ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" We compare, first, the SFRs to the binned rate we obtained by inverting the data (see Figure 9)) and we calculate the \? for both 1/3 and 1/2 binning."," We compare, first, the SFRs to the binned rate we obtained by inverting the data (see Figure \ref{fig:SFRsplot}) ) and we calculate the $\chi^2$ for both $1/3$ and $1/2$ binning."3 We find acceptable reduced \? values (see Table 4)) for all the functions., We find acceptable reduced $\chi^2$ values (see Table \ref{tbl:SFRsstats}) ) for all the functions.4" However, a comparison of the overall observed redshift and luminosity distributions with those predicted by models in which the GRB rate is fixed by a given SFR reveals that the 2D K-S or the K-S tests for the peak flux and the redshift distributions show inconsistency for the first three functions (ΗΒ. PM SF2, R-R)."," However, a comparison of the overall observed redshift and luminosity distributions with those predicted by models in which the GRB rate is fixed by a given SFR reveals that the 2D K-S or the K-S tests for the peak flux and the redshift distributions show inconsistency for the first three functions (HB, PM SF2, R-R)."5" We find, however, consistency for the last one (B09)."," We find, however, consistency for the last one (B09)."6" Next, we optimize the for a given SFR."," Next, we optimize the for a given SFR."7 We take the GRB rate as known following a model of the SFR and obtain the best fit by solving equation 12.., We take the GRB rate as known following a model of the SFR and obtain the best fit by solving equation \ref{eqn:lumf}.8 We now perform a 2D K-S test as well as K-S tests for the peak flux distribution and for the redshift distribution., We now perform a 2D K-S test as well as K-S tests for the peak flux distribution and for the redshift distribution.9 The results of the statistical tests are shown in Table 4.., The results of the statistical tests are shown in Table \ref{tbl:SFRsstats}.10 Even though the fit improves still the first three SFR models fail the KS tests., Even though the fit improves still the first three SFR models fail the KS tests.11" The last SFR model (B09) is, of course, consistent."," The last SFR model (B09) is, of course, consistent."12 We attribute the consistency of the GRB rate with the B09 SER model but not with the first, We attribute the consistency of the GRB rate with the B09 SFR model but not with the first13Kyus IS a reliable distance indicator for globular clusters with known metal content and HB type.,$k_{puls}$ is a reliable distance indicator for globular clusters with known metal content and HB type.14" We wish to mention that the occurrence of a Period-Luminosity-Amplitude relation for RR,» stars was originally suggested by Sandage (1981a.b) and that the present use of detailed evolutionary and pulsational predictions provides the opportunity to constrain the dependence on the globular cluster HB type and metal content."," We wish to mention that the occurrence of a Period-Luminosity-Amplitude relation for $_{ab}$ stars was originally suggested by Sandage (1981a,b) and that the present use of detailed evolutionary and pulsational predictions provides the opportunity to constrain the dependence on the globular cluster HB type and metal content."15 On this ground. we find that the RR; in Ool clusters and in Ooll clusters with HB types bluer than +0.8 do obey to well defined νι relations.," On this ground, we find that the $_{ab}$ in OoI clusters and in OoII clusters with HB types bluer than +0.8 do obey to well defined $M_V$ $k_{puls}$ relations."16" In particular. we find and while the RR,, in Ooll clusters with moderately blue HB morphology present. at fixed &j,,. a zero-point that is ~ 0.05 mag brighter."," In particular, we find and while the $_{ab}$ in OoII clusters with moderately blue HB morphology present, at fixed $k_{puls}$, a zero-point that is $\sim$ 0.05 mag brighter."17" Regarding the variables in the solar neighborhood. additional pulsation models with //H,,=1.5 and Z >0.006 together with the predicted metallicity dependence of the mass of metal-rich ({Fe/H]> —1.0) RR Lyrae stars yield with —1.0 <|Pe/H]< —0.5 and with —0.5 <|Fe/H]<0."," Regarding the variables in the solar neighborhood, additional pulsation models with $l/H_p$ =1.5 and $Z>$ 0.006 together with the predicted metallicity dependence of the mass of metal-rich $\ge-$ 1.0) RR Lyrae stars yield with $-1.0\le$ $\le -$ 0.5 and with $-0.5\le$ $\le$ 0."18" Once the PA,-based absolute magnitude M\(RR) is derived. the resulting correlation with the globular cluster metallicity [Fe/H], has a slope of 0.2020.06 mag dex. regardless of the adopted mixing-length parameter. while the zero-point changes from 0.9440.10 to 0.82+0.10 mag when using pulsation models constructed by assuming a mixing length parameter //H,,—1.5 and //H,=2.0. respectively."," Once the $PA_V$ -based absolute magnitude $M_V$ (RR) is derived, the resulting correlation with the globular cluster metallicity $_K$ has a slope of $\pm$ 0.06 mag $^{-1}$, regardless of the adopted mixing-length parameter, while the zero-point changes from $\pm$ 0.10 to $\pm$ 0.10 mag when using pulsation models constructed by assuming a mixing length parameter $l/H_p$ =1.5 and $l/H_p$ =2.0, respectively."19 However. the inclusion of the metal-rich field variables vields that over the total metallicity range from [Fe/H-2.5 to ~ the relation becomes quadratic as in agreement with the results presented by by Bono et al. (," However, the inclusion of the metal-rich field variables yields that over the total metallicity range from $-$ 2.5 to $\sim$ the relation becomes quadratic as in agreement with the results presented by by Bono et al. ("202003) and Sandage (2006).,2003) and Sandage (2006).21" Finally. in order to constrain the most appropriate value of the mixing-length parameter. we adopt the RR,, stars in co Cen. but the PAy-based true distance moduli. fo=13.6840.09 mag for //H, 21.5 and 13.80x0.09 mag for //H, 22.0. agree within Io with the distance 44:5,213.7550.04. mag based on the eclipsing binary OGLEGC-17 (Thompson et al."," Finally, in order to constrain the most appropriate value of the mixing-length parameter, we adopt the $_{ab}$ stars in $\omega$ Cen, but the $PA_V$ -based true distance moduli, $\mu_0$ $\pm$ 0.09 mag for $l/H_p$ =1.5 and $\pm$ 0.09 mag for $l/H_p$ =2.0, agree within $\sigma$ with the distance $\mu_0$ $\pm0.04$ mag based on the eclipsing binary OGLEGC-17 (Thompson et al."22 2001: Kaluzny et al., 2001; Kaluzny et al.23 2002)., 2002).24 Therefore. we adopt the FOBE method that provides cluster apparent distance moduli which decrease with increasing the mixing-length parameter.," Therefore, we adopt the FOBE method that provides cluster apparent distance moduli which decrease with increasing the mixing-length parameter."25" Eventually. we find that distance estimates based on the PAy and on the FOBE method agree for an intermediate mixing-length parameter. namely //H,,~ 1.7."," Eventually, we find that distance estimates based on the $PA_V$ and on the FOBE method agree for an intermediate mixing-length parameter, namely $l/H_p\sim$ 1.7."26 — E= μή] wherevp is the velocity of radial motion of the outside medium., - )^2= ] where$v_0$ is the velocity of radial motion of the outside medium.27 We assume highly supersonic flows ancl neglect for simplicity the ciffereuce between the ram aud the post-shock thermal pressures Below we refer to Eq. (2)), We assume highly supersonic flows and neglect for simplicity the difference between the ram and the post-shock thermal pressures Below we refer to Eq. \ref{Komp}) )28 as the lxoimpaneets equation., as the Kompaneets equation.29 It describes the evolution of non-spherical shocks with energy supply., It describes the evolution of non-spherical shocks with energy supply.30 The Wompaneets equation (2)) shows that uou-sphericity of the expauding shock at a given uoument cepeucds both ou the anisotropic driving (η(0) teri)end collimating effects of the stellar uaterial - the term in parenthesis. which wader certain coucditious tends to amplify non-sphericity. (," The Kompaneets equation \ref{Komp}) ) shows that non-sphericity of the expanding shock at a given moment depends both on the anisotropic driving $L_{\rm iso}(\theta)$ term) collimating effects of the stellar material - the term in parenthesis, which under certain conditions tends to amplify non-sphericity. ("31We asstune that the density. distribution is sphericallysyiumetric).,We assume that the density distribution is sphericallysymmetric).32 Most importantly. Eq. (2))," Most importantly, Eq. \ref{Komp}) )"33 is ion-linear aud tucer certain conditions even a small anisotropy driven by either the luminosity of he central source or by the initial non-sphlierical shape of the shock cau be amplified aud may lead o formation of highly collimated jets., is non-linear and under certain conditions even a small anisotropy driven by either the luminosity of the central source or by the initial non-spherical shape of the shock can be amplified and may lead to formation of highly collimated jets.34 This is incleed what Lappeus in a steep deusity part of the yost-SN shock profile of a star., This is indeed what happens in a steep density part of the post-SN shock profile of a star.35 Interaction of the SN ejecta with the stellar envelope have been cousidered by ???..," Interaction of the SN ejecta with the stellar envelope have been considered by \cite{Chevalier82,Nadezhyn85,TrueloveMcKee}."36 After the SN shock passed through the progenitor star. it Creates an expanidiug SNR with expansion velocity linearly increasing with distance. ryty=t where rj=vol is the outer radius of ejecta freely expanding with velocity eo.," After the SN shock passed through the progenitor star, it creates an expanding SNR with expansion velocity linearly increasing with distance, v= v_0 = where $r_0 = v_0 t$ is the outer radius of ejecta freely expanding with velocity $v_0$."37 The density structure consists of a nearly coustaut deusity core. aud an euvelope with a steep cleusity profile created by the SN shock breakout from the surface of the progenitor.," The density structure consists of a nearly constant density core, and an envelope with a steep density profile created by the SN shock breakout from the surface of the progenitor."38 If. we asstume sell-similar expansion. so that at each moment the relative size of tlie core remiaius coustant. reΞero=eto. aud that the envelope density profile is a power law px r7. the deusity at time / is p= gfr|," If we assume self-similar expansion, so that at each moment the relative size of the core remains constant, $r_c = \eta_c r_0= \eta_c v_0 t$, and that the envelope density profile is a power law $\rho \propto r^{-\om}$ , the density at time $t$ is = g(r)"39As an indicator of dust abundance. we take dust-to-gas ratio.,"As an indicator of dust abundance, we take dust-to-gas ratio."40" For the gas mass. we adopt gas mass Vg estimated from 21 em emission, observations."," For the gas mass, we adopt gas mass $M_\mathrm{H\, I}$ estimated from 21 cm emission observations."41" The data of Ag, are already compiled by HO8 for the common sample tthe latter seven BCDs in Table 2)."," The data of $M_\mathrm{H\, I}$ are already compiled by H08 for the common sample the latter seven BCDs in Table \ref{tab:mdust}) )."42 Among the newly added sample. there is no available data for UM 420 and Mrk 59. while the data for Mrk 487 and SBS 13194579 are obtained from Hopkins.Schulte-Ladbeck.&Drozdovsky(2002) and Huchtmeieretal.(2007). respectively (for the latter. we used the formula in Lisenfeld&Ferrara1998 to convert the flux to Λη τ).," Among the newly added sample, there is no available data for UM 420 and Mrk 59, while the data for Mrk 487 and SBS 1319+579 are obtained from \citet*{hopkins02} and \citet{huchtmeier07}, respectively (for the latter, we used the formula in \citealt{lisenfeld98} to convert the flux to $M_\mathrm{H\, I}$ )."43" The dust-to-gas ratio PD is defined as D.= AMaf/AMgt,."," The dust-to-gas ratio $\mathcal{D}$ is defined as $\mathcal{D}\equiv M_\mathrm{d}/M_\mathrm{H\, I}$ ."44 We adopt AZ467.=1) for the dust mass. but the following discussion does not change if we adopt M4(.7=2).," We adopt $M_\mathrm{d}(\beta =1)$ for the dust mass, but the following discussion does not change if we adopt $M_\mathrm{d}(\beta =2)$."45 i, Fig.46" shows the relations between FIR colour ((60/100). or ( 140/100),1) and dust-to-gas ratio.", \ref{fig:dg_clr} shows the relations between FIR colour $(60/100)_\mathrm{cl}$ or $(140/100)_\mathrm{cl}$ ) and dust-to-gas ratio.47 We observe correlations with correlation coefficients ——0.65 for the log(60/100). οςD relation and +0.50 for the los( 1H0/100).4-10&P relation., We observe correlations with correlation coefficients $r=-0.65$ for the $\log (60/100)_\mathrm{cl}$ $\log\mathcal{D}$ relation and $r=0.89$ for the $\log (140/100)_\mathrm{cl}$ $\log\mathcal{D}$ relation.48 These correlations indicate that the dust temperature tends to be high in dust-poor objects., These correlations indicate that the dust temperature tends to be high in dust-poor objects.49 We present not only the sample BCDs but also the data of the Milky Way. the LMC and the SMC.," We present not only the sample BCDs but also the data of the Milky Way, the LMC and the SMC."50 The dust-to-gas ratio of the Milky Way is assumed to be 0.006 1978).. while the dust-to-gas ratios of the LMC and the SMC are assumed to be 1/3 and 1/5 times of the value of the Milky Way 1992).," The dust-to-gas ratio of the Milky Way is assumed to be 0.006 \citep{spitzer78}, while the dust-to-gas ratios of the LMC and the SMC are assumed to be 1/3 and 1/5 times of the value of the Milky Way \citep{pei92}."51 For the FIR colours. we adopt the peak of the contours in for the Milky Way. and the average of the data points for the LMC andthe SMC.," For the FIR colours, we adopt the peak of the contours in \\ref{fig:clrdat}52 for the Milky Way, and the average of the data points for the LMC andthe SMC."53 Those three points also follow the trend found by the BCDs., Those three points also follow the trend found by the BCDs.54 A possible interpretation of the correlation in reftig:dg Fristhatlherelativelylowdustltempoeraluresindusl richDC Dsresull fromtheshieldinglertinetion of stellarradiatlion, A possible interpretation of the correlation in \\ref{fig:dg_clr} is that the relatively low dust temperatures in dust-rich BCDs result from the shielding (extinction) of stellar radiation.55ef pes lealal μα by using the models (same as ," In order to examine this possibility, we calculate the relation between FIR colours and $A_V$ by using the models (same as )."56"Pheresullsareshowninf'ig. caeherewefindlhalbolhthevarialionofte0/ VOOY4 and that of (1H0/100), with a single value of \ are too small to explain the observed large diversity in these colours in reftig:dg,Fi."," The results are shown in \\ref{fig:Av_clr}, where we find that both the variation of $(60/100)_\mathrm{cl}$ and that of $(140/100)_\mathrm{cl}$ with a single value of $\chi$ are too small to explain the observed large diversity in these colours in \\ref{fig:dg_clr}."57 PF hecoloursacrenolsosensitivetothechangeof Ax parly because the strongest contribution from sly)~0. where the dust temperature is the highest. is always present.," The colours are not so sensitive to the change of $A_V$ partly because the strongest contribution from $A_V\sim 0$, where the dust temperature is the highest, is always present."58 In particular. if elyο2. the colour is insensitive to ly: since the dust temperature at such deep optical depths is too low to contribute to the total emission.," In particular, if $A_V\ga 2$, the colour is insensitive to $A_V$ since the dust temperature at such deep optical depths is too low to contribute to the total emission."59 Thus. the variation of the FIR colours cannot be reproduced only with a variation of dust optical depth. but rather it should reflect he correlation 4) between dust-to-gas ratio and dust heating itsef (re. ISRF). or (tii) between dust-to-gas raio and dust properties (1.e.. absorption coefficient and/or grain size distribution).," Thus, the variation of the FIR colours cannot be reproduced only with a variation of dust optical depth, but rather it should reflect the correlation (i) between dust-to-gas ratio and dust heating itself (i.e., ISRF), or (ii) between dust-to-gas ratio and dust properties (i.e., absorption coefficient and/or grain size distribution)."60 It is difficult to survey all the possible cases for (i). since there are few. if any. constraints on the dust properties in BCDs.," It is difficult to survey all the possible cases for (ii), since there are few, if any, constraints on the dust properties in BCDs."61 However. we can discuss some cases for Gi) as follows.," However, we can discuss some cases for (ii) as follows."62 HHS07 show that (140/100)... changes only slightly along with the change of grain size distribution. since it reflects the equilibrium grain emperature.," HHS07 show that $(140/100)_\mathrm{cl}$ changes only slightly along with the change of grain size distribution, since it reflects the equilibrium grain temperature."63" Thus. it is hard to reproduce the clear correlation between (1207100), and dust-to-gas ratio only with the change of grain size distribution."," Thus, it is hard to reproduce the clear correlation between $(140/100)_\mathrm{cl}$ and dust-to-gas ratio only with the change of grain size distribution."64 The change of grain material as a function of dust-to-gas ratio may change the grain absorption coefficient. eading to variation of dust temperature as a function of dust-to-gas ratio.," The change of grain material as a function of dust-to-gas ratio may change the grain absorption coefficient, leading to variation of dust temperature as a function of dust-to-gas ratio."65 However. we have shown that the colour-eolour relation of he BCDs can be explained by the emissivity that also explains the colour-colour relation of the Milky Way.," However, we have shown that the colour–colour relation of the BCDs can be explained by the emissivity that also explains the colour–colour relation of the Milky Way."66 In this context. it is nof orobable that the dust property is the main driver for the change of FIR colours.," In this context, it is not probable that the dust property is the main driver for the change of FIR colours."67 The possibility (1) is interesting. to investigate. since the correlation in end," The possibility (i) is interesting to investigate, since the correlation in \\ref{fig:dg_clr} is a natural extension of the sequence of the Milky Way, the LMC, and the SMC."68s ΤΠ has ΙΙ gasral," For those “nearby” three galaxies, it is known that the typical ISRFs are different \citep[e.g.][]{welty06}, and indeed the FIR colour sequence can be explained by the variation of the ISRF \citealt{hibi06}, , HHS07)."69io.," Thus, in the following subsection, we discuss a possibility that the ISRF changes as a function of dust-to-gas ratio."70towards the CRB aud iarvacted on t1ο early hisorv of agerceatesCoco in the nebula.,towards the GRB and impacted on the early history of aggregates in the nebula.71 T1ο choudanles were combined and compacted to forum mactoorites a1 this same ]ILOCCSS should have operated throtorout the nehla aud led to the ination of the terrestrial planes auc ]ossibly the cores he eiut planets;, The chondrules were combined and compacted to form meteorites and this same process should have operated throughout the nebula and led to the formation of the terrestrial planets and possibly the cores of the giant planets.72 The ΙΙ o 27 ALI is close to the nount estimated (30-LOA ) to forli he cores of tje four elaut plauets asstuine that chonudrues constituted most he mass., The minimum of 27 $\oplus$ is close to the amount estimated (30-40 $\oplus$ ) to form the cores of the four giant planets assuming that chondrules constituted most of the mass.73 However for choudzru.CS o foll he terrestrial planets. then a laver of at cast2 oο D7 was prodiced ou to a few AU. implying sieulficau easOS ¢ispersal frou the immer nebula by about :i factor of Ίθα t1ο tine of the GRB.," However for chondrules to form the terrestrial planets, then a layer of at least2 g $^{-2}$ was produced out to a few AU, implying significant gas dispersal from the inner nebula by about a factor of 10 at the time of the GRB."74 The composition of he Earth 15 1O luicolisseut wi ha complee chondrule origin because tie inner solar systeu experienced higher aubienut tenipereures than the asteroid belt aid would have been more effently cleaned of gas containiue volatile bearing dust (?).., The composition of the Earth is not inconsistent with a complete chondrule origin because the inner solar system experienced higher ambient temperatures than the asteroid belt and would have been more efficiently cleaned of gas containing volatile bearing dust \cite{hh:1996}.75 Twre Is a niajor chanec in the aerodyuauic properties on melting of the fiuffv precursor iuatcql to form choudrules with stopping times increasi18o oa factor of about 100., There is a major change in the aerodynamic properties on melting of the fluffy precursor material to form chondrules with stopping times increasing by a factor of about 100.76 Towever. tiere sects to be little cudency for them to settle to the widplane because vertica settliug requires verv low intesusities of urbuC1e (22PrT).," However, there seems to be little tendency for them to settle to the midplane because vertical settling requires very low intensities of turbulence \cite{weid:1980,vm:1991,cam3:1995}."77" Somehow the cloudsCS WOYO SIZ SOLed. xobablv by an acrodyinne process, and couceitr‘ated by a larec factor to orn plauctesimals and metesorites of size of order LOO zu."," Somehow the chondrules were size sorted, probably by an aerodynamic process, and concentrated by a large factor to form planetesimals and meteorites of size of order 100 km."78 A turbulent couccutratio Lot aLicles Las been showi to be size-seective aleL effective for partic‘les with the choudrule size distribution (?) where a uniform volue distribution of articles texd Q Vacae the ecdclics and couceitrate in stagnant zones with coucenutration Actors o order 109., A turbulent concentration of particles has been shown to be size-selective and effective for particles with the chondrule size distribution \cite{cd:1996} where a uniform volume distribution of particles tend to vacate the eddies and concentrate in stagnant zones with concentration factors of order $^{6}$.79 T1ο subsecAon evolution of 1ο dense coicentratious las not been nodelled in detail out it is probable that hey desceuded to the uicdpla and comunenced. aud continued the accretioun process of foruduug planetesinals that inchcle the meteorite went bodies., The subsequent evolution of the dense concentrations has not been modelled in detail but it is probable that they descended to the midplane and commenced and continued the accretion process of forming planetesimals that include the meteorite parent bodies.80 Subsequeut collisions nuust luerge t1c anetesiaals of size about LOO kin to orn he terrestrial auets aud cores of elaut plaucts., Subsequent collisions must merge the planetesimals of size about 100 km to form the terrestrial planets and cores of giant planets.81 The foruatiou of the cores of the eiait planets could have proceeded at a uuch faster rate than the terrestrial planet:s because the eax was cooler. ess dense and less turbuwt ancl also 16 chondrules were probably. coated with ice axd mixed with ice particles that should have significavy naproved je Μολις co-cthicicuts (2)...," The formation of the cores of the giant planets could have proceeded at a much faster rate than the terrestrial planets because the gas was cooler, less dense and less turbulent and also the chondrules were probably coated with ice and mixed with ice particles that should have significantly improved the sticking co-efficients \cite{cam3:1995}."82 These effects «Iold have PAeeded. up. the ormation of planctesimals iu he outer rebula., These effects should have speeded up the formation of planetesimals in the outer nebula.83 The composition of conets is approximate vosolar and 1ο GRB should have formed choudrules iu ti6 reelon where comes formed., The composition of comets is approximately solar and the GRB should have formed chondrules in the region where comets formed.84 Tje favoured region is near the Urauus-Nepune zone where perturbations by fhe proto-ieptunian eroup could move the vouns comes out to he Oort cloud (?:?)..," The favoured region is near the Uranus-Neptune zone where perturbations by the proto-neptunian group could move the young comets out to the Oort cloud \cite{whi:1989,mum:1993}."85 οher models advocate colletary onuatiou firther out in the solar svstem., Other models advocate cometary formation further out in the solar system.86 There| are onlv wo Ways dn which comets can avoid having choudrules: (1) they formed before tie GRD. or (2) there were no iron rich «ust balls sufficiently laree to be melted to form. chourules.," There are only two ways in which comets can avoid having chondrules: (1) they formed before the GRB, or (2) there were no iron rich dust balls sufficiently large to be melted to form chondrules."87 The presence or abseuce of choudrules in comets will vield valuable clues to the cometary aud chondiule formation processes., The presence or absence of chondrules in comets will yield valuable clues to the cometary and chondrule formation processes.88 The high precision results that will coue from outstanding and ambitious rendezvous and sauple return iiissious will ereatlv improve our nuderstanding of conditions iu the comet forming regions of the solar svstoi., The high precision results that will come from outstanding and ambitious rendezvous and sample return missions will greatly improve our understanding of conditions in the comet forming regions of the solar system.89 The yequency of nearby supernovae. aud hence CRοι.Los assundue they are linked to massive sar formation like supernovae. depend ou where the solar svstem was locatec withiithe galaxy when it formed.," The frequency of nearby supernovae, and hence GRBs assuming they are linked to massive star formation like supernovae, depend on where the solar system was located within the galaxy when it formed."90 The hiighest rate of tvp II syernovae occurs iu the two priucioil spiral aris 16 galaxy., The highest rate of type II supernovae occurs in the two principal spiral arms of the galaxy.91 The molecular cloud wel5 COupressed euteri 10 oral avin to a condition for star fe»yTuation aux this oeiteractiou resulted iu a new star cluser that traveESOC 1ο Sviral aria., The molecular cloud was compressed entering the spiral arm to a condition for star formation and this interaction resulted in a new star cluster that traversed the spiral arm.92 Massive stars in the cluster evolve raDnlv over vears terminating in type IT supernovac., Massive stars in the cluster evolve rapidly over years terminating in type II supernovae.93 The width of is supernova zone is about 1 kpe )ecase the stars nove tabout 100 kins + for vears (?).., The width of this supernova zone is about 1 kpc because the stars move at about 100 km $^{-1}$ for years \cite{cmcs:1977}.94 It is likely that a nearby superuova cause ie collapse of the presolar clouc alcL also seedec he vebula with the radioactive. ΑΙ needed to explain he :26MMg in CATs (2)..., It is likely that a nearby supernova caused the collapse of the presolar cloud and also seeded the nebula with the radioactive $^{26}$ Al needed to explain the Mg in CAIs \cite{chmc:1995}.95 The anilY of supernovac akne 16 spiral avin. within the 1 kpe zo10 and over a perioc of vears. has bee1 estimated at 250 supernovae per 100 X ," The number of supernovae along the spiral arm, within the 1 kpc zone and over a period of years, has been estimated at 250 supernovae per 100 pc \cite{cmcs:1977}."96BATSE observes ou average about one GRB per c, BATSE observes on average about one GRB per day.97 This corresponds o one burst per mullion vears ealaxy αππο that the rate of GRBs does not chaiege with cosimological iue (7)., This corresponds to one burst per million years per galaxy assuming that the rate of GRBs does not change with cosmological time \cite{fm:1995}.98 The average rate chaigeseos if allowance is nue for beamine or a cosmic evolution of the rate of GRBs., The average rate changes if allowance is made for beaming or a cosmic evolution of the rate of GRBs.99" The observations that CRB lost ealaxies are star forming svstenus {ελ,1),7) dudicates hat he rate of GRBs may follow the star formatio1 rafe 7).."," The observations that GRB host galaxies are star forming systems \cite{hf:1998,ftm:1999,bd:1998} indicates that the rate of GRBs may follow the star formation rate \cite{wbb:1998,tot:1999}."100 Tn this case CRBs are further away aud οcour at a ower rate and have significantly ereater euergv outut., In this case GRBs are further away and occur at a lower rate and have significantly greater energy output.101 At present there is no agrecment on the nature of the xogenitors of the GRB explosion although netiron star ucrecrs are a pronudsing candidate (22ολ," At present there is no agreement on the nature of the progenitors of the GRB explosion although neutron star mergers are a promising candidate \cite{eich:1989,pir:1999}."102 The Bist also include failed superuovae (?).. white dwarf collapse (?) and hivperuovae (?)..," The list also include failed supernovae \cite{woo:1993}, white dwarf collapse \cite{usov:1992} and hypernovae \cite{pac:1998}."103 All these models are consistent with he possibility that CRBs are associated with sar forming regions., All these models are consistent with the possibility that GRBs are associated with star forming regions.104 The lifetime of massive stars is quite short alc hat of a neutron star binary coul be sufficieuIv short to e close to a star forming region., The lifetime of massive stars is quite short and that of a neutron star binary could be sufficiently short to be close to a star forming region.105 There is considerable uucertaiity in the cosimologica rate of GRBs (?:?:2) and a rate of one CRB per ealaxy per LOE vears is adopted wuich is about 10? times less than the supernova rate (7). ," There is considerable uncertainty in the cosmological rate of GRBs \cite{cen:1998,kth:1998,che:1999} and a rate of one GRB per galaxy per $^{7}$ years is adopted which is about $^{5}$ times less than the supernova rate \cite{pac:1998}. ."106It js also asstuic that CRBs are Buked to massive stars and the explosiou occurs in the supernova zone offje spiral aria., It is also assumed that GRBs are linked to massive stars and the explosion occurs in the supernova zone of the spiral arm.107 There is, There is108The hierarchical builc-up of self-gravitating dark matter is thought to drive evolution in the observable universe.,The hierarchical build-up of self-gravitating dark matter is thought to drive evolution in the observable universe.109 The formation of clumps of cark matter precipitates the formation of galaxies by providing a potential well into which gas can fall ancl subsequently. cool., The formation of clumps of dark matter precipitates the formation of galaxies by providing a potential well into which gas can fall and subsequently cool.110 Violent mergers between equally. sized. halos and their associated: galaxics are thought to be important for starbursts ancl quasar activation., Violent mergers between equally sized halos and their associated galaxies are thought to be important for starbursts and quasar activation.111 In order to model and understand the observable universe it is therefore essential to understand the build-up of the dark structure., In order to model and understand the observable universe it is therefore essential to understand the build-up of the dark structure.112 The most widely used analytic model for the distribution of mass in isolated halos at any epoch comes from Press-Schechter (PS) theory (Press&Schechter1974)., The most widely used analytic model for the distribution of mass in isolated halos at any epoch comes from Press-Schechter (PS) theory \cite{ps}.113. By smoothing the initial Geld of density Ductuations on clillerent scales. information on the clistribution of perturbation sizes can be obtained.," By smoothing the initial field of density fluctuations on different scales, information on the distribution of perturbation sizes can be obtained."114 Linking the time at which these perturbations collapse to the initial overdensities using the simplified spherical top-hat collapse model allows the distribution of mass in isolated halos at any epoch to be determined. (Press&Schechter1974:Peacock&Lleavens1990:Bond.efa£ 1991).," Linking the time at which these perturbations collapse to the initial overdensities using the simplified spherical top-hat collapse model allows the distribution of mass in isolated halos at any epoch to be determined \cite{ps,peacock,bond}."115 In Pereival Miller (1999). (hereafter paper 1). we used he tenets of PS theory to model the related. but. clistinet xoblem of determining the distribution of times at which alos of a given mass are created.," In Percival Miller \shortcite{ev1} (hereafter paper I), we used the tenets of PS theory to model the related, but distinct problem of determining the distribution of times at which halos of a given mass are created."116 Here. ‘creation’ is defined as the epoch at. which non-linear collapse is. predicted.," Here, `creation' is defined as the epoch at which non-linear collapse is predicted."117 Two derivations were given. one of which directly used the rajectories invoked in PS theory (Peacock&Lleavens1990:Boneο)aL LOOL).. and one of which used Bayes’ theorem to convert from the PS mass function to a time distribution.," Two derivations were given, one of which directly used the trajectories invoked in PS theory \cite{peacock,bond}, and one of which used Bayes' theorem to convert from the PS mass function to a time distribution."118 The second. derivation required the prior for the creation ime which was calculated. by examining the trajectories model., The second derivation required the prior for the creation time which was calculated by examining the trajectories model.119 In this paper we extend the Bayesian link between the mass function and the creation time distribution to cover any mass function., In this paper we extend the Bayesian link between the mass function and the creation time distribution to cover any mass function.120 This is important. not only because it is known that standard PS theory is wrong in detail (e.g. Sheth Tormen 1999). but especially because the new extension applies to mass functions derived from more general density ficlds including non-Gaussian mocdoels (e.g. Mlatarrese. Verde Jimenez 2000).," This is important, not only because it is known that standard PS theory is wrong in detail (e.g. Sheth Tormen 1999), but especially because the new extension applies to mass functions derived from more general density fields including non-Gaussian models (e.g. Matarrese, Verde Jimenez 2000)."121 First. we adopt the assumption that all clumps monotonically increase in mass on the cosmological time scales of interest.," First, we adopt the assumption that all clumps monotonically increase in mass on the cosmological time scales of interest."122 This monotonic growth is an inevitable aspect of gravitational instability., This monotonic growth is an inevitable aspect of gravitational instability.123 Every epoch should. now, Every epoch should now124llence. the shock breakout interpretation does nol seen to γα correct (stronger arguments are eiven in Section 3: see also Xu et al.,"Hence, the shock breakout interpretation does not seem to be correct (stronger arguments are given in Section \ref{shock}; see also Xu et al."125 2008)., 2008).126 The transient. OSOLO9 was in the field. of view of the Durst Alert Telescope (BAT) onboard. beginning half an hour before and continuing throughout he outburst., The transient 080109 was in the field of view of the Burst Alert Telescope (BAT) onboard beginning half an hour before and continuing throughout the outburst.127 However. no gamma-ray counterpart was detected. (Burrowsctal.2008).," However, no gamma-ray counterpart was detected \citep{bur08}."128.. Hence. it is also unlikely hat the transient was an X-ray [lare of a GRB.," Hence, it is also unlikely that the transient was an X-ray flare of a GRB."129 Then. the only remaining interpretation on the nature of the transient 050100 is that it is an NRE.," Then, the only remaining interpretation on the nature of the transient 080109 is that it is an XRF."130 In this paper 1 will show that. despite its extremely soft spectrum compared to that of a normal SRE or a GRB. the transient. 0501090 is naturally interpreted. as an NRE in the context of the GRB-SN connection.," In this paper I will show that, despite its extremely soft spectrum compared to that of a normal XRF or a GRB, the transient 080109 is naturally interpreted as an XRF in the context of the GRB-SN connection."131 An important cliscovery in the observation of CRBs has been the connection between long-cluration (αλ1ὸς (with a duration 2 s) and SNe (Piran2004:DellaValle2006: therein)..," An important discovery in the observation of GRBs has been the connection between long-duration GRBs (with a duration $>2$ s) and SNe \citep[and 132references therein]{pir04,del06,woo06,nom08}."133 So far. four pairs of spectroscopically confirme CRBs/SNe have been discovered: CAB 980425 SN 1998bw (Calamactal.1998).. GRB 030329/8N 2003dh (Stanckeal.2003:Ljorthet 2003).. CRB 081203/SN 20031 (Cobbetal.2004:MalesaniPhomsen 2004)... anc GRB 060218/SN 2006aj (Campanaetal.2006:Cobbct2006:Sollermanctal.Soderberget 2006b).," So far, four pairs of spectroscopically confirmed GRBs/SNe have been discovered: GRB 980425/ SN 1998bw \citep{gal98}, GRB 030329/SN 2003dh \citep{sta03,hjo03}, GRB 031203/SN 2003lw \citep{cob04,mal04,tho04}, and GRB 060218/SN 2006aj \citep{cam06,cob06,mir06,mod06,pia06,sol06,sod06}."134. ALL of the four SNe are among a special class of Evpoe Ic. called the broad-lined SNe indicative of à very large expansion velocity (Iwamotoetal.1998:Mazzali2003:DellaValle2006:Woosley&Bloom2006.andreferences therein).," All of the four SNe are among a special class of Type Ic, called the broad-lined SNe indicative of a very large expansion velocity \citep[and references 135therein]{iwa98,maz03,del06,woo06}."136 All the above four GRBs are nearby GRBs. among which GRB 030329 is the farthest (at 2= 0.17).," All the above four GRBs are nearby GRBs, among which GRB 030329 is the farthest (at $z=0.17$ )."137 Observing SN signatures in hieh-recdshift GRBs is dillicult. since by selection elfects the observable GRBs at high redshift are bright and hence the underlving SNe are casily overshone by the GIU afterglows.," Observing SN signatures in high-redshift GRBs is difficult, since by selection effects the observable GRBs at high redshift are bright and hence the underlying SNe are easily overshone by the GRB afterglows."138 Despite this challenge. a handful of GRBs have shown rebrightening and Uattening in their late optical afterglows. which can be interpreted. as the emergence of the underlying SN lighteurves (Bloomctal.Jersieretal. 2006).," Despite this challenge, a handful of GRBs have shown rebrightening and flattening in their late optical afterglows, which can be interpreted as the emergence of the underlying SN lightcurves \citep{blo99,zeh04,sod05,bers06}."139. A systematic study on the GRB altcrelows with this approach suggests that all long-cluration GRBs are associated with SNe (Zeh.Wlose&Llartmann 2004)., A systematic study on the GRB afterglows with this approach suggests that all long-duration GRBs are associated with SNe \citep{zeh04}.140. Llowever. exceptions to the GRB-SN connection exist.," However, exceptions to the GRB-SN connection exist."141 Extensive observations of two nearby long GRBs. 060614 al ο=0.125 and 060505 at z=0.089. had not detected SNe associated with them down to limits fainter than any SN Ic ever observed (DellaValleetal.2006:EPvnbo2006:Gehrelsetal. 2006).," Extensive observations of two nearby long GRBs, 060614 at $z=0.125$ and 060505 at $z=0.089$, had not detected SNe associated with them down to limits fainter than any SN Ic ever observed \citep{del06b,fyn06,geh06}."142. This has been considered to be a challenge to the standard GRB classification scheme based on burst durations (Zhang2006:Watsonetal.2007).," This has been considered to be a challenge to the standard GRB classification scheme based on burst durations \citep{zha06,wat07}."143. On the other hand. whether a normal (not broad-lined) core-collapse SN is associated with a GRB or a GRB-like event is uncertain.," On the other hand, whether a normal (not broad-lined) core-collapse SN is associated with a GRB or a GRB-like event is uncertain."144 Considering the fact that GRBs are beamecl so that many of them may have been missed. by us. people have proposed to look for the GIU. signature in nearby SNe by observing the late brightening in radio emissions of nearby SNe as expected when the GRB ejecta are slowed down and the radio emission becomes more or less isotropic2003).," Considering the fact that GRBs are beamed so that many of them may have been missed by us, people have proposed to look for the GRB signature in nearby SNe by observing the late brightening in radio emissions of nearby SNe as expected when the GRB ejecta are slowed down and the radio emission becomes more or less isotropic."145. Llowever. L[ate-time radio observations of GS local Type Ibe SNe. including six events with broad optical absorption lines. have found. none exhibiting raclio emission. attributable to oll-axis GRB jets spreading into our line of sight (Soderbereetal.2006a).," However, late-time radio observations of 68 local Type Ibc SNe, including six events with broad optical absorption lines, have found none exhibiting radio emission attributable to off-axis GRB jets spreading into our line of sight \citep{sod06a}."146. This leads to a severe constraint on the fraction of SNe Lhe associated with normal GBs., This leads to a severe constraint on the fraction of SNe Ibc associated with normal GRBs.147 With the four spectroscopically confirmed pairs of GRBs/SNe. a relation between the peak spectral energy of GRBs and the maximum bolometric luminosity or the mass of in the ejecta of the underlving SNe was derived. by Li(2006).," With the four spectroscopically confirmed pairs of GRBs/SNe, a relation between the peak spectral energy of GRBs and the maximum bolometric luminosity or the mass of in the ejecta of the underlying SNe was derived by \citet{li06}."148. A remarkable conclusion inferred from the relation was that “if normal Evpe the SNe are accompanied. by GRBs. the GRBs should be extremely underluminous in the ganuna-ray band: despite their close distances.," A remarkable conclusion inferred from the relation was that “if normal Type Ibc SNe are accompanied by GRBs, the GRBs should be extremely underluminous in the gamma-ray band despite their close distances."149 Their peas spectral energy is expected to be in the soft X-ray and. UV band. so they may be easier to detect with an X-ray or UV detector than with a gamma-ray detector.," Their peak spectral energy is expected to be in the soft X-ray and UV band, so they may be easier to detect with an X-ray or UV detector than with a gamma-ray detector."150(Li 2006. page 1362).,"”(Li 2006, page 1362)."151" For several SNe Lhe that are not as luminous as SN 199s8bw. the ""expected ο) derived. from the relation has a peak spectral energy in the range of 0.01. 1 keV. and a total energy 107 1077 ere in the energy band. 1-10000 keV. Lt appears that NRE 080109 and SN 2008D agree with the relation (Section 4))."," For several SNe Ibc that are not as luminous as SN 1998bw, the `expected GRB' derived from the relation has a peak spectral energy in the range of $0.01$ –1 keV, and a total energy $10^{44}$ $10^{48}$ erg in the energy band 1-10000 keV. It appears that XRF 080109 and SN 2008D agree with the relation (Section \ref{xrf}) )."152 The paper is arranged. as follows., The paper is arranged as follows.153 In Section 2. the analvsis of the NICE. data is. presented., In Section \ref{data} the analysis of the XRT data is presented.154 In. Section 3 it is argued that the N-rav transient 050100 cannot be interpreted as a SN shock breakout event., In Section \ref{shock} it is argued that the X-ray transient 080109 cannot be interpreted as a SN shock breakout event.155 Section 4. shows that the most natural explanation of the nature of the transient. 050109 is that it is a faint NRE with a very soft spectrum., Section \ref{xrf} shows that the most natural explanation of the nature of the transient 080109 is that it is a faint XRF with a very soft spectrum.156 Ln Section 5 models for producing [aint and soft AREs by à normal core-collapse SN are discussed., In Section \ref{model} models for producing faint and soft XRFs by a normal core-collapse SN are discussed.157 La Section 6 summary ancl conclusions are crawn. and future observational strategies are proposed.," In Section \ref{concl} summary and conclusions are drawn, and future observational strategies are proposed."158 The SRY software was used to extract the lighteurve and the spectrum of the X-ray transient 050109 in the NICE energy band 0.3. LO keV from the Level 2 event data file (in Photon Counting mode) downloaded from the oonline archive., The XRT software was used to extract the lightcurve and the spectrum of the X-ray transient 080109 in the XRT energy band $0.3$ –10 keV from the Level 2 event data file (in Photon Counting mode) downloaded from the online archive.159 The lightcurve has a FRED (Fast Rise anc Exponential Decay) shape and a duration 600 s. Although the X-ray emission was already in progress when the observation began ancl hence the start time of the burst is uncertain. from the shape of the lighteurve it is expected that the start time of the burst should not be too much earlier than the start time of observation (see. c.g... Fig.," The lightcurve has a FRED (Fast Rise and Exponential Decay) shape and a duration $\sim 600$ s. Although the X-ray emission was already in progress when the observation began and hence the start time of the burst is uncertain, from the shape of the lightcurve it is expected that the start time of the burst should not be too much earlier than the start time of observation (see, e.g., Fig."160 1 of Soderberg et al., 1 of Soderberg et al.161 2008)., 2008).162 In extraction of the source and background spectra over a time interval of 600 s containing the burst and beginning at the start time of observation. only events. with &rades )d (ic. single ancl double pixel events) were selected. in order to achieve better spectral resolution.," In extraction of the source and background spectra over a time interval of 600 s containing the burst and beginning at the start time of observation, only events with grades 0–4 (i.e., single and double pixel events) were selected in order to achieve better spectral resolution."163 A fit of the hing unction to the point. spread. function. (PSE) of the image showed that the core region with a radius of three pixels was led up. so the core region was removed from the analysis.," A fit of the King function to the point spread function (PSF) of the image showed that the core region with a radius of three pixels was piled up, so the core region was removed from the analysis."164 Then the source region where the spectrum was extracted was an annular aperture with an inner radius of four pixels (0.47) and an outer radius of 30 pixels (717). centered at," Then the source region where the spectrum was extracted was an annular aperture with an inner radius of four pixels $9.4^{\prime\prime}$ ) and an outer radius of 30 pixels $71^{\prime\prime}$ ), centered at"165aadarciuiu.. Cleee et ((1992) found substantial fluctuations in RAL on linear scales of ~ 0.1 - 10 pe. which they could explain by electron density fluctuations alone.,"and, Clegg et (1992) found substantial fluctuations in $RM$ on linear scales of $\sim$ 0.1 - 10 pc, which they could explain by electron density fluctuations alone."166 However. Minter Spaneler (1996) observed RAL fluctuations iu extragalactic source components that cannot be explained bv only electron. density fctuatious: they need an additional turbulent maguctic field of ~luG to fit the observations.," However, Minter Spangler (1996) observed $RM$ fluctuations in extragalactic source components that cannot be explained by only electron density fluctuations; they need an additional turbulent magnetic field of $\sim 1 \,\mu$ G to fit the observations."167 Observations of polarization of starlight (Jones et al., Observations of polarization of starlight (Jones et al.168 1992) eive mich arecr estimates of the cell size. of up to a kpc.," 1992) give much larger estimates of the cell size, of up to a kpc."169" Usine pulsars aud extragalactic radio sources for the determination of the RAL of the Calactic ISAL is clearly not ideal. because they only provide information in particular directions which sample the ISAL ταν sparsely,"," Using pulsars and extragalactic radio sources for the determination of the $RM$ of the Galactic ISM is clearly not ideal, because they only provide information in particular directions which sample the ISM very sparsely."170 On the contrary. the Calactic raclio backeround provides esscutially complete filling over large solid angles.," On the contrary, the Galactic radio background provides essentially complete filling over large solid angles."171 Therefore. rotation measure maps of the diffuse cimission can be produced that eive iuformation ou the electron-deusitv-weighted magnetic field over a large range of scales.," Therefore, rotation measure maps of the diffuse emission can be produced that give information on the electron-density-weighted magnetic field over a large range of scales."172 The distribution of polarized intensity. when interpreted as mostly bee due to depolarization. can vield estimates of several properties of the wari. ISM such as correlation length. ratio of randoni over regular magnetic field aud the distance out to which diffuse xilurization can be observed.," The distribution of polarized intensity, when interpreted as mostly being due to depolarization, can yield estimates of several properties of the warm ISM such as correlation length, ratio of random over regular magnetic field and the distance out to which diffuse polarization can be observed."173 Early RAL maps of the «iMfuse svuchrotron emission in the Calaxw were construced bx Bingham Shakeshaft (1967) aud Broww Spoclsra (1976) who confirmed a Galactic magnetic field in the Galactic plane., Early $RM$ maps of the diffuse synchrotron emission in the Galaxy were constructed by Bingham Shakeshaft (1967) and Brouw Spoelstra (1976) who confirmed a Galactic magnetic field in the Galactic plane.174 Junkes et (1987) prescuted a polarizaion survey of the Galactic plane at 97<7«τοῦ and |b«15? showing sinall-scale structure in diffuse polarization., Junkes et (1987) presented a polarization survey of the Galactic plane at $4.9\dg < l < 76\dg$ and $|b| < 1.5\dg$ showing small-scale structure in diffuse polarization.175 The existence of polarization fibunenuts at iutermediate latitudes. without correlated structure iu total intensity Z. was discovered by Wieringa et ((1993) at 325 AMUIz.," The existence of polarization filaments at intermediate latitudes, without correlated structure in total intensity $I$, was discovered by Wieringa et (1993) at 325 MHz."176 Polavization surveys have been performed at frequencies from 1.4 GIIz to 2.695 GIIz (Duncan ot 11997. Duncan et 11999. Uviuuker et 11999. Laucdecser et 22001. Cacusler et 22001). mostly iu he Galactic plane.," Polarization surveys have been performed at frequencies from 1.4 GHz to 2.695 GHz (Duncan et 1997, Duncan et 1999, ker et 1999, Landecker et 2001, Gaensler et 2001), mostly in the Galactic plane."177" Iu this paper. we discuss the results of uulti-frequeucyv observations at low frequencies around 350. MIIZ of a field iu the constellation Auriga. in the second Galactic quadrant (fo=161"". b= 16"")."," In this paper, we discuss the results of multi-frequency observations at low frequencies around 350 MHz of a field in the constellation Auriga, in the second Galactic quadrant $l = 161^{\circ}$, $b =17816^{\circ}$ )."179 Due to the low requencies. we probe low rotation licasures tha are xedonmunant at iuterinediae and high latiticles.," Due to the low frequencies, we probe low rotation measures that are predominant at intermediate and high latitudes."180 This eives the opportunity to study the liglatitude RAL without concrete objects suc vas III regions or superuova relmnauts in the liue of sight. and estimate structure in the ISM above the thin stelew disk.," This gives the opportunity to study the high-latitude $RM$ without concrete objects such as HII regions or supernova remnants in the line of sight, and estimate structure in the ISM above the thin stellar disk."181 Section 2 contains deails of the ulti-frequeney polarization observations., Section \ref{s4:obs} contains details of the multi-frequency polarization observations.182 Iji Sect. 3..," In Sect. \ref{s4:res},"183 we analyze the observations. iu particular the small-scale structure in polarized intensity. and polarization angle.," we analyze the observations, in particular the small-scale structure in polarized intensity and polarization angle."184 Faraday rotation is discussed in Sect. L.," Faraday rotation is discussed in Sect. \ref{s4:rm},"185 where we also. prescut he map of rotaion measure., where we also present the map of rotation measure.186 Iu Sect. 5..," In Sect. \ref{s4:depol},"187 depolarization nechaiisius are described. that cause the structure in D. uid the constraints hat the observations provide for he parameters that describe the warm ISM.," depolarization mechanisms are described that cause the structure in $P$ , and the constraints that the observations provide for the parameters that describe the warm ISM."188 In Sect. 6.. ," In Sect. \ref{s4:sources}, ,"189he polarization properties of 13 polarized extragalactic »)iut sources found in the Auriga region are discussed., the polarization properties of 13 polarized extragalactic point sources found in the Auriga region are discussed.190" In Sect. τν,"," In Sect. \ref{s4:disc},"191 we discuss the information that our data provides ou the streneth and structure of the Calactic magnetic field., we discuss the information that our data provides on the strength and structure of the Galactic magnetic field.192 Finally. our couclusious are stated im Sect. 8..," Finally, our conclusions are stated in Sect. \ref{s4:conc}."193" We used the Westerbork Svuthesis Radio Telescope (WSRT) for iuulti-frequeney polarimetric observations of the Galactic raclio background in a field iu the constellation of Ariea centered on (a. d) (D19050) = (620"",52*30"") (|=16b. b=)"," We used the Westerbork Synthesis Radio Telescope (WSRT) for multi-frequency polarimetric observations of the Galactic radio background in a field in the constellation of Auriga centered on $\alpha$, $\delta$ ) (B1950) = $(6^h20^m, 52^{\circ}30^m)$ $l =194161^{\circ}$, $b = 16^{\circ}$ )."195 This field was observed in 8 frequency bands between 325 and 390 MIIz simmiltancoushy. each with a baud width of 5 MIIz.," This field was observed in 8 frequency bands between 325 and 390 MHz simultaneously, each with a band width of 5 MHz."196 Due o radio interference and hardware problems ouly data iu 5 of the 8 bands. tthose centered on 311. 319. 2355. 360. and 375 MIIz. could be used.," Due to radio interference and hardware problems only data in 5 of the 8 bands, those centered on 341, 349, 355, 360, and 375 MHz, could be used."197 The regiou in Auriga was observed iu six {δν periods. which resulted in ai baseline iucreiueut of 1214. The shortest baseline obtaimec is 361i. and the longest is 270011. which eives a imaxinmiu resolution of ~1.," The region in Auriga was observed in six 12hr periods, which resulted in a baseline increment of 12m. The shortest baseline obtained is 36m, and the longest is 2700m, which gives a maximum resolution of $\sim 1$."198 A taper was applied to the (£u.0)-data to increase the to-nolso ratio. so as to obain a resolution of 5.0%&5.0 cosee 6=5ςο in all 5 frequeney bau4," A taper was applied to the $(u,v)$ -data to increase the signal-to-noise ratio, so as to obtain a resolution of $5.0\arcmin\times5.0\arcmin$ cosec $\delta =1995.0\arcmin\times6.3\arcmin$ in all 5 frequency bands."200 As an interferometer has a finite shorest baseline. it is insensitive to large-scale structure.," As an interferometer has a finite shortest baseline, it is insensitive to large-scale structure."201 The shortest spacing of Όσα in the WSRT constiutes effectively a hüeli-pass filter for all scales above approximacly a degree., The shortest spacing of 36m in the WSRT constitutes effectively a high-pass filter for all scales above approximately a degree.202 The Auriga region was selected from diffuse polarization maps that were produced as a by-product of the Westerbork Northern Sky Survey (WENSS. Reugcliuk et al.," The Auriga region was selected from diffuse polarization maps that were produced as a by-product of the Westerbork Northern Sky Survey (WENSS, Rengelink et al."203 1997). which is a sinele-frequency radio survey at 325 MIIZ.," 1997), which is a single-frequency radio survey at 325 MHz."204 The WENSS diffuse polarization maps contain several regions of hieh polarization which show conspicuous sinallscale structure in polarized iuteusity and polarization angle., The WENSS diffuse polarization maps contain several regions of high polarization which show conspicuous small-scale structure in polarized intensity and polarization angle.205 We reobserved two of those regions at multiple requenceies and with higher scusitivity to obtain rotation measure information., We reobserved two of those regions at multiple frequencies and with higher sensitivity to obtain rotation measure information.206 The first region iu Auriga is described iu this paper. aud the other oue in a forthcoming paper (ITaverkorn et 22003a).," The first region in Auriga is described in this paper, and the other one in a forthcoming paper (Haverkorn et 2003a)."207 The data reduction process is described in detail in Ilaverkoru (2002). aud we ouly eive a brief summary here.," The data reduction process is described in detail in Haverkorn (2002), and we only give a brief summary here."208 The observatIOUS Were recποσα usimg tιο cata reduction package., The observations were reduced using the data reduction package.209 Poluized aud unpolarized standard calibrator sources were used. where the absolute flix scale at 325 MIIZ is based on a value of 26.93 Jy for 3C286 (Baars ct 1977).," Polarized and unpolarized standard calibrator sources were used, where the absolute flux scale at 325 MHz is based on a value of 26.93 Jy for 3C286 (Baars et 1977)."210 From this value the flux scales of the other calibraor sources 3€18. 3C117. 3€315. and 3€305 were derived.," From this value the flux scales of the other calibrator sources 3C48, 3C147, 3C345, and 3C303 were derived."211 As the area to be mapped is lareer than the primary beanofthe WSRT. the mosaicking technique was used," As the area to be mapped is larger than the primary beamofthe WSRT, the mosaicking technique was used"212observation.,observation.213 We reduced and analyzed the ASCA data and found that both flux and spectral shape of the ASCA spectrum are consistent with our data within the uncertainties., We reduced and analyzed the ASCA data and found that both flux and spectral shape of the ASCA spectrum are consistent with our data within the uncertainties.214" This indicates that the source does not show evidence for long term variability in excess of about, that is our uncertainty on the flux."," This indicates that the source does not show evidence for long term variability in excess of about, that is our uncertainty on the flux."215" This is consistent with the idea that the observed flux is not seen directly, but is reprocessed by a large scale (> 1 pc) medium."," This is consistent with the idea that the observed flux is not seen directly, but is reprocessed by a large scale $\ge$ 1 pc) medium."216 The ASCA data of NGC 1386 were also analyzed by Iyomoto et al. (1997)), The ASCA data of NGC 1386 were also analyzed by Iyomoto et al. \cite{iyomoto}) )217 who interpret the observed spectrum with a Compton thin transmission model (Ny5’2.8—5.4x 10%3em7?)., who interpret the observed spectrum with a Compton thin transmission model $_H\approx 2.8-5.4\times 10^{23}$ $^{-2}$ ).218" As discussed above, statistically the transmission model would fit also our data, but is inconsistent with the large EW(Fe Ka)."," As discussed above, statistically the transmission model would fit also our data, but is inconsistent with the large EW(Fe $\alpha$ )."219" Finally, we estimated the contribution to the soft X rays from the Fornax cluster thermal emission by extracting the spectrum in two regions of the sky located"," Finally, we estimated the contribution to the soft X rays from the Fornax cluster thermal emission by extracting the spectrum in two regions of the sky located"220 feroidesweshowthec'A Bde fincdbyk οσα Lypegaleaciesthalarespeclroscopicallyeon firmed Anttianenbersomeluded tro,we show the CMR defined by FS90 early-type galaxies that are spectroscopically confirmed Antlia members or were considered as definite members (status 1) in the FS90 Antlia catalogue.221che ditsdant ο defi CNTR, We have added the new dwarf galaxies presented in the previous section.222 Sito Ecatalogue. M refajustes)).," Several biweight fits to the observed relation have been performed, some of them considering only spectroscopically confirmed members (see \\ref{ajustes}) )."223PollowingCrebel(2005)... wewilleonsiderasdiear f gal siniilat/soatter/té mag. which corresponds to 7;14 mag at the Antlia distance (seetable3afromFukugita.Shimasaku&Ichikawa 1993).," Following \citet{G05}, we will consider as dwarf galaxies those with $M_V\sim -18$ mag, which corresponds to $T_1>14$ mag at the Antlia distance \citep*[see table 3a from][]{F95}. ."224. In order to test the results found by Barazzaetal.(2009) in Abell 901/902 regarding the existence of a colour-density relation in the projected radial distribution. we divided our dwarf galaxy sample into systems displaying redder and bluer colours than the mean CMR.," In order to test the results found by \citet{Barazza09} in Abell 901/902 regarding the existence of a colour–density relation in the projected radial distribution, we divided our dwarf galaxy sample into systems displaying redder and bluer colours than the mean CMR."225" From refCMR,5 feroidesandable refajustes.. weeansee halspeel roscopicallycon firmedmembersde relation,of. candidatesFS90 mag with no change of slope or increase in the scatter."," From \\ref{CMR_esferoides} and \\ref{ajustes}, , we can see that spectroscopically confirmed members define a tight relation down to $T_{1_0}=20$ mag with no change of slope or increase in the scatter."226" The new dwarf galaxy candidates seem to extend the relation down to Ti,22 mag. although introducing a considerable dispersion in the .CMR at :its very faint.. end."," The new dwarf galaxy candidates seem to extend the relation down to $T_{1_0}>22$ mag, although introducing a considerable dispersion in the CMR at its very faint end."227" In particular,. dSph- candidates. tend to increase the scatter towards bluer colours than the mean relation."," In particular, dSph candidates tend to increase the scatter towards bluer colours than the mean relation."228 In comparison with the results presented in Paper the CMR gets slightly steeper with the addition of the new contirmedIT. members.," In comparison with the results presented in I, the CMR gets slightly steeper with the addition of the new confirmed members."229 When FS90 non contirmed members are included in the fit. both the slope of the CMR and its scatter increase.," When FS90 non confirmed members are included in the fit, both the slope of the CMR and its scatter increase."230 The selection of the spectroscopic targets was performed independently of their location in the photometric relations analyzed in this paper., The selection of the spectroscopic targets was performed independently of their location in the photometric relations analyzed in this paper.231 The GEMINI-GMOS tields were chosen to include as many FS90 galaxy candidates as possible., The GEMINI-GMOS fields were chosen to include as many FS90 galaxy candidates as possible.232 Therefore. i is remarkable that all early-type contirmed members suite so well in he CMR.," Therefore, it is remarkable that all early-type confirmed members suite so well in the CMR."233 In addition. we can see that speetroscopically contirmec background galaxies included in the FS90 Antlia catalogue. as wel as dI and BCD confirmed members. would introduce a substantia dispersion to the relation if they were wrongly considered as ype cluster members.," In addition, we can see that spectroscopically confirmed background galaxies included in the FS90 Antlia catalogue, as well as dI and BCD confirmed members, would introduce a substantial dispersion to the relation if they were wrongly considered as early-type cluster members."234 The new confirmed cE galaxies share the same CMR as “normal” early-type dwarf galaxies., The new confirmed cE galaxies share the same CMR as “normal” early-type dwarf galaxies.235 However. as can be seen from he data included in Table |.. they increase the dispersion of the relation defined by dwarf contirmed members towards the red side of the colour-magnitude diagram.," However, as can be seen from the data included in Table \ref{ajustes}, they increase the dispersion of the relation defined by dwarf confirmed members towards the red side of the colour-magnitude diagram."236 When these peculiar galaxies are ΜΕνΗΝpebaesüibéns axi Mat traced by brightones.," When these peculiar galaxies are excluded from the fit, faint early-type members define a CMR with a similar scatter to that traced by brightones."237 The location of both cEs in the CMR diagram is consistent with a luminosity fading (2.5 mmag for 1110. and z3.7 mmag for FS901192) at constant colour.," The location of both cEs in the CMR diagram is consistent with a luminosity fading $\approx 2.8$ mag for 110, and $\approx 3.7$ mag for 192) at constant colour."238" In refmueff,s feroideswepresentlhereeisedluminosilg ΙΙ randouiloQUA definite and confirmed members. and new dwarf μα and laumMembers."," In \\ref{mueff_esferoides} we present the revised $\langle\mu_{\rm eff}\rangle$ relation of FS90 Antlia definite and confirmed members, and new dwarf candidates and members."239" We. show. as a dashed line. the locus of constant effective radius (4p Lkkpe) found for galaxies fainter than 71,=13 mag in PaperII. Recall tha lines. parallel to this. locus towards fainterον luminositiesD correspond to smaller effective radii (see L1 in Π)."," We show, as a dashed line, the locus of constant effective radius $r_{\rm eff}\sim 1$ kpc) found for galaxies fainter than $T_{1_0}=13$ mag in I. Recall that lines parallel to this locus towards fainter luminosities correspond to smaller effective radii (see 1 in I)."240" For our new sample of dwarf early-type members. and candidates. we obtain a mean effective radius of roar)=OSL (rms 0.31) kpe. considering 57 galaxies with 71,13 mag anc excluding the two cEs which represent extreme cases."," For our new sample of dwarf early-type members and candidates, we obtain a mean effective radius of $\langle r_{\rm eff} \rangle = 0.81$ (rms 0.31) kpc, considering 57 galaxies with $T_{1_0} > 13$ mag and excluding the two cEs which represent extreme cases."241" However. we see that both FS90 and new contirmed members fainter than Ti,LS mag tend to depart from the linear relation towards smaller effective radii."," However, we see that both FS90 and new confirmed members fainter than $T_{1_0} \sim 18$ mag tend to depart from the linear relation towards smaller effective radii."242" When only dwarf galaxies in the range 13«7),<18 are considered. the mean effective radius increases to Crap?=0.93 (rms 0.28) kpe."," When only dwarf galaxies in the range $13 < T_{1_0} < 18$ are considered, the mean effective radius increases to $\langle r_{\rm eff} \rangle = 0.93$ (rms 0.28) kpc."243 One possible explanation for the faint break is that it arises due to the isophotal limit of our photometry. which causes different fractions of galaxy luminosity to be lost outside the limiting isophote for galaxies with different profile shapes.," One possible explanation for the faint break is that it arises due to the isophotal limit of our photometry, which causes different fractions of galaxy luminosity to be lost outside the limiting isophote for galaxies with different profile shapes."244 In order to quantify this effect. we considered a set of Sérrsic models spanning an appropriate magnitude range. with shape parameters (7) following the luminosity — shape relation given by Graham& 10).," In order to quantify this effect, we considered a set of Sérrsic models spanning an appropriate magnitude range, with shape parameters $n$ ) following the luminosity – shape relation given by \citet[][see their fig.\,10]{Graham03}. ."245. We fixed the effective radii of all the models at Kkpe (5.87 arcsecat the Antlia cluster distance). and wethen computed for each model the fraction of light lost outside," We fixed the effective radii of all the models at kpc (5.87 arcsecat the Antlia cluster distance), and wethen computed for each model the fraction of light lost outside"246"For the case of the outflowing cloud (5002), we also see a larger spread of the sickle-shaped cloud in radial direction.","For the case of the outflowing cloud (SC02), we also see a larger spread of the sickle-shaped cloud in radial direction."247" For the case of even higher column densities than displayed, the amount of compression decreases, as gravitational acceleration dominates over radiation pressure effects."," For the case of even higher column densities than displayed, the amount of compression decreases, as gravitational acceleration dominates over radiation pressure effects."248" Radiation pressure effects are only effective at the cloud edges, where cometary-shaped tails build up, which develop Kelvin-Helmholtz-instabilities and form a turbulent wake behind the cloud."," Radiation pressure effects are only effective at the cloud edges, where cometary-shaped tails build up, which develop Kelvin-Helmholtz-instabilities and form a turbulent wake behind the cloud."249" Only the inner boundary of the cloud forms small cloudlets and filaments, whereas the outer part keeps a continuous density distribution."," Only the inner boundary of the cloud forms small cloudlets and filaments, whereas the outer part keeps a continuous density distribution."250" On its way towards the centre, the cloud shrinks due to gravitational forces, gas cooling and the ablation of gas at the outer edges."," On its way towards the centre, the cloud shrinks due to gravitational forces, gas cooling and the ablation of gas at the outer edges."251" In summary, clouds can encounter two fates, depending on their radial column density: (i) Low column density clouds will be pushed outwards, whereas (ii) high column density clouds always show both, in- and outflow motion, due to the formation of tails at the low column density edges of the clouds."," In summary, clouds can encounter two fates, depending on their radial column density: (i) Low column density clouds will be pushed outwards, whereas (ii) high column density clouds always show both, in- and outflow motion, due to the formation of tails at the low column density edges of the clouds."252 Fig., Fig.253" 9 shows the radial distribution of mass for clouds with different densities for an early snapshot (upper panel, after yyr) and a late snapshot (lower panel, after yyr)."," \ref{fig:dens_study_massonshells} shows the radial distribution of mass for clouds with different densities for an early snapshot (upper panel, after yr) and a late snapshot (lower panel, after yr)."254" It clearly shows the dependence of the density distribution on the initial condition: whereas the high density case remains peaked, it spreads out more and more for the lower column density clouds."," It clearly shows the dependence of the density distribution on the initial condition: whereas the high density case remains peaked, it spreads out more and more for the lower column density clouds."255 'The shearing of the cloud is quantified in Fig. 10.., The shearing of the cloud is quantified in Fig. \ref{fig:density_study_shell_thickness}.256" First of all, we determine the centre of mass of the cloud."," First of all, we determine the centre of mass of the cloud."257" Then we add up the mass in the spherical shell defined by the radial cell, which contains the COM."," Then we add up the mass in the spherical shell defined by the radial cell, which contains the COM."258 We extend the spherical shell (symmetrically with respect to the centre of mass) until it includes of the mass of the initial condition within the spherical shell embracing the initial cloud., We extend the spherical shell (symmetrically with respect to the centre of mass) until it includes of the mass of the initial condition within the spherical shell embracing the initial cloud.259" This is done for the standard model (96000, black line), the model with half the mass of the standard model (5001, blue line) and a model with a quarter of the mass of the standard model with an outer radius extended to ppc (5011, red line)."," This is done for the standard model (SC00, black line), the model with half the mass of the standard model (SC01, blue line) and a model with a quarter of the mass of the standard model with an outer radius extended to pc (SC11, red line)."260" In the beginning of the simulation, the contraction of the cloud is visible, before the differential forces lead to a shearing."," In the beginning of the simulation, the contraction of the cloud is visible, before the differential forces lead to a shearing."261" Two types of shearing occur: (i) due to the column density differences between the cloud centre and the cloud's outer edge, as visible in the extended tails and (ii) due to the small scale column density differences which emerge in a later stage of the evolution."," Two types of shearing occur: (i) due to the column density differences between the cloud centre and the cloud's outer edge, as visible in the extended tails and (ii) due to the small scale column density differences which emerge in a later stage of the evolution."262" After the compression phase, the half mass shell size increases almost linearly for the case where the COM moves outward (see Fig. 11))."," After the compression phase, the half mass shell size increases almost linearly for the case where the COM moves outward (see Fig. \ref{fig:density_study_cloud_com_r}) )."263" The evolution is fastest for the low density case, where radiation pressure dominates the radial forces."," The evolution is fastest for the low density case, where radiation pressure dominates the radial forces."264" The infalling high density case behaves differently, as the dense inner shell which forms due to the initial contraction seems to prevent efficient shearing."," The infalling high density case behaves differently, as the dense inner shell which forms due to the initial contraction seems to prevent efficient shearing."265 Fig., Fig.266 12 quantifies the different velocities reached., \ref{fig:dens_study_radvel_hist} quantifies the different velocities reached.267" Whereas the highest density cores reach the smallest outflow and the highest inflow velocities, respectively, the highest outflow velocities are reached by the material within the tails expelled from the cloud edges."," Whereas the highest density cores reach the smallest outflow and the highest inflow velocities, respectively, the highest outflow velocities are reached by the material within the tails expelled from the cloud edges."268 This material shows up as the extended tails ofthe distributions in Fig. 12.., This material shows up as the extended tails ofthe distributions in Fig. \ref{fig:dens_study_radvel_hist}. .269lt may be the natural definition to use if one wishes to compare with analyses which model the distortion. of a galaxy (for example. the warping of the \lilkyw Way due to tidal interaction with the Alagellanie Clouds) as excitations ofa regular svstem driven by external gravitational forcing.,"It may be the natural definition to use if one wishes to compare with analyses which model the distortion of a galaxy (for example, the warping of the Milky Way due to tidal interaction with the Magellanic Clouds) as excitations of a regular system driven by external gravitational forcing."270" We dub this barvcentre Fia. so the position ollset between the halo and its core Aman, Can be written as where Foore is the barvcentre of the LOO most. bound particles in the main subhalo and Fa is that of the main subhalo as a whole."," We dub this barycentre $r_{\rm main}$, so the position offset between the halo and its core $\Delta r_{\rm main}$ can be written as where $\vec{r}_{\rm core}$ is the barycentre of the $100$ most bound particles in the main subhalo and $\vec{r}_{\rm main}$ is that of the main subhalo as a whole."271 For comparison. we will also show some results for olfsets where the centre of a halo is defined as the barveentre of the corresponding group.," For comparison, we will also show some results for offsets where the centre of a halo is defined as the barycentre of the corresponding group."272 For this purpose we take the group centre to be the particle with the greatest potential energy and we define the halo as all. particles (inelucing& substructures and unbound 1particles) within the largest sphere for which the mean enclosed overdensity is at least 200 times the critical value., For this purpose we take the group centre to be the particle with the greatest potential energy and we define the halo as all particles (including substructures and unbound particles) within the largest sphere for which the mean enclosed overdensity is at least 200 times the critical value.273 With this definition the core olfset is where £a is the barvceentre of all members of the halo., With this definition the core offset is where $\vec{r}_{\rm so}$ is the barycentre of all members of the halo.274 Clearly since the halo is bounded by a sphere which is effectively centred on μοι we can expect typical olfsets to be smaller in this case than with our preferred definition.," Clearly since the halo is bounded by a sphere which is effectively centred on $\vec{r}_{\rm core}$, we can expect typical offsets to be smaller in this case than with our preferred definition."275 We define mean velocities for halos as a whole in direc analogy to the mean positions defined. above by averaging either over all particles of the main subhalo (Vas) OF Over all particles of the halo (1)., We define mean velocities for halos as a whole in direct analogy to the mean positions defined above by averaging either over all particles of the main subhalo $\vec{V}_{\rm main}$ ) or over all particles of the halo $\vec{V}_{\rm so}$ ).276 Note that again the firs definition excludes substructures but the second. does not., Note that again the first definition excludes substructures but the second does not.277" Aleasuring a velocity ollset for the core is more dillieult than measuring a position ollset because of the ""noise"" introduce by the large random motions of particles in the inner halo.", Measuring a velocity offset for the core is more difficult than measuring a position offset because of the “noise” introduced by the large random motions of particles in the inner halo.278 We rank particles by their distance from the centre of the core (taken as Pose) and we estimate the square of the velocity olfset for the N innermost particles as where Vinuk is either αμ or ων. and Vere and (vus are defined by and With these definitions we expect our estimator of velocity offset. (squared) to be unbiased. but it will give negative values for some halos.," We rank particles by their distance from the centre of the core (taken as $\vec{r}_{\rm core}$ ) and we estimate the square of the velocity offset for the $N$ innermost particles as where $\vec{V}_{\rm bulk}$ is either $\vec{V}_{\rm main}$ or $\vec{V}_{\rm279so}$, and $\vec{V}_{\rm core}$ and $\sigma_{\rm core}$ are defined by and With these definitions we expect our estimator of velocity offset (squared) to be unbiased but it will give negative values for some halos."280 Choosing large IN. will reduce the noise but will result in overly large scores” for the lower mass halos., Choosing large $N$ will reduce the noise but will result in overly large “cores” for the lower mass halos.281 We investigate the appropriate conipromise below., We investigate the appropriate compromise below.282 We now examine how the above position and velocity olfsets are distributed. for large samples of halos drawn from the Millennium Simulation., We now examine how the above position and velocity offsets are distributed for large samples of halos drawn from the Millennium Simulation.283 Lt is clearly of interest to understand how such distributions depend on halo mass., It is clearly of interest to understand how such distributions depend on halo mass.284 Naively. lower mass haloes were assembled earlier than more massive ones. so it seems natural that they should. typically be more relaxed. anc have smaller asvimametries both in position and in velocity.," Naively, lower mass haloes were assembled earlier than more massive ones, so it seems natural that they should typically be more relaxed and have smaller asymmetries both in position and in velocity."285 We select. four sets. of. halos randomly from the Millennium Simulation in four dillerent mass ranges., We select four sets of halos randomly from the Millennium Simulation in four different mass ranges.286" “Phere are 1636 “Alilky Way"" haloes with Adoug in the range 2.0.4.0]10775. 1M.: there are G40 “poor group” halos in the mass range 0.7.2.0]10h1M: there are 280 ""rich group"" halos in the mass range 0.7.2.0].1075.1M: finally. there are 227 “cluster” halos with masses greater than 2.lothΤΑ."," There are $1636$ “Milky Way” haloes with $M_{200}$ in the range $[2.0,4.0] \times 10^{12}h^{-1}{\rm M_\odot}$ ; there are $640$ “poor group” halos in the mass range $[0.7,2.0] \times 10^{13}h^{-1}{\rm287M_\odot}$; there are $280$ “rich group” halos in the mass range $[0.7,2.0]288\times 10^{14}h^{-1}{\rm M_\odot}$; finally, there are $227$ “cluster” halos with masses greater than $2 \times 10^{14}h^{-1}{\rm M_\odot}$."289 Cumulative distributions of the spatial ollset between the barycentre of the core and that of the halo as a whole are plotted in Figure 1 for halos in our four disjoint mass ranges., Cumulative distributions of the spatial offset between the barycentre of the core and that of the halo as a whole are plotted in Figure \ref{fig:fig1} for halos in our four disjoint mass ranges.290 In the left panel the centre of cach halo is taken to be Pa. while in the right. panel it is taken to be Ps.," In the left panel the centre of each halo is taken to be $\vec{r}_{\rm main}$, while in the right panel it is taken to be $\vec{r}_{\rm so}$."291 In order to facilitate comparison of the cillerent mass ranges. the olfset. for cach halo is expressed as a fraction of rooo. the radius of the corresponding group.," In order to facilitate comparison of the different mass ranges, the offset for each halo is expressed as a fraction of $r_{200}$, the radius of the corresponding group."292" The ollsets are substantially smaller when we use 7, to define the halo centre. so the symmetry. imposed. artificially by the spherical boundary. assumed. for the halos clearly allects the results much more stronely than the omission of substructure when calculating Pu."," The offsets are substantially smaller when we use $\vec{r}_{\rm so}$ to define the halo centre, so the symmetry imposed artificially by the spherical boundary assumed for the halos clearly affects the results much more strongly than the omission of substructure when calculating $\vec{r}_{\rm main}$."293 bor the reasons discussed: above. we consider ollsets based on. Fun to be the appropriate indicator of the kind. of asymmetry. which could drive galaxy distortions. so we concentrate on results in the left panel of Figure 1. for the rest of this subsection.," For the reasons discussed above, we consider offsets based on $\vec{r}_{\rm main}$ to be the appropriate indicator of the kind of asymmetry which could drive galaxy distortions, so we concentrate on results in the left panel of Figure \ref{fig:fig1} for the rest of this subsection."294 lt is clear that more massive haloes tend to have larger asvnimetries., It is clear that more massive haloes tend to have larger asymmetries.295 Thus the cores of of cluster halos are oll rom the barvcentre of the main subhalo by more than ol rogo (~200 !kpe). while only a few percent of Milky Way haloes have such large asvmmetries: the typical olfset or these lower mass halos is about of ου (~105 1κρο.," Thus the cores of of cluster halos are offset from the barycentre of the main subhalo by more than of $r_{200}$ $\sim 200 h^{-1}$ kpc), while only a few percent of Milky Way haloes have such large asymmetries; the typical offset for these lower mass halos is about of $r_{200}$ $\sim 10296h^{-1}$ kpc)."297 This mass dependence. presumably. rellects the fact that massive halos typically assemble at [ater times and so are arther from equilibrium todav., This mass dependence presumably reflects the fact that massive halos typically assemble at later times and so are farther from equilibrium today.298 We come back to this issue xdow: in our discussion. section., We come back to this issue below in our discussion section.299 Notice inb even for the Milkv Way. halos. the typical offsets are as large as the visible size of the galaxy.," Notice that even for the Milky Way halos, the typical offsets are as large as the visible size of the galaxy."300 In cluster halos theyare easily arge enough to be measured reliably from. X-ray images or ensing Heaps., In cluster halos theyare easily large enough to be measured reliably from X-ray images or lensing maps.301can be seen by comparing Tables | and 3..4 the fitted values for absorbing column density. temperature. metallicity. and normalisation of the thermal spectrum are not affected by the addition of the 6.4 keV-line component.,"can be seen by comparing Tables \ref{tab:psfit} and \ref{tab:psfit_line}, the fitted values for absorbing column density, temperature, metallicity, and normalisation of the thermal spectrum are not affected by the addition of the 6.4 keV-line component."302 The null-hypothesis probability of all the fits improves. except for “see1”. for which the null-hypothesis probability decreases marginally.," The null-hypothesis probability of all the fits improves, except for “seg1”, for which the null-hypothesis probability decreases marginally."303" Indeed. an excess of emission at 6.4 keV does not appear to be present at all in this spectrum. so that there is no reason to add an extra line component at 6.4 keV. We have also added this component to the spectral fit of ""segl"" to make the fits homogeneous and directly comparable."," Indeed, an excess of emission at 6.4 keV does not appear to be present at all in this spectrum, so that there is no reason to add an extra line component at 6.4 keV. We have also added this component to the spectral fit of “seg1” to make the fits homogeneous and directly comparable."304" The equivalent. width of the fitted line appears to vary significantly from the 13 eV of ""segl"" (where the excess emission at 6.4 keV does not seem to be present) to the 249 eV of ""seg2"".", The equivalent width of the fitted line appears to vary significantly from the 13 eV of “seg1” (where the excess emission at 6.4 keV does not seem to be present) to the 249 eV of “seg2”.305" reftab:psfitine,,ossununarise sthere sultso fthe simultaneous specteahinstone TY ait ny dgeewütufiBlisarbodWE nlesfocausdlalandanadd theresultsobtainedf romthis jointspectralanalysisareagatn fullvewecsas Mebane lee et Ael BN rette psfitineandA)).", \\ref{tab:psfit_line_mos} summarises the results of the simultaneous spectral fitting of PN and MOS data with an absorbed 1T plasma model and an additional Gaussian line component at 6.4 keV: the results obtained from this joint spectral analysis are again fully consistent with the results from the PN data alone (compare \\ref{tab:psfit_line} and \ref{tab:psfit_line_mos}) ).306"Thestrongvariationintheintensitvo Πο μονο αμα sAkgddeenween"" segV'and""seg2"" isconfirmed:thebest— Fitlineequivalentwidthvariesfroml0eVin""seglV'(wherethelineal sedgegecosst obOO sautiaom ΜΑΙ ΜΑΝ od inübsarbeOvMiserhee xcess —seeFig. reffig: psfit).", The strong variation in the intensity of the excess emission at 6.4 keV between “seg1” and “seg2” is confirmed; the best-fit line equivalent width varies from 10 eV in “seg1” (where the line also appears to be absent in the MOS2 data) to 194 eV in “seg2” (where the excess of emission is also strong in the MOS2 data -- see \\ref{fig:psfit}) ).307"For""seg3 and""κος. theequivalentwidtho f theetsgintisttbatée ek fitsdif fersby~ from the value derived. from the PN data alone. but best-fit values of the line’s flux are consistent within the two data-sets: for ""seg5"". the equivalent width of the emission at 6.4 keV derived from the two spectral analysis are very similar."," For “seg3” and “seg4”, the equivalent width of the emission at 6.4 keV derived from the joint fits differs by $\sim $ from the value derived from the PN data alone, but best-fit values of the line's flux are consistent within the two data-sets; for “seg5”, the equivalent width of the emission at 6.4 keV derived from the two spectral analysis are very similar."308" As described in refsec:sim.. we have performed à set of Monte Carlo simulations of the PN spectra to assess whether the line at 6.4 keV seen in the spectra from ""seg2"" to ""seg5"" is real rather than the result of statistical fluctuations in the data."," As described in \\ref{sec:sim}, we have performed a set of Monte Carlo simulations of the PN spectra to assess whether the line at 6.4 keV seen in the spectra from “seg2” to “seg5” is real rather than the result of statistical fluctuations in the data."309 The results of these simulations are summarised in the last column of reftab:psfitine.. probability whichgivesthe thatalineat6o AkeV.," The results of these simulations are summarised in the last column of \\ref{tab:psfit_line}, , which gives the probability that a line at 6.4 keV, with equivalent width equal to, or greater than, the best-fit value, could be the result of random fluctuations for each segment."310 withalurOQ mtsién r," This probability is high for “seg1” and the “flare” segment, for which the data are consistent with the absence of a line in the spectrum."311ege thebest— fitvalue.," Conversely, the probability that the excess of emission in “seg2” and “seg5” is due to noise fluctuations is low and, respectively)."312 f random couldbetheresultofluctuations f o," For time intervals “seg3” and “seg4” the situation is less clear, since with a probability of and, respectively, that the excess at 6.4 keV could be due to random fluctuations, the evidence for intrinsic emission is less compelling."313reachsegment.T dleV eghé psfitiine).," Nevertheless an analysis of the spectrum of the source integrated over the time intervals “seg3”, “seg4”, and “seg5” shows that the evidence for the presence of the line is very strong, with a probability that the excess at 6.4 keV is due to random fluctuation of less than one in a thousand (as summarised in the last line of \\ref{tab:psfit_line}) )."314 The simulations described in refsec:sim. also show that the variation in the line’s equivalent width seen between “seg!” (where the line appear to be absent or extremely weak) and “seg?” are very likely intrinsic (with a probability of 99.9%))., The simulations described in \\ref{sec:sim} also show that the variation in the line's equivalent width seen between “seg1” (where the line appear to be absent or extremely weak) and “seg2” are very likely intrinsic (with a probability of ).315" To further constrain the properties of the Fe 6.4 keV emission from Elias 29. we derived the spectrum of the source integrated over the quiescent time intervals where the excess at 6.4 keV appears to be present (although with varying significance). Le. intervals “seg2”. ""seg37. κος, and “segs” (PN data only)."," To further constrain the properties of the Fe 6.4 keV emission from Elias 29, we derived the spectrum of the source integrated over the quiescent time intervals where the excess at 6.4 keV appears to be present (although with varying significance), i.e. intervals “seg2”, “seg3”, “seg4”, and “seg5” (PN data only)."316 The summed spectrum between 4 and 8 keV is shown in reffig:psint.. where the emission line at 6.4 keV is very clear thanks to the the improved statistic.," The summed spectrum between 4 and 8 keV is shown in \\ref{fig:psint}, , where the emission line at 6.4 keV is very clear thanks to the the improved statistic."317 A fit with an absorbed IT model to this spectrum yields N(H)=6.7x107 em. kT=3.7 keV and Z=0.7Ze with a null hypothesis probability P=3.5x10%.," A fit with an absorbed 1T model to this spectrum yields $N({\rm H}) = 6.7 \times 10^{22}$ $^{-2}$, $kT = 3.7$ keV and $Z=0.7~Z_{\sun}$ with a null hypothesis probability $P = 3.5 \times31810^{-5}$."319 The spectral parameters are very similar to the average values derived above from the fits to the individual five quiescent time intervals. although the fit probability is rather low.," The spectral parameters are very similar to the average values derived above from the fits to the individual five quiescent time intervals, although the fit probability is rather low."320 With the addition of a line at 6.4 keV. the fit probability increases substantially to P=2.1x107 (and the values of the parameters of the IT model hardly change).," With the addition of a line at 6.4 keV, the fit probability increases substantially to $P=2.1 \times 10^{-3}$ (and the values of the parameters of the 1T model hardly change)."321 In this case we left the position of the Gaussian line free to vary during the fit. together with its normalisation.," In this case we left the position of the Gaussian line free to vary during the fit, together with its normalisation."322 The fitted line equivalent width is Waii;v=143 eV and its position is 6.44+0.03. fully consistent with being Fe K fluorescent emission.," The fitted line equivalent width is $W_{\rm3236.4~keV} = 143$ eV and its position is $6.44 \pm 0.03$, fully consistent with being Fe K fluorescent emission."324 Indeed. although the reliability ts limited (the quoted error is at ο). the line peak energy of 6.44 keV would suggest that the fluorescing Fe is Neon-like: or so.," Indeed, although the reliability is limited (the quoted error is at $\sigma$ ), the line peak energy of 6.44 keV would suggest that the fluorescing Fe is Neon-like: or so."325 The Fe K fluorescent emission line energy ts. in fact. a slowly increasing function of tonisation state. rising from 6.40 keV in Ferto 6.45 keV in George&Fabian.1991)).," The Fe K fluorescent emission line energy is, in fact, a slowly increasing function of ionisation state, rising from 6.40 keV in to 6.45 keV in \citealp{house69}; \citealp{gf91}) )."326 To quantify the reliability of the detection of the 6.4 keV at sitem Bpcera," To quantify the reliability of the detection of the 6.4 keV emission in the different spectra of Elias 29, we performed a set of Monte Carlo simulations of the PN spectra."327chabdve Phe fitted to the spectrum the additional Gaussiat X deN fperoilelioint 506€reftab:psfit)) were generated usingxspec.," For each time interval discussed in \\ref{sec:res}, 1000 random realisations of the absorbed 1T-model fitted to the spectrum the additional Gaussian component at 6.4 keV (as per \\ref{tab:psfit}) ) were generated using."328 These random realisations have the same noise characteristics of the data anc the same energy binning of the real data (for which channels are combined to à minimum of 20 counts per energy bin)., These random realisations have the same noise characteristics of the data and the same energy binning of the real data (for which channels are combined to a minimum of 20 counts per energy bin).329 The 1000 simulated spectra were then fitted with the same procedure used for the real data., The 1000 simulated spectra were then fitted with the same procedure used for the real data.330 First a fit with an absorbed IT plasma model was performed then a Gaussian line component at 6.4 keV with a narrow c of 10 eV was added to the model and the simulated data were re-fitted., First a fit with an absorbed 1T plasma model was performed then a Gaussian line component at 6.4 keV with a narrow $\sigma$ of 10 eV was added to the model and the simulated data were re-fitted.331 The line position and width were kept fixec during this fit. while its normalisation was left unconstrained.," The line position and width were kept fixed during this fit, while its normalisation was left unconstrained."332 The equivalent width of the fitted line was then computed for tio mgtexxalthan. lBiwyoco, The equivalent width of the fitted line was then computed for all 1000 fits for each time interval.333fbibiditpisiial csidalbitéduspeeceuidid. farwhichthed contain any emission line at 6.4 keV. the number (over 1000) of fitted spectra with a fitted line with a given Wa4ων gives the probability that a line with that equivalent width could be measured in the real spectrum because of the noise's random fluctuations.," Since the input model to the simulated spectra did not contain any emission line at 6.4 keV, the number (over 1000) of fitted spectra with a fitted line with a given $W_{\rm 6.4~keV}$ gives the probability that a line with that equivalent width could be measured in the real spectrum because of the noise's random fluctuations."334" For example. in the case of “seg!” the number of simulated spectra with Weyney=13 eV οων= being the best-fit equivalent width in the real data) is 453. thus. the probability of deriving a spurious line with Wajoy eV from the spectrum of ""segl1"" is 45%."," For example, in the case of “seg1” the number of simulated spectra with $W_{\rm 6.4~keV} \ge 13$ eV $W_{\rm 6.4~keV} = 13$ eV being the best-fit equivalent width in the real data) is 453, thus, the probability of deriving a spurious line with $W_{\rm 6.4~keV} \ge 13$ eV from the spectrum of “seg1” is ."335". This can be seen by looking at the top panel of reffig:simzqu. . whichgivesthedistributiono FWyv for the fitted lines for the simulation of ""segl""."," This can be seen by looking at the top panel of \\ref{fig:sim_eqw}, which gives the distribution of $W_{\rm 6.4~keV}$ for the fitted lines for the simulation of “seg1”."336" Note that. in the case of ""segl"". there is no visible excess of emission at 6.4 keV. so a high incidence of simulated spectra with Wesον213 eV is consistent with the absence of the line in the intrinsic spectrum."," Note that, in the case of “seg1”, there is no visible excess of emission at 6.4 keV, so a high incidence of simulated spectra with $W_{\rm 6.4~keV} \ge 13$ eV is consistent with the absence of the line in the intrinsic spectrum."337" In the case of ""seg2"". on the other hand. the number of simulated spectra with ον2249 eV is ] (over 1000simulations). indicating that the excess at 6.4 keV seen in the spectrum of""seg2"" is very likely intrinsic to the source."," In the case of “seg2”, on the other hand, the number of simulated spectra with $W_{\rm 6.4~keV} \ge 249$ eV is 1 (over 1000simulations), indicating that the excess at 6.4 keV seen in the spectrum of“seg2” is very likely intrinsic to the source."338 The results of all thesesimulations for all the different time intervals. in terms of the probability of by chance observing a line with a value of Ποιον greater or equal to the one," The results of all thesesimulations for all the different time intervals, in terms of the probability of by chance observing a line with a value of $W_{\rm 6.4~keV}$ greater or equal to the one"339redshift of this galaxy of z=0.0276 (IXochaneketal.2001).. the physical offset between the ealaxv center and the ART position is 220 kpc.,"redshift of this galaxy of $z = 0.0276$ \citep{kpf+01}, the physical offset between the galaxy center and the XRT position is 230 kpc."340 11292 is a very massive galaxy fal Mj=—25.4 il is probably several (mes as massive as Gx)., 11292 is a very massive galaxy (at $M_K = -25.4$ it is probably several times as massive as $G*$ ).341 Even with conservative assumptions about the galaxy mass and the position of the progenitor birthplace within it. a large kick (6= 500 km +) would be required to eject an object to this.," Even with conservative assumptions about the galaxy mass and the position of the progenitor birthplace within it, a large kick $v \age$ 500 km $^{-1}$ ) would be required to eject an object to this."342. An intriguing alternative possibility might be that the GRB was ejected from a much smaller ancl much less notable host (hat itself is associated wilh UGC 11292., An intriguing alternative possibility might be that the GRB was ejected from a much smaller and much less notable host that itself is associated with UGC 11292.343 Perhaps the spiral galaxy. mentioned above is a member of such an association: its eravitational potential well would be much more shallow and the offset would be only ~70 kpe., Perhaps the spiral galaxy mentioned above is a member of such an association; its gravitational potential well would be much more shallow and the offset would be only $\sim$ 70 kpc.344 This is within (he range of predicted short-harcd GRB ollsets., This is within the range of predicted short-hard GRB offsets.345 However. although there is some evidence that some short-harcd GRBs may originale from the local universe 2005).. no specilic short GRB has vet been associated wilh any host with 2<0.2.," However, although there is some evidence that some short-hard GRBs may originate from the local universe \citep{tcl+05}, no specific short GRB has yet been associated with any host with $z < 0.2$."346 Until the local population of short GRBs and their hosts (if real) has been better characterized or other low-probability chance associations with nearby galaxies are observed. this alternative hypothesis remains extremely speculative. and theposteriori probability argument alone is not sufficient to consider 11292 or its hypothetical group a likely host.," Until the local population of short GRBs and their hosts (if real) has been better characterized or other low-probability chance associations with nearby galaxies are observed, this alternative hypothesis remains extremely speculative, and the probability argument alone is not sufficient to consider 11292 or its hypothetical group a likely host."347 The large offset [rom what we have argued is a plausible host. if true. holds important ramifications for both the sort of viable progenitors and where they are born.," The large offset from what we have argued is a plausible host, if true, holds important ramifications for both the sort of viable progenitors and where they are born."348 First. the large olfset would seem to be at odds with the hypothesis of a degenerate binary origin where systematic kicks are small (such as in globular clusters [GCs]: Grindlayetal. 2006)).," First, the large offset would seem to be at odds with the hypothesis of a degenerate binary origin where systematic kicks are small (such as in globular clusters [GCs]; \citealt{gpm06}) )."349 While the expected number density of GCs at 75 kpe is exceedingly suiall (e.g..Dekkietal.2005). there certainly could be à GC at 2=0.287 in the ART error circle Gt would appear as [aint ved point source wilh magnitude fe29. in principle observable with LST imaging).," While the expected number density of GCs at 75 kpc is exceedingly small \citepeg{bbb+05}, there certainly could be a GC at $z = 0.287$ in the XRT error circle (it would appear as faint red point source with magnitude $R \approx 29$, in principle observable with HST imaging)."350 Alternatively. G* could have undergone a major merger leaving behind a progenitor svstem al the ART position.," Alternatively, $G^*$ could have undergone a major merger leaving behind a progenitor system at the XRT position."351" Second. if the progenitor was created during what appears to be the laststarburst in the putative host. then the lime since zero age main sequence would be T71.d0.2 Gyr confidence),"," Second, if the progenitor was created during what appears to be the laststarburst in the putative host, then the time since zero age main sequence would be $\tau \approx 1.3 \pm 0.2$ Gyr confidence)."352 At the inferred offset. this would imply a minimum avstemic kick velocity of eudgauin=n/7£2DOAH4 km |.," At the inferred offset, this would imply a minimum systemic kick velocity of $v_{\rm kick, min} = r/\tau \approx 55 \pm 14$ km $^{-1}$."353 Such a kick velocity is comparable to the models for degenerate binaries (Frverοἱal.1999). and observations of Galactie double NS systems (Dewietal. 2005).., Such a kick velocity is comparable to the models for degenerate binaries \citep{fwh99} and observations of Galactic double NS systems \citep{dpp05}. .354 The kick could have been significantly larger. implving that," The kick could have been significantly larger, implying that"355 ↖↖↽⋜⋯≼∐∖↥⋅↕∐∶↴∙∷∖↴↕∐↻∐⋜↧↴∖↴↸∖↥⋅↸∖↴∖↴∏↕↑↕⋟↥⋅∪⋯↕∐↑↸∖↥⋅↕≯↸∖↥⋅↸∖∐↸⊳↸∖↕≯↥⋅∪⋯↑∐↸∖ other periods present. and also appear to correlate with the outbursts.,"wanderings in phase result from interference from the other periods present, and also appear to correlate with the outbursts."356 We show the 2D DFT for davs 200 to 275 in Figure 16.., We show the 2D DFT for days 200 to 275 in Figure \ref{fig: 2dDFTq4}.357 Tere we used a window width of davs. aud shifted the window by L/ath of a day between transforms.," Here we used a window width of 2 days, and shifted the window by 1/8th of a day between transforms."3582 We show amplitude per cadence., We show amplitude per cadence.359 The orbial signal appears to be increasing in amplitude slehtly dming QL. rhaps as a result of the buillup of mass 1u the outer disk after several DN outbursts.," The orbital signal appears to be increasing in amplitude slightly during Q4, perhaps as a result of the buildup of mass in the outer disk after several DN outbursts."360 The huge auplitudes ound for the orbital signal in Figure 15. during outbursts l? aud 19 (starting davs ~216.5 and 266. res)ectively) are spurious. resulting from the hiehier-frequeucy. signals ound on the decline from maxima in each case.," The large amplitudes found for the orbital signal in Figure \ref{fig: omc200275} during outbursts 17 and 19 (starting days $\sim$ 246.5 and 266, respectively) are spurious, resulting from the higher-frequency signals found on the decline from maximum in each case."361 AS ciseussed below. outbursts 17 aud 19 both show evideuce or trigecringao a negative superliunu signal. ar the light curve for outburst 19 vields a complex Fourier traustforii that shows power at the orbital frequency. the negative superliuup frequency. and at 12.3 6/0 (1.95 hir).," As discussed below, outbursts 17 and 19 both show evidence for triggering a negative superhump signal, and the light curve for outburst 19 yields a complex Fourier transform that shows power at the orbital frequency, the negative superhump frequency, and at 12.3 c/d (1.95 hr)."362 The light curve for V31L Lyv ds rich im detail aud in particular provides the best data vot for exploring the time evolution of positive superlumops.," The light curve for V344 Lyr is rich in detail, and in particular provides the best data yet for exploring the time evolution of positive superhumps."363 As discussed above. the superluuups are first driven fo resonance durinugthe DN outburst that precedes the superoutburst as the heating wave transitions the outer disk to the hieh-viscositv state allowing the resonance to be driveu to amplitudes that can modulate the svsteui Iuninosity.," As discussed above, the superhumps are first driven to resonance during the DN outburst that precedes the superoutburst as the heating wave transitions the outer disk to the high-viscosity state allowing the resonance to be driven to amplitudes that can modulate the system luminosity."364 Close inspection of the positive superlauups in Fieures 7 and S shows that in both cases the amplitude of, Close inspection of the positive superhumps in Figures \ref{fig: reslc1} and \ref{fig: reslc2} shows that in both cases the amplitude of365Several astrophysical and cosmological probes have firmly established that baryons — which stars. planets. and (known) living creatures are made of — constitute only some 15% of the total content in the Universe adding to the dominant dark energy component.,"Several astrophysical and cosmological probes have firmly established that baryons – which stars, planets, and (known) living creatures are made of – constitute only some $15\%$ of the total content in the Universe adding to the dominant dark energy component."366" The rest is in the form of ""cold dark matter’ (DM). Le.. Massive particles that were non-relativistic at decoupling. do not emit/absorb radiations. and basically do not interact with themselves and with the baryons except via long-range gravitational forces."," The rest is in the form of `cold dark matter' (DM), i.e., massive particles that were non-relativistic at decoupling, do not emit/absorb radiations, and basically do not interact with themselves and with the baryons except via long-range gravitational forces."367 However. no ‘direct’ detection of the DM has been made so far. other than(2008).," However, no `direct' detection of the DM has been made so far, other than."368. Thus the microscopic nature of the DM remains largely a mystery: several clues suggest as a promising candidate or component the lightest supersymmetric particle. the “neutralino”2009).," Thus the microscopic nature of the DM remains largely a mystery; several clues suggest as a promising candidate or component the lightest supersymmetric particle, the `neutralino'."369. Given that the latter's mass. depending on the specific supersymmetric model. ranges from several GeVs to tens of TeVs. its laboratory production requires an accelerator at least as powerful as the newly-born Large Hadron Collider2009):: the discovery of supersymmetry and specifically of the neutralino is one of the main aims for the current experiments in high-energy physics.," Given that the latter's mass, depending on the specific supersymmetric model, ranges from several GeVs to tens of TeVs, its laboratory production requires an accelerator at least as powerful as the newly-born Large Hadron Collider; the discovery of supersymmetry and specifically of the neutralino is one of the main aims for the current experiments in high-energy physics."370 Meanwhile. evidence for the DM can be looked for “indirectly” in the sky.," Meanwhile, evidence for the DM can be looked for `indirectly' in the sky."371 In fact. the basic aims of the recently launched satellite include the search for y-ray signals due to the annihilation of DM particles at the Galactic Center (GC) and in nearby galaxies (see discussion in§ 4).," In fact, the basic aims of the recently launched satellite include the search for $\gamma$ -ray signals due to the annihilation of DM particles at the Galactic Center (GC) and in nearby galaxies (see discussion in 4)."372 The former provides a favorable target being closest to us. with the DM density expected to merease in moving toward the inner regions of a galaxy.," The former provides a favorable target being closest to us, with the DM density expected to increase in moving toward the inner regions of a galaxy."373 However. the GC is also a crowded region. and it remains a challenging task to separate the DM signal from the contributions of other astrophysical sources and backgrounds whose energy spectrum and angular distribution are poorly known.," However, the GC is also a crowded region, and it remains a challenging task to separate the DM signal from the contributions of other astrophysical sources and backgrounds whose energy spectrum and angular distribution are poorly known."374 In principle. if one can predict the strength and angular distribution of the annihilation signal itself. then the y-ray observations would elicit. or put ‘Indirect’ constraints on the (combined) properties of the DM particles like mass. annihilation cross section and channels.," In principle, if one can predict the strength and angular distribution of the annihilation signal itself, then the $\gamma$ -ray observations would elicit, or put `indirect' constraints on the (combined) properties of the DM particles like mass, annihilation cross section and channels."375 This approach has been pursued extensively but suffers yet of large uncertainties2004).. mainly related to the poor knowledge of the macroscopic DM distribution (rp) throughout the Galaxy.," This approach has been pursued extensively but suffers yet of large uncertainties, mainly related to the poor knowledge of the macroscopic DM distribution $\rho(r)$ throughout the Galaxy."376" Since the annihilation rate scales like 70""). such uncertainties are maximized near the center right where detection is favored."," Since the annihilation rate scales like $\rho^2(r)$, such uncertainties are maximized near the center right where detection is favored."377 Note that similar if milder uncertainties affect the source function of the electrons originated from DM annihilations by production or cascading: these diffuse outwards and interact with the Galactic magnetic field and with the interstellar light to produce synchrotron emission observed in the radio band2009).. and inverse Compton radiation observable in. y rays2009)..," Note that similar if milder uncertainties affect the source function of the electrons originated from DM annihilations by production or cascading; these diffuse outwards and interact with the Galactic magnetic field and with the interstellar light to produce synchrotron emission observed in the radio band, and inverse Compton radiation observable in $\gamma$ rays."378 Traditionally. the density profile of an equilibrium DM structure. or “halo”. is rendered in terms of different empirical formulas that fit the results of N-body simulations and to some extent the stellar observations.," Traditionally, the density profile of an equilibrium DM structure, or `halo', is rendered in terms of different empirical formulas that fit the results of $N$ -body simulations and to some extent the stellar observations."379 Perhaps the most popular one 1s the Navarro. Frenk White profile. that has an asymptotic inner slope ptr)«rl. goes over to a powerlaw behavior p(r)e77 in the halo's middle. and declines as pO)«777 in the outer regions.," Perhaps the most popular one is the Navarro, Frenk White profile, that has an asymptotic inner slope $\rho(r)\propto r^{-1}$, goes over to a powerlaw behavior $\rho(r)\propto r^{-2}$ in the halo's middle, and declines as $\rho(r)\propto r^{-3}$ in the outer regions."380 Despite its widespread use in the literature. clearly this expression cannot account for the actual DM distribution in the inner regions of a galaxy halo where it would imply a centrally angled gravitational potential well and an infinite pressure. nor in the halo outskirts where it would yield a diverging overall mass.," Despite its widespread use in the literature, clearly this expression cannot account for the actual DM distribution in the inner regions of a galaxy halo where it would imply a centrally angled gravitational potential well and an infinite pressure, nor in the halo outskirts where it would yield a diverging overall mass."381 Other empirical density profiles have been proposed but suffer of similarly unphysical features: e.g.. the Moore profile goes like ptr)&777 and implies a gravitational force divereing towards the center. while the Einasto profile behaves like (7) eso it yields a vanishing pressure there.," Other empirical density profiles have been proposed but suffer of similarly unphysical features; e.g., the Moore profile goes like $\rho(r)\propto r^{-1.2}$ and implies a gravitational force diverging towards the center, while the Einasto profile behaves like $\rho(r)\propto e^{-a\,r^{b}}$ , so it yields a vanishing pressure there."382 We stress that the 1n the predicted annihilation signals under these DM distributions turn out to be quite considerable: for example. the ratio of the NFW to the Einasto squared density averaged over | degree (about 150 pe) comes to a factor 10 when normalized at the Sun's location (see also discussion in 4).," We stress that the in the predicted annihilation signals under these DM distributions turn out to be quite considerable; for example, the ratio of the NFW to the Einasto squared density averaged over $1$ degree (about $150$ pc) comes to a factor $10$ when normalized at the Sun's location (see also discussion in 4)."383catalogue and carry an estimated £0.8 error for the Ho band and. £0.5 for the Ori] band.,catalogue and carry an estimated $\pm$ 0.3 error for the $\alpha$ band and $\pm$ 0.5 for the ] band.384 Of the 69 possible or proven planetary nebulae and VLIE objects known in the field of the survey (NLAO3. SAIP7TS). only 23 are found in the catalogue.," Of the 69 possible or proven planetary nebulae and VLE objects known in the field of the survey (MA93, SMP78), only 23 are found in the catalogue."385 This is due entirely to the limitations of the wide field CCD format of the images., This is due entirely to the limitations of the wide field CCD format of the images.386 In total. 236 objects of unknown identity appear in the catalogue.," In total, 236 objects of unknown identity appear in the catalogue."387 The catalogue contains LOT previously unknown PN candidates and 218 emission line star candidates. only 113 of which are known.," The catalogue contains 107 previously unknown PN candidates and 218 emission line star candidates, only 113 of which are known."388 We can make no definitive estimate of the fraction of our candidates that will be true PN or VLE objects., We can make no definitive estimate of the fraction of our candidates that will be true PN or VLE objects.389 However. we note that if only one half of our PN candidates are in fact PN. estimates of the total number of PN in the SAIC (27 2500) seem much larger than the values suggested by common wisdom (500 1000).," However, we note that if only one half of our PN candidates are in fact PN, estimates of the total number of PN in the SMC $> 2500$ ) seem much larger than the values suggested by common wisdom $\sim 500{\rm ~-~}1000$ )."390 In order to determine the true identity of the catalogued objects. follow-up observations of cach object must be mado.," In order to determine the true identity of the catalogued objects, follow-up observations of each object must be made."391 This mav be dillicult in some cases due to the relative imprecision of the object co-ordinates (we allow a 12 arc second error for most objects)., This may be difficult in some cases due to the relative imprecision of the object co-ordinates (we allow a 12 arc second error for most objects).392 However. these observations must be carried out in order to obtain a better survey of the planetary. nebulae content of the SAIC and to evaluate the viability of the methods used. to find the objects.," However, these observations must be carried out in order to obtain a better survey of the planetary nebulae content of the SMC and to evaluate the viability of the methods used to find the objects."393 Several observations subsequent. to the formation of the catalogue have revealed. that many of the potential PN objects are indeed PN., Several observations subsequent to the formation of the catalogue have revealed that many of the potential PN objects are indeed PN.394 X disadvantage. of the wide field. format of the SAIC images was apparent in many cases: more than one object occupied the 12 are seconds surrounding the catalogue co-ordinates., A disadvantage of the wide field format of the SMC images was apparent in many cases: more than one object occupied the 12 arc seconds surrounding the catalogue co-ordinates.395 Details of these observations will be published elsewhere., Details of these observations will be published elsewhere.396 However. the usefulness. of the catalogue in Tables 1 and 2. as à supplement to those in MA93 and SMPTS. is clear.," However, the usefulness of the catalogue in Tables 1 and 2, as a supplement to those in MA93 and SMP78, is clear."397 Phe. methods. of finding PN detailed in Sections 24 will be applied to the Large Magellanic Cloud where we have already retrieved the data., The methods of finding PN detailed in Sections 2–4 will be applied to the Large Magellanic Cloud where we have already retrieved the data.398 Also. bv comparing different narrow band images to those used here. many more emission objects. such as Be stars. could be identified in the Magellanic Clouds.," Also, by comparing different narrow band images to those used here, many more emission objects, such as Be stars, could be identified in the Magellanic Clouds."399 lt is à pleasure to acknowledge Michael Burton ancl John Webb for proof reading the manuscript and for many helpful comments., It is a pleasure to acknowledge Michael Burton and John Webb for proof reading the manuscript and for many helpful comments.400 We would also like to thank Stefan Weller. Jill Rathborne and John Storey for useful cüscussions.," We would also like to thank Stefan Keller, Jill Rathborne and John Storey for useful discussions."401 We also acknowledge the referee. €. HI. Jacoby. for many helpful suggestions.," We also acknowledge the referee, G. H. Jacoby, for many helpful suggestions."402surface acts to make (he magnetic field a dipole.,surface acts to make the magnetic field a dipole.403 The diffusivity near the surface enhances mainlv the coupling of the poloidal field near the surface between the hemispheres. leading to the eeneration of dipolar magnetic field.," The diffusivity near the surface enhances mainly the coupling of the poloidal field near the surface between the hemispheres, leading to the generation of dipolar magnetic field."404 The second result is (hat the thinner laver of the strong surface diffusivity also works to cause the magnetic field to become dipolar., The second result is that the thinner layer of the strong surface diffusivity also works to cause the magnetic field to become dipolar.405 The thinner surface depth suppresses the coupling of the toroidal field between the hemispheres since most of the toroidal field exists around (he tachocline., The thinner surface depth suppresses the coupling of the toroidal field between the hemispheres since most of the toroidal field exists around the tachocline.406 The third result is that the [ast meridional How causes the magnetic field to become a quadrupole., The third result is that the fast meridional flow causes the magnetic field to become a quadrupole.407 The fast meridional flow prevents the poloidal field from coupling near the surface of the equator because the flow (transports the poloidal field poleward., The fast meridional flow prevents the poloidal field from coupling near the surface of the equator because the flow transports the poloidal field poleward.408 In addition. the flow transports the toroidal field around the tachocline equatorward. (hus causing the coupling of the toroidal fiekl.," In addition, the flow transports the toroidal field around the tachocline equatorward, thus causing the coupling of the toroidal field."409 These three results quantitatively constrain the distribution and (he amplitude of turbulent diffusivityv. which cannot be determined by observation and is a important [actor for the dvnamo problem.," These three results quantitatively constrain the distribution and the amplitude of turbulent diffusivity, which cannot be determined by observation and is a important factor for the dynamo problem."410 In this study. we did not investigate the dependence of the parity ou (he a-ellect in the convection zone. which may be a strong [actor in causing the magnetic field to become a dipole.," In this study, we did not investigate the dependence of the parity on the $\alpha$ -effect in the convection zone, which may be a strong factor in causing the magnetic field to become a dipole."411 The poloidal field generated by this effect around the tachocline is transported equatorward by (he meridional flow. and (his process enhances the coupling of the poloidal Ποια between (he hemispheres (Dikpati&Gilman2001:etal. 2004)..," The poloidal field generated by this effect around the tachocline is transported equatorward by the meridional flow, and this process enhances the coupling of the poloidal field between the hemispheres \citep{2001ApJ...559..428D,2002A&A...390..673B,2004A&A...427.1019C}."412 It is possible that the criterion for a dipole field we obtain in Chis study mar be mocdified with this (wpe of a-effect., It is possible that the criterion for a dipole field we obtain in this study may be modified with this type of $\alpha$ -effect.413 We will discuss (he possibility of the existence and the inlluence of the a-effect in a forthcoming paper., We will discuss the possibility of the existence and the influence of the $\alpha$ -effect in a forthcoming paper.414 Another interesting issue to be addressed is the possibility that (he variation of the velocity field in Che solar evele affects the parity., Another interesting issue to be addressed is the possibility that the variation of the velocity field in the solar cycle affects the parity.415 In the ealeulations for the earth diamo there is the significant difference between the kinematic and the MIID cases in (he parity issue (Nishikawa&Kusano2008).., In the calculations for the earth dynamo there is the significant difference between the kinematic and the MHD cases in the parity issue \citep{nishikawa2008simulation}.416 Thus. in the [uture we will investigate the parity issue with the Lorentz feedback (Rempel 2006)..," Thus, in the future we will investigate the parity issue with the Lorentz feedback \citep{2006ApJ...647..662R}. ."417at pressures greater than ~10 bar.,at pressures greater than $\sim$ 10 bar.418 In Figure 4 we plot vertical velocities throughout the model., In Figure \ref{fig:d_vert} we plot vertical velocities throughout the model.419" Although the primitive equations used in this code replace the vertical momentum equation with hydrostatic balance, vertical motions are still present through the continuity equation: dw/dP=—V :ὔ, where w=dP/dt and @ is the horizontal wind."," Although the primitive equations used in this code replace the vertical momentum equation with hydrostatic balance, vertical motions are still present through the continuity equation: $d\omega/dP = -\nabla \cdot \vec{v}$ , where $\omega = dP/dt$ and $\vec{v}$ is the horizontal wind."420" We integrate the continuity equation down from the top of the model, where the boundary condition imposes w=0 at P=0."," We integrate the continuity equation down from the top of the model, where the boundary condition imposes $\omega=0$ at $P=0$."421 We then convert to a vertical velocity (dz/dt) through use of the hydrostatic equation: dP/dz=—pg., We then convert to a vertical velocity $dz/dt$ ) through use of the hydrostatic equation: $dP/dz = - \rho g$.422 We note that snapshots of the vertical wind profiles taken at other points in the run match the main features shown here., We note that snapshots of the vertical wind profiles taken at other points in the run match the main features shown here.423" The strength of vertical motion in the atmosphere has important implications for the mixing of chemical species throughout the atmosphere, which can introduce chemical disequilibrium and influence the observable properties of the planet (Mosesetal.2011)."," The strength of vertical motion in the atmosphere has important implications for the mixing of chemical species throughout the atmosphere, which can introduce chemical disequilibrium and influence the observable properties of the planet \citep{Moses2011}."424". For example, titanium oxide (TiO) and vanadium oxide (VO) have been identified as possible candidates for the absorbing species responsible for stratospheric temperature inversions, but Spiegeletal.(2009) demonstrated that very strong vertical mixing would be required to keepthese absorbers aloft in the atmosphere."," For example, titanium oxide (TiO) and vanadium oxide (VO) have been identified as possible candidates for the absorbing species responsible for stratospheric temperature inversions, but \citet{Spiegel2009} demonstrated that very strong vertical mixing would be required to keepthese absorbers aloft in the atmosphere."425 From, From426Zuckerman et al. (,Zuckerman et al. (427"2007) provide an analysis of the white dwarf GD 362, including an estimate of the abundance of 17 elements accreted by that star.","2007) provide an analysis of the white dwarf GD 362, including an estimate of the abundance of 17 elements accreted by that star."428 They conclude that an asteroid-mass object (either a remnant asteroid or the residual of a disrupted terrestrial planet) is needed to explain the abundance pattern., They conclude that an asteroid-mass object (either a remnant asteroid or the residual of a disrupted terrestrial planet) is needed to explain the abundance pattern.429" A very rough estimate of the size of an object needed to account for the metals seen in that star (107 ο) is of order 80 km: such an object would produce a transit with a depth of 0.01%, or 100 ppm."," A very rough estimate of the size of an object needed to account for the metals seen in that star $10^{22}$ g) is of order $80$ km; such an object would produce a transit with a depth of $0.01\%$, or $100$ ppm."430" For every asteroid that is tidally disrupted, there must be many more with perihelia located much farther trom the white dwart."," For every asteroid that is tidally disrupted, there must be many more with perihelia located much farther from the white dwarf."431 Direct detection of these asteroids is challenging., Direct detection of these asteroids is challenging.432 They have very little gravitational influence on their star and cannot presently be detected through cither Doppler or ground-based photometric transit methods., They have very little gravitational influence on their star and cannot presently be detected through either Doppler or ground-based photometric transit methods.433" Transits of white dwarfs by large asteroids can, however, be detected byKepler, a space mission designed to detect the transits of Sun-like a ra"," Transits of white dwarfs by large asteroids can, however, be detected by, a space mission designed to detect the transits of Sun-like stars by Earth-like planets."434dius of , Consider a white dwarf with a radius of $8000$ km.435100 km (1000) km will produce a fractional decrease in the amount of light received of 150 ppm (15.000 ppm). within Kepler's detection limit.," An asteroid with a radius of $100$ km $1000$ ) km will produce a fractional decrease in the amount of light received of 150 ppm (15,000 ppm), within Kepler's detection limit."436" Many such asteroids of this size are known in our own solar system [an estimated 80.000 in the Kuiper Belt alone (Trujillo, Jewett, Luu 2001)]. so it is reasonable to expect that they exist elsewhere as well."," Many such asteroids of this size are known in our own solar system [an estimated $80,000$ in the Kuiper Belt alone (Trujillo, Jewett, Luu 2001)], so it is reasonable to expect that they exist elsewhere as well."437 In $2 we show that theKepler observatory can discover asteroids orbiting white dwarfs by identifying short-lived downward deviations from the baseline flux in white dwarfs associated with transits by asteroids., In 2 we show that the observatory can discover asteroids orbiting white dwarfs by identifying short-lived downward deviations from the baseline flux in white dwarfs associated with transits by asteroids.438 In 3 we discuss what we can learn throughKepler monitoring of a small set of white dwarts., In 3 we discuss what we can learn through monitoring of a small set of white dwarfs.439 Asteroid transits or significant limits on white-dwart asteroid systems are a certain science return., Asteroid transits or significant limits on white-dwarf asteroid systems are a certain science return.440" In addition, depending on the structure of white-dwarf planetary systems. transits by rings and/or moons may also be detected by monitoring a modest number of white dwarfs."," In addition, depending on the structure of white-dwarf planetary systems, transits by rings and/or moons may also be detected by monitoring a modest number of white dwarfs."441 The depth of a transit and its time duration determine its level of detectability., The depth of a transit and its time duration determine its level of detectability.442" If Aj is the projected. area ofB the asteroid.. and ΑνατπRy,y the cross-sectional. area ofB the white. dwarf.B the depth of the transit is (A,4/A«4). The calculations for asteroids transiting white dwarfs mirror the results for an Earth-like planet transiting a Sun-like star, because the relative size scales are similar."," If $A_{\rm ast}$ is the projected area of the asteroid, and $A_{\rm wd}= \pi\, R_{\rm wd}^2$ the cross-sectional area of the white dwarf, the depth of the transit is $(A_{\rm ast}/A_{\rm wd}).$ The calculations for asteroids transiting white dwarfs mirror the results for an Earth-like planet transiting a Sun-like star, because the relative size scales are similar."443" For an asteroid of a given size, the depth is greatest for more massive white dwarfs, which are smaller."," For an asteroid of a given size, the depth is greatest for more massive white dwarfs, which are smaller."444range of stellar ages is fro disk to center).,range of stellar ages is from disk to center).445 Tn summary. all the objects presented in these two panels have colour profiles cousisteut with the evolutionary tracks of Bica.. but incousistcut with either of the other two models shown in Figure 17..," In summary, all the objects presented in these two panels have colour profiles consistent with the evolutionary tracks of Bica, but inconsistent with either of the other two models shown in Figure \ref{f10}."446 Changes in metallicity would have ouly a minor effect (for iustancemay be responsible for the shehtly differiug slopes of the profiles). as if is apparent from the virtually overlapping Worthey models for a wide range of inetallicitics.," Changes in metallicity would have only a minor effect (for instance may be responsible for the slightly differing slopes of the profiles), as it is apparent from the virtually overlapping Worthey models for a wide range of metallicities."447 The Charlot Bruzual models for differcut star formation (not shown in Figure 17)) do not resenible our colour profiles aud lic far from our data points., The Charlot Bruzual models for different star formation (not shown in Figure \ref{f10}) ) do not resemble our colour profiles and lie far from our data points.448 Although the influence ofthe ACN makes it more difficult to interpret the Sevfert L inverse colour gradients. it is likely at least for the Sevtert 2s. hat their colour eradieunts mainly represcut stellar age effects. if extinction. was to be ignored (dust extinction would have a similar effect on the colour xofiles).," Although the influence of the AGN makes it more difficult to interpret the Seyfert 1 inverse colour gradients, it is likely at least for the Seyfert 2s, that their colour gradients mainly represent stellar age effects, if extinction was to be ignored (dust extinction would have a similar effect on the colour profiles)."449 Although for a simple Calactic exctiuctiou aw such an effect could not be uch larger than ~0.5 nagin V. band a ealaxy. different assumptions or the dust distribution could result in larger effects DeJong1996. aud references therein). (," Although for a simple Galactic exctinction law such an effect could not be much larger than $\sim$ 0.5 mag in $V$ band a galaxy, different assumptions for the dust distribution could result in larger effects \cite{jong96c} and references therein). ("450c) Lower panelsanels: In these: plots: we show: objects: with complex aud unusual colour profiles that caunot be explained casily bv a simple comparison with population models.,c) Lower panels: In these plots we show objects with complex and unusual colour profiles that cannot be explained easily by a simple comparison with population models.451" The Sevfert 1s plotted im the left panel are TRAS 00509|1225, 23016|2221 and 21299|095."," The Seyfert 1s plotted in the left panel are IRAS 00509+1225, 23016+2221 and 21299+095."452 The first oue (bluest of the three) is au early type spiral with kuotty emission in its (one-sided) spiral avin., The first one (bluest of the three) is an early type spiral with knotty emission in its (one-sided) spiral arm.453 What makes if uuusual is its very blue unclear region., What makes it unusual is its very blue nuclear region.454 Its disk colours could be fitted with a very voung starburst <0.5 Cvr old. superposed on the old galaxy population.," Its disk colours could be fitted with a very young starburst $\leq$ 0.5 Gyr old, superposed on the old galaxy population."455 IRAS 23016|2221 (with the bluest (WR) nuclear colour) is au object with peculiar morphology. reminiscent of a recent merger. originally given an carly Hubble classification.," IRAS 23016+2221 (with the bluest $(V-R)$ nuclear colour) is an object with peculiar morphology, reminiscent of a recent merger, originally given an early Hubble classification."456 Its strong Ta ciission within the central —5 kpe (sce Appendix of Paper ILD) is probably respousible for the Ὀ (WR) disk compared to its nucleus;, Its strong $\alpha$ emission within the central $\sim$ 5 kpc (see Appendix of Paper III) is probably responsible for the bluer $(V-R)$ disk compared to its nucleus.457 Modeling its colours with Bica Alloin’s tracks indicates a very vouug starburst of mean age 0.07207. Cr., Modeling its colours with Bica Alloin's tracks indicates a very young starburst of mean age 0.07-0.7 Gyr.458 The las object is IRAS 21299|095. an carly type spiral which also shows strong cicumnuclear Ho emission. tha causes ifs mean disk colours to become siguificautlv bluer (compared to the nucleus).," The last object is IRAS 21299+095, an early type spiral which also shows strong circumnuclear $\alpha$ emission, that causes its mean disk colours to become significantly bluer (compared to the nucleus)."459" They can be fitted by a starburst of mean age 0.02-0.5 Cyr,", They can be fitted by a starburst of mean age 0.02-0.5 Gyr.460 It is difficul to explain its very red (V.—R) umelear colour. thoueh.," It is difficult to explain its very red $(V-R)$ nuclear colour, though."461 On the right panel we show some extreme Sevfer 2 cases: IRAS 1311111508. 11298|5313. (WW and E members). 19251-7215 aud 13536|1836 Gu order of bluening (WR) nuclear. colours).," On the right panel we show some extreme Seyfert 2 cases: IRAS 13144+4508, 11298+5313 (W and E members), 19254-7245 and 13536+1836 (in order of bluening $(V-R)$ nuclear colours)."462 The fist three objects have sinilar (BR) colours as the rest of the Seytert 2 sample aud their colour profiles are {roughly} following the evolutionary tracks of Bica Alloin., The first three objects have similar $(B-R)$ colours as the rest of the Seyfert 2 sample and their colour profiles are (roughly) following the evolutionary tracks of Bica Alloin.463 However. their (WR) colours ave. strongly shifted to the red by ~0.2-0.3 mag. distinguishing them. from the rest of the sample.," However, their $(V-R)$ colours are strongly shifted to the red by $\sim$ 0.2-0.3 mag, distinguishing them from the rest of the sample."464 They are all πιονους of inultiple strongly interacting systems. suffering tidal distortions and they all have very blue (BV) integrated) disk colours. indicating recent star formation events," They are all members of multiple strongly interacting systems, suffering tidal distortions and they all have very blue $(B-V)$ (integrated) disk colours, indicating recent star formation events."465 They fit the description given bv Larson&Tinsley1978 of strongly iteracting galaxies (at a particular stage of their ανασα] evolution. involving tidal features). showing very blue (5VJ colours. off the normal sequence in colour-colour plots.," They fit the description given by \cite{larson78} of strongly interacting galaxies (at a particular stage of their dynamical evolution, involving tidal features), showing very blue $(B-V)$ colours, off the normal sequence in colour-colour plots."466 The latter two objects are examples of on-going mergers. with double nuclei embedded in a cohnunon body and large tidal tails extending radially outwards.," The latter two objects are examples of on-going mergers, with double nuclei embedded in a common body and large tidal tails extending radially outwards."467 Actually. the colours of IRAS 19251-7215 can be explained with a Bica Alloiu tvpe of iiodel. indicating starbursts with age ~0.1-5 Gyr or younger if we allow for the (certainly very significant) dust effects. invoked in order to explain the steep colour gradicut aud the VON red unclear colour.," Actually, the colours of IRAS 19254-7245 can be explained with a Bica Alloin type of model, indicating starbursts with age $\sim$ 0.1-5 Gyr or younger if we allow for the (certainly very significant) dust effects, invoked in order to explain the steep colour gradient and the very red nuclear colour."468 Ou the other haud. n ver’ difficult fo explain the colour rofile of IRAS m13536|1836. part o the wohlem being the very blue W uucleus that affects the mean nuclear colour at 2 kpe.," On the other hand, it is very difficult to explain the colour profile of IRAS 13536+1836, part of the problem being the very blue W nucleus that affects the mean nuclear colour at 2 kpc."469 We have not presented colou-colour profiles for any of the Cold saniple objects., We have not presented colour-colour profiles for any of the Cold sample objects.470 The only two objects among them with three-colour information are IRAS 0751115327 and 06506|5025. both late-type barre spirals.," The only two objects among them with three-colour information are IRAS 07514+5327 and 06506+5025, both late-type barred spirals."471 On colour-colour diapruus as the ones of Figure l7.. their colour profiles are similar to those of the third group Sevfert 2 galaxies (lower panels).," On colour-colour diagrams as the ones of Figure \ref{f10}, their colour profiles are similar to those of the third group Seyfert 2 galaxies (lower panels)."472 They show very red colours that cannot be interprete by any of the population svuthesis iiodels and their profiles vary alinost perpendicular to the normal colourcolour sequence., They show very red colours that cannot be interpreted by any of the population synthesis models and their profiles vary almost perpendicular to the normal colour-colour sequence.473 These effects secu to be independen of the unclear activity type (one object is a starburst. the other a Sevfert 1 galaxy).," These effects seem to be independent of the nuclear activity type (one object is a starburst, the other a Seyfert 1 galaxy)."474 We stuummarize our couclusious in the next section., We summarize our conclusions in the next section.475" Iu this paper we have examined the colour distributions characterizingοBway]3 theH host: galaxies»»""GN of: our. WanriiTua aud"" 1Cold siuuples.", In this paper we have examined the colour distributions characterizing the host galaxies of our Warm and Cold samples.476" Our main conclusions are as follows: 1,", Our main conclusions are as follows: 1.477 The Wn Sevfert 1 galaxies show bluer nuclei, The Warm Seyfert 1 galaxies show bluer nuclei478The analvsis of different absorption liues of the optical star reveals a strong heating. cffect) in: the illmuinated.: stars atmosphere.,The analysis of different absorption lines of the optical star reveals a strong heating effect in the illuminated star's atmosphere.479 During the disk eclipse eeress low-excitation∙∙ absorption∙ lines∙ strougly weaken., During the disk eclipse egress low-excitation absorption lines strongly weaken.480 The stellar hemisphere iluninmated by the bright accretion disk iu⋅ SS133 probably has a temperature of ~20.000 Ix. as the presence of CITA1267 absorption Chussion liue sugecstsOO (the top spectzuii in Fie. 15)).," The stellar hemisphere illuminated by the bright accretion disk in SS433 probably has a temperature of $\sim 20,000$ K, as the presence of $\lambda 4267$ absorption + emission line suggests (the top spectrum in Fig. \ref{fig:SPklass}) )."481 This absorption line is the stronecst oue in this spectral region alone supcreiauts with temperatures I2TLTTo15.000 K. The evolution of the blend A272 (Fol\ Fol273.3 | CITA 275.5) is seen: in the eclipse center the low-cxcitatiou Fel line is stronger. while out of the eclipse. FellΟΤΙ lines are chhanced.," This absorption line is the strongest one in this spectral region among supergiants with temperatures $ > 15,000$ K. The evolution of the blend $\lambda4273$ $\lambda 4271.7$ + $\lambda 4273.3$ + $\lambda 4275.5$ ) is seen: in the eclipse center the low-excitation FeI line is stronger, while out of the eclipse FeII+CrII lines are enhanced."482 Other Fel lines also appear oulv in the eclipse., Other FeI lines also appear only in the eclipse.483 These effects are illustrated by Fig. 16.," These effects are illustrated by Fig. \ref{fig:demo21},"484" iu which spectra of the staudard stars with effective temperatures δ,1060. Is and 22.000 I& are shown together with spectra of SS133 obtained on 9.05. 10.05. 28.01111.05. 12.05. and 13.05 (orbital eclipses fell on nights 10.05 aud 28.01111.05)."," in which spectra of the standard stars with effective temperatures 8,400 K and 22,000 K are shown together with spectra of SS433 obtained on 9.05, 10.05, 28.04+11.05, 12.05 and 13.05 (orbital eclipses fell on nights 10.05 and 28.04+11.05)."485 The orbital phase rises from bottom to top in the fieure., The orbital phase rises from bottom to top in the figure.486 There are enmussion lines in these spectral fraeimoeuts the broad structured cussion of CITAI267..— and strougser enüssions FeIIA5169 MeIAD167.51723 and FoIIAD197.," There are emission lines in these spectral fragments — the broad structured emission of $\lambda 4267$, and stronger emissions $\lambda 5169$ $\lambda4875167, 5173$ and $\lambda 5197$."488 Note that enussion lines. which prestmably are formed in the disk wind. should move bluewird Gu phase with the compact object) iu the orbital phases of our observations.," Note that emission lines, which presumably are formed in the disk wind, should move blueward (in phase with the compact object) in the orbital phases of our observations."489 In coutrast. absorption nes. which are formed in the donor plotosphere. must move redward during our observations.," In contrast, absorption lines, which are formed in the donor photosphere, must move redward during our observations."490 The streneth of the CTIA1267 absorption compoucut Guarked by vertical bars in Fig. 16)), The strength of the $\lambda 4267$ absorption component (marked by vertical bars in Fig. \ref{fig:demo21}) )491 increases uotablv out of the eclipse., increases notably out of the eclipse.492 The comples blend Al273 (FOIE|FellCIT) is marked by the dotted Hues in the figure., The complex blend $\lambda4273$ (FeI+FeII+CrII) is marked by the dotted lines in the figure.493 Fig., Fig.494 16 illustrates absorption lines narked bv the vertical ars) the blend AL3LL of THA1313 FoILA131 THA£315: ScTA320. Hine aud the blend ScIIA1325 | FelA1326.1327.," \ref{fig:demo21} illustrates absorption lines (marked by the vertical bars) — the blend $\lambda 4314$ of $\lambda4954313$ $\lambda 4314$ $\lambda 4315$; $\lambda 4320$ line and the blend $\lambda 4325$ + $\lambda 4326, 4327$."496 However the last bleud mav be distorted by the strong blue wing of I5 12 the middle of eclipse., However the last blend may be distorted by the strong blue wing of $\gamma$ in the middle of eclipse.497 Other| absorption lines shown in Fie., Other absorption lines shown in Fig.498 16 απο panel) are ASLOL (Ta|Fel) aud. A5227 (Ti|Fel}.," \ref{fig:demo21}499 (right panel) are $\lambda 5154$ (TiII+FeII) and $\lambda 5227$ (TiII+FeI)."500" It is seen that these Hines shift redward with tie,", It is seen that these lines shift redward with time.501 Iu Fie., In Fig.502 16 we also show the spectrum of SS133 averaged over all nights of observations (the third from. bottom)., \ref{fig:demo21} we also show the spectrum of SS433 averaged over all nights of observations (the third from bottom).503 When averaging spectra obtained ou individual nights we shifted them to zero velocity according to the radial velocity curve from Fie. 18s.., When averaging spectra obtained on individual nights we shifted them to zero velocity according to the radial velocity curve from Fig. \ref{fig:radvel}.504 The average spectrum las ai better signal-to-noise ratio., The average spectrum has a better signal-to-noise ratio.505 All the absorptou lines remain in the spectrum and they are simular to the corresponding lines in the spectrum of the staudard supereiant (8.100 IN).," All the absorpton lines remain in the spectrum and they are similar to the corresponding lines in the spectrum of the standard supergiant (8,400 K)."506 The shallow emission line (prestunably CIIA1267) has an absorption component., The shallow emission line (presumably $\lambda 4267$ ) has an absorption component.507" Iu our recent spectral observations of 5ο20, which were carried out around primary minima on Aueust 21. 2001 and September 6. 2001 (the precession phase is the same. ie. the maxinuun disk opeuiug) we confirmed the preseuce"," In our recent spectral observations of SS433, which were carried out around primary mimima on August 24, 2004 and September 6, 2004 (the precession phase is the same, i.e. the maximum disk opening) we confirmed the presence"508We investigate the contribution of stellar proper motions to microlensing statistics bv looking for the transverse velocity (equivalent transverse velocity) that produces a derivative histogram closest to the one produced by the proper motions of the point masses in the same fields.,We investigate the contribution of stellar proper motions to microlensing statistics by looking for the transverse velocity $equivalent$ $transverse$ $velocity$ ) that produces a derivative histogram closest to the one produced by the proper motions of the point masses in the same fields.509 Phe similarity of two cumulative distributions £ and £ is quantified by their INS difference D where This procedure leads to the natural definition of a constant. which following Ixundic. Witt Chang (1993). and Wambseanss Ixundie (1993) we call the cllectivencss parameter Note that this value dillers to that defined by Wanmbseanss Ixundic (1993). as it takes account of all microlensing as opposed to only LIMES.," The similarity of two cumulative distributions $P_{1}$ and $P_{2}$ is quantified by their KS difference D where This procedure leads to the natural definition of a constant, which following Kundic, Witt Chang (1993), and Wambsganss Kundic (1993) we call the effectiveness parameter Note that this value differs to that defined by Wambsganss Kundic (1993), as it takes account of all microlensing as opposed to only HMEs."510" For the sake of ‘larity. we therefore refer to the quantity. defined. by Eqn 20 as the total effectiveness parameter (e, ).", For the sake of clarity we therefore refer to the quantity defined by Eqn \ref{a} as the total effectiveness parameter $a_{tot}$ ).511 ligure shows the images of a source line as well as 10 corresponding point source light curve for a simulation iwing an optical depth of &=0.4., Figure \ref{imlc} shows the images of a source line as well as the corresponding point source light curve for a simulation having an optical depth of $\kappa=0.4$.512 The source trajectory is aligned at 45 degrees to the wy y-axis., The source trajectory is aligned at 45 degrees to the $x_{1}$ -axis.513 Figure 2. displays 1e cumulative histogram of derivatives that was calculated clirectly from. the combination of this light curve with a ransverse velocity (clot-dashecl line)., Figure \ref{dertest} displays the cumulative histogram of derivatives that was calculated directly from the combination of this light curve with a transverse velocity (dot-dashed line).514 Each of the point masses in this simulation were given a velocity equal to 10 transverse velocity and parallel to the source line., Each of the point masses in this simulation were given a velocity equal to the transverse velocity and parallel to the source line.515 In 10 absence of a shear. the transverse ancl stream motions we equivalent.," In the absence of a shear, the transverse and stream motions are equivalent."516 “Phe distribution of derivatives at stationary source points along the source line was then calculated using re expression LO. and is shown as the solid light line in Figure 2..," The distribution of derivatives at stationary source points along the source line was then calculated using the expression \ref{der}, and is shown as the solid light line in Figure \ref{dertest}."517 In addition. the histogram: of derivatives in 1ο transverse motion case was also calculated: using the combination of the analvtical expression for the light curve derivative (eqn 3)). with the transverse velocity.," In addition, the histogram of derivatives in the transverse motion case was also calculated using the combination of the analytical expression for the light curve derivative (Eqn \ref{der_stat}) ), with the transverse velocity."518 The histograms calculated from the analytical derivatives agree to within the numerical resolution of the computer (as they must if our expressions are correct)., The histograms calculated from the analytical derivatives agree to within the numerical resolution of the computer (as they must if our expressions are correct).519 The histograms calculated. from the analytical and numerical derivatives (calculated from a 5-point derivative along the light-curve) display excellent agreement. having a maximum IxS dilference of 0.008.," The histograms calculated from the analytical and numerical derivatives (calculated from a 5-point derivative along the light-curve) display excellent agreement, having a maximum KS difference of 0.008."520 Figure 2. shows the simple nature of the derivative distribution. even when computed over a relatively short sample length.," Figure \ref{dertest} shows the simple nature of the derivative distribution, even when computed over a relatively short sample length."521 This is in stark contrast to the highly disordered parent light curve., This is in stark contrast to the highly disordered parent light curve.522 As a further check of our method. the stars are again given parallel motions resulting in a stream velocity. but this time the direction of this motion is perpencdieular to that of the transverse velocity.," As a further check of our method, the stars are again given parallel motions resulting in a stream velocity, but this time the direction of this motion is perpendicular to that of the transverse velocity."523 In this case our simulation consists of 100. fields of point masses. cach with an optical depth of 0.4.," In this case our simulation consists of 100 fields of point masses, each with an optical depth of 0.4."524 Phe best fit was obtained between the histogram of derivatives due to stream motions. and that due to a transverse velocity. by finding the equivalent: transverse velocity that minimised. the WS cilference between the histograms.," The best fit was obtained between the histogram of derivatives due to stream motions, and that due to a transverse velocity, by finding the equivalent transverse velocity that minimised the KS difference between the histograms."525 This procedure produced a ratio between the value of the stellar stream motion and the caleulatect equivalent transverse motion of 0.9993 with a minimised AS cillerenee of 0.007., This procedure produced a ratio between the value of the stellar stream motion and the calculated equivalent transverse motion of 0.9993 with a minimised KS difference of 0.007.526 These simulations demonstrate that the methocl emploved is working correctIv., These simulations demonstrate that the method employed is working correctly.527 In order to investigate the dependence of the relative ellects of a transverse motion and that of a collection of random. proper motions. we start by following the example of Ixundic. Witt Chang (1993) who explore the unrealistic situation in which the point masses are all solar mass objects that have a motion of fixed. magnitude. but a random direction. [ving in the lens plane.," In order to investigate the dependence of the relative effects of a transverse motion and that of a collection of random proper motions, we start by following the example of Kundic, Witt Chang (1993) who explore the unrealistic situation in which the point masses are all solar mass objects that have a motion of fixed magnitude, but a random direction lying in the lens plane."528 We label simulations with this form for the stellar velocity distribution hy CONST.DISP. These. models allow us to. explore the relationship between the microlensing properties of the two types of motion in a simple situation without the added complexities of velocity ancl mass functions., We label simulations with this form for the stellar velocity distribution by $CONST.DISP.$ These models allow us to explore the relationship between the microlensing properties of the two types of motion in a simple situation without the added complexities of velocity and mass functions.529 These. are discussed in sections 6.2. and 6.3., These are discussed in sections \ref{mass_func_sect} and \ref{vel_disp_sect}.530 We consider the ellect. of optical depth on the value of eus, We consider the effect of optical depth on the value of $a_{tot}$.531 MSOLAR tvpe simulations were made at optical depths between α=0.025 and κ=0.6 (simulations 1-N in Table 13)., $MSOLAR$ type simulations were made at optical depths between $\kappa=0.025$ and $\kappa=0.6$ (simulations 1-8 in Table \ref{parameters}) ).532 Table 2. displays the value of ai.) obtained as well as the best fit INS dillerence. and the derivative at which the IWS dillerence was found. (in brackets).," Table \ref{opt_dept_val} displays the value of $a_{tot}$ obtained as well as the best fit KS difference, and the derivative at which the KS difference was found (in brackets)."533 Table 2 also clisplays the results of sections 6.2 and 6.3.., Table \ref{opt_dept_val} also displays the results of sections \ref{mass_func_sect} and \ref{vel_disp_sect}.534" Phe quoted error in these. and all values of ανω, presented in this paper have been estimated by dividing the total simulation at each optical depth into 5 smaller simulations. and calculating the standard deviation in the resulting values."," The quoted error in these, and all values of $a_{tot}$ presented in this paper have been estimated by dividing the total simulation at each optical depth into 5 smaller simulations, and calculating the standard deviation in the resulting values."535 ligure 3. shows graphically the relationship between &s , Figure \ref{optical_gr} shows graphically the relationship between $\kappa$ 536reeious further outside are cither not targeted by observations or their X-ray huuinositv sensitivity uit is uuch licher.,regions further outside are either not targeted by observations or their X-ray luminosity sensitivity limit is much higher.537 Cousequeutly a significant umuber of NRBs medicted by the models to have moved to distances vevoud 10 kpe could remain uudetected., Consequently a significant number of XRBs predicted by the models to have moved to distances beyond $\sim10$ kpc could remain undetected.538 Qur above findines strongly depeud ou our choice to set jatal kicks for direct collapse BIs to be as strong as our Aaswellian natal kick distribution., Our above findings strongly depend on our choice to set natal kicks for direct collapse BHs to be as strong as our Maxwellian natal kick distribution.539 If we set direct collapse natal kicks to be strictly zero. we find a large »pulatiou of persistent sources in the SAIC bar with uunostv Ly>LY? 1. containing CIleB donors and massive DIT accretors. aud having orbital periods ou he order of thousands of davs.," If we set direct collapse natal kicks to be strictly zero, we find a large population of persistent sources in the SMC bar with luminosity $L_X>10^{35}$ $^{-1}$, containing CHeB donors and massive BH accretors, and having orbital periods on the order of thousands of days."540 As these svsteius are not oulv unobserved in the SAIC. but throughout all Πλ »»pulatious. we enable snall direct collapse kicks which split these loosely bound. «πο».," As these systems are not only unobserved in the SMC, but throughout all HMXB populations, we enable small direct collapse kicks which split these loosely bound systems."541" Lastly. while the Be star phenomena is not understood youn first principles. making it difficult to determine the absolute umber of systems with Be-driven luuinositics above Ly>LO ο, we note that our sinmlatious are cousistent with the lack of observed supereiauts with spherically driven winds."," Lastly, while the Be star phenomena is not understood from first principles, making it difficult to determine the absolute number of systems with Be-driven luminosities above $L_X>10^{34}$ $^{-1}$, we note that our simulations are consistent with the lack of observed supergiants with spherically driven winds."542 For cach 1illiou initial binaries. Wwe Iv 7.5 such sources with luninositv LyBud>dO bt prostatewhich have travelled less than 1 kpe.," For each million initial binaries, we find approximately 7.5 such sources with luminosity $L_X>10^{34}$ $^{-1}$ which have travelled less than 1 kpc."543 Using standard assuniptious for imitial mass function aud star formation rate in thebar region. this is consistent with a Poisson distribution of supereiaut svsteuis.," Using standard assumptions for initial mass function and star formation rate in the bar region, this is consistent with a Poisson distribution of supergiant systems."544 These results demonstrate the promise of using the ECS process in order to correctly model the great overabundance of Be-TAINB sources in the SAIC., These results demonstrate the promise of using the ECS process in order to correctly model the great overabundance of Be-HMXB sources in the SMC.545 Because of the low natal kicks iuparted to ECS SVvstenas. TAINBs formed through the EC'S process are able to replicate the lone period of Be-TAINB sources aud biel concentration of these systems in the SAIC bar.," Because of the low natal kicks imparted to ECS systems, HMXBs formed through the ECS process are able to replicate the long period of Be-HMXB sources and high concentration of these systems in the SMC bar."546 While several models exist which allow for low natal lick velocities. we show that the ECS process should be ‘favored due to its ability to create a dominant population of svstenis at times matching SAIC observations.," While several models exist which allow for low natal kick velocities, we show that the ECS process should be favored due to its ability to create a dominant population of systems at times matching SMC observations."547 In addition. the EC'S mechanisi produces JAINBs through he same plysical process suspected to produce a Be-IINMD population (?)..," In addition, the ECS mechanism produces HMXBs through the same physical process suspected to produce a Be-HXMB population \citep{2005ApJS..161..118M}."548" Detailed iiodeliug of the TAINB xopulatiou iu the SAIC. taking iuto account the duration. age and spatial distribution of star formation activity. he motion of the star forming clusters. aud the lower uetallicitv of the SAIC is bevoud the scope of thispaper, but is currently underway."," Detailed modeling of the HMXB population in the SMC, taking into account the duration, age and spatial distribution of star formation activity, the motion of the star forming clusters, and the lower metallicity of the SMC is beyond the scope of this, but is currently underway."549 We anticipate that such studies of the SAIC aud potentially other nearby galaxies with recent starburst activity will ereatlv. contribute to efforts of understanding SNe aud compact object formation., We anticipate that such studies of the SMC and potentially other nearby galaxies with recent starburst activity will greatly contribute to efforts of understanding SNe and compact object formation.550 We thank Valia Antoniou. Jay Callagher. and Andreas Zezas for useful discussions reearding recent observations of starbursts and hiehauass X-ray binaries.," We thank Valia Antoniou, Jay Gallagher, and Andreas Zezas for useful discussions regarding recent observations of starbursts and high-mass X-ray binaries."551 This work was supported by the NSF CAREER eraut AST-0119558 and a Packard Fellowship in Science Eneinecring to VIX., This work was supported by the NSF CAREER grant AST-0449558 and a Packard Fellowship in Science Engineering to VK.552 Numerical simulations were performed ou the IPC cluster, Numerical simulations were performed on the HPC cluster553Additionally. we set up two templates which have a lexible core plus an edge radius. ie. a well-defined: bulk. rut can also fit the region beyond the edge radius in à more sophisticated wav than by just a constant background.,"Additionally, we set up two templates which have a flexible core plus an edge radius, i.e. a well-defined bulk, but can also fit the region beyond the edge radius in a more sophisticated way than by just a constant background."554The figures lor the (wo smallest. values of 4 correspond to a Neptuneanass. planet and an Earth-mass planet. respectively. orbiting a star wilh 0.25M... In each case. the lower-right panel zooms in on the perlirbecl region. to reveal (hat. in a small region of the annulus around £2. isomagnilication contours from larger values of r are pulled in to smaller values of r. wilh the contours from smaller 7 pushed out on either side.,"The figures for the two smallest values of $q$ correspond to a Neptune-mass planet and an Earth-mass planet, respectively, orbiting a star with $0.25\, M_\odot.$ In each case, the lower-right panel zooms in on the perturbed region, to reveal that, in a small region of the annulus around $R_\alpha$, isomagnification contours from larger values of $r$ are pulled in to smaller values of $r$, with the contours from smaller $r$ pushed out on either side."555 When a source with larger transverse (han radial speed passes behind (his region. the magnilication will deviate upward from the point lens form. then downward and up again before descending back to the point-lens value.," When a source with larger transverse than radial speed passes behind this region, the magnification will deviate upward from the point lens form, then downward and up again before descending back to the point-lens value."556" As shown in the top panel of all three figures and in the portion of the lieht curve shown in the lower left-hand. panel of each figure. this characteristic ""up-down-up-down' form of the light curve is exhibited when both a and q are small."," As shown in the top panel of all three figures and in the portion of the light curve shown in the lower left-hand panel of each figure, this characteristic “up-down-up-down” form of the light curve is exhibited when both $\alpha$ and $q$ are small."557 The isomagnification contours in the lower-right-hand panels for (he Neptune-amnass and Earth-mass planets exhibit small closed curves. which enclose caustics.," The isomagnification contours in the lower-right-hand panels for the Neptune-mass and Earth-mass planets exhibit small closed curves, which enclose caustics."558 The caustics are tiny and (heir positions are not marked here: in fact. (he causties do not play an important role in the light curve deviations.," The caustics are tiny and their positions are not marked here; in fact, the caustics do not play an important role in the light curve deviations."559 The light curve deviations are dominated instead by (he more subtle affects associated with the perturbations of the low-maenilication isomaegnification contours., The light curve deviations are dominated instead by the more subtle affects associated with the perturbations of the low-magnification isomagnification contours.560 Nevertheless. the positions of (he caustics. which can be vanishinely small. provide a convenient wav (o measure the size of the perturbed region.," Nevertheless, the positions of the caustics, which can be vanishingly small, provide a convenient way to measure the size of the perturbed region."561" We define Ay. to be the straight-Iine distance between the (inv. caustics discussed above. expressed in units of Rp. We compute a normalized separation. Y,,,. bv dividing Ay. bv C,=2x,. the cireiumdference of a circle of radius R,. Consider the bottom panel of Figure 2."," We define $\Delta y_c$ to be the straight-line distance between the tiny caustics discussed above, expressed in units of $R_E.$ We compute a normalized separation, $\Delta\, Y_{norm},$ by dividing $\Delta y_c$ by $C_\alpha=2\, \pi\, R_\alpha$, the circumference of a circle of radius $R_\alpha.$ Consider the bottom panel of Figure 2."562 The variable along (he vertical axis is (he logaritlim of the normalized separation. A Vion: lis plotted against Jogy(q). There are 5 colored curves for values of a ranging from 0.10 to 0.33: these curves are almost indistinguishable.," The variable along the vertical axis is the logarithm of the normalized separation, $\Delta\, Y_{norm}$ ; it is plotted against $log_{10}(q).$ There are $5$ colored curves for values of $\alpha$ ranging from $0.10$ to $0.33$; these curves are almost indistinguishable."563 Moving to wider orbits. the green curve for a=0.40 can be distinguished [rom the others. but it is close to them.," Moving to wider orbits, the green curve for $\alpha=0.40$ can be distinguished from the others, but it is close to them."564 All in all. there is very little alpha dependence. indicating that the linear dimensions of the perturbed area depend primarily on the value of q.," All in all, there is very little alpha dependence, indicating that the linear dimensions of the perturbed area depend primarily on the value of $q$."565" The curves for small a and small q are well approximated bv the equation: fogy(AVice)=0.5logju(q)—0.2. Thus. the physical separation. expressed in units of Ap. can be expressed as a product of a factor that depends only on a and one that depends only on gq: Ay.=253R4AVion(@). Fieures 4 and 5 clearly show that the perturbed region is larger than the distance between the centers of the closed curves. which is an approximate measure of the separation Ay, between caustics."," The curves for small $\alpha$ and small $q$ are well approximated by the equation: $log_{10}(\Delta\, Y_{norm}) = 0.5\, log_{10}(q) - 0.2.$ Thus, the physical separation, expressed in units of $R_E$, can be expressed as a product of a factor that depends only on $\alpha$ and one that depends only on $q$: $\Delta\, y_c = 2\, \pi\, R_\alpha \Delta\, Y_{norm}(q).$ Figures 4 and 5 clearly show that the perturbed region is larger than the distance between the centers of the closed curves, which is an approximate measure of the separation $\Delta\, y_c$ between caustics."566 Let L(o.q) represent the linear dimensions of the perturbed region. expressed in units of Rp.," Let $L(\alpha, q)$ represent the linear dimensions of the perturbed region, expressed in units of $R_E$."567 On an empirical level. (he size of the region is determined by the size of the smallest deviations that can be reliably detected lor anv given observational scheme.," On an empirical level, the size of the region is determined by the size of the smallest deviations that can be reliably detected for any given observational scheme."568 If deviations like those shown in the light cures in the top panels of Figures 3 through are detectable. then we find. empirically. that ία.)22.5.y. For the three cases shown in Figures 3. 4. aud 5. (he linear. dimensions. L(a.q). are approximately 0.932p.0.387Rye. and 0.09Re. respectively.," If deviations like those shown in the light cures in the top panels of Figures 3 through are detectable, then we find, empirically, that $L(\alpha, q) \approx 2.5\, \Delta\, y_c.$ For the three cases shown in Figures 3, 4, and 5, the linear dimensions, $L(\alpha, q),$ are approximately $0.93\, R_E, 0.37\, R_E,$ and $0.09\, R_E,$ respectively."569 In theabsence of orbital rotalion. the event rate would be proportional to these linear dimensions.," In theabsence of orbital rotation, the event rate would be proportional to these linear dimensions."570 The event, The event571effeclive temperature or Iuminositv: however. it is now known that (he derivations of those quantities were inadequate at that time.,"effective temperature or luminosity; however, it is now known that the derivations of those quantities were inadequate at that time."572 The debate was settled by a purely morphological demonstration of the detailed correlations between (he wind profiles in the data ancl the optical spectral tvpes. which had in (urn been calibrated in terms of Fandamental parameters (Walborn et 11935. 1995. 2009: Rountree Sonneborn 1991. 1993: Penny et 11996).," The debate was settled by a purely morphological demonstration of the detailed correlations between the wind profiles in the data and the optical spectral types, which had in turn been calibrated in terms of fundamental parameters (Walborn et 1985, 1995, 2009; Rountree Sonneborn 1991, 1993; Penny et 1996)."573 The database provided by the (FUSE)) supported the extension of those correlations to (he rich spectral region below Lyman-a (Walborn et 22002. Pellerin et 22002).," The database provided by the ) supported the extension of those correlations to the rich spectral region below $\alpha$ (Walborn et 2002, Pellerin et 2002)."574 Of course. morphology. does not explain anything. but it may pave (he wav toward the ultimate objective of physical understanding.," Of course, morphology does not explain anything, but it may pave the way toward the ultimate objective of physical understanding."575 The (and NALM-Newlon)) X-ray satellites have provided the first stellar spectroscopic data of adequate quality to investigate the svstematics of that regime., The (and ) X-ray satellites have provided the first stellar spectroscopic data of adequate quality to investigate the systematics of that regime.576 The samples remain small to date because the required high-resolution data are time-consuming (o acquire wilh (hose systems., The samples remain small to date because the required high-resolution data are time-consuming to acquire with those systems.577 Nevertheless. (μον are sufficient for an initial morphological survey. which is presented here based on the data. with results Chat may be surprising.," Nevertheless, they are sufficient for an initial morphological survey, which is presented here based on the data, with results that may be surprising."578 Allofthe observations were obtained with the Advanced CCD Imaging Spectrometer (ACIS) in its Iligh. Energy. Transmission Grating Spectrometer (IIETGS) conliguration. which in turn simultaneously provides Medium Energv Grating (MEG) and IHieh Energy Grating (IIEG) data.," All of the observations were obtained with the Advanced CCD Imaging Spectrometer (ACIS) in its High Energy Transmission Grating Spectrometer (HETGS) configuration, which in turn simultaneously provides Medium Energy Grating (MEG) and High Energy Grating (HEG) data."579 The resolving powers are 660 al 15 and 1000 al 12.4À., The resolving powers are 660 at 15 and 1000 at 12.4.580. We have combined the (vo datasets whenever possible. i.e.. whenever ihe HEG S/N was adequate.," We have combined the two datasets whenever possible, i.e., whenever the HEG S/N was adequate."581 The data discussed here were obtained trom the TGCat (IIuenemoerder et 22009) web-based catalog of erating data., The data discussed here were obtained from the TGCat (Huenemoerder et 2009) web-based catalog of grating data.582 TGCat processing starts with the Level 1 event data downloaded from the archive., TGCat processing starts with the Level 1 event data downloaded from the archive.583 Updated calibrations and responses are applied to the data and the zeroth order position is determined to hish accuracy., Updated calibrations and responses are applied to the data and the zeroth order position is determined to high accuracy.584 The resulting FGCat Level 2 extracted spectral data were used to create the plots shown here., The resulting TGCat Level 2 extracted spectral data were used to create the plots shown here.585 Most of the data discussed here were archival. but three of the four targets observed in our program (PI Waldron. ID. 6200204) to fill gaps in the extant coverage of the IIR. Diagram are included.," Most of the data discussed here were archival, but three of the four targets observed in our program (PI Waldron, ID 6200204) to fill gaps in the extant coverage of the HR Diagram are included."586 They are HD 93250. 9 Ser. and 15 Mon: our fourth target. IID 93129AD. presents a complex. composite spectrum that will be discussed. separately (Nichols et al..," They are HD 93250, 9 Sgr, and 15 Mon; our fourth target, HD 93129AB, presents a complex, composite spectrum that will be discussed separately (Nichols et al.,"587 in preparation.), in preparation.)588 Stellar and observational parameters are listed in Table 1. in the order in which the objects appear in Figures 16. together with extensive references (o previous analvses of these stars.," Stellar and observational parameters are listed in Table 1, in the order in which the objects appear in Figures 1–6, together with extensive references to previous analyses of these stars."589 Further explanation of several columns in the table is given below., Further explanation of several columns in the table is given below.590stellar variability can produce transit depth variations.,stellar variability can produce transit depth variations.591 These can be recognized and taken into account by monitoring the star outside of transits. as is done automatically by theKepler satellite.," These can be recognized and taken into account by monitoring the star outside of transits, as is done automatically by the satellite."592 We are not aware of any atmospheric phenomena associated with the exoplanet that would result in variations in the projected area at the level. mimicking those due to uniform spin precession.," We are not aware of any atmospheric phenomena associated with the exoplanet that would result in variations in the projected area at the level, mimicking those due to uniform spin precession."593 However. we can think of two plausible phenomena that would affect the TÓV signal: moons and rings.," However, we can think of two plausible phenomena that would affect the $\delta$ V signal: moons and rings."594 If the planet has any moons then the precession period may be shorter than we have calculated., If the planet has any moons then the precession period may be shorter than we have calculated.595 Satellites provide more leverage for the star to torque the exoplanetary system., Satellites provide more leverage for the star to torque the exoplanetary system.596 Mathematically. satellites augment the effective values of J+ and C.," Mathematically, satellites augment the effective values of $J_2$ and $\mathds{C}$."597 Following Ward Hamilton (2004) we may write the enhanced values as «οj and C 4c. where where #;. a;. T; and are the satellites’ masses. orbital radit. orbital inclinations Pas(relative to the planetary equator). and orbital periods.," Following Ward Hamilton (2004) we may write the enhanced values as $J_2+j$ and $\mathds{C}+c$ , where where $m_i$, $a_i$, $I_i$ and $p^i_{\rm orb}$ are the satellites' masses, orbital radii, orbital inclinations (relative to the planetary equator), and orbital periods."598 For example. in the Saturnian system //J5»z3.2 while efCx0.01 such that (C+e)/0+4f)z3.2 (as compared to CJ.= 13.5).," For example, in the Saturnian system $j/J_2 \approx 3.2$ while $c/\mathds{C} \approx 0.01$ such that $(\mathds{C}+c)/(J_2+j) \approx5993.2$ (as compared to $\mathds{C}/J_2 = 13.5$ )."600 Titan alone is responsible for about 90% of j and c. shortening Saturn's precession period by a factor of four relative to a satellite-free Fig. (3))," Titan alone is responsible for about $90\%$ of $j$ and $c$, shortening Saturn's precession period by a factor of four relative to a satellite-free Fig. \ref{fig:times}) )"601 shows the effect of Titàn analogs at various distances around the Saturn analog considered in this paper., shows the effect of Titan analogs at various distances around the Saturn analog considered in this paper.602 The distances are expressed as fractions of the Hill radius 7j., The distances are expressed as fractions of the Hill radius $r_H$.603 This effect might be used to implicate the presence of exomoons. if a ΤΟΝ signal were observed and found to correspond to an effective 7» too large to be plausibly attributed to the planet alone.," This effect might be used to implicate the presence of exomoons, if a $\delta$ V signal were observed and found to correspond to an effective $J_2$ too large to be plausibly attributed to the planet alone."604 Ring systems would increase the amplitude of the signal. while leaving the period unchanged.," Ring systems would increase the amplitude of the signal, while leaving the period unchanged."605 Optically thick rings that lie within the equatorial plane of the planet would increase the fractional variation of the sky-projected area. as the planet precesses.," Optically thick rings that lie within the equatorial plane of the planet would increase the fractional variation of the sky-projected area, as the planet precesses."606 In contrast to exomoons. ring systems have little mass. and would not significantly reduce the precessional period.," In contrast to exomoons, ring systems have little mass, and would not significantly reduce the precessional period."607 This is the situation in the Saturnian system (Ward Hamilton 2004)., This is the situation in the Saturnian system (Ward Hamilton 2004).608 It is not certain that rings could exist around planets having orbital periods between 15 and 30 days., It is not certain that rings could exist around planets having orbital periods between 15 and 30 days.609 Rings- around planets with orbital periods less than Panz15 days would likely be short-lived as a result of Poynting-Roberston drag amongst other destructive effects (Barnes Fortney 2004).," Rings around planets with orbital periods less than $P_{\rm orb}610\approx15$ days would likely be short-lived as a result of Poynting-Roberston drag amongst other destructive effects (Barnes Fortney 2004)."611 Also. we would be unlikely to find rings composed of water ice SSaturn’s rings) around planets whose orbits are interior to the snow line (c| AU).," Also, we would be unlikely to find rings composed of water ice Saturn's rings) around planets whose orbits are interior to the snow line $< 1$ AU)."612 Nevertheless. rings of other compositions may exist.," Nevertheless, rings of other compositions may exist."613 In short. rings and moons would each affect the observed ΤΟΝ signal. and in complementary ways.," In short, rings and moons would each affect the observed $\delta$ V signal, and in complementary ways."614 This may introduce some ambiguity in the estimation of the shape parameters of the rotating planet. but may also allow the rings and moons to be detectable. issues that we leave for future work.," This may introduce some ambiguity in the estimation of the shape parameters of the rotating planet, but may also allow the rings and moons to be detectable, issues that we leave for future work."615 For simplicity we have considered only circular. orbits., For simplicity we have considered only circular orbits.616 Planets on eccentric orbits will undergo apsidal precession and nodal precession. which will result in time variable stellar torques on the planet and consequent modifications to the spin-axis precession.," Planets on eccentric orbits will undergo apsidal precession and nodal precession, which will result in time variable stellar torques on the planet and consequent modifications to the spin-axis precession."617" For Saturn orJupiter analogs at Psp215 days. the apsidal and nodal precession periods are 210"" yr and therefore likely to be irrelevant (Ragozzine Wolf 2009)."," For Saturn or Jupiter analogs at $P_{\rm orb} \gtrsim 15$ days, the apsidal and nodal precession periods are $\gtrsim$$10^7$ yr and therefore likely to be irrelevant (Ragozzine Wolf 2009)."618 In addition. we restricted our attention to the simplest case of uniform spin precession. but in reality the perturbations from other bodies may cause the spin axis to perform a more complex ballet.," In addition, we restricted our attention to the simplest case of uniform spin precession, but in reality the perturbations from other bodies may cause the spin axis to perform a more complex ballet."619 For example. Mars's spin axis tumbles chaotically (Touma Wisdom 1992).," For example, Mars's spin axis tumbles chaotically (Touma Wisdom 1992)."620 Saturn's moon Titan causes a 700 yr modulation of Saturn's spin. precession frequency. due to its inclined orbit.," Saturn's moon Titan causes a 700 yr modulation of Saturn's spin precession frequency, due to its inclined orbit."621" Furthermore. Saturn's spin axis may be trapped in à resonance with Neptune's orbit. causing it to librate with an angular amplitude of 731"" as it circulates about the second Cassini state (Ward Hamilton 2004)."," Furthermore, Saturn's spin axis may be trapped in a resonance with Neptune's orbit, causing it to librate with an angular amplitude of $\gtrsim$$31^\circ$ as it circulates about the second Cassini state (Ward Hamilton 2004)."622" These effects would be manifested as additional time dependences (""noise"") in the TóVsignal.", These effects would be manifested as additional time dependences (“noise”) in the signal.623 The effects are impossible to forecast for exoplanets. depending as they do on the existence of other bodies and any resonances that may occur.," The effects are impossible to forecast for exoplanets, depending as they do on the existence of other bodies and any resonances that may occur."624 We thank Dan Fabrycky. Darin Ragozzine. and members of the MIT exoplanet discussion group. for helpful conversations.," We thank Dan Fabrycky, Darin Ragozzine, and members of the MIT exoplanet discussion group, for helpful conversations."625 We also thank an anonymous referee for helpful comments on an earlier draft of this manuscript., We also thank an anonymous referee for helpful comments on an earlier draft of this manuscript.626 We model the planet as an oblate spheroid. illustrated in Figure (1)).," We model the planet as an oblate spheroid, illustrated in Figure \ref{fig:dia}) )."627 The sky plane projected shadow of the spheroidal planet is bounded by an ellipse., The sky plane projected shadow of the spheroidal planet is bounded by an ellipse.628 The polar axis. s. of the spheroid ts tilted by the obliquity angle 0> from the orbital axis 7 and by theangle 0!0 from the axis 2’ which is perpendicular to the plane that is perpendicular to the sky plane.," The polar axis, $\hat{s}$, of the spheroid is tilted by the obliquity angle $\theta > 0$ from the orbital axis $\hat{n}$ and by theangle $\theta' > 0$ from the axis $\hat{n}'$ which is perpendicular to the plane that is perpendicular to the sky plane."629 Let v be the axis which, Let $\hat{y}$ be the axis which630As shown in Figures 16 and 17.. the projected mass distribution of A2163 is complex and two mass peaks are sienificautly detected im the ceutral region.,"As shown in Figures \ref{fig:opt+kappa} and \ref{fig:kappa+den}, the projected mass distribution of A2163 is complex and two mass peaks are significantly detected in the central region."631 It is of prime inportance for understanding cluster merecr plenomena to iueasure asses of the main- and sub- clusters., It is of prime importance for understanding cluster merger phenomena to measure masses of the main- and sub- clusters.632 Furthermore. since numerical simulations (Meneghettietal.2010:Decker&Iravtsov2010) aud observatious (Okabeetal.2010b) have shown that a tanecutial shear profile is affected by significant substructures. talking iuto account substructures in modchug is also important for understanding such a leusine bias.," Furthermore, since numerical simulations \citep{men10,bec10} and observations \citep{oka10b}633 have shown that a tangential shear profile is affected by significant substructures, taking into account substructures in modeling is also important for understanding such a lensing bias."634 Iu the imas lcasurement using the tangential shear profile (Section 1)) it is very difficult to distinguish which structure contributes in part to the tangential distortion signals. because the full lensing information frou both the main and subcelusters must be couvolved to express the one dimensional distortion profile with respect to a eiven center (Okabeetal.2010a).," In the mass measurement using the tangential shear profile (Section \ref{sec:1d}) ), it is very difficult to distinguish which structure contributes in part to the tangential distortion signals, because the full lensing information from both the main and subclusters must be convolved to express the one dimensional distortion profile with respect to a given center \citep{oka10a}."635. The two dimensional shear pattern. on the other hind. enables us to casily model lensing signals by a superposition of leusimg siguals.," The two dimensional shear pattern, on the other hand, enables us to easily model lensing signals by a superposition of lensing signals."636 Iu this section. we conduct two-dimensional shear fitting iu order to measure the masses of three components (the sub and main components for A2L63-A and A2163-B) revealed by MOS aud D11.," In this section, we conduct two-dimensional shear fitting in order to measure the masses of three components (the sub and main components for A2163-A and A2163-B) revealed by M08 and B11."637 We pixelize the shear pattern into a regular erid of 1!« without auv spatial s100thiue procedure. whereas we adopted Caussian smoothing im the map making (Section ??)).," We pixelize the shear pattern into a regular grid of $1\farcm \times 1\farcm$ without any spatial smoothing procedure, whereas we adopted Gaussian smoothing in the map making (Section \ref{sec:map}) )."638" The pixelized. distortion signals aud statistical weight. (6) aud 0.(0, ). in the nth pixol are estimated with a weight function «; for cach backeround source residing iu the pixel (see also Equations. (1))"," The pixelized distortion signals and statistical weight, $\langle{g_{\alpha}}\rangle(\btheta_n)$ and $\sigma_{g}^2(\btheta_n)$ , in the $n$ th pixel are estimated with a weight function $u_i$ for each background source residing in the pixel (see also Equations. \ref{eq:g}) )"639 and (5)))., and \ref{eq:sig_g+}) )).640 The representative position for the nth pixel is also estimated with a weight functiou us., The representative position for the $n$ th pixel is also estimated with a weight function $u_i$.641" The \? fitting is eiven by where p ds the parameters and νι is the eror covariance matrix shape measurements in the form of €C,45(0,)=οof(01)."," The $\chi^2$ fitting is given by where $\mbox{\boldmath $ $}$ is the parameters and $C_{\alpha\beta}$ is the error covariance matrix of shape measurements in the form of $C_{\alpha\beta}(\btheta_n)=\delta^{\rm642K}_{\alpha\beta}\sigma_g^2(\btheta_n)$."643" Tere. db. js a Kronecker delta function aud 05(0,) is the statistical error of the jXxelized shear (Ogurietal.2010:Watanabe2011)."," Here, $\delta^{\rm644K}_{\alpha\beta}$ is a Kronecker delta function and $\sigma_g^2(\btheta_n)$ is the statistical error of the pixelized shear \citep{ogu10,wat11}."645. We first consider a single mass modol of the NEW xofile in order to compare the mass estimates bv aueeutial shear measurement., We first consider a single mass model of the NFW profile in order to compare the mass estimates by tangential shear measurement.646 We here treat the center of NEW mass Geo. ye} as à parameter.," We here treat the center of NFW mass $x_c$, $y_c$ ) as a parameter."647 In total. we use our parameters (AL. e.c. and 9g.) for fitting.," In total, we use four parameters $M$, $c$, $x_c$, and $y_c$ ) for fitting."648 We adopt he Markov Chain Monte Carlo method with stancard Metropolis-Tastines sampling., We adopt the Markov Chain Monte Carlo method with standard Metropolis-Hastings sampling.649 Werestrict the sample range of Maax5«10TALL. eus<20.," Werestrict the sampling range of $M_{\rm650vir}\leq5\times10^{15}h^{-1}M_\odot$, $c_{\rm vir}\le 20$."651 We refer to he mean of the posterior probability distribution of cach xwanmeter., We refer to the mean of the posterior probability distribution of each parameter.652 The resultant masses are consistent with the aueeutial shear measurements (Table 53)., The resultant masses are consistent with the tangential shear measurements (Table \ref{tab:mass}) ).653 The ceutral »osition of mass is consistent with the peak position of he MC chump in the mass map., The central position of mass is consistent with the peak position of the MC clump in the mass map.654 The MC chip. which is associated with BCC. is therefore likely to be the main colmpoucut.," The MC clump, which is associated with BCG1, is therefore likely to be the main component."655 We next add a ass niodel for the mass chunp MW. to the main cluster., We next add a mass model for the mass clump MW to the main cluster.656 From Ανταν and optical spectroscopic studies (MOS and Bil). the mass chup ATW is likely ο be a merging substructure in A2163-À. Since cluster substructure size is not determined by the virial theorem mt bv the strong tidal force of the main cluster (6.8...Tormenetal.1998).. we adopt the truucated SIS CTSIS) nodel (Okabeetal.2010a) to describe the MW clump.," From X-ray and optical spectroscopic studies (M08 and B11), the mass clump MW is likely to be a merging substructure in A2163-A. Since cluster substructure size is not determined by the virial theorem but by the strong tidal force of the main cluster \citep[e.g.,][]{tor98}, we adopt the truncated SIS (TSIS) model \citep{oka10a}657 to describe the MW clump."658 The TSIS model is au extreme case of the truncation: nass deusitv becomes zero at a radius ry., The TSIS model is an extreme case of the truncation; mass density becomes zero at a radius $r_t$ .659" The TSIS mass xofile is expressed as The subchunp mass for the TSIS model is estimated as The TSIS inodel is specified by one-dineusioual velocity dispersion o, aud the truucation radius ry.", The TSIS mass profile is expressed as The subclump mass for the TSIS model is estimated as The TSIS model is specified by one-dimensional velocity dispersion $\sigma_v$ and the truncation radius $r_t$.660 We rave an additional four parameters(7). rg aud ceuters) or the TSIS model aud a total of eight parameters for he fitting.," We have an additional four parameters$\sigma_v$, $r_t$ and centers) for the TSIS model and a total of eight parameters for the fitting."661 We assume that the redshift of the ATW chuup is the same as that of the main cluster., We assume that the redshift of the MW clump is the same as that of the main cluster.662 We adopt WekX25 and peak!<25 where suo aud Yoork peak!ALC peak. coordinates[ue appearing m a weak-leusiug nass nup.," We adopt $|x_c-x_{\rm peak}|<2\farcm$ and $|y_c-y_{\rm peak}|<2\farcm$, where $x_{\rm663peak}$ and $y_{\rm peak}$ are peak coordinates appearing in a weak-lensing mass map."664 The resultant mass aud ceutral positions are shown in Table 6.., The resultant mass and central positions are shown in Table \ref{tab:mass2}.665 The centroid of the ATW chup. is consistent with the peak found iu the massmap., The centroid of the MW clump is consistent with the peak found in the massmap.666" The runcation radius r,=~L4tMpe. is an intermediate size comparedO74 to the virial radius of the nain cluster ray16'6—2.35iMpe."," The truncation radius, $r_t=9\farcm7_{-2.9}^{+3.4}\sim 1.4h^{-1}{\rm Mpc}$, is an intermediate size compared to the virial radius of the main cluster $r_{\rm vir} = 16\farcm6\sim 2.3h^{-1}{\rm Mpc}$."667 Since the sub-cluster size after sone maüpacts is significantly decreased w the stroug tidal field. such a large truucation radius uieht sugeest that the MAW chup is a imeregiug cluster at the first impact.," Since the sub-cluster size after some impacts is significantly decreased by the strong tidal field, such a large truncation radius might suggest that the MW clump is a merging sub-cluster at the first impact."668 Next. we take into account the northeru component A2163-B (MOS. and Bill ) which coutaius Dhnumiuous ealaxies (optical chuup D) aud au ταν cinitting core.," Next, we take into account the northern component A2163-B (M08 and B11 ), which contains luminous galaxies (optical clump B) and an X-ray emitting core."669 We consider two possibilities for the dwuanüc state of A2163-D: one scenario is the pre-merger phase that A2163-B is infalline toward A2163-A. aud the other is that A2163-B has already undergoue a mergimg event with the main cluster of A2163-A. B11 found uo evidence of the close interaction between À2163-À and A2163-D. and therefore coucluded that they are Likely to he separated more than (oj aligning along the liue of sight.," We consider two possibilities for the dynamic state of A2163-B; one scenario is the pre-merger phase that A2163-B is infalling toward A2163-A, and the other is that A2163-B has already undergone a merging event with the main cluster of A2163-A. B11 found no evidence of the close interaction between A2163-A and A2163-B, and therefore concluded that they are likely to be separated more than $r_{500}$ aligning along the line of sight."670 ILowever. in MOS. a filament of faint galaxies was detected along a north/south axis between A2163-A aud A2163-B which might sugecst a previous interaction between the wo coniponeuts.," However, in M08, a filament of faint galaxies was detected along a north/south axis between A2163-A and A2163-B which might suggest a previous interaction between the two components."671 Although this post-merger hvpothliesis is very unlikely from the N-rav approach. the origin of lis faint ealaxy filamentary structure is still an open issue.," Although this post-merger hypothesis is very unlikely from the X-ray approach, the origin of this faint galaxy filamentary structure is still an open issue."672 In this paper. we investigate two possibilities in the fittine.," In this paper, we investigate two possibilities in the fitting."673 If A2163-D is physically separated from A2163-À. its mass profile is not likely to be affected by the strong idal field of A2163-A and we therefore adopt the NEW nodel for the first scenario.," If A2163-B is physically separated from A2163-A, its mass profile is not likely to be affected by the strong tidal field of A2163-A and we therefore adopt the NFW model for the first scenario."674 Here. the halo couceutration is ill constrained because the shear signals fou A2163-B are sinaller than those fromA2163-A. and it is difficult in the cuviroument of the massive cluster to find the curvature of the distortion profile. asshown in Figure 19..," Here, the halo concentration is ill constrained because the shear signals from A2163-B are smaller than those fromA2163-A, and it is difficult in the environment of the massive cluster to find the curvature of the distortion profile, asshown in Figure \ref{fig:g+}. ."675 We therefore assume the mass - concentration. relation of ea=7.85(Aba/2«101ptaryIIqpuyvH (Dittyetal. 2008).., We therefore assume the mass - concentration relation of $\cvir=7.85\left(\Mvir/2\times10^{12}h^{-1}\Msun\right)^{-0.081}(1+z_c)^{-0.71}$ \citep{duf08}. .676 Tere. we assume a redshift of το. is the same as that of A2163-À. This assumption," Here, we assume a redshift of A2163-B, $z_c$ , is the same as that of A2163-A. This assumption"677ligure 2. under the assumption of non-evolving ratio: we get AL=101777744. (a= 3/2) and M=1072252ar. (a— 0).,Figure \ref{fig2} under the assumption of non-evolving ratio; we get $M=10^{12.5\pm0.2}M_\odot$ $\alpha=3/2$ ) and $M=10^{12.3\pm0.2}M_\odot$ $\alpha=0$ ).678" 1E a fraction ο of dark matter halos contain SMDlls. then the total lifetime of the quasar can be estimated (Martini Weinberg 2001: Haiman Lui 2001) by dividing the quasar number density Ψ(Αντου<26.7.2) bvο times the number density ΑςAL) of halos larger than AM. and then multiplving by the Hubbletime (for &,«Lf ly "," If a fraction $\epsilon$ of dark matter halos contain SMBHs, then the total lifetime of the quasar can be estimated (Martini Weinberg 2001; Haiman Hui 2001) by dividing the quasar number density $\Psi(M_{1450}<-26.7,z)$ by $\epsilon$ times the number density $N(>M)$ of halos larger than $M$, and then multiplying by the Hubbletime (for $t_{\rm q} < H^{-1}$ )."679"The probability for the product e£, is where (dPd) is the observed: Gaussian probability for VW.", The a-posteriori probability for the product $\epsilon t_{\rm q}$ is where $(dP/d\Psi)$ is the observed Gaussian probability for $\Psi$.680 Under the assumption of a SMDII to halo mass ratio that does not evolve with redshift. (see. Figure 2..right hand panel) we lind lifetimes of 1017776+ and LOEEee1 ears (respectively) for a=3/2 and a= 0. in à cosmology where ox= O.S4.," Under the assumption of a SMBH to halo mass ratio that does not evolve with redshift (see Figure \ref{fig2},right hand panel), we find lifetimes of $10^{4.8\pm0.3}\epsilon^{-1}$ and $10^{4.3\pm0.4}\epsilon^{-1}$ years (respectively) for $\alpha=3/2$ and $\alpha=0$ , in a cosmology where $\sigma_8=0.84$ ."681 In addition (not shown), In addition (not shown)682they are modelled as spheres in the cylindrical coordinate system.,they are modelled as spheres in the cylindrical coordinate system.683" The computational domain extended 530 AU in the r direction, and 1060 AU in the z direction."," The computational domain extended 530 AU in the $r$ direction, and 1060 AU in the $z$ direction."684 The adopted geometrical system configuration implied imposition of an axisymmetric (reflecting) boundary condition at rmin=0 and outflow conditions at the remaining boundaries., The adopted geometrical system configuration implied imposition of an axisymmetric (reflecting) boundary condition at $r\rs{min} = 0$ and outflow conditions at the remaining boundaries.685" In order to compare the results of the 2D simulations with those derived from the 3D simulation, we reconstructed the 3D spatial distributions of all the physical variables (e.g. mass density and temperature) derived with the 2D simulations, by rotating the 2D slab about the z axis, according to the symmetry of the problem."," In order to compare the results of the 2D simulations with those derived from the 3D simulation, we reconstructed the 3D spatial distributions of all the physical variables (e.g. mass density and temperature) derived with the 2D simulations, by rotating the 2D slab about the $z$ axis, according to the symmetry of the problem."686" Thus we passed from the cylindrical coordinate system to the cartesian one, orienting the cartesian coordinate system in such a way that both the WD and the companion star lie on the x axis, as in the 3D simulation."," Thus we passed from the cylindrical coordinate system to the cartesian one, orienting the cartesian coordinate system in such a way that both the WD and the companion star lie on the $x$ axis, as in the 3D simulation."687 The explosion and subsequent blast wave was followed for a total of 60 days in order to explore the evolution of the X-ray emission and study the effects of the circumstellar environment on the evolution of the blast during the evolutionary phase that was characterized by a pronounced peak of X-ray emission in the 2010 outburst (?))., The explosion and subsequent blast wave was followed for a total of 60 days in order to explore the evolution of the X-ray emission and study the effects of the circumstellar environment on the evolution of the blast during the evolutionary phase that was characterized by a pronounced peak of X-ray emission in the 2010 outburst \citealt{2011A&A...527A..98S}) ).688" As with the modeling of the U Sco blast, the small scale of the stellar system compared with the size of the rapidly expanding blast wave over the 60 day period of interest presents a major computational challenge."," As with the modeling of the U Sco blast, the small scale of the stellar system compared with the size of the rapidly expanding blast wave over the 60 day period of interest presents a major computational challenge."689" To this end, we exploited the adaptive mesh capabilities of the FLASH code by using 12 nested levels of adaptive mesh refinement, with resolution increasing twice at each refinement level."," To this end, we exploited the adaptive mesh capabilities of the FLASH code by using 12 nested levels of adaptive mesh refinement, with resolution increasing twice at each refinement level."690" This grid configuration yielded an effective maximum resolution of zz5x106km at the finest level, corresponding to zz20 grid points per initial radius of the blast and =66 grid points per radius of the Mira companion."," This grid configuration yielded an effective maximum resolution of $\approx 5\times 10^6$km at the finest level, corresponding to $\approx69120$ grid points per initial radius of the blast and $\approx 66$ grid points per radius of the Mira companion."692 The calculations were performed using an automatic mesh derefinement scheme in the whole spatial domain except in the Mira (where the resolution does not vary during the blast evolution) that kept the computational cost approximately constant as the blast expanded., The calculations were performed using an automatic mesh derefinement scheme in the whole spatial domain except in the Mira (where the resolution does not vary during the blast evolution) that kept the computational cost approximately constant as the blast expanded.693" The effective mesh size was 16384x32768 for the 2D simulations, and 32768x16384 for the 3D simulation."," The effective mesh size was $16384\times 32768$ for the 2D simulations, and $32768\times 16384\times 16384$ for the 3D simulation."694" Solar abundances of ? (GS) were assumed for the wind and circumstellar density enhancement, while ejecta metal abundances were assumed to be enhanced by a factor of ten."," Solar abundances of \citet{1998SSRv...85..161G} (GS) were assumed for the wind and circumstellar density enhancement, while ejecta metal abundances were assumed to be enhanced by a factor of ten."695" This latter choice was guided by theSwift spectra that ? found to be rich in both N and O—by possibly more than a factor of ten—and by observations of He-rich ejecta in the outburst of U Sco (see?), as well as the ? high-resolution X-ray spectroscopic study of the 2006 RS Oph blast that found evidence for metal-rich ejecta."," This latter choice was guided by the spectra that \citet{2011A&A...527A..98S} found to be rich in both N and O—by possibly more than a factor of ten—and by observations of He-rich ejecta in the outburst of U Sco \citep[see][]{2010ApJ...720L.195D}, as well as the \citet{2009ApJ...691..418D} high-resolution X-ray spectroscopic study of the 2006 RS Oph blast that found evidence for metal-rich ejecta."696" The adopted abundances are relevant for the radiative losses from shocked ejecta, and for the local absorption by the shocked CSM (with GS abundances) and by the ejecta (with GS abundances x10) encountered within the blast wave."," The adopted abundances are relevant for the radiative losses from shocked ejecta, and for the local absorption by the shocked CSM (with GS abundances) and by the ejecta (with GS abundances $\times 10$ ) encountered within the blast wave."697 The choice of abundances is also relevant for computation of the emitted X-ray intensityof the blast., The choice of abundances is also relevant for computation of the emitted X-ray intensityof the blast.698 Such emission was synthesized from the model results using the methodology described by ?.., Such emission was synthesized from the model results using the methodology described by \citet{2009A&A...493.1049O}.699" T'he synthesis includes: thermal broadening of emission lines, Doppler shift of lines due to the component of plasma velocity along the line-of-sight, photoelectric absorption by the interstellar medium (ISM), CSM, and ejecta."," The synthesis includes: thermal broadening of emission lines, Doppler shift of lines due to the component of plasma velocity along the line-of-sight, photoelectric absorption by the interstellar medium (ISM), CSM, and ejecta."700 The absorption by the ISM was calculated assuming a column density Ny=2x10?! cm?; the local absorption was calculated self-consistently from the distributions of shocked CSM and shocked ejecta., The absorption by the ISM was calculated assuming a column density $N_{\rm H} = 2\times 10^{21}$ $^{-2}$; the local absorption was calculated self-consistently from the distributions of shocked CSM and shocked ejecta.701" 'The influence of the different system parameters was investigated through the 2D simulations, by exploring models with an initial energy of explosion, Eo, in the range 10**-10*"" erg, ejecta mass, Mj, in the range 10 7—10* Mo, wind density in the range 10'-10!? cm~3, CDE density in the range 109—10* cm (see Table 1))."," The influence of the different system parameters was investigated through the 2D simulations, by exploring models with an initial energy of explosion, $E_0$, in the range $10^{44}$ $10^{47}$ erg, ejecta mass, $M\rs{ej}$, in the range $10^{-7}$ $10^{-4}$ $M_\odot$, wind density in the range $10^7$ $10^{10}$ $^{-3}$ , CDE density in the range $10^6$ $10^7$ $^{-3}$ (see Table \ref{t:params}) )."702" The ranges of ejected mass and outburst energy? include those typical of recurrent novae (10:«Μα«1075 Mo, 10**<Eo«1035 erg),"," The ranges of ejected mass and outburst energy include those typical of recurrent novae $10^{-7}< M\rs{ej} < 10^{-6}$ $M_\odot$ , $10^{44} < E_0 < 10^{45}$ erg),"703anunihilation.,annihilation.704 Usine this study. we cau derive the value of the matter deusitv above the black hole or Which the energy deposited by neutrinos is able ο drive au explosion. aud obtain au estimate of he mass of the black hole remunaut left οἱήπιο by lis explosion.," Using this study, we can derive the value of the matter density above the black hole for which the energy deposited by neutrinos is able to drive an explosion, and obtain an estimate of the mass of the black hole remnant left behind by this explosion."705 We will define the onset of the explosion as he moment when ueutrino momenta deposition exceeds the pull of eravity on matter flowing onto he accretion disk along the rotation axis., We will define the onset of the explosion as the moment when neutrino momentum deposition exceeds the pull of gravity on matter flowing onto the accretion disk along the rotation axis.706" The scattering opacity (A) for neutrinos is roughly (Jauka 2001): ↖↖↽∐↸∖↥⋅↸∖∣⊔⊓≈⊥⋅∢⋔∖⊥∪−↓↽⋅⋅↽⋅≻ ee is atonic lass unit. ο5=n 0.511MeV. -.is electron restauass energy. oy=1.456«10 tem. ei is the neutrino energy. p is the density above the rotation axis. Y,ΠΠ aud Y,=yf, are the iuuber fractions of free neutrons aud protons."," The scattering opacity $\kappa_{\rm sc}$ ) for neutrinos is roughly (Janka 2001): where $m_{\rm u} \approx 1.66 \times 10^{-24}$ g is atomic mass unit, $m_{\rm e} \, c^2 = 0.511$ MeV is electron rest-mass energy, $\sigma_0 = 1.76 \times 10^{-44}$ $^2$ , $\epsilon_{\nu}$ is the neutrino energy, $\rho$ is the density above the rotation axis, $Y_{\rm n} = 707n_{\rm n}/n_{\rm b}$ and $Y_{\rm p} = n_{\rm p}/n_{\rm b}$ are the number fractions of free neutrons and protons."708" The correspondiug absorption opacity (&45,) for neutrinos is (Janka 2001) For the conditions in our disks. electron capture produces over half of the total ucutrinos aud electron neutrinos are the most abundaut neutrino species."," The corresponding absorption opacity $\kappa_{\rm ab}$ ) for neutrinos is (Janka 2001) For the conditions in our disks, electron capture produces over half of the total neutrinos and electron neutrinos are the most abundant neutrino species."709" Asstuning this species dominates the absorption aud scattering. the total ucutrino opacity is Uere we have used the following assuniptious: axial-vector couplings set to the chareged-curreut axial-vector coupling coustant idu a να. a= 1.260 34=X,0.5. the ueutriuo eiperature (7, ) is related to neutrino euerev wo ay2LATL2=<ee7> aud that the cutire: reutring flux is in the clectrou ποππο species."," Assuming this species dominates the absorption and scattering, the total neutrino opacity is Here we have used the following assumptions: axial-vector couplings set to the charged-current axial-vector coupling constant in a vacuum, $\alpha=-1.26$ , $Y_{\rm n} \approx Y_{\rm p} \approx 0.5$, the neutrino temperature $T_{\nu_{\rm e}}$ ) is related to neutrino energy by $21 (kT_{\nu_{\rm e}})^2=<\epsilon^2_{\nu}>$ and that the entire neutrino flux is in the electron neutrino species."710 Tack we assmued an equal mix of electron and anti-clectron neutrinos. the total opacity would iot be different bv more than," Had we assumed an equal mix of electron and anti-electron neutrinos, the total opacity would not be different by more than."711" As a shell of uatter falls towards the black hole. it is supported w the momentum ofthe scattered aud absorbed ieutrinos: where £, is the neutrino hDmuuimositv. muaLpzi?dr is the mass. dr the thickness. kc the radius of the shell. e is neutrino velocity z the speed of light."," As a shell of matter falls towards the black hole, it is supported by the momentum ofthe scattered and absorbed neutrinos: where $L_{\nu}$ is the neutrino luminosity, $m_{\rm shell} = 4 \rho \pi r^2712dr$ is the mass, $dr$ the thickness, $r$ the radius of the shell, $c$ is neutrino velocity $\approx$ the speed of light."713 The corresponding acceleration from ueutriuo inibilation requires detailed models of the black hole accretion disk svstem., The corresponding acceleration from neutrino annihilation requires detailed models of the black hole accretion disk system.714 The disk models aud inibilation calculations frou Popham ot al. (, The disk models and annihilation calculations from Popham et al. (7151999) led to a value for the cnerey deposited iong a surface per unit path length (ὁ=CLERSlen+).,"1999) led to a value for the energy deposited along a surface per unit path length $[\dot{e}]= {\rm ergs \, s^{-1} \, cm^{-1}}$ )."716 With this deposition rate ο). which is a function of height above the disk. we can calculate the acceleration due to neutriuo annililation inside a 30° cone aloug the rotation axis: The onset of the explosion occurs when ay|Gy|ee>0 where ay=(αλ.ντDi ds. the eravitational acceleration with gravitational coustant G. aud black hole mass ή.," With this deposition rate $\dot{e}(r)$, which is a function of height above the disk, we can calculate the acceleration due to neutrino annihilation inside a $30^{\circ}$ cone along the rotation axis: The onset of the explosion occurs when $a_g+a_\nu+a_{\nu \bar{\nu}} >7170$ where $a_g=-G M_{\rm BH}/r^2$ is the gravitational acceleration with gravitational constant $G$, and black hole mass $M_{\rm718BH}$."719 Using equations [ aud 5. the acceleration condition for the ouset of the explosion cau be translated iuto a threshold coudition ou the deusitv: For our estimates. we take the radi where the enerev deposition frou neutrino annihilation peaks (~20kkin).," Using equations 4 and 5, the acceleration condition for the onset of the explosion can be translated into a threshold condition on the density: For our estimates, we take the radii where the energy deposition from neutrino annihilation peaks $\sim$ km)."720" Figure 1 eives critical deusitics for set values of ὁ versus au effective Iuninositv (kT, ο ΕΕ ", Figure 1 gives critical densities for set values of $\dot{e}$ versus an effective luminosity $(kT_{\nu_{\rm e}}/4 {\rm MeV})^2 L_{\nu}$ ].721critical deusity rises sharply as the “Eddinetou” Iuminosity for neutrinos is reached., The critical density rises sharply as the “Eddington” luminosity for neutrinos is reached.722" The data (6 at and L,) for a series of disks from Popham ct al. (", The data $\dot{e}$ at km and $L_{\nu}$ ) for a series of disks from Popham et al. (7231999) are also shown for comparison.,1999) are also shown for comparison.724 These critical deusities correspoucd to iui accretion rate inside the 30° coues alougthe rotation axes of where s=20kmsud cg=V2GMpni r.," These critical densities correspond to an accretion rate inside the $30^{\circ}$ cones alongthe rotation axes of where $r=20\,{\rm km}$and $v_{\rm ff}=\sqrt{2 G M_{\rm BH}/r}$ ."725 The accretion rates for massive stars are initially wich hieher than these critical values. but the accretion vate) decreases as iaterial froin increasingly," The accretion rates for massive stars are initially much higher than these critical values, but the accretion rate decreases as material from increasingly"726We can estimate the number of expected extragalactic X-ray sources by combining information ou the expected sky density of such objects. as a function of unabsorbed. flix 2001).. with our knowledge of the total extinctiou due to the Oriou Molecular Cloud (Goldsmith.Bergin.&Lis1997).,"We can estimate the number of expected extragalactic X-ray sources by combining information on the expected sky density of such objects, as a function of unabsorbed flux \citep{gia01,toz01}, with our knowledge of the total extinction due to the Orion Molecular Cloud \citep{gol97}."727". For this exercise we make the following assumptions: 1) Extragalactic sources have power law spectra of photon index D between 1.3 and 1.5. compatible with values derived by Ciacconietal. (2001): 2) The sky density pLF] of extragalactic objects as a function of unabsorbed fIux follows the descriptious of Ciacconietal.(2001) aud (2001) respectively.:: 3) Observed photon [lus is determined by intrinsic fix aud au absorptiou proportional to the molecular cloud total optical absorption (Nj,=2-10?At ). as estimated [rom radio data by Coklsimith.Bergii.&Lis(1997): we use CFON,,) to denote the unabsorbed flux to HRC couut rate conversion factor computed with PIMMS. which depends ou Nyy. the assumed source spectrum aud the spectral band tucer consideratiou: aud. 1) We cau detect sources above count rate thresholds. C25. computed as the photon threshold (viz."," For this exercise we make the following assumptions: 1) Extragalactic sources have power law spectra of photon index $\Gamma$ between 1.3 and 1.5, compatible with values derived by \citet{gia01}; ; 2) The sky density $\rho[F]$ of extragalactic objects as a function of unabsorbed flux follows the descriptions of \citet{gia01} and \citet{toz01} ; 3) Observed photon flux is determined by intrinsic flux and an absorption proportional to the molecular cloud total optical absorption $N_H=2\cdot 10^{21}A_V^{tot}$ ), as estimated from radio data by \citet{gol97}; we use $CF(N_H)$ to denote the unabsorbed flux to HRC count rate conversion factor computed with PIMMS, which depends on $N_H$, the assumed source spectrum and the spectral band under consideration; and 4) We can detect sources above count rate thresholds, $CR_{th}$, computed as the photon threshold (viz."728 6. 8 or 10) divided by exposure time.," 6, 8 or 10) divided by exposure time."729" With these assumptions. the surface density of extragalactic sources seen through a giveu hydrogen column deusity becomes p[CHj-CRUN,)] and we can compute the expected numberof extragalactic sources detected in au area $ as: where dais the infiuitesiimial area element aud. Ny is a function of position ou the sky."," With these assumptions, the surface density of extragalactic sources seen through a given hydrogen column density becomes $\rho[CR_{th} \cdot CF(N_H)]$ and we can compute the expected numberof extragalactic sources detected in an area $S$ as: where $da$is the infinitesimal area element and $N_H$ is a function of position on the sky."730" Computing the integral (1)) for the given values of P. CR), and energy band (and therefore p[F]). we find expected numbers of detectable extragalactic objects in the inner 5/x5! of our FOV ranging from 0.6 to 1.2."," Computing the integral \ref{eq:agn}) ) for the given values of $\Gamma$, $CR_{th}$ and energy band (and therefore $\rho[F]$ ), we find expected numbers of detectable extragalactic objects in the inner $5'\times5'$ of our FOV ranging from 0.6 to 1.2."731" An extragalactic nature for most of our unidentified sources is therefore excluded. aud most ""uou-IDs can indeed be highly embedded ONC members uever observed with optical or near-IR instruments."," An extragalactic nature for most of our unidentified sources is therefore excluded, and most “non-IDs” can indeed be highly embedded ONC members never observed with optical or near-IR instruments."732 We can get a rough estimate for the size of this hidden population if we assume that counterparts ofthe 20 unidentified field-ceuter sources (expected to be real) have masses larger thau 1AL. (ct., We can get a rough estimate for the size of this hidden population if we assume that counterparts of the $\sim$ 20 unidentified field-center sources (expected to be real) have masses larger than $\sim 1~M_{\odot}$ (cf.733 Figure 16)) aud that the ratio of the number of stars with AZ>1.0AL. to stars with M«1.0AL. is the same as for oursample. namely. ~25% [or the field center and ~16% for the entire FOV.," Figure \ref{fig:noid}) ) and that the ratio of the number of stars with $M >7341.0~M_{\odot}$ to stars with $M < 1.0~M_{\odot}$ is the same as for our, namely, $\sim$ for the field center and $\sim$ for the entire FOV."735 We obtain the interesting result that the uidiscovered. population numbers between 50 aid. 125 stars. Le.H about halfH ofH the optically-wellH characterizedH members yo.in the same regionH aud about a quarter of the optical objects studied by Hillenubraud(1997).," We obtain the interesting result that the undiscovered population numbers between 80 and 125 stars, i.e., about half of the optically-well characterized members in the same region and about a quarter of the optical objects studied by \citet{hil97}."736. For comparison. there are ~600stars seen iu the infrared with A< ELLO. implying masses that roughly correspond to the mass range spauned by our sample.," For comparison, there are $\sim 600$stars seen in the infrared with $K < 14.0$ , implying masses that roughly correspond to the mass range spanned by our ."737 We conclude. therefore. that the central regiou of the ONC," We conclude, therefore, that the central region of the ONC"738temperature of the stellar system essentially negates the effects of radiative cooling.,temperature of the stellar system essentially negates the effects of radiative cooling.739 Such a small amount of gas implies that most of the mass shed by stars has either been accreted by the central supermassive black hole or has been expelled from the central region in a wind., Such a small amount of gas implies that most of the mass shed by stars has either been accreted by the central supermassive black hole or has been expelled from the central region in a wind.740 The point source labeled AGN in Fig., The point source labeled AGN in Fig.741 | is located within 1” of the optical centroid of the galaxy. and is probably associated with the central supermassive black hole with a dynamically measured mass of 1.03.9ΙΟΣΜ. (Magorrian et al.," 1 is located within $1^{\prime\prime}$ of the optical centroid of the galaxy, and is probably associated with the central supermassive black hole with a dynamically measured mass of $1.0-3.9 \times 10^8 \Mo$ (Magorrian et al."742 1998. Haring Rix 2004).," 1998, Haring Rix 2004)."743" The central black hole in NGC3379 is also a weak 14 GHz radio source with a luminosity of vL,=4.3«108 eres sc! (Condon et al.", The central black hole in NGC3379 is also a weak 1.4 GHz radio source with a luminosity of $\nu L_{\nu} = 4.3 \times 10^{35}$ ergs $^{-1}$ (Condon et al.744 1998)., 1998).745 There are too few net counts in the S3 data to fit the spectrum of the AGN. but assuming an absorbed power-law model with [=1.6 and galactic absorption gives L(0.3-10.0 keV)=8.0«IO? eres s7!. corresponding to ~3«107% of its Eddington limit.," There are too few net counts in the S3 data to fit the spectrum of the AGN, but assuming an absorbed power-law model with $\Gamma=1.6$ and galactic absorption gives L(0.3-10.0 $8.0 \times 10^{38}$ ergs $^{-1}$, corresponding to $\sim 3 \times 10^{-8}$ of its Eddington limit."746" Using the density and temperature of the ambient gas derived above gives an accretion radius for the central black hole of Ry=ολcz—7 pe. and a Bondi accretion rate M,=AzR;p,c,6«ΙΟΜ.Μ, which is a factor of 10 below the cooling rate within the central 770 kpe."," Using the density and temperature of the ambient gas derived above gives an accretion radius for the central black hole of $R_a = GM_{bh}/c_a^2 = 7$ pc, and a Bondi accretion rate $\dot {\rm M}_b = 4 \pi R_a^2 \rho_g c_a = 6 \times 10^{-5} \Mo yr^{-1}$, which is a factor of 10 below the cooling rate within the central 770 kpc."747 The implied efficiency. €=L/Mc. of the central AGN assuming Bondi aecretion is 2«1079.," The implied efficiency, $\epsilon = L/\dot {\rm M} c^2$, of the central AGN assuming Bondi accretion is $2 \times 10^{-6}$."748 This low efficieney is typical of that found for supermassive black holes at the centers of ellipticals (Lowenstein et al., This low efficiency is typical of that found for supermassive black holes at the centers of ellipticals (Lowenstein et al.749 2001. DiMatteo et al.," 2001, DiMatteo et al."750 2003)., 2003).751 The low luminosity of the central black holes in ellipticals can be explained by either a very low radiative efficiency. as in the advection dominated accretion flow model (ADAF: Narayan Yi 1994) or radiatively inefficient accretion flow model (RIAF: Yuan Narayan 2005). or a reduction 1n the aceretion rate. as in models with both inflow and AGN driven outflows (e.g.. Blandford Belgelman 1999).," The low luminosity of the central black holes in ellipticals can be explained by either a very low radiative efficiency, as in the advection dominated accretion flow model (ADAF; Narayan Yi 1994) or radiatively inefficient accretion flow model (RIAF; Yuan Narayan 2005), or a reduction in the accretion rate, as in models with both inflow and AGN driven outflows (e.g., Blandford Belgelman 1999)."752" While the uncertainty on the temperature of the diffuse gas is large. the best-fit temperature is twice the temperature associated with the velocity dispersion of the stars (KT-4un,O;/k=0.3 keV for 6,=217 km s': Prugniel/— Simien 1996)."," While the uncertainty on the temperature of the diffuse gas is large, the best-fit temperature is twice the temperature associated with the velocity dispersion of the stars $\mu m_p \sigma_p^2 /k=0.3$ keV for $\sigma_p = 217$ km $^{-1}$; Prugniel Simien 1996)."753 This suggests that the gas is being heated by the central AGN and is presently flowing out of the system in a galactic wind., This suggests that the gas is being heated by the central AGN and is presently flowing out of the system in a galactic wind.754" Assuming the gas is in a steady-state wind (1.e.. M,—Ati,putt, at 770 pe) gives i,=20 km s7! and an energy outflow rate (mostly thermal) of 5«IO eres s7!. which is 4 orders of magnitude greater than the radio luminosity of the AGN."," Assuming the gas is in a steady-state wind (i.e., $\dot M_s = 4 \pi r^2 \rho_g u_w$ at 770 pc) gives $u_w=20$ km $^{-1}$ and an energy outflow rate (mostly thermal) of $5 \times 10^{39}$ ergs $^{-1}$, which is 4 orders of magnitude greater than the radio luminosity of the AGN."755 The low wind velocity near the galactic center is typical of galactic wind models since the wind velocity continues to increase with increasing radius (e.g.. David. Forman Jones 1991).," The low wind velocity near the galactic center is typical of galactic wind models since the wind velocity continues to increase with increasing radius (e.g., David, Forman Jones 1991)."756 The lack of detectable diffuse emission at large radi in NGC 3379 may be due to the greater wind velocities and lower gas densities., The lack of detectable diffuse emission at large radii in NGC 3379 may be due to the greater wind velocities and lower gas densities.757 Chandra has detected X-ray cavities filled with radio emitting plasma and AGN driven shocks in many cluster cooling flows and individual elliptical galaxies (e.g.. MeNamara et al.," Chandra has detected X-ray cavities filled with radio emitting plasma and AGN driven shocks in many cluster cooling flows and individual elliptical galaxies (e.g., McNamara et al."758 2000. Finoguenov Jones 2002. Fabian et al.," 2000, Finoguenov Jones 2002, Fabian et al."759 2003. Blanton et al.," 2003, Blanton et al."760 2003. Forman et al.," 2003, Forman et al."761 2005. Nulsen et al.," 2005, Nulsen et al."762 2005a. Nulsen et al.," 2005a, Nulsen et al."763 2005b. MeNamara et al.," 2005b, McNamara et al."764 2005)., 2005).765 Based on the analysis of cavities found in à sample of 16 clusters. one group and one galaxy. Birzan et al. (," Based on the analysis of cavities found in a sample of 16 clusters, one group and one galaxy, Birzan et al. ("7662004) found that the ratio of mechanical to radio power of the central AGN varies from 10 in. the most radio luminous AGNs. up to 10 in systems with less radio luminous AGNs.,"2004) found that the ratio of mechanical to radio power of the central AGN varies from 10 in the most radio luminous AGNs, up to $10^4$ in systems with less radio luminous AGNs."767 In clusters with AGN driven shocks. the shock energies are typically a few times the energy in the cavities. which further increases the ratio of mechanical to radio power.," In clusters with AGN driven shocks, the shock energies are typically a few times the energy in the cavities, which further increases the ratio of mechanical to radio power."768 The largest shock and cavity energies yet observed are found in MS0735.6+7421 (McNamara et al., The largest shock and cavity energies yet observed are found in MS0735.6+7421 (McNamara et al.769 2005). which has a ratio between mechanical and radio power of 10°.," 2005), which has a ratio between mechanical and radio power of $10^5$."770 Thus. at least on energetics grounds. the hypothesis that the lack of a significant reservoir of hot gas in NGC 3379 is due to an AGN driven wind is consistent with Chandra observations of systems perturbed by radio outbursts.," Thus, at least on energetics grounds, the hypothesis that the lack of a significant reservoir of hot gas in NGC 3379 is due to an AGN driven wind is consistent with Chandra observations of systems perturbed by radio outbursts."771 The low luminosities of the central supermassive black holes in ellipticals may. in general. arise from the same feedback mechanism between the central AGN and hot gas as that observed in cluster cooling flows.," The low luminosities of the central supermassive black holes in ellipticals may, in general, arise from the same feedback mechanism between the central AGN and hot gas as that observed in cluster cooling flows."772 Based on ROSAT and Chandra observations. approximately of late-type galaxies and less that of early-type galaxies contain ULXs (Ptak Colbert 2004. Irwin et al.," Based on ROSAT and Chandra observations, approximately of late-type galaxies and less that of early-type galaxies contain ULXs (Ptak Colbert 2004, Irwin et al."773 2004)., 2004).774 In late-type galaxies. the ULXs are primarily associated with regions of star formation. indicating that they are most likely black hole binaries (BHBs) with high-mass companions.," In late-type galaxies, the ULXs are primarily associated with regions of star formation, indicating that they are most likely black hole binaries (BHBs) with high-mass companions."775 However. Colbert et al. (," However, Colbert et al. ("7762004) recently estimated that of the ULXs in spirals are not associated with recent star formation and could have low mass companions as ts likely in early-type galaxies.,2004) recently estimated that of the ULXs in spirals are not associated with recent star formation and could have low mass companions as is likely in early-type galaxies.777 As noted in the introduction. ULXs could arise from non-isotropic. sub-Eddington emission from stellar mass black holes. super-Eddington emission from stellar mass black holes. or sub-Eddington emission from IMBHs.," As noted in the introduction, ULXs could arise from non-isotropic, sub-Eddington emission from stellar mass black holes, super-Eddington emission from stellar mass black holes, or sub-Eddington emission from IMBHs."778 van der Marel (2003) has noted that the X-ray luminosity function of X-ray point sources m galaxies can be fit by a single power- even to luminosities above 10°° ergs s7!. suggesting that the accreting objects in ULXs are not a separate class of objects (e.g.. IMBHs).," van der Marel (2003) has noted that the X-ray luminosity function of X-ray point sources in galaxies can be fit by a single power-law, even to luminosities above $10^{39}$ ergs $^{-1}$, suggesting that the accreting objects in ULXs are not a separate class of objects (e.g., IMBHs)."779" There are 18 BHBs in our Galaxy with dynamically measured black hole masses between Mj),=318M. (McClintock Remillard 2004).", There are 18 BHBs in our Galaxy with dynamically measured black hole masses between $M_{bh}=3-18~\Mo$ (McClintock Remillard 2004).780 Assuming isotropic emission. 3 of these binaries are super-Eddington. with peak luminosities up to 7 times their Eddington-limit. suggesting that some of the extragalactic ULXs could be stellar mass black holes.," Assuming isotropic emission, 3 of these binaries are super-Eddington, with peak luminosities up to 7 times their Eddington-limit, suggesting that some of the extragalactic ULXs could be stellar mass black holes."781 King (2003) has proposed that ULXs comprise two separate classes of super-Eddington mass aceretion rate systems., King (2003) has proposed that ULXs comprise two separate classes of super-Eddington mass accretion rate systems.782 In regions of recent star formation in spiral galaxies. ULXs would arise from thermal-timescale mass transfer in high mass X-ray binaries. while in elliptical galaxies. the ULXs would be similar to the micro-quasars observed in our galaxy.," In regions of recent star formation in spiral galaxies, ULXs would arise from thermal-timescale mass transfer in high mass X-ray binaries, while in elliptical galaxies, the ULXs would be similar to the micro-quasars observed in our galaxy."783 The long term stability of the ULX in NGC 3379 as determined from the ROSAT HRI and Chandra observations. may pose a problem for the micro-quasar interpretation of ULXs in type galaxies.," The long term stability of the ULX in NGC 3379 as determined from the ROSAT HRI and Chandra observations, may pose a problem for the micro-quasar interpretation of ULXs in early-type galaxies."784" The mass of the central compact object in a ULX can be estimated. if thermal emission from an accretion disk car be detected. since the temperature at the inner edge of ar accretion disk scales as 77,e«Mh,"," The mass of the central compact object in a ULX can be estimated, if thermal emission from an accretion disk can be detected, since the temperature at the inner edge of an accretion disk scales as $T_{in} \propto M_{bh}^{1/4}$."785 Spectral analysis of ASCA data on ULXs indicated that these objects could be described by the MCD model with inner disk temperatures of &T=1.1.1.8 keV. implying stellar masses for the accreting objects (Makishima et al.," Spectral analysis of ASCA data on ULXs indicated that these objects could be described by the MCD model with inner disk temperatures of $kT=1.1-1.8$ keV, implying stellar masses for the accreting objects (Makishima et al."786 2000)., 2000).787 More recent analysis of Chandra and XMM-Newton data. however. indicate that some ULXs ca be described as pure power-laws with D—1.52.2. while others require à power-law plus disk model (e.g.. Roberts et al.," More recent analysis of Chandra and XMM-Newton data, however, indicate that some ULXs can be described as pure power-laws with $\Gamma=1.5-2.2$, while others require a power-law plus disk model (e.g., Roberts et al."788 2001. Zezas et al.," 2001, Zezas et al."789 2002a. Zezas et al.," 2002a, Zezas et al."790 2002b. Humphrey et al.," 2002b, Humphrey et al."791 2003. Miller et al.," 2003, Miller et al."792 2004. Liu. Bregman Seitzer 2002).," 2004, Liu, Bregman Seitzer 2002)."793 Soft accretion disks have been detected in two ULXs in NGC 1313 with inner disk temperatures of 150 eV. implying masses of 100|1000M. (Miller et al.," Soft accretion disks have been detected in two ULXs in NGC 1313 with inner disk temperatures of 150 eV, implying masses of $100-1000 \Mo$ (Miller et al."794 2003)., 2003).795 While we cannot estimate the black hole mass in the ULX in NGC 3379 due to the, While we cannot estimate the black hole mass in the ULX in NGC 3379 due to the796iuts in the VAIS IME will not significantly impact our conchisions. owing to the narrow mass rouge of clement svuthesis from VAIS SNe. aud to the uear-ideutical ionizing Xioton production per stellar baryon in all stars with nasses 2300AL.. (Brometal.200Lb)..,"limits in the VMS IMF will not significantly impact our conclusions, owing to the narrow mass range of element synthesis from VMS SNe, and to the near-identical ionizing photon production per stellar baryon in all stars with masses $\ga 300 M_\odot$ \citep{bkl}."797 We do not include cases where the conversion efficiency is derived includius the metal vield from iuteriuediate-nass stars. as pee ronaadus approximately the same for oxvgen and exactly the same for Si.," We do not include cases where the conversion efficiency is derived including the metal yield from intermediate-mass stars, as $\eta_{\rm Lyc}$ remains approximately the same for oxygen and exactly the same for Si."798 For carbon. gn decreases by a factor of a few with iutermecdiate-miass stars owing to their large vield in €. For the purposes of this paper. we wish to track the erowth of ionizing radiation which is dominated by the massive stars in the IATF.," For carbon, $\eta_{\rm Lyc}$ decreases by a factor of a few with intermediate-mass stars owing to their large yield in C. For the purposes of this paper, we wish to track the growth of ionizing radiation which is dominated by the massive stars in the IMF."799 We do uot include the vield from Ἔνρο la SNe in our calculations., We do not include the yield from Type Ia SNe in our calculations.800 Recent studies iudicate that such SNe may not occur iu metaltee stellar populations (sNobavaslictal.1998).. although this is a seusitive function of the SN mechanisi itself aud of the unknown binarityv in Z=0 stars.," Recent studies indicate that such SNe may not occur in metal-free stellar populations \citep{kobayashi}, although this is a sensitive function of the SN mechanism itself and of the unknown binarity in $Z=0$ stars."801 As shown in Venkatesan&Truman(2003) auc Miralda-Escude&Rees (1997).. calculations of ive cani be used to compute the nuniber of ionizing photons per barvou eenerated in association with a metallicity that is observed in a giveu system.," As shown in \citet{venktruran} and \citet{mirrees97}, calculations of $\eta_{\rm Lyc}$ can be used to compute the number of ionizing photons per baryon generated in association with a metallicity that is observed in a given system."802 These papers focussed on the ICAL and pointed out that the universe first generates about LO iouiziug photous per ΤΝΤ birvou for the observed IGAL metallicity of ~10.27Z..," These papers focussed on the IGM, and pointed out that the universe first generates about 10 ionizing photons per IGM baryon for the observed IGM metallicity of $\sim 10^{-2.5} Z_\odot$."803 This estimate is however subject to the uncertainties of star formation efficicucy and the escape fraction of ionizing radiation from carly ealaxies., This estimate is however subject to the uncertainties of star formation efficiency and the escape fraction of ionizing radiation from early galaxies.804 Here. we examine the ionizing eficiency in the environieut of EXIPs. aud calculate INΑλ the nuuber of ionizing photos created per barvon in stars; which is uot related to the above highlv uncertain astrophysical piraueters.," Here, we examine the ionizing efficiency in the environment of EMPs, and calculate $N_{\gamma}/N_{\rm b}$, the number of ionizing photos created per baryon in stars, which is not related to the above highly uncertain astrophysical parameters."805 Following Veukatesan&Titan(2003).. for an clement ἐν NSLN=tye\Zis (1 GeV/CELGJE we asstune the IME-averaged. energy of a Ly-coutimmiun photon. (2uve) = 27 eV (30 eV) for metal-free stars in a preseut-day. (VAIS) TTF.," Following \citet{venktruran}, for an element $i$, $N_{\gamma,i}/N_{\rm b} = \eta_{\rm Lyc,i} \times Z_i \times$ (1 $\langle806E_{\rm Lyc} \rangle)$; we assume the IMF-averaged energy of a Ly-continuum photon, $\langle E_{\rm Lyc} \rangle$ = 27 eV (30 eV) for metal-free stars in a present-day (VMS) IMF."807 For our calculations here. we take the values of gp or carbon aud oxvecu computed in Veukatesau&Traran (2003).. aud compute them iudepeudenutlv for silicon.," For our calculations here, we take the values of $\eta_{\rm Lyc}$ for carbon and oxygen computed in \citet{venktruran}, and compute them independently for silicon."808 We fil that for the 1100 AL. Salpeter-slope IME. νο has values of 0.18. 0.2 and 1.31 for C. O aud Si respectively: or a VAIS IME. the corresponding values are 0.098. 0.01. and 0.057.," We find that for the 1–100 $M_\odot$ Salpeter-slope IMF, $\eta_{\rm Lyc}$ has values of 0.48, 0.2 and 1.34 for C, O and Si respectively; for a VMS IMF, the corresponding values are 0.098, 0.01, and 0.057."809 Usine these nunibers. we show the results of our calculations iu Figure 2. where the umber of iouizine Notons created per barvou iu ENP stars. NX.δρ ds shown as a function of |Fe/II| for the eleiieuts C. O aud Si in three separate panels," Using these numbers, we show the results of our calculations in Figure 2, where the number of ionizing photons created per baryon in EMP stars, $N_{\gamma}/N_{\rm b}$, is shown as a function of [Fe/H] for the elements C, O and Si in three separate panels."810 Iu cach case. the ionizing ioton contribution frou a prescut-dav aud a VMS IME are plotted.," In each case, the ionizing photon contribution from a present-day and a VMS IMF are plotted."811 A uunuber of treuds seeu in Figure 2 are of relevance to he first-stars field., A number of trends seen in Figure 2 are of relevance to the first-stars field.812 First. VMS make a low but persisteut contribution to the overall ionizing plotou budget iu association with the metals locked iu EXIP stars. typically an order of magnitude less than the 1100 AL. INE.," First, VMS make a low but persistent contribution to the overall ionizing photon budget in association with the metals locked in EMP stars, typically an order of magnitude less than the 1–100 $M_\odot$ IMF."813 This is because VMSs are in general less efficieut at generating total ionizing racliation per uuit metal vield relative to other metal-free stellar populations. owiug to the large metal production frou VMSs.," This is because VMSs are in general less efficient at generating total ionizing radiation per unit metal yield relative to other metal-free stellar populations, owing to the large metal production from VMSs."814 Secoud. the slow buildup of metals and the associated ionizing radiation is apparent. for cach clement and for cach IME.," Second, the slow buildup of metals and the associated ionizing radiation is apparent, for each element and for each IMF."815 This treud appears most obvious for oxvecn. although there is a siguificaut scatter in the correlation between NV.δαν aud |Fo/TI] at any given ΙΕοΤΗ.," This trend appears most obvious for oxygen, although there is a significant scatter in the correlation between $N_{\gamma}/N_{\rm b}$ and [Fe/H] at any given [Fe/H]."816 As we stated earlier. the notable exceptious are the two stars at the lowest values of |Fo/1I].," As we stated earlier, the notable exceptions are the two stars at the lowest values of [Fe/H]."817 Third. we show im cach panel the approximate criterion to generate an optical depth iu the cosmic microwave backegrouud (CMD) of about 0.1. consistent with data fron theProbe (VALAP: Spereeletal.2006)). of about ΑνΑνν 31.000 CTPuuliusou2006:Tumliusonetal.2001).," Third, we show in each panel the approximate criterion to generate an optical depth in the cosmic microwave background (CMB) of about 0.1, consistent with data from the $WMAP$; \citealt{spergel06}) ), of about $N_\gamma/N_{\rm b} \sim$ 34,000 \citep{tum06,tvs04}."818. This number is derived from interpolating between cases studied by Tuulinsonetal.(20015. where the lifetime-iuteerated ionizing photon xoduction from various stellar populatious aud IMES were calculated and used as inputs in detailed cosmological relonization models., This number is derived from interpolating between cases studied by \citet{tvs04} where the lifetime-integrated ionizing photon production from various stellar populations and IMFs were calculated and used as inputs in detailed cosmological reionization models.819 Latercstinely. the EMP data indicates hat this lue is crossed at least oncetuwicc οποσα -ἰ x [Fe/TI] x -3 by a present-day IME.," Interestingly, the EMP data indicates that this line is crossed at least once between -4 $\leq$ [Fe/H] $\leq$ -3 by a present-day IMF."820" This is jest seen dn the panel correspouding to Si, where a clear dip in N/M, occurs between. -3.6 < [Fe/TH]. x -3."," This is best seen in the panel corresponding to Si, where a clear dip in $N_\gamma/N_{\rm b}$ occurs between -3.6 $\leq$ [Fe/H] $\leq$ -3."821 The VAIS IMP appears to never mect this criterion over the uctallicity ranges considered here. consistent with the role of VMSs in ICAL reionization predicted by Veukatesan&Truran (2003).," The VMS IMF appears to never meet this criterion over the metallicity ranges considered here, consistent with the role of VMSs in IGM reionization predicted by \citet{venktruran}."822 Conducting a imetal census of the universe from EXIP stars aud from the ΤΝΤ is important iu both chvirouments. despite their differing svstcmatics.," Conducting a metal census of the universe from EMP stars and from the IGM is important in both environments, despite their differing systematics."823 The TGAL contains ucarly all of the barvous at high redshifts but the former case permits a detailed. star-ly-star analysis ofthe cosiuic curichiment history., The IGM contains nearly all of the baryons at high redshifts but the former case permits a detailed star-by-star analysis of the cosmic enrichment history.824 By working with nucleosvuthetic data in EXIP stars rather than the ICAL we have not assigned a elobal fixed ietallicitv with the appropriately scaled individual clement values according to their solar ratios.," By working with nucleosynthetic data in EMP stars rather than the IGM, we have not assigned a global fixed metallicity with the appropriately scaled individual element values according to their solar ratios."825 Rather. we lave derived parallel constraints for reionization from a nunber of clements independently. which is a considerably strouger approach.," Rather, we have derived parallel constraints for reionization from a number of elements independently, which is a considerably stronger approach."826disrupt the disk. the angular momentum loss becomes less efficient. and the star has to lose a larger amount of mass to keep the rotation velocity below the critical one.,"disrupt the disk, the angular momentum loss becomes less efficient, and the star has to lose a larger amount of mass to keep the rotation velocity below the critical one."827 Consequently. we expect larger disk mass-Ioss in close binaries aud iu very dense star clusters.," Consequently, we expect larger disk mass-loss in close binaries and in very dense star clusters."828 Iu the analvsis presented here we used an assuniptiou of constant required angular momentum loss rate. which enabled us to use stationary equations.," In the analysis presented here we used an assumption of constant required angular momentum loss rate, which enabled us to use stationary equations."829 This assumption is reasonable iu most phases of the stellar evolution. as 1e evolutionary timescale is match longer than the typical nuescale of the disk buili-up. which is of the order of vears (Okazaki2001.Jonesetal.2008).," This assumption is reasonable in most phases of the stellar evolution, as the evolutionary timescale is much longer than the typical timescale of the disk build-up, which is of the order of years \citep{okaform,josip}."830. This also mecaus iat the transitional processes that occur when the star reaches or leaves the critical limut are more complicated ian studied here., This also means that the transitional processes that occur when the star reaches or leaves the critical limit are more complicated than studied here.831 Tu the course of the stellay evolution. when je surface rotational velocity reaches the critical lint. iu a first time je disk appears because it is feeded by the nechanical uass loss.," In the course of the stellar evolution, when the surface rotational velocity reaches the critical limit, in a first time the disk appears because it is feeded by the mechanical mass loss."832 The dise grows and part of it is ablated and out is transported away wa viscous coupling until au equilibrium between the required angular momentum loss rate aud mass-loss rate is achieved., The disc grows and part of it is ablated and part is transported away via viscous coupling until an equilibrium between the required angular momentum loss rate and mass-loss rate is achieved.833 During this process the disk own angular momentum could be of some muportance., During this process the disk own angular momentum could be of some importance.834 Ou the other haud. when the star leaves the critical limit. an inner part of the remaimineg disk is accreted ou the star while other parts are expelled iuto the interstellar mecditun (Okazaki20010...," On the other hand, when the star leaves the critical limit, an inner part of the remaining disk is accreted on the star while other parts are expelled into the interstellar medium \citep{okaform}."835 The processes discussed here might be relevant also for other stars with disks., The processes discussed here might be relevant also for other stars with disks.836 For example. the disk radiative ablation uuelt be one of the reasons why the Be phenomenon is typical for B stars oulv. whereas for more luminous O stars auv disk could be destroved by the radiative force.," For example, the disk radiative ablation might be one of the reasons why the Be phenomenon is typical for B stars only, whereas for more luminous O stars any disk could be destroyed by the radiative force."837 Sinular effects should also be present iu accretion disks duriug star formation., Similar effects should also be present in accretion disks during star formation.838 Tn amore luninous stars he radiative ablation could contribute to the disk. xiotoevaporation (e...Adamsetal.2001.Alexanderal.2006) iu dispersing of the disk.," In more luminous stars the radiative ablation could contribute to the disk photoevaporation \citep[e.g.,][]{adams,alexander} in dispersing of the disk."839 Moreover. a similar oxocess of the angular momentum transfer is present also iu the accretion disks of these stars. consequentlv influencing the distribution of the rotational speeds on he ZANIS.," Moreover, a similar process of the angular momentum transfer is present also in the accretion disks of these stars, consequently influencing the distribution of the rotational speeds on the ZAMS."840 Mechanical mass loss through a decretion disk can be a ubiquitous phenomenon especially for Pop III or very metal poor stars., Mechanical mass loss through a decretion disk can be a ubiquitous phenomenon especially for Pop III or very metal poor stars.841 Indeed as shown by Ekstrónictal.(2008a) pure hydrogeu-heliuu Pop ITI stars with masses above 60 ML. beeinnine their evolution ou the ZAMS with a surface velocity aronud of the critical aueular velocity. will reach the critical velocity during the AIS phase.," Indeed as shown by \citet{ekmemaba} pure hydrogen-helium Pop III stars with masses above 60 $_\odot$, beginning their evolution on the ZAMS with a surface velocity around of the critical angular velocity, will reach the critical velocity during the MS phase."842 This arises because of two effects: first aneular moment ds transported frou. the immer regions to the surface during the MS phase: second. the aneular momentum accumulates at the surface since it is not renioved by stellar winds.," This arises because of two effects: first angular momentum is transported from the inner regions to the surface during the MS phase; second, the angular momentum accumulates at the surface since it is not removed by stellar winds."843 Note that in the absence of metals hwdroseu aud helium are unable to drive a diven wind being ucarly completely ionized (xiticka&Ixubát2006)., Note that in the absence of metals hydrogen and helium are unable to drive a line-driven wind being nearly completely ionized \citep{bezvi}.844. As bydrogen-lelimm first stars are unable to launch a lne-driven wind. we expect the radiative ablation to o inefficient close to the star.," As hydrogen-helium first stars are unable to launch a line-driven wind, we expect the radiative ablation to be inefficient close to the star."845 Ou the other laud. at arecr distances a nounceligible fraction of hydrogen couk )comie neutral. enabling the possibility of disk radiative ablation.," On the other hand, at larger distances a nonnegligible fraction of hydrogen could become neutral, enabling the possibility of disk radiative ablation."846 The disk wind mass-loss rate in such case couk νο deseribed as a flow with a very low value of @ (correspondiug likely just to Ένα line force)., The disk wind mass-loss rate in such case could be described as a flow with a very low value of $\bar Q$ (corresponding likely just to $\alpha$ line force).847 Α τοις]o[um estimate of the disk wind mass-loss rate in this case couk © obtaine inserting instead of Mea the single line uass-loss rate estimate AL=Líc. (Lucy&Solomon1970) in Eq., A rough estimate of the disk wind mass-loss rate in this case could be obtained inserting instead of $\dot M_\text{CAK}$ the single line mass-loss rate estimate $\dot M\approx L/c^2$ \citep{lusol} in Eq.848"(20).. Ανάν, in most cases such flow would be likely ineficieut. especially because the disk wind nass-loss rate originates close to the star (see Fig. À3))."," Anyway, in most cases such flow would be likely inefficient, especially because the disk wind mass-loss rate originates close to the star (see Fig. \ref{palfaobr}) )."849 Cousequeutlv. the relation between the iass-loss rate required for a given angular momentum loss rate would )o eiven. by the wiud-free condition Eq.," Consequently, the relation between the mass-loss rate required for a given angular momentum loss rate would be given by the wind-free condition Eq."850(15).. The most uncertain ineredicuts of a proposed model are the viscous coupling. the disk temperature distribution and the radiative ablation.," The most uncertain ingredients of a proposed model are the viscous coupling, the disk temperature distribution and the radiative ablation."851 To include these processes we applied the same description used iu the accretion disk theory and the theory of radiativelv driven winds of hot stars., To include these processes we applied the same description used in the accretion disk theory and the theory of radiatively driven winds of hot stars.852 This may not be completely adequate for the description of decretion disk especially at large distances from the star studied here., This may not be completely adequate for the description of decretion disk especially at large distances from the star studied here.853 Consequeutbe future work should address these problems.," Consequently, future work should address these problems."854 We examine the imechanismi of the mass and aneular momentum loss via decretion disks associated with near-critical rotation., We examine the mechanism of the mass and angular momentum loss via decretion disks associated with near-critical rotation.855 The disk mass loss is set by the aneular moment needed to keep the stellar rotation at or below the critica rate., The disk mass loss is set by the angular momentum needed to keep the stellar rotation at or below the critical rate.856 We study he potentially important role of viscous coupling m outward angular momoentuii transport in the decretion disk. emphasizius that the specific angular momoeutuim at the outer edge of the disk can be much larger than at the stellar surface.," We study the potentially important role of viscous coupling in outward angular momentum transport in the decretion disk, emphasizing that the specific angular momentum at the outer edge of the disk can be much larger than at the stellar surface."857 For a given stellar interior augular moment excess. the mass loss required from a decretion disk cau be sieuificautly less than invoked iu previous models assuming a direct. release.," For a given stellar interior angular momentum excess, the mass loss required from a decretion disk can be significantly less than invoked in previous models assuming a direct, near-surface release."858and median values of the spectral index in cach frequency interval are listed in Table 4..,and median values of the spectral index in each frequency interval are listed in Table \ref{tab.alpha}.859 Both samples show a general steepening of the radio spectrum with increasing frequency., Both samples show a general steepening of the radio spectrum with increasing frequency.860 A similar elfeet has been noted by Waldram et ((2007) ancl \lassarei et (0005)., A similar effect has been noted by Waldram et (2007) and Massardi et (2008).861 Figure 7 shows a radio twocolour diagram comparing the S20 and CGlIIz spectral indices., Figure \ref{fig.2col} shows a radio two–colour diagram comparing the 8–20 and GHz spectral indices.862" As discussed bv Sacer et ((2006). this diagram: provides a useful wav of classifying objects which (like many of the AT20C sources) have ονο, rather than powerlaw radio spectra."," As discussed by Sadler et (2006), this diagram provides a useful way of classifying objects which (like many of the AT20G sources) have curved, rather than power–law radio spectra."863 The diagonal dotted line in Figure T shows the powerlaw relation., The diagonal dotted line in Figure \ref{fig.2col} shows the power–law relation.864 As noted earlier. inverted.spectrum objects (which account for of all Αθ sources at GCGLIZ). are almost absent (< 2/4)) at GCLz.," As noted earlier, inverted–spectrum objects (which account for of all AT20G sources at GHz), are almost absent $<2$ ) at GHz."865 We used the Supercosmos catalogue (Llambly et 22001) to obtain optical identifications for the radio sources observed in this study., We used the Supercosmos catalogue (Hambly et 2001) to obtain optical identifications for the radio sources observed in this study.866 We accepted an optical object as the correct ID i£ it was brighter than Dj=22nunag and lav within 5aaresee of the radio position. since Monte Carlo tests imply that at. least of such objects are. likely to be genuine associations (Sadler et 22006).," We accepted an optical object as the correct ID if it was brighter than $_{\rm J}=22$ mag and lay within arcsec of the radio position, since Monte Carlo tests imply that at least of such objects are likely to be genuine associations (Sadler et 2006)."867 Optica identifications were not attempted for three sources within lOddegrees of the Galactic plane. ancl one source in the Huxlimtecl sample. 3837). was so close to a brigh foreground star that no optical identification was possible.," Optical identifications were not attempted for three sources within degrees of the Galactic plane, and one source in the flux–limted sample $-$ 3837) was so close to a bright foreground star that no optical identification was possible."868 Table 5. summarizes the optical properties of the two samples., Table \ref{tab.opt} summarizes the optical properties of the two samples.869 While QSOs make up the majority of the optica IDs in both samples. the inverted.spectrum. sample has a slightly higher fraction of galaxies and a median value of By 0.4 mag fainter than the Dux.limited sample.," While QSOs make up the majority of the optical IDs in both samples, the inverted–spectrum sample has a slightly higher fraction of galaxies and a median value of $_{\rm J}$ 0.4 mag fainter than the flux–limited sample."870 Published recshifts are available for fewer than half the optical IDs. so the redshift. distribution needs to be interpreted with caution.," Published redshifts are available for fewer than half the optical IDs, so the redshift distribution needs to be interpreted with caution."871 Llowever. the lower median redshift for the inverted.spectrum sample is consistent with it containing a higher fraction of galaxies (which generally. [ie αἲ ο<0.5 if visible on DSS images) than the Hlux.limited sample.," However, the lower median redshift for the inverted–spectrum sample is consistent with it containing a higher fraction of galaxies (which generally lie at $z<0.5$ if visible on DSS images) than the flux–limited sample."872 Owen Mulfson (1977) found a correlation between optical magnitude and millimetre (90GCGIIz) [lux density for à sample of flatspectrum QSOs. ancl noted. that this was surprising because of the 20-25 vear interval between their 90€Cllz measurements and the sky. survey plates from. which the optical magnitudes were measured.," Owen Mufson (1977) found a correlation between optical magnitude and millimetre GHz) flux density for a sample of flat–spectrum QSOs, and noted that this was surprising because of the 20-25 year interval between their GHz measurements and the sky survey plates from which the optical magnitudes were measured."873 They showed that the correlation was significant at the level at Gllz. vet the €iCLlz lux densities of the same sources were uncorrelated with optical magnitude.," They showed that the correlation was significant at the level at GHz, yet the GHz flux densities of the same sources were uncorrelated with optical magnitude."874 They interpreted this as evidence that the sources were optically thin at millimetre wavelengths but optically thick at. centimetre wavelengths. and that a correlation existed between the radiation mechanisms in the optical ancl millimetre regimes.," They interpreted this as evidence that the sources were optically thin at millimetre wavelengths but optically thick at centimetre wavelengths, and that a correlation existed between the radiation mechanisms in the optical and millimetre regimes."875 Figure S. shows a plot of 95CLIz Hux density against optical By magnitude for our [luxlimited sample. with separate symbols used for QSOs ancl galaxies.," Figure \ref{fig.opt} shows a plot of GHz flux density against optical $_{\rm J}$ magnitude for our flux–limited sample, with separate symbols used for QSOs and galaxies."876 Blank fields are indicated by upper limits in By., Blank fields are indicated by upper limits in $_{\rm J}$.877 We see a trend similar to that found by Owen Mufson. (1977). in the sense that brighter GCLz sources are associated with brighter optical objects.," We see a trend similar to that found by Owen Mufson (1977), in the sense that brighter GHz sources are associated with brighter optical objects."878 The correlation for QSOs in Figure S. is statistically significant at a level of »99.6% in a rank correlation test., The correlation for QSOs in Figure \ref{fig.opt} is statistically significant at a level of $>99.6$ in a rank correlation test.879 One possible explanation is that many of the strongest Gllz sources are brightened by relativistic beaming at both optical ancl millimetre wavelengths. which would require that they are viewed at very small angles to the jet axis.," One possible explanation is that many of the strongest GHz sources are brightened by relativistic beaming at both optical and millimetre wavelengths, which would require that they are viewed at very small angles to the jet axis."880 1n this orientation. the millimetre continuum emission can be Doppler-boostecd bv. factors. of up. to twenty (Làhhteenmàákki Valtaoja 1999) and the optical continuum brightened by at least one magnitude (Browne Wright 1985).," In this orientation, the millimetre continuum emission can be Doppler-boosted by factors of up to twenty (Lähhteenmäkki Valtaoja 1999) and the optical continuum brightened by at least one magnitude (Browne Wright 1985)."881Calibration and editing was done in AIPS: Bad data points were flagged: phase. amplitude. and flux were calibrated using the continuum data of the calibrator sources. and bandpass calibration was applied.,"Calibration and editing was done in AIPS: Bad data points were flagged; phase, amplitude, and flux were calibrated using the continuum data of the calibrator sources, and bandpass calibration was applied."882 In (?).. Doppler correction was done and the channels were averaged to a width of 1 km s'. covering LSR velocities of 48-87 km s in G10.47+0.03 and 27-93 km s! in SgrB2.," In \citep{Sault95}, Doppler correction was done and the channels were averaged to a width of 1 km $^{-1}$, covering LSR velocities of 48–87 km $^{-1}$ in G10.47+0.03 and 27–93 km $^{-1}$ in SgrB2."883 The continuum was fitted using line-free channels (excluding 58-77. 44-80. and 42-82 km s! in G10.47+0.03. SerB2-N. and SerB2-M. respectively) and subtracted from the line data.," The continuum was fitted using line-free channels (excluding 58–77, 44–80, and 42–82 km $^{-1}$ in G10.47+0.03, SgrB2-N, and SgrB2-M, respectively) and subtracted from the line data."884" Imaging was done with almost uniform weighting for continuum maps (MIRIAD robust parameter -2. resulting in beams of 0.12""x0.06"" for GIO.47 and 0.12""x0.08"" for SgrB2) and nore —atural weighting for line maps (robust 0.5. resulting in beams NF 0.147x0.1"" for GIO.J47 and 0.15""«0.11"" for SgrB2)."," Imaging was done with almost uniform weighting for continuum maps (MIRIAD robust parameter -2, resulting in beams of $0.12'' \times 0.06''$ for G10.47 and $0.12'' \times 0.08''$ for SgrB2) and more natural weighting for line maps (robust 0.5, resulting in beams of $0.14'' \times 0.1''$ for G10.47 and $0.15'' \times 0.11 ''$ for SgrB2)."885 For total fluxes and lower noise levels. the continuum was also naged in natural weighting.," For total fluxes and lower noise levels, the continuum was also imaged in natural weighting."886" A pixel size of 0.02” and a cutoff for cleaning of twice the ""ms noise in the image was used.", A pixel size of $''$ and a cutoff for cleaning of twice the rms noise in the image was used.887" Table 1. summarizes beam ""aizes and noise levels.", Table \ref{tab:obs} summarizes beam sizes and noise levels.888 For G10.47+0.03. the continuum clean components were csed to self-calibrate the phases and apply the solutions to the line data.," For G10.47+0.03, the continuum clean components were used to self-calibrate the phases and apply the solutions to the line data."889 The absorption lines in this source were almost visible before self-calibration., The absorption lines in this source were almost invisible before self-calibration.890 The procedure did not improve the SgrB2 data. presumably due to the good calibration with SerA* only 0.7° away.," The procedure did not improve the SgrB2 data, presumably due to the good calibration with SgrA* only $^\circ$ away."891" All figures shown in this paper were created with the GILDASsoftware"".", All figures shown in this paper were created with the GILDAS.892 With the Effelsberg 100-m telescope of the Max-Planck-Institut fürr Radioastronomie. we observed several sources in HCN direct /-typelines in 2000 (2).. 2002. and 2007.," With the Effelsberg 100-m telescope of the Max-Planck-Institut fürr Radioastronomie, we observed several sources in HCN direct $\ell$ -typelines in 2000 \citep{Thorwirth01}, , 2002, and 2007."893 The lines were the 7-9 transition at 20.18 GHz. 7-210 at 24.66 GHz. J=!1 at 29.58 GHz. and 7/212 at 34.95 GHz.," The lines were the $J$ =9 transition at 20.18 GHz, $J$ =10 at 24.66 GHz, $J$ =11 at 29.58 GHz, and $J$ =12 at 34.95 GHz."894" Beam sizes are 37. 31. 26. and 22"", respectively."," Beam sizes are 37, 31, 26, and $''$, respectively."895" Pointing was done on nearby quasars. and Is accurate to about 10""."," Pointing was done on nearby quasars, and is accurate to about $''$."896 The different polarizations and scans were averaged. and a baseline was subtracted by fitting a polynomial of order 0 to 5 to line-free channels.," The different polarizations and scans were averaged, and a baseline was subtracted by fitting a polynomial of order 0 to 5 to line-free channels."897 The noise tube units measured by the telescope were converted to fluxes by comparison with a source of known flux. mostly NGC7027 (?).. which was observed once per day.," The noise tube units measured by the telescope were converted to fluxes by comparison with a source of known flux, mostly NGC7027 \citep{Ott94}, which was observed once per day."898 To correct the deformation of the telescope at low elevations. the resulting flux was multiplied by an additional factor of (1—0.01κ(30°eh)! (Q9). which is 1.25 at an elevation of 10°. typical for SgrB2.," To correct the deformation of the telescope at low elevations, the resulting flux was multiplied by an additional factor of $\left(1-0.01\times (30^\circ - elv)\right)^{-1}$ \citep{Gallimore01}, which is 1.25 at an elevation of $10^\circ$, typical for SgrB2."899 The observations were complemented by data from the millimeter-wave line survey of SgrB2 with the IRAM 30-m telescope (?).., The observations were complemented by data from the millimeter-wave line survey of SgrB2 with the IRAM 30-m telescope \citep{Belloche08}.900 For each source we show spectra (Fig. 1)).," For each source we show spectra (Fig. \ref{fig:spectra}) ),"901 continuum and integrated line maps. as well as position-velocity diagrams.," continuum and integrated line maps, as well as position-velocity diagrams."902 Absorption lines are summarized in Table 2. and emission lines in Table 3.., Absorption lines are summarized in Table \ref{tab:abslines} and emission lines in Table \ref{tab:emlines}.903 From Gaussian fits to the absorption lines. lower limits C1 the optical depth τ and on the column density of hot HCN can be derived: The line-to-continuum ratio is e7 if line emission can be neglected. ie. if the beam-averaged (excitation) temperature of the absorbing gas is much lower than the beam-averaged background brightness temperature - else the line-to-continuum ratio is larger than ο.," From Gaussian fits to the absorption lines, lower limits on the optical depth $\tau$ and on the column density of hot HCN can be derived: The line-to-continuum ratio is $e^{-\tau}$ if line emission can be neglected, i.e. if the beam-averaged (excitation) temperature of the absorbing gas is much lower than the beam-averaged background brightness temperature - else the line-to-continuum ratio is larger than $e^{-\tau}$."904 The background radiation 1s provided by free-free emission from ionized gas of around 10 K. which is at least an order of magnitude larger than the temperature of the absorbing gas.," The background radiation is provided by free-free emission from ionized gas of around $^4$ K, which is at least an order of magnitude larger than the temperature of the absorbing gas."905 However. the observed continuum is lower than 10 K due to optically thin free-free radiation in parts of the beam (see e.g. ? for spectral energy distributions of regions with density gradient).," However, the observed continuum is lower than $^4$ K due to optically thin free-free radiation in parts of the beam (see e.g. \citet{Cesaroni10} for spectral energy distributions of regions with density gradient)."906 Additionally. the hot molecular gas could emit over the whole beam.," Additionally, the hot molecular gas could emit over the whole beam."907 Therefore. the real optical depths can be much higher than derived from the line-to-continuum ratio. and the values given in Table 2. are only lower limits.," Therefore, the real optical depths can be much higher than derived from the line-to-continuum ratio, and the values given in Table \ref{tab:abslines} are only lower limits."908 From r and the observed line width Av(FWHM). the HCN column density can be derived. assuming Local Thermodynamic Equilibrium (LTE. see also Sect. ??))," From $\tau$ and the observed line width $\Delta v$(FWHM), the HCN column density can be derived, assuming Local Thermodynamic Equilibrium (LTE, see also Sect. \ref{sec:assumptions}) )"909" at a temperature 7: Usingwith frequency v=40.7669 GHz. Einstein A coefficient Au=3.75x1078 s! and profile function at Gaussian line center. ᾧ_=πιX20,94 πες. the total algocolumn densityUe NATcanone be obtained from the column density in the upper state"," at a temperature $T$ : Usingwith frequency $\nu=40.7669$ GHz, Einstein A coefficient $A_{\rm ul}=3.75\times 10^{-8}$ $^{-1}$ and profile function at Gaussian line center $\Phi= \sqrt{\frac{ln(2)}{\pi}} \times \frac{2}{\Delta v} \approx \frac{0.94}{\Delta v}$ , the total column density $N$can be obtained from the column density in the upper state"910ab O.7O8 yam).,at 0.768 $\mu m$ ).911 Therelore. for this object we model the degree of polarization at different wavelengths.," Therefore, for this object we model the degree of polarization at different wavelengths."912 The real part of the refractive index is lixed al 1.65 and the imaginary part is taken by interpolating the data given in Scott&Dulev(1996)., The real part of the refractive index is fixed at 1.65 and the imaginary part is taken by interpolating the data given in \citet{sco96}.913. It should be mentioned that the relractive index of amorphous condensates mieht differ under different. physical conditions., It should be mentioned that the refractive index of amorphous condensates might differ under different physical conditions.914 Apart [rom the caleulation of the grain number density. the location of the cloud in the almosphere plays ai important role in determining (he amount of polarization.," Apart from the calculation of the grain number density, the location of the cloud in the atmosphere plays an important role in determining the amount of polarization."915 The location of the cloud base lor different atmospheric models and different chemical species is determined bv the intersection of the T-P profile of the atmosphere model and the condensation curve ; as prescribed in C03.," The location of the cloud base for different atmospheric models and different chemical species is determined by the intersection of the T-P profile of the atmosphere model and the condensation curve $P_{c,l}$ as prescribed in C03."916 Taking the condensation curve lor forsterite. we determine the base of the cloud for each spectral type. [rom LO (to L8.," Taking the condensation curve for forsterite, we determine the base of the cloud for each spectral type, from L0 to L8."917 Figure 2. presents (he atmospheric pressure height al which the cloud base is situated for models with different spectral tvpes., Figure \ref{pbase} presents the atmospheric pressure height at which the cloud base is situated for models with different spectral types.918 As the elleetive temperature decreases from LO to L8. the cloud base is pushed deeper into ihe atmosphere.," As the effective temperature decreases from L0 to L8, the cloud base is pushed deeper into the atmosphere."919 According to the condensation curve given in CO3. the base of forsterite cloud. for a L8 object (Zig 21480 IX) is situated al about 10.0 bar pressure height when the surface gravity of the object is assumed to be 10? em 7.," According to the condensation curve given in C03, the base of forsterite cloud for a L8 object $T_{\rm eff} \simeq$ 1480 K) is situated at about 10.0 bar pressure height when the surface gravity of the object is assumed to be $10^5$ cm $^{-2}$."920 For a similar model. found the base of Του at 9.4 bar pressure height.," For a similar model, \citet{woi04} found the base of $_2$ at 9.4 bar pressure height."921" Similarly. for a L4 (Teg 01820 IX) object. the forsterite cloud. base is lound to be situated al 2.2 bar while Woitke&IIelling,(2004) found it to be at 2.7 bar for TiOs cloud."," Similarly, for a L4 $T_{\rm eff}\simeq$ 1820 K) object, the forsterite cloud base is found to be situated at 2.2 bar while \citet{woi04} found it to be at 2.7 bar for $_2$ cloud."922 Theoretical investigation (Tsuji2004a) claims that the thickness of the dust clouds and hence the location of the cloud deck influences the spectral energy distribution of L and T chwarls., Theoretical investigation \citep{tsuji04a} claims that the thickness of the dust clouds and hence the location of the cloud deck influences the spectral energy distribution of L and T dwarfs.923" Also. 1 is suggested that the vertical height of dust cloud may vary [or a given T,jy and surface gravity (IXnappetal.2004:Tsuji2004a)."," Also, it is suggested that the vertical height of dust cloud may vary for a given $T_{eff}$ and surface gravity \citep{knap04, tsuji04a}."924. The degree of polarization too is stronglv dependent on the vertical height of the dust cloud and hence on the location of the eloud deck., The degree of polarization too is strongly dependent on the vertical height of the dust cloud and hence on the location of the cloud deck.925 In C03. the cloud deck is considered to be at one scale height above the base.," In C03, the cloud deck is considered to be at one scale height above the base."926 The condensation curve {δι decreases exponentially with the decrease in the atmospheric temperature and the value of 72.; become neelieibly small at 7=1600A.," The condensation curve $P_{c,l}$ decreases exponentially with the decrease in the atmospheric temperature and the value of $P_{c,l}$ become negligibly small at $T=1600 K$."927 For different atmospheric models. this temperature is attained at different atmospheric pressure height.," For different atmospheric models, this temperature is attained at different atmospheric pressure height."928 The position of the cloud deck for different spectral types is also presented in figure 2., The position of the cloud deck for different spectral types is also presented in figure 2.929 From ligure 2 we note that the thickness of the cloud decreases as one goes [rom L3 to LO., From figure \ref{pbase} we note that the thickness of the cloud decreases as one goes from L8 to L0.930 In other words. the thickness of the dust cloud decreases with the increase in effective temperature for a fixed value of surface gravity.," In other words, the thickness of the dust cloud decreases with the increase in effective temperature for a fixed value of surface gravity."931 For L chwarls hotter than L2. the eloud is very (thin. much less than one scale height.," For L dwarfs hotter than L2, the cloud is very thin, much less than one scale height."932 For à L3 object. the forsterite cloud deck is ealeulated to be situated at about 4 bar pressure height.," For a L8 object, the forsterite cloud deck is calculated to be situated at about 4 bar pressure height."933 For a similar atmospheric model. calculated the Γιος cloud deck at 0.24 bar.," For a similar atmospheric model, \citet{woi04} calculated the $_2$ cloud deck at 0.24 bar."934 For à L4 object the forsterite cloud deck in our model is al 0.5 bar pressure height while the TiO» cloud deck caleulated by. [or a similar object is al 0.1 bar., For a L4 object the forsterite cloud deck in our model is at 0.5 bar pressure height while the $_2$ cloud deck calculated by \citet{woi04} for a similar object is at 0.1 bar.935 Therefore the cloud thickness in our model, Therefore the cloud thickness in our model936stream al £zz0. and an upwarel stream al (6221807.,"stream at $\ell \approx 0$, and an upward stream at $\ell \approx 180\degr$."937 Obviously. the pattern in Fig.," Obviously, the pattern in Fig."938 4 is completely inconsistent with this prediction., \ref{tt.fig} is completely inconsistent with this prediction.939 Assuming for simplicity that the Sun lies on the line of nodes. the linear Tavlor expansion of the local velocity field (2)) should be expanded to include a vertical CZ) component of velocity. Pyyee b The corresponding tangential velocity field is = ," Assuming for simplicity that the Sun lies on the line of nodes, the linear Taylor expansion of the local velocity field \ref{taylor.eq}) ) should be expanded to include a vertical $Z$ ) component of velocity, _0) b. The corresponding tangential velocity field is = ^2 r _2^1)."940Thus. the differential warp motion is expressed bv two OMM parameters. Ly; ancl Mq.," Thus, the differential warp motion is expressed by two OMM parameters, $L_{13}$ and $M_{13}$."941 These two fitted parameters vield discrepant estimates of the warp velocity gradient. A=—12 and A=6elct+4kms1.," These two fitted parameters yield discrepant estimates of the warp velocity gradient, $\Lambda = -2\, h_1^{-1}942\simeq -12$ , and $\Lambda = 6\, e_2^{1} \simeq +4$."943 The former estimate [rom the magnetic harmonic has the wrong sign. and its modulus is too large for a credible differential warp.," The former estimate from the magnetic harmonic has the wrong sign, and its modulus is too large for a credible differential warp."944 The electric harmonic Li has the right sign. but it nearly vanishes for more clistant stars (II<10 mas).," The electric harmonic $\vec{E}_2^1$ has the right sign, but it nearly vanishes for more distant stars $\Pi < 10$ mas)."945 Thus. the kinematical model of Galactic warp does not furnish an adequate explanation to the presence of magnetic harmonics li! and IL," Thus, the kinematical model of Galactic warp does not furnish an adequate explanation to the presence of magnetic harmonics $\vec{H}_1^{-1}$ and $\vec{H}_2^{-1}$."946",Samples of larger volumes are needed (o find out if these two harmonics are not a local feature. and to lind evidence of warp in the motion of fielcl stars."," Samples of larger volumes are needed to find out if these two harmonics are not a local feature, and to find evidence of warp in the motion of field stars."947 Interestingly. Drimmeletal.(2000) also found a negative vertical motion of distant OD stars in (he direction of Galactic anticenter. in obvious contradiction to the predieted warp motion.," Interestingly, \citet{dri} also found a negative vertical motion of distant OB stars in the direction of Galactic anticenter, in obvious contradiction to the predicted warp motion."948 A non-stationary warp is one of the possibilities considered by them., A non-stationary warp is one of the possibilities considered by them.949 A precessing line of nodes is conceivable. but we find it difficult to reconcile the observed pattern of vertical motion. should it bear ou the subject at all. with a plausible precession model.," A precessing line of nodes is conceivable, but we find it difficult to reconcile the observed pattern of vertical motion, should it bear on the subject at all, with a plausible precession model."950 It appears instead. that the line of nodes is stationary. but the shape of warp changes to ils opposite every 50 Myr or so. curling (his way ancl (he other.," It appears instead, that the line of nodes is stationary, but the shape of warp changes to its opposite every 50 Myr or so, curling this way and the other."951 llipparcos stars wilh accurate trigonometric parallaxes represent only a tiny traction of the Galactic population., Hipparcos stars with accurate trigonometric parallaxes represent only a tiny fraction of the Galactic population.952 Half of stars considered in this paper are within 112 pe. and 75," Half of stars considered in this paper are within 112 pc, and 75"953non-axisvmmetric ones.,non-axisymmetric ones.954 For example. Janiuketal.(2008) found that in fully 3-D simulations the inner torus processes.," For example, \citet{janiuk:2008} found that in fully 3-D simulations the inner torus processes."955 Lt would be important to check if the torus will also precess in the MIID limit and what consequences it would have on the outflow formation and the polar-funnel accretion., It would be important to check if the torus will also precess in the MHD limit and what consequences it would have on the outflow formation and the polar-funnel accretion.956 Recent work on outllows driven by radiation from a precessing disc show that the low geometry can be dramatically changes although the mass accretion rate can be similar to that in the non-precessing disc case (Ixurosawa&Proga2008)., Recent work on outflows driven by radiation from a precessing disc show that the flow geometry can be dramatically changes although the mass accretion rate can be similar to that in the non-precessing disc case \citep{kurosawa:2008}.957. We plan to address these issues in our future work., We plan to address these issues in our future work.958 Future simulations should also include radiative cooling and heating processes., Future simulations should also include radiative cooling and heating processes.959 Recently. Fragile&Aleier(2009) pointed. out that. the radiative. cooling may be of the same order as artificial. cooling caused by lack of the treatment of kinetic ancl magnetic dissipative processes in non-conservative codes (as one used. by us).," Recently, \citet{fragile:2009} pointed out that the radiative cooling may be of the same order as artificial cooling caused by lack of the treatment of kinetic and magnetic dissipative processes in non-conservative codes (as one used by us)."960 Our. mocels also do not resolve the gcometricallv thin discs., Our models also do not resolve the geometrically thin discs.961 Currently. elobal simulations of the magnetized geometrically thin disc is bevond computational abilities.," Currently, global simulations of the magnetized geometrically thin disc is beyond computational abilities."962 We acknowledge support provided by the Chandra awards TAIT-SOOSNO (ALAL and D.) and TMS-9004X (D.D.) issued by the Chandra. X-Ray Observatory Center. which is operated by the Smithsonian Astrophysical Observatory for and on behalf o£NASA under contract NAS S-39073.," We acknowledge support provided by the Chandra awards TM7-8008X (M.M. and D.P.) and TM8-9004X (D.P.) issued by the Chandra X-Ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS 8-39073."963While these six classes of Ixuiyer belt surfaces provide an overall frauework for uuderstaudiug the the composition of ΔΕΟ suraces. there are opel questions abou umultiple aspects of this framework tha must be answerec before we can be ce‘tatu that our first-order understaucding of these surfaces is correct.,"While these six classes of Kuiper belt surfaces provide an overall framework for understanding the the composition of KBO surfaces, there are open questions about multiple aspects of this framework that must be answered before we can be certain that our first-order understanding of these surfaces is correct."964 La additiOL. some overall αιestious still remai1," In addition, some overall questions still remain."965 We stinimarize some of the most impo‘taut questions to be auswered by futu'e research:, We summarize some of the most important questions to be answered by future research:966We now convolve the processed spectra of Section 3. with the star-formation histories of Section 2. to calculate the ccontribution to the CURB.,We now convolve the processed spectra of Section \ref{specsec} with the star-formation histories of Section \ref{sfrsec} to calculate the contribution to the CIRB.967 The background. is evaluated with (e.g. Peebles 1993).," The background is evaluated with (e.g., Peebles 1993)."968" Here μις is the observed frequency. Ll, ds the observed specific intensity. vfs)=(1|z)e6u. and ζωές) is the comoving specific emission coellicient."," Here $\nu_{\mathrm obs}$ is the observed frequency, $I_{\nu}$ is the observed specific intensity, $\nu(z)=(1+z)\nu_{\mathrm obs}$ and $j^{\mathrm c}_{\nu}(z)$ is the comoving specific emission coefficient."969" Both the star-formation history and the assumed. recombination history. determine j5(z): where /,. is either (? or 4. 72LO""vr is the fiducial main-sequence lifetime of a sstar (Brommetal.2001b) and os) is either o,(2) or Charafs). the SER per comoving volume."," Both the star-formation history and the assumed recombination history determine $j^{\mathrm970c}_{\nu}(z)$: where $l_{\nu}$ is either $l_{\nu}^{0}$ or $l_{\nu}^{1}$ $\tau=2\times 10^6~\yr$ is the fiducial main-sequence lifetime of a star \cite{bro01c} and $\psi(z)$ is either $\psi_{\mathrm971on}(z)$ or $\psi_{\mathrm burst}(z)$, the SFR per comoving volume."972 Results for fos.=0 and | are shown in6., Results for $f_{\mathrm esc}=0$ and $1$ are shown in.973. There are a total of eight curves in the figure. generated by varving each of three parameters over two values: fos.=0 or 1: Lona=400 or 107Ix: star-formation mode of ongoing or single-burst.," There are a total of eight curves in the figure, generated by varying each of three parameters over two values: $f_{\mathrm esc}=0$ or $1$ ; $\tcrit=400$ or $10^4~\kelvin$; star-formation mode of ongoing or single-burst."974. Models with fos.=0 alwaws produce more CIRB at all wavelengths than f;=1 models., Models with $f_{\mathrm esc}=0$ always produce more CIRB at all wavelengths than $f_{\mathrm esc}=1$ models.975" Models with 25,5;=400Ix produce more CIRD than To,—10!Kx models at all wavelengths except near 1san for single-burst star-[ormation models.", Models with $\tcrit=400~\kelvin$ produce more CIRB than $\tcrit=10^4~\kelvin$ models at all wavelengths except near $1~\mu$ m for single-burst star-formation models.976 The ongoing star-formation mocels produce more CIRB at all wavelengths than single-burst star-formation models. except near Ly for the fi...=0 case.," The ongoing star-formation models produce more CIRB at all wavelengths than single-burst star-formation models, except near $1~\mu$ m for the $f_{\mathrm esc}=0$ case."977 The sharp edge at. 1yam in all of the curves is a result of ow sharp truncation of sstag formation at tent=7., The sharp edge at $1~\mu$ m in all of the curves is a result of our sharp truncation of star formation at $z_{\rm end}=7$.978 The edge occurs at the redshifted wavelength. of Lya [rom stars at zegq. be. soyL216 A.," The edge occurs at the redshifted wavelength of $\lya$ from stars at $z_{\rm979end}$, i.e., $(1+z_{\rm end})1216$ ."980". The reason that the CURB curves for 25,4;=400 and 107IX have similar values at 1.fm for single-burst star-formation models is that the corresponding SElIts at =7 are similar (sce Fig. 1))", The reason that the CIRB curves for $\tcrit=400$ and $10^4~\kelvin$ have similar values at $1~\mu$ m for single-burst star-formation models is that the corresponding SFRs at $z=7$ are similar (see Fig. \ref{sfretafig}) ).981 The “bump” in the CIR curves from 0.7jii to 1jan results from stellar. emission. between rest-frame 912 and 1216 ((sco Figs., The “bump” in the CIRB curves from $0.7~\mu$ m to $1~\mu$ m results from stellar emission between rest-frame 912 and 1216 (see Figs.982 3. and 5)) by sources at z=7., \ref{procspec15fig} and \ref{igmspec15fig}) ) by sources at $z=7$.983 From A=1jum to roughly 2 im the CCLBD is dominated by Ljo emission from sources at 1]2=A/1216 A., From $\lambda=1~\mu$ m to roughly $2~\mu$ m the CIRB is dominated by $\lya$ emission from sources at $1+z=\lambda/1216~\ang$ .984 The inflection points of the curves. particularly clear in the f;=0 panel. occur at the wavelength where the COIRB transitions from being dominated by Lya emission to being dominated by continuum emission from sources at =song.," The inflection points of the curves, particularly clear in the $f_{\mathrm985esc}=0$ panel, occur at the wavelength where the CIRB transitions from being dominated by $\lya$ emission to being dominated by continuum emission from sources at $z=z_{\rm end}$."986 Phe continuum radiation for the fi...=0 spectrum is dominated. by free-free. emission. (see E 3)).," The continuum radiation for the $f_{\mathrm esc}=0$ spectrum is dominated by free-free emission (see Fig. \ref{procspec15fig}) ),"987 whereas stellar continuum. is important as well for the fi...=1 continuum spectrum (see Fig. 5))., whereas stellar continuum is important as well for the $f_{\mathrm esc}=1$ continuum spectrum (see Fig. \ref{igmspec15fig}) ).988 Consequently. the nmunmid-Ilt background is determined. predominantly by the choice of za rather than the SER at extremely. high redshifts.," Consequently, the mid-IR background is determined predominantly by the choice of $z_{\rm989end}$ rather than the SFR at extremely high redshifts."990 The ccontribution to the optical background (for τρ2 7) is due to the stellar “bump” described above and the high-energy tail of [ree-free emission. which is only significant for the fou=0 spectrum: this is a consequence of the temperature of the gas. which is elfectively much higher in the fas.=0 case than for the fis.=1 case (see 833).," The contribution to the optical background (for $z_{\rm end}\ge7$ ) is due to the stellar “bump” described above and the high-energy tail of free-free emission, which is only significant for the $f_{\mathrm991esc}=0$ spectrum; this is a consequence of the temperature of the gas, which is effectively much higher in the $f_{\mathrm esc}=0$ case than for the $f_{\mathrm esc}=1$ case (see 3)."992 The points with error bars in show the cdilference tween the total extragalactic background. and. the extragalactic background. clue to. resolved sources., The points with error bars in show the difference between the total extragalactic background and the extragalactic background due to resolved sources.993 At wavelengths. e.g. 0.3 jm. where the lower limit is an arrow. he contribution from resolve| sources is sullicient to explain of the background. at he 26 level.," At wavelengths, e.g., $0.3~\umu$ m, where the lower limit is an arrow, the contribution from resolved sources is sufficient to explain of the background, at the $2\sigma$ level."994 At wavelengths where data points have lower limits plotted. e.g..2.2 fun. he light. from resolved. sources is not enoughto account or the measured background.," At wavelengths where data points have lower limits plotted, e.g.,$2.2~\umu$ m, the light from resolved sources is not enoughto account for the measured background."995 Lt is this unexplained excess. measured by Cambréssy et:d.," It is this unexplained excess, measured by Cambréssy et al."996 (2001) at 1.25 jim and by Cambréssy et al., \shortcite{cam01} at $1.25~\umu$ m and by Cambréssy et al.997 (2001). anc Wright Johnson (2001) at 2.2 yam. that we are trving to fit with our mocoels. while conforming to upper limits a other wavelenths.," \shortcite{cam01} and Wright Johnson \shortcite{wri01} at $2.2~\umu$ m, that we are trying to fit with our models, while conforming to upper limits at other wavelenths."998There are two key differences between NSs and BHs - the presence or the absence of a solid surface and a (dipole) magnetic field.,There are two key differences between NSs and BHs – the presence or the absence of a solid surface and a (dipole) magnetic field.999" These differences give rise respectively to Type 1 X-ray bursts, which are thermonuclear explosions in the surface layers of NSs, and coherent pulsations, which are the signals resulting from the dipolar magnetic fields anchored in NSs (Done et al."," These differences give rise respectively to Type I X-ray bursts, which are thermonuclear explosions in the surface layers of NSs, and coherent pulsations, which are the signals resulting from the dipolar magnetic fields anchored in NSs (Done et al."1000 2007)., 2007).1001" These two phenomena are very common in NS X-ray binaries, but have never seen in the BH systems."," These two phenomena are very common in NS X-ray binaries, but have never seen in the BH systems."1002 It is believed that both the solid surface and the magnetic field can also atfect the accretion flow. and show some observable effects.," It is believed that both the solid surface and the magnetic field can also affect the accretion flow, and show some observable effects."1003" For comparable mass aceretion rates, the observational data suggest that BH LMXBs are fainter than NS LMXBs by a factor of ~ 100-1000 in quiescent state."," For comparable mass accretion rates, the observational data suggest that BH LMXBs are fainter than NS LMXBs by a factor of $\sim$ 100-1000 in quiescent state."1004 The large X-ray luminosity difference can be naturally explained by the advection-dominated aceretion flow (ADAF) model., The large X-ray luminosity difference can be naturally explained by the advection-dominated accretion flow (ADAF) model.1005" The bulk of thermal energy is trapped in the advective flow entering into the BH event horizon, and is lost from sight."," The bulk of thermal energy is trapped in the advective flow entering into the BH event horizon, and is lost from sight."1006" Whereas in the case of NS, the thermal energy is radiated from its solid surface, and makes NS LMXB much brighter than BH system (Narayan MeClintock 2008)."," Whereas in the case of NS, the thermal energy is radiated from its solid surface, and makes NS LMXB much brighter than BH system (Narayan McClintock 2008)."1007" However, ADAF model overestimates the luminosity of quiescent NS LMXB, unless most of the accretion flow is prevented from reaching the NS surface on account of the ""propeller"" effect (Zhang et al."," However, ADAF model overestimates the luminosity of quiescent NS LMXB, unless most of the accretion flow is prevented from reaching the NS surface on account of the “propeller"" effect (Zhang et al."1008 1998; Menou et al., 1998; Menou et al.1009 1999)., 1999).1010 The interaction of accretion flow with magnetic field can be characterized by the size of magnetosphere co-rotating with the central NS: the boundary of the magnetosphere is determined where the ram pressure of the flow is balanced by the magnetic pressure., The interaction of accretion flow with magnetic field can be characterized by the size of magnetosphere co-rotating with the central NS; the boundary of the magnetosphere is determined where the ram pressure of the flow is balanced by the magnetic pressure.1011" When falling into the magnetosphere, the acereting gas is forced to co-rotate with the magnetosphere/NS, since the magnetic force dominates the flow dynamics in this region (Lamb et al."," When falling into the magnetosphere, the accreting gas is forced to co-rotate with the magnetosphere/NS, since the magnetic force dominates the flow dynamics in this region (Lamb et al."1012 1973)., 1973).1013" The radius of an NS magnetosphere increases with decreasing accretion rate (ram pressure), that is. given by Cui (1997), where Lx is the bolometric X-ray luminosity, B is the NS surface magnetic field strength, and Rs is the NS radius."," The radius of an NS magnetosphere increases with decreasing accretion rate (ram pressure), that is, given by Cui (1997), where $L_{\rm X}$ is the bolometric X-ray luminosity, $B$ is the NS surface magnetic field strength, and $R_{\rm NS}$ is the NS radius."1014" If the magnetosphere expands beyond the radius, the centrifugal barrier prevents most material accreting onto NS, and the disk is truncated at the magnetosphere radius."," If the magnetosphere expands beyond the co-rotation radius, the centrifugal barrier prevents most material accreting onto NS, and the disk is truncated at the magnetosphere radius."1015" It is well known as ""propeller"" effect, and its evidence has been reported in some X-ray pulsars and Atoll sources (Cui 1997: Zhang et al."," It is well known as “propeller"" effect, and its evidence has been reported in some X-ray pulsars and Atoll sources (Cui 1997; Zhang et al."1016 1998: Campana ct al 1998)., 1998; Campana et al 1998).1017 The Atoll source 4U1608-52? is found to undergo an abrupt spectral change during the luminosity declines of its 2004 outburst (Chen et al., The Atoll source 4U1608–522 is found to undergo an abrupt spectral change during the luminosity declines of its 2004 outburst (Chen et al.1018 2006)., 2006).1019 Chen et al. (, Chen et al. (1020"2006) argued that this event can be interpreted as the propeller driven spectral state transition, similar to that found in Aql X-1 (Zhang et al.","2006) argued that this event can be interpreted as the propeller driven spectral state transition, similar to that found in Aql X-1 (Zhang et al."1021 1998; Campana et al 1998)., 1998; Campana et al 1998).1022" In the next section, we investigate the 2007 outburst of 4U1608-522, that was observed with Swift and the Rossi X-ray Timing Explorer (RXTE) simultancously."," In the next section, we investigate the 2007 outburst of 4U1608–522, that was observed with Swift and the Rossi X-ray Timing Explorer (RXTE) simultaneously."1023 We compare the BH LMXBs with NS LMXBs from low to super-Eddington luminosity in, We compare the BH LMXBs with NS LMXBs from low to super-Eddington luminosity in1024original papers.,original papers.1025 In particular. we have distinguished the EROs for which there is firm evidence for the presence of lutrinsic obscuration on the basis of their Xταν and/or optical spectrum (squares) from the EROs for which Xrav obscuration is onlv sugeested from the broadbaud Xrav photometry. io. harduess ratios (triangles).," In particular, we have distinguished the EROs for which there is firm evidence for the presence of intrinsic obscuration on the basis of their X–ray and/or optical spectrum (squares) from the EROs for which X--ray obscuration is only suggested from the broad–band X–ray photometry, i.e. hardness ratios (triangles)."1026" Non active galaxies. EROs for which Xrav properties do not suggest iutrinsic obscuration and EROs for which the information available is insufficient to constrain their physical nature are grouped together aud indicated with Crosses,"," Non active galaxies, EROs for which X–ray properties do not suggest intrinsic obscuration and EROs for which the information available is insufficient to constrain their physical nature are grouped together and indicated with crosses."1027 More details on the svunbols are reported in the caption of the figure., More details on the symbols are reported in the caption of the figure.1028" A large fraction of the EROs having Log(Fx /E,,4) 21 (at least 15 out of the 10) are obscured Αννα,", A large fraction of the EROs having $_X$ $_{opt})>$ 1 (at least 45 out of the 70) are obscured AGNs.1029 This is indeed what is expected on the basis of he observational results found so far bv deep. mediuu and bright XNrav surveys (Fiore et al. 2003)).," This is indeed what is expected on the basis of the observational results found so far by deep, medium and bright X–ray surveys (Fiore et al. \cite{Fiore03}) )."1030 The act hat S2F1.1113 and S2F1.7711 lic in this region of the diagram strongly supports the hypothesis derived from the wrduess ratio analysis. 1.0. that strong X.ray obscuration is likely present in these hieh luminosity ACNs.," The fact that 443 and 714 lie in this region of the diagram strongly supports the hypothesis derived from the hardness ratio analysis, i.e. that strong X–ray obscuration is likely present in these high luminosity AGNs."1031 Moreover. hese 2 EROs also appear exteuded in the optical and rwear-IR images sugecsting that the ACNs are likely to 0 strongly absorbed also in the optical/neariutrared domain.," Moreover, these 2 EROs also appear extended in the optical and near-IR images suggesting that the AGNs are likely to be strongly absorbed also in the optical/near–infrared domain."1032 All the XNταν and optical properties make the xesence in these sources of Xrav obscured type 2 QSO ikcly., All the X–ray and optical properties make the presence in these sources of X–ray obscured type 2 QSO likely.1033 As for ERO S2F1.1193. it is detected only iu he 0.52 keV energy baud and it has au IIR value jo;~ 0.9) which caunot exclude a starburst origin of the XNrav cuuission observed.," As for ERO 493, it is detected only in the 0.5–2 keV energy band and it has an HR value $_{493}\sim$ –0.9) which cannot exclude a starburst origin of the X–ray emission observed."1034 We have calculated the vienetting corrected count rates for this object iu the detection baud (0.52 keV) and we have estimated the 0.52 keV flux corrected. for the Galactic absorption using both a powerlaw model with a photon iudex of LO (Prosog; 0.920.110.ο ere 2 1) and a Ravinoud-Siuith model with WT=0.7 aud Solar abundance (Fyy5ogm0 SEO. LS10. Perec 2s 1)., We have calculated the vignetting corrected count rates for this object in the detection band (0.5–2 keV) and we have estimated the 0.5–2 keV flux corrected for the Galactic absorption using both a power–law model with a photon index of 1.9 $_{(0.5-2\rm keV)}$ $\pm$ $\times$ $^{-15}$ erg $^{-2}$ $^{-1}$ ) and a Raymond-Smith model with KT=0.7 and Solar abundance $_{(0.5-2\rm keV)}$ $\pm$ $\times$ $^{-15}$ erg $^{-2}$ $^{-1}$ ).1035 Iu both cases. taking iuto account the photometric redshift," In both cases, taking into account the photometric redshift"1036(c.e..Fabian1999,"\citep[e.g.,][]{fabian99}."1037").. Drandt ~30 ~50% Nyy=ar!~LO?ten 2. ~504 Sevtert 2s contain a Comptou-thick nucleus (Risalitietal.1999:Akvlas&Ceoreautopoulos 2009):: about 50 objects - mostlv local - have been certified as ""bona-fide” Comptou-thick ACN by X-ray spectral analvsis (Comastri2001)."," \citealt{bh05} $\sim$ $\sim$ $N_H=\sigma_T^{-1}\sim10^{24}$ $^{-2}$ $\sim50\%$ Seyfert 2s contain a Compton-thick nucleus \citep{guido99,akylas09}; about 50 objects - mostly local - have been certified as ``bona-fide'' Compton-thick AGN by X-ray spectral analysis \citep{c04}."1038. Svuthesis models of the N-rawv backerouud (XRD) Sugeest that Comptou-thick ACN aust be abundaut at least up to 2~1 to explain the peak of the NRB at 30 keV (seece.Callietal.2007:Treister2009.andreferences therein)..," Synthesis models of the X-ray background (XRB) suggest that Compton-thick AGN must be abundant at least up to $z\sim1$ to explain the peak of the XRB at 30 keV \citep[see e.g.,][and references therein]{gch07,tuv09}."1039 A population of distant. Conmptou-thick AGN. as abundant as that predicted by ARD svuthesis models. is also required to matchthe SMBIT mass function measured m nearby galaxies with that of “relic” SMDIIS erown by accretion (6.8...Alarconictal. 2001).," A population of distant, Compton-thick AGN, as abundant as that predicted by XRB synthesis models, is also required to matchthe SMBH mass function measured in nearby galaxies with that of “relic” SMBHs grown by accretion \citep[e.g.,][]{marconi04}."1040". In recent vears it has been proposed that Copton-thick ACN represent ai key plase of the DlII/salaxv coevolution. during which the DIT is producing most of its feedback into the host galaxy (6.8.Daddietal.2007:Mencei 2005), and it Las also been sugeested that their nunuber density steeply increases with redshift (Treisteretal.2009)."," In recent years it has been proposed that Compton-thick AGN represent a key phase of the BH/galaxy coevolution, during which the BH is producing most of its feedback into the host galaxy \citep[e.g.,][]{daddi07,menci08}, and it has also been suggested that their number density steeply increases with redshift \citep{tuv09}."1041. The observation of heavily obscured ACN at hieli-:. 2D223. remains challenging and it is very difficult to estimate their abundance since they produce only a sanall fraction of the NRB cutission and are thus poorly constrained by svuthesis models," The observation of heavily obscured AGN at $z$, $z\gtrsim2-3$, remains challenging and it is very difficult to estimate their abundance since they produce only a small fraction of the XRB emission and are thus poorly constrained by synthesis models."1042 Deep ταν surveys have proven effective in revealing a few “bona fide” Comptou-thick ACN at high-z. For instance. four such objects at L543<2<3.70 have been discovered in the ChandraXALAL - Deep field South (CDES:seeNorman 2011)..," Deep X-ray surveys have proven effective in revealing a few “bona fide” Compton-thick AGN at high-z. For instance, four such objects at $1.53<z<3.70$ have been discovered in the $Chandra/XMM$ - Deep field South \citep[CDFS; see][]{norman02,comastri11,feruglio11}. ."1043 Other examples of candidate Couptou-thick ACN at hieh-z have been reported (ce...Tozzietal.2006:Pol 2008).. even up to z=5.8 (Braudtetal. 2001).. albeit with poorer X-ray photon statistics.," Other examples of candidate Compton-thick AGN at high-z have been reported \citep[e.g.,][]{tozzi06,polletta08}, , even up to z=5.8 \citep{brandt01}, , albeit with poorer X-ray photon statistics."1044 Selection, Selection1045well with the observed EUVE data. even beyond the Chandra range fort>170A.,"well with the observed EUVE data, even beyond the Chandra range for $\lambda>170$."1046. Again. these data cannot help to choose between model | and 2. although model 2 describes the data in the 170—250 rrange slightly better.," Again, these data cannot help to choose between model 1 and 2, although model 2 describes the data in the $170-250$ range slightly better."1047 In Fig., In Fig.1048 5. we compare the fluxed EUVE spectrum of HZ 43A with our models | and 2., \ref{fig:hz_euve} we compare the fluxed EUVE spectrum of HZ 43A with our models 1 and 2.1049 In the SW band (below 180 Ay) the EUVE flux is typically 15 below our model flux. while in the MW band fluctuations up to 10 occur.," In the SW band (below 180 ) the EUVE flux is typically 15 below our model flux, while in the MW band fluctuations up to 10 occur."1050 Note also the relatively large systematic fluctuations in both bands of up to a few in the SW band to 5 in the LW band., Note also the relatively large systematic fluctuations in both bands of up to a few in the SW band to 5 in the LW band.1051 We have compared our model calculations with ? by evaluating our model using exactly the same parameters as obtained by these authors (their Table 2)., We have compared our model calculations with \citet{beuermann2006} by evaluating our model using exactly the same parameters as obtained by these authors (their Table 2).1052 We show this comparison in Table 7.., We show this comparison in Table \ref{tab:comparebeuermann}.1053 We have used here the long cut-off of the Lyman pseudo-continuum (see Sect. 2.2.2))., We have used here the long cut-off of the Lyman pseudo-continuum (see Sect. \ref{sect:pseudo}) ).1054 It should be noted that Table 2 and Table 3 of ? contain errors. as explained in an erratum on that paper (in press).," It should be noted that Table 2 and Table 3 of \citet{beuermann2006} contain errors, as explained in an erratum on that paper (in press)."1055 This erratum was triggered by our present results., This erratum was triggered by our present results.1056 Accordingly. we used their updated temperatures of 24897 and 51111 K for Sirius B and HZ 43A. as well as the updated fluxes (Table | of the erratum).," Accordingly, we used their updated temperatures of 24897 and 51111 K for Sirius B and HZ 43A, as well as the updated fluxes (Table 1 of the erratum)."1057 For HZ 43A there is an excellent agreement between both codes: only at the shortest wavelength listed (48 A)). there is a small difference.," For HZ 43A there is an excellent agreement between both codes; only at the shortest wavelength listed (48 ), there is a small 4 difference."1058 However. for Sirius B there are large differences.," However, for Sirius B there are large differences."1059 It is striking that at all wavelengths our predicted flux is smaller than the flux given by ?.. also because we used exactly the same interstellar absorption column as well as normalisation R2/d=4.877x1077! as these authors.," It is striking that at all wavelengths our predicted flux is smaller than the flux given by \citet{beuermann2006}, also because we used exactly the same interstellar absorption column as well as normalisation $R^2/d^2=4.877\times 10^{-21}$ as these authors."1060 We verified that the (unabsorbed) and integrated spectrum of our model obeys with high precision the normalisation condition that fF(vdv=στην with c the Stefan-Boltzmann constant and F(v) the emitted surface flux.," We verified that the (unabsorbed) and integrated spectrum of our model obeys with high precision the normalisation condition that $\int1061F(\nu) {\mathrm d}\nu = \sigma T_{\mathrm {eff}}^4$ with $\sigma$ the Stefan-Boltzmann constant and $F(\nu)$ the emitted surface flux."1062 As we both use the same effective temperature of 8897 K. the conclusion must be that the spectrum for Sirius B as calculated by ? is probably not correct.," As we both use the same effective temperature of 897 K, the conclusion must be that the spectrum for Sirius B as calculated by \citet{beuermann2006} is probably not correct."1063 Independently. we compare the ratio of the spectra of both stars as calculated by ? to the ratio that we measured with the LETGS.," Independently, we compare the ratio of the spectra of both stars as calculated by \citet{beuermann2006} to the ratio that we measured with the LETGS."1064 Again. the measured ratio is smaller by on average," Again, the measured ratio is smaller by on average"1065in discriminating different competing models (e.g. see the recent reviews by Cheng 2009; Harding 2009).,in discriminating different competing models (e.g. see the recent reviews by Cheng 2009; Harding 2009).1066" This will definitely shed detailed light on many unsettled debates, such as whether the high-energy emission and radio emission are originated from the same accelerating region."," This will definitely shed detailed light on many unsettled debates, such as whether the high-energy emission and radio emission are originated from the same accelerating region."1067" In this paper, we report the results from the investigation of the multiwavelength properties ofJ20214-4026."," In this paper, we report the results from the investigation of the multiwavelength properties of."1068". In Section 2, we describe the searches for the possible X-ray and radio counterpart for the pulsar with both archival and dedicated observations."," In Section 2, we describe the searches for the possible X-ray and radio counterpart for the pulsar with both archival and dedicated observations."1069 We have also analyzed all the first-year y—ray data collected by LAT in order to constrain its spectral and temporal properties., We have also analyzed all the first-year $\gamma-$ ray data collected by LAT in order to constrain its spectral and temporal properties.1070" In Section 3, we model the emission properties of iin the context of the outer gap model."," In Section 3, we model the emission properties of in the context of the outer gap model."1071 We have further discussed if it is possible that hhas any association with G78.2+2.1., We have further discussed if it is possible that has any association with G78.2+2.1.1072" Finally, we summarize our results in Section 4."," Finally, we summarize our results in Section 4."1073" In order to search for possible X-ray counterparts of detected in a blind search with LAT, we firstly cross-correlated the second serendipitous source catalogue (hereafter XMM SSC) (Watson et al."," In order to search for possible X-ray counterparts of detected in a blind search with LAT, we firstly cross-correlated the second serendipitous source catalogue (hereafter XMM SSC) (Watson et al."1074" 2009) with the LAT bright y-ray source list, in which is denoted as OFGL J2021.5+4026 (Abdo et al."," 2009) with the LAT bright $\gamma$ -ray source list, in which is denoted as 0FGL J2021.5+4026 (Abdo et al."1075 2009a)., 2009a).1076" XMM SSC is the largest catalogue ever constructed in X-ray astronomy, which contains 221012 unique sources!."," XMM SSC is the largest catalogue ever constructed in X-ray astronomy, which contains 221012 unique sources."1077". In particular, we search for all the X-ray sources in XMM SSC which are located within its 9596 confidence circle."," In particular, we search for all the X-ray sources in XMM SSC which are located within its $95\%$ confidence circle."1078" In this search, we have identified only one X-ray object,J202131.0+402645,, in the 95% error circle of with a radius of 0.053°."," In this search, we have identified only one X-ray object, in the $95\%$ error circle of with a radius of $0.053^{\circ}$."1079 This X-ray source is located less than 1 arcmin away from the reported —ray position of the LAT pulsar., This X-ray source is located less than 1 arcmin away from the reported $\gamma-$ ray position of the LAT pulsar.1080 The corresponding observation was carried out on 1 December 2003 with MOS1/2 (Metal Oxide Semicondutor) and EPIC-PN (the European Photon Imaging Camera-Positive Negative) detectors operated in full frame mode (Obs., The corresponding observation was carried out on 1 December 2003 with MOS1/2 (Metal Oxide Semicondutor) and EPIC-PN (the European Photon Imaging Camera-Positive Negative) detectors operated in full frame mode (Obs.1081 ID: 150960801)., ID: 150960801).1082 This observation was pointed to the geometrical center of the supernova remnant G78.2+2.1 with llocated ~8.5 arcmin off-axis., This observation was pointed to the geometrical center of the supernova remnant G78.2+2.1 with located $\sim8.5$ arcmin off-axis.1083" Examining this dataset for times of high background, we notice that this observation was contaminated by soft-proton flares."," Examining this dataset for times of high background, we notice that this observation was contaminated by soft-proton flares."1084 Cleaning the data by removing these flares results in the effective exposure of ~5 ks and ~2.6 ks in MOS1/2 and PN detectors respectively., Cleaning the data by removing these flares results in the effective exposure of $\sim5$ ks and $\sim2.6$ ks in MOS1/2 and PN detectors respectively.1085 The combined MOS1/2+PN image of the full field-of-view is displayed in Figure 1 with the error circles of aand 3EG J2020--4017 illustrated., The combined MOS1/2+PN image of the full field-of-view is displayed in Figure \ref{lat_ssc} with the error circles of and 3EG J2020+4017 illustrated.1086 An 8x arcmin? close-up view centered at the nominal position of iis displayed in Figure 2.., An $8\times8$ $^{2}$ close-up view centered at the nominal position of is displayed in Figure \ref{xmm_closeup}.1087 iis located just outside the 95% confidence circle of 3EG J2020--4017 (see Fig. 1)), is located just outside the $95\%$ confidence circle of 3EG J2020+4017 (see Fig. \ref{lat_ssc}) )1088 which is the brightest unidentified 4-ray source discovered by (Hartman et al., which is the brightest unidentified $\gamma$ -ray source discovered by (Hartman et al.1089 1999)., 1999).1090 Searches for X-ray counterparts of 3EG J2020+4017 have been reported by Becker et al. (, Searches for X-ray counterparts of 3EG J2020+4017 have been reported by Becker et al. (10912004) and Weisskopf et al. (,2004) and Weisskopf et al. (10922006) with Advanced CCD Imaging Spectrometer (ACIS) spectro-imaging observations.,2006) with Advanced CCD Imaging Spectrometer (ACIS) spectro-imaging observations.1093 The observation made by Weisskopf et al. (, The observation made by Weisskopf et al. (10942006) partly covered the error circle ofJ20214-4026.,2006) partly covered the error circle of.1095. This ACIS-I observation took place on 6 February 2005 with an effective exposure time of ~14 ksec (Obs., This ACIS-I observation took place on 6 February 2005 with an effective exposure time of $\sim14$ ksec (Obs.1096 ID: 5533)., ID: 5533).1097" The ACIS-I image centered at the nominal y—ray position of iis displayed in Figure 3,, which has the same field-of-view as that in Figure 2.."," The ACIS-I image centered at the nominal $\gamma-$ ray position of is displayed in Figure \ref{cxc_closeup}, which has the same field-of-view as that in Figure \ref{xmm_closeup}."1098 The position of source $21 (as labeled in Weisskopf et al., The position of source S21 (as labeled in Weisskopf et al.1099" 2006) is found to be consistent with that ofJ202131.0+402645,, and hence we concluded that they are the same object."," 2006) is found to be consistent with that of, and hence we concluded that they are the same object."1100" As it is located outside the error circle of 3EG J2020+4017, it did not receive enough attention in Weisskopf et al. ("," As it is located outside the error circle of 3EG J2020+4017, it did not receive enough attention in Weisskopf et al. ("11012006).,2006).1102 We note that two other X-ray sources detected by Weisskopf et al. (, We note that two other X-ray sources detected by Weisskopf et al. (1103"2006), namely S25 and 828 in their paper, are also found to be located within the 95% error circle of ((see Fig. 3)).","2006), namely S25 and S28 in their paper, are also found to be located within the $95\%$ error circle of (see Fig. \ref{cxc_closeup}) )."1104 As a number of important parameters, As a number of important parameters1105"We deal with a 1D erid composce Lot N,=200 cells. with periodic boundary conditions","We deal with a 1D grid composed of $N_s=200$ cells, with periodic boundary conditions."1106 The cell width is Av=(000311. the isothermal xmud speed ds ος= 0.01.," The cell width is $\Delta x=0.0314$, the isothermal sound speed is $c_s=0.04$ ."1107 The equilibrium deusitv is Sy=6-101., The equilibrium density is $\Sigma_0=6\cdot 10^{-4}$.1108 These paranueters correspond roughly to the ones used in the uunercal study of a protoplanct «n a circular orbit at 5 A.U. embedded in a ΙΙ mass protoplanetary disk (Πανάς 1985 or Brvclen 19985). that are described in section 5)). when the central star mass aud the protoplauet orbit radius are taken to be respectively the units of mass and distance.," These parameters correspond roughly to the ones used in the numerical study of a protoplanet on a circular orbit at 5 A.U. embedded in a minimum mass protoplanetary disk (Hayashi 1985 or Bryden 1998), that are described in section \ref{sec:2d}) ), when the central star mass and the protoplanet orbit radius are taken to be respectively the units of mass and distance."1109 We present the results of different test ruus in fie. 1.., We present the results of different test runs in fig. \ref{fig:res}.1110 The thick solid liue represents the initial profile. which corresponds to a rightward propagating acoustic wave. with wavelength A=lOAr=1.256.," The thick solid line represents the initial profile, which corresponds to a rightward propagating acoustic wave, with wavelength $\lambda=40\Delta x=1.256$."1111" The relative amplitude of this sound wave ds. s=,10D7.", The relative amplitude of this sound wave is $s=10^{-2}$.1112 The: thick. dashed line. represeuts the density profile at time ty=220. ie. after the wave has raveled ούρα=7 times its own wavelcneth. when studied im the matter frame. ie. when the velocity at t= O0is set to be only the perturbed velocity associated o the sound wave.," The thick dashed line represents the density profile at time $t_0=220$, i.e. after the wave has traveled $c_st_0/\lambda=7$ times its own wavelength, when studied in the matter frame, i.e. when the velocity at $t=0$ is set to be only the perturbed velocity associated to the sound wave."1113 The thick dashed profile is obtained with the transport algorithin (there is no uced or the modified one in this case since we work in the uatter frame). with a timestep Af—5-1027.," The thick dashed profile is obtained with the transport algorithm (there is no need for the modified one in this case since we work in the matter frame), with a timestep $\Delta t=5\cdot 10^{-3}$."1114 The curves obtained by choosing a uch smalcr timestep appear to coincide exactly with this one. heuce we can consider this hick dashed line as the actual state the svsteii must have at the date ty.," The curves obtained by choosing a much smaller timestep appear to coincide exactly with this one, hence we can consider this thick dashed line as the actual state the system must have at the date $t_0$."1115 This profile docs no exactly comede with he initial one because ty ix ~i of he profile steepeniug nue fy~3\, This profile does not exactly coincide with the initial one because $t_0$ is $\sim\frac{1}{7}$ of the profile steepening time $t_{ps}\sim\frac{\lambda}{2c_ss}$.1116 Now if we just change the initia velocity by uniformly adding 1.0 to them at tf=0. whicli umeaus that we are 10 more in the matter frame. aud we still work with he standard transport alegorithin. then we ect the dotted xofile. which has ~1/5 the auuplitide obtained from the computation in the matter frame.," Now if we just change the initial velocity by uniformly adding $1.0$ to them at $t=0$, which means that we are no more in the matter frame, and we still work with the standard transport algorithm, then we get the dotted profile, which has $\sim 1/5$ the amplitude obtained from the computation in the matter frame."1117 Tn this run the CFL ratio ix cAt/Aw= 0.16., In this run the CFL ratio is $v\Delta t/\Delta x= 0.16$ .1118 In order to check the timestep dependency of this result. we redo this test with twice as smaller a timestep (At=2.5-10 3) aud we ect the dash-dotted profile. which has about twice as simaller a density contrast than the previous curve.," In order to check the timestep dependency of this result, we redo this test with twice as smaller a timestep $\Delta t= 2.5\cdot 10^{-3}$ ) and we get the dash-dotted profile, which has about twice as smaller a density contrast than the previous curve."1119 N«te that if this effect were to be due to a physical kinematic viscosity 1’. then its value should bx Mdos5~OS.LO! auch higher than the expected viscosity iu a niniWU Lass protoplauetary disk Gv~10. in our dimensioness undts).," Note that if this effect were to be due to a physical kinematic viscosity $\nu$, then its value should be: $\nu\sim \frac{\lambda^2\log 5}{2\pi^2 t_0}\sim 5.8\cdot 10^{-4}$, much higher than the expected viscosity in a minimum mass protoplanetary disk $\nu \sim 10^{-5}$ in our dimensionless units)."1120 Now. instead of decreasing the timestep. we incrense it aud set At=24-10.7 (hence the CFL ratio is alout 0.6L).," Now, instead of decreasing the timestep, we increase it and set $\Delta t=2.0\cdot 10^{-2}$ (hence the CFL ratio is about $0.64$ )."1121 We then eet at time ty the dot-dot-dot-dashlied profile. which is nof wmuerically damped but slightly amplified.," We then get at time $t_0$ the dot-dot-dot-dashed profile, which is not numerically damped but slightly amplified."1122 With such a lareec timestep. we cau use the modified transport algorithm. which in that case correspouds tc ya rielitwards one cell shift and a Ieftwards normal trasport wit la renaming CFL ratio of l0.61=0.36.," With such a large timestep, we can use the modified transport algorithm, which in that case corresponds to a rightwards one cell shift and a leftwards normal transport with a remaining CFL ratio of $1-0.64=0.36$."1123 In that case we ect the thin loug-dashed profile., In that case we get the thin long-dashed profile.1124 If we use the nodifect FARGO transport algorithm. we can stil Increase the iuestep.," If we use the modified FARGO transport algorithm, we can still increase the timestep."1125 The thin solid profile aud the thin short-dasred xofile have been obtained respectively with Af=L1p2 (effective CFL ratio ~ 1.3) and At=1.2+1Q03 (effecive CFL ratio ~ 3.8)., The thin solid profile and the thin short-dashed profile have been obtained respectively with $\Delta t=4\cdot 10^{-2}$ (effective CFL ratio $\sim 1.3$ ) and $\Delta t=1.2\cdot 10^{-1}$ (effective CFL ratio $\sim 3.8$ ).1126 We clearly see from these results that ιο FARGO trausport algorithin leads to CSS 1ΗΙΟΥical lissipation than the standard transport., We clearly see from these results that the FARGO transport algorithm leads to less numerical dissipation than the standard transport.1127 From the first wo tests in the non-comoving frame. one can couclude iat increasing the of timesteps over a eiven time oeterval with the standard transport aleorithui iucreascs je nunierical dissipation (f the exid is moving w.r.t the uatter frame with a velocity ey4O0 and if the main part X the velocity comes from co).," From the first two tests in the non-comoving frame, one can conclude that increasing the of timesteps over a given time interval with the standard transport algorithm increases the numerical dissipation (if the grid is moving w.r.t the matter frame with a velocity $v_0\neq 0$ and if the main part of the velocity comes from $v_0$ )."1128" A simple explanation for 1e lower numerical dissipation of the FARGO aleorithim is that itrequires less iterations as the timestep increases, and since most of the distance swept is achieved through"," A simple explanation for the lower numerical dissipation of the FARGO algorithm is that itrequires less iterations as the timestep increases, and since most of the distance swept is achieved through"1129Warped accretion discs may occur across a wide variety of astrophysical systems. from the large scales of accretion discs around supermassive black holes (SMBH). down to the small scales of planet forming disces.,"Warped accretion discs may occur across a wide variety of astrophysical systems, from the large scales of accretion discs around supermassive black holes (SMBH), down to the small scales of planet forming discs."1130 Observationally. warps are found in galactic binary systems. such as the hyperaccreting X-ray binary 88433 (2). and the X-ray binary Her X-1 (2).. and in several microquasars. including GRO 11655-40 (2) and V4641 Ser (2)..," Observationally, warps are found in galactic binary systems, such as the hyperaccreting X-ray binary SS433 \citep{begelman06b} and the X-ray binary Her X-1 \citep{wijers99}, and in several microquasars, including GRO J1655-40 \citep{martin08a} and V4641 Sgr \citep{martin08b}."1131" On the much less energetic side. a warped protostellar dise is found around the young star KH 15D (2),"," On the much less energetic side, a warped protostellar disc is found around the young star KH 15D \citep{chiang04}."1132 Warps are also found in the thin accretion discs in Active Galactic Nuclei (AGN). as in the case of NGC 4258 (22)..," Warps are also found in the thin accretion discs in Active Galactic Nuclei (AGN), as in the case of NGC 4258 \citep{herrnstein96,papaloizou98}."1133 The dynamics of warped accretion can play a fundamental role in these cases. as it in turn regulates the spin history of the growing SMBH and. as a consequence. its very ability to grow rapidly (22)..," The dynamics of warped accretion can play a fundamental role in these cases, as it in turn regulates the spin history of the growing SMBH and, as a consequence, its very ability to grow rapidly \citep{king06,KPH08}."1134 The torques which produce the warp can be very different., The torques which produce the warp can be very different.1135 For protostellar dises. they include tidal interactions with a companion star (22).. and dynamical effects during the formation of the disc. which might affect the relative orientation of the stellar spin and the planetary orbits (2)..," For protostellar discs, they include tidal interactions with a companion star \citep{larwood96,martin09}, and dynamical effects during the formation of the disc, which might affect the relative orientation of the stellar spin and the planetary orbits \citep{BLP09}."1136 For accretion dises around black holes there are additional torques arising from the general relativistic Lense-Thirring precession around a spinning black hole (222222)... and self-induced warping caused by radiation pressure (2)..," For accretion discs around black holes there are additional torques arising from the general relativistic Lense-Thirring precession around a spinning black hole \citep{bardeen75,scheuer96,KLOP,LP06,martin07b,perego09}, and self-induced warping caused by radiation pressure \citep{pringle96}."1137 Recently. some attention has also been given to the process of dise warping and black hole spin alignment in the case of supermassive black hole binaries (2)..," Recently, some attention has also been given to the process of disc warping and black hole spin alignment in the case of supermassive black hole binaries \citep{dotti09}."1138 In all such cases. the evolution of the system is strongly dependent on the speed at which warping disturbances ean propagate inthe disc.," In all such cases, the evolution of the system is strongly dependent on the speed at which warping disturbances can propagate inthe disc."1139 Analytic theories of warp propagation have been discussed extensively in the past (22222) (see Section 2)).," Analytic theories of warp propagation have been discussed extensively in the past \citep{pappringle83,pringle92,paplin95,ogilvie99,ogilvie00} (see Section \ref{sec:theory}) )."1140 These theories predict that while for thick dises warps should propagate as dispersive waves. with a velocity of the order of half the sound speed in the disc. in the limit of thin and viscous dises the propagation is diffusive. with a diffusion coefficient. inversely proportional to the dise viscosity (2)..," These theories predict that while for thick discs warps should propagate as dispersive waves, with a velocity of the order of half the sound speed in the disc, in the limit of thin and viscous discs the propagation is diffusive, with a diffusion coefficient inversely proportional to the disc viscosity \citep{pappringle83}. ."1141 Numerical simulations of, Numerical simulations of1142where the binary fraction is taken to be around a few percent suitable for a typical region of the cluster outside the core (?)..,where the binary fraction is taken to be around a few percent suitable for a typical region of the cluster outside the core \citep{2008arXiv0803.0005D}.1143 The power produced by the binaries is of course proportional to the number density of the binaries and inversely proportional to the velocity dispersion that sets the Cross-section per binary., The power produced by the binaries is of course proportional to the number density of the binaries and inversely proportional to the velocity dispersion that sets the cross-section per binary.1144 Comparing Eq. (8)), Comparing Eq. \ref{eq:binary_power}) )1145 to (5)) shows that the power sources are similar lor the region of NGC 6397 observed by ?.., to \ref{eq:kickpower2}) ) shows that the power sources are similar for the region of NGC 6397 observed by \citet{2007arXiv0708.4030R}.1146 To look at the relative importance of binaries and kicks early in the life of the cluster. some assumptions about. the mass function of the eluster in the past are needed.," To look at the relative importance of binaries and kicks early in the life of the cluster, some assumptions about the mass function of the cluster in the past are needed."1147 First. the mass function becomes more and more top heavy with time as the low mass stars are lost from the cluster: therefore. it is natural to assume that àc Lin the past ane possibly a72 near the turnoll.," First, the mass function becomes more and more top heavy with time as the low mass stars are lost from the cluster; therefore, it is natural to assume that $\alpha>1$ in the past and possibly $\alpha>2$ near the turnoff."1148 In this regime. the derivation of Eq. (5))," In this regime, the derivation of Eq. \ref{eq:kickpower2}) )"1149 is not valid., is not valid.1150 The result in general is where the various slopes are evaluated at the turn-oll., The result in general is where the various slopes are evaluated at the turn-off.1151 Using the IME of ? below one solar mass and ? above gives |LaleL7 compared το.αzz1.9 currently., Using the IMF of \citet{1993MNRAS.262..545K} below one solar mass and \citet{1986FCPh...11....1S} above gives $|1-\alpha|\approx 1.7$ compared to $2-\alpha \approx 1.9$ currently.1152 Also the value of the 3 only changes with time slightly (for mro~1M.. jz 3). so the bulk of the increase comes from the replacement of the turn-olf mass with the mean mass in the denominator of the expression.," Also the value of the $\beta$ only changes with time slightly (for $m_\rmscr{TO} \sim11531\msun$, $\beta\approx 3$ ), so the bulk of the increase comes from the replacement of the turn-off mass with the mean mass in the denominator of the expression."1154 Of course as the cluster evolves. the velocity dispersion of the cluster should also evolve.," Of course as the cluster evolves, the velocity dispersion of the cluster should also evolve."1155 Because the mass of the eluster was larger in the past. one would expect that the velocity dispersion was also larger.," Because the mass of the cluster was larger in the past, one would expect that the velocity dispersion was also larger."1156 On the other hand. the kick velocity may also change with the turn-olf mass. so it is natural to introduce both of these quantities as variables.," On the other hand, the kick velocity may also change with the turn-off mass, so it is natural to introduce both of these quantities as variables."1157 The power from binaries also depends sensitively on the velocity dispersion and mean stellar mass., The power from binaries also depends sensitively on the velocity dispersion and mean stellar mass.1158" Taking the ratio of the kick power to the binary power vields. where the approximation holds for z=10""10? vr."," Taking the ratio of the kick power to the binary power yields, where the approximation holds for $\tau = 10^7 - 10^9$ yr."1159 After about a billion vears. one would expect the cluster to have evolved structurally. ejecting many of the low mass stars.," After about a billion years, one would expect the cluster to have evolved structurally, ejecting many of the low mass stars."1160 This would change the mass function ancl twpically decrease this ratio further., This would change the mass function and typically decrease this ratio further.1161 The increased. velocity dispersion of the cluster actually increases the relative importance of kicks early. in the life of the cluster by increasing the relaxation time (decreasing the binary power)., The increased velocity dispersion of the cluster actually increases the relative importance of kicks early in the life of the cluster by increasing the relaxation time (decreasing the binary power).1162 On the other hand. the number density of binaries was likely to be larger in the past than today simply because the number of density of stars was larger then.," On the other hand, the number density of binaries was likely to be larger in the past than today simply because the number of density of stars was larger then."1163 Over the life of a globular cluster such as NGC 6397. white-thwarts kicks may provide a significant energv source.," Over the life of a globular cluster such as NGC 6397, white-dwarfs kicks may provide a significant energy source."1164 In a region outside the core todayt. kicks provide about about one-half of energy. input. from binaries.," In a region outside the core todayt, kicks provide about about one-half of energy input from binaries."1165 Early in the life of the globular cluster when stars of several solar masses are leaving the main sequence. the white-dwarl kicks may actually dominate over binaries as an energy source: consequently. voung globular clusters such as those in starburst galaxies niv actually differ structurally from their older peers.," Early in the life of the globular cluster when stars of several solar masses are leaving the main sequence, the white-dwarf kicks may actually dominate over binaries as an energy source; consequently, young globular clusters such as those in starburst galaxies may actually differ structurally from their older peers."1166 ? founcl that an energy source bevond binaries was required to avoid core collapse in. M1: perhaps white cwarl kicks could explain this discrepancy., \citet{1992ApJ...386..106D} found that an energy source beyond binaries was required to avoid core collapse in M71; perhaps white dwarf kicks could explain this discrepancy.1167 Regardless. these calculations indicate that further study of the elfects of white-cwarl kicks on the dvnamies of globular clusters is warranted.," Regardless, these calculations indicate that further study of the effects of white-dwarf kicks on the dynamics of globular clusters is warranted."1168 Lwould like to thank Harvey Richer and Saul Davis for κο discussions and the referee. James Binney. would. provided many useful comments.," I would like to thank Harvey Richer and Saul Davis for useful discussions and the referee, James Binney, would provided many useful comments."1169 The Natural Sciences and Engineering Research Council of Canada. Canadian. Foundation for Innovation and the British Columbia Ixnowledge Development Fund supported this work.," The Natural Sciences and Engineering Research Council of Canada, Canadian Foundation for Innovation and the British Columbia Knowledge Development Fund supported this work."1170 Correspondence ancl requests for materials should be addressed. to. hevEephas.ube.ca., Correspondence and requests for materials should be addressed to heylphas.ubc.ca.1171 This research has mace use of NASAs Astrophysics Data System sibliographic Services, This research has made use of NASA's Astrophysics Data System Bibliographic Services1172where we choose ο=1l. f is couformal time and a(t) denotes the scale factor.,"where we choose $c=1$ , $t$ is conformal time and $a(t)$ denotes the scale factor."1173" For tensor perturbations. the metric fluctuations m satisty the conditions LT,ο =003) where k is the wave vector which mav be set equal to (0.0.4). such that the conditions (2)) reduce tohi. =0"," For tensor perturbations, the metric fluctuations $h^T_{ij}$ satisfy the conditions _i=0, =0 where ${\bf k}$ is the wave vector which may be set equal to $(0,0,k)$, such that the conditions \ref{cond}) ) reduce to, =0."1174 We describe dynamics of tensor perturbations nm a media coutainue↰ collision-less particles. ↖↖⇁∐∪↴∖↴↸∖⋜∐∐↴∖↴∪⊓⋅∪↻↕↸⊳↴∖↴⊓⋅↸∖↴∖↴↴∖↴↸∖↴∖↴⋜∐⋅↸∖∐∪↑≼↧⋜⋯∏⋉," We describe dynamics of tensor perturbations in a medium containing collision-less particles, whose anisotropic stresses are not damped by collisions."1175∖≼∏⋝∙↖↽≼⊳∪∐↕↴∖↴↕∪∐↴∖↴∙⊀≚↴∖↴↕∪∐∶↴∙⊾⋜↕↴∖↴↑↕∐∖↸⊳∪∐↕↴∖↴↕∪∐≓↕↸∖↴∖∷∖↴↸⊳∪∐∏⋯∐↸∖∐↑ ↕↴∖↴↥⋅↸∖↕⋜↧↑↕↖↽↕↴∖↴↑↕↸⊳∙↕↑↻↥⋅∪↖," As long as the collision-less component is relativistic, it provides a source for gravitational waves."1176⇁↕≼∐∖↴∖↴⋜↧↴∖↴≺∏∐⋅∩∖↕⋟∪↥⋅∶↴∙⊾↥⋅⋜↧↖⇁↕↑⋜↧↑↕∪∐⋜↧↕↖↖↽⋜↧↖↽↸∖↴∖↴∙↽∕∏∐∖↸∖↖↽∪↕∏↑↕∪∐↸∖≺∣∏⋜↧↑↕∪∐↕⋟∪↥⋅↑↸∖∐↴∖↴∪↥⋅ ↻↸∖↥⋅⊓∐⋅↴⋝⋜↧↑↕∪∐↴∖↴∪↕⋟↑∐↸∖∐∐∖⊓⋅↕↸⊳↕↴∖↴∶↴∙⊾↕↖↽↸∖∐↴⋝∙↖⇁∩∷ | BLο ἀπDE ρΠ, The evolution equation for tensor perturbations of the metric is given by \cite{Review}: + k^2 G a^2p.1177 Tere pis the pressure of the collisiou-less component and II denotes the tensor contribution to the anisotropic stresses. which iu our case are due to the presence of relativistic. particles.," Here $p$ is the pressure of the collision-less component and $\Pi$ denotes the tensor contribution to the anisotropic stresses, which in our case are due to the presence of relativistic, collision-less particles."1178 Denoting the tensor part of the perturbed distribution function of the collisiou-less component by F. ILis given by where s; is a spatial unit vector. denoting the photon directions. e is the redshift corrected velocity and q the redshift corrected energy of the collisiou-less particles (see [0])).," Denoting the tensor part of the perturbed distribution function of the collision-less component by $F$, $\Pi$ is given by = where $n_{i}$ is a spatial unit vector, denoting the photon directions, $v$ is the redshift corrected velocity and $q$ the redshift corrected energy of the collision-less particles (see \cite{Review}) )."1179 Tn the case of massless particles (massless neutrini) g=c., In the case of massless particles (massless neutrini) $q \equiv v$.1180 Liouville’s equation leads to the following perturbation equation for F 0). qk I chP= qen'ijhi(7) f denotes the unperturbed distribution function.," Liouville's equation leads to the following perturbation equation for $F$ \cite{Review}, q +v n^jk_jF=qv n^i n_j, $f$ denotes the unperturbed distribution function."1181 The set of Eqs. (2)), The set of Eqs. \ref{exp}) )1182 to (2)) fully describes the evolution of teusor perturbations iu inedia contaimine perfect fluids and collisiou-less particles., to \ref{Liou}) ) fully describes the evolution of tensor perturbations in media containing perfect fluids and collision-less particles.1183 Iu our models we have in principle three kinds of collisiou-less particles: Wot dark matter. massless neutriui aud. after recombination. the photons.," In our models we have in principle three kinds of collision-less particles: Hot dark matter, massless neutrini and, after recombination, the photons."1184 Studving the imitial conditions. we shall &ud that for the erowing mode anisotropic stresses are extremely sinall on super horizou scales.," Studying the initial conditions, we shall find that for the growing mode anisotropic stresses are extremely small on super horizon scales."1185 However. when the scales relevant for teusor CMD anisotropies (AZ9 tu.) euter the horizon. £29t... DAL particles are alveady non relativistic.," However, when the scales relevant for tensor CMB anisotropies $\la\gg t_{dec}$ ) enter the horizon, $t\gg t_{dec}$ HDM particles are already non relativistic."1186 We may thus neelect their contribution to anisotropic stresses., We may thus neglect their contribution to anisotropic stresses.1187 Hence. we just consider the pressure anisotropy frommassless neutrini aud. after recombination. from the photons theiiselves.," Hence, we just consider the pressure anisotropy frommassless neutrini and, after recombination, from the photons themselves."1188 For massless particles we can simply Eqs. (2)), For massless particles we can simplify Eqs. \ref{Pi}) )1189 aud (2)) by introducing the brigltuess perturbation A , and \ref{Liou}) ) by introducing the brightness perturbation $M$ 1190"photosphere as 700Ro, whereas we have adopted 650Ro, hence we obtain the outer limit for the chromosphere as £z'1.53Ro rather than 7Ro.","photosphere as $700 R_{\odot}$, whereas we have adopted $650 R_{\odot}$, hence we obtain the outer limit for the chromosphere as $\approx 7.53 R_0$ rather than $7R_0$."1191 Silicate dust later condenses at large distances ~30Ro., Silicate dust later condenses at large distances $ \sim 30R_0$.1192 It is implicitly assumed in this model that alumina dust is transparent so as not to reveal any dust signature between 1.5Ro and 30Ro., It is implicitly assumed in this model that alumina dust is transparent so as not to reveal any dust signature between $1.5R_0$ and $30R_0$.1193 The third possibility is we can assume formation of alumina in the region r<1.5Ho (in small and large quantities; explored in respectively)., The third possibility is we can assume formation of alumina in the region $r \leq 1.5R_0$ (in small and large quantities; explored in respectively).1194 This dust then gets destroyed at a distance of 1.5Ro due to perhaps convective turbulence in regions closer to the photosphere and changes in pressure or perhaps due to temperature variability in the chromosphere., This dust then gets destroyed at a distance of $1.5R_0$ due to perhaps convective turbulence in regions closer to the photosphere and changes in pressure or perhaps due to temperature variability in the chromosphere.1195" Whatever the reason may be, dust is not seen between 1.5Ro and about 20—30Ro."," Whatever the reason may be, dust is not seen between $1.5R_0$ and about $20-30R_0$."1196 Silicate dust later condenses at large distances., Silicate dust later condenses at large distances.1197" 'The purpose of these scenarios is not to elaborate on the details of dust spallation, but rather to ask the pertinent question that, within the framework of the hybrid-MHD-dust-driven wind theory, is it possible to achieve an efflux, should alumina first form and perhaps even be destroyed in the wind, at some distance?"," The purpose of these scenarios is not to elaborate on the details of dust spallation, but rather to ask the pertinent question that, within the framework of the hybrid-MHD-dust-driven wind theory, is it possible to achieve an efflux, should alumina first form and perhaps even be destroyed in the wind, at some distance?"1198" In addition, it is to be kept in mind that for the models presented in Scenarios 2—4 the photospheric temperature was considered to be 2600 K. Figure 4 shows both Scenarios 2 and 3 each containing two hybrid wind models."," In addition, it is to be kept in mind that for the models presented in Scenarios $2-4$ the photospheric temperature was considered to be $T_0=2600~$ K. Figure \ref{fig:figure4} shows both Scenarios 2 and 3 each containing two hybrid wind models."1199 Scenario 2 is shown in the upper panel of Figure 4 while Scenario 3 is shown in the lower panel., Scenario 2 is shown in the upper panel of Figure \ref{fig:figure4} while Scenario 3 is shown in the lower panel.1200" 'The red and green solid lines represent the dust velocity profiles in these scenarios for small and large amounts of alumina condensation, respectively."," The red and green solid lines represent the dust velocity profiles in these scenarios for small and large amounts of alumina condensation, respectively."

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