ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" The only exception was G337.826+0.0 for which we calculated the integrated intensity by determining the area within the FHWM of the '?CO emission, as this line-of-sight shows complex velocity structure."," The only exception was G337.826+0.0 for which we calculated the integrated intensity by determining the area within the FHWM of the $^{13}$ CO emission, as this line–of–sight shows complex velocity structure."3 Based on the !?CO line parameters we identify 58 π]] components associated with dense molecular gas., Based on the $^{13}$ CO line parameters we identify 58 ] components associated with dense molecular gas.4" All of them also show ""CO emission while 12 show C!*O emission.", All of them also show $^{12}$ CO emission while 12 show $^{18}$ O emission.5 The remaining diffuse atomic and/or diffuse molecular u]]-emitting clouds that do not have ?CO counterparts are discussed by ? and ?..," The remaining diffuse atomic and/or diffuse molecular ]–emitting clouds that do not have $^{13}$ CO counterparts are discussed by \citet{Langer2010}6 and \citet{Velusamy2010}."7" In the left panel of Figure 2,, we summarize the observed characteristics by plotting the u]]CO and [Cnu]]/?CO integrated intensity ratios for the identified components as a function of the u]] integrated intensity."," In the left panel of Figure \ref{fig:results_pdr}, we summarize the observed characteristics by plotting the $^{12}$ CO and $^{13}$ CO integrated intensity ratios for the identified components as a function of the ] integrated intensity."8 The ratios are calculated from integrated intensities in units of ss!, The ratios are calculated from integrated intensities in units of $^{-1}$.9 The mean value and standard deviation are 0.29 and 0.6 for the n]]/?CO integrated intensity ratio and 1.75 and 2.54 for n]]/?CO., The mean value and standard deviation are 0.29 and 0.6 for the $^{12}$ CO integrated intensity ratio and 1.75 and 2.54 for $^{13}$ CO.10 The ratios vary over 2 orders of magnitude suggesting a wide range of physical conditions in our sample., The ratios vary over 2 orders of magnitude suggesting a wide range of physical conditions in our sample.11 We use the 1]]/? CO and i]]/?CO integrated intensity ratios to constrain the physical conditions of the line-emitting gas., We use the $^{12}$ CO and $^{13}$ CO integrated intensity ratios to constrain the physical conditions of the line–emitting gas.12" The '*CO emission, which becomes optically thick quickly after a modest fraction of the gas-phase carbon is converted to CO, is not very sensitive to the FUV radiation field, as the temperature at the C*/C°/CO transition layer is also insensitive to this quantity (??).."," The $^{12}$ CO emission, which becomes optically thick quickly after a modest fraction of the gas–phase carbon is converted to CO, is not very sensitive to the FUV radiation field, as the temperature at the $^+$ $^0$ /CO transition layer is also insensitive to this quantity \citep{Wolfire1989,13Kaufman99}. ."14" Therefore, the u]]/"" CO ratio is determined by the column density of C* and the temperature at the surface of the PDR, which are in turn dependent on the FUV radiation field and H5 density."," Therefore, the $^{12}$ CO ratio is determined by the column density of $^+$ and the temperature at the surface of the PDR, which are in turn dependent on the FUV radiation field and $_2$ density."15 The n]]/?CO ratio is proportional to the ratio between the Ct and CO column densities., The $^{13}$ COratio is proportional to the ratio between the $^+$ and $^{13}$ CO column densities.16" It therefore gives, provided that extra constraints on the total column of material are available and that there are no significant variations of the FUV field within the beam, a constraint on the location of the C*/C°/CO transition layer which in turn depends on the strength of the FUV field and H» density."," It therefore gives, provided that extra constraints on the total column of material are available and that there are no significant variations of the FUV field within the beam, a constraint on the location of the $^+$ $^0$ /CO transition layer which in turn depends on the strength of the FUV field and $_2$ density."17 We compare the observed 1]]/2ΟΟ and [Cu]]/CO integrated intensity ratios with the results of a PDR model grid in order to constrain physical conditions of the u]]-emitting clouds., We compare the observed $^{12}$ CO and $^{13}$ CO integrated intensity ratios with the results of a PDR model grid in order to constrain physical conditions of the ]–emitting clouds.18 The model grid was calculated using the KOSMA-r PDR model (??) which is available online?.," The model grid was calculated using the $\tau$ PDR model \citep{Stoerzer96,Roellig06} which is available ."19". The model provides a self-consistent solution of the chemistry and thermal balance of a spherical cloud, with a truncated density profile, which is illuminated isotropically by a FUV radiation field."," The model provides a self–consistent solution of the chemistry and thermal balance of a spherical cloud, with a truncated density profile, which is illuminated isotropically by a FUV radiation field."20" The density distribution has the form, n(r)2n,(r/r.)|? for 02r. <r€re and a constant density of n(r)= n5(0.2)-!? in the central region of the cloud (r« 0.2r,)."," The density distribution has the form, $n(r)$ $n_{s}(r/r_c)^{-1.5}$ for $r_c$ $\leq$ $ r \leq r_c$ and a constant density of $n(r)=n_s$ $^{-1.5}$ in the central region of the cloud $r <210.2r_c$ )."22 Here γε is the cloud radius and n; is the density at the cloud surface., Here $r_c$ is the cloud radius and $n_{s}$ is the density at the cloud surface.23" Note that with a power-law index of 1.5, the average density of the clump is about twice the density at the cloud surface."," Note that with a power--law index of 1.5, the average density of the clump is about twice the density at the cloud surface."24 The line intensities are calculated using a non-LTEradiativetransfer code by ?.., The line intensities are calculated using a non–LTEradiativetransfer code by \cite{Gierens92}. .25" Each model is characterized by the clump mass, the density at the cloud surface, and strength of the FUV field."," Each model is characterized by the clump mass, the density at the cloud surface, and strength of the FUV field."26" The clump mass ranges from 107? to 100 ΜΜΕ, the density at the cloud surface from 10? to 106 ccm?, and the strengthof the FUV field from Xo=1 to 10° (in units of the 2 field?))."," The clump mass ranges from $10^{-2}$ to $100$ $_\odot$, the density at the cloud surface from $^3$ to $^6$ $^{-3}$, and the strengthof the FUV field from $\chi_{\rm270}=1$ to $^6$ (in units of the \citealt{Draine78} )."28 We do not use and, We do not use and29The search for molecular lines at high redshifts ἐς21) offers one of the richest and most exciting avenues to follow in the study of galaxy formation and evolution (Solomon Vanden Bout 2005).,The search for molecular lines at high redshifts $z\gs 1$ ) offers one of the richest and most exciting avenues to follow in the study of galaxy formation and evolution (Solomon Vanden Bout 2005).30" The detections of rotational transitions of CO in extremely distant quasars (Carilli et 22002: Walter et 22003). high-z radio galaxies (Papadopoulos οἱ 22000: De Brenek et 22005) and submillimeter (submnm) selected. galaxies (Fraver et 11998. 1999: Neri οἱ 22003). have established that the most luminous ancl extreme objects in the early Universe harbour vast amounts of molecular gas (~LOM1M, | Neri οἱ 22003: Greve οἱ 22005) and have large dynamical masses (~LOYDAL. Genzel et 22003: Tacconi et 22006)."," The detections of rotational transitions of CO in extremely distant quasars (Carilli et 2002; Walter et 2003), high-z radio galaxies (Papadopoulos et 2000; De Breuck et 2005) and submillimeter (submm) selected galaxies (Frayer et 1998, 1999; Neri et 2003), have established that the most luminous and extreme objects in the early Universe harbour vast amounts of molecular gas $\sim 10^{10-11}\,\Msolar$ – Neri et 2003; Greve et 2005) and have large dynamical masses $\sim 10^{11}\,\Msolar$ – Genzel et 2003; Tacconi et 2006)."31 Modelling of the bulk physical conditions of the molecular gas in hieh-z QSOs have even been possible in cases where several CO lines have been detected eel 22005)., Modelling of the bulk physical conditions of the molecular gas in $z$ QSOs have even been possible in cases where several CO lines have been detected et 2005).32 The success of CO observations is primarily due to its much larger abundance compared to other species as well asils easily excitable low-/ (CO J4-1—JJ« 3) rotational lines. whieh makes it an excellent tracer of the total amount of 7) molecular gas.," The success of CO observations is primarily due to its much larger abundance compared to other species as well asits easily excitable $J$ (CO $J+1\longrightarrow J, J<3$ ) rotational lines, which makes it an excellent tracer of the total amount of $n(\mbox{H}_2) \sim 10^{2-3}$ $^{-3}$ ) molecular gas."33 However. the diffuse gas only serves as a reservoir olpolential fuel available for star formation. and is not actively involved in forming stars.," However, the diffuse gas only serves as a reservoir of fuel available for star formation, and is not actively involved in forming stars."34 In our own Galaxy. the sites of active star formation coincide with the dense cores of giant molecular clouds (G\ICs).," In our own Galaxy, the sites of active star formation coincide with the dense cores of giant molecular clouds (GMCs)."35 This dense gas phase (n(IIs)2I0 7?) is best traced using molecules with high critical densities such as HCN., This dense gas phase $n(\mbox{H}_2) \gs 10^{4}$ $^{-3}$ ) is best traced using molecules with high critical densities such as HCN.36" This basic picture also appears {ο hold in nearby galaxies. as suggested by IICN(1—0) survevs of local (2z 0.1) Luminous Infrared Galaxies (LIRGs Ly,~10 EL.) and Ultra Luminous Infrared Galaxies (ULIRGs LycLOL. ). which found a remarkably tight correlation between IB. luminosity and ICN line luminosity (Solomon et 11992: Gao Solomon 2004a.b)."," This basic picture also appears to hold in nearby galaxies, as suggested by $(1-0)$ surveys of local $z\ls 0.1$ ) Luminous Infrared Galaxies (LIRGs – $L_{\mbox{\tiny{IR}}}\sim 10^{11}\,\Lsolar$ ) and Ultra Luminous Infrared Galaxies (ULIRGs – $L_{\mbox{\tiny{IR}}}\sim 10^{12}\,\Lsolar$ ), which found a remarkably tight correlation between IR luminosity and HCN line luminosity (Solomon et 1992; Gao Solomon 2004a,b)."37 Recently. this relation was shown to extend all the way clown to single GMCs. thus extending over 7-8 orders of magnitude in IR. luminosity (Wu et 22005).," Recently, this relation was shown to extend all the way down to single GMCs, thus extending over 7-8 orders of magnitude in IR luminosity (Wu et 2005)."38 This was interpreted as suggesting that the (rue star formation elliciency (the star formation rate per unit mass of dense gas) is the same in these widely different svstems., This was interpreted as suggesting that the true star formation efficiency the star formation rate per unit mass of gas) is the same in these widely different systems.39behind the detonation can have significant amounts of cucdothermic reactions. violating the assumptions of the CJ structure.,"behind the detonation can have significant amounts of endothermic reactions, violating the assumptions of the CJ structure."40 Because in the case of a pathological detonation some fraction of the reactions powering the detonation are decoupled from the shock. calculating the speed of a pathological detonation requires detailed integration of the detonation structure. rather than simply using jump conditions.," Because in the case of a pathological detonation some fraction of the reactions powering the detonation are decoupled from the shock, calculating the speed of a pathological detonation requires detailed integration of the detonation structure, rather than simply using jump conditions."41 For either kind of detonation. oue can estimate where most burning occurs with slock speed D. Gvhich. even in non-CJ case. can be estimated with CJ speed) aud 7: /;=Dr; is the position behind the shock at which the induction zone chads and rapid burning takes place.," For either kind of detonation, one can estimate where most burning occurs with shock speed $D$ (which, even in non-CJ case, can be estimated with CJ speed) and $\tau_i$; $l_i = D \tau_i$ is the position behind the shock at which the induction zone ends and rapid burning takes place."42" Iu the case of a detonation iuto a very low-density. cold material. the material immediately behind the shock will still not burn significantly uutil a leugth of time equal to the ignition time passes. resulting in a ""quare wave detonation."," In the case of a detonation into a very low-density, cold material, the material immediately behind the shock will still not burn significantly until a length of time equal to the ignition time passes, resulting in a `square wave' detonation."43 For conditious relevant to near the core of a white dwarf. however. the post-shock fluid will typically have temperatures on order 75225 that is. temperatures which are already. near the aNd temperature which will be obtaiued by burning.," For conditions relevant to near the core of a white dwarf, however, the post-shock fluid will typically have temperatures on order $T_9 \approx 5$ – that is, temperatures which are already near the maximum temperature which will be obtained by burning."44 Even in these cases. this estimate of 7; provides a good measure of the thickness of the detonation structure behind the shock.as is shown in Fig & where it naeasures the position of maxima burniug.," Even in these cases, this estimate of $l_i$ provides a good measure of the thickness of the detonation structure behind the shock,as is shown in Fig \ref{fig:detstructure} where it measures the position of maximum burning."45 One mechanisin for ignition of a detonation by a hotspot is au initial rapid input of enerey which leads to a Sedov blast wave: the material shocked by the outgoing spherical blast ignites. aud as the outeoiug wave slows. a steady outeoing detonation results.," One mechanism for ignition of a detonation by a hotspot is an initial rapid input of energy which leads to a Sedov blast wave; the material shocked by the outgoing spherical blast ignites, and as the outgoing wave slows, a steady outgoing detonation results."46 A steady detonation cannot form until the outgoing shock wave speed drops to the detonation velocity detouation. or else the energy released. by reactions behind the blast wave will not be able to cateli up! to the outgoing shock to drive it.," A steady detonation cannot form until the outgoing shock wave speed drops to the detonation velocity detonation, or else the energy released by reactions behind the blast wave will not be able to `catch up' to the outgoing shock to drive it."47 Ou the other Iud. if the shock drops sienificautly below the detonation speed before ignition takes place. not enough material will be burning per nuit time to sustain a detonation wave.," On the other hand, if the shock drops significantly below the detonation speed before ignition takes place, not enough material will be burning per unit time to sustain a detonation wave."48 We denote the position of the shock when it reaches the detonation speed. froii above as Rp., We denote the position of the shock when it reaches the detonation speed from above as $R_{D}$.49 Naively. the condition for successful detonation ignition would be that Rpz Hf. ," Naively, the condition for successful detonation ignition would be that $R_{D} \gtrsim l_{i}$ "50The angle approximation Z5δρ is au estimate to b/p=2sin(Z/2). a Πιτ of a bascline so short that it does uot matter whether it is measured along a straight line (as drawn in refPoint Rho.ps)) or alone the circular perimeter.,"The angle approximation $Z\approx b/\rho$ is an estimate to $b/\rho =2\sin (Z/2)$, a limit of a baseline so short that it does not matter whether it is measured along a straight line (as drawn in \\ref{PointRho.ps}) ) or along the circular perimeter."51 The relative error in this approNimationu ds zc Z/2|. oy z10H for the example of b=100 ll. Pointingοπήπιο is a functionality of the individual telescopes: the existence of à nonzero pointing difference is absorbed in the telescope operation. aud any delay originating from there is to first order recovered in the tracking.," The relative error in this approximation is $\approx Z^2/24$ , or $\approx 10^{-11}$ for the example of $b=100$ m. Pointing/guiding is a functionality of the individual telescopes: the existence of a nonzero pointing difference is absorbed in the telescope operation, and any delay originating from there is to first order recovered in the tracking."52" We hereby explicitly discard auv “separation” term of Gubler and Tytler enmünent from their consideration of suele telescopes(ὃν, and acknowledge that both telescopes are ""1uispoinutiug"" at the same time."," We hereby explicitly discard any “separation” term of Gubler and Tytler eminent from their consideration of single telescopes, and acknowledge that both telescopes are “mispointing” at the same time."53 This cross-eved geometry iudirectly trausforis into a contibution to the delay that may boe understoodand calculated to lowest orderon the basis of what is said in refsec flatearth.. but has no parallel with sinele telescopes as long as their diameters are much sanaller than the earth radius: The example of 3.2 arcsec frou above translates into an additional anele of refraction of AR~Azg(1|tan?το)(η1)As(nyl)eZ(ng—z650 pas at 2600 ni above sea level. which is the first derivative of (1)) zy.," This cross-eyed geometry indirectly transforms into a contribution to the delay that may be understood—and calculated to lowest order—on the basis of what is said in \\ref{sec.flatearth}, but has no parallel with single telescopes as long as their diameters are much smaller than the earth radius: The example of $3.2$ arcsec from above translates into an additional angle of refraction of $\Delta R\approx \Delta z_0(1+\tan^2z_0)(n_0-1)>\Delta z_0(n_0-1)\approx54Z (n_0-1)\approx 650$ $\mu$ as at 2600 m above sea level, which is the first derivative of \ref{eq.Rofnflat}) ) $z_0$."55 Dropping the term tau?zy hore niens this is a lower estimate in the Init of stars at the zenith., Dropping the term $\tan^2z_0$ here means this is a lower estimate in the limit of stars at the zenith.56" The effect on the delay could be uuderstood in the ""staudard model of delay line correction.” where the two ravs of the star that will eventually ut the two telescopes ""eeucrate a phase difference in the vacuna (undone later ou in the delay. line uunel) as they hit the top laver of the earth atinosphiere with a path difference D rofDelModl.ps))."," The effect on the delay could be understood in the “standard model of delay line correction,” where the two rays of the star that will eventually hit the two telescopes “generate” a phase difference in the vacuum (undone later on in the delay line tunnel) as they hit the top layer of the earth atmosphere with a path difference $D$ \\ref{DelModl.ps}) )."57 The curvature correction means hat this top laver “bends back” a bit more for he telescope further away from) the star. which slightly increases the anele of incidence on the atimosplicre.," The curvature correction means that this top layer “bends back” a bit more for the telescope further away from the star, which slightly increases the angle of incidence on the atmosphere."58 refBase.ps shows that the ouly obvious definition of the baseline leneth b is on carth., \\ref{Base.ps} shows that the only obvious definition of the baseline length $b$ is on earth.59 Three alternatives have been narked withquestion marks m the figure: lu a formal way. I define an effective baseline leugth 5 above the atimosphere via," Three alternatives have been marked withquestion marks in the figure: In a formal way, I define an effective baseline length $b^*$ above the atmosphere via"60responsible for the radio enission. rather than tle amount of soft X-ray cussion. provided they account for the suppressed radio cussion du the soft state.,"responsible for the radio emission, rather than the amount of soft X-ray emission, provided they account for the suppressed radio emission in the soft state."61 Such a hypothesis ueath explains the behavior of Cre N-3. which is quite bright iu all the three energy ranges and hence the observational uncertaiutv is quite low.," Such a hypothesis neatly explains the behavior of Cyg X-3, which is quite bright in all the three energy ranges and hence the observational uncertainty is quite low."62 It cau also be noticed from Table 1 that the most significant correlation for (νο XN-3 is between the radio enüssiou and the ratio of hard. N-rav. flux to soft N-ravs., It can also be noticed from Table 1 that the most significant correlation for Cyg X-3 is between the radio emission and the ratio of hard X-ray flux to soft X-rays.63 Though such au explanation is not very clear in other sources. all the available observations are consisteut with this.," Though such an explanation is not very clear in other sources, all the available observations are consistent with this."64 Since the radio ciission too shows mereasing Clissio—-c from ‘off state to low-hard state (iu GN 339-1 aud VLO Cre). correlated. behavior m low-hard state (the above two sources and Cre X-1). aud high radio emission in au intermediate state very close to the high state (n CRS 19151105 and (νο XN-3) and suppressed radio enissio- in the high state (Cvg N-3. CRS 19151105. (νο N-1& CX 339-1). we speculate that the soft N-rav intensity deteriuues the spectral shape aud the accretion disc condition iu these sources. which iu turn determines the αλλο of radio enussion (in the X-ray quiescent hd state of these sources).," Since the radio emission too shows increasing emission from `off' state to low-hard state (in GX 339-4 and V404 Cyg), correlated behavior in low-hard state (the above two sources and Cyg X-1), and high radio emission in an intermediate state very close to the high state (in GRS 1915+105 and Cyg X-3) and suppressed radio emission in the high state (Cyg X-3, GRS 1915+105, Cyg X-1 GX 339-4), we speculate that the soft X-ray intensity determines the spectral shape and the accretion disc condition in these sources, which in turn determines the amount of radio emission (in the X-ray quiescent hard state of these sources)."65 The trausition of the svsteuis (Cre νο GRS 19151105) iuto flaring state απ their correspouding behavior in the radio as well as X-ray bands Is an issue not discussed here., The transition of the systems (Cyg X-3 GRS 1915+105) into flaring state and their corresponding behavior in the radio as well as X-ray bands is an issue not discussed here.66 Though there are models describing the accretion disk enüssion (Zdziarski=2000)— or jet cimission (ALarkotfetal. 2003). there are very few inodels which self solve the accretion aud. ejection phenomena seen in black hole sources.," Though there are models describing the accretion disk emission \citep{zdz00} or jet emission \citep{mar03}, there are very few models which self-consistently solve the accretion and ejection phenomena seen in black hole sources."67 Since our ficdines sugeest a close connection between these two phenomena. we attempt below to qualitatively explain the N-rayv radio association using one such model: the Two Conmponeut Advective Flow (TCAF) model of Chakrabarti(1996).," Since our findings suggest a close connection between these two phenomena, we attempt below to qualitatively explain the X-ray radio association using one such model: the Two Component Advective Flow (TCAF) model of \citet{cha96}."68. According to this model. the Compton scattered N-ravs iu a black hole source originates froun a region close to the compact object. coufined within the Ceutrifugal Boundary Laver (CENBOL).," According to this model, the Compton scattered X-rays in a black hole source originates from a region close to the compact object, confined within the Centrifugal Boundary Layer (CENBOL)."69 The N-vay spectral shape iu various ‘states’ of the source essentially depends on the location of the CENBOL and a detailed. description can be found in Chakrabarti&Titarchul1905} anc Ebisawaetal. (1996)., The X-ray spectral shape in various `states' of the source essentially depends on the location of the CENBOL and a detailed description can be found in \citet{cha95} and \citet{ebi96}.70. At low accretion rates. the CENBOL is far away from the compact object aud the N-vay spectrum is dominated by a thermalCompton spectra. originating roni the hieh temperature region within the CENBOL.," At low accretion rates, the CENBOL is far away from the compact object and the X-ray spectrum is dominated by a thermal-Compton spectrum, originating from the high temperature region within the CENBOL."71 Iu the transition state. the CENBOL comes closer to he compact object aud the CENBOL can sometimes eive rise to radial shocks. causing iuteuse quasi-periodic oscillations. as seen in GRS 1915|105.," In the transition state, the CENBOL comes closer to the compact object and the CENBOL can sometimes give rise to radial shocks, causing intense quasi-periodic oscillations, as seen in GRS 1915+105."72 Tn the high state. he increased accretion rate produces copious photons i- he accretion dise which cool the Compton region. giving rise to very intense disk blackbody cussion along with ilk inotiou Comptonization (a power-law in hard N-aravs with a photon index of —2.5).," In the high state, the increased accretion rate produces copious photons in the accretion disc which cool the Compton region, giving rise to very intense disk blackbody emission along with bulk motion Comptonization (a power-law in hard X-rays with a photon index of $\sim$ 2.5)."73 At some critical accretio- rates. the state transitions could be oscillatory as seen in GRS 19151105 (Chakrabarti&Mauickiun|20001," At some critical accretion rates, the state transitions could be oscillatory as seen in GRS 1915+105 \citep{cha00}."74", The behavior of TCAF disks aud the outflow has been stucied in detail in Das&Chakrabarti(1998).", The behavior of TCAF disks and the outflow has been studied in detail in \citet{das98}.75. The outflow rate is found to be a monotonic function of the conrpressiou ratio. BR. of the eas at the shock region.," The outflow rate is found to be a monotonic function of the compression ratio, R, of the gas at the shock region."76 Iu this scenario. at low accretion rates. the CENBOL is far away from the compact object. and a weal shock can forma with low compression ratio. eiviug low aud steady outflow.," In this scenario, at low accretion rates, the CENBOL is far away from the compact object, and a weak shock can form with low compression ratio, giving low and steady outflow."77 If this outflow gives rise to radio emission. one can expect a relation between the radio enission aud the N-ray cussion.," If this outflow gives rise to radio emission, one can expect a relation between the radio emission and the X-ray emission."78 In this state (off state to low-hard state). an ducreased accretion rate increases the overall amount of energv available to the Couptouizine region and heuce inercasing the XN-rav cuissionu.," In this state (off state to low-hard state), an increased accretion rate increases the overall amount of energy available to the Comptonizing region and hence increasing the X-ray emission."79 The CENBOL location would be pushed imward. increasing the compression ratio (aud hence inereasiug the radio Cluission) and also can increase the temperature aud optical depth of the Comptouizing region. thus eiving rise to a pivoting behavior at hard N-vavs (50. 90 keV) as seen in Cve X-1 and GN 339-1.," The CENBOL location would be pushed inward, increasing the compression ratio (and hence increasing the radio emission) and also can increase the temperature and optical depth of the Comptonizing region, thus giving rise to a pivoting behavior at hard X-rays (50 – 90 keV) as seen in Cyg X-1 and GX 339-4."80 At increased accretion rate. the CENBOL can come closer to the compact region. giving the spectral aud radio properties as seen im GRS 1915|105 and Cye N-3.," At increased accretion rate, the CENBOL can come closer to the compact region, giving the spectral and radio properties as seen in GRS 1915+105 and Cyg X-3."81 For a eiven accretion rate the compression ratio. after reaching a critical value (with the shock region comune correspondinely closer to the eveut horizou). causes the source to transit iuto the high-soft state state. for which the radio enuüssiou is progressively suppressed (Chakrabarti1999).," For a given accretion rate the compression ratio, after reaching a critical value (with the shock region coming correspondingly closer to the event horizon), causes the source to transit into the high-soft state state, for which the radio emission is progressively suppressed \citep{cha99}."82. This model qualitatively explains all the observed. X-ray spectral aud radio properties of Galactic black hole sources preseuted here., This model qualitatively explains all the observed X-ray spectral and radio properties of Galactic black hole sources presented here.83 A complete understaundiug of the accretion-ejection physics in Galactic icroquasars demands proper interpretation and modeling of all the varied states of X-rav and radio enuüssion. euconipassing the various flaring and steady enüssious covering all ranges of time scales.," A complete understanding of the accretion-ejection physics in Galactic microquasars demands proper interpretation and modeling of all the varied states of X-ray and radio emission, encompassing the various flaring and steady emissions covering all ranges of time scales."84 Iu this paper we have taken a first step in this direction by atteniptiug to understand the loug term variation of the (non flaring) radio enüssion associated with the X-rav chuission in the steady hard aud soft states;, In this paper we have taken a first step in this direction by attempting to understand the long term variation of the (non flaring) radio emission associated with the X-ray emission in the steady hard and soft states.85 We have analyzed the (quasi) smmltaueous observations on CRS 19151105 and (νο X-1 using the RVTE-ASAL CCRO-BATSE and GBI data and made a detailed study of correlation between radio aud X-ray fluxes.," We have analyzed the (quasi) simultaneous observations on GRS 1915+105 and Cyg X-1 using the -ASM, }-BATSE and GBI data and made a detailed study of correlation between radio and X-ray fluxes."86 Dased on this analvsis along with discussion of earlier published results ou Galactic niücroquasars we find that:, Based on this analysis along with discussion of earlier published results on Galactic microquasars we find that:87AMpgy.,$M_{BH}$.88 Black hole virialm 1iasses may be estimatedB as AfpyxRe.Di where Rois B the broad lineB regionB size.B and eds the velocity dispersion of the eas emiting the broad. emission lines.," Black hole virial masses may be estimated as $M_{BH} \propto R v^2$ , where $R$ is the broad line region size, and $v$ is the velocity dispersion of the gas emitting the broad emission lines."89 A correlation has been found between the luminosity of à source aud tie size of it’s broad line region 2005).," A correlation has been found between the luminosity of a source and the size of it's broad line region \citep[the $R$--$L$ relationship, e.g.,][]{kaspi05}."90. One can then exploit this τεJatiolsup. and use the broad line FWTAL as an estimate for 0. obtaining virial mass estimates MpXLee? (¢NOOO.Wandeletal.1999).. where the expoucut is 0zz0.5 (c.g...Vestereaard&Peterson2006).," One can then exploit this relationship, and use the broad line $FWHM$ as an estimate for $v$, obtaining virial mass estimates $\hat{M}_{BH}91 \propto L^{\theta} v^2$ \citep[e.g.,][]{wand99}, where the exponent is $\theta \approx 0.5$ \citep[e.g.,][]{vest06}."92". Uuortulaelv. the uncertainty ou the broad line estimates of Apry can be considerable. having a standard deviati1i of o,~0.1 dex (e.g...Mebure&Jarvis2002:&Peterson2006:Kellyetal."," Unfortunately, the uncertainty on the broad line estimates of $M_{BH}$ can be considerable, having a standard deviation of $\sigma_m \sim 0.4$ dex \citep[e.g.,][]{bhmmgii,vest06,kelly06a}."93 2007).. For οase 0: coniparison with previous work. 1 cstimate Afpy using oulv the IL cussion liue.," For ease of comparison with previous work, I estimate $M_{BH}$ using only the $\beta$ emission line."94 The logarithua of t1ο viria lnass estimates were calculated using tje ID) huuiuositv axd FT7M according to the relatioushi) even by Vestereaard&Peterson (2006).., The logarithm of the virial mass estimates were calculated using the $\beta$ luminosity and $FWHM$ according to the relationship given by \citet{vest06}. .95 Ay snple consists ofa subset of the sample o‘Ivelly&Bechtold(2007)., My sample consists of a subset of the sample of\citet{kelly06b}.96. These sources lave measurements Q “the N-rav photon index. Py=ay|Ll. obtained from observations. aud measurements of the QticalJUV BIuuinositv at 2500-4. denoted as Losyy. obtained from SDSS spectra.," These sources have measurements of the X-ray photon index, $\Gamma_X = \alpha_X + 1$, obtained from observations, and measurements of the optical/UV luminosity at $2500\AA$, denoted as $L_{2500}$, obtained from SDSS spectra."97 The IL} profile was modeled as a stn of (απουσίας and extracted from the SDSS xs]vectra according to the procedure cescribed in (2007).., The $\beta$ profile was modeled as a sum of Gaussians and extracted from the SDSS spectra according to the procedure described in \citet{kelly06a}.98 I estimated the I+ £TPAL aud luminosity from the line profile fits., I estimated the $\beta$ $FWHM$ and luminosity from the line profile fits.99" Tostimate the bolometric Inuinositv. L5. from the Iuininositv at 2500.4. assuming a constant bolometric correction £5,=5.6Lo5yy (Elviseta.199D.."," I estimate the bolometric luminosity, $L_{bol}$, from the luminosity at $2500\AA$, assuming a constant bolometric correction $L_{bol} = 5.6 L_{2500}$ \citep{elvis94}."100". The standard deviatici iu this bolometric correction reported by Elvisetal.(1991). is 3.l. nuplviugo an uncertainty in logL5, of σι0.25 dex."," The standard deviation in this bolometric correction reported by \citet{elvis94} is 3.1, implying an uncertainty in $\log L_{bol}$ of $\sigma_{bol} \sim101 0.25$ dex."102" Combining this with the ~0.1 dex uucertaimtv on loBMpy. tie total ueasureiment error o1i logLawπιω bocomes o,~0.17 dex."," Combining this with the $\sim 0.4$ dex uncertainty on $\log M_{BH}$, the total `measurement error' on $\log L_{bol} /103 L_{Edd}$ becomes $\sigma_x \sim 0.47$ dex."104 The distribution of Dy as a fiction o flosLi/Lg; is shown in Fiewe 10.., The distribution of $\Gamma_X$ as a function of $\log L_{bol} / L_{Edd}$ is shown in Figure \ref{f-gamx_eddrat}.105" As can be seen. the iicasureimeut errors on both Dy aud logZí4/Lr are large and make a considerable contribution to t1e observed scatter in both variables. where A,~ ü.laid Ry~OS."," As can be seen, the measurement errors on both $\Gamma_X$ and $\log L_{bol} / L_{Edd}$ are large and make a considerable contribution to the observed scatter in both variables, where $R_y \sim 0.1$ and $R_x \sim 0.8$."106 Therefore. we expect the moeasurenieit errors to have a sjeuificaut effect on the correlation aid regression analysis.," Therefore, we expect the measurement errors to have a significant effect on the correlation and regression analysis."107 I performed the regression assuwing the linear form Dya|Sloeο aud modellehue the intrinsic distribution of logLayLi; using A— 2€Guissans.," I performed the regression assuming the linear form $\Gamma_X =108 \alpha + \beta \log L_{bol} / L_{Edd}$, and modelleling the intrinsic distribution of $\log L_{bol} / L_{edd}$ using $K = 2$ Gaussians."109 Draws from the posterior were obtained using the Cabbs sampler., Draws from the posterior were obtained using the Gibbs sampler.110 The mareinal posterior distzilnitions for 2.0. and the correlation between Pay aud logLawfLead. p. are shown in Figure 11.. and the posteric imediau and 95% (26) poiutwise intervals on the regression line are show rin Fieure 10.," The marginal posterior distributions for $\beta, \sigma$ , and the correlation between $\Gamma_X$ and $\log L_{bol} / L_{edd}$, $\rho$, are shown in Figure \ref{f-posthb}, and the posterior median and $95\%$ $2\sigma$ ) pointwise intervals on the regression line are shown in Figure \ref{f-gamx_eddrat}."111 The posterior mclan estimate of the paracters are a=3.1240.11 for the coustaut. Jj=1.35+£0.51 for the slope. ¢=0.2640.11 for the intrinsic scatter about the regressiou line. µεOrrEOL| for the mean of logLy.7/Leag. aud σε0.3240.12 dex for the dispersion iu logLi/L4.," The posterior median estimate of the parameters are $\hat{\alpha} = 3.12 \pm 0.41$ for the constant, $\hat{\beta} = 1.35 \pm 0.54$ for the slope, $\hat{\sigma} = 0.26 \pm 0.11$ for the intrinsic scatter about the regression line, $\hat{\mu}_{\xi} = -0.77 \pm 0.10$ for the mean of $\log L_{bol} / L_{Edd}$, and $\hat{\sigma}_{\xi} = 0.32 \pm 0.12$ dex for the dispersion in $\log L_{bol} / L_{edd}$."112 Hore. I have used a robust estimate of the posterior standard deviation as au error bar on the parameters.," Here, I have used a robust estimate of the posterior standard deviation as an `error bar' on the parameters."113" These resuts naply that the observed scatter in logοLg; is dominated by measurement error. GfTo~1.5. as oxected. from the large value of Π,."," These results imply that the observed scatter in $\log L_{bol} / L_{Edd}$ is dominated by measurement error, $\sigma_x / \tau \sim 1.5$, as expected from the large value of $R_x$."114 For comparison. the DCES(Y[VX) estimate of the sope is Opers=329£3.31. the FITENY estimate is Jexyy=1.τος.LO. are the OLS estimate is Jops=0.5640.11: the standard error on Jpgvyy was estimated using bootstrapping.," For comparison, the $Y|X$ ) estimate of the slope is $\hat{\beta}_{BCES} = 3.29 \pm 3.34$, the FITEXY estimate is $\hat{\beta}_{EXY} = 1.76 \pm 0.49$, and the OLS estimate is $\hat{\beta}_{OLS} = 0.56 \pm 0.14$; the standard error on $\hat{\beta}_{EXY}$ was estimated using bootstrapping."115 Fieure 10 also compares the OLS. BCES. aud FITENY best-fit lines with the posterior median estimate.," Figure \ref{f-gamx_eddrat} also compares the OLS, BCES, and FITEXY best-fit lines with the posterior median estimate."116" The 95% coufideuce region ou the slo2ο implied by the posterior draws is 0.16<9<< 11. whereas the approximate 9554 confidence region implied by the BCES. FITENY. aud OLS standard errors are o2.26«P<OSL 050<>«2,12. aud 0.12«30,10. --espectivelv."," The $95\%$ confidence region on the slope implied by the posterior draws is $0.46 < \beta117 < 3.44$ , whereas the approximate $95\%$ confidence region implied by the BCES, FITEXY, and OLS standard errors are $-3.26 < \beta <118 9.84$, $0.80 < \beta < 2.72$, and $0.42 < \beta < 0.70$, respectively."119 The OLS aud FITENY cstimates aud the Davesiaiapproach eive “statistically significait” evience for a correlation between logLi;/Lead and Py: however the BCES estimate is too variable to rule out the null livpothesis of uo correlation., The OLS and FITEXY estimates and the Bayesianapproach give `statistically significant' evidence for a correlation between $\log L_{bol} / L_{Edd}$ and $\Gamma_X$; however the BCES estimate is too variable to rule out the null hypothesis of no correlation.120" As noted before. the large measurement errors on logL5,[πιω bias the OLS estimate of. towardshalloswer values aud the FITENY estiuate of JJ toward steeper values."," As noted before, the large measurement errors on $\log121 L_{bol} / L_{Edd}$ bias the OLS estimate of $\beta$ towardshallower values and the FITEXY estimate of $\beta$ toward steeper values."122 Because of this bias. coufideuce regious based O1 ons and Jpyyare not valid because they are not centered ou the true value of 2. aud thus do not," Because of this bias, confidence regions based on $\hat{\beta}_{OLS}$ and $\hat{\beta}_{EXY}$are not valid because they are not centered on the true value of $\beta$ , and thus do not"1232230.. a niuis. pulsar. was discovered in a radio survev of wnicentified EGRET eamuna rax sources using the Parkes Radio Telescope (Ilesselsal. 2005).,", a ms pulsar, was discovered in a radio survey of unidentified EGRET gamma ray sources using the Parkes Radio Telescope \citep{discovery}."124. Subsequeutlv. N-vay cussion from XAJM (Robertsetal.2007). aud 5-av enmuüssion frouTelescope (Abdo2010) was detected.," Subsequently, X-ray emission from \citep{xraypwn}125 and $\gamma$ -ray emission from \citep{fermi} was detected."126 Like most nüllisecond pulsars (MISPs}. is mn a binary svsteni.," Like most millisecond pulsars (MSPs), is in a binary system."127 The circular orbit is consistent with the pulsar having uudergoue mass trausfer aud spun up., The circular orbit is consistent with the pulsar having undergone mass transfer and spun up.128 The mass function derived from pulsar timine indicated a companion with mass Mao>O.LAL. (Iessels 2005)..," The mass function derived from pulsar timing indicated a companion with mass $M_2>0.4\,M_\odot$ \citep{discovery}."129 The svsteni recently came into prominence when Demorestetal.(2010). reported the mass of the pulsar to be LOFAOOLAL....," The system recently came into prominence when \citet{heavy} reported the mass of the pulsar to be $1.97\pm0.04\,$."130 The detection of such a massive ueutron star (NS) places very strong constraints ou the equation of state of matter at extreme uuclear deusities (sec.forexample.Lattimer&Prakash2001.2005).," The detection of such a massive neutron star (NS) places very strong constraints on the equation of state of matter at extreme nuclear densities \citep[see, for example,][]{lattimer,lattimertable}."131.. The rather exquisite precision of this mass measurement was xossible due to the orbit beiug almost perpeudicular to he plane ofthe sky., The rather exquisite precision of this mass measurement was possible due to the orbit being almost perpendicular to the plane of the sky.132 As a result. the Shapiro delay caused w the companion is very larvec. resulting iu a precise estimate of the mass of the companion. A»=0.5004006 ," As a result, the Shapiro delay caused by the companion is very large, resulting in a precise estimate of the mass of the companion, $M_2=1330.500\pm 0.006\,M_\odot$ ."134The s.7dday orbital period is siguificauth shorter AZ...than ~120 davs expected for a low-ass Nav ünary with such a massive secondary (Rappaportotal. sugecsting a peculiar evolutionary historvw for his binary.," The day orbital period is significantly shorter than $\sim120\,$ days expected for a low-mass X-ray binary with such a massive secondary \citep{massperiod} — suggesting a peculiar evolutionary history for this binary."135 Given the importance of the result of Demorestctal.(2010). additional verification or consistency checks of physicalparameters of οσα be expected to be of some value., Given the importance of the result of \cite{heavy} additional verification or consistency checks of physicalparameters of can be expected to be of some value.136 A wwhite dwarf (WD) at the interred distance of (GT~1.2 kkpe). even if a few Cyr old. is within the reach of preseut-day optical telescopes.," A white dwarf (WD) at the inferred distance of $d\sim 1.2$ kpc), even if a few Gyr old, is within the reach of present-day optical telescopes."137 It is this search for the WD that coustitutes the principal focus of this Letter., It is this search for the WD that constitutes the principal focus of this Letter.138 We observed 1)) ing and R bands using the imaging mode of +16 Low Resolutionlnaging Spectrograph (ERIS) ou the yumm I&eck-I telescope (Okeetal.1995).. with uperaded aud blue cameras (MeCarthvetal.1998:Steidelal 2001).," We observed ) in $g$ and $R$ bands using the imaging mode of the Low Resolution Imaging Spectrograph (LRIS) on the m Keck-I telescope \citep{lris}, with upgraded and blue cameras \citep{lrisb1,lrisb2}."139 Several nuages were acquired at cach target location. dithering the telescope by small amouuts between cach exposure.," Several images were acquired at each target location, dithering the telescope by small amounts between each exposure."140" The observing conditions ou UT 2010x May 15 were poor (secius 1"".1). so onlv data acquired. on UT 2010 July 5S (Ro band xccing 07.85 FWIIM) were used in this analysis."," The observing conditions on UT 2010 May 15 were poor (seeing .4), so only data acquired on UT 2010 July 8 $R$ band seeing .85 FWHM) were used in this analysis."141 The total exposure ou this night was 9608s in the R baud and LOLOss in the g baud., The total exposure on this night was s in the $R$ band and s in the $g$ band.142 The plate scale is | for both Calieras The images were processed usingIRAF., The plate scale is $^{-1}$ for both cameras The images were processed using.143. After bias correction and flat fielding. cosmic ravs wererejected using (vanDokkun 2001)..," After bias correction and flat fielding, cosmic rays wererejected using \citep{lacosmic}. ."144 The tages were then aligned with aud averaged to produce the final image for each baud (see 1))., The images were then aligned with and averaged to produce the final image for each band (see ).145 A World Coordinate Svstem was calculated using, A World Coordinate System was calculated using146blackbody contributions (hirley2000).. while the AXPs had softer spectra. with P~4 and ~0.5 keV blackbocdies contributing up to ol the X-ray flix (Mereghetti2000).,"blackbody contributions \citep{h99}, while the AXPs had softer spectra, with $\Gamma \sim 4$ and $\sim 0.5$ keV blackbodies contributing up to of the X-ray flux \citep{m99}."147. But this situation has been changing., But this situation has been changing.148 Observations ol the quiescent [found a photon index of 3.2.) closer to the nominal ANP index than to the that of the other SGRs and possible evidence for a 0.5 keV blackbody (hulkarnietal.2001a)., Observations of the quiescent found a photon index of 3.2 – closer to the nominal AXP index than to the that of the other SGRs – and possible evidence for a 0.5 keV blackbody \citep{k+00}.149. This may put the value of the photon index on a continuum related (o burst activity. ancl magnetic Ποια geometry for both groups., This may put the value of the photon index on a continuum related to burst activity and magnetic field geometry for both groups.150 Observations of iin quiescent and active states demonstrated (he presence of an underlying ~0.5 keV blackbody (Woodsοἱal.1999a.2001).," Observations of in quiescent and active states demonstrated the presence of an underlying $\sim$ 0.5 keV blackbody \citep{wkp+99a,wkg+01}."151. Updated spectral fits of archival ddata of SGRs and AXPs have shown that both groups seem to possess blackbody components whose fraction of the overall X-ray emission may constitute another unilving continuum (Pernaοἱal.2001)., Updated spectral fits of archival data of SGRs and AXPs have shown that both groups seem to possess blackbody components whose fraction of the overall X-ray emission may constitute another unifying continuum \citep{phh+01}.152. Spectral fits to the ANP LE 1043.1—5937 show that it has a hard power-law component reminiscent of the SGRs (lNaspietal.2001).., Spectral fits to the AXP 1E $-$ 5937 show that it has a hard power-law component reminiscent of the SGRs \citep{kgc+01a}.153. And finally. optical and infrared observations of SGRs (kaplanetal.2001a:πα900110) and ANPs (IIullemanetal.2000:ILulleman2000) have shown that the groups have similar rav-to-optical flux ratios. so that this ratio may be a distinguishing characteristic of the two. as à group (Ilullemanetal.2000).," And finally, optical and infrared observations of SGRs \citep{k+00c,k+01} and AXPs \citep{hvkk00,hvkvk00} have shown that the groups have similar X-ray-to-optical flux ratios, so that this ratio may be a distinguishing characteristic of the two, as a group \citep{hvkk00}."154.. All of these findings have strengthened. arguments for association between the AXNPs and SGRs., All of these findings have strengthened arguments for association between the AXPs and SGRs.155 The blackbody component of the sspeclatun. wilh Api80.5 keV and 2j215d; kim. has parameters (hat are similar (o those of other isolated NS candidates (c.f.Verbuntetal.1994).," The blackbody component of the spectrum, with $kT_{\rm156BB}\approx 0.5$ keV and $R_{\rm BB}\approx 1.5 d_5$ km, has parameters that are similar to those of other isolated NS candidates \citep[c.f.][]{vbj+94}."157. The relatively small emitting radius (hat we find. significantly smaller Caan (he nominal 210 km-radius NS. is twpically interpreted as either due to restricted emission Irom. e.g.. the NS polar caps. or as the result of temperature-dependent opacity effects in (he NS atmosphere (Rutledge 2001).," The relatively small emitting radius that we find, significantly smaller than the nominal $\approx$ 10 km-radius NS, is typically interpreted as either due to restricted emission from, e.g., the NS polar caps, or as the result of temperature-dependent opacity effects in the NS atmosphere \citep{rbb+99,phh+01}."158". The latter scenario would allow for closer distances. lower surface temperatures. and, potentially. emission [rom (he entire NS surface (Pernaetal.2001)."," The latter scenario would allow for closer distances, lower surface temperatures, and, potentially, emission from the entire NS surface \citep{phh+01}."159. The absence of anv narrow spectral features. to equivalent widths of less Chan 150 eV. is somewhat surprising given the detection bx Strohmaver&Ibrahim(2000) of à strong. 400-eV equivalent width. 226.4-keV. emission line in the sspectrum of a 1998 August 29 burst of1900--L4.," The absence of any narrow spectral features, to equivalent widths of less than 150 eV, is somewhat surprising given the detection by \citet{si00} of a strong, 400-eV equivalent width, $\approx$ 6.4-keV emission line in the spectrum of a 1998 August 29 burst of."160. Strohmaver&Ibrahim(2000) discuss two possible interpretations for the feature they observe: first. (hat it may result from fluorescence of relatively cool iron in the near vicinity of the NS: and second. that it may result [rom proton or alpha particle (He!) evclotron transitions in the SGR magnetosphere: {hese ions would have been liberated by the closely-prececling giant flare of 1998 August 27.," \citet{si00} discuss two possible interpretations for the feature they observe: first, that it may result from fluorescence of relatively cool iron in the near vicinity of the NS; and second, that it may result from proton or alpha particle $^4$ ) cyclotron transitions in the SGR magnetosphere; these ions would have been liberated by the closely-preceding giant flare of 1998 August 27."161 llowever. if the line resulted. [rom iron (norescence (hen we would expect. with," However, if the line resulted from iron fluorescence then we would expect, with"162out that most of the curve described by L passes through reeions of few electrous.,out that most of the curve described by \ref{cosphi_s} passes through regions of few electrons.163 The result is that the negative absorption coefficient are very sinall in absolute value. or that there are no negative absorption coefficients at all for these PEUT ratios.," The result is that the negative absorption coefficient are very small in absolute value, or that there are no negative absorption coefficients at all for these $\nu_p/\nu_B$ ratios."164 We performed nuucerical caleulatious of the absorption cocfiicicnt 5 using the power law distribution 7 with index à=3. and the loss cone distribution & with ουσία).=(LAL.costada)O83.," We performed numerical calculations of the absorption coefficient \ref{gyroe} using the power law distribution \ref{powerlaw}165 with index $\delta=3$, and the loss cone distribution \ref{losscone} with $\cos(\alpha)=0.81,166\cos(\alpha-\delta\alpha)=0.83$."167" The calculation were performed with a standard magnetic Ποια B=360 gauss, and an ambient munber density which was chauged to give differeut ratios of 1/rp."," The calculation were performed with a standard magnetic field $B=360\ gauss$ , and an ambient number density which was changed to give different ratios of $\nu_p/\nu_B$."168 For every cosine of enission angle cos(0) to the magnetic field the largest in absolute magnitude negative absorption coefficient was und by scamming in frequeucy from sp to (s|1)rj/p., For every cosine of emission angle $\cos(\theta)$ to the magnetic field the largest in absolute magnitude negative absorption coefficient was found by scanning in frequency from $s\nu_B$ to $(s+1)\nu_B$.169" The requency of this largest in absolute magnitude negative absorption cocficient is compared with the approximation 1l aud with our new approximation 19 in the figures 6 ο δν,"," The frequency of this largest in absolute magnitude negative absorption coefficient is compared with the approximation \ref{DM} and with our new approximation \ref{multiD} in the figures \ref{100-81-1}170 to \ref{140-81-2}."171 Iu figure 6 the comparison is mace for frequencies jetween vp sand 2»pp. and he feure shows that for sanall cos(0) the Dulk-Moelrose approximation 11 Is vorv siuilar to our new approximation.," In figure \ref{100-81-1} the comparison is made for frequencies between $\nu_B$ and $2\nu_B$, and the figure shows that for small $\cos(\theta)$ the Dulk-Melrose approximation \ref{DM} is very similar to our new approximation."172 However. for lareer cos(0). the now approximation is mach better.," However, for larger $\cos(\theta)$, the new approximation is much better."173 The new approximation is identical with the result of the full Munerical computation for most of the cos(0) range where here is negative absorption., The new approximation is identical with the result of the full numerical computation for most of the $\cos(\theta)$ range where there is negative absorption.174 In figure 7 the comparison is made for frequencies vetween 2vp and 237p., In figure \ref{100-81-2} the comparison is made for frequencies between $2\nu_B$ and $3\nu_B$.175 Here the relevant cos(0) rauge is huger. aud again for small cosines the Dulk-Moelrose approximation ll ids similar to the ummerical results aud ο our new approximation.," Here the relevant $\cos(\theta)$ range is larger, and again for small cosines the Dulk-Melrose approximation \ref{DM} is similar to the numerical results and to our new approximation."176 However. for angles smaller han about 60 degrees. the Dulk-Melrose approximation vceins to diverge. while the new approximation reais virtually identical with the numerical results.," However, for angles smaller than about $60$ degrees, the Dulk-Melrose approximation begins to diverge, while the new approximation remains virtually identical with the numerical results."177" For the ratio v,=L.I1rp our conclusions in section 5 ead us to expect that negative absorption exists ouly for requencies 7227g. aud the uuuercal computations bear lis out."," For the ratio $\nu_p=1.4\nu_B$ our conclusions in section \ref{general properties} lead us to expect that negative absorption exists only for frequencies $\nu > 2\nu_B$, and the numerical computations bear this out."178 Figure 5 shows again that for large cos(0) the approximation of equation JL begins to diverge from the miuerical results. while our new approximation reais ideutical to it.," Figure \ref{140-81-2} shows again that for large $\cos(\theta)$ the approximation of equation \ref{DM} begins to diverge from the numerical results, while our new approximation remains identical to it."179 We do not show results for the Z-1mode. since we are interested iu presenting estimates for the frequencies of occurrence of observable cuiission.," We do not show results for the Z-mode, since we are interested in presenting estimates for the frequencies of occurrence of observable emission."180 The Zauode is nuportaut in quenching the maser. but it is necessary fo compute the absorption coefficieuts for all the 11odes aud conrpare them to determine whether it docs.," The Z-mode is important in quenching the maser, but it is necessary to compute the absorption coefficients for all the modes and compare them to determine whether it does."181 We develop a new approximation for the frequencies at which the absorption cocficient is negative. aud therefore the Electron Cyclotron Maser mechanisin operates.," We develop a new approximation for the frequencies at which the absorption coefficient is negative, and therefore the Electron Cyclotron Maser mechanism operates."182 This new approxiuation is eiven by equation 13.. and is casy to compute.," This new approximation is given by equation \ref{multiD}, and is easy to compute."183 Our approximation gives results which are much more accurate than previous approximations. id are practicallythe same as the results of a full munerical calculation.," Our approximation gives results which are much more accurate than previous approximations, and are practicallythe same as the results of a full numerical calculation."184 The frequencies derived with the approxination are within 0.010.02vp of the numerically calculated frequencies., The frequencies derived with the approximation are within $0.01-0.02\ \nu_B$ of the numerically calculated frequencies.185" The paramcters cutering the approximation are the anele of emission to the magnetic field 0. the loss-cone opening angle o. the ratio r,/75. aud the ratio 1/1]."," The parameters entering the approximation are the angle of emission to the magnetic field $\theta$, the loss-cone opening angle $\alpha$, the ratio $\nu_p/\nu_B$, and the ratio $\nu/\nu_B$."186" The new approximation can be used to define a range ofpossible frequencies of millisecond spike cussion. given the ratio r,/rg."," The new approximation can be used to define a range of possible frequencies of millisecond spike emission, given the ratio $\nu_p/\nu_B$ ."187 Or. when spike cuuission is detected. the i»proxination can be used to eive the range of plivsical paraiaeters iu the emission region.," Or, when spike emission is detected, the approximation can be used to give the range of physical parameters in the emission region."188"and, accordingly, the probability distribution function of yf, is The precise functional form (11)) is not crucial, only that cannot be taken to be uniform.","and, accordingly, the probability distribution function of $\psi_0'$ is The precise functional form \ref{eq:psi1-distrib}) ) is not crucial, only that $p(\psi_0')$ cannot be taken to be uniform."189" After the sudden baryonic blowout,p(w) collisionless particles enter their new orbit in a special phase — preferentially near pericentre — so that they subsequently migrate outwards in unison."," After the sudden baryonic blowout, collisionless particles enter their new orbit in a special phase – preferentially near pericentre – so that they subsequently migrate outwards in unison."190 It is this difference in knowledge of phases before and after sudden changes that allows irreversibility in the real universe to appear in the model., It is this difference in knowledge of phases before and after sudden changes that allows irreversibility in the real universe to appear in the model.191 Only if all collisionless particles were near their pericentre just before the baryons returned would the statistical properties of the reversed picture match those of the actual model., Only if all collisionless particles were near their pericentre just before the baryons returned would the statistical properties of the reversed picture match those of the actual model.192" While this is dynamically possible, it is statistically unlikely."," While this is dynamically possible, it is statistically unlikely."193" Finally note that if the changes in potential are introduced gradually, the process should become adiabatic and hence reversible."," Finally note that if the changes in potential are introduced gradually, the process should become adiabatic and hence reversible."194" The dashed line in Figure 3 shows a numerical solution for which € changes smoothly over several orbital times from (9 to €, then back to @p."," The dashed line in Figure \ref{fig:harmonic-oscillator}195 shows a numerical solution for which $\omega$ changes smoothly over several orbital times from $\omega_0$ to $\omega_1$, then back to $\omega_0$."196" As expected from equation (4)), the final orbital amplitude is the same as its initial value, confirming the qualitatively different results to be expected from gradual variation as opposed to sudden jumps."," As expected from equation \ref{eq:adiabatic-Efinal}) ), the final orbital amplitude is the same as its initial value, confirming the qualitatively different results to be expected from gradual variation as opposed to sudden jumps."197 To test the picture expounded above we start by generating a time-dependent effective toy potential from the simulations (Section ??))., To test the picture expounded above we start by generating a time-dependent effective toy potential from the simulations (Section \ref{sec:first-sims}) ).198" This is given by equation (1)), with V(r;t) calculated from the spherically averaged density profile."," This is given by equation \ref{eq:veff}) ), with $V(r;t)$ calculated from the spherically averaged density profile."199 The starting energy Ep and the value of j can be determined by specifying initial orbital parameters., The starting energy $E_0$ and the value of $j$ can be determined by specifying initial orbital parameters.200 The angular momentum is necessarily conserved because of the spherical symmetry of the modelling (restriction 1 of Section ??))., The angular momentum is necessarily conserved because of the spherical symmetry of the modelling (restriction 1 of Section \ref{sec:virial-eqs}) ).201" In the simulations the changes in potential are not exactly symmetric (e.g. lower panel of Figure 2)); however we will see below that, for the purposes of calculating real-space density profiles, the symmetric approximation which enforces constant j actually works extremely well."," In the simulations the changes in potential are not exactly symmetric (e.g. lower panel of Figure \ref{fig:HT-fluctuations}) ); however we will see below that, for the purposes of calculating real-space density profiles, the symmetric approximation which enforces constant $j$ actually works extremely well."202" As before, the energy shift for one jump is given by averaging over possible orbital phases."," As before, the energy shift for one jump is given by averaging over possible orbital phases."203" However the potential Vphere is no longer an exact power law, so the calculation required is where the time integrals are evaluated over an orbital period; after changing variables to r this corresponds to integrating over the region where the integrand is real."," However the potential $V_{\mathrm{sphere}}$ is no longer an exact power law, so the calculation required is where the time integrals are evaluated over an orbital period; after changing variables to $r$ this corresponds to integrating over the region where the integrand is real."204 Equation (12)) agrees with equation (3)) for the special case of power-law potentials., Equation \ref{eq:delta-E1}) ) agrees with equation \ref{eq:deltaE-virial}) ) for the special case of power-law potentials.205" The remainder of this Section applies expression (12)) recursively to a time-series of potentials from the HT flattening) simulation, at each step updating AV, E and Verepriately?.."," The remainder of this Section applies expression \ref{eq:delta-E1}) ) recursively to a time-series of potentials from the HT (cusp-flattening) simulation, at each step updating $\Delta V$ , $E$ and $V_{\mathrm{eff}}$."206 The energy gain is evaluated at every stored simulation timestep; the relevant outputs are written every δί~27Myr.," The energy gain is evaluated at every stored simulation timestep; the relevant outputs are written every $\delta t\simeq 27\,\Myr$."207 Thus changes occurring on timescales <δί will implicitly be classified as “rapid” (composed of one jump) whereas those occurring on timescales >>dt will automatically be treated as “adiabatic” (composed of many small steps)., Thus changes occurring on timescales $\le \delta t$ will implicitly be classified as “rapid” (composed of one jump) whereas those occurring on timescales $\gg \delta t$ will automatically be treated as “adiabatic” (composed of many small steps).208" While the boundary between these limits cannot be uniquely defined, the change in behaviour must occur at around the orbital period for a particle, which is indeed ~25Myr."," While the boundary between these limits cannot be uniquely defined, the change in behaviour must occur at around the orbital period for a particle, which is indeed $\sim 25\, \Myr$."209 We verified by running checks with only every second timestep (dt~ 54Myr) that the results presented are insensitive to the precise time-slicing.," We verified by running checks with only every second timestep $\delta t \simeq 54\,\Myr$ ) that the results presented are insensitive to the precise time-slicing."210" The solid lines in Figure 4 show the resulting mean radius (ή) of orbits as a function of time, where The values of j and Eo for each orbit are chosen by requiring the initial motion to be circular at a range of different radii."," The solid lines in Figure \ref{fig:radial-migration} show the resulting mean radius $\langle r \rangle$ of orbits as a function of time, where The values of $j$ and $E_0$ for each orbit are chosen by requiring the initial motion to be circular at a range of different radii."211" As time progresses, the orbits starting interior to 1kpc migrate outwards, reflecting a net gain in energy."," As time progresses, the orbits starting interior to $1\,\kpc$ migrate outwards, reflecting a net gain in energy."212 Orbits outside this radius are largely unaffected., Orbits outside this radius are largely unaffected.213" In the LT run, by contrast, no tracer particles gain energy;those that start on circular orbits, for instance, are predicted to remain at the same radius for the entire run."," In the LT run, by contrast, no tracer particles gain energy;those that start on circular orbits, for instance, are predicted to remain at the same radius for the entire run."214[or Carina not to develop winds before each star formation episode is completed. again. unrealistically high numbers.,"for Carina not to develop winds before each star formation episode is completed, again, unrealistically high numbers."215 A carina.wind mocdel would give as=0.37. only mareinally acceptable from the point of view of more complete models of gas heating in small svstems. although it would: vield present cay average metallicities. matching the observed central values.," A carina.wind model would give a $\gamma=0.37$, only marginally acceptable from the point of view of more complete models of gas heating in small systems, although it would yield present day average metallicities matching the observed central values."216 The temporal evolution of model carina.dm is shown in figure 4. with the different panels. ancl curves. being totally analogous to those of figure 1.," The temporal evolution of model carina.dm is shown in figure 4, with the different panels and curves being totally analogous to those of figure 1."217 In. panel (a) we see the S£Iges. and the one used by the model. having very similar time structures. except for the total cessation in star forming activity. between the two main bursts assumed by the model. and not seen in the directly inferred star formation history.," In panel (a) we see the $SFR_{HGV}$, and the one used by the model, having very similar time structures, except for the total cessation in star forming activity between the two main bursts assumed by the model, and not seen in the directly inferred star formation history."218 This probably reflects second. order ellects. not contemplated by the simple modeling attempted here. which however. does include the broad. behaviour of the galaxy. and hence we expect to give valuable constraints on the physics of the evolution. if only at an approximate level.," This probably reflects second order effects, not contemplated by the simple modeling attempted here, which however, does include the broad behaviour of the galaxy, and hence we expect to give valuable constraints on the physics of the evolution, if only at an approximate level."219 In panel (b) we see that the average metallicity of the stars falls a little during the second. accretion. phase. which we take as being composed of primordial material.," In panel (b) we see that the average metallicity of the stars falls a little during the second accretion phase, which we take as being composed of primordial material."220 Again. the observed. metallicity range falls well within the eas metallicity during the two periods of star formation. so that our model comfortably accounts for the presence of a significant number of stars within the observed range.," Again, the observed metallicity range falls well within the gas metallicity during the two periods of star formation, so that our model comfortably accounts for the presence of a significant number of stars within the observed range."221 Panel (c) shows clearly how the star formation process is limited. by the appearance of galactic winds. once the thermal energv of the gas surpasses the gravitational potential energv.," Panel (c) shows clearly how the star formation process is limited by the appearance of galactic winds, once the thermal energy of the gas surpasses the gravitational potential energy."222 In Panel (d) we see the rates of the cdillerent types of SNea. with the memory of the first star formation episode alfecting the dynamics of the second. through the extended SNla rates.," In Panel (d) we see the rates of the different types of SNea, with the memory of the first star formation episode affecting the dynamics of the second, through the extended SNIa rates."223 Panel (ο) gives the cumulative amounts of stars and gas present. with the gas content being totally cleared. olf after the second wind.," Panel (e) gives the cumulative amounts of stars and gas present, with the gas content being totally cleared off after the second wind."224 This is seen in the final panel. where the two accretion phases and the two galactic winds are shown.," This is seen in the final panel, where the two accretion phases and the two galactic winds are shown."225 Leo Ll is very similar to Carina in its star formation history. this is rellectecd in the second set of models shown in table 2. where all numbers very closely follow what was obtained for Carina.," Leo I is very similar to Carina in its star formation history, this is reflected in the second set of models shown in table 2, where all numbers very closely follow what was obtained for Carina."226 In figure 5 we show the tempora evolution of model. ουσ., In figure 5 we show the temporal evolution of model leoi.dm.227 This figure again closely resembles the results of Carina. with the only cdillercnce being accordance in the predicted average metallicities an observed: values.," This figure again closely resembles the results of Carina, with the only difference being accordance in the predicted average metallicities and observed values."228 Our physical assumptions are shown to be consistent with observational data in predicting the tota clearing of the σας from this galaxy., Our physical assumptions are shown to be consistent with observational data in predicting the total clearing of the gas from this galaxy.229 Bowen et al. (, Bowen et al. (2301997) finc no gas around Leo | using three lines of sight towards distan QSOs. and searching for absorption features in the spectra.,"1997) find no gas around Leo I using three lines of sight towards distant QSOs, and searching for absorption features in the spectra."231 The values of fpi slightly. above unity. Le. the requirement of à core radius in the dark matter halo slightly above current observational estimates for the tidal radii of these systems. is totally consistent with the very recent dynamical studies of Ixlevna et. al. (," The values of $f_{DM}$ slightly above unity, i.e. the requirement of a core radius in the dark matter halo slightly above current observational estimates for the tidal radii of these systems, is totally consistent with the very recent dynamical studies of Kleyna et al. ("2322001) and the photomertic surveys of Odenkichen ct al. (,2001) and the photomertic surveys of Odenkichen et al. (2332001) viclcling precisely this conclusion.,2001) yielding precisely this conclusion.234 Llere the values of extra metal loss required. by. the models to agree with the ranges of observed. metallicities. are given by Asy.," Here the values of extra metal loss required by the models to agree with the ranges of observed metallicities, are given by $\Delta\gamma_Z$."235 We see that for Carina. in all cases. we require between and of metal expulsion for our models to agree with the data.," We see that for Carina, in all cases, we require between and of metal expulsion for our models to agree with the data."236 In the case of Leo 1. very little of this elfect is needed to agree with the upper limits of the measurements. although high. values of are again needed to reach the lower bound in the observed. metallicities.," In the case of Leo I, very little of this effect is needed to agree with the upper limits of the measurements, although high values of are again needed to reach the lower bound in the observed metallicities."237 In our treatment of Ursa Minor in section 3.1 we fixed our mocels in order to comply with S£Cge. however. as mentioned in the description of our method. the inference of LIGY loses all temporal resolution for ages greater than 10 Gyr.," In our treatment of Ursa Minor in section 3.1 we fixed our models in order to comply with $SFG_{HGV}$, however, as mentioned in the description of our method, the inference of HGV loses all temporal resolution for ages greater than 10 Gyr."238 In this wav. the time structure inferred for Ursa Minor. could well be only an artifact of the method.," In this way, the time structure inferred for Ursa Minor could well be only an artifact of the method."239 As remarked in the description of our present results for this ealaxy. the clement ratios we obtain are all similar to wha was obtained for Leo LL with values of O/Fe] always above about 0.2.," As remarked in the description of our present results for this galaxy, the element ratios we obtain are all similar to what was obtained for Leo II with values of [O/Fe] always above about 0.2."240 In comparing with the detailed observationa determinations for Ursa Minor. we find that for values of Η]ς- 1.6 our corresponding predictions for O/Fo] closely match observations for this galaxy.," In comparing with the detailed observational determinations for Ursa Minor, we find that for values of $<$ -1.6 our corresponding predictions for [O/Fe] closely match observations for this galaxy."241 On the other hand. the most metal-rich data point for Ursa Minor of Fe/L1]e-1.4 corresponds to an upper limit of O/Fe] 0.0.," On the other hand, the most metal-rich data point for Ursa Minor of $\approx$ -1.4 corresponds to an upper limit of [O/Fe] $\approx$ 0.0."242 Our single, Our single243There are two classes of persistent sources at cosniüc distances: galaxies and quasars/Active Calactic Nuclei (AGN).,There are two classes of persistent sources at cosmic distances: galaxies and quasars/Active Galactic Nuclei (AGN).244 Stars power galaxies while accretion outo and/or spin down of supermassive black holes power quasars., Stars power galaxies while accretion onto and/or spin down of supermassive black holes power quasars.245 τι. receutlv. ealactic and quasar phenomena were thought to be separate on both observational and theoretical grounds.," Until recently, galactic and quasar phenomena were thought to be separate on both observational and theoretical grounds."246" However. the discovery of the black hole mass — bulee stellar mass relation (Af,— AS.) iu nearby elliptical galaxies and the black hole mass stellar velocity dispersion relationteeinaineg2M. indicates that ealactic aud black hole activity are closely connected to one another."," However, the discovery of the black hole mass – bulge stellar mass relation $M_{\bullet}-M_{\star}$ ) in nearby elliptical galaxies and the black hole mass – stellar velocity dispersion relation indicates that galactic and black hole activity are closely connected to one another."247 The natural iuplication is that the energy release resulting from the »xiüld-up of the black hole mass limits auy further erowth of both the stellar bulge aud the black hole., The natural implication is that the energy release resulting from the build-up of the black hole mass limits any further growth of both the stellar bulge and the black hole.248" The fact hat the AJ,AZ, relation holds for nearlv four decades in black hole mass seecnis to suggest that aq""ieersal.sclf-sinilur oy process is at work. which acts ο self-regulate the ratio between black hole and bulge nass. irrespective of their combined mass."," The fact that the $M_\bullet-M_{\star}$ relation holds for nearly four decades in black hole mass seems to suggest that a, or process is at work, which acts to self-regulate the ratio between black hole and bulge mass, irrespective of their combined mass."249 Apparcutly. he only question that remains is with regard to the exact physical miechamisin responsible for black hole feedback and seltxegulation.," Apparently, the only question that remains is with regard to the exact physical mechanism responsible for black hole feedback and self-regulation."250 The aremuent. aloug with the work of?.. indicates hat the mass of supermassive black holes is mostly accrued ο an optically-huninous radiativelv-eficieut “quasar phase.”," The argument, along with the work of, indicates that the mass of supermassive black holes is mostly accrued during an optically-luminous radiatively-efficient “quasar phase.”"251" The energy released during the accretion oocess, Which is carried away primarily by photous and/or a “quasar wind.” may couple to the interstellaro uediu of the host galaxy aud eject it from the ealactic eravitational potential?)."," The energy released during the accretion process, which is carried away primarily by photons and/or a “quasar wind,” may couple to the interstellar medium of the host galaxy and eject it from the galactic gravitational potential."252. Tn doing so. fucl or any further galactfie aud 2227???quasar activity is removed. and the mass of the black hole. as well as of the stellar »ilee. is selt-Iuuited.," In doing so, fuel for any further galactic and quasar activity is removed and the mass of the black hole, as well as of the stellar bulge, is self-limited."253 The energy released during the accretion process lay ο carried away uot solely in the forme of photons., The energy released during the accretion process may be carried away not solely in the form of photons.254" Iu he so called ""radio-loud (as opposed to “racdio-quict™} 6jects. relativistic collumated outflows. or “jets.” put out a significant amount of enerev m mechanical form."," In the so called “radio-loud” (as opposed to “radio-quiet”) objects, relativistic collimated outflows, or “jets,” put out a significant amount of energy in mechanical form."255 Although radio-loud phenomena are also observed iu objects that are not actively accreting??7j.. the radio jet is more likely to affect the evolution of the system when a significant amount of mass is boiug built up.," Although radio-loud phenomena are also observed in objects that are not actively accreting, the radio jet is more likely to affect the evolution of the system when a significant amount of mass is being built up."256 As this work focuses on the selfreeulation of black hole growth. which occurs at high accretion rates. our itention rests on objects that are both siguificautlv accreting and racio-lIoud.," As this work focuses on the self-regulation of black hole growth, which occurs at high accretion rates, our attention rests on objects that are both significantly accreting and radio-loud."257" The kinetic power of radio jets is dissipated in sub-pc scale ""radio cores” aud kpe to AIpe scale “radio lobes.” with comparable amounts of energy dissipated at cach ste."," The kinetic power of radio jets is dissipated in sub-pc scale “radio cores” and kpc to Mpc scale “radio lobes,” with comparable amounts of energy dissipated at each site."258 The radio-loud quasar phase could be responsible for black hole selt-regulatiou if the cucrey release from the radio core. unlike that from the distant radio lobes. has the opportunity to couple to the interstellar medi of the host galaxy.," The radio-loud quasar phase could be responsible for black hole self-regulation if the energy release from the radio core, unlike that from the distant radio lobes, has the opportunity to couple to the interstellar medium of the host galaxy."259 , 260spectral tvpes were derived [rom visual classification (visual pattern matching of our smoothed program star spectra wilh standard star spectra) supported by quantitative analvsis of some spectral indices.,Spectral types were derived from visual classification (visual pattern matching of our smoothed program star spectra with standard star spectra) supported by quantitative analysis of some spectral indices.261 In (his section. we provide descriptions of (he absorption lines used to classifiv three broad groups. starting with the earliest spectral (wpe stars (D-À). moving to the F-IxX stars. ancl finally the AI stars.," In this section, we provide descriptions of the absorption lines used to classifiy three broad groups, starting with the earliest spectral type stars (B-A), moving to the F-K stars, and finally the M stars."262 We conclude the section. with a diseussion of eravitv-sensitive absorption features in the 5820-8700 sspectral range., We conclude the section with a discussion of gravity-sensitive absorption features in the 5820-8700 spectral range.263 For the purposes of matching spectral features with those of standard stars. our Ivdra spectra were smoothed using a gaussian filler to the resolution of the standaxd stars for direct comparison.," For the purposes of matching spectral features with those of standard stars, our Hydra spectra were smoothed using a gaussian filter to the resolution of the standard stars for direct comparison."264 All spectra have been normalized to 1 by dividing out a fit to the continuae. carefully. excluding regions with emission lines or broad absorption due to TiO and VO.," All spectra have been normalized to 1 by dividing out a fit to the continuae, carefully excluding regions with emission lines or broad absorption due to TiO and VO."265 Normalized spectra smoothled to a resolution of 5.7 aare shown in Fig., Normalized spectra smoothed to a resolution of 5.7 are shown in Fig.266 1 for a representative sample of program objects. wilh earlv-tvpe stars in Fig.," 1 for a representative sample of program objects, with early-type stars in Fig."267 la (B3-G9). IN stars in Fig.," 1a (B3-G9), K stars in Fig."268 Ib. early-to-micl M stars in Fig.," 1b, early-to-mid M stars in Fig."269 le. and mid-to-late M stars in Fig.," 1c, and mid-to-late M stars in Fig."270 ld., 1d.271 Both photospheric and telluric spectral features are labeled., Both photospheric and telluric spectral features are labeled.272 Two main sets of standards were used for classification (both qualitative and cuantitative)., Two main sets of standards were used for classification (both qualitative and quantitative).273 First. optical spectra from the WIYN/IIvcdra study of the Praesepe by Allen Strom (1995) were used to derive spectral types from Οδ) - ALLY. The effective resolution of these spectra was 5.7A.," First, optical spectra from the WIYN/Hydra study of the Praesepe by Allen Strom (1995) were used to derive spectral types from B8V - M4V. The effective resolution of these spectra was 5.7."274. For giants and later tvpe dwarls (AISV - M9V). optical spectra from the study of Ixirkpatrick. Ilenrv. AMeCarthy (1991) were used with an effective resolution of either 5 or 18A.," For giants and later type dwarfs (M5V - M9V), optical spectra from the study of Kirkpatrick, Henry, McCarthy (1991) were used with an effective resolution of either 8 or 18."275. In addition to these. optical spectra of very late (ype subgiants in IC 348 (Luhman 1999) and p Oph (Luhman. Liebert. Rieke 1997) were used for comparison with the coolest stars in our sample.," In addition to these, optical spectra of very late type subgiants in IC 348 (Luhman 1999) and $\rho$ Oph (Luhman, Liebert, Rieke 1997) were used for comparison with the coolest stars in our sample."276 For stars ealier (han DSV. we referred to the spectral atlas of and Weaver (1993).," For stars ealier than B8V, we referred to the spectral atlas of Torres-Dodgen and Weaver (1993)."277 Absorption lines [rom the Balmer (n22) and Paschen (1=3) series of hvdrogen are prominent in (he spectra of early (vpe stus., Absorption lines from the Balmer (n=2) and Paschen (n=3) series of hydrogen are prominent in the spectra of early type stars.278 In our spectra. we see tnblenced absorption lines from Ha (6563 À)) and Paschen 14 (8598 A)) (see Fig.," In our spectra, we see unblended absorption lines from $\alpha$ (6563 ) and Paschen 14 (8598 ) (see Fig."279 la) that reach a maximum around AO ancl weaken in warmer stars., 1a) that reach a maximum around A0 and weaken in warmer stars.280 The Ca II triplet (S498À.. 8542Α.. 8662 À)) is also observed aud decreases in strength toward early-(wpe stars until overtaken by Pa 16. 15. and 13(8502AÀ..8545A.. and 8665À)).," The Ca II triplet (8498, 8542, 8662 ) is also observed and decreases in strength toward early-type stars until overtaken by Pa 16, 15, and 13, and )."281 lence an F2 star may have a similar EWí(l1la) as a D5 star. but will be distinct by displaving stronger absorption from the Ca II triplet.," Hence an F2 star may have a similar $\alpha$ ) as a B5 star, but will be distinct by displaying stronger absorption from the Ca II triplet."282 We note that all of the alorementioned lines can appear in emission. aud (hat the observed absorption line strengths could be lower limits to the true strengths.," We note that all of the aforementioned lines can appear in emission, and that the observed absorption line strengths could be lower limits to the true strengths."283 We estimate that the uncertainties, We estimate that the uncertainties284 (Zwicky (c.g...Fabricautetal.1980)..," \citep[e.g.,][and references285therein]{cirsmf,rines08,vikhlinin09b,henry09,mantz08,rozo08}."286 1972).. (e.g.Majumdar&Moblr2001).. (Ixravtsov2008).," \citep[][]{zwicky1937} \citep[e.g.,][]{flg80}, \citep[e.g.,][]{smith05,richard10}, \citep[SZE][]{sz72}. \citep[e.g.,][]{majumdar04}. \citep[][]{kravtsov06,rozo08}."287. (Nagaictal.2007) (Motletal.2005) 2008)..," \citep{nagai07} \citep{motl05} \citep[e.g.,][]{henry09,lopes09b,mantz09b,locutushuang09}. ,"288 aud recent results from hydrodynamical simulations indicate that virial masses may have scatter as snall as ~5% (Lauctal.2010)., and recent results from hydrodynamical simulations indicate that virial masses may have scatter as small as $\sim$ \citep{lau10}.289.. Previous studies lave compared SZE signals to lydrostatic X-ray masses (Bonamenteetal.2008:Plageeetal.2010) and gravitational lensing masses (ALarroueetal.2009.hereafter AIO9).," Previous studies have compared SZE signals to hydrostatic X-ray masses \citep{bonamente08,plagge10} and gravitational lensing masses \citep[][hereafter M09]{marrone09}."290. Here. we make the first conrparison between virial masses of galaxy clusters and their SZE signals.," Here, we make the first comparison between virial masses of galaxy clusters and their SZE signals."291 We use SZE measurements from the literature and newly-measured virial masses of 15 clusters from extensive MIAIT/Tectospec spectroscopy., We use SZE measurements from the literature and newly-measured virial masses of 15 clusters from extensive MMT/Hectospec spectroscopy.292 This comparison tests the robustuess of the SZE as a proxy for cluster mass and the physical relatiouship between the SZE sienal and cluster mass., This comparison tests the robustness of the SZE as a proxy for cluster mass and the physical relationship between the SZE signal and cluster mass.293 Large SZ cluster surveys are underway aud are begining to vield cosmological constraints (Carlstrometal.2010:IBucksetal.2010:Staniszewskiot 2009).," Large SZ cluster surveys are underway and are beginning to yield cosmological constraints \citep{carlstrom10,hincks10,staniszewski09}."294". We assune a cosinoloey of 0,,20.3. O4-—0.7. aud Πιτ kins + + for all cealeulatious."," We assume a cosmology of $\Omega_m$ =0.3, $\Omega_\Lambda$ =0.7, and $H_0$ =70 km $^{-1}$ $^{-1}$ for all calculations."295 We are completing the Hectospec Cluster Survey (IleCS). a study of an N-vayv flux-limited sample of 53 ealaxy clusters at moderate redshift with extensive spectroscopy from ADIT/Iectospec.," We are completing the Hectospec Cluster Survey (HeCS), a study of an X-ray flux-limited sample of 53 galaxy clusters at moderate redshift with extensive spectroscopy from MMT/Hectospec."296 HeCS includes all clusters with ROSAT X-ray fluxes of fy>5«10 Pere tat [0.5-2.0]keV from the Bright Cluster Survey Ebelingetal.L998) or REPLEN siuvex (Bohringerctal.2001) with optical imaging in the Sixth. Data Release (DRG) of SDSS (Adchluan-AIcCarthyetal.2008)., HeCS includes all clusters with ROSAT X-ray fluxes of $f_X>5\times10^{-12}$ erg $^{-1}$ at [0.5-2.0]keV from the Bright Cluster Survey \citep[BCS][]{bcs} or REFLEX survey \citep{reflex} with optical imaging in the Sixth Data Release (DR6) of SDSS \citep{dr6}.297. We use DR6 photometry to select IHectospec targets., We use DR6 photometry to select Hectospec targets.298 The ITeCS targets are allbrighter than r=20.8 (SDSS catalogs are coniplete for point sources to 722.2)., The HeCS targets are allbrighter than $r$ =20.8 (SDSS catalogs are complete for point sources to $r$$\approx$ 22.2).299 Out of the Πος5 siuuple. 15 clusters have published SZ measurements.," Out of the HeCS sample, 15 clusters have published SZ measurements."300(oxvgen is a typical a-clement) for several models: as one can see. modela2e.. with the vields by HNV02.. predicts exactly the same behaviour of the O/Ec] ratio as model (standard case withot pair-creation SNe) except for the very carly phases.,"(oxygen is a typical $\alpha$ -element) for several models: as one can see, model, with the yields by HW02, predicts exactly the same behaviour of the [O/Fe] ratio as model (standard case withot pair-creation SNe) except for the very early phases."301 The case with poplll pair- creation SNe and LIWO2 vields. in fact. starts with a quite lower O/Fe] ratio. relative to the standard case. due to the fact that pair creation SNe favor the xoduction of Fe (at variance with the results of OFES3).," The case with popIII pair- creation SNe and HW02 yields, in fact, starts with a quite lower [O/Fe] ratio, relative to the standard case, due to the fact that pair creation SNe favor the production of Fe (at variance with the results of OFE83)."302 This ratio stavs constant while the οΗ] decreases and then increases to reach the value of the stancard case when the pair-creation supernovae disappear., This ratio stays constant while the [Fe/H] decreases and then increases to reach the value of the standard case when the pair-creation supernovae disappear.303 This inversion in case is due to the presence of infall of material of primordial chemical composition., This inversion in case is due to the presence of infall of material of primordial chemical composition.304 In fact. when the first very massive stars die. the ΠΟΠΗ] in the ISM jumps immediately at the value of be/LJ=-1.0 but soon this value decreases due to the infalling gas.," In fact, when the first very massive stars die, the [Fe/H] in the ISM jumps immediately at the value of [Fe/H]=-1.0 but soon this value decreases due to the infalling gas."305 Model is the equivalent of the standard model without infall (CB)., Model is the equivalent of the standard model without infall (CB).306 In this case. the model predicts a lower O/Fe] ratio at the beginning which increases later on. but no inversion in the Le/Ll].," In this case, the model predicts a lower [O/Fe] ratio at the beginning which increases later on, but no inversion in the [Fe/H]."307 In figure 2 we show {1e same plot of O/Fe] vs. ο] for the models ancl bl (shown again for comparison)., In figure 2 we show the same plot of [O/Fe] vs. [Fe/H] for the models and b1 (shown again for comparison).308 Model cilfers from mocel only for the nucleosvnthesis in pair-creation SNe. which is [rom OFES3.," Model differs from model only for the nucleosynthesis in pair-creation SNe, which is from OFE83."309 One can inimediately. notice the large dilference in the predictions of the two models: model predicts a very high oxveen overabundance relative to Fe in the very carly phases. due to the lack of Fe-peak elements in the ΟΙΤΗ vields.," One can immediately notice the large difference in the predictions of the two models: model predicts a very high oxygen overabundance relative to Fe in the very early phases, due to the lack of Fe-peak elements in the OFE83 yields."310 1n Figure 3 we show the O/Fe] vs. Fe/l for the strongly bimodal star formation cases (only very massive stars in the early phases) lasting for 0.1. Gar., In Figure 3 we show the [O/Fe] vs. [Fe/H] for the strongly bimodal star formation cases (only very massive stars in the early phases) lasting for 0.1 Gyr.311 Models. (yields IIWO2) and. (sields UN) show a rather constant O/Fc] ratio over the whole Fel] range., Models (yields HW02) and (yields UN) show a rather constant [O/Fe] ratio over the whole [Fe/H] range.312 This is due to the fact that the very massive pop LLL stars. in the most. recent nucleosvnthesis calculations. produce an almost solar O/Lc ratio and this will predominate also in the subsequent evolution.," This is due to the fact that the very massive pop III stars, in the most recent nucleosynthesis calculations, produce an almost solar O/Fe ratio and this will predominate also in the subsequent evolution."313 On the other hand. model shows a very high oxvgen overabundance relative to Fe. again due to the lack of Fe-peak elements in the vields of OEESS.," On the other hand, model shows a very high oxygen overabundance relative to Fe, again due to the lack of Fe-peak elements in the yields of OFE83."314 The other models not included in the Figure. where the pop LL stars form only for a very short time interval (0.01 Gyr) do not produce noticeable dillerences in the results relative to the standard el moclel.," The other models not included in the Figure, where the pop III stars form only for a very short time interval (0.01 Gyr) do not produce noticeable differences in the results relative to the standard $a1$ model."315 While the abundances in Figures |. 2 and 3 refer to the eas. in Figures 4 and 5 we show the predicted distributions of stars as functions of Fe/1] for models -age.52s. ese adc.," While the abundances in Figures 1, 2 and 3 refer to the gas, in Figures 4 and 5 we show the predicted distributions of stars as functions of [Fe/H] for models -, - ."316 In models afe-- the predicted stellar distributions are almost indistinguishable except for the absence of stars with Fe/L]«3.0 in the case with pop ILE stars., In models - the predicted stellar distributions are almost indistinguishable except for the absence of stars with $<-3.0$ in the case with pop III stars.317 Ehe reason [or this resides in the fact that the pop LL phase is very short and at the same time the star formation rate is small at carly stages when there is little gas., The reason for this resides in the fact that the pop III phase is very short and at the same time the star formation rate is small at early stages when there is little gas.318 In the closed-box cases (models and 62)) the dillerence is more noticeable since at the beginning the star formation is quite high., In the closed-box cases (models and ) the difference is more noticeable since at the beginning the star formation is quite high.319 In both models. in fact. no stars with metallicity lower than -3.0 ancl -2.0. respectively. are predicted (sce Figure 4).," In both models, in fact, no stars with metallicity lower than -3.0 and -2.0, respectively, are predicted (see Figure 4)."320 The, The321relativistic Cengine-«driven) supernovae (e.g. Chakrabortietal.301001.,relativistic (`engine-driven') supernovae (e.g. \citealt{Chakraborti+10}) ).322 The arrival directions of UHECRs provide a potentially important probe of their origin., The arrival directions of UHECRs provide a potentially important probe of their origin.323 Measurements by the Pierre Auger Observatory (PAO) rule out isotropy for the highest energy cosmic rays at ~98% confidence (Armengaud20050). and PAO has furthermore discovered a correlation between the arrival directions of UHECRs with energies E>57 EeV and nearby εἰς75 Mpc) AGN (Abrahametal. 2008)).," Measurements by the Pierre Auger Observatory (PAO) rule out isotropy for the highest energy cosmic rays at $\sim98\%$ confidence \citealt{Armengaud+08}) ), and PAO has furthermore discovered a correlation between the arrival directions of UHECRs with energies $E > 57$ EeV and nearby $\lesssim 75$ Mpc) AGN \citealt{Abraham+08}) )."324 This result does not. however. imply that UHECRSs necessarily originate from AGN. because AGN trace local Galactic structure. such that the correlation is consistent with a variety of other sources (Kashti&Waxman2008:: Ghisellinietal. 2008:: Takamietal. 2009:: Takami&Sato2009)).' At present the sources of UHECR cannot therefore be deduced from their arrival directions alone.," This result does not, however, imply that UHECRs necessarily originate from AGN, because AGN trace local Galactic structure, such that the correlation is consistent with a variety of other sources \citealt{Kashti&Waxman08}; \citealt{Ghisellini+08}; \citealt{Takami+09}; \citealt{Takami&Sato09}) At present the sources of UHECR cannot therefore be deduced from their arrival directions alone."325 The composition of UHECRs also provides important clues to their origin., The composition of UHECRs also provides important clues to their origin.326" Although the composition is measured directly at low energies €x10"" eV). at ultra-high energies it must be inferred indirectly by measuring the shower depth at maximum elongation Xy."," Although the composition is measured directly at low energies $\lesssim 10^{14}$ eV), at ultra-high energies it must be inferred indirectly by measuring the shower depth at maximum elongation $X_{\rm max}$."327" Recent measurements by PAO show that the average shower depth (X4,) and its RMS variation decrease systematically moving to the highest energies (Abrahametal.2010).", Recent measurements by PAO show that the average shower depth $\langle X_{\rm max} \rangle$ and its RMS variation decrease systematically moving to the highest energies \citep{Abraham+10}.328. This suggests that the UHECR composition transitions from being dominated by protons below the ankle to being dominated by heavier nuclei with average masses similar to Si or Fe at ~5x10! eV. We caution. however. that HiRes has not verified this finding (Abbasietal.2008).," This suggests that the UHECR composition transitions from being dominated by protons below the ankle to being dominated by heavier nuclei with average masses similar to Si or Fe at $\sim 5\times 10^{19}$ eV. We caution, however, that HiRes has not verified this finding \citep{Abbasi+05}."329 The UHECR composition measured by Auger is puzzling., The UHECR composition measured by Auger is puzzling.330" One possible explanation is that the accelerated material has an intrinsically ""mixed"" composition (with e.g. solar abundances). such that protons are accelerated to a maximum energy E=Esma~10? eV. beyond which only heavier nuclei are accelerated."," One possible explanation is that the accelerated material has an intrinsically `mixed' composition (with e.g. solar abundances), such that protons are accelerated to a maximum energy $E = E_{\rm p,max} \sim 10^{18.5}$ eV, beyond which only heavier nuclei are accelerated."331 This seems plausiblepriori because accelerator size considerations show that the maximum achievable energy increases linearly with the nuclear charge Z (Hillas1984)., This seems plausible because accelerator size considerations show that the maximum achievable energy increases linearly with the nuclear charge $Z$ \citep{Hillas84}.332. On the other hand. this explanation appears to require fine tuning because the maximum energy to which. for instance. Fe nuclei are accelerated Eia~ZXEpnay8XLo (Z/26) eV must (by coincidence) be close to the cut-off observed at ~6x10! eV and expected to occur independently from the GZK ettect.," On the other hand, this explanation appears to require fine tuning because the maximum energy to which, for instance, Fe nuclei are accelerated $E_{\rm Fe,max} \sim Z\times E_{\rm p,max} \sim 8\times 10^{19}$ (Z/26) eV must (by coincidence) be close to the cut-off observed at $\sim 6\times 10^{19}$ eV and expected to occur independently from the GZK effect."333 A “mixed” composition with metal abundance ratios similar to the Sun or Galactic cosmic rays also appears inconsistent with modeling of the propagation of UHECRs through the EBL (Allardetal. 2008). which suggest that the injected composition has a fairly narrow distribution in charge (e.g. Hooper&Taylor 2010).," A `mixed' composition with metal abundance ratios similar to the Sun or Galactic cosmic rays also appears inconsistent with modeling of the propagation of UHECRs through the EBL \citealt{Allard+08}) ), which suggest that the injected composition has a fairly narrow distribution in charge (e.g. \citealt{Hooper&Taylor10}) )."334 A second possibility is that the accelerated material is dominated by heavy nuclei., A second possibility is that the accelerated material is dominated by heavy nuclei.335 In this case the proton-dominated composition measured near the ankle may be explained as secondary particles produced by the interaction of the nuclei with the EBL (e.g. Hooper&Taylor 20101)., In this case the proton-dominated composition measured near the ankle may be explained as secondary particles produced by the interaction of the nuclei with the EBL (e.g. \citealt{Hooper&Taylor10}) ).336 A heavy-rich composition is unlikely in the case of AGN. galaxy clusters. and supernova shocks because the accelerated material originates from the interstellar medium.," A heavy-rich composition is unlikely in the case of AGN, galaxy clusters, and supernova shocks because the accelerated material originates from the interstellar medium."337 For a solar composition. the fraction of the total mass in Fe nuclei and heavier is just Xi;~LOὃς such that only for extremely super-solar metallicity (~10?Z;) could heavy nuclei dominate the total UHECR mass.," For a solar composition, the fraction of the total mass in Fe nuclei and heavier is just $X_{\rm Fe} \sim 10^{-3}$, such that only for extremely super-solar metallicity $\sim 10^{3} Z_{\odot}$ ) could heavy nuclei dominate the total UHECR mass."338 In this paper we show that UHECRs from GRBs. unlike AGN. may indeed be composed of almost entirely very heavy nuclei.," In this paper we show that UHECRs from GRBs, unlike AGN, may indeed be composed of almost entirely very heavy nuclei."339 In particular. if the outflow from the central engine is strongly magnetized we find that Fe-group nuclei and possibly heavier elements (A > 90) are synthesized during its expansion.," In particular, if the outflow from the central engine is strongly magnetized we find that Fe-group nuclei and possibly heavier elements (A $\gtrsim$ 90) are synthesized during its expansion."340 Although it is well established that long duration GRBs originate from the core collapse of massive stars Woosley&Bloom2006).. it remains debated whether the central engine is a hyper-aeereting black hole (Woosley1993) ora rapidly spinning. strongly magnetized neutron star (à proto-magnetar: e.g. Usov1992)).," Although it is well established that long duration GRBs originate from the core collapse of massive stars \citep{Woosley&Bloom06}, it remains debated whether the central engine is a hyper-accreting black hole \citep{Woosley93} or a rapidly spinning, strongly magnetized neutron star (a `proto-magnetar'; e.g. \citealt{Usov92}) )."341 We focus here on the proto-magnetar model. which recent work has shown can explain many of the observed properties of GRBs (Thompsonetal.2004:: Metzgeretal.2007:: Bucciantinietal.2007:: Metzgeretal.2010).," We focus here on the proto-magnetar model, which recent work has shown can explain many of the observed properties of GRBs \citealt{Thompson+04}; \citealt{Metzger+07}; \citealt{Bucciantini+07}; \citealt{Metzger+10}) )."342 However. similar considerations may apply to acecretion-powered models. provided that the jet is magnetically-dominated rather than a thermally-driven fireball ($2.2).," However, similar considerations may apply to accretion-powered models, provided that the jet is magnetically-dominated rather than a thermally-driven fireball $\S\ref{sec:BH}$ )."343 The high temperatures 7> | MeV near the central engine imply that all nuclei are dissociated into free neutrons and protons., The high temperatures $T >$ 1 MeV near the central engine imply that all nuclei are dissociated into free neutrons and protons.344 Heavier elements form only once lower temperatures and densities are reached at larger radii in the outflow., Heavier elements form only once lower temperatures and densities are reached at larger radii in the outflow.345" If the outflow forms as a fireball dominated by thermal energy (as would occur if the jet is powered by neutrino annihilation along the rotational axis: e.g. Eichleretal. 1989)). its entropy is necessarily high S.>10"" &, '."," If the outflow forms as a fireball dominated by thermal energy (as would occur if the jet is powered by neutrino annihilation along the rotational axis; e.g. \citealt{Eichler+89}) ), its entropy is necessarily high $S \gtrsim 10^{5}$ $k_{\rm b}$ $^{-1}$."346 Free nuclei recombine into Helium only once the deuterium bottleneck is broken., Free nuclei recombine into Helium only once the deuterium bottleneck is broken.347 Since this occurs at low densities when the entropy is high. few elements heavier than He are formed. similar to Big Bang nucleosynthesis (Lemoine2002:: Beloborodov 2003).," Since this occurs at low densities when the entropy is high, few elements heavier than He are formed, similar to Big Bang nucleosynthesis \citealt{Lemoine02}; \citealt{Beloborodov03}) )."348 Pure fireballs are therefore unlikely to produce jets enriched in heavy elements., Pure fireballs are therefore unlikely to produce jets enriched in heavy elements.349 The situation is different if the jet is accelerated magnetically. as occurs from proto-magnetars or magnetized accretion disk winds.," The situation is different if the jet is accelerated magnetically, as occurs from proto-magnetars or magnetized accretion disk winds."350" In this case most of the energy is stored in the magnetic field (Poynting flux) at small radii and the flow has a much lower entropy S.-LO—300K, ! (see Fig."," In this case most of the energy is stored in the magnetic field (Poynting flux) at small radii and the flow has a much lower entropy $S \sim 10-300\,k_{\rm b}$ $^{-1}$ (see Fig."351 |. and eg. [IT] , \ref{fig:wind} and eq. \ref{eq:SNRNM}] ]352below)., below).353 Under these conditions Helium recombination occurs at higher densities. such that heavier nuclei can be formed efficiently via e.g. the triple-a reaction and subsequent a captures.," Under these conditions Helium recombination occurs at higher densities, such that heavier nuclei can be formed efficiently via e.g. the $\alpha$ reaction and subsequent $\alpha$ captures."354 Below we focus on the nucleosynthesis in proto-magnetar winds because the outflow properties can be calculated with relative contidence (Metzgeretal.2010):: however. in $2.2 we briefly discuss the composition of accretion-powered outflows.," Below we focus on the nucleosynthesis in proto-magnetar winds because the outflow properties can be calculated with relative confidence \citep{Metzger+10}; however, in $\S\ref{sec:BH}$ we briefly discuss the composition of accretion-powered outflows."355 When a massive star runs out of nuclear fuel. its core undergoes gravitational collapse.," When a massive star runs out of nuclear fuel, its core undergoes gravitational collapse."356" This results in a hot ""proto-neutron' star (proto-NS). which radiates the energy released during the collapse in neutrinos (e.g. Burrows&Lattimer |986))."," This results in a hot `proto-neutron' star (proto-NS), which radiates the energy released during the collapse in neutrinos (e.g. \citealt{Burrows&Lattimer86}) )."357 As neutrinos escape. they heat the material above the proto-NS surface. potentially powering a supernova (SN) explosion during the first few hundred milliseconds after core bounce (e.g. Bethe&Wilson 19855).," As neutrinos escape, they heat the material above the proto-NS surface, potentially powering a supernova (SN) explosion during the first few hundred milliseconds after core bounce (e.g. \citealt{Bethe&Wilson85}) )."358 However. regardless of how the star explodes. if the core does not collapse into a black hole. neutrinos continue to heat the proto-NS atmosphere on longer timescales t ~|—100 s. This drives mass from the proto-NS into the expanding cavity behind the outgoing," However, regardless of how the star explodes, if the core does not collapse into a black hole, neutrinos continue to heat the proto-NS atmosphere on longer timescales t $\sim 1-100$ s. This drives mass from the proto-NS into the expanding cavity behind the outgoing"359some of these sources. a change in the column density of the absorber. rather than a switchingolf of the source. cannot be completely ruled. out. ancl indeed. Hisaliti ct al. (,"some of these sources, a change in the column density of the absorber, rather than a switching–off of the source, cannot be completely ruled out, and indeed Risaliti et al. ("3602002) claimed that variations in the absorbing column densitv are common in Sevfert. 2 galaxies.,2002) claimed that variations in the absorbing column density are common in Seyfert 2 galaxies.361 However. the changing absorbers in the Risaliti et al. (," However, the changing absorbers in the Risaliti et al. ("3622002) sample are all Comptonthin. and in most cases the variations are too small to rule out the possibility that they are an artifact due to comparing spectra obtained: with dilleren instruments.,"2002) sample are all Compton–thin, and in most cases the variations are too small to rule out the possibility that they are an artifact due to comparing spectra obtained with different instruments."363 Moreover. this solution is clearly untenable for GC 2992 (Cail et al.," Moreover, this solution is clearly untenable for NGC 2992 (Gilli et al."364 2000: see Sec., 2000; see Sec.365 2.4). which has been well monitored over the vears. showing a gradual change of 10 nuclear [lux and a costant absorber.," 2.4), which has been well monitored over the years, showing a gradual change of the nuclear flux and a costant absorber."366 We find. cillieul o imagine a situation in which a Comptonthick absorber on the pescale (as suggeste by the lack of variability. of e reflection components) and. with a large covering factor (to allow for the rather large reflection components) can Pvary so dramatically on timescales of vears., We find difficult to imagine a situation in which a Compton–thick absorber on the pc–scale (as suggested by the lack of variability of the reflection components) and with a large covering factor (to allow for the rather large reflection components) can vary so dramatically on time–scales of years.367 Pherefore. in 1e following we will assume that the observed. variations re due to the switchingolf of the nucleus.," Therefore, in the following we will assume that the observed variations are due to the switching–off of the nucleus."368 After reviewing jo current observation status of this field (Sect., After reviewing the current observation status of this field (Sect.369 2). we will discuss some possible implications (Sect.," 2), we will discuss some possible implications (Sect."370 3), 3).371 UGC 4203 (a.k.a., UGC 4203 (a.k.a.372 Mkn 1210) has been recently observed by NAIALNewton (Guainazzi ct al., Mkn 1210) has been recently observed by XMM–Newton (Guainazzi et al.373 2002). unveiling a XNταν bright nucleus. absorbed by Ny2«1077 em7.," 2002), unveiling a X–ray bright nucleus, absorbed by $N_H \simeq 2 \times 10^{23}$ $^{-2}$."374 Llowever. in an ASCA observation performed about five and half vears earlier (Awaki et al.," However, in an ASCA observation performed about five and half years earlier (Awaki et al."375 2000). the prominent iron line 1 keV) and the factor of 5 lower 210 keV [ux indicated a rellection.dominated spectrum. (Fig. 5)).," 2000), the prominent iron line $EW \simeq 1$ keV) and the factor of 5 lower 2–10 keV flux indicated a reflection–dominated spectrum (Fig. \ref{polittico}) ),"376 with the nuclear emission too faint to be visible., with the nuclear emission too faint to be visible.377 The limited. bandpass of ASCA. along with the low Ilux of the source. does not permit to distinguish bewteen different column densities of the rellecting matter. provided that it exceeds about 107 7 (see Fie. 4)).," The limited bandpass of ASCA, along with the low flux of the source, does not permit to distinguish bewteen different column densities of the reflecting matter, provided that it exceeds about $10^{23}$ $^{-2}$ (see Fig. \ref{refl}) )."378 Ht is therefore possible that in this case the absorbing and rellecting materials are one and the same., It is therefore possible that in this case the absorbing and reflecting materials are one and the same.379 NGC 6300. discovered: serendipitouslv by (Awaki et al.," NGC 6300, discovered serendipitously by (Awaki et al."380 1991). was observed in a Comptonthick rellection-dominated state by RAPE on February 1997 (Leighly et al.," 1991), was observed in a Compton–thick reflection-dominated state by RXTE on February 1997 (Leighly et al."381 1999)., 1999).382 Two and half vears later a remarkably strong Seviert nucleus (210 keV Hux ~1.3.10.+ erg em7s +) seen through a column density with Nyc21075 en7 (Fig. 5)).," Two and half years later a remarkably strong Seyfert nucleus (2–10 keV flux $\sim 1.3 \times 10^{-11}$ erg $^{-2}$ $^{-1}$ ) seen through a column density with $N_H \simeq 2 \times 10^{23}$ $^{-2}$ (Fig. \ref{polittico}) ),"383 was discovered. in a BeppoSAN observation., was discovered in a BeppoSAX observation.384 An XMMNewton observation performed carly in. 2001 caught the source still in the high lux. Comptonthin state (Maclelox et al.," An XMM–Newton observation performed early in 2001 caught the source still in the high flux, Compton–thin state (Maddox et al."385 2002)., 2002).386 As the RAPE bandpass extends up to 20 keV. for this source jt is possible to distinguish between Comptonthin and Comptonthick reflection (Fig. 4)).," As the RXTE bandpass extends up to 20 keV, for this source it is possible to distinguish between Compton–thin and Compton–thick reflection (Fig. \ref{refl}) )."387 The detection in the PCA highest energy. band is too strong to be explained as pure reflection by matter with Ny&2107 7., The detection in the PCA highest energy band is too strong to be explained as pure reflection by matter with $N_H\simeq 2 \times 10^{23}$ $^{-2}$.388 In this case. therefore. the (thick) reflector must be dillerent from the (thin) absorber.," In this case, therefore, the (thick) reflector must be different from the (thin) absorber."389 A BeppoSAX observation on August 1997 detected in this source a bright Sevfert nucleus. seen through a Comptonthin (Ngc41077: Risaliti et al.," A BeppoSAX observation on August 1997 detected in this source a bright Seyfert nucleus, seen through a Compton--thin $N_H \simeq 4 \times 10^{23}$$^{-2}$; Risaliti et al."390 2000) absorber., 2000) absorber.391 On the contrary. an ASCA observation. performed three vears earlier. detected a very [lat X-ray continuum (E2 0.8) and a 2.1 keV We iron line. both indicating a rellection.dominated state (Fie. 5)).," On the contrary, an ASCA observation, performed three years earlier, detected a very flat X-ray continuum $\Gamma \simeq 0.8$ ) and a 2.1 keV $\alpha$ iron line, both indicating a reflection–dominated state (Fig. \ref{polittico}) )."392 Due to the limited bandwidth of ASCA. and similarly to UGC 4203. the possibility that the reflector. is simply the inner wall of the absorber cannot be ruled out.," Due to the limited bandwidth of ASCA, and similarly to UGC 4203, the possibility that the reflector is simply the inner wall of the absorber cannot be ruled out."393 The brightest anc best studied source in our little sample is NGC 2992. a Sevlert 1.9 galaxy with an X.ταν absorbing column clensity Ng9107 ?.," The brightest and best studied source in our little sample is NGC 2992, a Seyfert 1.9 galaxy with an X–ray absorbing column density $_{H}\sim9\times10^{21}$ $^{-2}$ ."394 The Xrav Dux of NGC 2992 steadily declined since LOTS. when it was observed," The X–ray flux of NGC 2992 steadily declined since 1978, when it was observed"395on identified clusters from ??????.. ,"on identified clusters from \cite{2001AJ....122.1796M, 2002ChJAA...2..197M, 2002AJ....123.3141M,396 2002AcA....52..453M, 2004ChJAA...4..125M, 2004A&A...413..563M}."397The SM catalogue contains 595 objects of which 428 are classified as high-confidence clusters (based on7/9T and high-resolution ground-based imaging)., The SM catalogue contains 595 objects of which 428 are classified as high-confidence clusters (based on and high-resolution ground-based imaging).398 The most recent work. currently not within the SM catalogue. includes work based on CFIUT/MeeaCam imagingby ? and? and JST imagine by ?.. thal contain 3554. 599 and 91 new star cluster candidates. respectively. (," The most recent work, currently not within the SM catalogue, includes work based on CFHT/MegaCam imagingby \cite{2008AcA....58...23Z} and \cite{2010arXiv1007.1042S} and $HST$ imaging by \cite{2009AcA....59...47Z}, that contain 3554, 599 and 91 new star cluster candidates, respectively. ("399All of these M33 studies cover only the inner one square degree.),All of these M33 studies cover only the inner one square degree.)400 ? claim that. 222054. of the 3554 cluster candidates identified in ? are likely to be genuine clusters.," \cite{2009AcA....59...47Z}401 claim that $\approx$ $\%$ of the 3554 cluster candidates identified in \cite{2008AcA....58...23Z} are likely to be genuine clusters."402 Unlike the GCSs of the MW and M31. AI33 is host to intermediate-age clusters (?2).. suggesting that the evolution of M33 was ditferent rom that of both the MW or M3I.," Unlike the GCSs of the MW and M31, M33 is host to intermediate-age clusters \citep{1998ApJ...508L..37S, 2002ApJ...564..712C}, suggesting that the evolution of M33 was different from that of both the MW or M31."403 Studying the Local Group gives us the best chance to observe the remnants of galaxy formation in detail. but. M33 remains to be scrutinized in as much detail as either of its larger neighboring galaxies. or the Magellanic Clouds.," Studying the Local Group gives us the best chance to observe the remnants of galaxy formation in detail, but M33 remains to be scrutinized in as much detail as either of its larger neighboring galaxies, or the Magellanic Clouds."404 The work on the M33 GCS has so [ar been constrained to the classical disk regions. with the exception of the four outer halo clusters found by ? between projected radii of 9.6 and 28.5 kpe and one cluster by ? al a projected radius of 12.5 kpc.," The work on the M33 GCS has so far been constrained to the classical disk regions, with the exception of the four outer halo clusters found by \cite{2009ApJ...698L..77H} between projected radii of 9.6 and 28.5 kpc and one cluster by \cite{2008AJ....135.1482S} at a projected radius of 12.5 kpc."405 The outer halo clusters ave important. not least because the most distant clusters may be the last that were accreted (e.g.. 2)).," The outer halo clusters are important, not least because the most distant clusters may be the last that were accreted (e.g., \citealt{2005MNRAS.360..631M}) )."406 ? have shown that AI3I's outer halo is rich with clusters., \cite{2010ApJ...717L..11M} have shown that M31's outer halo is rich with clusters.407 ? undertook a search for M33 outer halo clusters through 12 sq., \cite{2009ApJ...698L..77H} undertook a search for M33 outer halo clusters through 12 sq.408 degrees of the Isaac Newton Telescope Wide-Field Camera data reaching to Ve-24.5 and 123.5., degrees of the Isaac Newton Telescope Wide-Field Camera data reaching to $\sim$ 24.5 and $\sim$ 23.5.409 The PÁndAS data allow this search to be extended to larger τας. deeper depths aud better image quality.," The PAndAS data allow this search to be extended to larger radii, deeper depths and better image quality."410 This is the project that we undertake in (his paper., This is the project that we undertake in this paper.411 We define outer halo clusters to be those which are projected bevond the isophotal radius of M33 (ο kpc. 2)).," We define outer halo clusters to be those which are projected beyond the isophotal radius of M33 $\sim$ 9 kpc, \citealt{2011Cockcroftinprep}) )."412 Such objects are sufficiently. remote Chat they are unlikely to be associated with the main disk component of the ealaxv: ? find little evidence Irom clirect stellar photometry that the disk extends bevond (hat point., Such objects are sufficiently remote that they are unlikely to be associated with the main disk component of the galaxy: \cite{2010ApJ...723.1038M} find little evidence from direct stellar photometry that the disk extends beyond that point.413 For comparison. the isophotal radius of NGC 253. an Sc-tvpe galaxy of similar size. is re9.8 kpe (?).. ," For comparison, the isophotal radius of NGC 253, an Sc-type galaxy of similar size, is $r \sim 9.8$ kpc \citep{2003AJ....125..525J}. ."414Ultimately however. we will require metallicity ancl velocity measurements to determine more definitely," Ultimately however, we will require metallicity and velocity measurements to determine more definitely"415" Johansenetal.(2006a.2007)and Balsaraetal.(2009)..(Jin1996;Sano&Mivama 1999)..Atthesametime.erowthwavelenethbecomes Sanoetal.(1993)..Thevfoundthatsustained.MIIDturbulencerequiresthemagneticionized).. 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\tikzmark{mainBodyCitationStart607}\citet{lyra08} \citet{lyra08} \tikzmark{mainBodyCitationEnd607} \tikzmark{mainBodyStart608}showed\tikzmark{mainBodyEnd608} \tikzmark{mainBodyStart609}that\tikzmark{mainBodyEnd609} \tikzmark{mainBodyStart610}gravitationally\tikzmark{mainBodyEnd610} \tikzmark{mainBodyStart611}bound\tikzmark{mainBodyEnd611} \tikzmark{mainBodyStart612}embryos\tikzmark{mainBodyEnd612} \tikzmark{mainBodyStart613}can\tikzmark{mainBodyEnd613} \tikzmark{mainBodyStart614}form\tikzmark{mainBodyEnd614} \tikzmark{mainBodyStart615}in\tikzmark{mainBodyEnd615} \tikzmark{mainBodyStart616}the\tikzmark{mainBodyEnd616} \tikzmark{mainBodyStart617}regions\tikzmark{mainBodyEnd617} \tikzmark{mainBodyStart618}of\tikzmark{mainBodyEnd618} \tikzmark{mainBodyStart619}enhanced\tikzmark{mainBodyEnd619} \tikzmark{mainBodyStart620}dust\tikzmark{mainBodyEnd620} \tikzmark{mainBodyStart621}density.\tikzmark{mainBodyEnd621} 425 426\tikzmark{mainBodyCitationStart622}\citet[][; hereafter referred to as Paper I]{kato08} "427Extra bodies can be added in circular orbits about the center of mass.,Extra bodies can be added in circular orbits about the center of mass.428 Llaves(2003) demonstrates that as the number of moving bodies in a Ηχος potential increases the shadow clurations decrease., \cite{Hayes} demonstrates that as the number of moving bodies in a fixed potential increases the shadow durations decrease.429 Le would be of interest to determine if a similar relationship holds for the Sitnikoy N-body problem., It would be of interest to determine if a similar relationship holds for the Sitnikov $N$ -body problem.430 It should. be stressed. again that the failure ol the refinement procedure does not necessarily mean that a shaclow does not exist for a given pseudo-orbit., It should be stressed again that the failure of the refinement procedure does not necessarily mean that a shadow does not exist for a given pseudo-orbit.431 It may very well be that shadows do exist for orbits in regions where the refinement procedure fails., It may very well be that shadows do exist for orbits in regions where the refinement procedure fails.432 We are encouraged that this may »¢ the case., We are encouraged that this may be the case.433 Both the Sitnikovy problem and the approximate 'oincaré map possess à hyperbolic invariant set. A. near he escape boundaries (see Moser(1973). and Urminsky respectively).," Both the Sitnikov problem and the approximate Poincaré map possess a hyperbolic invariant set, $\Lambda$, near the escape boundaries (see \cite{Moser} and \cite{UrminskyThesis}434 respectively)."435 Despite the fact that iX is near the x»undary. ODy. the shadowing theorems by Anosov(1967) and Bowen(1972). guarantee that any pseudo-orbit on A has an associated shacdow-orbit.," Despite the fact that $\Lambda$ is near the boundary $\partial \mathcal{D}_0$, the shadowing theorems by \cite{Anosov} and \cite{Bowen} guarantee that any pseudo-orbit on $\Lambda$ has an associated shadow-orbit."436 Phis demonstrates that being in he vicinity on the escape boundary does not necessarily rule out the existence of shadow-orbits., This demonstrates that being in the vicinity on the escape boundary does not necessarily rule out the existence of shadow-orbits.437 DU was supported by the National Acronautics and Space Administration through grant. NNX-07ALIII5CG. The author would like to thank D. Hegegie. D. Merritt and D. Dicken for their helpful suggestions.," DU was supported by the National Aeronautics and Space Administration through grant NNX-07AH15G. The author would like to thank D. Heggie, D. Merritt and D. Dicken for their helpful suggestions."438 In addition. the author would like to thank the anonymous referee for his/her careful reading of the manuscript and useful suggestions.," In addition, the author would like to thank the anonymous referee for his/her careful reading of the manuscript and useful suggestions."439"The main point of the following analysis is the determination of the Bollzmann entropy SCM.Q.V) and of the total οποιον £7,V.Q.V) along Che sequence of models. ie. as a [function of the concentration parameter V. defined above.","The main point of the following analysis is the determination of the Boltzmann entropy $S(M, Q, \Psi)$ and of the total energy $E_{tot}(M, Q, \Psi)$ along the sequence of models, i.e. as a function of the concentration parameter $\Psi$ defined above."440 These functions. at constant AL and Q. ave illustrated in Fig.," These functions, at constant $M$ and $Q$, are illustrated in Fig."441"1. They have been obtained by noting that. from (he definitions of S and f"". From the definitions Q=Adabd!YrOb) and M=Aa2dV""ALOV) andthe definition of . we can express (he variables (21.0.d) in terms of the variables (V/.Q.Y) anclthus find that (he entropy per unit mass can be written as $/M=$40M.Q)+ o(V). where Sy is constant when the values of M. and Q are fixed. with Here E=E(w) is the dimensionless (otal energy defined from Ej,=AaFd?""E."," They have been obtained by noting that, from the definitions of $S$ and $f^{(\nu)}$, From the definitions $Q = A a^{-9/4}d^{-1 - 3/\nu} \hat{Q}(\Psi)$ and $M = A a^{-9/4}d^{- 3/\nu} \hat{M}(\Psi)$ andthe definition of $\gamma$, we can express the variables $(A, a, d)$ in terms of the variables $(M, Q, \Psi)$ andthus find that the entropy per unit mass can be written as $S/M=S_0(M,Q)+\sigma(\Psi)$ , where $S_0$ is constant when the values of $M$ and $Q$ are fixed, with Here $\hat{E} = \hat{E}(\Psi)$ is the dimensionless total energy defined from $E_{tot} = A a^{-13/4} d^{-3/\nu}\hat{E}$."442" From the identity «f),,/Al=E/M and the expression of a=a(M.Q.V) obtained previously. we lind £,,/M=H(M.Q)e(V). with: The factor Z£(M.Q) is à constant when A aud (Q are taken to be constant."," From the identity $a E_{tot}/M = \hat{E}/\hat{M}$ and the expression of $a = a(M, Q, \Psi)$ obtained previously, we find $E_{tot}/M = H(M,Q)\epsilon(\Psi)$, with: The factor $H(M,Q)$ is a constant when $M$ and $Q$ are taken to be constant."443" The quantities ο], VOY). QQU). and LOY) that enter the expression of σ ancl € depend only on V and are evaluated numerically on the equilibrium sequence."," The quantities $\gamma (\Psi)$, $\hat{M}(\Psi)$, $\hat{Q}(\Psi)$, and $\hat{E}(\Psi)$ that enter the expression of $\sigma$ and $\epsilon$ depend only on $\Psi$ and are evaluated numerically on the equilibrium sequence."444 This completes the derivation that allows us to craw the analogy with the classical paper of Lynden-BellandWood(1963)., This completes the derivation that allows us to draw the analogy with the classical paper of \citet{lyn68}.445". This step. straightforward [or the /"" models. is by itself interesting ancl new."," This step, straightforward for the $f^{(\nu)}$ models, is by itself interesting and new."446 In fact. other attempts at applving theparadigm of the gravothermal cabastrophe to stellar ανασα equilibrium sequences were either based on an unjustified ansalz [οι the identification of the relevant temperature (e.g.. see Appendix V in the article bv Lynelen-BellanclWood 1968: Katz 1980: Magliocchettiοἱal. 1993)) or onthe use of non-standard entropies (for less realistic models: Chavanis 2002)).," In fact, other attempts at applying theparadigm of the gravothermal catastrophe to stellar dynamical equilibrium sequences were either based on an unjustified for the identification of the relevant temperature (e.g., see Appendix V in the article by \citealt{lyn68}; ; \citealt{kat80}; ; \citealt{mag98}) ) or onthe use of non-standard entropies (for less realistic models; \citealt{cha02}) )."447 When the /' models wereconstructed (StiavelliandBertin 1987). it was immediatelv," When the $f^{(\nu)}$ models wereconstructed \citep{sti87}, , it was immediately"448metal ionization in the convection zone and the mean molecular weight of the solar core.,metal ionization in the convection zone and the mean molecular weight of the solar core.449" In à comprehensive review, Basu&Antia(2008) found that increases in neon did not reduce the need for a high oxygen in the convection zone (c.f."," In a comprehensive review, \citet{BA08} found that increases in neon did not reduce the need for a high oxygen in the convection zone (c.f."450 their Figure 21)., their Figure 21).451" One would therefore need to invoke multiple errors in distinct interiors and atmospheric input physics, with the same sign and magnitude, to produce an acceptable high Ne - low O mixture."," One would therefore need to invoke multiple errors in distinct interiors and atmospheric input physics, with the same sign and magnitude, to produce an acceptable high Ne - low O mixture."452" Our best interiors estimate for composition is A(O)=8.86+0.04, A(Ve)=8.15£0.17 and A(Fe)=7.50£0.05."," Our best interiors estimate for composition is $A(O)=8.86\pm0.04 $ , $A(Ne)=8.15\pm0.17 $ and $A(Fe)=7.50\pm0.05$."453 Loddersetal.(2009) combined recent atmospheres measurements for estimates of A(O)=8.732:0.07. A(Ne)=8.05£0.10 and A(Fe)=7.45+£0.08: these two scales are consistent within the errors.," \citet{Lodders2009} combined recent atmospheres measurements for estimates of $A(O)=8.73\pm0.07 $, $A(Ne)=8.05\pm0.10 $ and $A(Fe)=7.45\pm0.08$; these two scales are consistent within the errors."454 A weighted mean of the two leads to A(O)=8.83+0.04. A(Ne)=8.08£0.09 and A(Fe)=7.49--0.05 which we contend is the most precise current estimate for abundances.," A weighted mean of the two leads to $A(O)=8.83\pm0.04 $, $A(Ne)=8.08\pm0.09 $ and $A(Fe)=7.49\pm0.05$ which we contend is the most precise current estimate for abundances."455" In DPO6 we derived relationships quantifying combinations of C. Ν. O, and Ne with the same Rey and Y,,,."," In DP06 we derived relationships quantifying combinations of C, N, O, and Ne with the same $R_{CZ}$ and $Y_{surf}$."456" In the case of Ne, nonlinear effects can be induced when the change in the Ne/O ratio is too large and a better fitting relationship 1s A(Q)2—71.52x(Ne/OY49.03(Ne/Oy—3.10(Ne/O)—0.32O)-8.98 Our abundance scale is consistent with some photospheric abundance measurements (Caffauetal.2010;Pinsonneault&Delahaye2009) but not the lower AGSSO9 values."," In the case of Ne, nonlinear effects can be induced when the change in the Ne/O ratio is too large and a better fitting relationship is $A(O)= -7.52\times (Ne/O)^4 +9.03\times (Ne/O)^3 - 3.10\times (Ne/O)^2 -0.32\times (Ne/O) + 8.98$ Our abundance scale is consistent with some photospheric abundance measurements \citep{caffau10,PD09} but not the lower AGSS09 values."457" This is not a conflict between modern and primitive atmospheres treatments, or between one- and three-dimensional studies, but rather reflects differences between competing atmospheres models and judgment calls on the choice of indicators, continuum levels, and the proper treatment of blending features."," This is not a conflict between modern and primitive atmospheres treatments, or between one- and three-dimensional studies, but rather reflects differences between competing atmospheres models and judgment calls on the choice of indicators, continuum levels, and the proper treatment of blending features."458 We are therefore hopeful that helioseismology may provide an absolute abundance standard which can be used to discriminate between competing models and which can be used to calibrate the appropriate composition diagnostics for the next generation of stellar models., We are therefore hopeful that helioseismology may provide an absolute abundance standard which can be used to discriminate between competing models and which can be used to calibrate the appropriate composition diagnostics for the next generation of stellar models.459 FD would like to thank C. Stehlé for financial support and A. Formicola for information onupdated nuclear reaction cross-sections., FD would like to thank C. Stehlé for financial support and A. Formicola for information onupdated nuclear reaction cross-sections.460 MP would like to acknowledge support from DOE, MP would like to acknowledge support from DOE461radio eniission.,radio emission.462 Because of the claims in the literature that SMCis are radio bright. we do not favor these models.," Because of the claims in the literature that SMGs are radio bright, we do not favor these models."463" The sugeested relative radio brightuess of high-: SAIGs therefore provides some evidence that. in fact. Box rather than Boxpl?95, "," The suggested relative radio brightness of $z$ SMGs therefore provides some evidence that, in fact, $B \propto \Sigma_g^{0.7 - 0.8}$ rather than $B \propto \rho^{0.5 - 0.6}$."464Towever. the matter of whether high-: SALGs are in fact radio bright is not vet settled.," However, the matter of whether $z$ SMGs are in fact radio bright is not yet settled."465 Although LTQ couclided that D iust increase dramatically from normal galaxies to dense starbursts 2)). they were unable to distinguish between these two possibilities with the :z0 FRC aloue.," Although LTQ concluded that $B$ must increase dramatically from normal galaxies to dense starbursts \ref{sec:Theory}) ), they were unable to distinguish between these two possibilities with the $z \approx 0$ FRC alone."466 For this reason. higeh-: starbursts and their qualitatively ciffercut morphologies compared to those at z&0 can distiuguisli theories of the FRC.," For this reason, $z$ starbursts and their qualitatively different morphologies compared to those at $z \approx 0$ can distinguish theories of the FRC."467 A prediction of all of our variants is that puffv starbursts like submillimeter galaxies should have steep nou-thermal radio spectra. with azOA1 (Seo Table À2))," A prediction of all of our variants is that puffy starbursts like submillimeter galaxies should have steep non-thermal radio spectra, with $\alpha \approx 0.8 - 1.0$ (see Table \ref{table:Models}) )."468 The steep spectra are caused by strong synchrotron cooling in the BoxLVFYS case aud the relatively stronger IC cooling off starlight in the Dxpe?0 case., The steep spectra are caused by strong synchrotron cooling in the $B \propto \Sigma_g^{0.7-0.8}$ case and the relatively stronger IC cooling off starlight in the $B \propto \rho^{0.5 - 0.6}$ case.469" Tu. general. putty starbursts should lave roughly the same a as normal salaxies in the local universe, which tends to be somewhat higher (aστ0.7. 1.0) than in compact starbursts (aτς 0.7)."," In general, puffy starbursts should have roughly the same $\alpha$ as normal galaxies in the local universe, which tends to be somewhat higher $\alpha \approx 0.7 - 1.0$ ) than in compact starbursts $\alpha \la 0.7$ )."470 The slope should hold even out to extremely ligh X. as loug as starbursts are putty.," The slope should hold even out to extremely high $\Sigma_g$, as long as starbursts are puffy."471 In coutrast. we fud that a=0.5 In compact starbursts because of efficieut ionization aud emisstraliluug losses. which flatten the equilibiiunii CR spectruni because of their euergev dependence.," In contrast, we find that $\alpha \approx 0.5$ in compact starbursts, because of efficient ionization and bremsstrahlung losses, which flatten the equilibrium CR spectrum because of their energy dependence."472 As we rote in LTQ. our predicted spectral iudex for normal ealaxies is somewhat too high. and this difference in a nay carry over to the puffv starbursts.," As we note in LTQ, our predicted spectral index for normal galaxies is somewhat too high, and this difference in $\alpha$ may carry over to the puffy starbursts."473 Towever. the sienificaut difference iu a between compact and putty starbursts should remain as a general prediction of our uodel: compact starbursts should have flatter spectra han puffy starbursts.," However, the significant difference in $\alpha$ between compact and puffy starbursts should remain as a general prediction of our model: compact starbursts should have flatter spectra than puffy starbursts."474 The high spectral slopes can be observed either with direct ieasurements of iultifrequency data of individual subimüilluneter galaxies. or with single frequency observations at a variety of redshifts.," The high spectral slopes can be observed either with direct measurements of multifrequency data of individual submillimeter galaxies, or with single frequency observations at a variety of redshifts."475" There are relatively few measurements of à for submillimeter ealaxies specifically: faint radio sources have a220.5.0.7 (IIuvuh.etal.2007:Dondict2007).. though. that sample iucludes both compact starbursts and Αν,"," There are relatively few measurements of $\alpha$ for submillimeter galaxies specifically; faint radio sources have $\alpha \approx 0.5 - 0.7$ \citep{Huynh07,Bondi07}, though that sample includes both compact starbursts and AGNs."476 Sajinaunmaetet;al.(2008)SOS do find that; ozLi1CGIlzNile~0.?ge for SMCs. comparable to our predictions.," \citet{Sajina08} do find that $\alpha_{610~\MHz}^{1.4~\GHz} \approx 0.8$ for SMGs, comparable to our predictions."477 They also find that subiuüllineter ealaxies have a radio-excess. m agereenmient with Figure 1..," They also find that submillimeter galaxies have a radio-excess, in agreement with Figure \ref{fig:LFIRRadioRest}."478 More τοσα]. Ibaroetal.(2010) found oean averageο aLIGIEZMIIZLzcοτεo6. which: is). somewji flatter than610 our imo0dels.," More recently, \citet{Ibar10} found an average $\alpha_{610~\MHz}^{1.4~\GHz} \approx 0.75 \pm 0.06$, which is somewhat flatter than our models."479 These spectral slopes arc not different from normal star-forming ealaxies. but are noticeably steeper than local ULIRGs (Clemensetal.2Kos)...," These spectral slopes are not different from normal star-forming galaxies, but are noticeably steeper than local ULIRGs \citep{Clemens08}."480 ILowever. we do not account for frec-free absorpti3. Which probably flattens the spectra of local ULIRGs ike Arp 220 at low frequency (Condoetal. 1991).. aud is not well uuderstood in SAICs.," However, we do not account for free-free absorption, which probably flattens the spectra of local ULIRGs like Arp 220 at low frequency \citep{Condon91}, and is not well understood in SMGs."481" Since puffv sfarbursts lave steeper spectra than compact starburs swe expect their inferred Loup/L7, will increase witi redshift: if the true radio spectral slopes of SAICs are greater than the assumed à by Ao. they will appear to become radio dinuuer by a factor (11:)59"", or up to ~IU at 2=2."," Since puffy starbursts have steeper spectra than compact starbursts, we expect their inferred $L_{\rm TIR}^{\prime}/L_{\rm radio}^{\prime}$ will increase with redshift: if the true radio spectral slopes of SMGs are greater than the assumed $\alpha$ by $\Delta\alpha$, they will appear to become radio dimmer by a factor $(1 + z)^{\Delta \alpha}$, or up to $\sim 40\%$ at $z = 2$."482 Iu Figure 3.. we show the expected radio svuchrotrou spectra of starburst galaxies. without correcting for thermal absorption or thermal cmission.," In Figure \ref{fig:StarburstSpectra}, , we show the expected radio synchrotron spectra of starburst galaxies, without correcting for thermal absorption or thermal emission."483 At a rest-frame frequency of 1 CIIz. putty starbursts (dashed) have steeper radio spectra than compact starbursts (solid).," At a rest-frame frequency of 1 GHz, puffy starbursts (dashed) have steeper radio spectra than compact starbursts (solid)."484 Note that at high frequencies 0”210 GIIz). the ratio of the radio huuinosities per unit star formation of the conrpact and putty starbursts asvinptotes to a value sot by the ratio of Up aud Uy iu these starbursts.," Note that at high frequencies $\nu^{\prime} \ga 10\ \GHz$ ), the ratio of the radio luminosities per unit star formation of the compact and puffy starbursts asymptotes to a value set by the ratio of $U_B$ and $U_{\rm ph}$ in these starbursts."485 At these lieh frequencies. ouly svuchrotron aud IC cooling are effective. aud IC cooling would be the same for puffy aud conipact starbursts because of the Schinidt Law 2)).," At these high frequencies, only synchrotron and IC cooling are effective, and IC cooling would be the same for puffy and compact starbursts because of the Schmidt Law \ref{sec:Theory}) )."486 For BxSy. Up is the same for putty aud. compact starbursts. but for Boxp. puffy starbursts have iumch snaller τω.," For $B \propto \Sigma_g^a$, $U_B$ is the same for puffy and compact starbursts, but for $B \propto \rho^a$, puffy starbursts have much smaller $U_B$."487 Thus. measuremcuts of the svuchrotron radio cuuission of SAIGs at hieh ν΄ could determine the magnetic feld streneth of SAIGs and determine which scenario applies.," Thus, measurements of the synchrotron radio emission of SMGs at high $\nu^{\prime}$ could determine the magnetic field strength of SMGs and determine which scenario applies."488 Of course. there are unlikely to be two perfectly distinct. populations of compact starbursts and putty starhbursts.," Of course, there are unlikely to be two perfectly distinct populations of compact starbursts and puffy starbursts."489 DIusteacd. there may be a continu variatio1 iji scale. heights from teis fo thousands of parsecs.," Instead, there may be a continuum variation in scale heights from tens to thousands of parsecs."490" We would then expectto see a larger scatter. both i Spf, aud o. ina ""ll sample of both the mos conrpact and the most pifiv starbursts."," We would then expectto see a larger scatter, both in $L_{\rm TIR}^{\prime}/L_{\rm radio}^{\prime}$ and $\alpha$, in a full sample of both the most compact and the most puffy starbursts."491 πηρανctal. fud that ποτιueter galaxies do have a largeLad scatter d ὅτε than other galaxies., \citet{Murphy09} find that submillimeter galaxies do have a larger scatter in $q_{\rm TIR}^{\prime}$ than other galaxies.492 However. Tharο fud a relatively simall scatterof ~0.3 1- SMG radio spectral index.," However, \citet{Ibar10} find a relatively small scatterof $\sim 0.3$ in SMG radio spectral index."493" huportautlv. for lareer Ph both Linn/radio aud a’ asviuptote as CR electron ai positron losses are entirely determined by svuchrotre- and IC: fx1.kpe starbursts are already: near this Πατ,"," Importantly, for larger $h$ , both $L_{\rm TIR}^{\prime}/L_{\rm radio}^{\prime}$ and $\alpha^{\prime}$ asymptote as CR electron and positron losses are entirely determined by synchrotron and IC; $h \approx 1~\kpc$ starbursts are already near this limit."494thick. ecometrically thin state and. viclels both an observable radio jet anc narrow-line emission.,"thick, geometrically thin state and yields both an observable radio jet and narrow-line emission."495 ‘Tables 2. and 3 suggest this is not the case for the later (control early types) stages of evolution., Tables \ref{tab:fracOpticalAGN_dustlanes} and \ref{tab:fracAllAGN} suggest this is not the case for the later (control early types) stages of evolution.496 This is likely to be because the merger-driven GN. activity. has mostly expelled the available gas. and the galaxy migrated to a quiescent state.," This is likely to be because the merger-driven AGN activity has mostly expelled the available gas, and the galaxy migrated to a quiescent state."497 Phe mean starburst age for the control sample is TOO Myr. which is much larger than both the transition time of ~200 Myr between the starburst and transition (i.c. starburst|ACGN) phase argued by and the maximum AGN lifetime of up to a few hundred. Myr2008).," The mean starburst age for the control sample is $700$ Myr, which is much larger than both the transition time of $\sim 200$ Myr between the starburst and transition (i.e. starburst+AGN) phase argued by and the maximum AGN lifetime of up to a few hundred Myr."498. Therefore. most of these objects are not. expected to host. AGN that would have a common origin with the starburst.," Therefore, most of these objects are not expected to host AGN that would have a common origin with the starburst."499 Conversely. with their mean starburst ages of 300 Myr. dust. lane early. types fall in the “sweet spot of being old enough to host an AGN. but not so old that AGN activity has been terminated.," Conversely, with their mean starburst ages of $\sim 300$ Myr, dust lane early types fall in the `sweet spot' of being old enough to host an AGN, but not so old that AGN activity has been terminated."500 We test this paradigm by deriving radio AGN ages for those galaxies that were classified as having excess 1.4-Cillz luminosity., We test this paradigm by deriving radio AGN ages for those galaxies that were classified as having excess 1.4-GHz luminosity.501 This was done by generating a library of tracks in racio buminositv- linear size space., This was done by generating a library of tracks in radio luminosity- linear size space.502 As discussed at length in(2008).. given a clensity profile for the atmosphere into which the radio source is expanding. anc aspect ratio of the source. its Luminosity and size allow je power and age of the radio source to be determined uniquely.," As discussed at length in, given a density profile for the atmosphere into which the radio source is expanding, and aspect ratio of the source, its luminosity and size allow jet power and age of the radio source to be determined uniquely."503 We use observations of local early-type galaxies for the X-ray gas density. profile. and adopt an axia ratio of Ap=2.," We use observations of local early-type galaxies for the X-ray gas density profile, and adopt an axial ratio of $R_{\rm T}=2$."504 X number of caveats are associated: with this analysis., A number of caveats are associated with this analysis.505 Our assumption for the gas density profile may not be applicable for dust. lane earlv-tvpe galaxies. most of which show disturbed morphologies (Paper D).," Our assumption for the gas density profile may not be applicable for dust lane early-type galaxies, most of which show disturbed morphologies (Paper I)."506 Furthermore. hotspot contribution to radio Luminosity can be comparable with that of the lobes at 1.4 1.," Furthermore, hotspot contribution to radio luminosity can be comparable with that of the lobes at 1.4 GHz."507 However. estimate that the derived time-scales are accurate to better than a factor of two.," However, estimate that the derived time-scales are accurate to better than a factor of two."508 Importantly. the radio source models of and are only applicable for edge-brightened: Fanaroll- tvpe EL (ETC LD] sources.," Importantly, the radio source models of and are only applicable for edge-brightened [Fanaroff-Riley type II (FR II)] sources."509 On the other hand. most radio AGN in the local universe are core-dominated ETC 1 objects.," On the other hand, most radio AGN in the local universe are core-dominated FR I objects."510 Llowever. most of the resolved objects in our sample are FR IL objects. for which the modelling is applicable.," However, most of the resolved objects in our sample are FR II objects, for which the modelling is applicable."511 Only upper limits on ages can be placed for unresolved radio sources., Only upper limits on ages can be placed for unresolved radio sources.512 ‘Table 4 eives the size distribution of radio AGN [or the dust lanes ancl the matched. control sample., Table \ref{tab:radioSizesAges} gives the size distribution of radio AGN for the dust lanes and the matched control sample.513 The distributions are statistically indistinguishable at the LO per cent level., The distributions are statistically indistinguishable at the 10 per cent level.514 However. the number of dust lane racio AGN in our sample (46) is small. and most of these are unresolved.," However, the number of dust lane radio AGN in our sample (46) is small, and most of these are unresolved."515 Lighresolution imaging will be required to address this issue properly., High resolution imaging will be required to address this issue properly.516 lig., Fig.517 S compares the derived radio source ages with the ages of stellar populations for dust lane early-type galaxies., \ref{fig:SFtimescales} compares the derived radio source ages with the ages of stellar populations for dust lane early-type galaxies.518 Sevlerts ancl LINERS have similar age distributions. with median values around 300 Myr.," Seyferts and LINERs have similar age distributions, with median values around 300 Myr."519 There is no cillerence between radio-Ioud and. radio-quiet emission-line ACN., There is no difference between radio-loud and radio-quiet emission-line AGN.520 We interpret this as evidence for the simultaneous trigeering of the radio jet and line emission., We interpret this as evidence for the simultaneous triggering of the radio jet and line emission.521 Sevfert-lHike line emission will come from the raciativelv ellicient AGN clise. while LINER-like emission can either come from the disce or be distributed throughout the radio cocoon2011).," Seyfert-like line emission will come from the radiatively efficient AGN disc, while LINER-like emission can either come from the disc or be distributed throughout the radio cocoon."522. This picture is further supported. by the 100150 Mr olfset between radio and starburst ages in Fig. N((, This picture is further supported by the $100-150$ Myr offset between radio and starburst ages in Fig. \ref{fig:SFtimescales}( (523b) being consistent with the age dillerence. between starburst) and ransition objects in Fig S((a).,b) being consistent with the age difference between starburst and transition objects in Fig \ref{fig:SFtimescales}( (a).524 Our interpretation of the origin and evolution of dust ane earlv-tv galaxies is then as follows., Our interpretation of the origin and evolution of dust lane early-type galaxies is then as follows.525 (X. quiescent earlv-tvpe galaxy.pe. undergoes a gaserich. minor merger., A quiescent early-type galaxy undergoes a gas-rich minor merger.526 The resulting gas inllow triggers a starburst., The resulting gas inflow triggers a starburst.527 Some time later (tvpically <200 Myr) the AGN switches on., Some time later (typically $<200$ Myr) the AGN switches on.528 Cireumnuclear starbursts could be the reason Lor this delav. with powerful winds driven by OB stars and supernovae suppressing ACN uclling temporarily2007).," Circumnuclear starbursts could be the reason for this delay, with powerful winds driven by OB stars and supernovae suppressing AGN fuelling temporarily."529.. Alternatively. mass loss from newly formed stars could. help [απο AGN activity. providing a possible mechanism of [Tunneling gas owards the central engine.," Alternatively, mass loss from newly formed stars could help fuel AGN activity, providing a possible mechanism of funneling gas towards the central engine."530 Once the ACGN switches on. the accretion rate onto the central black hole is high. enough (tvpically at least a few per cent of the Eddington value) for he accretion cise to be in a classical. raclatively ellicient hin disc state. and the AGN is observed in both emission ines and at radio wavelengths.," Once the AGN switches on, the accretion rate onto the central black hole is high enough (typically at least a few per cent of the Eddington value) for the accretion disc to be in a classical, radiatively efficient thin disc state, and the AGN is observed in both emission lines and at radio wavelengths."531 This phase is accompanied w the presence of significant amounts of dust. ancl the earlv-tvpe galaxy. is observed as having a dust lane feature.," This phase is accompanied by the presence of significant amounts of dust, and the early-type galaxy is observed as having a dust lane feature."532" Eventually, AGN feedback heats up and/or expels the gas rom the galaxy2009)."," Eventually, AGN feedback heats up and/or expels the gas from the galaxy."533 oth the star formation and AGN activity are truncated. with the galaxy returning to à quiescent state.," Both the star formation and AGN activity are truncated, with the galaxy returning to a quiescent state."534 In Paper Lowe showed that the mass of dust. in the observed. features is too great to come from stellar mass oss. sugeesting stronely an external origin for this dust.," In Paper I we showed that the mass of dust in the observed features is too great to come from stellar mass loss, suggesting strongly an external origin for this dust."535 Since dust ane gas are typically coupled. one might expect dust lane earlv-type galaxies to be gas rich. consistent with he gas-rich merger origin of these objects.," Since dust and gas are typically coupled, one might expect dust lane early-type galaxies to be gas rich, consistent with the gas-rich merger origin of these objects."536" As shown in ""aper L dust lane carly types do show enhanced. levels of star formation compared to a control saniple of all early-vpe galaxies."," As shown in Paper I, dust lane early types do show enhanced levels of star formation compared to a control sample of all early-type galaxies."537 However. Fig.," However, Fig."538 7 shows that galaxies with dust eatures also have vounger starburst ages. and it is therefore possible that the higher star formation rates in these objects," \ref{fig:t2control} shows that galaxies with dust features also have younger starburst ages, and it is therefore possible that the higher star formation rates in these objects"539momentum of the accretor. i.e. we mimick in this way helium nova explosions) yielded virtually identical abundances as function of orbital period.,"momentum of the accretor, i.e. we mimick in this way helium nova explosions) yielded virtually identical abundances as function of orbital period."540 We also ran two sets of calculations. completely conservative and completely non-conservative. for the case of a neutron star accretor with initial helium donor masses of 0.35. 0.65 and 1M. and again found no significant difference in the abundances as function of orbital period.," We also ran two sets of calculations, completely conservative and completely non-conservative, for the case of a neutron star accretor with initial helium donor masses of 0.35, 0.65 and $1\,\msun$ and again found no significant difference in the abundances as function of orbital period."541 Because the onset of mass transfer from the helium star the helium burning3imainBodyCitationEnd1576]skh86. the chemical composition of the core of the donor depends sensitively on the at which the helium star fills its Roche lobe.," Because the onset of mass transfer from the helium star the helium burning, the chemical composition of the core of the donor depends sensitively on the at which the helium star fills its Roche lobe."542 We use evolutionary calculations for binaries that start mass transfer almost immediately after the common-envelope phase in which the helium star is formed. as well as systems that fill their Roche lobe just before core helium exhaustion.," We use evolutionary calculations for binaries that start mass transfer almost immediately after the common-envelope phase in which the helium star is formed, as well as systems that fill their Roche lobe just before core helium exhaustion."543 In this way the complete range of expected abundances can be probed. although we would like to note that the extremes of this range will likely be rare in practice. because the periods need to be fine tuned.," In this way the complete range of expected abundances can be probed, although we would like to note that the extremes of this range will likely be rare in practice, because the periods need to be fine tuned."544 We discuss this in more detail in Section 3.., We discuss this in more detail in Section \ref{population}.545 In Fig., In Fig.546 + we show a representative set of evolutionary sequences for binaries with helium donors and white dwarf/neutron star accretors., \ref{fig:heabund} we show a representative set of evolutionary sequences for binaries with helium donors and white dwarf/neutron star accretors.547 The full set of sequences is published on-line., The full set of sequences is published on-line.548 For each sequence we plot the abundances of the transferred material. the mass transfer rate. donor mass and orbital period as function of the time since the onset of RLOF.," For each sequence we plot the abundances of the transferred material, the mass transfer rate, donor mass and orbital period as function of the time since the onset of RLOF."549 This allows full assessment of the evolution. both in the initial phase when the binary evolves to shorter periods at almost constant mass transfer rate of a few times LO7M.vr.J| as. well as later. when the system has passed its period minimum.," This allows full assessment of the evolution, both in the initial phase when the binary evolves to shorter periods at almost constant mass transfer rate of a few times $10^{-8}\,\myr$, as well as later, when the system has passed its period minimum."550 Before the period minimum stars lose matter that was outside the convective core in the helium-burning stage so the material is heltum rich. with CNO abundances corresponding to the CNO cycle equilibrium for relatively massive stars that are typical progenitors of heliumstars!.," Before the period minimum stars lose matter that was outside the convective core in the helium-burning stage so the material is helium rich, with CNO abundances corresponding to the CNO cycle equilibrium for relatively massive stars that are typical progenitors of helium."551. Shortly after the »eriod. minimum tor for the most evolved donors already before oriod. minimum) helium burning products. most notably C and ater O. come to the surface.," Shortly after the period minimum (or for the most evolved donors already before period minimum) helium burning products, most notably C and later O, come to the surface."552 Depending on the initial period of he binary the enrichment by C and O can be very mild. or C and O can dominate even He.," Depending on the initial period of the binary the enrichment by C and O can be very mild, or C and O can dominate even He."553 In the top row of Fig., In the top row of Fig.554 4. we plot sequences for an initially VAAL. helium star donor transferring material to an initially 6M. white dwarf aecretor.," \ref{fig:heabund} we plot sequences for an initially $0.4\,\msun$ helium star donor transferring material to an initially $0.6\,\msun$ white dwarf accretor."555 The leftmost plot is for the case of a post-common-envelope period of 20 min. in which RLOF starts almost immediately after formation of the helium star and very ittle helium burning occurs. so He. N. O and Νο abundances are virtually unchanged.," The leftmost plot is for the case of a post-common-envelope period of 20 min, in which RLOF starts almost immediately after formation of the helium star and very little helium burning occurs, so He, N, O and $^{22}$ Ne abundances are virtually unchanged."556 However. after the period minimum the carbon abundance increases substantially.," However, after the period minimum the carbon abundance increases substantially."557 For an intermediate post-common-envelope period of mmin. there is a dramatic change of abundances around period minimum because the layers which were in the core and experienced some He-burning are exposed and for most of the AM CVn evolution C and © (and even 77 Ne) dominate over N. The He abundance is noticeably reduced.," For an intermediate post-common-envelope period of min, there is a dramatic change of abundances around period minimum because the layers which were in the core and experienced some He-burning are exposed and for most of the AM CVn evolution C and O (and even $^{22}$ Ne) dominate over N. The He abundance is noticeably reduced."558 Finally for the most evolved donor. with initial period of 130 min (helium abundance in the core at RLOF Y;z 0.07). the changes are even more dramatic and O and C dominate even over He.," Finally for the most evolved donor, with initial period of 130 min (helium abundance in the core at RLOF $Y_{\rm c} \approx 0.07$ ), the changes are even more dramatic and O and C dominate even over He."559" Nitrogen becomes extinguished even before /2,,.4,4."," Nitrogen becomes extinguished even before $ P_{\rm orb, min} $."560 Note that in the most extreme cases He-burning continues for some time after RLOF but He is still not completely burnt so significant amounts of He should still be detectable. contrary to hybrid white dwarf donors.," Note that in the most extreme cases He-burning continues for some time after RLOF but He is still not completely burnt so significant amounts of He should still be detectable, contrary to hybrid white dwarf donors."561 In the bottom row of Fig., In the bottom row of Fig.562 + a number of evolutionary sequences for systems with neutron star accretors are shown., \ref{fig:heabund} a number of evolutionary sequences for systems with neutron star accretors are shown.563 The leftmost panel is again for fairly short initial period of mmin and shows quite a change in C but not much in the other elements., The leftmost panel is again for fairly short initial period of min and shows quite a change in C but not much in the other elements.564 The middle plot is for the sequence with the longest initial period for which RLOF starts when the star almost totally burnt helium in its core (3.zz0.06) and looks very similar to the most evolved donor shown for the sequence with a white dwarf accretor., The middle plot is for the sequence with the longest initial period for which RLOF starts when the star almost totally burnt helium in its core $ Y_{\rm c} \approx 0.06 $ ) and looks very similar to the most evolved donor shown for the sequence with a white dwarf accretor.565 The bottom right plot is for a He star plus neutron star system with initial donor mass of 0.65M. and initial orbital period close to the minimum possible for such a system. mmin It shows that at a given orbital period there may be a scatter of a factor of several in abundance ratios. depending on the initial mass of the donor.," The bottom right plot is for a He star plus neutron star system with initial donor mass of $0.65\,\msun$ and initial orbital period close to the minimum possible for such a system, min It shows that at a given orbital period there may be a scatter of a factor of several in abundance ratios, depending on the initial mass of the donor."566 A peculiar evolutionary path is followed by initially relatively massive helium stars (more than about 0.65ΔΕ. ) with neutron star companions.," A peculiar evolutionary path is followed by initially relatively massive helium stars (more than about $0.65\,\msun$ ) with neutron star companions."567 These overfill their Roche lobes after burning of a substantial fraction of helium in the core and continue He-burning during the semidetached stage of evolution., These overfill their Roche lobes after burning of a substantial fraction of helium in the core and continue He-burning during the semidetached stage of evolution.568" For instance. the system with Mg.=O.SOAL. and £4=TOmmin starts mass loss when Y,=0.643 and proceeds along a conventional evolutionary track."," For instance, the system with $M_{\rm He}=0.80\,\msun$ and $569 P_0=70$ min starts mass loss when $Y_c \approx 0.643$ and proceeds along a conventional evolutionary track."570" In a slightly wider initially system with /3, 75mmin. RLOF occurs when 3;=0.56 (see Fig. 59)."," In a slightly wider initially system with $ P_0=75$ min, RLOF occurs when $Y_c \approx 0.56$ (see Fig. \ref{fig:evolHe}) )."571" In this system the donor detaches from its Roche lobe when its mass ws decreased to 0.52M. and Y,z0.006."," In this system the donor detaches from its Roche lobe when its mass has decreased to $0.52\,\msun$ and $Y_c \approx 0.006$."572 The orbit continues o shrink and mass exehange resumes in the helium-shell burning stage., The orbit continues to shrink and mass exchange resumes in the helium-shell burning stage.573 However. when the donor mass is more than about 0.45M.. mass loss cannot be stabilised by mass and angular-momentum oss from the system and the ensuing mass loss proceeds on a dynamical time scale (see Fig. 59).," However, when the donor mass is more than about $0.45\,\msun$, mass loss cannot be stabilised by mass and angular-momentum loss from the system and the ensuing mass loss proceeds on a dynamical time scale (see Fig. \ref{fig:evolHe}) )."574 Thus. such a system does not contribute to the heltum star channel or UCXBs.," Thus, such a system does not contribute to the helium star channel for UCXBs."575 Evolutionary sequences for 1M... donor stars follow a similar path irrespective of the amount of He burnt prior to RLOF.," Evolutionary sequences for $1\,\msun$ donor stars follow a similar path irrespective of the amount of He burnt prior to RLOF."576 The details of this type of evolution will be discussed in a forthcoming paper (Yungelson et al., The details of this type of evolution will be discussed in a forthcoming paper (Yungelson et al.577 in Thus. there are two factors limiting the helium star channel for the formation of ultra-compact binaries. the maximum post-common-envelope period for which mass transfer still starts during core helium burning and a limiting mass above which the system detaches as described above (see also Fig. 105.," in Thus, there are two factors limiting the helium star channel for the formation of ultra-compact binaries, the maximum post-common-envelope period for which mass transfer still starts during core helium burning and a limiting mass above which the system detaches as described above (see also Fig. \ref{fig:hechannel_MP}) )."578 The formation of ultra-compact binaries from main-sequence donors requires two conditions., The formation of ultra-compact binaries from main-sequence donors requires two conditions.579 First. the initial periods are such that the progenitors fill their Roche lobe close to the end of the main sequence.," First, the initial periods are such that the progenitors fill their Roche lobe close to the end of the main sequence."580 Second. angular momentum loss drives the components together at a sufficient rate that the ultra-short periods can. be reached within the Hubble time (222?)..," Second, angular momentum loss drives the components together at a sufficient rate that the ultra-short periods can be reached within the Hubble time ."581 Radiative transfer is an important phenomena in star formation., Radiative transfer is an important phenomena in star formation.582 Radiation sets the temperature of the gas during the collapse of a molecular cloud core., Radiation sets the temperature of the gas during the collapse of a molecular cloud core.583 This both influences the degree of fragmentation of the eloud. and sets the minimum mass of brown dwarfs (theopacitylimitforfragmentation:2)..," This both influences the degree of fragmentation of the cloud, and sets the minimum mass of brown dwarfs \citep[the opacity limit for fragmentation;][]{LL1976}."584 Once protostars have formed in a cloud. radiative and mechanical feedback from them can affect subsequent star formation.," Once protostars have formed in a cloud, radiative and mechanical feedback from them can affect subsequent star formation."585 Such feedback mechanisms include protostellar jets and outflows from low-mass stars. and ionisation from massive stars which creates HII regions and destroys a cloud.," Such feedback mechanisms include protostellar jets and outflows from low-mass stars, and ionisation from massive stars which creates HII regions and destroys a cloud."586 Computer simulations are vital in our efforts to understand the complex problem of star formation., Computer simulations are vital in our efforts to understand the complex problem of star formation.587 Many previous simulations have used the smoothed particle hydrodynamics method (SPH) (e.g.222222).," Many previous simulations have used the smoothed particle hydrodynamics method (SPH) \citep[e.g.][]{GM1981,PCDNDW1991MmSAI,BMBAB1991,NP1993,BBP1995,KBB1998}."588 Other methods used are typically based around grid-based codes (e.g.222222).," Other methods used are typically based around grid-based codes \citep[e.g.][]{L1969b,BB1979,BM1992,BB1993,TKMHHG1997,BFKM2000}."589 SPH is a Lagrangian method firs developed by ? and ? (see?.forareview)..., SPH is a Lagrangian method first developed by \citet{L1977} and \citet{GM1977} \citep[see][for a review]{M1992}.590 It approximates the fluid as a series of discrete fluid elements denoted by individual SPH particles and uses interpolation to obtain the fluic variables at any point in the simulation., It approximates the fluid as a series of discrete fluid elements denoted by individual SPH particles and uses interpolation to obtain the fluid variables at any point in the simulation.591 SPH is conceptually simple to understand. and can naturally adapt its resolution to the local density distribution. unlike grid-based codes which require complex adaptive-mesh refinement algorithms to perform the same task.," SPH is conceptually simple to understand, and can naturally adapt its resolution to the local density distribution, unlike grid-based codes which require complex adaptive-mesh refinement algorithms to perform the same task."592 This property makes it ideal for use in star formation. where densities may range over many orders of magnitude in a single simulation.," This property makes it ideal for use in star formation, where densities may range over many orders of magnitude in a single simulation."593 Despite these advantages. few attempts have been made to include radiative transfer into SPH (22227). and until recently SPH with radiative transfer has not been applied to star formation.," Despite these advantages, few attempts have been made to include radiative transfer into SPH \citep{L1977,B1985,B1986,OW2003,WB2004}, and until recently \citep*{BCV2004,BCV2005} SPH with radiative transfer has not been applied to star formation."594 Instead. many past simulations have simply used isothermal or barotropic equations of state to model the collapse of a molecular cloud.," Instead, many past simulations have simply used isothermal or barotropic equations of state to model the collapse of a molecular cloud."595 The former is only valid up to densities of ~10U & ? at which point the cloud traps radiation etficiently enough for the cloud to begin to heat up., The former is only valid up to densities of $\sim 10^{-13}$ g $^{-3}$ at which point the cloud traps radiation efficiently enough for the cloud to begin to heat up.596 The latter is usually based on the evolution of the temperature at the highest density. during the collapse of spherically symmetric clouds as calculated using radiative transfer (e.g.222)..," The latter is usually based on the evolution of the temperature at the highest density during the collapse of spherically symmetric clouds as calculated using radiative transfer \citep[e.g.][]{L1969b,WN1980,MI2000}."597 However. a barotropic equation of state can at best only hope to provide an adequate description of temperature at the density maximum: it is unlikely to give an accurate temperature distribution during a three-dimensional calculation with complex density and velocity structure.," However, a barotropic equation of state can at best only hope to provide an adequate description of temperature at the density maximum; it is unlikely to give an accurate temperature distribution during a three-dimensional calculation with complex density and velocity structure."598 Indeed. ? performed grid-based calculations of the collapse of a molecular cloud core both with a barotropic equation of state and with radiative transfer in the Eddington approximation and found they dittered somewhat.," Indeed, \citet{BFKM2000} performed grid-based calculations of the collapse of a molecular cloud core both with a barotropic equation of state and with radiative transfer in the Eddington approximation and found they differed somewhat."599 However. they did not examine in detail how the relation between temperature and density dittered from that of the barotropic equation of state spatially and temporally. or its dependence on initial conditions.," However, they did not examine in detail how the relation between temperature and density differed from that of the barotropic equation of state spatially and temporally, or its dependence on initial conditions."600 ? recently presented an implicit algorithm for calculating radiative transfer using the flux-limited diffusion approximation within the SPH formalism., \citet*{WBM2005} recently presented an implicit algorithm for calculating radiative transfer using the flux-limited diffusion approximation within the SPH formalism.601 This paper describes a three-dimensional implementation of this algorithm) and uses it to examine the thermodynamics during the collapse of molecular cloud cores., This paper describes a three-dimensional implementation of this algorithm and uses it to examine the thermodynamics during the collapse of molecular cloud cores.602 Section 2. describes the changes necessary to the radiative transfer algorithm of 2? for use in three dimensions and the initial conditions for our star formation calculations.," Section \ref{sec:method}603 describes the changes necessary to the radiative transfer algorithm of \citet{WBM2005} for use in three dimensions and the initial conditions for our star formation calculations."604 Section 3 presents the results of simulations of the collapse of molecular cloud cores with different initial conditions and examines the evolution of their temperature structure., Section \ref{sec:results} presents the results of simulations of the collapse of molecular cloud cores with different initial conditions and examines the evolution of their temperature structure.605 Finally. section 5 summarises the main conclusions of this paper.," Finally, section \ref{sec:conclusions} summarises the main conclusions of this paper."606Each person has their own favorite list of future observational needs.,Each person has their own favorite list of future observational needs.607 Here is mine: ο We need a high rate (>100 GRBs 1) of bursts with good locations. in order to change the sociology of ground-based optical and radio observations.," Here is mine: $\bullet$ We need a high rate $> 100$ GRBs $^{-1}$ ) of bursts with good locations, in order to change the sociology of ground-based optical and radio observations."608 This many good GRB positions to follow-up each year would make it possible to propose and carry out GRB afterglow monitoring programs at many medium-to-large aperture telescopes., This many good GRB positions to follow-up each year would make it possible to propose and carry out GRB afterglow monitoring programs at many medium-to-large aperture telescopes.609 e The diversity of GRBs. GRB afterglows. and host galaxies means that we need a large number (71000) of good GRB positions in order to be able to study the correlations between these properties.," $\bullet$ The diversity of GRBs, GRB afterglows, and host galaxies means that we need a large number $> 1000$ ) of good GRB positions in order to be able to study the correlations between these properties."610 This is important for determining whether or not there are distinct subclasses of bursts. and more than one burst mechanism.," This is important for determining whether or not there are distinct subclasses of bursts, and more than one burst mechanism."611 Any correlations found will also impose important constraints on burst mechanisms and models., Any correlations found will also impose important constraints on burst mechanisms and models.612 e We need many rapid (near real time) one areminute GRB positions in order to determine whether or not significant optical emission accompanies the bursts (Park 1999). and to make it possible to take spectra of the burst afterglows while the afterglows are still bright — and thereby obtain redshifts of the bursts themselves from absorption line systems. and if there are bursts at high redshifts. from the Ενα break.," $\bullet$ We need many rapid (near real time) one arcminute GRB positions in order to determine whether or not significant optical emission accompanies the bursts (Park 1999), and to make it possible to take spectra of the burst afterglows while the afterglows are still bright – and thereby obtain redshifts of the bursts themselves from absorption line systems, and if there are bursts at high redshifts, from the $\alpha$ break."613" e All of the GRBs that BeppoSAX has detected are ""long"" bursts.", $\bullet$ All of the GRBs that BeppoSAX has detected are “long” bursts.614" Currently we know nothing about the afterglow properties. the distance scale. and the hosts (1f any) of ""short"" bursts."," Currently we know nothing about the afterglow properties, the distance scale, and the hosts (if any) of “short” bursts."615 Therefore we need good/quick positions for short bursts. in order to determine these properties for short bursts in the same way that BeppoSAX has enabled us to determine these properties for long bursts.," Therefore we need good/quick positions for short bursts, in order to determine these properties for short bursts in the same way that BeppoSAX has enabled us to determine these properties for long bursts."616 e Currently. there is a largely unexplored gap in our knowledge of the X-ray and optical behavior of burst afterglows of ~10!Lo’ seconds immediately following the bursts. corresponding to the time needed to bring the BeppoSAX NFlIs to bear on a burst.," $\bullet$ Currently, there is a largely unexplored gap in our knowledge of the X-ray and optical behavior of burst afterglows of $\sim 10^4 - 10^5$ seconds immediately following the bursts, corresponding to the time needed to bring the BeppoSAX NFIs to bear on a burst."617 We need to fill in this unexplored gap. in order to see if bursts always. often. or rarely join smoothly onto their X-ray and optical afterelows. and to explore the geometry and kinematics of GRB afterglows (Sari 1999).," We need to fill in this unexplored gap, in order to see if bursts always, often, or rarely join smoothly onto their X-ray and optical afterglows, and to explore the geometry and kinematics of GRB afterglows (Sari 1999)."618 e We also need to search for variability in the X-ray and optical afterglows., $\bullet$ We also need to search for variability in the X-ray and optical afterglows.619" Observations of such variability would impose severe constraints on. models. including the widely-discussed relativistic fireball model of burst afterelows (see. e.g.. Fenimore 1999),"," Observations of such variability would impose severe constraints on models, including the widely-discussed relativistic fireball model of burst afterglows (see, e.g., Fenimore 1999)."620 The Rome Workshop provided a feast of observational and theoretical results. and the opportunity to discuss them.," The Rome Workshop provided a feast of observational and theoretical results, and the opportunity to discuss them."621 On behalf of all of the Workshop participants. | would like to thank Enrico Costa. Luigi Piro. Filippo Fontana. and everyone else who helped to organize this meeting for bringing all of us together and for providing us with such “fine dining.”," On behalf of all of the Workshop participants, I would like to thank Enrico Costa, Luigi Piro, Filippo Fontana, and everyone else who helped to organize this meeting for bringing all of us together and for providing us with such “fine dining.”"622Physical properties of cometary dust can be obtained from the solar radiation scattered by the cometary dust. which. in the process. gets. polarised.,"Physical properties of cometary dust can be obtained from the solar radiation scattered by the cometary dust which, in the process, gets polarised."623 The degree of polarisation and its direction mainlv depend. on the size clistribution. composition of the particles. phase angle and the wavelength of the incident. solar radiation.," The degree of polarisation and its direction mainly depend on the size distribution, composition of the particles, phase angle and the wavelength of the incident solar radiation."624 However. the real situation is not that straight forward.," However, the real situation is not that straight forward."625 In an attempt to study the detailed behaviour of polarisation with phase. Dolllusetal.CI988). synthesized the polarisation observation data on l1P/LHallev by various researchers ancl derived: curves of polarisation as a function of the phase angle.," In an attempt to study the detailed behaviour of polarisation with phase, \citet{Dollfus1988} synthesized the polarisation observation data on 1P/Halley by various researchers and derived curves of polarisation as a function of the phase angle."626 Phase curve below about 20° shows negative polarisation while it is positive at. higher. phase angles., Phase curve below about $ 20^{\circ}$ shows negative polarisation while it is positive at higher phase angles.627 They find slight modification in the polarisation phase curve as one moves away [rom the nucleus indicating the change in the nature of the dust. particles., They find slight modification in the polarisation phase curve as one moves away from the nucleus indicating the change in the nature of the dust particles.628 Also an anomalously high transient polarisation was noted between October 17 and 80. 1985. at phase angle 25°. attributed to sudden. release of large number of smaller particles.," Also an anomalously high transient polarisation was noted between October 17 and 30, 1985, at phase angle $25^{\circ}$, attributed to sudden release of large number of smaller particles."629 On the basis of this work on 1P/Hallev. Dollfus(1989). derived the physical properties of the dust. erains indicating the presence of large particles - aggregates comprising of submicron sized grains. very rough and dark.," On the basis of this work on 1P/Halley, \citet{Dollfus1989} derived the physical properties of the dust grains indicating the presence of large particles - aggregates comprising of submicron sized grains, very rough and dark."630 These rather large grains are mixed with the clouds of small particles ancl they are usually responsible for almost all the polarisation elfects in. visible light. except. during temporary specific dust. release events (as seen in case of 1P/Halley curing October 17-30. 1985) bv the nucleus. (Dollfus1989).," These rather large grains are mixed with the clouds of small particles and they are usually responsible for almost all the polarisation effects in visible light, except during temporary specific dust release events (as seen in case of 1P/Halley during October 17-30, 1985) by the nucleus \citep{Dollfus1989}."631. The complex. behaviour of the dust is also seen in comet ς105 (Llale-Bopp). especially the region. around. the nucleus shows complex structure (Llacdameik&Levasseur-Itegourd.2003).," The complex behaviour of the dust is also seen in comet C/1995 (Hale-Bopp), especially the region around the nucleus shows complex structure \citep{hadamcik2003}."632. Though the comets. in general. show similar polarisation behaviour with phase angle. they are divided into three classes based on the maximum in polarisation(Levasseur-Itegourd.1999).," Though the comets, in general, show similar polarisation behaviour with phase angle, they are divided into three classes based on the maximum in \citep{levasseur1999}."633. Varving polarisation observed in the coma or in the features (jets. shells. etc.)," Varying polarisation observed in the coma or in the features (jets, shells, etc.)"634 indicates a diversity of dust. particles., indicates a diversity of dust particles.635 Issues related to the dust. characteristics are adequately reviewed by Ixolokolovactal.(2005)., Issues related to the dust characteristics are adequately reviewed by \citet{kolokolova2005}.636. One of the main objective behind the study of comets is to uncerstand the origin of the solar svstem., One of the main objective behind the study of comets is to understand the origin of the solar system.637 Since comets spend. substantial part of their life away from the sun. their sub-surface material is considered. pristine.," Since comets spend substantial part of their life away from the sun, their sub-surface material is considered pristine."638" Space mission Deep Lupact was launehed on January 12. 2005 to study the composition of the interior of the comet 9P""Tempel 1 by colliding a part of the spacecraft with the comet CXLearnetal.2005b:Aleech 2000)."," Space mission Deep Impact was launched on January 12, 2005 to study the composition of the interior of the comet 9P/Tempel 1 by colliding a part of the spacecraft with the comet \citep{hearn2005b, meech2000}."639. At 5:52 UPC on July 4. 2005. the impactor of the Deep Impact. probe successfully collicled with the comet's nucleus. excavating huge amount," At 5:52 UTC on July 4, 2005, the impactor of the Deep Impact probe successfully collided with the comet's nucleus, excavating huge amount"640The orientation of the white loops as drawn is based upon comparison between the HMI magnetic field contours and the loops actually observed by for at least 2.5 days following the initial eruption.,The orientation of the white loops as drawn is based upon comparison between the HMI magnetic field contours and the loops actually observed by for at least 2.5 days following the initial eruption.641" We attribute the slight difference in loop appearance between those in panels c) and d) in this core region as being due to using a potential extrapolation near the limb, 2 days of additional rotation, and possible shear (a typical characteristic of pre-eruptive regions along polarity inversion lines (Su,Golub,&VanBallegooijen||2007))))."," We attribute the slight difference in loop appearance between those in panels c) and d) in this core region as being due to using a potential extrapolation near the limb, 2 days of additional rotation, and possible shear (a typical characteristic of pre-eruptive regions along polarity inversion lines \citep{su-golub-vanball_2007}) )."642 The green lines correspond to the development of the field in the green region of interest., The green lines correspond to the development of the field in the green region of interest.643 These loops appear kinked and stretched in the SECCHI images and are therefore highly non-potential., These loops appear kinked and stretched in the SECCHI images and are therefore highly non-potential.644" The western footpoints of these loops migrate after several hours possibly due to reconnection higher in the corona where the field lines have different footpoints, as is noted above in the PFSS extrapolations."," The western footpoints of these loops migrate after several hours possibly due to reconnection higher in the corona where the field lines have different footpoints, as is noted above in the PFSS extrapolations."645 The actual flaring site is located within the red region of interest where the first post-eruption arcade develops., The actual flaring site is located within the red region of interest where the first post-eruption arcade develops.646 This region also corresponds to the strongest polarity inversion., This region also corresponds to the strongest polarity inversion.647" Due to limb obscuration, the original erupting flux rope is not imaged by AIA nor is it readily apparent in the SECCHI observations. ("," Due to limb obscuration, the original erupting flux rope is not imaged by AIA nor is it readily apparent in the SECCHI observations. ("648A long filamentary structure is seen in the SECCHI images in the far south of the region but is not noticeably involved with the eruption.),A long filamentary structure is seen in the SECCHI images in the far south of the region but is not noticeably involved with the eruption.)649" Fortuitously, two eruptions originate from this region over the following several days wherein a flux rope is observed to erupt from the red core region. ("," Fortuitously, two eruptions originate from this region over the following several days wherein a flux rope is observed to erupt from the red core region. ("650Refer to the available online movie.),Refer to the available online movie.)651" By analyzing the subsequent eruptions and combining this information with the PFSS extrapolations, we infer that a relatively small flux rope erupts from within the core red region."," By analyzing the subsequent eruptions and combining this information with the PFSS extrapolations, we infer that a relatively small flux rope erupts from within the core red region."652" As it travels into the corona, it encounters the overlying field traversing the entire region in the general east-west direction (Figure 6| b))."," As it travels into the corona, it encounters the overlying field traversing the entire region in the general east-west direction (Figure \ref{mag_pfss} b))."653 This overlying field combines with the original erupting flux rope (possibly via reconnection or entanglement) to create a larger erupting flux rope which disrupts the field above the entire region., This overlying field combines with the original erupting flux rope (possibly via reconnection or entanglement) to create a larger erupting flux rope which disrupts the field above the entire region.654" This process may be likened to the flare breakout model (MacNeiceetal.| 20047; DeVore,&Klimchuk| [1999)) although not a necessary scenario due to the uncertainty in the original flux rope and overlying field structure; however, a truly 3-D model addressing the various overlying field line orientations, bend in the core polarity inversion line, and complex photospheric polarity organization is necessary in order understand the evolution of the flux rope."," This process may be likened to the flare breakout model \citeauthor{macneiceEA_2004} \citeyear{macneiceEA_2004}; \citeauthor{antiochos-devore-klimchuk_1999} \citeyear{antiochos-devore-klimchuk_1999}) ) although not a necessary scenario due to the uncertainty in the original flux rope and overlying field structure; however, a truly 3-D model addressing the various overlying field line orientations, bend in the core polarity inversion line, and complex photospheric polarity organization is necessary in order understand the evolution of the flux rope."655" 'The focus of this paper is to discuss the flows occurring in the wake of the flux rope; therefore, we will refer to the erupting flux rope for this region as the large, combined one traversing the region since it is required to create the post-eruption arcade in the green domain — where the flows of interest are occurring. ("," The focus of this paper is to discuss the flows occurring in the wake of the flux rope; therefore, we will refer to the erupting flux rope for this region as the large, combined one traversing the region since it is required to create the post-eruption arcade in the green domain – where the flows of interest are occurring. ("656The post-eruption arcade within the core red region could develop independently due to the original smaller flux rope eruption.),The post-eruption arcade within the core red region could develop independently due to the original smaller flux rope eruption.)657" Using these image sets and the magnetic field topological information as aguide combined with the basic reconnection scenario depicted in Figure D], a simplified description of the orientations of the most"," Using these image sets and the magnetic field topological information as aguide combined with the basic reconnection scenario depicted in Figure \ref{cartoon_all}, , a simplified description of the orientations of the most"658overestimated by up to 0.5 mag 7.,overestimated by up to 0.5 mag $^{-2}$.659 Late type spirals ane irregulars will only have a negligible effect., Late type spirals and irregulars will only have a negligible effect.660 However late types will be more elfected by inclination., However late types will be more effected by inclination.661 To model this. we have assumed. that a disk galaxy is optically thin and has no internal extinction.," To model this, we have assumed that a disk galaxy is optically thin and has no internal extinction."662 A galaxy of area Aj... was assumed to have an isophotal radius ri;;. given bv: The isophotal magnitude ancl radius were used to calculate the total magnitude and the cllective surface brightness yr as described in Cross et al.," A galaxy of area $A_{iso}$, was assumed to have an isophotal radius $r_{iso}$, given by: The isophotal magnitude and radius were used to calculate the total magnitude and the effective surface brightness $\mu_e$ as described in Cross et al."663 2001., 2001.664 However a disk galaxy. inclined at an angle. / with major axis e and minor axis > has an area where The surface brightness has increased at cach point by a [actor i zs inereasing the semi-major axis until pla) Mtm ," However a disk galaxy, inclined at an angle, $i$ with major axis $a$ and minor axis $b$ has an area where The surface brightness has increased at each point by a factor $\frac{1}{\cos(i)}$ , increasing the semi-major axis until $\mu(a)=\mu_{lim}$ ."665where à is the disk scale length., where $\alpha$ is the disk scale length.666 This increases the isophotal [lux of the galaxy. as well as the isophotal radius.," This increases the isophotal flux of the galaxy, as well as the isophotal radius."667 An exponential profile is fitted to these parameters as in Cross et al. (, An exponential profile is fitted to these parameters as in Cross et al. (6682001).,2001).669 The central surface brightness and total magnitude are calculated for this galaxy assuming that the ealaxy is [ace on., The central surface brightness and total magnitude are calculated for this galaxy assuming that the galaxy is face on.670 The error in the central surface surface brightness is the difference between the true central surface brightness and the caleulated: central surface. brightness., The error in the central surface surface brightness is the difference between the true central surface brightness and the calculated central surface brightness.671 The error in the elective surface brightness is exactly the same. as the dillerence between central and effective surface brightness is a constant for an exponential profile.," The error in the effective surface brightness is exactly the same, as the difference between central and effective surface brightness is a constant for an exponential profile."672Phe total,The total673fast. reliable. and sufficiently accurate compared to line-by-line calculations.,"fast, reliable, and sufficiently accurate compared to line-by-line calculations."674 We compared spectra computed by line-by-line and correlated-A models. and found that the mean difference between the two techniques is less than 5 per cent. which is considerably smaller than the range of uncertainties on available exoplanet measurements.," We compared spectra computed by line-by-line and $k$ models, and found that the mean difference between the two techniques is less than 5 per cent, which is considerably smaller than the range of uncertainties on available exoplanet measurements."675 In the &-distribution method. the absorption spectrum over an interval is sorted in order of increasing absorption and the fraction of the interval with absorption less than a certain value A(g) is represented in terms of the fraction of the interval g.," In the $k$ -distribution method, the absorption spectrum over an interval is sorted in order of increasing absorption and the fraction of the interval with absorption less than a certain value $k(g)$ is represented in terms of the fraction of the interval $g$."676 Since A(g) is a smoothly varying function of g. it may be integrated with relatively few quadrature points /V to determine the mean transmission over the interval as: where m is the amount of a molecule: and A; and Ag; are the k-coefficients and quadrature weights at each quadrature point (Irwinetal.2008).," Since $k(g)$ is a smoothly varying function of $g$, it may be integrated with relatively few quadrature points $N$ to determine the mean transmission over the interval as: where $m$ is the amount of a molecule; and $k_{i}$ and $\Delta g_{i}$ are the $k$ -coefficients and quadrature weights at each quadrature point \citep{irw08}."677. The A-coefficients are calculated from line data for a range of temperatures and pressures expected in the atmosphere in advance of the retrieval to enable rapid calculation of the transmission during each iteration., The $k$ -coefficients are calculated from line data for a range of temperatures and pressures expected in the atmosphere in advance of the retrieval to enable rapid calculation of the transmission during each iteration.678 The molecular line lists used in this study were taken from HITEMP2010 (Rothmanetal.2010) for H»O. the Carbon Dioxide Spectroscopic Databank (CDSD-(Tashkunetal.2003) (also used for HITEMP2010) for CO». HITEMP1995 (Rothmanetal.1995) for CO. and the Spherical Top Data System (STDS) (Wenger&Champion1998). for CH.," The molecular line lists used in this study were taken from HITEMP2010 \citep{rot10} for $_{2}$ O, the Carbon Dioxide Spectroscopic Databank (CDSD-1000)\citep{tas03} (also used for HITEMP2010) for $_{2}$, HITEMP1995 \citep{rot95} for CO, and the Spherical Top Data System (STDS) \citep{wen98} for $_{4}$."679 The absorption coefficients for the extreme atmospheric temperatures found within exoplanetary atmospheres are continuously being improved. so the conclusions of this study are considerably limitec by the quality of the available spectroscopic data.," The absorption coefficients for the extreme atmospheric temperatures found within exoplanetary atmospheres are continuously being improved, so the conclusions of this study are considerably limited by the quality of the available spectroscopic data."680 We have made use of the best available spectroscopic parameters at the time of writing. and our line database will be updated as new sources of data become available.," We have made use of the best available spectroscopic parameters at the time of writing, and our line database will be updated as new sources of data become available."681 The combination of the optimal estimation retrieval scheme and the correlated-# method enhances the efficiency of the retrieva process in terms of time and computational resources., The combination of the optimal estimation retrieval scheme and the $k$ method enhances the efficiency of the retrieval process in terms of time and computational resources.682 Furthermore. NEMESIS calculates the matrix. of the partial derivatives of radiances at each wavelength with respect to each retrieved variable. which are called the frnedional derivatives (or Jacobrans). in order that the contribution of different atmospheric yurameters at each wavelength can be easily interpreted by comparing the elements of this matrix.," Furthermore, NEMESIS calculates the matrix of the partial derivatives of radiances at each wavelength with respect to each retrieved variable, which are called the $functional$ $derivatives$ (or $Jacobians$ ), in order that the contribution of different atmospheric parameters at each wavelength can be easily interpreted by comparing the elements of this matrix."683" Our e priori dayside atmosphere of HD 19597330 extends Tom "" to IO bar to capture the full atmospheric range of »otential spectral contributions.", Our $a$ $priori$ dayside atmosphere of HD 189733b extends from $^{-9}$ to 10 bar to capture the full atmospheric range of potential spectral contributions.684 For initial modelling we assumed hat all species were well-mixed throughout the atmosphere and he molecular abundanee was defined in terms of a single sealing yarameter., For initial modelling we assumed that all species were well-mixed throughout the atmosphere and the molecular abundance was defined in terms of a single scaling parameter.685 This is because the retrieval of a continuous profile of composition would be under-constrained considering the small number of data points and the low spectral resolutions available. eading to non-physical oscillations in the retrieved profile.," This is because the retrieval of a continuous profile of composition would be under-constrained considering the small number of data points and the low spectral resolutions available, leading to non-physical oscillations in the retrieved profile."686 The « priori estimate for the abundance scaling parameter is assumed to dave a large uncertainty so that retrieved values are not weighted by initial guesses since a simple scaling parameter already includes vertical smoothing., The $a$ $priori$ estimate for the abundance scaling parameter is assumed to have a large uncertainty so that retrieved values are not weighted by initial guesses since a simple scaling parameter already includes vertical smoothing.687 The @ priori for temperature. however. is assumed to have a continuous profile and the assumed error on he « priori profile was adjusted to achieve the optimal balance between the quality of the fit to the measured data and the vertical smoothing.," The $a$ $priori$ for temperature, however, is assumed to have a continuous profile and the assumed error on the $a$ $priori$ profile was adjusted to achieve the optimal balance between the quality of the fit to the measured data and the vertical smoothing."688 This will be further discussed in Section 5.3.1., This will be further discussed in Section 5.3.1.689 As an important source of absorption in exoplanetary atmospheres. collisional-induced absorption (CIA) between principle gases are included in the model atmosphere.," As an important source of absorption in exoplanetary atmospheres, collisional-induced absorption (CIA) between principle gases are included in the model atmosphere."690 We consider the interactions between H»—-H» and He—-He and the coefficients are taken from Borysowetal.(1989). Borysow&Frommhold(1989). Borysow&Frommhold(1990).. Zheng&Borysow(1995)... Borysowetal.(1997).. and Borysow(2002).," We consider the interactions between $_{2}$ $_{2}$ and $_{2}$ –He and the coefficients are taken from \citet{bor89}, \citet{bor892}, \citet{bor90}, \citet{zhe95}, \citet{bor97}, and \citet{bor02}."691. The mole fractions of H» and He are assumed to be related to the fractions of atomic H and He. which are close to the typical solar value of 0.91 and 0.0887 each (Burrows&Sharp1999).," The mole fractions of $_{2}$ and He are assumed to be related to the fractions of atomic H and He, which are close to the typical solar value of 0.91 and 0.0887 each \citep{bur99}."692. The implications of this assumption will be tested in Section 5.5., The implications of this assumption will be tested in Section 5.5.693 Seattering by clouds and hazes has been reported from fiS7 observations at visible wavelengths. yielding a featureless ransmission spectrum of HD 189733b (Pontetal.2008:Singetal.2011).," Scattering by clouds and hazes has been reported from $HST$ observations at visible wavelengths, yielding a featureless transmission spectrum of HD 189733b \citep{pon08,sin11}."694 Recently. Hengetal.(2011) showed that the effect of scattering by clouds and hazes modifies the inferred emperature profile. and that an isothermal temperature structure above an adiabatic troposphere could also be caused by a cloud-op or haze layer.," Recently, \citet{hen11} showed that the effect of scattering by clouds and hazes modifies the inferred temperature profile, and that an isothermal temperature structure above an adiabatic troposphere could also be caused by a cloud-top or haze layer."695 We consider. however. that the inclusion of scattering. clouds and hazes in our retrieval model is beyond he scope of the present study for a number of reasons: (1) the scattering properties of possible clouds and hazes is insufficiently known: (1) adding such particles would greatly enlarge an already arge and poorly constrained parameter space and: (i) modelling scattering. processes will significantly increase the computation ime.," We consider, however, that the inclusion of scattering clouds and hazes in our retrieval model is beyond the scope of the present study for a number of reasons: (i) the scattering properties of possible clouds and hazes is insufficiently known; (ii) adding such particles would greatly enlarge an already large and poorly constrained parameter space and; (iii) modelling scattering processes will significantly increase the computation time."696 In summary. the addition of scattering would increase the complexity of the model and does not appear to be warranted by he dayside emission spectra studied here.," In summary, the addition of scattering would increase the complexity of the model and does not appear to be warranted by the dayside emission spectra studied here."697 We intend to assess the ikely effects of scattering on our modelling of folJipilers in a ollow-up study., We intend to assess the likely effects of scattering on our modelling of $hot Jupiters$ in a follow-up study.698 To retrieve the 7-7 profile and compositional abundances. we used three measurement. sets of the secondary. eclipse for HD 189733b. representing all of the available infrared dayside eclipse measurements at the present time. ranging over a wide wavelength range from [.45 jim to 24 jim: Go eighteen 7/5 77NICMOS (Swain channels covering the range 1.45—2.5 jim: (1) forty seven Spitzer IRS (Grillmairetal.2008) channels covering the range 5—14.5 jim and one IRS photometry (Deming channel at 16 sam: and (i) five Spi/zer TRAC (Infrared. Array Camera) and MIPS (Multiband Imaging Photometer for pil zer) (Charbonneauetal.2008). photometry channels at 3.6. 4.5. 5.8. 8.0. and 24 jim. The measurement errors on the three observational datasets are directly obtained from the studies referenced above.," To retrieve the $P$ $T$ profile and compositional abundances, we used three measurement sets of the secondary eclipse for HD 189733b, representing all of the available infrared dayside eclipse measurements at the present time, ranging over a wide wavelength range from 1.45 $\mu$ m to 24 $\mu$ m: (i) eighteen $HST$ /NICMOS \citep{swa09} channels covering the range 1.45–2.5 $\mu$ m; (ii) forty seven $Spitzer$ IRS \citep{gri08} channels covering the range 5–14.5 $\mu$ m and one IRS photometry \citep{dem06} channel at 16 $\mu$ m; and (iii) five $Spitzer$ IRAC (Infrared Array Camera) and MIPS (Multiband Imaging Photometer for $Spitzer$ ) \citep{cha08} photometry channels at 3.6, 4.5, 5.8, 8.0, and 24 $\mu$ m. The measurement errors on the three observational datasets are directly obtained from the studies referenced above."699 To integrate the binned flux in each channel. we use (i) filter widths taken from the literature for Sp/fzer broadband channels (Fazioetal.2004:RiekeDeming2006): (i) ILSTINICMOS widths of ~10 nm at 2 jim: and (ii) Spit zer/IRS widths of ~ 100 nm at 8 jam. The reference stellar spectrum for HD 189733 is taken from the Kurucz grid model’.," To integrate the binned flux in each channel, we use (i) filter widths taken from the literature for $Spitzer$ broadband channels \citep{faz04,rie04,dem06}; (ii) $HST$ /NICMOS widths of $\sim$ 10 nm at 2 $\mu$ m; and (iii) $Spitzer$ /IRS widths of $\sim$ 100 nm at 8 $\mu$ m. The reference stellar spectrum for HD 189733 is taken from the Kurucz grid ."700 Despite the substantial efforts towards finding and reducing the errors from the data. uncertainties on the given datasets still remain and are widely distributed over the wavelengths due to various error sources.," Despite the substantial efforts towards finding and reducing the errors from the data, uncertainties on the given datasets still remain and are widely distributed over the wavelengths due to various error sources."701 First of all. techniques to decorrelate a transit light curve from the combined light of a planetary system are not consistent each other fe.g. Swainetal.(2008). vs. Gibsonetal. D]].," First of all, techniques to decorrelate a transit light curve from the combined light of a planetary system are not consistent each other [e.g. \citet{swa08} vs. \citet{gib11}] ]."702 We will discuss the effects of underestimated errors on, We will discuss the effects of underestimated errors on703We simulate the scenario described. setting the background cleusity to be 5%Ut of the value in the dense chimps. aud the initial velocity of this gas to be zero.,"We simulate the scenario described, setting the background density to be $5\%$ of the value in the dense clumps, and the initial velocity of this gas to be zero."704 We focus just ou the collision region. so that the right and left sides ο ‘the domain are set to “clump” conditions. as in Equation (19)).," We focus just on the collision region, so that the right and left sides of the domain are set to “clump"" conditions, as in Equation \ref{cflIC}) )."705 When the two dense «lumps meet each other. a stroug shock forms (Fig. 5)).," When the two dense clumps meet each other, a strong shock forms (Fig. \ref{CC3}) )."706 Since all [uid variables (à. By. Up) are s and continuous prior to shock formation. the features produced are not a consequence of discontilous initial coucitious.," Since all fluid variables $n$, $B_y$, $v_x$ ) are smooth and continuous prior to shock formation, the features produced are not a consequence of discontinuous initial conditions."707 This test case eventually evolves to profile similar to that in the simpe convergent [low test (Fie. 6))., This test case eventually evolves to profile similar to that in the simple convergent flow test (Fig. \ref{CC4}) ).708 The central peaks in deusity auc ratio show up as well., The central peaks in density and mass-to-flux ratio show up as well.709 Susequent evolution leads to a decline in the central peak iu 5 aud niBy (Fig. 6))., Subsequent evolution leads to a decline in the central peak in $n$ and $n/B_y$ (Fig. \ref{CC4}) ).710 Peaks in density above the “steady” shock solution have also been observed in other ambipolar diffusion simulations using different MHD codes (e.g..Choietal.2009)..," Peaks in density above the “steady"" shock solution have also been observed in other ambipolar diffusion simulations using different MHD codes \citep[e.g.,][]{2009ApJS..181..413C}."711 In. addition. similar transient behavior of C shocks has been noted i1 models with more complex chemistry impleineuted (e.g.Chiezeοἱa.1998:vanLooetal.2009:Ashinore2010)..," In addition, similar transient behavior of C shocks has been noted in models with more complex chemistry implemented \citep[e.g.][]{1998MNRAS.295..672C, 2009MNRAS.395..319V, 2010A&A...511A..41A}."712" Physically. we believe these peaks arise becaise the neutrals are effectivey Cunmaegnetized"" when the shock first forms."," Physically, we believe these peaks arise because the neutrals are effectively “unmagnetized"" when the shock first forms."713 As a COllsecquence. 1ie ueutrals cau be very stroiely compressed. forming what is seen as a central density peak in Figs.," As a consequence, the neutrals can be very strongly compressed, forming what is seen as a central density peak in Figs."714 1-6.., \ref{cvg1}$ $-$ \ref{CC4}.715 The magnetic field. however. does not follow the inital strong compression of the ueutrals.," The magnetic field, however, does not follow the initial strong compression of the neutrals."716 Iustead. the overv-conupressed ueutrals generate higher pressure in the central regions. inhibiting the magnetic [lux from gettiug in.," Instead, the overly-compressed neutrals generate higher pressure in the central regions, inhibiting the magnetic flux from getting in."717 Fig., Fig.718 7 slows the total p 5 ⋅ ↠∖⊽∖⊽⊳∖↕↩⋯⋅∖∖↽∐≺↵↕⋅↩∫⋟≜≕⊳⋮↳∖∶∣↗⊔≬⋡⊽∖−⋜↕∐≺⇂∫⋟∠↗∶≵≩−↙∕∕↖∖∣⊤⋅∖∖↽∐∐∣⋅∣∣∐↕≺↵⋜↕⊳∖⋯⋅≺↵≺⇂∐⊔∐≺↵↥⋜↕∣⋉∐⋅⋜↕↕∩↥⋅⊽∖⊽⊔⋅⋜⋃∐≺↵⋅⊺∐≺↵⊳∖≺↵ tlire," \ref{pressure} shows the total pressure $P_\mathrm{tot} = \rho_n {v_n}^2 + P_\mathrm{gas} + P_B$ of the system, where $P_\mathrm{gas} = \rho_n {c_s}^2$ and $P_B = B^2/8\pi$, with $v_n$ measured in the “laboratory"" frame."719"e terms correspoxd to ACUgrj. ry. and rg7/?Jg respective""y. ln. Equation (11))."," These three terms correspond to ${\cal M}^2/r_n$, $r_n$, and ${r_B}^2/\beta$ respectively, in Equation \ref{up_down}) )."720 Since uses the conservative [ori1 of the momentum equation (OUA(pe)/0f+OP/Or= 0). P iust become coustant in the posttock region at late times.," Since uses the conservative form of the momentum equation $ \partial \left(\rho v\right) / \partial t + \partial P_\mathrm{tot} / \partial x = 0$ ), $P_\mathrm{tot}$ must become constant in the post-shock region at late times."721 For stroiο shocks. the maguetic pressure term dominates at late tiides in the post-shock region.," For strong shocks, the magnetic pressure term dominates at late times in the post-shock region."722 At early times. there is a slight depression of the magnetic field streng at the center of the shock. in order to balauce the extremely Ligh neutral £as pressure in the «sity peak.," At early times, there is a slight depression of the magnetic field strength at the center of the shock, in order to balance the extremely high neutral gas pressure in the density peak."723 Combining he strong ueutral compression aL slight magnetic exclusion. the —jass-Lo-Iux ratio is elevated in tle ce “when a shock forms.," Combining the strong neutral compression and slight magnetic exclusion, the mass-to-flux ratio is elevated in the center when a shock forms."724 The αςlisious between neutrals aud lous will gradually slow down the iucoο neutrals auc compress iois and maguetic field to the center., The collisions between neutrals and ions will gradually slow down the incoming neutrals and compress ions and magnetic field to the center.725 Meauwhile. the neutrals in the 'eutral peak diffuse outward in order to balance tle increasing maguetic pressure auc keep the total )ressture constalr.," Meanwhile, the neutrals in the central peak diffuse outward in order to balance the increasing magnetic pressure and keep the total pressure constant."726 Eventually. the ious aud weutrals interact sufficiently that a steady-state C shiocJ structure deveops.," Eventually, the ions and neutrals interact sufficiently that a steady-state C shock structure develops."727" The post-shock n/B, is the same as the upstream value.", The post-shock $n/B_y$ is the same as the upstream value.728 However. the ambivolar diffusion process takes tiue. aud during the trausieut stage. a region of very strongly compressed ueutrals will be present.," However, the ambipolar diffusion process takes time, and during the transient stage, a region of very strongly compressed neutrals will be present."729 Our finding that there is a transieut stage of very strong deusity compression. with au enliauced," Our finding that there is a transient stage of very strong density compression, with an enhanced"730Aapni~A20.,$\lambda_{MRI}\sim\Delta/20$.731 Ou general erounds. however. we note hat we would expect that the transition poiut would lic at Aarg&SA.," On general grounds, however, we note that we would expect that the transition point would lie at $\lambda_{MRI}\ll 8\Delta$."732 A eiven vertical field is unstable uot just o the fastest erowing mode. but also to a whole spectrum of slower-growing modes that have longer wavelengths hat are more casily resolvable ποσααν.," A given vertical field is unstable not just to the fastest growing mode, but also to a whole spectrum of slower-growing modes that have longer wavelengths that are more easily resolvable numerically."733 Plausibe he transition point will then correspond to the condition hat we resolve the slowest erowing mode that grows appreciably before it is truncated by non-linear coupling o other MRI modes or some other aspect of the plivsics (ee. a dynamo evele).," Plausibly, the transition point will then correspond to the condition that we resolve the slowest growing mode that grows appreciably before it is truncated by non-linear coupling to other MRI modes or some other aspect of the physics (e.g. a dynamo cycle)."734 Tf this is the case. then it is uusirprising that the transition poiut varies between ocal and elobal simulations. since the time scale available or a mode to grow may well depeud on the presence or absence of a low density disk corona within which the AIRI is not active.," If this is the case, then it is unsurprising that the transition point varies between local and global simulations, since the time scale available for a mode to grow may well depend on the presence or absence of a low density disk corona within which the MRI is not active."735" To consider this more quautitativelv. consider purely vertical AIRT modes (4,=&, 0) in a thin accretiou disk (so that radial eracieuts of pressure and eutropy can be neglected)."," To consider this more quantitatively, consider purely vertical MRI modes $k_r=k_\phi=0$ ) in a thin accretion disk (so that radial gradients of pressure and entropy can be neglected)."736 Let the spacetime dependence of the modes he (€{οςobz), Let the spacetime dependence of the modes be $e^{i(\omega t-kz)}$.737 The dispersion relation for these modes (Balbus&Hawley1991). reads where 2?=4heer and # is the radial epicyclic (angular) frequency., The dispersion relation for these modes \citep{mri1} reads where $\tilde{\omega}^2=\omega^2-k^2v_A^2$ and $\kappa$ is the radial epicyclic (angular) frequency.738 We wish to examine modes with wavelengths much longer than the fastest growing mode. ic. with |keV/O9|< 1.," We wish to examine modes with wavelengths much longer than the fastest growing mode, i.e., with $|kv_A/\Omega_0|\ll 1$ ."739 Rewriting in terms of the growth rate. d=fw and expanding the dispersion relation to lowest order in k?267/08 gives Suppose that a eiven mode cau erow exponcutially for a time 7 before it is truncated by mode coupling or some other unspecified physical process.," Rewriting in terms of the growth rate, $\sigma=-i\omega$ and expanding the dispersion relation to lowest order in $k^2v_A^2/\Omega_0^2$ gives Suppose that a given mode can grow exponentially for a time $\tau$ before it is truncated by mode coupling or some other unspecified physical process."740 Then. the slowest erowing inode that actually experiences siguificaut erowth (hereafter. the slowest appreciably eroxwing mode [SAGAL)) has ση=20/7 and a saveumuber given by Our lypothesis is that the transition point iu the fiux-stress relation correspouds to the point where the slowest appreciably erowiug mode is just resolvable. ie.. where Asayin=28hugs~SA.," Then, the slowest growing mode that actually experiences significant growth (hereafter, the slowest appreciably growing mode [SAGM]) has $\sigma_{sagm}=2\pi/\tau$ and a wavenumber given by Our hypothesis is that the transition point in the flux-stress relation corresponds to the point where the slowest appreciably growing mode is just resolvable, i.e., where $\lambda_{sagm}\equiv7412\pi/k_{sagm}\sim 8\Delta$."742 This predicts a transition point at where r'—Titan. topp bouge the orbital period at that radius.," This predicts a transition point at where $\tau^\prime\equiv\tau/t_{orb}$, $t_{orb}$ being the orbital period at that radius."743 Equation 13. offers some insight iuto the transition point found in the flux-stress relations that we have been considering., Equation \ref{eq:lmri} offers some insight into the transition point found in the flux-stress relations that we have been considering.744" In the local uustratified simulations of Pessaletal.(2007).. the implicit potential is Newtonian (ne= OF) and we find that Agra, A. imiplving 7~ f,5,."," In the local unstratified simulations of \citet{boxscaling}, the implicit potential is Newtonian $\kappa^2=\Omega_0^2$ ) and we find that $\lambda_{MRI}\sim \Delta$ , implying $\tau\sim t_{orb}$ ."745" lu the global sinuuations presented here. we find the transition point at Aaya,cA/20 which (accounting for the fact that #7?<o2 in the pseudo-Newtoniau poteutial) eijvoes το—θέ "," In the global simulations presented here, we find the transition point at $\lambda_{MRI}\sim \Delta/20$ which (accounting for the fact that $\kappa^2<\Omega_0^2$ in the pseudo-Newtonian potential) gives $\tau\sim 5-10t_{orb}$."746Thus. within the framework of this argument. the difference iu the location of the transition point between the local wustratified and the global siuulations is due to a difference iu the robustness of the long waveleneth aud slowly erowiug modes: slowing erowius nodes appear to be able to erow for longer withiu the elobal simulation before being truncated.," Thus, within the framework of this argument, the difference in the location of the transition point between the local unstratified and the global simulations is due to a difference in the robustness of the long wavelength and slowly growing modes; slowing growing modes appear to be able to grow for longer within the global simulation before being truncated."747 The nature of this differeuce. which must be closely related to the saturation of the turbulent state. is bevoud the scope of this paper aud will be explored in future work.," The nature of this difference, which must be closely related to the saturation of the turbulent state, is beyond the scope of this paper and will be explored in future work."748 The results of refsec:fluxstress sugecsts that the Guctuating) magnetic Hux threading a local patch of the disk determines the ro0 component of the magnetic stress generated by he turbulence in that patch., The results of \\ref{sec:fluxstress} suggests that the (fluctuating) magnetic flux threading a local patch of the disk determines the $r-\phi$ component of the magnetic stress generated by the turbulence in that patch.749 If the vertical maguetic Hux is indeed the causal ageut i determine the stress. we expect a temporal lag between fluctuations in the maeuectic flux and the resulting variations in he stress," If the vertical magnetic flux is indeed the causal agent in determining the stress, we expect a temporal lag between fluctuations in the magnetic flux and the resulting variations in the stress."750 On the basis of experiments with local sinulations (ILuwvlevetal.1996).. we expect this lag to © approximately two (local) orbital periods.," On the basis of experiments with local simulations \citep{hawley96}, we expect this lag to be approximately two (local) orbital periods."751 Thus. we expect the temporal lag to imerease with radius in the disk due to the increasing orbital period.," Thus, we expect the temporal lag to increase with radius in the disk due to the increasing orbital period."752 To search for this lag. we use and output the 3-d structure of the disk once every 0.1 ISCO orbits during the interval between 5090 ISC'O orbits (this is 10 times the nominaldata output rate).," To search for this lag, we use and output the 3-d structure of the disk once every 0.1 ISCO orbits during the interval between 50–90 ISCO orbits (this is 10 times the nominaldata output rate)."753" Using these 100 snapshots of the disk structure. we then colputed the instantaneous vertical magnetic faxes aud maguctic ro stresses in families of co-moving wedges at three radi rC[SryLey.12r,}."," Using these 400 snapshots of the disk structure, we then computed the instantaneous vertical magnetic fluxes and magnetic $r-\phi$ stresses in families of co-moving wedges at three radii $r\in754\{8r_g, 10r_g, 12r_g\}$."755" The azunutballv averaged value of c, at cach radius was used to track a given comoving wedee between tinesteps.", The azimuthally averaged value of $v_\phi$ at each radius was used to track a given comoving wedge between timesteps.756 This procedure is uot fully lagrangian. because it docs not account for the radial movement or fluctuating azimuthal velocity of a comoving patch. but we expect these effects to be uceleible for the short timeframe uudoer consideration.," This procedure is not fully lagrangian, because it does not account for the radial movement or fluctuating azimuthal velocity of a comoving patch, but we expect these effects to be negligible for the short timeframe under consideration."757 The time-series of maguetic fux and stress for cach wedge were then cross-correlated aud. finally. the cross-correlations for all wedges at a given radius were averaged.," The time-series of magnetic flux and stress for each wedge were then cross-correlated and, finally, the cross-correlations for all wedges at a given radius were averaged."758 The resulting averaged temporal cross-correlations are shown in Fie. L., The resulting averaged temporal cross-correlations are shown in Fig. \ref{crosscorr}.759 At each radius we see a strong lustautaneous correlation. Likely due to the nmuuediate sheariug of perturbed vertical fields.," At each radius we see a strong instantaneous correlation, likely due to the immediate shearing of perturbed vertical fields."760 However. in general. 16 cross-correlation is biased toward positive lag.," However, in general, the cross-correlation is biased toward positive lag."761 Tis is consistent with what we would expect. namely that the xeseuce of vertical flux will feed the MBI aud result in rosthanced transport.," This is consistent with what we would expect, namely that the presence of vertical flux will feed the MRI and result in enhanced transport."762 Of note is the fact that the imner-lost radius considered. R=sry exhibits a double peak structure whereas this is unresolved at higher radii.," Of note is the fact that the inner-most radius considered, $R=8r_g$ exhibits a double peak structure whereas this is unresolved at higher radii."763" Also seculiar is the fact that the outermost radius. R=I2r, is senificautlv less biased towards positive lag than the other radii under consideration."," Also peculiar is the fact that the outer-most radius, $R=12r_g$ is significantly less biased towards positive lag than the other radii under consideration."764 A further exploration of hese issues is bevoud the scope of this paper. aud will ο explored iu future work cmplovine orbital advection algoritlins aud test-particle tracers in order to correctly ollow the evolution of a local patc[u," A further exploration of these issues is beyond the scope of this paper, and will be explored in future work employing orbital advection algorithms and test-particle tracers in order to correctly follow the evolution of a local patch."765"m Whenconsidering the correlation between vertical fux and stress we workdirectly with AM, but when studving possible trends in average stress with domain size we instead define au effective o-paraneter"," Whenconsidering the correlation between vertical flux and stress we workdirectly with $M_{r\phi}$ , but when studying possible trends in average stress with domain size we instead define an effective $\alpha$ -parameter"766shear signal may suffer [rom such a bias (Whiteetal.2002)..),shear signal may suffer from such a bias \citep{white:clusters-completeness}. .)767 On intermediate scales. the orientation of nearby filamentary structure correlated with the cluster lens (as well as the angular distribution of nearby correlated halos} must also be random for a large statistical sample.," On intermediate scales, the orientation of nearby filamentary structure correlated with the cluster lens (as well as the angular distribution of nearby correlated halos) must also be random for a large statistical sample."768 Since such structure is correlated wilh the lens. itdoes contribute to (he tangential shear on large scales: indeed. as we have argued above. it dominates the signal from clusters on scales above afew ft\Mpe and simply represents the large-scale chister-mass correlation funelion.," Since such structure is correlated with the lens, it contribute to the tangential shear on large scales; indeed, as we have argued above, it dominates the signal from clusters on scales above a few $h^{-1}$ Mpc and simply represents the large-scale cluster-mass correlation function."769 Again. as shown above. the effects of correlated structure along the line of sight appear to be negligible out to the virial radius of massive clusters.," Again, as shown above, the effects of correlated structure along the line of sight appear to be negligible out to the virial radius of massive clusters."770 The only residual problem for the statistical inversion method is anisotropic sample variance ab large scales (discussed above in Section 6)): Chis finite-volume ellect creates a small scatter in the inferred mass but does not create a bias., The only residual problem for the statistical inversion method is anisotropic sample variance at large scales (discussed above in Section \ref{section:tests}) ); this finite-volume effect creates a small scatter in the inferred mass but does not create a bias.771 We have developed. a non-parametric method lor inverüing cross-correlation lensing measurements to obtain average densitv and mass profiles of halos., We have developed a non-parametric method for inverting cross-correlation lensing measurements to obtain average density and mass profiles of halos.772 We have demonstrated the method on an N-body simulation and shown that it successfully recovers the 3D proliles., We have demonstrated the method on an N-body simulation and shown that it successfully recovers the 3D profiles.773 We argued that asphericitv of halos and Iarge-scale structure along the line of sight do not introduce bias or substantial uicertaintv in the inferred mass estimates., We argued that asphericity of halos and large-scale structure along the line of sight do not introduce bias or substantial uncertainty in the inferred mass estimates.774 This method should find several useful applications in survevs., This method should find several useful applications in surveys.775 Applied to galaxv-galaxy lensing measurements. this method can be used to measure «Αρη=Ὁροῃ£y(r) Lor samples of lens galaxies (e.g.. Sheldon. et al.," Applied to galaxy-galaxy lensing measurements, this method can be used to measure $\Delta\rho(r) = \Omega_m\rho_{crit}~\xi_{gm}(r)$ for samples of lens galaxies (e.g., Sheldon, et al."776 2004)., 2004).777 On small scales. (his provides information about galaxy dark matter halos and should thereby constrain models of galaxy formation ancl evolution. including the details of hierarchical structure formation and merging.," On small scales, this provides information about galaxy dark matter halos and should thereby constrain models of galaxy formation and evolution, including the details of hierarchical structure formation and merging."778 Statistical nass profiles around galaxies can provide virial mass measurements and. combined with the average lieht profile around these galaxies. determine mass-to-lieht ratios as a Iunction of scale.," Statistical mass profiles around galaxies can provide virial mass measurements and, combined with the average light profile around these galaxies, determine mass-to-light ratios as a function of scale."779 On larger scales. galaxv-galaxy lensing inversions should tell us more about cosmology.," On larger scales, galaxy-galaxy lensing inversions should tell us more about cosmology."780" The autocorrelation function of galaxies allows us to measure £4,(7)=b(r)&,,,(r). where b(r) is the scale-dependent bias and £,,;00) is the mass autocorrelation function."," The autocorrelation function of galaxies allows us to measure $\xi_{gg}(r) = b^2(r) \xi_{mm}(r)$, where $b(r)$ is the scale-dependent bias and $\xi_{mm}(r)$ is the mass autocorrelation function."781" Lensine allows us to measure O,,£,,(r)=OQ,bir)r«(r)Sianeli). where the eross-bias. κ). is sometimes referred to as stochastic bias (a term we do not recommend using in this context. since it is not bounded by 41)."," Lensing allows us to measure $\Omega_m~\xi_{gm}(r) =782\Omega_m~b(r)~\mbox{r}_{\times}(r)~\xi_{mm}(r)$, where the cross-bias, $\mbox{r}_{\times}(r)$, is sometimes referred to as stochastic bias (a term we do not recommend using in this context, since it is not bounded by $\pm1$ )."783 The presence of these (vo bias functions. b(r) aad ry(7). allows for the most general model of the relative clustering of galaxies and mass. (," The presence of these two bias functions, $b(r)$ and $\mbox{r}_{\times}(r)$, allows for the most general model of the relative clustering of galaxies and mass. ("784See also (2005)..),See also \cite{neyrinck:halo-model}. .)785 Simulations indicate that rz(7) is consistent with unity on scales larger than, Simulations indicate that $\mbox{r}_{\times}(r)$ is consistent with unity on scales larger than786by svuchrotvon photons plavs an important role in the internal shock model (Guetta. Spada Waxman 2001: Asano Kobavashi 2002).,"by synchrotron photons plays an important role in the internal shock model (Guetta, Spada Waxman 2001; Asano Kobayashi 2002)."787 In order to obtain hieh radiative efficiency. ancl the characteristic clustering of spectral break energies of GRBs in the range 0.1-1 MeV. the collision radii are required to be similar to the photosphere radius.," In order to obtain high radiative efficiency and the characteristic clustering of spectral break energies of GRBs in the range 0.1-1 MeV, the collision radii are required to be similar to the photosphere radius."788 Since collisions producing narrow pulses occur at small radii xD. the photosphere might obscure these. leaving only the wider pulses visible.," Since collisions producing narrow pulses occur at small radii $\propto D$, the photosphere might obscure these, leaving only the wider pulses visible."789 This will make (he temporal profile smooth., This will make the temporal profile smooth.790 In a wider jet. (he tvpical Lorentz lactor Dis smaller. a larger fraction of the collisions occur at small radii xE? below the photosphere. therefore. the smoothing effect is expected to be stronger.," In a wider jet, the typical Lorentz factor $\Gamma$ is smaller, a larger fraction of the collisions occur at small radii $\propto \Gamma^2$ below the photosphere, therefore, the smoothing effect is expected to be stronger."791 This might explain the correlation between luminosity ancl variability in GRBs., This might explain the correlation between luminosity and variability in GRBs.792 We discuss the smoothing effect. by using a multiple-shell model., We discuss the smoothing effect by using a multiple-shell model.793 We represent the irregular wind bv relativistic shells in a manner similar to that in INPS., We represent the irregular wind by relativistic shells in a manner similar to that in KPS.794" Because of the relativistic beaming effect. we can study (he emission [rom a jet by using spherical shells with an isotropic explosion energv. Ej,(0)=46/6? where E is the geometrically corrected explosion energv and 8 is the opening angle."," Because of the relativistic beaming effect, we can study the emission from a jet by using spherical shells with an isotropic explosion energy $E_{iso}(\theta)=4 E/\theta^2$ where $E$ is the geometrically corrected explosion energy and $\theta$ is the opening angle."795" The eanuna-ray energy released troma GRD is narrowly clustered around 10"" ere (Frail et al.", The gamma-ray energy released froma GRB is narrowly clustered around $10^{51}$ erg (Frail et al.796 2001). and the conversion elliciency [rom (he explosion energv into the gamma-rays is about 1056(Guetta. Spada Waxman 2001: IXobavashi Sari 2001).," 2001), and the conversion efficiency from the explosion energy into the gamma-rays is about $10\%$(Guetta, Spada Waxman 2001; Kobayashi Sari 2001)."797 Then. E~LO” erg.," Then, $E \sim 10^{52}$ erg."798 Cousider a two shell collision which is the elementary process in the multiple shell evolution., Consider a two shell collision which is the elementary process in the multiple shell evolution.799" A rapid shell with Lorentz [actor D, and mass m, catches up to a slower one with D; and m. and the two merge to temporarily form a single shell."," A rapid shell with Lorentz factor $\Gamma_r$ and mass $m_r$ catches up to a slower one with $\Gamma_s$ and $m_s$, and the two merge to temporarily form a single shell."800" Using conservation ol energv and momentum we calculate (he Lorentz factor of the merged shell to be The internal energy. of the merged shell is the difference of kinetic energy before ancl alter the collision. Ej;=m,c(T,—Ty)-mic(D. D,)."," Using conservation of energy and momentum we calculate the Lorentz factor of the merged shell to be The internal energy of the merged shell is the difference of kinetic energy before and after the collision, $E_{int}=m_rc^2(\Gamma_r-\Gamma_m)+m_sc^2(\Gamma_s-\Gamma_m)$ ."801" We assume that electrons are accelerated to a power-law distribution of Lorentz factor ορ. with a minimum. Lorentz factor mi Nelda,ox8,Uds,2 am."," We assume that electrons are accelerated to a power-law distribution of Lorentz factor $\gamma_e$, with a minimum Lorentz factor $\gamma_m$ : $N(\gamma_e)d\gamma_e \propto \gamma_e^{-p}d\gamma_e, \gamma_e \ge802\gamma_m$ ."803 Throughout this paper. we use thestandard choice," Throughout this paper, we use thestandard choice"804comparison with observational data.,comparison with observational data.805 We estimate the cllipcity coniponeuts of cach halo by nicasmiug the second moments of the projected mass distribution m a vay analogous to that used for the surface brightuess distribution of galaxies (Valdes 1983. Alivalda-Escudé 1991): where and Tere. i6 and g ave the coordinates of the ceuter of mass of the halo iu question. which contains VY particles of equal mass.," We estimate the ellipcity components of each halo by measuring the second moments of the projected mass distribution in a way analogous to that used for the surface brightness distribution of galaxies (Valdes 1983, Miralda-Escudé 1991): where and Here, $\overline{x}$ and $\overline{y}$ are the coordinates of the center of mass of the halo in question, which contains $N$ particles of equal mass."806 In the observational case. these moments are often calculated using the surface brightuess weielted by a function chosen to maximize the S/N of the measurement (see c.g. WW).," In the observational case, these moments are often calculated using the surface brightness weighted by a function chosen to maximize the S/N of the measurement (see e.g., VW)."807 In our case. as we have mentioned above. we will probe the seusitivitv of our iueasuremeuts to varatious of this sort by comparing halos chosen with a laree FOF linking leueth to those using a small value which cfectively give a non-zero weight oulv to the dense central reelous.," In our case, as we have mentioned above, we will probe the sensitivity of our measurements to variations of this sort by comparing halos chosen with a large FOF linking length to those using a small value which effectively give a non-zero weight only to the dense central regions."808 When working with ραπνο statistics. such as the ellipticity correlation fiction (see 833). it will be advantageous to redefine ey aud e» for cach pair of halos. with the w-axis defined to be line joinine the halo ceutres aud the y-axis a line perpendicular to it.," When working with pairwise statistics, such as the ellipticity correlation function (see 3), it will be advantageous to redefine $e_{1}$ and $e_{2}$ for each pair of halos, with the $x$ -axis defined to be line joining the halo centres and the $y$ -axis a line perpendicular to it."809 The quantity (61.609) defines a pseudovector. of leneth C=VG| 3.," The quantity $(e_{1},e_{2})$ defines a pseudovector, of length $e=\sqrt{e_{1}^{2}+e_{2}^{2}}$ ."810 A positive c4 component indicates a stretching along the. axis. aud a negative compoucut a stretching along the yo axis.," A positive $e_{1}$ component indicates a stretching along the $x-$ axis, and a negative component a stretching along the $y-$ axis."811 The e» component is likewise a nieasure of the stretching along axes at Lodeg to the .c aud y axes., The $e_{2}$ component is likewise a measure of the stretching along axes at $45 \deg$ to the $x$ and $y$ axes.812 If we have au cllipse of ellipticity e (6—(1.«λα147). where q is the ratio of winmor and major axis leneths). then where s is the augle between the major axis aud the CO naxbs," If we have an ellipse of ellipticity $e$ $e \equiv (1-q^{2})/(1+q^{2})$, where $q$ is the ratio of minor and major axis lengths), then where $\beta$ is the angle between the major axis and the $x-$ axis."813 Iu the bottom three panels of Fig. l..," In the bottom three panels of Fig. \ref{halo},"814 we plot the elliptidties of the halos chosen by the three eroupfinders., we plot the ellipticities of the halos chosen by the three groupfinders.815 For each halo. we show a bar with leneth proportional to c. oriented along the direction of the major axis.," For each halo, we show a bar with length proportional to $e$, oriented along the direction of the major axis."816 It is dathicult to pick out bv eve auv tendency for halos to be aligned., It is difficult to pick out by eye any tendency for halos to be aligned.817 One worry which we mieht have had concerus the tendency of close halos to be joined together bv thin vuecks” of particles and for the eroupfinder to count such pairs as oue halo., One worry which we might have had concerns the tendency of close halos to be joined together by thin “necks” of particles and for the groupfinder to count such pairs as one halo.818 If these halos are distributed along fiunenuts. then we might expect au artificial alieuneut to arise.," If these halos are distributed along filaments, then we might expect an artificial alignment to arise."819 This does not seen to be au obvious problem here., This does not seem to be an obvious problem here.820" For example. if we look at halos picked out bv the FOE,4 aud FOF)» eroupfiuders. the ellipticities and. directions appear to be faitly similar even though differeut parts of the halo are being used to caleulate them."," For example, if we look at halos picked out by the $_{0.1}$ and $_{0.2}$ groupfinders, the ellipticities and directions appear to be fairly similar even though different parts of the halo are being used to calculate them."821 We will check the statistical endencies for aliguiments iu the next section., We will check the statistical tendencies for alignments in the next section.822 The TOP alos do in several cases appear to be made frou several sanall halos joined together., The HOP halos do in several cases appear to be made from several small halos joined together.823 Presuinablv this could be alleviated by tuning the free parameters which govern the uethod. but we have not attempted to do this.," Presumably this could be alleviated by tuning the free parameters which govern the method, but we have not attempted to do this."824 Tn Fig. 2..," In Fig. \ref{ehist},"825 we show the probabilitv distribution of « values for the halos (again with >20 member particles) Xcked out bv the three groupfuders., we show the probability distribution of $e$ values for the halos (again with $>20$ member particles) picked out by the three groupfinders.826" They are all fairly simular. with a mean e around 0.Ll. slightly higher than the 43 typical of real galaxies (σοι, Wittinan 2000)."," They are all fairly similar, with a mean $e$ around $0.4$, slightly higher than the $0.3$ typical of real galaxies (e.g., Wittman 2000)."827 Observationally. ellipticity correlations are measured as a function of augular separation. ou the plane of the sky (at least for weak lensing survevs).," Observationally, ellipticity correlations are measured as a function of angular separation, on the plane of the sky (at least for weak lensing surveys)."828 With distance information (for example. using redshifts}. it would be possible to measure them as a function of separation iu three dimensions. and this is what it is most natural to do using our Nbody simulations.," With distance information (for example, using redshifts), it would be possible to measure them as a function of separation in three dimensions, and this is what it is most natural to do using our Nbody simulations."829 Iu this section. we will do this. and later convert the measurements to angular correlations which cau be compared to weak lensing survey results.," In this section, we will do this, and later convert the measurements to angular correlations which can be compared to weak lensing survey results."830 This conversion will be done iu two different wavs., This conversion will be done in two different ways.831 The first is an analytical projection of our three dimensional results using Linwber’s equation (Limber. 1959].," The first is an analytical projection of our three dimensional results using Limber's equation (Limber, 1959)."832 The second is a direct measurement from sinmlated surveys made bv projecting the halo distributions im the box. and applying a radial selection fuuctiou.," The second is a direct measurement from simulated surveys made by projecting the halo distributions in the box, and applying a radial selection function."833 In the prescut section. although we will be dealing with halo separations in three dimensions. if is worth bearing im mind that we restrict ourselves to quantities which can be measured directly observationally (albeit with redshifts). so that the cllipticitics wewill be correlating are projected ellipticities (defined in Equation 1)).," In the present section, although we will be dealing with halo separations in three dimensions, it is worth bearing in mind that we restrict ourselves to quantities which can be measured directly observationally (albeit with redshifts), so that the ellipticities wewill be correlating are projected ellipticities (defined in Equation \ref{e1}) )."834 Two cllipticity correlations cau be defined (following Aliralda-Escudé 1991) as, Two ellipticity correlations can be defined (following Miralda-Escudé 1991) as835during the evolution of structure at early times. anc visible as an isotropic eamma-rav backeround at the present cay.,"during the evolution of structure at early times, and visible as an isotropic gamma-ray background at the present day."836 In this paper. we calculate. the Dux produced. by annihilations in simple CDAL halos. relative to the tux ooduced in a uniform background.," In this paper, we calculate the flux produced by annihilations in simple CDM halos, relative to the flux produced in a uniform background."837 We correct this result or halo substructure. and. integrate over a large. volume o determine the cosmological background. from WIAIP annihilation as a function of redshift.," We correct this result for halo substructure, and integrate over a large volume to determine the cosmological background from WIMP annihilation as a function of redshift."838 The outline of this yaper is as follows., The outline of this paper is as follows.839 In section 2. we define a climensionless lux multiplier f. that accounts for the enhanced. rate of two-body interactions produced. by inhomogeneities in he dark matter distribution. and. determine its value for simple virialisecd halos.," In section 2, we define a dimensionless flux multiplier $f$ that accounts for the enhanced rate of two-body interactions produced by inhomogeneities in the dark matter distribution, and determine its value for simple virialised halos."840 In section 3 we caleulate { for cosmological volumes. using analytic estimates of the halo mass function and halo concentrations. ancl determine its redshift’ dependence.," In section 3 we calculate $f$ for cosmological volumes, using analytic estimates of the halo mass function and halo concentrations, and determine its redshift dependence."841 Finally. in section. 4 we study. the contribution to f. from substructure within virialisecl halos. and calculate f for à set of realistic halos generated: using a semi-analvtie model of halo substructure.," Finally, in section 4 we study the contribution to $f$ from substructure within virialised halos, and calculate $f$ for a set of realistic halos generated using a semi-analytic model of halo substructure."842 Throughout this paper we assume a Lambda-CDM (LODM) cosmology with a cosmological constant Ag=0.7. a matter density Oo=0.3 and a Hubble parameter 40=fhlO00knmis with 5—0.65.," Throughout this paper we assume a Lambda-CDM (LCDM) cosmology with a cosmological constant $\Lambda_0 = 0.7$, a matter density $\Omega_{{\rm m},0} = 0.3$ and a Hubble parameter $H_0 = h \times\ 100 {\rm km\,s^{-1}}$, with $h = 0.65$."843 In current hierarchical models. cold dark matter is expected to. form centrally concentrated: halos with a characteristic density profile.," In current hierarchical models, cold dark matter is expected to form centrally concentrated halos with a characteristic density profile."844 Dense substructure is abundant within these halos. as a relic from earlier stages of the hierarchical merging process.," Dense substructure is abundant within these halos, as a relic from earlier stages of the hierarchical merging process."845 Since the annihilation Hux is quadratic in the density. these inhomogeneities will increase the πας from a halo of a given mean density.," Since the annihilation flux is quadratic in the density, these inhomogeneities will increase the flux from a halo of a given mean density."846 We begin hy computing a cimensionless quantity that describes this enhancement., We begin by computing a dimensionless quantity that describes this enhancement.847 In the next section we will then stuck the evolution ofthis quantity with epoch., In the next section we will then study the evolution of this quantity with epoch.848 If clark matter consists of neutralinos with a mass my ancl a velocity-averaged cross-section for annihilation (ec then the annihilation Uux produced within a volume V. will be where p is the local density ofCDM.," If dark matter consists of neutralinos with a mass $m_\chi$ and a velocity-averaged cross-section for annihilation ${\langle \sigma v \rangle}$, then the annihilation flux produced within a volume $V$ will be where $\rho$ is the local density of CDM."849 For non-relativistic xuticles. £00? is approximately independent of e so the Dux will just be proportional to p.," For non-relativistic particles, ${\langle \sigma v \rangle}$ is approximately independent of $v$ so the flux will just be proportional to $\rho^2$."850 Since the rate depends equadratically on the density. the otal rate from a given mass within a given. volume will be ueher ifthe dark matter is distributed inhomogeneously.," Since the rate depends quadratically on the density, the total rate from a given mass within a given volume will be higher if the dark matter is distributed inhomogeneously."851 We can study thisenhancement. by defining the dimensionless lux multiplier for a distribution within a volume V. where p is the average density within this volume.," We can study thisenhancement by defining the dimensionless flux multiplier for a distribution within a volume $V$, where ${\bar \rho}$ is the average density within this volume."852 This function can also be written as à mass-weighted density average: where A is the total mass within V., This function can also be written as a mass-weighted density average: where $M$ is the total mass within $V$ .853 Clearly. f=1 for a homogeneous distribution. while for a power-law density profile pxrmm provided à«1.5.," Clearly $f = 1$ for a homogeneous distribution, while for a power-law density profile $\rho \propto r^{-\alpha}$, provided $\alpha < 1.5$."854" For à—1.5. integrating equation (2)) from luin lO Mux ΟΙΝΟΝ: so f diverges logarithmically as rii, goes to zero."," For $\alpha = 1.5$, integrating equation \ref{fluxm1}) ) from $r_{\rm min}$ to $r_{\rm max}$ gives: so $f$ diverges logarithmically as $r_{\rm min}$ goes to zero."855 Two analytic density profiles are commonly used to fit the spherically averaged: properties of dark matter halos. the NEW profile (Navarro. Frenk White 1996. 1997). and the Moore profile (Moore et 11998).," Two analytic density profiles are commonly used to fit the spherically averaged properties of dark matter halos, the NFW profile (Navarro, Frenk White 1996, 1997), and the Moore profile (Moore et 1998)."856 We can specify. these generically as with à=31.5—2 for the NEW profile and a= for the Moore profile.," We can specify these generically as with $\alpha = \beta = 1, \gamma = 2$ for the NFW profile and $\alpha = \beta = 1.5, \gamma = 1$ for the Moore profile."857 Ehe total mass within radius r is with for the NEW profile and for the Moore. profile. while the mean density. within this radius is simply where.—rfr.," The total mass within radius $r$ is with for the NFW profile and for the Moore profile, while the mean density within this radius is simply where $x \equiv r/r_s$."858" 1n a cosmological setting. halos are virialised out to a radius r« corresponding to an overdensity A, of roughly 200 relative to the background."," In a cosmological setting, halos are virialised out to a radius $r_v$ corresponding to an overdensity $\Delta_c$ of roughly 200 relative to the background."859" The concentration ο—refr, ofa halo describes the size of this radius relative tor...", The concentration $c \equiv r_v/r_s$ of a halo describes the size of this radius relative to $r_s$ .860 Calculating the (ux multiplier over the virialised region of a halo. we get a function which depends only on e," Calculating the flux multiplier over the virialised region of a halo, we get a function which depends only on$c$ :"861"To properly assess the contribution of the various mono-abundance sub-populations to the mass or surface-mass budget in the Solar neighborhood, we must convert the number of spectroscopically-observed stars in each bin to a surface-mass density at the Solar neighborhood.","To properly assess the contribution of the various mono-abundance sub-populations to the mass or surface-mass budget in the Solar neighborhood, we must convert the number of spectroscopically-observed stars in each bin to a surface-mass density at the Solar neighborhood."862" On the one hand, this requires incorporation of a model for the sselection function (see A of B11)) and our exponential-disk fits (B11))."," On the one hand, this requires incorporation of a model for the selection function (see A of ) and our exponential-disk fits )."863" On the other hand, this requires the use of stellar-population models that can relate the observed number of G-type dwarfs to the total mass of the stellar population, given the metallicity of the sub-population and an assumed star formation history for it."," On the other hand, this requires the use of stellar-population models that can relate the observed number of G-type dwarfs to the total mass of the stellar population, given the metallicity of the sub-population and an assumed star formation history for it."864 This is described in detail in ??.., This is described in detail in \ref{sec:surfmass}.865" Briefly, for G-type dwarfs in a given ([Fe/H],,[a/Fe])) bin we calculate their total number per square pc over vertical height) by adjusting the normalization(integrated of the number-density profile such that after running it through our model for the sselection function it predicts the observed number of stars in each bin."," Briefly, for G-type dwarfs in a given ) bin we calculate their total number per square pc (integrated over vertical height) by adjusting the normalization of the number-density profile such that after running it through our model for the selection function it predicts the observed number of stars in each bin."866 Then we relate the number density of G-type dwarfs to the total stellar surface-mass density by multiplying the number density by the average mass of a G-type dwarf—calculated using Padova isochrones (Marigoetal. dividing it by the fraction of the mass in a stellar 2008)-—andpopulation in G-type dwarfs (calculated using the same isochrones and assuming a lognormal Chabrier(2001) initial mass function)., Then we relate the number density of G-type dwarfs to the total stellar surface-mass density by multiplying the number density by the average mass of a G-type dwarf—calculated using Padova isochrones \citep{Marigo08a}- —and dividing it by the fraction of the mass in a stellar population in G-type dwarfs (calculated using the same isochrones and assuming a lognormal \citet{Chabrier01a} initial mass function).867" At a given abundance, this fraction of course depends on the age of the population, and here is calculated by marginalizing over a flat age distribution between 0.5 and 10 Gyr for each bin."," At a given abundance, this fraction of course depends on the age of the population, and here is calculated by marginalizing over a flat age distribution between 0.5 and 10 Gyr for each bin."868" However, averaging only over older ages for a-enhanced stars would be appropriate, as a-enhanced stars likely represent the oldest part of the disk."," However, averaging only over older ages for $\alpha$ -enhanced stars would be appropriate, as $\alpha$ -enhanced stars likely represent the oldest part of the disk."869" As we show in ??,, this gives similar results, with a slightly steeper decline in X(HRo) with h,."," As we show in \ref{sec:surfmass}, this gives similar results, with a slightly steeper decline in $\Sigma(R_0)$ with $h_z$."870 We calculate uncertainties on the surface-mass densities by varying the density-parameters according to the posterior probability distribution for the parameters inB11.., We calculate uncertainties on the surface-mass densities by varying the density-parameters according to the posterior probability distribution for the parameters in.871 These uncertainties do not include systematic uncertainties due to the use of the stellar isochrones., These uncertainties do not include systematic uncertainties due to the use of the stellar isochrones.872" This procedure results in an estimate of the stellar surface-mass density contribution at the Solar radius for any abundance-selected sub-population, which in turn has a vertical scale height associated with it."," This procedure results in an estimate of the stellar surface-mass density contribution at the Solar radius for any abundance-selected sub-population, which in turn has a vertical scale height associated with it."873" The relative total stellar surface-mass densities of different mono-abundance bins are not affected by assuming a different initial mass function although assuming a different IMF can systematically (IMF),shift all surface-mass densities by a few percent (see below)."," The relative total stellar surface-mass densities of different mono-abundance bins are not affected by assuming a different initial mass function (IMF), although assuming a different IMF can systematically shift all surface-mass densities by a few percent (see below)."874 'The results from this mass estimation are shown in s1 and 2.., The results from this mass estimation are shown in s \ref{fig:mass_afe_feh} and \ref{fig:mass_hz_afe}.875" The left panel of 1 is simply a more coarsely binned version of the unweighted GG-dwarf sample abundance distribution, which shows two distinct maxima, one considerably more metal poor and o-enhanced than the other, seemingly reflecting a chemically-distinct thick-disk component."," The left panel of \ref{fig:mass_afe_feh} is simply a more coarsely binned version of the unweighted G-dwarf sample abundance distribution, which shows two distinct maxima, one considerably more metal poor and $\alpha$ -enhanced than the other, seemingly reflecting a chemically-distinct thick-disk component."876" It is important to note that the marginalized mmetallicity distribution (left [Fe/H]panel, top) shows no hint of any bi-modality."," It is important to note that the marginalized metallicity distribution (left panel, top) shows no hint of any bi-modality."877" There is distinct bi-modality in the marginalized ddistribution, but [a/Fe]Schónrich&Binney already showed that even for a smooth age distribution(2009a) such bi-modality arises, simply separating stars that formed before and after enrichment by SN Ia became important."," There is distinct bi-modality in the marginalized distribution, but \citet{Schoenrich08a} already showed that even for a smooth age distribution such bi-modality arises, simply separating stars that formed before and after enrichment by SN Ia became important."878" The right panel of 1 shows the stellar mass density at the solar radius Ro in each elemental-abundance bin, corrected for selection effects due to the spectroscopic sselection as described above."," The right panel of \ref{fig:mass_afe_feh} shows the stellar surface-mass density at the solar radius $R_0$ in each elemental-abundance bin, corrected for selection effects due to the spectroscopic selection as described above."879" It represents the properly mass-weighted, underlying distribution of disk stars in the elemental-abundance space spanned by aand[a/Fe],, and dramatically differs from the raw sample distribution in the left panel: it does not have the strong bi-modality apparent in the raw nnumber distribution."," It represents the properly mass-weighted, underlying distribution of disk stars in the elemental-abundance space spanned by and, and dramatically differs from the raw sample distribution in the left panel: it does not have the strong bi-modality apparent in the raw number distribution."880 It also shows no hint of a bi-modal mmetallicity distribution and the remaining hint of bbi-modality is explained as in the left panel., It also shows no hint of a bi-modal metallicity distribution and the remaining hint of bi-modality is explained as in the left panel.881 The right panel of 1 now provides the relevant weights of each mono-abundance bin to a surface-mass- distribution of disk scale heights., The right panel of \ref{fig:mass_afe_feh} now provides the relevant weights of each mono-abundance bin to a surface-mass-weighted distribution of disk scale heights.882 The colored symbols in 2 show exactly these surface-mass, The colored symbols in \ref{fig:mass_hz_afe} show exactly these surface-mass883lass concentration iu the local universe.,mass concentration in the local universe.884" Throughout. the following cosmological parameters are adopted: Q,,=0.3. O4=O7. and IZ,=100h=T0 5. which Πάρος a scale of 1.6 Alpe + (77 kpe t) at the ~20.000 nuuean redshift of the IRS."," Throughout, the following cosmological parameters are adopted: $\Omega _m = 0.3$ , $\Omega _\Lambda = 0.7$ , and $H_o = 100h885= 70 $ $^{-1}$, which implies a scale of 4.6 Mpc $^{-1}$ (77 kpc $^{-1}$ ) at the $\sim$ 20,000 mean redshift of the HRS."886 The UK Schinidt Telescope (UIST) six-deerce field (dE). multi-fiber system is uniquely suited to survey large supercluster regious im the nearby universe.," The UK Schmidt Telescope (UKST) six-degree field (6dF), multi-fiber system is uniquely suited to survey large supercluster regions in the nearby universe."887 6dE deploys 150 fibers over a circular field of caameter wwith a nuninnun required spacing between fibers of 677. set bv the magnetic prism buttons.," 6dF deploys 150 fibers over a circular field of diameter with a minimum required spacing between fibers of 7, set by the magnetic prism buttons."888 Light is fed from the fibers iuto a fast f/0.9 CCD spectrograph (Parkeretal.19908)., Light is fed from the fibers into a fast f/0.9 CCD spectrograph \citep{par98}.889. Two interchangeable field plate units allow for the simultaneous observation of the current feld aud configuration of the next., Two interchangeable field plate units allow for the simultaneous observation of the current field and configuration of the next.890 A practical limiting magnitude for the svstem is b; = 17.5., A practical limiting magnitude for the system is $_J$ = 17.5.891 All of these attributes taken together iuply that the 6dF is most effectively used to probe the large-scale iuter-cluster euvironnieuts of local superclusters. while avoiding the more densely crowded cluster members.," All of these attributes taken together imply that the 6dF is most effectively used to probe the large-scale inter-cluster environments of local superclusters, while avoiding the more densely crowded cluster members."892 Consequently. in studviug the TRS our goal was to produce a catalog of galaxies iu the iuter-cluster region.," Consequently, in studying the HRS our goal was to produce a catalog of galaxies in the inter-cluster region."893" Galaxy solectiou took place in the following manner,", Galaxy selection took place in the following manner.894" A . aarea of the sky centered upon a=3""19.5 wwas chosen for the region of observation based upon previously published literature (Zuccaetal. 1993)."," A $\times$ area of the sky centered upon $\alpha = 3^h19^m, \delta =895-$ was chosen for the region of observation based upon previously published literature \citep{zuc93}."896. A complete catalog of all galaxies dow ο à by imaegnitude of 17.5 was extracted iu four equivalent « 67) regions from the UKST survey ates previously scanned by. the SuperCOSMOS nachine (ILuublvetal.2001)., A complete catalog of all galaxies down to a $_J$ magnitude of 17.5 was extracted in four equivalent $\times$ ) regions from the UKST survey plates previously scanned by the SuperCOSMOS machine \citep{ham01}.897". There was also he addition of a fifth rectaugular region « 6"")) in the far Southeru portion to incorporate he feld surrounding ACO clusters 3106 αμα 3161.", There was also the addition of a fifth rectangular region $\times$ ) in the far Southern portion to incorporate the field surrounding ACO clusters 3106 and 3164.898 The ealaxy classification flag assigned bv SuperCOSAIOS was used for the initial suuple selection., The galaxy classification flag assigned by SuperCOSMOS was used for the initial sample selection.899 The b;=17.5 maguitude lait was adopted as a practical limiting magnitude for the L2an aperture UNST., The $_J= 17.5$ magnitude limit was adopted as a practical limiting magnitude for the 1.2-m aperture UKST.900 To avoid expeuding fibers on galaxies within clusters. our original intention was to excise from the catalog all ealaxies within a 17 radius circle of sixteen ACO clusters listed by Zuccaetal.(1993). απο νους of the URS aud intersecting our observing region.," To avoid expending fibers on galaxies within clusters, our original intention was to excise from the catalog all galaxies within a $^{\circ}$ radius circle of sixteen ACO clusters listed by \cite{zuc93} as members of the HRS and intersecting our observing region."901" The 1"" radius exclusion corresponds to ~2 Abell radi (where 1 Ry»= 2 Alpe) at the mean redshift of the TRS.", The $^{\circ}$ radius exclusion corresponds to $\sim$ 2 Abell radii (where 1 $_A=$ 2 Mpc) at the mean redshift of the HRS.902 This would cusure that new spectroscopic information relates onlv to the iuter-cluster regions of the IIRS., This would ensure that new spectroscopic information relates only to the inter-cluster regions of the HRS.903 Iowever. a coding error was discovered in the programs. that excises galaxies from the cluster regions oulv after the observations were made.," However, a coding error was discovered in the program that excises galaxies from the cluster regions only after the observations were made."904 The cos(ó) conversion factor in the Right Ascension (RA) coordinate. when expressed in degrees. was not included. in the calculation of angular distances of galaxies from cluster ceuters.," The $\cos$ $\delta$ ) conversion factor in the Right Ascension (RA) coordinate, when expressed in degrees, was not included in the calculation of angular distances of galaxies from cluster centers."905 As a result. the actual excision regious are fhtened in the RA coordinate and correspondingly more flattened at higher Declination.," As a result, the actual excision regions are flattened in the RA coordinate and correspondingly more flattened at higher Declination."906 The typical fattening is a factor of 1.6., The typical flattening is a factor of 1.6.907 Nevertheless. the result remains that we have generated a sample that is alinost entirely conrprised. of iuter-cluster galaxies.," Nevertheless, the result remains that we have generated a sample that is almost entirely comprised of inter-cluster galaxies."908 After the above coustraiuts were applied. there relmained 28LS ealaxies (Figure |).," After the above constraints were applied, there remained 2848 galaxies (Figure \ref{f1}) )."909 The πιακα uunber of optical ealaxy redshifts that could be obtained uncer optimal observing conditions was estimated at 1500., The maximum number of optical galaxy redshifts that could be obtained under optimal observing conditions was estimated at 1500.910 Consequeuth. we produced a subcatalog of 1500 targets from the original list of 2818.," Consequently, we produced a subcatalog of 1500 targets from the original list of 2848."911 This was accomplished as follows., This was accomplished as follows.912 Calaxies in cach ος region were assigued a random) Πο aud then arranged in ascending order., Galaxies in each $\times$ region were assigned a random number and then arranged in ascending order.913 This ordering provides a basis for selecting an unbiased subsample from the larger complete sample., This ordering provides a basis for selecting an unbiased subsample from the larger complete sample.914" The uuuberius schemes from the iadividual SO"" iregious were merged into a final catalog of 1500 objects with cach region weighted according to the fraction of galaxies found in that region.", The numbering schemes from the individual $\times$ regions were merged into a final catalog of 1500 objects with each region weighted according to the fraction of galaxies found in that region.915 That is. if of the ealaxies in the original catalog came from a particular region. the subcatalog of 1500 ealaxics also contaiuc from that region.," That is, if of the galaxies in the original catalog came from a particular region, the subcatalog of 1500 galaxies also contained from that region."916 Hence the method preserves natural galaxy overdeusities while randomlysuupling theeutire extracted region., Hence the method preserves natural galaxy overdensities while randomlysampling theentire extracted region.917 Finally. a Digitized Sky Survey (DSS) nuage of cach target was cxamuned to further reduce the uuuber of misclassified galaxies iun the," Finally, a Digitized Sky Survey (DSS) image of each target was examined to further reduce the number of misclassified galaxies in the"918but not exactly: it is not possible to derive C! when the two dips are perfectly superposed).,but not exactly: it is not possible to derive $C$ when the two dips are perfectly superposed).919 lt appears [rom Fig., It appears from Fig.920 1 that C could be represented with a polynomial with terms less and less significant when the order increases: the most important is Cy. aid a slope may possibly be added. since C may be as large as Co|O.1 when [V1E is large.," \ref{fig:C_V2} that $C$ could be represented with a polynomial with terms less and less significant when the order increases: the most important is $C_0$, and a slope may possibly be added, since $C$ may be as large as $C_0 + 0.1$ when $|V_1-V_2|$ is large."921 Then. €'CoΟτοvs].," Then, $C=C_0 + C_1|V_1-V_2|$."922 The (6η.ον) coellicients. were calculated: as terms of he orbital solution for 7 of the S svstems with more than 10 blended measurements that are presented in. Fig.," The $(C_0, C_1)$ coefficients were calculated as terms of the orbital solution for 7 of the 8 systems with more than 10 blended measurements that are presented in Fig."923 2 (the triple system 2:54B was set aside)., \ref{fig:orblend} (the triple system 2:54B was set aside).924 It appeared. t Cy was never significant. since its maximum value. t was obtained for system. 2:74B. was only 2.35 times its uncertainty.," It appeared that $C_1$ was never significant, since its maximum value, that was obtained for system 2:74B, was only 2.35 times its uncertainty."925 Moreover. negative values were found for 3 systems (1:19D. 2:58D. and 2:79B). although this should no happen in theory.," Moreover, negative values were found for 3 systems (1:19B, 2:58B, and 2:79B), although this should not happen in theory."926 We conclude then that the Ct term. is sullicient for deriving the blended. velocities., We conclude then that the $C_0$ term is sufficient for deriving the blended velocities.927 This is easilv confirmed by a visual inspection of Eig. 2..," This is easily confirmed by a visual inspection of Fig. \ref{fig:orblend},"928 where the mocde velocity curves derived by assuming only the €t term in the expression of Care represented., where the model velocity curves derived by assuming only the $C_0$ term in the expression of $C$ are represented.929 The blended measurements are equally distributed: around the theoretical curves. anc no deviation related with |Viio is visible in practice.," The blended measurements are equally distributed around the theoretical curves, and no deviation related with $|V_1-V_2|$ is visible in practice."930 Lt was possible to derive the orbital elements for 51 stars. inclucling a triple-system solution which consists of 2 orbits.," It was possible to derive the orbital elements for 51 stars, including a triple-system solution which consists of 2 orbits."931 The spectroscopic orbits are presented. in Tables 40 to 6.., The spectroscopic orbits are presented in Tables \ref{tab:orb1} to \ref{tab:orb3}.932 We count 40 first orbits: 27 91 and 13 SB2., We count 40 first orbits: 27 SB1 and 13 SB2.933 The 12 other orbits are. distributed. as follows: Six are new orbits that were computed taking into account other measurements in addition to ours: these caleulations were done including the olfset oetween the 2 RW sources as a free. parameter of the model., The 12 other orbits are distributed as follows: Six are new orbits that were computed taking into account other measurements in addition to ours; these calculations were done including the offset between the 2 RV sources as a free parameter of the model.934 Two other orbits are. published orbits which were partly based on our measurements: they are just expressed with the same conventions as the others: RY in the system. and epochs in Julian davs: the last 4 orbits are new orbits derived [rom our measurements alone. since including the others did not ameliorate the solution.," Two other orbits are published orbits which were partly based on our measurements; they are just expressed with the same conventions as the others: RV in the system, and epochs in Julian days; the last 4 orbits are new orbits derived from our measurements alone, since including the others did not ameliorate the solution."935 The phase plots of 49 orbits ave available in electronic form., The phase plots of 49 orbits are available in electronic form.936 “Phe two orbits that were already. published are not drawn again., The two orbits that were already published are not drawn again.937 In Table 3.. we count 15 stars for which it was not possible to derive a spectroscopic orbit.," In Table \ref{tab:Vmoy}, we count 15 stars for which it was not possible to derive a spectroscopic orbit."938 In addition. we still found two triple svstems (2:16 ancl 2:981). with a short-period SB and a clit in the residual RV.," In addition, we still found two triple systems (2:16A and 2:98B), with a short-period SB and a drift in the residual RV."939 Ehe figures showing the racial velocities of these 17 stars as functions of the epochs are given in electronic form., The figures showing the radial velocities of these 17 stars as functions of the epochs are given in electronic form.940 In addition to the two triple svstems alreacly mentioned. we still count 7 long period SBI (2:sL.," In addition to the two triple systems already mentioned, we still count 7 long period SB1 (2:8B,"941can be described by a Kings law (Lada&Lacla2003).. although the present objects are not virialised.,"can be described by a King's law \citep{Lada03}, although the present objects are not virialised."942 Llowever. the differential dust absorption produces conspicuous variations in the RDPs of the present objects.," However, the differential dust absorption produces conspicuous variations in the RDPs of the present objects."943 Wing profile describes the structure of clusters close to spherical symmetry ancl centrally concentrated., King profile describes the structure of clusters close to spherical symmetry and centrally concentrated.944 However. many voung clusters are substructurecl or asymmetric. deviating significantly. fron this shape. and therefore. cannot be fitted hy Ixing's. law (Cartwright&Whitworth2004:Cutermuthctal," However, many young clusters are substructured or asymmetric, deviating significantly from this shape, and therefore cannot be fitted by King's law \citep{Cartwright04, Gutermuth05}."945.2005).. 1n Fig. 14..," In Fig. \ref{fig:14},"946 we show the spatial distribution of stars in the decontaminated photometry of the three EC's that follow a Ixine-like wolile (FSR 784. Sh2-235 Cluster ancl Sh2-235E2)} and two representative cases of objects that do not (AWC 11 and BDSB 73).," we show the spatial distribution of stars in the decontaminated photometry of the three ECs that follow a King-like profile (FSR 784, Sh2-235 Cluster and Sh2-235E2) and two representative cases of objects that do not (KKC 11 and BDSB 73)."947 The former are centrally concentrated and nearly circularly svimmetric., The former are centrally concentrated and nearly circularly symmetric.948 Phe cavities anc overdensities in the stellar distribution (Eig. 14)), The cavities and overdensities in the stellar distribution (Fig. \ref{fig:14}) )949 can be seen as bumps and dips in the RDP (Fig. 11))., can be seen as bumps and dips in the RDP (Fig. \ref{fig:11}) ).950 On the other hand. objects like BDSB τὸ that are not centrally condensed and WAC 11 with more elongated shape do not follow a Wing profile.," On the other hand, objects like BDSB 73 that are not centrally condensed and KKC 11 with more elongated shape do not follow a King profile."951 Phe multiple peaks in the RDPs of these ECs may be a fractal ellect., The multiple peaks in the RDPs of these ECs may be a fractal effect.952 these objects survive the primordial gas expulsion. they may undergo merging evolving into a relatively smooth structure.," If these objects survive the primordial gas expulsion, they may undergo merging evolving into a relatively smooth structure."953 The angular distribution of decontaminated stars (Fig. 14)).," The angular distribution of decontaminated stars (Fig. \ref{fig:14}) ),"954 used. in the CALD construction. reprocuces the distribution of stars in the RDPs built with filtered photometry (Figs.," used in the CMD construction, reproduces the distribution of stars in the RDPs built with filtered photometry (Figs."955 12. and 13)). supporting the consistency οἱ our results.," \ref{fig:12} and \ref{fig:13}) ), supporting the consistency of our results."956 Given the poorly-populated nature of the MS. we simply counted stars in the CAIDs (within the region P<Rapp). and summed their masses as estimated. from the mass-luminosity relation implied by the respective isochrone solution (Sect. 3.2)).," Given the poorly-populated nature of the MS, we simply counted stars in the CMDs (within the region $R<R_{RDP}$ ), and summed their masses as estimated from the mass-luminosity relation implied by the respective isochrone solution (Sect. \ref{sec:3.2}) )."957 The results are given in Table 4.., The results are given in Table \ref{tab8}.958 All the ECs clearly present. clistinet populations of MIS and PAIS stars (Figs., All the ECs clearly present distinct populations of MS and PMS stars (Figs.959 4 o S))., \ref{fig:04} to \ref{fig:08}) ).960 However. given the cillcrential recldening. it is not pessible to attribute a prec“Isc mass value for cach PAm star.," However, given the differential reddening, it is not possible to attribute a precise mass value for each PMS star."961 Thus. we simply count the number of PAIS stars anc adop an average mass value [ου he PMS stars to estin enpars and mpars.," Thus, we simply count the number of PMS stars and adopt an average mass value for the PMS stars to estimate $n_{PMS}$ and $m_{PMS}$."962 Assuming that he mass distribution of the PMS stars also follows Ixroupa's (2001) ME. the zsc. average PAS mass - for masses wilin he range 0.08m(A.)i is <ΠΕΙ=~06A.," Assuming that the mass distribution of the PMS stars also follows Kroupa's (2001) MF, the zsc, average PMS mass - for masses within the range $0.08\la m(\ms)\la7$ - is $<m_{PMS}>\approx0.6\ms$."963 ‘Thus. we simply multiply the number of PAIS stars (Pablc S) w this value to estimate the PAS mass.," Thus, we simply multiply the number of PMS stars (Table 8) by this value to estimate the PMS mass."964 Finally. we add the alter value to the AIS mass to obtain an estimate of the otal stellar mass.," Finally, we add the latter value to the MS mass to obtain an estimate of the total stellar mass."965 Vhese values should. be taken as lower inits., These values should be taken as lower limits.966 N-body simulations of massive star clusters that include the οσοι of eas removal (e.g.Goodwin&Bastian2006) show that the phase of dramatic core radii increase may Last about 10-30 Myr., N-body simulations of massive star clusters that include the effect of gas removal \citep[e.g.][]{Goodwin06} show that the phase of dramatic core radii increase may last about 10-30 Myr.967 Mass segregation may also lead to a phase of core contraction. with high mass stars more concentrated in the core while low mass stars are transferred to outer parts of the cluster.," Mass segregation may also lead to a phase of core contraction, with high mass stars more concentrated in the core while low mass stars are transferred to outer parts of the cluster."968 In this context. we suggest that most objects of our," In this context, we suggest that most objects of our"969The satellite (2)). launched in October 2002. ts an ESA space mission specifically designed to study the gamma-ray sky.,"The satellite \citealt{winkler}) ), launched in October 2002, is an ESA space mission specifically designed to study the gamma-ray sky."970 In particular the IBIS (Imager on Board of the Satellite)telescope (2)) 1s the main hard X-ray/soft gamma-ray coded aperture Imaging mstrument (?)). and is responsible for surveying and cataloguing the sky above 17 keV. Here we discuss the point source location accuracy (PSLA) of the ISGRI low energy detector (15-1000 keV) of IBIS (?)).," In particular the IBIS (Imager on Board of the Satellite)telescope \citealt{ubertini03}) ) is the main hard X-ray/soft gamma-ray coded aperture imaging instrument \citealt{goldwurm03}) ), and is responsible for surveying and cataloguing the sky above 17 keV. Here we discuss the point source location accuracy (PSLA) of the ISGRI low energy detector (15-1000 keV) of IBIS \citealt{lebrun03}) )."971 Due to the continuing necessity to follow-up the growing unidentified source population in other wavebands (particularly optical and infrared). it is of great interest to assure the correctness of the IBIS/ISGRI PSLA.," Due to the continuing necessity to follow-up the growing unidentified source population in other wavebands (particularly optical and infrared), it is of great interest to assure the correctness of the IBIS/ISGRI PSLA."972 In particular. it is hoped that with the release of new and updated Offline Science Analysis (OSA 7.0) software the PSLA could have improved substantially compared to the already published estimates based on early mission data and software releases (?.con-structedthePSLAbaseduponOSA 3.0)..," In particular, it is hoped that with the release of new and updated Off-line Science Analysis (OSA 7.0) software the PSLA could have improved substantially compared to the already published estimates based on early mission data and software releases \citep[][constructed the PSLA based upon OSA 3.0]{gros}."973 Any improvement in the PSLA is important in reducing the chance of random or multiple source associations in other wavebands., Any improvement in the PSLA is important in reducing the chance of random or multiple source associations in other wavebands.974 In order to empirically determine the PSLA of the IBIS/ISGRI telescope. we can extract the positions of objects from the IBIS/ISGRI Science (SeWs) and compare these with their best known positions.," In order to empirically determine the PSLA of the IBIS/ISGRI telescope, we can extract the positions of objects from the IBIS/ISGRI Science (ScWs) and compare these with their best known positions."975 This can then be used to estimate the 90% error offset as a function of detected significance. allowing us to define the 90% PSLA.," This can then be used to estimate the $90\%$ error offset as a function of detected significance, allowing us to define the $90\%$ PSLA."976 In particular. the IBIS/ISGRI telescope (and coded mask telescopes in general) PSLA depends strongly on detection significance. but also on the position of the source within the field of view.," In particular, the IBIS/ISGRI telescope (and coded mask telescopes in general) PSLA depends strongly on detection significance, but also on the position of the source within the field of view."977 We therefore require for our analysis a set of sources spanning a wide range of significances and off-axis positions in order to allow our analysis to be useful for all detected IBIS/ISGRI sources., We therefore require for our analysis a set of sources spanning a wide range of significances and off-axis positions in order to allow our analysis to be useful for all detected IBIS/ISGRI sources.978 We begin by compiling a list of sources with good positions., We begin by compiling a list of sources with good positions.979 It is best at this stage to be conservative and only select sources where accurate nominal positions are known rather than to bias our sample by also including sources with large nominal error radi. like many newly discovered sources.," It is best at this stage to be conservative and only select sources where accurate nominal positions are known rather than to bias our sample by also including sources with large nominal error radii, like many newly discovered sources."980" To do this we take the latest General Reference Catalog (Version 30. ?.. http://isdc.unige.ch/Data/cat/latest/)) and make a selection on the error radius. selecting those sources with an error less than 30"": at this level. the error on the true position should give a negligible contribution to the measured offsets to the IBIS position."," To do this we take the latest General Reference Catalog (Version 30, \citealt{ebisawa}, ) and make a selection on the error radius, selecting those sources with an error less than $''$; at this level, the error on the true position should give a negligible contribution to the measured offsets to the IBIS position."981 Thus the total number of objects used in our sample is 332. spanning a wide range of detection significances and off-axis angles.," Thus the total number of objects used in our sample is 332, spanning a wide range of detection significances and off-axis angles."982 This number might seem small when compared to the 72] sources detected in ?.. however we note that many objects in that catalog are newly discovered sources for which X-ray follow-up is not yet available. and that therefore have relatively large nominal error radi.," This number might seem small when compared to the 721 sources detected in \cite{cat4}, however we note that many objects in that catalog are newly discovered sources for which X-ray follow-up is not yet available, and that therefore have relatively large nominal error radii."983 After performing an imaging analysis with the OSA 7.0 pipeline. we inspected all available ScW images and extracted the fitted positions which. resulted from the image deconvolution: these are the columns FFIN and .FFIN from the file for all pointings where any of the 332 objects was present.," After performing an imaging analysis with the OSA 7.0 pipeline, we inspected all available ScW images and extracted the fitted positions which resulted from the image deconvolution; these are the columns FIN and FIN from the file for all pointings where any of the 332 objects was present."984 The dataset was divided into fully coded field of view (FCFOV) and partially coded field of view (PCFOV)., The dataset was divided into fully coded field of view (FCFOV) and partially coded field of view (PCFOV).985 The IBIS coded aperture mask has a field of view of 30°.. the FCFOV is the central 9*x9* region:," The IBIS coded aperture mask has a field of view of , the FCFOV is the central $\degr\times$ $\degr$ region;"986After separating variables. and projecting the forcing terms appropriately. as done above for the interactions in à warpec disc. the equations describing the coupling between the trapped r mode. eccentric dise and à=1 intermediate mode read,"After separating variables, and projecting the forcing terms appropriately, as done above for the interactions in a warped disc, the equations describing the coupling between the trapped r mode, eccentric disc and $n=1$ intermediate mode read"987XX-ray Center (CXC. operated for NASA by SAO). and the ESA'S SScience Archive (XSA).,"X-ray Center (CXC, operated for NASA by SAO), and the ESA's Science Archive (XSA)."988" PE acknowledges financial support from the Autonomous Region of Sardinia through a research grant under the program PO Sardegna FSE 2007-2013. Τ.Κ. 7/2007 “Promoting scientific research and innovation technology in Sardinia""."," PE acknowledges financial support from the Autonomous Region of Sardinia through a research grant under the program PO Sardegna FSE 2007–2013, L.R. 7/2007 “Promoting scientific research and innovation technology in Sardinia”."989 This work was partially supported by the ASI/INAF contract 1009/10/0., This work was partially supported by the ASI/INAF contract I/009/10/0.990one would see multiple scintles. possibly in different stages of development.,"one would see multiple scintles, possibly in different stages of development."991 Our observing bandwidth of 192 MHz is at least four times more narrow than the expected Avpiss (see Table 3)., Our observing bandwidth of 192 MHz is at least four times more narrow than the expected $\Delta\nu_{\rm DISS}$ (see Table 3).992 It means that at any given time we are usually able to see only a fraction of a single seintle., It means that at any given time we are usually able to see only a fraction of a single scintle.993 Following Cordes Lazio (1991)) we estimated our number of seintles in both frequency and time. and calculations yielded ΔΝ to be very close to unity (as expected) and ΑΔ54.6.," Following Cordes Lazio \cite{cordes91}) ), we estimated our number of scintles in both frequency and time, and calculations yielded $N_f$ to be very close to unity (as expected) and $N_t \simeq 4.6$."994 The latter leads to the expected DISS modulation index of 0.466. much lower than the observed values.," The latter leads to the expected DISS modulation index of 0.466, much lower than the observed values."995 However. after including the contribution from RISS (εις=0.56: the value found via structure. function analysis. see next sections of the paper). and using the total intensity variance formula (Rickett 1990)). we obtained the final expected value of mu=0.889.," However, after including the contribution from RISS $m_{\rm RISS}=0.56$; the value found via structure function analysis, see next sections of the paper), and using the total intensity variance formula (Rickett \cite{rick}) ), we obtained the final expected value of $m_{\rm tot}=0.889$."996 This value is still somewhat lower than the observed modulation indices. but not by a huge margin.," This value is still somewhat lower than the observed modulation indices, but not by a huge margin."997 Because every individual session was at least several hours long. we believe that diffractive scintillations (which happen at the timescale of ca.," Because every individual session was at least several hours long, we believe that diffractive scintillations (which happen at the timescale of ca."998 40 minutes. see subsection 2.4)) should not affect our average flux measurements.," 40 minutes, see subsection \ref{sect_sf}) ) should not affect our average flux measurements."999 On the other hand. refractive timescales. which are significantly longer. may have affected our results.," On the other hand, refractive timescales, which are significantly longer, may have affected our results."1000 Figure 2. shows the results of the average flux density measurement versus the observing epoch., Figure \ref{flux_long} shows the results of the average flux density measurement versus the observing epoch.1001 Clearly (conf., Clearly (conf.1002 Table 1) there is significant variation in the average values., Table 1) there is significant variation in the average values.1003 Using these data. we calculated the modulation index of the average flux density measurements. which yielded the value of m=0.57.," Using these data, we calculated the modulation index of the average flux density measurements, which yielded the value of $m=0.57$."1004 Assuming that the pulsar itself is not varying in intensity. this modulation could be caused by only the refractive scintillations. which happen at significantly long timescales. close to the length of a single observing session.," Assuming that the pulsar itself is not varying in intensity, this modulation could be caused by only the refractive scintillations, which happen at significantly long timescales, close to the length of a single observing session."1005" To take that into account. we calculated the errors of average flux measurements following Κάπρι Stinebring (1992.. KS92) as where Top, 1s [fiasthe length of a given observing session. and fjiss Is the RISS timescale."," To take that into account, we calculated the errors of average flux measurements following Kaspi Stinebring \cite{kasp}, KS92) as where $T_{\rm obs}$ is the length of a given observing session, and $t_{\rm RISS}$ is the RISS timescale."1006 To calculate the error values shown on Figure 2 we used the value of rss obtained via the structure function analysis (305 minutes. see subsection 2.4))," To calculate the error values shown on Figure \ref{flux_long} we used the value of $t_{\rm RISS}$ obtained via the structure function analysis (305 minutes, see subsection \ref{sect_sf}) )."1007 Using those error estimates. we were able to calculate the weighted average flux density (wj=o ) for our entire observing session. which ts (Fi)=11.69 mJy.," Using those error estimates, we were able to calculate the weighted average flux density $w_i = \sigma_i^{-2}$ ) for our entire observing session, which is $\left<F_{\rm tot}\right> = 11.69$ mJy."1008 This value ts shown in Figure 2 as a dashed-dotted horizontal line. along with the simple arithmetic average from Table | (dashed line).," This value is shown in Figure \ref{flux_long} as a dashed-dotted horizontal line, along with the simple arithmetic average from Table \ref{t1} (dashed line)."1009 As we mentioned above. the average flux values and their respective uncertainties for the last two sessions in our project differ significantly from the remaining observations.," As we mentioned above, the average flux values and their respective uncertainties for the last two sessions in our project differ significantly from the remaining observations."1010 However. a proper calculation of the error estimates improves the picture.," However, a proper calculation of the error estimates improves the picture."1011 Por relatively short sessions. which we had towards the end of the project. RISS can play a huge role. but the duration of the session is included in the uncertainty estimates. which makes them more reliable than the formal errors cited in Table 1.," For relatively short sessions, which we had towards the end of the project, RISS can play a huge role, but the duration of the session is included in the uncertainty estimates, which makes them more reliable than the formal errors cited in Table 1."1012 The, The1013All the necessary X-ray data were obtained from theChandra (NGC 6543:630: DD--303639: 587: and NGC 7027: 588)) and (NGC 7009). science archives.,All the necessary X-ray data were obtained from the (NGC 6543:; $+$ 303639:; and NGC 7027: ) and (NGC 7009) science archives.1014" The Chandra observations were carried out with the ACIS-S cleteetor and the corresponding Science Threads for Image Spectroscopy in CLAO were used for extracting the X-ray spectra,", The Chandra observations were carried out with the ACIS-S detector and the corresponding Science Threads for Image Spectroscopy in CIAO were used for extracting the X-ray spectra.1015 For (ae NMM-Newton observation of NGC 7009. the most recent version of SAS was used for the spectral extraction.," For the XMM-Newton observation of NGC 7009, the most recent version of SAS was used for the spectral extraction."1016 Given the goal of our study. only the EPIC PN spectrum was used in the following analysis due to its better photon statistics compared to those of the EPIC MOSI and MOS2.," Given the goal of our study, only the EPIC PN spectrum was used in the following analysis due to its better photon statistics compared to those of the EPIC MOS1 and MOS2."1017 The periods of high background count rates were excluded [rom the EPIC PN data., The periods of high background count rates were excluded from the EPIC PN data.1018 Finally. for each object. X-ray spectra were extracted corresponding to the entire object and that part within the optical slit.," Finally, for each object, X-ray spectra were extracted corresponding to the entire object and that part within the optical slit."1019 The X-ray spectra were fit within XSPEC 11.3 (Arnancd1996) using theΠάρος model for the emission from opticallv-thin plasma., The X-ray spectra were fit within XSPEC 11.3 \citep{arnaud1996} using the model for the emission from optically-thin plasma.1020 We note that the derived parameters of the A-ray emitting plasma do not depend on this choice and using a different model (e.g. mekal) leads to the same results within the expected., We note that the derived parameters of the X-ray emitting plasma do not depend on this choice and using a different model (e.g. ) leads to the same results within the expected.1021 Thus. the model was chosen to make caleulations of the aand eenissions technically more straightforward.," Thus, the model was chosen to make calculations of the and emissions technically more straightforward."1022 The hot plasma abundances were taken [rom Alaness&Vrtilek(2003) for NCC: 65423. from Manessetal.(2003). lor NGC 1027. and from Guerreroetal...(2002). [or NGC 1009.," The hot plasma abundances were taken from \citet{manessvrtilek2003} for NGC 6543, from \citet{manessetal2003} for NGC 7027, and from \citet{guerreroetal2002} for NGC 7009."1023 ForBD+30°3639.. two abundance sets were used. the first being a variant of the Manessetal...(2003). abundance set (fourth column in Table 3:: henceforth. we denote this set as ‘wind’ abundances) and the second a new set derived here (last column in Table 3: nebular’ abuucdances) based partly upon the nebular abundances of Aller&Ivune(1995) and which have values similar to the ‘nebular’ abundances derived bv Arnaudοἱal.(1996) from the analvsis of the ASC'A data of this object.," For, two abundance sets were used, the first being a variant of the \citet{manessetal2003} abundance set (fourth column in Table \ref{table_xrayfit3}; henceforth, we denote this set as `wind' abundances) and the second a new set derived here (last column in Table \ref{table_xrayfit3}; `nebular' abundances) based partly upon the nebular abundances of \citet{allerhyung1995} and which have values similar to the `nebular' abundances derived by \citet{arnaud1996a} from the analysis of the ASCA data of this object."1024 The two fits are incdistinguishable in fitting the data., The two fits are indistinguishable in fitting the data.1025 Figure 3. presents our fits to the X-ray spectra., Figure \ref{figure_xrayspec} presents our fits to the X-ray spectra.1026 The parameters used in these fits. including elemental abundances. are listed in Tables 3. and 4..," The parameters used in these fits, including elemental abundances, are listed in Tables \ref{table_xrayfit3} and \ref{table_7027par}."1027 Our fits to the total X-ray spectra olf these PNe are consistent with those obtained by other eroups using the same data sets., Our fits to the total X-ray spectra of these PNe are consistent with those obtained by other groups using the same data sets.1028 Finally. we note that. if the Gorenstein(1975). conversion," Finally, we note that, if the \citet{gorenstein1975} conversion"1029At the end of the 20th ceutury. observations of tvpe In supernovae (δα) revealed that the Universe expansion is accelerating (27)..,"At the end of the 20th century, observations of type Ia supernovae (SNIa) revealed that the Universe expansion is accelerating \citep{riess98,perlmutter99}."1030 Siuce these publications. several efforts wave been mace to explain these observatious (?????? aud references therem).," Since these publications, several efforts have been made to explain these observations \citet{cunha09, frieman08, linder08, linder05, samsing10, freaza02, ishida05,ishida08} and references therein)."1031 Iu a standard analvsis. dark-euergy models are characterized by a small set of paramcters.," In a standard analysis, dark-energy models are characterized by a small set of parameters."1032 These are placed iuto the cosmic expansion rate by means oftje Friedman equations. iu substitution for the conveutional cosinological-constant terim.," These are placed into the cosmic expansion rate by means of the Friedman equations, in substitution for the conventional cosmological-constant term."1033 This approach assmmes a specific dependence of the dark-euergy equation of state (0) on redshift :xd provides some insight iuto the probable valies of the parameters involved., This approach assumes a specific dependence of the dark-energy equation of state $w$ ) on redshift and provides some insight into the probable values of the parameters involved.1034 IHowever. the results remain restricted to that particular parametrization.," However, the results remain restricted to that particular parametrization."1035 An interesting question to attempt to answer is what can be inferred about the cosmic expansion rate from observations withmit any reference to a specific model for the energy. coutent of the Universe?, An interesting question to attempt to answer is what can be inferred about the cosmic expansion rate from observations without any reference to a specific model for the energy content of the Universe?1036 To perforui an iudepeudenu analvsis we used principal component analysis (PCA).," To perform an independent analysis, we used principal component analysis (PCA)."1037 Iu simple terms. PCA idcutifies the cirectious of daa poluts c‘lustering in the phase space defined by the parameters of a given model.," In simple terms, PCA identifies the directions of data points clustering in the phase space defined by the parameters of a given model."1038 Cousequeutly. it allows a cimenusioialitv redction with as nininimn an information loss as possible (2)..," Consequently, it allows a dimensionality reduction with as minimum an information loss as possible \citep{tegmark97}."1039 The importance of a reconsruction o the cosmüc expansion rate las already been investigated iu the literature (72???7)..," The importance of a model-independent reconstruction of the cosmic expansion rate has already been investigated in the literature \citep{Huterer99,Huterer00,Tegmark02,Wang05,mignone08}."1040" Tn this coutest. PCA has be4 used to reconstruct the dark-cnerey equation of state (777) and the deceleration paraueter (7) asa ""unction o “redshift."," In this context, PCA has been used to reconstruct the dark-energy equation of state \citep{huterer03,Crittenden09,simpson06} and the deceleration parameter \citep{shapiro06} as a function of redshift."1041 The use of PCA was also proposed in the interpretation of future experiments results by ?.., The use of PCA was also proposed in the interpretation of future experiments results by \citet{albretch09}.1042 In the face of growing interest in the application of PCA to cosinology. ?. recall that some care must be taken in choosing the basic expansion functiois and the interpretation assigned to the components.," In the face of growing interest in the application of PCA to cosmology, \citet{kitching09} recall that some care must be taken in choosing the basic expansion functions and the interpretation assigned to the components."1043 The main goal of this work is to apply PCA to reconstruct directly the piriuneter redshift dependence without auv reference to a specific cosmological model., The main goal of this work is to apply PCA to reconstruct directly the parameter redshift dependence without any reference to a specific cosmological model.1044 In this contest. the eieeuvectors aud cigenvalucs of the Fisher matrix form a new basis in which the parameter is expanded.," In this context, the eigenvectors and eigenvalues of the Fisher matrix form a new basis in which the parameter is expanded."1045 For the first time. we show that it is possible," For the first time, we show that it is possible"1046Preprint The hwdrogeu between galaxies was reiouized more than 12.5 Cer ago (7)., The hydrogen between galaxies was reionized more than $12.5~$ Gyr ago \citep{fan06}.1047 After this event. a larecly nuiforma t-ionizing radiatiou backeround pervaded the intergalactic πουπα (IGM) and kept the hydrogen lughly ionized everywhere except within rare. dense pockets (2222??2)..," After this event, a largely uniform -ionizing radiation background pervaded the intergalactic medium (IGM) and kept the hydrogen highly ionized everywhere except within rare, dense pockets \citep{gunn65, cen94, miralda96, hernquist96, haardt96, katz96}."1048 The amplitude of this backerouud appears to have declined quickly above a redshift of :=6 (o.@.. 2)) and to havestaved relatively coustaut over Doc Lee. ?)).," The amplitude of this background appears to have declined quickly above a redshift of $z=6$ (e.g., \citealt{fan06}) ) and to havestayed relatively constant over $2<z<4$ (e.g., \citealt{faucher08b}) )."1049 It is of some debate whether this decline owed to the overlap stage of cosinological reionization or to something more nundaue (e.g... ?77]).," It is of some debate whether this decline owed to the overlap stage of cosmological reionization or to something more mundane (e.g., \citealt{gnedin00, fan06, becker07}) )."1050 Iu addition. the deuse selfshiclding svstenis that remained in the TGAL called Exauau-Init svstems. provide a window iuto structure formation in a different density regime than explored by other large-scale structure probes.," In addition, the dense self-shielding systems that remained in the IGM, called Lyman-limit systems, provide a window into structure formation in a different density regime than explored by other large-scale structure probes."1051 This paper aims to study interealactic radiative transfer aud the properties of Lsaiuan-liuüt| svstenis (systems with ccoluuus of 100152.Nyy<1019 2)., This paper aims to study intergalactic radiative transfer and the properties of Lyman-limit systems (systems with columns of $10^{17.2} < N_{\rm HI} < 10^{19}~$ $^{-2}$ ).1052 To do so. we post-process cosmological simulations (both with and without ealactic feedback muiplemeutations) with lonizing radiative transfer.," To do so, we post-process cosmological simulations (both with and without galactic feedback implementations) with ionizing radiative transfer."1053 The abuudance of Lyman-iuit svstenis in the post-processed simulations is then compared with measurements of their abundance frou quasar absorption line studies., The abundance of Lyman-limit systems in the post-processed simulations is then compared with measurements of their abundance from quasar absorption line studies.1054 This comparison tests row cosmological simulations fare at the outskirts of ealactic halos., This comparison tests how cosmological simulations fare at the outskirts of galactic halos.1055 Previous attempts to model Exaiuau-Inuit systelus in simulations had reported various levels of agreement with observations aud had used much smaller ON Sizes and particle uuuboers than are preseutly feasible QUT). ," Previous attempts to model Lyman-limit systems in simulations had reported various levels of agreement with observations and had used much smaller box sizes and particle numbers than are presently feasible \citep{katz96, gardner01, kohler07}. ."1056Tu addition. recent observations have significantly nuproved the coustraints on the abundance of svstems (2?7)..," In addition, recent observations have significantly improved the constraints on the abundance of systems \citep{prochaska09, prochaska10, songaila10}."1057 Our caleulatious also provide au estimate for the -ionizius cuussivity of star-forming galaxies and quasars since. after cosmological reionization. the production rate of ionizing photons was in balance with the number of absorptions.," Our calculations also provide an estimate for the -ionizing emissivity of star-forming galaxies and quasars since, after cosmological reionization, the production rate of ionizing photons was in balance with the number of absorptions."1058 These absorptious occured primarily witlin ΓιατιΠΠ systems., These absorptions occurred primarily within Lyman-limit systems.1059 Our determinations of the cluissivity using the simulations aeree with observations at redshifts where it can be measured observationallv (2<2« 1l) and they also provide a meaus to estimate the enüssivitv at higher redshifts.," Our determinations of the emissivity using the simulations agree with observations at redshifts where it can be measured observationally $2 < z<4$ ), and they also provide a means to estimate the emissivity at higher redshifts."1060 We also study the relationship between the cuissivity of ionizing photons and the intensity of the ioniziug background., We also study the relationship between the emissivity of ionizing photons and the intensity of the ionizing background.1061 luterestiuglv. we find that small changes in the cuissivity at hieh redshifts could have resulted iu much larger changes in the ioniziug backeround.," Interestingly, we find that small changes in the emissivity at high redshifts could have resulted in much larger changes in the ionizing background."1062 This finding has interesting nuplicatious for the observed trends in this backerounud., This finding has interesting implications for the observed trends in this background.1063 This paper is organized as follows., This paper is organized as follows.1064 Section 2. describes the observations aud our nuucerical techniques., Section \ref{sec:thecase} describes the observations and our numerical techniques.1065 Section 3 compares our ininerical calculatious of 02A/0:ONY the umuber of absorption svstcms per uuit redshift per ccoluun (Nyy) with observations.," Section \ref{sec:comparison} compares our numerical calculations of $\partial^2{\cal N}/\partial z\,\partial N_{\rm HI}$ – the number of absorption systems per unit redshift per column $N_{\rm HI}$ ) – with observations."1066 Section | studies the relationship between dense absorption systelus. the jouizine cnussivity. and the ionizing vackerouncd.," Section \ref{sec:relationship} studies the relationship between dense absorption systems, the ionizing emissivity, and the ionizing background."1067 Section 5 considers how plivsical effects that may not be captured in the simulations could alter our conclusions., Section \ref{sec:other} considers how physical effects that may not be captured in the simulations could alter our conclusions.1068 Finally. Appendix A xoviles supplementary information reearcding the xoperties of the simulated Lyian-limit systems.," Finally, Appendix \ref{ap:properties} provides supplementary information regarding the properties of the simulated Lyman-limit systems."1069 Our calculations assume a flat ACDAL cosmolosv with (QuQn.ηνσε.ο).=(0.28.0.016.0.70.0.82.0.96) ancl a lvdrogen nass fraction of 0.75. consistent with the atest Wilkinson Microwave Anisotropy Probe analysis (?)..," Our calculations assume a flat $\Lambda$ CDM cosmology with $(\Omega_m,\Omega_b,h,\sigma_8,n_s) = (0.28,0.046,0.70,0.82,0.96)$ and a hydrogen mass fraction of $0.75$ , consistent with the latest Wilkinson Microwave Anisotropy Probe analysis \citep{komatsu10}."1070derived roni the cross-correlations (see section 6) cau be fou in the Áppeudix. A (table A.l. A.2. A.B. ALL X ALND).,"derived from the cross-correlations (see section 6) can be found in the Appendix A (table A.1, A.2, A.3, A.4 and A.5)."1071" The cataloge lists all the sources detected iu all the 303. fields analvzed. ie. we did not associate ""OIECON «etected iu dittvent observations of the same area he sky."," The catalogue lists all the sources detected in all the 4,303 fields analyzed, i.e. we did not associate sources detected in different observations of the same area of the sky."1072" Am estimae of the nuuber of indepenudoeut rees m the catalogue can be obtained compressing the uber of sources using an error on the source position 10"" (a conservative init dictated bv the uncertainties conneced wih the boxsight correction).", An estimate of the number of independent sources in the catalogue can be obtained compressing the number of sources using an error on the source position of $10''$ (a conservative limit dictated by the uncertainties connected with the boresight correction).1073 We fouud 20.153 epeideut objects.," We found 20,453 independent objects."1074 Iu Fig., In Fig.1075 1 we plot the distribution of source offaxis aneles showiis the typical trend due to the increase of the coIectingo area together with the decreasing «ft the sensitivity with offaxis., 4 we plot the distribution of source off–axis angles showing the typical trend due to the increase of the collecting area together with the decreasing of the sensitivity with off–axis.1076" Clearly. the peak at zero o[axis is due to poiited sources,"," Clearly, the peak at zero off–axis is due to pointed sources."1077 Oue of the most importait characteristics of wavelet algoritlas is the ability to determine the source exteusion. Le. the scale of the wavelet ransforiu where the S/N is maximized after the application of the fitting refinement procedure (see Lazzati ct al. 1909).," One of the most important characteristics of wavelet algorithms is the ability to determine the source extension, i.e. the scale of the wavelet transform where the S/N is maximized after the application of the fitting refinement procedure (see Lazzati et al. \cite{lazzati99}) ),"1078 aud. if a criterion is eiven. also to discutangle poiit and extended sources (see Campana et al. 19993).," and, if a criterion is given, also to disentangle point and extended sources (see Campana et al. \cite{campana99}) )."1079 To assess the source extension criterion we considered al SOTIEECS detecte iu the observatious that have a star(5) as a target (ROR ποτ beeiuning with 2) axd that were available im the public archives iu a preliminary phase of our catalogue: 6.013 sources iu 756 IIRI fields.," To assess the source extension criterion we considered all sources detected in the observations that have a star(s) as a target (ROR number beginning with 2) and that were available in the public archives in a preliminary phase of our catalogue: 6,013 sources in 756 HRI fields."1080 Tιο clistribution of the source extension as a fiction of fie source offaxis angele has ceu divided iuto bius of 1: wemln each., The distribution of the source extension as a function of the source off–axis angle has been divided into bins of 1 arcmin each.1081 To each bin we jen applied a c cli»piug aleorithiu ο ciscarcl iteratively rulv exteuded sources aud ο derive the mean value of je source extension in the iu for pointed sources., To each bin we then applied a $\sigma-$ clipping algorithm to discard iteratively truly extended sources and to derive the mean value of the source extension in the bin for pointed sources.1082 We ien determined the 39 dis]version on the mean for cach iu.," We then determined the $3\,\sigma$ dispersion on the mean for each bin."1083 The mean value plus he 36 dispersion provides je threshold for the source extension.," The mean value plus the $3\,\sigma$ dispersion provides the threshold for the source extension."1084 We conservativev lassifv a source as extended if it ies 1uore than 20 fro us limit (1.6. if the source csxtension error bar lies more an twice from the 20 limit described above).," We conservatively classify a source as extended if it lies more than $2\,\sigma$ from this limit (i.e. if the source extension error bar lies more than twice from the $3\,\sigma$ limit described above)."1085 Combining us threshold with the 36 ou the iutrinsic dispersion. we obtain a Lo coufkence level for the exteusion classification (sce also Rosaict al. 1995)).," Combining this threshold with the $3\,\sigma$ on the intrinsic dispersion, we obtain a $\sim\,4.5\,\sigma$ confidence level for the extension classification (see also Rosati et al. \cite{rosati95}) )."1086 In Fie., In Fig.1087 5 we alot the distribution of the source extension versus offaxis angle for the 29.089 DÀW-IRI sources (small dots).," 5 we plot the distribution of the source extension versus off--axis angle for the 29,089 BMW-HRI sources (small dots)."1088 The solid line in Fig., The solid line in Fig.1089 5 represeuts the mean value of source extension for poiute sources as described above. while the dashed line is the 3c dispersion on this nean.," 5 represents the mean value of source extension for pointed sources as described above, while the dashed line is the $3\,\sigma$ dispersion on this mean."1090 Open squares in Fie., Open squares in Fig.1091 5 repreent sources we classified as extended. ic. with a confence level for the extensiou classification of ~1ωσ.," 5 represent sources we classified as extended, i.e. with a confidence level for the extension classification of $\sim\,4.5\,\sigma$."1092 We eud up with 2.717 exended sources (open squares in Fig.," We end up with 2,717 extended sources (open squares in Fig."1093 5) containing supernova remnants. galaxies. cluster of galaxies ete; (," 5) containing supernova remnants, galaxies, cluster of galaxies etc. ("1094as well as blering of nearby sources).,as well as blending of nearby sources).1095" The distributions of source extensious for the truv exteided SOTCCS, he full sai.je aud only the high-ealactic latitude MU| ) one (2.139 sources). are reported in Figο"," The distributions of source extensions for the truly extended sources, the full sample and only the high-galactic latitude $|b| > 20^{\degr}$ ) one (2,139 sources), are reported in Fig."1096", ϐ,", 6.1097 We assuued that a] the ligrh-ealactic latitude exteided sources are oxtragalactic in natire., We assumed that all the high-galactic latitude extended sources are extragalactic in nature.1098 In the plot we also report the onaxis angular resolution of t1ο ROSAT PSPC., In the plot we also report the on–axis angular resolution of the ROSAT PSPC.1099 Xrav exte1s1olis are calculated subtractiig du quacrattre the relaive PSF extension at a given offaxis anele (solid. line in Fie., X–ray extensions are calculated subtracting in quadrature the relative PSF extension at a given off–axis angle (solid line in Fig.1100 5)., 5).1101 The extended sources were used to select a is of candidate Xrav selected cluster of galaxies that we then studie wih optical folkW-Up (Moretti et al., The extended sources were used to select a list of candidate X–ray selected cluster of galaxies that we then studied with optical follow-up (Moretti et al.1102 2002 in prepuation: €uzzo et al., \cite{moretti02} in preparation; Guzzo et al.1103 209 iu preparation)., \cite{guzzo02} in preparation).1104 As the scusitivity of the WRI Πισίναment is not uniforui over the entire field of view. for a eiven Πιο flux the surveved area does not coiucide with he detector oue but it is ecnerally simaller.," As the sensitivity of the HRI instrument is not uniform over the entire field of view, for a given limiting flux the surveyed area does not coincide with the detector one but it is generally smaller."1105 We calculated the sky coverage of the cutive survey as a fuuctiou of the flux. (calculated with the full cohuun deusity) by mncaus of simulations., We calculated the sky coverage of the entire survey as a function of the flux (calculated with the full column density) by means of simulations.1106 To, To1107shifts and asymmetric profiles is an obvious indication that their winds are much more transparent in N-ravs than originally believed.,shifts and asymmetric profiles is an obvious indication that their winds are much more transparent in X-rays than originally believed.1108 This result. along with the small filling [actors of the X-ray emitting plasma in OB stars as found in previous AT) studies (Ixudritzkietal.1996).. lends support to a physical picture in which the stellar winds are clumpy and/or porous.," This result, along with the small filling factors of the X-ray emitting plasma in OB stars as found in previous ) studies \citep{ku_96}, lends support to a physical picture in which the stellar winds are clumpy and/or porous."1109 Alternatively. if the winds are smooth and homogeneous. the mass-oss rates should have values appreciably smaller (a factor ~5 or more) than those presently accepted (Ixramer.Cohen&Owocki2003: Cohenetal. 2006)).," Alternatively, if the winds are smooth and homogeneous, the mass-loss rates should have values appreciably smaller (a factor $\sim$ 5 or more) than those presently accepted \citealt{kr_03}; \citealt{co_06}) )."1110 Wind clumping ancl porosity elfects. on the X-ray emission from OB stars. anc specifically on the shape of the line profiles. have been explored in recent analytical and numerical models (e.g. Feldmeier.Oskinova& 2003:: Oskinova. Feldmoeier Lamann 2004. 2006: Owocki&Cohen 2006)).," Wind clumping and porosity effects on the X-ray emission from OB stars, and specifically on the shape of the line profiles, have been explored in recent analytical and numerical models (e.g., \citealt{feld_03}; Oskinova, Feldmeier Hamann 2004, 2006; \citealt{ow_06}) )."1111 It has been shown that under given conditions (such as reduced mass loss and. assumed tvpical! distance between clumps) their inclusion may lead. to results much more Consistent with the observations., It has been shown that under given conditions (such as reduced mass loss and assumed `typical' distance between clumps) their inclusion may lead to results much more consistent with the observations.1112 Given the complexity of these models and the fact that they are not vet fully selt-consistent. it is important to gather empirical information about the physical conditions in the regions responsible for the X-ray. emission to put further constraints on numerical nmoclels.," Given the complexity of these models and the fact that they are not yet fully self-consistent, it is important to gather empirical information about the physical conditions in the regions responsible for the X-ray emission to put further constraints on numerical models."1113 Various diagnostics have been used in this respect: analvsis of helium-like triplet ratios. global [its with ciscrete-tompcrature models. constructing a distribution of cmussion measures as function. of temperature. based.on fits to individual-lineHuxes and to the total X-ray spectra (Cassinellietal. 2001: Wahnctal.2001: Walelron&Cassinelli 2000: Miller.ctal. 2002: Cohenetal. 2003:: Schulzetal. 2003:: Sanz-Forcada.Franciosini&Pallavicini 2004: Wojdowski Schulz 2004. 2005: Gagnectal.2005:: Leuteneggeretal. 2006)).," Various diagnostics have been used in this respect: analysis of helium-like triplet ratios, global fits with discrete-temperature models, constructing a distribution of emission measures as function of temperature, basedon fits to individual-linefluxes and to the total X-ray spectra \citealt{cass_01}; ; \citealt{kahn_01}; \citealt{wa_00}; \citealt{mi_02}; \citealt{co_03}; \citealt{schu_03}; \citealt{sa_04}; Wojdowski Schulz 2004, 2005; \citealt{ga_05}; \citealt{leu_06}) )."1114 These studies indicate that X-rays are produced close to the stellar surface (likely. in the wind acceleration zone). and that the corresponding hot. plasma has a temperature stratification.," These studies indicate that X-rays are produced close to the stellar surface (likely, in the wind acceleration zone), and that the corresponding hot plasma has a temperature stratification."1115 The latter point reinforces the idea that the X-ray emission originates in an ensemble of shocks., The latter point reinforces the idea that the X-ray emission originates in an ensemble of shocks.1116 Guided by this background. we have developed a simple model which bears all the basic charateristics of the X-ray production in wind shocks.," Guided by this background, we have developed a simple model which bears all the basic charateristics of the X-ray production in wind shocks."1117 Ehe model is described in 2: the data sample is given in 3: the results are presented in 4 and diseussed in 5.., The model is described in \ref{sec:mod}; the data sample is given in \ref{sec:obs}; the results are presented in \ref{sec:res} and discussed in \ref{sec:dis}.1118 Phe conclusions close the paper., The conclusions close the paper.1119 As in the case of the RDL and ALICWS models. our basic assumption is that the X-ray. emission of hot massive stars originates in shocks.," As in the case of the RDI and MCWS models, our basic assumption is that the X-ray emission of hot massive stars originates in shocks."1120 Given the relatively high densities in he wind. the energy losses by the shock-heated plasma are considerable: thus. shocks should. beradialive.," Given the relatively high densities in the wind, the energy losses by the shock-heated plasma are considerable: thus, shocks should be."1121" ""This conclusion follows from simple estimates which show that he tvpical cooling time of a parcel of σας at the postshock emperature and density issmaller than the typical dynamic ime of the Dow.", This conclusion follows from simple estimates which show that the typical cooling time of a parcel of gas at the postshock temperature and density issmaller than the typical dynamic time of the flow.1122" Namely. for the shock position at a distance r [rom the star. the ratio of the cooling time (£. πριν.) o the dvnamic time of the [low (5,= rfe) is: ⋜⋯∠⇂↿↓↕⋖⋅↓⋅⋜∐⊲⊓⋯⇂⋅↿↓∐⊾↿↓↥⊀⊔⇍↓∡⊔⋖⊾⊳∖⊳∖∪⇂⋅↿↓∐⋅↓⋅⋯⇂⊲↓⋜⊔⊀↓∖⇁⋖⋅⊳∖↓↕⋯⇍↳↿∖⊀⊔⊾↦ the cooling length of a parcel of hot eas at the postshock temperature: f=Logd, ) and shock ""radius! is: where 72, is the postshock temperature given in keV. CQouo is the terminal stellar wind. velocity. (in units of 9). and Aly is the stellar niass loss (in units of 1O""MA. P "," Namely, for the shock position at a distance $r$ from the star, the ratio of the cooling time $t_c = \frac{5}{2}p_{sh}/Q_c$ ) to the dynamic time of the flow $t_d = r/v$ ) is: and the ratio of the thickness of the radiative shock (i.e., the cooling length of a parcel of hot gas at the postshock temperature: $l_c = \frac{1}{4} v_{sh} t_c$ ) and shock `radius' is: where $T_{sh}$ is the postshock temperature given in keV, $v_{1000}$ is the terminal stellar wind velocity (in units of ), and $\dot{M}_6$ is the stellar mass loss (in units of $10^{-6}$ $_\odot$ $^{-1}$ )."1123"Fora strong shock. the relation between the postshock temperature (in keV) and the shock velocity (in units of )) is given by Zi,=1.9565/02,,,4. and pois the mean atomic weight."," For a strong shock, the relation between the postshock temperature (in keV) and the shock velocity (in units of ) is given by $T_{sh} = 1.956\mu v_{shock}^2$, and $\mu$ is the mean atomic weight."1124 The relative number density of hydrogen is assumed rg=0.9: thus. the relative electron number density is or.=1.1 for a fully ionized. plasma.," The relative number density of hydrogen is assumed $x_H = 0.9$; thus, the relative electron number density is $x_e = 1.1$ for a fully ionized plasma."1125 The gascvnamical quantities and the cooling function. are described in 2.1.., The gasdynamical quantities and the cooling function are described in \ref{subsec:shock}.1126 For typical mass-loss rates (AlyxsOL1) anc wind velocities (P100071.5. 2.5). the cooling time ancl cooling ength of a shock developed in a wind. are appreciably smaller than the corresponding twpical characteristics of he flow (see eqs. 1]. 2]].," For typical mass-loss rates $\dot{M}_6 \approx 0.1 - 1$ ) and wind velocities $v_{1000} \approx 1.5 - 2.5$ ), the cooling time and cooling length of a shock developed in a wind are appreciably smaller than the corresponding typical characteristics of the flow (see eqs. \ref{eq:tcool}] ], \ref{eq:lcool}] ])."1127" This is true for postshock emperatures below 1 keV. ναι, shock velocities smaller than for solar abundances) ancl shock locations rom a lew to several tens of stellar radii."," This is true for postshock temperatures below 1 keV (i.e., shock velocities smaller than for solar abundances) and shock locations from a few to several tens of stellar radii."1128 VPherelore. the asstunption of a steady-state. plane-parallel raciative shock is a good approximation for our analysis.," Therefore, the assumption of a steady-state, plane-parallel, radiative shock is a good approximation for our analysis."1129 This conclusion inds support in numerical simulations of both the RDI and ALOWS models., This conclusion finds support in numerical simulations of both the RDI and MCWS models.1130 In fact. as à result of ellicient cooling. the shocks ‘collapse’ in geometrically thin shells and. clisk-like structures. respectively (e.g. Feldimeicr.Puls&Pauldrach 1997:: ud-Doula&Owocki 2002: Gagneetal. 2005)).," In fact, as a result of efficient cooling, the shocks `collapse' in geometrically thin shells and disk-like structures, respectively (e.g. \citealt{feld_97}; \citealt{ud_02}; \citealt{ga_05}) )."1131 The description of our shock mocdel and the ensemble of shocks is given below., The description of our shock model and the ensemble of shocks is given below.1132 The models were then used. in he recent version (11.3.2). of the software. package for analysis of X-ray spectra. (Arnaucl1996).," The models were then used in the recent version (11.3.2) of the software package for analysis of X-ray spectra, \citep{a_96}."1133.. A elobal-it approach was adopted in our analysis for the following reasons: (i) the fit can automatically take into account he quasi-continuum due to numerous weak lines: (ii) by itting the shape of the underlying continuum. the mocel laces: additional constraints on the plasma temperature: (ii) the model can constrain the column clensitw of the X-rav absorbing eas: and (iv) it can vield estimates of relative clement abuncances.," A global-fit approach was adopted in our analysis for the following reasons: (i) the fit can automatically take into account the quasi-continuum due to numerous weak lines; (ii) by fitting the shape of the underlying continuum, the model places additional constraints on the plasma temperature; (iii) the model can constrain the column density of the X-ray absorbing gas; and (iv) it can yield estimates of relative element abundances."1134" Finally. the X-ray emission is assumed o originate [rom a hot optically-thin plasma in collisional ionization equilibrium (CLE). as is the case for various types of astrophysical objects. including hot massive stars (e.g. ""uerels&Ixahn 2006))."," Finally, the X-ray emission is assumed to originate from a hot optically-thin plasma in collisional ionization equilibrium (CIE), as is the case for various types of astrophysical objects, including hot massive stars (e.g., \citealt{pa_03}) )."1135 We consider a steady-state. plane-parallel. shock moving in a gas with adiabatic index ~= 5/3.," We consider a steady-state, plane-parallel, shock moving in a gas with adiabatic index $\gamma = 5/3$ ."1136" The basic phwsical quantities of the Dow (density or nucleon number density. velocity. ancl pressure) have their standard postshock values for a strong shock: pi,=Apo (n.i,= dno). Pu,= ca/4. and po,= 3/4por5. where the subscript7Q denotes the preshock values (the gas velocity is given in the rest [rame of the shock front)."," The basic physical quantities of the flow (density or nucleon number density, velocity, and pressure) have their standard postshock values for a strong shock: $\rho_{sh} = 4\rho_0$ $n_{sh} = 4n_0$ ), $v_{sh} = v_0/4$ , and $p_{sh} = 3/4\rho_0v_0^2$ , where the subscript`0' denotes the preshock values (the gas velocity is given in the rest frame of the shock front)."1137 The mass and. momentum, The mass and momentum1138For a given surlace brightness profile twpe. there exists a relation between. absolute magnitude and apparent axis ratio.,"For a given surface brightness profile type, there exists a relation between absolute magnitude and apparent axis ratio."1139 Contour plots of mean apparent axis ratio as a function ol both and AZ. are given in Figure 2.. (, Contour plots of mean apparent axis ratio as a function of both and $M_r$ are given in Figure \ref{fig:fdevmag}. (1140"To give a feel for the absolute magnitude scale. fitting a Schechter function to the luminosity function of SDSS galaxies vields 3,,sz—21.4 (Nakamuraetal. 2003)..)","To give a feel for the absolute magnitude scale, fitting a Schechter function to the luminosity function of SDSS galaxies yields $M_{*,r} \approx -21.4$ \citep{na03}. .)"1141" The upper panel of the figure shows that the trend in (q,,,) runs from the flattest galaxies at fracDeV©0 and M,z—18. where (qu)20.52. to the roundest galaxies al fracDeVzz| and M,ez—23. where (qu)7&0.83."," The upper panel of the figure shows that the trend in $\langle q_{\rm am} \rangle$ runs from the flattest galaxies at $\texttt{fracDeV} \approx 0$ and $M_r \approx -18$, where $\langle q_{\rm am} \rangle \approx 0.52$, to the roundest galaxies at $\texttt{fracDeV} \approx 1$ and $M_r \approx -23$, where $\langle q_{\rm am} \rangle \approx 0.83$."1142 This result is not surprising. since moderatelv bright galaxies with exponential profiles are intrinsically fattened clisk ealaxies. while extremely bright galaxies with de Vaucouleurs profiles are intrinsically nearly spherical eiant elliptical galaxies (Tremblay&Merritt1996)..More surprising are (he results shown in the bottom panel of Figure 2.. which shows (02). the mean isophotal axis ratio.," This result is not surprising, since moderately bright galaxies with exponential profiles are intrinsically flattened disk galaxies, while extremely bright galaxies with de Vaucouleurs profiles are intrinsically nearly spherical giant elliptical galaxies \citep{tm96}.More surprising are the results shown in the bottom panel of Figure \ref{fig:fdevmag}, which shows $\langle q_{25} \rangle$, the mean isophotal axis ratio."1143" ]lere. we find that the apparently [attest galaxies. as nieasured by qos. are nol exponential ealaxies. bul galaxies wilh fracDeVzz0.7 (corresponding (o Sérrsic index nx2.5) and M,£g—20.5: these galaxies have (qo3)220.53."," Here, we find that the apparently flattest galaxies, as measured by $q_{25}$, are not exponential galaxies, but galaxies with $\texttt{fracDeV} \approx 0.7$ (corresponding to Sérrsic index $n \approx 2.5$ ) and $M_r \approx -20.5$; these galaxies have $\langle q_{25} \rangle \approx 0.53$."1144" The roundest galaxies. measured by (055). are nol bright de Vaucouleurs galaxies. but bright exponential galaxies: the masxinnun value of (qos) is 8Ο.Τ. at fracDeVzz0. M,zz—22.5."," The roundest galaxies, measured by $\langle q_{25} \rangle$, are not bright de Vaucouleurs galaxies, but bright exponential galaxies; the maximum value of $\langle q_{25} \rangle$ is $\approx 0.74$, at $\texttt{fracDeV} \approx 0$, $M_r \approx -22.5$."1145" Note also that [or bright galaxies (M,S —21). the contours of constant (001) in Figure 2) are nearly horizontal."," Note also that for bright galaxies $M_r \la -21$ ), the contours of constant $\langle q_{25} \rangle$ in Figure \ref{fig:fdevmag}1146 are nearly horizontal."1147 That is. among bright galaxies. the flattening of the outer isophotes doesnt depend strongly on the surface briehtuess profile (wpe.," That is, among bright galaxies, the flattening of the outer isophotes doesn't depend strongly on the surface brightness profile type."1148 A view of the dependence of (q) on absolute magnitude for each of our four profile types. ον. ‘ex/de’. de/ex'. and ‘ce’. is given in Figure 3..," A view of the dependence of $\langle q \rangle$ on absolute magnitude for each of our four profile types, `ex', `ex/de', 'de/ex', and `de', is given in Figure \ref{fig:mag}."1149 In the upper panel. which shows (qa). note that for each prolile type. there is a critical absolute magnitude Mag at which(qu) is al a minimum.," In the upper panel, which shows $\langle q_{\rm am} \rangle$ , note that for each profile type, there is a critical absolute magnitude $M_{\rm crit}$ at which$\langle q_{\rm am} \rangle$ is at a minimum."1150" This οσα] absolute magnitude ranges from M4;~—20.6 for the ‘de’ galaxies to Magc—19.4 for the ""ex! galaxies.", This critical absolute magnitude ranges from $M_{\rm crit} \sim -20.6$ for the `de' galaxies to $M_{\rm crit} \sim -19.4$ for the `ex' galaxies.1151" At AL.<Mag. the value of (gun) increases relatively rapidly with increasing luminosity: at M,>Mig. the value of (gy) increases less rapidly with decreasing Iuminositv."," At $M_r < M_{\rm crit}$, the value of $\langle q_{\rm am} \rangle$ increases relatively rapidly with increasing luminosity; at $M_r > M_{\rm crit}$, the value of $\langle q_{\rm am} \rangle$ increases less rapidly with decreasing luminosity."1152" At a fixed absolute magnitude. the average axis ratio of ‘cle’ galaxies is always greater than (hat of ex’ galaxies: however. for M,<<—20. the flattest ealaxies. on average. al a given absolute magnitude are not (he ‘ex galaxies. butthose with the mixed ‘de/ex’ and ‘ex/de’ prolile types."," At a fixed absolute magnitude, the average axis ratio of `de' galaxies is always greater than that of `ex' galaxies; however, for $M_r \la -20$, the flattest galaxies, on average, at a given absolute magnitude are not the `ex' galaxies, butthose with the mixed `de/ex' and `ex/de' profile types."1153" The bottom panel of Figure 3. shows (q@5) versus AM, for the different profile types.", The bottom panel of Figure \ref{fig:mag} shows $\langle q_{25} \rangle$ versus $M_r$ for the different profile types.1154" In the interval —20<V,—22. we see that ‘ex’ galaxies have values of (q55) than galaxies of other profile types."," In the interval $-20 \la M_r \la -22$, we see that `ex' galaxies have values of $\langle1155q_{25} \rangle$ than galaxies of other profile types."1156 Tremblay&Merritt(1996). divided elliptical galaxies into (wo classes: galaxies brighter than Aj8—20 are rounder on average than [anter ellipticals., \citet{tm96} divided elliptical galaxies into two classes; galaxies brighter than $M_B \approx -20$ are rounder on average than fainter ellipticals.1157" Using a tvpical color for elliplical galaxiesof 5—V.zz 0.9. this corresponds (to an absolute magnitude in the r band ol M,zz —21.2. using the transformation r=2—1.4408V)20.12 (Smithetal. 2002).."," Using a typical color for elliptical galaxiesof $\bv \approx 0.9$ , this corresponds to an absolute magnitude in the $r$ band of $M_r \approx -21.2$ , using the transformation $r = B - 1.44 (B-V) + 0.12$ \citep{sm02}. ."1158 In, In1159luterestinglw. both x-ray sources are transient and have been much brighter iu the past 6)).,"Interestingly, both x-ray sources are transient and have been much brighter in the past \ref{s:temporal}) )."1160" No known backeround or foreground objects were found coincident with the $3 ssources,", No known background or foreground objects were found coincident with the S3 sources.1161 Up to ~25 backerouncd objects are expected im he $3 field above S/N =3.5 based upon our analysis of he calibration Ποια CRSS J0030.5|2618 (see also Draudt 22000)., Up to $\sim$ 25 background objects are expected in the S3 field above S/N $=3.5$ based upon our analysis of the calibration field CRSS J0030.5+2618 (see also Brandt 2000).1162 This estimate ignores anv obscurtion bv MSI., This estimate ignores any obscurtion by M81.1163 Based on results of the stellar survey (Topka 11982). we estimate roughly 0.1 F- and C-stars could be detectable in our field but these should all be extremely soft (Alageio 11987. Todekin Pye 1991. Scliunitt 1997).," Based on results of the stellar survey (Topka 1982), we estimate roughly 0.4 F- and G-stars could be detectable in our field but these should all be extremely soft (Maggio 1987, Hodgkin Pye 1994, Schmitt 1997)."1164 Α soft spectrum was observed οι 3 catalogued stars detected ou CCD S2., A soft spectrum was observed from 3 catalogued stars detected on CCD S2.1165 The total source counts in the hard xay baud (2.0. 8.0 keV) is shown in figure 2 against the soft (0.2 2.0 keV) baud for the subset of sources with S/N223.5 excluding the uucleus., The total source counts in the hard x-ray band (2.0 – 8.0 keV) is shown in figure 2 against the soft (0.2 – 2.0 keV) band for the subset of sources with $\ge$ 3.5 excluding the nucleus.1166 There is no adjustineut for pileup which tends to harden spectra of the brightest sources., There is no adjustment for pileup which tends to harden spectra of the brightest sources.1167 Also shown are the hardness ratios of the stun of all the bulge sources. and of all the disk sources. the harduess ratio ofthe excess bulge emission (backeround aud unclear PSF subtracted). aud of the typical background (scaled to a 2« area).," Also shown are the hardness ratios of the sum of all the bulge sources, and of all the disk sources, the hardness ratio of the excess bulge emission (background and nuclear PSF subtracted), and of the typical background (scaled to a $2\arcmin \times 2\arcmin$ area)."1168 The nucleus aud the bright soft source are olutted from the summed bulee poiut. aud N-6 is omitted from the sununaed disk poiut as these sources are clearly spectroscopically atypical.," The nucleus and the bright soft source are omitted from the summed bulge point, and X-6 is omitted from the summed disk point as these sources are clearly spectroscopically atypical."1169 The line shown corresponds to an absorbed power law of spectral iudex D=1.6. typical of x-ray binaries. with the Galactic absorbing cola deusity of Ny=bx102? cm? (Stark 11992).," The line shown corresponds to an absorbed power law of spectral index $\Gamma = 1.6$, typical of x-ray binaries, with the Galactic absorbing column density of $N_H = 4 \times 10^{20}$ $^{-2}$ (Stark 1992)."1170 Though iudicative aud useful to euide the eve. this canonical spectral shape is not a model fit result.," Though indicative and useful to guide the eye, this canonical spectral shape is not a model fit result."1171 Most sources fall near this curve., Most sources fall near this curve.1172 Notable exceptions are the soft sources at the lower right of figure 2., Notable exceptions are the soft sources at the lower right of figure 2.1173 The softest bulee sources have no known associations but the 3 softest disk sources all lie on spiral axis., The softest bulge sources have no known associations but the 3 softest disk sources all lie on spiral arms.1174 The softest source is also tinme-variable 63) aud is the third brightest source in the entire sample., The softest source is also time-variable \ref{s:temporal}) ) and is the third brightest source in the entire sample.1175 The harduess ratios for the sunmuued bulee and sumuued disk spectra are also typical of x-rav binarics., The hardness ratios for the summed bulge and summed disk spectra are also typical of x-ray binaries.1176 The excess bulge cinissiou is softer indicating some of the excess chussion is from truly diffuse. hot. iuterstellar gas and not cutirely from unresolved point sources.," The excess bulge emission is softer indicating some of the excess emission is from truly diffuse, hot, interstellar gas and not entirely from unresolved point sources."1177 The ummber of sources above a lanitine brieltucss. NSS). is shown against the 0.2. δ keV. count rate. S. iu figure 3.," The number of sources above a limiting brightness, $N(>$$S)$, is shown against the 0.2 – 8.0 keV count rate, $S$, in figure 3."1178 The nucleus is excluded as are sources with S/N<3.5., The nucleus is excluded as are sources with $<$ 3.5.1179 Backerouncl sources were taken from the calibration field CRSS J0030.5|2618 3)). by applying our sale analysis methods. aud have been subtracted after scaling to the fractional areas of the bulee and disk.," Background sources were taken from the calibration field CRSS J0030.5+2618 \ref{s:spatial}) ), by applying our same analysis methods, and have been subtracted after scaling to the fractional areas of the bulge and disk."1180" The curve shown in figure 3 represcuts the best power law fit to the disk distribution, Vo=0.135 """", over the entire range of S,"," The curve shown in figure 3 represents the best power law fit to the disk distribution, $N =0.43S^{-0.50}$ , over the entire range of $S$."1181" Similarly, N=0.119"""" for the bulee source distribution for S-«0.001 1."," Similarly, $N = 0.44 S^{-0.57}$ for the bulge source distribution for $S$$<$ 0.004 $^{-1}$."1182 There is a break iu the slope of the distribution of bulge sources above this point but no such break iu the disk source distribution., There is a break in the slope of the distribution of bulge sources above this point but no such break in the disk source distribution.1183 Of the LO disk sources with 570.001 s1. 7 ave coincident with spiral arius.," Of the 10 disk sources with $S$$>$ 0.004 $^{-1}$, 7 are coincident with spiral arms."1184 The huuinositv of cach source can be estimated by assunune the P—1.6 power law spectral model of and a distance of 3.6 AIpe to M81 (Freecanan 11991)., The luminosity of each source can be estimated by assuming the $\Gamma = 1.6$ power law spectral model of \ref{s:spectral} and a distance of 3.6 Mpc to M81 (Freedman 1994).1185" For our 50-ks observation. therefore. S=0.001 3 in the 0.2 — 8.0 keV baud corresponds to a huuinosity Ly=3.04107 cress | ane the faintest source iu the field corresponds to a luminosity of ~3«1076 eres st,"," For our 50-ks observation, therefore, $S=0.004$ $^{-1}$ in the 0.2 – 8.0 keV band corresponds to a luminosity $L_X = 3.7 \times 10^{37}$ ergs $^{-1}$ and the faintest source in the field corresponds to a luminosity of $\sim 3 \times 10^{36}$ ergs $^{-1}$."1186 Excluding the nucleus. the total bulee luuinosity is Ly~2.1.10 eres bof which is excess (unresolved) cluission.," Excluding the nucleus, the total bulge luminosity is $L_X \sim 2.4 \times 10^{39}$ erg $^{-1}$ of which is excess (unresolved) emission."1187 The total hmuuimositv of the disk sources is Ly~3.9&1079 cre 1., The total luminosity of the disk sources is $L_X \sim 3.9 \times 10^{39}$ erg $^{-1}$.1188 The bluniuositv of the nucleus is Ly~Ls10! cre ft based ou spectral fits to the trailed image., The luminosity of the nucleus is $L_X \sim 4 \times 10^{40}$ erg $^{-1}$ based on spectral fits to the trailed image.1189 This is within the ASCA-obscrved range of huninositics (Ishisali 11996) and comparable to the BeppoSAX observed huninosity (Pellegrini 22000)., This is within the ASCA-observed range of luminosities (Ishisaki 1996) and comparable to the BeppoSAX observed luminosity (Pellegrini 2000).1190 The uucleus coutributes approximately of the total luminosity in the 87.3.8:3 S3 field of view., The nucleus contributes approximately of the total luminosity in the $8\arcmin.3 \times 8\arcmin.3$ S3 field of view.1191 A simple test for time viuiabilitv was made by binning the light curves of all sources on 1000. 2000. and 000 second intervals.," A simple test for time variability was made by binning the light curves of all sources on 1000, 2000, and 4000 second intervals."1192 Applying a 4? test for the lypothesis of consistency with a mean value found only oue. clearly siguificant deviation ou all three timescales., Applying a $\chi^2$ test for the hypothesis of consistency with a mean value found only one clearly significant deviation on all three timescales.1193 This source is also the softest source oi $3 aud the third brightest., This source is also the softest source on S3 and the third brightest.1194 It is present iu at least 3 of 6 IIIRI observations spauuiug 1993 - 1998 but is too close to the nucleus to be identified in amy other previous x-ray observation., It is present in at least 3 of 6 HRI observations spanning 1993 - 1998 but is too close to the nucleus to be identified in any other previous x-ray observation.1195 ΑΙΣ1 has been observed in x-ravs at moderate spatial resolution by in 1979 and bv oover the period 19911998., M81 has been observed in x-rays at moderate spatial resolution by in 1979 and by over the period 1991–1998.1196 There are 6 ssources (E88) within the $3 field of view and another 1 ROSAT—detected sources according to our analysis., There are 6 sources (F88) within the S3 field of view and another 4 -detected sources according to our analysis.1197 rresolves six ssource regions into two or more sources inchiding ssources X-7 and N-1O. and. of course. the nucleus.," resolves six source regions into two or more sources including sources X-7 and X-10, and, of course, the nucleus."1198 Long-term variability has been detected in the vvariahle source. the nucleus. N-2 and the ROSAT—detected source comcideut with au uudocumoeuted star-like object 3)).," Long-term variability has been detected in the variable source, the nucleus, X-2 and the -detected source coincident with an undocumented star-like object \ref{s:spatial}) )."1199 Both of the latter sources are moderately weak in the preseut observations (~3 and ~6<107 sto respectively) but have been much brighter in the past.," Both of the latter sources are moderately weak in the present observations $\sim$ 3 and $\sim 6 \times 10^{37}$ $^{-1}$, respectively) but have been much brighter in the past."1200" The location of another ssource, X-12. places it on the eastern edge of 53."," The location of another source, X-12, places it on the eastern edge of S3."

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