ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2brielituess being within 1” of oue of the 128 GCs ij 2410 7.,brightness being within $''$ of one of the 428 GCs is $\times$ $^{-5}$.3 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}."4 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."5 We preseut iu Fie., We present in Fig.6 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.,"7 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."8 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.9 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."10" 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."11 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}."12 Do 153 is the 87th most massive. but the 36th richest.," Bo 153 is the 87th most massive, but the 36th richest."13 Bo 163 is the 20th mos Πιννο aud the 2ist richest., Bo 163 is the 20th most massive and the 21st richest.14 Bo 185 is the 53d most massive aud the 75th richest., Bo 185 is the 53rd most massive and the 75th richest.15 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."16 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."17 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."18 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}."19 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."20 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."21 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."22 Four of the outbursts occurred over LLOO davs., Four of the outbursts occurred over 1100 days.23 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."24 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}."25 We shall now discuss alternative explanations or the observed behaviour., We shall now discuss alternative explanations for the observed behaviour.26 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."27 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."28" 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."29" 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."30" 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."31 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 variation32"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 $^{-1}$."33" 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)."34" 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."35" The SHS was detected in these observations, the NHS was not."," The SHS was detected in these observations, the NHS was not."36" 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."37" 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)."38" 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."39" 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."40 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 14.1.0.41 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.42" 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."43 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.44" 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}."45. There have been noHST observations of the NHS., There have been no observations of the NHS.46 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.47 The fluxes were reddening-corrected using the dust maps of (1998)., The fluxes were reddening-corrected using the dust maps of \citet{sch98}.48. The correction to the flux densities is ~25% in the visual., The correction to the flux densities is $\sim$ in the visual.49 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}.50". 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."51 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}.52 The data were calibrated and reduced in the standard manner using AIPS., The data were calibrated and reduced in the standard manner using AIPS.53 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}.54". 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."55 The hot spots were not detected inany of the UV images., The hot spots were not detected inany of the UV images.56 The observation, The observation57"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)."58 '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.59" 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."60" 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."61" 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}."62. 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.63" 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."64" 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."65 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.66" 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."67" 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."68" 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."69" 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."70" 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."71" 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)."72" 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'."73" 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."74" 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."75" 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."76The 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.77 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)."78 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)."79 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 $\simgt 10^7\msun$.80 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.81" 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)."82" 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."83" 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"84"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."85 The RRd variable stars are discussed separately in section 3.2.., The RRd variable stars are discussed separately in section \ref{sec:rrd}.86" 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."87" 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."88 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}. (89"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."90 1995.), 1995.)91 Notes on some of the individual stars are in the following subsections., Notes on some of the individual stars are in the following subsections.92 Table 2 contains the photometric data for the variable stars., Table \ref{phottable} contains the photometric data for the variable stars.93 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}. .94" 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,"95physical) 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.96 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 $\theta$.97 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."98 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."99 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 $\mu\propto r^{-\Re(\varepsilon)}\exp100[-\hbox{i}\Im(\varepsilon)\ln r]$ where $\Re(\varepsilon)$ and $\Im(\varepsilon)$ are the real and imaginary parts of $\varepsilon$."101 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 $-m+1<\Re(\varepsilon)<m+2$ (Qian 1992).102 Without loss of generality. we assume a set of logarithmic spiral density perturbations and the resulting eravitational potential perturbation in a mathematically consistent (Ixalnajs 1971: Sver Premaine: Shu et al.," Without loss of generality, we assume a set of logarithmic spiral density perturbations and the resulting gravitational potential perturbation in a mathematically consistent (Kalnajs 1971; Syer Tremaine; Shu et al."103 2000: Lou 2002: Lou Fan 2002: Lou Shen 2003: Lou Zou 2004: Lou Wu 2004)., 2000; Lou 2002; Lou Fan 2002; Lou Shen 2003; Lou Zou 2004; Lou Wu 2004).104 Specifically. we write," Specifically, we write"105criteria have exclucled all sources with radio spectral index between 151. Alllz and 1.4 11 flatter than 1. or with radio angular size larger than 13 aresec.,"criteria have excluded all sources with radio spectral index between 151 MHz and 1.4 GHz flatter than 1, or with radio angular size larger than 13 arcsec."106 The final sample consists of GS objects over an area of skv of 0.421 sr. and is statistically complete at an angular size limit. of 6<ll aresec.," The final sample consists of 68 objects over an area of sky of 0.421 sr, and is statistically complete at an angular size limit of $\theta < 11$ arcsec."107 Full details of how the 6C**. sample was selected can be found in Cruz et al. (, Full details of how the 6C** sample was selected can be found in Cruz et al. (1082006. hereafter Paper 1).,"2006, hereafter Paper I)."109 The selection eriteria just described are similar to those of the 6C* sample (Blundell et al., The selection criteria just described are similar to those of the 6C* sample (Blundell et al.110 1998: Jarvis οἱ al., 1998; Jarvis et al.111 2001a.b). which was one of the samples usec by Jarvis et al. (," 2001a,b), which was one of the samples used by Jarvis et al. ("112200160) to constrain the co-moving space density of Iow-frequeney. selected radio sources.,2001c) to constrain the co-moving space density of low-frequency selected radio sources.113 The 6C* sample was crucial in that study in sampling to high redshift (2— 4.4).," The 6C* sample was crucial in that study in sampling to high redshift $z \simeq1144.4$ )."115 The οςἘν sample. being larger (cf.," The 6C** sample, being larger (cf."116 0.13 sr) and deeper (cf., 0.13 sr) and deeper (cf.117 0.06<Sys)2.0 Jv) than 6C. aims to improve on the small-numboer statistics limitation of this previous work. anc ultimately to extend it to higher redshifts (22 5).," $0.96 \leq S_{151} \leq 2.0$ Jy) than 6C*, aims to improve on the small-number statistics limitation of this previous work, and ultimately to extend it to higher redshifts $z \,\,\gtsim\,\, 5$ )."118 Deep imaging follow-up with UETL/UIST on ΕΙΗΕ. NIRD on Gemini. anc NIRC on Weck provide photometry for all members of the ος* sample (Paper I).," Deep imaging follow-up with UFTI/UIST on UKIRT, NIRI on Gemini and NIRC on Keck provided photometry for all members of the 6C** sample (Paper I)."119 Optical spectroscopy provided: redshifts for 32 per cent of the sources (Paper Land references therein)., Optical spectroscopy provided redshifts for 32 per cent of the sources (Paper I and references therein).120 A summary of key observational information is given in Table , A summary of key observational information is given in Table \ref{tab:6cssummary1_median}.121In this paper we describe a. method. of. redshif estimation based on the Az diagram of radio galaxies., In this paper we describe a method of redshift estimation based on the $K-z$ diagram of radio galaxies.122 ‘This is presented in Section ?77.., This is presented in Section \ref{sec:estimation}.123 In Section 3.. we use the complete set of magnitudes of the 6€ sample to estimate redshifts for all its optically identified members.," In Section \ref{sec:estimates}, we use the complete set of magnitudes of the 6C** sample to estimate redshifts for all its optically identified members."124 These are compared to spectroscopic redshifts in Section 4.. in order to assess the robustness of the method.," These are compared to spectroscopic redshifts in Section \ref{sec:comparison}, in order to assess the robustness of the method."125 The resulting estimated redshift cüstribution is discussed in Section 5.., The resulting estimated redshift distribution is discussed in Section \ref{sec:est-zdist}.126 In Section 6 we summarize the model radio luminosity function (IRLE) of Jarvis et al. (, In Section \ref{sec:JarvisRLF} we summarize the model radio luminosity function (RLF) of Jarvis et al. (12720010).,2001c).128 This is the most relevant model to compare our data to. because ib. takes into account the selection ellects. of the 6C7. sample.," This is the most relevant model to compare our data to, because it takes into account the selection effects of the 6C* sample."129 In. Section. 77. we compare the redshift distribution (including spectroscopic and discuss the evolution of the co-moving space density of the most radio luminous. low-frequencey selected: sources.," In Section \ref{sec:RLF} we compare the redshift distribution (including spectroscopic redshifts) of the 6C** sample with the model predictions, and discuss the evolution of the co-moving space density of the most radio luminous, low-frequency selected sources."130" Unless otherwise stated. we assume throughout that ff=τοkms*\Ipe 1 On,=03 and O4—0.7."," Unless otherwise stated, we assume throughout that $H_{0}=70~ {\rm km~s^{-1}Mpc^{-1}}$ , $\Omega_ {\mathrm131M} = 0.3$ and $\Omega_ {\Lambda} = 0.7$."132" The convention used. for radio spectral index is S,xν""o where S, is the IIux-density at frequency v."," The convention used for radio spectral index is $S_{\nu} \propto \nu^{-\alpha}$, where $S_{\nu}$ is the flux-density at frequency $\nu$."133 Infrarecd-photometry provides a method of. recdshif estimation by utilising the tightness of the relation between magnitude and recshift. which is characteristic of he near-infrared. Hubble. clagran of radio galaxies (Lilly Loneair 1984: Eales et al.," Infrared-photometry provides a method of redshift estimation by utilising the tightness of the relation between magnitude and redshift, which is characteristic of the near-infrared Hubble diagram of radio galaxies (Lilly Longair 1984; Eales et al."134 1997: Jarvis ct al., 1997; Jarvis et al.135 2001a: De Breuck et al., 2001a; De Breuck et al.136 2002. Willott et al.," 2002, Willott et al."137 2003)., 2003).138 Phe physica xls for the A> relation is not well understood., The physical basis for the $K-z$ relation is not well understood.139 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."140 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 $z >1413$ )."142 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."143 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).144 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."145 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."146 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. (1472003) 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."148 1997: Rawlines. Eales Lacy 2001). 6C (Jarvis et al.," 1997; Rawlings, Eales Lacy 2001), 6C* (Jarvis et al."149 2001a.b) and TORS (Lacy ct al.," 2001a,b) and 7CRS (Lacy et al."150 2000. Willott ct al.," 2000, Willott et al."151 2003) Ilux-lipited. samples., 2003) flux-limited samples.152" 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."153 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."154 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.155" 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."156 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 $S_{178}157\geq 10.9$ 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."158 The intermediate samples are GCE and 6€7 selected. at MAIIz. with llux-density limits of 2.0<Sys)x3.93 JJv and O.OG<<Sys)2.00 JJ. respectively.," The intermediate samples are 6CE and 6C* selected at MHz, with flux-density limits of $2.0159\leq S_{151} \leq 3.93$ Jy and $0.96 \leq S_{151} \leq 2.00$ Jy, respectively."160 This. results in a wide range in radio luminosity. which has made the investigation of the radio-Iuminosity dependence of the Az relation possible in an unprecedented. way.," This results in a wide range in radio luminosity, which has made the investigation of the radio-luminosity dependence of the $K-z$ relation possible in an unprecedented way."161 The correlation between luminosity and racio luminosity has been one of the major worries with redshift estimates based on the A zorelation., The correlation between luminosity and radio luminosity has been one of the major worries with redshift estimates based on the $K-z$ relation.162 Willott ct al. (, Willott et al. (1632003). found a statistically significant mean luminosity dillerence between the ὃςRR. and. TORS radio galaxies of 0.55 mae in A-band. over all redshilts.,"2003) found a statistically significant mean luminosity difference between the 3CRR and 7CRS radio galaxies of 0.55 mag in $K$ -band, over all redshifts."164 Llowever. the 6C radio galaxies were found to cdiller on average from the 3€ ones by only 2:0.3 mag. which is much smaller than the value (20.6 mag) reported previously," However, the 6C radio galaxies were found to differ on average from the 3C ones by only $\simeq 0.3$ mag, which is much smaller than the value $\simeq1650.6$ mag) reported previously"166derived.,derived.167 These equations (38)) surpass in consistency the usual Fokker-Planck equations (49)) — (52)) — (532)., These equations \ref{LAequation}) ) surpass in consistency the usual Fokker-Planck equations \ref{formeFP}) ) – \ref{Asanseffetscoll}) ) – \ref{Bsanseffetscoll}) ).168 The latter are unsatisfactory [rom a principle point of view. being local and. non-collective.," The latter are unsatisfactory from a principle point of view, being local and non-collective."169 ὃν contrast. the proposed. equations Lully account for the system's inhomogencity ancl for the collective gravitational dressing of the colliding particles.," By contrast, the proposed equations fully account for the system's inhomogeneity and for the collective gravitational dressing of the colliding particles."170 Equations (38)) describe the evolution of distribution functions in action and angle space. which is possible when the hamiltonian associated with the average potential is integrable.," Equations \ref{LAequation}) ) describe the evolution of distribution functions in action and angle space, which is possible when the hamiltonian associated with the average potential is integrable."171 Physically. these equations describe the evolution of the distribution functions in action space as a result of the weak eravitational noise caused. by. the cliscreteness of the particles. dressed. with the polarization clouds that their own gravity induces in the system.," Physically, these equations describe the evolution of the distribution functions in action space as a result of the weak gravitational noise caused by the discreteness of the particles, dressed with the polarization clouds that their own gravity induces in the system."172 This gravitational polarization is accounted for in equation (38)) in à manner that is fully consistent with the distribution functions. as they are at the moment.," This gravitational polarization is accounted for in equation \ref{LAequation}) ) in a manner that is fully consistent with the distribution functions, as they are at the moment."173 Equation (38)) is the sum. of a second. order derivative term with respect to actions and of a first order one., Equation \ref{LAequation}) ) is the sum of a second order derivative term with respect to actions and of a first order one.174 It therefore basically is of the Fokker-Planck type. although it is definitely simpler in the form of expression (38)).," It therefore basically is of the Fokker-Planck type, although it is definitely simpler in the form of expression \ref{LAequation}) )."175 The dillusion coelIicient involved depends on the l-bocly distributions theniselves. in particular through the factor |D|> 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."176 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."177 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.178 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}) )."179 ]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 $\omega = {\mathbf{k}}\! \cdot \! {\mathbf{\Omega}}$."180 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.181" 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.182 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."183" 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."184 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."185 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.186 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."187 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.188 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."189 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."190 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."191 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."192 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."193" 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."194 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.195 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.196 The usefulness, The usefulness197positions.,positions.198 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).199"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."200 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.201" 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."202" 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."203" (1),Unlike the scenario of the classical Nice model (Tsiaganis et al.", Unlike the scenario of the classical Nice model (Tsiaganis et al.204" 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."205" 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."206 Thommes et al. (, Thommes et al. (207"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."208" 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."209" 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."210" 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."211. It appears that somewhat larger eccentricities are needed., It appears that somewhat larger eccentricities are needed.212" 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."213" 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."214" 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)."215" 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."216" 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."217γάμο on observations of the local universe.,based on observations of the local universe.218 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."219 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."220 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.221 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."222 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."223 Another constraint on our models comes from the recdshift distributions., Another constraint on our models comes from the redshift distributions.224 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}) )."225 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."226 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."227 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 $z=1.5$."228 There are at least a couple of reasons for this behaviour., There are at least a couple of reasons for this behaviour.229 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."230 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"231independent. 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."232 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 $M_{vir}$."233" 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 $\rho_{\rm NFW} 234\propto r^{-1}$ for $r \rightarrow 0$, and a profile/amplitude which is controlled by a free parameter $M_{vir}$."235 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."236" 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}) )."237 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."238" 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.239 This density cistribution has an even sleeper cusp (ptsXV Laefor r: 0) than the previous one.," This density distribution has an even steeper cusp $\rho_{\rm Moore} 240\propto r^{-1.5}$ for $r \rightarrow 0$ ) than the previous one."241 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."242 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}."243 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."244" 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 $8 \times 10^{11}$ $_{\odot}$.245 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}246 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}) )."247 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}.248. 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.249 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}."250". 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}) )."251" The total 47 value to be mininiised then is xz,=No,|Ns", The total $\chi^2$ value to be minimised then is $\chi^2_{tot}=\chi^2_{vel}+\chi^2_{\nabla}$.252 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."253 μα Figs., In Figs.254 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."255 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."256 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)."257 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}) )."258 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 $^{-3}$."259 In Fig., In Fig.260 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."261 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.262 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.263 Moreover. there is à systematic," Moreover, there is a systematic"264"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."265" 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 $M_{WD}$ ).266 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."267" 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 $^{-1}$."268 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."269" 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 $^{-1}$."270The 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 $^{-1}$."271 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."272 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."273 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).274 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."275 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."276 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."277 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."278 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)."279 JO acknowledges support from. STEC., JO acknowledges support from STFC.280. 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)."281 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.282Iu 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."283 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}."284 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}."285". 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}."286 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}."287. 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}."288. 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}."289. 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."290 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}."291. 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 $10^{32}$ $10^{-14}$ )."292Unfortuately. 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."293 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."294" ds both a faiut transient svsteni aud οΓΕ,", is both a faint transient system and a low-luminosity295The 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."296 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."297 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.298 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.299 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 6302.300 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."301 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."302 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.303 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.304 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."305 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."306 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.307 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 10.0.308 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"309These 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}) ).310 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."311" 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."312 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)."313 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.314 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.315 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."316 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.317 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}) ).318 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."319 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."320 A ‘lassical design with classical components could be chosen if preferred., A classical design with classical components could be chosen if preferred.321 “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.322 The following items give 1e &eneral framework of our experimental study., The following items give the general framework of our experimental study.323 The following sections summarize the “VIP bench structure., The following sections summarize the THT bench structure.324 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."325 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.326 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."327 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.328 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.329 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.330 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 $23.75 \mu rad$."331 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}) )."332 The experimental setup can be seen in fig.6.., The experimental setup can be seen in \ref{photo_objet}.333 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.334 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."335 Consequently. our telescope array must periodically sample the spatial frequency domain.," Consequently, our telescope array must periodically sample the spatial frequency domain."336 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.337 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 :338Of the 17 galaxies in the Noo et al. (1995)),Of the 17 galaxies in the Koo et al. \cite{koo95}) )339 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."340 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}) ).341 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."342 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 1997.343" The sixth galaxy. SÀ57-5182. was not observed due to tine constraints,"," The sixth galaxy, SA57-5482, was not observed due to time constraints."344" 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.345 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.346 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)."347 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."348 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.349 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."350 The remaining spectra were averaged togetlier. weighted by their rus noise.," The remaining spectra were averaged together, weighted by their rms noise."351 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}) )."352 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)."353 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}) ).354 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."355 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}) ).356" 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.357 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}) ),"358 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."359 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.360 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}) )"361 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}) ),"362 while our 30 upper linits rauge from 2 to 8 Jv lau +., while our $\sigma$ upper limits range from 2 to 8 Jy km $^{-1}$.363 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."364 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."365. 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 $z \sim 0.5$."366 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."367 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};368 Sage et al. 1992))., Sage et al. \cite{sage}) ).369 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 $z\sim 0.5$."370" 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}) )."371 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."372 In ealactic nuclei. the three trausitious have," In galactic nuclei, the three transitions have"373is 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.374 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.375 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."376 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."377 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.378 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."379 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.380 1998: Fabricant et al., 1998; Fabricant et al.381" 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)."382 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."383 2001: Busha et al., 2001; Busha et al.384 2005: Rines et al., 2005; Rines et al.385 2005: Tran et al., 2005; Tran et al.386 2005)., 2005).387 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."388 2009: Umetsu et al., 2009; Umetsu et al.389 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.390 2011)., 2011).391 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)."392 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."393 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.394 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."395 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."396 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.397 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."398 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.399 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.400 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)."401 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"402his paper.,this paper.403 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."404 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}."405". 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 $^+$."406 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."407 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}."408 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."409 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 Q2231-00.410 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."411 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}.412. 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."413 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."414 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.415" 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."416 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.417 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."418 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."419 Ehe. validity of this relation is discussed in section 3.3.., The validity of this relation is discussed in section \ref{section:CMBR}.420 DLA svstenis have very high. neutral hydrogen column densities (logN(LLEI) 20.3).," DLA systems have very high neutral hydrogen column densities $\log\rmn{N}(\hbox{H\,{\sc i}})>20.3$ )."421 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}. ."422 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.423 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."424 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"425Figures | 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 $(e -426\log P)$ 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)."427 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.428 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."429 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."430 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)."431 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."432 Fig., Fig.433 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."434 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}."435 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.436 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.437" 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 $M_2 =4380.6$ $_\odot$."439 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."440 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}) )."441 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}.442 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."443" 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}."444 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."445 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.446 The reason for this may be the following., The reason for this may be the following.447 When à system is close to filling its, When a system is close to filling its448"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."449 It is part of a large-scale structure (see fig., It is part of a large-scale structure (see fig.450 1 in (09 and fig., 1 in G09 and fig.451 3 in Scoville et al., 3 in Scoville et al.452 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 $z=0.37$ ).453" 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."454 2010)., 2010).455" 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."456 It is isolated and its BCG has M;=—23.87., It is isolated and its BCG has $M_{i} = -23.87$.457 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 1.458" 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."459" 5), where quantities are estimated at 0.7 R2oo."," 5), where quantities are estimated at $0.7 R_{200}$ ."460 This is particularly true for 0095951--0212.6., This is particularly true for $+$ 0212.6.461" As from GO095,, the stellar mass", As from the stellar mass462" 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)."463 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."464 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."465 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.466 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."467 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."468 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)."469 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 of470"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."471" 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."472" 3 to 5)) that emanate from SGL~200°, SGB~30°."," \ref{Fig:3} to \ref{Fig:5}) ) that emanate from $SGL\sim 200^\circ$, $SGB\sim 30^\circ$."473 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.474 2008)., 2008).475" 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."476" 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."477" 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."478 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.479(EW) baseline vectors.,(EW) baseline vectors.480 Next. we cdeseribe the. estimation of array geometry.," Next, we describe the re-estimation of array geometry."481 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.482 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.483 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)."484 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."485 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.486 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.487 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."488 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.489 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)."490 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.491" 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."492" 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"493"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 $M(R) = 1.4\times49410^{11}\,M_{\odot}$ (Côtté et 2001)."495 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.496 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."497 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."498 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."499 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."500 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."501 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."502 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."503 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.504 These also are seen in the 90 em image (see Fig., These also are seen in the 90 cm image (see Fig.505 11. fora composite X-ray-radio view of M87)., \ref{fig:overlay} for a composite X-ray-radio view of M87).506 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.507 2001. Molendi 2002).," 2001, Molendi 2002)."508 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.509 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}) )."510 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."511 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."512 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},"513 and 4))., and \ref{fig:divking}) ).514 At the base of the filament (Fig., At the base of the filament (Fig.515" 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.516 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).517 Fig., Fig.518" 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.519 lee)., \ref{fig:bl1sum}c c).520 The temperature structure (Fig. 6)), The temperature structure (Fig. \ref{fig:xmm_tmap}) )521 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.522 2001)., 2001).523 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)."524" 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."525 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."526 11. and Fig., \ref{fig:overlay} and Fig.527 3 and 4 in Churazov et al., 3 and 4 in Churazov et al.528 2001)., 2001).529 A projection along the arm. Fig. 10..," A projection along the arm, Fig. \ref{fig:eastern_arm_proj},"530 shows a brightening at the radial distance of the 14 kpe ring., shows a brightening at the radial distance of the 14 kpc ring.531 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.532 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}) )."533 [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."534" 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}) ),"535 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.536 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)."537 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. (5382001). this could account for the rather filamentary appearance of this feature.,"2001), this could account for the rather filamentary appearance of this feature."539 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}) )"540" 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).541 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}) )542which 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}) ).543 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.544 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).545 The two enhancements. labeled andE2 in Fig.," The two enhancements, labeled and in Fig."546 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)."547 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."548 The southwestern X-ray arm originates (see Fig., The southwestern X-ray arm originates (see Fig.549 | and Fig. 2))," \ref{fig:inner_cocoon}550 and Fig. \ref{fig:adapt}) )"551 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)."552 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).553 As seen in Fig. 11..," As seen in Fig. \ref{fig:overlay},"554 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.555 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."556 4ec)., \ref{fig:divking}c c).557 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.558 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.559 Young et al (, Young et al. (5602002) suggested that the arms are overpressurized.,2002) suggested that the arms are overpressurized.561 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."562 We found no elemental abundance differences that could explain, We found no elemental abundance differences that could explain563In 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 $>3\times 10^{10}\ \lsol$.564 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}) ).565 $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}) ).566"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}) )."567" 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 $\sim300-400\kms$ ."568" 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 $\sim50-150~\kms$."569" 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."570 $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.571" 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."572 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.573" 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."574" 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."575" 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."576 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.577" 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."578" 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."579" 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 $M_{\mbox{\tiny580HII}}\sim 10^5\ \msol$ in the two components of the $\beta$ line $L_{H\beta}581= 2\times 10^{39}\ \ergsec$ )."582 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.583" 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."584 For, For585"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."586" 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 $277.46^{\circ}$.587 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 $^{-1}$ )."588 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}."589. 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.590 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.591 But observations. of extended sources need to be conducted with caution., But observations of extended sources need to be conducted with caution.592" 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}) ). ("59311) 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.594 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). ("595"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. ("5961v) The stability of the 620.701 GHz masers 15 remarkable.,iv) The stability of the 620.701 GHz masers is remarkable.597 The variation over a three week periodis profile<1% (see Figure 2). (, The variation over a three week period is $\lesssim1\%$ (see Figure 2). (598v) 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,"599The 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.600. 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}."601 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 $|l|<30^\circ$, $|b|<3^\circ$."602 This covers less than of the sky., This covers less than of the sky.603 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)."604 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}. .605The 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.606 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."607 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."608 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}.609 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."610 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}."611. 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."612 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."613 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.614 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}."615 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."616" 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}."617. 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."618 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.619 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.620 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."621 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."622 Besides. lis not classified as a FR [E type radio galaxy.," Besides, is not classified as a FR I type radio galaxy."623 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."624 It possesses, It possesses625ist 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."626 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.627 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."628" 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 $\sigma629_{\mu}$ and $\chi^{2}$ ) an estimate of the error associated with each measure of position is required."630 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."631 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."632 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.633 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.634 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."635 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."636 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.637We therefore iteratively remove points lying 3o from the fitted line.,We therefore iteratively remove points lying $3\sigma$ from the fitted line.638 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."639 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.640 “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.641 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.642 1990 ancl references. therein)., 1990 and references therein).643 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."644 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).645 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.646 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."647 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.648 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}) )."649 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."650 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."651 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."652 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.653 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.654 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."655 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."656 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}.657 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"658does not exceed ~30 for the scattering inside the light cylinder.,does not exceed $\sim 30^\circ$ for the scattering inside the light cylinder.659 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.660 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."661 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.662 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."663 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.664" 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, $I_{\nu_b}(\nu_b)\sim665I_{\nu_a}^{(0)}(\nu_a)$."666 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 $\nu_b$."667 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."668 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."669" 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 $\sim 30^\circ$."670 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."671 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."672 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."673 This is indeed the main distinctive feature of the observed. precursors., This is indeed the main distinctive feature of the observed precursors.674 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 $[{\bmath k}\times{\bmath b}]\not\parallel[{\bmath675k_1}\times{\bmath b}]$ , i.e. in the main pulse and precursor the position angles of linear polarization should somewhat differ."676 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}."677.. 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}."678. 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."679" 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."680" Secondly. the scattering ellicieney is proportional to B,."," Secondly, the scattering efficiency is proportional to $B_\star$."681 Short periods ancl large radio luminosities also favour significant scattering., Short periods and large radio luminosities also favour significant scattering.682 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.683 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."684 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}."685" 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, $I_{\nu_a}\to 0$, $I_{\nu_b}\to I_{\nu_a}^{(0)}$."686 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."687" 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 $I_{\nu_a}^{(0)}$."688 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.689 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."690 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.691 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."692" 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."693continu 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.694 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."695 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.696" 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."697 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}.698. 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).699 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."700 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."701 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 $\mathcal{L}=2\sqrt{R^{2}-(R-\Delta R)^{2}}$ ."702 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.703 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."704" 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 $K=Mv^{2}_{\mathrm{exp}}/2$."705" 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 $P_{\mathrm{shell}}=2n_{{e}}kT=2.76\times 10^{-12}n_{{e}}$ ."706 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."707 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.708 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.709 Couvolving the two profiles. we found an uncertainty of 11L.," Convolving the two profiles, we found an uncertainty of 11."710 Calculated quantities are listed in Table 2.., Calculated quantities are listed in Table \ref{snrtable}.711 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."712 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 $u(t)=0.351(E/\rho t^3)^{1/5}$."713 Solving js system vields f=θα)., Solving this system yields $t=0.3(r/u)$.714 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.715 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."716 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 $^{-1}$.717 Tnhomogencitics i the ambicut medium also affect the expansion rate., Inhomogeneities in the ambient medium also affect the expansion rate.718 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."719 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.720 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.721 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."722 sshows the simplest structure of the three reninaunts presented here., shows the simplest structure of the three remnants presented here.723 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.724 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."725 The bright eenissiou to the cast of, The bright emission to the east of7261992))).,).727 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."728 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 $h$."729 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 $H_0$.730" At the same time the procedure allows to quantify this ""systeniatic errors.", At the same time the procedure allows to quantify this “systematic” errors.731 )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."732 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.733 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 $34\%$."734 This percentage obviously. changes if we simulate other lens svstenms., This percentage obviously changes if we simulate other lens systems.735" 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).736 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.737 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.738 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."739 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 to740 General Relativity predicts redshift of photons due to a gravitational field.,] General Relativity predicts redshift of photons due to a gravitational field.741 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."742 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."743 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."744 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 $z_{g}$."745 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."746" 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."747 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."748 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."749 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."750 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."751 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."752 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.753 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."754 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."755 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."756 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."757 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.758 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.759 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.760 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."761 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.762 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."763 Towever. massive clusters are rare.," However, massive clusters are rare,"764REFERENCES Riess. A.aL.. 2001. ApJ.. 560. 49-71. “,"REFERENCES Riess, A. 2001, 560, 49-71. “"765"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."766deusities 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}) ).767 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."768" 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."769 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.770" 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.771 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."772 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}."773" 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.774 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.775 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."776 Density eulianceiments suc las these are accolupanied by pressure maxima., Density enhancements such as these are accompanied by pressure maxima.777 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}.778" 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 $25\ r_{\rm p}$."779In 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 $\sim 5\%$."780The 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.781 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.782 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."783 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."784 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."785 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."786 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.787 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, $\alpha$."788 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."789 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."790 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 $\alpha \geq 10^{-3}$ 791parameters simultaneously. which would probably become prohibitive first.),"parameters simultaneously, which would probably become prohibitive first.)"792 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 $\jones{E}{p}$.793" 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}."794 A number of approaches have shown that this is feasible., A number of approaches have shown that this is feasible.795 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."796 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).797 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."798 ? 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."799 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."800 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)."801 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."802" 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.803 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."804 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.805 [ 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."806 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},"807 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)."808" 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."809 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."810 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."811" 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."812 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.813 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},"814" 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."815 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.816 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."817 Pointing errors introduce an E-Jones às given by Eq. (9))., Pointing errors introduce an $E$ -Jones as given by Eq. \ref{eq:mispointing}) ).818 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}) )"819 and differential gains (Sect. 2.4.3))., and differential gains (Sect. \ref{sec:dEs}) ).820 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."821 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.822 comm.).," comm.),"823 but is not publicly available at time of writing., but is not publicly available at time of writing.824 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."825 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.826" 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)."827" 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."828 Differential gains uses an equation like (16))., Differential gains uses an equation like \ref{eq:de}) ).829" 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."830" 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."831 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."832 This is especially severe when sources have comparable flux., This is especially severe when sources have comparable flux.833 Differential gains overcomes this by solving for all sources simultaneously., Differential gains overcomes this by solving for all sources simultaneously.834 In principle. it should," In principle, it should"835"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."836 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. ("837"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.)"838 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."839 1997)., 1997).840 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 $^{-1}$ $^2$."841 For the 3e flux. limit for CO J—5-I. agalu assuimniug a linewidth of 200 kns Ly ho.<eod)x10 Ix kin ! pc?. If obta," For the $3\sigma$ flux limit obtained for CO J=5–4, again assuming a linewidth of 200 km $^{-1}$, $L^{'}_{CO}(5-4) < 3.0 \times 10^{10}$ K km $^{-1}$ $^2$."842inedthe assumed linewidth were two times larger. then these luminosity liinitis be V2 times higher.," If the assumed linewidth were two times larger, then these luminosity limits would be $\sqrt{2}$ times higher."843 Conversion of these CO luminosity limits to molecular gas mass limits is faught witl uncertaluties., Conversion of these CO luminosity limits to molecular gas mass limits is fraught with uncertainties.844 But a simple conversiou factor from CO luminosity to Πο mass is commony taken to be L5AM. (Ix km 1 pc)> 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)."845 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).846 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.847 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.848 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.849 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."850 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."851 1996. Ohta et al.," 1996, Ohta et al."852 1996) and. BRIL335-O117 at 1.1 (Guilloteau et al., 1996) and BRI1335-0417 at $z=4.4$ (Guilloteau et al.853" 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).854 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.855 1900)., 1999).856 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."857 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. ("8582001) [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.859 For the SDSS 1011-0125 observations. such [features," For the SDSS 1044-0125 observations, such features"860(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 $Q^{2-k}\setminus861Q^{1-k}$, 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 $j$ ."862 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 $m$."863 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}. .864 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:"865the 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.866 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.867 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."868 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}."869 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)."870 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}."871 Our model includes two cool spots on the more-massive. hotter componet.," Our model includes two cool spots on the more-massive, hotter component."872 The spotted model ts supported by the X-ray observations., The spotted model is supported by the X-ray observations.873 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.874 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."875 A good fit could not be, A good fit could not be876of BBLPO2.,of BBLP02.877 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."878 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.879 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."880 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."881 [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.882 1999)., 1999).883 This treatineut. however. is only appropriate for low mass alos.," This treatment, however, is only appropriate for low mass halos."884 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."885 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."886 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."887 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.888 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."889" 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.890" 2000). where AN—AT,3*"," 2000), where $K \equiv 891kT_e n_e^{-2/3}$."892 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)."893 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."894 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."895 The complicated: effects of radiative cooling are neglected by these models., The complicated effects of radiative cooling are neglected by these models.896 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 $\vec{r}$."897 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.898 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.899 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 $P_e(\vec{r})$."900 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."901 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."902 1 of NDBDB02)., 1 of MBB02).903 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."904 2 of NBD02)., 2 of MBB02).905 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."906 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."907" 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)."908 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.909 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."910 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.911 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."912 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, $y(\theta = 0) \equiv y_0$ ]."913 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"914It 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}) ).915 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."916 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."917 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 1982.918 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."919 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 2004.920 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.921 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.922 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."923 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."924 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}.925 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."926 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."927 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.928 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.929 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.930 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}."931 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.932 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."933 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.934 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:935"they are indeed observed allows us to conclude that Rina,> A.",they are indeed observed allows us to conclude that $R_{\rm{max}} > A$ .936 Nevertheless. we cannot discard a possible relationship between truncations and warps.," Nevertheless, we cannot discard a possible relationship between truncations and warps."937 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."938Low 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.939 While/-GRBs differ from typical long GRBs (LGRBs) in many aspects. (μον also share some common features.," While differ from typical long GRBs (LGRBs) in many aspects, they also share some common features."940 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."941 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."942 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."943 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.944 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.945 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}946 947\tikzmark{mainBodyStart185}\begin{document}"948According 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."949 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."950 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.951 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}. ."952 (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}."953(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.954 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.955 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."956 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."957 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}) )."958 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."959 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."960 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.961 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."962 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}) )."963 Inspecting the ATCA image in Fig. 2..," Inspecting the ATCA image in Fig. \ref{Fig:ATCA-CXO},"964 we seea ring of emission centered ~2' south of the pulsar location., we seea ring of emission centered $\sim$ $'$ south of the pulsar location.965 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."966 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?967 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."968 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.969 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.970 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."971 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."972 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."973 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."974 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."975 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."976 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."977 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.978 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."979 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."980 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 NAS8-03060.981 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.982 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.983 S.B. gratefully acknowledges the support of STFC in his PhD studentship., S.B. gratefully acknowledges the support of STFC in his PhD studentship.984 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. , , ."985“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."986 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."987 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.988 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."989 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 $^{-1}$ $^{-2}$."990 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}."991 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.992 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 $^{-1}$.993" 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}."994 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."995 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.996 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."997 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 $_e\sim 0.3$."998 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."999 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."1000 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."1001 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."1002 ?— 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."1003 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}."1004 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."1005 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."1006 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.1007 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.1008 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.1009and 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."1010" 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."1011 In the case of Alfvénn and fast waves (Fig., In the case of Alfvénn and fast waves (Fig.1012 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."1013 So. the larger ἕμοι. the smaller K?.," So, the larger $\xi_\ion{He}{i}$, the smaller $k_{\rm c}^{\rm a}$."1014" 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. ("101538) 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."1016 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.1017 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, $\eta_{\rm C}$."1018 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."1019 Turning our attention to the slow wave (Fig., Turning our attention to the slow wave (Fig.1020 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 $k$."1021 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 $\tdp$.1022 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}) )"1023 causes this displacement of the curve of r5/P., causes this displacement of the curve of $\tdp$.1024 As for Alfvénn and fast waves. this effect is of minor importance.," As for Alfvénn and fast waves, this effect is of minor importance."1025" 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}."1026 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."1027 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.1028 Next. we study the thermal mode.," Next, we study the thermal mode."1029 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}) )."1030 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 $k$.1031 For &>107 m. thermal conduction is the dominant damping mechanism.," For $k \gtrsim 10^{-4}$ $^{-1}$, thermal conduction is the dominant damping mechanism."1032 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."1033 On the other hand. radiative losses are more relevant for k€1077 m.," On the other hand, radiative losses are more relevant for $k \lesssim 10^{-4}$ $^{-1}$."1034 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."1035 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."1036 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.1037 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."1038 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"10392003).,.1040". 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 $L_{\rm1041X,bol} \approx 0.25 \times 10^{42} h^{-2}$ 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 $R_{200}$ )."1042 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, $R_{500} \sim 0.59 \times1043R_{200}$ )."1044 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}."1045. 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}."1046. 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."1047 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."1048 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}."1049. 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."1050 Cooler fossil groups also show lower entropy than their non-fossil counterparts., Cooler fossil groups also show lower entropy than their non-fossil counterparts.1051 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."1052 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."1053 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."1054 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.1055 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."1056 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."1057 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.1058 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."1059 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."1060 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."1061 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."1062 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."1063 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."1064 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}.1065. Below we summarize the main characteristics of the above simulations., Below we summarize the main characteristics of the above simulations.1066 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 $\Lambda$."1067 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."1068" 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."1069" 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: $\Omega_\Lambda = 0.75, \Omega_M = 0.25, \Omega_b = 0.045, h = 0.73, n1070= 1$ , 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}1071 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."1072 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 $\times 10^{10}h^{-1}$ $_{\odot}$."1073 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."1074 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."1075 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 $z=0$ ."1076 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."1077"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.1078" 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.1079 The other (homogeneous) waves are those measured by a distant observer., The other (homogeneous) waves are those measured by a distant observer.1080" 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)."1081 The interferometer is placed in a plane defined at a constant way=zui., The interferometer is placed in a plane defined at a constant $w_{\rm ant} = z_{\rm ant}/\lambda$.1082 Typically one ean assume Wyn.=0., Typically one can assume $w_{\rm ant}=0$.1083" 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$."1084 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.1085 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 $w_{\rm ant}$.1086 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."1087. 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)."1088 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.1089 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."1090 In Section5 we show how to unravel this information., In Section 5 we show how to unravel this information.1091 In radio interferometry one does not analyze the electric field itself., In radio interferometry one does not analyze the electric field itself.1092 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."1093 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."1094 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 $w=w_{\rm ant}$."1095" 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."1096 The averaging 1s assumed to be over time., The averaging is assumed to be over time.1097 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."1098. 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.1099 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."1100 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.1101 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."1102 However. the sky is an incoherent emitterfields).," However, the sky is an incoherent emitter."1103. 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."1104 This equation forms the basis for further discussions in the paper., This equation forms the basis for further discussions in the paper.1105 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.1106" 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 $s_{v}$."1107 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."1108 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."1109 Multiplied with its complex conjugate. this recovers the point source intensity.," Multiplied with its complex conjugate, this recovers the point source intensity."1110 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 ."1111. 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.1112 Hence. squared.," Hence, ."1113 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."1114First we investigate the effects of outer truncation.,First we investigate the effects of outer truncation.1115 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}."1116 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.1117 Agam we extracted the jet width from emission maps like these., Again we extracted the jet width from emission maps like these.1118 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}.1119 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.1120 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."1121 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."1122 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)."1123 In principle. we can reproduce even smaller values than the observed ones.," In principle, we can reproduce even smaller values than the observed ones."1124 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."1125 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.1126 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.1127 Unfortunately. only one run met our scaling requirements (Sect. 3.1)):," Unfortunately, only one run met our scaling requirements (Sect. \ref{sec_norm}) ):"1128 model SC3 and run (---. 100. 0.2).," model SC3 and run $\cdots$, 100, 0.2)."1129 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}."1130 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."1131 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 $R_0$.1132 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.1133 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.1134 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.1135 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.1136 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."1137 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."1138 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)."1139 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}.1140. 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."1141 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}."1142" 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."1143 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."1144 This gives the following results:, This gives the following results:1145this 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.1146" 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."1147 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.1148 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.1149 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."1150 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."1151 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. ("1152In 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"1153of Equation (35).,of Equation (35).1154" 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."1155" 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."1156" 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)."1157" But this does not mean that 6, cannot grow.", But this does not mean that $\delta_\kappa$ cannot grow.1158" 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."1159" Moreover, there is no Jeans length scale."," Moreover, there is no Jeans length scale."1160" 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."1161" 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 $R_{\rm h}$.1162" 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 $\lambda<<R_{\rm h}$ ),"11631993))).,).1164 The values of the που thus derived for all the regions are listed in Table 2., The values of the $I_{TRGB}$ thus derived for all the regions are listed in Table 2.1165 The distance modulus is eiveu by where fyrgeip is the dereddened Z-baud magnitude of the TRGB.," The distance modulus is given by where $I_{0, TRGB}$ is the dereddened $I$ -band magnitude of the TRGB."1166" BC, is the bolometric correction to the I magnitude which depeuds on color as follows: where (V.Dorpep is the dereddened color of the TRGB."," $BC_{I}$ is the bolometric correction to the I magnitude which depends on color as follows: where $(V-I)_{0, TRGB}$ is the dereddened color of the TRGB."1167 The bolometric maenitude of the TRGD. ΑΙτης. ds given as a function of mictallicity [Fe/TI] by: Metallicity can be estimated from the (V.£) color at the absolute Z-baud magnitude of M;=3.5 eiven bv Lee.Freediman.&Madore(1993) (see also Saviane (2000))) as follows: We have enploved an iterative procedure iu which an initial guess at the distance is used to estimate the metallicity which is iu turn used to refine the distauce uutil the solution converges. which occurs after only a few iterations.," The bolometric magnitude of the TRGB, $M_{bol,TRGB}$, is given as a function of metallicity [Fe/H] by: Metallicity can be estimated from the $(V-I)$ color at the absolute $I$ -band magnitude of $M_I = -3.5$ given by \citet{lee93}1168 (see also \citet{sav00}) ) as follows: We have employed an iterative procedure in which an initial guess at the distance is used to estimate the metallicity which is in turn used to refine the distance until the solution converges, which occurs after only a few iterations."1169 It is important to note that the regions used for this study. are located in various euvironnienuts iuchiding voung to old stellar populations: thus. the broad ROBs seen in the CALDs are actually à uüxture of itermediate-age to old populations. as well as a range of metallicities.," It is important to note that the regions used for this study are located in various environments including young to old stellar populations; thus, the broad RGBs seen in the CMDs are actually a mixture of intermediate-age to old populations, as well as a range of metallicities."1170" Tf we simply use the mean color |WLy, απ of the cutire apparent RGB iu this case. the resulting metallicity will be an underestimate. because there are vounecr populations with bluer color on the blue side of the ROB."," If we simply use the mean color $(V-I)_{0, -3.5}$ ] of the entire apparent RGB in this case, the resulting metallicity will be an underestimate, because there are younger populations with bluer color on the blue side of the RGB."1171 For this reason we tried to use the median value of the color of the stars along the RGB to reduce the effect of iuteriiecdiate-age populations., For this reason we tried to use the median value of the color of the stars along the RGB to reduce the effect of intermediate-age populations.1172 As a check of our method. we Lave also derived the mean metallicity using the slope of the RGB as calibrated by Sarajedinietal.(2000).. obtainins verv simular results to those from the median color of the RGB stars.," As a check of our method, we have also derived the mean metallicity using the slope of the RGB as calibrated by \citet{sar00}, obtaining very similar results to those from the median color of the RGB stars."1173 The mean metallicities resulting from this procedure are listed in Table 2., The mean metallicities resulting from this procedure are listed in Table 2.1174 The mean metallicity ranges frou Fe/H]| = 0.6 to 0.9 dex., The mean metallicity ranges from [Fe/H] $\approx$ –0.6 to –0.9 dex.1175 Figure 5 displays the mean uctallicity versus the deprojected radial distance of the regions (filled circles)., Figure 5 displays the mean metallicity versus the deprojected radial distance of the regions (filled circles).1176 Iu Figure 5 there is clearly a weeative radial eracicut of the metallicity., In Figure 5 there is clearly a negative radial gradient of the metallicity.1177" The mean uctallicity data ave fit by [Fe/H] —05ΕΟΟ,L55|x0.02] ([Fe/H| =COO8,010.061. using the metallicity obtained with the RGD slope uethod) for all the data. where Ry, is given in feriis of spe (10=0.27 kpe is assumed)."," The mean metallicity data are fit by [Fe/H] $= -0.05[\pm0.01] R_{dp} - 0.55[\pm0.02]$ ([Fe/H] $= -0.04[\pm0.02] R_{dp} - 0.51[\pm0.06]$, using the metallicity obtained with the RGB slope method) for all the data, where $R_{dp}$ is given in terms of kpc $1^\prime=0.27$ kpc is assumed)."1178" If we exclude the two innermost regious where the erowding is severe. we obtaiu a fit. |Fe/II] = O.07|4Q.01R,,0.5ΕΟΟ οσο =μεςµηνΟΦΗ using the metallicity obtained with the RGB slope ΕΟΟ)method). similar to values found iu our Galaxys disk using open clusters aud Πο] saute (d|Fe/H|/dR=0.050+0.008. 1) 1979)."," If we exclude the two innermost regions where the crowding is severe, we obtain a fit, [Fe/H] $= -0.07[\pm0.01] R_{dp} - 0.48[\pm0.04]$ ([Fe/H] $= -0.08[\pm0.03] R_{dp} - 0.34[\pm0.10]$ using the metallicity obtained with the RGB slope method), similar to values found in our Galaxy's disk using open clusters and field giants $d[Fe/H]/dR = - 0.050 \pm 0.008$ $^{-1}$ ) \citep{jan79}."1179. Iu Fiewre 5 the metallicity of the red eiauts is compare’ with that of ΠΠ regious in MO., In Figure 5 the metallicity of the red giants is compared with that of HII regions in M33.1180 The metallicity of the ΠΠ regions was converted from [O/II| values given in the literature (Iswitter&Aller1981:AIcCall.Rybska.IIuchra1991). using the following relation taken frou King(2000) ΙΟΡο=015ΗΕΠ|0.019.," The metallicity of the HII regions was converted from [O/H] values given in the literature \citep{kwi81, mcc85, vil88, zar94} using the following relation taken from \citet{kin00}: $[O/Fe]=-0.184[Fe/H]+0.019$ ."1181 The deprojected radius for the TWD regious was calculated as above., The deprojected radius for the HII regions was calculated as above.1182" The metallicity of the ΠΤΙ regions is fit by |Fe/II| =0.12]2:0.02]|0.33[250.07]. which is somewhat steeper hau that for Ru,the field red giants."," The metallicity of the HII regions is fit by [Fe/H] $= -0.12[\pm0.02] R_{dp} + 0.33[\pm0.07]$ , which is somewhat steeper than that for the field red giants."1183 The relation for tle WI reeious slows a trend that is similar to that of the field red elauts. but with a larger scatter.," The relation for the HII regions shows a trend that is similar to that of the field red giants, but with a larger scatter."1184 It is natural that the ποσα metallicity of the field red giants is lower than that of the WIT regions. because the red giauts are wich older han the IIII regions.," It is natural that the mean metallicity of the field red giants is lower than that of the HII regions, because the red giants are much older than the HII regions."1185 Then we derive the distance modulus of each region using the information eiven above., Then we derive the distance modulus of each region using the information given above.1186" Table 2 lists the xumuueters related to the TRGD icthod: the observed f-hand magnitude of the TRGD Uren). the extinction corrected L-band magnitude of the TROB (της). the nean color of the TROB άτυπο]. the mean color measured at M,=3.5 [AVPy.as]. the mean netallicity (|FeTI) of the RGB. the absolute magnitude ofthe TROB (Wyrgep). aud the distance modulus (iMy]."," Table 2 lists the parameters related to the TRGB method; the observed $I$ -band magnitude of the TRGB $I_{TRGB}$ ), the extinction corrected $I$ -band magnitude of the TRGB $I_{0,TRGB}$ ), the mean color of the TRGB $(V-I)_{0,TRGB}$ ], the mean color measured at $M_I = -3.5$ $(V-I)_{0, -3.5}$ ], the mean metallicity ([Fe/H]) of the RGB, the absolute magnitude of the TRGB $M_{I, TRGB}$ ), and the distance modulus $(m-M)_{0}$ ]."1187 Figure 6 displavs Ipper versus [Fe/THI] for the tecre regions iu M33., Figure 6 displays $I_{TRGB}$ versus [Fe/H] for the ten regions in M33.1188 The value of τραμ varies little. wit uo obvious net metallicity dependence.," The value of $I_{TRGB}$ varies little, with no obvious net metallicity dependence."1189 The mean vali of τομ for the ten regions is Zprge;p=20.58c0.0 showing a remarkably small dispersion.," The mean value of $I_{TRGB}$ for the ten regions is $I_{TRGB} = 119020.88\pm0.04$, showing a remarkably small dispersion."1191 The average value of the distance moduli for all of the fields is calculated to be (avMoyrere=2L81cx0.0[Grandoni) Uri (systematic).," The average value of the distance moduli for all of the fields is calculated to be $(m-M)_{0,TRGB}=24.81\pm0.04$ $^{+0.15}_{-0.11}$ (systematic)."1192 The errors for the cistauce modulus are based ou the error budget listed in. Table 3., The errors for the distance modulus are based on the error budget listed in Table 3.1193 The calibration of the TRGD is based. ou Galactic elobular clusters with [Fe/II] = 2.1 to 0.7 dex. vet the derived mean metallicities of the four iuner regions iu our saluple ([Fo/II] = 0.61 to 0.68 dex) are slightly larger than the upper boundary of the calibration range.," The calibration of the TRGB is based on Galactic globular clusters with [Fe/H] = –2.1 to –0.7 dex, yet the derived mean metallicities of the four inner regions in our sample ([Fe/H] = –0.61 to –0.68 dex) are slightly larger than the upper boundary of the calibration range."1194" If we use only the six other regions. excluding these four iuner ones, we obtain an average distance modulus of (11) .j(svstematic)."," If we use only the six other regions, excluding these four inner ones, we obtain an average distance modulus of $(m-M)_{0,TRGB}=24.83\pm0.06$ $^{+0.15}_{-0.11}$ (systematic)."1195"un If the theoretical calibration given by Salavis&Cassisi(1998). is adopted CMrpge;p=3.953|LL.IT|OLLALHp? and [ALT]2.39.2:0|OLG87|Do,ss].36.851,""Do,as)?opGas3s| μὴν— the average distance modulus will be GaMorpep=2190940.0 statistical). which is 0.2 mae fainter than that derived usine the enipirical calibration of Lee.Freediman.&Madore(1993)."," If the theoretical calibration given by \citet{sal98} is adopted $M_{I,TRGB} = -3.953 + 0.437[M/H] + 0.147[M/H]^2$ and $[M/H]=-39.270+64.687[(V-I)_{0,-3.5}] -36.351[(V-I)_{0,-3.5}]^2 1196+6.838 [(V-I)_{0,-3.5}]^3 $ ), the average distance modulus will be $(m-M)_{0,TRGB}=24.99\pm0.04$ (statistical), which is 0.2 mag fainter than that derived using the empirical calibration of \citet{lee93}."1197.. However. it las beeu found that the distance obtained with the theoretical calibration is not consistent with other results as shown by Dolphinctal.(2001) in IC 1613.," However, it has been found that the distance obtained with the theoretical calibration is not consistent with other results as shown by \citet{dol01} in IC 1613."1198 So we prefer to use the empirical calibration ratler than the theoretical oue iu this study., So we prefer to use the empirical calibration rather than the theoretical one in this study.1199 Finally we adopt GnADytrop=2L81£0.0Lrandou) |irit (svstematic) as the TRGB distance modulus to N23.," Finally we adopt $(m-M)_{0,TRGB}=24.81\pm0.04$ $^{+0.15}_{-0.11}$ (systematic) as the TRGB distance modulus to M33."1200 We lave deteriined the distance to M33 using the red chunip as well., We have determined the distance to M33 using the red clump as well.

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