ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 This discovery was simultaneously ramed in terms of ollset. pseudobulges by Hu (2008). with Ην pseudobulge sample effectively a barred. galaxyslot.," This discovery was simultaneously framed in terms of offset pseudobulges by Hu (2008), with Hu's pseudobulge sample effectively a barred galaxy."3 Graham. (20082) reported that there was a Q.1 to 01 per cent. probability of the galaxy saniple being olfset ον chance., Graham (2008a) reported that there was a 0.1 to 0.01 per cent probability of the galaxy sample being offset by chance.4 The deviant nature of these barred/pseudobulse ealaxies. which has included the Milky Way. was again the focus in Craham (2008b). Graham Li (2009). αςοιτὰ Ixaullmann (2009). Greene et ((2010). and. discussed extensively in mid 2010 by Graham et ((2010).," The deviant nature of these barred/pseudobulge galaxies, which has included the Milky Way, was again the focus in Graham (2008b), Graham Li (2009), Gadotti Kauffmann (2009), Greene et (2010), and discussed extensively in mid 2010 by Graham et (2010)."5 This latter work expanded the sample of galaxies used. in 2008-2000 from ~50 to 64 (including 39 disc galaxies. 20 of which are barred galaxies) and constructed new relations after having identified ancl corrected an additional sample bias an artificial black hole mass floor in the cata set allecting past studies.," This latter work expanded the sample of galaxies used in 2008-2009 from $\sim$ 50 to 64 (including 39 disc galaxies, 20 of which are barred galaxies) and constructed new relations after having identified and corrected an additional sample bias — an artificial black hole mass floor in the data set — affecting past studies."6 The classical Miu -0 relation. was constructed: using galaxies of all morphological type (Ferrarese Merritt 2000: Gebhardt et 22000: Merritt Ferrarese 2001: Tremaine et 22002).," The classical $M_{\mathrm{bh}\,}$ $\,\sigma$ relation was constructed using galaxies of all morphological type (Ferrarese Merritt 2000; Gebhardt et 2000; Merritt Ferrarese 2001; Tremaine et 2002)."7" To distinguish from this. Graham. (2008a) introduced. the barless Adv-0 relation and. the elliptical-ealaxv Mig, -0 relation (see also Llu 2008 in regard to the latter) and reported that “Removal of the seven barred ealaxies [rom the Tremaine et ((2002) set of 31 galaxies gives à barless Alia -0 relation with an intrinsic scatter of 0.17 dex 00.27 dex for the 31 galaxies) and a total scatter of 0.25 dex 00.34 dex for the 31 galaxies)."," To distinguish from this, Graham (2008a) introduced the barless $M_{\mathrm{bh}\,}$ $\,\sigma$ relation and the elliptical-galaxy $M_{\mathrm{bh}\,}$ $\,\sigma$ relation (see also Hu 2008 in regard to the latter), and reported that ""Removal of the seven barred galaxies from the Tremaine et (2002) set of 31 galaxies gives a barless $M_{\mathrm{bh}\,}$ $\,\sigma$ relation with an intrinsic scatter of 0.17 dex 0.27 dex for the 31 galaxies) and a total scatter of 0.25 dex 0.34 dex for the 31 galaxies)""."8 The Afin -0 relation was predicted (Silk Rees 1998: IHachnelt. Natarajan Rees 1998: Fabian 1999. 2010) before Π was observed.," The $M_{\mathrm{bh}\,}$ $\,\sigma$ relation was predicted (Silk Rees 1998; Haehnelt, Natarajan Rees 1998; Fabian 1999, 2010) before it was observed."9 The Silk Rees (1998). Migjy-0 relation with a slope of 5 is now observationally supported by both the harless Mig -0 relation ancl the elliptical-onlv. μι e relation (Graham et 22010: see also Ferrarese Forcl’s 2005 classical Mia- 0 relation).," The Silk Rees (1998) $M_{\mathrm{bh}\,}$ $\,\sigma$ relation with a slope of 5 is now observationally supported by both the barless $M_{\mathrm{bh}\,}$ $\,\sigma$ relation and the elliptical-only $M_{\mathrm{bh}\,}$ $\,\sigma$ relation (Graham et 2010; see also Ferrarese Ford's 2005 classical $M_{\mathrm{bh}\,}$ $\,\sigma$ relation)."10 As revealed by Novak. Faber Dekel (2006). it is not vet established which physical property of the host bulge best correlates with the mass of the central black hole.," As revealed by Novak, Faber Dekel (2006), it is not yet established which physical property of the host bulge best correlates with the mass of the central black hole."11 What is known is that the scatter about the classical Ali -0 relation has increased as the number of barred. and likely pseudobulge. galaxies has increased. (Llu 2008: Graham 2008b: Gülltekin et 22009: Graham οἱ 22010).," What is known is that the scatter about the classical $M_{\mathrm{bh}\,}$ $\,\sigma$ relation has increased as the number of barred, and likely pseudobulge, galaxies has increased (Hu 2008; Graham 2008b; Gülltekin et 2009; Graham et 2010)."12 Graham (2008a) wrote “Bar instabilities are believed: to lead to the formation of pseudobulges.," Graham (2008a) wrote ""Bar instabilities are believed to lead to the formation of pseudobulges."13 Such evolution may have resulted. in. (pseudo)bulges with an increased. velocity dispersion and luminosity but a relatively anemic SMDLIL (unless it also grew. during the formation of the pseudobulge)., Such evolution may have resulted in (pseudo)bulges with an increased velocity dispersion and luminosity but a relatively anemic SMBH (unless it also grew during the formation of the pseudobulge).14" HE the barred. galaxies do indeed have cliscrepantly low SALBIL masses rather than high e-values. they should also appear as systematic outliers in the AM -L diagram."""," If the barred galaxies do indeed have discrepantly low SMBH masses rather than high $\sigma$ -values, they should also appear as systematic outliers in the $M_{\mathrm{bh}\,}$ $L$ diagram."""15 The work by Graham and collaborators does not rule out this possibility which is what the Nature paper in question has attempted to answer., The work by Graham and collaborators does not rule out this possibility which is what the Nature paper in question has attempted to answer.16 Pseudobulges are notoriously hard to identify. and there is not vet a consensus as to how to define them.," Pseudobulges are notoriously hard to identify, and there is not yet a consensus as to how to define them."17 For example. at odds with the Nature article. Pecbles’ (2011) review of," For example, at odds with the Nature article, Peebles' (2011) review of"18which is the same limit because of (2.113).,which is the same limit because of \ref{fin_est_lam}) ).19 From (2.11)). (2.12)) and (2.13)). inequality (2.2)) directly The fact that A is independent of ej follows directly from the comparison principle aud inequality (2.2)).," From \ref{l+}) ), \ref{lambda+}) ) and \ref{lambda-}) ), inequality \ref{ergo_eq1}) ) directly The fact that $\l$ is independent of $v_{0}$ follows directly from the comparison principle and inequality \ref{ergo_eq1}) )."20 LI We can now present the proof of Propositions 1.1. aud 1..., $\hfill{\Box}$ We can now present the proof of Propositions \ref{AM7Z} and \ref{ganaza}.21 Using inequality (2.2)) of Proposition 2.1.. we can easilv see that (1.2)) directly follows.," Using inequality \ref{ergo_eq1}) ) of Proposition \ref{ergo}, , we can easily see that \ref{Ymala1}) ) directly follows."22 It remains to show (1. 1))., It remains to show \ref{Ymala3}) ).23 We argue in two Let axà., We argue in two Let $u\leq \tilde{u}$.24 Call A=f(u.f) aud \=fict).," Call $\l=\o{f}(u,t)$ and $\tilde{\l}=\o{f}(\tilde{u},t)$."25" Lot eaud 6 be the solutions of: aud respectively,", Let $v$and $\tilde{v}$ be the solutions of: and respectively.26 Assume without loss of generality that vy=0., Assume without loss of generality that $u_{0}=0$.27 Using CÀ3). we deduce that f(t.7.0.£)xft.T.uf).," Using (A3), we deduce that $f(\tilde{v},\tau,\tilde{u},t)\leq f(\tilde{v},\tau,u,t)$."28 ence. the comparison principle gives: From inequality (2.2)) of Proposition 2.1.. we have: We then casily couchide that À<A as a consequence of (2.15)) aud (2.16) We refor the reader to Proposition 3.2. which inuplies in particular the coutiuuitv of f.," Hence, the comparison principle gives: From inequality \ref{ergo_eq1}) ) of Proposition \ref{ergo}, we have: We then easily conclude that $\tilde{\l}\leq \l$ as a consequence of \ref{argu_contra}) ) and \ref{argu_contra1}) We refer the reader to Proposition \ref{lwt3b} which implies in particular the continuity of $\o{f}$."29 The main idea of the proof is to apply aperturbation argument using the inequality |AT(T})A|«x3, The main idea of the proof is to apply aperturbation argument using the inequality $|\l^{\pm}(T)-\l|\leq \frac{\xi}{T}$.30 N This is a direct consequence of the Cauchy-Péaane theoreur using in particular the continuity of f (see 1.1)). Assume that there exists ulcCH0.xX) another solution of (1.6)).," $\hfill{\Box}$ This is a direct consequence of the Cauchy-Péaano theorem, using in particular the continuity of $f$ (see \ref{Ymala3}) Assume that there exists $u^{1}\in31C^{1}([0,\infty);\R)$ another solution of \ref{homog_eq}) )."32 Define k(t)=[a(f) utt]. we conipute (with the sign function sgu(rc)—.c/L.e| if;zx 0): where for the last liue we lave used the monotonicity of f£ (see (L0).," Define $k(t)=|u^{0}(t)-u^{1}(t)|$ , we compute (with the sign function $\sgn(x)=x/|x|$ if $x\neq 0$ ): where for the last line we have used the monotonicity of $\o{f}$ (see \ref{Ymala3})))."33 This imunediately implies that uy— , This immediately implies that $u^{0}=u^{1}$ .34"ul, L1 ", $\hfill{\Box}$ 35values of q. at different magnitudes of the primary component. produces a broadening of the sinele-star MS. (o its bright- and red-haud side.,"values of $q$, at different magnitudes of the primary component, produces a broadening of the single-star MS, to its bright- and red-hand side."36" In principle. (he ratio between (he number of stars Iving on (he red side of the single-star MS ancl the total number of stars observed along the ""broadened MS provides the cluster binary fraction."," In principle, the ratio between the number of stars lying on the red side of the single-star MS and the total number of stars observed along the “broadened MS” provides the cluster binary fraction."37" In. practice. depending on the photometric error of the data. a minimum value of the mass ralio (q,;,) exists below which it is impossible to observationally disünguish a binary system [rom a single MS star."," In practice, depending on the photometric error of the data, a minimum value of the mass ratio $q_{min}$ ) exists below which it is impossible to observationally distinguish a binary system from a single MS star."38 Moreover. it is necessary to take into account a number of effects. like stellar blends aud the contamination bv foregroundbackground lield stars. which can add spurious sources in the CMD.," Moreover, it is necessary to take into account a number of effects, like stellar blends and the contamination by foreground/background field stars, which can add spurious sources in the CMD."39 Indeed. chance superposiGons of (vo stars (blends) ean produce a Iuminosity enhancement that mimics the magnitude shift characteristic of a genuine binarv svstem.," Indeed, chance superpositions of two stars (blends) can produce a luminosity enhancement that mimics the magnitude shift characteristic of a genuine binary system."40 In order to correct for this effect we analvzed (he distribution of the residuals between the input ancl the output magnitudes of the artificial star catalogue built by 10 for the completuess study (see previous section)., In order to correct for this effect we analyzed the distribution of the residuals between the input and the output magnitudes of the artificial star catalogue built by B10 for the completness study (see previous section).41 From the asymmetry of the distribution (vhich is skewed Coward brighter output magnitudes because of the blending between artificial and real stus) we estimated that the percentage of blended sources Chat would mimick binary svstems will 4>qu. varies [rom ~6% in the core. to less (han 0.2% in the external regions.," From the asymmetry of the distribution (which is skewed toward brighter output magnitudes because of the blending between artificial and real stars) we estimated that the percentage of blended sources that would mimick binary systems with $q>q_{min}$ , varies from $\sim426\%$ in the core, to less than $0.2\%$ in the external regions."43 D10 also estimated the Galactic field contamination in the direction of MIO. finding that it is verv low: even in the worst case (he WFPC2 data-set). where the munhber of cluster sources is small. the field stars are just ~37€ of the total sample.," B10 also estimated the Galactic field contamination in the direction of M10, finding that it is very low: even in the worst case (the WFPC2 data-set), where the number of cluster sources is small, the field stars are just $\sim 3\%$ of the total sample."44 Despite such a low value. for a proper measurement of the binary fraction we performed a detailed study of the field contamination as a function of the magnitude.," Despite such a low value, for a proper measurement of the binary fraction we performed a detailed study of the field contamination as a function of the magnitude."45 From the Galaxy model of Robinοἱal.(2003) we retrieved a catalogue covering an area of 0.5deg? in the direction of MIO. and we randomly extracted two sub-samples ol svnthetie stars. scaled to the fields of view of the ACS and WFPC2 data-sets.," From the Galaxy model of \citet{robin03} we retrieved a catalogue covering an area of $0.5\deg^2$ in the direction of M10, and we randomly extracted two sub-samples of synthetic stars, scaled to the fields of view of the ACS and WFPC2 data-sets."46 Their magnitudes were converted Irom the Johnson to the VEGAMAG photometric svstem adopting (he prescriptions of Siriannietal.(2005)., Their magnitudes were converted from the Johnson to the VEGAMAG photometric system adopting the prescriptions of \citet{sirianni05}.47. Finally. by. exploiting the artilicial-star catalogue used for the completeness (Sect. 2)).," Finally, by exploiting the artificial-star catalogue used for the completeness (Sect. \ref{data}) ),"48 we obtained a catalogue of svnthetic field stars that includes the observational biases (1incompleteness and blending). for both the ACS and WEDPC? data-sets.," we obtained a catalogue of synthetic field stars that includes the observational biases (incompleteness and blending), for both the ACS and WFPC2 data-sets."49 Once all (he contaminant effects are taken into account. the binary fraction was estimated as (he number of stars in the dividedby the total number of stars.," Once all the contaminant effects are taken into account, the binary fraction was estimated as the number of stars in the dividedby the total number of stars,"50"where Ad, is the mass of the galaxy and ry is the Gaussian scale length.",where $M_g$ is the mass of the galaxy and $r_g$ is the Gaussian scale length.51 In modeling. 9 is no longer a constant and depeuds on r as. Successful solutions a'e listed in Table 3..," In modeling, $\delta$ is no longer a constant and depends on $r$ as, Successful solutions are listed in Table \ref{fermion.table}."52 The geueral treud is tliat ‘or the saime g. the sinaller he particle mass. nr. the arger the trausition radius. ri.," The general trend is that for the same $g$ , the smaller the particle mass, $m$, the larger the transition radius, $r_t$."53 If we measure he significance of a model wy the radial coverage. which also corresponds the largest encircled mass coverage. the smallest i solution is tlie most Πάρο‘aut for a given g.," If we measure the significance of a model by the radial coverage, which also corresponds the largest encircled mass coverage, the smallest $m$ solution is the most important for a given $g$."54 For the simallest mass solutious. tlie rauge of particle nass ds gà=3.9~2.7 eV [or g ο the cosmic baryonu-DM raio of 0.2.," For the smallest mass solutions, the range of particle mass is $m = 3.9 \sim 2.7$ eV for $g=1 \sim 4$ for the cosmic baryon-DM ratio of 0.2."55 A larger ALVOL ractiou 'educes the parti(‘le mass., A larger baryon fraction reduces the particle mass.56 For the sinallest me solutions. resultant voltume- aud column density profiles are aliost identical as shown in Figs.10 aud 12..," For the smallest $m$ solutions, resultant volume- and column density profiles are almost identical as shown in \ref{fermion.rho} and \ref{fermion.Sigma}."57 There are πεsme deficiencies of nass ceusities inside the ocation of the radial critical curve. 7.," There are some deficiencies of mass densities inside the location of the radial critical curve, $r_c$."58 However. in 3D aud 2D encircled uass profiles shown in Figs.11 aud 13.. these mass deficiencies. which amount to at most of he 3D encircled mass usi(le rj (2x101234. ). are not noticeable.," However, in 3D and 2D encircled mass profiles shown in \ref{fermion.M3} and \ref{fermion.M2}, these mass deficiencies, which amount to at most of the 3D encircled mass inside $r_E$ $2 \times 10^{12} M_\odot$ ), are not noticeable."59" The maxiuum allowed particle mass. ni. is obtained by eqtating Q, aud ODip as 3.27 eV. As can be seen in Table £L. successful solutious lave smaller particle masses."," The maximum allowed particle mass, $m$, is obtained by equating $\Omega_\nu$ and $\Omega_{\rm DM}$ as 3.27 eV. As can be seen in Table \ref{neutrino.table}, successful solutions have smaller particle masses."60 Thereore we are clealing with the cases that dark matter consists of neutrinos aud atother form of yarticles. possibly. iondegenerate cold. dark matter particles.," Therefore we are dealing with the cases that dark matter consists of neutrinos and another form of particles, possibly, nondegenerate cold dark matter particles."61 The volume aud coumn deusity proliles are given iu Fies.ll and 16 respectively., The volume and column density profiles are given in \ref{neu.rho} and \ref{neu.Sigma} respectively.62 Again he model profiles are always lower than tie observed profile lear the center., Again the model profiles are always lower than the observed profile near the center.63 However. the cdiscrepaucy. between the models and observation is negligible in the inear plots of the eucircled masses shown in Fies.15 and 17..," However, the discrepancy between the models and observation is negligible in the linear plots of the encircled masses shown in \ref{neu.M3} and \ref{neu.M2}."64 Athough η depeids on the ratio. A. the resultant. profiles a'e essentially identical aud they are uot distingulshable from he general leriuiou cases.," Although $m$ depends on the baryon-DM ratio, $R$, the resultant profiles are essentially identical and they are not distinguishable from the general fermion cases."65 For /?=0.2 aud 0.5. the simallest nass solutions are for im=1.6 aud 1.1 eV respectively.," For $R=0.2$ and 0.5, the smallest mass solutions are for $m = 1.6$ and 1.1 eV respectively."66" Π is typical to have asmall [raction (<2%)) of deficiency in the mocel 3D encircled mass iuside re 1011A, ).", It is typical to have asmall fraction $<$ ) of deficiency in the model 3D encircled mass inside $r_E$ $\times10^{14}M_\odot$ ).67 A brightest cluster galaxy at the center of a cluster. typically has a stellar mass," A brightest cluster galaxy at the center of a cluster, typically has a stellar mass"68aximitun luminosity. of tie. nearby aid clistaut salupes.,"maximum luminosity, of the nearby and distant samples."69" The early light-curve beliavior should be intlrencecdl by the aiout of ""Ni synthesize in tlie exjiosion. as well as 1le opacity of the ejecta (Shieevamaetal.1992:BranchIlokhlov1903:Vacca&Leibundgut1996:Hóllicletal.1993.1995:Domíuguez2001)."," The early light-curve behavior should be influenced by the amount of $^{56}\mbox{Ni}$ synthesized in the explosion, as well as the opacity of the ejecta \citep{Shigeyama:92,Branch:92,70Khokhlov:93,Vacca:96,Hoflich:93,Hoflich:98,Dominguez:01}."71 . Changes iu either of these. for exaimple. due to chaugilg progenitor metalicity with redshilt. cotld affect the tse of SNe Ja as standard cauctles.," Changes in either of these, for example, due to changing progenitor metallicity with redshift, could affect the use of SNe Ia as standard candles."72 An ewAutiouary ellect of ().2 mag to 0.5 WotId nullify the SN Ia evidence hat the Universe ls acceerating. and measuring w to requires that any eflec be sinaller that 0.01 mag.," An evolutionary effect of 0.2 mag to $z=0.5$ would nullify the SN Ia evidence that the Universe is accelerating, and measuring $w$ to requires that any effect be smaller than 0.04 mag."73 There are other routes to studying evolution with redsult: comparing SNe Ia in different host. galaxy euvirouiments (Hamuyetal.2000:Sullivan2003:Crallagrer2005).. and via detailed spectroscopic studies (Hook 22005. Blouclit O06. Broncler 22000. in preparation).," There are other routes to studying evolution with redshift: comparing SNe Ia in different host galaxy environments \citep{Hamuy:00,Sullivan:03,74Gallagher:05}, and via detailed spectroscopic studies (Hook 2005, Blondin 2006, Bronder 2006, in preparation)."75 Neither approach has ttrued up auy evidence of evolution., Neither approach has turned up any evidence of evolution.76 The rise-time has implicatious for SNe Ia explosion mocels., The rise-time has implications for SNe Ia explosion models.77 Varying the rise time from 20 to 16 days at a fixed peak luminosity changes the 1uplied amour( of PONi synthesized in the explosion wv —10Ut (Conarcoetal.2000.., Varying the rise time from 20 to 16 days at a fixed peak luminosity changes the implied amount of $^{56}$ Ni synthesized in the explosion by $-10\%$ \citep{Contardo:00}.78 Models of single white dwar. progenitor syseuis generaly predict ‘Ise times 11 ile range 13-19 davs. while systems iuvolviug two white dwarls allow for konger rise πο because interaction with he disk of unace'eLed materia [rom the clisruj»ted compajon slows je. clifTusion «. photons (Hóllic1&Whokhlov1996:Hóllichetal.2002).," Models of single white dwarf progenitor systems generally predict rise times in the range 13–19 days, while systems involving two white dwarfs allow for longer rise times because interaction with the disk of unaccreted material from the disrupted companion slows the diffusion of photons \citep{Hoflich:96, Hoflich:02}."79. The cdeermination of the ‘ise times has been the stbjec oL some dispue., The determination of the rise times has been the subject of some dispute.80 Historicaly. well-c:dlibrated. photoiet'v of SNe Ia has been quite clificult to obtain.," Historically, early-time, well-calibrated photometry of SNe Ia has been quite difficult to obtain."81 Some of the earliest uclies of Se Ta light-curve shapes examiner the rise 1ime (Pskovskii1981., Some of the earliest studies of SNe Ia light-curve shapes examined the rise time \citep{Pskovskii:84}.82h R99) presented early observatious of a set of jiearby. SNe Ia deteced 10-18 days before Danityum B lunilosity., \citet[hereafter R99]{Riess:99a} presented early observations of a set of nearby SNe Ia detected 10–18 days before maximum $B$ luminosity.83 This data set was co1911:icted primarily from. uufilte'ed early detections. solue [roni alateus observers.," This data set was constructed primarily from unfiltered early detections, some from amateur observers."84 They transforme| these observatious to staard pass bands (in »articular. B8) usiie moclels of early-timme SN las)ectra aid colors.," They transformed these observations to standard pass bands (in particular, $B$ ) using models of early-time SN Ia spectra and colors."85 They Cousicdered various αἰθ-ἰine light-cu've parameterlzations. concuciig that the rise time for a [iducial SN Ia was 19.5+0.2 days.," They then considered various late-time light-curve parameterizations, concluding that the rise time for a fiducial SN Ia was $19.5 \pm 0.2$ days."86 Riessetal.(1999b)| compare this number with the preπαν analysis of Coldlaberetal.(2001.hereafter.GOL) for disat SNe Ia and conclued liat the rise times differec| by 2.540.1 days. a siguificauce of ~6o. and a ¢ear slguature of evoIulon.," \citet{Riess:99b} compared this number with the preliminary analysis of \citet[hereafter G01]{Goldhaber:01} for distant SNe Ia and concluded that the rise times differed by $2.5 \pm 0.4$ days, a significance of $\sim 6\ \sg$, and a clear signature of evolution."87 Alderiugetal.(2000.hereafterAINNOO)| argued that this cotiparison was based ou analyses that had ignored the significant correlatious between the light-curve parameters. aud that taking these p‘operly into account increased tlie errors o ithe rise time tod-1.2 days lor the distant sample.," \citet[hereafter AKN00]{AKN:00} argued that this comparison was based on analyses that had ignored the significant correlations between the light-curve parameters, and that taking these properly into account increased the errors on the rise time to $\pm 1.2$ days for the distant sample."88 They coucluded that the significance of the dille‘ence was closer to 1.5o., They concluded that the significance of the difference was closer to $1.5\ \sg$.89 Qir purpose here is uot to revisit this σοιtroversy: rather. we present a new. siguilicantly lore p'ecise (~6 times) measurement of the hieredshift rise time anc compare it with the value for nearby SNe.," Our purpose here is not to revisit this controversy; rather, we present a new, significantly more precise $\sim 6$ times) measurement of the high-redshift rise time and compare it with the value for nearby SNe."90 This has particular relevance because current SN projects place more stringent requirenents on the staudard-caucdle assuimptio1., This has particular relevance because current SN projects place more stringent requirements on the standard-candle assumption.91 This paper preseuts measurements of tlie rise, This paper presents measurements of the rise92This form is correct onlv in very near the critical point /=1: for laree teniperatures. ΕΙ}»to πο that the overall form expected for the mass of the quasi-glion becomes m(l) bi. where @ and b are constants.,"This form is correct only in very near the critical point $t=1$; for large temperatures, $\xi(t) \sim t$, so that the overall form expected for the mass of the quasi-gluon becomes m(t) + b t, where $a$ and $b$ are constants."93 The resulting behavior is illustrated in releritmass (left)., The resulting behavior is illustrated in \\ref{critmass} (left).94 It. would certainly be of interest to cheek this form clirectly through caleulations in SU(2) gauge theory: unfortunately. there does not seem (o exist any lattice study providing an extrapolation to the continuum. thus eliminating finite lattice size effects.," It would certainly be of interest to check this form directly through calculations in $SU(2)$ gauge theory; unfortunately, there does not seem to exist any lattice study providing an extrapolation to the continuum, thus eliminating finite lattice size effects."95 Older studies of e(7) and P(P) in terms of a gluon mass (7T). [25]. did in fact lead to the form shown in re[mass.., Older studies of $\e(T)$ and $P(T)$ in terms of a gluon mass $m(T)$ \cite{Golo93} did in fact lead to the form shown in \\ref{mass}.96" For 5U(3). the transition is of first order. [2.3].. so that all quantitites remain finite al T, and an equivalent form cannot be given."," For $SU(3)$, the transition is of first order \cite{Celik83,Kogut83}, so that all quantitites remain finite at $T_c$ and an equivalent form cannot be given."97 Nevertheless. in all cases we have a strong increase of both e(£) and ACF) in some range above Ti. and so we shall maintain the unctional dependence (4//4)) with an open exponent c.," Nevertheless, in all cases we have a strong increase of both $\e(T)$ and $\Delta(T)$ in some range above $T_c$, and so we shall maintain the functional dependence \ref{critmass4}/ \ref{critmass5}) ) with an open exponent $c$."98 The resulting quasi-particle mass is (hus expected to have the form with constants a.b.€.," The resulting quasi-particle mass is thus expected to have the form m(T) = + bt, with constants $a,~b,~c$."99 Using Chis mass. we now determine (he parameters a.b.e by calculating the enerey density [rom ((17) and A(T) from (4)).," Using this mass, we now determine the parameters $a,b,c$ by calculating the energy density from (17) and $\Delta(T)$ from \ref{delta-run}) )."100 The resulting mass and the corresponding parameters are shown in (right)., The resulting mass and the corresponding parameters are shown in \\ref{critmass} (right).101 The fits to energv density and interaction measure are given in, The fits to energy density and interaction measure are given in102In order to determine the absolute wavelength scales for the LiF LÀ spectra from the three pointings. we used the airglow emission lines as reference wavelengths.,"In order to determine the absolute wavelength scales for the LiF 1A spectra from the three pointings, we used the airglow emission lines as reference wavelengths."103 We then (he spectra from the (hree poinüngs ancl shifted to the Local Standard of Rest (LS) reference frame., We then co-added the spectra from the three pointings and shifted to the Local Standard of Rest (LSR) reference frame.104 The 1020 to 1045 rreeion of the resulting satellite-night and day + night spectra are displaved in Figure 5.., The 1020 to 1045 region of the resulting satellite-night and day $+$ night spectra are displayed in Figure \ref{fig:coadd}.1055 We [ound the continuum level in the satellite-night spectrum bx fitting a smooth curve to the surrounding spectral region., We found the continuum level in the satellite-night spectrum by fitting a smooth curve to the surrounding spectral region.106 We then searched (he residual spectrum for emission features., We then searched the residual spectrum for emission features.107 None were lound in close proximity (o the rresonance line rest wavelengths in the LSR reference frame., None were found in close proximity to the resonance line rest wavelengths in the LSR reference frame.108 If cosmic features had existed. their widths would have equaled or exceeded the instrumental width function. their signals would have been calculated Irom the numbers of counts in excess of (he continuum within the extraction width. and their random uncertainties would have been caleulated from the square roots of the numbers of spectral counts (not residual counts) within the extraction width.," If cosmic features had existed, their widths would have equaled or exceeded the instrumental width function, their signals would have been calculated from the numbers of counts in excess of the continuum within the extraction width, and their random uncertainties would have been calculated from the square roots of the numbers of spectral counts (not residual counts) within the extraction width."109 We have followed this method. using the total instrumental width (generously set to 0.43 À)) as the extraction width. to determine the upper limits.," We have followed this method, using the total instrumental width (generously set to 0.43 ) as the extraction width, to determine the upper limits."110" The “signal” and 1 sigma statistical uncertainty intensities lor the rresonance lines al their rest wavelengths in the LSR reference [rame are 180 + 330 and -180 + 310 photons 7? F !. for the 1032 and 1038 llines. respectively,"," The “signal” and 1 sigma statistical uncertainty intensities for the resonance lines at their rest wavelengths in the LSR reference frame are 180 $\pm$ 330 and -180 $\pm$ 310 photons $^{-2}$ $^{-1}$ $^{-1}$, for the 1032 and 1038 lines, respectively."111 These measurements are subject to the above mentioned svstematic uncertainties of 14%., These measurements are subject to the above mentioned systematic uncertainties of $14\%$.112 We validated our technique by applving the following alternate extraction technique to sample spectra., We validated our technique by applying the following alternate extraction technique to sample spectra.113 We fit (he spectrum to a continuum and small emission feature. ihen varied the size of the feature to determine the 1 sigma uncertainties.," We fit the spectrum to a continuum and small emission feature, then varied the size of the feature to determine the 1 sigma uncertainties."114 The results were similar {ο those found by applying our techiiques to the same spectra., The results were similar to those found by applying our techniques to the same spectra.115 When the satellite-day portions of the data sets were added. the spectrum became more ragged.," When the satellite-day portions of the data sets were added, the spectrum became more ragged."116 From the variations between (he 120505. 120506. and. D12901 satellite-day. spectra we surmise (hat (he raggedness is primarily due to seattered lisht.," From the variations between the I20505, I20506, and B12901 satellite-day spectra we surmise that the raggedness is primarily due to scattered light."117 For the combined cay and night spectrum. the “signal” and 1 sigma statistical uncertainty intensities are 20 c 230 and 50 + D210 photons 27? ! JF. fort the 1032IBI and 1038J llines. respectively.," For the combined day and night spectrum, the “signal” and 1 sigma statistical uncertainty intensities are 20 $\pm$ 230 and 80 $\pm$ 210 photons $^{-2}$ $^{-1}$ $^{-1}$, for the 1032 and 1038 lines, respectively."118 The measurements are subject to the 14% svstematie uncertainties., The measurements are subject to the $14\%$ systematic uncertainties.119 For relerence. Table 2. tabulates these results and lists the Gghtest 1 and 2 sigma upper limits.," For reference, Table \ref{table:measurements} tabulates these results and lists the tightest 1 and 2 sigma upper limits."120 The l and 2 sigma upper limits were caleulated from the unrounded numbers., The 1 and 2 sigma upper limits were calculated from the unrounded numbers.121 We also searched [orT..IL.TIL. EL. IL. TL. IE. IL. IL. HL. IV.. VL. IL. and eemission lines in (he spectra taken with the LiF LÀ. SiC 1B. LiF 2A. and SiC 2A detector seenmientis.," We also searched for, and emission lines in the spectra taken with the LiF 1A, SiC 1B, LiF 2A, and SiC 2A detector segments."122 We relied on the satellite-night portion of the data when we searched for emission, We relied on the satellite-night portion of the data when we searched for emission123ÁN zo relations inferred.,$K$ $z$ relations inferred.124 We first. consider what. cllect the small Ποια of view (~357) of ΙΟΑΔΗ might have had on T96's modelling., We first consider what effect the small field of view $\sim 35\arcsec$ ) of IRCAM1 might have had on T96's modelling.125 While the much larger field of view of IRCAAIS provides a significant amount of blank sky in our images and therefore allows an accurate determination of the background level. this was not the case with ΕιςΑΔΗ.," While the much larger field of view of IRCAM3 provides a significant amount of blank sky in our images and therefore allows an accurate determination of the background level, this was not the case with IRCAM1."126 As T96 explain. they may have overestimated the sky. level in their images. ane we discuss here why this can lead to an underestimation of the host galaxy. brightness.," As T96 explain, they may have overestimated the sky level in their images, and we discuss here why this can lead to an underestimation of the host galaxy brightness."127 T96's radio galaxies have a typical ellective radius of a few areseconcds., T96's radio galaxies have a typical effective radius of a few arcseconds.128 At the edge of their field of view. a de Vaucouleurs profile does not have a negligible surface brightness. but rather will have frz23 = (for à typical j7;5z20.5 and ro 67).," At the edge of their field of view, a de Vaucouleurs profile does not have a negligible surface brightness, but rather will have $\mu \approx12923$ $^{-2}$ (for a typical $\mu_{1/2} \approx 20.5$ and $r_{\rm e} \approx 6\arcsec$ )."130 We have investigated the elIects of this on mocified dy-band images of some of our galaxies. by subtracting a constant value from all the pixels to simulate overestimation of the sky level.," We have investigated the effects of this on modified $K$ -band images of some of our galaxies, by subtracting a constant value from all the pixels to simulate overestimation of the sky level."131 We find that for small deviations from the true value. the effective. radius of the best-fitting model does. not change significantly. but the [Lux normalization of the stellar component is decreased.," We find that for small deviations from the true value, the effective radius of the best-fitting model does not change significantly, but the flux normalization of the stellar component is decreased."132" ""This. normalization is primarily determined at 72(7. since the signal-to-noise ratio is much lower at larger radii. while the sampling errors can be large near the centre. and the flux of the nuclear source can be varied to compensate for deficiencies in the quality. of the fit."," This normalization is primarily determined at $r \approx r_{\rm e}$, since the signal-to-noise ratio is much lower at larger radii, while the sampling errors can be large near the centre, and the flux of the nuclear source can be varied to compensate for deficiencies in the quality of the fit."133 For a tvpical galaxy with an error in. background determination of the level indicated: above. we find an increase of ~20 increase in the Dux attributed to the nucleus.," For a typical galaxy with an error in background determination of the level indicated above, we find an increase of $\sim 20$ increase in the flux attributed to the nucleus."134 Phe value of the 47 statistic also increases. and it is therefore worth considering whether more accurate results might be obtained if the sky level is included as an extra fitting parameter in the modelling process.," The value of the $\chi^2$ statistic also increases, and it is therefore worth considering whether more accurate results might be obtained if the sky level is included as an extra fitting parameter in the modelling process."135 Phere is also evidence that T96 may have systematically overestimated the scale lengths of their galaxies., There is also evidence that T96 may have systematically overestimated the scale lengths of their galaxies.136 Optical imaging with the (Dunlop ct 22000) produced a median scale length of kkpe. compared to kkpe determined by LOG.," Optical imaging with the (Dunlop et 2000) produced a median scale length of kpc, compared to kpc determined by T96."137 The ellect of overestimating the ns ds also to lower the contribution from the host galaxy in the central regions. and therefore to overestimate the contribution from a nuclear point source.," The effect of overestimating the $r_{\rm e}$ is also to lower the contribution from the host galaxy in the central regions, and therefore to overestimate the contribution from a nuclear point source."138 A systematic error of ~|70% in the scale lengths determined. by T96 would serve to produce central surface brightnesses 1 mmag too faint (again. the fitting procedure will tend to match the model to the data ator er.) and the model Dux within a aaperture will. be underestimated by ~—0.4 mmag. depending on the size of the galaxy.," A systematic error of $\sim +70$ in the scale lengths determined by T96 would serve to produce central surface brightnesses $\sim 1$ mag too faint (again, the fitting procedure will tend to match the model to the data at $r \approx r_{\rm e}$ ) and the model flux within a aperture will be underestimated by $\sim1390.4$ mag, depending on the size of the galaxy."140 Since this is very much in line with the shift determined by POG. it would seem to »e a Likely explanation for their result.," Since this is very much in line with the shift determined by T96, it would seem to be a likely explanation for their result."141 We can make a direct comparison between our results and those of LOG for the two objects which are common ο both samples., We can make a direct comparison between our results and those of T96 for the two objects which are common to both samples.142 We present the results of our A-band fits and those of T96 in Table 7.., We present the results of our $K$ -band fits and those of T96 in Table \ref{tab:compare}.143 Phe agreement for ὃς 234 is excellent. but it is less good for 3€ 79.," The agreement for 3C 234 is excellent, but it is less good for 3C 79."144 Optical imaging with he (Dunlop ct 22000) produces an elfective radius ο=9.4 kkpc. somewhere between the values we determine from our / ancl A-band images. and clearly indicating that “POG overestimated the true value.," Optical imaging with the (Dunlop et 2000) produces an effective radius $r_{\rm e} = 9.4$ kpc, somewhere between the values we determine from our $J$ and $K$ -band images, and clearly indicating that T96 overestimated the true value."145 A visual inspection of their Fig., A visual inspection of their Fig.146 2 appears to indicate that the larger effective radius is influenced by the companion source approximately nnorth of the radio galaxy., A2 appears to indicate that the larger effective radius is influenced by the companion source approximately north of the radio galaxy.147 Alternatively. there may have been additional scattered light within ICAMI which would artificially enhance the surface. brightness at large. racial distances and hence cause the scale length to be incorrectly overdetermined. although the good. agreement for 3€. 234 (where the bright nuclear point source would be expected to produce a large effect). seems to argue against this explanation.," Alternatively, there may have been additional scattered light within IRCAM1 which would artificially enhance the surface brightness at large radial distances and hence cause the scale length to be incorrectly overdetermined, although the good agreement for 3C 234 (where the bright nuclear point source would be expected to produce a large effect) seems to argue against this explanation."148 ]t is quite possible that cilferent elfects are at work for different objects., It is quite possible that different effects are at work for different objects.149 Since we can think of no likely elfect which would serve to the host galaxy brightnesses. we can expect a significant systematic error in the results of ‘LOG. even if we cannot be certain what the dominant cause of this error might be.," Since we can think of no likely effect which would serve to the host galaxy brightnesses, we can expect a significant systematic error in the results of T96, even if we cannot be certain what the dominant cause of this error might be."150 We have analysed near-infraredAL images of an ellectively complete sample of ten 8CRR radio galaxies with strong emission lines. and have separated them. into their nuclear and stellar components.," We have analysed near-infrared images of an effectively complete sample of ten 3CRR radio galaxies with strong emission lines, and have separated them into their nuclear and stellar components."151 We find that the colours of the nuclear components are well-moclellecd by a. reddened power-law. and the derived. unobscured. Lumiinositics are in excellent. agreement with the values predicted. from. the emission-line Iuminosities.," We find that the colours of the nuclear components are well-modelled by a reddened power-law, and the derived unobscured luminosities are in excellent agreement with the values predicted from the emission-line luminosities."152 We find evidence that the nuclear extinction increases with viewing angle. suggesting a [lattened. distribution for the obscuring material.," We find evidence that the nuclear extinction increases with viewing angle, suggesting a flattened distribution for the obscuring material."153 The contributions from the nuclear components make the model host galaxy. magnitudes fainter than the observed A magnitudes. and support a shift of the ÁN zo relation to fainter magnitudes by mamas for low-redshift 3CRR galaxies.," The contributions from the nuclear components make the model host galaxy magnitudes fainter than the observed $K$ magnitudes, and support a shift of the $K$ $z$ relation to fainter magnitudes by mag for low-redshift 3CRR galaxies."154 Using our observed L magnitudes and the assumption that the nuclear sources in radio galaxies are intrinsically no bluer than quasar nuclei; we can rule out a shift of more than mmag. independent of our two-dimensional mocdel-fitting procedure.," Using our observed $L'$ magnitudes and the assumption that the nuclear sources in radio galaxies are intrinsically no bluer than quasar nuclei, we can rule out a shift of more than mag, independent of our two-dimensional model-fitting procedure."155 We have investigated: possible causes of the dillerent results obtained by Vavlor ct ((1996) ancl ourselves., We have investigated possible causes of the different results obtained by Taylor et (1996) and ourselves.156 While we believe that Εθθς sample is hiasecl towards sources with [ow nuclear obscuration and therefore a relatively large nuclear fraction. this should not alleet their hostgalaxy magnitudes.," While we believe that T96's sample is biased towards sources with low nuclear obscuration and therefore a relatively large nuclear fraction, this should not affect their hostgalaxy magnitudes."157 We believe that their fainter magnitudes. are, We believe that their fainter magnitudes are158Lt has been suggested that UL processes resembling that ound in the Jovian svstem can occur in double degenerate xnarv svstenis. (Wu ct al.,It has been suggested that UI processes resembling that found in the Jovian system can occur in double degenerate binary systems (Wu et al.159 2002). and in degenerate star-planet systems (Li. Ferrario Wickramasinghe 1998: Willes Wu 2004. 2005).," 2002), and in degenerate star-planet systems (Li, Ferrario Wickramasinghe 1998; Willes Wu 2004, 2005)."160 “Pwo candidates for Ul double degenerate binary svstems are the »eeuliar X-rav sources ΗΝ JOSOG|15 and RA J1914|24., Two candidates for UI double degenerate binary systems are the peculiar X-ray sources RX J0806+15 and RX J1914+24.161 These objects show light curves which are modulated. on »eriods of 5.4 and 9.5 min respectively - these periods rave widely been taken to represent the binary orbital »eriods (Ramsay et al 2000. Ramsay. Hakala Cropper 2002. Israel ct al 2002).," These objects show light curves which are modulated on periods of 5.4 and 9.5 min respectively - these periods have widely been taken to represent the binary orbital periods (Ramsay et al 2000, Ramsay, Hakala Cropper 2002, Israel et al 2002)."162 Alost of the models which have »en put forward to account for these systems have two white chvarls orbiting around a common center of gravity (eg Cropper et al 2004)., Most of the models which have been put forward to account for these systems have two white dwarfs orbiting around a common center of gravity (eg Cropper et al 2004).163 Wu et al (2002) proposed that the X-ray emission from both these systems were powered. by Ul., Wu et al (2002) proposed that the X-ray emission from both these systems were powered by UI.164 Since their orbital periods are much shorter than the rotation period of Jupiter's satellites. and since the magnetic lied. of the magnetic white dwarf is much greater. than Jupiter. the currents are much greater and. therefore heat the footpoints to N-rav rather than UV. temperatures (in the case of Jupiter).," Since their orbital periods are much shorter than the rotation period of Jupiter's satellites, and since the magnetic field of the magnetic white dwarf is much greater than Jupiter, the currents are much greater and therefore heat the footpoints to X-ray rather than UV temperatures (in the case of Jupiter)."165 An essence of the Ul mocel for these svstemis is the large current flows. driven by the induced eam...," An essence of the UI model for these systems is the large current flows, driven by the induced e.m.f.,"166 along magnetic field lines connecting the two objects., along magnetic field lines connecting the two objects.167 For a magnetic object with a dipolar field. the field lines converge to its magnetic polar regions.," For a magnetic object with a dipolar field, the field lines converge to its magnetic polar regions."168 In such a field configuration. kinetic instabilities such as loss-cone instability can develop easily. leacing to cleetron-evelotron masers (Wu Lee 1979: see also Dulk 1985).," In such a field configuration, kinetic instabilities such as loss-cone instability can develop easily, leading to electron-cyclotron masers (Wu Lee 1979; see also Dulk 1985)."169 Moreover. while there is sullicient. plasma to provide the charge particles for the current. the plasma density. should be low enough to have a low plasma cut-olf frequency for the transmission. of masers.," Moreover, while there is sufficient plasma to provide the charge particles for the current, the plasma density should be low enough to have a low plasma cut-off frequency for the transmission of masers."170 For. double degenerate binaries ancl stellar planetary systems. some iuwnmonices of these masers are in radio wave-bands (Willes Wu 2004: Willes. Wu Ixuncic 2005).," For double degenerate binaries and stellar planetary systems, some harmonics of these masers are in radio wave-bands (Willes Wu 2004; Willes, Wu Kuncic 2005)."171 Moreover. these celectron-cvclotron masers are narrowly beamed. have a high xiehtness teniperature >10 I) and are almost. circularly polarized.," Moreover, these electron-cyclotron masers are narrowly beamed, have a high brightness temperature $\gg 10^8$ K) and are almost circularly polarized."172 Thus. the detection of strongly. circularly polarized. emission. (modulated. at. the orbital »eriod). would. provide an unambiguous proof of the oesence of UL in these compact systems.," Thus, the detection of strongly circularly polarized emission, (modulated at the orbital period), would provide an unambiguous proof of the presence of UI in these compact systems."173 We sought evidence of UL in various astrophysical systems., We sought evidence of UI in various astrophysical systems.174 ‘These include the systems ΗΝ J0806|15 and RA 21914|24 and as a control. we also observed the ultra-compact svstem ES Cet which has an orbital period of 10.3 min (Warner Wouelt 2002) and shows clear evidence of accretion (Espaillat ct al.," These include the systems RX J0806+15 and RX J1914+24 and as a control, we also observed the ultra-compact system ES Cet which has an orbital period of 10.3 min (Warner Woudt 2002) and shows clear evidence of accretion (Espaillat et al."175 2005)., 2005).176 While the presence of an accretion How should suppress Ul. it is interesting to search for racio emission around such short period binaries.," While the presence of an accretion flow should suppress UI, it is interesting to search for radio emission around such short period binaries."177 Our other arget was Ποσο ST6 (Gi STG) which is a dMA star at à distance of 4.7 pe with 3 known planets., Our other target was Gliese 876 (GJ 876) which is a dM4 star at a distance of 4.7 pc with 3 known planets.178 GJ S76d has an orbital period. of 1.94 days ancl has a mass ol ~ (Rivera οἱ al 2005)., GJ 876d has an orbital period of 1.94 days and has a mass of $\sim7.5_{\earth}$ (Rivera et al 2005).179 I£ the planet GJ ST6d. has a negligible154 magnetic field and a metallic core. UL could occur which may drive electron. evelotron. maser emission. analogous to the Jovian svstem.," If the planet GJ 876d has a negligible magnetic field and a metallic core, UI could occur which may drive electron cyclotron maser emission, analogous to the Jovian system."180 On the other hand if GJ STÓd has a substantial surface magnetic field. its field will interact directly with the Ποια of the host star and shield its core from being threaded by the Field lines of its dMA host-," On the other hand if GJ 876d has a substantial surface magnetic field, its field will interact directly with the field of the host star and shield its core from being threaded by the field lines of its dM4 host-star."181 In this case. field reconnection may. lead: to particle acceleration. and any radio emüssion would probably be due to svnchrotron radiation and not electron. evclotron maser emission.," In this case, field reconnection may lead to particle acceleration, and any radio emission would probably be due to synchrotron radiation and not electron cyclotron maser emission."182 While the radiation would be expected to be linearly polarized. we would not expect a clear periodicity related. to its orbital motion. unless the emission region is Iocalised and eclipsed for a fraction of the orbit.," While the radiation would be expected to be linearly polarized, we would not expect a clear periodicity related to its orbital motion, unless the emission region is localised and eclipsed for a fraction of the orbit."183 Willes. Wu Ixuncic (2004) presented calculations for the peak radio flux expected. from. ultra-compact binaries such as RN JOSOG|15 and RN 1914]24.," Willes, Wu Kuncic (2004) presented calculations for the peak radio flux expected from ultra-compact binaries such as RX J0806+15 and RX J1914+24."184 For systems with orbital periods in the range 510 min. the optimum observing frequency is close to 5 Gllz (Gem).," For systems with orbital periods in the range 5–10 min, the optimum observing frequency is close to 5 GHz (6cm)."185 For terrestrial planets orbiting around a low-mass magnetic star. the UL model described in Willes Wu (2005) predicted that the peak frequency is likely to be between 50500 CGllIz Gmm) although this was rather uncertain.," For terrestrial planets orbiting around a low-mass magnetic star, the UI model described in Willes Wu (2005) predicted that the peak frequency is likely to be between 50–500 GHz (0.6--6mm) although this was rather uncertain."186 ES Cet and GJ S76 were observed. using the Australian ‘Telescope Compact Array (ATCA) in New South Wales. Australia.," ES Cet and GJ 876 were observed using the Australian Telescope Compact Array (ATCA) in New South Wales, Australia."187 RX JOSOG|15 and RN 1914]24 were observed using the Very Large Array (VLA) in New Mexico. USA.," RX J0806+15 and RX J1914+24 were observed using the Very Large Array (VLA) in New Mexico, USA."188 We obtained full polarisation information. with the intention of determining the fractional polarisation of any detected source.," We obtained full polarisation information, with the intention of determining the fractional polarisation of any detected source."189 The observation log is shown in Table 1.., The observation log is shown in Table \ref{log}.190 In. cach case. observations took place at two adjacent [requency bands: this provides an increase in sensitivity by a factor of V2 when imaged altogether.," In each case, observations took place at two adjacent frequency bands; this provides an increase in sensitivity by a factor of $\sqrt 2$ when imaged altogether."191 All data were reduced using standard. Uageine. calibration and imaging routines within the ane packages for the ATCA and VLA observations respectively.," All data were reduced using standard flagging, calibration and imaging routines within the and packages for the ATCA and VLA observations respectively."192 We determined the rms noise level in regions of sky near the known position of each source., We determined the rms noise level in regions of sky near the known position of each source.193 We set upper limits on the Ες density to be three times the rms noise level., We set upper limits on the flux density to be three times the rms noise level.194 For the one source from which we detected radio emission (RN JOSOG|15: see Section 3.3). the integrated. [ux density was obtained by performing a 2-d Gaussian fit to the image.," For the one source from which we detected radio emission (RX J0806+15; see Section 3.3), the integrated flux density was obtained by performing a 2-d Gaussian fit to the image."195 The arrav was in the GA configuration anc observations took place at frequeney. bands centered: on 4800 and. 4928 MllIz., The array was in the 6A configuration and observations took place at frequency bands centered on 4800 and 4928 MHz.196 Conditions were good throughout the observations., Conditions were good throughout the observations.197variatious that lag slightlv (~30 degrees in phase) diud Barrosetal. (2007) photoimetrv.,variations that lag slightly $\sim$ 30 degrees in phase) behind \citet{Bar07}' 's photometry.198 This is not unexpected eiven. in particular.78 the uncertainty in the veriod derivative measured by Barrosetal.(2007). which translates into a phase uucertaiutv of about this uaenitudoe.," This is not unexpected given, in particular, the uncertainty in the period derivative measured by \citet{Bar07}, which translates into a phase uncertainty of about this magnitude."199 By matching the phases of the variable g-baud flux in our time-resolved spectra with the g-baud photometry of Barrosctal.(2007).. we can obtain a refined ephemeris or HIM. C€nc.," By matching the phases of the variable $g$ -band flux in our time-resolved spectra with the $g$ -band photometry of \citet{Bar07}, we can obtain a refined ephemeris for HM Cnc."200 This will not be a very precise refinemen since our spectra only imareinally sample the orbita oeriod. aud since atimospheric trausparcucy and secing were variable.," This will not be a very precise refinement since our spectra only marginally sample the orbital period, and since atmospheric transparency and seeing were variable."201 However. because we have hundreds of spectra and the folding period is much shorter than the vpical timescales for sky quality variations. we can stil resolve this shift.," However, because we have hundreds of spectra and the folding period is much shorter than the typical timescales for sky quality variations, we can still resolve this shift."202 The easiest wav to correct the phase shift is to reduce the frequency v and its time derivative roni Barrosetal.(2007). by approximately 1.30: where umnbers iu parentheses are the uucertainties in the corresponding uuuber of last decimals., The easiest way to correct the phase shift is to reduce the frequency $\nu$ and its time derivative from \citet{Bar07} by approximately $\sigma$: where numbers in parentheses are the uncertainties in the corresponding number of last decimals.203 The new error ou the frequency derivative is estimated as the error that eives the sue phase uncertainty (at our epoch) as the error on the frequency., The new error on the frequency derivative is estimated as the error that gives the same phase uncertainty (at our epoch) as the error on the frequency.204 The error ou the frequency has been kept the same., The error on the frequency has been kept the same.205 This ephemeris is used throughout this paper., This ephemeris is used throughout this paper.206 The left panels of reffie:trails show the time-resolved (trailed) spectrum of aaround the 1171 line. folded ou the above ephemeris CI.," The left panels of \\ref{fig:trails} show the time-resolved (trailed) spectrum of around the 4471 line, folded on the above ephemeris \ref{eq:ephemeris}) ))."207 The continui fux is seen to follow broadly the same pattern as in Barrosctal.(2007) after aligning the phases: diuxiug a cvcle the conutiuuua flux increases slowly and decreases more rapidly., The continuum flux is seen to follow broadly the same pattern as in \citet{Bar07} after aligning the phases: during a cycle the continuum flux increases slowly and decreases more rapidly.208 The scatter im our continua fluxes. shown in the left-anost panel of Fie. 2..," The scatter in our continuum fluxes, shown in the left-most panel of Fig. \ref{fig:trails},"209 is due to differences in the average sky. quality between phase bius rather than due to noise in iudividual spectra., is due to differences in the average sky quality between phase bins rather than due to noise in individual spectra.210 Clear spectral line variatious are seen in the £171 line. iu the form of an S-wvave feature that is visible for about half the period while it moves frou red-shifted to bluc-shifted wavelengths.," Clear spectral line variations are seen in the 4471 line, in the form of an `S-wave' feature that is visible for about half the period while it moves from red-shifted to blue-shifted wavelengths."211 The intensity of the S-wave in the [171 line follows the intensity of the variable continu flux. sugecsting that they originate from the sale region.," The intensity of the S-wave in the 4471 line follows the intensity of the variable continuum flux, suggesting that they originate from the same region."212 Iu the remaining paucls of reffie:trails the intrinsically variable coutimuum fux has been fitted— aud subtracted to highlieht the line variability., In the remaining panels of \\ref{fig:trails} the intrinsically variable continuum flux has been fitted and subtracted to highlight the line variability.213 Here theHeit £686 line is plotted as well as the sum ofthe three strongest Pickeriug series li1ο (1100. 1328AA: sce ," Here the 4686 line is plotted as well as the sum of the three strongest Pickering series lines (4100, 4338; see \\ref{fig:spectrum}) )."214The lines behave quite differently roni the Lift line., The lines behave quite differently from the 4471 line.215 The L686 line is double-»ealsed aud appears to wobble iu anti-phase with respect o the 11471 line., The 4686 line is double-peaked and appears to wobble in anti-phase with respect to the 4471 line.216 The Pickering lines have a strouely modulated. narrow component which may be noving from blue-shifted. to red-shifted iu phase with (auc at the same racial velocity of) the 1686 line.," The Pickering lines have a strongly modulated, narrow component which may be moving from blue-shifted to red-shifted in phase with (and at the same radial velocity of) the 4686 line."217 Iu addition the Pickering lines have a fairly constant. road component with a FWA of ~2500kkuss |. which matches the EWIIM of the (double-peaked) L686 profile.," In addition the Pickering lines have a fairly constant, broad component with a FWHM of $\sim$ $^{-1}$, which matches the FWHM of the (double-peaked) 4686 profile."218 We measure. froma linear back-projection. Doppler tomoeram (Marsh&Toric1988).. a radial velocity ;uplitude of ffor the Savave feature in the Li7l lue (corrected for a ~5% bias due to finite exposure times. which we modeled using svuthetic data).," We measure, froma linear back-projection Doppler tomogram \citep{Mar88}, a radial velocity semi-amplitude of for the S-wave feature in the 4471 line (corrected for a $\sim$ bias due to finite exposure times, which we modeled using synthetic data)."219" The error was estimated from a large cusemble of Doppler tomograms calculated frou, bootstrap samples of our 100 spectra.", The error was estimated from a large ensemble of Doppler tomograms calculated from bootstrap samples of our 400 spectra.220 For the double-peakedtt 1686 line moving iu auti-plhase. we sinularly measure a racial velocity senmuüeunplitude of+.," For the double-peaked 4686 line moving in anti-phase, we similarly measure a radial velocity semi-amplitude of."221.. The two peaks in the profile are red- and bluc-shifted by |., The two peaks in the profile are red- and blue-shifted by .222 Finally. the spectra were plase-folded ou trial periods of up to 6 hours. but no racial-velocity or iutensity," Finally, the spectra were phase-folded on trial periods of up to 6 hours, but no radial-velocity or intensity"223" L4. Agi Af,=ΑμLOCAL... Loe—VE, Lois=Los10%cres+. jj. Lg 2«0.5 Mp 4 Apa. Lopων Liz;XMasa MasaoAdiiec μον Affe. MiseXVou. Looe/Mypy. LiLead. LotxLope: LiafLgaaf>O0 ζωπια 4 A/pyp Loy A ~30 lower than iu the PG sample (RII. Eie.12). as expected frou equation 1 above."," $L_{\rm opt}$ $\Mbh$ $M_8=\Mbh/10^8 \Msun$ $L_{\rm opt} \equiv \nu L_\nu$ $L_{\rm opt,45}=L_{\rm opt}/{\rm 10^{45} \; erg \; s^{-1}}$ $\eta$ $L_{\rm bol}$ $z<0.5$ $\Mbh$ $\eta$ $\Mbh$ $L_{\rm opt}/L_{\rm host}>1$ $L_{\rm host}\propto M_{\rm host}$ $M_{\rm host}\ge M_{\rm bulge}$ $M_{\rm host}$ $M_{\rm bulge}$ $M_{\rm bulge}\propto \Mbh$ $L_{\rm opt}/\Mbh$ $L_{\rm bol}/L_{\rm Edd}$ $L_{\rm bol}\propto L_{\rm opt}$ $L_{\rm bol}/L_{\rm Edd}>0.1$ $L_{\rm bol}/L_{\rm Edd}$ $\eta$ $\Mbh$ $L_{\rm opt}$ $\Mdot$ $\sim 30$ lower than in the PG sample (R11, Fig.12), as expected from equation 1 above."224 The implied typical jj values are 3 times lieher than for the PC quasars at simular My (RIL. Fig.16). as expected from equation 2 above. if Li has the same characteristic ratio as iu the PCLope suuple.," The implied typical $\eta$ values are $\sim 3$ times higher than for the PG quasars at similar $\Mbh$ (R11, Fig.16), as expected from equation 2 above, if $L_{\rm opt}/L_{\rm bol}$ has the same characteristic ratio as in the PG sample."225 R11 also analyzed a handful of higher : SDSS quasars. simular iu properties to the PC quasars. and derive jj values similar to the PCs for similar Mp values (R11. Fig.16).," R11 also analyzed a handful of higher $z$ SDSS quasars, similar in properties to the PG quasars, and derive $\eta$ values similar to the PGs for similar $\Mbh$ values (R11, Fig.16)."226 R11 study carefully the rauge of parameters covered by the PO sample. asstmuing a Έπος ratio for LorLit. aud conclude that the a vs. My relation found /for the PG quasar sample is an artifact of the sample selection criteria.," R11 study carefully the range of parameters covered by the PG sample, assuming a fixed ratio for $L_{\rm227 opt}/L_{\rm bol}$, and conclude that the $\eta$ vs. $\Mbh$ relation found for the PG quasar sample is an artifact of the sample selection criteria."228 Below we explain why the y vs. Mp relation in the PC sample is not an artifact., Below we explain why the $\eta$ vs. $\Mbh$ relation in the PG sample is not an artifact.229 There are two indepeudenu relations among the observables that generate the correlation. and cach needs to be carefully uuderstood.," There are two independent relations among the observables that generate the correlation, and each needs to be carefully understood."230 The first comes from the PC sample sclection criterion., The first comes from the PG sample selection criterion.231 As explained above. this leads to a lower limit on Lor/ Lead. aud thus to a lower limit on AL for a given My.," As explained above, this leads to a lower limit on $L_{\rm232 opt}/L_{\rm Edd}$ , and thus to a lower limit on $\Mdot$ for a given $\Mbh$."233 But. this selection effect. alone docs not produce ana vs. Mp relation.," But, this selection effect alone does not produce an $\eta$ vs. $\Mbh$ relation."234 The second. and essential relation is the observed ziiall spread in Lopr/Lo. (DE. Fig.12).," The second, and essential relation is the observed small spread in $L_{\rm opt}/L_{\rm bol}$ (DL, Fig.12)."235" Applying both relations. Loy,XMp and XZia iu eqs.l 2 above. leads inevitably to a riseLope of j with Mou Gothi a power of 0.39. in the abseuce of scatter)."," Applying both relations, $L_{\rm opt}\propto \Mbh$ and $L_{\rm opt}\propto L_{\rm236 bol}$ in eqs.1 2 above, leads inevitably to a rise of $\eta$ with $\Mbh$ (with a power of 0.39, in the absence of scatter)."237 The observed correlation between 4 and Afpg is only an artifact if selection effects gcucrate the ZoxL4 relation., The observed correlation between $\eta$ and $\Mbh$ is only an artifact if selection effects generate the $L_{\rm opt}\propto L_{\rm bol}$ relation.238" Therefore. it is crucial to muderstand that the Lorxfy, relation is not a selection effect of the PC sample."," Therefore, it is crucial to understand that the $L_{\rm opt}\propto L_{\rm239 bol}$ relation is not a selection effect of the PG sample."240" The value of £),4) 1s mostly set by the far UV to soft N-vay part of the SED. which is independent of L4."," The value of $L_{\rm bol}$ is mostly set by the far UV to soft X-ray part of the SED, which is independent of $L_{\rm opt}$."241" The value of Loy should come predominantly from larger disk radii than the UV and N-ravs. aud is not expected to provide a measure of Zj,4."," The value of $L_{\rm opt}$ should come predominantly from larger disk radii than the UV and X-rays, and is not expected to provide a measure of $L_{\rm242 bol}$."243 The expected SEDs of the PG sample. if all had a fixed ij (~ 0.1). are shown in DL Fie.7.There isno selectioneffect whichpreventsthePCquasars from showingthe predicted fixed η SED.," The expected SEDs of the PG sample, if all had a fixed $\eta$ $\sim 0.1$ ), are shown in DL Fig.7.There isno selectioneffect whichpreventsthePGquasars from showingthe predicted fixed $\eta$ SED."244 Yet.at lowApitheobservedSEDissystematicallycolderthan the expected fixed 4 SED. while at the highest Afpiy the observed SED is systematically hotter.," Yet,at low$\Mbh$theobservedSEDissystematicallycolderthan the expected fixed $\eta$ SED, while at the highest $\Mbh$ the observed SED is systematically hotter."245 Thejj20.1 SED is expected to peak at ~10 Rydborg for the Apu PO sample objects. and at <1 Rydborg for the," The$\eta=0.1$ SED is expected to peak at $\sim 10$ Rydberg for the $\Mbh<10^7\Msun$ PG sample objects, and at $< 1$ Rydberg for the"246It will also be convenient to define the global upstream Alfvénn transit time and the corresponding Lundquist number,"It will also be convenient to define the global upstream Alfvénn transit time , and the corresponding Lundquist number"247The current paradigm for stellar mass loss uses Equation to scale mass loss rates with stellar rotation for stars at constant luminosity and effective temperature.,The current paradigm for stellar mass loss uses Equation \ref{eqn:1Dscale} to scale mass loss rates with stellar rotation for stars at constant luminosity and effective temperature.248 As discussed in Section 1.. this elect has been seen observationallv (Vardva1985:Nieuwenhuijzen&deJager1988). alhough the magnitude of the effect appears {ο be somewhat uncertain. ranging [rom a [ew tens of percent to two orders of magnitude.," As discussed in Section \ref{intro}, this effect has been seen observationally \citep{vardya,nieuwenhuijzen}, although the magnitude of the effect appears to be somewhat uncertain, ranging from a few tens of percent to two orders of magnitude."249 Llowever. stellar models use mass as the independent: variable. and the luminosity ancl effective temperature are allowed to vary.," However, stellar models use mass as the independent variable, and the luminosity and effective temperature are allowed to vary."250" Caculations of fully 2D rotating stars indicate that the situation may be more complicated. and Equation 1. may be used inc""orrectiv in some situations."," Calculations of fully 2D rotating stars indicate that the situation may be more complicated, and Equation \ref{eqn:1Dscale} may be used incorrectly in some situations."251 We find that for models ab consant mass. the overall mass loss rates as the rotatior1 rale increases. as shown in Figure 7 for 20 mnmocdes.," We find that for models at constant mass, the overall mass loss rates as the rotation rate increases, as shown in Figure \ref{time} for 20 models."252 As the rotation rate increases. the cllective tempor:uure and luminosity also decrease. as shown in Table l.. whicth leads to lower mass loss rates in all cases.," As the rotation rate increases, the effective temperature and luminosity also decrease, as shown in Table \ref{models}, which leads to lower mass loss rates in all cases."253 The decrease is about 0.06 dex for the IxXS9 rates. and about 0.15 dex. for the VOL rates.," The decrease is about 0.06 dex for the K89 rates, and about 0.15 dex for the V01 rates."254 At 30 and. 40AL... the decrease is betweer1 0.03 - 0.05 dex for all three rates. although these models do not extend to as rapid rotation as the mmocels.," At 30 and 40, the decrease is between 0.03 - 0.05 dex for all three rates, although these models do not extend to as rapid rotation as the models."255Equation (2) aud the plot of [N Πα vs Galactic latitude presented in Figure 8 of Hallner et al (1999) were then combiued to produce the T. vs relation [or the Perseus arm in Figure 1.,Equation (2) and the plot of [N $\alpha$ vs Galactic latitude presented in Figure 8 of Haffner et al (1999) were then combined to produce the $_e$ vs $|$ $|$ relation for the Perseus arm in Figure 1.256" This result covers the Galactic latitude rauge —31"">5—6"" averaged over the lougitude interval 125"">(1252""."," This result covers the Galactic latitude range $-34^{\rm o} \geq b \geq257-6^{\rm o}$ averaged over the longitude interval $125^{\rm o} \geq \ell258\geq 152^{\rm o}$."259 The distauce to the Perseus arm is assumed to be 2.5 kpc (Beynolds et al 1995. ancl references therein).," The distance to the Perseus arm is assumed to be 2.5 kpc (Reynolds et al 1995, and references therein)."260" The electron deusity n. within the WIM a a distance Zt 'om the midplane cau be derived [rom the Ha iuteusity. which is related to tle eluISSIOLL Leastre El through the relation EM = 2.75 T?[ya (from Martin LOSS). where EN ( Juz> ds) is. iu. utriso Cem+ ""6 pe aud Zjj is. in. rayleighs"" (1 R = 10°/Ie photons ? | sp1 "," The electron density $_e$ within the WIM at a distance $|$ $|$ from the midplane can be derived from the $\alpha$ intensity, which is related to the emission measure EM through the relation EM = 2.75 $T^{0.9}_{4}261I_{\mathrm{H}\alpha}$ (from Martin 1988), where EM (= $\int262\mathrm{n}_{e}^{2}$ ds) is in units of $^{-6}$ pc and $I_{H\alpha}$ is in rayleighs (1 R = $^6$ $\pi$ photons $^{-2}$ $^{-1}$ $^{-1}$ )."263"LAOLoOes he line «M sight through the Perseus arm. EM can be expressed as nzDE /L. where L is"" the pxuli euet1 throug iile arm. f the fraction of L occupied by ionized hydrogen. aud n the rius elect‘OM cleusity withi iude loized regious."," Along the line of sight through the Perseus arm, EM can be expressed as $^{2}_{e}f$ L, where L is the path length through the arm, $f$ the fraction of L occupied by ionized hydrogen, and $_e$ the rms electron density within the ionized regions."264" HalIner et al (1999) showed that for the same ranges of € alle b represeuted ii Figure l. dy(|z|) c 5.7 Hl qu Therefore. if L is assumed to have a vaue of|1000 pe (see Fiο,"," Haffner et al (1999) showed that for the same ranges of $\ell$ and $b$ represented in Figure 1, $I_{\mathrm{H}\alpha}$ $|$ $|$ ) $\simeq$ 5.7 $^{-|\mathrm{z}|/500}$ R. Therefore, if L is assumed to have a value of 1000 pc (see Fig."265 l in Becker Fenkart 1970). We consider two situations: 1) a constatt filling fraction. / = 0.2 (Reynolds 1991). aud 9)a fillingOm fraction that increases with accordi& to the relation given by Ixulkarui Heiles (1937). that is. f(\z|)=O.1el4|/350 [or Zuw1710 pc.," 1 in Becker Fenkart 1970), We consider two situations: 1) a constant filling fraction $f$ = 0.2 (Reynolds 1991), and 2) a filling fraction that increases with $|$ $|$ according to the relation given by Kulkarni Heiles (1987), that is, $f(|\mathrm{z}|) = 0.1 \, e^{|\mathrm{z}|/750}$ for $|\mathrm{z}| < 1740$ pc."266 There is some evideuce that f does in [act increase with distance from the midplaue (neviiolds 1991): however. the results are sullicieutly uucertaiu that both a constant aud varyiug f are cousidered here.," There is some evidence that $f$ does in fact increase with distance from the midplane (Reynolds 1991); however, the results are sufficiently uncertain that both a constant and varying $f$ are considered here."267" Weasstume that tle temperature Is cetermined by a balance between the cooling rate per unit voluije (An?) in the di[use ionized gas aud two heating rates: the uet heating by pliotoiouization. eiven by >Cauz. plus a1 additional |eallug teiu. given either by Gyu, or by just a coustaut Cio."," We assume that the temperature is determined by a balance between the cooling rate per unit volume $\Lambda$ $^{2}_{e}$ ) in the diffuse ionized gas and two heating rates: the net heating by photoionization, given by $_{0}$ $^{2}_{e}$, plus an additional heating term, given either by $_1$ $_e$ or by just a constant $_2$."268 The jeat]ug-cooliug balauce cau theu be expressed as eiher Cy4-Ci{αν=A. or Qu4Go/nzP0=A. represelting. lor exaunje. suppleumertal heatit& by turbilent dissipation (Gy). or by maguetic field reconnection (Cis). res»ectively.," The heating–cooling balance can then be expressed as either $\mathrm{G}_{0} +269\mathrm{G}_{1}/\mathrm{n}_{e} = \Lambda$, or $\mathrm{G}_{0} +270\mathrm{G}_{2}/\mathrm{n}^{2}_{e} = \Lambda$, representing, for example, supplemental heating by turbulent dissipation $_{1}$ ), or by magnetic field reconnection $_{2}$ ), respectively."271 The'efore. de;»eudiug upon the values of Cy or Go relative to C. slenificanly increased jeatiug (relative to phooionizatiou) can occur as the deusity decreases.," Therefore, depending upon the values of $_{1}$ or $_{2}$ relative to $_{0}$, significantly increased heating (relative to photoionization) can occur as the density decreases."272 This will result iu higher equilibrium teu)eratures at lower ceusities., This will result in higher equilibrium temperatures at lower densities.273 We |ave adopted the cooling fuiction A or low density photoiouized gas giveu in Osterbrock (1989)., We have adopted the cooling function $\Lambda$ for low density photoionized gas given in Osterbrock (1989).274" While this particular cooling function may not be exactly appropriate for the WIM. for T, ) Ik (the temperature range cousidered here) it is a very good approximation. because"," While this particular cooling function may not be exactly appropriate for the WIM, for $_e \,>$ 7000 K (the temperature range considered here) it is a very good approximation, because"275calculations to follow. these were treated. as O4V. stars.,"calculations to follow, these were treated as O4V stars."276" From dillerent studies proposing tvpical mass-Ioss rates and terminal velocities with respect to spectral tvpes (Prinjaοἱ 2004).. AL, and DAS were respectively estimated at « "" Mo + ancl 30000 km s.1 for standard OLV stars."," From different studies proposing typical mass-loss rates and terminal velocities with respect to spectral types \citep{Pri1990,Lam1999,Mar2004}, , $\dot{M}_{w}$ and $v_{\infty}$ were respectively estimated at $\times$ $^{-6}$ $_{\bigodot}$ $^{-1}$ and 000 km $^{-1}$ for standard O4V stars."277 Given pugpus © 225 7 (see above). nebular material found within 20 pc of Melotte 15 is likely to have been previously. disrupted bv stellar winds emanating from the current cluster.," Given $\rho_{diffuse}$ $\sim$ 25 $^{-3}$ (see above), nebular material found within $-$ 20 pc of Melotte 15 is likely to have been previously disrupted by stellar winds emanating from the current cluster."278 Fhis was caleulatecl assuming radiative (non-acliabatic) shocks (Lozinskava1992.Equation13.5).., This was calculated assuming radiative (non-adiabatic) shocks \citep[Equation 13.5]{Loz1992}.279 Given that interstellar shocks are usually aciahbatic at the earliest. times of. the expansion. the non-radiative model. vields a distance. of roughly 40 pe in the vicinity. of Alelotte 15. (Lozinskaya1992.Equation 13.9).. ≧∪⇂↓↥∠," Given that interstellar shocks are usually adiabatic at the earliest times of the expansion, the non-radiative model yields a distance of roughly 40 pc in the vicinity of Melotte 15 \citep[Equation 13.9]{Loz1992}."280∐⋡∖∣⋜⋯≼↛⋖⋅⋡∖⋖⊾⇀∖⊓⋅⋯⇂⇂↓↥⋖⊾⋖⋅⇀∖∩⊾⊔↿∪⇂⋅ our FOV (15.99 pc ) and support the fact that shocks. attributed to the current star cluster. have had: sullicient time to reach the bright structure in central 11805.," Both distances exceed the extent of our FOV $\times$ 9 $^{2}$ ) and support the fact that shocks, attributed to the current star cluster, have had sufficient time to reach the bright structure in central 1805."281 Besicles the bright. central structure observed. near the most massive stars of the Alelotte 15. cluster. our FOV mostly reveals diffuse ionizecl gas. partially obscured by interstellar dust.," Besides the bright, central structure observed near the most massive stars of the Melotte 15 cluster, our FOV mostly reveals diffuse ionized gas, partially obscured by interstellar dust."282 Llowever. two structures are. nonetheless detected. particularly well-defined. in (see 5& 4.1).," However, two structures are nonetheless detected, particularly well-defined in (see $\S$ 4.1)."283 In order to investigate the presence of shock excitation in other portions of our FOV. a similar approach. to what was carried on in & 5.2.1. is used. here on these two features.," In order to investigate the presence of shock excitation in other portions of our FOV, a similar approach, to what was carried on in $\S$ 5.2.1, is used here on these two features."284 Pancl (a) of Figure 19 reveals the shape of the ionization front observed. at the periphery of the CO fragment found in the south-east portion of our FOV (see Figure 8)., Panel (a) of Figure 19 reveals the shape of the ionization front observed at the periphery of the CO fragment found in the south-east portion of our FOV (see Figure 8).285 As in Figures 3 to 9. North is up ancl East is left.," As in Figures 3 to 9, North is up and East is left."286 Phe molecular feature is well-defined in the millimeter regime and its western side shows signs of crosion by the nearby star cluster., The molecular feature is well-defined in the millimeter regime and its western side shows signs of erosion by the nearby star cluster.287 The ionized gas associated to the ionization [ront was Dist circumscribed while weaker areas near the bright feature were selected and used. to extract the foregroundbackground: spectrum., The ionized gas associated to the ionization front was first circumscribed while weaker areas near the bright $^{+}$ feature were selected and used to extract the foreground/background spectrum.288 In. order. to obtain a post-subtraction sample containing a sullicient number of emission-line profiles. only the first condition of § 4.2.2 was used.," In order to obtain a post-subtraction sample containing a sufficient number of emission-line profiles, only the first condition of $\S$ 4.2.2 was used."289 Fherefore. results presented here should be cautiously interpreted.," Therefore, results presented here should be cautiously interpreted."290 Prior to the subtraction. all points were initially found inside the regions” area areaof the logio|joiePAO) vs. logio|--k diagnostic diagram ancl black filled: circles were used as symbols.," Prior to the subtraction, all points were initially found inside the regions” area of the $_{10}\left[\frac{\textnormal{I}(\textnormal{H}\alpha)}{\textnormal{I}([\textnormal{S}\,\textsc{ii}])}\right]$ vs. $_{10}\left[\frac{\textnormal{I}(\textnormal{H}\alpha)}{\textnormal{I}([\textnormal{N}\,\textsc{ii}])}\right]$ diagnostic diagram and black filled circles were used as symbols."291 Panel (b) displays the diagram for post-subtraction spectra only., Panel (b) displays the diagram for post-subtraction spectra only.292 These results reveal. as in § 5.2.1. that. points are displaced: toward. the shock-cominatecl 7SNItS area although the tail is much less developed when compared to ligure165.," These results reveal, as in $\S$ 5.2.1, that points are displaced toward the shock-dominated “SNRs” area although the tail is much less developed when compared to Figure."293. No post-subtraction point actually enters. the hatched area defined. earlier., No post-subtraction point actually enters the hatched area defined earlier.294 Shock excitation hence appears to have plaved a much more minor role in the ionization of this cloud's envelope when compared to the central structure of our FOV., Shock excitation hence appears to have played a much more minor role in the ionization of this cloud's envelope when compared to the central structure of our FOV.295 The apparent shape of the ionization front indicates that. the ionizing sources are located behind the molecular cloud (sce ὃ∣ 4.1)., The apparent shape of the ionization front indicates that the ionizing sources are located behind the molecular cloud (see $\S$ 4.1).296 Using kinematical information retrieved. [ron ⇂↓↕⋖⋅↓≻↓↥⋖⋟∩⋈⊾∖⇁⋜↧↓≻∪↓⋅⋜⋯⊾∠⇂↓↥↓⋜↧↿⋖⊾↓⋅↕⋜↧↓↕↓↥⇂↓↕⋖⊾∖⇁↕≼∼↕↓↕↕↿∙∖⇁∪⇂⋅⇂↓↥∢⊾≼⇍∪⋯⇂⊳ Lagrois&Joncas(2009a) suggested. that. an appreciable distance could. exist. between the CO fragment. ancl the AMelotte 15 cluster (see the authors’ Figure 11. and. their associated Flow €).," Using kinematical information retrieved from the photoevaporated material in the vicinity of the cloud, \citet{Lag2009a} suggested that an appreciable distance could exist between the CO fragment and the Melotte 15 cluster (see the authors' Figure 11 and their associated Flow G)."297 Hence. larec distances could. signifv here that. stellar-wind shocks may have been partially dissipated before they could. reach the molecular cloud.," Hence, large distances could signify here that stellar-wind shocks may have been partially dissipated before they could reach the molecular cloud."298 Shock excitation is therefore likely measurable only within a certain distance of the shock sources Le. stars with strong stellar winds in our case.," Shock excitation is therefore likely measurable only within a certain distance of the shock sources i.e., stars with strong stellar winds in our case."299 Obviously. the stronger the shocks are. the greater this corresponding distance is.," Obviously, the stronger the shocks are, the greater this corresponding distance is."300 We reiterate that only the first 15 to 40 pe in the vicinity of Moelotte 15 may have been disrupted by stellar winds (see § 5.2.1)., We reiterate that only the first 15 to 40 pc in the vicinity of Melotte 15 may have been disrupted by stellar winds (see $\S$ 5.2.1).301 At this point. the strongest wind shocks (fuelled up by the O4 stars) would have receded to the subsonic regime with velocities between 4 and 9 km + depending on the model used. (radiative or non-radiative respectively).," At this point, the strongest wind shocks (fuelled up by the O4 stars) would have receded to the subsonic regime with velocities between 4 and 9 km $^{-1}$ depending on the model used (radiative or non-radiative respectively)."302 LE by. any chance. the molecular fragment found near the south-eastern boundary of our FOV is Located. relatively far from. the ionizing sources ( 115 pe). this could explain the apparent absence of strong. compressive shocks at its periphery.," If, by any chance, the molecular fragment found near the south-eastern boundary of our FOV is located relatively far from the ionizing sources $\gtrsim$ 15 pc), this could explain the apparent absence of strong, compressive shocks at its periphery."303 Panel (c) of Figure 19 shows the very tenuous. but well-defined. ionized counterpart of a cigar-like structure pointing toward a nearby star with strong emission line.," Panel (c) of Figure 19 shows the very tenuous, but well-defined, ionized counterpart of a cigar-like structure pointing toward a nearby star with strong emission line."304 Again. North is up and. Last is left.," Again, North is up and East is left."305 The star is particularly visible on the left-hand side of Figure S and has been cataloged bv I[xohoutek.&Webmever(1999) as 66211-05 with a V-band magnitude of 14.6 and no known spectral type., The star is particularly visible on the left-hand side of Figure 8 and has been cataloged by \citet{Koh1999} as 6211-05 with a V-band magnitude of 14.6 and no known spectral type.306" Is coordinates are (62000 002434"" 10.06. δουυυ 66172435"". 7)."," Its coordinates are $\alpha_{2000}$ $^{\textnormal{h}}$ $^{\textnormal{m}}$ $^{\textnormal{s}}$ .06, $\delta_{2000}$ $\arcdeg$ $\arcmin$ $\arcsec$ .7)."307 Phe elongated. feature was briellyv introduced in ὃ 4.1., The elongated feature was briefly introduced in $\S$ 4.1.308 Emission in and. N Lextscii]isdelectedonthceoulskirtsoflhecigqar fealurcwhiledscenterappearsmostlygasde pleted, Emission in and $[$ $]$ is detected on the outskirts of the cigar-like feature while its center appears mostly gas depleted.309 Ehisoverallschemceiap fertsciiregions(e.g..Car," This overall scheme is particularly similar to what is expected from elephant trunks in regions (e.g., \citealt{Car2003}) )."310lqvistel ad200911 Shadowinge ffeels.," Shadowing effects, caused by a dense neutral globule located in a radiation field, allow the warm gas behind it to recombine which could explain the absence of ionized material at the center of the elongated structure."311 cau, The bright ionized rims are formed of photoevaporated material created by the erosion of the neutral globule.312"sedbyadei likeshape,", These flows move away from the ionizing star creating the cigar-like shape.313 Both the FORAO €O(1-0) survey and the Canadian Galactic Plane Survey at 21 cm (Normandoeauefaf1997) reveal no indication for either molecular or atomic gas associated to the elongated. feature., Both the FCRAO CO(1-0) survey and the Canadian Galactic Plane Survey at 21 cm \citep{Nor1997} reveal no indication for either molecular or atomic gas associated to the elongated feature.314 Theoretically. Ll. σας is expected to constitute the main component of the eroded elobule while material should result. from recombinations in the tail," Theoretically, $_{2}$ gas is expected to constitute the main component of the eroded globule while material should result from recombinations in the tail."315 The whole structure. however. has relatively small angular dimensions (457 « 777) which suggests that emission from the neutral gas could be beam οπέος in the low-resolution radio observations.," The whole structure, however, has relatively small angular dimensions $\arcsec$ $\times$ $\arcsec$ ) which suggests that emission from the neutral gas could be beam diluted in the low-resolution radio observations."316" Theory has suggested. that shocks. will develop. in elephant trunks (Mackay&Lim2010:Ragaefa£.2010) although. in ⋠⋅first approximation.. the logioemu]liHa Vs. logiejog,Ην} diagram has shown nothing particular using the first set of Gaussian fits toe. allpoints associated to the elongated structure are well-confined into the regions"" area."," Theory has suggested that shocks will develop in elephant trunks \citep{Mac2010,Rag2010} although, in first approximation, the $_{10}\left[\frac{\textnormal{I}(\textnormal{H}\alpha)}{\textnormal{I}([\textnormal{S}\,\textsc{ii}])}\right]$ vs. $_{10}\left[\frac{\textnormal{I}(\textnormal{H}\alpha)}{\textnormal{I}([\textnormal{N}\,\textsc{ii}])}\right]$ diagram has shown nothing particular using the first set of Gaussian fits i.e., allpoints associated to the elongated structure are well-confined into the regions” area."317 However. subtracting the [oregroundbackground material vields the diagram clisplavecl in Panel (d) of Figure 19.," However, subtracting the foreground/background material yields the diagram displayed in Panel (d) of Figure 19."318 None of the conditions listed in ὃ 4.2.2 were considered., None of the conditions listed in $\S$ 4.2.2 were considered.319 Only à S/N greater than 3 (sullicientlv. high. to confirm a physical detection: see ¢; 4.2.2) was here required., Only a S/N greater than 3 (sufficiently high to confirm a physical detection; see $\S$ 4.2.2) was here required.320 Therefore. the results are highly," Therefore, the results are highly"321fireball with the ambient medium also produces a short-lived reverse shock that propagates backwards through the expanding shell?0.,"fireball with the ambient medium also produces a short-lived reverse shock that propagates backwards through the expanding \cite{zk05,zkm03}."322" Exploiting the ability of robotic optical telescopes to respond rapidly and automatically to the discovery of new GRBs. a custom, fast-response, optical polarimeter!!! (RINGO) was deployed on the 2.0 meter robotic. Liverpool. Telescope!”5 (La Palma) with the goal of measuring the degree of polarization of optical emission from GRBs at early time."," Exploiting the ability of robotic optical telescopes to respond rapidly and automatically to the discovery of new GRBs, a custom, fast-response, optical \cite{ringo} (RINGO) was deployed on the 2.0 meter robotic Liverpool \cite{lt} (La Palma) with the goal of measuring the degree of polarization of optical emission from GRBs at early time."323" RINGO uses a rotating Polaroid to modulate the incoming beam, followed by corotating deviating optics that transter cach star image into a ring that is recorded on a CCD (Figure 1)."," RINGO uses a rotating Polaroid to modulate the incoming beam, followed by corotating deviating optics that transfer each star image into a ring that is recorded on a CCD (Figure 1)."324 Any polarization signal present in the incoming light is mapped out around the ring in a 5/728 pattern., Any polarization signal present in the incoming light is mapped out around the ring in a $sin 2\theta$ pattern.325" RINGO was first used in 2006, when it observed GRB 060418 at 203s after the gamma ray burst and coincident with the time of deceleration of the fireball."," RINGO was first used in 2006, when it observed GRB 060418 at 203s after the gamma ray burst and coincident with the time of deceleration of the fireball."326 At this time the reverse (assuming it was present) and forward shock components would have contributed equally to the observed light., At this time the reverse (assuming it was present) and forward shock components would have contributed equally to the observed light.327" For GRB 060418 a 2c upper limit on optical polarization of P«85c was measured in the combined light from the emitting regions"".", For GRB 060418 a $\sigma$ upper limit on optical polarization of $<$ was measured in the combined light from the emitting \cite{mun07a}.328 Until the burst reported here this was the only limit on early-time optical GRB polarization., Until the burst reported here this was the only limit on early-time optical GRB polarization.329" GRB 090102 was detected by theSwfr satellite on 2 January 2009 at 02:55:45 UT. with a pulse of gamma rays lasting To;227 s and comprising four overlapping peaks starting 14-s before the trigger time""..."," GRB 090102 was detected by the satellite on 2 January 2009 at 02:55:45 UT, with a pulse of gamma rays lasting $_{90}$ =27 s and comprising four overlapping peaks starting 14-s before the trigger \cite{man09}."330" The automatic localization provided by the spacecraft was communicated to ground-based facilities, and a single 60-second RINGO exposure was obtained starting 160.8 seconds after the trigger time."," The automatic localization provided by the spacecraft was communicated to ground-based facilities, and a single 60-second RINGO exposure was obtained starting 160.8 seconds after the trigger time."331" Simultancously with our polarization observation of GRB 090102,"," Simultaneously with our polarization observation of GRB 090102,"332",UadtiunB . sd(ul πο. Wwrere d((r) is the differential leueth element along the closed path D.","r) r) = ) r) , where $d\ell(\vec r)$ is the differential length element along the closed path $\Gamma$."333" Dx collectiug the «ata ou the ""accumulated phase” trDyQUUdDAEEAP) audA the! “probed eravitatiotal potential” fbor()d((r) for a set of D. and fitting a straigit line. one may extract {QsBUSιο)."," By collecting the data on the “accumulated phase” $\oint_\Gamma334{\Omega^\prime_{a\rightleftharpoons b}} (\vec r) d\ell(\vec r)$ and the “probed gravitational potential” $335\oint_\Gamma{\phi_E(\vec r)} d\ell(\vec r)336$ for a set of $\Gamma$, and fitting a straight line, one may extract $\{{\Omega^{\infty}_{a\rightleftharpoons b}},337\phi_{GA}\}$."338 Rigorously speaking. whatone obtains is Q7D alc the constant oc;4 as modified by other cosmic cotributions.," Rigorously speaking, whatone obtains is ${\Omega^{\infty}_{a\rightleftharpoons b}}$ and the constant $\phi_{GA}$ as modified by other cosmic contributions."339 Furtlky. these additional contributions may iucluceyencral-rclativrstic coutrinitions from he vet-unkuown iuteractious ha may completo he variou:4 parameters associaed with the superimpose qlanuni states.," Further, these additional contributions may include contributions from the yet-unknown interactions that may couple to the various parameters associated with the superimposed quantum states."340 Asiuple consicration on the maeuitiucle ¢rf variens eravitationa poteutiaE involve aud the accuracy of clocks based ou cταιitun superposilous of atomlc states leHids to the tentative conclusion that the SUee(fed experiuel is feasile withiu tje existing techuoloey., A simple consideration on the magnitude of various gravitational potentials involved and the accuracy of clocks based on quantum superpositions of atomic states leads to the tentative conclusion that the suggested experiment is feasible within the existing technology.341 Iu this regi note is taken thaf varlous donlc aud atoiic clocks have reached an accuracy ο da aL in 107 witrarelmarkal e long ter ustability., In this regard note is taken that various ionic and atomic clocks have reached an accuracy of $1$ part in $10^{15}$ with a remarkable long term stability.342 In addition. workers in this fied are optimistic that a sever:d orders o “πασάο inprovenieut iav be expected im the next few vears (see. e.g. Darvara Levis recent coverage of this subject iu the Eebnary 1998 d5 of Plisies Toda? )) lutje present study sve emprasized observability of the constaut potential of the Creat attractor by micas of flavor oscillation clocks.," In addition, workers in this field are optimistic that a several orders of magnitude improvement may be expected in the next few years (see, e.g, Barbara Levi's recent coverage of this subject in the February 1998 issue of Physics \cite{clocks}) ) In the present study we emphasized observability of the constant potential of the Great attractor by means of flavor oscillation clocks."343 While iu a classical coutext. the force F=mgVole) experienced by au object is independeut of eracieutless eravitational poteutials such as 0c;4. the frequency of the favor οσοlation clocks depeucds directly ou oc;4 [in addition to F ορ].," While in a classical context, the force $\vec F = - m_g \vec344\nabla \phi (\vec r)$ experienced by an object is independent of gradientless gravitational potentials such as $\phi_{GA}$, the frequency of the flavor oscillation clocks depends directly on $\phi_{GA}$ [in addition to $\phi_E(\vec r)$ ]."345 The above considerations sugeest that in a free fall the space-time interval (at cast in the quanti couext) is given by ds? right)jdt right)ydi?., The above considerations suggest that in a free fall the space-time interval (at least in the quantum context) is given by ds^2 ) .346", Sinultaucouslv. Eq. (:?) ))"," Simultaneously, Eq. \ref{gmunu}) )"347 should be replaced by, should be replaced by348For the galaxies with higher-quality distances. the quoted errors range from 0.1 to 0.2 magnitudes with an average of slightly under 0.15. giving a distance error of7.,"For the galaxies with higher-quality distances, the quoted errors range from 0.1 to 0.2 magnitudes with an average of slightly under 0.15, giving a distance error of."3492%... As noted above. the brightest-star errors are not as well known: but taking 0.4 magnitudes as an estimate vields an average distance error of20%.," As noted above, the brightest-star errors are not as well known; but taking 0.4 magnitudes as an estimate yields an average distance error of."350. Putting these into the above formula gives contributions of 67 and 21 km J| of distance errors to the total rms velocity dispersion for the brightest-star and better distances. respectively: which leaves 97 km | of real motion in the 98-galaxy isotropic solution. τὸ km ! in the 98-ealaxyv anisotropic solution. and 86and 74 kms ! for the respective 35-ealaxvsolutions?.," Putting these into the above formula gives contributions of 67 and 21 km $^{-1}$ of distance errors to the total rms velocity dispersion for the brightest-star and better distances, respectively; which leaves 97 km $^{-1}$ of real motion in the 98-galaxy isotropic solution, 78 km $^{-1}$ in the 98-galaxy anisotropic solution, and 86and 74 km $^{-1}$ for the respective 35-galaxy."351. Compared to the dillerences in solar reflex velocity amoung the various calculations it is perhaps reassuring to find among the tensor model results a stable. high value of 82-84 kin sIMpe.! close to the supergalactie plane and not [ar [rom the direction of Virgo.," Compared to the differences in solar reflex velocity among the various calculations it is perhaps reassuring to find among the tensor model results a stable, high value of 82-84 km ${\rm s}^{-1} {\rm Mpc}^{-1}$ close to the supergalactic plane and not far from the direction of Virgo."352 However. there appears to be no agreement in direction among the other eigenvectors and very. wide variation in eigenvalues: indeed. in the solution with the most reliable data the Virgo-pointing eigenvector does not correspond to the largest eigenvalue.," However, there appears to be no agreement in direction among the other eigenvectors and very wide variation in eigenvalues; indeed, in the solution with the most reliable data the Virgo-pointing eigenvector does not correspond to the largest eigenvalue."353 Clearly. the reliablility of these results must be investigated.," Clearly, the reliablility of these results must be investigated."354 An appropriate wav to compare solutions as a whole is the F-ratio(UU., An appropriate way to compare solutions as a whole is the F-ratio.355 One finds (heir respective variances (average square of the deviation from the model: here. the square ol (he velocity dispersions) and the number of degrees of freedom in each. and then calculates the probability that the larger variance could be produced by the model which better fits the data.," One finds their respective variances (average square of the deviation from the model; here, the square of the velocity dispersions) and the number of degrees of freedom in each, and then calculates the probability that the larger variance could be produced by the model which better fits the data."356" Essentially, while a model with more parameters will always eive a smaller dispersion. one demands that il eive asignificantly smaller dispersion."," Essentially, while a model with more parameters will always give a smaller dispersion, one demands that it give a smaller dispersion."357 For the 98-ealaxy sample. the difference is quite significant: (hie anisotropic solution is a better fit at the level.," For the 98-galaxy sample, the difference is quite significant: the anisotropic solution is a better fit at the level."358 For the 35-galaxv. sample the probability is lower. 77%... but," For the 35-galaxy sample the probability is lower, , but"359"After performing several catalog cross-correlations, a new association with nearby T Tauri stars inside the well-known possiblep Ophiuchi star forming region clearly emerges for theFermi source IFGL J1625.8 —2429c.","After performing several catalog cross-correlations, a new possible association with nearby T Tauri stars inside the well-known $\rho$ Ophiuchi star forming region clearly emerges for the source 1FGL J1625.8 $-$ 2429c."360" Indeed, inside the 95% confidence error ellipse of thisFermi source we find four T Tauri stars: 2MASS J16260160—2429449 (Casanova et al."," Indeed, inside the $95\%$ confidence error ellipse of this source we find four T Tauri stars: 2MASS $-$ 2429449 (Casanova et al."361" 1995), 2MASS J16253958—2426349 (Wilking et al."," 1995), 2MASS $-$ 2426349 (Wilking et al."362" 1989), JCMTSF J162556.8—243014 (Di Francesco et al."," 1989), JCMTSF $-$ 243014 (Di Francesco et al."363" 2008), and 2MASS J16255752—2430317 (Grasdalen et al."," 2008), and 2MASS $-$ 2430317 (Grasdalen et al."364 1973)., 1973).365 Their observational properties are summarized in Table 3.., Their observational properties are summarized in Table \ref{tableIII}. .366" In Figs. 7,,"," In Figs. \ref{ir_map},"367" 8 and 9 we show this field (J 2353?0, b 217200) as observed in the infrared, X-ray and radio wavelengths."," \ref{x_map}368 and \ref{radio_map} we show this field $l=$ 0, $b=$ 0) as observed in the infrared, X-ray and radio wavelengths."369" These have been public data retrieved (and calibratedimages when necessary) producedfrom usingthe Spitzer-GLIMPSE, and NRAO Very Large Array (VLA) archives, respectively."," These images have been produced using public data retrieved (and calibrated when necessary) from the -GLIMPSE, and NRAO Very Large Array (VLA) archives, respectively."370" As discussed below, we tentatively suggest that this source be the result of the emission of at least these four Tauri stars mightthat lay inside the location error box of 1FGL J1625.8 —2429c."," As discussed below, we tentatively suggest that this source might be the result of the emission of at least these four Tauri stars that lay inside the location error box of 1FGL J1625.8 $-$ 2429c."371 In order to estimate the probability of a pure chance association we have implemented Monte Carlo simulations of computer-generated Fermi sources following the approach developed by Romero et al. (, In order to estimate the probability of a pure chance association we have implemented Monte Carlo simulations of computer-generated sources following the approach developed by Romero et al. (3721999) for unidentified EGRET sources.,1999) for unidentified EGRET sources.373" After 10 simulations of artificial populations we find 47 coincidences at 1-degree binning and 4 at 2-degree binning, indicating a probability of chance association of 10."," After $10^4$ simulations of artificial populations we find 47 coincidences at 1-degree binning and 4 at 2-degree binning, indicating a probability of chance association of $\sim 10^{-3}$ ."374 These results do not change with larger samples (we run to 10° simulations)., These results do not change with larger samples (we run up to $10^6$ simulations).375" upLet F(E\,£2)+A[F(E,,Ε2)] be the integratedFermi flux in the energy range [Ε1, Ε2] and its error."," Let $F(E_{1},E_{2}) \pm \bigtriangleup[F(E_{1},E_{2})]$ be the integrated flux in the energy range $E_{1}, E_{2}$ ] and its error."376" To reproduce the observed fluxes, we consider in first approximation that the four T Tauri stars emit the same y-ray luminosity."," To reproduce the observed fluxes, we consider in first approximation that the four T Tauri stars emit the same $\gamma$ -ray luminosity."377" Then, we can compute the integrated flux from: Here Lj(E) is the total y-ray luminosity produced by an individual T Tauri star according to our model (E» 20 MeV) and d is the distance to p Ophiuchi cloud, ~ 120 pc (Loinard et al."," Then, we can compute the integrated flux from: Here $L_{\gamma}(E)$ is the total $\gamma$ -ray luminosity produced by an individual T Tauri star according to our model $E >$ 20 MeV) and $d$ is the distance to $\rho$ Ophiuchi cloud, $\sim$ 120 pc (Loinard et al."378 2008)., 2008).379 The integratedFermi fluxes (Abdo et al., The integrated fluxes (Abdo et al.380 2010) and the calculated fluxes in five energy bands are shown in Table 2.., 2010) and the calculated fluxes in five energy bands are shown in Table \ref{tableII}.381 Figure 10 shows the luminosity obtained with the model and the upper bound given byChandra andFermi data., Figure \ref{LumiF} shows the luminosity obtained with the model and the upper bound given by and data.382" Radio data from VLA are also shown, but this radiation issurely acombination of non-thermal and thermal emission and hence must be considered just as an upper value to constrain the model."," Radio data from VLA are also shown, but this radiation issurely acombination of non-thermal and thermal emission and hence must be considered just as an upper value to constrain the model."383and 2.8AU had significantly non-zero eccentricities.,and $2.8\AU$ had significantly non-zero eccentricities.384 This is because. as discussed at the top ol rels:sweeping.. an initially cold asteroid belt swept bv the 5j resonance would either lose all its asteroids or none. and very low initial eccentricities would result in final asteroid eccenlricilies in à very narrow range of values (cf.," This is because, as discussed at the top of \\ref{s:sweeping}, an initially cold asteroid belt swept by the $\nu_6$ resonance would either lose all its asteroids or none, and very low initial eccentricities would result in final asteroid eccentricities in a very narrow range of values (cf."385 equation 32)). in contradiction with the fairly wide eccentricitw dispersion (hat is observed.," equation \ref{e:finalebounds}) ), in contradiction with the fairly wide eccentricity dispersion that is observed."386 This conclusion supports recent results from studies of planetesimal accretion and asteroid ancl planet formation that the asteroids were modestly excited at the end of their formation (e.g..Petitetal.2002)..," This conclusion supports recent results from studies of planetesimal accretion and asteroid and planet formation that the asteroids were modestly excited at the end of their formation \citep[e.g.,~][]{Petit:2002p170}."387 In Appendix Α we show that the double-gaussian distribution is a slightlv better fit to the main belt asteroid eccentricity distribution. but the statistical tests do not rule out a single-peaked distribution.," In Appendix \ref{sec:sweeprate-appendix-fitting} we show that the double-gaussian distribution is a slightly better fit to the main belt asteroid eccentricity distribution, but the statistical tests do not rule out a single-peaked distribution."388 We boldly proceed with considering the implications of the double-peaked eccentricity distribution to further constrain the migration rate of Saturn. with the caveat that these results can only be said to be consistent with the observations. rather (han uniquely constrained by (hem.," We boldly proceed with considering the implications of the double-peaked eccentricity distribution to further constrain the migration rate of Saturn, with the caveat that these results can only be said to be consistent with the observations, rather than uniquely constrained by them."389 If the pre-sweeping asteroid belt had a Gaussian eccentricity distribution. then the lower peak of the post-sweeping asteroid belt should be equal to the lower bound of equation (32)).," If the pre-sweeping asteroid belt had a Gaussian eccentricity distribution, then the lower peak of the post-sweeping asteroid belt should be equal to the lower bound of equation \ref{e:finalebounds}) )."390 We use the analvlical (theory (o make a rough estimate of the parameter A (and hence (5) that would yield a final distribution with lower peak near 0.09 and upper peak near 0.19 (which is similar to the best-fit double Gaussian in Fig. 5))., We use the analytical theory to make a rough estimate of the parameter $\lambda$ (and hence $\dot a_6$ ) that would yield a final distribution with lower peak near $0.09$ and upper peak near $0.19$ (which is similar to the best-fit double Gaussian in Fig. \ref{f:MBA-big-dist}) ).391" Applying equation (32)). we see that there are two possible solutions: (6;)=0.14.9, and (ο= 0.05.0,=0.14."," Applying equation \ref{e:finalebounds}) ), we see that there are two possible solutions: $\langle e_i\rangle=0.14$ $\delta_e=0.05$ and $\langle e_i\rangle=0.05$ $\delta_e=0.14$."392" A corresponding migration rate of Saturn can be estimated from the value of 6, using equation (33)). and the parameter relationships plotted in Figs."," A corresponding migration rate of Saturn can be estimated from the value of $\delta_e$ using equation \ref{e:deltaedef}) ), and the parameter relationships plotted in Figs."393 and 3.., \ref{f:g6vsasat} and \ref{f:epsvsanu6}.394 The former solution (0.= 0.05) requires a migration rate for Saturn of 4., The former solution $\delta_e=0.05$ ) requires a migration rate for Saturn of $\dot{a}_6=30\AU\My^{-1}$ .395 We mention this implausible solution here for completeness. but we will not discuss it any further.," We mention this implausible solution here for completeness, but we will not discuss it any further."396" The latter solution (9,= 0.14) requires a migration rate for Saturn of fi;=4AUMy.+.", The latter solution $\delta_e=0.14$ ) requires a migration rate for Saturn of $\dot{a}_6=4\AU\My^{-1}$.397" We dub this solution the ""cold belt” solution.", We dub this solution the “cold belt” solution.398" This rate is comparable to the rates of planet mieration found in the ""Jumping Jupiter"" scenario proposed by (2009)...", This rate is comparable to the rates of planet migration found in the “Jumping Jupiter” scenario proposed by \cite{Brasser:2009p3022}.399 A third solution exists if we consider Chat eccentricities in (he main belt are restricted by (he orbits of Mars and Jupiter on either side. such (hat stable asteroid orbits do not cross the planetary orbits.," A third solution exists if we consider that eccentricities in the main belt are restricted by the orbits of Mars and Jupiter on either side, such that stable asteroid orbits do not cross the planetary orbits."400 This limits asteroid eccentricities to values such that neither the aphelion of the asteroid crosses the perihelion distance of Jupiter. nor the perihelion of (he asteroid crosses (he aphelion distance of Mars.," This limits asteroid eccentricities to values such that neither the aphelion of the asteroid crosses the perihelion distance of Jupiter, nor the perihelion of the asteroid crosses the aphelion distance of Mars."401" Maximum asteroid eccentricity is therefore a function of semimajor axis. where e,,,,=min(1l—Qarars/LeQuupier/a1). where Q and q are planet aphelion and perihelion. respectively. aud α is (he semimajor axis of the asteroid."," Maximum asteroid eccentricity is therefore a function of semimajor axis, where $e_{max}=\min(1-Q_{Mars}/a-1,q_{Jupiter}/a-1)$, where $Q$ and $q$ are planet aphelion and perihelion, respectively, and $a$ is the semimajor axis of the asteroid."402 In this case. an initial single Gaussian eccentricity distribution with a mean greater than 0.3 would be severely truncated. therefore we need only fit the lower peak of the," In this case, an initial single Gaussian eccentricity distribution with a mean greater than $\sim0.3$ would be severely truncated, therefore we need only fit the lower peak of the"4032008): and hint at a local correlation of galaxy spins at distances less than~0.5 Mpe - the first experimental evidence for chiral correlation of spins (Slosaretal.2009).,; and hint at a local correlation of galaxy spins at distances less than$\sim 0.5$ Mpc - the first experimental evidence for chiral correlation of spins \citep{Slosar2009}.404. Intriguingly there are also hints of a correlation between star formation history and spin alignments (Jimenezetal.2010)., Intriguingly there are also hints of a correlation between star formation history and spin alignments \citep{Jimenez2010}.405. The sample of merging galaxies has been used to show that the local fraction of mergers is about and to study the global properties of merging galaxies (Dargetal.2010a.b).," The sample of merging galaxies has been used to show that the local fraction of mergers is about and to study the global properties of merging galaxies \citep{Darg2010a, Darg2010b}."406. Multi-mergers (where more than two galaxies are merging at once) - which are much rarer than binary mergers have also recently been studied (Dargetal.2011)., Multi-mergers (where more than two galaxies are merging at once) - which are much rarer than binary mergers have also recently been studied \citep{Darg2011}.407 The GZI classifications also. revealed interesting correlations between galaxy morphology and black hole growth., The GZ1 classifications also revealed interesting correlations between galaxy morphology and black hole growth.408 By splitting both the normal galaxy population and the active galaxy population by morphology. two fundamentally different modes of black hole feeding and feedback in early- and late-type galaxies were found (Schawinskietal.2010b).," By splitting both the normal galaxy population and the active galaxy population by morphology, two fundamentally different modes of black hole feeding and feedback in early- and late-type galaxies were found \citep{Schawinski2010b}."409. Early-type active galactic nucleus (AGN) host galaxies are systematically lower mass and bluer than the general early-type population., Early-type active galactic nucleus (AGN) host galaxies are systematically lower mass and bluer than the general early-type population.410 Black hole growth is concentrated strongly in the “green valley” between the blue cloud and the low-mass end of the red sequence.," Black hole growth is concentrated strongly in the “green valley"" between the blue cloud and the low-mass end of the red sequence."411 These ewuly-type AGN host galaxies furthermore feature strong post-starburst stellar populations (Schawinskietal.2007b) and thus are migrating from the blue cloud to passive evolution at the low mass end of the red sequence - they are thus building up the red sequence today., These early-type AGN host galaxies furthermore feature strong post-starburst stellar populations \citep{Schawinski2007b} and thus are migrating from the blue cloud to passive evolution at the low mass end of the red sequence - they are thus building up the red sequence today.412" Late-type AGN host galaxies dominate by number (up to if ""indeterminate"" are included) and reside predominantly in massive host galaxies with no indications of recent suppression of star formation."," Late-type AGN host galaxies dominate by number (up to if ""indeterminate"" are included) and reside predominantly in massive host galaxies with no indications of recent suppression of star formation."413 Black hole growth in these disk-dominated galaxies is likely stochastic and has no significant connection to the evolutionary trajectory of the host galaxy., Black hole growth in these disk-dominated galaxies is likely stochastic and has no significant connection to the evolutionary trajectory of the host galaxy.414" Intriguingly. the Milky Way galaxy resides in the locus of mass and colour where black hole growth is most likely. potentially making the Milky Way and Sagittarius A* a prototype for this ""secular"" mode of black hole feeding in late-type galaxies."," Intriguingly, the Milky Way galaxy resides in the locus of mass and colour where black hole growth is most likely, potentially making the Milky Way and Sagittarius A* a prototype for this “secular"" mode of black hole feeding in late-type galaxies."415" GZl has brought to light several rare classes of object. """, GZ1 has brought to light several rare classes of object. “416"Hanny's Voorwerp"" is perhaps the most famous of such objects and many are familiar with the story of the Dutch school teacher Hanny. who first noted this object (she was not the first volunteer to see it. but the first to ask about it) which is now memorialized in a ComieBook"".","Hanny's Voorwerp” is perhaps the most famous of such objects and many are familiar with the story of the Dutch school teacher Hanny, who first noted this object (she was not the first volunteer to see it, but the first to ask about it) which is now memorialized in a Comic."417. The Voorwerp is an unusual emission line nebula neighbouring the spiral galaxy IC 2497 and has been studied in several follow-up projects (e.g.Lintottetal.2009:Rampadarath2010:Schawin-skietal. 20102).. and also features in much of the education material from Galaxy Zoo.," The Voorwerp is an unusual emission line nebula neighbouring the spiral galaxy IC 2497 and has been studied in several follow-up projects \citep[e.g.][]{Lintott2009, Rampadarath2010, Schawinski2010a}, and also features in much of the education material from Galaxy Zoo."418" Another unusual class of objects discovered by the Galaxy Zoo volunteers are the ""Green Peas""."," Another unusual class of objects discovered by the Galaxy Zoo volunteers are the “Green Peas""."419 The properties of these emission-line galaxies. which appear green in the SDSS composite eri colour images because of their strong [OIL] emission. are studied in detail in Cardamoneetal.(2009).," The properties of these emission–line galaxies, which appear green in the SDSS composite $gri$ colour images because of their strong [OIII] emission, are studied in detail in \citet{Cardamone2009}."420. As the original Galaxy Zoo was the first time such a project had been attempted. the Galaxy Zoo team was cautious with their. classification scheme. only asking for simple information about the appearance of the galaxies.," As the original Galaxy Zoo was the first time such a project had been attempted, the Galaxy Zoo team was cautious with their classification scheme, only asking for simple information about the appearance of the galaxies."421 Thanks to the overwhelming response. and prompted by requests from the volunteers who wanted to provide more detailed classifications. the team realized they could harvest much more information from the SDSS images than in GZI.," Thanks to the overwhelming response, and prompted by requests from the volunteers who wanted to provide more detailed classifications, the team realized they could harvest much more information from the SDSS images than in GZ1."422 Therefore. Galaxy Zoo 2 (GZ2) was designed around asking more detailed questions about the ~250.000 brightest SDSS galaxies from the original GZI sample of galaxies.," Therefore, Galaxy Zoo 2 (GZ2) was designed around asking more detailed questions about the $\sim250,000$ brightest SDSS galaxies from the original GZ1 sample of galaxies."423 Once again. the response was tremendous and in the fourteen months the site was live. Galaxy Zoo 2 users provided over 60 million classifications.," Once again, the response was tremendous and in the fourteen months the site was live, Galaxy Zoo 2 users provided over 60 million classifications."424" Along the way. deeper SDSS images were added for a subset of GZ2 galaxies. taken from a patch of the sky known as ""Stripe 82"" which allows fainter structures in these galaxies to be visible."," Along the way, deeper SDSS images were added for a subset of GZ2 galaxies, taken from a patch of the sky known as “Stripe 82"" which allows fainter structures in these galaxies to be visible."425 The first science results from GZ2 classifications are now appearing., The first science results from GZ2 classifications are now appearing.426 In. Mastersetal. (2011).. we showed that the fraction of barred disk galaxies (as compared to unbarred," In \citet{Masters2011}, , we showed that the fraction of barred disk galaxies (as compared to unbarred"427of the Solar System)?,of the Solar System)?428 And how do the particles stay at an eccentricity lower than 0.1 all the time?, And how do the particles stay at an eccentricity lower than $0.1$ all the time?429 These questions can be resolved by better modeling the origin and the evolution of planetary migration., These questions can be resolved by better modeling the origin and the evolution of planetary migration.430 In any realistic simulation. the orbit of the planet will be subject to secular evolution.," In any realistic simulation, the orbit of the planet will be subject to secular evolution."431 There is even no need for other planets for this., There is even no need for other planets for this.432 The interaction with the disk particles themselves can be sufficient to significantly affect the planetary orbit., The interaction with the disk particles themselves can be sufficient to significantly affect the planetary orbit.433 Thus taking into account. the influence of the disk on the planets ts necessary to derive realistic simulations., Thus taking into account the influence of the disk on the planets is necessary to derive realistic simulations.434" Several studies have already discussed the origin of planetary migration either by ""planet-planetesimals"" (??) interactions or by “planet-planet™ interactions (?).."," Several studies have already discussed the origin of planetary migration either by “planet-planetesimals” \citep{2000ApJ...534..428I,2004Icar..170..492G}435 interactions or by “planet-planet” interactions \citep{2006DPS....38.5403M}."436" Depending on the scenario and on the initial conditions, one can observe migration on low-eccentricity orbit or more chaotic migration after a short time on an eccentric orbit."," Depending on the scenario and on the initial conditions, one can observe migration on low-eccentricity orbit or more chaotic migration after a short time on an eccentric orbit."437 We have studied the problem of the presence of observable structures in planetesimal disks due to mean motion resonance with ar unseen planet migrating outward in the disk., We have studied the problem of the presence of observable structures in planetesimal disks due to mean motion resonance with an unseen planet migrating outward in the disk.438 Using numerical simulations. we have explored a large range of parameters for the planet (mass and orbital eccentricity) and the disk (initial distribution of planetesimal eccentricities).," Using numerical simulations, we have explored a large range of parameters for the planet (mass and orbital eccentricity) and the disk (initial distribution of planetesimal eccentricities)."439 In the case of a planet on a circular orbit migrating inside a dynamically cold disk. our results are in agreement with previous analytical studies.," In the case of a planet on a circular orbit migrating inside a dynamically cold disk, our results are in agreement with previous analytical studies."440 In the cases not already addressed. namely planets on eccentric orbits or dynamically warm disks. we have found that the observability of resonant structures demands very specific orbital configurations.," In the cases not already addressed, namely planets on eccentric orbits or dynamically warm disks, we have found that the observability of resonant structures demands very specific orbital configurations."441 The clumps produced by MMRs with a planet on a circular orbit are smoothed in the case of a planet on an even moderately eccentric orbit., The clumps produced by MMRs with a planet on a circular orbit are smoothed in the case of a planet on an even moderately eccentric orbit.442 An eccentricity as low as 0.05 is enough to smooth all the resonant structures. except for the most massive planets.," An eccentricity as low as $0.05$ is enough to smooth all the resonant structures, except for the most massive planets."443 These results indicate that although trapping planetesimals in MMRs is an efficient mechanism to generate clumpy disks. stringent conditions must be fulfilled for this scenario to occur.," These results indicate that although trapping planetesimals in MMRs is an efficient mechanism to generate clumpy disks, stringent conditions must be fulfilled for this scenario to occur."444 Theoretical modeling of the origin. of the planetary migration therefore. will have to explain how planetary systems can remain under these conditions., Theoretical modeling of the origin of the planetary migration therefore will have to explain how planetary systems can remain under these conditions.445 Moreover. we only consider a planet migrating at a constant rate.," Moreover, we only consider a planet migrating at a constant rate."446 A more realistic model with a variable. stochastic migrattor rate can reduce the population of resonances and thus their observability.," A more realistic model with a variable, stochastic migration rate can reduce the population of resonances and thus their observability."447 A better model of planet migration thus should be developed in future studies., A better model of planet migration thus should be developed in future studies.448eniploved. to explore them in more detail.,employed to explore them in more detail.449 The uncertain cases are FSR 815. FSR 585. PSR 902. PSR 921. and FSR 951.," The uncertain cases are FSR 815, FSR 883, FSR 902, FSR 921, and FSR 951."450 Iu Fig., In Fig.451 10. we show the decontaminated J.(FfLF) CNDs of a represeutative sample of the uncertain cases. alc in Fig.," \ref{fig:10} we show the decontaminated $J\times(J-H)$ CMDs of a representative sample of the uncertain cases, and in Fig."452 12. their RDP»., \ref{fig:12} their RDPs.453" Decoutanunated CAIDs of this eroup have Ny,-values sienificautly lower. aud the RDPs much more megular. than those of the other two groups (Sect. 3.1))."," Decontaminated CMDs of this group have $N_{1\sigma}$ -values significantly lower, and the RDPs much more irregular, than those of the other two groups (Sect. \ref{sec:3.1}) )."454 Iu Fig.10 we present the decoutaminated J.(4IT) CMDs of a representative sample of the possible field fluctuations aud Fig., In \ref{fig:10} we present the decontaminated $J\times(J-H)$ CMDs of a representative sample of the possible field fluctuations and Fig.455 12. shows RDPs for some these overdeusities., \ref{fig:12} shows RDPs for some these overdensities.456 Civeu the somewhat limited 2\LASS photometric depth and the relatively large distance (Table 5)) of our confirmed OC's. the CAIDs in Fies.," Given the somewhat limited 2MASS photometric depth and the relatively large distance (Table \ref{tab5}) ) of our confirmed OCs, the CMDs in Figs."457 6 - 8. do not contain the whole mass range expected especially for OC's older than ~SOM., \ref{fig:6} - \ref{fig:8} do not contain the whole mass range expected especially for OCs older than $\sim50$ Myr.458 Thus. we estimate the stellar mass by means of the mass function (ATF). built for the observed AMIS amass rauge according to Bicaetal.(2006).," Thus, we estimate the stellar mass by means of the mass function (MF), built for the observed MS mass range according to \citet{Bica06}."459". The AIS MIF is then fitted with the function off)xaGM,", The MS MF is then fitted with the function $\phi(m)\propto{m}^{-(1+\chi)}$.460 Details of this approach are given in Table 7.. where we also show the nuuber aud mass of the evolved stars.," Details of this approach are given in Table \ref{tab7}, where we also show the number and mass of the evolved stars."461 Clearly. we do not lave access to the lower MS.," Clearly, we do not have access to the lower MS."462" Thus. asstnune that the low-mass content is still present. we use Kroupa’s (2001) to estimate the total stellar mass, down to the IT-burnius mass Iuüt (0.08AZ..."," Thus, assuming that the low-mass content is still present, we use Kroupa's (2001) to estimate the total stellar mass, down to the H-burning mass limit $0.08\,M_{\odot}$ )."463 The results are eiven in the last two colhuuus of Table 7.., The results are given in the last two columns of Table \ref{tab7}.464 Tuterestinely. the extrapolation suggests that FSR 911 may be a relatively massive OC.," Interestingly, the extrapolation suggests that FSR 941 may be a relatively massive OC."465 For the voung OC's we built the AIS ME in a similar way to the old ones. aud count the mmuber of PAISstars (Table 8)).," For the young OCs we built the MS MF in a similar way to the old ones, and count the number of PMSstars (Table \ref{tab8}) )."466 Tuterestinely. the MIF slopes are. in general. flatter than those of the older OC's (Table 7)). which may reflect the longer timescale for the evolution tows the MS of the low-mass PAIS: stars.," Interestingly, the MF slopes are, in general, flatter than those of the older OCs (Table \ref{tab7}) ), which may reflect the longer timescale for the evolution towards the MS of the low-mass PMS stars."467 Given the differcutial reddening. it is not possible to attribute a precise lass value for each PAIS stir.," Given the differential reddening, it is not possible to attribute a precise mass value for each PMS star."468 Thus. we simply coun the munber of PAIS stars aud adopt an average mass value for the PAIS stars to estimate pars aud pars.," Thus, we simply count the number of PMS stars and adopt an average mass value for the PMS stars to estimate $n_{PMS}$ and $m_{PMS}$."469 Assuniug that he mass distribujon of the PAIS stars also ollows Ίντοxis (2001) ME. the average PAIS imass - for HaASKOS witlii the range 0.08λεν}ST - is <ο.0.637 s," Assuming that the mass distribution of the PMS stars also follows Kroupa's (2001) MF, the average PMS mass - for masses within the range $0.08\la m(\ms)\la7$ - is $<m_{PMS}>\approx0.6\ms$ ."470 Thus. we sumaaly immultiplv the nwuuber o| PAIS stars (Table 8) by this value to estimate the PAIS mass.," Thus, we simply multiply the number of PMS stars (Table 8) by this value to estimate the PMS mass."471 Finalvy. we add the later value to the MS mass to obtain all Csuate of the tota] stellar mass.," Finally, we add the latter value to the MS mass to obtain an estimate of the total stellar mass."472 Obviously. similarly to the MS stars. 2\TASS cannot detect the very low mass PAIS stars.," Obviously, similarly to the MS stars, 2MASS cannot detect the very low mass PMS stars."473 Cousequeuthy. these values should be taken as lower limits.," Consequently, these values should be taken as lower limits."474 After cluster formation. structural piriuueters change with stellar and dynamical evolution.," After cluster formation, structural parameters change with stellar and dynamical evolution."475 As a consequence of the rapid expulsion of primordial eas and the new lower eravitational potential. the cluster increases on all scales reaching for virtalisation.," As a consequence of the rapid expulsion of primordial gas and the new lower gravitational potential, the cluster increases on all scales reaching for virialisation."476 Coodwin&Bastian(2006) show that this carly core radii expansion phase occurs within 10 - 30 Myr and can be explained as an effect of rapid residual gas expulsion., \citet{Goodwin06} show that this early core radii expansion phase occurs within 10 - 30 Myr and can be explained as an effect of rapid residual gas expulsion.477 After eas expulsion (a ew LOO vr) when some enerev equipartition is reached. he core radius of the OC survivors shrink. whereas the outer parts keep iucreasing in size.," After gas expulsion (a few $10^7$ yr), when some energy equipartition is reached, the core radius of the OC survivors shrink, whereas the outer parts keep increasing in size."478" Mass loss due to stellar evolution also affects the structural. parameters t this effect is neelieible because the most massive stars (AL,o 30M.) hardly contribute to the mass of he cluster (Lamers&Cucles. 2006)."," Mass loss due to stellar evolution also affects the structural, parameters but this effect is negligible because the most massive stars $M_{\star}>30M_{\odot}$ ) hardly contribute to the mass of the cluster \citep{Lamers06b}. ."479 Iu this coutest. PortegiesZwartetal.(1999) show that the maxima," In this context, \citet{Portegies99} show that the maximum"480Spin temperature can be thought of as a short hand notation to represent the level population of the hypertine states of the ground level of a hydrogen atom.,Spin temperature can be thought of as a short hand notation to represent the level population of the hyperfine states of the ground level of a hydrogen atom.481 Depending on the physical processes and background radiation that dominate a medium. T. is either coupled to the background CMB temperature or to the kinetic temperature of the hydrogen gas in the medium.," Depending on the physical processes and background radiation that dominate a medium, $\mathrm{T_s}$ is either coupled to the background CMB temperature or to the kinetic temperature of the hydrogen gas in the medium."482" Formally Field(1958) derived T. as a weighted sum of Ty and Tear. as: where ;,, and yo. are parameters that reflect the coupling of I. to Ti via Lye excitation and collisions respectively."," Formally \cite{field58} derived $\mathrm{\mathrm{T_s}}$ as a weighted sum of $\mathrm{\mathrm{T_k}}$ and $\mathrm{\mathrm{T_{CMB}}}$, as; where $y_\alpha$ and $y_{coll}$ are parameters that reflect the coupling of $\mathrm{T_s}$ to $\mathrm{T_k}$ via $\alpha$ excitation and collisions respectively."483 The efficiency. of Lya-coupling dominates over that of collisions. especially further away from the source (Thomas&Zaroubi2008:Chuzhoy.Alvarez.&Shapiro 2006).," The efficiency of $\alpha$ -coupling dominates over that of collisions, especially further away from the source \citep{thomas08,chuzhoy06}."484". In our treatment of calculating T.. we estimate both 5, and your."," In our treatment of calculating $\mathrm{\mathrm{T_s}}$, we estimate both $y_\alpha$ and $y_{coll}$."485 The coefficient your Is a function of Ti and the ionized fraction of the medium. XH.," The coefficient $y_{coll}$ is a function of $\mathrm{\mathrm{T_k}}$ and the ionized fraction of the medium, $\mathrm{x_{HII}}$."486 These informations on ionization and heating are available from the prescription outlined in the previous section., These informations on ionization and heating are available from the prescription outlined in the previous section.487" While simulating the |-D profiles we simultaneously calculate j,, as: Here. J.(|r]) is the Ένα flux density at distance + from the source."," While simulating the 1-D profiles we simultaneously calculate $y_\alpha $ as; Here, $J_o(|r|)$ is the $\alpha$ flux density at distance $r$ from the source."488 For miniqsos with high energyphotons. Lya coupling is mainly caused by collisional excitation due to secondary electrons (Chuzhoy.Alvarez.&Shapiro2006).," For miniqsos with high energyphotons, $\alpha$ coupling is mainly caused by collisional excitation due to secondary electrons \citep{chuzhoy06}."489". This process is accounted for by the following integral. where .N(Jc:r:£) is the number of photons with energy ""E at radius τς and time ""t per unit area (Zaroubi&Silk2005)."," This process is accounted for by the following integral, where $N(E;r;t)$ is the number of photons with energy 'E' at radius 'r', and time 't' per unit area \citep{zaroubi05}."490. This number is obtained directly from the 1-D radiative transfer by taking into account the the absorption due to the optical depth along the line-of-sight to the source at a distance r., This number is obtained directly from the 1-D radiative transfer by taking into account the the absorption due to the optical depth along the line-of-sight to the source at a distance 'r'.491 The I-D profiles generated are catalouged also as a function of time., The 1-D profiles generated are catalouged also as a function of time.492" Therefore the profiles that are embedded within the simulation are chosen to obey causality"".", Therefore the profiles that are embedded within the simulation are chosen to obey causality.493". The ionization cross-section of neutral hydrogen in the ground state is given by (47). ιο=0.416 is the oscillator strength of the Ένα transition. ο m,. are the electron's charge and mass. respectively. ©,, is the fraction of the absorbed photon energy that goes into excitation (Shull&vanSteenberg1985:Di-jkstra.Haiman.&Loeb 2004).."," The ionization cross-section of neutral hydrogen in the ground state is given by $\sigma(E),$ $\mathrm{f_{12}} = 0.416$ is the oscillator strength of the $\alpha$ transition, $e$ $m_e$ are the electron's charge and mass, respectively, $\phi_\alpha$ is the fraction of the absorbed photon energy that goes into excitation \citep{shull85,dijkstra04a}."494 Note here that the fitting formula is a function of both ionization fraction and energy as given in the appendix of Dijkstra.Haiman., Note here that the fitting formula is a function of both ionization fraction and energy as given in the appendix of \citet{dijkstra04a}.495&Loeb(2004 For the case of stars. the dominant source of Lye flux results from the redshifting of the source spectrum blueward of Ένα into the resonant line at different distances from the source.," For the case of stars, the dominant source of $\alpha$ flux results from the redshifting of the source spectrum blueward of $\alpha$ into the resonant line at different distances from the source."496 Frequency “vy at the redshift of emission (or the source) z is redshifted into Vey at redshift z(|r|) such that: Now. instead of embedding a sphere of theapn “PL. as in the ease of i. we embed instead the a bubble of Lya flux. Jl(|r[). as estimated from Eg. 3..," Frequency $\nu$ ' at the redshift of emission (or the source) $z$ ' is redshifted into $\nu_{Ly\alpha}$ at redshift $z(|r|)$ such that; Now, instead of embedding a sphere of the $\mathrm{T_s}$, as in the case of $\mathrm{T_k}$, we embed instead the a bubble of $\alpha$ flux, $J_o(|r|)$, as estimated from Eq. \ref{eq:lyalphaflux}. ."497" Since JJ.(|r|) is basically the number of Lya photons at a given location. the overlap of two 7.J,, bubbles"" implies that the photons and hence the J,, has to be added. ie.. at à given spatial (pixel) location. 7. jf. Sand time /. the total Ένα flux is given where J/(Foy.2.1) is the Ένα flux contributed by i!” source at the pixel location in the box. 7. jj. and time /."," Since $J_o(|r|)$ is basically the number of $\alpha$ photons at a given location, the overlap of two $\mathrm{J_o}$ bubbles” implies that the photons and hence the $\mathrm{J_o}$ has to be added, i.e., at a given spatial (pixel) location, $\vec{x}$, $\vec{y}$, $\vec{z}$ and time $t$, the total $\alpha$ flux is given by; where $J_{o}^{i}(\vec{x},\vec{y},\vec{z},t)$ is the $\alpha$ flux contributed by $i^{th}$ source at the pixel location in the box, $\vec{x}$, $\vec{y}$, $\vec{z}$ and time $t$."498" Equipped with the quantities Ty(1). and 4.07). we can calculate j4, as in Eq. 2.."," Equipped with the quantities $\mathrm{\mathrm{T_k}(\vec{r})}$, and $J_o(\vec{r})$, we can calculate $y_\alpha$ as in Eq. \ref{eq:yalpha},"499 and subsequently the spin temperature through Eq. 1.., and subsequently the spin temperature through Eq. \ref{eq:tspin}.500 Now all terms required for the caleulation of oT). as in Eq. 6..," Now all terms required for the calculation of $\delta \mathrm{T_b}$, as in Eq. \ref{eq:dtb},"501 are obtained., are obtained.502 In this section we apply with its extended feature of including heating of the IGM. to three different scenarios of reionization.," In this section we apply with its extended feature of including heating of the IGM, to three different scenarios of reionization."503" The models described in this section are not ""template"" reionization scenarios by any measure nor is any particular model favoured w.r.t the other.", The models described in this section are not “template” reionization scenarios by any measure nor is any particular model favoured w.r.t the other.504 In fact. these models may be far from reality and only serve as examples of the potential of to provide a reasonable estimate of the 21-em brightness temperature for widely different scenarios of reionization.," In fact, these models may be far from reality and only serve as examples of the potential of to provide a reasonable estimate of the 21-cm brightness temperature for widely different scenarios of reionization."505 The first scenario explored using is the case in which the sources of reionization are stars., The first scenario explored using is the case in which the sources of reionization are stars.506 In this section we describe the model used to describe the stellar component and the prescription adopted to embed these stars into haloes of dark matter identified in an N-body simulation., In this section we describe the model used to describe the stellar component and the prescription adopted to embed these stars into haloes of dark matter identified in an N-body simulation.507 Most stars. to first order. behave as blackbodies at a given temperature. although the detailed features in the SED depends on more complex physical processes. age. metallicity and mass of the star.," Most stars, to first order, behave as blackbodies at a given temperature, although the detailed features in the SED depends on more complex physical processes, age, metallicity and mass of the star."508 This blackbody nature imprints characteristic signatures on the IGM heating and ionization patterns (Thomas&Zarou, This blackbody nature imprints characteristic signatures on the IGM heating and ionization patterns \citep{thomas08}. .509bi 2008).. Schaerer(2002). showed that the temperature of the star only weakly depends on its mass., \cite{schaerer02} showed that the temperature of the star only weakly depends on its mass.510 The blackbody temperature of the stars in our simulation was thus fixedat 5—104Ix to perform the radiative transfer., The blackbody temperature of the stars in our simulation was thus fixedat $5 \times 10^4~\mathrm{K}$ to perform the radiative transfer.511 We sample the parametre space of redshifts (12 to 6). density profiles around the source and masses €10 to," We sample the parametre space of redshifts (12 to 6), density profiles around the source and masses (10 to"512resolved: mergers.,resolved mergers.513 Symbols mark the last output bin before this limiting recdshift. where we believe we resolve enough of the mergers to robustIy study their properties.," Symbols mark the last output bin before this limiting redshift, where we believe we resolve enough of the mergers to robustly study their properties."514 Since the assumption used for the dashed lines is extreme. we expect that the solid lines are generally closer to the true rates.," Since the assumption used for the dashed lines is extreme, we expect that the solid lines are generally closer to the true rates."515 For the high mass sample. the limiting redshifts for fuss290.125.0.25 and 0.5 are se.=0.5.1.0 and 2.6. respectively.," For the high mass sample, the limiting redshifts for $\rmerg > 0.125, 0.25$ and $0.5$ are $\zres = 0.5, 1.0$ and $2.6$, respectively."516 For medium masses. merger ratios of Zoos and 0.5 can be resolved to ο=(0.6 and 1.0. respectively.," For medium masses, merger ratios of $\rmerg > 0.25$ and $0.5$ can be resolved to $\zres = 0.6$ and $1.0$, respectively."517 For the low mass sample. eios270.5 can be resolved only to σος=0.5.," For the low mass sample, $\rmerg > 0.5$ can be resolved only to $\zres = 0.5$."518 To compare all three samples. we must therefore restrict ourselves to Risers70.5 and zx0.5.," To compare all three samples, we must therefore restrict ourselves to $\rmerg>0.5$ and $z \leq 0.5$ ."519 Figure 5 quantifies the mass dependence of merger rates seen in Figures 3. and 4.., Figure \ref{fig:mass} quantifies the mass dependence of merger rates seen in Figures \ref{fig:resh} and \ref{fig:resl}.520 Fo maximize statistics. we count all mergers with Zeusc0.5 occurring between z=0 and >= (45.," To maximize statistics, we count all mergers with $\rmerg > 0.5$ occurring between $z=0$ and $z=0.5$ ."521 The mean number of mergers per galaxy in this interval follows a best-fit relation 10145 where τω is the galaxy mass ad = 0.," The mean number of mergers per galaxy in this interval follows a best-fit relation = 0.0145 )+0.0175, where $M_{\rm gal}$ is the galaxy mass at $z=0$ ."522 We can herefore anticipate a strong dependence of Hubble type requencics on galaxy mass., We can therefore anticipate a strong dependence of Hubble type frequencies on galaxy mass.523 We find an even steeper best-fit slope for his>0.25. but with only two points it is hard ο draw meaningful conclusions from this clillcrence.," We find an even steeper best-fit slope for $\rmerg > 0.25$, but with only two points it is hard to draw meaningful conclusions from this difference."524 Figure 6 shows the distribution of parent mass ratios or main branch mergers in the interval 0<z«0.5., Figure \ref{fig:ratio} shows the distribution of parent mass ratios for main branch mergers in the interval $0 < z < 0.5$.525 In the igh mass sample. the number of mergers is proportional to li>»liucr1..," In the high mass sample, the number of mergers is proportional to $\rmerg^{-1.2}$."526 Phere are not enough bins in the low and. medium mass samples to reliably infer a dependence (or lack thereof) on galaxy mass., There are not enough bins in the low and medium mass samples to reliably infer a dependence (or lack thereof) on galaxy mass.527 Phe —1.2 slope for the high mass sample implies that high mass ratio mergers dominate the merger erowth rate. since the average rate at which a galaxy. gains mass by mergers above a threshold Misia. MasRita: has already reached half of its asymptotic. value. for Hau042.," The $-1.2$ slope for the high mass sample implies that high mass ratio mergers dominate the merger growth rate, since the average rate at which a galaxy gains mass by mergers above a threshold $R_{\rm min}$, ), has already reached half of its asymptotic value for $R_{\rm min}=0.42$."528 We now turn to the voltume-averaged merger rate of ealaxies (the mean number of mergers per comoving Alpe? per Gyr). which can be estimated obscrvationally by counting either recent merger remnants or close pairs that will merge in the near future. ancl dividing by an estimated. merger timescale.," We now turn to the volume-averaged merger rate of galaxies (the mean number of mergers per comoving $^3$ per Gyr), which can be estimated observationally by counting either recent merger remnants or close pairs that will merge in the near future, and dividing by an estimated merger timescale."529 Phe merger rate of all galaxies (not just the main progenitor branch) is shown in Figure 7. for mergers with Jaess290.5.," The merger rate of all galaxies (not just the main progenitor branch) is shown in Figure \ref{fig:rate}530 for mergers with $\rmerg > 0.5$."531 We plot the result. for all branches because observations cannot determine which merger remnants will end up merging with other galaxies at future times., We plot the result for all branches because observations cannot determine which merger remnants will end up merging with other galaxies at future times.532 Dashed lines include the possible contribution of unresolved mergers., Dashed lines include the possible contribution of unresolved mergers.533 We continue curves past the limiting redshift 2... adopted in Figures 8 and 4 because the range of possible merger rates is still an interesting prediction. even though the contribution of unresolved mergers may be significant.," We continue curves past the limiting redshift $z_{\rm res}$ adopted in Figures \ref{fig:resh} and \ref{fig:resl}534 because the range of possible merger rates is still an interesting prediction, even though the contribution of unresolved mergers may be significant."535 Although we are likely to be missing some mergers above zi. we think that the resolved: merger rates (solid lines) are. probably closer to the true merger rate predictions than the dashed. lines. which are upper limits based on extreme assuniptions.," Although we are likely to be missing some mergers above $z_{\rm res}$ , we think that the resolved merger rates (solid lines) are probably closer to the true merger rate predictions than the dashed lines, which are upper limits based on extreme assumptions."536 The naked error bars in Figure 7 show the observational estimates of 2. derived [rom the DEEDP2 survey (2)... for ealaxies with [uminosities 19«Alp21.," The naked error bars in Figure \ref{fig:rate} show the observational estimates of \citet{lin:04} derived from the DEEP2 survey \citep{davis:03}, for galaxies with luminosities $-19 < M_B < -21$."537 These points lio below our mocdel predictions. especially at z1.," These points lie below our model predictions, especially at $z>1$."538 The luminosity range roughly corresponds to the mass range of our high mass sample. except that these are the galaxy luminosities at. the observed: redshift. not at z= 0.," The luminosity range roughly corresponds to the mass range of our high mass sample, except that these are the galaxy luminosities at the observed redshift, not at $z=0$ ."539 If we restrict ourselves to galaxies that are in that mass range at the plotted redshift. then we ect the clot-dash line with crosses in Figure 7.. which agrees fairly well with the observations at 2<1 but remains high by a factor ~ 2a 2m1.," If we restrict ourselves to galaxies that are in that mass range at the plotted redshift, then we get the dot-dash line with crosses in Figure \ref{fig:rate}, which agrees fairly well with the observations at $z<1$ but remains high by a factor $\sim 2$ at $z>1$."540 Evolution of stellar mass-to-light ratios changes the correspondence between Luminosity anc stellar mass. anc the range of mass-to-leht ratios becomes larger at earlier epochs. so a full assessment of this mild. discrepancy. wil require more detailed. modeling of the stellar populations of the simulated. galaxies. and more detailed replication of the observational procedures for estimating merger rates.," Evolution of stellar mass-to-light ratios changes the correspondence between luminosity and stellar mass, and the range of mass-to-light ratios becomes larger at earlier epochs, so a full assessment of this mild discrepancy will require more detailed modeling of the stellar populations of the simulated galaxies, and more detailed replication of the observational procedures for estimating merger rates."541 The svstematic uncertainties in matching theoretical anc observational samples are minimized if merger rates are given divided. by the number density of objects. being sampled. as in our Figures 3. and 4.," The systematic uncertainties in matching theoretical and observational samples are minimized if merger rates are given divided by the number density of objects being sampled, as in our Figures \ref{fig:resh} and \ref{fig:resl}."542 When data are presented as in Figure 7.. the number of mergers per galaxy is convolved with evolution of the number density of galaxies ancl of their properties. making it more dillieult to isolate the source of discrepancies.," When data are presented as in Figure \ref{fig:rate}, the number of mergers per galaxy is convolved with evolution of the number density of galaxies and of their properties, making it more difficult to isolate the source of discrepancies."543 Figure S. shows the distribution of the total number of mergers agalaxy undergoesduring its history. for cilferent mass samples and mass ratio thresholds.," Figure \ref{fig:num} shows the distribution of the total number of mergers agalaxy undergoesduring its history, for different mass samples and mass ratio thresholds."544 Figure legencds list theaverage number ofmergers per galaxy. for. eachmass bin ancl parent mass ratio., Figure legends list theaverage number ofmergers per galaxy for eachmass bin and parent mass ratio.545 Curves in each panel show, Curves in each panel show546above the theoretical expectation.,above the theoretical expectation.547 In fact. when we normalize our simulations by requirine that the umber of events with E>101? eV equals the AGASA . —ao ∪↴⋝↴∖↴↸∖↥⋅↖↽⋜↧⊓∪∐↴∖↴≺∣−⋗≺∖⋝∙↖↖⇁↸∖∏∐≼↧↑∐⋜↧↑↑↕∐∖↕∐∐⊔↴⋝↸∖↥⋅∪↸∖⊼↻↸∖↸⊳↑↸∖≼⊓∖↖⇁↸∖∐↑↴∖↴↕∪↥⋅⊏≧⊥∪−∪ . : ] ⋡↽⋅≻ ↸∖∖⊽↕↴∖↴∪∐⋅↖⇁↕∙⊇∶∶⊓∣↕⋟∪↥⋅↑∐↸∖↕⋟≋≼⊲∑↸⊳⋜↧↴∖↴↸∖∙↕∙↸∖∙∙ ↘⇁⊓⊔∎⋪⋜↧↖↖⇁⋜↧⋅↖↽↕≯↥⋅∪⋯↑∐↸∖∪↴⋝↴∖↴," In fact, when we normalize our simulations by requiring that the number of events with $E548\ge 10^{19}$ eV equals the AGASA observations (728), we find that the number of expected events for $E \ge 10^{20}$ eV is only $1.2 \pm 1.0$ for the PSCz case, i.e., “6 $\sigma$ ” away from the observed 8 events."549↸∖↥⋅↖↽↸∖≺↧≺∖∖ ↸∖↖↽↸∖∐↑↴∖↴∙ ↽∕∏∐∖∶↴∙⊾⋜⋯↴⋝↸∖↑↖↖↽↸∖↸∖∐∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≼↧↕−⊓↕⊼⋜⋯≼↧⋯∪∩∖↕↻↥⋅↸∖≼∐↸⊳↑↕∪∐↴∖↴∐⋜∐⋅↥⋅∪↖↖⇁↴∖↴⋜↧↴∖↴↑∐↸∖ ↕∐⋅↿≱↸∖↸⊳↑↕∪↕↴∖↴↻↸∖↸⊳⊓⋅⋯⊔∪↕≯↑∐↸∖↕↸∐⊏≼⊲↕, The gap between observed flux and model predictions narrows as the injection spectrum of the UHECR sources becomes much harder than $\gamma = 3$ .550⊰↴∖↴≺∏∐⋅↸⊳↸∖↴∖↴↴⋝↸∖↸⊳∪⋯↸∖↴∖↴⋯⋯⊳∐∐⋜∐⋅≼∐∖↥⋅↑∐⋜⋯↷↴∶∶≩∙ For >=2.1 (shown in Figure yy. the nuuber of expected events above Lor? eV reaches 3.323:1.6 for à homogeneous distribution while for the PSCz catalog itis 3.7£2.0.," For $\gamma = 2.1$ (shown in Figure \cite{BBO00}) ), the number of expected events above $10^{20}$ eV reaches $3.3 \pm 1.6$ for a homogeneous distribution while for the PSCz catalog it is $3.7\pm 2.0$."551 This trend cau be seen also in Figure 6. where moan fluxes for ~=1.5.2.1 and 2.7 are shown.," This trend can be seen also in Figure 6, where mean fluxes for $\gamma =1.5,5522.1$ and 2.7 are shown."553 Iu addition to the preseuce of events past the CZIN cutoff. there has beeu uo clear counterparts identified in the arrival direction of the highest energy eveuts.," In addition to the presence of events past the GZK cutoff, there has been no clear counterparts identified in the arrival direction of the highest energy events."554 If these events are protons or photons. these observations should be astrononucal. ic. them arrival directions should be the angular position of sources.," If these events are protons or photons, these observations should be astronomical, i.e., their arrival directions should be the angular position of sources."555 At these hieh energies the Calactic and extragalactic maenetic fields should not affect proton orbits significantly so that even protons would poit back to their sources within a few deerces., At these high energies the Galactic and extragalactic magnetic fields should not affect proton orbits significantly so that even protons would point back to their sources within a few degrees.556 Protons at 1079 eV propagate mainly in straight lines as they traverse the Galaxy since their gvroradi are ~ 100 kpe in pC fields which is typical in the Galactic disk., Protons at $10^{20}$ eV propagate mainly in straight lines as they traverse the Galaxy since their gyroradii are $\sim $ 100 kpc in $ \mu$ G fields which is typical in the Galactic disk.557 Extragalactic fields are expected to be « pollte aud induce at most ~ 1° deviation from the source.," Extragalactic fields are expected to be $\ll558\mu$ \cite{KronVallee,BBO99} and induce at most $\sim$ $^o$ deviation from the source."559 Even if the Local Supercluster has relatively stroug fields. the highestcucrey," Even if the Local Supercluster has relatively strong fields, the highestenergy"560therefore these variations are regarded as real.,therefore these variations are regarded as real.561" The residual signals appear at similar, 0.0155-0.0150 cd! separations from fo in the 1971-1977 and 1978-1993 data, indicating that the modulation period is about 64 d (Fig. 5))."," The residual signals appear at similar, 0.0155–0.0150 $^{-1}$ separations from $f_0$ in the 1971–1977 and 1978–1993 data, indicating that the modulation period is about 64 d (Fig. \ref{v08sp}) )."562 We failed to detect periodic light-curve modulation in the photographic data before 1971., We failed to detect periodic light-curve modulation in the photographic data before 1971.563 The pulsation period has been steadily increasing but the period increase is not linear., The pulsation period has been steadily increasing but the period increase is not linear.564 Goranskij(1980a) determined a 75-d Blazhko-modulation period for V14., \cite{g80a} determined a 75-d Blazhko-modulation period for V14.565" The CCD (R96, Κ00) light curves show strong amplitude modulation."," The CCD (R96, K00) light curves show strong amplitude modulation."566 The maximum- variation is 0.7-mag in the V band., The maximum-brightness variation is 0.7-mag in the $V$ band.567" The pulsation-period variation is strong and irregular, which makes the analysis of the light curve difficult."," The pulsation-period variation is strong and irregular, which makes the analysis of the light curve difficult."568 The star can be easily measured; the photographic data are not biased., The star can be easily measured; the photographic data are not biased.569 A 47.8-d (0.021 cd~') modulation period was determined for the 1971-1981 interval (see upper panel in Fig. 6))., A 47.8-d (0.021 $^{-1}$ ) modulation period was determined for the 1971–1981 interval (see upper panel in Fig. \ref{v14sp}) ).570" Although strong light-curve modulation was present in the other parts of the photographic data also, a modulation period close to"," Although strong light-curve modulation was present in the other parts of the photographic data also, a modulation period close to"5711999).,.572". Note that Q,,,=90° represents the worst case. since the tolerance angle criterion now is fulfilled for every particle with minimal Ο per search through the nearest neighbour list."," Note that $\Theta_{\rm tol}=90^\circ$ represents the worst case, since the tolerance angle criterion now is fulfilled for every particle with minimal $\Theta$ per search through the nearest neighbour list."573 The particles which are most allectecl by the tolerance anele criterion lie next to the borders of shadows cast by optically thick regions. since here the path for the integration along the line of sight may be bent through the optically thick region. thus decreasing the ionizing [ux artificially.," The particles which are most affected by the tolerance angle criterion lie next to the borders of shadows cast by optically thick regions, since here the path for the integration along the line of sight may be bent through the optically thick region, thus decreasing the ionizing flux artificially."574 In the opposite case. the path may lead around. the opaque region. increasing the ionizing Lux a i6 position of a particle in the shadow.," In the opposite case, the path may lead around the opaque region, increasing the ionizing flux at the position of a particle in the shadow."575 These extreme cases lead to the tail in the error histograms in Fig. 3.., These extreme cases lead to the tail in the error histograms in Fig. \ref{fig:raterrs}.576 Applying the tolerance angle criterion thus numerically blurs shadows., Applying the tolerance angle criterion thus numerically blurs shadows.577" The mean errors in 7 are 1.3 per cent for Οι=0.5 2.2 per cent for Ομ= 1.07. 3.4 per cent for O,,,=2.0 and 11.2 per cent for QO...=907."," The mean errors in $\tau$ are $1.3$ per cent for $\Theta_{\rm578tol}=0.5^\circ$, $2.2$ per cent for $\Theta_{\rm tol}=1.0^\circ$ , $3.4$ per cent for $\Theta_{\rm tol}=2.0^\circ$ and $11.2$ per cent for $\Theta_{\rm tol}=90^\circ$."579 The correspnding mean errors in Z are 2.8. 4.1. 5.7 and 13.3 per cent. respectively.," The correspnding mean errors in ${\cal I}$ are $2.8$, $4.1$, $5.7$ and $13.3$ per cent, respectively."580 For the remaining test cases presented in this paper the choice of Οἱ. has no ellect. since they deal with one-climensiona problems. in which the optical depth. is only a function of distance from the source.," For the remaining test cases presented in this paper the choice of $\Theta_{\rm tol}$ has no effect, since they deal with one-dimensional problems, in which the optical depth is only a function of distance from the source."581 Applying the tolerance angle criterion only shifts the evaluation points [from the lines of sight in directions perpendicular to these. along which there is no change in the optical depth.," Applying the tolerance angle criterion only shifts the evaluation points from the lines of sight in directions perpendicular to these, along which there is no change in the optical depth."582" Indeed. even the choice Qj,=90 gives the same results in the one-dimensiona test cases as for Q4=07.", Indeed even the choice $\Theta_{\rm tol} = 90^\circ$ gives the same results in the one-dimensional test cases as for $\Theta_{\rm tol}=0^\circ$.583 Thus the errors introduced. by the angle criterion must be checked with problems in which this svmumetry is broken and shadows are present. as the one mentioned above.," Thus the errors introduced by the angle criterion must be checked with problems in which this symmetry is broken and shadows are present, as the one mentioned above."584 For reasons of noise reduction we smooth the ionization front. which is not resolvable by the representation. over a distance of the order of one local smoothing length.," For reasons of noise reduction we smooth the ionization front, which is not resolvable by the representation, over a distance of the order of one local smoothing length."585 Nature provides a simple way for doing this., Nature provides a simple way for doing this.586 The width of the ionization zone Is of the order of one photon mean free path length. where m is the net absorption cross section for ionizing photons as clelined in Ίσα. 2..," The width of the ionization zone is of the order of one photon mean free path length, where $\bar{\sigma}$ is the net absorption cross section for ionizing photons as defined in Eq. \ref{eq:crossect}."587 Since we cannot resolve the ionization region anyway. we are free to adjust o in a way that the width of the ionization region given by Eq.," Since we cannot resolve the ionization region anyway, we are free to adjust $\sigma$ in a way that the width of the ionization region given by Eq."588 12. is equal to a constant factor Co<1 times the local smoothing length . but never larger than the value 7 given by Eq. 2:," \ref{eq:width} is equal to a constant factor $C \leq 1$ times the local smoothing length $h$, but never larger than the value $\bar{\sigma}$ given by Eq. \ref{eq:crossect}:"589 lest caculations have shown that à good value is C—0.1., Test calculations have shown that a good value is $C=0.1$.590 1 has proven to sullicicnthy reduce. numerical noise introcluced. into the ionization structure by noise in the particle distribution and at the same time to keep the resolution of ionization fronts better than the resolution of thespl ormalism in order not to worsen the overall resolution., It has proven to sufficiently reduce numerical noise introduced into the ionization structure by noise in the particle distribution and at the same time to keep the resolution of ionization fronts better than the resolution of the formalism in order not to worsen the overall resolution.591" Note that. when smoothing"" the ionization front over 0.1 times the smoothing length. the noise reducing elfect is not caused by the spatial smoothing. since it is ten times smaller than the smoothing."," Note that, when “smoothing” the ionization front over $0.1$ times the smoothing length, the noise reducing effect is not caused by the spatial smoothing, since it is ten times smaller than the smoothing."592 Ht rather results [rom a larger number of time steps needed. to ionize a particle in the front. from an ionization fraction of .r=0 to.rc1., It rather results from a larger number of time steps needed to ionize a particle in the front from an ionization fraction of $x=0$ to $x \simeq 1$.593 This gives the neighbouring particles the opportunity to react to the changed state in a smoother wav., This gives the neighbouring particles the opportunity to react to the changed state in a smoother way.594 We assume that heating anc cooling ellects lead to an equilibrium temperature of 100000 Ix. in the tonizect gas vcnetrated by ionizing radiation., We assume that heating and cooling effects lead to an equilibrium temperature of 000 K in the ionized gas penetrated by ionizing radiation.595 The cross sections [for elastic electron.electron and electron.proton scattering are of the order 10.Pem?., The cross sections for elastic electron–electron and electron–proton scattering are of the order $10^{-13} {\rm cm}^2$.596 Together with a mean velocity of he electrons of the order of 600uns+ the twrmalization imeseale for the energies of the ejected electrons. is. [ar ess than a vear for densities of 1 particle cm which is many orders of magnitude smaller than the dynamical imescale.," Together with a mean velocity of the electrons of the order of $600 \rm{\,km\, s}^{-1}$ the thermalization timescale for the energies of the ejected electrons is far less than a year for densities of 1 particle $^{-3}$, which is many orders of magnitude smaller than the dynamical timescale."597 Phermalization thus occurs quasi instantaneously., Thermalization thus occurs quasi instantaneously.598 This process runs even morerapidly for higher densities., This process runs even morerapidly for higher densities.599 Thus we are allowed to treat the gas behind the ionization ront as thermalized., Thus we are allowed to treat the gas behind the ionization front as thermalized.600 We set the internal energy. to:, We set the internal energy to:601have available Lla Dux measurements. but fall outside one of the limits on brightness. Galactic latitude. or morphological tvpe.,"have available $\alpha$ flux measurements, but fall outside one of the limits on brightness, Galactic latitude, or morphological type."602 Lt is a composite of targets that were either observed by Kennicutt et al. (, It is a composite of targets that were either observed by Kennicutt et al. (6032008) as telescope time allowed. or had Ilo fluxes published in the literature.,"2008) as telescope time allowed, or had $\alpha$ fluxes published in the literature."604 Subsequent statistical tests. às functions of B-band apparent magnitudes anc HE Iluxes (compiled from the literature). show that the subset of galaxies with |b]ο20 is relatively complete to Mi&15 and Mg72.107 AL. at 1e edge of the 11 Alpe volume Lee et al. (," Subsequent statistical tests, as functions of B-band apparent magnitudes and HI fluxes (compiled from the literature), show that the subset of galaxies with $|b|>20^{\circ}$ is relatively complete to $\mathrm{M}_{\mathrm{B}} \lta -15$ and $\mathrm{M}_{\mathrm{{HI}}}> 2 \times 10^8$ $_{\odot}$ at the edge of the 11 Mpc volume Lee et al. ("6052009).,2009).606 Subsequent CLALIEN. UV. imagine primarily targeted the |b)>307. Bo<15.5 subset of the sample.," Subsequent GALEX UV imaging primarily targeted the $|b|>30^{\circ}$, $B<15.5$ subset of the sample."607 The more restrictive latitude limit was imposed to avoid excessive Galactic extinction and fields with bright foreground. stars and/or high background levels for which observations would be prohibited due to CLALISN brightness safety restrictions., The more restrictive latitude limit was imposed to avoid excessive Galactic extinction and fields with bright foreground stars and/or high background levels for which observations would be prohibited due to GALEX's brightness safety restrictions.608 Deep. single orbit (71500 sec) simaging was obtained for each ealaxy. following the strategy ofthe GALEN Nearby Galaxy Survey (τὸ.," Deep, single orbit $\sim$ 1500 sec) imaging was obtained for each galaxy, following the strategy of the GALEX Nearby Galaxy Survey \citep{Gil-de-Paz:2007aa}."609 GALEN observations for a significant [raction of the remaining galaxies bevoned these limits were also taken by other GL programs., GALEX observations for a significant fraction of the remaining galaxies beyond these limits were also taken by other GI programs.610 Overall. GALEN cata are available for 90% of the 436 galaxy sample.," Overall, GALEX data are available for $\sim90$ of the 436 galaxy sample."611 Finally. Spitzer URAC mid-infrared. and MIDPS. infrared imaging was also obtained Lor the 0]307. D« subset of the sample through the Local Volume Legacy program.," Finally, Spitzer IRAC mid-infrared and MIPS far-infrared imaging was also obtained for the $|b|>30^{\circ}$, $B<15.5$ subset of the sample through the Local Volume Legacy program."612 This sub-sample with both UV and Ht coverage contains 257 galaxies and is used in the following analysis., This sub-sample with both UV and IR coverage contains 257 galaxies and is used in the following analysis.613 The resulting dataset provides an unprecedented multi-wavelength. view of star formation in the nearby. Universe., The resulting dataset provides an unprecedented multi-wavelength view of star formation in the nearby Universe.614 In particular. the multi-band Spitzer HX observations allow for bolometric luminosities to be calculated: (using the algorithms provided by 2)) in à manner consistent with the LRAS fluxes available for our larger datasets.," In particular, the multi-band Spitzer IR observations allow for bolometric luminosities to be calculated (using the algorithms provided by \citealt{2002ApJ...576..159D}) ) in a manner consistent with the IRAS fluxes available for our larger datasets."615" The ‘classic way of constructing a luminosity function is based on the estimator Where Vias is the volume enclosed by the maximum distance at which ealaxy / would be observable. given the Ilux limits of the survey OS!"" - defined by the IR. and UV respectively for the LR- ancl UV-selected. samples. anc the D-band for the LVL. sample) and the ealaxy’s luminosity - this “maximum volume is then used to weight each ealaxies’ contribution to the final function &(L)."," The `classic' way of constructing a luminosity function is based on the estimator Where $_{\mathrm{max}}$ is the volume enclosed by the maximum distance at which galaxy $i$ would be observable, given the flux limits of the survey $S^{lim}_{\nu}$ - defined by the IR and UV respectively for the IR- and UV-selected samples, and the B-band for the LVL sample) and the galaxy's luminosity - this `maximum volume' is then used to weight each galaxies' contribution to the final function $\Phi$ (L)."616 This inverse volume weighting is designed to counteract the \lalniquist-type bias which would be encountered. by a pure number counting exercise: the voltume probed. by a flux limited survey varies as a function of luminosity. and as such faint galaxies (which are only seen nearby) are under-represented: conversely. bright galaxies seen out to large distances are over-represented.," This inverse volume weighting is designed to counteract the Malmquist-type bias which would be encountered by a pure number counting exercise: the volume probed by a flux limited survey varies as a function of luminosity, and as such faint galaxies (which are only seen nearby) are under-represented; conversely, bright galaxies seen out to large distances are over-represented."617 Weighting by Vises eliminates this ellect. and reconstructs the true underlving luminosity distribution.," Weighting by $_{\mathrm{max}}$ eliminates this effect, and reconstructs the true underlying luminosity distribution."618 This particular form of the weighting (as opposed to first binning into luminosity bins. then applying a mean μις to all galaxies within the bin) reduces error resulting from binning of the data - in essence. cach galaxy is assigned its own bin of width dL. The L/Vinex method has the great. advantage of being à Non-parametric estimator. as it does not assume any orm of e(L).," This particular form of the weighting (as opposed to first binning into luminosity bins, then applying a mean $_{\mathrm{max}}$ to all galaxies within the bin) reduces error resulting from binning of the data - in essence, each galaxy is assigned its own bin of width dL. The $_{\mathrm{max}}$ method has the great advantage of being a non-parametric estimator, as it does not assume any form of $\Phi$ (L)."619 However. it does suller from two weaknesses: irstls. binning in luminosity space is sometimes required. which necessarily involves some loss of information. and the resulting form of @(L) can be somewhat sensitive to the xuticular binning used.," However, it does suffer from two weaknesses: firstly, binning in luminosity space is sometimes required, which necessarily involves some loss of information, and the resulting form of $\Phi$ (L) can be somewhat sensitive to the particular binning used."620 Secondly. and more seriously. it is hiehly sensitive to local density enhancements (see ? or à detailed discussion).," Secondly, and more seriously, it is highly sensitive to local density enhancements (see \citealt{1988MNRAS.232..431E} for a detailed discussion)."621 The Local Volume represents a significant overdensity compared to the cosmic mean. which will manifest in a flux limited survey as an enhancement at he faint end. of the Iuminosity function.," The Local Volume represents a significant overdensity compared to the cosmic mean, which will manifest in a flux limited survey as an enhancement at the faint end of the luminosity function."622 7. compared. the D-band luminosity density in the local 8 Alpe and find that it is 1.7-2.0 times the global luminosity density (as derived rom both the Sloan Digital Sky Survey and the Millennium Galaxy. Catalogue)., \cite{2004AJ....127.2031K} compared the B-band luminosity density in the local 8 Mpc and find that it is 1.7-2.0 times the global luminosity density (as derived from both the Sloan Digital Sky Survey and the Millennium Galaxy Catalogue).623 We therefore correct the local density downwards by a factor 1.5540.15. and. incorporate this uncertainty in the error on the derived. faint end. slope.," We therefore correct the local density downwards by a factor $1.85 \pm 0.15$, and incorporate this uncertainty in the error on the derived faint end slope."624 ‘This is consistent with the values found by ? and ? by comparing the LVL and the the field mass function (the Local Volume is over-clense by a factor of 1.43). the DB-band LE (a factor of 2.3) and the UW LE (a factor of 2).," This is consistent with the values found by \cite{2009ApJ...706..599L} and \cite{2010arXiv1009.4705L} by comparing the LVL and the the field mass function (the Local Volume is over-dense by a factor of 1.4), the B-band LF (a factor of 2.3) and the UV LF (a factor of 2)."625 The weakness to density [Iuctuations can be overcome by acopting à parametric estimator. which assumes the form of the luminosity funetion is universal (with the precise shape being determined. by some free. parameters). which allows the density to be factored oul.," The weakness to density fluctuations can be overcome by adopting a parametric estimator, which assumes the form of the luminosity function is universal (with the precise shape being determined by some free parameters), which allows the density to be factored out."626" One such statistic is the ""maximum likelihood method. as described by (ος) ? and ? "," One such statistic is the `maximum likelihood' method, as described by (e.g.) \cite{1988MNRAS.232..431E} and \cite{1991ApJ...372..380Y}. ."627"We take a 7. function to be the assumed. form of the luminosity function: When fitting this to data using a maximum likelihood method. the [ree parameters are obtained by maximising the value of A with respect to a and L where and where V={Φα, is the cumulative luminosity function (equal to P. the normal incomplete gamma function for a Schechter LE). and ων, is the minimum luminosity at which the sample is complete."," We take a \cite{1976ApJ...203..297S} function to be the assumed form of the luminosity function: When fitting this to data using a maximum likelihood method, the free parameters are obtained by maximising the value of $\Delta$ with respect to $\alpha$ and $L^*$, where and where $\Psi = \int \Phi(L) dL$ is the cumulative luminosity function (equal to $\Gamma$, the normal incomplete gamma function for a Schechter LF), and $L_{lim}$ is the minimum luminosity at which the sample is complete."628 Essentially. a eric of Schechter functions with varving parameters is explored. and cach is assigned a Tikelihood! using the data.," Essentially, a grid of Schechter functions with varying parameters is explored, and each is assigned a `likelihood' using the data."629 Our adopted function is taken to be the function which maximises the ‘likelihood’., Our adopted function is taken to be the function which maximises the `likelihood'.630 While this method. has the aforementioned. advantage that it is insensitive to local density [uctuations. it has the disadvantage of being similarly insensitiveto the absolute normalisation of the luminosity. function (note that d cancels out in the expression for £5).," While this method has the aforementioned advantage that it is insensitive to local density fluctuations, it has the disadvantage of being similarly insensitiveto the absolute normalisation of the luminosity function (note that $\Phi^*$ cancels out in the expression for $F_i$ )."631 This can be recovered, This can be recovered632As mentioned in(4.5).. the solution IX of does not explode almost surely. and this can be rewritten as An interesting question about this is that. how fast does the above probability converge to zero?,"As mentioned in, the solution $ X^{x,t}$ of does not explode almost surely, and this can be rewritten as An interesting question about this is that, how fast does the above probability converge to zero?"633 The answer to (his question is indeed useful to obtain the convergence rate of the truncated approximation., The answer to this question is indeed useful to obtain the convergence rate of the truncated approximation.634 Finally. we are now ready fo the proof ofTheorem 1..," Finally, we are now ready fo the proof ofTheorem \ref{thm:conv}. ."635more massive aud had diferent prope‘ties al he time of formation (2)..,more massive and had different properties at the time of formation \citep{PenarrubiaNM08}.636 It is intriguing that both the tidal scenario and the pre-reionizaion fossil scenario are ale o produce a population of cbwarfs that fclow very similar salistical trends in ternis of size. surlace briglitness. nass to liehtel ration and inetallicitv-Lumiduosits relation.," It is intriguing that both the tidal scenario and the pre-reionization fossil scenario are able to produce a population of ultra-faint dwarfs that follow very similar statistical trends in terms of size, surface brightness, mass to light ration and metallicity-luminosity relation."637 The jury is stillo ul., The jury is still out.638 This paper is out as follows., This paper is laid out as follows.639 Li ?7?.. we collect published lata on the uew dwarf population auc. after correcting for completeness of the strveys. we estimate the total number of Local Group satellites (which increases [rom 32 toa out LOO).," In \ref{sec:data}, we collect published data on the new dwarf population and, after correcting for completeness of the surveys, we estimate the total number of Local Group satellites (which increases from 32 to about 100)."640 Using the restlis of publiιδ N-bocly simulatious. we compare tlie oevec muuber of Ituninous satellites to the estimated number of dark satellites that have or had in the past a circilar velocity a using the results of published N-bods simulations. ΤΕ that some ult‘a-faint chwarls must be pre-reionizaion fossils.," Using the results of published N-body simulations, we compare the observed number of luminous satellites to the estimated number of dark satellites that have or had in the past a circular velocity $>v_{c}^{cr}$, using the results of published N-body simulations, concluding that some ultra-faint dwarfs must be pre-reionization fossils."641 In ?? we show that the properies of the new Milky Way aud M31 dwarls are in reujarkable agreement with tlie theoretical data on the “fossils” from RCOS aud with their Galactocettric distribution around the Milky Way calclated in CHUx06., In \ref{sec:comp} we show that the properties of the new Milky Way and M31 dwarfs are in remarkable agreement with the theoretical data on the “fossils” from RG05 and with their Galactocentric distribution around the Milky Way calculated in GK06.642 In 2? we diseuss the implications of tle new cdwarls on the formation of the firs @alaxies and the missing ealactic satellite problem., In \ref{sec:disc} we discuss the implications of the new dwarfs on the formation of the first galaxies and the missing galactic satellite problem.643 Iu Table 1. we sumauuarize the observed. properties of the new dwads.," In Table 1, we summarize the observed properties of the new dwarfs."644 The new Milky Way satellites were discovered. using SDSS Data Release { aud 5 (??)..," The new Milky Way satellites were discovered using SDSS Data Release 4 and 5 \citep{Adelman-McCarthyetal06,Adelman-McCarthyetal07}."645 Whe1 multiple references are available for a dwarl property. we defer to the measurement with the smalest error bars.," When multiple references are available for a dwarf property, we defer to the measurement with the smallest error bars."646" Excepting Bootes I and II. Canes Venatici Iand Leo T. where ceutral surlace |xightuess measurements were avallable. tlie average surface brightuess inside the half light. racS.ry.D. Was used: f(29211,4)."," Excepting Bootes I and II, Canes Venatici I and Leo T, where central surface brightness measurements were available, the average surface brightness inside the half light radius,$r_{1/2}$, was used: $\Sigma_{V} = L_{V}/(2 \pi647r_{1/2}^{2})$ ."648 Recent surveys of N31 (2?) Lave covered approximately a quarter of he space arouLd the M31 spiral.," Recent surveys of M31 \citep{Martinetal06,Ibataetal07} have covered approximately a quarter of the space around the M31 spiral."649 The survey have found 6 new M31 satellites., The survey have found 6 new M31 satellites.650 If we make a simple correction for tje covered are of the survey. we fixl that. inclucing the new dwa‘ts. the estμια(ος number of M31 satellites increases [rom 9 to 33d-10.," If we make a simple correction for the covered are of the survey we find that, including the new dwarfs, the estimated number of M31 satellites increases from $9$ to $33 \pm 10$."651 Two new 131 satellites. Atdà NIT αιd And XIV. have velocities Leal Or above their hosts escape velocity (??)..," Two new M31 satellites, And XII and And XIV, have velocities near or above their host's escape velocity \citep{Chapmanetal07,Majewskietal07}."652 Both galaxies aο classilie as dwarf splieroidals and show a lack of gas. and both are likely oi their first approach towards a massive halo.," Both galaxies are classified as dwarf spheroidals and show a lack of gas, and both are likely on their first approach towards a massive halo."653 Winematic data is not yet available on these two dwarls to determine whether t1eir circular velocities are below the 20 kus  threshold. however their ctrrently kuown properties meet the RGOS criteria for fossils.," Kinematic data is not yet available on these two dwarfs to determine whether their circular velocities are below the $20$ km $^{-1}$ threshold, however their currently known properties meet the RG05 criteria for fossils."654 Ti esinating the completeness correctson for the mumber o ‘the MiIky Way clwarls. oue sliould also accouit for selection effects from the liiniting sirlace brigl1lles5 sensitivity of the Sloan of ~30 magarcsec7 Dogs(?)..," In estimating the completeness correction for the number of the Milky Way dwarfs, one should also account for selection effects from the limiting surface brightness sensitivity of the Sloan of $\sim$ 30 ${\rm655 mag~arcsec}^{-2}$ \citep{Koposovetal07}."656" The seusitivity""mm"" limi.it is shown as a solic| liue in Figure L..", The sensitivity limit is shown as a solid line in Figure \ref{Kor}.657" Identification of uew satellites depends ou the visibilitv of the horizontal brauch in the color-magnitude cdiagrain. which. for the typical luminosity of the uew faint dwafs CM,2 —1) drops below SDSS detection limits at Galactocentric distauces beymudd 200—250 kpe (2).."," Identification of new satellites depends on the visibility of the horizontal branch in the color-magnitude diagram, which, for the typical luminosity of the new faint dwarfs $M_V \approx -4$ ) drops below SDSS detection limits at Galactocentric distances beyond $\sim 200-250$ kpc \citep{Koposovetal07}. ."658 Of the new Milky Way cwarls. ouly," Of the new Milky Way dwarfs, only"659trending!.,.660. In principle. as La Silla and Cerro Tololo are ⊽↼ above⊽the sea⊽ lev el and−latitude. 3 3∇∊↴∇∔∃⋅−⇥∖⇁⊔⋅∃∣≼∖⇁∣∃∃∶ differences similarareeles ationsexpected in 4 aS so that so far the extinction curves theforextinction 5 ιο. observatories have been widely used to correct the 6 IS obtained at Paranal.," In principle, as La Silla and Cerro Tololo are placed at similar elevations above the sea level and latitude, no significant differences are expected in the extinction wavelength dependency, so that so far the extinction curves for these two observatories have been widely used to correct the optical spectra obtained at Paranal."661 However. Cerro Paranal is 7 |? closer to the Pacific Ocean (12 km). and this 8 3 into a different composition of the tropospheric = Total in a different extinction law.," However, Cerro Paranal is situated much closer to the Pacific Ocean (12 km), and this might turn into a different composition of the tropospheric aerosols, resulting in a different extinction law."662 Moreover. the extinction curves currently in use for these observatories were more than years ago. before 2. Observations major eruptions derivedof ΕΙ Chichónn (1982) 15and Pinatubo (1991). so that they are most likely outdated.," Moreover, the extinction curves currently in use for these observatories were derived more than 15 years ago, before the two major eruptions of El Chichónn (1982) and Pinatubo (1991), so that they are most likely outdated."663 The available — 2.7. for Paranal are not sufficient to address these ., The available broad-band data for Paranal are not sufficient to address these issues.664 . it was decided to undertake the PARanal All observations Spectral Extinction. Curve project (hereafter PARSEC). Spectrograph the manifold aim of a) obtaining a spectroscopic function for the extinction correction of optical spectra. b) getting an estimate of the variability of the various extirction components in a time lapse free of major volcanic eruptions affecting South America. and C) setting a term of reference for future studies and trend analyses at this site.," Therefore, it was decided to undertake the PARanal Spectral Extinction Curve project (hereafter PARSEC), with the manifold aim of a) obtaining a spectroscopic function for the extinction correction of optical spectra, b) getting an estimate of the variability of the various extinction components in a time lapse free of major volcanic eruptions affecting South America, and c) setting a term of reference for future studies and trend analyses at this site."665 This ts particlarly important in the view of the construction of the Europea Extremely Large Telescope on Cerro Armazones. which is located only 30 km away from Cerro Paranal.," This is particularly important in the view of the construction of the European Extremely Large Telescope on Cerro Armazones, which is located only 30 km away from Cerro Paranal."666 In this article we present the results of the PARSEC project. which was carried o between October 2008 and March 2009.," In this article we present the results of the PARSEC project, which was carried on between October 2008 and March 2009."667 Very briefly. the optical extinction. cai be described by three separate components (Hayes Latham 1975)); Rayleigh scattering by air molecules. aerosol scatteriig. and molecular absorption (O*. Os and HO).," Very briefly, the optical extinction can be described by three separate components (Hayes Latham \cite{hayes}) ): Rayleigh scattering by air molecules, aerosol scattering, and molecular absorption $_2$ , $_3$ and $_2$ O)."668 The contribution of the various components is illustrated in Fig. ]..," The contribution of the various components is illustrated in Fig. \ref{fig:trans},"669 where we present the transmittance computed for Paranal usi£g the LBLRTM code (Clough et al. 2005))., where we present the transmittance computed for Paranal using the LBLRTM code (Clough et al. \cite{clough}) ).670 While the Rayleigh scattering. and aerosols act at all wavelengths. the effect of ozone in the optical is limited to the so-called Chappuis bands (Chappuis 1880)) between 5000 and 7000A.. and the Huggin8 bands (Huggins. 1890)) below 3400A.," While the Rayleigh scattering and aerosols act at all wavelengths, the effect of ozone in the optical is limited to the so-called Chappuis bands (Chappuis \cite{chappuis}) ) between 5000 and 7000, and the Huggins bands (Huggins, \cite{huggins}) ) below 3400."671. The molecular bands of O» and HO are relevant only above 6500, The molecular bands of $_2$ and $_2$ O are relevant only above 6500.672A.. were carried. out. usingissues. the FOcalTherefore. with Reducer/low-dispersion (hereafter FORS D). mounted at the Cassegrain focus of the ESO-Kueyen 8.2 m telescope (Appenzeller et al. 1998:;," All observations were carried out using the FOcal Reducer/low-dispersion Spectrograph (hereafter FORS1), mounted at the Cassegrain focus of the ESO-Kueyen 8.2 m telescope (Appenzeller et al. \cite{appenzeller};"673 Szeifert et al. 2007)), Szeifert et al. \cite{szeifert}) ).674 At the time of the observations discussed in this paper. FORSI was equipped with a mosaic of two blue-optimised. 2048x4096 l5jm pixel (px) E2V CCDs.," At the time of the observations discussed in this paper, FORS1 was equipped with a mosaic of two blue-optimised, $\times$ 4096 $\mu$ m pixel (px) E2V CCDs."675 The spectra were obtained with the low-resolution G300V_ grism coupled to a long. 5.0 aresee wide slit. giving a useful spectral range 3100-9330A.. and a dispersion of ~3.3 !.," The spectra were obtained with the low-resolution G300V grism coupled to a long, 5.0 arcsec wide slit, giving a useful spectral range 3100–9330, and a dispersion of $\sim$ 3.3 $^{-1}$."676 The spatial scale along the slit is 0.252 aresee px!, The spatial scale along the slit is 0.252 arcsec $^{-1}$.677 The G300V grism shows a rather pronounced second order contamination. starting at about 6100 (Szeifert et al. 2007).," The G300V grism shows a rather pronounced second order contamination, starting at about 6100 (Szeifert et al. \cite{szeifert}) )."678 To cover the widest possible wavelength range we run the observations using two setups. one with no filter (blue setting) and one with the order sorting filter GG435 (red setting).," To cover the widest possible wavelength range we run the observations using two setups, one with no filter (blue setting) and one with the order sorting filter GG435 (red setting)."679 The latter provides a wavelength range free of second order contamination 4400-8100A., The latter provides a wavelength range free of second order contamination 4400–8100.680. The E2V detectors suffer from a marked fringing above 6500 (Szeifert et al. 2007))., The E2V detectors suffer from a marked fringing above 6500 (Szeifert et al. \cite{szeifert}) ).681 This becomes extremely strong for A 28000Α.. reaching a peak-to-peak amplitude of ~20%.. and it is not possible toremove it from the data.," This becomes extremely strong for $\lambda>$ 8000, reaching a peak-to-peak amplitude of $\sim$, and it is not possible toremove it from the data."682 Therefore. the spectral region above this wavelength is practically unusable for our purposes.," Therefore, the spectral region above this wavelength is practically unusable for our purposes."683overhead of and additional memory consumption ofax)» both of which are small compared to the total CPU and storage requirements.,"overhead of and additional memory consumption of, both of which are small compared to the total CPU and storage requirements."684" uuses sub-maps of roughly 100 or ΝΡ/10 rings (or ring pairs), whichever is larger."," uses sub-maps of roughly 100 or $N_\vartheta/10$ rings (or ring pairs), whichever is larger."685 The arrangement described above is sufficient for a single SHT., The arrangement described above is sufficient for a single SHT.686" Since ssupports multiple simultaneous SHTs, another loop hierarchy had to be introduced."," Since supports multiple simultaneous SHTs, another loop hierarchy had to be introduced."687 A pseudo-code listing illustrating the complete design of the SHT algorithm (including the subdominant parts performing the FFTs) is presented in Fig. [I]., A pseudo-code listing illustrating the complete design of the SHT algorithm (including the subdominant parts performing the FFTs) is presented in Fig. \ref{loopstruct}.688" To make use of multiple CPU cores, if available, the algorithm's loop over m, as well as the code blocks performing the FFTs, have been parallelised using directives, requesting dynamic scheduling for every iteration; this is indicated by the tag in Fig. [I]."," To make use of multiple CPU cores, if available, the algorithm's loop over $m$, as well as the code blocks performing the FFTs, have been parallelised using directives, requesting dynamic scheduling for every iteration; this is indicated by the tag in Fig. \ref{loopstruct}."689" As long as the SHTs are large enough, this results in very good scaling with the number of cores available (see also refopenmp;caling))."," As long as the SHTs are large enough, this results in very good scaling with the number of cores available (see also \\ref{openmp_scaling}) )."690" If the target machine supports the SSE2 instruction (which is the case for all AMD/Intel CPUs introduced sinceset] around 2003), its ability to perform two arithmetic operations of the same kind with a single machine instruction is used to process two ring (pairs) simultaneously, greatly improving the overall execution speed."," If the target machine supports the SSE2 instruction (which is the case for all AMD/Intel CPUs introduced since around 2003), its ability to perform two arithmetic operations of the same kind with a single machine instruction is used to process two ring (pairs) simultaneously, greatly improving the overall execution speed."691 The relevant loop is marked with in Fig. [I]., The relevant loop is marked with in Fig. \ref{loopstruct}.692" The necessary changes are straightforward for the most part; however, special attention must be paid to the / recursion, because the two sequences of wwill cross the threshold to IEEE-representable numbers at different /j."," The necessary changes are straightforward for the most part; however, special attention must be paid to the $l$ recursion, because the two sequences of will cross the threshold to IEEE-representable numbers at different $l_{\text{th}}$."693 Fortunately this complication can be addressed without a significant slowdown of the algorithm., Fortunately this complication can be addressed without a significant slowdown of the algorithm.694" The data types used and the functions called in order to use the SSE2 instruction set are not part of the C90 language standard, and will therefore not be known to all compilers and on all hardware platforms."," The data types used and the functions called in order to use the SSE2 instruction set are not part of the C90 language standard, and will therefore not be known to all compilers and on all hardware platforms."695" However there is a portable way to detect compiler and hardware support for SSE2; if the result of this check is negative, only the standard-compliant point implementation of wwill be compiled, without the necessity of user intervention."," However there is a portable way to detect compiler and hardware support for SSE2; if the result of this check is negative, only the standard-compliant floating-point implementation of will be compiled, without the necessity of user intervention."696" Similarly, the OpenMP functionality is accessed using so-called compiler directives, which are simply ignored by compilers lacking the required capability, reducing the source code to a single-threaded version."," Similarly, the OpenMP functionality is accessed using so-called compiler directives, which are simply ignored by compilers lacking the required capability, reducing the source code to a single-threaded version."697 Both extensions are supported by the widely used and Intel compilers., Both extensions are supported by the widely used and Intel compilers.698 Only a high-level overview of the provided functionality can be given here., Only a high-level overview of the provided functionality can be given here.699" For the level of detail necessary to actually interface with the library, the reader is referred to the technical documentation provided alongside the source code."," For the level of detail necessary to actually interface with the library, the reader is referred to the technical documentation provided alongside the source code."700" Due to libpsht'ss universality goal, it must be able to accept input data and produce output data in a wide variety of storage schemes, and therefore only makes few assumptions about how maps and aare arranged in memory."," Due to s universality goal, it must be able to accept input data and produce output data in a wide variety of storage schemes, and therefore only makes few assumptions about how maps and are arranged in memory."701 A tesselation of the sphere and the relative location of its pixels in memory is described to bby the following set of data:, A tesselation of the sphere and the relative location of its pixels in memory is described to by the following set of data:702UCACH enS 2 observed magnitudes. based ou the volue ofthe inage profile model fitted. aud a true aperture photometry. respectively.,"UCAC3 gives 2 observed magnitudes, based on the volume of the image profile model fitted, and a true aperture photometry, respectively."703 Extinction coefficients: arc| derived for cach exposure with respect o Tycho-2 stars adopting a linear model with V cokx., Extinction coefficients are derived for each exposure with respect to Tycho-2 stars adopting a linear model with $-$ V color.704 Thus a photometric zero-poiut was determi«d for cach CCD exposure and applied to the instrumental magnitudes to arrive at our bapass magnitudes based ou the available Tycho-2 stars ina eiven field., Thus a photometric zero-point was determined for each CCD exposure and applied to the instrumental magnitudes to arrive at our bandpass magnitudes based on the available Tycho-2 stars in a given field.705 An estimate of the photometric qiwlitv of a nieht is made from the average exinction coefficients of all CCD frames taken that night aud compared to other nights” results., An estimate of the photometric quality of a night is made from the average extinction coefficients of all CCD frames taken that night and compared to other nights' results.706 Magnuitudes οstained from nights flagece as non-phooletric are excluded in the calculation of a ican magnitude for cach star., Magnitudes obtained from nights flagged as non-photometric are excluded in the calculation of a mean magnitude for each star.707" If all images are excluded. a ""bes euess for the zero-point of the maguitide scale on cach CCD frame is macο and a mean magnitude for stch stars is derived over a] available CCD frames and the error of the magnitude is set to Lin those cases."," If all images are excluded, a “best guess” for the zero-point of the magnitude scale on each CCD frame is made and a mean magnitude for such stars is derived over all available CCD frames and the error of the magnitude is set to $-1$ in those cases."708 Normally. for «ach individual star 2 photometric errors have hee1 derived.," Normally, for each individual star 2 photometric errors have been derived."709 The model error is based ontie S/N ratio of the images of a star. while the scater error is determined from the distribution of the incividual uaenitudes per star froin different frames.," The model error is based on the S/N ratio of the images of a star, while the scatter error is determined from the distribution of the individual magnitudes per star from different frames."710 The lareer of these is then published iu the UCAC?23 catalog., The larger of these is then published in the UCAC3 catalog.711 It is expectec that the photometry of the UCAC3 CCD data is vastly improved over UCAC?. which was ou the 0.3 imag level," It is expected that the photometry of the UCAC3 CCD data is vastly improved over UCAC2, which was on the 0.3 mag level."712 Ilowewver. no detailed vestienOzion iuto the precision or accuracy of photonietric errors in. UCACS has been made so far.," However, no detailed investigation into the precision or accuracy of photometric errors in UCAC3 has been made so far."713 For well exposed stars 5 to photometric accuracy is expected., For well exposed stars 5 to photometric accuracy is expected.714 The UCAC observing οστά Was never envisioned to provide reliable photometry., The UCAC observing program was never envisioned to provide reliable photometry.715" No photometric standard stars were observed to derive. photonetric constauts for anv observing uieht. aud all t""CAC observatious were performed in a single bandpass."," No photometric standard stars were observed to derive photometric constants for any observing night, and all UCAC observations were performed in a single bandpass."716 Positious in UCACS are on the Iuternational Celestial Reference System (ICRS) as realized by the Tycho-2 catalog.Oo which was used as refereuce star catalog i a conventional. frame-by-frame. astrometric reduction affer various corrections were applied.," Positions in UCAC3 are on the International Celestial Reference System (ICRS) as realized by the Tycho-2 catalog, which was used as reference star catalog in a conventional, frame-by-frame, astrometric reduction after various corrections were applied."717 Residuals of the final reductions are shown in Fies., Residuals of the final reductions are shown in Figs.718 6 aud 7 or the CTIO aud NOFS data. respectively.," 6 and 7 for the CTIO and NOFS data, respectively."719 Roaalnus svstematic errors are on the 5 mas level., Remaining systematic errors are on the 5 mas level.720 It is possible that these are Iuhereif dn the Twe10-2 data. see discussion below.," It is possible that these are inherent in the Tycho-2 data, see discussion below."721" Tl|a"" coordinate| djs along right asccusion (RA). whiο vis along declination (Dec)."," The $x$ coordinate is along right ascension (RA), while $y$ is along declination (Dec)."722 Fortunaτον. the 2NASS observations were made at roughly the sale epoch as UCAC observatiois. aud the 2M.ASS catalog was exteusivelv used to erive systematic error corrections in UCAC data.," Fortunately, the 2MASS observations were made at roughly the same epoch as UCAC observations, and the 2MASS catalog was extensively used to derive systematic error corrections in UCAC data."723" Complex lookup ables were generated enipirncallv to correct for purely geometric field distortions (depending ouly ou μον, y coordinates of stars on CCD framics) as wel as colma-lilke terms involving magnitude and ον4 coordinates."," Complex look-up tables were generated empirically to correct for purely geometric field distortions (depending only on the $x,y$ coordinates of stars on CCD frames) as well as coma-like terms involving magnitude and $x,y$ coordinates."724 Tlose types of systematic errors cai be attribute to be in the UCAC data due to the correlation with weg pixel coordinates.," These types of systematic errors can be attributed to be in the UCAC data due to the correlation with $x,y$ pixel coordinates."725 However. a pure imaenitude equation (systematic positiona error as a function of brightuess) could either o in UCAC or 24ASS data.," However, a pure magnitude equation (systematic positional error as a function of brightness) could either be in UCAC or 2MASS data."726 Thus the overall pure magnitude equation correcions of the UCAC «ata were derived from the “flip” calibration data alone., Thus the overall pure magnitude equation corrections of the UCAC data were derived from the “flip” calibration data alone.727 These calibration fields ie heen observed hroughout the UCAC projec with the telescope being on one side of the pier (East or West) then ou the other., These calibration fields have been observed throughout the UCAC project with the telescope being on one side of the pier (East or West) then on the other.728 These flip observatious provide pais of CCD exposures which are rotated by I507 with respect to each other. revealing the magnitude equalon offsets independent of external catalog data.," These flip observations provide pairs of CCD exposures which are rotated by $180^{\circ}$ with respect to each other, revealing the magnitude equation offsets independent of external catalog data."729 The asstuuption here of course is that the magnitude equation stavs constant over the set of East/West exposures and other systematic errors like coma enus have been removed., The assumption here of course is that the magnitude equation stays constant over the set of East/West exposures and other systematic errors like coma terms have been removed.730 No corrections as a function of color were applied., No corrections as a function of color were applied.731 Differential color refraction cffects are vpically bclow- 5n iuas due to the narrow UCAC xuidpass., Differential color refraction effects are typically below 5 mas due to the narrow UCAC bandpass.732 For a detailed discussion of the astrometric uctious leading to UCACS the reader is referred o the separate paper by Finch et al., For a detailed discussion of the astrometric reductions leading to UCAC3 the reader is referred to the separate paper by Finch et al.733 For UCACS the complete set of the secondKatalog (GIN2) plates. taken around 1930. could be utilized from scans maceon the StarScan machine (Zachariasetal.2008).," For UCAC3 the complete set of the second (AGK2) plates, taken around 1930, could be utilized from scans made on the StarScan machine \citep{starscan}."734. This set comprises about 1950 plates taken at the Boun and Ihuuburs observatories. covering the," This set comprises about 1950 plates taken at the Bonn and Hamburg observatories, covering the"735from 5 to 37A.,from 5 to 37.736 The EPIC spectra. which have a lower resolution but higher sensitivity. are used to constrain the high-temperature part of Procyon’s EM distribution.," The EPIC spectra, which have a lower resolution but higher sensitivity, are used to constrain the high-temperature part of Procyon's EM distribution."737 Because of the high resolution of the grating spectrometers we will focus on the spectra from these instruments., Because of the high resolution of the grating spectrometers we will focus on the spectra from these instruments.738 In Fig., In Fig.739 1. we show the RGS spectra together with an extract of the LETGS spectrum covering the wavelength range from 10 to 37A.," 1, we show the RGS spectra together with an extract of the LETGS spectrum covering the wavelength range from 10 to 37."740. No notable features are observed below 10 im the LETGS and RGS spectra., No notable features are observed below 10 in the LETGS and RGS spectra.741 However. the EPIC-MOS detects the H- and He-like lines of Μα.," However, the EPIC-MOS detects the H- and He-like lines of Mg."742 The remaining part of the LETGS spectrum is shown in Fig., The remaining part of the LETGS spectrum is shown in Fig.743 2., 2.744 From Fig., From Fig.745 | the gaps in the two RGS spectra due to CCD failure of CCD 7 (RGSI) and 4 (RGS2) are obvious., 1 the gaps in the two RGS spectra due to CCD failure of CCD 7 (RGS1) and 4 (RGS2) are obvious.746 The spectral lines from all three instruments have been measured individually., The spectral lines from all three instruments have been measured individually.747 We folded monochromatic delta functions through the instrumental response matrices in order to derive the integrated line fluxes., We folded monochromatic delta functions through the instrumental response matrices in order to derive the integrated line fluxes.748 No additional width was needed to fit the shape of the lines., No additional width was needed to fit the shape of the lines.749" A constant ""background"" level was adjusted in order to account for the real continuum and for the pseudo-continuum created by the overlap of several weak. neglected lines."," A constant ""background"" level was adjusted in order to account for the real continuum and for the pseudo-continuum created by the overlap of several weak, neglected lines."750 In Table 1. we have collected the measured wavelengths and fluxes of the emission lines in the RGS instruments together with those in the LETGS in the," In Table 1, we have collected the measured wavelengths and fluxes of the emission lines in the RGS instruments together with those in the LETGS in the"751to be unreachable by high weight particles.,to be unreachable by high weight particles.752 Thus any further increasing of ρω does not influence the resulting spectra in à visible wav., Thus any further increasing of $t_{max}$ does not influence the resulting spectra in a visible way.753 In the simulations. we inject test. particles with initial energv fy = 2 AleV in the vicinity of the reconnection null point and we follow their trajectories by numerical integration of particle equations of motion.," In the simulations, we inject test particles with initial energy $E_0$ = $2$ MeV in the vicinity of the reconnection null point and we follow their trajectories by numerical integration of particle equations of motion."754" The integration is completed when a particle either crosses the boundary of the considered reconnection region (escape boundary). or the time limit /,,,;=100 s is reached."," The integration is completed when a particle either crosses the boundary of the considered reconnection region (`escape boundary'), or the time limit $t_{max} = 100$ s is reached."755 Particles were scattered. in a small region around the reconnection null point only., Particles were scattered in a small region around the reconnection null point only.756 This region is shown in the two upper panels of Fig., This region is shown in the two upper panels of Fig.757 1 as black rectangles. and in expanded form in the lower panel.," 1 as black rectangles, and in expanded form in the lower panel."758 Phe trajectory computation times are much longer for low energy. particles and this is the main reason why we start with initial proton energies substantially larger than the thermal energy: for the discussion of the injection problem of cnerectic solar Dare particles one can consult the cliscussion in. Miller et al. (, The trajectory computation times are much longer for low energy particles and this is the main reason why we start with initial proton energies substantially larger than the thermal energy; for the discussion of the injection problem of energetic solar flare particles one can consult the discussion in Miller et al. (759L997).,1997).760 As the long integrations performed here require high accuracy we use a variable step fourth-order Itunge-Ixutta integration with the parameters chosen in such a way that any further accuracy increase does not alfect. the simulated. trajectories., As the long integrations performed here require high accuracy we use a variable step fourth-order Runge-Kutta integration with the parameters chosen in such a way that any further accuracy increase does not affect the simulated trajectories.761 In. the simulation we use only LOO particles because the required high accuracy of integration leads to extensive integration times., In the simulation we use only 100 particles because the required high accuracy of integration leads to extensive integration times.762 Let us remember that with the applied: trajectory splitting technique the number of particles forming. the spectrum at dillerent energies is the same., Let us remember that with the applied trajectory splitting technique the number of particles forming the spectrum at different energies is the same.763 We performed a number of numerical tests of the code applied in the simulations., We performed a number of numerical tests of the code applied in the simulations.764 We checked by hand the derivation of the resulting particle phase space co-ordinates ina few randomly chosen individual integration steps of the code algorithm., We checked by hand the derivation of the resulting particle phase space co-ordinates in a few randomly chosen individual integration steps of the code algorithm.765 Phen we derived. particle trajectories within a few simple uniform magnetic fields oriented randomly with respect to the chosen reference frame., Then we derived particle trajectories within a few simple uniform magnetic fields oriented randomly with respect to the chosen reference frame.766 The results coincided within the numerical accuracy with the derived analytic trajectories., The results coincided within the numerical accuracy with the derived analytic trajectories.767 Finally. for the actual considered magnetic field structure in the reconnection volume we positively checked conservation of particle energy with the plasma velocity set equal to zero.," Finally, for the actual considered magnetic field structure in the reconnection volume we positively checked conservation of particle energy with the plasma velocity set equal to zero."768 In the simulations particles gain energy mostly in the vicinity. of the reconnection laver when drifting in the VAB electric fields., In the simulations particles gain energy mostly in the vicinity of the reconnection layer when drifting in the $\vec{V} \wedge \vec{B}$ electric fields.769 Away [rom this region. while moving across the magnetic field. eracicnt. particles can eain and lose energy. but the mean energy change is small.," Away from this region, while moving across the magnetic field gradient, particles can gain and lose energy, but the mean energy change is small."770 Somov Ixosugi (1997) estimated the accelerated: particle οποιον as a product. of the magnetic field. the plasma velocity and the reconnection area length.," Somov Kosugi (1997) estimated the accelerated particle energy as a product of the magnetic field, the plasma velocity and the reconnection area length."771 The. energy gains derived. in ourΠΟΡΟ reconnection model. are in agreement with this estimate if we take the distance raversed by a particle within the reconnection area as he required. length., The energy gains derived in our reconnection model are in agreement with this estimate if we take the distance traversed by a particle within the reconnection area as the required length.772 The. οσο of particle escape from he reconnection volume has been discussed. by Speiser (1965) for a highky simplified reconnection model., The effect of particle escape from the reconnection volume has been discussed by Speiser (1965) for a highly simplified reconnection model.773 We confirm his results showing that a small vertical magnetic ield Component within the reconnection laver increases the xuticle escape substantially., We confirm his results showing that a small vertical magnetic field component within the reconnection layer increases the particle escape substantially.774 In the simulations we consider the particle scattering process only in a small volume containing the reconnection null point. where the magnetic energy ds clissipatecl (see Fig.," In the simulations we consider the particle scattering process only in a small volume containing the reconnection null point, where the magnetic energy is dissipated (see Fig."775 1)., 1).776 The real reconnection regions are expected to garow analogous structures. with the turbulence amplitude erowing toward the centre. including null points of the magnetic field.," The real reconnection regions are expected to show analogous structures, with the turbulence amplitude growing toward the centre, including null points of the magnetic field."777 This choice also resulted from. the fact iu the Craig et al. (, This choice also resulted from the fact that the Craig et al. (7781995) three dimensional mocel of 10 stationary reconnection is not too realistic at large istances from the null point. as. for example. it. involves 1e inflow velocity growing without a limit when increasing istance [rom the centre.,"1995) three dimensional model of the stationary reconnection is not too realistic at large distances from the null point, as, for example, it involves the inflow velocity growing without a limit when increasing distance from the centre."779 For the perturbed trajectories model we use a simple pitch-anele scattering approach (c.g. Ostrowski 1991) intended to model the particle scattering at MIID. waves., For the perturbed trajectories model we use a simple pitch-angle scattering approach (e.g. Ostrowski 1991) intended to model the particle scattering at MHD waves.780 In this case integration of the particle equations of motion Is performed in the electromagnetic field defined by the unperturbed analytic model. but. trajectory perturbations are introduced. every constant time interval Af. when the particle momentum. vector. is. randomly scattered within a narrow cone along its original clirection.," In this case integration of the particle equations of motion is performed in the electromagnetic field defined by the unperturbed analytic model, but trajectory perturbations are introduced every constant time interval $\Delta t$, when the particle momentum vector is randomly scattered within a narrow cone along its original direction."781 The scattering is performed in the localplasme rest frame and it conserves particle energy in this frame., The scattering is performed in the local rest frame and it conserves particle energy in this frame.782 In the present simulations we consider the uniform momentum scattering within a cone with the half opening angle equal to 11., In the present simulations we consider the uniform momentum scattering within a cone with the half opening angle equal to $11^\circ$.783 The perturbation intensity is controlled by changing At and it is characterized with NS—wifry. the ratio of the cross-Licld diffusion cocllicient to the diffusion cocllicient along the magnetic field.," The perturbation intensity is controlled by changing $\Delta t$ and it is characterized with $\aleph \equiv \kappa_\perp / \kappa_\|$, the ratio of the cross-field diffusion coefficient to the diffusion coefficient along the magnetic field."784 The value of δ was determined in auxiliary simulations performed in the uniform magnetic field with the value characteristic for a region close outside the reconnection current sheet (see section 2.3)., The value of $\aleph$ was determined in auxiliary simulations performed in the uniform magnetic field with the value characteristic for a region close outside the reconnection current sheet (see section 2.3).785 One should also note that decrease of the magnetic field. toward the reconnection site leads to increasing the ellective turbulence amplitude (ic. the value of N: in the limit of B=0 we have N= 1.0). but in the present simulations the particle evroracius is always larger than the reconnection laver thickness near the considered. X-tvpe null point.," One should also note that decrease of the magnetic field toward the reconnection site leads to increasing the effective turbulence amplitude (i.e. the value of $\aleph$; in the limit of $B = 0$ we have $\aleph = 1.0$ ), but in the present simulations the particle gyroradius is always larger than the reconnection layer thickness near the considered X-type null point."786 As the mean scattering time Af is assumed to. be constant within a given simulation run. particle trajectories are alfected by perturbations with intensity depending on particle energy and the background magnetic field.," As the mean scattering time $\Delta t$ is assumed to be constant within a given simulation run, particle trajectories are affected by perturbations with intensity depending on particle energy and the background magnetic field."787 For non-relativistic particles with constant angular velocities of their evration movements. assuming constant Af is equivalent to introducing scattering acts at constant evrophasc steps.," For non-relativistic particles with constant angular velocities of their gyration movements, assuming constant $\Delta t$ is equivalent to introducing scattering acts at constant gyrophase steps."788 Thus the resulting value of N does not depend on energy. as expected Lor the Hat wave power spectrum E(k)xkt.," Thus the resulting value of $\aleph$ does not depend on energy, as expected for the flat wave power spectrum $F(k) \propto 789k^{-1}$."790 This slightly. unrealistic wave spectrum allows. on the other hand. evaluation of the role of diffusive elfects for the same scattering amplitude at all considered: particle energies.," This slightly unrealistic wave spectrum allows, on the other hand, evaluation of the role of diffusive effects for the same scattering amplitude at all considered particle energies."791 A discussion. of a more realistic Wolmogoroy wave spectrum within the finite wave vector range will be presented. in the next. paper (in. preparation)., A discussion of a more realistic Kolmogorov wave spectrum within the finite wave vector range will be presented in the next paper (in preparation).792 However. as such a wave spectrum carries more energy in long waves. the results are expected to show a transition from our low RN results to the large N ones.," However, as such a wave spectrum carries more energy in long waves, the results are expected to show a transition from our low $\aleph$ results to the large $\aleph $ ones."793 In attempting to compare our simplified. scattering model with the real turbulence with an amplitude of waves, In attempting to compare our simplified scattering model with the real turbulence with an amplitude of waves794of synthetic spectra computed with different temperatures. bx using SYNTHE code (Ixurucz 1993).,"of synthetic spectra computed with different temperatures, by using SYNTHE code (Kurucz 1993)."795 Tvpical uncertainties lor the temperatures are of the order of ~50 Ix for the DS5s. and 100—150 Ix for the eiants.," Typical uncertainties for the temperatures are of the order of $\sim 50$ K for the BSSs, and $\sim796100-150$ K for the giants."797 Since the adopted technique is efficient only for rotational velocities up to ©50—G0kms.J|. the values of £44 for faster stars have been estimated by comparing the observations in the triplet region with rotationally broacdenecl synthetic speclra.," Since the adopted technique is efficient only for rotational velocities up to $\simeq 50 - 60\kms$, the values of $I_{\rm rot}$ for faster stars have been estimated by comparing the observations in the triplet region with rotationally broadened synthetic spectra."798" Figure 2. presents the derived rotational index distributions: (hat of the giants is peaked ab J,—00kms +. with the highest value being 13.42:3.4kms.| for a SGD."," Figure \ref{rotisto} presents the derived rotational index distributions: that of the giants is peaked at $I_{\rm rot}=0.0 \kms$ , with the highest value being $13.4\pm 3.4\kms$ for a SGB."799 The rotational index distribution for the BSSs (see Table 1) is quite different. with eight stars of the total) being fast rotators. Le.. rotating at more than 50kms.| (while normal F-G tvpe stars tvpically spin at less than ~30kms.|: Cortéss et al.," The rotational index distribution for the BSSs (see Table 1) is quite different, with eight stars of the total) being fast rotators, i.e., rotating at more than $50\kms$ (while normal F-G type stars typically spin at less than $\sim 30\kms$; Cortéss et al."800 2009)., 2009).801 Interestingly. three (out of five) DS5s with anomalous V4 also are [ast rotators.," Interestingly, three (out of five) BSSs with anomalous $V_{\rm rad}$ also are fast rotators."802 As the relerence population needed to identilv possible anomalies in the BSS surface abundances. we have considered the SGDs. since episodes of mixing ancl dredge-up may have modified (he primordial abundance patterns in the RGBs.," As the reference population needed to identify possible anomalies in the BSS surface abundances, we have considered the SGBs, since episodes of mixing and dredge-up may have modified the primordial abundance patterns in the RGBs."803 Chemical abundances have been derived Irom the equivalent width measurements by using the WIDTII9 code (Ixurucz 1993: Sbordone et al., Chemical abundances have been derived from the equivalent width measurements by using the WIDTH9 code (Kurucz 1993; Sbordone et al.804 2004)., 2004).805 Gravilies have been determined (within 0.2 dex) bv comparing the (target position in the CMD with a grid of evolutionary tracks extracted [rom the (Pietrinferni et al., Gravities have been determined (within 0.2 dex) by comparing the target position in the CMD with a grid of evolutionary tracks extracted from the (Pietrinferni et al.8062006)*.. This also vielded to a mass distribution for (he observed. BSSs. which peaks al ~LV... with the most massive object being al eL3AL..," This also yielded to a mass distribution for the observed BSSs, which peaks at $\sim 1807M_\odot$, with the most massive object being at $\sim 1.3 M_\odot$."808 Abundance errors have been computed by taking into account the uncertainties on the atmospheric parameters ancl those on the equivalentwidth measurements., Abundance errors have been computed by taking into account the uncertainties on the atmospheric parameters and those on the equivalentwidth measurements.809 For each star thev (vpically are of the order of 0.1—0.2 dex., For each star they typically are of the order of $0.1-0.2$ dex.810 The iron content for the SGDs and BSSs has been derived from the equivalent widths of about ten and 27 lines. respectively.," The iron content for the SGBs and BSSs has been derived from the equivalent widths of about ten and 2–7 lines, respectively."811 For the SGDs the resulting average iron abundance is |Fe/II]|——1.102z£0.01. with a dispersion ¢=0.07 about the mean. in good agreement with previous values (ranging between —1.20 and —1.07: Harris 1996: Ivans et al.," For the SGBs the resulting average iron abundance is $= -1.10 \pm8120.01$, with a dispersion $\sigma = 0.07$ about the mean, in good agreement with previous values (ranging between $-1.20$ and $-1.07$; Harris 1996; Ivans et al."813 1999: Marino et al., 1999; Marino et al.814 2008: Carrel(a οἱ al., 2008; Carretta et al.815 2009)., 2009).816 Because of the significant deformation of the spectral line profiles. no iron abundance has been derived for the eight fast rotators.," Because of the significant deformation of the spectral line profiles, no iron abundance has been derived for the eight fast rotators."817 Moreover. technical failures in (he spectrograph fiber positioning prevented us to measure it for two additional objects (see Table 1).," Moreover, technical failures in the spectrograph fiber positioning prevented us to measure it for two additional objects (see Table 1)."818 The iron abundance obtained for the remaining ten BSSs has a mean value of—1.27 and a dispersion σ= 0.10. consistent. within the errors. with the values," The iron abundance obtained for the remaining ten BSSs has a mean value of$-1.27$ and a dispersion $\sigma=0.10$ , consistent, within the errors, with the values"819"probabilities maps of our targets with an accurate age measurment, and therefore excluding HIP114046 and 2M0443.","probabilities maps of our targets with an accurate age measurment, and therefore excluding HIP114046 and 2M0443."820" The decreasing detection probability for very large semi-major axis reflects the fact that such objects can be observed within our 19.5x19.5"" field of vue only on a fraction of their orbit and for favorable combination of excentricity and angle of sight.", The decreasing detection probability for very large semi-major axis reflects the fact that such objects can be observed within our $\times$ $\arcsec$ field of vue only on a fraction of their orbit and for favorable combination of excentricity and angle of sight.821" Using the full 52 star sample, these limits could be used to derive constraints on the existence of around late-type stars and consequently on planetary formation models around low-mass stars."," Using the full 52 star sample, these limits could be used to derive constraints on the existence of around late-type stars and consequently on planetary formation models around low-mass stars."822" However, the sub-sample of 16 stars we present here is too small to be derive meaningful statistics and more observations are needed to bring it to a statistically more robust size. (?,Bonfilsetal,submitted), ?,,"," However, the sub-sample of 16 stars we present here is too small to be derive meaningful statistics and more observations are needed to bring it to a statistically more robust size. \citep[][Bonfils823 et al, submitted]{Gould.2010}, \citet{Chauvin.2004},"824 (?) ," \citep{Halbwachs.2000}825 "826"currently only supports grains of a single type. so we adopt he default ""standard SM mixture’ comprising erains which mimic a 53:437 mixture of silicate anc graphite grains from Draine Lee (1984).","currently only supports grains of a single type, so we adopt the default `standard ISM mixture' comprising grains which mimic a 53:47 mixture of silicate and graphite grains from Draine Lee (1984)."827 The DUSTY wavelength: grid spans 3.6«107pim... so the elleets of harder. radiation are not mocdelled.," The DUSTY wavelength grid spans $3.6 \times 10^{4}$, so the effects of harder radiation are not modelled."828 Since sources A and D. are likely to be Compton-thin with Αμον1077107 (as inferred rom the hardness ratios in FOO and from αν synthesis models for the NIB. ο. Wilman Fabian 1999). they are transparent to photons above a few keV: there are hus about 1.5 decades of frequency. below where ohotons would. be absorbed. but which are not nee," Since sources A and B are likely to be Compton-thin with $N_{\rm{H}} \sim 10^{22}-10^{23}$ (as inferred from the hardness ratios in F00 and from AGN synthesis models for the XRB, e.g. Wilman Fabian 1999), they are transparent to photons above a few keV; there are thus about 1.5 decades of frequency below where photons would be absorbed but which are not included."829 Given that the input SED cuts olf sharply below 0.03.jr. his omission is unimportant.," Given that the input SED cuts off sharply below 0.03, this omission is unimportant."830 We adopt the cosmological parameters Lf)5O0kms and qo=0.5 throughout the paper., We adopt the cosmological parameters $H_{\rm{0}}=50$ and $q_{\rm{0}}=0.5$ throughout the paper.831 Léómmonon et al. (, Lémmonon et al. (832"1998) eive 6.7 andLSOCULAL Duxes ⋅or source D of⋅ 110.5,Lo and 350.⋅4,νι. respectively.","1998) give 6.7 and fluxes for source B of $110^{+40}_{-60}$ and $350^{+50}_{-40}$, respectively."833: From a total of 33 counts. FOO estimate 0.5r2 and Dluxes of 5.9 and 23-10Mereem4. respectively: the upper init at ds 5.7 mJv (00).," From a total of 33 counts, F00 estimate 0.5–2 and fluxes of 5.9 and $\times 10^{-15}$, respectively; the upper limit at is 5.7 mJy (F00)."834 We use the relative Duxes in theD. V(E555W). It. I(ESIAW). Janel IN? filters provided » Léómmonon et aL," We use the relative fluxes in the B, V(F555W), R, I(F814W), J and $'$ filters provided by Lémmonon et al."835 along with IIYPEIZ to compute a Xhotometrie redshift. (Ν.Ο. the LIST F555W. and. ESIAW magnitudes given by Lémmonon et. al., along with HYPERZ to compute a photometric redshift (N.B. the HST F555W and F814W magnitudes given by Lémmonon et al.836 dilfer from. those isteck in FOO. but for internal consistency. we adopt. the former values).," differ from those listed in F00, but for internal consistency we adopt the former values)."837 We consider 2 [amilies ofLYPERZ mocels:(i) where at least SO per cent of the Is! light. jm) is host galaxy starlight: (i) where at least 50 per cent of it is nuclear dust emission., We consider 2 families of HYPERZ models:(i) where at least 80 per cent of the $'$ light ) is host galaxy starlight; (ii) where at least 50 per cent of it is nuclear dust emission.838 A satisfactory HEYPIEIZ mocel could not be found. for the case where all the Ix light. is from the nucleus., A satisfactory HYPERZ model could not be found for the case where all the $'$ light is from the nucleus.839 LEYPERZ uses Bruzual Charlot (1993) spectral svnthesis models and. varies the redshift. age and extinction. of the population.," HYPERZ uses Bruzual Charlot (1993) spectral synthesis models and varies the redshift, age and extinction of the population."840 The elliptical galaxy moclel we use has an exponentiallv-declining star formation rate with an e-folding time of 1 Gyr: other models with longer star-Formation timescales(SOdesSd and Im). as well as bursts. were also considered. but do not significantly change the fitted. redshift. (essentially because the break between the V(E555W) and I. points is assumed to be the redshifted break).," The elliptical galaxy model we use has an exponentially-declining star formation rate with an e-folding time of 1 Gyr; other models with longer star-formation timescales (S0–Sd and Im), as well as bursts, were also considered, but they do not significantly change the fitted redshift (essentially because the break between the V(F555W) and R points is assumed to be the redshifted break)."841 For case (). UYPERZ fits a 500 Myr old. elliptical ealaxy with ely=240 mag at z=0.575.," For case (i), HYPERZ fits a 500 Myr old elliptical galaxy with $A_{\rm{V}}=2.40$ mag at $z=0.575$."842" n""For this recshilt. we generated a grid. of DUSTY with 7=10. 20...100 (equivalent to Nyc1077Wem fora Galactic dust:gas ratio. and appropriate for the mocoeratelvy Compton-thin obscuration implied. by the X-ray fluxes). di,=100.200...1500]x.. and /!=5. 50. 250 and 1000."," For this redshift, we generated a grid of DUSTY models, with $\tau =10$, 20,..,100 (equivalent to $N_{\rm{H}} \simeq 10^{22}-10^{23}$ for a Galactic dust:gas ratio, and appropriate for the moderately Compton-thin obscuration implied by the X-ray fluxes), $T_{\rm{in}}=100$, and $R=5$, 50, 250 and 1000."843 After integration over the filter bandpasses. the models were normalised to the observed. Dux density. anc deemed: acceptable if the G.7/15 Εαν ratio fell within the range allowed by the errors on the data. if the Εαν fell below the limit. and if the [N flux was less than 20 per cent of that observed.," After integration over the filter bandpasses, the models were normalised to the observed flux density, and deemed acceptable if the 6.7/15 flux ratio fell within the range allowed by the errors on the data, if the flux fell below the limit, and if the $'$ flux was less than 20 per cent of that observed."844 Fig., Fig.845 1 shows which models meet these criteria. and Fig.," 1 shows which models meet these criteria, and Fig."846 2 the SED fits for three such cases. with (Ror.Zin)5(250.50.1500). (50.100.700) ancl (5.60.200).," 2 the SED fits for three such cases, with $(R,\tau,T_{\rm{in}})=$ (250,50,1500), (50,100,700) and (5,60,200)."847 Phe implied optical-UV“DUSTY input luminosity. Χ-rav absorption corrected luminosity (derived. from the observed Bux. assuming an intrinsic power-law spectrum with a photon index P=2). optical (2500.A)) to X-ray keV) spectral index. e. and the inner radius. rin. for each are shown in Table 1.," The implied optical-UV DUSTY input luminosity, X-ray absorption corrected luminosity (derived from the observed flux, assuming an intrinsic power-law spectrum with a photon index $\Gamma=2$ ), optical ) to X-ray ) spectral index, $\alpha_{\rm{ox}}$, and the inner radius, $r_{\rm{in}}$, for each are shown in Table 1."848" Phe best fits to the portion of the SED covered by the data are obtained with hot dust. (heated. close to its sublimation temperature of IX). with an inner raclius within a parsec of the central engine: the implied o, in this case is. however. somewhat Hatter than the canonical value of 1.35 for quasars (Elvis et al."," The best fits to the portion of the SED covered by the data are obtained with hot dust (heated close to its sublimation temperature of ), with an inner radius within a parsec of the central engine; the implied $\alpha_{\rm{ox}}$ in this case is, however, somewhat flatter than the canonical value of 1.35 for quasars (Elvis et al."849 1994)., 1994).850 Figs., Figs.851" 1 and 2 also show. however. that models with warm dust at Zi,=9001 cannot be ruled out at present: such models have inner radii of tens of and oi values close to those of quasars."," 1 and 2 also show, however, that models with warm dust at $T_{\rm{in}}=200$ cannot be ruled out at present; such models have inner radii of tens of and $\alpha_{\rm{ox}}$ values close to those of quasars."852 Discrimination between the warm and hot dust models would be possible using data atjm: e.g. the model shown in Fig., Discrimination between the warm and hot dust models would be possible using data at; e.g. the model shown in Fig.853 2 has à Εαν density of 16 mJ. which is well within the capability. of SIRE (see c.g. Brandl ct al.," 2 has a flux density of 16 mJy, which is well within the capability of SIRTF (see e.g. Brandl et al."854 2000), 2000).855" For case ""(ii). HYΙΟ fits a 3.5phe Cyr old elliptical ue at z=0.505 Ay=0.60 mae."," For case (ii), HYPERZ fits a 3.5 Gyr old elliptical galaxy at z=0.505 with $A_{\rm{V}}=0.60$ mag."856" need for DUSTY reproduce at least half of the Ix! light in this case means that the dust must be hot (Z5,=10001500 I0) ancl not too optically thick at (725. 40): £2 is not very well constrained. with a value of 100 for r=35. although a more compact structure. (2.7)=(5.40). is also acceptable."," The need for DUSTY to reproduce at least half of the $'$ light in this case means that the dust must be hot $T_{\rm{in}}=1000-1500$ ) and not too optically thick at $\tau \sim 25-40$ ); $R$ is not very well constrained, with a value of 100 for $\tau=35$, although a more compact structure, $(R,\tau)=(5,40)$, is also acceptable."857" For (Ror)=(100.35). we find Lo40—4.6«LOM and Qo,=1.42: the latter model SED is shown in Fig."," For $(R,\tau)=(100,35)$, we find $L_{\rm{2-10}}=4.6 \times 10^{43}$ and $\alpha_{\rm{ox}}=1.12$; the latter model SED is shown in Fig."858 2., 2.859 We conclude that the best-fitting. models. are. those in which the dust is hot. with an inner radius within lpc of the nucleus.," We conclude that the best-fitting models are those in which the dust is hot, with an inner radius within $\sim 1$ of the nucleus."860 Several models. with warm. dust I5) are also formally acceptable. but for /?=50 some of these uncderprecict the upper limit by only a small [actor ( 2). which. if this source is representative of the new IINB sources. seems unlikely given the non-detection of large samples of them by (see references in section 1).," Several models with warm dust ) are also formally acceptable, but for $R=50$ some of these underpredict the upper limit by only a small factor $\sim 2$ ), which, if this source is representative of the new HXB sources, seems unlikely given the non-detection of large samples of them by (see references in section 1)."861 This is the brightest. source in the 322909 field. coincident with a slightly reddened L mid-type spiral at a photometric redshift of2=0.85z:0.15 (00).," This is the brightest source in the A2390 field, coincident with a slightly reddened $L^{\star}$ mid-type spiral at a photometric redshift of $z=0.85 \pm 0.15$ (F00)."862" From a total of 90 counts. LO) ""m""performed crude X-ray spectral fitting are deduced an Ng=(642)(93)107 with a de-absorbed Lo4072.3l0 (after correction for a lensing magnification by a factor of abou 2). for 2=O.7 l. respectively."," From a total of $\sim 90$ counts, F00 performed crude X-ray spectral fitting and deduced an intrinsic $N_{\rm{H}}=(6 \pm 2)-(9 \pm 3) \times 10^{22}$, with a de-absorbed $L_{\rm{2-10}} \simeq 2-3 \times 10^{44}$ (after correction for a lensing magnification by a factor of about 2), for $z=0.7-1$, respectively."863 Lt is thus an X-ray type IL quasar., It is thus an X-ray type II quasar.864 It also. has /SOCAAL counterparts at 6.7 ane (Altieri et al., It also has counterparts at 6.7 and (Altieri et al.865 1999) but the source Luxes have no been published., 1999) but the source fluxes have not been published.866 We proceed on the assumption that they are equal to those of source D. which appears reasonable from the images in Altieri ct al.," We proceed on the assumption that they are equal to those of source B, which appears reasonable from the images in Altieri et al."867coutalling the PN. potential is saved. aud the coutribution to this potential mace by the tree itself is subtacted out. leaving the tidal potential due to all external mass.,"containing the PM potential is saved, and the contribution to this potential made by the tree itself is subtracted out, leaving the tidal potential due to all external mass."868 See for details., See for details.869" 5lice ϐ, cau only be calculated ouce per PM step. it will be calculated at midsep."," Since $\Phi_{ext}$ can only be calculated once per PM step, it will be calculated at midstep."870 PM j»articles are thus already in 1the proper locaion for this. but t‘ee particles. with positions at the ορ]μίας of tje PM tine step. are uot.," PM particles are thus already in the proper location for this, but tree particles, with positions at the beginning of the PM time step, are not."871 However. since ree regious are spatially separated aud the ialo density p‘ofiles are evoving ou slower timescales than any individual particle's orbita period. i1 approximate positicMl ds Ss=liciently accurate. (," However, since tree regions are spatially separated and the halo density profiles are evolving on slower timescales than any individual particle's orbital period, an approximate position is sufficiently accurate. ("872Note that since a given tree's own contributiou Dey ds exactly subtracted back out. oily 1je effect on other ‘ees needs to be cousiderec).,"Note that since a given tree's own contribution to $\Phi_{ext}$ is exactly subtracted back out, only the effect on other trees needs to be considered)."873" Th 1 approximation of tle tree j»articles"" positlous at the micelle ol the PM step is taken to be Ositiou one ful partice timeje step aliead: sitce tree pa‘ticle tije steps are hal“the PM time s ‘less. this is no more than the PM miclstep."," Thus, an approximation of the tree particles' positions at the middle of the PM step is taken to be the position one full particle time step ahead; since tree particle time steps are half the PM time step or less, this is no more than the PM midstep."874 With these advanced positious. 1le potential ou 3d is found in the staidard P] mauner.," With these advanced positions, the potential on the grid is found in the standard PM manner."875 For each tree the PN. poteial in a cubical subvoluime is saved., For each tree the PM potential in a cubical subvolume is saved.876 Tis voltLje. is slightly larger than the active ceLl regon (iu order to alow for finding the gradient of Ihe poteitial through finite differencing) plus One exira ce Lon a side in case particles migrate ot of lre active cell region during the time integr:ion., This volume is slightly larger than the active cell region (in order to allow for finding the gradient of the potential through finite differencing) plus one extra cell on a side in case particles migrate out of the active cell region during the time integration.877 Siice the PM tiue step is limitecl by a CoiWal οςidition (see re[sec:timestep)) such that PN particles cannot move more than a ractiol of a cell per step. one extra cell is sullicieut— particles near t1ο edge of a tree region are al [9]uy a slightly higher overdeusity thau the ¢ensest PAI regions. au hence have similar velocities.," Since the PM time step is limited by a Courant condition (see \\ref{sec:timestep}) ) such that PM particles cannot move more than a fraction of a cell per step, one extra cell is sufficient— particles near the edge of a tree region are at only a slightly higher overdensity than the densest PM regions, and hence have similar velocities."878 At the beeinnine of a tree step the portion «X the PM potential ἆIe to the tree particles themselves is subtracted out. leaving tle tidal potertial.," At the beginning of a tree step the portion of the PM potential due to the tree particles themselves is subtracted out, leaving the tidal potential."879" With $,,, saved i1 this muanuer. every time a particles acceleratiou is upcatec. the tidal force Is calculated from 11e erid in the same manuer that PM forces are fou."," With $\Phi_{ext}$ saved in this manner, every time a particle's acceleration is updated, the tidal force is calculated from the grid in the same manner that PM forces are found."880 This is au improvenietr1 over the methocl usec inBOX., This is an improvement over the method used in.881 Iutegate each tree regio1 forward to the uiddle of the PM step., Integrate each tree region forward to the middle of the PM step.882 This is done with a tree code. adding ii the tidal forces.," This is done with a tree code, adding in the tidal forces."883 Tie tree code we use was written by Lars Hernquist. (HeruquistHenqist 1990).," The tree code we use was written by Lars Hernquist \citep{Hern87, HernKatz89, Hern90}."884". Any other potential solver could be used. but a tree code is well siited for this type of »roblem. iu that it can efficiently. hauxdle a wide variety of pa‘ticle distributi1s. Can incl«cle inci""dual particle time steps. auc scales as Vlog’."," Any other potential solver could be used, but a tree code is well suited for this type of problem, in that it can efficiently handle a wide variety of particle distributions, can include individual particle time steps, and scales as $N$ $N$."885 Note hat for each tree this portion of the code is sell-contained: tha is. once the pa‘ticle data al yotential mes1 lor a given tree have been collected together uo further inormnation is required to evolve that tree forward.," Note that for each tree this portion of the code is self–contained; that is, once the particle data and potential mesh for a given tree have been collected together no further information is required to evolve that tree forward."886 This makes TPM well suited lor yarallel processlue@D>oO on distributed. memory SVsenr., This makes TPM well suited for parallel processing on distributed memory systems.887 Once the tree data is received by a given processor tis step— which is the most couiputationally expeusive part of the algorithuu— cau ye performer| without auy [further commatuicedion., Once the tree data is received by a given processor this step— which is the most computationally expensive part of the algorithm— can be performed without any further communication.888 Given this coarse-grained parallelis. one cau ise widely distributect auc heterogeneously οςiigured processors. with more capable processors (or groups of p'OCessors) reserved for the lafeest trees.," Given this coarse–grained parallelism, one can use widely distributed and heterogeneously configured processors, with more capable processors (or groups of processors) reserved for the largest trees."889 (FilippenkoaudRiess2000)::," \citep{ost95,tur97,chi97,cal98,zla99,pmw99}. \citep{fil00}:"890Weak eravitationa lensing. the shearing of ealaxv images by gravitational beudiug o: light. Is an effective. tool to. probe the large-scale matter distribution o| fhe universe.,"Weak gravitational lensing, the shearing of galaxy images by gravitational bending of light, is an effective tool to probe the large-scale matter distribution of the universe."891 It is also a lucas to measure the cosmolocical parameters colparing observatioi fo nmuuerical sunulatious of large scale structiro erowth (BartchuannSchneider 2001)., It is also a means to measure the cosmological parameters by comparing observation to numerical simulations of large scale structure growth \citep{bartelmann01}.892. There are many weak ens (WL) survevs underway to obtain the cosinological paralcters to higher precision. aud iu particular to probe the evolution of the dark cnerev bx observing its effects cn the evolution of matter distribution(DLS!.. ‘FIITLS?}).," There are many weak lensing (WL) surveys underway to obtain the cosmological parameters to higher precision, and in particular to probe the evolution of the dark energy by observing its effects on the evolution of matter distribution, )."893 The WL sienalOo is verv subtle. however: it Is necessary fo measure these μια. distortions (tvpica shear 5—1% jin the presence of optical cistortions aud the asvunnuetric porut-spread-functio1i (PSF) of real-life imaging.," The WL signal is very subtle, however; it is necessary to measure these small distortions (typical shear $\gamma\sim 1\%$ ) in the presence of optical distortions and the asymmetric point-spread-function (PSF) of real-life imaging."894 The level of systematic error in the WL measurement methods are cirreutly above the statistical accuracy expected fron future wide and deep WL survevsSTARRS?..SNAP!..LSST.. SKA)).," The level of systematic error in the WL measurement methods are currently above the statistical accuracy expected from future wide and deep WL surveys, )."895 Because there are no “standard shear” lenses onu the skv. shearaneasurenient techuiques are tested by applying them o artificial ealaxy images and seeimg if one cai correctly extract a shear applied to the sinnation.," Because there are no “standard shear” lenses on the sky, shear-measurement techniques are tested by applying them to artificial galaxy images and seeing if one can correctly extract a shear applied to the simulation."896 lu most Cases. the recovered shear cau bο written as sour=Min|6.," In most cases, the recovered shear can be written as $\gamma_{\rm out} = m \gamma_{\rm in} + c$."897" Departures frou the ideal a=1 we will term ""calibration or ""uuipliceative errors and quote as percentages.", Departures from the ideal $m=1$ we will term “calibration” or “multiplicative” errors and quote as percentages.898" Deviations from the ideal e=0 cau result from unucorreced asvuumetrics in the PSF and optics. aud will © termed cadditive errors? or “Incomplete PSF suppression."""," Deviations from the ideal $c=0$ can result from uncorrected asymmetries in the PSF and optics, and will be termed “additive errors” or “incomplete PSF suppression.”"899 Such tests of the uost widely applied. analysis iiethod (Naiser.Squires.&Droadlist 1995)||kSD].," Such tests of the most widely applied analysis method \citep{KSB}[ [KSB],"900Flattened astrophysical objects like disks are known to genrally produce gravitational fields weaker than spherical bodies of comparable mass.,Flattened astrophysical objects like disks are known to genrally produce gravitational fields weaker than spherical bodies of comparable mass.901 However. the gravity of low-mass disks evolving on long time scales may play a significant role in their own dynamics and environment (??)..," However, the gravity of low-mass disks evolving on long time scales may play a significant role in their own dynamics and environment \citep{gt78,subrkaras05}."902 Gravitational forces from disks are not easily accessible by numerical computation. and this domain still represents an interesting challenge.," Gravitational forces from disks are not easily accessible by numerical computation, and this domain still represents an interesting challenge."903 For various reasons (misknowledge of boundary conditions. sensitivity and inaccuracy of solutions. relevant physical scales. kernel singularities. computational cost. ete.).," For various reasons (misknowledge of boundary conditions, sensitivity and inaccuracy of solutions, relevant physical scales, kernel singularities, computational cost, etc.),"904 neither the Poisson equation nor Newton's integral law offers a simple and straightforward tool. and each must be handled with some caution.," neither the Poisson equation nor Newton's integral law offers a simple and straightforward tool, and each must be handled with some caution."905 Truncated expansions of solutions generally suffer from inaccuracy and instability (22)..," Truncated expansions of solutions generally suffer from inaccuracy and instability \citep{clement74,hachisu86}."906 Softened Gravity for continuous systems may help in some circumstances. but the influence of the softening length — a free-parameter. classically — 1s spurious. and it fundamentally destroys the Newtonian character of thegravitational interaction (??)..," Softened Gravity for continuous systems may help in some circumstances, but the influence of the softening length | a free-parameter, classically | is spurious, and it fundamentally destroys the Newtonian character of thegravitational interaction \citep{he88,ars89}."907 Each disk configuration (symmetry. edges. mass profile. shape. etc.)," Each disk configuration (symmetry, edges, mass profile, shape, etc.)"908 must therefore be investigated individually for a given application., must therefore be investigated individually for a given application.909 Geometrically thin disks probably constitute the main class of astrophysical disks., Geometrically thin disks probably constitute the main class of astrophysical disks.910 These exhibit various shapes. density profiles and sizes.," These exhibit various shapes, density profiles and sizes."911 For those orbiting a massive central object (star or black hole). a self-similar behavior may develop secularly. leading to a mass density profile varying close to a power law of the radius.," For those orbiting a massive central object (star or black hole), a self-similar behavior may develop secularly, leading to a mass density profile varying close to a power law of the radius."912 Such a profile is widely supportec by theory and it is a typical initial. ingredient of numerical simulations (e.g.?2)..," Such a profile is widely supported by theory and it is a typical initial ingredient of numerical simulations \citep[e.g.][]{pringle81,edgar07}."913 Even in quasi-Keplerian rotation. thi disks can be influenced by their own gravity.," Even in quasi-Keplerian rotation, thin disks can be influenced by their own gravity."914 ? (hereafter Paper D) have shown that the midplane gravitational potential of flat. power-law disks obey an ordinary differential equatio (ODE) accounting for edges which are usually ignored (??)..," \cite{hh07} (hereafter Paper I) have shown that the midplane gravitational potential of flat, power-law disks obey an ordinary differential equation (ODE) accounting for edges which are usually ignored \citep{bisnovatyi75,ge99}."915 Analytical solutions in the form of very rapidly converging series have been reported in ?.., Analytical solutions in the form of very rapidly converging series have been reported in \cite{hhcb08}.916" At the same time. ? have show that the model of ""Softened Gravity"" offers a good framework for determining the Newtonian potential of thin disks (whatever the mass density profile). provided the ""softening length"" takes a very specific form. locally."," At the same time, \cite{hp09} have shown that the model of “Softened Gravity” offers a good framework for determining the Newtonian potential of thin disks (whatever the mass density profile), provided the “softening length” takes a very specific form, locally."917 In the present paper. we show that the ODE for the gravitational potential deseribed by ? can be extended to the whole physical space. and we combine this result with an appropriate softening length to describe the potential of disks of non vanishing thickness.," In the present paper, we show that the ODE for the gravitational potential described by \cite{hh07} can be extended to the whole physical space, and we combine this result with an appropriate softening length to describe the potential of disks of non vanishing thickness."918 The paper is organized as follows., The paper is organized as follows.919 We recall the basic configuration and useful formulae of potential in flat. power-law disks in Sect. 2..," We recall the basic configuration and useful formulae of potential in flat, power-law disks in Sect. \ref{sec:basic}."920 The derivation of the generalized ODE. non-dimensionalization and asymptotic behavior of solutions. are found in Sect. 3..," The derivation of the generalized ODE, non-dimensionalization and asymptotic behavior of solutions, are found in Sect. \ref{sec:ugode}."921 The numerical solutions are given in Sect. 4.., The numerical solutions are given in Sect. \ref{sec:num}. .922 Thickness effects. including the introduction of the softening length. are discussed in Sect 5..," Thickness effects, including the introduction of the softening length, are discussed in Sect \ref{sec:lambda}."923 The last section ts devoted to a conclusion., The last section is devoted to a conclusion.924" Following ?— (hereafter Paper D. we consider a flat axisymmetrical disk with inner edge oj,>0. outer edge diy (see Fig. 1))."," Following \cite{hh07} (hereafter Paper I), we consider a flat axisymmetrical disk with inner edge $\ain \ge 0$, outer edge $\aout > \ain$ (see Fig. \ref{fig:scheme2.xfig}) ),"925 and a power-law surface density of the form where « Σια).is the cylindrical radius. oo some reference radius. and Xj=Xap) the corresponding surface density.," and a power-law surface density of the form where $a$ is the cylindrical radius, $a_0$ some reference radius, and $\Sigma_0 \equiv \Sigma(a_0)$ the corresponding surface density."926 This profile can serve as a basis for defining more complex mass distributions. by mixing power laws with different indices (positive and negative).," This profile can serve as a basis for defining more complex mass distributions, by mixing power laws with different indices (positive and negative)."927 For such a disk. the gravitational potential in space Is given exactly by the expression (?) where is the complete elliptic integral of the first kind. and is the (a+RPmodulus (0€κ I). R and Z are the cylindrical coordinates. and r is the spherical radius (i.e. 7=R+ Z ," For such a disk, the gravitational potential in space is given exactly by the expression \citep[][]{durand64}928 where is the complete elliptic integral of the first kind, and is the modulus $0 \le k \le 1$ ), $R$ and $Z$ are the cylindrical coordinates, and $r$ is the spherical radius (i.e. $r^2 =R^2+Z^2$ )."929Known properties about this configuration are the followings., Known properties about this configuration are the followings.930 The integral in Eq., The integral in Eq.931 2 has a diverging kernel as soon as the modulus & reaches unity., \ref{eq:psi} has a diverging kernel as soon as the modulus $k$ reaches unity.932 This occurs everywhere inside the disk., This occurs everywhere inside the disk.933 Standard quadrature schemes fail to give accurate potential values unless a specifictreatment is considered (?).., Standard quadrature schemes fail to give accurate potential values unless a specifictreatment is considered \citep{hurepierens05}. .934 The potential is not a power law of the radius. because of edges.," The potential is not a power law of the radius, because of edges."935The central regious of galaxy clusters are the places with the highest galaxw density in the universe.,The central regions of galaxy clusters are the places with the highest galaxy density in the universe.936 Dwarf ellipticals (dE) are expecially the most strongly clustered types of galaxies in ligh-density euvironmoeuts (6.8. review bv Ferguson DBiugeelhOO 1991. aud references therein).," Dwarf ellipticals (dE) are especially the most strongly clustered types of galaxies in high-density environments (e.g. review by Ferguson Binggeli \cite{ferg94}, and references therein)."937 Several striking characteristics are seen in the center region of clusters: (1) most central galaxies possess extraordinarily rich elobular cluster systems (CC'S) (see Tarris 1991.. Richtler 1995 and references therein). but see also apparent counter-cxamples (see Table 11 in MeLanellin et al. 19913): (," Several striking characteristics are seen in the center region of clusters: (1) most central galaxies possess extraordinarily rich globular cluster systems (GCS) (see Harris \cite{harr91a}, , Richtler \cite{rich95} and references therein), but see also apparent counter-examples (see Table 14 in McLaughlin et al. \cite{mcla94b}) ); ("9382) there often exists a cD ealaxy in the ceuter of clusters (e.g. Schombert 1988]). (,2) there often exists a cD galaxy in the center of clusters (e.g. Schombert \cite{scho88}) ). (9393) different types of dwarf galaxies have differeut. clusteriug properties (e.g. Vader Saudage 1991)): C1) iun some cases the faint cud slope of the disvarf galaxy Iuninosity function (LF) seems to depend on the chlister-ceutiic distauce (c.g. tn Coma: Lobo et al. 19973).,3) different types of dwarf galaxies have different clustering properties (e.g. Vader Sandage \cite{vade91}) ); (4) in some cases the faint end slope of the dwarf galaxy luminosity function (LF) seems to depend on the cluster-centric distance (e.g. in Coma: Lobo et al. \cite{lobo}) ).940 The question arises ou whether these properties may be related through the accretion of cwarf ealaxies., The question arises on whether these properties may be related through the accretion of dwarf galaxies.941 The answer to this question is imost probably associated to the formation epoch of galaxy clusters., The answer to this question is most probably associated to the formation epoch of galaxy clusters.942 At that time. it is expected that ealaxics were τον gus-vich and that interactions between galaxies were more frequent.," At that time, it is expected that galaxies were very gas-rich and that interactions between galaxies were more frequent."943 The παν density of galaxies at that epoch in the central region nmst have been larger than today., The number density of galaxies at that epoch in the central region must have been larger than today.944 Therefore. the initial population of chwart galaxies played an miportaut role.," Therefore, the initial population of dwarf galaxies played an important role."945 The favoured theoretical models of ealaxv cluster formation predict a steep slope of the iifial mass function towards the low-mass eud (see a more detailed discussion and references in Sect., The favoured theoretical models of galaxy cluster formation predict a steep slope of the initial mass function towards the low-mass end (see a more detailed discussion and references in Sect.946 2.1)., 2.1).947 Tu contrast. the faint cud slope of the observed LF iu nearV eroups and clusters are siguificautlv flatter (sec Fergusou DBiueeeli 1991. Trentham 1998)).," In contrast, the faint end slope of the observed LF in nearby groups and clusters are significantly flatter (see Ferguson Binggeli \cite{ferg94}, Trentham \cite{tren98}) )."948 One possibility that would explain this diserepaucy is the accretion and dissolution of dwarf galaxies iu cluster centers., One possibility that would explain this discrepancy is the accretion and dissolution of dwarf galaxies in cluster centers.949 It is posible to mnderstand the formation of à rich GC system aud a cD halo from the iufall of &as-poor and eas-rich chwarts iuto a dense cluster cuviroument., It is posible to understand the formation of a rich GC system and a cD halo from the infall of gas-poor and gas-rich dwarfs into a dense cluster environment.950 During the iufall of eas-poor as well as eas-rich clwarfs mm a deuse cluster ceuter environment several scenarios are thiukable for forming a rich CCS aud a cD halo (see Sect., During the infall of gas-poor as well as gas-rich dwarfs in a dense cluster center environment several scenarios are thinkable for forming a rich GCS and a cD halo (see Sect.951 5)., 5).952 Support for such a scenario from the observational side cones from Lóppez-Cruz et al. (1997)), Support for such a scenario from the observational side comes from Lóppez-Cruz et al. \cite{lope}) )953 who compared the properties of clusters with and without a ceutral Iuninous cD galaxy., who compared the properties of clusters with and without a central luminous cD galaxy.954 They fouud that clusters without a prominent cD ealaxy teud to have a steep LF at the faint cud aud a ligh fraction of late-tvpe galaxies. and thus seem to be less evolved than clusters with pronounced cD ealaxics and relatively flat LF at the faintcud.," They found that clusters without a prominent cD galaxy tend to have a steep LF at the faint end and a high fraction of late-type galaxies, and thus seem to be less evolved than clusters with pronounced cD galaxies and relatively flat LF at the faintend."955 They explain this finding by the disruptiou of dwarf galaxies., They explain this finding by the disruption of dwarf galaxies.956"definitely the requirements for strong confinement. ie. 77,>>1. are fulfilled.","definitely the requirements for strong confinement, i.e. $\eta_{*} \gg 1$, are fulfilled."957 While at first analytic studies of rigidly rotating magnetospheres indicated that in the case of strong magnetic confinement an equatorial disk builds up from corotation radius outwards (?).. its formation is also present in MHD simulation when including effects of stellar rotation.," While at first analytic studies of rigidly rotating magnetospheres indicated that in the case of strong magnetic confinement an equatorial disk builds up from corotation radius outwards \citep{tow05}, its formation is also present in MHD simulation when including effects of stellar rotation."958 These models predict the formation of a rigidly rotating disk by the accumulation of wind material. however episodes of infall and breakouts limit the build-up of the disk and lead to a dynamic but quasi-stationary behavior (?):: moreover the location of the temporary confined plasma around the equatorial plane can be estimated with the formalism presented in these works.," These models predict the formation of a rigidly rotating disk by the accumulation of wind material, however episodes of infall and breakouts limit the build-up of the disk and lead to a dynamic but quasi-stationary behavior \citep{dou08}; moreover the location of the temporary confined plasma around the equatorial plane can be estimated with the formalism presented in these works."959" For moderate rotation and very strong confinement the inner edge of disk is roughly given by the ""associated Kepler-radius’ with W2Via/Van and Vin=VGM/R.; using Via=50 ss! we obtain Ry5R..", For moderate rotation and very strong confinement the inner edge of disk is roughly given by the 'associated Kepler-radius' $R_{\rm K}= W^{-2/3}$ with $W=V_{\rm rot}/V_{\rm orb}$ and $V_{\rm orb}=\sqrt{GM/R_{*}}$; using $V_{\rm rot}=50$ $^{-1}$ we obtain $R_{\rm K} \sim 5 R_{*}$.960" The outer edge is determined by the extent of the closed magnetosphere Re50.7R,. slightly below the Alfvénn radius given by Ra=η.*R,."," The outer edge is determined by the extent of the closed magnetosphere $R_{\rm C} \approx 0.7 R_{\rm A}$, slightly below the Alfvénn radius given by $R_{\rm A} \approx \eta_{*}^{1/4} \times R_{*}$."961" For IQ Aur we obtain Ry=30R,: clearly we are m a regime where Ry> and thus the conditions required by the model for the formation of a rigid disk are fulfilled.", For IQ Aur we obtain $R_{A} \approx 30~R_{*}$; clearly we are in a regime where $R_{\rm A} > R_{\rm K}$ and thus the conditions required by the model for the formation of a rigid disk are fulfilled.962" The disk of IQ Aur is expected to be roughly located between =5—20R, anc breakout events are mainly launched at distances of =20—30 R.."," The disk of IQ Aur is expected to be roughly located between $\approx 5\,-\,20~R_{*}$ and breakout events are mainly launched at distances of $\approx 20\,-\,30~R_{*}$ ."963 We caution that these models assume an aligned dipole and were derived for more massive stars. thus an extrapolatior to our Ap/Bp stars may not be straightforward.," We caution that these models assume an aligned dipole and were derived for more massive stars, thus an extrapolation to our Ap/Bp stars may not be straightforward."964 Nevertheless. the model is generally applicable for magnetically channellec line-drive stellar winds and thus appears sufficient for the discussion of the overall phenomenology of X-ray emisstor presented in the following.," Nevertheless, the model is generally applicable for magnetically channelled line-drive stellar winds and thus appears sufficient for the discussion of the overall phenomenology of X-ray emission presented in the following."965" The X-ray luminosity produced by MCWS follows the relation LxoΜΥ ΡΟ, whereas the plasma temperature is given by Tx=LI8xIOK(V4,/100kms!y (BM97)."," The X-ray luminosity produced by MCWS follows the relation $L_{\rm X}\propto \dot M V_{\infty} B^{0.4}_{*}$ , whereas the plasma temperature is given by $T_{\rm X} \approx 1.15 \times10^{5} {\rm K}\,(V_{\rm sh}/100~\rm{km\,s}^{-1})^{2}$ (BM97)."966 Adopting similar wind speed and mass loss rate. one expects a7 CCVn to be comparably bright or even moderately X-ray brighter than [Q Aur.," Adopting similar wind speed and mass loss rate, one expects $\alpha^2$ CVn to be comparably bright or even moderately X-ray brighter than IQ Aur."967" However. it is at least a factor thousand X fainter than ""expected? from the simplified assumption."," However, it is at least a factor thousand X-ray fainter than 'expected' from the simplified assumption."968 This implies that either the mass loss rates differ by orders of magnitudes or that shock-speeds for a CCVn are so low. that the plasma does not reach X-ray temperatures.," This implies that either the mass loss rates differ by orders of magnitudes or that shock-speeds for $\alpha^{2}$ CVn are so low, that the plasma does not reach X-ray temperatures."969 Since stellar wind speeds are likely comparable and strong confinement is achieved for both stars. à very low plasma temperature of Tx€3x10° K as would be required to explain the tight upper limit on Lx for a7 CCVn. is virtually ruled out.," Since stellar wind speeds are likely comparable and strong confinement is achieved for both stars, a very low plasma temperature of $T_{\rm X} \lesssim 3 \times 10^{5}$ K as would be required to explain the tight upper limit on $L_{\rm X}$ for $\alpha^{2}$ CVn, is virtually ruled out."970 It also appears unlikely that small differences in the magnetic topology of both stars lead to completely different wind channelling and wind shock configurations., It also appears unlikely that small differences in the magnetic topology of both stars lead to completely different wind channelling and wind shock configurations.971 A more reasonable explanations would be to propose a different mass loss rate and that IQ Aur differs by intrinsic. properties that promote mass loss and thus X-ray generation. for example it is more luminous and hotter than « CCVn.," A more reasonable explanations would be to propose a different mass loss rate and that IQ Aur differs by intrinsic properties that promote mass loss and thus X-ray generation, for example it is more luminous and hotter than $\alpha^{2}$ CVn."972 In this ease the X-ray generation would depend very sensitively on the underlying stellar parameter(s)., In this case the X-ray generation would depend very sensitively on the underlying stellar parameter(s).973 Alternatively. the MCWS phenomenon could be a transient one and currently only IQ Aur is in an active wind phase with a high mass loss rate.," Alternatively, the MCWS phenomenon could be a transient one and currently only IQ Aur is in an active wind phase with a high mass loss rate."974 Unfortunately. mass loss rates of Ap stars usually cannot be independently measured. but are determined via modeling of e.g. their X-ray properties.," Unfortunately, mass loss rates of Ap stars usually cannot be independently measured, but are determined via modeling of e.g. their X-ray properties."975 However. the strong wind phase is believed to be connected to abundance anomalies. that are also observed in a7 CCVn.," However, the strong wind phase is believed to be connected to abundance anomalies, that are also observed in $\alpha^{2}$ CVn."976 It was already noticed by BM97. that any abundance anomalies should be removed by the rather high mass loss rate. thus requiring that IQ Aur only recently. t.e. before a few Myr. entered the active wind phase.," It was already noticed by BM97, that any abundance anomalies should be removed by the rather high mass loss rate, thus requiring that IQ Aur only recently, i.e. before a few Myr, entered the active wind phase."977 Although the details of the onset of the strong wind phase are rather unknown. they estimate that Ap stars would spends a few percent of their lifetime in the strong wind phase. thus explaining that most Ap stars are no X-ray sources. at least at the moment.," Although the details of the onset of the strong wind phase are rather unknown, they estimate that Ap stars would spends a few percent of their lifetime in the strong wind phase, thus explaining that most Ap stars are no X-ray sources, at least at the moment."978 Nevertheless. additional criteria might be necessarily fulfilled to make an AOp star a bright X-ray source.," Nevertheless, additional criteria might be necessarily fulfilled to make an A0p star a bright X-ray source."979 Given the very different findings for IQ Aur and a7 CCVn. we searched the and archives. for observations of similar Ap/Bp stars. to derive some information on theirgeneral X-ray properties.," Given the very different findings for IQ Aur and $\alpha^{2}$ CVn, we searched the and archives for observations of similar Ap/Bp stars, to derive some information on theirgeneral X-ray properties."980 As a comparison sample we choose late-B to early-A magnetic CP stars with well, As a comparison sample we choose late-B to early-A magnetic CP stars with well981can appear before the LC peak depending on the optical depth of the wiud.,can appear before the LC peak depending on the optical depth of the wind.982 If we apply the model of (2001).. the ratio C. of the uuscattered Wa line fix to the total Πα line flix of the Loreutzian profile is For the case of flat density slopes. 7 remains too high until the forward shock reaches thesurface (Figure 13) and UC is expected to be very simall for a long time before the LC peak.," If we apply the model of , the ratio $U$ of the unscattered $\alpha$ line flux to the total $\alpha$ line flux of the Lorentzian profile is For the case of flat density slopes, $\tau$ remains too high until the forward shock reaches thesurface (Figure \ref{fig1}) ) and $U$ is expected to be very small for a long time before the LC peak."983 On the other haud. if the density decline is steep. the optical depth decreases gradually. with time and the suitable optical depth for the appearance of Loreutzian profiles would be realized for a long while.," On the other hand, if the density decline is steep, the optical depth decreases gradually with time and the suitable optical depth for the appearance of Lorentzian profiles would be realized for a long while."984 Therefore. Loreutzian lines are expected to be observe well before the LC peak for Tvpe Tn LSNe.," Therefore, Lorentzian lines are expected to be observed well before the LC peak for Type IIn LSNe."985 The LC evolution of Type II LSNe is also cousisteu with our models., The LC evolution of Type II LSNe is also consistent with our models.986 Ii our inodels for both Type Thi anc Type TL LSNe. the forward shock stavs in the dense wind until the LC peak.," In our models for both Type IIn and Type IIL LSNe, the forward shock stays in the dense wind until the LC peak."987 As the wind with r>J is shocked with the timescale of fj. the dense wine adiabatically cools down after the LC peak.," As the wind with $\tau>1$ is shocked with the timescale of $t_d$, the dense wind adiabatically cools down after the LC peak."988 Thus. the LCs of Type II LSNe are supposed to follow the shocked. diffusion model preseuted by(2007).," Thus, the LCs of Type II LSNe are supposed to follow the shell-shocked diffusion model presented by."989.. The shell-shocked diffusion model is based on the aciabatic cooling of the shocked dense wind. which is basically the same as the LC model suggested for Type IL SNe by(1980).. aud the model had been already shown to be consistent with the declining plase of the LC of SN 200Gev2007).," The shell-shocked diffusion model is based on the adiabatic cooling of the shocked dense wind, which is basically the same as the LC model suggested for Type II SNe by, and the model had been already shown to be consistent with the declining phase of the LC of SN 2006gy."990.. However. it should be noted that the model is too simplified aud many effects which cannot be treated by the formulation of are ignored in the model.," However, it should be noted that the model is too simplified and many effects which cannot be treated by the formulation of are ignored in the model."991 For example. the model assumes a constant opacity aud it ignores the preseuce of recombination wave which is supposed to be created iu thea diffusing shocked shell.," For example, the model assumes a constant opacity and it ignores the presence of a recombination wave which is supposed to be created in the diffusing shocked shell."992 Thus. we caunot confirm that our model is consistent with the LCs of Type II LSNe just by the comparison with the shellshocked. diffusion model and nuuerical LC modeling is required to see if our models are consistent with Type II Τον LCs.," Thus, we cannot confirm that our model is consistent with the LCs of Type II LSNe just by the comparison with the shell-shocked diffusion model and numerical LC modeling is required to see if our models are consistent with Type II LSN LCs."993" Iu the previous section. we have shown that. if the shock breakout occurs inside a deuse wind Ge<1). the ratio of the timescale of the photon diffusion to that of the shock propagation iu the wind depends on the wind density slope aud thus the different density slope can result iu two kinds of Type II LSNe. Ίο, Type Tn aud Type TL LSNe."," In the previous section, we have shown that, if the shock breakout occurs inside a dense wind $(x<1)$, the ratio of the timescale of the photon diffusion to that of the shock propagation in the wind depends on the wind density slope and thus the different density slope can result in two kinds of Type II LSNe, i.e., Type IIn and Type IIL LSNe."994 As an example. we apply our model to two LSNe: Type Tn SN 2006ev and Type TL SN 2008es.," As an example, we apply our model to two LSNe: Type IIn SN 2006gy and Type IIL SN 2008es."995 If we look into Type Tn LSN 2006e8v and Type TIL LSN 2008es. oue inportaut difference is the existence of narrow P-Cveni profiles in the spectra of SN 2006ev after the LC peak.," If we look into Type IIn LSN 2006gy and Type IIL LSN 2008es, one important difference is the existence of narrow P-Cygni profiles in the spectra of SN 2006gy after the LC peak."996 Based on the observational feature. we can guess that Type TL Τον 2008es cune from the dense wind with t/t.21 while Type Tn LSN 2006ev resulted from the dense wind with t/t.« 1.," Based on the observational feature, we can guess that Type IIL LSN 2008es came from the dense wind with $t_d/t_s \simeq 1$ while Type IIn LSN 2006gy resulted from the dense wind with $t_d/t_s < 1$ ."997 We apply those models to the two LSNo., We apply those models to the two LSNe.998 In this section. & is set to O3lem?&||," In this section, $\kappa$ is set to $0.34~\mathrm{cm^{2}~g^{-1}}$."999 SN 2006ev is extensively studied by e$...(2010).," SN 2006gy is extensively studied by, e.g.,."1000.. Tt is classified. as Type Tn and the huninosity reaches ~22 mag in the 7? baud2007)., It is classified as Type IIn and the luminosity reaches $\sim -22$ mag in the $R$ band.1001. The detailed spectral evolution is sununarized in(2010)., The detailed spectral evolution is summarized in.1002. The narrow P-Creni Ho lines with the absorption minim of ~100kins|! are considered to come frou the wind surroundiug the progenitor of SN 2000ον., The narrow P-Cygni $\alpha$ lines with the absorption minimum of $\simeq 100~\mathrm{km~s^{-1}}$ are considered to come from the wind surrounding the progenitor of SN 2006gy.1003 As SN. 200G6e. shows narrow P-Cyeui profiles after the maxima huninosity. an unshocked wind is supposed to remain after the maxunumn.," As SN 2006gy shows narrow P-Cygni profiles after the maximum luminosity, an unshocked wind is supposed to remain after the maximum."1004 Thus. models with fj/f;<land gq<1l are preferred.," Thus, models with $t_d/t_s <1 $ and $y_1<1$ are preferred."1005 Based on the observatious of(2010).. we adopt the following parameters: C. Is coustrained by the evolution of the blackbody radius and ty is obtained from the rising time of the LC.," Based on the observations of, we adopt the following parameters: $v_s$ is constrained by the evolution of the blackbody radius and $t_d$ is obtained from the rising time of the LC."1006 As the narrow Πα P-Cweui profile is detected at 179 and disappears at 209 days2010)... we presune that the forward shock has goue through the eutire wiud between 179 days aud 209 davs.," As the narrow $\alpha$ P-Cygni profile is detected at 179 and disappears at 209 days, we presume that the forward shock has gone through the entire wind between 179 days and 209 days."1007 We simply take the ceutral date (191 davs) as the time when the forward shock has goue through the eutire sviud. ic. davs.," We simply take the central date (194 days) as the time when the forward shock has gone through the entire wind, i.e., $t_s\simeq194$ days."1008" With fj. μι aud ey. we cau estimate c aud I, for a eiven w from Equations (10)) aud (11))."," With $t_d$, $t_s$ , and $v_s$, we can estimate $x$ and $R_o$ for a given $w$ from Equations \ref{td}) ) and \ref{ts}) )."1009 If we adopt the model with w=2. for example. wand Πρ are estimated to be 0.0095 and 8.8«107 cni. respectively.," If we adopt the model with $w=2$, for example, $x$ and $R_o$ are estimated to be $0.0095$ and $8.8\times10^{15}$ cm, respectively."1010" In this case. shock breakout occurs at wR,~3.2s10:5 em and the last scattering surface ds quR,c3.2.10 ens"," In this case, shock breakout occurs at $xR_o\simeq3.2\times 10^{14}$ cm and the last scattering surface is $y_1R_o\simeq3.2\times 10^{15}$ cm."1011 The total wind mass is MagcιδM. (e£, The total wind mass is $M_\mathrm{wind}\simeq0.81~M_\odot$ (c.f.1012 R; FR) and is much smaller than the value estimated from the shell-shocked diffusion LC model2007).. Towever. the shell-shocked diffision model is a too simplified model and we cannot exclude this model just because of the inconsistency with it. as is noted iu the previous section.," $R_i\ll R_o$ ) and is much smaller than the value estimated from the shell-shocked diffusion LC model However, the shell-shocked diffusion model is a too simplified model and we cannot exclude this model just because of the inconsistency with it, as is noted in the previous section."1013" Alternatively. if we adopt a steeperdensity eradicut how and A, are estimated to be 0.17 and 1.05<1019 αι, respectively. and thus 2,2L8«1017emi aud yk,~L9«Lo cni"," Alternatively, if we adopt a steeperdensity gradient $w=5$ , $x$ and $R_o$ are estimated to be $0.17$ and $1.05\times10^{16}$ cm, respectively, and thus $xR_o\simeq1.8\times 10^{15}~\mathrm{cm}$ and $y_1R_o\simeq4.9\times 10^{15}$ cm."1014" gtB, is consistent with the blackbody radius at the LC peak estimated from the observatious (6«1019 cin).", $y_1R_o$ is consistent with the blackbody radius at the LC peak estimated from the observations $6\times10^{15}$ cm).1015 Tf we asstune that R;~101?cin. the mass contained in the optically thick region (R;<r<yh.) is 22AL. in our wt=Ὁ anodel.," If we assume that $R_i\simeq10^{15}~\mathrm{cm}$, the mass contained in the optically thick region $(R_i<r<y_1R_o)$ is $22~M_\odot$ in our $w=5$ model."1016 In this case. tle mass of the entire wind becomes Αρz23AL...," In this case, the mass of the entire wind becomes $M_\mathrm{wind}\simeq23~M_\odot$."1017 The left paucl of Figure L is the optical depth aud the euclosed mass distributions., The left panel of Figure \ref{fig4} is the optical depth and the enclosed mass distributions.1018 The existence of the wushocked wiud may also account for the weakness of the N-vay cussion of SN 20066v. 2007)., The existence of the unshocked wind may also account for the weakness of the X-ray emission of SN 2006gy .1019. The spectral evolution of SN 2006ev isalso consistent with our model., The spectral evolution of SN 2006gy isalso consistent with our model.1020 Loreutziau II Daliuer lines secu iu the spectra of SN 200698. are presumed to becaused by the optically thick wind 2009)..For example. for the case a= 5. 7 become z10 at around 3«104? οι (Figure 1)).," Lorentzian H Balmer lines seen in the spectra of SN 2006gy are presumed to becaused by the optically thick wind .For example, for the case $w=5$ , $\tau$ become $\simeq 10$ at around $3\times 10^{15}$ cm (Figure \ref{fig4}) )."1021 This is consistent with 7~15 at 36 davs which is estimated from the, This is consistent with $\tau\simeq15$ at 36 days which is estimated from the1022signal maps in the left column of Fig. 1)).,signal maps in the left column of Fig. \ref{FigObs}) ).1023 We present in the middle column of Fig., We present in the middle column of Fig.1024 | the corresponding noise maps that show our sensitivity limit as a function of the position in the field of view., \ref{FigObs} the corresponding noise maps that show our sensitivity limit as a function of the position in the field of view.1025 The right column of Fig., The right column of Fig.1026 1. shows the signal-to- ratio maps obtained in each case by dividing of the signal map by the noise map., \ref{FigObs} shows the signal-to-noise ratio maps obtained in each case by dividing of the signal map by the noise map.1027 From these. we conclude that only the central point source is detected with à SNR»3.," From these, we conclude that only the central point source is detected with a $>3$."1028 Previous interferometric observations. at. mmm were reported by ? and ?.., Previous interferometric observations at mm were reported by \citet{Koerner_2001} and \citet{Wilner_2002}.1029" With an angular resolution of 3.3 x2.9"", ? found an are ring at 95 AU with four peaks located between I] and oof flux density ranging from 2.4 to mmJy (3 to 4c level) after correcting for primary beam attenuation."," With an angular resolution of 3.3 x, \citet{Koerner_2001} found an arc ring at 95 AU with four peaks located between 11 and of flux density ranging from 2.4 to mJy (3 to $\sigma$ level) after correcting for primary beam attenuation."1030" In addition to the central point source. ? reported two emission peaks located at 8.0 and9.5""... after tapering their data to à 5.3 x rresolution."," In addition to the central point source, \citet{Wilner_2002} reported two emission peaks located at 8.0 and, after tapering their data to a 5.3 x resolution."1031 From a Gaussian fit in the plane. they obtained fluxes (corrected for the primary beam attenuation) of 7.1+1.4 and 4.3€1.0 mmJy. respectively (4 to 5c level).," From a Gaussian fit in the plane, they obtained fluxes (corrected for the primary beam attenuation) of $7.1\pm1.4$ and $4.3\pm1.0$ mJy, respectively (4 to $\sigma$ level)."1032 The positior of these dust peaks is reported in Fig. 1..," The position of these dust peaks is reported in Fig. \ref{FigObs},"1033 with their Io error ellipse derived from the signal-to-noise ratio and synthesizec beam., with their $1 \sigma$ error ellipse derived from the signal-to-noise ratio and synthesized beam.1034 These two results clearly do not agree. as none of the error ellipse overlap.," These two results clearly do not agree, as none of the error ellipse overlap."1035 We also note that the comparison of the different results need to take into account that their single field maps are not corrected for primary beam attenuation. in contrast to the maps we present here.," We also note that the comparison of the different results need to take into account that their single field maps are not corrected for primary beam attenuation, in contrast to the maps we present here."1036 At the position of the peaks reported by ?.. our observations have a lor sensitivity of 0.35 mJy/beam (0.54 for the most distant peak). a factor of between two and three better than the OVRO observations.," At the position of the peaks reported by \citet{Koerner_2001}, our observations have a $\sigma$ sensitivity of 0.35 mJy/beam (0.54 for the most distant peak), a factor of between two and three better than the OVRO observations."1037 If real. these peaks should have been detected at the >6—8c level.," If real, these peaks should have been detected at the $>10386-8\sigma$ level."1039 Similarly. our observations reach a Io sensitivity limit of 0.26 mJy/beam (1.1 mK) or O.45mJy/beam (0.6 mK) at the position of the ? peaks for the untapered and tapered maps. respectively.," Similarly, our observations reach a $1\sigma$ sensitivity limit of 0.26 mJy/beam (1.1 mK) or 0.45mJy/beam (0.6 mK) at the position of the \citet{Wilner_2002} peaks for the untapered and tapered maps, respectively."1040 Thus. depending on their size. the two structures should have been detected at the 10—I5c and 6—10c level in our maps.," Thus, depending on their size, the two structures should have been detected at the $10-15 \sigma$ and $6-101041\sigma$ level in our maps."1042Classical C'epheids are the kev standard candles. which are used to set the zero point of the extragalactic distance scale (Freedmanetal.2001) and also serve as voung-population tracers of great importance (BinneyanclMerrifield1998).,"Classical Cepheids are the key standard candles, which are used to set the zero point of the extragalactic distance scale \citep{F01} and also serve as young-population tracers of great importance \citep{BM}."1043. They owe their popularity to their high. luminosities and photometric variability (which make them easy. to identify and observe even at [large distances) and the fact that the Iuminosities. intrinsic colours. and ages of these stars are closely related to such an easy to determine quantity as the variability. period.," They owe their popularity to their high luminosities and photometric variability (which make them easy to identify and observe even at large distances) and the fact that the luminosities, intrinsic colours, and ages of these stars are closely related to such an easy to determine quantity as the variability period."1044 Li would be best το calibrate the Cepheid Iuminosity (PL). period-colour (PC). and period-Iuminosity-colour relations via distances based on trigonomoetric parallaxes. however. the most precisely measured. parallaxes ol even the nearest Cepehleids remain insulliciently accurate and. more importantly. they may be fraught with so far uncovered systematic errors.," It would be best to calibrate the Cepheid period-luminosity (PL), period-colour (PC), and period-luminosity-colour relations via distances based on trigonometric parallaxes, however, the most precisely measured parallaxes of even the nearest Cepeheids remain insufficiently accurate and, more importantly, they may be fraught with so far uncovered systematic errors."1045 Here the BaaceBeckerWesselink method. (BaacleL926:Decker.1940:Wesselink1946) comes in handy. because d allows the Cepheid distances (along with the physical parameters of these stars) to be inferred. thereby. providing an independent. check for the results based on geometric methods (e.g.. trigonometric and statistical parallax).," Here the Baade--Becker--Wesselink method \citep{Baa26, Beck40, Wes46} comes in handy, because it allows the Cepheid distances (along with the physical parameters of these stars) to be inferred, thereby providing an independent check for the results based on geometric methods (e.g., trigonometric and statistical parallax)."1046 However. all the so far proposed. versions of the BaaceBeckerWesselink method. (surface. brightness technique (Barnesand.Evans1976).. maximumclikelihood. technique dona 1977))) depend. in one way or another. on the adopted: reddening value.," However, all the so far proposed versions of the Baade--Becker--Wesselink method (surface brightness technique \citep{BE76}, maximum-likelihood technique \citep{B77}) ) depend, in one way or another, on the adopted reddening value."1047 Both techniques are. based. on he same astrophysical background but make use somewhat cillerent calibrations (limb-darkened surface brightness xwameter. bolometric correction — elfective. temperature air) on the normal colour.," Both techniques are based on the same astrophysical background but make use somewhat different calibrations (limb-darkened surface brightness parameter, bolometric correction – effective temperature pair) on the normal colour."1048 Here we propose a generalization of the Balona(1977) technique. which allows one to independently determine not only the stars distance and ηνποσα] parameters. but also the amount of interstellar reddening. and even calibrate the dependence of a linear combination of the bolometric correction and. effective emperature on intrinsic colour.," Here we propose a generalization of the \citet{B77} technique, which allows one to independently determine not only the star's distance and physical parameters, but also the amount of interstellar reddening, and even calibrate the dependence of a linear combination of the bolometric correction and effective temperature on intrinsic colour."1049 We now brielly outline the method., We now briefly outline the method.1050 First. the bolometric luminosity of a star at any time instant is given by the following relation. which inimeciately follows from the StefanBoltzmann law: Here L. HR. and ZY are the stars bolometric luminosity. radius. and elective temperature. respectively. ancl the subscript denotes the corresponding solar values.," First, the bolometric luminosity of a star at any time instant is given by the following relation, which immediately follows from the Stefan–Boltzmann law: Here $L$, $R$, and $T$ are the star's bolometric luminosity, radius, and effective temperature, respectively, and the $\odot$ subscript denotes the corresponding solar values."1051 Given that the bolometric absolute magnitude Mo; is related to bolometric Luminosity as we can simply derive from Eq. (, Given that the bolometric absolute magnitude $M_{bol}$ is related to bolometric luminosity as we can simply derive from Eq. (10521):,1):1053"almost completely optically thick, this suggest that the CO temperature might be higher in this side, or that the CO extends to slightly larger distances from the central star.","almost completely optically thick, this suggest that the CO temperature might be higher in this side, or that the CO extends to slightly larger distances from the central star."1054" Note, however, that the CO asymmetry might also be due to the lack of short spatial frequency in SMA observations as discussed in Section 3.."," Note, however, that the CO asymmetry might also be due to the lack of short spatial frequency in SMA observations as discussed in Section \ref{sec:res}."1055 Figure 5 shows the comparison between the observed SED and the SED of the best fitting model to the millimeter data., Figure \ref{fig:sed} shows the comparison between the observed SED and the SED of the best fitting model to the millimeter data.1056" At millimeter wavelengths, a good agreement with the observations is obtained with a grain size distribution slope q=3.5 (see,e.g.,??).. (see,e.g,?),, ?,, (seealso?).. 5,, (??).. 5)"," At millimeter wavelengths, a good agreement with the observations is obtained with a grain size distribution slope $q=3.5$ \citep[see, e.g.,][]{Ricci10,Natta04}. \citep[see, e.g,][]{Isella05}, \citet{Isella08}, \citep[see also][]{Benisty10}. \ref{fig:sed}, \citep{Vinkovic06, Mulders10}. \ref{fig:sed})"1057"). (??) (?).. (?,WheelwrightH.private"," \citep{Pietu06,Espaillat07} \citep{Mulders10}. \citep[][Wheelwright H. 1058private communication]{Wheelwright10}."1059et al.,et al.1060 2004. Casali et al.," 2004, Casali et al."1061 2006). mounted on of the Very Large Telescope (Paranal. Chile).," 2006), mounted on of the Very Large Telescope (Paranal, Chile)."1062 HAWK-I is composed of four Hawan-2RG chips. each measuring 2048x2048 pixels.," HAWK-I is composed of four Hawaii-2RG chips, each measuring 2048x2048 pixels."1063 Its pixel scale is 0.106/pixel. providing a total field of view of 7:55 x 7:55.," Its pixel scale is 0.106""/pixel, providing a total field of view of 5 x 5."1064 Observations were obtained on 2009 May 03 from 23h06 to 05h17 UT., Observations were obtained on 2009 May 03 from 23h06 to 05h17 UT.1065 The broadband Z-band filter was used Clay = |.620um. FWHM = 4m).," The broadband $H$ -band filter was used $\lambda_{\rm eff}$ = $\mu$ m, FWHM = $\mu$ m)."1066 The airmass ranged from 1.09 to 2.62 during the run and the transparency conditions were good., The airmass ranged from 1.09 to 2.62 during the run and the transparency conditions were good.1067 A total of 405 exposures. each comprising 10 integrations of ss. were obtained.," A total of 405 exposures, each comprising 10 integrations of s, were obtained."1068 We used a pattern of six Offsets. with the aim of producing an accurate sky map for each image from the neighbouring images.," We used a pattern of six offsets, with the aim of producing an accurate sky map for each image from the neighbouring images."1069 For a given offset. we kept the stars on the same pixels to minimise the effect of the small-scale spatial variations in the sensitivity of the detector chips.," For a given offset, we kept the stars on the same pixels to minimise the effect of the small-scale spatial variations in the sensitivity of the detector chips."1070 As the pomting was changed once early in the run. each star sampled a total of 12 detector positions.," As the pointing was changed once early in the run, each star sampled a total of 12 detector positions."1071 To avoid saturation of the target and reference stars. the telescope was heavily defocused. resulting in asymmetric stellar images with FWHMs of13-28”.," To avoid saturation of the target and reference stars, the telescope was heavily defocused, resulting in asymmetric stellar images with FWHMs of."1072.. In our analysis. we used only the images obtained with the QI chip. which contained1 WASP-19 and several reference stars.," In our analysis, we used only the images obtained with the $Q1$ chip, which contained WASP-19 and several reference stars."1073 After a standard pre-reduction1 (dark subtraction and flat-field division). a localised smoothing was applied to each image: the count level of each pixel was compared to the median count level of the neighbouring pixels and. if the difference exceeded a threshold of 4c” (or 30«0 for pixels belonging to stellar images). then the pixel’s count level was set to the median of its neighbours.," After a standard pre-reduction (dark subtraction and flat-field division), a localised smoothing was applied to each image: the count level of each pixel was compared to the median count level of the neighbouring pixels and, if the difference exceeded a threshold of $\sigma$ (or $\sigma$ for pixels belonging to stellar images), then the pixel's count level was set to the median of its neighbours."1074 At this stage. a sky map was constructed for and removed from each image using a median-filtered set of the adjacent images taken at different offsets.," At this stage, a sky map was constructed for and removed from each image using a median-filtered set of the adjacent images taken at different offsets."1075 For each of the 12 offsets. aperture photometry was then performed using the software (Stetson. 1987).," For each of the 12 offsets, aperture photometry was then performed using the software (Stetson, 1987)."1076 An aperture radius of 30 pixels was used., An aperture radius of 30 pixels was used.1077 A similar flux extraction was also performed on the non-sky-subtracted images and found to provide a more reliable result., A similar flux extraction was also performed on the non-sky-subtracted images and found to provide a more reliable result.1078 We attribute this to the incomplete removal of the large. asymmetric stellar images from the sky maps.," We attribute this to the incomplete removal of the large, asymmetric stellar images from the sky maps."1079 We thus decided to use the fluxes extracted from the non-sky-subtracted images in our analysis. though we did measure the sky level in an annulus and subtract it from the stellar aperture.," We thus decided to use the fluxes extracted from the non-sky-subtracted images in our analysis, though we did measure the sky level in an annulus and subtract it from the stellar aperture."1080 After a careful choice of reference stars. differential photometry was performed and a light curve was produced for each of the 12 offsets (Fig.," After a careful choice of reference stars, differential photometry was performed and a light curve was produced for each of the 12 offsets (Fig."1081 1)., 1).1082 The light curve of one offset is signifcantly poorer than the 11 others. probably because of a detector defect in the image of either WASP-19 or a reference star. and we discarded this light curve from our analysis.," The light curve of one offset is signifcantly poorer than the 11 others, probably because of a detector defect in the image of either WASP-19 or a reference star, and we discarded this light curve from our analysis."1083 For each of the 11 remaining light curves. the scatter is much larger during one half-hour period.," For each of the 11 remaining light curves, the scatter is much larger during one half-hour period."1084 This period corresponds to the minimum of the FWHM of the stellar images and to the maximum pixel value (above kKkKADU) for the target star., This period corresponds to the minimum of the FWHM of the stellar images and to the maximum pixel value (above kADU) for the target star.1085 The larger scatter in this portion of the light curves ts therefore probably caused by a non-linearity effect. and so we discarded these data.," The larger scatter in this portion of the light curves is therefore probably caused by a non-linearity effect, and so we discarded these data."1086 The 276 measurements remaining (from an original 405 measurements) after rejection are shown in Fig., The 276 measurements remaining (from an original 405 measurements) after rejection are shown in Fig.1087 1., 1.1088 Each light curve varies. differently with time. and we found that these variations are strongly correlated with the background amplitudes.," Each light curve varies differently with time, and we found that these variations are strongly correlated with the background amplitudes."1089 We chose not to simply detrend the light curves for external parameters and analyse the resulting corrected light curves., We chose not to simply detrend the light curves for external parameters and analyse the resulting corrected light curves.1090 To avoid underestimating the error bars of our final parameters. we included trend models in our global analysis (Sect. 3)).," To avoid underestimating the error bars of our final parameters, we included trend models in our global analysis (Sect. \ref{data-analysis}) )."1091 To place às many observational constraints as possible on the occultation parameters. we performed a global analysis of our HAWK-I occultation photometry combined with the 34 radial velocities (RVs) and the FTS z-band transit light curve presented m Hebb et al. (," To place as many observational constraints as possible on the occultation parameters, we performed a global analysis of our HAWK-I occultation photometry combined with the 34 radial velocities (RVs) and the FTS $z$ -band transit light curve presented in Hebb et al. ("10922010).,2010).1093 In addition. the SuperWASP transit epoch reported by Hebb et al. (," In addition, the SuperWASP transit epoch reported by Hebb et al. ("10942010) was used to constrain the orbital period of the planet.,2010) was used to constrain the orbital period of the planet.1095 These data were adopted as input of the adaptative Markov-Chain Monte Carlo (MCMC) algorithm presented in Gillon et al. (, These data were adopted as input of the adaptative Markov-Chain Monte Carlo (MCMC) algorithm presented in Gillon et al. (109620092. 2009b).,"2009a, 2009b)."1097 This MCMC implementation uses the Metropolis-Hasting algorithm (e.g.. Carlin Louis 2008) to sample the posterior probability distribution of adjusted parameters for a given model.," This MCMC implementation uses the Metropolis-Hasting algorithm (e.g., Carlin Louis 2008) to sample the posterior probability distribution of adjusted parameters for a given model."1098 Our model was based on an occulting star and a transiting planet on a Keplerian orbit about their common centre of mass., Our model was based on an occulting star and a transiting planet on a Keplerian orbit about their common centre of mass.1099 We used a classical Keplerian model for the RVs obtained outside of transit (we discarded the single RV, We used a classical Keplerian model for the RVs obtained outside of transit (we discarded the single RV1100on the detector for the source photons [rom the inner 130 arcseconds (35 kpe) around the ealaxv in this observation.,on the detector for the source photons from the inner 130 arcseconds (35 kpc) around the galaxy in this observation.1101 For observation 10530. the galaxy is 200 arcsec olf the edge of the 11/12 chips. but the aimpoint is now on the same side of the center of the array. so the conjugate point is close to the edge of the 10/12 chips.," For observation 10530, the galaxy is 200 arcsec off the edge of the I1/I3 chips, but the aimpoint is now on the same side of the center of the array, so the conjugate point is close to the edge of the I0/I2 chips."1102 But since the ealaxv is off the detector. we do not have a measurement of the source for the inner 200 areseconds (50 kpc) around the galaxy in this observation.," But since the galaxy is off the detector, we do not have a measurement of the source for the inner 200 arcseconds (50 kpc) around the galaxy in this observation."1103 For observation 10531. the galaxy is on the 13 chip. near the 12 chip. 210 arcseconds rom the aimpoint.," For observation 10531, the galaxy is on the I3 chip, near the I2 chip, 270 arcseconds from the aimpoint."1104 The conjugate point is also on the detector. on the boundary between the [0/11 chips.," The conjugate point is also on the detector, on the boundary between the I0/I1 chips."1105 So for this observation. we have measurements οἱ the source and background emission out to 270 areseconds (75 kpc}: bevond this radius the backeround and source annuli beein (o overlap.," So for this observation, we have measurements of the source and background emission out to 270 arcseconds (75 kpc); beyond this radius the background and source annuli begin to overlap."1106 We excluded the data bevond this radius for observation 10531 for the rest of the analvsis. but did also repeat (hie analvsis with these points included. aud found Chat Chev have no effect on the results since the halo emission has disappeared by 50 or GO kpc.," We excluded the data beyond this radius for observation 10531 for the rest of the analysis, but did also repeat the analysis with these points included, and found that they have no effect on the results since the halo emission has disappeared by 50 or 60 kpc."1107 This vielded similar backgrounds| to the results of the modeling for 10528 and 10530. but the results were much better for 10529 and 10531. so we adopted this approach for the rest of the analvsis.," This yielded similar backgrounds to the results of the modeling for 10528 and 10530, but the results were much better for 10529 and 10531, so we adopted this approach for the rest of the analysis."1108 To help verily the reliability of (his technique. we also tested the conjugate technique 90° on either side of the source. and obtained zero signal.," To help verify the reliability of this technique, we also tested the conjugate technique $^{\circ}$ on either side of the source, and obtained zero signal."1109 It is critically important to be sure we are measuring the hot diffuse emission and not a collection. of N-rav. binaries in and around the galaxy. whose surface density also falls olf with radius like the halo gas.," It is critically important to be sure we are measuring the hot diffuse emission and not a collection of X-ray binaries in and around the galaxy, whose surface density also falls off with radius like the halo gas."1110 The first step to ensuring a clean measurement is the automated point source removal using WAVDETECT. described above. which removed six point sources within the inner 50 arcseconds. with the faintest point source having a luminosity of Logsge~3xLO eres lif at the assumed distance of 56 Mpc.," The first step to ensuring a clean measurement is the automated point source removal using WAVDETECT, described above, which removed six point sources within the inner 50 arcseconds, with the faintest point source having a luminosity of $ L_{\text{0.6-2 keV}} \sim 3\times10^{38}$ erg $^{-1}$ if at the assumed distance of 56 Mpc."1111 One of these »oint sources falls on the egalactic nucleus. which hosts a low-Iuminositv AGN (Roberts and Warwick 2000) for which we measured a luminosity of LxLO! erg sf.," One of these point sources falls on the galactic nucleus, which hosts a low-luminosity AGN (Roberts and Warwick 2000) for which we measured a luminosity of $1\times10^{40}$ erg $^{-1}$."1112 To estimate (he contribution of point source emission lo the surlace brightness prolile. we exlracted and reduced ai image of the 2-6 keV emission. using (he identical procedure as we used for the 0.6-2 keV images.," To estimate the contribution of point source emission to the surface brightness profile, we extracted and reduced an image of the 2-6 keV emission, using the identical procedure as we used for the 0.6-2 keV images."1113 We expect no contribution from the <1 keV gas in (his higher-energv. band. so all the emission should come from point sources in the galaxy or the background.," We expect no contribution from the $< 1$ keV gas in this higher-energy band, so all the emission should come from point sources in the galaxy or the background."1114 Using (he in-fiekl conjugate subtraction technique. we subtracted the backeround emission aud derived radial surface brightness profiles for the 2-6 keV. galactic enussion.," Using the in-field conjugate subtraction technique, we subtracted the background emission and derived radial surface brightness profiles for the 2-6 keV galactic emission."1115 We attributed all this emission (to unresolved point sources., We attributed all this emission to unresolved point sources.1116the primary source term in eq (??)).,the primary source term in eq \ref{eq:pert}) ).1117 Therefore. ὃρε decrease rapidly. more than it would for wpgz~—1.," Therefore, $\dlt$ decrease rapidly, more than it would for $\ww \sim -1$."1118" When the equation of state transitions from Ww,=—O.1 to woΞ--1.0 at a;=0.2. the source term —3H(e2pp—wpip becomes larger and therefore the decreasing pj starts to increase. though not fast enough to change signs again. as seen in figure |. (e)."," When the equation of state transitions from $\wm = -0.1$ to $\w = -1.0$ at $a_t = 0.2$, the source term $-3 \HH (\cs - \ww) \dlt$ becomes larger and therefore the decreasing $\dlt$ starts to increase, though not fast enough to change signs again, as seen in figure \ref{fig:example}1119 (e)."1120" dp is therefore still of opposite sign to 6,,. but less negative than for a ρε=constant——1 ease."," $\dlt$ is therefore still of opposite sign to $\delta_m$, but less negative than for a $\ww = {\rm constant} \sim -1$ case."1121 Thus the ISW contribution is decreased from what it would be in the no perturbation case. but still is larger than that for the ACDM model. while the matter perturbations at low Κ. which source the through 21+irp.)W’. become smaller at late times as Wye becomes more negative.," Thus the ISW contribution is decreased from what it would be in the no perturbation case, but still is larger than that for the $\ld$ CDM model, while the matter perturbations at low $k$, which source the through $3(1+\ww) \Psi^{\pr}$ , become smaller at late times as $\ww$ becomes more negative."1122 Thus matter perturbations at low & for EDE models are strongly suppressed at late times as compared to ACDM. or the no perturbation case (fig 1. (f).," Thus matter perturbations at low $k$ for EDE models are strongly suppressed at late times as compared to $\ld$ CDM, or the no perturbation case (fig \ref{fig:example} (f))."1123 The change in potential ©’ in eq (??)) is therefore enhanced., The change in potential $\phi^{\pr}$ in eq \ref{eq:dpotl}) ) is therefore enhanced.1124 So effectively. we expect a strong enhancement off the transfer function and therefore the matter power spectrum at large scales (low κ).," So effectively, we expect a strong enhancement off the transfer function and therefore the matter power spectrum at large scales (low $k$ )."1125 Thus the matter power spectrum at late times. when normalized at low Κ. would show a strong suppression on the small scales at high Κ). and this suppression is effected due to the variation of the equation of state.," Thus the matter power spectrum at late times, when normalized at low $k$, would show a strong suppression on the small scales at high $k$ ), and this suppression is effected due to the variation of the equation of state."1126 The effect of can be understood also from the scalar field formalism., The effect of can be understood also from the scalar field formalism.1127 From eq (??)). the scalar field Q can be viewed as a fluid with comoving Jeans mode given by the curvature of the potential. i.e. the mass of the field. ky2ανα/dQ-.," From eq \ref{eq:2q}) ), the scalar field $Q$ can be viewed as a fluid with comoving Jeans mode given by the curvature of the potential, i.e. the mass of the field, $k_J = a1128\sqrt{d^2V/dQ^2}$."1129 Therefore scales which corresponds to modes k«ky will collapse under gravitational instability. while modes &>&; will undergo a series of damped oscillations due to pressure waves in the quintessence fluid.," Therefore scales which corresponds to modes $k <1130k_J$ will collapse under gravitational instability, while modes $k >1131k_J$ will undergo a series of damped oscillations due to pressure waves in the quintessence fluid."1132 This has two major effects., This has two major effects.1133 Firstly. the large scale clustering of enhances the amplitude of the [SW effect in CMB at low /.," Firstly, the large scale clustering of enhances the amplitude of the ISW effect in CMB at low $l$."1134 Secondly. as a consequence of the homogeneity of of the component on small scales and the fact that the growth of the linear matter perturbations is suppressed due to the lower values of Oo. the linear matter power spectrum at small scales will have an amplitude which is smaller than in ACDM.," Secondly, as a consequence of the homogeneity of of the component on small scales and the fact that the growth of the linear matter perturbations is suppressed due to the lower values of $\omt$, the linear matter power spectrum at small scales will have an amplitude which is smaller than in $\ld$ CDM."1135 We thus expect that on the very large scales (&<ky ) the dark energy clustering enhances the matter power spectrum compared to the unclustered case. while on small scales (&7ky ) the opposite occurs.," We thus expect that on the very large scales $k < k_J$ ) the dark energy clustering enhances the matter power spectrum compared to the unclustered case, while on small scales $k > k_J$ ) the opposite occurs."1136 If we CMB normalize the matter power spectrum normalize it at large scales). the small scale matter power spectrum will show a stronger suppression of power than in the no case. thus giving a smaller value of σε at present.," If we CMB normalize the matter power spectrum normalize it at large scales), the small scale matter power spectrum will show a stronger suppression of power than in the no case, thus giving a smaller value of $\sig$ at present."1137 Fig 2. (a). (b) show the CMB Cy's and the matter power spectrum at z20 normalized to CMB for the DE model.," Fig \ref{fig:obs} (a), (b) show the CMB $C_l$ 's and the matter power spectrum at $z = 0$ normalized to CMB for the DE model."1138 As expected from the arguments in the previous paragraphs. we see that there is a slight shift in the CMB peak position as well as enhanced power at low / for the DE model as compared to ACDM.," As expected from the arguments in the previous paragraphs, we see that there is a slight shift in the CMB peak position as well as enhanced power at low $l$ for the DE model as compared to $\ld$ CDM."1139 The main effect is at low /. a region which is cosmic variance limited. therefore difficult to rule out observationally.," The main effect is at low $l$ , a region which is cosmic variance limited, therefore difficult to rule out observationally."1140 For the matter power spectrum. as expected. there is a small suppression of power at high & (since the normalization is done at low &).," For the matter power spectrum, as expected, there is a small suppression of power at high $k$ (since the normalization is done at low $k$ )."1141 The value of os in the no case Is 0.79. while that in the perturbed case Is σε=0.80. and that for ACDM is oy20.82.," The value of $\sig$ in the no case is $\sig = 0.79$ , while that in the perturbed case is $\sig1142= 0.80$, and that for $\ld$ CDM is $\sig = 0.82$."1143 Neither the effect on CMB nor that on the matter power spectrum is in itself good enough to rule out the DE model. even for the case where DE perturbations have been accounted for.," Neither the effect on CMB nor that on the matter power spectrum is in itself good enough to rule out the DE model, even for the case where DE perturbations have been accounted for."1144 For the EDE model. as seen in fig 2. (c) (d). the non-perturbative case shows effect mostly in the low / regime through the ISW effect. which is cosmic variance limited.," For the EDE model, as seen in fig \ref{fig:obs}1145 (c) (d), the non-perturbative case shows effect mostly in the low $l$ regime through the ISW effect, which is cosmic variance limited."1146 The results for the matter power spectrum today also show a very slight difference from the cosmological constant., The results for the matter power spectrum today also show a very slight difference from the cosmological constant.1147 These results appear to suggest that just the non-perturbative effects of are not sufficient to discriminate this EDE model from ACDM. especially if we factor in degeneracies with other cosmological parameters. such as Ho.," These results appear to suggest that just the non-perturbative effects of are not sufficient to discriminate this EDE model from $\ld$ CDM, especially if we factor in degeneracies with other cosmological parameters, such as $H_0$."1148 When we consider the perturbative case. the ISW effect is actually muted. however. there is a slightly larger shift in the CMB peak position. (see inset of fig 1. (¢)) which is a tightly constrained observable.," When we consider the perturbative case, the ISW effect is actually muted, however, there is a slightly larger shift in the CMB peak position, (see inset of fig \ref{fig:example} (c)) which is a tightly constrained observable."1149 The matter power spectrum at present shows a stronger suppression at small scales which leads to à much smaller value of 0.69 (as compared to the non-perturbative case. where 0.81. which is close to the ACDM value).," The matter power spectrum at present shows a stronger suppression at small scales which leads to a much smaller value of $\sig = 0.69$ (as compared to the non-perturbative case, where $\sig = 0.81$ , which is close to the $\ld$ CDM value)."1150 Thus. although the background expansion of this model is very similar to ACDM at late times. its early time behaviour leaves signatures for discriminating it from the ACDM model provided the are accounted for properly.," Thus, although the background expansion of this model is very similar to $\ld$ CDM at late times, its early time behaviour leaves signatures for discriminating it from the $\ld$ CDM model provided the are accounted for properly."1151 The effect of adding the 1s seen in fig 2 (e). (f) for both DE and ΕΡΕ. models.," The effect of adding the is seen in fig \ref{fig:obs} (e), (f) for both DE and EDE models."1152 In obtaining the scalar Cjs. for the DE model. there ts a fairly large difference at low /. while at high / the perturbed anc non-perturbed models behave similarly.," In obtaining the scalar $C_l$ s, for the DE model, there is a fairly large difference at low $l$, while at high $l$ the perturbed and non-perturbed models behave similarly."1153 For the EDE model. there 1s a large difference at low /. and also a significant difference at the higher /s. For the matter power spectrum today. the EDE model shows a larger difference in in the perturbed and non-perturbed case.," For the EDE model, there is a large difference at low $l$, and also a significant difference at the higher $l$ s. For the matter power spectrum today, the EDE model shows a larger difference in in the perturbed and non-perturbed case."1154 Thus. a model close to ACDM today as also in the past (as in the DE model chosen) would be difficult to discriminate from ACDM from current observatiors. but a model with a different expansion history m the past. even if it is very similar to ACDM today (such as the EDE 1nodel). could be discriminated using the perturbative observatiois such as CMB and the matter power spectrum provided the are not neglected.," Thus, a model close to $\ld$ CDM today as also in the past (as in the DE model chosen) would be difficult to discriminate from $\ld$ CDM from current observations, but a model with a different expansion history in the past, even if it is very similar to $\ld$ CDM today (such as the EDE model), could be discriminated using the perturbative observations such as CMB and the matter power spectrum provided the are not neglected."1155 These results are commensurate with those found in (Maetal.1999) where constart equation of state models of were considered. ad those in (Alimietαἱ.2009).. where quintessence models of were studied.," These results are commensurate with those found in \citep{pert1} where constant equation of state models of were considered, and those in \citep{pert11}, where quintessence models of were studied."1156 We note here that. since in addition to the ISW effect. dark energy also makes itself felt in a shift of the CMB first peak position. we expect that the parameters may be degenerate with OI? if the flatness condition is removed in the analysis.," We note here that, since in addition to the ISW effect, dark energy also makes itself felt in a shift of the CMB first peak position, we expect that the parameters may be degenerate with $\omk h^2$ if the flatness condition is removed in the analysis."1157 We study the effect of curvature on the scalar Cy's in figure 3.., We study the effect of curvature on the scalar $C_l$ 's in figure \ref{fig:curv}.1158 A non-flat ACDM model will differ from a flat ACDM model with all other parameters identical mainly in a shift of the peak positions., A non-flat $\ld$ CDM model will differ from a flat $\ld$ CDM model with all other parameters identical mainly in a shift of the peak positions.1159" Figure 3. shows this shift for à XCDM model with Q,,20.06.", Figure \ref{fig:curv} shows this shift for a $\ld$ CDM model with $\omk = 0.06$.1160" An EDE model with wo2—0.65.,,0.1.0;=0.2.A, 20.1. and a curvature O,=0.06 is also shown."," An EDE model with $\w = -0.65, \wm = -0.1, \at =11610.2, \dt = 0.1$ , and a curvature $\omk = 0.06$ is also shown."1162 For the EDE model. the dark energy component compensates for the curvature of the universe. thus the peak position 1s the same as for the flat XCDM model.," For the EDE model, the dark energy component compensates for the curvature of the universe, thus the peak position is the same as for the flat $\ld$ CDM model."1163 However. as seen in the previous paragraphs. EDE manifests itself not only in the shift of the peaks. but also in the shape of the peaks and in the low-/ [SW effect.," However, as seen in the previous paragraphs, EDE manifests itself not only in the shift of the peaks, but also in the shape of the peaks and in the $l$ ISW effect."1164 In this example. the height of the first peak is different for the EDEmodel. as is the low / behaviour. rendering it distinct from the flat XCDM model.," In this example, the height of the first peak is different for the EDEmodel, as is the low $l$ behaviour, rendering it distinct from the flat $\ld$ CDM model."1165 Thus. although we expect some degeneracy betweenthe parameters and the curvature. this degeneracy is not very strong. since both the position and the height of the first peak are strongly constrained by current CMB data.," Thus, although we expect some degeneracy betweenthe parameters and the curvature, this degeneracy is not very strong, since both the position and the height of the first peak are strongly constrained by current CMB data."1166 We first study the results using only the CMB data., We first study the results using only the CMB data.1167 The primary parameters to be varied are the standard CMB, The primary parameters to be varied are the standard CMB1168a small bullet on a much larger target.,a small bullet on a much larger target.1169 Initially the bullet would transfer most of its energy to a volume the size of itself at the impact site: much of this energv would escape from the site via a small amount of fast ejecta. though some would propagate through the target as a shock.," Initially the bullet would transfer most of its energy to a volume the size of itself at the impact site; much of this energy would escape from the site via a small amount of fast ejecta, though some would propagate through the target as a shock."1170" somewhal more quantitatively, we can think of a collision between a very small bullet and a large target as a point explosion on the planar surface between a vacuum and a space filled with matter."," Somewhat more quantitatively, we can think of a collision between a very small bullet and a large target as a point explosion on the planar surface between a vacuum and a half-infinite space filled with matter."1171 The analogous explosion in a uniform infinite material leads to the Sedov-Tavlor blast wave. a sell-similar solution of the first (wpe in which total energy is conserved as the spherical shock propagates (?2?)..," The analogous explosion in a uniform infinite material leads to the Sedov-Taylor blast wave, a self-similar solution of the first type in which total energy is conserved as the spherical shock propagates \citep{sedov46,taylor50}."1172 By contrast. a point explosion in a hal[-infinite space is a self-similar solution of the second twpe (2): the shock moving into the half-space must lose energy. as some of the shocked material Lows into the vacuum.," By contrast, a point explosion in a half-infinite space is a self-similar solution of the second type \citep{zeldovich67}; the shock moving into the half-space must lose energy as some of the shocked material flows into the vacuum."1173 Also. the nonzero pressure increases (he momentum in the shock.," Also, the nonzero pressure increases the momentum in the shock."1174 So as the shock propagates. its velocity should fall off faster than it would have given conservation of energy but slower than jit would have in the case of momentunm conservation.," So as the shock propagates, its velocity should fall off faster than it would have given conservation of energy but slower than it would have in the case of momentum conservation."1175 We can use (hese considerations to constrain μή) scalings for catastrophic collisions., We can use these considerations to constrain $r_B(r)$ scalings for catastrophic collisions.1176 We assume that a given target is destroved if the velocity of the shock wave when it reaches the antipode of the impact site exceeds the escape velocity. (see.[orexample.?)..," We assume that a given target is destroyed if the velocity of the shock wave when it reaches the antipode of the impact site exceeds the escape velocity \cite[see, for1177example,][]{melosh94}."1178 Let the shock velocity decay as (uuX73 where x is the distance traveled by the shock.," Let the shock velocity decay as $v_{\rm1179shock}\propto x^{-\beta}$ where $x$ is the distance traveled by the shock."1180 If the enereve. in the shock were conserved. we would expect ¢=3/2/ [rom dimensional analysis: if (he monmentunr were conserved. we would expect 2=3.," If the energy in the shock were conserved, we would expect $\beta=3/2$ from dimensional analysis; if the momentum were conserved, we would expect $\beta=3$."1181" Then the actual point explosion solution must have 3/2""ο«3.", Then the actual point explosion solution must have $3/2<\beta<3$.1182 The criterion for target destruction is where we have assumed (he bullet initially deposits its energv in a volume the size of itself., The criterion for target destruction is where we have assumed the bullet initially deposits its energy in a volume the size of itself.1183 This implies The 3/2«93 condition requires 4/3<a«5/3 and 23/8<q22/1. both of which are satisfied by all of the impact simulation and dimensional analysis results.," This implies The $3/2<\beta<3$ condition requires $4/3 < \alpha < 5/3$ and $23/8<q<22/7$, both of which are satisfied by all of the impact simulation and dimensional analysis results."1184 ? mentions (hat energv and momentum conservation should represent limiting cases [ον the impact process and (hat laboratory experiments involving impacts into sand. rock. and water salisfv (hose limits.," \citet{holsapple94}1185 mentions that energy and momentum conservation should represent limiting cases for the impact process and that laboratory experiments involving impacts into sand, rock, and water satisfy those limits."1186 Note that the range in q found in previous studies. 2.95<qx 3.11. spans most of the allowed range for q.," Note that the range in $q$ found in previous studies, $2.95\leq q\leq 3.11$ , spans most of the allowed range for $q$."1187 This suggests that the catastrophic impact process and a depend on more specific details of the collisionssuch as the equation of state., This suggests that the catastrophic impact process and $\alpha$ depend on more specific details of the collisionssuch as the equation of state.1188scaes during the whole free fall. whereas for ¢=0.0 the index becomes. ó20. over the whole dynamical range. durug a period of —.r7g.,"scales during the whole free fall, whereas for $a=0.0$ the index becomes, $\delta>0$, over the whole dynamical range, during a period of $\sim 0.71189\tau_{\rm ff}$."1190 That is. 350 AZ; are not suffideut to develop πα scale phase-space correlations in a dissipatiouless svstei.," That is, 350 $M_{\rm J}$ are not sufficient to develop small scale phase-space correlations in a dissipationless system."1191 Iu order to show the dependence of the result ou the initial Poisson noise. the absolutely cold simulation with Vo=160000 is compared with a Vo= 32000-body sn," In order to show the dependence of the result on the initial Poisson noise, the absolutely cold simulation with $N=160000$ is compared with a $N=32000$ -body simulation."1192As. above. it follows ⋅⋅⋅that the initial roughucss⋜↧≻⋉∖⋜∐⋅↕∐↖∩⊾↕∐⋯∐↴∖↴↖↽↴∖↴↑↸∖⋯↴∖↴∪↥⋅↕∐↴∖↴↖↽↴∖↴↑↸∖⋯↴∖↴↖↖⇁↕↑∐↖⇁↸∖↥⋅↖↽↸∖∎↸∖↸⊳↑↕↖↽↸∖ ! ofthe two svstenis ciffers⋅⋅ by a factor. ~a.2.2.," As above, it follows that the initial roughness of the two systems differs by a factor $\sim11932.2$."1194 Fig., Fig.1195 lí shows that the non-equilibenuu structures LOSIuting form the simulations with equal & but unequal particle nuniber differ from cach other during the whole free fall., \ref{ff_1} shows that the non-equilibrium structures resulting form the simulations with equal $a$ but unequal particle number differ from each other during the whole free fall.1196 Indeed. during the first half ofthe free fall tune the two initial conditions produce velocitycorrelations that differ ou small and large scales.," Indeed, during the first half of the free fall time the two initial conditions produce velocitycorrelations that differ on small and large scales."1197 After f=(0.5τη the differences approximately disappear., After $t=0.5\;\tau_{\rm ff}$ the differences approximately disappear.1198 However. the behavior of the spatial correlations (see lower panels of Fig. 17))," However, the behavior of the spatial correlations (see lower panels of Fig. \ref{ff_1}) )"1199 is inverse. meaning that differing spatial correlations appear after 0.5mg and persist for the rest 9 the free fall.," is inverse, meaning that differing spatial correlations appear after $0.5\;\tau_{\rm ff}$ and persist for the rest of the free fall."1200 These results suggest that non-equilibrium structures Dou ⋅ ulation. enerev dissipation depend more strongly ou initial. noise than those appearing iu warn svstenis with less effective dissipation (sce also Fig. 15))., These results suggest that non-equilibrium structures appearing in cold systems or in systems with very effective energy dissipation depend more strongly on initial noise than those appearing in warm systems with less effective dissipation (see also Fig. \ref{mf2_1}) ).

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