gas." + We found no elemental abundance differences that could explain, We found no elemental abundance differences that could explain +In the local universe extraplanar gas is detected in most highly inclined galaxies that have total infrared luminosities >3x10Lo,In the local universe extraplanar gas is detected in most highly inclined galaxies that have total infrared luminosities $>3\times 10^{10}\ \lsol$. + Our IFU observations include three such super-group 2005).galaxies and we discover that two have extraplanar emission with Ha and [ΝΤ FWHM line-widths of 50—150kms! (Fig. 3))., Our IFU observations include three such super-group galaxies and we discover that two have extraplanar emission with $\alpha$ and [NII] FWHM line-widths of $50-150\kms$ (Fig. \ref{fig:s23}) ). + $G1120-82 is a disk-dominated member viewed nearly edge-on that lies on the infrared-radio relation for local star-forming galaxies and is not detected with , SG1120-S2 is a disk-dominated member viewed nearly edge-on that lies on the infrared-radio relation for local star-forming galaxies and is not detected with (Table \ref{tab:sour}) ). +"We detect [NII] and Ha emission in the disk (Tableand, 1)).surprisingly, also at projected heights of ry~7.5 kpc above the disk (Fig. 3))"," We detect [NII] and $\alpha$ emission in the disk and, surprisingly, also at projected heights of $r_{h}\sim7.5$ kpc above the disk (Fig. \ref{fig:s23}) )." +" In the spaxels sampling the disk, the ratios of 0 to 0.2 are consistent with shocked gas and log[NII]/Hathe measured line-widths correspond to gas velocities of ~300—400km s!."," In the spaxels sampling the disk, the $\log$ $\alpha$ ratios of 0 to 0.2 are consistent with shocked gas and the measured line-widths correspond to gas velocities of $\sim300-400\kms$ ." +" In the extraplanar spaxels (τι>5 kpc), the log[NII|/Ha ratios of -0.2 to -0.4 are consistent with photoionization by starlight and the line-widths correspond to gas velocities of ~50—150kmsο."," In the extraplanar spaxels $r_{h}>5$ kpc), the $\log$ $\alpha$ ratios of -0.2 to -0.4 are consistent with photoionization by starlight and the line-widths correspond to gas velocities of $\sim50-150~\kms$." +" Our multi-wavelength observations indicate that as with SG1120-S1, the shocked gas in the central region of $G1120-82 is due to star formation and not an AGN."," Our multi-wavelength observations indicate that as with SG1120-S1, the shocked gas in the central region of SG1120-S2 is due to star formation and not an AGN." + $G1120-S3 is also an inclined disk-dominated member with comparable IR luminosity to SG1120-S2 (Table 1)); it is not detected in the radio nor X-ray observations., SG1120-S3 is also an inclined disk-dominated member with comparable IR luminosity to SG1120-S2 (Table \ref{tab:sour}) ); it is not detected in the radio nor X-ray observations. +" The IFU maps show and Ha emission in both the disk and extraplanar spaxels[NIJ] (rj~10 kpc), and the line- are consistent with photoionization by starlight."," The IFU maps show [NII] and $\alpha$ emission in both the disk and extraplanar spaxels $r_{h}\sim10$ kpc), and the line-ratios are consistent with photoionization by starlight." + The FWHM line-widths correspond to velocities of ~200—300kms! iin the disk spaxels and decrease to —50150kms! above the disk., The FWHM line-widths correspond to velocities of $\sim200-300~\kms$ in the disk spaxels and decrease to $\sim50-150~\kms$ above the disk. +" With no signs of an AGN, the gas motion is most likely driven by the ongoing star formation."," With no signs of an AGN, the gas motion is most likely driven by the ongoing star formation." +" In both group members where we detect extraplanar ionized gas, the emission lines vary in terms of relative velocity and width from spaxel to spaxel indicating that there is no PSF broadening in these sources."," In both group members where we detect extraplanar ionized gas, the emission lines vary in terms of relative velocity and width from spaxel to spaxel indicating that there is no PSF broadening in these sources." +" As with $G1120-S1, we measure only motion along the line-of-sight while the gas is likely to be primarily moving perpendicular to the disk, i.e. the true gas velocities are likely to be higher."," As with SG1120-S1, we measure only motion along the line-of-sight while the gas is likely to be primarily moving perpendicular to the disk, i.e. the true gas velocities are likely to be higher." + We cannot determine a net flow direction for the extraplanar gas because the errors on the systemic velocity (~100kms !) for these two galaxies are large compared to the velocity shifts (~10—65kms 1) in their extraplanar spaxels., We cannot determine a net flow direction for the extraplanar gas because the errors on the systemic velocity $\sim100~\kms$ ) for these two galaxies are large compared to the velocity shifts $\sim 10-65 \kms$ ) in their extraplanar spaxels. +" However, we do confirm the existence of ionized gas at large scale heights above the disk of both members."," However, we do confirm the existence of ionized gas at large scale heights above the disk of both members." +" To determine what happens to the gas in these three members, we first estimate how much ionized gas is in the observed outflow."," To determine what happens to the gas in these three members, we first estimate how much ionized gas is in the observed outflow." +" For SG1120-S1, using the H5 lines from our single-slit data and the relation inoutflow.,, we assume case B recombination and an electron of 100cm? to estimate a total ionized gas mass of My;~10° in the two components of the HG line (Lag=2Mox1099erg s~!)."," For SG1120-S1, using the $\beta$ lines from our single-slit data and the relation in, we assume case B recombination and an electron of $100 \cmc$ to estimate a total ionized gas mass of $M_{\mbox{\tiny +HII}}\sim 10^5\ \msol$ in the two components of the $\beta$ line $L_{H\beta} += 2\times 10^{39}\ \ergsec$ )." + Next we estimate an outflow rate (M) for the ionized gas by comparing the mass inferred from the Hj emission to a dynamical timescale., Next we estimate an outflow rate $\dot{M}$ ) for the ionized gas by comparing the mass inferred from the $\beta$ emission to a dynamical timescale. +" Using the single- data we assume a radius of 1 kpc, consistent with the extent of the emission lines, and an outflow velocity of 900kms! from the most blueshifted component on the [OIIIJA5007 line, giving us tayn—R/V~10° yr."," Using the single-slit data we assume a radius of 1 kpc, consistent with the extent of the emission lines, and an outflow velocity of $900 \kms$ from the most blueshifted component on the $\lambda$ 5007 line, giving us $t_{dyn}=R/V\sim10^6$ yr." + For, For +"fraction and angle. respectively. with We have applied this polarisation analysis to. our observations of the 620.701 GHz H»O 53».44, ortho-transition.","fraction and angle, respectively, with We have applied this polarisation analysis to our observations of the 620.701 GHz $\mathrm{H}_{2}\mathrm{O}$ $5_{32}-4_{41}$ ortho-transition." +" Our results shown in Figure | were obtained from the two aforementioned observations made at epochs of corresponding position angles of 261.27"" and 277.46"",", Our results shown in Figure \ref{fig:spectra} were obtained from the two aforementioned observations made at epochs of corresponding position angles of $261.27^{\circ}$ and $277.46^{\circ}$. + Although there are no obvious strong polarisation signals from the maser emission peaks. we clearly detect polarisation levels ranging from pz1.5% to pz6% in regions of significant line intensity (e.. from approximately -5 to 45 km s7!).," Although there are no obvious strong polarisation signals from the maser emission peaks, we clearly detect polarisation levels ranging from $p\simeq1.5\%$ to $p\simeq 6\%$ in regions of significant line intensity (i.e., from approximately -5 to 45 km $^{-1}$ )." + Furthermore. the observed anti-correlation of the polarisation fraction with the Stokes 7 intensity is similar to previous ground-based polarisation observations (Girartetal.. aimed at the detection of the Goldreich-Kylafis effect 1n. non-masing molecular lines (Goldreich&Kylafis.1981:Cortesetal.2005). which appears to have first been detected in evolved stars (Glennetal.. 1997).," Furthermore, the observed anti-correlation of the polarisation fraction with the Stokes $I$ intensity is similar to previous ground-based polarisation observations \citep{Girart2004,Hezareh2010} aimed at the detection of the Goldreich-Kylafis effect in non-masing molecular lines \citep{GK1981,Cortes2005}, which appears to have first been detected in evolved stars \citep{Glenn1997}." +. We will discuss the relevance of the Goldreich-Kylatis effect for our observations in section 7 below., We will discuss the relevance of the Goldreich-Kylafis effect for our observations in section 7 below. + Several instrumental capabilities of HIFI and the observations obtained with them may be noted: (i) The two orthogonally polarised HIFI. receivers. are well matched and extremely stable., Several instrumental capabilities of HIFI and the observations obtained with them may be noted: (i) The two orthogonally polarised HIFI receivers are well matched and extremely stable. + But observations. of extended sources need to be conducted with caution., But observations of extended sources need to be conducted with caution. +" A slight misalignment of H and V receivers can lead to a ""false polarisation"" that reverses polarity at half-year intervals (see Appendix Appendix A:)) ("," A slight misalignment of H and V receivers can lead to a “false polarisation"" that reverses polarity at half-year intervals (see Appendix \ref{sec:1557}) ). (" +11) The misalignment of the HIFI receivers does not appear to affect observations of unresolved sources.,ii) The misalignment of the HIFI receivers does not appear to affect observations of unresolved sources. + Our observations realised at two observing epochs indicate that instrumental polarisation. which could be in part due to errors in the relative calibration between the two receiver chains of Band 1B. cannot exceed a measure of order |2% (see section 7 below). (," Our observations realised at two observing epochs indicate that instrumental polarisation, which could be in part due to errors in the relative calibration between the two receiver chains of Band 1B, cannot exceed a measure of order $1-2\%$ (see section 7 below). (" +"it) The polarisation of VY CMais not significant near the peak of the 620.701 GHz H2O 53».44, line. but rises up to ~6% in the wings of the spectrum in a manner consistent with polarisation due to the Goldreich-Kylafis effect discussed in greater detail in section 7 below. (","iii) The polarisation of VY CMa is not significant near the peak of the 620.701 GHz $\mathrm{H}_{2}\mathrm{O}$ $5_{32}-4_{41}$ line, but rises up to $\sim 6\%$ in the wings of the spectrum in a manner consistent with polarisation due to the Goldreich-Kylafis effect discussed in greater detail in section 7 below. (" +1v) The stability of the 620.701 GHz masers 15 remarkable.,iv) The stability of the 620.701 GHz masers is remarkable. + The variation over a three week periodis profile<1% (see Figure 2). (, The variation over a three week period is $\lesssim1\%$ (see Figure 2). ( +v) As Figure3. shows. the spectral of the 620.701 GHz and 22.235 GHz masers appears remarkably similar.,"v) As Figure \ref{fig:22vs621} shows, the spectral profile of the 620.701 GHz and 22.235 GHz masers appears remarkably similar," +The number of known astronomical sources of very-high-energy (VHE) y-rays grew ten-fold over the last five.,The number of known astronomical sources of very-high-energy (VHE) s grew ten-fold over the last five. +. A large part of the newly discovered sources lie in the Galaxy and were revealed via a systematic scan of the inner Galactic Plane by the HESS telescope (Aharonianetal..2005a.2006).," A large part of the newly discovered sources lie in the Galaxy and were revealed via a systematic scan of the inner Galactic Plane by the HESS telescope \citep{HESS_survey_science,HESS_survey}." + The HESS survey has covered an area 0.1 srin a strip ή<307. |b]<37.," The HESS survey has covered an area 0.1 sr in a strip $|l|<30^\circ$, $|b|<3^\circ$." + This covers less than of the sky., This covers less than of the sky. + Surveys of larger regions on the VHE ssky with the existing ground based Cherenkov ttelescopes are difficult because the size of the field of view Is too narrow (5° for HESS. 3.5° VERITAS telescopes and 3° for MAGIC telescope).," Surveys of larger regions on the VHE sky with the existing ground based Cherenkov telescopes are difficult because the size of the field of view is too narrow $5^\circ$ for HESS, $3.5^\circ$ VERITAS telescopes and $3^\circ$ for MAGIC telescope)." + A previous survey of the northern hemisphere using the Cherenkov telescope Whipple has resulted only in derivation of upper limits on the flux of persistent VHE ssources (Weekesetal. 1979). , A previous survey of the northern hemisphere using the Cherenkov telescope Whipple has resulted only in derivation of upper limits on the flux of persistent VHE sources \citep{whipple_survey}. . +The wide field of view MILAGRO (Atkinsetal..2004) and Tibet (Amenomonrtetal..2005) arrays have produced a systematic survey of the VHE ssky., The wide field of view MILAGRO \citep{milagro} and Tibet \citep{tibet} arrays have produced a systematic survey of the VHE sky. + However. the energy threshold of the air shower arrays like MILAGRO and TIBET is rather high (in the multi-TeV band) so that only sources with spectra extending well above | TeV could be detected.," However, the energy threshold of the air shower arrays like MILAGRO and TIBET is rather high (in the multi-TeV band) so that only sources with spectra extending well above 1 TeV could be detected." + Contrary to the ground-based Cherenkov ttelescopes.Fermi has a wide field-of-view and continuously surveys the whole sky on a timescale of 3.2 hr.," Contrary to the ground-based Cherenkov telescopes, has a wide field-of-view and continuously surveys the whole sky on a timescale of $3.2$ hr." + Over the first year of operation has detected some 1.5x10? Galactic and extragalactic sources of y-rays with energies above | GeV (Abdoetal..2009).., Over the first year of operation has detected some $1.5\times 10^{3}$ Galactic and extragalactic sources of s with energies above 1 GeV \citep{fermi_catalog}. + The smaller collection area of C Lim’. compared to ~10? n? for the ground-based ttelescopes) prevents an extension of the all-sky monitoring with to the VHE bband.," The smaller collection area of $\sim 1$ $^2$, compared to $\sim 10^5$ $^2$ for the ground-based telescopes) prevents an extension of the all-sky monitoring with to the VHE band." + However. the collection area of is still sutficient for detecting the brightest ssources at the energies above 100 GeV. The power of the all- monitoring capabilities of at the highest energies was clearly demonstrated by discoveries of new VHE ssources motivated by detections of these sources above 10 GeV (Ong.2009.2010).," However, the collection area of is still sufficient for detecting the brightest sources at the energies above 100 GeV. The power of the all-sky monitoring capabilities of at the highest energies was clearly demonstrated by discoveries of new VHE sources motivated by detections of these sources above 10 GeV \citep{ATEL2260,ATEL2486}." +. The all-sky survey capabilities of space-based ttelescope EGRET at the energies above 10 GeV were used for the search of new VHE bblazars by Dingus&Bertsch(2001):Gorbunovetal.(2005) via cross-correlation of arrival directions of highest energy EGRET photons with positions of known sources.," The all-sky survey capabilities of space-based telescope EGRET at the energies above 10 GeV were used for the search of new VHE blazars by \citet{dingus01,10GeV_EGRET} via cross-correlation of arrival directions of highest energy EGRET photons with positions of known sources." + Below we use data to produce a survey of extragalactic sky at the energies above 100 GeV. re. in the energy range accessible for the ground-based ttelescopes.," Below we use data to produce a survey of extragalactic sky at the energies above 100 GeV, i.e. in the energy range accessible for the ground-based telescopes." + We find that most of the sources visible with at the energies above 100 GeV are known TeV blazars., We find that most of the sources visible with at the energies above 100 GeV are known TeV blazars. + The only source which has not previously been reported as a VHE ssource turns out to be IC 310. which is a head-tail radio galaxy (Sibring&deBruyn.1998). with. possibly a BL Lae type nucleus (Rectoretal..1999).," The only source which has not previously been reported as a VHE source turns out to be IC 310, which is a head-tail radio galaxy \citep{sijbring98} with possibly a BL Lac type nucleus \citep{rector}." + Two radio galaxies have previously been reported to be the sources of y-rays with energies above 100 GeV: M87 (Aharonianetal..2005b:Albert2008:Acciari2009) and Cen A (Aharonianetal..2009).. These two sources are the two closest Fanaroff-Riley type | (FR D) radio galaxies.," Two radio galaxies have previously been reported to be the sources of s with energies above 100 GeV: M87 \citep{m87,m87_magic,m87_veritas} and Cen A \citep{cena}.. These two sources are the two closest Fanaroff-Riley type I (FR I) radio galaxies." +" The FR I radio galaxies form the ""parent population of BL Lac type blazars (Urry&Padovani.1995)."," The FR I radio galaxies form the ""parent"" population of BL Lac type blazars \citep{urry95}." +. They are expected to be weak VHE eemitters. because the ffülux from these sources is not boosted by the relativistic Doppler effect.," They are expected to be weak VHE emitters, because the flux from these sources is not boosted by the relativistic Doppler effect." + In this respect it is not surprising that only the two nearest FR I radio galaxies have been seen in the VHE bband so far., In this respect it is not surprising that only the two nearest FR I radio galaxies have been seen in the VHE band so far. + Both Cen A and M87 are too weak to be detected at 100 GeV in the 1.5 yr exposure ofFermi., Both Cen A and M87 are too weak to be detected at 100 GeV in the 1.5 yr exposure of. + iis situated in Perseus galaxy cluster at the distance of 80 Mpc. which is a factor of 22 and 5 larger than the distances of Cen A and M 87. respectively.," is situated in Perseus galaxy cluster at the distance of 80 Mpc, which is a factor of 22 and 5 larger than the distances of Cen A and M 87, respectively." + iis. therefore. by 1-2 orders of magnitude more luminous than that of Cen A and M87.," is, therefore, by 1-2 orders of magnitude more luminous than that of Cen A and M87." + Besides. lis not classified as a FR [E type radio galaxy.," Besides, is not classified as a FR I type radio galaxy." + Instead. it 15 à head-tail radio galaxy (Sijbring&deBruyn. 1998)..the type of galaxiesusually foundin galaxy clusters.," Instead, it is a head-tail radio galaxy \citep{sijbring98}, ,the type of galaxiesusually foundin galaxy clusters." + It possesses, It possesses +ist of x and ν coordinates for cach object. one set for each stack the object is found. on.,"list of x and y coordinates for each object, one set for each stack the object is found on." + Calculating proper motions is then simply a matter of performing a linear regression it to each object's x and v coordinates as a function of ime., Calculating proper motions is then simply a matter of performing a linear regression fit to each object's x and y coordinates as a function of time. + Llowever. erroneous pairing inevitably occurs between stacks. and. we therefore wish to perform some form of bad »oint rejection to reduce contamination by spurious proper motions.," However, erroneous pairing inevitably occurs between stacks, and we therefore wish to perform some form of bad point rejection to reduce contamination by spurious proper motions." +" In order to reject deviant points (and. calculate xwanpeters such as o, and "" 47) an estimate of the error associated with cach measure of position is required."," In order to reject deviant points (and calculate parameters such as $\sigma +_{\mu}$ and $\chi^{2}$ ) an estimate of the error associated with each measure of position is required." + We assume this error is simply a function of magnitude and hat it will vary from stack to stack. but. not across the survey area.," We assume this error is simply a function of magnitude and that it will vary from stack to stack, but not across the survey area." + This error is calculated. using the deviation of an objects position on a particular stack [rom the mean »osition over the 20 stacks used. and is determined: over 10 magnitudeὃν bins.," This error is calculated using the deviation of an object's position on a particular stack from the mean position over the 20 stacks used, and is determined over 10 magnitude bins." + A 3e iterative rejection procedure. is implemented. to reject. spurious pairings or high proper motion objects which are not reflecting the true positional errors sought., A $3\sigma$ iterative rejection procedure is implemented to reject spurious pairings or high proper motion objects which are not reflecting the true positional errors sought. + The calculated errors are much as one might expect: decreasing for brighter objects until factors such as saturation and blended. images makes positional measures more uncertain., The calculated errors are much as one might expect: decreasing for brighter objects until factors such as saturation and blended images makes positional measures more uncertain. + A straight line fit can now be applied to the x and v data for cach object. the gradient. of which is taken to be the measured. proper motion. ji. and fry respectively.," A straight line fit can now be applied to the x and y data for each object, the gradient of which is taken to be the measured proper motion, $\mu_{x}$ and $\mu_{y}$ respectively." + An example is shown in Figure 2.. the points showing the deviation at each epoch from the average object position with error bars caleulated as above.," An example is shown in Figure \ref{pmplot}, the points showing the deviation at each epoch from the average object position with error bars calculated as above." + Deviant points arising [rom spurious pairings often lic fu from the other data ancl will give rise to spurious high proper motion detections if not removed., Deviant points arising from spurious pairings often lie far from the other data and will give rise to spurious high proper motion detections if not removed. +We therefore iteratively remove points lying 3o from the fitted line.,We therefore iteratively remove points lying $3\sigma$ from the fitted line. + Εις can occasionally lead to further problems if there are several bad. points associated. with the object. and the result. of several iterations can be a larger spurious motion detection.," This can occasionally lead to further problems if there are several bad points associated with the object, and the result of several iterations can be a larger spurious motion detection." + This source of contamination is generally eliminated. by insisting sample objects are detected on virtually every stack., This source of contamination is generally eliminated by insisting sample objects are detected on virtually every stack. + “Phe validity of the positional error estimation scheme described above has been verified by confirming that scatter plots of log reduced 47 as à function of magnitude cluster around. zero for all magnitudes in all regions of the survey arena., The validity of the positional error estimation scheme described above has been verified by confirming that scatter plots of log reduced $\chi^{2}$ as a function of magnitude cluster around zero for all magnitudes in all regions of the survey area. + Instrumental magnitudes are calculated [or every object. detected. on. cach stack in. the. standard COSMOS/SuperCOSMOS. fashion (Beard et al., Instrumental magnitudes are calculated for every object detected on each stack in the standard COSMOS/SuperCOSMOS fashion (Beard et al. + 1990 ancl references. therein)., 1990 and references therein). + Brielly. an object. detection is defined by a given number of interconnected: pixels. with intensity above a given threshold (ce.," Briefly, an object detection is defined by a given number of interconnected pixels with intensity above a given threshold (eg." + S interconnected pixels with intensity above a 2.57 sky noise threshold. for SuperCOSMOS data)., 8 interconnected pixels with intensity above a $2.5\sigma$ sky noise threshold for SuperCOSMOS data). + An objects instrumental magnitude is then calculated. as the log of the sum of the intensity above background. across the object area., An object's instrumental magnitude is then calculated as the log of the sum of the intensity above background across the object area. + This. quantity varies monotonically with true magnitude. and is therefore suitable. for use in constructing calibration curves using a CCD sequence.," This quantity varies monotonically with true magnitude, and is therefore suitable for use in constructing calibration curves using a CCD sequence." + A sequence of ~200 stars with CCD magnitudes measured. in a variety of passbands exists. in ficld 287 (αννκας et al., A sequence of $\sim 200$ stars with CCD magnitudes measured in a variety of passbands exists in field 287 (Hawkins et al. + 1998). vielding U. D. V. IG and 1 photometry to a tvpical accuracy of 0.15 magnitudes (see Section 5.2)).," 1998), yielding U, B, V, R and I photometry to a typical accuracy of 0.15 magnitudes (see Section \ref{photom}) )." + Significantly smaller errors are theoretically obtainable from photographic material. ancl the larger uncertainties we find appear to be caused. by systematic deviations of sequence objects from the calibration curve.," Significantly smaller errors are theoretically obtainable from photographic material, and the larger uncertainties we find appear to be caused by systematic deviations of sequence objects from the calibration curve." + This is not a colour or field effect. and is probably caused by dillerences in detection media.," This is not a colour or field effect, and is probably caused by differences in detection media." + The ceatalogue! resulting from the implementation of the procedure deseribed. in the previous section. consists. of astrometric and. photometric measures for. over. 200.000 objects.," The `catalogue' resulting from the implementation of the procedure described in the previous section consists of astrometric and photometric measures for over 200,000 objects." + Criteria for. inclusion. in this preliminary sample is merely detection in both By ancl 1t passbands. (since these are required. for construction of the reduced. proper motion clagram (RPALD)) and a measure of proper motion in both these passbancs., Criteria for inclusion in this preliminary sample is merely detection in both $\rm B_{J}$ and R passbands (since these are required for construction of the reduced proper motion diagram (RPMD)) and a measure of proper motion in both these passbands. + Lt is from these objects that an uncontaminated proper motion sample is to be drawn: and we require well defined universal survey limits so that space densities can be calculated from the final survey. sample., It is from these objects that an uncontaminated proper motion sample is to be drawn; and we require well defined universal survey limits so that space densities can be calculated from the final survey sample. + Number count plots from this survey cata increase linearly with increasing magnitude. as shown for the It data in Figure 3.. before dropping precipitously.," Number count plots from this survey data increase linearly with increasing magnitude, as shown for the R data in Figure \ref{Rhist}, before dropping precipitously." + Εις eut-olf is attributed to the survey detection. limit. and the position of the turnover is used to determine photometric survey limits.," This cut-off is attributed to the survey detection limit, and the position of the turnover is used to determine photometric survey limits." + The limits used are 21.2 in It and 22.5 in D. The proper motion distribution for all objects in. our survey area detected on at least 15 stacks in both D and 1H is shown in Figure 4.., The limits used are 21.2 in R and 22.5 in B. The proper motion distribution for all objects in our survey area detected on at least 15 stacks in both B and R is shown in Figure \ref{pmhist}. + Low proper motions are generally an artifact of measuring machine error. thus the distribution indicates a typical error in measured. proper motions of I0mas/vr. Our criteria for choosing a survey proper motion limit," Low proper motions are generally an artifact of measuring machine error, thus the distribution indicates a typical error in measured proper motions of $ \rm \sim10mas/yr$ Our criteria for choosing a survey proper motion limit" +does not exceed ~30 for the scattering inside the light cylinder.,does not exceed $\sim 30^\circ$ for the scattering inside the light cylinder. + We have considered the induced Compton scattering by the particles of the ultrarelativistic electron-positron plasma in the presence of a superstrong magnetic field., We have considered the induced Compton scattering by the particles of the ultrarelativistic electron-positron plasma in the presence of a superstrong magnetic field. + In. particular. we have examined the scattering. of pulsar. radio beam into background. which takes place in the open field. line tube of a pulsar.," In particular, we have examined the scattering of pulsar radio beam into background, which takes place in the open field line tube of a pulsar." + Le has been demonstrated that the photons are predominantly scattered. approximately along the ambient magnetic field., It has been demonstrated that the photons are predominantly scattered approximately along the ambient magnetic field. + This contrasts with the non-magnetic scattering. in which case the scattered: photons concentrate in the backward. direction.," This contrasts with the non-magnetic scattering, in which case the scattered photons concentrate in the backward direction." + This dillerence. is solely determined by a specific role of the superstrong magnetic field in the scattering process and does not depen on a detailed form of the particle distribution function., This difference is solely determined by a specific role of the superstrong magnetic field in the scattering process and does not depend on a detailed form of the particle distribution function. +" InclueecL scattering in a superstrong magnetic Lick transfers the photons from lower to higher. frequencies. py,~d757οon10e,. and if the process is ellicient. the scattered Component may. become as strong as the origina racio. bean. Z,,Gn)~£5,iGh)."," Induced scattering in a superstrong magnetic field transfers the photons from lower to higher frequencies, $\nu_b\sim\nu_a\theta^2\gamma^2\sim n\cdot 10\nu_a$, and if the process is efficient, the scattered component may become as strong as the original radio beam, $I_{\nu_b}(\nu_b)\sim +I_{\nu_a}^{(0)}(\nu_a)$." + As the beam has a decreasing. spectrum. Ρα...τοeoqn(7). the intensity of the scatterec component may dominate the original beam intensity at the same frequency. d£.," As the beam has a decreasing spectrum, $I_{\nu_a}^{(0)}(\nu_a)\gg I_{\nu_a}^{(0)}(\nu_b)$, the intensity of the scattered component may dominate the original beam intensity at the same frequency $\nu_b$." + For steep enough original spectra. of pulsar radiation. ac2. the induced. scattering in a superstrong magnetic field is most elficient at. distances roughly comparable to the radius of evelotron resonance.," For steep enough original spectra of pulsar radiation, $\alpha>2$, the induced scattering in a superstrong magnetic field is most efficient at distances roughly comparable to the radius of cyclotron resonance." + Because of rotational aberration. the scattered component appears in the pulse profile as a precursor to the main pulse.," Because of rotational aberration, the scattered component appears in the pulse profile as a precursor to the main pulse." +" This elfect provi""sS the main pulse-precursor separationsin longitude rsinc/2ri. which may run up to 30°."," This effect provides the main pulse-precursor separationsin longitude $\Delta\lambda\sim r\sin\zeta/2r_L$ , which may run up to $\sim 30^\circ$." + Since the length of the scattering region is larger than the height. of the emission region. the intrinsic radiuseto-frequencey. mapping of the radio emission is smeared.," Since the length of the scattering region is larger than the height of the emission region, the intrinsic radius-to-frequency mapping of the radio emission is smeared." + The cllective height of the scattering region is an extremely weak function of the wave [requeney. so that the main pulse-precursor. separation is practically independent of frequency. just as is observed.," The effective height of the scattering region is an extremely weak function of the wave frequency, so that the main pulse-precursor separation is practically independent of frequency, just as is observed." + Since the induced scattering in. the superstrong magnetic Ποιά holds only between the ordinary waves. the scattered. component should have complete linear polarization.," Since the induced scattering in the superstrong magnetic field holds only between the ordinary waves, the scattered component should have complete linear polarization." + This is indeed the main distinctive feature of the observed. precursors., This is indeed the main distinctive feature of the observed precursors. + Note that in general &«5][/Ry 6]. ic. in the main pulse and. precursor the position angles of linear. polarization should somewhat cdiller.," Note that in general $[{\bmath k}\times{\bmath b}]\not\parallel[{\bmath +k_1}\times{\bmath b}]$ , i.e. in the main pulse and precursor the position angles of linear polarization should somewhat differ." + Such a dillerence can be noticed. e... in PSR. DB1822-09 (Fowleretal. 1981).," Such a difference can be noticed, e.g., in PSR B1822-09 \citep{f81}." +.. Besides that. if the main pulse is dominated by the extraordinary rather than ordinary. polarization. the position angle of the precursor should additionally diller by 90. as is the case in the Vela pulsar. (Ixrishnamohan&Downs 1983).," Besides that, if the main pulse is dominated by the extraordinary rather than ordinary polarization, the position angle of the precursor should additionally differ by $90^\circ$, as is the case in the Vela pulsar \citep{kd83}." +. As first noted by Fowlerctal.CI981).. the precursor components are met in pulsars with relatively large surface magnetic field.," As first noted by \citet{f81}, the precursor components are met in pulsars with relatively large surface magnetic field." +" Firstly. large D, are necessary for the regime ol superstrong magnetic field to hold well above the emission region."," Firstly, large $B_\star$ are necessary for the regime of superstrong magnetic field to hold well above the emission region." +" Secondly. the scattering ellicieney is proportional to B,."," Secondly, the scattering efficiency is proportional to $B_\star$." + Short periods ancl large radio luminosities also favour significant scattering., Short periods and large radio luminosities also favour significant scattering. + The pulse-to-pulse variations of the incident intensity ancl of the physical parameters in the scattering region may result in strong Uuctuations of the precursor emission., The pulse-to-pulse variations of the incident intensity and of the physical parameters in the scattering region may result in strong fluctuations of the precursor emission. + The former variations imply the main pulse-precursor connection. which may have civersiform observational manifestations.," The former variations imply the main pulse-precursor connection, which may have diversiform observational manifestations." + Lor example. PSR J1826-6700 shows occasional main pulse nullings accompanied by the strong precursor emission. (Wangetal.2007).," For example, PSR J1326-6700 shows occasional main pulse nullings accompanied by the strong precursor emission \citep{w07}." +" This can he interpreted as a consequence of extremely strong scattering. (Lp,iU!ἐν)exp(U)Z91. when the main pulse intensity is almost completely. transferred to the precursor. Z,,—70. laii""Note ."," This can be interpreted as a consequence of extremely strong scattering, $(I_{\nu_b}^{(0)}/I_{\nu_a}^{(0)})\exp (\Gamma)\gg 1$, when the main pulse intensity is almost completely transferred to the precursor, $I_{\nu_a}\to 0$, $I_{\nu_b}\to I_{\nu_a}^{(0)}$." + that this. may happen only ifep the originalM intensity is mainly in the ordinary modo. which is subject to the scattering.," Note that this may happen only if the original intensity is mainly in the ordinary mode, which is subject to the scattering." +" In case of a moderately strong scattering. VIPiii1)exp(E)H~I. the main. pulse intensity. Z5,iU. is almost unchanged. whereas the precursor grows exponentially with I5"," In case of a moderately strong scattering, $(I_{\nu_b}^{(0)}/I_{\nu_a}^{(0)})\exp (\Gamma)\sim 1$, the main pulse intensity $I_{\nu_a}^{(0)}$ is almost unchanged, whereas the precursor grows exponentially with $I_{\nu_a}^{(0)}$." + Phovefore even weak lucetuations of the latter quantity mav alleet the scattered. component. dramatically., Therefore even weak fluctuations of the latter quantity may affect the scattered component dramatically. + La some pulsars the precursors are indeed met only in strong pulses (Llankins&Cordes1981:Ciletal.1994:Weltevredect2006).. and one can expect that the transient. precursors are much more abundant in the pulsar population and are vet to be studied observationally.," In some pulsars the precursors are indeed met only in strong pulses \citep{hc81,g94,welt06}, and one can expect that the transient precursors are much more abundant in the pulsar population and are yet to be studied observationally." + The precursor component can Uuetuate not only in intensity. but. also in pulse longitude., The precursor component can fluctuate not only in intensity but also in pulse longitude. + In the Vela pulsar. stronger precursors exhibit larger separations [rom the main pulse. which is thought to result. from the fluctuations of the physical. parameters in the scattering region.," In the Vela pulsar, stronger precursors exhibit larger separations from the main pulse, which is thought to result from the fluctuations of the physical parameters in the scattering region." +" Larger separations imply Larger scattering heights. AAxor. in which case the angle of incidence of the photons is also larger. @x r. and at a fixed. [requeney. v, the precursor is formed by the photonscoming from. lower frequencies We=anf0ye? which are more numerous ancl stimulate stronger scattering."," Larger separations imply larger scattering heights, $\Delta\lambda\propto r$ , in which case the angle of incidence of the photons is also larger, $\theta\propto r$ , and at a fixed frequency $\nu_b$ the precursor is formed by the photonscoming from lower frequencies $\nu_a=\nu_b/\theta^2(r)\gamma^2$ , which are more numerous and stimulate stronger scattering." +continu exposures were used to subtract the coufinmmun contribution to the oenüsson line nuaees.,continuum exposures were used to subtract the continuum contribution to the emission line images. + Iu addition. we have long-slit. high-cispersion echelle spectra of the SNR caudidates from the CTIO bu telescope.," In addition, we have long-slit, high-dispersion echelle spectra of the SNR candidates from the CTIO 4m telescope." + The data have a tan pixel size that corresponds to 0.082 ((3.65 1)) along the dispersion axis aud ~0726 along the skv., The data have a $\mu$ m pixel size that corresponds to 0.082 (3.65 ) along the dispersion axis and $\sim 0\farcs 26$ along the sky. +" The spatial coverage alone the slit is roughly 3"". limited by the optics of the calcera."," The spatial coverage along the slit is roughly $3'$, limited by the optics of the camera." + Details of the reduction of these data can be found in Sinithetal.(2011.iupreparation)., Details of the reduction of these data can be found in \citet{inprep}. +. The echelle profile of the liue is broadened along the dispersion axis both by the inherent iustrunental profile (—Ll 13) aud by thermal Doppler broadening (~IS at N-rav teniperatures)., The echelle profile of the line is broadened along the dispersion axis both by the inherent instrumental profile $\sim14$ ) and by thermal Doppler broadening $\sim18$ at X-ray temperatures). + To assign au expansion velocity to cach remmaut. we extract profiles aloug the dispersion axis where he enuüsson shows the greatest dispersion aud neasure the peaks of the profile.," To assign an expansion velocity to each remnant, we extract profiles along the dispersion axis where the emission shows the greatest dispersion and measure the peaks of the profile." + Using the fux-calibrated AICELS nuages. we ueasured an ssurtace brightness aud the average radius AP aud hickuess AR of the shell.," Using the flux-calibrated MCELS images, we measured an surface brightness and the average radius $R$ and thickness $\Delta R$ of the shell." + For a uniform spherical shell. the ereatest line of sight through the shell is L=2\/R?(R AR).," For a uniform spherical shell, the greatest line of sight through the shell is $\mathcal{L}=2\sqrt{R^{2}-(R-\Delta R)^{2}}$ ." + The measured surface xiehtuess then duplics au enuüssion nmieasure EM=u2£5«1075OSB where SD is the surface briehtuess i ces units aud arcsecouds., The measured surface brightness then implies an emission measure $\mathrm{EM}\equiv n^{2}_{e}\mathcal{L}=5\times10^{17}\times \mathrm{SB}$ where SB is the surface brightness in cgs units and arcseconds. + The total mass of the warm. ionized shell is AL=L2vYnangVaar where Vac is the volhune of the shell aud assuuiug singly ionized elim.," The total mass of the warm ionized shell is $M=1.27n_{{e}}m_{{p}}\Vshell$, where $\Vshell$ is the volume of the shell and assuming singly ionized helium." +" Expausonu velocities (a4, have been determined from echelle spectra of the ecnissiou-Iue. aud thus we may determine kinetic euergies for the warin shells by A=2."," Expansion velocities $v_\mathrm{exp}$ have been determined from echelle spectra of the emission-line, and thus we may determine kinetic energies for the warm shells by $K=Mv^{2}_{\mathrm{exp}}/2$." +" It we assuune that T=101 K. we can also Mey,calculate the pressure in the shell as Pop=2».kT2.16«10 στης."," If we assume that $T=10^{4}$ K, we can also calculate the pressure in the shell as $P_{\mathrm{shell}}=2n_{{e}}kT=2.76\times 10^{-12}n_{{e}}$ ." + Tn calculating the volume of the shell. we assuned an cllipsoidal ecometry. mneasudues two axes from the projected face of the shell aud takine the third line-ofsielit axis to be the average of these two.," In calculating the volume of the shell, we assumed an ellipsoidal geometry, measuring two axes from the projected face of the shell and taking the third line-of-sight axis to be the average of these two." + We then took the mucertaiutv in the radius along this third axis to be the deviation of the first two axes from their iiem., We then took the uncertainty in the radius along this third axis to be the deviation of the first two axes from their mean. + We also considered the iustruuieutal aud Doppler broadening of our echelle spectra as an additional source of error., We also considered the instrumental and Doppler broadening of our echelle spectra as an additional source of error. + Couvolving the two profiles. we found an uncertainty of 11L.," Convolving the two profiles, we found an uncertainty of 11." + Calculated quantities are listed in Table 2.., Calculated quantities are listed in Table \ref{snrtable}. + The age of the SNR may be estimated using the analytic expressions of the Sedov-Tavlor solution for blast wave expansion. iu which the shell radius is given as a fiction of time by rt)=LATERps where E ds the explosion euergv and p is the ambicut density.," The age of the SNR may be estimated using the analytic expressions of the Sedov-Taylor solution for blast wave expansion, in which the shell radius is given as a function of time by $ r(t)=1.17(Et^2/\rho)^{1/5}$, where $E$ is the explosion energy and $\rho$ is the ambient density." + TaXiug 1ο time derivative aud applying the BRaukiuc-IIugoniot conditions for a strong shock to relate ie blast wave velocity to the post-shock eas velocity 4. we find a(f)=0.351(E/pt?H.," Taking the time derivative and applying the Rankine-Hugoniot conditions for a strong shock to relate the blast wave velocity to the post-shock gas velocity $u$, we find $u(t)=0.351(E/\rho t^3)^{1/5}$." + Solving js system vields f=θα)., Solving this system yields $t=0.3(r/u)$. + We then obtain ie ages bv plugeiugOO in the radius observed iu ie optical mages and the velocities from the echelle spectra., We then obtain the ages by plugging in the radius observed in the optical images and the velocities from the echelle spectra. + These procedures apply best to remnants that are still in the Sedov-Tavlor phase of evolution. since post-Sedov-phase roemuauts continue to expand at a slower rate.," These procedures apply best to remnants that are still in the Sedov-Taylor phase of evolution, since post-Sedov-phase remnants continue to expand at a slower rate." + The Sedov-Tavlor phase is expected to cud when the post-shock gas velocity drops to ~190 kin |., The Sedov-Taylor phase is expected to end when the post-shock gas velocity drops to $\sim190$ km $^{-1}$. + Tnhomogencitics i the ambicut medium also affect the expansion rate., Inhomogeneities in the ambient medium also affect the expansion rate. + Iun addition. the observed velocities aud radii are found for individual parts of the SNRs aud. due to asviuuetries in the SNRs may uot adequately represent the whole objects.," In addition, the observed velocities and radii are found for individual parts of the SNRs and, due to asymmetries in the SNRs may not adequately represent the whole objects." + All of these effects combine to make the ages estimated from t=0:3(c0/4) approximate., All of these effects combine to make the ages estimated from $t = 0.3(r/u)$ approximate. + The suaulatious cescribed previously also provide an independent numerical estimate of the age., The simulations described previously also provide an independent numerical estimate of the age. + Alternatively. given the present values of r aud 0. one may solve for the ratio Ep. or equivalently Lf where vis the ambient number density. aud compare this with the value estimatedusing the X-ray spectral modeling aud Tea surface brightness techuiqucs as described above.," Alternatively, given the present values of $r$ and $u$, one may solve for the ratio $E/\rho$, or equivalently $E/n$ where $n$ is the ambient number density, and compare this with the value estimatedusing the X-ray spectral modeling and $\alpha$ surface brightness techniques as described above." + sshows the simplest structure of the three reninaunts presented here., shows the simplest structure of the three remnants presented here. + Its well defined sshell smrounds a smoothelliptical distribution of soft N-rav. emission with radii of 1:14«0.757 or 19.1.«11.25 pe., Its well defined shell surrounds a smoothelliptical distribution of soft X-ray emission with radii of $1.3'\times0.75'$ or $19.4\times11.25$ pc. + The shell has typical values for oof ~ 0.6. as opposed to πιαπα values ~0.2 elsewhere.," The shell has typical values for of $\sim0.6$ , as opposed to maximum values $\sim0.2$ elsewhere." + The bright eenissiou to the cast of, The bright emission to the east of +1992))).,). + Llere. we want briellv to analyze the biases and the errors due to the use of an “incorrect” parametric mocel to fit the observable data.," Here, we want briefly to analyze the biases and the errors due to the use of an “incorrect” parametric model to fit the observable data." + A wav to face this important question consists in to build simulated. svstems for a lens model and then to fit the image positions and time delays eencrated by it. using an other functional form. studving the change in the lens parameters ancl above all in .," A way to face this important question consists in to build simulated systems for a lens model and then to fit the image positions and time delays generated by it, using an other functional form, studying the change in the lens parameters and above all in $h$." + We can furnish a qualitative estimate of he effect. of he model depen:ence on Z£o., We can furnish a qualitative estimate of the effect of the model dependence on $H_0$. +" At the same time the procedure allows to quantify this ""systeniatic errors.", At the same time the procedure allows to quantify this “systematic” errors. + )v means of a simulated system built using t1e LEubble model. we fit to the image positions and the time cdelavs so obtained the and2.," By means of a simulated system built using the Hubble model, we fit to the image positions and the time delays so obtained the and." + The analysis of the most significant. parameters shows interesing trends which are partially already well Known., The analysis of the most significant parameters shows interesting trends which are partially already well known. + In particular. in our simulated system f=0.7. and the fitting of the other models gives us the means values =0.35 for the anc h0.46 for the3. respectively with a percentage change of 50% and 344.," In particular, in our simulated system $h=0.7$, and the fitting of the other models gives us the means values $h=0.35$ for the and $h=0.46$ for the, respectively with a percentage change of $50\%$ and $34\%$." + This percentage obviously. changes if we simulate other lens svstenms., This percentage obviously changes if we simulate other lens systems. +" This shows that if the ""correct? model for a lens is one with constant mass-to-light ratio and it tries to shape it with a separable model we obtain a lower estimate of 5 than that obtained with the first one: this veriies some previous results in Ditcrature (see (Ixochanek202) for an analysis mace on Leal systems).", This shows that if the “correct” model for a lens is one with constant mass-to-light ratio and it tries to shape it with a separable model we obtain a lower estimate of $h$ than that obtained with the first one; this verifies some previous results in literature (see \cite{Koch02} for an analysis made on real systems). + Similar trends are obtained if we create a simuaded system. using a de Vatσυ(ος model., Similar trends are obtained if we create a simulated system using a de Vaucouleurs model. + Leis also possib eto analyze he uncertainies introduced. by the lack of the internal ellipticitv of t1e lens galaxy., It is also possible to analyze the uncertainties introduced by the lack of the internal ellipticity of the lens galaxy. + IHE we try to fit wih the the observades generated with the2 we obtain a ower mean / rut i£ we consider the errors this «stinate is in agreement wih the simulated: value. instead t10 estimated value for à raises.," If we try to fit with the the observables generated with the we obtain a lower mean $h$ but if we consider the errors this estimate is in agreement with the simulated value, instead the estimated value for $\alpha$ raises." + ὃν means of simulated systems we can also obtain statistical correlations anions paranietCrs in order to, By means of simulated systems we can also obtain statistical correlations among parameters in order to + General Relativity predicts redshift of photons due to a gravitational field.,] General Relativity predicts redshift of photons due to a gravitational field. + When a photon with wavelength Ais cluitted iu a gravitational potential &. it will lose energv when it climbs up in the eravitational field aud will consequently be redshitted.," When a photon with wavelength $\lambda$ is emitted in a gravitational potential $\Phi$, it will lose energy when it climbs up in the gravitational field and will consequently be redshifted." + The redshift observed at infinity is given in the weak field linüt by: where AA. Ad are respectively the difference in wavelength. and difference im potential between where the photon is cluitted and where it is observed.," The redshift observed at infinity is given in the weak field limit by: where $\Delta \lambda$, $\Delta \Phi$ are respectively the difference in wavelength, and difference in potential between where the photon is emitted and where it is observed." + If we consider galaxies as sources of the photons. the eravitational redshift effect is so tiny that we take it for eranted that a measurement of the total galaxy redshift can be asstuned to be the stun of Thibble expansion and peculiar velocities.," If we consider galaxies as sources of the photons, the gravitational redshift effect is so tiny that we take it for granted that a measurement of the total galaxy redshift can be assumed to be the sum of Hubble expansion and peculiar velocities." + In this paper we examine whether this is always the case. aud in particular whether galaxies im galaxy clusters could have measurable values of τρ.," In this paper we examine whether this is always the case, and in particular whether galaxies in galaxy clusters could have measurable values of $z_{g}$." + Since the eravitational potential depends ou the mass distribution around galaxies. the eravitational redshift. if observable. should be most evident iu dense environments.," Since the gravitational potential depends on the mass distribution around galaxies, the gravitational redshift, if observable, should be most evident in dense environments." +" Iu an early study by Nottale (1976). the redshitt difference between pairs of clusters was compared to the richness difference,"," In an early study by Nottale (1976), the redshift difference between pairs of clusters was compared to the richness difference." + À supposed strong effect was found. with the pair ου. of higher richness having a svstcmatically lnieh redshift.," A supposed strong effect was found, with the pair member of higher richness having a systematically high redshift." + ILlowever. when Rood Struble (1982) rexanuned this with a larger sample. their result showed no such correlation.," However, when Rood Struble (1982) rexamined this with a larger sample, their result showed no such correlation." + Nottale (19900). discussed. that. the effect should be looked for in galaxies at the centers of ealaxv clusters. by comparing them redshifts with those of galaxies at the cluster edges.," Nottale (1990) discussed that the effect should be looked for in galaxies at the centers of galaxy clusters, by comparing their redshifts with those of galaxies at the cluster edges." + Stiavelli Setti (1993) carried out a related test in iudividual elliptical ealaxies. finding at 99.9% confidence that elliptical galaxy cores are redshifted with respect to the galaxw outer regions. explaining this as a result of eravitational redshift.," Stiavelli Setti (1993) carried out a related test in individual elliptical galaxies, finding at $99.9\%$ confidence that elliptical galaxy cores are redshifted with respect to the galaxy outer regions, explaining this as a result of gravitational redshift." + The study of gravitational redshifts in galaxy clusters was taken further by Cappi (1995). who modelled clusters using differcut density profiles iucludiug a de Vaucouleurs law.," The study of gravitational redshifts in galaxy clusters was taken further by Cappi (1995), who modelled clusters using different density profiles including a de Vaucouleurs law." + It was predicted that the eravitational redshift is non-ueelieible in very rich clusters., It was predicted that the gravitational redshift is non-negligible in very rich clusters. + For example. the centers of clusters of masses 10195.EXD. should be vedshifted by as nich as 300nis with respect to infinity.," For example, the centers of clusters of masses $10^{16} \msun$ should be redshifted by as much as $300 \kms$ with respect to infinity." + Broadlurst Scannapieco (2000) modelled the effect using a Navarro Freuk White (1997) (hereafter NEW) density profile. and sugeested that the gravitational redshift of ictal lunes iu the cluster eas could eventually be used to nap out the potential directly.," Broadhurst Scannapieco (2000) modelled the effect using a Navarro Frenk White (1997) (hereafter NFW) density profile, and suggested that the gravitational redshift of metal lines in the cluster gas could eventually be used to map out the potential directly." + As the gravitational redshitt is sensitive to the distribution of mass in the mnerost regions of clusters. it could be used as à probe to coustrain the amount of dark matter there.," As the gravitational redshift is sensitive to the distribution of mass in the innermost regions of clusters, it could be used as a probe to constrain the amount of dark matter there." + Ciavitational redshifts would provide complinentary information to eravitational lensing (e... Sand 2003). as uulike leusiug they do uot depend on the mass deusity projected along the line of sight.," Gravitational redshifts would provide complimentary information to gravitational lensing (e.g., Sand 2003), as unlike lensing they do not depend on the mass density projected along the line of sight." + Tere we use an N-body saulation mace publically available by the Virgo Consortimu (Freak et al., Here we use an $N$ -body simulation made publically available by the Virgo Consortium (Frenk et al. + 2000) to estimate the magnitude of the effect of gravitational redshifts on ealaxy clusters in a ACDAL universe., 2000) to estimate the magnitude of the effect of gravitational redshifts on galaxy clusters in a $\rm{\Lambda CDM}$ universe. + We examine possible observational strategies and determine if ealaxv eravitational redshifts could be detected with a reasonable uunuber of clusters., We examine possible observational strategies and determine if galaxy gravitational redshifts could be detected with a reasonable number of clusters. + By using tle umucrical simulation. we will be able to study the effect of substructure in the density aud the potentially complex velocity field of realistic clusters.," By using the numerical simulation, we will be able to study the effect of substructure in the density and the potentially complex velocity field of realistic clusters." + We will see if Nottale’s suggestion of measuring the difference iu eravitational redshift between the ceutral galaxy aud galaxies at the οσο of the cluster is realizable iu practice., We will see if Nottale's suggestion of measuring the difference in gravitational redshift between the central galaxy and galaxies at the edge of the cluster is realizable in practice. + The poteutial wells should be deeper for the most massive clusters. which mieaus Ilurger eravitational redshitts.," The potential wells should be deeper for the most massive clusters, which means larger gravitational redshifts." + Towever. massive clusters are rare.," However, massive clusters are rare," +REFERENCES Riess. A.aL.. 2001. ApJ.. 560. 49-71. “,"REFERENCES Riess, A. 2001, 560, 49-71. “" +"The Farthest Known Supernova: Support for an Accelerating Universe and a Glimpse of the Epoch of Deceleration™” quote [rom abstract: ""It is inconsistent with erev dust or simple luminosity - Regos. E.. Tout. C.. Wickramasinghe. D.. Hurley. J. Pols. O. 2001. astro-ph/0112355. ""Could Edge-Lit Type Ia Supernovae be Standard Candles"" quote from abstract: ""we find à svstematie shift in Chis relation that would make distant SNe Ia fainter than those nearby"" Perlmutter. S. 11999.ÀpJ.. 517. 565-586.","The Farthest Known Supernova: Support for an Accelerating Universe and a Glimpse of the Epoch of Deceleration” quote from abstract: “It is inconsistent with grey dust or simple luminosity ' Regos, E., Tout, C., Wickramasinghe, D., Hurley, J. Pols, O. 2001, astro-ph/0112355, “Could Edge-Lit Type Ia Supernovae be Standard Candles” quote from abstract: “we find a systematic shift in this relation that would make distant SNe Ia fainter than those nearby” Perlmutter, S. 1999, 517, 565-586." +deusities exist iu the outer regions of these disks εrere ds stil sjenificaut amounts of gas cing transported ot js region (see Figure 5)).,densities exist in the outer regions of these disks there is still significant amounts of gas being transported to this region (see Figure \ref{fig:mass_transfer}) ). + ενis that solids :we carried along with the eas as] is transported outward. there is sufficient hass present for saollie formation.," Assuming that solids are carried along with the gas as it is transported outward, there is sufficient mass present for satellite formation." +" Caven a solar abuudaice of solids. wὉ calculated that there is rearly wice as mich nass in solids transported outwar¢ over a 10"" vr ine period than is needed o fonu Callisto."," Given a solar abundance of solids, we calculated that there is nearly twice as much mass in solids transported outward over a $10^5$ yr time period than is needed to form Callisto." + There are reasons το belicve hat the solids-to-gas mass ratio would be higher han soar and therefore we take lis value as an tunerCRuate., There are reasons to believe that the solids-to-gas mass ratio would be higher than solar and therefore we take this value as an underestimate. +" We plan to investigate the actual clistyinion and transport of solids in the near ""ture wath a more comprehensive model that is currently in developiieut.", We plan to investigate the actual distribution and transport of solids in the near future with a more comprehensive model that is currently in development. + Another aspect of our simulations that may Lave COlsCQ(quenceos oli satellite formation is the density cuhancement seen i our sinulations at ~25F» the location of peak mass infall.," Another aspect of our simulations that may have consequences on satellite formation is the density enhancement seen in our simulations at $\sim 25\ r_{\rm p}$, the location of peak mass infall." + A simular density cauhaucement was secu in ?.. but was nof preseut in more recent simulations wuc1 include radiative trauster (7?)..," A similar density enhancement was seen in \citet{machida08}, but was not present in more recent simulations which include radiative transfer \citep{ayliffe09}." +" Tt is unclear at this time if these density euhlhaucenienuts woukl be present in a more realistic model in whi11011 the viscosity was determined locally,", It is unclear at this time if these density enhancements would be present in a more realistic model in which the viscosity was determined locally. + This is an interesting question aud one which we plan to vesieate in the near future., This is an interesting question and one which we plan to investigate in the near future. + If it is real. fLOSC chhawcelments would have a siguificaut impact on satelite formation.," If it is real, these enhancements would have a significant impact on satellite formation." + Density eulianceiments suc las these are accolupanied by pressure maxima., Density enhancements such as these are accompanied by pressure maxima. + It has been shown that migrating solids cau be rapped Histch pressure niaxinia and rapidly erow iuto satelitesimials (7)., It has been shown that migrating solids can be trapped in such pressure maxima and rapidly grow into satellitesimals \citep{kretke09}. +" Iu an effort to test what effect the ocation at which iufalliug material intersects ιο disk las ou steady-state disk morphology. we have yerformecd oιο test sinuulatiou ia which 1e peak of the infalliue material occured at 35+, rather han at 25+» "," In an effort to test what effect the location at which infalling material intersects the disk has on steady-state disk morphology, we have performed one test simulation in which the peak of the infalling material occurred at $35\ r_{\rm p}$ rather than at $25\ r_{\rm p}$." +In the test simulation. the ocation of the disk outer edee was shifted farther out aud the otal disk iuass ducreased bv ," In the test simulation, the location of the disk outer edge was shifted farther out by $\sim 3 \%$ and the total disk mass increased by $\sim 5\%$." +The changes are a result of a greater Traction of he iufaling mass being traisported outward ratjor thaji inward., The changes are a result of a greater fraction of the infalling mass being transported outward rather than inward. + This test indicates hat it is nuyortant to ideutifv the exact location at which the iufalΠιο παν» accretes onto the circunplaueary clisk., This test indicates that it is important to identify the exact location at which the infalling mass accretes onto the circumplanetary disk. + Ilowever. the current 3-D ivdrodyvuauuical παπαΊος used to mocel imfall rou the solar ueula onto cireiunplauetarv disks have insufficient resolutio1 to ideutifv the location exactly.," However, the current 3-D hydrodynamical simulations used to model infall from the solar nebula onto circumplanetary disks have insufficient resolution to identify the location exactly." + We are satisfiec that our treatment is πιaficient for this stidy. vet we plan on inchiding more precise results as they become available.," We are satisfied that our treatment is sufficient for this study, yet we plan on including more precise results as they become available." + While the streugho | fhe viscosity. plavs uo 1e iun the location of: v clisks outer bouudary. it does play a siguificau role in the toal niss COtained iu a given disk.," While the strength of the viscosity plays no role in the location of a disks outer boundary, it does play a significant role in the total mass contained in a given disk." + In a steady sate. the mass accretion rate. ALXEM. 1 coustaut.," In a steady state, the mass accretion rate, $\dot{M}\propto \nu \Sigma$, is constant." + A Cistant mass accretion rate implies tlat he nass surface density mst be proportional to the inverse of the viscosity., A constant mass accretion rate implies that the mass surface density must be proportional to the inverse of the viscosity. + Iu our models. this niens that the surface density is nwerscly proportional to the viscosity. paraieteor. o.," In our models, this means that the surface density is inversely proportional to the viscosity parameter, $\alpha$." + Oue would naivelv assume that a arecr surface deusitv would result in larger satellites. but in actuality he opposite is true due to he increased rate of mügration.," One would naively assume that a larger surface density would result in larger satellites, but in actuality the opposite is true due to the increased rate of migration." + A MOLE Massive. ower viscosity disk results in a less luassive satellite system.," A more massive, lower viscosity disk results in a less massive satellite system." + thud that satellites will ouly survive against type I uueration for values of a>107. , \citet{canup02}f find that satellites will only survive against type I migration for values of $\alpha \geq 10^{-3}$ +parameters simultaneously. which would probably become prohibitive first.),"parameters simultaneously, which would probably become prohibitive first.)" + The DoF issue can be addressed if the DDE in question can be represented by a parametrized model for E., The DoF issue can be addressed if the DDE in question can be represented by a parametrized model for $\jones{E}{p}$. +" We can then solve for the parameters of that model (presumably. few in number). and then correct for the resulting £, estimate using one of the methods of Sect. 2.3.."," We can then solve for the parameters of that model (presumably, few in number), and then correct for the resulting $\jones{E}{p}$ estimate using one of the methods of Sect. \ref{sec:dde-correction}." + A number of approaches have shown that this is feasible., A number of approaches have shown that this is feasible. + For the tonosphere. the (FBC) method of ? uses the position offsets of sources (1n individual snapshot images) to fit a global phase screen over the array.," For the ionosphere, the (FBC) method of \citet{Cotton:FBC} uses the position offsets of sources (in individual snapshot images) to fit a global phase screen over the array." + The (SPAM) algorithm of ? does a similar fit to phase solutions obtained via peeling (in AIPS)., The (SPAM) algorithm of \citet{Intema:SPAM} does a similar fit to phase solutions obtained via peeling (in AIPS). + Both methods show how to work around the limitations of 2GC packages: since direct fits to visibilities are impossible in the framework of the latter. especially without a fully-fledged RIME. they rely on standard calibration methods (including peeling). and fit a model to the of calibration.," Both methods show how to work around the limitations of 2GC packages: since direct fits to visibilities are impossible in the framework of the latter, especially without a fully-fledged RIME, they rely on standard calibration methods (including peeling), and fit a model to the of calibration." + ? have demonstrated a similar approach for E-Jones. using source fluxes to fit the FWHM parameter of the ATA beam.," \citet{Hull:ata-beam-fitting} have demonstrated a similar approach for $E$ -Jones, using source fluxes to fit the FWHM parameter of the ATA beam." + Given an explicit RIME. it should be possible to fit parametrized models directly to the observed visibilities.," Given an explicit RIME, it should be possible to fit parametrized models directly to the observed visibilities." + The (MIM) approach proposed by Noordam is similar to FBC and SPAM. in that it purports to fit a smooth model for ionospheric phase. but is different in that it uses visibilities (but also other sources of data. such as GPS measurements).," The (MIM) approach proposed by Noordam is similar to FBC and SPAM, in that it purports to fit a smooth model for ionospheric phase, but is different in that it uses visibilities (but also other sources of data, such as GPS measurements)." + This requires a software system where explicit RIMEs may be implemented. and so cannot be adapted to 2GC packages. but it has been demonstrated in the LOFAR BBS system. using a simple linear-slope MIM.," This requires a software system where explicit RIMEs may be implemented, and so cannot be adapted to 2GC packages, but it has been demonstrated in the LOFAR BBS system, using a simple linear-slope MIM." +" The pointing selfcal method (?) already mentioned above is an application of the same approach to pointing errors,", The pointing selfcal method \citep{SB:pointing} already mentioned above is an application of the same approach to pointing errors. + All these methods have the common feature of relying onsources.. that 1s. having enough sources in the field to constrain the solutions.," All these methods have the common feature of relying on, that is, having enough sources in the field to constrain the solutions." + The availability of a sufficient number of beacons ts a crucial question for the calibratability of future instruments., The availability of a sufficient number of beacons is a crucial question for the calibratability of future instruments. + [ will return to this in the conclusion to Paper III (?).. after the results presented therein have been considered.," I will return to this in the conclusion to Paper III \citep{RRIME3}, after the results presented therein have been considered." + Note that. just as in the DFT-vs.-FFT debate discussed in Sect. 2.3.3...," Note that, just as in the DFT-vs.-FFT debate discussed in Sect. \ref{sec:subtraction-uv-plane}," + there is a related dichotomy between the parametrized model approach. and methods based on direction-dependent solutions (peeling. differential gains).," there is a related dichotomy between the parametrized model approach, and methods based on direction-dependent solutions (peeling, differential gains)." +" The latter methods the use of DFTs at the predict stage. since the FFT approach (AW-projection) cannot be applied without a model of £,,(/) for the entire field."," The latter methods the use of DFTs at the predict stage, since the FFT approach (AW-projection) cannot be applied without a model of $\jones{E}{p}(\vec l)$ for the entire field." + Parametrized models. on the other hand. may be applied both via DFT and FFT.," Parametrized models, on the other hand, may be applied both via DFT and FFT." + Once again. [ suggest that the two approaches should be treated as complementary.," Once again, I suggest that the two approaches should be treated as complementary." +" Looking ahead. the results of Paper HI (2). will show that brighter off-axis sources exhibit all sorts of complicated structure in their AZ, solutions. even in the relatively uncomplicated (1.6. low-DDE) case of WSRT 21 em observations."," Looking ahead, the results of Paper III \citep{RRIME3} will show that brighter off-axis sources exhibit all sorts of complicated structure in their $\Delta\jones{E}{p}$ solutions, even in the relatively uncomplicated (i.e. low-DDE) case of WSRT 21 cm observations." + It is hard to see how this can be captured by a parametrized DDE model to a precision sufficient for error-free subtraction of such sources., It is hard to see how this can be captured by a parametrized DDE model to a precision sufficient for error-free subtraction of such sources. + This suggests a similar trade-off in accuracy vs. computing cost as that deseribed in Sect. 2.3.3..," This suggests a similar trade-off in accuracy vs. computing cost as that described in Sect. \ref{sec:subtraction-uv-plane}," +" leading to the following hybrid approach for dealing with DDEs: Note that the sets of sources involved at steps 2. 3 and 4 are conceptually similar to ""Cat I and ""Cat II sources proposed for LOFAR calibration (?).. but here I suggest three sets rather than two."," leading to the following hybrid approach for dealing with DDEs: Note that the sets of sources involved at steps 2, 3 and 4 are conceptually similar to “Cat I” and “Cat II” sources proposed for LOFAR calibration \citep{JEN:LOFAR3}, but here I suggest three sets rather than two." + The exact partitioning of sources into sets determines the accuracy vs. computing cost trade-off., The exact partitioning of sources into sets determines the accuracy vs. computing cost trade-off. + It may be interesting to compare the different approaches to a particular class of DDE. for instance pointing error.," It may be interesting to compare the different approaches to a particular class of DDE, for instance pointing error." + Pointing errors introduce an E-Jones às given by Eq. (9))., Pointing errors introduce an $E$ -Jones as given by Eq. \ref{eq:mispointing}) ). + To date. three relevant approaches have been proposed: pointing selfcal (?).. peeling (Sect. 2.4.2))," To date, three relevant approaches have been proposed: pointing selfcal \citep{SB:pointing}, peeling (Sect. \ref{sec:peeling}) )" + and differential gains (Sect. 2.4.3))., and differential gains (Sect. \ref{sec:dEs}) ). + Of these. peeling is by far the best tested. since it Is available with all 2GC software packages.," Of these, peeling is by far the best tested, since it is available with all 2GC software packages." + Differential gains are available in MeqTrees: pointing selfcal is implemented in an experimental version of CASA (Bhatnagar priv., Differential gains are available in MeqTrees; pointing selfcal is implemented in an experimental version of CASA (Bhatnagar priv. + comm.).," comm.)," + but is not publicly available at time of writing., but is not publicly available at time of writing. + This makes a quantitative comparison impossible. but the algorithms may be compared in principle.," This makes a quantitative comparison impossible, but the algorithms may be compared in principle." + The peeling approach and differential gains are very similar in that they attempt to solve for the same effect: a direction-dependent complex gain term., The peeling approach and differential gains are very similar in that they attempt to solve for the same effect: a direction-dependent complex gain term. +" In essence. peeling approximates a full-sky RIME as: where X,,, is the model coherency PMof 5source(GT. s (typically à phase-shifted delta function. for a point source model. but Gaussian sources are also possible in e.g. NEWSTAR)."," In essence, peeling approximates a full-sky RIME as: where $\coh{X}{spq}$ is the model coherency of source $s$ (typically a phase-shifted delta function, for a point source model, but Gaussian sources are also possible in e.g. NEWSTAR)." +" Peeling consists of a least-squares solution for for one set of gams at a time (as in regular selfcal). followed by ""temporary"" subtraction of sources for which a solution has been obtained."," Peeling consists of a least-squares solution for for one set of gains at a time (as in regular selfcal), followed by “temporary” subtraction of sources for which a solution has been obtained." + Differential gains uses an equation like (16))., Differential gains uses an equation like \ref{eq:de}) ). +" First. a regular selfcal step is done to obtain G,, solutions on short time/frequency scales."," First, a regular selfcal step is done to obtain $\jones{G}{p}$ solutions on short time/frequency scales." +" This is followed by à simultaneous least-squares solution for all the AE,, terms. on longer time/frequency scales."," This is followed by a simultaneous least-squares solution for all the $\jones{\Delta E}{sp}$ terms, on longer time/frequency scales." + Peeling 1s subject to selfeal contamination at each stage of the process. due to the as-yet-unsolved-for contributions of fainter sources.," Peeling is subject to selfcal contamination at each stage of the process, due to the as-yet-unsolved-for contributions of fainter sources." + This is especially severe when sources have comparable flux., This is especially severe when sources have comparable flux. + Differential gains overcomes this by solving for all sources simultaneously., Differential gains overcomes this by solving for all sources simultaneously. + In principle. it should," In principle, it should" +"with the expression where SeoAvu is the limit on the velocity integratec ine [lux iu Jy km lop is the observing frequency iu GHz. and D, is the luminosity clistauce iu xc.","with the expression where $S_{CO} \Delta v$ is the limit on the velocity integrated line flux in Jy km $^{-1}$, $\nu_{obs}$ is the observing frequency in GHz, and $D_L$ is the luminosity distance in Mpc." + The choice of cosmological parameters euters in Dy. aud we adopt. Ay=τὸ καν ο οτα i ) lor consistency. with most work in this field. (," The choice of cosmological parameters enters in $D_L$ , and we adopt $H_0 = 75$ km $^{-1}$, $\Omega = 1$ and $\Omega_{\Lambda} = 0$ for consistency with most work in this field. (" +"An alternative cosmology with Hy=f)T Nlb 5 ] and O4—Q.T results in D, largere by a factor of 1.51 for this redshil.)","An alternative cosmology with $H_0 = 75$ km $^{-1}$, $\Omega = 1$ and $\Omega_{\Lambda} = 0.7$ results in $D_L$ larger by a factor of 1.54 for this redshift.)" + The effective lirewidth is 1ot known. but it likely falls iu the range 150 t0 550 kins + found for a large sample of tItralumiuous galaxies in the local universe (Solomon et al.," The effective linewidth is not known, but it likely falls in the range 150 to 550 km $^{-1}$ found for a large sample of ultraluminous galaxies in the local universe (Solomon et al." + 1997)., 1997). + For the 3o flux limit obtained in he tore sesitive part of the CO J=2-1 spectrum. assuming a linewidth of 200 kim Lo Leo—]1)«5.1x10! N kin . Ρο," For the $3\sigma$ flux limit obtained in the more sensitive part of the CO J=2–1 spectrum, assuming a linewidth of 200 km $^{-1}$, $L^{'}_{CO}(2-1) < 5.1 \times 10^{10}$ K km $^{-1}$ $^2$." + For the 3e flux. limit for CO J—5-I. agalu assuimniug a linewidth of 200 kns Ly ho. Lale value deteriniued for Milky Way molecular clouds (Sauders. Scoville Soifer 1991).," But a simple conversion factor from CO luminosity to $_2$ mass is commonly taken to be $4.5~M_{\odot}$ (K km $^{-1}$ $^2$ $^{-1}$, the value determined for Milky Way molecular clouds (Sanders, Scoville Soifer 1991)." + There is evidence [rom comparisous of luminosity based mass estinales with dynamical nass estimates tiat the couversiou factor may be perhaps five times lower in ultraluimious objects {Downes Soloi101 1998)., There is evidence from comparisons of luminosity based mass estimates with dynamical mass estimates that the conversion factor may be perhaps five times lower in ultraluminous objects (Downes Solomon 1998). + Additioual corrections of order unity are also ueede| to accotut properly Or excitatiou from t1e elevated«cosmic background radiation at high recshilt., Additional corrections of order unity are also needed to account properly for excitation from the elevated cosmic background radiation at high redshift. + Adopting the Galactic conversion factor for CO J=2-1 liue luminosity gives a limit ou the molecular gas nass of~2.310H. iu the SDSS 1011-0122 system., Adopting the Galactic conversion factor for CO J=2–1 line luminosity gives a limit on the molecular gas mass of $\sim2.3\times10^{11}~M_{\odot}$ in the SDSS 1044-0125 system. + Using the same couversion factor for the CO J=5-1 inelmiosity gives a liiil ou the molecular gas mass of of ~1.3:10H.AL. in the SDSS 1011-0120 system., Using the same conversion factor for the CO J=5–4 line luminosity gives a limit on the molecular gas mass of of $\sim1.3\times10^{11}~M_{\odot}$ in the SDSS 1044-0125 system. + These mass limits are comparable to the mass indicated. [roin the detection of CO etuission [rom some z>| quasars. iucludiug at least two thought uot be amplified by eravitatioual leusine.," These mass limits are comparable to the mass indicated from the detection of CO J=5--4 emission from some $z>4$ quasars, including at least two thought not to be amplified by gravitational lensing." + In particular. observatious of CO J=5-1 emission [rom BRI202-0722 at =L7 (Omont al.," In particular, observations of CO J=5–4 emission from BR1202-0725 at $z=4.7$ (Omont al." + 1996. Ohta et al.," 1996, Ohta et al." + 1996) and. BRIL335-O117 at 1.1 (Guilloteau et al., 1996) and BRI1335-0417 at $z=4.4$ (Guilloteau et al. +" 1997) indicate molecular gas masses in excess of LOM ML, (adjusted for the cosmology aud CO to H» conversion factor adopted here).", 1997) indicate molecular gas masses in excess of $10^{11}$ $_{\odot}$ (adjusted for the cosmology and CO to $_2$ conversion factor adopted here). + There is uo clear physical argument to explain why some quasar environments show CO emission at this sensitivity level while others do not (Cuilloteatu et al., There is no clear physical argument to explain why some quasar environments show CO emission at this sensitivity level while others do not (Guilloteau et al. + 1900)., 1999). + In any case. the CO J=2-1 and J—5-1 luminosity limits suggest that the e1virouruent ol SDSS 1011-0125 does not possess an euo‘MOUS mass reservoir of either low excitation or high excitation molecular gas.," In any case, the CO J=2–1 and J=5–4 luminosity limits suggest that the environment of SDSS 1044-0125 does not possess an enormous mass reservoir of either low excitation or high excitation molecular gas." + The CO 22-1 limit is comparable to the amount of molecular gas detected toware the leused quasar APM 08279-5255. wherePapacopoulos et al. (," The CO J=2–1 limit is comparable to the amount of molecular gas detected toward the lensed quasar APM 08279+5255, wherePapadopoulos et al. (" +2001) [ouud several CO —2-] emission features with total luminosity 6.6+3.1x10! lx kins | pe? attributed to (unleused) molecular gas rich companion galaxies to the αιasar host.,2001) found several CO J=2–1 emission features with total luminosity $6.6\pm3.1 \times 10^{11}$ K km $^{-1}$ $^2$ attributed to (unlensed) molecular gas rich companion galaxies to the quasar host. + For the SDSS 1011-0125 observations. such [features," For the SDSS 1044-0125 observations, such features" +(Estimate of A3). Sincee the integral. appearing. in. Ay is.done over Q?>\(Qt; we obtain⋅ Usiug this inequality together with the fact that we Cal estimate the term Ay as follows: where the above series converges for17>n4-2. (Estimate of A). Using Lemma 2.10... and the fact that ||.αςπα& on Qe\Qt the term Ay can be estimated as follows: where the aboveseries also converges for 10>n+2. From (2.26)). (2.29)) aud (2.30)). inequality (2.23)) directly follows with a coustaut C>0 indepeudent of j.,"(Estimate of $A_3$ Since the integral appearing in $A_{3}$ isdone over $Q^{2-k}\setminus Q^{1-k}$, we obtain Using this inequality together with the fact that we can estimate the term $A_{3}$ as follows: where the above series converges for$\o{m}>n+2$ (Estimate of $A_4$ Using Lemma \ref{mean_est}, and the fact that $\|2^{(j-1)a}z\|^{\o{m}}\geq 2^{\o{m}(j-k)}$ on $Q^{2-k}\setminus +Q^{1-k}$, the term $A_{4}$ can be estimated as follows: where the aboveseries also converges for $\o{m}>n+2$ From \ref{key_eq-1}) ), \ref{key_eq8}) ) and \ref{key_eq9}) ), inequality \ref{key_eq1}) ) directly follows with a constant $C>0$ independent of $j$ ." + a The constauts that will appear may differ from line to line. but only depend on » aud 1.," $\hfill{\blacksquare}$ The constants that will appear may differ from line to line, but only depend on $n$ and $m$." + The proof of this lemina combines somehow the proof of Lemimas 2.9 and 2.11.., The proof of this lemma combines somehow the proof of Lemmas \ref{BSI_lelemme} and \ref{key_lemma}. . + We write down ui as a finite stun of a telescopie sequencefor NV> 1: From Lemuna 2.10.. we deduce that:," We write down $u_{Q^{1}}$ as a finite sum of a telescopic sequencefor $N\geq 1$ : From Lemma \ref{mean_est}, , we deduce that:" +the mass ratio of 0.915 and emphasized the need for a new photometric analysis of the system to attain the absolute physical parameters.,the mass ratio of 0.915 and emphasized the need for a new photometric analysis of the system to attain the absolute physical parameters. + Zascheetal.(2009) updated the light elements after having analyzed all photometric and astrometric data available for the system., \citet{zasche09} updated the light elements after having analyzed all photometric and astrometric data available for the system. + According to the observational indicators. MR Del has properties similar to stars of BY Dra type or of RS CVn stars.," According to the observational indicators, MR Del has properties similar to stars of BY Dra type or of short-period RS CVn stars." + The results of our photometric analysis. based on updated spectroscopic elements of Pribullaetal.(2009b).. are given in Table 7..," The results of our photometric analysis, based on updated spectroscopic elements of \citet{pribb09}, are given in Table \ref{TabMRDel}." + Figure 3. shows the observed (LCO) and the synthetic (LCC) light curves 1n the B. V. and R filters (upper left). the B—V and V-B color indices (lower left). the O—C residuals (upper right) and the geometrical model of the system in representative phases 0.3 and 0.7 (lower right).," Figure \ref{fMRDel} shows the observed (LCO) and the synthetic (LCC) light curves in the B, V, and R filters (upper left), the $B-V$ and $V-B$ color indices (lower left), the $O-C$ residuals (upper right) and the geometrical model of the system in representative phases 0.3 and 0.7 (lower right)." + Table 7 lists parameter uncertainties estimated by combining the formal nonlinear least-squared fitting errors with the errors arising from the uncertainty of the spectroscopic mass ratio (q=0.915+ 0.012). as described in Section 3..," Table \ref{TabMRDel} lists parameter uncertainties estimated by combining the formal nonlinear least-squared fitting errors with the errors arising from the uncertainty of the spectroscopic mass ratio $q=0.915 \pm 0.012$ ), as described in Section \ref{analysis}." + Our model includes two cool spots on the more-massive. hotter componet.," Our model includes two cool spots on the more-massive, hotter component." + The spotted model ts supported by the X-ray observations., The spotted model is supported by the X-ray observations. + Another activity indicator is the flare event observed by Clausenetal.(2001) which was most pronounced in the u band., Another activity indicator is the flare event observed by \citet{clau01} which was most pronounced in the u band. + In addition. there are night-to-night differences in the light curves. increasing in strength from the y to the u band. so cool spots can be expected on one or both components: however. the uniqueness of the spot locations obtained in our solution is questionable to some degree.," In addition, there are night-to-night differences in the light curves, increasing in strength from the y to the u band, so cool spots can be expected on one or both components; however, the uniqueness of the spot locations obtained in our solution is questionable to some degree." + A good fit could not be, A good fit could not be +of BBLPO2.,of BBLP02. + The models cau be sununuanzed as follows: the dominant dark matter component. which is unaffected bv the enerev injection. collapses and virializes to form. bound halos.," The models can be summarized as follows: the dominant dark matter component, which is unaffected by the energy injection, collapses and virializes to form bound halos." + The distribution of the dark matter iu such halos is assunued to be the same as for the selfsimular clusters described above., The distribution of the dark matter in such halos is assumed to be the same as for the self-similar clusters described above. + While the dark component is unaffected by energy injection. the collapse of the barvouic conrponeut is hiudered by the pressure forces induced x eutropy injection.," While the dark component is unaffected by energy injection, the collapse of the baryonic component is hindered by the pressure forces induced by entropy injection." + If the maxima iufall velocity due surely to eravity of the dark halo is subsonic. the flow will )o stronely affected by the pressure aud it will not uudereo accretion shocks.," If the maximum infall velocity due purely to gravity of the dark halo is subsonic, the flow will be strongly affected by the pressure and it will not undergo accretion shocks." + [It is assmmed that the barvous will accumulate outo the halosZsentropicallg at the adiabatic Bouc accretion rate (as described iu Balogh et al., It is assumed that the baryons will accumulate onto the halos at the adiabatic Bondi accretion rate (as described in Balogh et al. + 1999)., 1999). + This treatineut. however. is only appropriate for low mass alos.," This treatment, however, is only appropriate for low mass halos." + Ifthe eravity of the dark halos is strong enough (as it is expected to be in the hot clusters being considered vere) that the maxima iufall velocity is frausonulc or supersonic. the eas will experience an additional (generally dominant) cutropy increase due to accretion shocks.," If the gravity of the dark halos is strong enough (as it is expected to be in the hot clusters being considered here) that the maximum infall velocity is transonic or supersonic, the gas will experience an additional (generally dominant) entropy increase due to accretion shocks." + Iu order to trace the shock history of the eas. a detailed knowledge of the merger history of the cluster/eroup is required but is not considered by BDBLDPU2.," In order to trace the shock history of the gas, a detailed knowledge of the merger history of the cluster/group is required but is not considered by BBLP02." + ILustead. it js asstuned that at some earlier time the most massive cluster progenitor will have had a mass low euouch such that shocks were uceleible in its formation. simular to the low mass halos discussed above.," Instead, it is assumed that at some earlier time the most massive cluster progenitor will have had a mass low enough such that shocks were negligible in its formation, similar to the low mass halos discussed above." + This progenitor forms au iscutropic gas core of radius rat the cluster ceuter., This progenitor forms an isentropic gas core of radius$r_{c}$ at the cluster center. + The cutropy of eas outside of the core. however. will be affected by shocks.," The entropy of gas outside of the core, however, will be affected by shocks." +" Receut high resolution numerical simulatious sugecst that the ""entropy profile for gas outside this core can be adequately represented by a simple analytic expression given bv luA(r)=InAy|olu(re£r.) (bewis et al.", Recent high resolution numerical simulations suggest that the “entropy” profile for gas outside this core can be adequately represented by a simple analytic expression given by $\ln{K(r)} = \ln{K_0} + \alpha \ln{(r/r_c)}$ (Lewis et al. +" 2000). where AN—AT,3*"," 2000), where $K \equiv +kT_e n_e^{-2/3}$." + For the massive. hot clusters (Ty23 keV) of interest here. a~1.1 (Tozzi Norman 2001: DBLDPO2).," For the massive, hot clusters $T_X \gtrsim 3$ keV) of interest here, $\alpha \sim 1.1$ (Tozzi Norman 2001; BBLP02)." + Following this prescription aud specitvine the paraluctors ον Pyas(e). aud a (as discussed in BBLPO2) colmpletely determines the models.," Following this prescription and specifying the parameters $r_c$, $\rho_{gas}(r_c)$, and $\alpha$ (as discussed in BBLP02) completely determines the models." + Under all conditions. the gas is assuned to be iu hverostatic equilibria within the dark halo potential.," Under all conditions, the gas is assumed to be in hydrostatic equilibrium within the dark halo potential." + The complicated: effects of radiative cooling are neglected by these models., The complicated effects of radiative cooling are neglected by these models. + The amplitude of the SZ effect is directly proportional to the “Compton parameter” (y) which is given by where 0 is the projected position from the cluster center. στ is the Thomson cross-section. and {σε2o(yal(GP) is the electron pressure of the ICAL at the 3-cimensioual position ©.," The amplitude of the SZ effect is directly proportional to the “Compton parameter” $y$ ) which is given by where $\theta$ is the projected position from the cluster center, $\sigma_T$ is the Thomson cross-section, and $P_e(\vec{r}) \equiv n_e(\vec{r}) kT_e(\vec{r})$ is the electron pressure of the ICM at the 3-dimensional position $\vec{r}$." + The iutegral is performed over the line-ofsight (7) through the cluster., The integral is performed over the line-of-sight $l$ ) through the cluster. + All of the plivsics of the SZ effect is contained within the Compton parameter., All of the physics of the SZ effect is contained within the Compton parameter. + It is the SZ effect analog of the vay surface brightuess of a cluster and is a measure of the average fractional energy. gain of a photon due to iuverse-Compton scattering while passing through a cloud of gas (n this case. the ICM) with an electron pressure profile of PAF).," It is the SZ effect analog of the X-ray surface brightness of a cluster and is a measure of the average fractional energy gain of a photon due to inverse-Compton scattering while passing through a cloud of gas (in this case, the ICM) with an electron pressure profile of $P_e(\vec{r})$." + As discussed by BBELPO2 aud MDD02. the presence of excess cutropy will modify both a clusters density aud temperature profiles.," As discussed by BBLP02 and MBB02, the presence of excess entropy will modify both a cluster's density and temperature profiles." + In the case where it is preheating 0.1iu that eives rise to an eutropy core. as iu the present study. the temperature of the gas near the center of the cluster is increased and. therefore. so is the global emission-woeiehted temperature of the cluster (e.9.. Fie.," In the case where it is preheating 0.1in that gives rise to an entropy core, as in the present study, the temperature of the gas near the center of the cluster is increased and, therefore, so is the global emission-weighted temperature of the cluster (e.g., Fig." + 1 of NDBDB02)., 1 of MBB02). + At the sale time. the density of the eas at the cluster center is dramatically reduced (e.g.. Fig.," At the same time, the density of the gas at the cluster center is dramatically reduced (e.g., Fig." + 2 of NBD02)., 2 of MBB02). + It turns out that. relatively speaking. preheating las a stronger influence on the density than it docs ou the temperature. at least at the centers of massive clusters.," It turns out that, relatively speaking, preheating has a stronger influence on the density than it does on the temperature, at least at the centers of massive clusters." + The result is that he eas pressure in central regious of a cluster is reduced by xelieatiug and. cousequeutly. so is the clusters Compton xuanueter.," The result is that the gas pressure in central regions of a cluster is reduced by preheating and, consequently, so is the cluster's Compton parameter." +" To demonstrate this. we plot cluster pressure xofiles (2= 0.2) for several values of the cutropy floor iu Figure 1 CR, is the radius of the cluster)."," To demonstrate this, we plot cluster pressure profiles $z = 0.2$ ) for several values of the entropy floor in Figure 1 $R_{halo}$ is the radius of the cluster)." + The addition of an cutropy floor leads to a decrease in the eas pressure acar the claster core., The addition of an entropy floor leads to a decrease in the gas pressure near the cluster core. + The eas pressure in the outer regions of the clusters. however. remains relatively uuchauged as he eutropv increase due to eravitational shock heating dominates the nou-eravitational eutropy injection.," The gas pressure in the outer regions of the clusters, however, remains relatively unchanged as the entropy increase due to gravitational shock heating dominates the non-gravitational entropy injection." + Also of rote is that the difference between the various nodels is greatest for the lower mass cluster., Also of note is that the difference between the various models is greatest for the lower mass cluster. + This is expected since the lower mass cluster has a shallower votential well aud. thus. is more stronely mfüuenced by he presence of an entropy floor.," This is expected since the lower mass cluster has a shallower potential well and, thus, is more strongly influenced by the presence of an entropy floor." + With an cutropy floor significantly affecting the pressure of the ICAL near the center of a cluster. the Comptou waralucter will be most stronely modified if it is evaluated within the smallestpossible projected radius [ic the central Compton parameter. g(0=0) yy.," With an entropy floor significantly affecting the pressure of the ICM near the center of a cluster, the Compton parameter will be most strongly modified if it is evaluated within the smallestpossible projected radius [i.e., the Compton parameter, $y(\theta = 0) \equiv y_0$ ]." + Tutegrating (or averaging) the Compton parameter within larger projected radi (for example. Rpg. the radius of the," Integrating (or averaging) the Compton parameter within larger projected radii (for example, $R_{halo}$ , the radius of the" +It has been known for niuiv vears that radio pulses frou he Crab pulsar are affected both by a variable delay due to changes im dispersion and by a variable pulse xoadeniues due to scattering along the line of sight (?:: ?)).,It has been known for many years that radio pulses from the Crab pulsar are affected both by a variable delay due to changes in dispersion and by a variable pulse broadening due to scattering along the line of sight \cite{rc73}; ; \cite{ir77}) ). + Both phenomena vary ou a typical time scale of about 100 days. but iu previous observations their variations lave appeared to be impertectly correlated anc possibly even uneorrelated.," Both phenomena vary on a typical time scale of about 100 days, but in previous observations their variations have appeared to be imperfectly correlated and possibly even uncorrelated." + At our two observatories. we have naintained for several vears two series of observations o separately monitor these two phenomena. and can iow report a discrete event that shows a remarkably good correlation between variations in scattering and in dispersion measure.," At our two observatories, we have maintained for several years two series of observations to separately monitor these two phenomena, and can now report a discrete event that shows a remarkably good correlation between variations in scattering and in dispersion measure." + Observations of dispersion iueasure are made at least once a week at Jodrell Bank Observatory as part of the Crab pulsar timine ephemeris which has Όσοι xoduced. aud made generally available since 1982., Observations of dispersion measure are made at least once a week at Jodrell Bank Observatory as part of the Crab pulsar timing ephemeris which has been produced and made generally available since 1982. + The ephemeris is based on daily observations of time of arrival of pulses at 610 MIIz. while the dispersion delay is ueasured by comparison with similar observations at 1100 MIIz.," The ephemeris is based on daily observations of time of arrival of pulses at 610 MHz, while the dispersion delay is measured by comparison with similar observations at 1400 MHz." + Observations at Pusheching Badio Astronomi Observatorv monitoring the pulse shape at 111 MIIz iive continued since 20014., Observations at Pushchino Radio Astronomy Observatory monitoring the pulse shape at 111 MHz have continued since 2004. + Both before and durius the event the pulse is broadened with a steep rise aud au approximately exponeutial decay with a time constant of several nuülliseconds: this characteristic decay time is monitored almost daily., Both before and during the event the pulse is broadened with a steep rise and an approximately exponential decay with a time constant of several milliseconds; this characteristic decay time is monitored almost daily. + A distinctive property of the Crab pulsar low frequency observations ds that the scatter broadening iav he comparable with or ereater than the pulsar period., A distinctive property of the Crab pulsar low frequency observations is that the scatter broadening may be comparable with or greater than the pulsar period. + To avoid the resulting confusion we use for observations the eiut pulses of this pulsar. which stand out of the regular pulses as rare. strong. well defined sinele pulses.," To avoid the resulting confusion we use for observations the giant pulses of this pulsar, which stand out of the regular pulses as rare, strong, well defined single pulses." + The pulse broadening is measured bv fitting the convolution of a Gaussian template pulse with a truncated exponent as the thin screen scatter function. to the observed pulsar pulse.," The pulse broadening is measured by fitting the convolution of a Gaussian template pulse with a truncated exponent as the thin screen scatter function, to the observed pulsar pulse." + The results of these measurements over a period of G00 davs are shown in Figure 2.., The results of these measurements over a period of 600 days are shown in Figure \ref{fig:dmscat}. + This shows a cliscrete event. lasting 200 davs (ALJD 53950 51150). during which the dispersion aud scattering changed together.," This shows a discrete event, lasting 200 days (MJD 53950 – 54150), during which the dispersion and scattering changed together." + The two curves are shown as recorded: note especially the sharp rise at the start of the event. aud the delay of 30 davs between the ouset of the rise in scattering aud the rise 1u DM.," The two curves are shown as recorded; note especially the sharp rise at the start of the event, and the delay of 30 days between the onset of the rise in scattering and the rise in DM." + Both before aud afer this event there are smaller variations which are less obviously correlated., Both before and after this event there are smaller variations which are less obviously correlated. + The event appears as a distinct phenomenon which stands out from the ecnueral level of variation iu both parameters., The event appears as a distinct phenomenon which stands out from the general level of variation in both parameters. + The dispersion nieasure is proportional to the total electron coutent along the line of sight., The dispersion measure is proportional to the total electron content along the line of sight. + Most of this is attributed to the interstellar medimu. aud this componcut is not expected to show such large aud rapid variations: observations of other pulsars show only comparatively sunall and slow variations. as shown bv ?..," Most of this is attributed to the interstellar medium, and this component is not expected to show such large and rapid variations: observations of other pulsars show only comparatively small and slow variations, as shown by \cite{you07}." + The base level of the dispersion mcasure appears to be 56715 pe: the event increases this by ADAI z 0.03 bpe., The base level of the dispersion measure appears to be 56.745 $^{-3}$ pc; the event increases this by $\Delta$ DM $\approx$ 0.03 $^{-3}$ pc. + The observed scattering. by contrast. is more than doubled at the event. increasiug from 10 to 25 is.," The observed scattering, by contrast, is more than doubled at the event, increasing from 10 to 25 ms." + Scattering bv radon variations in refractive iudex depends on irregular fluctuations of electron deusitv within anv part of the propagation path: the simplest interpretation is that the increased scattering aud the increased dispersion are both due to a discrete electron. cloud or filament within the Nebula., Scattering by random variations in refractive index depends on irregular fluctuations of electron density within any part of the propagation path; the simplest interpretation is that the increased scattering and the increased dispersion are both due to a discrete electron cloud or filament within the Nebula. + Three leneth scales are involved in estimating the size of a sinele cloud respousible both for mereased dispersion andscatterme:, Three length scales are involved in estimating the size of a single cloud responsible both for increased dispersion andscattering: +"they are indeed observed allows us to conclude that Rina,> A.",they are indeed observed allows us to conclude that $R_{\rm{max}} > A$ . + Nevertheless. we cannot discard a possible relationship between truncations and warps.," Nevertheless, we cannot discard a possible relationship between truncations and warps." + It appears that optical warps always start closer in than HI warps. although we note that the low resolution of the HI data makes it difficult to detect warps.," It appears that optical warps always start closer in than HI warps, although we note that the low resolution of the HI data makes it difficult to detect low-amplitude warps." +Low luminosity gamma-ray bursts (LGIhRDs) constitute a sub-class of eanmnma-rav bursts (GRBs) that plavs a central role in the GRD-supernova connection.,Low luminosity gamma-ray bursts () constitute a sub-class of gamma-ray bursts (GRBs) that plays a central role in the GRB-supernova connection. + While/-GRBs differ from typical long GRBs (LGRBs) in many aspects. (μο�� also share some common features.," While differ from typical long GRBs (LGRBs) in many aspects, they also share some common features." + Therefore. the question whether ihe gamma-ray emission of/-GRBs and LGRBs has a common origin is of great interest.," Therefore, the question whether the gamma-ray emission of and LGRBs has a common origin is of great interest." + Llere we address this question by testing whether/-GRBs. like LGRBs according to the Collapsar model. can be generated by relativistic jets that punch holes in the envelopes of (heir progenitor stars.," Here we address this question by testing whether, like LGRBs according to the Collapsar model, can be generated by relativistic jets that punch holes in the envelopes of their progenitor stars." + The collapsar model predicts (hat the durations of most observed bursts will be comparable to. or longer than. the lime it takes the jets to breakout of the star.," The collapsar model predicts that the durations of most observed bursts will be comparable to, or longer than, the time it takes the jets to breakout of the star." + We calculate the jet breakout (times of/EGRBs and compare them to the observed duratons., We calculate the jet breakout times of and compare them to the observed durations. + We find that there is a significant. access of/-GRBs with durations that are much shorter than the jet breakout time and (hat these are inconsistent with the Collapsar model., We find that there is a significant access of with durations that are much shorter than the jet breakout time and that these are inconsistent with the Collapsar model. + We conclude that the processes (hat dominate (he eamama-ray eniission of/-GIDs and of LGRBs are most likely fundamentally different. ," We conclude that the processes that dominate the gamma-ray emission of and of LGRBs are most likely fundamentally different. \end{abstract}\tikzmark{mainBodyEnd184} + +\tikzmark{mainBodyStart185}\begin{document}" +According to the Collapsar model (Paczenski19938:MacFadyen&Woosley1999) (he core collapse of a massive star results in the Formation of a compact object. a black hole or a rapidly rotating neutron star.," According to the Collapsar model \citep{Paczynski98,MacFadyen99} the core collapse of a massive star results in the formation of a compact object, a black hole or a rapidly rotating neutron star." + The compact object ejects a relativistic bipolar. barvon poor jel. along ils rotation axis.," The compact object ejects a relativistic bipolar, baryon poor jet, along its rotation axis." + The jet punctures the surrounding stellar envelope and it emits the observed 5-ravs at a laree distance from (he star where the optical depth is small aud the high energy photons can escape., The jet punctures the surrounding stellar envelope and it emits the observed $\gamma$ -rays at a large distance from the star where the optical depth is small and the high energy photons can escape. + This model. (hat is accepted as the standard model for long GRBs (LGRBs). explains naturally the association of some LGRDs with SNe. aud (heir general emergence in star forming regions reviews)..," This model, that is accepted as the standard model for long GRBs (LGRBs), explains naturally the association of some LGRBs with SNe, and their general emergence in star forming regions \citep[see][for recent reviews]{Woosley06, Hjorth11}. ." + (MeClintock&Remillard2004... <10 1) Williamsetal.2004:DiStefano2002:Trudolvuboyetal.2001:Osborne (Williamsetal.2005a.b.c..2004)..," \citealp{mcclintock2004}, $\gap10^{38}$ $^{-1}$ \citealp{williams2004hrc,distefano2004,kong2002acis,trudolyubov2001,osborne2001}; \citep{williams2005bh1,williams2005bh2,williams2005bh4,williams2004hrc}." +(Mereghetti 2008:: Camiloetal.2007a:; Halpernetal.2005)) in quiescence and larger ratios in outburst.,\citealp{Mer08}; ; \citealp{CamApJ666}; \citealp{Hal05}) ) in quiescence and larger ratios in outburst. + The radio emission from 1510-197 was discovered immediately following a strong X-ray outburst., The radio emission from J1810–197 was discovered immediately following a strong X-ray outburst. + It has since faded. both in the radio and the X-ray band. and the radio pulsations are no longer visible.," It has since faded, both in the radio and the X-ray band, and the radio pulsations are no longer visible." + For 11547-5408. the radio emission is also highly variable and appears to be revived in the periods after its X-ray outbursts.," For 1547–5408, the radio emission is also highly variable and appears to be `revived' in the periods after its X-ray outbursts." + PSR 11622-4950 on the other hand. has had at least two episodes of non-detections in the radio band lasting hundreds of days followed by periods of bright radio emission (see Fig. 1)).," PSR J1622–4950 on the other hand, has had at least two episodes of non-detections in the radio band lasting hundreds of days followed by periods of bright radio emission (see Fig. \ref{Fig:Lightcurve}) )." + In addition to the new observation. we searched archival data fromChandra...Newton...Rosat.. ASCA.. Beppo-SAX..Rossi-XTE and for an outburst. however no evidence for X-ray flux variability and no X-ray outburst at the level of the outbursts seen in [1810-197 and 11547—5408 in connection to the radio pulsations C7. 1079 ss!) were found since at least as early as 2005.," In addition to the new observation, we searched archival data from, and for an outburst, however no evidence for X-ray flux variability and no X-ray outburst at the level of the outbursts seen in 1810–197 and 1547–5408 in connection to the radio pulsations $\gtrsim$ $^{36}$ $^{-1}$ ) were found since at least as early as 2005." + It is possible therefore that an enhancement of X-ray activity is not a requirement for pulsed radio emission by magnetars. however. given the duty cycle of sensitive X-ray observations of the field containing JJ1622—4950. we cannot constrain the occurrence of fainter X-ray enhancements of the source.," It is possible therefore that an enhancement of X-ray activity is not a requirement for pulsed radio emission by magnetars, however, given the duty cycle of sensitive X-ray observations of the field containing J1622–4950, we cannot constrain the occurrence of fainter X-ray enhancements of the source." + What is instead certain is that the observed X-ray emission from JJ1622—4950 is at variance with what is observed for the other two radio pulsating magnetars., What is instead certain is that the observed X-ray emission from J1622--4950 is at variance with what is observed for the other two radio pulsating magnetars. + If the true age of PSRJJI622—4950 Is similar to its characteristic age of 4kkyr. we might expect to see a supernova remnant (SNR) surrounding the pulsar.," If the true age of J1622–4950 is similar to its characteristic age of kyr, we might expect to see a supernova remnant (SNR) surrounding the pulsar." + Indeed. 5 of the 9 AXPs and at least 1 of the 5 SGRs are located within SNRs (Mereghetti2008:: Gaensleretal. 2001)).," Indeed, 5 of the 9 AXPs and at least 1 of the 5 SGRs are located within SNRs \citealp{Mer08}; \citealp{Gae01}) )." + Inspecting the ATCA image in Fig. 2..," Inspecting the ATCA image in Fig. \ref{Fig:ATCA-CXO}," + we seea ring of emission centered ~2' south of the pulsar location., we seea ring of emission centered $\sim$ $'$ south of the pulsar location. + This ring lacks an infra-red counterpart and appears to be non thermal. whereas the extended radio source to the south of the ring is clearly thermal in nature.," This ring lacks an infra-red counterpart and appears to be non thermal, whereas the extended radio source to the south of the ring is clearly thermal in nature." + Could the ring be the SNR and the pulsar has escaped its bounds?, Could the ring be the SNR and the pulsar has escaped its bounds? + If we assume a distance of ~9 kkpe to the magnetar and further assume 1t was born in the centre of the ring. the magnetar would need a velocity of ~1300kkm ss! to reach its current location whereas the ring itself would have a lower expansion velocity.," If we assume a distance of $\sim$ kpc to the magnetar and further assume it was born in the centre of the ring, the magnetar would need a velocity of $\sim$ $^{-1}$ to reach its current location whereas the ring itself would have a lower expansion velocity." + Such a velocity is high (though not impossible) for pulsars but rather low for expanding SNRs., Such a velocity is high (though not impossible) for pulsars but rather low for expanding SNRs. + Although the link between the ring and the magnetar Is a possibility we consider it unlikely., Although the link between the ring and the magnetar is a possibility we consider it unlikely. + The HTRU survey has discovered a radio-luminous pulsar. which is highly polarized. has an inverted spectrum. and is highly variable 1n. both its pulse profile and flux density.," The HTRU survey has discovered a radio-luminous pulsar, which is highly polarized, has an inverted spectrum, and is highly variable in both its pulse profile and flux density." + The radio pulsar has a faint X-ray counterpart that appears to be stable in flux. with a value that is typical of a quiescent magnetar.," The radio pulsar has a faint X-ray counterpart that appears to be stable in flux, with a value that is typical of a quiescent magnetar." + The pulsar shares many of the properties of the two known radio magnetars and we therefore conclude that JJ1622—4950 is indeed a magnetar. the first discovered through its radio emission.," The pulsar shares many of the properties of the two known radio magnetars and we therefore conclude that J1622–4950 is indeed a magnetar, the first discovered through its radio emission." + This discovery not only adds a new member to the magnetar family. but also highlights unprecedented features of the emission of the magnetars across the electromagnetic band.," This discovery not only adds a new member to the magnetar family, but also highlights unprecedented features of the emission of the magnetars across the electromagnetic band." + At odds with what is observed in other sources. JJ1622-4950 indicates that bright radio emission can be present even when a magnetar displays an X-ray luminosity typical of a quiescent state.," At odds with what is observed in other sources, J1622–4950 indicates that bright radio emission can be present even when a magnetar displays an X-ray luminosity typical of a quiescent state." + Moreover. JJ1622-4950 shows that radio emission can either exist without the occurrence of a strong X-ray outburst. or occur a long time (2 5 years) after the outburst.," Moreover, J1622–4950 shows that radio emission can either exist without the occurrence of a strong X-ray outburst, or occur a long time $\gtrsim$ 5 years) after the outburst." + Alternatively. the radio pulsations could be triggered by a modest increment of X-ray activity. that escaped detection in this case.," Alternatively, the radio pulsations could be triggered by a modest increment of X-ray activity, that escaped detection in this case." + We finally note that the extreme variability in the flux density of JJ1622—4950 also demonstrates the advantages of surveying the radio sky at regular intervals with even modest sensitivity., We finally note that the extreme variability in the flux density of J1622–4950 also demonstrates the advantages of surveying the radio sky at regular intervals with even modest sensitivity. + This highlights the potential of the upcoming radio facilities like the LOFAR. ASKAP or the SKA which promise to characterize the dynamie radio sky at an unprecedented level.," This highlights the potential of the upcoming radio facilities like the LOFAR, ASKAP or the SKA which promise to characterize the dynamic radio sky at an unprecedented level." + The Parkes Observatory and the Australia Telescope Compact Array are part of the Australia Telescope. which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO.," The Parkes Observatory and the Australia Telescope Compact Array are part of the Australia Telescope, which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO." + The ChandraX-ray Observatory Centre is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NASS03060., The ChandraX-ray Observatory Centre is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060. + This work is partly supported by the Australian Research Council through its discovery programme., This work is partly supported by the Australian Research Council through its discovery programme. + The HYDRA supercomputer at the JBCA is supported by a grant from the UK Science and Technology Facilities Council., The HYDRA supercomputer at the JBCA is supported by a grant from the UK Science and Technology Facilities Council. + S.B. gratefully acknowledges the support of STFC in his PhD studentship., S.B. gratefully acknowledges the support of STFC in his PhD studentship. + This work is partly supported by theAustralian Research Couneil through its discovery programme. Parkes.. ATCA.. (ASIS-D..," This work is partly supported by theAustralian Research Council through its discovery programme. , , ." +“classical” LBCs like QU317-383 C5. but also galaxies selected with other UV-based criteria.,"“classical” LBGs like Q0347-383 C5, but also galaxies selected with other UV-based criteria." + Overall. this illustrates the difficulties related to purely morphological aud photometric studies and lighlielts the need to iuclude inteeral-field kinciatics for statistically robust samples of the various lLiel-vedshift ealaxy populations. if we want to understaud the wuderlving mechanisius governing galaxy evolution iu the carly wniverse.," Overall, this illustrates the difficulties related to purely morphological and photometric studies and highlights the need to include integral-field kinematics for statistically robust samples of the various high-redshift galaxy populations, if we want to understand the underlying mechanisms governing galaxy evolution in the early universe." + We presented an analysis of rest-frame optical iuteeral-field spectroscopy of the +=3.23 Lyiman-Break Calaxy QO317-383 C5 in he I baud., We presented an analysis of rest-frame optical integral-field spectroscopy of the $z=3.23$ Lyman-Break Galaxy Q0347-383 C5 in the K band. + This galaxy is oue of the largest 1-1i0wn LBGs. and iu particular large enough for secine-limited observations.," This galaxy is one of the largest known LBGs, and in particular large enough for seeing-limited observations." + QU317-383 C5 was first described by ?.. who obtained E702W IIST continua oeuaeiue aud longsli spectroscopy in the I-baud We detect the |OTMJAA 959.5007 doublet with line oxoperties that are similar to those discussed in ?.. but oe1 addition. we also identify with a flux of 9«10.008 erg I 7.," Q0347-383 C5 was first described by \citet{pettini01}, who obtained F702W HST continuum imaging and longslit spectroscopy in the K-band We detect the $\lambda\lambda$ 4959,5007 doublet with line properties that are similar to those discussed in \citet{pettini01}, but in addition, we also identify $\beta$ with a flux of $9\times10^{-18}$ erg $^{-1}$ $^{-2}$." + The [OTII[/TI./ line ratio is high. o»ut not oo high for a low-nctalicity star-forming ogalaxy. aud corresponds to an oxvgen abundance within the range of uetallicities of LBGs measured by ?..," The $\beta$ line ratio is high, but not too high for a low-metalicity star-forming galaxy, and corresponds to an oxygen abundance within the range of metallicities of LBGs measured by \citet{pettini01}." + The observations do tot sugeest that the optical spectrum of QUJ17-383 C5 is dominated by an ACN., The observations do not suggest that the optical spectrum of Q0347-383 C5 is dominated by an AGN. + The |OIH]A5007 line image shows two knots at a xojected distance ~0.7 ((5.L kpe) with a small relative velocity of 33 kan |., The $\lambda$ 5007 line image shows two knots at a projected distance $\sim 0.7$ (5.4 kpc) with a small relative velocity of 33 km $^{-1}$. +" Line morphology aud sincluatics do not resemble those expected for au outflow or a rotating disk. and more ikely originate from a merger of either two imtermeciate-nass galaxies with a dvuamical mass of ΠΑΕ, each. or perhaps massive sub-chuups of a fragmented disk as ostulated by οον,"," Line morphology and kinematics do not resemble those expected for an outflow or a rotating disk, and more likely originate from a merger of either two intermediate-mass galaxies with a dynamical mass of $\le 10^{10} M_{\odot}$ each, or perhaps massive sub-clumps of a fragmented disk as postulated by \citet{immeli04,bournaud07}." + The arge inasses of individual knots uake it more likely that we see the merging of two galaxies cach tracing its individual dark matter halo or subhalo. although this is a very difficult distinction to make with oxeseut dav data.," The large masses of individual knots make it more likely that we see the merging of two galaxies each tracing its individual dark matter halo or subhalo, although this is a very difficult distinction to make with present day data." + The density of simularly huninous z~3 LBCes is consistent with predictions frou recent models of the cosmic evolution of the moereer rate., The density of similarly luminous $\sim 3$ LBGs is consistent with predictions from recent models of the cosmic evolution of the merger rate. + Stary-formation rates estimate from the observed IL? flux correspond to ~20LO AL. in each clamp. which is uot unusual for LDCs ecnerally.," Star-formation rates estimated from the observed $\beta$ flux correspond to $\sim 20-40$ $_{\odot}$ in each clump, which is not unusual for LBGs generally." + Most z—23 LBCs are significantly more compact than QO3L7-38e C5. with typical halflight radi of rs~0.37.," Most $\sim 3$ LBGs are significantly more compact than Q0347-388 C5, with typical half-light radii of $_e\sim 0.3$." + Such scales are difficult to resolve with 1ni class telescopes. even with adaptive optics assisted observations.," Such scales are difficult to resolve with 10-m class telescopes, even with adaptive optics assisted observations." + From. such observations 7? find that DSF2237a-C?2. their only target at z»3. has a velocity eracdicent aud velocity dispersions of the same magnitude as the shear.," From such observations \citet{law07} find that DSF2237a-C2, their only target at $>$ 3, has a velocity gradient and velocity dispersions of the same magnitude as the shear." + While superficially these characteristics could be suggestive of a rotating disk. ?.. from a comparison of their data to a simple exponeutial rotating disk model. cluphasize that this source is unlikely to be a thin. rotationallv-supported disk.," While superficially these characteristics could be suggestive of a rotating disk, \citet{law07}, from a comparison of their data to a simple exponential rotating disk model, emphasize that this source is unlikely to be a thin, rotationally-supported disk." + Both ealaxics are among the lareest LBCs aud are comparably bright. which sheds doubts as to whether the properties of the overall population of :~3 LDGs are well described by the properties of its largest members.," Both galaxies are among the largest LBGs and are comparably bright, which sheds doubts as to whether the properties of the overall population of $z\sim 3$ LBGs are well described by the properties of its largest members." + ?— found evidence for rotatiou on sub-kpe scales iu a stronely-lensed LDC: at z=3.2L. but such scales are well bevond reach for eecnerie LDGs even with adaptive optics.," \citet{nesvadba06} found evidence for rotation on sub-kpc scales in a strongly-lensed LBG at $=3.24$, but such scales are well beyond reach for generic LBGs even with adaptive optics." + While adaptive optics-assisted observations allow to probe the dyvuamics of lhiel-redshift galaxies at sub-kpe resolution. they niust concentrate ou galaxies with particularly bright line enission. to eusure reasonable observing times as poiuted out bv ?..," While adaptive optics-assisted observations allow to probe the dynamics of high-redshift galaxies at sub-kpc resolution, they must concentrate on galaxies with particularly bright line emission, to ensure reasonable observing times as pointed out by \citet{law07}." + This will inevitably lead to biases between observed LBC samples aud the pareut population of LBGs. aud Is a reason why studies of eravitationally leused are not superceded. but are rather complemented. bv high aneular resolution observations of LBCs with adaptive optics. in spite of uucertaiuties related to the eravitationa magnification.," This will inevitably lead to biases between observed LBG samples and the parent population of LBGs, and is a reason why studies of gravitationally lensed are not superceded, but are rather complemented, by high angular resolution observations of LBGs with adaptive optics, in spite of uncertainties related to the gravitational magnification." + More positively. observing galaxies with bright line cussion will plausibly provide information about particularly rapid phases of star-formation ac ealaxv growth. whatever mechanisni is responsible for initiating such phases;," More positively, observing galaxies with bright line emission will plausibly provide information about particularly rapid phases of star-formation and galaxy growth, whatever mechanism is responsible for initiating such phases." + Prudenuce aud caution however are certainly justified when ecueralizing the results of lugh redshift geealaxics eiven the current liuitatiou iu astronomical instrmucutation aud the small sample sizes with detailed 3-dimensioual spectroscopy observations., Prudence and caution however are certainly justified when generalizing the results of high redshift galaxies given the current limitation in astronomical instrumentation and the small sample sizes with detailed 3-dimensional spectroscopy observations. + We would like to thank an anonymous referee for. helpfi advice and suggestions that substantially. improved this paper and the stall at Paranal for their help and. suppor in obtaining these observations., We would like to thank an anonymous referee for helpful advice and suggestions that substantially improved this paper and the staff at Paranal for their help and support in obtaining these observations. + ΝΡΗΝ wishes to acknowledge financial support from. the European Commission through a Marie. Curie Postdoctoral Fellowship and MDL wishes to thank the Centre Nationale de Ia Recherche Scientifique for its continuing support of his research., NPHN wishes to acknowledge financial support from the European Commission through a Marie Curie Postdoctoral Fellowship and MDL wishes to thank the Centre Nationale de la Recherche Scientifique for its continuing support of his research. +and helium ionization degrees of jjj=0.8 and Oy.=O.1. respectively.,"and helium ionization degrees of $\mutilde_{\rm H} = 0.8$ and $\delta_{\rm He}=0.1$, respectively." +" We see that even in the case of the largest quantity of helium considered (£j,=20%). the presence of helium has a minor effect on the results."," We see that even in the case of the largest quantity of helium considered $\xi_\ion{He}{i} = 20\%$ ), the presence of helium has a minor effect on the results." + In the case of Alfvénn and fast waves (Fig., In the case of Alfvénn and fast waves (Fig. + 2aa.b). their critical wavenumber (1.e.. the value of & which causes the real part of the frequency to vanish) is shifted toward slightly smaller values.," \ref{fig:mhdwaves}a a,b), their critical wavenumber (i.e., the value of $k$ which causes the real part of the frequency to vanish) is shifted toward slightly smaller values." + So. the larger ἕμοι. the smaller K?.," So, the larger $\xi_\ion{He}{i}$, the smaller $k_{\rm c}^{\rm a}$." +" This result can be understood by considering that the Alfvénn wave critical wavenumber. κά, given by Eq. ("," This result can be understood by considering that the Alfvénn wave critical wavenumber, $k_{\rm c}^{\rm a}$ , given by Eq. (" +38) of Is. with v4=Bo/Vipo the Alfvénn speed.,"38) of \citet{forteza08} is, with $\va = B_0 / \sqrt{\mu \rho_0}$ the Alfvénn speed." + Equation (21)) is also approximately valid for the fast wave critical wavenumber., Equation \ref{eq:crit}) ) is also approximately valid for the fast wave critical wavenumber. + Then. we see that K? is inversely proportional to Cowling's diffusivity. ic.," Then, we see that $k_{\rm c}^{\rm a}$ is inversely proportional to Cowling's diffusivity, $\eta_{\rm C}$." + Since jc is larger in the presence of helium than in the pure hydrogen case due to additional collisions of neutral andsingly ionized helium species. ko is therefore smaller.," Since $\eta_{\rm C}$ is larger in the presence of helium than in the pure hydrogen case due to additional collisions of neutral andsingly ionized helium species, $k_{\rm c}^{\rm a}$ is therefore smaller." + Turning our attention to the slow wave (Fig., Turning our attention to the slow wave (Fig. + 2cc). we see that the maximum and the right-hand side minimum of rp/P are also slightly shifted toward smaller values of κ.," \ref{fig:mhdwaves}c c), we see that the maximum and the right-hand side minimum of $\tdp$ are also slightly shifted toward smaller values of $k$." + Results from Carbonellet and Fortezaetal.(2008) indicate that thermal conduction is responsible for these maximum and minimum of rp/P., Results from \citet{carbonell04} and \citet{forteza08} indicate that thermal conduction is responsible for these maximum and minimum of $\tdp$. + Thus. the additional contribution of neutral helium atoms to thermal conduction (Eq. 19))," Thus, the additional contribution of neutral helium atoms to thermal conduction (Eq. \ref{eq:cond}) )" + causes this displacement of the curve of r5/P., causes this displacement of the curve of $\tdp$. + As for Alfvénn and fast waves. this effect is of minor importance.," As for Alfvénn and fast waves, this effect is of minor importance." +" For comparison. equivalent results with £j.,=106€ and Oy.=0.5 are plotted by means of symbols in Fig. 2.."," For comparison, equivalent results with $\xi_\ion{He}{i} = 10\%$ and $\delta_{\rm He} = 0.5$ are plotted by means of symbols in Fig. \ref{fig:mhdwaves}." + We see that for realistic values of One. Its role is almost irrelevant. meaning that the presence of can be neglected.," We see that for realistic values of $\delta_{\rm He}$ , its role is almost irrelevant, meaning that the presence of can be neglected." + It is worth mentioning that we have repeated these calculations for other values of fij and similar results have been obtained., It is worth mentioning that we have repeated these calculations for other values of $\mutilde_{\rm H}$ and similar results have been obtained. + Next. we study the thermal mode.," Next, we study the thermal mode." + Since it is a purely damped. non-propagating disturbance (We= 0) we only plot the damping time. rp. as a function of & for jjj=0.8 and dye=0.ἱ (Fig. 3)).," Since it is a purely damped, non-propagating disturbance $\omega_{\rm R} = 0$ ), we only plot the damping time, $\td$, as a function of $k$ for $\mutilde_{\rm H} = 0.8$ and $\delta_{\rm He}=0.1$ (Fig. \ref{fig:therm}) )." + We can see that the effect of helium is different in two ranges of &., We can see that the effect of helium is different in two ranges of $k$. + For &>107 m. thermal conduction is the dominant damping mechanism.," For $k \gtrsim 10^{-4}$ $^{-1}$, thermal conduction is the dominant damping mechanism." + So. the larger the amount of helium. the smaller rp because of the enhanced thermal conduction by neutral helium atoms.," So, the larger the amount of helium, the smaller $\td$ because of the enhanced thermal conduction by neutral helium atoms." + On the other hand. radiative losses are more relevant for k€1077 m.," On the other hand, radiative losses are more relevant for $k \lesssim 10^{-4}$ $^{-1}$." + In this region. the thermal mode damping time grows as the helium abundance increases.," In this region, the thermal mode damping time grows as the helium abundance increases." + Since these variations of the damping time are very small. we have to conclude again that the damping time obtained in the absence of helium does not significantly change when helium is taken into account.," Since these variations of the damping time are very small, we have to conclude again that the damping time obtained in the absence of helium does not significantly change when helium is taken into account." + Computations with other values of /tj and oy. do not modify this statement., Computations with other values of $\mutilde_{\rm H}$ and $\delta_{\rm He}$ do not modify this statement. + We can estimate the effect of a magnetic structure. say a slab ora cylinder. which would act as a waveguide.," We can estimate the effect of a magnetic structure, say a slab ora cylinder, which would act as a waveguide." + To do so. weset the wavenumber component in the perpendicular direction to magnetic field lines to a fixed value. k-L= 2/2. with La typical length-scale in the perpendicular," To do so, weset the wavenumber component in the perpendicular direction to magnetic field lines to a fixed value, $k_z L = \pi/2$ , with $L$ a typical length-scale in the perpendicular" +2003).,. +". They are generally based on the detinition of fossil groups from Jonesetal.2003).. i.e. groups with a minimum X-ray luminosity of Lx70.251077) ""erg las well as minimum magnitude difference of two between the first and second ranked galaxies. within half the projected radius that encloses an overdensity of 200 times the mean density of the universe (ους)."," They are generally based on the definition of fossil groups from \citet{b65}, i.e. groups with a minimum X-ray luminosity of $L_{\rm +X,bol} \approx 0.25 \times 10^{42} h^{-2}$ erg $^{-1}$, as well as minimum magnitude difference of two between the first and second ranked galaxies, within half the projected radius that encloses an overdensity of 200 times the mean density of the universe $R_{200}$ )." + For an NFW profile (Navarro.Frenk 1996). this is roughly equivalent to /7?555. the radius enclosing an overdensity of SOO times the mean (for NFW haloes of the ypropriate concentration. {έτος~0.59 Royo)," For an NFW profile \citep{b123}, , this is roughly equivalent to $R_{500}$, the radius enclosing an overdensity of 500 times the mean (for NFW haloes of the appropriate concentration, $R_{500} \sim 0.59 \times +R_{200}$ )." + A few of these fossil groups have been the subject of detailed investigations (Khosroshahi.Jones&Ponman2004:Yoshiokaetal.Sunetal. 2006).," A few of these fossil groups have been the subject of detailed investigations \citep{b75,b185,b165,b167,b45,b100,b80}." +. While most previous studies have focused on X-ray properties of fossils. there is also emerging evidence that the galaxy properties in fossils are different from those in non-fossils (Khosroshahi.Ponman&Jones 2006).," While most previous studies have focused on X-ray properties of fossils, there is also emerging evidence that the galaxy properties in fossils are different from those in non-fossils \citep{b82}." +. For instance the isophotal shapes of the central fossil galaxies appear to be non-boxy. suggesting that they may have formed in gas rich mergers.," For instance the isophotal shapes of the central fossil galaxies appear to be non-boxy, suggesting that they may have formed in gas rich mergers." + Various observational and theoretical studies have suggested a significant fraction of galaxy groups to be fossils (Vikhlininetal.1999:Jones 2006).. though often the criteria used to detine fossils in theoretical work are not easy to relate to observational studies.," Various observational and theoretical studies have suggested a significant fraction of galaxy groups to be fossils \citep{b170,b65,b50,b115,b147}, though often the criteria used to define fossils in theoretical work are not easy to relate to observational studies." + Fossils may represent extreme examples of a continuum of group properties — they are consistently found to be outliers in the usual scaling relations involving optical. X-ray and dynamical properties (Khosroshahi.Ponman&Jones2007).," Fossils may represent extreme examples of a continuum of group properties – they are consistently found to be outliers in the usual scaling relations involving optical, X-ray and dynamical properties \citep{b85}." +. While fossils fall on the L-T relation of non-fossil groups and clusters. they appear to be both hotter and more X-ray luminous than non-fossils of the same mass.," While fossils fall on the L-T relation of non-fossil groups and clusters, they appear to be both hotter and more X-ray luminous than non-fossils of the same mass." + Cooler fossil groups also show lower entropy than their non-fossil counterparts., Cooler fossil groups also show lower entropy than their non-fossil counterparts. + According to Khosroshahi.Pon-man&Jones (2007). the haloes of fossil groups appear to be more concentrated than those of non-fossil systems. for a given mass. which suggests that fossils have an early formation epoch.," According to \citet{b85}, the haloes of fossil groups appear to be more concentrated than those of non-fossil systems, for a given mass, which suggests that fossils have an early formation epoch." + As such. we have much to learn from them. and the investigation of objects with similar properties in cosmological simulations can provide important insights into the physical processes that underly the scaling relations.," As such, we have much to learn from them, and the investigation of objects with similar properties in cosmological simulations can provide important insights into the physical processes that underly the scaling relations." + It can also reveal limitations in the numerical simulations. related to the treatment of physical effects like pre-heating. feedback and merging. which are difficult to model.," It can also reveal limitations in the numerical simulations, related to the treatment of physical effects like pre-heating, feedback and merging, which are difficult to model." + It is thus important to study the formation and evolution of these systems in the cosmological N-Body simulations which have become essential tools for studying formation of large scale structure in the Universe., It is thus important to study the formation and evolution of these systems in the cosmological N-Body simulations which have become essential tools for studying formation of large scale structure in the Universe. + In this paper we use the Millennium simulation (Springeletal.2005) together with the semi-analytic models (Crotonetal.2006) of galaxy formation within dark matter haloes and the Millennium gas simulation (Pearceetal.20073.. to identify fossil groups. study their properties in the simulations and make a comparison to the observations.," In this paper we use the Millennium simulation \citep{b160} together with the semi-analytic models \citep{b40} of galaxy formation within dark matter haloes and the Millennium gas simulation \citep{b128}, to identify fossil groups, study their properties in the simulations and make a comparison to the observations." + We begin with a brief discussion in 322 of the Millennium Simulation. and the implemented semi-analytic galaxy catalogues and gas simulations.," We begin with a brief discussion in 2 of the Millennium Simulation, and the implemented semi-analytic galaxy catalogues and gas simulations." + In $33 we discuss our method of identifying andX-rav fossil groups from these catalogues., In 3 we discuss our method of identifying and fossil groups from these catalogues. + In S44. we discuss the various properties of these fossil groups. their abundance in the local Universe and the evolution of simulated X-ray fossils with time.," In 4, we discuss the various properties of these fossil groups, their abundance in the local Universe and the evolution of simulated X-ray fossils with time." + Finally. in $55. we summarize the implications of our results in terms of the evolution of fossil groups in the context of multiwavelength observations.," Finally, in 5, we summarize the implications of our results in terms of the evolution of fossil groups in the context of multiwavelength observations." + Throughout the paper we adopt {ο=100/ kms + ¢ for the Hubble constant.," Throughout the paper we adopt $H_{0} = 100 \,h$ km $^{-1}$ $^{-1}$ for the Hubble constant." + In order to extract fossil groups in the Millennium simulation. using observational selection criteria. we require a simulation suite that includes the baryonic physics of hot gas and galaxies. as well as a high resolution dark matter framework and a sufficient spatial volume to limit the effects of cosmic variance.," In order to extract fossil groups in the Millennium simulation, using observational selection criteria, we require a simulation suite that includes the baryonic physics of hot gas and galaxies, as well as a high resolution dark matter framework and a sufficient spatial volume to limit the effects of cosmic variance." + For this study we use the dark matter Millennium Simulation (Springeletal.2005).. a 10-billion particle model of a comoving volume of side 5005.+ Mpc. on top of which a publicly available semi-analytic galaxy model (Crotonetal.2006). has been constructed.," For this study we use the dark matter Millennium Simulation \citep{b160}, a 10-billion particle model of a comoving volume of side $h^{-1}$ Mpc, on top of which a publicly available semi-analytic galaxy model \citep{b40} has been constructed." + For the hot gas we have repeated the Millennium simulation with a lower resolution simulation including gas physics utilising the same volume. phases and amplitudes as the original dark-matter-only model.," For the hot gas we have repeated the Millennium simulation with a lower resolution simulation including gas physics utilising the same volume, phases and amplitudes as the original dark-matter-only model." + This run accurately reproduces the structural framework of the Millennium Simulation (Pearceetal.20073., This run accurately reproduces the structural framework of the Millennium Simulation \citep{b128}. +. Below we summarize the main characteristics of the above simulations., Below we summarize the main characteristics of the above simulations. + The Millennium Simulation is based on a Cold) Dark Matter cosmological model of structure formation. with a Dark Energy field A.," The Millennium Simulation is based on a Cold Dark Matter cosmological model of structure formation, with a Dark Energy field $\Lambda$." + The basic assumptions are those of an inflationary universe. dominated by dark matter particles. leading to a bottom-up hierarchy of structure formation. via collapsing and merging of small dense haloes at high redshifts. into the large virialised systems such as groups and clusters that contain the galaxies that we observe today.," The basic assumptions are those of an inflationary universe, dominated by dark matter particles, leading to a bottom-up hierarchy of structure formation, via collapsing and merging of small dense haloes at high redshifts, into the large virialised systems such as groups and clusters that contain the galaxies that we observe today." +" The simulation was performed using the publiclyavailable parallel TreePM code Gadget? (Springeletal. 2001). achieving a 3D dynamic range of 10"" by evolving 2160* particles of individual mass 8.6.1075.+ M.. within a co-moving periodic box of side 500.+ Mpc. and employing a gravitational softening of Sf! kpc. from redshift >=127 to he present day."," The simulation was performed using the publiclyavailable parallel TreePM code Gadget2 \citep{b155}, achieving a 3D dynamic range of $10^5$ by evolving $^3$ particles of individual mass $8.6\times10^{8}h^{-1}$ $_{\odot}$, within a co-moving periodic box of side $h^{-1}$ Mpc, and employing a gravitational softening of $h^{-1}$ kpc, from redshift $z=127$ to the present day." +" The cosmological parameters for the Millennium Simulation were: (34.=0.75.0,,0.25.0),0.045.0)i3.nΞ ]. and oy=0.9. where the Hubble constant is characterised as 100kms.‘Alpe+. These cosmological xrameters are consistent with recent combined analysis from data (Spergeletal.2003) and the 2dF galaxy redshift survey (Collessetal.2001). although the value for ax is a little ligher than would perhaps have been desirable in retrospect."," The cosmological parameters for the Millennium Simulation were: $\Omega_\Lambda = 0.75, \Omega_M = 0.25, \Omega_b = 0.045, h = 0.73, n += 1$ , and $\sigma_8 = 0.9$, where the Hubble constant is characterised as $100 \,h \,{\rm km s^{-1} Mpc^{-1}}.$ These cosmological parameters are consistent with recent combined analysis from data \citep{b146} + and the 2dF galaxy redshift survey \citep{b31}, although the value for $\sigma_8$ is a little higher than would perhaps have been desirable in retrospect." + The derived dark matter halo catalogues include haloes down o a resolution limit of 20 particles. which yields a minimum xilo mass of 10775.! M..," The derived dark matter halo catalogues include haloes down to a resolution limit of 20 particles, which yields a minimum halo mass of $\times 10^{10}h^{-1}$ $_{\odot}$." + Haloes in the simulation are ound using a friends-of-friends (FOF) group. finder. tuned. to extract haloes with overdensities of at least 200 relative to the critical density.," Haloes in the simulation are found using a friends-of-friends (FOF) group finder, tuned to extract haloes with overdensities of at least 200 relative to the critical density." + Within a FOF halo. substructures or subhaloes are identified using the SUBFIND algorithm developed by Springelal. (2001). and the treatment of the orbital decay of satellites is deseribed in the next section.," Within a FOF halo, substructures or subhaloes are identified using the SUBFIND algorithm developed by \citet{b155}, and the treatment of the orbital decay of satellites is described in the next section." + During the Millennium Simulation. 64 time-slices of the locations and. velocities of all the particleswere stored. spread approximately logarithmically in time between +=127 and += 0.," During the Millennium Simulation, 64 time-slices of the locations and velocities of all the particleswere stored, spread approximately logarithmically in time between $z=127$ and $z=0$ ." + From these time-slices. merger trees are built by combining the tables of all haloes found at any given output time. a process which enables us to trace the growth of haloes and their subhaloes through time within the simulation.," From these time-slices, merger trees are built by combining the tables of all haloes found at any given output time, a process which enables us to trace the growth of haloes and their subhaloes through time within the simulation." +"with sz,=1—sz+97 for szxlors: =-(s2+52-1) otherwise.",with $s_{w}^{2}={1-s^{2}_{u}+s^{2}_{v}}$ for $s^{2}_{u}+s^{2}_{v}\le1$ or $s_{w}^{2}=- ({s^{2}_{u}+s^{2}_{v}-1})$ otherwise. +" Complex values of s, lead to exponentially decaying (evanescent) electric fields that are typically not measurable far from the scatterer.", Complex values of $s_{w}$ lead to exponentially decaying (evanescent) electric fields that are typically not measurable far from the scatterer. + The other (homogeneous) waves are those measured by a distant observer., The other (homogeneous) waves are those measured by a distant observer. +" If one further uses the Fourier transform of the scattering potential. (s)=(ffdane""Fu. one can write the scattered electric field üs where we assume a geometry where w=0 is the ground-plane below the ionosphere where 7=1. and that w>O is in the direction of the zenith or the phase reference center (see below)."," If one further uses the Fourier transform of the scattering potential, $\tilde{\Phi}(\vc{s}) = \iiint \Phi(\vc{u}) e^{-2 \pi i \vc{s} \cdot \vc{u}} d^{3}\vc{u},$ one can write the scattered electric field as where we assume a geometry where $w=0$ is the ground-plane below the ionosphere where $n=1$, and that $w>0$ is in the direction of the zenith or the phase reference center (see below)." + The interferometer is placed in a plane defined at a constant way=zui., The interferometer is placed in a plane defined at a constant $w_{\rm ant} = z_{\rm ant}/\lambda$. + Typically one ean assume Wyn.=0., Typically one can assume $w_{\rm ant}=0$. +" Thence. one finds a relation between the Fourter transform of the observed electric field in the plane of the interferometer at Wan, and the Fourter transform of the scattering potential with E'?(s,.5.)=ITVeWandedaddy."," Thence, one finds a relation between the Fourier transform of the observed electric field in the plane of the interferometer at $w_{\rm ant}$ and the Fourier transform of the scattering potential with $ \tilde{E}^{(s)}(s_{u}, s_{v}) = \iint E_{1}^{(s)}(u,v,w_{\rm ant}) e^{ + 2 \pi i (s_{u} u + s_{v} v)} du dv$." + This can be regarded as the Fourier Ea.transform of a two-dimensional slice through a three-dimensional scattered electric field., This can be regarded as the Fourier transform of a two-dimensional slice through a three-dimensional scattered electric field. + In this paper we do not treat the case of an interferometer with varying Way., In this paper we do not treat the case of an interferometer with varying $w_{\rm ant}$. + A planar array is an reasonable assumption for relatively compact kkm-seale) interferometers. but breaks down on large scales where the curvature of the Earth can not be neglected2009).," A planar array is an reasonable assumption for relatively compact km-scale) interferometers, but breaks down on large scales where the curvature of the Earth can not be neglected." +. For a planar array. however. the w-term due to the array can be neglected for small integration times unstantaneous sampling of the electric field in à plane). in contrast to visibilities from very different time frames where the array has rotated over a substantial angle compared to the phase center (only a linear east-west array does not suffer from the w-term).," For a planar array, however, the $w$ -term due to the array can be neglected for small integration times instantaneous sampling of the electric field in a plane), in contrast to visibilities from very different time frames where the array has rotated over a substantial angle compared to the phase center (only a linear east-west array does not suffer from the $w$ -term)." + The physical interpretation of Eqn.(8)) is the following: Every point of the two-dimensional Fourier transform of the scattered electric fieldin the plane of an interferometer probes a single three-dimensional mode of the scattering potential tthe scattering medium) for a single point source., The physical interpretation of \ref{eqn:scattered_field}) ) is the following: Every point of the two-dimensional Fourier transform of the scattered electric field in the plane of an interferometer probes a single three-dimensional mode of the scattering potential the scattering medium) for a single point source. + In the presence of N point sources. all in different directions. every point of the two-diminsional Fourier transform of the scattered electric field in the plane of an interferometer probes the sum of N independent three-dimensional modes of the scattering potential.," In the presence of $N$ point sources, all in different directions, every point of the two-diminsional Fourier transform of the scattered electric field in the plane of an interferometer probes the sum of $N$ independent three-dimensional modes of the scattering potential." + In Section5 we show how to unravel this information., In Section 5 we show how to unravel this information. + In radio interferometry one does not analyze the electric field itself., In radio interferometry one does not analyze the electric field itself. + In that case. Eqn.(8)) would directly yield the three-dimensional structure of the ionosphere (per integration time) because the phase information of the Fourier transform of the electron density of the tonosphere is fully retained in the phase information of the scattered electric field.," In that case, \ref{eqn:scattered_field}) ) would directly yield the three-dimensional structure of the ionosphere (per integration time) because the phase information of the Fourier transform of the electron density of the ionosphere is fully retained in the phase information of the scattered electric field." + In reality. only the cross-correlations of the electric field. measured at different antennae pairs. are stored tthe complex visibilities) and the phase information. of thetonospherie density fluctuationsis lost.," In reality, only the cross-correlations of the electric field, measured at different antennae pairs, are stored the complex visibilities) and the phase information of the ionospheric density fluctuations is lost." + In the following. we assume that the total electric field from the entire sky tthe antenna sensitivity is directionally independent) ismeasured over the infinite interferometer plane with w2Wane.," In the following, we assume that the total electric field from the entire sky the antenna sensitivity is directionally independent) ismeasured over the infinite interferometer plane with $w=w_{\rm ant}$." +" Visibilities are sampled from the cross-correlation of the electric field E(u)=A+Eu) with its complex conjugate. Vibb=«ΕΕια+b», with b. being the baseline between two points (antennae) in plane of the interferometer."," Visibilities are sampled from the cross-correlation of the electric field $E(\vc{u}) = E^{(i)}(\vc{u}) + E^{(s)}(\vc{u})$ with its complex conjugate, $V(\vc{b})\equiv \langle E(\vc{u}) E^{*}(\vc{u} + \vc{b}) \rangle_{\rm t}$ with $\vc{b}$ being the baseline between two points (antennae) in plane of the interferometer." + The averaging 1s assumed to be over time., The averaging is assumed to be over time. + The Fourier transform of the visibilities forms the incident intensity from the sky. as follows from the van Cittert-Zernike theorem2009).," The Fourier transform of the visibilities forms the incident intensity from the sky, as follows from the van Cittert-Zernike theorem." +. The same intensity is also the product of the Fourier transform of the electric field with its complex conjugate., The same intensity is also the product of the Fourier transform of the electric field with its complex conjugate. + A bit of algebra shows that the cross-correlation between the incident and scattered fields depends on the imaginarypart of the zero-mode. 4X0). of the ionosphere. and consequently is equal to zero.," A bit of algebra shows that the cross-correlation between the incident and scattered fields depends on the imaginary part of the zero-mode, $\tilde{\Phi}(0)$, of the ionosphere, and consequently is equal to zero." + The multiplication of the Fourier transform of the scattered electric field with its complex conjugate therefore provides the complete scattered intensity where the dependence on Wan --, The multiplication of the Fourier transform of the scattered electric field with its complex conjugate therefore provides the complete scattered intensity where the dependence on $w_{\rm ant}$ disappears. + Using Eqn.(8)). we find the following result This equation is exact for phase-coherent point sources to first order Born approximation.," Using \ref{eqn:scattered_field}) ), we find the following result This equation is exact for phase-coherent point sources to first order Born approximation." + However. the sky is an incoherent emitterfields).," However, the sky is an incoherent emitter." +. Hence. the cross-terms with 2zi depend on the electric field coming from incoherent point sources and vanish. such that we are left with where we dropped the subscript.," Hence, the cross-terms with $n\neq m$ depend on the electric field coming from incoherent point sources and vanish, such that we are left with where we dropped the subscript." + This equation forms the basis for further discussions in the paper., This equation forms the basis for further discussions in the paper. + The above equation is only correct for an interferometer and an electric field measured ina plane., The above equation is only correct for an interferometer and an electric field measured in a plane. +" In three dimensions. one would no longer be able to use simple Fourier transforms (see below). because 5, depends explicitly on s», and ον."," In three dimensions, one would no longer be able to use simple Fourier transforms (see below), because $s_{w}$ depends explicitly on $s_{u}$ and $s_{v}$." + To understand the physical interpretation of the above equation. one might suppose a point source in the zenith (or equivalently in the phase center) emitting a plane wave in the absence of the tonosphere.," To understand the physical interpretation of the above equation, one might suppose a point source in the zenith (or equivalently in the phase center) emitting a plane wave in the absence of the ionosphere." + Because the phase of the electric field 1s the same at each antenna (by construction). its Fourter transform yields a complex delta function in the zenith with a time-varying phase.," Because the phase of the electric field is the same at each antenna (by construction), its Fourier transform yields a complex delta function in the zenith with a time-varying phase." + Multiplied with its complex conjugate. this recovers the point source intensity.," Multiplied with its complex conjugate, this recovers the point source intensity." + If a two-dimensional thin phase-screen is placed in between the source and the array. exhibiting a single wave-mode in electron density perpendicular to the zenith or phase reference center direction. then part of the electric field amplitude will be modulated such that its phases show to first order the imprint of this ionospheric wave-mode description).," If a two-dimensional thin phase-screen is placed in between the source and the array, exhibiting a single wave-mode in electron density perpendicular to the zenith or phase reference center direction, then part of the electric field amplitude will be modulated such that its phases show to first order the imprint of this ionospheric wave-mode ." +. The modulated phase aa single wave over the array) can be interpreted as being identical in. the weak scattering limit to the modulated phase of a point source offset from the zenith in the direction of the ionospheric wave- by a distance set by the phase-frequency over the array., The modulated phase a single wave over the array) can be interpreted as being identical in the weak scattering limit to the modulated phase of a point source offset from the zenith in the direction of the ionospheric wave-vector by a distance set by the phase-frequency over the array. + Hence. squared.," Hence, ." + The sum of all speckles create à halo of scattered emission around the point source. when not corrected forthrough phase calibration.," The sum of all speckles create a halo of scattered emission around the point source, when not corrected forthrough phase calibration." +First we investigate the effects of outer truncation.,First we investigate the effects of outer truncation. + Convolved synthetic maps for the emission in [OI]. 6300 for some numerical models and run (500.1000.0.5) are given in Fig. 6..," Convolved synthetic maps for the emission in [OI] $\lambda$ 6300 for some numerical models and run (500,1000,0.5) are given in Fig. \ref{Fig_emissmaps_outertrunc}." + Truncation leads to collimation of the emission region with respect to the model ADO without any truncation., Truncation leads to collimation of the emission region with respect to the model ADO without any truncation. + Agam we extracted the jet width from emission maps like these., Again we extracted the jet width from emission maps like these. + The resulting widths derived from the synthetic [OI] images and sealed to AU are presented in Fig. 7.., The resulting widths derived from the synthetic [OI] images and scaled to AU are presented in Fig. \ref{jet_widths_modelSC}. + We found similarities in. behavior in the truncated. models to the untruncated model ADO., We found similarities in behavior in the truncated models to the untruncated model ADO. + The jet widths show again no dependency on the density. as described for model ADO in the previous section.," The jet widths show again no dependency on the density, as described for model ADO in the previous section." + Surprisingly. in. models SCla-c. SC2 and SC4 the runs (500.600.0.2) and (500.1000.0.5) and also (500.1000.0.8) lead to almost similar physical Jet widths.," Surprisingly, in models SC1a-c, SC2 and SC4 the runs (500,600,0.2) and (500,1000,0.5) and also (500,1000,0.8) lead to almost similar physical jet widths." + The first two also almost coincide in models SCId-e. As in model ADO. also in the truncated models the run (500.600.0.5) has the smallest jet widths (after the first bump).," The first two also almost coincide in models SC1d-e. As in model ADO, also in the truncated models the run (500,600,0.5) has the smallest jet widths (after the first bump)." + In principle. we can reproduce even smaller values than the observed ones.," In principle, we can reproduce even smaller values than the observed ones." + In paper I we also performed numerical simulations. in which we truncated the analytical solution in the interior. Le. at an inner truncation radius.," In paper I we also performed numerical simulations, in which we truncated the analytical solution in the interior, i.e. at an inner truncation radius." + The physical picture behind. this scenario is a stellar magnetosphere truncating the jet-emitting disk., The physical picture behind this scenario is a stellar magnetosphere truncating the jet-emitting disk. + We showed that inner truncation leads to a decrease of the jet radius and compression of the material in the inner region., We showed that inner truncation leads to a decrease of the jet radius and compression of the material in the inner region. + Unfortunately. only one run met our scaling requirements (Sect. 3.1)):," Unfortunately, only one run met our scaling requirements (Sect. \ref{sec_norm}) ):" + model SC3 and run (---. 100. 0.2).," model SC3 and run $\cdots$, 100, 0.2)." + For this model. a convolved synthetic map for the emission in [OI] 26300 is given in Fig. 8..," For this model, a convolved synthetic map for the emission in [OI] $\lambda$ 6300 is given in Fig. \ref{Fig_emissmaps_innertrunc}." + After rescaling the derived jet width to AU. we found an almost constant width in the range of the observed values.," After rescaling the derived jet width to AU, we found an almost constant width in the range of the observed values." + Note that our model does not provide results farther out than 100 AU due to a small Ro., Note that our model does not provide results farther out than 100 AU due to a small $R_0$. + We studied the jet widths derived from synthetic emission maps in different forbidden lines as the full-width half-maximum of the emission., We studied the jet widths derived from synthetic emission maps in different forbidden lines as the full-width half-maximum of the emission. + We found that the untruncated model ADO of Vlahakisetal.(2000). cannot account for the small jet widths found in recent optical images taken with HST and AO., We found that the untruncated model ADO of \citet{VTS00} cannot account for the small jet widths found in recent optical images taken with HST and AO. + The density normalization is not important for the resulting measured jet width as long as we are far from the critical regime., The density normalization is not important for the resulting measured jet width as long as we are far from the critical regime. + We investigated different effects for reducing the deriving jet width: by imposing an outer radius of the launching region of the underlying accreting disk and thus also of the outflow on the observable structure of the jet and by imposing an inner radius of the underlying aceretion disk due to interactions with the stellar magnetosphere., We investigated different effects for reducing the deriving jet width: by imposing an outer radius of the launching region of the underlying accreting disk and thus also of the outflow on the observable structure of the jet and by imposing an inner radius of the underlying accretion disk due to interactions with the stellar magnetosphere. + We created synthetic images based on our simulations of truncated disk winds (Stuteetal.2008) as well as new simulations and found that the extracted jet widths in the truncated models decrease for models SCla-lIg. compared to those of the untruncated model ADO. as naively expected.," We created synthetic images based on our simulations of truncated disk winds \citep{STV08} as well as new simulations and found that the extracted jet widths in the truncated models decrease for models SC1a–1g, compared to those of the untruncated model ADO, as naively expected." + In the present paradigm. Jets are emitted only by the inner part of the disk.," In the present paradigm, jets are emitted only by the inner part of the disk." + Hence in the other parts the disk can be described by a standard aceretion disk (SAD). in the inner parts by a jet-emitting disk JED).," Hence in the other parts the disk can be described by a standard accretion disk (SAD), in the inner parts by a jet-emitting disk (JED)." + Andersonetal.(2003) showed that one can estimate the launching region às This transition was. constrained observationally with measured jet rotation velocities and using the equation above and radi of the order of 0.I-] AU we used in several theoretical studies as e.g. Combet&Ferreira(2008)., \citet{ALK03} showed that one can estimate the launching region as This transition was constrained observationally with measured jet rotation velocities and using the equation above and radii of the order of 0.1–1 AU are used in several theoretical studies as e.g. \citet{CoF08}. +. Our results can be used to infer the “real” value of the truncation. radius Ay; in the observed sample of jets and interpret 1t as the transition. radius of the JED to the SAD. assuming the specific model of VOO applies.," Our results can be used to infer the “real” value of the truncation radius $R_{\rm trunc}$ in the observed sample of jets and interpret it as the transition radius of the JED to the SAD, assuming the specific model of V00 applies." + At the lower boundary in our simulations. the truncation radii are given in Table 1..," At the lower boundary in our simulations, the truncation radii are given in Table \ref{tbl_models}." +" They vary from 5.375 Ro in model SCla to 0.575 Ro m model SCIg. However. these radii are set atz=6R, (the lower boundary). not in the equatorial plane."," They vary from 5.375 $R_0$ in model SC1a to 0.575 $R_0$ in model SC1g. However, these radii are set at $z = 6\,R_0$ (the lower boundary), not in the equatorial plane." + Those can be calculated by extrapolating the field line. t.e. with. @uune=aretan(Ryunel-—_6/6)G(PBug: and G. taken from- the analytical solution of VOO.," Those can be calculated by extrapolating the field line, i.e. with $\theta_{\rm trunc} = \arctan ( R_{\rm trunc} |_{z = 6} / 6 )$ and $G$ taken from the analytical solution of V00." + This gives the following results:, This gives the following results: +this looks essentially the same as the window function is a eood indication that there are no periodicities in the cala which result from “PW Pic iself.,this looks essentially the same as the window function is a good indication that there are no periodicities in the data which result from TW Pic itself. +" Phe third panel is another ""dirty power spectrum of the time series. but this time with the mean value of the data removed. prior to caleulaion of the Fourier transform."," The third panel is another `dirty' power spectrum of the time series, but this time with the mean value of the data removed prior to calculation of the Fourier transform." + TEus cllectively removes the +irst order window function [rom the data allowing anv wcoals signals to be seen more clearIv., This effectively removes the `first order' window function from the data allowing any weak signals to be seen more clearly. + Note that the vertical sca eof this power spectrum is 100 imes greater than in the second panel., Note that the vertical scale of this power spectrum is 100 times greater than in the second panel. + Some residual structure ap»ears to be present in this power spectrum. but close inspecjon again reveals that all the peaks are at window function [recuencies.," Some residual structure appears to be present in this power spectrum, but close inspection again reveals that all the peaks are at window function frequencies." + The bottom panel shows the CLEANed. power spectrum. with the same vertical scale as he hird panel.," The bottom panel shows the ed power spectrum, with the same vertical scale as the third panel." + The two largest spikes in the CLEANed. [)0WeOr spectrum. near (o ⋅n . ⇀↗≻⋅⋅↱≻↓∪∐∠⊳⋜⊔⋅∢⋅⋜∐∖∖⋎↓⊔∠⇂∪∖∖⊽⇂⊔⊔≼∼⋅jon pequencies and so are unlikely to represent real signals. (," The two largest spikes in the ed power spectrum, near to $3.5 \times 10^{-4}$ Hz, are at window function frequencies and so are unlikely to represent real signals. (" +In act. their frequencies correspond. tofadf the orbital peloc of the satellite and,"In fact, their frequencies correspond to the orbital period of the satellite and" +of Equation (35).,of Equation (35). +" Fortunately, this transition is greatly simplified by the very simple equation of state implied by the condition Ry=cf. given by with w=—1/3. as we discussed earlier."," Fortunately, this transition is greatly simplified by the very simple equation of state implied by the condition $R_{\rm h}=ct$, given by with $w=-1/3$, as we discussed earlier." +" For a universe with density p and pressure p=wp. the linear relativistic version of Equation (35) is Therefore, for an Aj=cf universe, the dynamical equation tor ó, is We need to emphasize several important features of this equation."," For a universe with density $\rho$ and pressure $p=w\rho$, the linear relativistic version of Equation (35) is Therefore, for an $R_{\rm h}=ct$ universe, the dynamical equation for $\delta_\kappa$ is We need to emphasize several important features of this equation." +" First of all, the active mass in this universe is proportional to e+3p=0. and therefore the gravitational term normally appearing in the standard model is absent (see Equation 35)."," First of all, the active mass in this universe is proportional to $\rho+3p=0$, and therefore the gravitational term normally appearing in the standard model is absent (see Equation 35)." +" But this does not mean that 6, cannot grow.", But this does not mean that $\delta_\kappa$ cannot grow. +" Instead, because p<0, the (usually dissipative) pressure term in Equation (35) here becomes an agent of growth."," Instead, because $p<0$, the (usually dissipative) pressure term in Equation (35) here becomes an agent of growth." +" Moreover, there is no Jeans length scale."," Moreover, there is no Jeans length scale." +" In its place is the gravitational radius, which we can see most easily by writing Equation (42) in the form where Note, in particular, that both the gravitational radius A, and the fluctuation scale 2 vary with ¢ in exactly the same way, so A, is therefore a constant in time."," In its place is the gravitational radius, which we can see most easily by writing Equation (42) in the form where Note, in particular, that both the gravitational radius $R_{\rm h}$ and the fluctuation scale $\lambda$ vary with $t$ in exactly the same way, so $\Delta_\kappa$ is therefore a constant in time." +" But the growth rate of 6, depends critically on whether 2 is less than or greater than A.", But the growth rate of $\delta_\kappa$ depends critically on whether $\lambda$ is less than or greater than $R_{\rm h}$. +" A simple solution to Equation (43) is the power law where evidently so that Thus, for small fluctuations Cl<< Ry)."," A simple solution to Equation (43) is the power law where evidently so that Thus, for small fluctuations $\lambda<6.1(D/100pc] kii."," to describe the multi-wavelength data on , may be also applied to the radiation from, with the “soft” component of $^\infty_{\rm bb,s}<43$ eV and $^\infty_{\rm bb,s}>6.1\,({\rm D}/100\,{\rm pc})$ km." + Such a model. with N-vavs originating from a hot area on the stars surface and the optical fluxes emütted from the rest of the surface. 1nay explain the pulsatious of the N-vay radiation frouJo720.1-3125..," Such a model, with X-rays originating from a hot area on the star's surface and the optical fluxes emitted from the rest of the surface, may explain the pulsations of the X-ray radiation from." + In addition to the thermal componoetits. HIST. observations bv Kaplan ο al. (2003))," In addition to the thermal components, HST observations by Kaplan et al. \cite{kaplan03}) )" + reveal evidence for a uouthermal power law colpoucut., reveal evidence for a nonthermal power law component. + Towever. while tlis siniple iiultiple-coniponenut mode seclus to be idu agreement with the properties of the ciission detected fromJ0720.1-3125... it. ds hardly reconciled with the fact that. as stars are uot blackbodies. raclation enütted by a star shouk deviate from a blacAbodyv model.," However, while this simple multiple-component model seems to be in agreement with the properties of the emission detected from, it is hardly reconciled with the fact that, as stars are not blackbodies, radiation emitted by a star should deviate from a blackbody model." + Also. i the case ofRXJ1556.5-375L. the absence of pulsatious put severe constraluts on he two-blackbody model. requiring either a particular ecometrical coufiguration or strong eravitational detlectio1 (Ransom et al. 2002)).," Also, in the case of, the absence of pulsations put severe constraints on the two-blackbody model, requiring either a particular geometrical configuration or strong gravitational deflection (Ransom et al. \cite{ransom02}) )." +" All previous modes of neutron star surface radiation were based on a conventional assmuption that there is chough matter ο, BS.ο nue liverogon or iron. or a müxture of clemeuts) ou the icutron star surface to make the atmosphere lavers optically thick at all euergies of interest."," All previous models of neutron star surface radiation were based on a conventional assumption that there is enough matter (e. g., pure hydrogen or iron, or a mixture of elements) on the neutron star surface to make the atmosphere layers optically thick at all energies of interest." + A typical estimate for such au amount in terms of the total surface. column deusitv+ is. và;7+10—E100 & P= (depending ou the surface temperature) to provide the equilibrium (or diffusima) solution of the radiative transfer problein in the very cep lavers (see AMihalas 1978)).," A typical estimate for such an amount in terms of the total surface column density is $_{\rm +tot}>10-100$ g $^{-2}$ (depending on the surface temperature) to provide the equilibrium (or diffusion) solution of the radiative transfer problem in the very deep layers (see Mihalas \cite{mihalas78}) )." + Under this assuniption. spectra of the emitted radiation are solely determined by the temperature distribution in the atinosphere (Gvehich grows towards larger depths) and do uot depend «n properties of stars lavers ling uuderneath the atmosphere.," Under this assumption, spectra of the emitted radiation are solely determined by the temperature distribution in the atmosphere (which grows towards larger depths) and do not depend on properties of star's layers lying underneath the atmosphere." + In the case of a lieht-clement atmosphere composition. the model spectra were ound to be much larder at higherLad photon energies than dackbody. ones providing the same radiative fux.," In the case of a light-element atmosphere composition, the model spectra were found to be much harder at higher photon energies than blackbody ones providing the same radiative flux." + The reason. for this effect is that ligh-enerey photons with οσο mean-frec-patlis are ciitted from deep surface avers with temperatures larger than the so-called effective eniperature. the fourth power of which determines the otal enerev fux (x cae. Zavliu ct al.," The reason for this effect is that high-energy photons with longer mean-free-paths are emitted from deep surface layers with temperatures larger than the so-called effective temperature, the fourth power of which determines the total energy flux (see, e.g., Zavlin et al." + 1996. aud Zavlin Pavlov 2002 for details}., \cite{zavlin96} and Zavlin Pavlov \cite{zavlin02} for details). + Due to this property he model spectra. wwhen applied to observational data. usually vield lower toiuperatures by a factor of 2.3 and uuch larger enüttius areas by afactor of 50200 than estimates obtained froni blackbody fits.," Due to this property the model spectra, when applied to observational data, usually yield lower temperatures by a factor of $2-3$ and much larger emitting areas by afactor of $50-200$ than estimates obtained from blackbody fits." + IHowever. it is iof known a priori how mich. for example. hydrogen las," However, it is not known a priori how much, for example, hydrogen has" +"To approximate the probability of a chance superposition of the X-ray positions of the compact sources with random sources in the respective fields. we calculate P=|expeve '* where pa is the surface area number density of observed sources down to the limiting magnitude and Ar, is the area of the X-ray positional error.","To approximate the probability of a chance superposition of the X-ray positions of the compact sources with random sources in the respective fields, we calculate $P \approx 1-\exp^{-(\rho_N \times A_{Err})}$ ; where $\rho_N$ is the surface area number density of observed sources down to the limiting magnitude and $A_{Err}$ is the area of the X-ray positional error." + For aandJ18490—0000.. which have positions accurate at the sub-aresecond level. we find probabilities of chance superpositions of and respectively. making the positional coincidence of wwith a nIR object reasonably compelling evidence for its association.," For and, which have positions accurate at the sub-arcsecond level, we find probabilities of chance superpositions of and respectively, making the positional coincidence of with a nIR object reasonably compelling evidence for its association." + However. forJ1632—478.. with only an aresecond accurate position. the probability is much greater at50%.. though the source is in a relatively less densely populated region of the field. where the local probability is ~40%.," However, for, with only an arcsecond accurate position, the probability is much greater at, though the source is in a relatively less densely populated region of the field, where the local probability is $\sim 40\%$." + In this case. even if a source had been found within the error circle. its associatiol with the X-ray source would be weak. meaning source | at a distance of ~2.60 is likely unrelated.," In this case, even if a source had been found within the error circle, its association with the X-ray source would be weak, meaning source 1 at a distance of $\sim 2.6\sigma$ is likely unrelated." + To associate a nIR counterpart with this source based on positional coincidence will require a significantly. better constrained position from e.g.Chandra. Along with the optical extinction in their directions. the detection of extended emission from the PWNe is complicated by the high level of background in nIR observations as well as the generally high density of field sources in the Galactic plane which contaminate the background.," To associate a nIR counterpart with this source based on positional coincidence will require a significantly better constrained position from e.g. Along with the optical extinction in their directions, the detection of extended emission from the PWNe is complicated by the high level of background in nIR observations as well as the generally high density of field sources in the Galactic plane which contaminate the background." + Deep nIR images from larger telescopes better able to resolve field sources. may be able to detect PWN emission. as well as increasing the probability of detecting the compact sources. but in these directions source confusion will always be a major impediment to detection of point or extended sources.," Deep nIR images from larger telescopes better able to resolve field sources, may be able to detect PWN emission, as well as increasing the probability of detecting the compact sources, but in these directions source confusion will always be a major impediment to detection of point or extended sources." + We find no evidence of any extended nIR emission associated with the PWNe in any of the fields or any new counterparts to the X-ray point sources. but we do confirm the magnitude of the previously suggested counterpart. ofJ18490—0000.," We find no evidence of any extended nIR emission associated with the PWNe in any of the fields or any new counterparts to the X-ray point sources, but we do confirm the magnitude of the previously suggested counterpart of." +. While there is a low probability of chance coincidence of the X-ray position with à nIR object in this field. the candidate source is significantly brighter than most other isolated pulsars and brighter than a simple extrapolation of the X-ray spectra to the nIR. making its association with the X-ray source less certain.," While there is a low probability of chance coincidence of the X-ray position with a nIR object in this field, the candidate source is significantly brighter than most other isolated pulsars and brighter than a simple extrapolation of the X-ray spectra to the nIR, making its association with the X-ray source less certain." + If future observations can confirm the association it seems that an additional emission component will be necessary to explain the excess nIR flux., If future observations can confirm the association it seems that an additional emission component will be necessary to explain the excess nIR flux. +" The non-detection of the other two sources. aandJ1632—478.. may be understood by the high level of Galactic extinction in their direction and by the intrinsically faint nature of isolated neutron stars. which the compact objects are assumed to be: it may be reasonable to expect the counterparts ofthese sources to be at magnitudes K,z 18.6."," The non-detection of the other two sources, and, may be understood by the high level of Galactic extinction in their direction and by the intrinsically faint nature of isolated neutron stars, which the compact objects are assumed to be; it may be reasonable to expect the counterparts ofthese sources to be at magnitudes $K_s \gtrsim 18.6$ ." +Object hh-540 at redshift 2.80 had in fact already been identified as à good quasar candidate in a variability study. where we compared & magnitudes in frames taken at different epochs throughout the CADIS observing program.,"Object h-540 at redshift 2.80 had in fact already been identified as a good quasar candidate in a variability study, where we compared $R$ magnitudes in frames taken at different epochs throughout the CADIS observing program." + The Seyfert galaxy hh-644 was found by chance among the galaxies we selected for checking our photometric redshift estimates., The Seyfert galaxy h-644 was found by chance among the galaxies we selected for checking our photometric redshift estimates. + It has stellar shape and was classified as a starburst galaxy by our algorithm., It has stellar shape and was classified as a starburst galaxy by our algorithm. +" The quasar 16hh-429 looks morphologically stellar in some filters and extended in others. in the 7? filter and in the A"" band."," The quasar h-429 looks morphologically stellar in some filters and extended in others, in the $R$ filter and in the $K^\prime$ band." + The point source appears to be not precisely centered on the fuzz., The point source appears to be not precisely centered on the fuzz. + Our classification assigned a significant likelihood to this object for being a galaxy at 2—1.5., Our classification assigned a significant likelihood to this object for being a galaxy at $z\approx1.7$. + We can not decide at this point. whether the visible fuzz around this object is a luminous host galaxy or a foreground object projected onto the line of sight by chance.," We can not decide at this point, whether the visible fuzz around this object is a luminous host galaxy or a foreground object projected onto the line of sight by chance." + Interesting to note are three pairs of AGNs: Object hh-104 lies outside of the, Interesting to note are three pairs of AGNs: Object h-104 lies outside of the +οςLUpoleus appearing at velocities of —160 to —200 kin Land —135 kis 1 are located within a few hundred parsecs of the GC.,components appearing at velocities of $-$ 160 to $-$ 200 km $^{-1}$ and $-$ 135 km $^{-1}$ are located within a few hundred parsecs of the GC. + In the injer Galaxy. atomic gas Is most often associated with regions of molecular gas where it serves 10 shied the molecular gas agalust »hotodissociation (Dickey Lockinan 1990).," In the inner Galaxy, atomic gas is most often associated with regions of molecular gas where it serves to shield the molecular gas against photodissociation (Dickey Lockman 1990)." + Therefore. H] absorption features not described above 1uay be idenified with known GC molecular emission [ealures usiug correlatious in velocity stricture.," Therefore, HI absorption features not described above may be identified with known GC molecular emission features using correlations in velocity structure." + The CO survey carried out by Oka et al. (, The CO survey carried out by Oka et al. ( +"1998) usiig the Nojevauma .o-ur telescope provides the most [favorable resolution. velocity. aud spatial C""verage oL aLy σιrvey of molecular gas within the central Galaxy.","1998) using the Nobeyama 45-m telescope provides the most favorable resolution, velocity, and spatial coverage of any survey of molecular gas within the central Galaxy." + Iu addition. the multitude of “forbidden” (e.g. sigu opposite to galactic rotation) veουν components iu the GC region are thought to represeit the respouse of the molecular gas iu the GC to the Galaxys stroig stellar bar (Binney οἱ al.," In addition, the multitude of “forbidden” (e.g. sign opposite to galactic rotation) velocity components in the GC region are thought to represent the response of the molecular gas in the GC to the Galaxy's strong stellar bar (Binney et al." + 1991: Bally et al., 1991; Bally et al. + LOSS)., 1988). + Tie. CO survey data of Oka et al. (, The CO survey data of Oka et al. ( +1998). illstrated that the molecular gas taced by CO elission iu the central 200 pc is organized iutο filaijentary and shell-like features.,1998) illustrated that the molecular gas traced by CO emission in the central 200 pc is organized into filamentary and shell-like features. + This morphology ald kijet1c stricture indicates that violent kiiletic activity (such as supernova explosiois and stellar wluds from Wolt-Bayet type stars) plays an iiiportaut role in shaping the ISAL., This morphology and kinetic structure indicates that violent kinetic activity (such as supernova explosions and stellar winds from Wolf-Rayet type stars) plays an important role in shaping the ISM. + In aclclition to the hadio Are reeion (where the Quiutupet aud. Arcles clusters are located). the GC region is fillec wlth sites whe‘e compact thermal radio and inid-iufrared sources have been observed (e.g. Ser B. Serie C. aud at uauvy positions along the Calaetie plane: e.g.. Laltosa et al.," In addition to the Radio Arc region (where the Quintuplet and Arches clusters are located), the GC region is filled with sites where compact thermal radio and mid-infrared sources have been observed (e.g. Sgr B, Sgr C, and at many positions along the Galactic plane; e.g., LaRosa et al." + 2000: Egan et al., 2000; Egan et al. + 1995 al Lit is likely hat massive stars are eiher foriing or have formed in these regions., 1998) and it is likely that massive stars are either forming or have formed in these regions. + Iu addition. the spectrum of cli[use X-ray emission in this regiou suggests that the ISM is being strongly influence bst qnasslve staforming activities (Wang. Cothelf Lang 2002: Wane. Doug Lang 2006).," In addition, the spectrum of diffuse X-ray emission in this region suggests that the ISM is being strongly influenced by massive star-forming activities (Wang, Gotthelf Lang 2002; Wang, Dong Lang 2006)." + HI absorption toward the bright SerA ccdLiplex aud the compact SgrÁ* radio source has beet the sibjeet of a number of interferometric stidies over the last three clecacdes (Badlakrishnan et al., HI absorption toward the bright SgrA complex and the compact $^*$ radio source has been the subject of a number of interferometric studies over the last three decades (Radhakrishnan et al. + 1972. Schwa*. Ekers Coss 1982. Liszt et al.," 1972, Schwarz, Ekers Goss 1982, Liszt et al." + 1983: Dwarakanath et al., 1983; Dwarakanath et al. + 2001)., 2004). +" These studies illust""ate the wide variety of absorption au enission features towalc this complex. area of the Galaxy. many o “which have velocities that ineicate non-circular motions."," These studies illustrate the wide variety of absorption and emission features toward this complex area of the Galaxy, many of which have velocities that indicate non-circular motions." + On larger scales. Laseuby. Li1361by Yusel-Zadeh (1989) carried out the first VLA compact configration HI absorption study toward the cent‘al of the QC (corresponcliug to τὸ pe at a distance c LS kpc (Bekl et al.," On larger scales, Lasenby, Lasenby Yusef-Zadeh (1989) carried out the first VLA compact configuration HI absorption study toward the central of the GC (corresponding to 75 pc at a distance of 8 kpc (Reid et al." + 1993)). cente'ed on the well-known Radio Are uonthermal filaments anc includiο the bright SerA complex.," 1993)), centered on the well-known Radio Arc nonthermal filaments and including the bright SgrA complex." +" Tle spatial rescAution was 20-70"" with a veocity resolution of 10.2τν witha total velocity verage of 660L."," The spatial resolution was $\sim$ with a velocity resolution of 10.2, with a total velocity coverage of 660." + However. tlis spatial resolution o ule Lasenby et al. (," However, this spatial resolution of the Lasenby et al. (" +1989) data is not equate or detailed comparisons wit1 higher frequency continttun aud recombination liue datasets the HII regins in the Radio Are (e.e.. Lang e al.,"1989) data is not adequate for detailed comparisons with higher frequency continuum and recombination line datasets of the HII regions in the Radio Arc (e.g., Lang et al." + 1997. 2001) ancl ν'elocity. inormation on the 10izing sellar clusters.," 1997, 2001) and velocity information on the ionizing stellar clusters." + Iu. acklition. he spatial coverage cid 1ot iuclude the active Ser B region.," In addition, the spatial coverage did not include the active Sgr B region." + Athough high spatial resolution VLA HI absorption measurements have been mace toward several indivicdtua GC sources (e.g.. Uchida e al. (," Although high spatial resolution VLA HI absorption measurements have been made toward several individual GC sources (e.g., Uchida et al. (" +1992) and Roy e al. (,1992) and Roy et al. ( +2003)). a complete HI absorption sluly is djissiug [rom the growing canon of GC surΝΘΥΣ.,"2003)), a complete HI absorption study is missing from the growing canon of GC surveys." +" ""Therefore. we have carried out an HI absorption survey of the central κου (250 x 125 pc)"," Therefore, we have carried out an HI absorption survey of the central $\times$ (250 x 125 pc)" +change is very small compared to that between Galactic and SAIC’ abundanees.,change is very small compared to that between Galactic and `SMC' abundances. + The present discussion. of the relationship between temperature and. spectral tvpe in the recuced-metallicity environment. of the SMC has immediate implications for the eriteria used. to allocate. luminosity classes., The present discussion of the relationship between temperature and spectral type in the reduced-metallicity environment of the SMC has immediate implications for the criteria used to allocate luminosity classes. + At given spectral twpe. the temperature of an A-type SAIC star is lower than its Galactic counterpart: as a consequence. the 115 equivalent width will be different in the SAIC star.," At given spectral type, the temperature of an A-type SMC star is lower than its Galactic counterpart; as a consequence, the $\gamma$ equivalent width will be different in the SMC star." +" For example. Figure 13. shows the model Le line for =O000K. = Z. and —8500lx. = E = 2.0). corresponding to Galactic and SAIC A2 spectra. respectively: the EI, equivalent width is some 304 larger in the SAIC case."," For example, Figure \ref{ew} shows the model $\gamma$ line for = 9000K, = $_{\odot}$ and = 8500K, = $_{\odot}$ (at = 2.0), corresponding to Galactic and SMC A2 spectra, respectively; the $\gamma$ equivalent width is some $\%$ larger in the SMC case." + This is not (directly) a metallicity ellect. as the Ες lines for Galactic and SAIC metallicities are essentially identical at fixed temperature.," This is not (directly) a metallicity effect, as the $\gamma$ lines for Galactic and SMC metallicities are essentially identical at fixed temperature." + Table ο summarizes the differences in H. equivalent widths for stars of spectral twpes BsAT (averaged over al a given temperature)., Table \ref{factor} summarizes the differences in $\gamma$ equivalent widths for stars of spectral types B8–A7 (averaged over at a given temperature). + In eencral. equivalent widths are —10 30% Larger in the svnthetic SAIC spectra than in Galactic models at the same spectral type (but sof the same temperature).," In general, equivalent widths are $\sim$ $\%$ larger in the synthetic SMC spectra than in Galactic models at the same spectral type (but the same temperature)." + Note that the equivalent widths are larger in aff of the SMC spectra: in contrast to A-type dwarls where the equivalent width of the Balmer lines reaches a maximum around AO/A2. the maximum for supergiants occurs at a much later type (e.g.2). resulting in a positive ellect throughout the spectral types in Table 13..," Note that the equivalent widths are larger in $all$ of the SMC spectra; in contrast to A-type dwarfs where the equivalent width of the Balmer lines reaches a maximum around A0/A2, the maximum for supergiants occurs at a much later type \citep[e.g.][]{h66} resulting in a positive effect throughout the spectral types in Table \ref{ew}." + The clear implication is that if luminosity classifications are allocated from Calactic calibrations. the intrinsic brightness. of a star with a given classification cannot be assumed to be universal.," The clear implication is that if luminosity classifications are allocated from Galactic calibrations, the intrinsic brightness of a star with a given classification cannot be assumed to be universal." + Our work has demonstrated. that accurate A-supergiant temperatures require knowledge of the metallicity of a svstem (ancl vice versa)., Our work has demonstrated that accurate A-supergiant temperatures require knowledge of the metallicity of a system (and vice versa). + This οσο has important ramifications for studies of extragalactic A-type supergiants., This effect has important ramifications for studies of extragalactic A-type supergiants. + For example. from comparison with template Calactic spectra. ? assign a spectral twpe of Al la to a star in NGC 3621 (a spiral galaxy. at a distance of 6.7 Alpe).," For example, from comparison with template Galactic spectra, \citet{bk01} assign a spectral type of A1 Ia to a star in NGC 3621 (a spiral galaxy at a distance of 6.7 Mpc)." + From the spectral type they estimate a temperature (00001 £400) and then use Ixurucz model atmospheres and. the line. formation calculations of 2? το [ind the chemicalcomposition which best matches the observations: their, From the spectral type they estimate a temperature (9000K $\pm$ 400) and then use Kurucz model atmospheres and the line formation calculations of \citet{pryz02} to find the chemicalcomposition which best matches the observations; their +hose in the first reduction method. resulting in a decrease in the number of vectors selected after error clipping.,"those in the first reduction method, resulting in a decrease in the number of vectors selected after error clipping." + The change in the errors in polarisation are due to he binning., The change in the errors in polarisation are due to the binning. +" When the pixel size is set to3.09""... four ixels are produced. for every one when the size is6."," When the pixel size is set to, four pixels are produced for every one when the size is." +"18"".. A vector is then produced for cach pixel. with the vectors or the smaller pixels being binned together adding the »olarisations together in (quacdrature to calculate the error."," A vector is then produced for each pixel, with the vectors for the smaller pixels being binned together — adding the polarisations together in quadrature to calculate the error." +" ""his erroneously reduces the resultant errors.", This erroneously reduces the resultant errors. + The observing mode used means that one independent »olarisation measurement is taken at steps of every. the results of which can be superimposed over an intensity : ↓⊔↓⋜↧⋏∙≟∢⊾≼∼↓⋅∢⊾⋜⋯⋅∠⇂∖∖⊽↓↿↓↥↶∫≻⋡∪≤⋗∢⋅∕∕ pixels.," The observing mode used means that one independent polarisation measurement is taken at steps of every, the results of which can be superimposed over an intensity image created with pixels." +" The mass of the star-forming cores can be calculated by assuming: where g is the gas-to-dust ratio. 5, is the lux.d the distance. αγ the absorption cocllicient at frequency. ος and. Dita) is the Planek function for frequceney vat a temperature of Lint."," The mass of the star-forming cores can be calculated by assuming: where $g$ is the gas-to-dust ratio, $S_{\rm \nu}$ is the flux,$d$ the distance, $\kappa_{\rm \nu}$ the absorption coefficient at frequency $\rm \nu$, and $B_{\rm \nu}(T_{\rm dust})$ is the Planck function for frequency $\rm \nu$ at a temperature of $T_{\rm dust}$." + Using a gas-to-dust ratio of 100:1. (Hildebrand: 1983).. and an absorption coelficient of 0.15 m? ke! estimated [rom Ossenkopf&Llenning(1994) based on a numberdensity of ng 107 . thick ice mantles and a formation timescale of 107 vears. mass estimates for the cores were caleulated (listed in table 2.. along with the other parameters derived [rom the observations).," Using a gas-to-dust ratio of 100:1 \citep{hildebrand}, , and an absorption coefficient of 0.15 $^{2}$ $^{-1}$ estimated from \citet{ossen} based on a numberdensity of $_{H}$ = $^{5}$ $^{-3}$, thick ice mantles and a formation timescale of $^{5}$ years, mass estimates for the cores were calculated (listed in table \ref{tab:param}, along with the other parameters derived from the observations)." + The mass of these objects are subject to uncertainties within the used. parameters. especially any errors. in measuring the distance to the core.," The mass of these objects are subject to uncertainties within the used parameters, especially any errors in measuring the distance to the core." + The gas-to-dust ratio. which mav be as [ow as 45:1 (AleCutcheonet also introduces an error that may be up to a factor of 2.," The gas-to-dust ratio, which may be as low as 45:1 \citep{mccutcheon} also introduces an error that may be up to a factor of 2." + he absorption coellicient at SbOf/mi still has not been determined. precisely. (Hildebrand:1983:Chinietal.2001).. although the value adopted. in this paper from Ossenkopf&lHlenning(1994) agrees with the values determined by Bianchietal.(2008) ancl Visseretal.(2002).," The absorption coefficient at $\mu$ m still has not been determined precisely \citep{hildebrand,chini}, although the value adopted in this paper from \citet{ossen} agrees with the values determined by \citet{bianchi} and \citet{visser}." +. The masses we determine in this paper are therefore the upper limits for the temperature of the cores., The masses we determine in this paper are therefore the upper limits for the temperature of the cores. + The CF relation can be used to obtain the plane of the sky average magnetic field strength., The CF relation can be used to obtain the plane of the sky average magnetic field strength. + This method is based on equipartition and the ability of the magnetic field to retain straight field lines under the inlluence of turbulence., This method is based on equipartition and the ability of the magnetic field to retain straight field lines under the influence of turbulence. +" The plane of the sky. average field strength can be calculated vla where p is the mean density (g em 7). a. the line of sight velocity dispersion (cm ). ae isthe dispersion in polarisation position angles (measured cast of north) and is coprected for measurement errors (65=o7luensured6,CEPOL ) where @ is in radians. and. f. is a correction factor found to be 20.5 (Lleitschetal.2001)."," The plane of the sky average field strength can be calculated via: where $\rho$ is the mean density (g $^{-3}$ ), $\sigma_{v_{\rm los}}$ the line of sight velocity dispersion (cm $^{-1}$ ), $\sigma_{\theta}$ isthe dispersion in polarisation position angles (measured east of north) and is corrected for measurement errors $\sigma^{2}_{\theta}= \sigma^{2}_{\rm measured} - +\sigma^{2}_{\rm error}$ ) where $\theta$ is in radians, and $f$ is a correction factor found to be $\sim$ 0.5 \citep{heitsch}." +". ]5rrors on the position angle of the vectors are calculated based on the polarimetry signal-to-noise: where d89 is the error in the position angle and s, is the signal-to-noise in the polarisation.", Errors on the position angle of the vectors are calculated based on the polarimetry signal-to-noise: where $d\theta$ is the error in the position angle and $s_{\rm p}$ is the signal-to-noise in the polarisation. + Pherefore in regions where the polarisation percentage is low (e.g. across the main core of DhR21(OLID). then σας~torr resulting in misleaclingly small dispersion. angles. and very strong magnetic fields.," Therefore in regions where the polarisation percentage is low (e.g. across the main core of DR21(OH)), then $\sigma_{meas} \sim \sigma_{err}$ resulting in misleadingly small dispersion angles, and very strong magnetic fields." + By only selecting the vectors which have a signal-to-noise (in polarisation) of z 3. this problem is avoided. therefore all of the magnetic field strength estimates in this paper are based on vectors selected in this way.," By only selecting the vectors which have a signal-to-noise (in polarisation) of $>$ 3, this problem is avoided, therefore all of the magnetic field strength estimates in this paper are based on vectors selected in this way." + Please note. however. as mentioned. earlier. the vectors shown in the figures are not selected in this way. as in terms of magnetic field morphology. polarisation nulls and low levels of polarisation are valid. detections.," Please note, however, as mentioned earlier, the vectors shown in the figures are not selected in this way, as in terms of magnetic field morphology, polarisation nulls and low levels of polarisation are valid detections." + The CF method should. be used. with caution when calculating the magnetic field streneth in the plane of the sky., The CF method should be used with caution when calculating the magnetic field strength in the plane of the sky. + The beanrsize of the ΙΟΝΤΕ means that the small-scale taneline of the magnetic field. Geld can occur within the beam. and so the measured. vectors only represent the net magnetic field. direction. leading to over-cstimates of the Ποια strength.," The beam-size of the JCMT means that the small-scale tangling of the magnetic field field can occur within the beam, and so the measured vectors only represent the net magnetic field direction, leading to over-estimates of the field strength." + Mocelling studies of this effect (Ποκοetal.2001) have lead to the introduction of a correction [actor f. which has been found to be ~ 0.5 (see eq. 5)).," Modelling studies of this effect \citep{heitsch} have lead to the introduction of a correction factor $f$, which has been found to be $\sim$ 0.5 (see eq. \ref{bfield}) )." + Also. any underlving magnetic field. morphology. (c.g. intrinsic. field curvature) has not been accounted for in calculating the dispersion in position angles of the polarimetry vectors (i.e. his technique assumes that the magnetic field is uniform).," Also, any underlying magnetic field morphology (e.g. intrinsic field curvature) has not been accounted for in calculating the dispersion in position angles of the polarimetry vectors (i.e. this technique assumes that the magnetic field is uniform)." + Uneertaintics in) our estimations of the magnetic icld strength arise from calculating the density of the cores. which incorporates the errors involved in calculating he mass. they therefore. represent. the upper limits. of he magnetic field strength.," Uncertainties in our estimations of the magnetic field strength arise from calculating the density of the cores, which incorporates the errors involved in calculating the mass, they therefore represent the upper limits of the magnetic field strength." + There are also errors in calculating the volume of the core which contribute as a spherical geometry has been assumed. for cach core (except where otherwise stated). although with no density racer information. we lack the ability to modal the threc-dimensional structure of the cores. therefore the upper limits statecl are solely for spherical geometry.," There are also errors in calculating the volume of the core which contribute as a spherical geometry has been assumed for each core (except where otherwise stated), although with no density tracer information, we lack the ability to modal the three-dimensional structure of the cores, therefore the upper limits stated are solely for spherical geometry." + The velocity of the eas within the core introduces another error as a F\WLAL of ~2kmss 5 has been used but it may be anvwhiere between lknmss and 3 (Brandctal.2001:Thompsonet 2004).," The velocity of the gas within the core introduces another error as a FWHM of $\sim$ 2 $^{-1}$ has been used but it may be anywhere between 1 $^{-1}$ and 3 $^{-1}$ \citep{brand,thompson}. ." +. Measurement. errors are also introcuced by the angle 8. although these are relatively small in comparison to the other errors stated.," Measurement errors are also introduced by the angle $\theta$ , although these are relatively small in comparison to the other errors stated." + Cepheus A is a well-known star forming region., Cepheus A is a well-known star forming region. + Located at a distance of ~730 pe (Blaauw.Hiltner&Johnson 1959).. it is the closest star-forming region in the sample.," Located at a distance of $\sim$730 pc \citep{blaauw}, , it is the closest star-forming region in the sample." + The region, The region +The 2010 Eruption was discovered by us (BGI and SD) as part of svstematic nightly monitoring aimed specilically at the discovery of the eruption.,The 2010 Eruption was discovered by us (BGH and SD) as part of systematic nightly monitoring aimed specifically at the discovery of the eruption. + llarris imaged U dco al 2010 Jan 23.4385 UT (JD 2455224.9385). saw the bright star in the center of the field. and quickly realized that U Sco was in eruption.," Harris imaged U Sco at 2010 Jan 28.4385 UT (JD 2455224.9385), saw the bright star in the center of the field, and quickly realized that U Sco was in eruption." + Her first act was to send the observation io the AAVSO. and then she telephoned Schaefer.," Her first act was to send the observation to the AAVSO, and then she telephoned Schaefer." + Schaefer could not get confirmation from ROTSE. so he took his 6-inch telescope out into the front varcl ancl made. direct visual confirmation that U Sco was bright in eruption.," Schaefer could not get confirmation from ROTSE, so he took his 6-inch telescope out into the front yard and made direct visual confirmation that U Sco was bright in eruption." + Independenüly. Dvorak discovered the eruption. notified the AAVSO. and started a (ime series on U Seo to cover the short {ime interval until dawn got too bright to continue.," Independently, Dvorak discovered the eruption, notified the AAVSO, and started a time series on U Sco to cover the short time interval until dawn got too bright to continue." + These initial observations are included in Table 1., These initial observations are included in Table 1. + Circumstances. pictures. ancl anecdotes on (he (wo independent discoveries are eiven in Simonsen MacRobert (2010).," Circumstances, pictures, and anecdotes on the two independent discoveries are given in Simonsen MacRobert (2010)." + In practice. our organization worked perfectly.," In practice, our organization worked perfectly." + The AAVSO automated alert svstem woke up MT and AP., The AAVSO automated alert system woke up MT and AP. + Within an hour of the discovery. the eruption had been confirmed and worldwide notifications were started.," Within an hour of the discovery, the eruption had been confirmed and worldwide notifications were started." + The first was to the LAU Cirenlars (Schaefer et al., The first was to the IAU Circulars (Schaefer et al. + 2010a)., 2010a). +" The sun had already risen in Chile. so we started wilh more western observatories as well as spacecraft,"," The sun had already risen in Chile, so we started with more western observatories as well as spacecraft." + Within two hours. BES. AP. and NT. had worked through all the long-prepared contact lists.," Within two hours, BES, AP, and MT had worked through all the long-prepared contact lists." + The response to (hese contacts (both by members of our existing collaboration as well as by independent observers) was excellent ancl fast., The response to these contacts (both by members of our existing collaboration as well as by independent observers) was excellent and fast. + The discovery of the 2010 eruption was a fulfillment of the prediction in Schaefer (2005) that U Sco would next erupt in the vear 341.0., The discovery of the 2010 eruption was a fulfillment of the prediction in Schaefer (2005) that U Sco would next erupt in the year $\pm$ 1.0. + The eruption in 2010.1 falls well within the one-sigma region of the prediction., The eruption in 2010.1 falls well within the one-sigma region of the prediction. + This adds good. confidence to the physical method of summine the total accreted material based on the D-band flux in the prior inter-eruption interval., This adds good confidence to the physical method of summing the total accreted material based on the B-band flux in the prior inter-eruption interval. + The folded light curve (see Figure 3) shows (he primary eclipse at phases 0.0. 1.0. and 2.0. (," The folded light curve (see Figure 3) shows the primary eclipse at phases 0.0, 1.0, and 2.0. (" +The magnitudes are double plotted so as to make (he eclipse at phase 1.0 easily visible.),The magnitudes are double plotted so as to make the eclipse at phase 1.0 easily visible.) + The out-ol-eclipse brightness varies substantially. aud (his makes for a ragged eclipse light curve because each point is [rom a different epoch eclipse with a different amount of flickering lieht added.," The out-of-eclipse brightness varies substantially, and this makes for a ragged eclipse light curve because each point is from a different epoch eclipse with a different amount of flickering light added." +" The scatter around (he middle of the eclipse is much smaller than (he out-of-eclipse scatter, which implies that the fIickering region is small and centrally locatec."," The scatter around the middle of the eclipse is much smaller than the out-of-eclipse scatter, which implies that the flickering region is small and centrally located." + No secondary eclipse is visible in the B and V bands., No secondary eclipse is visible in the B and V bands. + However. in the I-band. the secondary eclipse is visible with aumplitude roughly 0.3 mag.," However, in the I-band, the secondary eclipse is visible with amplitude roughly 0.3 mag." + This is readily. understood. as, This is readily understood as +singular. it cannot be diagonalized aud therefore x caunot be whitened.,"singular, it cannot be diagonalized and therefore $\chib$ cannot be whitened." + In anv case. if iu Eq. (21))," In any case, if in Eq. \ref{eq:Cei}) )" +" matrix Cy is substituted for Cy aud one sets then it is a trivial matter to decorrelate 7,5 aud LN,je by aneaus of Eqs. (26))-(27))", matrix $C_{\xb}$ is substituted for $\Cb_{\chib}$ and one sets then it is a trivial matter to decorrelate $\zh_k$ and $\zh_{N_{\dag} + k}$ by means of Eqs. \ref{eq:norm}) \ref{eq:step3}) ) + aud to compute the periodograin through Eq. (28))., and to compute the periodogram through Eq. \ref{eq:step1}) ). +" This result cau be casily exteud to the case where. because of measurement errors. each entry of a has its own variance ση, aud a weighted mica is subtracted from the data sequence Xj=UÜUjS2,uteiNu gie with yy= 1o."," This result can be easily extend to the case where, because of measurement errors, each entry of $\xb$ has its own variance $\sigma^2_{x_j}$ and a weighted mean is subtracted from the data sequence $\chi_j = x_j - \sum _l +\eta_j x_l / \sum_l \eta_l$ , with $\eta_l = 1/ +\sigma^2_{x_l}$ ." + Indeed. it is sufficient to substitute Cy as given by Eq. (29))," Indeed, it is sufficient to substitute $\Cb_{\chib}$ as given by Eq. \ref{eq:chib}) )" + with ο...σιJL.," with where $\sigmab^2=[\sigma^2_{x_0}, \sigma^2_{x_1}, \ldots, \sigma^2_{x_{N-1}}]^T$." + The rest of the procedure remains uuniodified., The rest of the procedure remains unmodified. + The second cxample consists of zeroaneun colored noise., The second example consists of zero-mean colored noise. + The improvement in the quality of the results obtainable with the approach presented in the previous section is visible in Fig. l.., The improvement in the quality of the results obtainable with the approach presented in the previous section is visible in Fig. \ref{fig:color}. + The top left panel shows a discrete sigual vj=0.5in(2xfj)|nj. f=0.121. siuulated ou a regular erid of 120 time instauts but with missing data iu the ranges [3170| aud [76115].," The top left panel shows a discrete signal $x_j += 0.5 \sin{(2 \pi f j)} + n_j$, $f=0.127$, simulated on a regular grid of $120$ time instants but with missing data in the ranges $[31~70]$ and $[76~115]$." + Uere. nis the realization of a discrete. zeroanean. colored Loise process Whose autocovariance function ix elven iu he top right panel.," Here, $\nb$ is the realization of a discrete, zero-mean, colored noise process whose autocovariance function is given in the top right panel." + From the bottom left paucl. it is evideut that periodogram of the original sequence a provides rather ambienous results concerning he presence of a sinusoidal component.," From the bottom left panel, it is evident that periodogram of the original sequence $\xb$ provides rather ambiguous results concerning the presence of a sinusoidal component." + Ou the other rand. such componeut is well visible in the bottom right ul that shows the periodogran of the sequence| y=CTL1/2X.," On the other hand, such component is well visible in the bottom right panel that shows the periodogram of the sequence $\yb = \Cb_{\nb}^{-1/2} \xb$." + The formalisua proposed here is also useful iu the context of luore theoretical questions (but with nuportaut practical inplications)., The formalism proposed here is also useful in the context of more theoretical questions (but with important practical implications). + For example. a point often overlooked in the astronomical literature is the relationship between the periodogram aud the least-squares fit of sine functions.," For example, a point often overlooked in the astronomical literature is the relationship between the periodogram and the least-squares fit of sine functions." + Often these two methods are believed to be equivalent., Often these two methods are believed to be equivalent. + Actually. this is true only when the sampling is regular and the frequencies of the sinusoids are given by theFourier oucs.," Actually, this is true only when the sampling is regular and the frequencies of the sinusoids are given by the ones." +" Indeed. if f;=1j aud fy,=hin. bh=O01...egN—I. then Eq. (13) "," Indeed, if $t_j = \tilde{t}_j$ and $f_k = k / N$, $k=0, 1, +\ldots, N-1$, then Eq. \ref{eq:model}) )" +can be written in the form with and @=[ag.03.....ayyblusu.byil’.," can be written in the form with and $\ab = [a_0, a_1, \ldots, a_{N-1}, b_0, b_1, \ldots, b_{N-1}]^T$." + The least-squares solution à of svete (32)) is eiven by where πο denotespscudo-inverse (Byorck1996)., The least-squares solution $\bar{\ab}$ of system \ref{eq:ls}) ) is given by where ${}^+$ ” denotes \citep{bjo96}. +. Iu the case of even suupling. wwhen Fy= aud Fr=Επ. it happens that Iu other words. coefficients [a4] and (bi). as given by the least-squares approach. cau be obtained through the DET of a. because. as shown by means of Eqs. (11)). (S8)8=F," In the case of even sampling, when $\Fmatcb_{\Rmatc} = \Fb_{\Rmatc}$ and $\Fmatcb_{\Imatc} = \Fb_{\Imatc}$, it happens that In other words, coefficients $\{ a_k \}$ and $\{ b_k \}$, as given by the least-squares approach, can be obtained through the DFT of $\xb$, because, as shown by means of Eqs. \ref{eq:orth}) ), $(\Fmatfb \Fmatfb^T)^+ \Fmatfb = \Fmatfb$." + In the case of uneven saupline. this identitv is not fulfilled.," In the case of uneven sampling, this identity is not fulfilled." + Αν kind of periodogram coniputed hrough Eq. (22)), Any kind of periodogram computed through Eq. \ref{eq:irr4}) ) + and the least-squares fit of sine functions has to be expected to eive different results., and the least-squares fit of sine functions has to be expected to give different results. + Moreover. as only uuder the two above-mentioned couditious do the sine fictions constitute au orthonormal basis. the least-squares fit of a single sine fiction per time does not iu general provide the same result as the sinultauecous ft of all the sinusoids as in Eq. (31)) (6.8.SCC1973.page 150)..," Moreover, as only under the two above-mentioned conditions do the sine functions constitute an orthonormal basis, the least-squares fit of a single sine function per time does not in general provide the same result as the simultaneous fit of all the sinusoids as in Eq. \ref{eq:lsfit}) ) \citep[e.g. see][page 450]{ham73}." + Iu particulu. if an uneveulv- signal is eiven by the contribution of two or mere sa.imsoids. the one-at-a-time fit of a sinele sine functiou provides biased results.," In particular, if an unevenly-sampled signal is given by the contribution of two or more sinusoids, the one-at-a-time fit of a single sine function provides biased results." +" This also holds for the poriodogrsun. which is equivalent to the least-squares fit of a single sinusoid with a specifice frequelcy. with the coustraint that the correspouding cocfiicicuts ""a7 and ""hb are uncorrelated (Scarele1982:Zeclun"," This also holds for the periodogram, which is equivalent to the least-squares fit of a single sinusoid with a specified frequency, with the constraint that the corresponding coefficients $a$ ” and $b$ ” are uncorrelated \citep{sca82, zec09}." +cisterI&ürster 2009)... As cemoustrated in Sec. 3," As demonstrated in Sec. \ref{sec:generalization}," +. when noise has arbitrary statistical characteristics. the commutation of the periodogrami of an unevenulbv-saupled signal requires two steps: The first step. unavoidable even in the case of regular saluplue. is a computationally expensive operation.," when noise has arbitrary statistical characteristics, the computation of the periodogram of an unevenly-sampled signal requires two steps: The first step, unavoidable even in the case of regular sampling, is a computationally expensive operation." +" Therefore. for tine series containing more than a few housand data points. dedicated algorithnis exploitiug he specific structure of C, ooften this matrix is of banded type} have to be developed for implementing Eq. (21 jn"," Therefore, for time series containing more than a few thousand data points, dedicated algorithms exploiting the specific structure of $\Cb_{\nb}$ often this matrix is of banded type) have to be developed for implementing Eq. \ref{eq:whitey}) )." + Tlowever. this problem is bevoud the aim of he present paper.," However, this problem is beyond the aim of the present paper." + The secoud step is much less time consuuing., The second step is much less time consuming. + Indeed. iu the caseof time series containing sole thousands of poiuts and when the periodogram has o be computed on a simular nuuber of frequencies. the direct inipleiieutation of Eqs. (22))-(28))," Indeed, in the caseof time series containing some thousands of points and when the periodogram has to be computed on a similar number of frequencies, the direct implementation of Eqs. \ref{eq:irr4})\ref{eq:step1}) )" + results ina few seconds of computation time onlv., results in a few seconds of computation time only. + Iu other words. iu uany practical situations. no dedicated aleoritlini is really," In other words, in many practical situations, no dedicated algorithm is really" +html The Balbus-Tawley instability is the most seenerallv applicable iiechanisni known to initiate turbulence aud outward augular momoeutun transport m accretion disks (Balbus Hawley 1991)., The Balbus-Hawley instability is the most generally applicable mechanism known to initiate turbulence and outward angular momentum transport in accretion disks (Balbus Hawley 1991). + This is a line. local iustabilitv that exists for rotating flows threaded by a weal magnetic field with dO?/dre«0. conditions. satisfied in disks (for earlier discussions see Velikhov 1959. Chandrasekhar 1961).," This is a linear, local instability that exists for rotating flows threaded by a weak magnetic field with ${\rm d} \Omega^2 / {\rm d} r < 0$, conditions satisfied in disks (for earlier discussions see Velikhov 1959, Chandrasekhar 1961)." + A vigorous erowth rate is obtained for a wide variety of initial magnetic Ποια coufiguratious (Balbus Tawleyv 1992: Oevilvie Pringle 1996: Terquem Papaloizou 1996). iuiplving that the instability is inescapable for ionized disks where the field is wellkcoupled to the gas.," A vigorous growth rate is obtained for a wide variety of initial magnetic field configurations (Balbus Hawley 1992; Ogilvie Pringle 1996; Terquem Papaloizou 1996), implying that the instability is inescapable for ionized disks where the field is well-coupled to the gas." + Extensive nuuerical simulations have explored the 1onlinear development of the iustabilitv within the local. shearing box approxination (for a review. sce e.c. Came 1998).," Extensive numerical simulations have explored the nonlinear development of the instability within the local, shearing box approximation (for a review, see e.g. Gammie 1998)." +" Such sunulatious lave couvincingly established hat the nonlinear development of the Balbus-Tawley instability leads to sustained turbulence aud significant aneular moment trausport. typically finding a Shakura-Sunvacy (1973) azm10? Cawley, Gamunie Balbus 1995. 1996: Stone cet al 1996: Braudenbure et al."," Such simulations have convincingly established that the nonlinear development of the Balbus-Hawley instability leads to sustained turbulence and significant angular momentum transport, typically finding a Shakura-Sunyaev (1973) $\alpha \approx 10^{-2}$ (Hawley, Gammie Balbus 1995, 1996; Stone et al 1996; Brandenburg et al." + 1995)., 1995). + There is some evidence for cvclic behavior that might have iuportaut nuplicatious for disk variability (Draudeuburg oet al., There is some evidence for cyclic behavior that might have important implications for disk variability (Brandenburg et al. + 1996)., 1996). + Equally müportaut has been the funal cliniuation of convection (Stone Balbus 1996). aud the rear-clinunation of nonlinear lyvcodvuamic turbulence (Balbus. Tlawley Stone 1996). as plausible rival nechanisias for angular momentum transport in accretion disks.," Equally important has been the final elimination of convection (Stone Balbus 1996), and the near-elimination of nonlinear hydrodynamic turbulence (Balbus, Hawley Stone 1996), as plausible rival mechanisms for angular momentum transport in accretion disks." + Progress has also been made in tryiug to understand row the rich. phenomenology of accretion disk variability can arise within a dynamo driven disk model (Armitage. Livio Pringle 1996: Game Moenou 1998). although uuch more remaius to be done in this area.," Progress has also been made in trying to understand how the rich phenomenology of accretion disk variability can arise within a dynamo driven disk model (Armitage, Livio Pringle 1996; Gammie Menou 1998), although much more remains to be done in this area." + There are many further questions that one may hope simulations will address. aud not all of them are amcuable to a local treatiment.," There are many further questions that one may hope simulations will address, and not all of them are amenable to a local treatment." + Most obvioush. is the angular mionentun transport in a disk locally determined?," Most obviously, is the angular momentum transport in a disk locally determined?" + What is the structure of the spatial and time variability of the disk fields. aud are they suitable for launchius a magnetically driven disk wind or jet?," What is the structure of the spatial and time variability of the disk fields, and are they suitable for launching a magnetically driven disk wind or jet?" +" Uusurprisinely. the elobal calculations needed to investigate these issues are extremely demanding. both as a consequence of the larecr conrutational domain aud. especially, because of the ueed to simulate regions of low density where the high Alfvéun speed severely hits the timestep of explicit umuerical codes."," Unsurprisingly, the global calculations needed to investigate these issues are extremely demanding, both as a consequence of the larger computational domain and, especially, because of the need to simulate regions of low density where the high Alfvénn speed severely limits the timestep of explicit numerical codes." + Tn this paper. results are presented from a vertically uustratified global simulation of accretion disk turbulence.," In this paper, results are presented from a vertically unstratified global simulation of accretion disk turbulence." + Such a calculation is evideutly missing esseutial plivsics., Such a calculation is evidently missing essential physics. + There is no buovancy. no possibility of Parker instability (Parker 1979). and no magnetically dominated disk corona all features that are expected to arise iu a full disk model and which may be crucial for the disk dynamo problem (Tout Pringle 1992).," There is no buoyancy, no possibility of Parker instability (Parker 1979), and no magnetically dominated disk corona – all features that are expected to arise in a full disk model and which may be crucial for the disk dynamo problem (Tout Pringle 1992)." + ITowever the lesser computational demands pernut a preliminary investigation of some of the inportant questions raised by previous. local. simulations.," However the lesser computational demands permit a preliminary investigation of some of the important questions raised by previous, local, simulations." + The equations of ideal maguetolhydrodvuamics (MIID) are solved. uxiug the ZEUS-3D code developed by the Laboratory for Computational Astrophysics (Clarke. Norman Fiedler 1991: Stone Norman 1992a. 1992h).," The equations of ideal magnetohydrodynamics (MHD) are solved using the ZEUS-3D code developed by the Laboratory for Computational Astrophysics (Clarke, Norman Fiedler 1994; Stone Norman 1992a, 1992b)." + ZEUS is a time explicit culerian finite difference code that uses the method of characteristics (MoC') constrained transport scheme to evolve the magnetic fields (Lawley Stone 1995: Stone Norman L992)., ZEUS is a time explicit eulerian finite difference code that uses the method of characteristics (MoC) – constrained transport scheme to evolve the magnetic fields (Hawley Stone 1995; Stone Norman 1992b). + For this simulation an isothermal equation of state Po=pe? replaces the internal energv equation. so the remaining equations are:," For this simulation an isothermal equation of state $P = \rho c_s^2$ replaces the internal energy equation, so the remaining equations are:" +"including the models with lower T, and lower logg that seem to be preferred by the photometry¢¢ (right panel of Figure 4)).",including the models with lower $T_{eff}$ and lower $\log{g}$ that seem to be preferred by the photometry (right panel of Figure \ref{fig-4}) ). +" Since we have already ruled out a DA WD companion of similar temperature, we expect the shape of the higher order Balmer lines to be a reliable probe of the mass of12574-5428,, even if the underlying continuum is somewhat distorted."," Since we have already ruled out a DA WD companion of similar temperature, we expect the shape of the higher order Balmer lines to be a reliable probe of the mass of, even if the underlying continuum is somewhat distorted." +" 'The spectral models shown in Figure 7 translate into masses between 0.60 and 1.20Mo, which we will adopt as conservative lower and upper limits to My."," The spectral models shown in Figure \ref{fig-7} translate into masses between $0.60$ and $1.20\,\mathrm{M_{\odot}}$, which we will adopt as conservative lower and upper limits to $M_{A}$." +" It is unfortunate that the poor performance of the spectral models in this temperature range does not allow for a more accurate measurement of MA, but we believe that our estimate is reasonable, and probably the best that can be done with current tools."," It is unfortunate that the poor performance of the spectral models in this temperature range does not allow for a more accurate measurement of $M_{A}$, but we believe that our estimate is reasonable, and probably the best that can be done with current tools." +" We note that the models we contemplate here span a range of logg values around the best-fit solution that is comfortably larger than the reported increase (30.5)for T,;;«12000 K (~0.2,Kepleretal.2007;Bergeron 2007).."," We note that the models we contemplate here span a range of $\log{g}$ values around the best-fit solution $\pm 0.5$ ) that is comfortably larger than the reported increase for $T_{eff}<12000$ K \citep[$\sim +0.2$,][]{kepler07:WD_mass_distribution,bergeron07:mass_distribution_WDS}." +" Also, ourlower limit to MA is close to the mean mass of DA WDs with Tepe212000 K (0.58Mo,2007), which would be the best guess for the mass of a WD in absence of any spectral or photometric information."," Also, ourlower limit to $M_{A}$ is close to the mean mass of DA WDs with $T_{eff} \geq 12000$ K \citep[$0.58\,\mathrm{M_{\odot}}$, which would be the best guess for the mass of a WD in absence of any spectral or photometric information." +" For all these reasons, we are confident that the true mass of llies within the range of values that we propose here."," For all these reasons, we are confident that the true mass of lies within the range of values that we propose here." +" For comparison purposes, the best-fit hot spectral model (Tegg=35000 K, logg= translates into a value of 0.45Mefor My."," For comparison purposes, the best-fit hot spectral model $T_{eff}=35000$ K, $\log{g}=7.5$ ) translates into a value of $0.45\,\mathrm{M_{\odot}}$for $M_{A}$." +" With the set 7.5)of limiting spectral models around the best-fit cold solution shown in Figure 4,, the Holberg&Bergeron curves yield a cooling age of 2.0+1.0 Gyr."," With the set of limiting spectral models around the best-fit cold solution shown in Figure \ref{fig-4}, the \citeauthor{holberg06:WD_models_photometry} curves yield a cooling age of $2.0\pm1.0$ Gyr." +" The absolute g magnitude is 19.4104, which results in a distance of D=48719 pc for1257+5428.."," The absolute $g$ magnitude is $13.4^{+1.1}_{-0.4}$, which results in a distance of $D=48^{+10}_{-19}$ pc for." +" Combining our estimate for the mass of ((Ma=0.924035 Mo) with the values of P (4.5550+0.0007 hr) and X4 (322.74-6.3km s) derived in Section 3.2, we obtain Mpsin(i)=1.62*029Mo for its unseen companion, with Mg and the inclination angle { being degenerate as in all single-lined binaries."," Combining our estimate for the mass of $M_{A}=0.92^{+0.28}_{-0.32}\,\mathrm{M_{\odot}}$ ) with the values of $P$ $4.5550 \pm 0.0007$ hr) and $K_{A}$ $322.7 \pm 6.3\,\mathrm{km\,s^{-1}}$ ) derived in Section \ref{subsec:orbit}, , we obtain $M_{B}\sin(i)=1.62^{+0.20}_{-0.25}\,\mathrm{M_{\odot}}$ for its unseen companion, with $M_{B}$ and the inclination angle $i$ being degenerate as in all single-lined binaries." + A plot of the companion mass as a function of cos(i) is shown in Figure 8.., A plot of the companion mass as a function of $\cos(i)$ is shown in Figure \ref{fig-8}. +" We stress that the properties of the RV curve alone require a massive companion, regardless of the estimated value for M4: Mg must be more massive than 0.66Mo even for M4=0 (ie, assuming the value of MA is negligible for the dynamics of the system), and more massive than 1.08M, for M4=0.3Mo."," We stress that the properties of the RV curve alone require a massive companion, regardless of the estimated value for $M_{A}$: $M_{B}$ must be more massive than $0.66 \, +\mathrm{M_{\odot}}$ even for $M_{A}=0$ (i.e., assuming the value of $M_{A}$ is negligible for the dynamics of the system), and more massive than $1.08 \, \mathrm{M_{\odot}}$ for $M_{A}=0.3 \, \mathrm{M_{\odot}}$." +" With any reasonable range of masses for the primary, a nondegenerate stellar companion would have a spectral type G or earlier, which is clearly incompatible with the observations of1257+5428."," With any reasonable range of masses for the primary, a nondegenerate stellar companion would have a spectral type G or earlier, which is clearly incompatible with the observations of." +". The companion must therefore be a compact object, either another WD, a NS or a BH."," The companion must therefore be a compact object, either another WD, a NS or a BH." + Could the companion be a WD?, Could the companion be a WD? +" We have not been able to discard this possibility from the point of view of the optical spectrum alone, but the properties of the RV curve make it very unlikely."," We have not been able to discard this possibility from the point of view of the optical spectrum alone, but the properties of the RV curve make it very unlikely." +" The companion could only be a WD if our mass estimate for M4 was completely off, and even then, it would have to be a very massive object 1.0Μς for any reasonable value of MA), cool object, (abovewithout any prominent absorption lines (see discussion in Section 3.3.0))."," The companion could only be a WD if our mass estimate for $M_{A}$ was completely off, and even then, it would have to be a very massive object (above $1.0 \, +\mathrm{M_{\odot}}$ for any reasonable value of $M_{A}$ ), cool object, without any prominent absorption lines (see discussion in Section \ref{subsubsec:poorfits}) )." + Such massive WDs are extremely rare., Such massive WDs are extremely rare. +" But we have found no evidence to indicate that the shape of the Balmer lines in the spectrum of iis distorted in any way, so there is no reason to doubt our conservative estimate for M4."," But we have found no evidence to indicate that the shape of the Balmer lines in the spectrum of is distorted in any way, so there is no reason to doubt our conservative estimate for $M_{A}$." +" If this estimate holds, assuming the smallest possible value of M4 (0.6 Mo), the orbit would have to be nearly edge-on (i> 82°) for Mg to be below the Chandrasekhar limit Mg."," If this estimate holds, assuming the smallest possible value of $M_{A}$ $0.6\,\mathrm{M_{\odot}}$ ), the orbit would have to be nearly edge-on $i \geq 82^\circ$ ) for $M_{B}$ to be below the Chandrasekhar limit $M_{Ch}$ ." +" This inclination is expected to happen randomly in only 1496of binary systems, but ddoes have a strong observational bias towards finding high inclination systems."," This inclination is expected to happen randomly in only $14\%$of binary systems, but does have a strong observational bias towards finding high inclination systems." +" Even then, the companion would be more massive than the largest known WDs(1.33to Mo, 1995)."," Even then, the companion would be more massive than the largest known WDs\citep[$1.33$ to $1.35\,\mathrm{M_{\odot}}$ , ." +" In this unlikely circumstance, the"," In this unlikely circumstance, the" +confined iu size aud uever reach the overlap phase that defines the epoch of reiouization.,confined in size and never reach the overlap phase that defines the epoch of reionization. + The simulation data shown in this paper is the higher resolution ruu in ROSO2b. evolved further to redshift z=8.0 after the introduction of a bright source of ionizing radiation tliat completes relouization al z9 (see RGOS lor details).," The simulation data shown in this paper is the higher resolution run in RGS02b, evolved further to redshift $z=8.0$ after the introduction of a bright source of ionizing radiation that completes reionization at $z \sim 9$ (see RG05 for details)." + The ueed for introduciug a bright ionizatiou source is dictated by the simall volume of the simulation (1.5° MNpc*): otherwise the volume would be reionized too late., The need for introducing a bright ionization source is dictated by the small volume of the simulation $1.5^3$ $^3$ ); otherwise the volume would be reionized too late. + The ionizing source removes all the remaining gas from halos with ve<20 kimi and shuts down star formation., The ionizing source removes all the remaining gas from halos with $v_c<20$ km $^{-1}$ and shuts down star formation. + Here we compare the RC» predictions for tlie fossils of primordial galaxies to the observed properties (see Table 1)) of the new Milky Way aud M31 dwarls., Here we compare the RG05 predictions for the fossils of primordial galaxies to the observed properties (see Table \ref{tab:one}) ) of the new Milky Way and M31 dwarfs. + The symbols aud lines in Figs. 1-, The symbols and lines in Figs. \ref{Kor}- +-6 have the following meanings., \ref{ZS} have the following meanings. + All known Milky Way dSphs are shown by circles: Ancromecda’s dSplis satellites are shown by triangles: simulated fossils are shown by the small solid squares., All known Milky Way dSphs are shown by circles; Andromeda's dSphs satellites are shown by triangles; simulated fossils are shown by the small solid squares. + The solic auc open symbols refer to previously kuowu aud new cdSplis. respectively.," The solid and open symbols refer to previously known and new dSphs, respectively." + The trausition betwee fossils and non-fossil galaxies is gradual., The transition between fossils and non-fossil galaxies is gradual. +" La order to illustrate the different. statistical treuds of ""non-[fossil galaxies we show dwarf irregulars (dlrrs) with asterisks aud the dwarf ellipticals (dE as Crosses. and we show the statistical trends for more luminous galaxies as thick dashedlines oi the right side of each panel."," In order to illustrate the different statistical trends of “non-fossil” galaxies we show dwarf irregulars (dIrrs) with asterisks and the dwarf ellipticals (dE) as crosses, and we show the statistical trends for more luminous galaxies as thick dashedlines on the right side of each panel." + Figure 1 shows how the surface brightuess (top panel) and half light radius (bottom pauel) of all known Milky Way and Audromeca satellites as a function of V-baud luminosity compares to the simulated fossils., Figure \ref{Kor} shows how the surface brightness (top panel) and half light radius (bottom panel) of all known Milky Way and Andromeda satellites as a function of V-band luminosity compares to the simulated fossils. + The surface brightness limit of the SDSS is shown by the thin solid lines in botl pauels of the figure., The surface brightness limit of the SDSS is shown by the thin solid lines in both panels of the figure. + The new dwarfs agree with the predictious up to this tlireshold. suggesting the possible existence of an uudetected population of dwarls with X4: below the SDSS seusitivity limit.," The new dwarfs agree with the predictions up to this threshold, suggesting the possible existence of an undetected population of dwarfs with $\Sigma_{V}$ below the SDSS sensitivity limit." + The new M31 satellites have properties similar to their previously known Milky Way counterparts(e.g... Ursa Minor aud Draco).," The new M31 satellites have properties similar to their previously known Milky Way counterparts, Ursa Minor and Draco)." + Given the similar lost masses anc environments. is reasonable to assume a similar [formation history [or the halos of M31 aud the Milky Way.," Given the similar host masses and environments, is reasonable to assume a similar formation history for the halos of M31 and the Milky Way." + This suggestsMOD the existence of au undiscovered population dwarls orbiting M31 equivalent to the new SDSS clwarts., This suggests the existence of an undiscovered population dwarfs orbiting M31 equivalent to the new SDSS dwarfs. + The large mass outflows due to photo-heatiug by massive stars and the consequeut suppression oL star formation after an initial burst. make reiouization [ossils among the most dark matter dominated objects in the universe. with predicted M/L ratios as high as 10! and Ly~10*—10! L.. .," The large mass outflows due to photo-heating by massive stars and the consequent suppression of star formation after an initial burst, make reionization fossils among the most dark matter dominated objects in the universe, with predicted M/L ratios as high as $10^4$ and $L_V \sim +10^3-10^4$ $_{\odot}$ ." +distributions as described in Minton&Malhotra(2009)...,distributions as described in \cite{Minton:2009p280}. + This is likely due to the effects of (he sweeping r4; inclination-longitude of ascending node secular resonance. analogous to the sweeping 5j eccentricitv-pericenter secular resonance (hat we analvzed in the present studs;," This is likely due to the effects of the sweeping $\nu_{16}$ inclination-longitude of ascending node secular resonance, analogous to the sweeping $\nu_6$ eccentricity-pericenter secular resonance that we analyzed in the present study." + While the ellects of the sweeping i44 resonance are analogous to the 14. only affecting inclinations instead of eccentricities. a [ull analvsis of the asteroid belt inclinations is bevond the scope of the present work. but will be explored in a future study.," While the effects of the sweeping $\nu_{16}$ resonance are analogous to the $\nu_6$, only affecting inclinations instead of eccentricities, a full analysis of the asteroid belt inclinations is beyond the scope of the present work, but will be explored in a future study." + A number of other studies have derived limits on the speed of planetesimal-driven giant planet migration., A number of other studies have derived limits on the speed of planetesimal-driven giant planet migration. + Murrav-Clay&Chiang(2005) exclude an e—[olding migration timescale TXl]Mv to 99.65% confidence based on the lack of a large observed. asvimetry in the population of Nuiper belt objects in the two libration centers of the 2:1 Neptune mean motion resonance., \cite{MurrayClay:2005p209} exclude an $e-$ folding migration timescale $\tau\leq 1\My$ to $99.65\%$ confidence based on the lack of a large observed asymmetry in the population of Kuiper belt objects in the two libration centers of the 2:1 Neptune mean motion resonance. + Ποιόοἱal.(2009). exclude 70.15AUMy+ we derive based on the existence of the inner asteroid belt., The latter lower limit on the migration timescale is slightly incompatible with the lower limit on the rate of Saturn's migration of $\dot{a}_6>0.15\AU\My^{-1}$ we derive based on the existence of the inner asteroid belt. + One way these can be reconciled is if Saturns orbital eccentricity were a factor 2 smaller than its present value as it migrated from 8.5 AU to 9.2 AU: then. some mechanism would need to have increased Saturn's eccentricity up to its present value bv the time Saturn reached its present semimajor axis of ~9.6AU.," One way these can be reconciled is if Saturn's orbital eccentricity were a factor $\sim2$ smaller than its present value as it migrated from 8.5 AU to 9.2 AU; then, some mechanism would need to have increased Saturn's eccentricity up to its present value by the time Saturn reached its present semimajor axis of $\sim9.6\AU$." + The authors would like to thank the anonymous reviewer and (he editor Eric Feigelson for useful comments., The authors would like to thank the anonymous reviewer and the editor Eric Feigelson for useful comments. + This research was supported in part bv NSF grant no., This research was supported in part by NSF grant no. + AST-0806828 and NASA:NESSF grant no., AST-0806828 and NASA:NESSF grant no. + NNNOSAW?25II. The work of David Minton was additionally partially supported by NASA NLSI/CLOE research grant no., NNX08AW25H. The work of David Minton was additionally partially supported by NASA NLSI/CLOE research grant no. + NNAO9DD32AÀ The binned eccentricity distribution max be modeled as a Gaussian probability distribution function. given bv: where σ is the standard deviation. fois (he mean. and is the random variable: in our case vis the eccentricity.," NNA09DB32A The binned eccentricity distribution may be modeled as a Gaussian probability distribution function, given by: where $\sigma$ is the standard deviation, $\mu$ is the mean, and $x$ is the random variable; in our case $x$ is the eccentricity." + With an appropriate scaling factor. equation (AL)) can be used to model the number of asteroids per eccentricity bin.," With an appropriate scaling factor, equation \ref{e:gaussian}) ) can be used to model the number of asteroids per eccentricity bin." + However. rather than fit the binned distribution. we instead. perform a least squares fit of the unbinned sample to the Gaussian cumulative distribution function given bv:," However, rather than fit the binned distribution, we instead perform a least squares fit of the unbinned sample to the Gaussian cumulative distribution function given by:" +1998b).,. + Moreover. the frequency separation in the Atoll source 11636-536 seems not to (e consistent with the half of the frequency of the QPO in type L bursts (Méndez&vanParadijs.1998)..," Moreover, the frequency separation in the Atoll source 1636-536 seems not to be consistent with the half of the frequency of the QPO in type I bursts \cite{Mendez98c}." +-- Though he beat-frequeney. models are the most hopeful in explaining the QDPO-phenomenology it has to be awaited row the variation of the frequency separation and deviation rom the QPO frequency in bursts can be incorporated. to hese mocdels., Though the beat-frequency models are the most hopeful candidates in explaining the QPO-phenomenology it has to be awaited how the variation of the frequency separation and deviation from the QPO frequency in bursts can be incorporated to these models. + One of us (Ch., One of us (Ch. + 5$.) gratefully acknowledges the Bavarian State for financial support., S.) gratefully acknowledges the Bavarian State for financial support. + We would like to thank Norman CGlendenning and Jürrgen Schalfner-Bielich for providing us tables of their EOSs., We would like to thank Norman Glendenning and Jürrgen Schaffner-Bielich for providing us tables of their EOSs. +Mukherjee luminosity function.,Mukherjee luminosity function. + The integrated fluxes of each blazar for Fo>1 GeV and E-10 GeV were used to eenerale observed fluxes using Poisson distributions equivalent to (wo full vears of exposure., The integrated fluxes of each blazar for $E>1$ GeV and $E>10$ GeV were used to generate observed fluxes using Poisson distributions equivalent to two full years of exposure. + For each blazar. we caleulated the ratio between these fluxes.," For each blazar, we calculated the ratio between these fluxes." +" The error in each flux ratio Was""us sesel dO Dpatiomu=FUETI1GeV]OppLOσον]2|(ολο.FUEπαTDITrees.ο). where oy is the statistical error of the flix measurement in each energv range."," The error in each flux ratio was set to $\sigma_{ratio}=\frac{1}{F(E\,>\,1\,\rm~GeV)}\sqrt{{\sigma_{F(E\,>\,10\,\rm~GeV)}}^{2}+(\frac{F(E\,>\,10\,\rm~GeV)}{F(E\,>\,1\,\rm~GeV)}\sigma_{F(E\,>\,1\,\rm~GeV)})^{2}}$, where $\sigma_{F}$ is the statistical error of the flux measurement in each energy range." + The crosses in Figure 2 show the weighted mean ratio in each recdshilt bin., The crosses in Figure \ref{fig2} show the weighted mean ratio in each redshift bin. + To avoid the bias of small number Poisson statistics toward lower values. the flix ratio of each source was weighted by Cie Poisson error of the E>1 GeV flux. rather than the formal. propagated error of the fIux ratio.," To avoid the bias of small number Poisson statistics toward lower values, the flux ratio of each source was weighted by the Poisson error of the $E>1$ GeV flux, rather than the formal, propagated error of the flux ratio." + The diamonds show the same ratio when the intergalactic absorption is removed [rom the observed blazar [Iuxes., The diamonds show the same ratio when the intergalactic absorption is removed from the observed blazar fluxes. + In all cases the error bars are statistical. obtained by computing the rms scatter within each redshift bin and dividing by VN.," In all cases the error bars are statistical, obtained by computing the rms scatter within each redshift bin and dividing by $\sqrt{N}$." + The analvticallvy derived flux ratio using (he opacity model of Salamon Stecker is plotted as a solid curve., The analytically derived flux ratio using the opacity model of Salamon Stecker is plotted as a solid curve. + For comparison. the dashed lines in Figure 2. show the same results with no intergalactic absorption.," For comparison, the dashed lines in Figure \ref{fig2} show the same results with no intergalactic absorption." + We repeated (he entire analvsis with the blazar spectra changed from single power laws with mean index -2.15 to broken power laws with mean index -2.15 below 50 GeV (at the source) and -3.15 above., We repeated the entire analysis with the blazar spectra changed from single power laws with mean index -2.15 to broken power laws with mean index -2.15 below 50 GeV (at the source) and -3.15 above. + The results are plotted as crosses in Figure 4., The results are plotted as crosses in Figure \ref{fig3}. + Although fewer blazars have detected [ας above 10 GeV. the effects of absorption are still apparent.," Although fewer blazars have detected flux above 10 GeV, the effects of absorption are still apparent." + Note that sources wilh no detectable flux above 10 GeV (zero photons) still provide important information: indeed. neglecting them introduces a bias.," Note that sources with no detectable flux above 10 GeV (zero photons) still provide important information; indeed, neglecting them introduces a bias." + The modified 47 statistic used here (Mighell 1999) accounts for these sources., The modified $\chi^{2}$ statistic used here (Mighell 1999) accounts for these sources. + The ratio obtained without EBL absorption is presented as diamonds. along with the analytically derived. {lux ratio (dashed line).," The ratio obtained without EBL absorption is presented as diamonds, along with the analytically derived flux ratio (dashed line)." + As can be easily seen. this flux ratio is nol constant as a [unction of redshift.," As can be easily seen, this flux ratio is not constant as a function of redshift." + This is a consequence of defining the break in the index for a given energv at the source., This is a consequence of defining the break in the index for a given energy at the source. + Primack and collaborators combined. theoretical modeling with observational data to develop semi-analvtic models of galaxy. formation aud evolution (Primack et al., Primack and collaborators combined theoretical modeling with observational data to develop semi-analytic models of galaxy formation and evolution (Primack et al. + 1999)., 1999). + Their, Their +"We have performed a survey of the most massive galaxies present at z>3, over an area of 0.6 deg? of the UKIDSS UDS field.","We have performed a survey of the most massive galaxies present at $z \geq 3$, over an area of 0.6 $^2$ of the UKIDSS UDS field." +" To have the best possible proxy for a stellar mass complete sample, we made our selection in the Spitzer/IRAC band, which maps rest-frame near-IR wavelengths at these high redshifts."," To have the best possible proxy for a stellar mass complete sample, we made our selection in the /IRAC band, which maps rest-frame near-IR wavelengths at these high redshifts." +" We followed up our master 4.5mcatalogue of 50,321 sources in 10 broad bands, from the U-band through the IRAC 3.6 um channel."," We followed up our master catalogue of 50,321 sources in 10 broad bands, from the $U$ -band through the IRAC 3.6 $\rm \mu m$ channel." +" The multi-wavelength follow up has allowed us to model the SEDs of all our galaxies and, with this, obtain redshift estimates and derive stellar masses."," The multi-wavelength follow up has allowed us to model the SEDs of all our galaxies and, with this, obtain redshift estimates and derive stellar masses." + Our final sample consists of 1292 galaxies at redshifts 3.0 5., We have found the following: Another key result of our work is the absence of massive galaxies at redshifts $z>5$ . +" Within our surveyed area of 0.6 deg?, we find only two quite secure candidates at such high redshifts, and only one with stellar mass M>10! "," Within our surveyed area of 0.6 $^2$, we find only two quite secure candidates at such high redshifts, and only one with stellar mass $M>10^{11} \, \rm M_\odot$." +"Instead, optical surveys have discovered a substantial Mo.number of intermediate stellar-mass sources at these redshifts."," Instead, optical surveys have discovered a substantial number of intermediate stellar-mass sources at these redshifts." +" These findings strongly suggest that massive galaxies as a significant population only appear at later times, and that the epoch around redshifts z~3—6 is critical to understand the formation of the first massive Systems."," These findings strongly suggest that massive galaxies as a significant population only appear at later times, and that the epoch around redshifts $z\sim3-6$ is critical to understand the formation of the first massive systems." +" In addition, we have found that a significant fraction of the most massive galaxies present at 3€z«4 would be missed by optical surveys, even asdeep as R«27 or"," In addition, we have found that a significant fraction of the most massive galaxies present at $3\leq z<4$ would be missed by optical surveys, even asdeep as $R<27$ or" +Postage stamps images in the four bands are shown for one of the 142 fLSB candidates with photo-z<0.2 in Fig.,Postage stamps images in the four bands are shown for one of the 142 fLSB candidates with $-z<0.2$ in Fig. + ΑΙ (galaxy #1128 in Table A3))., \ref{fig:post} (galaxy 128 in Table \ref{tab:liste3}) ). + The corresponding surface brightness profile is given in Fig. A2.., The corresponding surface brightness profile is given in Fig. \ref{fig:prof}. + Based on the large spectroscopic and photometric catalogues aequired for Abell 496 (Boué et al., Based on the large spectroscopic and photometric catalogues acquired for Abell 496 (Boué et al. + 2008). we have estimated the spectral type of each galaxy with the Le Phare photometric redshift software.," 2008), we have estimated the spectral type of each galaxy with the Le Phare photometric redshift software." + Galaxies are then assigned a spectral type: type | for ellipticals. type 2 for early type spirals. type 3 for intermediate type spirals and type 4 for late type spirals.," Galaxies are then assigned a spectral type: type 1 for ellipticals, type 2 for early type spirals, type 3 for intermediate type spirals and type 4 for late type spirals." + In order to search for substructures. we applied the Serna Gerbal (1996) software to galaxies with measured spectroscopic redshifts and magnitudes.," In order to search for substructures, we applied the Serna Gerbal (1996) software to galaxies with measured spectroscopic redshifts and magnitudes." + This hierarchical method allows to extract galaxy substructures or groups from a catalogue containing positions. magnitudes and redshifts. based on the calculation of their relative (negative) binding energies.," This hierarchical method allows to extract galaxy substructures or groups from a catalogue containing positions, magnitudes and redshifts, based on the calculation of their relative (negative) binding energies." + The method gives as output a list of galaxies belonging to each group. as well as the information on the binding energy of the group itself. and on the mass of each substructure. assuming a mass to luminosity ratio (M/L).," The method gives as output a list of galaxies belonging to each group, as well as the information on the binding energy of the group itself, and on the mass of each substructure, assuming a mass to luminosity ratio (M/L)." + We used herea M/L ratio in the 7 band of 200. as previously assumed for the Coma cluster by Adami et al. (," We used herea M/L ratio in the $r'$ band of 200, as previously assumed for the Coma cluster by Adami et al. (" +2005). based on the Coma cluster M/L ratio given by Lokas Mamon (2003).,"2005), based on the Coma cluster M/L ratio given by okas Mamon (2003)." + The Serna Gerbal analysis shows the existence of three substructures (also see Section 4)., The Serna Gerbal analysis shows the existence of three substructures (also see Section 4). + These all have low masses (smaller than a few 10 M..) and therefore their existence does not contradict the overall relaxed structure of the cluster., These all have low masses (smaller than a few $10^{12}$ $_\odot$ ) and therefore their existence does not contradict the overall relaxed structure of the cluster. + If we analyze the morphological type distribution of the galaxies belonging to these three substructures (also see Fig. 5)).," If we analyze the morphological type distribution of the galaxies belonging to these three substructures (also see Fig. \ref{fig:type}) )," + we find that only one galaxy is of type 4 (late type spiral). corresponding to ~1% of all the galaxies in substructures.," we find that only one galaxy is of type 4 (late type spiral), corresponding to $\sim$ of all the galaxies in substructures." + If we estimate the percentage of type + galaxies in the cluster (1.5. 1n the [0.0229.0.0429] redshift range) that are not included in substructures. we find a value of 23%..," If we estimate the percentage of type 4 galaxies in the cluster (i.e. in the [0.0229,0.0429] redshift range) that are not included in substructures, we find a value of ." + The difference between these two values could be, The difference between these two values could be +equilibrium points are also made linearly stable by continuous corrections of their halo rq}).,equilibrium points are also made linearly stable by continuous corrections of their halo ). + In other words the collinear equilibrium points are metastable points in (he sense (hat. like a ball sitting on top of a hill.," In other words the collinear equilibrium points are metastable points in the sense that, like a ball sitting on top of a hill." + However. in practice these Lagrange points have proven to be very useful indeed since à spacecralt can be made {ο execute a small orbit about one of these Lagrange points with a very small expenditure of energy[please see 1969)]].," However, in practice these Lagrange points have proven to be very useful indeed since a spacecraft can be made to execute a small orbit about one of these Lagrange points with a very small expenditure of energy[please see \citet{Farquhar1967JSpRo,Farquhar1969AsAer}] ]." + We considered ihe Chermuvkh’s problem which is a new kind of restricted (hree body problem. il was first Gime studied by Chermauvkh(1987).," We considered the Chermnykh's problem which is a new kind of restricted three body problem, it was first time studied by \citet{Chermnykh1987}." +. This problem generalizes two Classical problems of Celestial mvechanics: (he two fixed center problem and the restricted three body problem., This problem generalizes two classical problems of Celestial mechanics: the two fixed center problem and the restricted three body problem. + This gives wide perspectives for applications of the problem in celestial mechanics and astronomy., This gives wide perspectives for applications of the problem in celestial mechanics and astronomy. + The importance of (he problem in astronomy has been addressed bv JiangandYeh(2004a).., The importance of the problem in astronomy has been addressed by \citet{Jiang2004IJBC}. + Some planetary systems are claimed (ο have discs of dust and thev are regarded (to be young analogues of the Ixuiper Bell in our Solar System., Some planetary systems are claimed to have discs of dust and they are regarded to be young analogues of the Kuiper Belt in our Solar System. + If these disces are massive enough. thev should play important roles in the origin of orbital elements.," If these discs are massive enough, they should play important roles in the origin of orbital elements." + Since (he belt of planetesimal often exists within a planetary svstem and provides (he possible mechanism of orbital circularization. it is important to understand the solutions of dynamical svstems with the planet-belt interaction.," Since the belt of planetesimal often exists within a planetary system and provides the possible mechanism of orbital circularization, it is important to understand the solutions of dynamical systems with the planet-belt interaction." +The Chermnykhs problem has been studied bv many scientists such as JiangandYeh(2004b).. Papaclakis(2004)..Papacdakis (2005) and JiangaudYeh(2006):and(2006)..,"The Chermnykh's problem has been studied by many scientists such as \citet{JiangYeh2004AJ}, \citet{Papadakis2004A&A}, \citet{Papadakis2005Ap&SS299} and \citet{JiangYeh2006Ap&SSI,YehJiang2006Ap&SSII}." + The present paper investigates the nature of collinear equilibrium point Lo because of the interested point to locate an artificial satellite., The present paper investigates the nature of collinear equilibrium point $L_2$ because of the interested point to locate an artificial satellite. + Although there are (vo new equilibrium points due to mass of the belt(larger than 0.15) as obtained by. (200G).. but they are left to be examined.," Although there are two new equilibrium points due to mass of the belt(larger than 0.15) as obtained by \citet{JiangYeh2006Ap&SSI,YehJiang2006Ap&SSII}, but they are left to be examined." + All the results are computed numerically using same technique as in GrebennikovandIxozak-Skoworodkin(2007).. because pure analvtical nuethods are not suitable.," All the results are computed numerically using same technique as in \cite{Grebennikov2007CMMPh}, because pure analytical methods are not suitable." + For specific time intervals. and initial values. (ese results provide jew information on the behavior of trajectories around (he Lagrangian point Le.," For specific time intervals, and initial values, these results provide new information on the behavior of trajectories around the Lagrangian point $L_2$." + It is supposed that the motion of an infinitesimal mass particle is influenced. by the eravitational force from primaries aud a belt of mass M., It is supposed that the motion of an infinitesimal mass particle is influenced by the gravitational force from primaries and a belt of mass $M_b$. + The units of the mass and the distance are taken such that sum of (he masses ancl (he distance between primaries are unities., The units of the mass and the distance are taken such that sum of the masses and the distance between primaries are unities. + The unit of the time ie. the time period of mn about m2 consists of 2x units such that the, The unit of the time i.e. the time period of $m_1$ about $m_2$ consists of $2\pi$ units such that the +hereafter discard filaments whose lengths are shorter than the smoothing length as non-physical.,hereafter discard filaments whose lengths are shorter than the smoothing length as non-physical. +" The traditional picture of large-scale structure as a ‘cosmic web’ (7) suggests that filaments are connected, one-dimensional strands that end abruptly at their points of intersection."," The traditional picture of large-scale structure as a `cosmic web' \citep{CosmicWeb} suggests that filaments are connected, one-dimensional strands that end abruptly at their points of intersection." +" As one filament begins and another ends, the local axis of structure should change direction rapidly."," As one filament begins and another ends, the local axis of structure should change direction rapidly." + The C parameter denotes the maximum angular rate of change in the axis of structure along a filament., The $C$ parameter denotes the maximum angular rate of change in the axis of structure along a filament. +" If this threshold is exceeded, filament tracing is stopped."," If this threshold is exceeded, filament tracing is stopped." +" In order to test the sensitivity of the output filaments to the value of the C parameter, we set K=1 and generated filament networks in the N-body simulation with a range of C."," In order to test the sensitivity of the output filaments to the value of the $C$ parameter, we set $K=1$ and generated filament networks in the N-body simulation with a range of $C$." +" In all of these tests, increasing the value of C led to an increase in the average length of the filaments and a decrease in the total number of filaments found."," In all of these tests, increasing the value of $C$ led to an increase in the average length of the filaments and a decrease in the total number of filaments found." +" If the curvature criterion is not strict enough, a filament will be traced past its vertex and into another filament."," If the curvature criterion is not strict enough, a filament will be traced past its vertex and into another filament." + Since our algorithm only prevents filaments from starting within previously-identified filaments (they are allowed to cross one this can lead to double detections of filaments.," Since our algorithm only prevents filaments from starting within previously-identified filaments (they are allowed to cross one another), this can lead to double detections of filaments." +" We can another),obtain a rough count of these double detections by comparing filament elements to one another, where a filament element is definedas a single step (of interval, A) on the grid."," We can obtain a rough count of these double detections by comparing filament elements to one another, where a filament element is definedas a single step (of interval, $\Delta$ ) on the grid." +" In other words, for each step along a given filament, we find the closest filament element that is not a member of that same filament."," In other words, for each step along a given filament, we find the closest filament element that is not a member of that same filament." +" If the closest filament element is within a smoothing length and has an axis of structure within C, then the original element is labelled a ‘repeat detection.’"," If the closest filament element is within a smoothing length and has an axis of structure within $C$, then the original element is labelled a `repeat detection.'" + The total number of repeat detections in an output filament network is denoted by R., The total number of repeat detections in an output filament network is denoted by $R$. + The total length of the network at this scale is therefore given by where ΔΝ. is the total number of filament elements found and A is the step size taken by the filament finder., The total length of the network at this scale is therefore given by where $N_e$ is the total number of filament elements found and $\Delta$ is the step size taken by the filament finder. +" Non-filamentary regions of space have already been excluded by the criteria in Equation 1, so an optimum set of parameters will maximize Ly while minimizing R."," Non-filamentary regions of space have already been excluded by the criteria in Equation \ref{eq:CellRemove}, so an optimum set of parameters will maximize $L_f$ while minimizing $R$." +" In the left panel of Fig. 4,,"," In the left panel of Fig. \ref{fig:Crit1Tots}," +" we plot both the fraction of repeat detections (R/N., dashed lines) and the total length of the network (Ly, solid lines) as a function of C."," we plot both the fraction of repeat detections $R/N_e$, dashed lines) and the total length of the network $L_f$, solid lines) as a function of $C$." +" On all smoothing scales, the fraction of false positives rises steadily with increasing C, with no obvious breaks or minima."," On all smoothing scales, the fraction of false positives rises steadily with increasing $C$, with no obvious breaks or minima." +" The total length, however, tends to rise until it reaches a maximum, after which point it either flattens or falls slowly."," The total length, however, tends to rise until it reaches a maximum, after which point it either flattens or falls slowly." +" This suggests that, as long as the curvature criterion is above a critical value, the algorithm will trace out the entire filament network."," This suggests that, as long as the curvature criterion is above a critical value, the algorithm will trace out the entire filament network." +" Since the fraction of false positives rises with C, we will hereafter use a curvature criterion near this value; that is, C—50, 40, and 30? for |—15, 10, and 5Mpc,, respectively."," Since the fraction of false positives rises with $C$ , we will hereafter use a curvature criterion near this value; that is, $C=50$, $40$, and $30$ for $l=15$, $10$, and $5$, respectively." +" As each filament is found,we wish to remove from the grid as much of it as possible without preventing the detection of further real filaments."," As each filament is found,we wish to remove from the grid as much of it as possible without preventing the detection of further real filaments." +" Using the previously-determined critical values of C, we ran the filament-finder with a range of K and computed the total length of the filament network and the fraction of repeat detections as a function of K."," Using the previously-determined critical values of $C$, we ran the filament-finder with a range of $K$ and computed the total length of the filament network and the fraction of repeat detections as a function of $K$." + The results are shown in the right panel of Fig. 4.., The results are shown in the right panel of Fig. \ref{fig:Crit1Tots}. . +" All of the curves are monotonic, with repeat detections and the network length decreasing with increasing K."," All of the curves are monotonic, with repeat detections and the network length decreasing with increasing $K$." +" Hereafter, we will set K=1 because it yields R/N,€20 per cent."," Hereafter, we will set $K=1$ because it yields $R/N_e\lesssim 20$ per cent." +Chemical inhomogeneities in light elements (C. N. O. Ε. Na. Al. Mg. and even S1) are intrinsic to globular clusters (GCs: see Grattonetal.2004. for an extensive review and references).,"Chemical inhomogeneities in light elements (C, N, O, F, Na, Al, Mg, and even Si) are intrinsic to globular clusters (GCs; see \citealt{araa04} for an extensive review and references)." + In particular. the striking anticorrelation between Na and O abundances in GC red giant branch (RGB) stars discovered and studied by the Texas-Lick group (see Kraft190 for a review on those pioneering efforts) is the most notable signature observed with high resolution spectroscopy.," In particular, the striking anticorrelation between Na and O abundances in GC red giant branch (RGB) stars discovered and studied by the Texas-Lick group (see \citealt{kraft94} for a review on those pioneering efforts) is the most notable signature observed with high resolution spectroscopy." + The pivotal discovery of the Na-O (and the Mg-Al) anticorrelation in unevolved cluster stars (Grattonetal..2001) led to the unambiguous conclusion that stars of different generations co-exist in the currently observed GCs., The pivotal discovery of the Na-O (and the Mg-Al) anticorrelation in unevolved cluster stars \citep{gratton01} led to the unambiguous conclusion that stars of different generations co-exist in the currently observed GCs. + The reason is that the high temperatures required for proton-capture reactions (Denisenkov&Denisenkova.1989:Langeretal..1993) to produce matter depleted in O. Mg and enriched in Na. AI are never reached in the interior of low-mass stars (temperature in excess of 25 or 70x10? K are required for the NeNa and MgAI cycles. respectively).," The reason is that the high temperatures required for proton-capture reactions \citep{denden89,langer93} to produce matter depleted in O, Mg and enriched in Na, Al are never reached in the interior of low-mass stars (temperature in excess of 25 or $\times10^6$ K are required for the NeNa and MgAl cycles, respectively)." + As a consequence. the observations by Gratton et al.," As a consequence, the observations by Gratton et al." + (laterconfirmedbye.g..Cohenetal..2002;Car-rettaetal..2004:D'Orazi2010) require the existence of a previous stellar generation of more massive stars with higher internal temperatures sufficient to activate the necessary nucleosynthesis. providing the ejecta from which the second-generation stars formed.," \citep[later confirmed by +e.g.,][]{cohen02,carretta04,dorazi10} require the existence of a previous stellar generation of more massive stars with higher internal temperatures sufficient to activate the necessary nucleosynthesis, providing the ejecta from which the second-generation stars formed." + Dilution processes with pristine gas left in the cluster may then reproduce the whole length of the Na-O anticorrelation (see Pranztos&Charbonnel20061: see however Gratton&Carretta 2010))., Dilution processes with pristine gas left in the cluster may then reproduce the whole length of the Na-O anticorrelation (see \citealt{pc06}; see however \citealt{gra010}) ). + The Na-O anticorrelation is so widespread among GCs (seee.g..Carrettaetal..2009a.b) that this feature is probably associated to the very same mechanism of cluster formation (Carretta.2006) and may be considered the main criterion to discriminate between GCs (Carrettaetal..2010) and other type of clusters. regardless of their old ages or even large mass (e.g.NGC6791.Bragagliaetal..2010b.inprep.).," The Na-O anticorrelation is so widespread among GCs \citep[see e.g.,][]{carretta09a,carretta09b} + that this feature is probably associated to the very same mechanism of cluster formation \citep{carretta06} and may be considered the main criterion to discriminate between GCs \citep{carretta10} and other type of clusters, regardless of their old ages or even large mass \citep[e.g. NGC~6791,][in prep.]{bragaglia6791}." +. However. while the overall pattern of the chemical composition of first and second-generation GC. stars. is currently. well assessed. several issues are still left open. the principal being the nature of the actual polluters. either intermediate-mass Asymptotic Giant Branch stars (IM-AGBs.Venturaetal..2001) or fast-rotating massive stars (FRMSs.Decressinetal.. 2007).," However, while the overall pattern of the chemical composition of first and second-generation GC stars is currently well assessed, several issues are still left open, the principal being the nature of the actual polluters, either intermediate-mass Asymptotic Giant Branch stars \citep[IM-AGBs,][]{ventura01} or fast-rotating massive stars \citep[FRMSs,][]{decressin07}." +. One of the main questions concerns the possible link between chemical signature and dynamical evolution of different stellar generations in GCs., One of the main questions concerns the possible link between chemical signature and dynamical evolution of different stellar generations in GCs. + This issue is puzzling and still poorly explored in a systematic way by theoretical nodels., This issue is puzzling and still poorly explored in a systematic way by theoretical models. + Models where a cooling-flow feeds gas enriched in IM-AGB ejecta to form second generation stars (D'Ercoleetal.. 2008).. intrinsically predict that this generation should be nore centrally concentrated. since the gas is re-collected at the cluster centre.," Models where a cooling-flow feeds gas enriched in IM-AGB ejecta to form second generation stars \citep{dercole08}, intrinsically predict that this generation should be more centrally concentrated, since the gas is re-collected at the cluster centre." + On the other hand. also second-generation stars formed by matter polluted by FRMS are expected to be nore centrally concentrated.," On the other hand, also second-generation stars formed by matter polluted by FRMS are expected to be more centrally concentrated." + They should have the same radial distribution of their progenitors. that are assumed to be born hear the cluster centre. being very massive objects.," They should have the same radial distribution of their progenitors, that are assumed to be born near the cluster centre, being very massive objects." + Even if the second generation formed at the cluster centre. there is the action of the dynamical evolution over a Hubble time to be taken into account.," Even if the second generation formed at the cluster centre, there is the action of the dynamical evolution over a Hubble time to be taken into account." + For instance. Decressinetal.(2008) compute that the second-generation stars are progressively spread out by dynamical encounters.," For instance, \cite{decressin08} compute that the second-generation stars are progressively spread out by dynamical encounters." + As a result. the radial distributions of first and second-generation stars can no longer be distinguished from their dynamics alone at the present time.," As a result, the radial distributions of first and second-generation stars can no longer be distinguished from their dynamics alone at the present time." + In this Note we combine information from our ongomg FLAMES survey of chemical abundances in giants in GCs (seeCarretta.2006) with newly derived photometry for the GC (Kravtsovetal..2009.2010) and we provide new insights on the radial distribution of first and second-generation stars in this GC. whose relaxation time at half-mass radius is about 1.6 Gyr Harris(1996).," In this Note we combine information from our ongoing FLAMES survey of chemical abundances in giants in GCs \cite[see][]{carretta06} with newly derived photometry for the GC \citep{kravtsov09,kravtsov10} and we provide new insights on the radial distribution of first and second-generation stars in this GC, whose relaxation time at half-mass radius is about 1.6 Gyr \cite{har96}." +. In Carrettaetal.(2009a) we showed that it is possible to separate a stellar component of first-generation (or primordial. P) stars in all GCs observed.," In \cite{carretta09a} we showed that it is possible to separate a stellar component of first-generation (or primordial, P) stars in all GCs observed." + The remaining second-generation stars can be further separated into intermediate (1) and extreme (E) components. according to the degree of O-depletion and Na-enhancement along the Na-O anticorrelation.," The remaining second-generation stars can be further separated into intermediate (I) and extreme (E) components, according to the degree of O-depletion and Na-enhancement along the Na-O anticorrelation." +losses have already. strougly depleted the umber of highly relativistic electrous when inverse Compton scattering becomes important.,losses have already strongly depleted the number of highly relativistic electrons when inverse Compton scattering becomes important. +" The assumed shape of the density distribution of the ICM implies that central deusity. p,;. auc core radius. e,. are not independent parameters."," The assumed shape of the density distribution of the IGM implies that central density, $\rho +_o$, and core radius, $a_o$, are not independent parameters." + The evolutionary tracks ouly depeud on a combination. pa). of the two.," The evolutionary tracks only depend on a combination, $\rho _o +a_o^{\beta}$, of the two." + This means that the effects of a ‘denser cuviromment are indistinguishable from those of a cmore extended’ euvironiieut aud Figure 5. may also be interpreted in this wav., This means that the effects of a `denser' environment are indistinguishable from those of a `more extended' environment and Figure \ref{fig:rhoredcom} may also be interpreted in this way. + The model for the iutrinsic source evolution described iu the previous section depends on source parameters (jet power. aspect ratio of the cocoou. distribution of energies of he relativistic clectrous at injection. source age. redshift) aud parameters cescribing its cuvirouuent (external density parameter pa). power law expoucut 3).," The model for the intrinsic source evolution described in the previous section depends on source parameters (jet power, aspect ratio of the cocoon, distribution of energies of the relativistic electrons at injection, source age, redshift) and parameters describing its environment (external density parameter $\rho _o a_o^{\beta}$, power law exponent $\beta$ )." + All of these wraleters are cither not directly observable or can ouly be imferred from observations at comparatively low redshift., All of these parameters are either not directly observable or can only be inferred from observations at comparatively low redshift. +" The ""birth function! of ERIT sources. ic. the comoving iuuber density of progenitors of radio galaxies starting to produce powerful jets as a ""uction of redshift. is of course also unknown."," The `birth function' of FRII sources, i.e. the comoving number density of progenitors of radio galaxies starting to produce powerful jets as a function of redshift, is of course also unknown." + In the following we will assume reasonable distribution functious of these source aud euviroument parameters which initially are asstuned to be indepeudent of cach other., In the following we will assume reasonable distribution functions of these source and environment parameters which initially are assumed to be independent of each other. +" For the birth fiction we assume a power aw of the form (1|2)"".", For the birth function we assume a power law of the form $(1+z)^n$. + Fora eiven cosimology it is then possible with the help of the uodel for the intrinsic radio huninositv-linear size evolution described iu the previous section to calculate a contiuuous distribution function iu the P-D plane., For a given cosmology it is then possible with the help of the model for the intrinsic radio luminosity-linear size evolution described in the previous section to calculate a continuous distribution function in the P-D plane. + This is theu conipared with the observed. binned source distribution of the complete. flux Iuuited sample of Laing et al. (," This is then compared with the observed, binned source distribution of the complete, flux limited sample of Laing et al. (" +"1983) using αν) Τοντ,","1983) using a $\chi +^2$ -test." + Using this technique we find that the steepenuing of the evolutionary tracks of FRI sources due to inverse Compton scattering of the CAIBR at large linear sizes alouc is not sufficicut to explain the observed decrease of the median linear size with redshift and/or radio huuinositv., Using this technique we find that the steepening of the evolutionary tracks of FRII sources due to inverse Compton scattering of the CMBR at large linear sizes alone is not sufficient to explain the observed decrease of the median linear size with redshift and/or radio luminosity. + More Iuuniuous sources at hieher redshift tend to host more powerful jets and this also implies higher hot spot advance speeds in these sources., More luminous sources at higher redshift tend to host more powerful jets and this also implies higher hot spot advance speeds in these sources. + The stecpening of their evolutionary tracks therefore occurs ouly at larger linear sizes: the opposite of what is observed., The steepening of their evolutionary tracks therefore occurs only at larger linear sizes; the opposite of what is observed. + Sources in denser enviromuents will not oulv be more Ipuuinous than those 1n more rarefied surroundings but their expiusiou speed will be lower as well., Sources in denser environments will not only be more luminous than those in more rarefied surroundings but their expansion speed will be lower as well. + The euviromucuts of sources at high redshift must have decoupled from the Ifubble flow earlier than those of low redshift objects;, The environments of sources at high redshift must have decoupled from the Hubble flow earlier than those of low redshift objects. +" This very simple picture implies that p,x(E|2)? which leads to a shortenine of the mean size of sources at high redshift."," This very simple picture implies that $\rho _o \propto +(1+z)^3$ which leads to a shortening of the mean size of sources at high redshift." + However. we fiud that this effect is not strong enough.," However, we find that this effect is not strong enough." + The single power law assumed for the birth fuuction predicts an monotonously Increasing nuniber of sources with increasing redshift., The single power law assumed for the birth function predicts an monotonously increasing number of sources with increasing redshift. + For low radio luninositics the Hux limit of the comparison sample iieaus that these sources will not be included in the sample., For low radio luminosities the flux limit of the comparison sample means that these sources will not be included in the sample. + For high radio liuinesities. however. we find that this birth fiction predicts nany more racio huuinous sources at high redshift than are observed.," For high radio luminosities, however, we find that this birth function predicts many more radio luminous sources at high redshift than are observed." + This implies at cast a flattening. if not a turn over. of the radio hunuiuositv function at redshifts of around 2 which is also iudicated by observations (0.8. Dunlop Peacock 1990).," This implies at least a flattening, if not a turn over, of the radio luminosity function at redshifts of around 2 which is also indicated by observations (e.g. Dunlop Peacock 1990)." + We find some evideuce for a population of eiat radio galaxies distinct from tle main »pulatiou by either their exceptionally high age aud/or τον rarefied environnmieuts., We find some evidence for a population of giant radio galaxies distinct from the main population by either their exceptionally high age and/or very rarefied environments. + There are three. possibly four. sources m the sample of Laing et al. (," There are three, possibly four, sources in the sample of Laing et al. (" +1983) which have ear sizes close to or above 1.5 Mype aud radio luminosities below 107 W bt t which belong to this class.,1983) which have linear sizes close to or above 1.5 Mpc and radio luminosities below $^{26}$ W $^{-1}$ $^{-1}$ which belong to this class. + The probability for finding sources in this region of the P-D diaeran is extremely low in any of the models discussed here and their inclusion in he models by allowing for extremely high lite times (>10 years) leads to au excess, The probability for finding sources in this region of the P-D diagram is extremely low in any of the models discussed here and their inclusion in the models by allowing for extremely high life times $> 10^9$ years) leads to an excess +For each bin. we calculate the structure functions [or all five bands of the quasars in that bin.,"For each bin, we calculate the structure functions for all five bands of the quasars in that bin." + ALL thirty structure functions (six bins times 5 bands) are shown in Figure &.., All thirty structure functions (six bins times 5 bands) are shown in Figure \ref{Fig3.3}. + Each structure function demonstrates the familiar relation between wavelength and variability: the & band in each bin shows the largest amplitude in its structure function.while the z-band. measurements show the least variability.," Each structure function demonstrates the familiar relation between wavelength and variability; the $u$ band in each bin shows the largest amplitude in its structure function,while the $z$ -band measurements show the least variability." + The structure functions shown in Figure S. have only nine points in Ar. rather than the ten seen in Figure 6: the high-redshift nature of these quasars (which is necessary to observe C 1v)) results in the largest rest-frame time lag bin containing no observations. after one translates from the observed. [rame to the quasar’s rest. frame.," The structure functions shown in Figure \ref{Fig3.3} have only nine points in $\Delta{\tau}$, rather than the ten seen in Figure \ref{Fig3.1}; the high-redshift nature of these quasars (which is necessary to observe C ) results in the largest rest-frame time lag bin containing no observations, after one translates from the observed frame to the quasar's rest frame." + One quickly. notices the large level of uncertainty in virtually all of these 30. structure functions in the filth bin in Ar. which is at approximately 00 days.," One quickly notices the large level of uncertainty in virtually all of these 30 structure functions in the fifth bin in $\Delta{\tau}$, which is at approximately 60 days." + This is due to the lack of observations separated by 180. clays in the observed frame: this bin spans 150davs/(1|i22). where (22 is the mean redshift at whieh € is observable (ic. z2 2.5).," This is due to the lack of observations separated by 180 days in the observed frame; this bin spans $180\ \mathrm{days}/(1 + \langle z\rangle)$, where $\langle z\rangle$ is the mean redshift at which C is observable (i.e., $z \approx 2.5$ )." + Additionallv. in certain time-lae bins. a reliable measurement of the variability cannot be mace. as the average uncertainty is greater than the average variability.," Additionally, in certain time-lag bins, a reliable measurement of the variability cannot be made, as the average uncertainty is greater than the average variability." + Γης is seen most often in v- and z-band structure functions. as those bands have the lowest signal-to-noise [Lux determinations.," This is seen most often in $u$ - and $z$ -band structure functions, as those bands have the lowest signal-to-noise flux determinations." + ὃν comparing the structure functions of quasars from adjacent bins in Figure 7.. we can isolate the dependences of variability upon luminosity ancl black hole mass.," By comparing the structure functions of quasars from adjacent bins in Figure \ref{Fig3.2}, we can isolate the dependences of variability upon luminosity and black hole mass." + l'or example. the left-hancl panel of Figure 9 shows the g-band structure functions for the quasars from bins 1. 2 ancl 3.," For example, the left-hand panel of Figure \ref{Fig3.4} shows the $g$ -band structure functions for the quasars from bins 1, 2 and 3." + Din 1 quasars are clearly more variable than those in bin 2. which are. in turn. more variable that those in bin 3.," Bin 1 quasars are clearly more variable than those in bin 2, which are, in turn, more variable that those in bin 3." + Table 3 shows the results of the power-law fits to these structure 'unctions (às well as those representing the quasars in bins 4. 5 and 6).," Table 3 shows the results of the power-law fits to these structure functions (as well as those representing the quasars in bins 4, 5 and 6)." + Phe progression from high to low variability. as one ravels from bin 1 to bin 3. seen in Figure 7. is rellected in he values for V(Nr=100) for those bins.," The progression from high to low variability, as one travels from bin 1 to bin 3, seen in Figure \ref{Fig3.2} is reflected in the values for $V(\Delta{\tau}=100)$ for those bins." + In the right-hand xuiel of Figure 7.. the same relation is observed for quasars at higher black hole mass.," In the right-hand panel of Figure \ref{Fig3.2}, the same relation is observed for quasars at higher black hole mass." + Quasars in bin 4 are of lower uminositv than those in bin 5. and are also more variable.," Quasars in bin 4 are of lower luminosity than those in bin 5, and are also more variable." + These results are not surprising. in that an anticorrclation between luminosity and variability has en. known for decades.," These results are not surprising, in that an anticorrelation between luminosity and variability has been known for decades." + However. this shows. for the first ime. that this dependence exists independent of black hole mass. à property known to be correlated with Iuminositv.," However, this shows, for the first time, that this dependence exists independent of black hole mass, a property known to be correlated with luminosity." + By comparing bins with quasars of similar Luminosity. rut clifferent black hole mass. one can isolate the dependence of variability on black hole mass.," By comparing bins with quasars of similar luminosity, but different black hole mass, one can isolate the dependence of variability on black hole mass." + This is seen with bins 2 and 4. as they cover the same range in luminosity. but un 2 contains objects with Mgg«510Εν while bin 4 contains quasars with between 510M.«Mage10 NL...," This is seen with bins 2 and 4, as they cover the same range in luminosity, but bin 2 contains objects with $M_{BH} < 5 \times 10^{8} {\rm M}_{\sun}$, while bin 4 contains quasars with between $5 \times 10^{8} {\rm M}_{\sun} < M_{\rm BH} < 10^{9} {\rm M}_{\sun}$ ." + Ehe left-hand. panel of Figure 10. shows these two xus g-band structure functions. which indicate that. the objects in bin 4or those with the higher average black hole massesare more variable than those in bin 2.," The left-hand panel of Figure \ref{Fig3.5} shows these two bins' $g$ -band structure functions, which indicate that the objects in bin 4–or those with the higher average black hole masses–are more variable than those in bin 2." + This is also reflected in their respective values of V(Nr=100) listed in ‘Table 3., This is also reflected in their respective values of $V(\Delta{\tau}=100)$ listed in Table 3. + This same trend. can be seen by comparing the three highest-luminosity bins: 3. 5 and 6.," This same trend can be seen by comparing the three highest-luminosity bins: 3, 5 and 6." + In the right-hand. panel of Figure 10. and. Table 3. it can be seen that variability appears to increase with increasing black hole mass.," In the right-hand panel of Figure \ref{Fig3.5} and Table 3, it can be seen that variability appears to increase with increasing black hole mass." + The increase is especially clear when one compares bin 3 with bin 6. the highest-black-hole-mass bin in our sample.," The increase is especially clear when one compares bin 3 with bin 6, the highest-black-hole-mass bin in our sample." + ὃν isolating the cependence of variability. upon luminosity and. black hole mass. we are. in cllect. able to probe the dependence of variability upon the LEclclineton ratio. Liafleas," By isolating the dependence of variability upon luminosity and black hole mass, we are, in effect, able to probe the dependence of variability upon the Eddington ratio, $L_{bol}/L_{Edd}$." + Vhe Eddington ratio of a quasar is a comparison of the actual bolometric luminosity. {ρω t0 the I5ddington luminosity. Lea. which is the maximum stable luminosity at which accretion can occur.," The Eddington ratio of a quasar is a comparison of the actual bolometric luminosity, $L_{bol}$, to the Eddington luminosity, $_{\rm Edd}$, which is the maximum stable luminosity at which accretion can occur." + Llowever. as we are measuring the optical luminosity. we can recast this as: where s represents the fraction of the bolometric uminosityv emitted in the optical.," However, as we are measuring the optical luminosity, we can recast this as: where $\varepsilon$ represents the fraction of the bolometric luminosity emitted in the optical." + This is likely to. be a function. of the bolometric Iuminosity: however. recent measurements for quasars with Lane2107L.; have shown his value to be approximately 0.1. (Mlopkins.Richarels.&Llernquist.2007:Richardsctal. 2006).," This is likely to be a function of the bolometric luminosity; however, recent measurements for quasars with $L_{bol} > 10^{10} L_{\sun}$ have shown this value to be approximately 0.1 \citep{hopkins07,richards06}. ." + Furthermore. since the Eclclington luminosity is directly. proportional to Xack hole mass (Rees1984).. we have that Lawflewcο ," Furthermore, since the Eddington luminosity is directly proportional to black hole mass \citep{rees84}, we have that $L_{bol}/L_{Edd} \sim L_{opt}/M_{BH}$ ." +Characteristic Edclington ratios have been calculated or each bin and are provided in Table 5.., Characteristic Eddington ratios have been calculated for each bin and are provided in Table \ref{bininfotab}. + Phese values do not represent an average Liawfleas Lor the bin. but rather he Eddington ratio one obtains from the average values or AL\(145004) and Myg also given in Table 5..," These values do not represent an average $L_{bol}/L_{Edd}$ for the bin, but rather the Eddington ratio one obtains from the average values for $\lambda L_{\lambda} (1450\AA)$ and $_{\rm BH}$ also given in Table \ref{bininfotab}." + The black 1ole mass is converted to an Eddington luminosity through he familiar Lg;=1.3I107(AI/MYz erg +., The black hole mass is converted to an Eddington luminosity through the familiar $L_{Edd} = 1.3 \times 10 ^{38} (M/{\rm M)_{\sun}}$ erg $^{-1}$. +" To get the Dolometric luminosity. we use the νι9AL\(5100.4) relation used in Waspietal.(2000) and Wollmeierctal.2106) and combine it with the a,=0.44 quasar spectral slope of VandenBerketal.(2001) to ect a new relation for he continuum near the € line: Liu.~5AL\(45024)."," To get the Bolometric luminosity, we use the $L_{bol} \sim 9\times \lambda L_{\lambda} (5100\AA)$ relation used in \citet{kaspi00} and \citet{kollmeier06} and combine it with the $\alpha_{\nu} = 0.44$ quasar spectral slope of \citet{vandenberk01} to get a new relation for the continuum near the C line: $L_{bol} \sim 5\times\lambda L_{\lambda} (1450\AA)$." + Five of the six bins have LogLg between 0.1 and 1. as did the vast majority of objects in Ixollmeierctal.(2006).," Five of the six bins have $L_{bol}/L_{Edd}$ between 0.1 and 1, as did the vast majority of objects in \citet{kollmeier06}." +. Even Bin 3. with a value of νι greater than 1 is not unreasonable: a number of objects stuclied in Ixollmeieretal.(2006) were calculated to have stuper-Eddington luminosities.," Even Bin 3, with a value of $L_{bol}/L_{Edd}$ greater than 1 is not unreasonable; a number of objects studied in \citet{kollmeier06} were calculated to have super-Eddington luminosities." + At any rate. the Edcington ratios calculated in ‘Table 5. should. primarily be used as a means for comparing the relative Eddington ratios of the quasars in cillerent bins.," At any rate, the Eddington ratios calculated in Table \ref{bininfotab} should primarily be used as a means for comparing the relative Eddington ratios of the quasars in different bins." + ὃν combining the established. (ancl herein reproduced) inverse dependence of variability upon optical luminosity with the newly demonstrated correlation of variability with black hole mass. we find that variability appears to be inversely. related to the Edelington ratio.," By combining the established (and herein reproduced) inverse dependence of variability upon optical luminosity with the newly demonstrated correlation of variability with black hole mass, we find that variability appears to be inversely related to the Eddington ratio." + Quasars with higher Eddington ratios are less variable than those with lower Edclington ratios., Quasars with higher Eddington ratios are less variable than those with lower Eddington ratios. + This suggests that the well-known anticorre[ation of variability with luminosity may in fact simply be a side ellect of a primary anticorrelation between variability and the Exldington ratio., This suggests that the well-known anticorrelation of variability with luminosity may in fact simply be a side effect of a primary anticorrelation between variability and the Eddington ratio. + In Figure 6.. lines of constant. Eddington ratio are simplv lines with intercept zero.," In Figure \ref{Fig3.1}, lines of constant Eddington ratio are simply lines with intercept zero." + In this plane. a higher Iddington ratio corresponds to a line with smaller positive slope.," In this plane, a higher Eddington ratio corresponds to a line with smaller positive slope." + We have avoided binning objects by their Eddington ratio in thispaper. simply because the shapes of those bins would not lend themselves to easy comparisons.," We have avoided binning objects by their Eddington ratio in thispaper, simply because the shapes of those bins would not lend themselves to easy comparisons." + We would.," We would," +carbon abundance predicted by stellar models gave rise to only a tiny change in the EW.,carbon abundance predicted by stellar models gave rise to only a tiny change in the EW. + Therefore we applied the maximum decrease in the carbon to oxygen ratio found by Erbetal.(2010) at z~2 so as to investigate the variation of the initial carbon/oxygen abundance ratio., Therefore we applied the maximum decrease in the carbon to oxygen ratio found by \citet{erb} at $z\sim2$ so as to investigate the variation of the initial carbon/oxygen abundance ratio. +" We present two sets of models, one with normal Solar-scaled carbon abundances and a second with the carbon abundance decreased by a factor of four."," We present two sets of models, one with normal Solar-scaled carbon abundances and a second with the carbon abundance decreased by a factor of four." +" We only perform this decrease for main-sequence OB stars when we use the OB model atmospheres of Smith,Norris&Crowther (2002).", We only perform this decrease for main-sequence OB stars when we use the OB model atmospheres of \citet{crow}. +. The result is general reduction in the strength of the absorption line as measured by the equivalent width., The result is general reduction in the strength of the absorption line as measured by the equivalent width. +" As Figure 1 demonstrates this reduction can go to explain some of the scatter in the observed EWs of in nearby galaxies, although the majority of the scatter is due to variations in their star formation history."," As Figure \ref{civew} demonstrates this reduction can go to explain some of the scatter in the observed EWs of in nearby galaxies, although the majority of the scatter is due to variations in their star formation history." + The procedure outlined above yields a synthetic spectrum appropriate to each time-step of a stellar evolution model., The procedure outlined above yields a synthetic spectrum appropriate to each time-step of a stellar evolution model. + We can then combine the spectra for each star together to produce the integrated spectrum for a synthetic stellar population., We can then combine the spectra for each star together to produce the integrated spectrum for a synthetic stellar population. + To do this we use the initial mass function described by Kroupa(2002)., To do this we use the initial mass function described by \citet{kroupa2002}. +". This uses an IMF power-law slope of -1.3 between 0.1 and MMo, and a slope of -2.35 from 0.5 to MMs."," This uses an IMF power-law slope of -1.3 between 0.1 and $_{\odot}$, and a slope of -2.35 from 0.5 to $_{\odot}$." + Finally in our spectral synthesis we include the contribution from nebular emission., Finally in our spectral synthesis we include the contribution from nebular emission. +" In star-forming galaxies, interstellar gas is ionised by the stellar continuum emitted blueward of912A,, and upon recombination it emits a nebular continuum."," In star-forming galaxies, interstellar gas is ionised by the stellar continuum emitted blueward of, and upon recombination it emits a nebular continuum." +" Neglecting this emission would lead to an incorrect estimate of the equivalent widths of emission lines and incorrect broad-band colours (Zackrisson,Bergvall&Leitet2008;Mollaetal."," Neglecting this emission would lead to an incorrect estimate of the equivalent widths of emission lines and incorrect broad-band colours \citep{zack,molla}." + 2009).. We use the radiative transfer program (Ferlandetal.1998) to produce a detailed model of the output nebular emission spectrum excited by our stellar spectra., We use the radiative transfer program \citep{cloudy} to produce a detailed model of the output nebular emission spectrum excited by our stellar spectra. +" The model output is sensitive to the chosen geometry, inner radius and composition of the gas used in the code."," The model output is sensitive to the chosen geometry, inner radius and composition of the gas used in the code." +" The details of our illustrative nebular emission model are identical to those in Eldridge&Stan-way (2009), and we output the final continuum and line strengths for use in our synthetic spectra."," The details of our illustrative nebular emission model are identical to those in \citet{ES09}, and we output the final continuum and line strengths for use in our synthetic spectra." +" We consider in this work the and spectral lines, both of which exhibit a broad component whose strength is determined by the stellar spectrum."," We consider in this work the and spectral lines, both of which exhibit a broad component whose strength is determined by the stellar spectrum." + We have already shown, We have already shown +A transit of GJ1I2I4b was observed in Sloan r-band (1.2627 nm) on May 26. 2010 between 2:57 UT and 5:15 UT with the Wide Field Camera (WFC) on the 2.5 meter Isaac Newton Telescope (INT).,"A transit of GJ1214b was observed in Sloan r-band $\lambda_c$ =627 nm) on May 26, 2010 between 2:57 UT and 5:15 UT with the Wide Field Camera (WFC) on the 2.5 meter Isaac Newton Telescope (INT)." + An exposure time of 60 seconds was used resulting in 89 frames with an average cycle time of 93 seconds., An exposure time of 60 seconds was used resulting in 89 frames with an average cycle time of 93 seconds. +" Only the central detector of the WFC (CCD4) was used for the analysis. with a pixel scale of 0.33°7/pixel. this CCD has a field of view of 675"" by 13507. sufficient to observe a number of reference stars of similar brightness simultaneously with the target."," Only the central detector of the WFC (CCD4) was used for the analysis, with a pixel scale of 0.33”/pixel, this CCD has a field of view of 675” by 1350”, sufficient to observe a number of reference stars of similar brightness simultaneously with the target." + The moon was almost full and the conditions were strongly non-photometric. with the transparency dropping to below during several frames (see top panel of Fig. 1)).," The moon was almost full and the conditions were strongly non-photometric, with the transparency dropping to below during several frames (see top panel of Fig. \ref{fig:LC_raw}) )." + On July 29. 2010. a transit of GJ214. was observed in I- 61.2822 nm) with the same instrument.," On July 29, 2010, a transit of GJ1214 was observed in I-band $\lambda_c$ =822 nm) with the same instrument." + The observations started at 21:23 UT and lasted for just over 3 hours., The observations started at 21:23 UT and lasted for just over 3 hours. + An exposure time of 50 seconds was used. resulting in a total of 142 frames with an average cycle time of 81 seconds.," An exposure time of 50 seconds was used, resulting in a total of 142 frames with an average cycle time of 81 seconds." + In this case the night was photometric., In this case the night was photometric. + Since GJI214b ts about 5.5 times brighter in I-band than in r-band. we significantly defocused the telescope in the I-band in order to keep the peak count-levels in the linear regime of the detector.," Since GJ1214b is about 5.5 times brighter in I-band than in r-band, we significantly defocused the telescope in the I-band in order to keep the peak count-levels in the linear regime of the detector." + This has the added benefit that the light is spread over more pixels. reducing the impact of flat-fielding errors.," This has the added benefit that the light is spread over more pixels, reducing the impact of flat-fielding errors." +" On the night of July 3. 2010. we obtained simultaneous observations of GJ1214b in the g 61,2459 nm). r 61.2622 nm). i Gl.2764 nm). and z-band 61,2899 nm) with the GROND instrument (?) on the 2.2 meter MPI/ESO telescope at La Silla in Chile."," On the night of July 3, 2010, we obtained simultaneous observations of GJ1214b in the g $\lambda_c$ =459 nm), r $\lambda_c$ =622 nm), i $\lambda_c$ =764 nm), and z-band $\lambda_c$ =899 nm) with the GROND instrument \citep{greineretal08} on the 2.2 meter MPI/ESO telescope at La Silla in Chile." + The field of view in each of the wavelength channels is 5.4. by 5.4. which ts sufficient to observe both GJI214 and a set of reference stars simultaneously.," The field of view in each of the wavelength channels is 5.4' by 5.4', which is sufficient to observe both GJ1214 and a set of reference stars simultaneously." + The observations started at 00:16 UT and lasted until 04:06 UT., The observations started at 00:16 UT and lasted until 04:06 UT. + During this time we obtained 280 frames in each of the four optical bands., During this time we obtained 280 frames in each of the four optical bands. + The exposure time was varied from 20 to 30 seconds to avoid saturation of the CCDs., The exposure time was varied from 20 to 30 seconds to avoid saturation of the CCDs. + The average cycle time was 50 seconds., The average cycle time was 50 seconds. +" We obtained a K, band transit observations with. the NOTCam instrument on the Nordic Optical Telescope (NOT) simultaneously with our INT r-band observations on May 26. 2010."," We obtained a $_s$ band transit observations with the NOTCam instrument on the Nordic Optical Telescope (NOT) simultaneously with our INT r-band observations on May 26, 2010." +" The observations were carried out in service mode. and the wide field imaging opties and a K,-band filter (1.22.15 um) were used."," The observations were carried out in service mode, and the wide field imaging optics and a $_s$ -band filter $\lambda_c$ =2.15 $\mu$ m) were used." + The pixelscale of this setup is 0.234pixel. resulting in a field of view of the detector of 4 by 4 areminutes.," The pixelscale of this setup is 0.234”/pixel, resulting in a field of view of the detector of 4 by 4 arcminutes." + This field of view is sufficient to allow simultaneous observations of one reference star of similar brightness to GJI214 as well as a reference star that is 4x fainter than GJI214., This field of view is sufficient to allow simultaneous observations of one reference star of similar brightness to GJ1214 as well as a reference star that is $\times$ fainter than GJ1214. + The field of view of the detector was rotated to make sure that bad regions on the detector were avoided for all three stars., The field of view of the detector was rotated to make sure that bad regions on the detector were avoided for all three stars. + Since the NOT is located on the same mountain as the INT. these observations suffer from the same non-photometric conditions. with the transparency dropping to for parts of the light curve (see Fig. 1)).," Since the NOT is located on the same mountain as the INT, these observations suffer from the same non-photometric conditions, with the transparency dropping to for parts of the light curve (see Fig. \ref{fig:LC_raw}) )." + This strongly affects the observations. since the sky background dominates over the object flux for the larger apertures. especially during times of low transparency.," This strongly affects the observations, since the sky background dominates over the object flux for the larger apertures, especially during times of low transparency." + Since GJI214 is bright at near-infrared wavelengths. we defocused the telescope in order to allow for the relatively long integration time and reducing the sensitivity to flat-fielding errors. although this also increases the impact of the sky background.," Since GJ1214 is bright at near-infrared wavelengths, we defocused the telescope in order to allow for the relatively long integration time and reducing the sensitivity to flat-fielding errors, although this also increases the impact of the sky background." + The exposure time was set to 4 seconds. to allow for relatively efficient. observations. with the large overheads induced by the NOTCam system.," The exposure time was set to 4 seconds, to allow for relatively efficient observations, with the large overheads induced by the NOTCam system." + The average cycle time was 16 seconds. allowing us to capture 518 frames in 2 hours and 25 minutes of observations.," The average cycle time was 16 seconds, allowing us to capture 518 frames in 2 hours and 25 minutes of observations." + In order to increase the stability of the system for the observations. and to decrease the telescope overheads. we observed in staring mode. with guiding. keeping the centroid of the star constant to within 4 pixels during the observations.," In order to increase the stability of the system for the observations, and to decrease the telescope overheads, we observed in staring mode, with guiding, keeping the centroid of the star constant to within 4 pixels during the observations." + Since this observation strategy does not allow us to subtract the background from the images. we obtained a set of dithered observations after our transit observation. from which we constructed a background map.," Since this observation strategy does not allow us to subtract the background from the images, we obtained a set of dithered observations after our transit observation, from which we constructed a background map." +ensing were recently studied in detail by ?.BAIL using clusters formed in a cosmological simulation independent of he MS run at. somewhat lower resolution.,lensing were recently studied in detail by \citet[BK11]{Becker_Kravtsov_2011} using clusters formed in a cosmological simulation independent of the MS run at somewhat lower resolution. + In this study. he mass derived from WL was found to be biased. low ato a level of ~5'A.," In this study, the mass derived from WL was found to be biased low at a level of $\sim -5\%$." + Considering that. these authors emploved a slightly dillerent reconstruction method in which xckeround. galaxies were used over a radial range [rom 1’ o 20. from the cluster centre and a shear profile formed. rom them. our results are in good quantitative agrecmicnt (sce also Fig.," Considering that these authors employed a slightly different reconstruction method in which background galaxies were used over a radial range from $^\prime$ to $^\prime$ from the cluster centre and a shear profile formed from them, our results are in good quantitative agreement (see also Fig." + B83 in the appendix. where we analyse our simulation using the same radial range as DIX11).," \ref{fig:cuttest} in the appendix, where we analyse our simulation using the same radial range as BK11)." + The scatter determined by DINXI1 (~20%) is very close to the evel we derive (~ 25%): we note. however. that these two numbers were derived: using two slightly. dillerent. analysis methocls.," The scatter determined by BK11 $\sim 20\%$ ) is very close to the level we derive $\sim 25\%$ ); we note, however, that these two numbers were derived using two slightly different analysis methods." + Biases in both mass and concentration have also been stucied by 2.OLILLI.. who found a mass bias similar to that in? and presented here.," Biases in both mass and concentration have also been studied by \citet[OH11]{Oguri_Hamana_2011}, who found a mass bias similar to that in \citet{Becker_Kravtsov_2011} and presented here." + However. in contrast to our results. they find a very laree. positive concentration bias of vs20%.," However, in contrast to our results, they find a very large, positive concentration bias of $\sim 20\%$." + ]t is presently unclear what the origin of this dillerence is., It is presently unclear what the origin of this difference is. + We speculate that it may originate from a dillerence in the weak lensing simulation method. between our two stuclies: while our results are based. on direct. fitting of a high resolution weak lensing simulation. OLLI] analyse an analytic circularly svmmoetric shear profile that was derived by stacking5 (mock) rav-traced lensing5 observations of 5galaxy clusters formed in à low resolution cosmological simulation.," We speculate that it may originate from a difference in the weak lensing simulation method between our two studies: while our results are based on direct fitting of a high resolution weak lensing simulation, OH11 analyse an analytic circularly symmetric shear profile that was derived by stacking (mock) ray-traced lensing observations of galaxy clusters formed in a low resolution cosmological simulation." + The azimuthal averagingDIA is expected to smooth out. the presence of substructure and triaxiality. both of which tend to bias the concentration low (see 5.3.3)).," The azimuthal averaging is expected to smooth out the presence of substructure and triaxiality, both of which tend to bias the concentration low (see \ref{sec:biasorigin}) )." + Having established the extent of the scatter and bias in WL reconstructions of cluster haloes. we now aim to find physical explanations for them.," Having established the extent of the scatter and bias in WL reconstructions of cluster haloes, we now aim to find physical explanations for them." + This is an interesting question in its own right. but might also allow an identification of possible ways to reduce these systematic errors.," This is an interesting question in its own right, but might also allow an identification of possible ways to reduce these systematic errors." + Any potential error sources can be broadly grouped into two categories: Those due to the background galaxies used in the reconstruction (ic. their unknown intrinsic ellipticities and finite number. in general also their intrinsic alignment due to cosmic shear). and those due to the cluster itself. such as halo triaxiality and substructure.," Any potential error sources can be broadly grouped into two categories: Those due to the background galaxies used in the reconstruction (i.e., their unknown intrinsic ellipticities and finite number, in general also their intrinsic alignment due to cosmic shear), and those due to the cluster itself, such as halo triaxiality and substructure." + In this section we show that. in the case of large statistical samples of clusters such as we have studied here and those to be derived. [rom the DES and LAST. the latter is dominated by the former only [or clusters with masses below a few 107M..," In this section we show that, in the case of large statistical samples of clusters such as we have studied here and those to be derived from the DES and LSST, the latter is dominated by the former only for clusters with masses below a few $10^{14} {\rm M}_\odot$." + Our strategy for assessing the importance of these various error contributions involves making two acelitional reconstructions of our cluster sample. designed. to. bridge the eap between the WL analysis based on particles within a lO h! Alpe box on the one side and the 3D fitting procedure within a radius ουυ on the other.," Our strategy for assessing the importance of these various error contributions involves making two additional reconstructions of our cluster sample, designed to bridge the gap between the WL analysis based on particles within a 10 $h^{-1}$ Mpc box on the one side and the 3D fitting procedure within a radius $r_{200}$ on the other." + In. the first of these. which we will refer to as “perfect WL. we use a very high density (η=3002 arcmin 7) of perfectly. circular background: galaxies πιο. o= 0.0). which eliminates the influence of shape noise and — essentially. we are now analysing the (reduced) shear field. g clirectly.," In the first of these, which we will refer to as “perfect WL”, we use a very high density $n = 300$ $^{-2}$ ) of perfectly circular background galaxies (i.e., $\sigma = 0.0$ ), which eliminates the influence of shape noise and — essentially, we are now analysing the (reduced) shear field $g$ directly." + In the second method. we approach the 3D fit even further by constructing the convergence field 5s and thus the shear only from those particles that lie within a (3D) distance of ους Crom the cluster centre. the same set of particles upon which the 3D fit is based.," In the second method, we approach the 3D fit even further by constructing the convergence field $\kappa$ — and thus the shear — only from those particles that lie within a (3D) distance of $r_{200}$ from the cluster centre, the same set of particles upon which the 3D fit is based." +" We will refer to this method as ""spherical WL.", We will refer to this method as “spherical WL”. + One problem with this approach is that the expression of ?. for g assumes à matter distribution extending to infinity. so fitting il to à catalogue of galaxy distortions based only on the matter distribution inside roug alone. which necessarily contains less total mass. will result in severe biases in both mass and.," One problem with this approach is that the expression of \citet{Wright_Brainerd_2000} for $g$ assumes a matter distribution extending to infinity, so fitting it to a catalogue of galaxy distortions based only on the matter distribution inside $r_{200}$ alone, which necessarily contains less total mass, will result in severe biases in both mass and." +. We overcome this by instead fitting the reduced shear fron an NEW profile that is. like our data. truncated: at σου (?: ?)).," We overcome this by instead fitting the reduced shear from an NFW profile that is, like our data, truncated at $r_{200}$ \citealt{Takada_Jain_2003a}; \citealt{Takada_Jain_2003b}) )." + We note that it is straightforward to also fit the projected mass profile of 7. directly to the projected matter within ους., We note that it is straightforward to also fit the projected mass profile of \citet{Takada_Jain_2003a} directly to the projected matter within $r_{200}$. +" This method approaches the 3D fit even closer. with the only remaining dillerence being a fit in 2D vs. one in 3D. We have done this. ancl found that the results are in very close agreement with those of the ""spherical. WL' methocl."," This method approaches the 3D fit even closer, with the only remaining difference being a fit in 2D vs. one in 3D. We have done this, and found that the results are in very close agreement with those of the `spherical WL' method." + The bias and scatter as defined. in equation in masses and concentrations resulting [rom both these methocs are shown in Fig., The bias and scatter as defined in equation in masses and concentrations resulting from both these methods are shown in Fig. + 4 and 5. respectively: the perfect WL fit represented by red lines. the spherical WL fit by blue ones.," \ref{medians} and \ref{fig:scatter} respectively, the perfect WL fit represented by red lines, the spherical WL fit by blue ones." + For ease of comparison. we also include the values determined from our default WL simulation as found in ‘Table 1 as black lines.," For ease of comparison, we also include the values determined from our default WL simulation as found in Table \ref{table} as black lines." +" We can judgee the influence of errors. associated with the background. galaxies by comparing the ""default and “perfect” WL reconstructions (black and red. curves. in Fies.", We can judge the influence of errors associated with the background galaxies by comparing the “default” and “perfect” WL reconstructions (black and red curves in Figs. +5 4 and 5)). the latter one. as explained1 above. not being allected by them.," \ref{medians} and \ref{fig:scatter}) ), the latter one, as explained above, not being affected by them." + Focusing first on scatter. in. default) vs. perfect WL (Fig. 5)).," Focusing first on scatter in default vs. perfect WL (Fig. \ref{fig:scatter}) )," + we find a very similar picture for both mass and concentration: it is comparable for the highest-mass clusters. but while the latter is almost. mass-independoent. the former increases considerably with decreasing. cluster mass.," we find a very similar picture for both mass and concentration: it is comparable for the highest-mass clusters, but while the latter is almost mass-independent, the former increases considerably with decreasing cluster mass." + This is what would be expected. from the influence of shape noise: Less massive haloes. producing a weaker shear signal. viel a lower signal-to-noise ratio than their high-mass counterparts: in the total absence of shape noise. however. the decreasing shear signal is irrelevant.," This is what would be expected from the influence of shape noise: Less massive haloes, producing a weaker shear signal, yield a lower signal-to-noise ratio than their high-mass counterparts; in the total absence of shape noise, however, the decreasing shear signal is irrelevant." + As with scatter. the variation in bias between default. and," As with scatter, the variation in bias between default and" +Additional evidence that we are distinguishiug regions domiuated by AGN activity from H I 'eejous iu NGCLILO comes [rom the line widths aud the lack of stroug contiuuuim in tle H II sources.,Additional evidence that we are distinguishing regions dominated by AGN activity from H II regions in NGC4410 comes from the line widths and the lack of strong continuum in the H II sources. + The nucleus of NGC [110A has relatively broad lines (FWHM ~ 600 kin 1j , The nucleus of NGC 4410A has relatively broad lines (FWHM $\sim$ 600 km $^{-1}$ ). +The NGC 10Η iucleus aud the filamentary features also appear to have somewhat broad lines (FWHM ~ LOO ans 1) compared to those of the knots(FWHM ~ 200 — 300 kins 1). which are only marginally 'esolved.," The NGC 4410B nucleus and the filamentary features also appear to have somewhat broad lines (FWHM $\sim$ 400 km $^{-1}$ ) compared to those of the knots(FWHM $\sim$ 200 $-$ 300 km $^{-1}$ ), which are only marginally resolved." + The knot sources have very little continuum. cousistent with their identification as H HH 'eglons.," The knot sources have very little continuum, consistent with their identification as H II regions." + The velocity structure of the ionized gas iu this system (Figure 2)) is intriguing., The velocity structure of the ionized gas in this system (Figure \ref{fig7}) ) is intriguing. + The two iuclei. the northwestern filament. aud the extended emission to the east of the NGC [110A nucleus are considerably redshifted (7110 ki | — 7500 kins 1) from the H LE regious and the extended emission to the southwest and east of the NGC 1110 nucleus. centered at 7130 — 7310 kin |).," The two nuclei, the northwestern filament, and the extended emission to the east of the NGC 4410A nucleus are considerably redshifted (7440 km $^{-1}$ $-$ 7500 km $^{-1}$ ) from the H II regions and the extended emission to the southwest and east of the NGC 4410A nucleus, centered at 7130 $-$ 7340 km $^{-1}$ )." + HH is possible that we are viewing line emission [rom two interacting systems with a velocity separation of ~200 km +. or that the H II regions were originally associated with one of the nuclei.," It is possible that we are viewing line emission from two interacting systems with a velocity separation of $\sim 200$ km $^{-1}$, or that the H II regions were originally associated with one of the nuclei." + The IUE data were extracted and. calibrated by the IUE New Spectral Imaging Processing System (NEWSIPS) software in two ways: the staudard extraction method which is optimized lor a poiut source. aud a re-extraction aud reprocessing using a method optimized for an extended source.," The IUE data were extracted and calibrated by the IUE New Spectral Imaging Processing System (NEWSIPS) software in two ways: the standard extraction method which is optimized for a point source, and a re-extraction and reprocessing using a method optimized for an extended source." + The two SWP spectra are plotted in Figure ) 3.., The two SWP spectra are plotted in Figure \ref{fig8}. . + The 1216A ἵνα feature is strongly detected in this source. with a total line lux of 1.0 + 0.2 x P erg tem 7.," The ${\rm \AA}$ $\alpha$ feature is strongly detected in this source, with a total line flux of 1.0 $\pm$ 0.2 $\times$ $^{-13}$ erg $^{-1}$ $^{-2}$." + A possible 15184-1551A. C IV feature may be present at the level of 6 + ‘ 9 −≻≍⋯⊔↩⋅∑≟⊳∖↓∢∙∐↕−⋅∣≻⋯↕∐⊳∖↥≺↵⋜↕⊓⊔⋅≺↵∢∙∩∐∐∙∐⇂≺↵⊳∖∖∖↽∐∐↕∐≺↵↥↽≻↓⋅≺↵⊳∖≺↵∐∢∙≺↵∩↥⊳∖∩⋯≺↵∢∙∩⊳∖∐∐∢∙↕⋅⋜↕⊽∖⊽⊳∖⋜↕∐≺⇂ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ the wavelength centroid of the feature places it significantly bluer (by about. £00 kin 1) of the centroid of the Lya feature. and lies about £5” south of the position of the continuum source.," A possible ${\rm \AA}$ C IV feature may be present at the level of 6 $\pm$ 2 $\times$ $^{-14}$ erg $^{-1}$ $^{-2}$, but this feature coincides with the presence of some cosmic rays and the wavelength centroid of the feature places it significantly bluer (by about 400 km $^{-1}$ ) of the centroid of the $\alpha$ feature, and lies about $''$ south of the position of the continuum source." + If real. it may be associated with Ixuot #2. but we are doubtful.," If real, it may be associated with Knot $\#$ 2, but we are doubtful." +" The mean contiuuum between 1350-1150 observed frame in the SWP spectrum is Peres 7 A1, ", The mean continuum between 1350-1450 observed frame in the SWP spectrum is $1.1\pm0.2 \times 10^{-15}$ erg $^{-1}$ $^{-2}$ $^{-1}$. +The contimuun flux from the SWP spectrum obtained with the extended source algoritlun is statistically equal to that fouud with the point source algoritlin centered ou the coutinuumn peak (1.2c0.2x1015 eres tem7 At). indicating that the continuum enmission ix unresolved by IUE (FWHM < 3755).," The continuum flux from the SWP spectrum obtained with the extended source algorithm is statistically equal to that found with the point source algorithm centered on the continuum peak $1.2\pm0.2 \times 10^{-15}$ erg $^{-1}$ $^{-2}$ $^{-1}$ ), indicating that the continuum emission is unresolved by IUE (FWHM $<$ 5)." + The LWP spectrum (uot shown) contains only faint. [lat continuum emission. at a mean level of b+ 2 x Meres Fem? Lat30004.," The LWP spectrum (not shown) contains only faint, flat continuum emission, at a mean level of 4 $\pm$ 2 $\times$ $^{-16}$ erg $^{-1}$ $^{-2}$ $^{-1}$ at." + Lya is clearly visible in both extracted spectra. and the fIux obtained with the extended source methocl is higher than that derived asstunineg a polut source.," $\alpha$ is clearly visible in both extracted spectra, and the flux obtained with the extended source method is higher than that derived assuming a point source." + In Figure 3.. the amplituce of the Lya emission line [rom the extendedsource extraction (71.210. theres Fem 7 4) is higher than that obtained from the point-source extraction (~0.5x10 theres tem 7 +). indicating that Lya is extendec.," In Figure \ref{fig8}, , the amplitude of the $\alpha$ emission line from the extendedsource extraction $\sim 1.2 \times 10^{-14}$ erg $^{-1}$ $^{-2}$ $^{-1}$ ) is higher than that obtained from the point-source extraction $\sim 0.5 \times 10^{-14}$ erg $^{-1}$ $^{-2}$ $^{-1}$ ), indicating that $\alpha$ is extended." +" The extent of the Lya emission is >20"". since the emission seems to fill the IUE aperture."," The extent of the $\alpha$ emission is $>20''$, since the emission seems to fill the IUE aperture." +candles in cosmology.,candles in cosmology. + Finally. we are very interested iu exploring the observational consequences of tlhe AITT in more detail.," Finally, we are very interested in exploring the observational consequences of the MTI in more detail." + In particular. we would like to understand theoretically the modification of the maguetic field measurement through inverse Compton and rotation measure methods. as the ecometiy of the magnetic field changes from isotropic to racially-biased.," In particular, we would like to understand theoretically the modification of the magnetic field measurement through inverse Compton and rotation measure methods, as the geometry of the magnetic field changes from isotropic to radially-biased." + With a theoretical undoerstaudiug. we could compute exact IC aud rotation measure maps from a Ισ]οποίο- simulated cluster for comparison with observational data.," With a theoretical understanding, we could compute exact IC and rotation measure maps from a high-resolution simulated cluster for comparison with observational data." + Iu short. clusters of galaxies provide a rich physics laboratory for testing Dragiuski-MIID. the MI. and mauv other phenomena.," In short, clusters of galaxies provide a rich physics laboratory for testing Braginskii-MHD, the MTI, and many other phenomena." + We have developed analytical and computational tools for understanding these phenomena. aud we will coutinue to apply these extended— AIITD inocdels to iuproviug our understanding of clusters of ealaxies.," We have developed analytical and computational tools for understanding these phenomena, and we will continue to apply these extended MHD models to improving our understanding of clusters of galaxies." + We thank Eliot Quataert. Prateck Sharma. and Ben Chaudran for αμα useful conversations.," We thank Eliot Quataert, Prateek Sharma, and Ben Chandran for many useful conversations." + We also acknowledge useful sugeestions from Chris Revuolds. Eve Ostriker. aud especially Jack Unehes.," We also acknowledge useful suggestions from Chris Reynolds, Eve Ostriker, and especially Jack Hughes." +" I. J. P. is supported by NASA through the Chandra Postdoctoral Fellowship erant PE?-80019 awarded by the N-Rav Center. which is operated by the Samüthsoniau| Astroplivsical Observatory for NASA under contract NASS-03060,"," I. J. P. is supported by NASA through the Chandra Postdoctoral Fellowship grant PF7-80049 awarded by the X-Ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060." + TJ. P. was previously supported by the Departinent of Energy. Computational Science Graduate Fellowship., I. J. P. was previously supported by the Department of Energy Computational Science Graduate Fellowship. + J. M. S. acknowledges support by the DOE through eraut DE-ECG52-06NA26217., J. M. S. acknowledges support by the DOE through grant DE-FG52-06NA26217. + This research was supported in part bv the National Science. Foundation through TeraCiid resources provided by the Natioual Center for Atmospheric Research aud the Pittsburgh Supercomputing Center., This research was supported in part by the National Science Foundation through TeraGrid resources provided by the National Center for Atmospheric Research and the Pittsburgh Supercomputing Center. + Parts of this work were also performed on the Oraugeua aud Della supercompiuters at Princeton University., Parts of this work were also performed on the Orangena and Della supercomputers at Princeton University. +are drawn in Section 6..,are drawn in Section \ref{concs}. +" Phroughout the paper. cosmological parameters of OQ= 1. X=0 and 44,=TOkkmss !Mpe. t are assumed."," Throughout the paper, cosmological parameters of $\Omega = 1$ , $\Lambda = 0$ and $H_{0}= 70$ $^{-1}$ $^{-1}$ are assumed." + With a redshift of z=0.83. 03 is the highest redshift cluster in the Extended Mecium Sensitivity Survey (I2MSS) Xray selected. cluster sample (2)... and also one of the most luminous in Xravs with a kkeV Xrav luminosity of 9«10! eergss.+.," With a redshift of $z=0.83$, $-$ 03 is the highest redshift cluster in the Extended Medium Sensitivity Survey (EMSS) X–ray selected cluster sample \cite{gio90}, and also one of the most luminous in X–rays with a keV X--ray luminosity of $9 \times 10^{44}$ $^{-1}$." + On account of its high redshift and richness (Abell class 3). a deep 5 by 5 arcminute mosaic was mace of the field around the cluster using the wideΠοια planetary camera 2 (WEDPC2) on the Hubble Space Telescope (ST). in two filters (E606. and ESI4M: van Dokkum 22000).," On account of its high redshift and richness (Abell class 3), a deep 5 by 5 arcminute mosaic was made of the field around the cluster using the wide–field planetary camera 2 (WFPC2) on the Hubble Space Telescope (HST), in two filters (F606W and F814W; van Dokkum 2000)." + This has subsequently. been supplemented. by. deep nearinfrared. imaging of the cluster in the J. ff and A wavebands. using the NT'T. and C. D. V. imagine using FORS on the VLT. to provide galaxy colours across a long wavelength baseline (Franx iin preparation).," This has subsequently been supplemented by deep near–infrared imaging of the cluster in the $J$, $H$ and $K$ wavebands using the NTT, and $U$, $B$, $V$ imaging using FORS on the VLT, to provide galaxy colours across a long wavelength baseline (Franx in preparation)." + These images show a conspicuous overdensity of red cluster galaxies with a somewhat irregular and elongated cistribution (2).. probably consisting of three sub-clumps of galaxies at the same radial velocity: this is consistent with the detection of substructure in the Nray image (7:?)..," These images show a conspicuous overdensity of red cluster galaxies with a somewhat irregular and elongated distribution \cite{dok00}, probably consisting of three sub-clumps of galaxies at the same radial velocity; this is consistent with the detection of substructure in the X–ray image \cite{don98,jel01}." + Alultiobject. spectroscopy carried. out on. the Keck Telescope has enabled: redshifts to be determined. for over 200 objects in this field. with more than 130 of these being confirmed as cluster members (van Dokkum 22000. Tran iin preparation)," Multi–object spectroscopy carried out on the Keck Telescope has enabled redshifts to be determined for over 200 objects in this field, with more than 130 of these being confirmed as cluster members (van Dokkum 2000, Tran in preparation)." +" ""These authors found that the fraction of all carly tvpe galaxies in the central regions of the cluster is much lower than that at. low recshift. (~ SOUL)."," These authors found that the fraction of all early type galaxies in the central regions of the cluster is, much lower than that at low redshift $\sim 80$ )." +" Further. à very high fraction 9 of cluster. galaxies are classified as ""merger/peculiar"" on the basis of double nuclei (separations lOkpc). tidal tails. and cistorted morphologics (?7).."," Further, a very high fraction ) of cluster galaxies are classified as “merger/peculiar” on the basis of double nuclei (separations $\ll 10\,$ kpc), tidal tails, and distorted morphologies \cite{dok99a}." + This high fraction strongly argues against monolithic collapse models of galaxy. formation., This high fraction strongly argues against monolithic collapse models of galaxy formation. + Interestingly.e many of the mergingo OOgalaxies are red. bulgeὃνdominated galaxies with no detected nebular line emission. and: colours offset. from the carlytype (0DB). colour magnitude relation bv only 0.07 magnitudes.," Interestingly, many of the merging galaxies are red, bulge--dominated galaxies with no detected nebular line emission, and colours offset from the early–type $(U-B)_z$ colour magnitude relation by only 0.07 magnitudes." + The fraction of blue galaxies in the cluster. calculated. in a manner equivalent to that. defined. by Butcher. Oemler (?).. is (7).. comparable to the mean value determined for clusters at redshifts 0.3«z0.5.," The fraction of blue galaxies in the cluster, calculated in a manner equivalent to that defined by Butcher Oemler \shortcite{but78}, is $0.22 \pm 0.05$ \cite{dok00}, comparable to the mean value determined for clusters at redshifts $0.3 < z < 0.5$." + 03 is clearly an interesting rich cluster with a wealth of observations over à wide varicty of wavelengths and. crucially. with spectroscopic redshifts for the majority of the objects. towards the cluster. centre: currently. spectroscopic redshifts have been. measured. for of all galaxies with 19.0<122.0 (the brightest cluster galaxy has L~ 19.5) within the bounds of the HIST. mosaic.," $-$ 03 is clearly an interesting rich cluster with a wealth of observations over a wide variety of wavelengths and, crucially, with spectroscopic redshifts for the majority of the objects towards the cluster centre: currently, spectroscopic redshifts have been measured for of all galaxies with $19.0 < {\rm I} <22.0$ (the brightest cluster galaxy has ${\rm I} \sim 19.5$ ) within the bounds of the HST mosaic." + As such. AISLO54 03 is an ideal target for a deep cluster racio survey.," As such, $-$ 03 is an ideal target for a deep cluster radio survey." + Indeed. it was one of the high redshift clusters in the L4GGllz survey of Stocke shortcitesto99b.. who detected three radio sources within the cluster down to a [lux density limit of 0.20].," Indeed, it was one of the high redshift clusters in the GHz survey of Stocke \\shortcite{sto99b}, who detected three radio sources within the cluster down to a flux density limit of 0.2mJy." + These are discussed later. together with the weaker sources identified in the eurrent observations.," These are discussed later, together with the weaker sources identified in the current observations." + 03 was observed using the Very Large. Array (VLA) at 5CGGllz in € array configuration during three 10-hour runs on April 3. 6 and 7 2000.," $-$ 03 was observed using the Very Large Array (VLA) at GHz in C array configuration during three 10-hour runs on April 3, 6 and 7 2000." + The total on- integration time was 06270 seconds., The total on-source integration time was 96270 seconds. + The observations were carried out simultaneously. at two frequencies. 4835 and MMlIz. cach with two circular polarisations and AAILI banedwieth.," The observations were carried out simultaneously at two frequencies, 4835 and MHz, each with two circular polarisations and MHz bandwidth." + With this setup. the fullwidthhalf»ower of the antenna primary beam is about 9 areniins and he angular resolution about 4 aresec.," With this set–up, the full--width--half--power of the antenna primary beam is about 9 arcmins and the angular resolution about 4 arcsec." + The observations were carried out using standard VLA procedures., The observations were carried out using standard VLA procedures. + Short observations of the primary (lux calibrator 3C286 (13311305) were used to calibrate the flux density scale. assumüng Lux densities of 7.46 and 7.51 Jv at the wo observing [requencies: these are the most. recently determined VLA values. ancl are approximately above he flux density scale of Baars shorteitehaaT7..," Short observations of the primary flux calibrator 3C286 (1331+305) were used to calibrate the flux density scale, assuming flux densities of 7.46 and 7.51 Jy at the two observing frequencies; these are the most recently determined VLA values, and are approximately above the flux density scale of Baars \\shortcite{baa77}." + Observations of ὃς286 separated. in time » about 6 hours were used to determine the absolute »olarisation position angle and to estimate the uncertainty in this calibration (42°) from the dillerence between he solutions for the two cillerent. scans.," Observations of 3C286 separated in time by about 6 hours were used to determine the absolute polarisation position angle and to estimate the uncertainty in this calibration $\pm +2^{\circ}$ ) from the difference between the solutions for the two different scans." + The secondary calibrator 10581015. olfset 5 degrees from MSI054. 03. was observed at. 30 minute intervals throughout the runs o provide accurate phase calibration.," The secondary calibrator 1058+015, offset 5 degrees from $-$ 03, was observed at 30 minute intervals throughout the runs to provide accurate phase calibration." +" ""The wide range of xwallactic angles at which this calibrator was observed enabled the on-axis antenna polarisation response ternis to xf accurately determined.", The wide range of parallactic angles at which this calibrator was observed enabled the on-axis antenna polarisation response terms to be accurately determined. + After first. ciscarcing data [from any antenna or baseline showing excessive noise (very little for the first run. about of the data from the second run and of the data rom the third run). the data were ed using the taskIMAGR.," After first discarding data from any antenna or baseline showing excessive noise (very little for the first run, about of the data from the second run and of the data from the third run), the data were ed using the task." +. Then. the presence of a just sullicientIx brig= (7mJv) point source towards the centre of the field. enable wo eveles of phase selfcalibration to be carried out. which reduced the map rms by15%.," Then, the presence of a just sufficiently bright (7mJy) point source towards the centre of the field, enabled two cycles of phase self–calibration to be carried out, which reduced the map rms by." +. Finalmaps of the fie were then produced in the Stokes parameters LQ and U w further eLEgANing the datasets.," Finalmaps of the field were then produced in the Stokes parameters I, Q and U, by further ing the datasets." + Phe maps were produce using an intermediate data weighting between those of natural and uniform weighting. bv setting the data weightine," The maps were produced using an intermediate data weighting between those of natural and uniform weighting, by setting the data weighting" +to the atmosphere.,to the atmosphere. + We can rewrite Eq. (2)), We can rewrite Eq. \ref{e:enthalpy}) ) + in terms of teniperature: where e is the specific heat at coustaut pressure., in terms of temperature: where $c_{\mathrm{p}}$ is the specific heat at constant pressure. + Duriug the atmospheric path. as the Mach umuber is large. the aeteoroid’s speed is close to the imaxiumn value corresponding to the stagnation temperature.," During the atmospheric path, as the Mach number is large, the meteoroid's speed is close to the maximum value corresponding to the stagnation temperature." + Changes iu the stream properties are mainly due to changes in the stagnation temperature Zy. which is a direct measure of the amount of heat trausfer.," Changes in the stream properties are mainly due to changes in the stagnation temperature $T_{0}$, which is a direct measure of the amount of heat transfer." + This argunient stresses the inuportance of the stagnation femiperature iu lwpersouic flow. since it is related to the maxinuun speed of the stream. which in turn is close to the speed of the cosmic body.," This argument stresses the importance of the stagnation temperature in hypersonic flow, since it is related to the maximum speed of the stream, which in turn is close to the speed of the cosmic body." + According to Shapiro (1951)). the relationship between stagnation temperature and maxima speed of the stream cau be expressed im the following wav: where 5 is the ratio of specific heats;," According to Shapiro \cite{SHAPIRO}) ), the relationship between stagnation temperature and maximum speed of the stream can be expressed in the following way: where $\gamma$ is the ratio of specific heats." + Dy meaus of the equation of state for the air. Vias can be expressed as a function of the stagnation pressure aud deusity: Tn order to obtain a condition. for the imeteoroicd breakup. the stagnation pressure py niust be set equal to the mechanical streneth S of the body.," By means of the equation of state for the air, $V_{\mathrm{max}}$ can be expressed as a function of the stagnation pressure and density: In order to obtain a condition for the meteoroid breakup, the stagnation pressure $p_0$ must be set equal to the mechanical strength $S$ of the body." + As for the stagnation density. we have PoPas)/Pair71 (Landau Lifshitz 1987)). where pair is the uncisturbed air density at the airburst height.," As for the stagnation density, we have $(\rho_{0}-\rho_{\mathrm{air}})/\rho_{\mathrm{air}}\approx 1$ (Landau Lifshitz \cite{LANDAU}) ), where $\rho_{\mathrm{air}}$ is the undisturbed air density at the airburst height." + Finally. bv expressing pair as a function of atmospheric height 2aud py. like iu Eq. (," Finally, by expressing $\rho_{\mathrm{air}}$ as a function of atmospheric height $h$and $\rho_{\mathrm{sl}}$, like in Eq. (" +1). we obtain a new equation to estimate Vias Which is close to the speed of the cosmic body at breakup V: For 5 we can use a value of about 1.7.resulting from. experinoenutal studies on plasina developed iu lypervelocity iupacts (Ikadono Fujiwara 1996).,"1), we obtain a new equation to estimate $V_{\mathrm{max}}$ , which is close to the speed of the cosmic body at breakup $V$: For $\gamma$ we can use a value of about $1.7$,resulting from experimental studies on plasma developed in hypervelocity impacts (Kadono Fujiwara \cite{KADONO}) )." + Comparing Eq. (6)), Comparing Eq. \ref{e:velo2}) ) + to Eq. (1)).," to Eq. \ref{e:velo}) )," + we see an additional factor of about 1.6., we see an additional factor of about $1.6$. + This comes from the fact that Eq. (6)), This comes from the fact that Eq. \ref{e:velo2}) ) + derives from Eq. CL).," derives from Eq. \ref{e:vmax}) )," + according to which the stagnation temperature cdepe1cs on speed when a body is travelling at Lypersonic velocity., according to which the stagnation temperature depends on speed when a body is travelling at hypersonic velocity. + Eq. (6)), Eq. \ref{e:velo2}) ) + shows that the airburst occurs thanks to f16 combined thermal aud mechanical effects acting on the neteoroid., shows that the airburst occurs thanks to the combined thermal and mechanical effects acting on the meteoroid. + In other words. thermodvuamic processes decrease the effective pressure crushing the body i a significaut way. so the same body can reach a lower altitude. or for a given airburst altitude a lower strength is required.," In other words, thermodynamic processes decrease the effective pressure crushing the body in a significant way, so the same body can reach a lower altitude, or for a given airburst altitude a lower strength is required." + By means of Eq. (6)), By means of Eq. \ref{e:velo2}) ) + we cau replace Table 1 with a new able for the breakup speeds of different types of cosmic xdv (see Tab. 23)., we can replace Table 1 with a new table for the breakup speeds of different types of cosmic body (see Tab. \ref{speed-new}) ). + Note that jw the inferred speed or an ion body would be too lugh. aud stony bodies xovide the most plausible solution.," Note that now the inferred speed for an iron body would be too high, and stony bodies provide the most plausible solution." + This i$ consisteut with the results of a detailed analysis of several hundreds ucteors carried out by Ceplecha AlcCrosky (1976)) aud Ceplecha (199 1). who found tha a height around 10 kin is fairly typical for stony objects.," This is consistent with the results of a detailed analysis of several hundreds meteors carried out by Ceplecha McCrosky \cite{JGR}) ) and Ceplecha \cite{CEPLECHA}) ), who found that a height around 10 km is fairly typical for stony objects." + We can now calculate other data for the Tuuguska eveut solving the equations of motion and the luminosity equation. according to the procedure described in Foschini (1995)).," We can now calculate other data for the Tunguska event solving the equations of motion and the luminosity equation, according to the procedure described in Foschini \cite{FOSCHINI}) )." + The results are sununarizec in Table 3.., The results are summarized in Table \ref{summary}. + The following assumptions have been made: (4) the Iuniuous eficicney 7 is D (i) the diameter of the object is calculated assimnuius a spherical shape and a deusityv of 3500 117. typical for a stoux object.," The following assumptions have been made: (i) the luminous efficiency $\tau$ is $5\%$; (ii) the diameter of the object is calculated assuming a spherical shape and a density of $3500$ $^{3}$, typical for a stony object." + Comparing these results to previous ones and to the available data (for a review see Vasilvey 1998)). we note a generally eood agreement. except for the trajectory inclination over the horizon.," Comparing these results to previous ones and to the available data (for a review see Vasilyev \cite{VASILYEV}) ), we note a generally good agreement, except for the trajectory inclination over the horizon." + The value obtained here is about 3°. while Vasilveyreported that the most likely inclination angle was about 157.," The value obtained here is about $3\degr$ , while Vasilyevreported that the most likely inclination angle was about $15\degr$ ." + ILoxcever. he also noted the possibility. of a good acrodvuamic shape of the," However, he also noted the possibility of a good aerodynamic shape of the" + , +In this section. we describe these simulations. and the relevant assumptions that go into our modeling.,"In this section, we describe these simulations, and the relevant assumptions that go into our modeling." + This involves combining a large number of simulation codes., This involves combining a large number of simulation codes. + In light of this. to guide the reader through the numerical details and equations in this section. we first summarise them more generally here.," In light of this, to guide the reader through the numerical details and equations in this section, we first summarise them more generally here." + We first simulate the hydrodynamic evolution of both dise galaxies and mergers., We first simulate the hydrodynamic evolution of both disc galaxies and mergers. + It is from these simulations that we know the global distribution of stars. gas and metals in the galaxy. and their physical properties.," It is from these simulations that we know the global distribution of stars, gas and metals in the galaxy, and their physical properties." + The radiative transfer occurs in post-processing., The radiative transfer occurs in post-processing. + We project the physical conditions of the particles onto an adaptive mesh using the SPH smoothing kernel., We project the physical conditions of the particles onto an adaptive mesh using the SPH smoothing kernel. + The base mesh is 5 spanning a 200 kpe box., The base mesh is $^3$ spanning a 200 kpc box. +" The cells refine recursively into 2° subcells based on the refinement criteria the relative density variations of metals (7,,,/.$ ) should be less than 0.1, and the $V$ -band optical depth across a cell be less than unity." + The maximum refinement level was L1. such that the smallest cells in this mesh are of order ~70 pe across.," The maximum refinement level was 11, such that the smallest cells in this mesh are of order $\sim70$ pc across." + The surface density of and velocity dispersion within the GMCs are set by the physical conditions in the hydrodynamic galaxy evolution simulations., The surface density of and velocity dispersion within the GMCs are set by the physical conditions in the hydrodynamic galaxy evolution simulations. + A subgrid prescription comes into play when GMCs are unresolved (i.e. when cells in the adaptive mesh are very large)., A subgrid prescription comes into play when GMCs are unresolved (i.e. when cells in the adaptive mesh are very large). + We assume that all of the mmass in the cell is in the GMC and we calculate the bbalance via analytic models (described below)., We assume that all of the mass in the cell is in the GMC and we calculate the balance via analytic models (described below). + From this. the complete physical conditions (except for the temperature) of the GMCs are described by the hydrodynamic galaxy evolution simulations.," From this, the complete physical conditions (except for the temperature) of the GMCs are described by the hydrodynamic galaxy evolution simulations." + The temperatures of the clouds are calculated by assuming thermal equilibrium between gas heating (by the grain photoelectric effect and cosmic rays). gas cooling (via molecular and atomic line cooling). dust heating (from the ambient radiation field). thermal dust cooling. and some energy exchange between gas and dust.," The temperatures of the clouds are calculated by assuming thermal equilibrium between gas heating (by the grain photoelectric effect and cosmic rays), gas cooling (via molecular and atomic line cooling), dust heating (from the ambient radiation field), thermal dust cooling, and some energy exchange between gas and dust." + With the physical properties of the galaxies and GMCs known. we then proceed to calculate the emergent CO emission from the clouds.," With the physical properties of the galaxies and GMCs known, we then proceed to calculate the emergent CO emission from the clouds." + We calculate the CO line emission from the GMCs utilising an escape probability formalism., We calculate the CO line emission from the GMCs utilising an escape probability formalism. + The radiation from these clouds then interacts with other clouds in the galaxy. and the level populations of CO are calculated by the balance of radiative absorptions. stimulated emission. spontaneous emission. and collisions with aand He.," The radiation from these clouds then interacts with other clouds in the galaxy, and the level populations of CO are calculated by the balance of radiative absorptions, stimulated emission, spontaneous emission, and collisions with and He." + At this point. the general reader should be equipped to understand the general results of this paper.," At this point, the general reader should be equipped to understand the general results of this paper." + For the remainder of this section. we elaborate on this abbreviated. description.," For the remainder of this section, we elaborate on this abbreviated description." + Throughout. we assume /=0.7.," Throughout, we assume $h=0.7$." + We simulate the hydrodynamic evolution of both idealised isolated dise galaxies. and mergers between these dises.," We simulate the hydrodynamic evolution of both idealised isolated disc galaxies, and mergers between these discs." + The purpose of the ivdrodynamie simulations is to calculate the spatial distribution of ye neutral ISM. stars and metals.," The purpose of the hydrodynamic simulations is to calculate the spatial distribution of the neutral ISM, stars and metals." + It is from the neutral ISM that we will calculate the molecular gas properties. and. as we will discuss. ye radiation from the stars and dust in the metals that determine ye IR. radiation field.," It is from the neutral ISM that we will calculate the molecular gas properties, and, as we will discuss, the radiation from the stars and dust in the metals that determine the IR radiation field." + Here. we describe the components of the model most pertinent to this study. namely the physics of the ISM and star formation preseriptions.," Here, we describe the components of the model most pertinent to this study, namely the physics of the ISM and star formation prescriptions." + For a more full understanding of ye underlying algorithms inGADGET-3.. please refer to and.," For a more full understanding of the underlying algorithms in, please refer to and." +processors... The galaxies are simulated with a moditied version of the publicly available SPH code.citepsprOSb.," The galaxies are simulated with a modified version of the publicly available SPH code,." +. The ISM is modeled as two-phase. with cold clouds embedded in a hot. pressure-contining medium2003).," The ISM is modeled as two-phase, with cold clouds embedded in a hot, pressure-confining medium." +. Numerically. this is realised via hybrid SPH particles.," Numerically, this is realised via hybrid SPH particles." + The cold gas mass grows via radiative cooling of the hot phase. and cold gas is converted to hot σας through the heating associated with star formation.," The cold gas mass grows via radiative cooling of the hot phase, and cold gas is converted to hot gas through the heating associated with star formation." + Stars form in the cold ISM according to a relation SFR pls ," Stars form in the cold ISM according to a relation SFR $\propto +\rho_{\rm cold}^{1.5}$ ." +"The normalisation of this relation is set in order to match the local spr|XV, relation2006b).", The normalisation of this relation is set in order to match the local $\Sigma_{\rm SFR}-\Sigma_{\rm gas}$ relation. +". Supernova pressurisation of the ISM is modeled via an ""effective"" equation of state2005b).", Supernova pressurisation of the ISM is modeled via an “effective” equation of state. +. Here. we assume a modest pressurisation of qgos=0.25 in the formalism.," Here, we assume a modest pressurisation of $q_{\rm EOS}=0.25$ in the formalism." + This corresponds to a mass-weighted ISM temperature of ~10K. In the Appendix we relax the star formation and equation of state assumptions in order to test the validity of our results., This corresponds to a mass-weighted ISM temperature of $\sim10^{4.5}$ K. In the Appendix we relax the star formation and equation of state assumptions in order to test the validity of our results. + The simulations here are not cosmological: the dises are set up in an idealised manner in order to maximise spatial resolution., The simulations here are not cosmological: the discs are set up in an idealised manner in order to maximise spatial resolution. + Here. the gravitational softening length for baryons is LOOh .. and 200h for dark matter.," Here, the gravitational softening length for baryons is 100 , and 200 for dark matter." + The disces are initialised according to the formalism. and are bulgeless.," The discs are initialised according to the formalism, and are bulgeless." + They are embedded in dark matter halos with density distributions., They are embedded in dark matter halos with density distributions. + In order to compare with observations in a. meaningful manner. we aim to simulate galaxies comparable to those found in the local Universe.," In order to compare with observations in a meaningful manner, we aim to simulate galaxies comparable to those found in the local Universe." + Accordingly. our isolated discs are initialised inside haloes of mass ~1.91077M.;.. baryonic mass of MORSo10!Μι. circular velocity of 160ὃς and with of the baryons in the form of gas.," Accordingly, our isolated discs are initialised inside haloes of mass $\sim1.9\times 10^{12}$, baryonic mass of $\sim8\times10^{10}$, circular velocity of 160, and with of the baryons in the form of gas." + The mergers are binary 1:1 mergers between discs constructed in the same manner., The mergers are binary 1:1 mergers between discs constructed in the same manner. + We simulate three mergers of slightly higher mass in order to ensure that they undergo a luminous starburst comparable to the most extreme ones seen in the local Universe (~100M.;vr. 1.," We simulate three mergers of slightly higher mass in order to ensure that they undergo a luminous starburst comparable to the most extreme ones seen in the local Universe $\sim100 +\ \msunyrend$ )." + In particular. the dises that comprise the binary mergers have a rotation speed of 2251. halo mass of ~ M... and baryonic mass of ~2.2.10!..," In particular, the discs that comprise the binary mergers have a rotation speed of 225, halo mass of $\sim 5 +\times 10^{12}$ , and baryonic mass of $\sim 2.2 \times +10^{11}$." + The mergers are set on an orbit with angles (61.64.05.05) = (30.60.- (-109.-30.71.-30) and (0.0.0.0).," The mergers are set on an orbit with angles $\theta_1,\phi_1,\theta_2,\phi_2$ ) = (30,60,-30,45), (-109,-30,71,-30) and (0,0,0,0)." +" The angles for the first two orbits are arbitrary. and were chosen to represent relatively ""normal"" orbits in our library of simulations."," The angles for the first two orbits are arbitrary, and were chosen to represent relatively “normal” orbits in our library of simulations." + The last merger is a coplanar one. and represents an extreme starburst with an extended duration. which we include simply for comparison.," The last merger is a coplanar one, and represents an extreme starburst with an extended duration, which we include simply for comparison." +" We choose the first merger as our ""fiducial"" merger for the remainder of this paper as this particular model is well-studied in theliterature. and focus particularly on the snapshot when the star formation rate is at its peak."," We choose the first merger as our “fiducial” merger for the remainder of this paper as this particular model is well-studied in the, and focus particularly on the snapshot when the star formation rate is at its peak." + The results from all simulations are similar. and we discuss the minor differences that do exist when necessary.," The results from all simulations are similar, and we discuss the minor differences that do exist when necessary." + We assume that the entire neutral mass in a given cell is locked in a cloud which is spherical. isothermal. and of constant density.," We assume that the entire neutral mass in a given cell is locked in a cloud which is spherical, isothermal, and of constant density." + We determine the surface density of the neutral gas via, We determine the surface density of the neutral gas via +"nearby cE galaxy made by the Virtual Observatory (VO) fed workflow, which became the second object of this class in the NGC 5846 group.","nearby cE galaxy made by the Virtual Observatory (VO) fed workflow, which became the second object of this class in the NGC 5846 group." + We study its internal properties using 3D-spectroscopy and datasets at different wavelength domains available in the VO and data archives., We study its internal properties using 3D-spectroscopy and datasets at different wavelength domains available in the VO and data archives. + ? describe a VO workflow constructed to search cE galaxies in nearby clusters., \citet{Chilingarian+09} describe a VO workflow constructed to search cE galaxies in nearby clusters. +" We extended it in order to detect cE candidates also in nearby groups, which would have higher extent on the sky because of smaller distances and, therefore, require different settings of theSEXTRACTOR software (?)."," We extended it in order to detect cE candidates also in nearby groups, which would have higher extent on the sky because of smaller distances and, therefore, require different settings of the software \citep{BA96}." +". To test the modified workflow, we decided to use HST images of the central part of the Virgo cluster and the NGC 5846 group known to contain ""legacy"" cEs, NGC 4486B and NGC 58464. Surprisingly, the workflow detected a new compact object in the HST WFPC2 images of the NGC 5846 group 3.1 arcmin south-east of the group centre, which turned to have a spectrum in the Sloan Digital Sky Survey Data Release 7 (SDSS DR7, ?)), proving its membership in the group."," To test the modified workflow, we decided to use HST images of the central part of the Virgo cluster and the NGC 5846 group known to contain “legacy” cEs, NGC 4486B and NGC 5846A. Surprisingly, the workflow detected a new compact object in the HST WFPC2 images of the NGC 5846 group 3.1 arcmin south-east of the group centre, which turned to have a spectrum in the Sloan Digital Sky Survey Data Release 7 (SDSS DR7, \citealp{SDSS_DR7}) ), proving its membership in the group." +" The galaxy is identified as SDSS J150634.27--013331.6, we will call it NGC 5846cE throughout the rest of theLetter."," The galaxy is identified as SDSS J150634.27+013331.6, we will call it NGC 5846cE throughout the rest of the." +". Recently, NGC 5846cE was mentioned by ? where it was classified as an UCD."," Recently, NGC 5846cE was mentioned by \citet{EZ10} where it was classified as an UCD." +" The NGC 5846 group, the third massive structure in the local Universe after the Virgo and Fornax clusters, has been intensively studied in the past and, therefore, numerous complementary datasets in different wavelength domains are available in the VO."," The NGC 5846 group, the third massive structure in the local Universe after the Virgo and Fornax clusters, has been intensively studied in the past and, therefore, numerous complementary datasets in different wavelength domains are available in the VO." + The group is located at a distance of 26.1 Mpc in the Virgo III cloud of galaxies (??) corresponding to a spatial scale 126 pc arcsec! and a distance modulus 32.08 mag.," The group is located at a distance of 26.1 Mpc in the Virgo cloud of galaxies \citep{Tully82,EZ10} + corresponding to a spatial scale 126 pc $^{-1}$ and a distance modulus $32.08$ mag." +" We used the calibrated optical WFPC2 HST images in F555W and F814W (total integration times 2200 and 2300 sec) available from the Hubble Legacy and found by the cE search workflow to studying the internal structure of NGC 5846cE. The galaxy has a small size on the sky, therefore we used other data sources only for the integrated photometric measurements."," We used the calibrated optical WFPC2 HST images in $F555W$ and $F814W$ (total integration times 2200 and 2300 sec) available from the Hubble Legacy and found by the cE search workflow to studying the internal structure of NGC 5846cE. The galaxy has a small size on the sky, therefore we used other data sources only for the integrated photometric measurements." + All photometric data provided in this are corrected for the Galactic extinction (?).., All photometric data provided in this are corrected for the Galactic extinction \citep{SFD98}. +" The NGC 5846 group is included in the footprints of (1) the GRA Data Release of the Medium Imaging Survey (MIS) by the Galaxy Evolution Explorer (GALEX) and (2) the Data Release 6plus (DR6+) of the Large Area Survey (LAS) of the UKIRT Infrared Deep Sky Survey (UKIDSS, ?)), thus providing photometric measurements in far-UV, near-UV, and four near-IR. broadband filters YJHK in addition to the 5-band optical ugriz photometry from SDSS DR7."," The NGC 5846 group is included in the footprints of (1) the GR4 Data Release of the Medium Imaging Survey (MIS) by the Galaxy Evolution Explorer (GALEX) and (2) the Data Release 6plus (DR6+) of the Large Area Survey (LAS) of the UKIRT Infrared Deep Sky Survey (UKIDSS, \citealp{Lawrence+07}) ), thus providing photometric measurements in far-UV, near-UV, and four near-IR broadband filters $YJHK$ in addition to the 5-band optical $ugriz$ photometry from SDSS DR7." +" We took Petrosian magnitudes from SDSS and UKIDSS, applying Vega-to-AB zero-point correction for the latter ones according to ?,, and total FUV and NUV magnitudes from GALEX."," We took Petrosian magnitudes from SDSS and UKIDSS, applying $AB$ zero-point correction for the latter ones according to \citet{HWLH06}, and total FUV and NUV magnitudes from GALEX." +" There are publicly available archival Spitzer Space Telescope images obtained with the Infrared Array Camera (IRAC) in four photometric bands centered at 3.6, 4.5, 5.8, and 8.0 wm. We obtained total AB magnitudes of NGC 5846cE in the IRAC bands usingSEXTRACTOR and parameters)."," There are publicly available archival Spitzer Space Telescope images obtained with the Infrared Array Camera (IRAC) in four photometric bands centered at 3.6, 4.5, 5.8, and 8.0 $\mu$ m. We obtained total $AB$ magnitudes of NGC 5846cE in the IRAC bands using and parameters)." +" Several central pixels of the galaxy image in all HST WFPC2 frames are saturated, therefore no analysis of the inner region is possible."," Several central pixels of the galaxy image in all HST WFPC2 frames are saturated, therefore no analysis of the inner region is possible." + The images were background-subtracted usingSEXTRACTOR., The images were background-subtracted using. +" Then we obtained light profiles of NGC 5846cE in both photometric bands by fitting elliptical isophotes with free orientation, ellipticity, and disky/boxy parameters using the task in the data processing environment."," Then we obtained light profiles of NGC 5846cE in both photometric bands by fitting elliptical isophotes with free orientation, ellipticity, and disky/boxy parameters using the task in the data processing environment." +" In Fig 1 we present the radial behaviour of ellipticity e=1—b/a, and positional angle (top and middle panels) and the F555W—F814W colour profile."," In Fig \ref{figpaell} we present the radial behaviour of ellipticity $e = 1 +- b/a$, and positional angle (top and middle panels) and the $F555W - F814W$ colour profile." + The positional angle remains stable at PA=127 deg at all radii., The positional angle remains stable at $PA = 127$ deg at all radii. + The galaxy has very round outer isophotes (e~ 0.05) becoming significantly prolate inwards with the ellipticity reaching (e— 0.3) at r=0.125 kpc=1 arcsec., The galaxy has very round outer isophotes $e \sim 0.05$ ) becoming significantly prolate inwards with the ellipticity reaching $e = 0.3$ ) at $r = 0.125$ $ = 1$ arcsec. +" Closer to the centre the ellipticity starts to decrease, however, we could not measure it at r«0.3 arcsec due to the saturation mentioned above."," Closer to the centre the ellipticity starts to decrease, however, we could not measure it at $r<0.3$ arcsec due to the saturation mentioned above." + The radial behaviour of PA and e is identical in the two photometric bands., The radial behaviour of $PA$ and $e$ is identical in the two photometric bands. + The isophotes remain purely elliptical without any signature of diskyness/boxiness., The isophotes remain purely elliptical without any signature of diskyness/boxiness. + The reconstructed colour profile is completely flat having a value of F555W—F814W=0.90 mag., The reconstructed colour profile is completely flat having a value of $F555W-F814W=0.90$ mag. + We computed a 2-dimensional colour map of NGC 5846cEapplying the Voronoi adaptive binning (?) with a, We computed a 2-dimensional colour map of NGC 5846cEapplying the Voronoi adaptive binning \citep{CC03} with a +" ACDAM cosmology with (O,,.Q4.h)=(0.27.0.73.0.044.0.71) (Spergeletal...2003).","$\Lambda$ CDM cosmology with $(\Omega_{m}, \Omega_{\Lambda}, \Omega_{b}, h) +=(0.27, 0.73, 0.044, 0.71)$ \citep{spergel03}." + We model the GRB allerelow source as a relativistic shell expanding into a homogeneous interstellar medium (15M) with particle number density 7 at redshift z., We model the GRB afterglow source as a relativistic shell expanding into a homogeneous interstellar medium (ISM) with particle number density $n$ at redshift $z$. +" The shell initially has an isotropic equivalent enerev £. a Lorentz [actor so. an opening hall-angle 9 and a width in the source frame eT(1-4-z)!. where we assume ,!c0 and the shell width being related to the observed GRD duration 7 (Ixobavashi.Piran.&Sari.1997)."," The shell initially has an isotropic equivalent energy $E$, a Lorentz factor $\gamma_{0}$, an opening half-angle $\theta$ and a width in the source frame $c T (1+z)^{-1}$, where we assume $\gamma_{0}^{-1}<\theta$ and the shell width being related to the observed GRB duration $T$ \citep{kobayashi97}." +. The true energv is given by E;=6?E/2., The true energy is given by $E_{j} = \theta^{2} E/2$. + Two shocks are formed: a forward shock heating the ISM and a reverse shock decelerating the shell., Two shocks are formed: a forward shock heating the ISM and a reverse shock decelerating the shell. + At these shocks electrons are accelerated. and magnetic fields are anmplilied. leading to the svnchrotron allerelow emission.," At these shocks electrons are accelerated and magnetic fields are amplified, leading to the synchrotron afterglow emission." +" We assume (hat. accelerated electrons have a power-law distribution of the Lorentz factor 54 as ολαx5,Pd, lor e>54, (ari.Piran.&Naravan1998).."," We assume that accelerated electrons have a power-law distribution of the Lorentz factor $\gamma_{e}$ as $N(\gamma_{e}) d\gamma_{e} +\propto \gamma_{e}^{-p} d\gamma_{e}$ for $\gamma_{e}>\gamma_{m}$ \citep{sari98b}." +". We also assume that fractions e; (e,,) and epy (egy) Of the shock energy go into electrons and magnetic fields. respectively. at the forward (reverse) shock. where the subscripts / and r indicate the forward and reverse shock. respectively."," We also assume that fractions $\epsilon_{e,f}$ $(\epsilon_{e,r})$ and $\epsilon_{B,f}$ $(\epsilon_{B,r})$ of the shock energy go into electrons and magnetic fields, respectively, at the forward (reverse) shock, where the subscripts $f$ and $r$ indicate the forward and reverse shock, respectively." + We also assume adiabatic shocks., We also assume adiabatic shocks. +" Under the above assumptions. we can calculate (he spectra and lieht curves of the afterglows as summarized in ο,"," Under the above assumptions, we can calculate the spectra and light curves of the afterglows as summarized in \ref{sec:model}." +" There are 10 model parameters: E. 0. n. p. eig. €gp. €or € n . d/(19-2). but we assume e,y= for simplicity. so the actual number of parameters is 9."," There are $10$ model parameters: $E$, $\theta$, $n$, $p$, $\epsilon_{e,f}$, $\epsilon_{B,f}$, $\epsilon_{e,r}$, $\epsilon_{B,r}$ , $\gamma_{0}$ , $T/(1+z)$, but we assume $\epsilon_{e,f}=\epsilon_{e,r}$ for simplicity, so the actual number of parameters is 9." +" We consider (he possible difference between (he magnetic field in the forward and reverse shocks. by using Ry=(ep,65,5)7 in equation (A23)) instead of ej). since the ejected shell may be endowed with magnetic fields from the central source Mészüros 2003).."," We consider the possible difference between the magnetic field in the forward and reverse shocks, by using ${\cal R}_{B}=(\epsilon_{B,r}/\epsilon_{B,f})^{1/2}$ in equation \ref{eq:rB}) ) instead of $\epsilon_{B,r}$, since the ejected shell may be endowed with magnetic fields from the central source \citep[e.g.,][]{zhang03b}." + We also take the sidewav expansion of the jet. (he non-relativistic regime. and the reverse shock emission into account (see ??)).," We also take the sideway expansion of the jet, the non-relativistic regime, and the reverse shock emission into account (see \ref{sec:model}) )." + In the following we examine several sets of model parameters (hat are physically motivated ab high redshilt. as summarized in Table 1..," In the following we examine several sets of model parameters that are physically motivated at high redshift, as summarized in Table \ref{tab:model}." + We estimate the maximum redshift out to which these alterglows could be detected with the VLA. LOFAR and SIXA.," We estimate the maximum redshift out to which these afterglows could be detected with the VLA, LOFAR and SKA." + We also evaluate the peak fluxes of the allerelows at the observed frequency around »~LOO MlIZ to discuss thedetectability of (he 21em absorption line later in ?? and ?7.., We also evaluate the peak fluxes of the afterglows at the observed frequency around $\nu \sim 100$ MHz to discuss thedetectability of the 21cm absorption line later in \ref{sec:z>6} and \ref{sec:z<6}. . +the clockwise disc by up to a few hundred. km/sec (which is the order of circular velocity at. these. clistances),the clockwise disc by up to a few hundred km/sec (which is the order of circular velocity at these distances). + The velocity dispersion even in a very compact Giant. Molecular Cloud. with mass of καν 3105M. and size of 1. parsee. is only ~10 km/sec.," The velocity dispersion even in a very compact Giant Molecular Cloud, with mass of say $3\times 10^4 \msun$ and size of 1 parsec, is only $\sim 10$ km/sec." + Vhus the only way to create the observed kinematically distinct population of stars would be to postulate the existence of two or more streams (filaments) inside the cloud that pass on opposite sides of aand doοί ect completely mixed. before. forming. stars., Thus the only way to create the observed kinematically distinct population of stars would be to postulate the existence of two or more streams (filaments) inside the cloud that pass on opposite sides of and do get completely mixed before forming stars. + Given our numerical experiments in this paper. this does not seem implausible if the cooling time is short 3%1.," Given our numerical experiments in this paper, this does not seem implausible if the cooling time is short $\beta \simlt 1$." + What is interesting in this scenario is that the massive stars of the counter-clockwise population would then have to form very quickly. Le. on a dynamical timescale. or else gaseous orbits would be mixed.," What is interesting in this scenario is that the massive stars of the counter-clockwise population would then have to form very quickly, i.e., on a dynamical timescale, or else gaseous orbits would be mixed." +" Lhe rotation period. scales approximately as Lon=3000(/5""""7. vears. so this is quite fast indeed."," The rotation period scales approximately as $T_{\rm rot} = +3000 (R/5'')^{3/2}$ years, so this is quite fast indeed." + 1t should also be noted that recent. N-bocly simulations (??7) imply that it would have been very dillieult. for the high eccentricities and inclinations of the dynamically hotter counter-clockwise feature to have been formed. [rom a Lat. cold dise via scattering processes.," It should also be noted that recent N-body simulations \citep{Cuadra08, Alexander07} imply that it would have been very difficult for the high eccentricities and inclinations of the dynamically hotter counter-clockwise feature to have been formed from a flat, cold disc via scattering processes." + A single disc progenitor for both GC stellar features is therefore largely. ruled out., A single disc progenitor for both GC stellar features is therefore largely ruled out. + 1n contrast. in the case of the collision of two clouds as considered here. it is almost too casy to obtain an inner near- disc and a kinematically diverse stellar population farther out.," In contrast, in the case of the collision of two clouds as considered here, it is almost too easy to obtain an inner near-circular disc and a kinematically diverse stellar population farther out." + We therefore favor a model where a GMC collided. with a pre-existing cloud. or structure. such as à massive larger-scale disc. c.g.. similar to the observed €ND.," We therefore favor a model where a GMC collided with a pre-existing cloud or structure, such as a massive larger-scale disc, e.g., similar to the observed CND." + The observed. well defined. Dat. geometrically thin and near-circular/mildly. eccentric clockwise stellar svstem (?) is best. created: via a gentle accumulation of gas.," The observed well defined, flat, geometrically thin and near-circular/mildly eccentric clockwise stellar system \citep{PaumardEtal06} is best created via a gentle accumulation of gas." + Several independent major gas deposition events lead to a warped disc. and/or mixed svstems consisting of several stellar rings or cliscs co-existing at the same radius.," Several independent major gas deposition events lead to a warped disc, and/or mixed systems consisting of several stellar rings or discs co-existing at the same radius." + To avoid this happening. the inner disc must be created: on time scale longer than the critical rotation time. which is estimated at Fo~ few c107 vears.," To avoid this happening, the inner disc must be created on time scale longer than the critical rotation time, which is estimated at $t_{\rm cr} \sim$ few $\times 10^4$ years." + While these results are based on analytical arguments (7) and our simplified one-parameter -cooling model. we note that the results of 2). corroborate this as their inner stellar disc appears to be too eccentric to match the data of 7).," While these results are based on analytical arguments \citep{NC05} and our simplified one-parameter $\beta$ -cooling model, we note that the results of \cite{Bonnell08} + corroborate this as their inner stellar disc appears to be too eccentric to match the data of \cite{PaumardEtal06}." +" Deposition of eas in the inner disc takes place on the longest of two timescales: the cooling time foo, and the collision time. feacBafea. where A and. ο are the cloud's size and. velocity. magnitude."," Deposition of gas in the inner disc takes place on the longest of two timescales: the cooling time $t_{\rm cool}$ and the collision time, $t_{\rm +coll} \sim R_{\rm cl}/v_{\rm cl}$, where $R_{\rm cl}$ and $v_{\rm cl}$ are the cloud's size and velocity magnitude." + In. the appendix we estimate the realistic cloud cooling timecollision. and show that it is always much shorter than the dynamical time unless magnetic fields are very important.," In the appendix we estimate the realistic cloud cooling time, and show that it is always much shorter than the dynamical time unless magnetic fields are very important." + We are thus left with the onlv option to require the collision itself be more prolonged than £4., We are thus left with the only option to require the collision itself be more prolonged than $t_{\rm cr}$. +" Estimating the velocity of the cloud at 04~150 km/sec. which is of order ol circular velocities in the inner Galaxy outside the inner parsec. we find £a=Rofera~10vearsF2,Lpe- Where Aa is the size of the cloud in parsecs."," Estimating the velocity of the cloud at $v_{\rm cl} +\sim 150$ km/sec, which is of order of circular velocities in the inner Galaxy outside the inner parsec, we find $t_{\rm coll} = R_{\rm cl}/v_{\rm cl} \sim +10^4 \hbox{years}\; R_{\rm cl, pc}$, where $R_{\rm cl, pc}$ is the size of the cloud in parsecs." + We hence require the cloud to be larger than a few parsees to satisfy Fogzfos., We hence require the cloud to be larger than a few parsecs to satisfy $t_{\rm coll}\simgt t_{\rm cr}$. + Note that this size is not necessarily the original size of the cloud if the cloud gets tidally disrupted before it makes the impact., Note that this size is not necessarily the original size of the cloud if the cloud gets tidally disrupted before it makes the impact. + In the latter case we can take A.) to be the radial clistance to the centre of the Galaxy at which the tidal disruption took place., In the latter case we can take $R_{\rm cl}$ to be the radial distance to the centre of the Galaxy at which the tidal disruption took place. + Finally. the location of the collision should. not be too far from the central parsec. or else too much angular momentum would have to be lost to deposit a significant amount of eas at 0.1 pe.," Finally, the location of the collision should not be too far from the central parsec, or else too much angular momentum would have to be lost to deposit a significant amount of gas at $\sim 0.1$ pc." + Another argument going in the same cirection comes rom a comparison of the radial distribution of gas and stars in our simulations with the observed. stellar. distribution (?).., Another argument going in the same direction comes from a comparison of the radial distribution of gas and stars in our simulations with the observed stellar distribution \citep{PaumardEtal06}. + Phe former is too compact. ic. all of our simulations deposited: mass within the inner arcesecond.," The former is too compact, i.e., all of our simulations deposited mass within the inner arcsecond." + La aclelition. if that was indeed the case 6 million. vears ago. hen wwould have received a significant amount of fuel. enough o become at least a bright AGN.," In addition, if that was indeed the case 6 million years ago, then would have received a significant amount of fuel, enough to become at least a bright AGN." + Given the long. viscous imes in the inner areseconc. ccould actually continue to acerete this fuel now.," Given the long viscous times in the inner arcsecond, could actually continue to accrete this fuel now." + However. it is well known that there is no geometricallv thin and optically thick disc inside the inner aresecond of citepbalcke9.Naravanü2.Cuacdraüd..," However, it is well known that there is no geometrically thin and optically thick disc inside the inner arcsecond of \\citep{Falcke97,Narayan02,Cuadra04}." + Eliminating the gaseous disc by star formation is not an option as there are not enough massive voung stars observed. there., Eliminating the gaseous disc by star formation is not an option as there are not enough massive young stars observed there. + Taking all these constraints together. we believe that the most realistic scenario would be a GALC of the order of a few parsecs in size striking the CND at the distance of a few pagsecs [romA.," Taking all these constraints together, we believe that the most realistic scenario would be a GMC of the order of a few parsecs in size striking the CND at the distance of a few parsecs from." +.. This scenario could perhaps explain the origin of the inner edge of the CND at /?z2 pe if the refilling time scale is longer than the age of the voung stars., This scenario could perhaps explain the origin of the inner edge of the CND at $R\approx2$ pc if the refilling time scale is longer than the age of the young stars. + Alternatively such a cloud. could. self-collide if the impact parameter with respect to iis small enough. but the cloud. needs to be very structured. c.g. essentially consist of several smaller clouds or filaments.," Alternatively such a cloud could self-collide if the impact parameter with respect to is small enough, but the cloud needs to be very structured, e.g., essentially consist of several smaller clouds or filaments." + In this paper we presented: several simulations. of cloud-cloud collisions aimed at reproducing gas flows that could have formed (a) gaseous disc(s) in the central parsee of our Galaxy. as well as the resulting star formation.," In this paper we presented several simulations of cloud-cloud collisions aimed at reproducing gas flows that could have formed (a) gaseous disc(s) in the central parsec of our Galaxy, as well as the resulting star formation." + We found the gas cooling time and the impact parameter of the collision to inlluence the outcome significantly., We found the gas cooling time and the impact parameter of the collision to influence the outcome significantly. +" Nevertheless. there are several robust results: (a) the inner near-circular and outer eccentric orbital structure of the stars formed. there: (b) a sharply peakecl mass distribution of stars V,(R)~ l/H7: (0) that the gaseous. and stellar discs are warped."," Nevertheless, there are several robust results: (a) the inner near-circular and outer eccentric orbital structure of the stars formed there; (b) a sharply peaked mass distribution of stars $\Sigma_*(R) \sim +1/R^2$ ; (c) that the gaseous and stellar discs are warped." + ‘These results are in good accordance with the observations., These results are in good accordance with the observations. + The breakdown of the stellar system into one or more components is sensitive to the initial conditions and. also the cooling parameter., The breakdown of the stellar system into one or more components is sensitive to the initial conditions and also the cooling parameter. + ]t appears that a GAIC with a size of one to a few parsees. self-colliding on a nearly radial orbit. or striking the CND at the cistanee of a few parsec from ccould. explain the known observational data satisfactorily.," It appears that a GMC with a size of one to a few parsecs, self-colliding on a nearly radial orbit, or striking the CND at the distance of a few parsec from could explain the known observational data satisfactorily." + Future observations and. modelling might put. interesting upper limits on the timescale over which the massive stars [ormed in the GC. and detail the structure and orbit of such a GMCC.," Future observations and modelling might put interesting upper limits on the timescale over which the massive stars formed in the GC, and detail the structure and orbit of such a GMC." +analysis of the two stars.,analysis of the two stars. + However. the temperatures adopted are supported by the Balmer lines. and we confirmed the assuned metallicity by computing svuthetic spectra near a few Fe lines with good gf values;," However, the temperatures adopted are supported by the Balmer lines, and we confirmed the assumed metallicity by computing synthetic spectra near a few Fe lines with good $gf$ values." + We did not explicitly took into account au cnhhancement in Ie in the stellar atmospheres: however. the expected effect on irou abundauce determination is uceleible (seediscussiousinCarettactal.2006:Bra-eachactal.2010) ancl this is most probably true for the other elemeuts.," We did not explicitly took into account an enhancement in He in the stellar atmospheres; however, the expected effect on iron abundance determination is negligible \citep[see discussions in][]{carretta06,bragagliahe} and this is most probably true for the other elements." + Although we did not do a detailed analysis of other heavy-clemeut species. we noted that lines of c.e.. Ti and Ca have approximately the same streneth iu both stars.," Although we did not do a detailed analysis of other heavy-element species, we noted that lines of e.g., Ti and Ca have approximately the same strength in both stars." + None of the suggested pollution sources that contribute hydrogseu-burniug products to newly forming stars should contribute elements bevoud $i., None of the suggested pollution sources that contribute hydrogen-burning products to newly forming stars should contribute elements beyond Si. + Heasier à oor Fo-peak abuudances should be the same in all NCC 2808 stars. and our spectra do not coutracict this expectation.," Heavier $\alpha$ or Fe-peak abundances should be the same in all NGC 2808 stars, and our spectra do not contradict this expectation." + Adopting the stellar parameters defined above. we used standard routines to compute svuthetic spectra for some particularly interesting Clements: N Grom the NIJ feature at 3360 A)). Al (from the 3961 rresonant line). Me (from the Mg b lines near 5180 À)). C (from the CII features in the C-band near 1300 Aj). and Na (from the 8183-01 ddoublet).," Adopting the stellar parameters defined above, we used standard routines to compute synthetic spectra for some particularly interesting elements: N (from the NH feature at 3360 ), Al (from the 3961 resonant line), Mg (from the Mg b lines near 5180 ), C (from the CH features in the G-band near 4300 ), and Na (from the 8183-94 doublet)." + The spectral svutheses shown in the figures were computed with the LTE spectroscopic analysis code ROSA (Οτο.1988) for the atomic lines (Al. Me. and Na) and MOOCG (Sueden1973). for the molecules (NIL CTL).," The spectral syntheses shown in the figures were computed with the LTE spectroscopic analysis code ROSA \citep{rosa} for the atomic lines (Al, Mg, and Na) and MOOG \citep{moog} for the molecules (NH, CH)." + However. all the svuthesis work was checked independently using both codes: results are in very good agreement.," However, all the synthesis work was checked independently using both codes; results are in very good agreement." + Abundances for all eleiieuts are presented in Table 1., Abundances for all elements are presented in Table \ref{info}. + The derived values have conservative error estinates (anostlv due to the uncertain coutimmiun placement) of 0.1 dex for Na (and Fe). aud 0.2 dex for N. €. Ale. and Al.," The derived values have conservative error estimates (mostly due to the uncertain continuum placement) of 0.1 dex for Na (and Fe), and 0.2 dex for N, C, Mg, and Al." + We stress however that the main result of our analysis les in the between the abundance patterns of the two stars. moro than in the absolute values for the chemical abundances.," We stress however that the main result of our analysis lies in the between the abundance patterns of the two stars, more than in the absolute values for the chemical abundances." + We will show that the light-clemeut differcuces between rMS-star aud bMS-star exceed their uncertainties., We will show that the light-element differences between rMS-star and bMS-star exceed their uncertainties. + Comparison of observed and svuthetie spectra are shown Fie., Comparison of observed and synthetic spectra are shown in Fig. + 2 for NTT. Ali. CIL and Ale features.," \ref{synth} for NH, Al, CH, and Mg features." + Frou the closestin observed/svuthetic matches we estimated the abuudances that are given in Table 1.., From the closest observed/synthetic matches we estimated the abundances that are given in Table \ref{info}. + The expectations are that N and Al should be increased. and C aud Ale should be decreased i bMS-star with respect to he values for rMS-star (tle one of supposedly.normal. xumnordial composition). following what has been fouud or evolved RGB stars (e... Ivausetal.2001:Cohen2002:Ramirez&Cohen2003:Carrettaetal. 20," The expectations are that N and Al should be increased, and C and Mg should be decreased in bMS-star with respect to the values for rMS-star (the one of supposedly, primordial composition), following what has been found for evolved RGB stars (e.g., \citealt{ivans01,cohen02,rc03,carretta09b}) )." +095)., Fig. + Fie. 2. demoustrates that the two stars have different ight-clement spectra., \ref{synth} demonstrates that the two stars have different light-element spectra. + This is most obvious for N: the NID absorption is mich stronger m bMS-star than iu rMS-star., This is most obvious for N: the NH absorption is much stronger in bMS-star than in rMS-star. + Neither details iu the spectimm normalization ror (πια) differences iu the atinosphlierie parameters cau account for this difference., Neither details in the spectrum normalization nor (small) differences in the atmospheric parameters can account for this difference. + The Al abundance was derived ouly from the 3961 rresonance line. since its doublet partner at 3011 jis a blend (Arpiguy&Magaiu 1983).," The Al abundance was derived only from the 3961 resonance line, since its doublet partner at 3944 is a blend \citep{arpigny83}." +. The svuthesis was computed acopting the Ca abundance appropriate for NGC 2808 (|Ca/Fe|2|0.31. Carrettaetal.200953) to reproduce the Ca II EK lines.," The synthesis was computed adopting the Ca abundance appropriate for NGC 2808 ([Ca/Fe]=+0.34, \citealt{carretta09b}) ) to reproduce the Ca H K lines." + The values for Al and Me given in Table 1 are corrected for NLTE effects according to (ιοποetal.(2001): the corrections are about |0.5 dex for Aland |0.06 dex for Me. respectively. cor both stars.," The values for Al and Mg given in Table \ref{info} are corrected for NLTE effects according to \cite{gehren04}; the corrections are about +0.5 dex for Al and +0.06 dex for Mg, respectively, for both stars." + The huge abundance of N found for bDATS-stay (which also had decreased €) can be explained oulv with the ransformiation of (virtually) all oxvecn iuto nitrogen., The huge abundance of N found for bMS-star (which also had decreased C) can be explained only with the transformation of (virtually) all oxygen into nitrogen. + Our findines sccm to indicate that we are secing. iu he eas from which this star formed. the outcome of he complete CNO cvele.," Our findings seem to indicate that we are seeing, in the gas from which this star formed, the outcome of the complete CNO cycle." + Actually. if we combine the C/Fe] and [N/Fo] values of Table 1. with the solar C. N. and O abuudances by Asplundetal.(2009) and with the maximum |O/Fe] ratio for RGB stars in NGC 2808 (Carrettaetal.2006)). even large depletions of O 'Fe|«1) cannot reproduce a coustaut sui of the(o CNO eleiieuts," Actually, if we combine the [C/Fe] and [N/Fe] values of Table \ref{info} with the solar C, N, and O abundances by \cite{asplund09} and with the maximum [O/Fe] ratio for RGB stars in NGC 2808 \citealt{carretta06}) ), even large depletions of O $<-1$ ) cannot reproduce a constant sum of the CNO elements." + This would be reproduced by assuning [N/Fe|-1.1 for bMS-star., This would be reproduced by assuming $\sim 1.4$ for bMS-star. + We uote that a systematic offset of ~0.6 dex in N abunudauces from our analysis would produce a roughly solar scaled [N/Fe] ratio for rMS-stir. which would agree fairly well with the values usually asstuned for feld halo stars (Crattouetal. 2000)).," We note that a systematic offset of $\sim 0.6$ dex in N abundances from our analysis would produce a roughly solar scaled [N/Fe] ratio for rMS-star, which would agree fairly well with the values usually assumed for field halo stars \citealt{gratton00}) )." + Ouce again. what is most important is the difference between the derived: abundauces. aud this is a sound result.," Once again, what is most important is the difference between the derived abundances, and this is a sound result." + Unufortunatelv. it was not possihle to iueasure OQ abundances for these two stars. since the O triplet at τπτ]τπτ lis weak and falls in a waveleneth region where the sky subtraction is difficult for these very faint objects.," Unfortunately, it was not possible to measure O abundances for these two stars, since the O triplet at 7771-7774 is weak and falls in a wavelength region where the sky subtraction is difficult for these very faint objects." + However. we were able to estimate the Na abundances.," However, we were able to estimate the Na abundances." + Fie., Fig. + 5 shows observed aud svuthetic spectra surroundiug the 5152-01 NNa lines., \ref{na} shows observed and synthetic spectra surrounding the 8183-94 Na lines. + We see in the figure that the Na lines are stronger iu bMS-star than in rMS-star and this is reflected iu the abundance ratios indicated im Table |, We see in the figure that the Na lines are stronger in bMS-star than in rMS-star and this is reflected in the abundance ratios indicated in Table \ref{info}. + These abundances inclide NLTE corrections (about -0.1 dex) as reccomended by Crattonetal.(1999)., These abundances include NLTE corrections (about -0.1 dex) as reccomended by \cite{gratton99}. +. The chief lanitation is the stroug telhwic-line contamination in this spectral region., The chief limitation is the strong telluric-line contamination in this spectral region. + The tellurics were climinated by division of the program star spectra with that of a hot. rapidly rotating star. using an IRAF routine for this task.," The tellurics were eliminated by division of the program star spectra with that of a hot, rapidly rotating star, using an IRAF routine for this task." + The cleaning quality is much better for the bluest of the two lines. so that our Na abundances rest ou that suele feature.," The cleaning quality is much better for the bluest of the two lines, so that our Na abundances rest on that single feature." + They are qualitatively confirmed by the other line and by the relative streneths of the Na D lues;, They are qualitatively confirmed by the other line and by the relative strengths of the Na D lines. + Unfortunately. strong interstellar absorption aud sky enussion made the derivation of Na abundance from the D lines less secure. given the radial velocity at the time of observation and the moderate resolution of the N-shooter spectra.," Unfortunately, strong interstellar absorption and sky emission made the derivation of Na abundance from the D lines less secure, given the radial velocity at the time of observation and the moderate resolution of the X-shooter spectra." + The present Al and Meg results are in good agreement with those found from high resohition UVES spectra of 12 red giauts im NGC 2808 bv Carrettaetal.(2009)b)., The present Al and Mg results are in good agreement with those found from high resolution UVES spectra of 12 red giants in NGC 2808 by \cite{carretta09b}. +. Iu Fig., In Fig. + 6 we plot the Me-Al auticorrelatiou for the RGB stars and the two MS stars analyzed here., \ref{almg} we plot the Mg-Al anticorrelation for the RGB stars and the two MS stars analyzed here. + Apart from a possible small zero-point effect due to the use of differeut lues. corrections for NLTE. ete..," Apart from a possible small zero-point effect due to the use of different lines, corrections for NLTE, etc.," + the two AIS stars do uicely participate in the same treud defined by the giauts., the two MS stars do nicely participate in the same trend defined by the giants. + The £MS and the bMS star fall iu the Mevich/Al-poor and Me-poor/Alvich groups. respectively.," The rMS and the bMS star fall in the Mg-rich/Al-poor and Mg-poor/Al-rich groups, respectively." + This result indicates that the extreme abundance pattern of the, This result indicates that the extreme abundance pattern of the +when the Lorentz factor of the ejecta drops toκ1/8. the edge of the jet becomes visible.,"when the Lorentz factor of the ejecta drops to$\gamma < 1/ \theta$, the edge of the jet becomes visible." +" Phus the light curve will steepen by £75, where f is the observed time.", Thus the light curve will steepen by $t^{-3/4}$ where $t$ is the observed time. + This is called the edge ellect (Mésszárros Rees 1999)., This is called the edge effect (Mésszárros Rees 1999). + Another ellect is called the lateral expansion effect., Another effect is called the lateral expansion effect. +" 1ο.joacls (1997. 19992. b) has shown that the lateral expansion (at sound speed) of a relativisticjet (5,2 2) will cause the blastwave to decelerate more quickly. leading to a sharp break in the afterglow light curve."," Rhoads (1997, 1999a, b) has shown that the lateral expansion (at sound speed) of a relativistic jet $\gamma \geq 2$ ) will cause the blastwave to decelerate more quickly, leading to a sharp break in the afterglow light curve." + The breaking point is again determined by 5ον1/6., The breaking point is again determined by $\gamma \sim 1/\theta$. + The power law decay indices of afterglows from CGIUS 9080326 and 980519 are anomalously large. a~2.0 (Ciroot et al.," The power law decay indices of afterglows from GRB 980326 and 980519 are anomalously large, $\alpha \sim 2.0$ (Groot et al." + 1908: Owens et al., 1998; Owens et al. + 1998: Halpern et al., 1998; Halpern et al. + 1999). and optical light curves of GRB 990123 and 990510 even show obvious steepening at {51 2 d (Ixulkarni et al.," 1999), and optical light curves of GRB 990123 and 990510 even show obvious steepening at $t \geq 1$ — 2 d (Kulkarni et al." + 1999: Harrison et al., 1999; Harrison et al. + 1999: C'astro-Tirado et al., 1999; Castro-Tirado et al. + 1999)., 1999). + Recently GRB 970228 was also reported to have a large index of à1.73 (Calama et al., Recently GRB 970228 was also reported to have a large index of $\alpha \sim 1.73$ (Galama et al. + 1999b3., 1999b). + Phese phenomena have been widely regarded as evidence for relativistic jets (Sari. Piran Llalpern 1999).," These phenomena have been widely regarded as evidence for relativistic jets (Sari, Piran Halpern 1999)." + llowever. numerical studies of some other authors (Panaitescu Mésszárros 1998: Mocerski. Sikora Bulik 1999) have shown that due to the increased swept-up matter and the time delay of the large angle emission. the sidewavy expansion of the jet does not lead to an obvious cdimming of the afterglow.," However, numerical studies of some other authors (Panaitescu Mésszárros 1998; Moderski, Sikora Bulik 1999) have shown that due to the increased swept-up matter and the time delay of the large angle emission, the sideway expansion of the jet does not lead to an obvious dimming of the afterglow." + Thus there are two opposite conclusions about the jet ellect: the analytical solution preclicts a sharp break. while the numerical calculation shows no such sharp breaks.," Thus there are two opposite conclusions about the jet effect: the analytical solution predicts a sharp break, while the numerical calculation shows no such sharp breaks." + The condition is quite confusing., The condition is quite confusing. + We need to clarify this question urgently., We need to clarify this question urgently. + In a recent paper (lluang et al., In a recent paper (Huang et al. + 1999c). we have developed a. refined: model to describe the evolution. of jetted GARB remnants.," 1999c), we have developed a refined model to describe the evolution of jetted GRB remnants." + Due. to some crucial refinemoents in the dynamics. we can follow the overall evolution of a realistic jet till its expanding velocity is as small as ~10c.," Due to some crucial refinements in the dynamics, we can follow the overall evolution of a realistic jet till its expanding velocity is as small as $\sim 10^{-3} c$." + Many new results were obtained in that paper. e.g.. (1) We found no obvious break in the optical light curve duringilself. ie. the time determined winc10 is not a breaking point.," Many new results were obtained in that paper, e.g., (i) We found no obvious break in the optical light curve during, i.e. the time determined by $\gamma \sim 1/\theta$ is not a breaking point." + But in some cases. obvious breaks does appear at the relativistic-Newtonian ransition point. (," But in some cases, obvious breaks does appear at the relativistic-Newtonian transition point. (" +i) Cenerally speaking. the Newtonian hase of jet evolution is characterized by a sharp decay. of optical afterglows. with the power law timing index àcL8 2.1..,"ii) Generally speaking, the Newtonian phase of jet evolution is characterized by a sharp decay of optical afterglows, with the power law timing index $\alpha \geq 1.8$ — $2.1$." + The most interesting finding may be that whether he relativistic-Newtonian break appears or not depends on £.. the parameter characterizing the energy. equipartition oetween electrons and protons.," The most interesting finding may be that whether the relativistic-Newtonian break appears or not depends on $\xi_{\rm e}$, the parameter characterizing the energy equipartition between electrons and protons." + This has given strong hints on the solution to the confusing problem. mentioned just above: whether an obvious break appears or not may depend On parvanietCrs., This has given strong hints on the solution to the confusing problem mentioned just above: whether an obvious break appears or not may depend on parameters. + In this paper. we go further to investigate what impact will other parameters have on the optical light curves. based on the model developed. by Huang et al. (," In this paper, we go further to investigate what impact will other parameters have on the optical light curves, based on the model developed by Huang et al. (" +19996).,1999c). + The organization of the paper is as follows., The organization of the paper is as follows. + For completeness. the model is briellv. described in Section 2.," For completeness, the model is briefly described in Section 2." + ln Section 3 we investigate various parameter effects. ancl present. our detailed numerical results. mainly in the form of optical light curves.," In Section 3 we investigate various parameter effects and present our detailed numerical results, mainly in the form of optical light curves." + We find that the light curve break is really alfected by many other parameters., We find that the light curve break is really affected by many other parameters. + Section 4 is our final conclusion. and Section 5 is a brief discussion.," Section 4 is our final conclusion, and Section 5 is a brief discussion." + We use the model developed by Luang ct al. (, We use the model developed by Huang et al. ( +19996).,1999c). +" ""Ehis model has the following advantages: (i) Lt is applicable to th radiative and acdiabatie blastwaves. and appropriate for roth ultra-relativistic and non-relativistic stages."," This model has the following advantages: (i) It is applicable to both radiative and adiabatic blastwaves, and appropriate for both ultra-relativistic and non-relativistic stages." + “Phe mocel even allows the radiative ellicieney € to evolve with time. so hat it can trace the evolution of a realistic GRB remnant. which is believed to evolve from the highly raciative regime o the adiabatic one (Dai. Huang Lu 1999). (," The model even allows the radiative efficiency $\epsilon$ to evolve with time, so that it can trace the evolution of a realistic GRB remnant, which is believed to evolve from the highly radiative regime to the adiabatic one (Dai, Huang Lu 1999). (" +ii) Lt takes he lateral expansion of the jet into account.,ii) It takes the lateral expansion of the jet into account. + The lateral speed is given by a reasonable expression. (, The lateral speed is given by a reasonable expression. ( +ii) Lt also akes many other ellects into account. for example. the cooling of electrons. ancl the equal arrival time surfaces.,"iii) It also takes many other effects into account, for example, the cooling of electrons, and the equal arrival time surfaces." + Vhe model is very convenient for numerical studies., The model is very convenient for numerical studies. + Llere. or completeness. we describe the model briellv.," Here, for completeness, we describe the model briefly." + For details ease see Huang et al. (, For details please see Huang et al. ( +19996).,1999c). + Let & be the radial coordinate in the burster frame: / be the observer's time: συ and M. be the initial Lorentz factor and ejecta mass and ϐ the half opening angle of the ejecta., Let $R$ be the radial coordinate in the burster frame; $t$ be the observer's time; $\gamma_0$ and $M_{\rm ej}$ be the initial Lorentz factor and ejecta mass and $\theta$ the half opening angle of the ejecta. + The burst energy is Ly=59M., The burst energy is $E_0 = \gamma_0 M_{\rm ej} c^2$. + The evolution of radius (2). the swept-up mass (m). the half opening angle (0) and the Lorentz factor (5) is described by (Lluane et al.," The evolution of radius $R$ ), the swept-up mass $m$ ), the half opening angle $\theta$ ) and the Lorentz factor $\gamma$ ) is described by (Huang et al." + 19996): where 3=VERl/s. n is the number density of surrounding interstellar medium.(18M). my is the mass of proton. e is the co-moving lateral radius of the ejecta (Rhoacs 1999a: Moderski. Sikora Bulik 1999). ος is the co-moving sound speed. and ο is the radiative efficiency.," 1999c): where $\beta = \sqrt{\gamma^2-1}/\gamma$, $n$ is the number density of surrounding interstellar medium(ISM), $m_{\rm p}$ is the mass of proton, $a$ is the co-moving lateral radius of the ejecta (Rhoads 1999a; Moderski, Sikora Bulik 1999), $c_{\rm s}$ is the co-moving sound speed, and $\epsilon$ is the radiative efficiency." + A reasonable expression for ὃς is where 4z(45|1)/(35) is the acliabatic index., A reasonable expression for $c_{\rm s}$ is where $\hat{\gamma} \approx (4 \gamma + 1)/(3 \gamma)$ is the adiabatic index. +" In the ultra-relativistic limit {51.52 4/3). equation (5)) gives ο2=e{91 and in the non-relativistic limit (5~1.52 5/3). we simply get ez25 η, "," In the ultra-relativistic limit $\gamma \gg 1, \hat{\gamma} \approx 4/3$ ), equation \ref{cs5}) ) gives $c_{\rm s}^2 = c^2/3$; and in the non-relativistic limit $\gamma \sim 1, \hat{\gamma} \approx 5/3$ ), we simply get $c_{\rm s}^2 = 5 \beta^2 c^2/9$ ." +"As usual.we assume that the magnetic energy. density in the co-moving frame is a fraction € of the total thermal energy density (Dai. Luang Lu 1999). BCssw=, £pc. and that the shock accelerated electrons. carry a fraction"," As usual,we assume that the magnetic energy density in the co-moving frame is a fraction $\xi_{\rm B}^2$ of the total thermal energy density (Dai, Huang Lu 1999), $B'^2 / 8 \pi = \xi_{\rm B}^2 e'$ , and that the shock accelerated electrons carry a fraction" +"When estimating a photometric redshift, we assume that there is a mapping between a galaxy's true redshift z, and photometry vector p such that z=Fp).","When estimating a photometric redshift, we assume that there is a mapping between a galaxy's true redshift $z$, and photometry vector $\mathbf{p}$ such that $z = F({\mathbf p})$." +" If such a mapping exists, then the information to find F should be latent in a large galaxy catalogue where both photometry and spectroscopic redshifts are available."," If such a mapping exists, then the information to find $F$ should be latent in a large galaxy catalogue where both photometry and spectroscopic redshifts are available." +" Self-organisation of such training set will naturally encode P, and therefore a SOM acan be used to predict the redshifts (or indeed any other parameter that was involved in the training) of new galaxies where, for example, only a subset of photometry is known."," Self-organisation of such a training set will naturally encode $F$, and therefore a SOM can be used to predict the redshifts (or indeed any other parameter that was involved in the training) of new galaxies where, for example, only a subset of photometry is known." + This technique could be easily applied to a large imaging survey that contains a smaller spectroscopic component in order to robustly estimate redshifts for those galaxies lacking spectroscopic coverage., This technique could be easily applied to a large imaging survey that contains a smaller spectroscopic component in order to robustly estimate redshifts for those galaxies lacking spectroscopic coverage. +" The advantage of using a SOM for photometric redshift estimation is that it is completely empirical, requires no assumptions about the spectral properties of the galaxies and involves no user intervention to guide the learning tthe learning is unsupervised)."," The advantage of using a SOM for photometric redshift estimation is that it is completely empirical, requires no assumptions about the spectral properties of the galaxies and involves no user intervention to guide the learning the learning is unsupervised)." +" However, there are two fundamental limitations to the method:"," However, there are two fundamental limitations to the method:" +constrain the photon cussion spectrum of the excess. shedding light ou its origin.,"constrain the photon emission spectrum of the excess, shedding light on its origin." + We perform a joiut analvsis of the CBI results aud the new ACBAR data at(>2000. assunune the coutributious frou primary auisotropy are known.," We perform a joint analysis of the CBI results and the new ACBAR data at$\ell>2000$, assuming the contributions from primary anisotropy are known." + In cach experiucut. the theoretical baud-powoers for priuary anisotropy are calculated from the product of the ACDME power spectrun and baud window fictions. which are then subtracted from the observed baud-powers.," In each experiment, the theoretical band-powers for primary anisotropy are calculated from the product of the $\Lambda$ CDM power spectrum and band window functions, which are then subtracted from the observed band-powers." +" A two-dimensional likelihood fuuctiou is calculated from these excess baud-powers aud thei uncertainties. where the two paraneters are the ratio of the 230CIIz and 150CIIz excess. C. and the power at 30CIIz. o3, (Gu "," A two-dimensional likelihood function is calculated from these excess band-powers and their uncertainties, where the two parameters are the ratio of the $30\,$ GHz and $150\,$ GHz excess, $\zeta$ and the power at $30\,$ GHz, $\sigma^2_{30}$ (in $\mu K_{CMB}^2$ )." +We thon marginalize over the oy parameter and plot ανα].the likelihood fuuctiou for the power ratio ¢ in Figure L., We then marginalize over the $\sigma^2_{30}$ parameter and plot the likelihood function for the power ratio $\zeta$ in Figure \ref{fig:excess}. + Since ACBAR iicasures siguificautlv less power at 150CIIz. the data disfavor sources that result in a blackbody spectrin(56. ¢= 1).," Since ACBAR measures significantly less power at $150\,$ GHz, the data disfavor sources that result in a blackbody spectrum, $\zeta=1$ )." + Using the ACDAR and CBI frequency response and equation (6)). we calculate the power ratio ¢=L3 for the thermal SZ effect.," Using the ACBAR and CBI frequency response and equation \ref{szs}) ), we calculate the power ratio $\zeta=4.3$ for the thermal SZ effect." + From the likehhood plot. we couclude that it is 1.5 times more likely that the excess seen by CBI aud ACBAR is the result of the thermal SZ effect (¢= L3) than a primordial process (ὁ= l1).," From the likelihood plot, we conclude that it is 4.5 times more likely that the excess seen by CBI and ACBAR is the result of the thermal SZ effect $\zeta=4.3$ ) than a primordial process $\zeta=1$ )." + Since the expected ratio of flux at 30 IIz to 150 GIIz from radio sources is expected to be «0.1. such sources are disfavored as being responsible for the excess power seen by CDI at about the same significance (~ 1.20) with which ACBAR detects excess power.," Since the expected ratio of flux at $30\,$ GHz to $150\,$ GHz from radio sources is expected to be $<$ 0.1, such sources are disfavored as being responsible for the excess power seen by CBI at about the same significance $\sim 1.2 \sigma$ ) with which ACBAR detects excess power." + Additional data from ACBAR or other higher frequency instruments will be required to make a cefinitive statement about the ore of the excess power seen by CDI and DIMÁ., Additional data from ACBAR or other higher frequency instruments will be required to make a definitive statement about the origin of the excess power seen by CBI and BIMA. +" Iu this section. we estimate cosimological parameters or a nunmal iuflation-based. spatially-flat.— tilted. eravitationally leused. ACDAM model characterized by. six xwanieters, and then investigate models including extra xuwanueters to test extensions of the theory."," In this section, we estimate cosmological parameters for a minimal inflation-based, spatially-flat, tilted, gravitationally lensed, $\Lambda$ CDM model characterized by six parameters, and then investigate models including extra parameters to test extensions of the theory." +" For our base uodel. the six parameters are: the plysical deusitv of xuvonie and dark matter. Oh? and 0,77: à coustaut spectral iudex ον and amplitude Iud, of the primordial vower spectu. the optical depth to last scatterine. Tr: and the ratio of the sound horizon at last scattering o the angular diameter distauce. 0."," For our base model, the six parameters are: the physical density of baryonic and dark matter, $\Omega_bh^2$ and $\Omega_ch^2$; a constant spectral index $n_s$ and amplitude $\ln A_s$ of the primordial power spectrum, the optical depth to last scattering, $\tau$ ; and the ratio of the sound horizon at last scattering to the angular diameter distance, $\theta$." +" The primordial comoving scalar curvature power spectrums is expressed as Paik)=Ah)Us where the normalization (pivot-»)ut) wavenunber is chosen to be fk,=0.05MpeB"," The primordial comoving scalar curvature power spectrum is expressed as ${\cal P}_s(k) = A_s (k/k_n)^{(n_s-1)}$, where the normalization (pivot-point) wavenumber is chosen to be $k_n += 0.05\, {\rm Mpc}^{-1}$." + The parameter @ maps angles observed at our location ο comoving spatial scales at recombination: changing 0 shifts the cutive acoustic peak/valley aud damping patte of the CAMB power spectra., The parameter $\theta$ maps angles observed at our location to comoving spatial scales at recombination; changing $\theta$ shifts the entire acoustic peak/valley and damping pattern of the CMB power spectra. + Additional paramcters are erived from the basic set., Additional parameters are derived from the basic set. +" These include: the energy chsityv of a cosmological coustaut in uuits of the critical density. O4: the age of universe: the cuerey density of non-relativistic matter. O,,: the (near) matter fluctuation ish !IMpe spheres. ox: the redshift to reionization. L4: aoeud the value of the present dav IIubble coustaut. fy. iu units of Mpc +."," These include: the energy density of a cosmological constant in units of the critical density, $\Omega_\Lambda$; the age of universe; the energy density of non-relativistic matter, $\Omega_m$; the (linear) matter fluctuation in $8h^{-1}$ Mpc spheres, $\sigma_8$; the redshift to reionization, $z_{re}$; and the value of the present day Hubble constant, $H_0$, in units of $^{-1}$ $^{-1}$." + Tilted primordial spectra indicate the presence of a tensor-incduced anisotropv componcut. however. we do not iuchide this potential contribution due to its uncertain amplitude.," Tilted primordial spectra indicate the presence of a tensor-induced anisotropy component, however, we do not include this potential contribution due to its uncertain amplitude." + The influence of the tensor COL)sent woulL only be significant at low-f. not iu the regine which ACBAR probes.," The influence of the tensor component would only be significant at $\ell$, not in the regime which ACBAR probes." + We also restrict this work to flat ACDAL models. inotivated by the observed. curvature being so close to zero.," We also restrict this work to flat $\Lambda$ CDM models, motivated by the observed curvature being so close to zero." +" However. we have run models with non-zero curvature Oy. and find that they reproduce the standard ecometrical degeneracy associated with 0 aud Ox,"," However, we have run models with non-zero curvature $\Omega_K$, and find that they reproduce the standard geometrical degeneracy associated with $\Omega_K$ and $\Omega_\Lambda$." + We have also considered two exteusious to the basic model which coul potentially inipact the interpretation of the ACBAR hancelpowers., We have also considered two extensions to the basic model which could potentially impact the interpretation of the ACBAR bandpowers. +" These extended models include flat AC'DAL inodccds with a runndus scalar spectral dex characterized by the derivative οΠα(κ). aud flat ACDAL aodels with a Sunvaev-Zeldovicl1 contribution to the angular power spectrum with amplitude parametrized by 077, "," These extended models include flat $\Lambda$ CDM models with a running scalar spectral index characterized by the derivative $dn_s/d\ln k (k_n)$, and flat $\Lambda$ CDM models with a Sunyaev-Zel'dovich contribution to the angular power spectrum with amplitude parametrized by $\alpha^{\rm SZ}$." +We also investigate a model where both a runing spectral iudex aud a SZ contribution are considered. stuultanecously., We also investigate a model where both a running spectral index and a SZ contribution are considered simultaneously. +" The parameter constraints are obtained using a Alonte Carlo Mawkov Chain (CMCMC) sampling of the uultidiueusional likelihood as a function of model xuauneters,", The parameter constraints are obtained using a Monte Carlo Markov Chain (MCMC) sampling of the multi-dimensional likelihood as a function of model parameters. + Our software is based ou tle ]mblicly available package λεν, Our software is based on the publicly available package \citep{Lewis:2002ah}. + CAIB angular power spectra aud matter power spectra are computes using the code (?).., CMB angular power spectra and matter power spectra are computed using the code \citep{lewis00}. + We approximate the ful non-Coussiun baudpower Usclihoods with an offset lognormal distribution (7) ound by explicit fits (see NOL for a detailed discussion of he calculation)., We approximate the full non-Gaussian bandpower likelihoods with an offset lognormal distribution \citep{bond2000} found by explicit fits (see K04 for a detailed discussion of the calculation). + Our παπάαχ results include he effects of weal eravitational lenxiug ou the CAIB (?7)..," Our standard results include the effects of weak gravitational lensing on the CMB \citep{seljak96,lewis00}." + Leusine effects in the telmpcrature spectruni are expected to become significant at scales (>1000. hence it is müportant to include this effect when interpreting the ACBAR results.," Lensing effects in the temperature spectrum are expected to become significant at scales $\ell > 1000$, hence it is important to include this effect when interpreting the ACBAR results." + The major effect of leusing ix a scale-depeudent smoothing of the angular power spectrun which diminishes the peaks aud vallevs of the spectrm., The major effect of lensing is a scale-dependent smoothing of the angular power spectrum which diminishes the peaks and valleys of the spectrum. + Tuclusion of lensing iuin the model improves the fit to the data for all experiment combinations., Inclusion of lensing in the model improves the fit to the data for all experiment combinations. + However. we fiud that the parameter mean values and 1:mcertaitics are largely unaffectec w the inclusion of lensine with some exceptions. in particular the iutroductiou of leuxing tends to increase the value of os.," However, we find that the parameter mean values and uncertainties are largely unaffected by the inclusion of lensing with some exceptions, in particular the introduction of lensing tends to increase the value of $\sigma_8$ ." + The typical computation consists of 5 separate chains. each having different initial random parameter choices.," The typical computation consists of $8$ separate chains, each having different initial random parameter choices." + The chains are run until the largest eigenvalue of the Cehnan-Rubin test is sumaller than 0.1 after accounting for burudn., The chains are run until the largest eigenvalue of the Gelman-Rubin test is smaller than 0.1 after accounting for burn-in. + ΕΠΟΠΠ priors with very broac cüstributions are assuned or the basic parameters., Uniform priors with very broad distributions are assumed for the basic parameters. + The standard run also includes a weak prior on the ITubble coustaut (15«90 + 1) and on the age ofthe uulverse (>LO Cars)., The standard run also includes a weak prior on the Hubble constant $45 < H_0 < 90$ $^{-1}$ $^{-1}$ ) and on the age of the universe $>10$ Gyrs). + We also investigate the influeuce of adding Large Seale Structure (LSS) data from the 2 deoree Field Cilaxy Redshitt Survey (2dFGRS) (2) aud 1ο Sloan Digital Sky Survev (SDSS) (?).., We also investigate the influence of adding Large Scale Structure (LSS) data from the 2 degree Field Galaxy Redshift Survey (2dFGRS) \citep{cole05} and the Sloan Digital Sky Survey (SDSS) \citep{tegmark04}. . + When iucludiuue the LSS data.we use only the baud powers for leugth scales larger than koeOAPApe ! to avoid non-linear clusering and scale- galaxybiasine effects.," When including the LSS data,we use only the band powers for length scales larger than $k \sim 0.1 h$ $^{-1}$ to avoid non-linear clustering and scale-dependent galaxybiasing effects." +" We nuwelnalize over a paranieter 55JD whichB describesH the (linear). biasing+ of. the ealaxy-galaxy power spectrum for L, σαaxies relative to the underlyingmass density power specrun.", We marginalize over a parameter $b^2_g$ which describes the (linear) biasing of the galaxy-galaxy power spectrum for $L_\star$ galaxies relative to the underlyingmass density power spectrum. +" We adopt a Cassial prior on centered. around b,=10 witha conservative width equivalentbo to ób,=0: 3: all parameters", We adopt a Gaussian prior on $b^2_g$ centered around $b_g=1.0$ with a conservative width equivalent to $\delta b_g = 0.3$ ; all parameters +(7)..,\citep{Soltan1982}. + We have only included solutions in both this and the following sections (Ligures 11- 16)) that describe. quasars which would lie in the SDSS catalog with Aeg=Aly and redshift corresponding to fy., We have only included solutions in both this and the following sections (Figures \ref{fig:allpl4panel}- \ref{fig:allintbothMgoverlap}) ) that describe quasars which would lie in the SDSS catalog with $M_{BH} = M_0$ and redshift corresponding to $t_0$. + We can also restrict the above solutions to lie at. least 0.2 dex from cach boundary to account for scatter. due to intrinsic variability in the observed quasar population., We can also restrict the above solutions to lie at least $0.2$ dex from each boundary to account for scatter due to intrinsic variability in the observed quasar population. + However. there are no non-trivial solutions lving at least 0.2 dex away from cach boundary with fy=4.5 Gyr.," However, there are no non-trivial solutions lying at least $0.2$ dex away from each boundary with $t_0 = 4.5$ Gyr." + This may be because the boundaries change discontinuously when the quasar redshift moves across a bin boundary in Table L.. and some bouncdaries in this table match poorly.," This may be because the boundaries change discontinuously when the quasar redshift moves across a bin boundary in Table \ref{table:boundaries}, and some boundaries in this table match poorly." + The greatest mismatches occur when virial masses transition from using to broad emission lines at z=0.8., The greatest mismatches occur when virial masses transition from using to $\beta$ broad emission lines at $z = 0.8$. + Phere are many wavs one might. correct. [or this binning problem., There are many ways one might correct for this binning problem. + As here we are simply developing models in an effort to establish rough guidelines for what properties are required of quasar evolution. we will just give the results of using a simple interpolation.," As here we are simply developing models in an effort to establish rough guidelines for what properties are required of quasar evolution, we will just give the results of using a simple interpolation." + In Figures 13. and 14. we take the boundaries in Table 1. to be correct at the midpoint (in time) of each in. and interpolate in both slope and intercept to find the roundaries used at other redshifts.," In Figures \ref{fig:plint4panel} and \ref{fig:expint4panel}, we take the boundaries in Table \ref{table:boundaries} to be correct at the midpoint (in time) of each bin, and interpolate in both slope and intercept to find the boundaries used at other redshifts." + Using these interpolated »»undaries. Figures 13. and 14 include parameters lor all racks of the sort included. in Figures 11. and 12.. with Πο1075.","1993), in the $7.5 - M_{up}$ mass range for $Z < 10^{-5}$ and in the $0.1 - M_{up}$ mass range for $Z > 10^{-5}$." + My is a free parameter adjusted to reproduce the observed O/H abundance ratio., $M_{up}$ is a free parameter adjusted to reproduce the observed O/H abundance ratio. + 4) We assume different stellar yields. dependent on initial stellar mass (71) and on initial stellar metallicity Z;. provided by different authors.," 4) We assume different stellar yields, dependent on initial stellar mass $m$ ) and on initial stellar metallicity $Z_i$, provided by different authors." + However they do not cover all the mass range., However they do not cover all the mass range. + In the case of LIMS. we have a complete library from ΜΜ. to MM.. and for MS. the mass range covered goes from MM. to 80 M...," In the case of LIMS, we have a complete library from $_\odot$ to $_\odot$ and for MS, the mass range covered goes from $_\odot$ to 80 $_\odot$." + In order to fill the mass gap (from MM.. to9 MMO). we proceeded as follows: for the 6Η/Μ.€7.5mass range we assigned the stellar yield values given by mass fraction (p;) of the MM.. star.," In order to fill the mass gap (from $_\odot$ to $\odot$ ), we proceeded as follows: for the $6 < m/M_\odot \leq 7.5 $mass range we assigned the stellar yield values given by mass fraction $p_i$ ) of the $_\odot$ star." + In the same way. for the 7.5«Η/Μ.«9 mass range we assigned the p; values of the MM. star.," In the same way, for the $7.5 < +m/M_\odot < 9$ mass range we assigned the $p_i$ values of the $_\odot$ star." +" Specifically. lem 4.1) For LIMS we adopt the stellar yields by Karakas Lattanzio (2007). and the integrated yields used by our model are given by: The results for ten elements. five initial stellar metallicities. and two different M,,, values are presented in Tables 4 and 5."," Specifically, 1cm 4.1) For LIMS we adopt the stellar yields by Karakas Lattanzio (2007), and the integrated yields used by our model are given by: The results for ten elements, five initial stellar metallicities, and two different $M_{up}$ values are presented in Tables 4 and 5." + lem 4.2) For MS. we consider the stellar yields obtained from models for the pre-SN stage and the SN stage.," 1cm 4.2) For MS, we consider the stellar yields obtained from models for the pre-SN stage and the SN stage." + The pre-SN yields are taken from the work of the Geneva group (Maeder 1992: Meynet Maeder 2002: Hirschi et al., The pre-SN yields are taken from the work of the Geneva group (Maeder 1992; Meynet Maeder 2002; Hirschi et al. + 2005: Hirschi 2007)., 2005; Hirschi 2007). + The SN yields are taken from Woosley Weaver (1995) adopting their models B for the 12 30MM. range and their models C. for the 35 - 40MM. range.," The SN yields are taken from Woosley Weaver (1995) adopting their models B for the 12 - $_\odot$ range and their models C, for the 35 - $_\odot$ range." + We combine the Geneva group vields with the Woosley Weaver yields using the prescription proposed by Carigi Hernandez (2008) where they connect the mass of the carbon-oxygen cores (Mca) from the Geneva group to Μου from Woosley Weaver. using the prescription given by Portinari et al. (," We combine the Geneva group yields with the Woosley Weaver yields using the prescription proposed by Carigi Hernandez (2008) where they connect the mass of the carbon-oxygen cores $_{CO}$ ) from the Geneva group to $_{CO}$ from Woosley Weaver, using the prescription given by Portinari et al. (" +1998).,1998). + Under these assumptions the He. C. N. and O yields are equal to the pre-SN ones. but for heavier elements the yields are similar to the SN ones.," Under these assumptions the He, C, N, and O yields are equal to the pre-SN ones, but for heavier elements the yields are similar to the SN ones." + Form>40 tthe adopted yields for the heavier elements are similar to those given for m=40 Μ., For $m > 40$ the adopted yields for the heavier elements are similar to those given for $m = 40$ . +... The chemical contribution of MS is in IRA. and the integrated yields are given by:," The chemical contribution of MS is in IRA, and the integrated yields are given by:" +" within nearborders.consideralsogalaxiesthatlocated2"" because the correct. estimation of Voronoi cell volume is not possible in this case.","consider also galaxies that located within } near borders, because the correct estimation of Voronoi cell volume is not possible in this case." +" Ο volunie-limited sample. is complete up to 17.7"" but contains also about LOO more fainter galaxies.", Our volume-limited sample is complete up to $17.7^{m}$ but contains also about 100 more fainter galaxies. + Final number of galaxies in the sample is 6186., Final number of galaxies in the sample is 6786. + We applied the second-order 3D. Voronoi tessellation to our sample 6786 galaxies and obtained 2196 eeometric pairs and 2394 single galaxies galaxies of whole sample are in pairs and are singles)., We applied the second-order 3D Voronoi tessellation to our sample 6786 galaxies and obtained 2196 geometric pairs and 2394 single galaxies galaxies of whole sample are in pairs and are singles). + We divided our samples of geometric pairs and singles on four equal parts by the parameter of isolation p and s. respectively.," We divided our samples of geometric pairs and singles on four equal parts by the parameter of isolation $p$ and $s$, respectively." + A quater of each sample with the highest isolation degree we called as (549 pairs and 598 singles)., A quater of each sample with the highest isolation degree we called as (549 pairs and 598 singles). + It means that the isolated. pairs and singles havep>Qs and s«(Qj. respectively. Q5 is third quartile and Qy is the first quartile.," It means that the isolated pairs and singles have $p > Q_{3}$ and $s < Q_{1}$, respectively, $Q_{3}$ is third quartile and $Q_{1}$ is the first quartile." + See values of quartiles in Table 1.., See values of quartiles in Table \ref{tab1d}. + Fig., Fig. + 3 shows the distributions of neighbouring galaxies number for galaxies that are members of pairs and singles., \ref{1} shows the distributions of neighbouring galaxies number for galaxies that are members of pairs and singles. + We can see from Fig., We can see from Fig. + 3. that number of neighbours is varricel through range from 4 to 30 galaxies., \ref{1} that number of neighbours is varried through range from 4 to 30 galaxies. + Isolated. galaxies have more neighbours than galaxies in other samples in average., Isolated galaxies have more neighbours than galaxies in other samples in average. + lt is a feature of the second-order Voronoi tessellation (see above)., It is a feature of the second-order Voronoi tessellation (see above). + Galaxies in isolated pairs have approximately less by half neighbours than isolated. galaxies because of the pair's neighbours distribute among two members., Galaxies in isolated pairs have approximately less by half neighbours than isolated galaxies because of the pair's neighbours distribute among two members. + Independently we applved the thirc-order 3D. Voronoi tessellation to our galaxy sample and obtained 1153 ecometric triplets of whole sample)., Independently we applyed the third-order 3D Voronoi tessellation to our galaxy sample and obtained 1182 geometric triplets of whole sample). + The/ quater (297)n of triplet sample with the highest isolation degree />(Q5 we called asisolated., The quater (297) of triplet sample with the highest isolation degree $t>Q_{3}$ we called as. +.. Values of all quartiles for triplets can be found in Table 1.., Values of all quartiles for triplets can be found in Table \ref{tab1d}. + The distribution. of number of neighbouring triplets is drawn in Vig. 4.., The distribution of number of neighbouring triplets is drawn in Fig. \ref{t1}. + As can be seen. this picture looks the same as for distribution of neighbouring galaxies number in case of the second-order Voronol tesscllation (Fig. 3)).," As can be seen, this picture looks the same as for distribution of neighbouring galaxies number in case of the second-order Voronoi tessellation (Fig. \ref{1}) )." + We cross-correlatecl our results with other samples., We cross-correlated our results with other samples. + In the first order we compared. pairs and triplets of our sample with “Tago et al. (, In the first order we compared pairs and triplets of our sample with Tago et al. ( +2008) groups selected by. modified friencs- method using the same release of SDSS.,2008) groups selected by modified friends-of-friends method using the same release of SDSS. + From 965, From 965 +lations that anv flight requiring a delav longer than one vear would have to be undertaken with a TAUVEX serformineg as originally planned.,nations that any flight requiring a delay longer than one year would have to be undertaken with a TAUVEX performing as originally planned. + Since the mirrors had con singled as the likely source of degradation. they would have to be recoated.," Since the mirrors had been singled as the likely source of degradation, they would have to be recoated." +" This, fortunately, could be done in India and would not require reshipping the wiVload to Israel. then back to Iudia."," This, fortunately, could be done in India and would not require reshipping the payload to Israel, then back to India." + The prolonged TAUVEN saga described above bees a 111111ver of conclusions reearding the structure of the TAUVEN project managed in Ixacl., The prolonged TAUVEX saga described above begs a number of conclusions regarding the structure of the TAUVEX project managed in Israel. + The first deals with ondssons bv the Isracli side: it was a iudstake ou je part of the science team to agree to continue the xoject after the national satellite and launcheLael pronised by ISA in the original call for proposals becaue unavailable., The first deals with omissions by the Israeli side; it was a mistake on the part of the science team to agree to continue the project after the national satellite and launcher promised by ISA in the original call for proposals became unavailable. +" This naive approach. that provided 10 exit. strateeies throughout the duration of the project. is uxerstandable ou the part of scientists, but ultinately did not pay off."," This naive approach, that provided no exit strategies throughout the duration of the project, is understandable on the part of scientists, but ultimately did not pay off." + The second imistake on the part of he TAUVEX Priicipal Duvestieators was to allow ISA to take full courol of the midget and of the final decisions regarding tlie conduct of the project at ELOp. xwule relegating themselves to an advisory role.," The second mistake on the part of the TAUVEX Principal Investigators was to allow ISA to take full control of the budget and of the final decisions regarding the conduct of the project at El-Op, while relegating themselves to an advisory role." + Duriug he long vears of this projec this caused the relaxatio1 of the tasks the Prime Contractor (ELOp) was require to perform. such as the iistallation of contamination inonitoring devices within TAUWVEN.," During the long years of this project this caused the relaxation of the tasks the Prime Contractor (El-Op) was required to perform, such as the installation of contamination monitoring devices within TAUVEX." + Similarly. uo insisting on a thorough iwestieation of the implicaions of the lone-term storage of the completed TAUVEN OU Was a uistake and the improper storage caused the throughput reduction presumably by degrading the nunror coatings.," Similarly, not insisting on a thorough investigation of the implications of the long-term storage of the completed TAUVEX OU was a mistake and the improper storage caused the throughput reduction presumably by degrading the mirror coatings." +" ISA also relaxed the requirement to inaliain full doctuuentation for the project: the conclusion is that now there is no wav to know what was doje with the flight model. when, or dy whom."," ISA also relaxed the requirement to maintain full documentation for the project; the conclusion is that now there is no way to know what was done with the flight model, when, or by whom." + On he Indian side. ISRO carries significant lane since it entered into an agreement with ISA to launch TAUVEN on-board GSAT-1 but was rot able to fulfil it.," On the Indian side, ISRO carries significant blame since it entered into an agreement with ISA to launch TAUVEX on-board GSAT-4 but was not able to fulfil it." +" ISA couk not enforce the launch :vereclnents with either RIXA «x ISRO because no punitive consequences were include Lin the launch aerecmens,", ISA could not enforce the launch agreements with either RKA or ISRO because no punitive consequences were included in the launch agreements. +" ISRO inisled, willingly or 1uwillinely both science teanis. Tuclian aud Ixacli, as to he status of the GSLV laaucher aud of the GSAT-I sateHite."," ISRO misled, willingly or unwillingly, both science teams, Indian and Israeli, as to the status of the GSLV launcher and of the GSAT-4 satellite." + The delavs certainly did not help the state of the TAUVEN iiirrors and catsed uinecessary and significaif expenses to the Israeli side., The delays certainly did not help the state of the TAUVEX mirrors and caused unnecessary and significant expenses to the Israeli side. +" If the one-vear delay (2008-2009) in the integrajon would have been known in advance, it is possible twat ELOp would have had time to consider refurbishing the TAUVEN optics to recover the original respouse instead of seeping TAUVEN i1 the clean room of ISRO."," If the one-year delay (2008-2009) in the integration would have been known in advance, it is possible that El-Op would have had time to consider refurbishing the TAUVEX optics to recover the original response instead of keeping TAUVEX in the clean room of ISRO." + Ilowever. one should also meution here t10 STICCCSSCS 6the project. in particular (a) the built-in flexibility of the pavload that allowed a relatively easv shift from SRG to GSAT-I. and (b) the stric adherence of the Prine) Contractor (ELOp) to the differeiut schedules imposed. by the two satellites.," However, one should also mention here the successes of the project, in particular (a) the built-in flexibility of the payload that allowed a relatively easy shift from SRG to GSAT-4, and (b) the strict adherence of the Prime Contractor (El-Op) to the different schedules imposed by the two satellites." + Additioially. the cooperaion of the technical teams at boh LaveΠΜ ludustries i1 Russia aud ISITE iu Tnclia facilitated t10 testingc» at various stagesOo and the easy aud oefficieit integration of the FAL wi↕↓≺∶≋∡≚⊺∟↓," Additionally, the cooperation of the technical teams at both Lavotchkin Industries in Russia and ISITE in India facilitated the testing at various stages and the easy and efficient integration of the FM with GSAT-4." +"∙ With an eve to the future, the Indian and. Isracli science teams expect ISA and ISRO to reach ali agreement very soon to allow a full-recovered TAUVENE to be launched and perform its original mission in a timely manner."," With an eye to the future, the Indian and Israeli science teams expect ISA and ISRO to reach an agreement very soon to allow a fully-recovered TAUVEX to be launched and perform its original mission in a timely manner." +" In particular, the science team proposed to refurbish and recoat the nirrors: this is expected to recover the original seusitivitv of TAUVEN."," In particular, the science team proposed to refurbish and recoat the mirrors; this is expected to recover the original sensitivity of TAUVEX." + Iowever. when this paper was completed no such decision. or indeed," However, when this paper was completed no such decision, or indeed" + Iowever. when this paper was completed no such decision. or indeed.," However, when this paper was completed no such decision, or indeed" +αἱ all.,at all. + Postponing for a moment seeking a correlation with more subtle statistical tools (han the human eve. we will first (av to find a plot which gives something more obvious.," Postponing for a moment seeking a correlation with more subtle statistical tools than the human eye, we will first try to find a plot which gives something more obvious." + Perhaps the problem lies in using blue Iuminosities., Perhaps the problem lies in using blue luminosities. + Ht is well known that starbursts can skew the mass-to-light ratio in this band. drastically: the nearby dwarl IC 10 is nearly as luminous as (he spiral M32 in D. but much fainter in (he infrared.," It is well known that starbursts can skew the mass-to-light ratio in this band drastically; the nearby dwarf IC 10 is nearly as luminous as the spiral M33 in $B$, but much fainter in the infrared." + Using A-band luminosity. which should be a much better measure of the actual mass of the galaxies. we arrive al the right panel of Figure (2)).," Using $K$ -band luminosity, which should be a much better measure of the actual mass of the galaxies, we arrive at the right panel of Figure \ref{scatter1}) )." + There is. again. no visible correlation.," There is, again, no visible correlation." + There are significantly fewer galaxies with A photometry (o contribute to the synthetic gravity. field. but the effect of the unmeasured objects should be slight: none are as bright as the Magellanic Clouds in D. and so the combined effect of all of them is less than about that of one giant galaxy.," There are significantly fewer galaxies with $K$ photometry to contribute to the synthetic gravity field, but the effect of the unmeasured objects should be slight: none are as bright as the Magellanic Clouds in $B$, and so the combined effect of all of them is less than about that of one giant galaxy." + Recalling that the anisotropic model was calculated to bea better fit to the data. we tum to the peculiar velocities based on that model for Figure (2)).," Recalling that the anisotropic model was calculated to be a better fit to the data, we turn to the peculiar velocities based on that model for Figure \ref{hscatter1}) )." + Again (here is no improvement apparent., Again there is no improvement apparent. + Perhaps the uncertainties in (he various quantiües are large enough to obscure any correlation: that is. perhaps the data are simply not good enough vet to see a signal.," Perhaps the uncertainties in the various quantities are large enough to obscure any correlation; that is, perhaps the data are simply not good enough yet to see a signal." + Adding (he uncertainties in svnthetic eravitv and peculiar velocitv as error bars eives Figure (4))., Adding the uncertainties in synthetic gravity and peculiar velocity as error bars gives Figure \ref{scatter2}) ). + Some points on the plots are clearly very uncertain indeed., Some points on the plots are clearly very uncertain indeed. + Though it appears that there are enough good data to delineate a (rend. if it existed. including all the errors serves {ο obscure the matter more than it helps.," Though it appears that there are enough good data to delineate a trend, if it existed, including all the errors serves to obscure the matter more than it helps." + Using only the 63 points with the best svnthetie gravity uncertainties. we have Figure (5)).," Using only the 63 points with the best synthetic gravity uncertainties, we have Figure \ref{scatter3}) )." + As one would expect. points have been preferentially removed at synthetic eravilies of large (positive and negative) magnitude. since these are most subject to distance errors in nearby. galaxies: and there is a bit of structure due to small-number statistics.," As one would expect, points have been preferentially removed at synthetic gravities of large (positive and negative) magnitude, since these are most subject to distance errors in nearby galaxies; and there is a bit of structure due to small-number statistics." + However. no real trend is visible. and the errors here are certainly small enough to show one.," However, no real trend is visible, and the errors here are certainly small enough to show one." + ] have claimed that there is no correlation on anv of the plots presented: however. it is very difficult to prove the absence ofany correlation. (," I have claimed that there is no correlation on any of the plots presented; however, it is very difficult to prove the absence of correlation. (" +In [act there could be a very. strong correlation of a particular kind. sav a high-[requency sine wave. which would be entirely masked by the errors.,"In fact there could be a very strong correlation of a particular kind, say a high-frequency sine wave, which would be entirely masked by the errors." + But we are looking lor something less general. à monotonic function.)," But we are looking for something less general, a monotonic function.)" + The [act that none is evident in the plots here presented is a strong indication in that direction. the human eve being very good at detecting correlations amidst noise (indeed. even when none exists): but we would like something quantitative.," The fact that none is evident in the plots here presented is a strong indication in that direction, the human eye being very good at detecting correlations amidst noise (indeed, even when none exists); but we would like something quantitative." + Consikler a linear relation., Consider a linear relation. + While we expect the Local Volume to be nonlinear as [ar as eravilational elfects are concerned. we should certainly be able to approximate il wilh a," While we expect the Local Volume to be nonlinear as far as gravitational effects are concerned, we should certainly be able to approximate it with a" +Figure 2. shows the light curves of models 3.4 while the inset provides the light curves of model 2. for the same set of parameters.,"Figure \ref{fig2} shows the light curves of models 3, while the inset provides the light curves of model 2, for the same set of parameters." + In. model 3. the peak of the light curves for Oo.2Oy is flatter compared to model 2. and is obtained at a somewhat latter time.," In model 3, the peak of the light curves for $\theta_{\rm obs}>\theta_0$ is flatter compared to model 2, and is obtained at a somewhat latter time." + The rise before the peak is not as sharp as in models | or 2. since in model 3 there is some material at the sides of the jet with a moderate Lorentz factor (Granot et al.," The rise before the peak is not as sharp as in models 1 or 2, since in model 3 there is some material at the sides of the jet with a moderate Lorentz factor (Granot et al." + 2001; Piran Granot 2001)., 2001; Piran Granot 2001). + The emission from this slower material tends to dominate the observed flux at early times for observers at (i.My. resulting 1n a gentler rise before the peak.," The emission from this slower material tends to dominate the observed flux at early times for observers at $\theta_{\rm obs}>\theta_0$, resulting in a gentler rise before the peak." +" The light curves for 0,4,>(Aj peak at a later time compared to model 2. and the flux during the decay stage grows faster with @,,),.. since in model 3 the curvature of the shock front is larger and the emission occurs within a shell of finite width. resulting in a larger photon arrival time. and implying that smaller radi contribute to a given observer time."," The light curves for $\theta_{\rm obs}>\theta_0$ peak at a later time compared to model 2, and the flux during the decay stage grows faster with $\theta_{\rm obs}$, since in model 3 the curvature of the shock front is larger and the emission occurs within a shell of finite width, resulting in a larger photon arrival time, and implying that smaller radii contribute to a given observer time." + The light-curves for model 2 3 are quantitatively similar for ην<(y., The light-curves for model 2 3 are quantitatively similar for $\theta_{\rm obs}<\theta_0$. + The main advantage of this model ts a reliable and rigorous treatment of the jet dynamics. which provides insight on the behavior of the Jet and the corresponding light curves.," The main advantage of this model is a reliable and rigorous treatment of the jet dynamics, which provides insight on the behavior of the jet and the corresponding light curves." + Its main drawback ts the long computational time it requires., Its main drawback is the long computational time it requires. + While the afterglow emission from a spherical outflow is expected to exhibit little or no linear polarization. as the polarization from the different parts of the afterglow image cancel out. a jetted outflow breaks the circular symmetry of the afterglow image and may exhibit a polarization of up to <20% (Ghisellint Lazatti 1999; Sart 1999).," While the afterglow emission from a spherical outflow is expected to exhibit little or no linear polarization, as the polarization from the different parts of the afterglow image cancel out, a jetted outflow breaks the circular symmetry of the afterglow image and may exhibit a polarization of up to $\lesssim 20\%$ (Ghisellini Lazatti 1999; Sari 1999)." +" One might therefore expect an even larger polarization for an observer at 0,4,7Oy.", One might therefore expect an even larger polarization for an observer at $\theta_{\rm obs}>\theta_0$. + An isotropic magnetic field configuration in the local rest frame will produce no linear polarization., An isotropic magnetic field configuration in the local rest frame will produce no linear polarization. + However. as the magnetic field is most likely produced at the shock itself. one might expect the magnetic field perpendicular (231) and parallel to the shock direction. to have different magnitudes (Gruzinov(4) 1999: Sari 1999).," However, as the magnetic field is most likely produced at the shock itself, one might expect the magnetic field perpendicular $B_\perp$ ) and parallel $B_\parallel$ ) to the shock direction, to have different magnitudes (Gruzinov 1999; Sari 1999)." + We calculate the linear polarization for model 2 following Ghisellini Lazatti and using their notations., We calculate the linear polarization for model 2 following Ghisellini Lazatti and using their notations. +" They assume the magnetic field is strictly in the plane of the shock (5=D, ).", They assume the magnetic field is strictly in the plane of the shock $B=B_{\perp}$ ). +" Figure 3. shows the polarization as a function of time for different 0,4, in terms of Py.", Figure \ref{fig3} shows the polarization as a function of time for different $\theta_{\rm obs}$ in terms of $P_{60}$. + For Pyy«0 the polarization is along the plane containing the line of sight and the jet axis. wile for Pay>O itis rotated by 907 (for (51520D5 this is reversed. e.g. Sart 1999).," For $P_{60}<0$ the polarization is along the plane containing the line of sight and the jet axis, wile for $P_{60}>0$ it is rotated by $90^\circ$ (for $\langle B_{\perp}\rangle < 2\langle B_{\parallel}\rangle$ this is reversed, e.g. Sari 1999)." + A more isotropic magnetic field configuration would result in à smaller degree of polarization. so the value of the polarization in Figure 1. (0j.," If GRB jets have well defined edges, the prompt gamma-ray flux drops very sharply outside the opening of the jet, and the prompt burst will be very hard to detect from $\theta_{\rm obs}>\theta_0$." +" On the other hand. the afterglow emission may be detected out to Oia~afewOy. where the exact value of 01,4. depends on the jet parameters (including its redshift). the observed band and the limiting flux for detection."," On the other hand, the afterglow emission may be detected out to $\theta_{\rm det}\sim\ {\rm a\ few}\ \theta_0$, where the exact value of $\theta_{\rm det}$ depends on the jet parameters (including its redshift), the observed band and the limiting flux for detection." +" Jetted GRBs with 0,