ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Such calculations would uo-doubt provide ither insight iuto the physical structure of extra-solar eas elants., Such calculations would no-doubt provide further insight into the physical structure of extra-solar gas giants.3"rate increases with time as £77"" wdülst the wind velocity decreases as fδν so the wind lias evolved from a case more suitable to an O-star.","rate increases with time as $t^{2/3}$ whilst the wind velocity decreases as $t^{-1/3}$, so the wind has evolved from a case more suitable to an O-star."4 The assumed bubble age is t=10! vr., The assumed bubble age is $t = 10^{4}$ yr.5 The interchunp medium varies as poxs2 )— 1/2) which is a flatter distribution than for a constaut velocity wind (e. 7)., The interclump medium varies as $\rho \propto r^{-1/2}$ $\beta = -1/2$ ) which is a flatter distribution than for a constant velocity wind $r^{-2}$ ).6 However. since the wind nass-loss rate is increasing and the velocity decreasing. aurDL? interchuup deusity profile is plivsically realistic Or such a scenario.," However, since the wind mass-loss rate is increasing and the velocity decreasing, an $r^{-1/2}$ interclump density profile is physically realistic for such a scenario."7 Tn comparison with the neglieiblv nass-loacded solution. the increase in deusitv duside the »bble for the highly mass-loaded solution can be clearly seen. along with a decrease in preshock velocity. preshock Mach number. aud postshock temperature.," In comparison with the negligibly mass-loaded solution, the increase in density inside the bubble for the highly mass-loaded solution can be clearly seen, along with a decrease in preshock velocity, preshock Mach number, and postshock temperature."8 laterestingly. he Mach uuuber of the postshock flow isAgher for the reavily miass-loaded solution.," Interestingly, the Mach number of the postshock flow is for the heavily mass-loaded solution."9 Note also that the heavily nass-loaded solution extends to a larger bubble radius., Note also that the heavily mass-loaded solution extends to a larger bubble radius.10 This is a consequence of the differcut preshock interchunp densities: for the heavily mass-loaded solution 1.=0.066. whilst 54=0.195 for the negligibly mass-loaded solution.," This is a consequence of the different preshock interclump densities: for the heavily mass-loaded solution $n_{e} = 0.066$, whilst $n_{e} = 0.195$ for the negligibly mass-loaded solution."11 Iu PDIT it was shown that there is a negative feed-back mechanisia caused by the evaporation of mass frou cmbedded chuups. which set a maxinuun lianit to the amount that a bubble could be massloaded.," In PDH it was shown that there is a negative feed-back mechanism caused by the evaporation of mass from embedded clumps, which set a maximum limit to the amount that a bubble could be massloaded."12 Additionally. for the bubble mass to be greater than the mass of the swept-up shell a large radial depeudence of the mass loading was required (A= 1).," Additionally, for the bubble mass to be greater than the mass of the swept-up shell, a large radial dependence of the mass loading was required $\lambda \geq 4$ )."13 Iu this work we iustead find that small values of A are required to satisfy this condition., In this work we instead find that small values of $\lambda$ are required to satisfy this condition.14" Our simulations show that it is impossible to obtain a sinularity solution with A,<Af, for A=>1 for A=1. Mj,2 2.1M;)."," Our simulations show that it is impossible to obtain a similarity solution with $M_{sh} < M_{b}$ for $\lambda \geq -1$ for $\lambda = 1$, $M_{sh} \gtsimm 2.4 M_{b}$ )."15" However. for smaller values of A. solutious satisfviug Ma,«AL, cau be found or A=2 (-3). we can obtain Af,z8 (29) M. where &,z7.6 (15))."," However, for smaller values of $\lambda$, solutions satisfying $M_{sh} < M_{b}$ can be found for $\lambda = -2$ (-3), we can obtain $M_{b} \approx 8$ (29) $M_{sh}$, where $\Phi_{b} \approx 7.6$ (15))."16" For a given value of AL,(AL, there appears to be a imaxiumun value for ὃν.", For a given value of $M_{sh}/M_{b}$ there appears to be a maximum value for $\Phi_{b}$.17 It occurs when lass loading starts very close to the bubble centre μη> 0) aud when the flow remains supersonic relative to the clumps over the cutive bubble radius., It occurs when mass loading starts very close to the bubble centre $x_{ml} \rightarrow 0$ ) and when the flow remains supersonic relative to the clumps over the entire bubble radius.18The lifetime of the progenitor star of each of these six objects has been derived by subtracting the estimated cooling time. shown in Table |. from the adopted cluster age. where. for the reasons outlined in Section 2. it has been assumed that 7=2434+40Myrs for NGC2287 and 7=300425Myrs for NGC3532.,"The lifetime of the progenitor star of each of these six objects has been derived by subtracting the estimated cooling time, shown in Table 1, from the adopted cluster age, where, for the reasons outlined in Section 2, it has been assumed that $\tau$ $\pm$ 40Myrs for NGC2287 and $\tau$ $\pm25$ Myrs for NGC3532."19 In this calculation. we have taken the errors in the cooling times to have magnitudes as shown within the brackets of the relevant column of Table |.," In this calculation, we have taken the errors in the cooling times to have magnitudes as shown within the brackets of the relevant column of Table 1."20 These are based on more likely levels of uncertainty in our effective temperature and surface gravity determinations of and 0.07dex respectively (e.g. Napiwotzki. Green Saffer 1999).," These are based on more likely levels of uncertainty in our effective temperature and surface gravity determinations of and 0.07dex respectively (e.g. Napiwotzki, Green Saffer 1999)."21 Subsequently. we have used cubic splines to interpolate between the lifetimes calculated for stars of solar by Girardi e al. (," Subsequently, we have used cubic splines to interpolate between the lifetimes calculated for stars of solar by Girardi et al. ("222000) and have constrained the masses of these six progenitors to the values shown in the final column of Table |.,2000) and have constrained the masses of these six progenitors to the values shown in the final column of Table 1.23 We note in this context and in the framework of main sequence turn-off based cluster age estimates that current eclipsing binary data are consistent with ao 0.2 (e., We note in this context and in the framework of main sequence turn-off based cluster age estimates that current eclipsing binary data are consistent with $\alpha_{\rm OV}$ =0.2 (ie.24 a moderate level of) convective core over-shooting across the broad mass range M-—2-30M.. (Clare 2007)., a moderate level of) convective core over-shooting across the broad mass range $\sim$ $_{\odot}$ (Claret 2007).25 However. we caution that the errors we quote here in progenitor mass are merely approximations since they have no been determined through a detailed statistical analysis (e.g. Salaris et al.," However, we caution that the errors we quote here in progenitor mass are merely approximations since they have not been determined through a detailed statistical analysis (e.g. Salaris et al."26 2008)., 2008).27 Nevertheless. their magnitudes should provide a guide to the impact of the uncertainties in both the white dwarf parameters and the cluster ages which are main sources of error on the final and initial masses respectively (Salaris et al.," Nevertheless, their magnitudes should provide a guide to the impact of the uncertainties in both the white dwarf parameters and the cluster ages which are main sources of error on the final and initial masses respectively (Salaris et al."28 2008), 2008).29 The locations of the six white dwarf members of NGC:22293523-7 and NGC2287 in initial mass-final mass space are shown plotted in Figure 3. with data from the extensively studied Sirius system (e.g. Barstow et al.," The locations of the six white dwarf members of NGC3532 and NGC2287 in initial mass-final mass space are shown plotted in Figure 3, with data from the extensively studied Sirius system (e.g. Barstow et al."30 2005) and a number of other clusters which have metalicities that are found to be reasonably close to the solar value (within 30-40%)x, 2005) and a number of other clusters which have metalicities that are found to be reasonably close to the solar value (within ).31" While Sirius B is not associated with a particular star cluster. we include it here since there are relatively few objects in the Mi, uM. regime and the uncertainties on individual points here are particularly large."," While Sirius B is not associated with a particular star cluster, we include it here since there are relatively few objects in the $_{\rm init}$$\simgreat$ $_{\odot}$ regime and the uncertainties on individual points here are particularly large."32 To determine the initial and final masses of the white dwarf members of these additional populations we have used the same model grids and methodology asapplied to NGC3532 and NGC2287., To determine the initial and final masses of the white dwarf members of these additional populations we have used the same model grids and methodology as applied to NGC3532 and NGC2287.33 For the MM we have the hite parameters bs Dine, For the Pleiades we have assumed an age of $\tau$ $\pm$ 25Myrs (e.g. Ferrario et al.3405) and have utilised Ww dwarf determined et al. (, 2005) and have utilised the white dwarf parameters determined by Dobbie et al. (352006a.2006b).,"2006a,2006b)."36 In the cases of NGC6819 (Kalirai et al., In the cases of NGC6819 (Kalirai et al.37 on NGC7789 (Kalirai et al.," 2008), NGC7789 (Kalirai et al."38 2008). the Hyades (Claver et N," 2008), the Hyades (Claver et al."39GCQxal. Praesepe (Claver et al.," 2001), Praesepe (Claver et al."40 2001. Casewell et al.," 2001, Casewell et al."41 2009). Sinus (Williams Bolte 2007). NGC1039 (Rubin et al.," 2009), NGC6633 (Williams Bolte 2007), NGC1039 (Rubin et al."42 2008) and (Liebert et al., 2008) and Sirius (Liebert et al.43 2005). we have adopted for the cluster age and the effective temperatures and surface gravities of the white dwarf members. the values listed in the relevant referenced work.," 2005), we have adopted for the cluster age and the effective temperatures and surface gravities of the white dwarf members, the values listed in the relevant referenced work."44 Although Kalirai et al. (, Although Kalirai et al. (452005) adopted an age of 7-650M yrs and a substantially subsolar composition for GC2099. the results from two recent spectroscopic studies suggest that the cluster has near solar metalicity.,"2005) adopted an age of $\tau$ =650Myrs and a substantially subsolar composition for NGC2099, the results from two recent spectroscopic studies suggest that the cluster has near solar metalicity."46 Marshall et al. (, Marshall et al. (472005) measure + 0.05 from. moderate resolution. spectroscopy. of eight giant members while Hartman et al. (,2005) measure $\pm$ 0.05 from moderate resolution spectroscopy of eight giant members while Hartman et al. (48"2008) determine [M/H]=+0.02+0 04 from. high resolution spectroscopy of candidate menibers. with 7,4774500K. Moreover. during the last fifteen years he bulk of age estimates for NGC2099 obtained using theoretical isochrones generated from. solar metalicity stellar models which include moderate levels of convectivecore overshooting. ave found values within the range 7—4150-550M yrs eg T=450Myrs. Mermilliod et al. (","2008) determine $\pm$ 0.04 from high resolution spectroscopy of candidate members with $T$$_{\rm eff}$$>$ 4500K. Moreover, during the last fifteen years the bulk of age estimates for NGC2099 obtained using theoretical isochrones generated from solar metalicity stellar models which include moderate levels of convectivecore overshooting, have found values within the range $\tau$ =450-550Myrs e.g. $\tau$ =450Myrs, Mermilliod et al. ("491996). 72520Mvrs. Kalirai et al. (,"1996), $\tau$ =520Myrs, Kalirai et al. ("502001). pU Kiss et al. (,"2001), $\tau$ =450Myrs, Kiss et al. ("512001) and 7—550M vrs. Hartman et al. (,"2001) and $\tau$ =550Myrs, Hartman et al. ("522008).,2008).53and. uveHere we have assumed the cluster has solar metaliciy adopted the mean of the above age determinations. T4904 FE70Myr. where the error bound has been tuned to envelope the bvUk of these estimates.," Here we have assumed the cluster has solar metalicity and have adopted the mean of the above age determinations, $\tau$$\sim$ $\pm$ 70Myr, where the error bound has been tuned to envelope the bulk of these estimates."54 Both Ferrario et al. (, Both Ferrario et al. (552005) and Dobbie et al. (,2005) and Dobbie et al. (562006a) adopted T2|58Mvrs for NGC?56. a key cluster for constraining the form of the top end of the IFMR.,"2006a) adopted $\tau$ =158Myrs for NGC2516, a key cluster for constraining the form of the top end of the IFMR."57 This age was drawn from the work of Sung Bessell (2002) and is marginally larger than that adopted by Koester Reimers {996). rz1HOM which is from the work of Mevnet. Mermilliod Maeder(1993).," This age was drawn from the work of Sung Bessell (2002) and is marginally larger than that adopted by Koester Reimers (1996), $\tau$ =140Myrs which is from the work of Meynet, Mermilliod Maeder (1993)."58 vrsKharchenko et al. (, Kharchenko et al. (592005) recently derived 7=120Tyrs using 2MASS PSC data. but this is based on only three cluster stars.,"2005) recently derived $\tau$ =120Myrs using 2MASS PSC data, but this is based on only three cluster stars."60 Since the work of Ferrario et al. (, Since the work of Ferrario et al. (612005) and Dobbie et al. (,2005) and Dobbie et al. (62200623). a new detailed photometric study of the cluster (Lyra et al.,"2006a), a new detailed photometric study of the cluster (Lyra et al."63 2006). which used the isochrones of Girardi et al. (," 2006), which used the isochrones of Girardi et al. ("64200!0). has concluded that 7 —|40Mvrs.,"2000), has concluded that $\tau$ =140Myrs."65 Looking at all these estimates collectively. we conclude that the age of NGC2516 most probably lies within the range 14523-30Myrs.," Looking at all these estimates collectively, we conclude that the age of NGC2516 most probably lies within the range $\pm$ 30Myrs."66 We have excluded a number of white dwarf candidate members of these clusters from our subsequent analvsis for the following reasons: WDO08374218 is more likely to be a field star than a member of Praesepe (Casewell et al., We have excluded a number of white dwarf candidate members of these clusters from our subsequent analysis for the following reasons: WD0837+218 is more likely to be a field star than a member of Praesepe (Casewell et al.67 20€09). WD08364201 is strongly magnetic and may have a substantially. different evolutionary history to that oa typical non-magnetic star (e.g. Wickramasinghe Ferrario 2000. Ux Toutet al.," 2009), WD0836+201 is strongly magnetic and may have a substantially different evolutionary history to that of a typical non-magnetic star (e.g. Wickramasinghe Ferrario 2000, Tout et al."68 2008). WDO08364+185. NGC6633 LAWDS 4 arid 7 may double-degenerate systems as suggested by photometric or radial velocity data. in which case close binary interaction could have significantly. impacted their evolution. NGC6633 LAWDS 16 is a DB white dwarf for which determinations of effective temperature and surface gravity are considerably less certain (e.g. Kepler et al.," 2008), WD0836+185, NGC6633 LAWDS 4 and 7 may be double-degenerate systems as suggested by photometric or radial velocity data, in which case close binary interaction could have significantly impacted their evolution, NGC6633 LAWDS 16 is a DB white dwarf for which determinations of effective temperature and surface gravity are considerably less certain (e.g. Kepler et al."69 2007). NGC2099 WD 6 and 21 do not have spectroscopic surface gravity determinations. NGC?099 WD 15.16 and 17 are found to be too old at the revised age of their putative parent cluster. NGCIO39 LAWDS 20. SI and 9 have proper motions. as listed in the SuperCOSMOS Sky Survey database (Hambly et al.," 2007), NGC2099 WD 6 and 21 do not have spectroscopic surface gravity determinations, NGC2099 WD 15,16 and 17 are found to be too old at the revised age of their putative parent cluster, NGC1039 LAWDS 20, S1 and 9 have proper motions, as listed in the SuperCOSMOS Sky Survey database (Hambly et al."70 21). which are ~3.30. ~4. 1 ~2.30 from the mean of their putative parent cluster and are thus," 2001), which are $\sim$ $\sigma$ , $\sim$ $\sigma$ $\sim$ $\sigma$ from the mean of their putative parent cluster and are thus"71 Jean. at least in principle. always be computed.,"$\beta$ can, at least in principle, always be computed."72 Llowever. in practice. the size of the computational domain (or the number of trajectories) required. may be extremely larec. and indeed. in some cases when small-scale dynamo action is present. may even be increasing exponentially in time.," However, in practice, the size of the computational domain (or the number of trajectories) required may be extremely large, and indeed, in some cases when small-scale dynamo action is present, may even be increasing exponentially in time."73 With the exception of the test field model all methocks (I5ulerian. and Lagrangian) are based on averages of the exact solution of the induction. equation. and. therefore should vield the same results.," With the exception of the test field model all methods (Eulerian and Lagrangian) are based on averages of the exact solution of the induction equation, and therefore should yield the same results."74 The test field procedure. by contrast. invokes a predetermined arbitrary mean field.," The test field procedure, by contrast, invokes a predetermined arbitrary mean field."75 The quantities à and 3 calculated through this technique will therefore be approximations to the true values of à and 3. whose quality will depend on how well the true mean field is approximated by the choice of test field.," The quantities $\alpha$ and $\beta$ calculated through this technique will therefore be approximations to the true values of $\alpha$ and $\beta$, whose quality will depend on how well the true mean field is approximated by the choice of test field."76 We now turn to the question of how e and 3 relate to the growth of a dynamo field., We now turn to the question of how $\alpha$ and $\beta$ relate to the growth of a dynamo field.77 First consider the case when no small-scale dynamo action is observed., First consider the case when no small-scale dynamo action is observed.78 Here. ας) £) must be small: for if it were not then. by equation (1)). one would observe cynamo action on a scale { Contrary to our assuniption.," Here, $\alpha \ell / \beta$ $k \ell$ ) must be small; for if it were not then, by equation \ref{eq:grate}) ), one would observe dynamo action on a scale $\ell$ — contrary to our assumption."79 One can conceive of a sequence of experiments of varying spatial extent £L., One can conceive of a sequence of experiments of varying spatial extent $L$.80 When £L—{ then. bv assumption. no dvnamo action is observed.," When $L \sim \ell$ then, by assumption, no dynamo action is observed."81 As Lis increased. dvnamo action will first set in when L=fa.," As $L$ is increased, dynamo action will first set in when $L = \beta / \alpha$."82 Increasing L further will lead to an increase in the growth rate until its maximum is reached at L=25/6., Increasing $L$ further will lead to an increase in the growth rate until its maximum is reached at $L = 2 \beta / \alpha$.83 Further increases in L will not [ead to any further increases in the erowth rate., Further increases in $L$ will not lead to any further increases in the growth rate.84 So in the absence of small-scale dynamo action. everything is fine. anc a and. determine the growth rate of the observed. magnetic structures.," So in the absence of small-scale dynamo action, everything is fine, and $\alpha$ and $\beta$ determine the growth rate of the observed magnetic structures."85 Consider now the case when small-scale dvnamo action is possible., Consider now the case when small-scale dynamo action is possible.86 What would. be the outcome of repeating the experiments described above?, What would be the outcome of repeating the experiments described above?87 By assumption. ανπαπιο action takes place even when L-—f.," By assumption, dynamo action takes place even when $L \sim \ell$."88 Furthermore. the dvnamo growth rate will be independent. of domain size.," Furthermore, the dynamo growth rate will be independent of domain size."89" Finally, any average of the magnetic field on intermediate scales will grow at exactlv the same rate."," Finally, any average of the magnetic field on intermediate scales will grow at exactly the same rate."90 Crucially. the erowth rate of the observed field has nothing to do with that predictedby equation (1)).," Crucially, the growth rate of the observed field has nothing to do with that predictedby equation \ref{eq:grate}) )."91 A particularly striking example can be seen for the case of a non-helical dynamo., A particularly striking example can be seen for the case of a non-helical dynamo.92 Here a is zero and equation (1)) therefore predicts that large-scale averages should. decay. exponentially at a scale-depencdent rate. whereas. as we have just argued. any average will grow exponentially at the small-scale dynamo growth rate.," Here $\alpha$ is zero and equation \ref{eq:grate}) ) therefore predicts that large-scale averages should decay exponentially at a scale-dependent rate, whereas, as we have just argued, any average will grow exponentially at the small-scale dynamo growth rate."93 As argued above. the validity of the mean field approach breaks down when small scale dynamo action occurs. which one anticipates at high em.," As argued above, the validity of the mean field approach breaks down when small scale dynamo action occurs, which one anticipates at high $Rm$."94 Interestingly. as pointed out by Alolfatt (1978). there are problems in the high n limit even within the mean field. formalism. since requiring that αἱ is small is inconsistent with traditional estimates for the urbulent a-ellect (a~ mw) and the turbulent -ellect (3 £u).," Interestingly, as pointed out by Moffatt (1978), there are problems in the high $Rm$ limit even within the mean field formalism, since requiring that $\alpha \ell / \beta$ is small is inconsistent with traditional estimates for the turbulent $\alpha$ -effect $\alpha \sim u$ ) and the turbulent $\beta$ -effect $\beta \sim \ell u$ )."95" In this case mean field theory preclicts by. equation (1)) hat the fastest growing “mean field"" has the same scale as he [uctuations namely a small-scale civnamo.", In this case mean field theory predicts by equation \ref{eq:grate}) ) that the fastest growing “mean field” has the same scale as the fluctuations — namely a small-scale dynamo.96 It should rc noted however that the growth rate of this small-scale dynamo predicted. by mean field theory is not the correct one since it relies on lack of rellectional symmetry whereas he actual growth rate does not., It should be noted however that the growth rate of this small-scale dynamo predicted by mean field theory is not the correct one since it relies on lack of reflectional symmetry whereas the actual growth rate does not.97 All the considerations above address the kinematic evolution of magnetic fields. which formally is the relevant regime for mean field electrodvnamics.," All the considerations above address the kinematic evolution of magnetic fields, which formally is the relevant regime for mean field electrodynamics."98 However. there have been attempts to extend. the mean field. approach to the nonlinear regime.," However, there have been attempts to extend the mean field approach to the nonlinear regime."99 We conclude this paper by considering a particular case in which many of the issues we have discussed here are pertinent., We conclude this paper by considering a particular case in which many of the issues we have discussed here are pertinent.100 It is possible to consider à case in which the velocity. rather than being prescribed. is the selt-consistent solution of à saturated small-scale dynamo.," It is possible to consider a case in which the velocity, rather than being prescribed, is the self-consistent solution of a saturated small-scale dynamo."101 Here both the velocity and magnetic [uetuations are stationary. and it is therefore possible. at least in. principle. to measure o and 2.," Here both the velocity and magnetic fluctuations are stationary, and it is therefore possible, at least in principle, to measure $\alpha$ and $\beta$ ."102 In. practice this process is tricky since any finite amplitude perturbation. such as the introduction of a mean field. will induce a corresponding change in the velocity.," In practice this process is tricky since any finite amplitude perturbation, such as the introduction of a mean field, will induce a corresponding change in the velocity."103 Putting aside the not inconsiderable technical dilliculties involved in calculating o and 2. it behoves us to ask whether these quantities convey. useful information about. magnetic field evolution.," Putting aside the not inconsiderable technical difficulties involved in calculating $\alpha$ and $\beta$ , it behoves us to ask whether these quantities convey useful information about magnetic field evolution."104 To make these ideas concrete we consider a very specific case., To make these ideas concrete we consider a very specific case.105 First suppose that a numerical experiment is conducted on a periodic domain L with L-f: we assume that small-scale dynamo action is observed. the magnetic field grows to a finite amplitude ancl saturates. and. by whatever means. à and of are Now suppose that a new computational domain of size NL. where Nis a largish positive integer. is constructed by replication of the original domain.," First suppose that a numerical experiment is conducted on a periodic domain $L$ with $L \sim \ell$; we assume that small-scale dynamo action is observed, the magnetic field grows to a finite amplitude and saturates, and, by whatever means, $\alpha$ and $\beta$ are Now suppose that a new computational domain of size $NL$, where $N$ is a largish positive integer, is constructed by replication of the original domain."106 Clearly. in the absence ofperturbation. the solution of the extended svsteni will continue to evolve as IN? replicas of the original system.," Clearly, in the absence of perturbation, the solution of the extended system will continue to evolve as $N^3$ replicas of the original system."107 If the system. is subject to a lone wavelength. perturbation then it will relax to a new state. which. in general. is not periodic on scales smaller than NL: in other words. the svstem will transfer some of its energy to scales with wavenumbers smaller than 2x/L.," If the system is subject to a long wavelength perturbation then it will relax to a new state, which, in general, is not periodic on scales smaller than $NL$; in other words, the system will transfer some of its energy to scales with wavenumbers smaller than $2 \pi /L$."108 The question is. will the coefficients à and: capture any aspect of this relaxation process?," The question is, will the coefficients $\alpha$ and $\beta$ capture any aspect of this relaxation process?"109 The final state could be similar to the initial state tthat obtained from replicating the smaller domain) or could be very dülferent with. sav. considerable energy at [arge scales.," The final state could be similar to the initial state that obtained from replicating the smaller domain) or could be very different with, say, considerable energy at large scales."110 However. irrespective of the nature of the final state. the relaxation process bv which it is achieved depends on the nonlinear interactions betweenall the scaleslarger than £ and is therefore not captured by averages over the scale £.," However, irrespective of the nature of the final state, the relaxation process by which it is achieved depends on the nonlinear interactions betweenall the scaleslarger than $L$ and is therefore not captured by averages over the scale $L$ ."111 Thus. in this case also. although a ," Thus, in this case also, although $\alpha$ "112bv the fact that we measure a cüllerent value for a in dilleren cosmologies. see Section 5.,"by the fact that we measure a different value for $\alpha$ in different cosmologies, see Section 5."113 Note that each. of the above cases consider. idealise observers who know the correct cosmology to compute distances and {1(0)., Note that each of the above cases consider idealised observers who know the correct cosmology to compute distances and $H(z)$.114 The measured mean of the distribution of pair angles (eq. 1)), The measured mean of the distribution of pair angles (Eq. \ref{sin2t}) )115 depends on the cosmological moce assumed to convert position on the sky ancl redshift to comoving distance., depends on the cosmological model assumed to convert position on the sky and redshift to comoving distance.116 The AAP function. also. depends on cosmologv through {ος, The AAP function also depends on cosmology through $H(z)$.117 As a result. the measure mean and the AAP function. will not agree if the wrong cosmology is assumed (the Alcock-Paczynski cllect).," As a result, the measured mean and the AAP function will not agree if the wrong cosmology is assumed (the Alcock-Paczynski effect)."118 Using two quintessence dark energy simulations (labellecl INV anc SUGRA). we have tested if the AAP function reproduces the measured mean of the distribution when. in the firs instance. we know the correct cosmology (the observer case). ancl in the second instance. when we insteac assume ACDAL (i.e. the observer who has no prior knowledge of the underlying cosmology).," Using two quintessence dark energy simulations (labelled INV and SUGRA), we have tested if the AAP function reproduces the measured mean of the distribution when, in the first instance, we know the correct cosmology (the observer case), and in the second instance, when we instead assume $\Lambda$ CDM (i.e. the observer who has no prior knowledge of the underlying cosmology)."119 Vhe two clark energy models we consider have an evolving equation of state which is compatible with current observations of the CMD. BAO and Type la SN distances.," The two dark energy models we consider have an evolving equation of state which is compatible with current observations of the CMB, BAO and Type Ia SN distances."120 We find that. for a perfect observer who knows //(2) and à exactly. the AAP function and the measured means are in very good agreement Lor both the SUCGILAX and the INV models.," We find that, for a perfect observer who knows $H(z)$ and $\alpha$ exactly, the AAP function and the measured means are in very good agreement for both the SUGRA and the INV models."121 Consider now performing the same exercise using the SUGRA and INV simulations. as à real observer who does not know the underlving cosmology and so assumes a ACDAL cosmology. and who uses the best. fit value for a at each redshift.," Consider now performing the same exercise using the SUGRA and INV simulations, as a real observer who does not know the underlying cosmology and so assumes a $\Lambda$ CDM cosmology, and who uses the best fit value for $\alpha$ at each redshift."122 We might expect that the theory should not match the measured mean for the dynamical dark energy. mocels., We might expect that the theory should not match the measured mean for the dynamical dark energy models.123 Llowever. we find that. by fitting for a using the observe distribution in the simulations. we instead recover a moce which incorrectly matches the observations extremely wel or both dark energy cosmologies. even though we have assumed. a ACDAL model.," However, we find that, by fitting for $\alpha$ using the observed distribution in the simulations, we instead recover a model which incorrectly matches the observations extremely well for both dark energy cosmologies, even though we have assumed a $\Lambda$ CDM model."124 The consequences are that. in a universe with evolving dark energy. we would fim hat a ACDAL model incorrectly matches the observations invalidating the methodology.," The consequences are that, in a universe with evolving dark energy, we would find that a $\Lambda$ CDM model incorrectly matches the observations invalidating the methodology."125 In this paper we have proposed a new formulation of he test of Marinoni Buzzi in which the distribution of galaxy pairs can be analysed without. prior knowledge of he cosmology., In this paper we have proposed a new formulation of the test of Marinoni Buzzi in which the distribution of galaxy pairs can be analysed without prior knowledge of the cosmology.126 The measured clistribution of angles shoulc »: compared. with predictions for the AAD function using a reference N-body simulation to directly measure a., The measured distribution of angles should be compared with predictions for the AAP function using a reference N-body simulation to directly measure $\alpha$.127" We rave shown that the subhalo pairs in two quintessence clark energv simulations. which are treated as the ""observed? »ür sample in this instance. produce a different measured distribution. to that. predicted. in. a ΑςΟΝΕ simulation even when analvsec after assuming (incorrectly) a AC'DAL cosmology."," We have shown that the subhalo pairs in two quintessence dark energy simulations, which are treated as the “observed” pair sample in this instance, produce a different measured distribution to that predicted in a $\Lambda$ CDM simulation even when analysed after assuming (incorrectly) a $\Lambda$ CDM cosmology."128 In the new test. the AAP function is normalized with reference to a simulation with the same cosmology assumed. to analyse the observations.," In the new test, the AAP function is normalized with reference to a simulation with the same cosmology assumed to analyse the observations."129 The precictec AAP function and. measurement will only agree if the assumed cosmology matches the true cosmology., The predicted AAP function and measurement will only agree if the assumed cosmology matches the true cosmology.130 ΙΕ this is not the case. then à new reference simulation must be generated with a revised expansion history. to see if an improved match to the observed distribution of galaxy pair angles can be obtained.," If this is not the case, then a new reference simulation must be generated with a revised expansion history, to see if an improved match to the observed distribution of galaxy pair angles can be obtained."131 We find that. by measuring the mean of the distribution as a function of redshift. we should be able to detect deviations [rom a AC'DAL (?) (2)..," We find that, by measuring the mean of the distribution as a function of redshift, we should be able to detect deviations from a $\Lambda$ \citep{2011ApJ...730..119R} \citep{2006astro.ph..9591A}. \citet{ 1994MNRAS.269.1077P}."132 7.. 2? (7) (2). (2)..," \citet{2010Natur.468..539M} \citep{2010SPIE.7733E..12K}133 \citep{2009arXiv0912.0201L}134 \citep{2011PhRvD..83d3004B}."135of RC stars as a function of vertical heielt below the Calactic plane is consistent with the adopted RC star distances. if the bulee structures studied here are roughly svuuuetric from frout to back.,"of RC stars as a function of vertical height below the Galactic plane is consistent with the adopted RC star distances, if the bulge structures studied here are roughly symmetric from front to back."136 This removes auy lingering doubt about the interpretation of the RC Αα maguitudes as due to distance. and strengtheus the couchision that the bulge contains an N-shape structure.," This removes any lingering doubt about the interpretation of the RC $K$ -band magnitudes as due to distance, and strengthens the conclusion that the bulge contains an X-shape structure."137 Our densities are slightly higher for the backgromuc structure: this possibility should be investigatcc with more sophisticated techniques., Our densities are slightly higher for the background structure; this possibility should be investigated with more sophisticated techniques.138 Several galaxies are kuowu to host X-shape bulges (e.g.. NGC. Ls. NGC 3625. NGC. L169). and some imuuerical simulations predict their formation. with a particularly strong buckling of a bar (Patsisctal.2002:Athauassoula2005:Mi-hosetal. 1995).. MeW," Several galaxies are known to host X-shaped bulges (e.g., NGC 128, NGC 3625, NGC 4469), and some numerical simulations predict their formation, with a particularly strong buckling of a bar \citep{2002MNRAS.337..578P, 2005MNRAS.358.1477A,139 1995ApJ...447L..87M}."140illiiun&Zoccali(2010) review some of the proposed mechauisuis to form such structures., \cite{2010ApJ...724.1491M} review some of the proposed mechanisms to form such structures.141 The X-shape structure secs to be relatively concentrated. with respect to other galaxies (oem. NOC 1710) aud. probably is the dominant conmpoueut ii the ier 2 kpc.," The X-shape structure seems to be relatively concentrated, with respect to other galaxies (e.g., NGC 4710) and probably is the dominant component in the inner 2 kpc."142 It remaius to be understood low the bulee 3D structure cau be reconciled with the other features. such as the presence of a radial wmetallicity eradicut (Zoccalietal.2008:Brownot 2010).. the kinematic difference between the metal poor aud metal rich conrponeut iu Baade’s Window (Dabusauxctal.2010) aud the behavior of the alpha οσοι! ratios. Which secius to be constant in different fields (Gonzalez et al.," It remains to be understood how the bulge 3D structure can be reconciled with the other features, such as the presence of a radial metallicity gradient \citep{2008A&A...486..177Z, 2010ApJ...725L..19B}, the kinematic difference between the metal poor and metal rich component in Baade's Window \citep{2010A&A...519A..77B} and the behavior of the alpha element ratios, which seems to be constant in different fields (Gonzalez et al."143 2011)., 2011).144 It should be kept iu wind. however. that all the properties listed above rave been derived from observations on /z07 ouly.," It should be kept in mind, however, that all the properties listed above have been derived from observations on $l\simeq0^{\circ}$ only."145 Just as the shape turned out to be much nore complex as soon as we analyzed a larger other properties um out to bea area.uwtial theview of the elobal luitpicture.," Just as the shape turned out to be much more complex as soon as we analyzed a larger area, the other properties might turn out to be a partial view of the global picture."146 Radial velocities of stars in the two RCs. at b=S&S revealed no differences (DePropris↽↽ ⋅⋅ ⋅ ⋜↧↕∙⊇∩⊔∙," Radial velocities of stars in the two RCs, at $b=-8^{\circ}$ revealed no differences \citep{2011arXiv1104.0223D}."147"∙∐∪↖↖⇁↸∖↖⇁↸∖↥⋅⋜↧↴∖↴⋃∐↕⋜∐⋅⋜⋯⋜↧↕⋅↖⇁↴∖↴↕↴∖↴⋜↧↑∣↗∶ reveals the presence of two peaks at e,=100 ! iu the faint/bright RC. respectively (Vasquez et al."," However a similar analysis at $b=-6^{\circ}$ reveals the presence of two peaks at $v_r=+100~/-100~$ $^{-1}$ in the faint/bright RC, respectively (Vasquez et al."148 2011. iu preparation).," 2011, in preparation)."149 Proper motions also do not ποσα to differ betweeu stars in the two chumps (Vieiraetal.2007).., Proper motions also do not seem to differ between stars in the two clumps \citep{2007AJ....134.1432}.150 Further investigations are clearly necessary to completely understand our bulge structure. kinematics. chemistry aud. ultimately. origin.," Further investigations are clearly necessary to completely understand our bulge structure, kinematics, chemistry and, ultimately, origin."151 The present imappine traces the N-shaped structure across the whole bulge area and may help to euide further analysis. as well as to design future observations of the Milky Way bulec.," The present mapping traces the X-shaped structure across the whole bulge area and may help to guide further analysis, as well as to design future observations of the Milky Way bulge."152 We thank the anonymous referee for the useful columucuts on our nizanuscript., We thank the anonymous referee for the useful comments on our manuscript.153 We also thank Alvio Renzini for the constructive discussious while we were preparing this paper., We also thank Alvio Renzini for the constructive discussions while we were preparing this paper.154 RS acknowledges financial support from CONICYT throughGEMINI Project Nr., RS acknowledges financial support from CONICYT through GEMINI Project Nr.155 32080016., 32080016.156" MZ and DM are partly supported by Proyectos FONDECYT. Regular 1110393 and 1090213. and by Provecto Couicy Auillo ΑςΤσο,"," MZ and DM are partly supported by Proyectos FONDECYT Regular 1110393 and 1090213, and by Proyecto Conicyt Anillo ACT-86."157 We eratefully ackuowledee use of data from the ESO Public Survey programune ID 179.D-2002 taken with the VISTA telescope. iux data products from the Cambridge Astronomica Survey Unit. and finding trom the FONDAP Ceuter for Astrophysics 15010003. the BASAL CATA Center for Astrophysics and Associate Technologies PFB-06. the NILENIO Milley Way Afillenunium Nucleus from the Ministry of Economyaτν ICM. grant DOT-021-F.. aud the FONDECYT from CONICYT.," We gratefully acknowledge use of data from the ESO Public Survey programme ID 179.B-2002 taken with the VISTA telescope, and data products from the Cambridge Astronomical Survey Unit, and funding from the FONDAP Center for Astrophysics 15010003, the BASAL CATA Center for Astrophysics and Associated Technologies PFB-06, the MILENIO Milky Way Millennium Nucleus from the Ministry of Economy´s ICM grant P07-021-F, and the FONDECYT from CONICYT."158 2MASS is a joint project of the University of Massachusetts aud the Iufrared Processing aud Analysis Center/Calitornia Iustitute of Technology. funded by the National Aeronautics and Space Administration aud the National science Foundation.," 2MASS is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation."159that of the old stellar component of the galaxy.,that of the old stellar component of the galaxy.160 The Sérrsic index. n is mostly in the range 0.5 - 2.0. with some outliers near O and 3.," The Sérrsic index, $n$ is mostly in the range 0.5 - 2.0, with some outliers near 0 and 3."161 Our (FUV-NUY) gradients and the residual images show tha ye FUV excess stars are more centrally concentrated than the yopulation which contributes the bulk of the light at longer wavelengths., Our (FUV-NUV) gradients and the residual images show that the FUV excess stars are more centrally concentrated than the population which contributes the bulk of the light at longer wavelengths.162 All normal ellipticals. all liners. and all bar one of 1e starforming sample show positive (FUV-NUV) gradients. ye dere is no clear correlation between the gradients and the absolute value of the FUV excess.," All normal ellipticals, all liners, and all bar one of the starforming sample show positive (FUV-NUV) gradients, yet there is no clear correlation between the gradients and the absolute value of the FUV excess."163 The FUV excess is centally concentrated irrespective of its absolute level., The FUV excess is centally concentrated irrespective of its absolute level.164 There is no clear indication tha 1ο FUV excess depends upon environment. for instance it is no j»urticularly strong in either NGC4A874 in the core of the Coma cluster. or NGC4486 in the centre of the X-ray distribution in Virgo.," There is no clear indication that the FUV excess depends upon environment, for instance it is not particularly strong in either NGC4874 in the core of the Coma cluster, or NGC4486 in the centre of the X-ray distribution in Virgo."165 It can be moderately strong in galaxies which show evidence of recent minor mergers. for instance the shell ellipticals NGC4552 Talin 1979). NGC3608 (Forbes Thomson 1992). NGC3923 Talin Carter 1980) and NGC5982 (Sikkema et al.," It can be moderately strong in galaxies which show evidence of recent minor mergers, for instance the shell ellipticals NGC4552 (Malin 1979), NGC3608 (Forbes Thomson 1992), NGC3923 (Malin Carter 1980) and NGC5982 (Sikkema et al."166 20073. bu in galaxies with evidence of recent major mergers such as NGC474 (Turnbull et al.," 2007), but in galaxies with evidence of recent major mergers such as NGC474 (Turnbull et al."167 1999). NGCI316 (Schweizer 1980) and NGC2865 (Hau et al.," 1999), NGC1316 (Schweizer 1980) and NGC2865 (Hau et al."168" 1999). and the kinematically decoupled core galaxy 06506, the FUV excess is weak."," 1999), and the kinematically decoupled core galaxy NGC596, the FUV excess is weak."169 The UV bright stars appear to be part of an old population. ormed in a short period of time early in the process of galaxy ormation.," The UV bright stars appear to be part of an old population, formed in a short period of time early in the process of galaxy formation."170 Pipino Matteucci (2004) and Pipino et al. (, Pipino Matteucci (2004) and Pipino et al. (1712006. 2008. 2010) present a number of hydrodynamic models for the ormation of ellipticals. a key prediction of these models is that star formation ceases earlier in the outer regions of the galaxies (“outside-in” formation).,"2006, 2008, 2010) present a number of hydrodynamic models for the formation of ellipticals, a key prediction of these models is that star formation ceases earlier in the outer regions of the galaxies (“outside-in” formation)."172 These models are successful in predicting he observed steep metallicity gradients determined from the optical spectra (Nopec 0.3) and. by taking into account difference in initial conditions. they can reproduce the observed variety in Woyeae.," These models are successful in predicting the observed steep metallicity gradients determined from the optical spectra $\nabla_{[Fe/H]} \simeq -0.3$ ) and, by taking into account difference in initial conditions, they can reproduce the observed variety in $\nabla_{[\alpha/Fe]}$ ."173 However Figure 7. shows that the FUV excess is more a eature of a-enhanced than of metal-rich populations so it is likely hat some other factor is driving the steepness and ubiquity of the UV-IR colour gradients., However Figure \ref{fig:PopsPlots} shows that the FUV excess is more a feature of $\alpha$ -enhanced than of metal-rich populations so it is likely that some other factor is driving the steepness and ubiquity of the UV-IR colour gradients.174 Helium abundance is a clear candidate. it has long been suspected that enhanced helium facilitates the ormation. of Extreme Horizontal Branch (EHB) stars.," Helium abundance is a clear candidate, it has long been suspected that enhanced helium facilitates the formation of Extreme Horizontal Branch (EHB) stars."175 Norris (2004) and Lee et al. (, Norris (2004) and Lee et al. (1762005) suggest that a large enhancement in he helium abundance (XY.20.15) can explain the extended blue yorizontal branch in part of the stellar population of the globular cluster «e Centauri.,2005) suggest that a large enhancement in the helium abundance ${\Delta}Y \simeq 0.15$ ) can explain the extended blue horizontal branch in part of the stellar population of the globular cluster $\omega$ Centauri.177 Sohn et al. (, Sohn et al. (1782006) investigate the UV properties of the globular clusters associated with NGC4486.,2006) investigate the UV properties of the globular clusters associated with NGC4486.179 Many of these clusters are very blue in (FUV-V). but in contrast with elliptical galaxies the bluest UV colours are found for the clusters with the weakest Adg» index.," Many of these clusters are very blue in (FUV-V), but in contrast with elliptical galaxies the bluest UV colours are found for the clusters with the weakest $Mg_2$ index."180 Kaviraj et al. (, Kaviraj et al. (1812007) propose that this indicates that these clusters have a small fraction of a helium enhanced population.,2007) propose that this indicates that these clusters have a small fraction of a helium enhanced population.182 Globular clusters are of course metal-poor populations compared with massive elliptical galaxies. but these observations strongly suggest that large variations in helium content can be generated by some process or processes.," Globular clusters are of course metal-poor populations compared with massive elliptical galaxies, but these observations strongly suggest that large variations in helium content can be generated by some process or processes."183 Suggestions include self-enrichment by winds from the first generation of massive AGB stars (D'Antona Ventura 2007) or by winds from massive rapidly rotating stars (Decressin et al., Suggestions include self-enrichment by winds from the first generation of massive AGB stars (D'Antona Ventura 2007) or by winds from massive rapidly rotating stars (Decressin et al.184 2007)., 2007).185 However whether the helium is primordial of the product of early self-enrichment. we need a mechanism to generate the strong gradients in the FUV excess that we observe.," However whether the helium is primordial of the product of early self-enrichment, we need a mechanism to generate the strong gradients in the FUV excess that we observe."186 A number of authors. including Chuzhoy Loeb (2004) and Peng Nagai (2009). propose that helium sedimentation in cooling gus can generate enhanced helium abundances in brightest cluster galaxies.," A number of authors, including Chuzhoy Loeb (2004) and Peng Nagai (2009), propose that helium sedimentation in cooling gas can generate enhanced helium abundances in brightest cluster galaxies."187 The efficiency of this process is a strong function of the emperature of the cooling gas (Diffusion velocity x T. and it is supressed by turbulence and by small scale magnetic fields.," The efficiency of this process is a strong function of the temperature of the cooling gas (Diffusion velocity $\propto$ $^{1.5}$, and it is supressed by turbulence and by small scale magnetic fields."188 evertheless both of these studies conclude that sedimentation can lead to an enhancement of Helium by a factor up to 1.2 in cD type galaxies. where the gas temperature is & LOK. At first sight this sedimentation process is an attractive candidate for he origin of the central gradients in the FUV excess. however here are two problems with this hypothesis. The first is that it is supressed at high gas concentrations. as the pressure gradient causes outward diffusion which supresses sedimentation.," Nevertheless both of these studies conclude that sedimentation can lead to an enhancement of Helium by a factor up to 1.2 in cD type galaxies, where the gas temperature is $\approx$ $^7$ K. At first sight this sedimentation process is an attractive candidate for the origin of the central gradients in the FUV excess, however there are two problems with this hypothesis, The first is that it is supressed at high gas concentrations, as the pressure gradient causes outward diffusion which supresses sedimentation."189 Thus the yelium abundance enhancement peaks at ~0Τους where rzoo is the radius within which the mean enclosed mass density is 500 imes the critical density of the universe (Peng Nagai 2009).," Thus the helium abundance enhancement peaks at $\sim 0.1 r_{500}$, where $r_{500}$ is the radius within which the mean enclosed mass density is 500 times the critical density of the universe (Peng Nagai 2009)."190" A urther problem is the sedimentation timescale. which is given by: where f, is the local gas fraction: T is temperature: and {ο is a suppression factor due to the magnetic tield (Chuzhoy Loeb 2004)."," A further problem is the sedimentation timescale, which is given by: where $f_{g}$ is the local gas fraction; T is temperature; and $F_B$ is a suppression factor due to the magnetic field (Chuzhoy Loeb 2004)."191 7 is likely to be a few Gyrs. and so it is difficult to set up a strong gradient in the early stages of galaxy formation.," $\tau$ is likely to be a few Gyrs, and so it is difficult to set up a strong gradient in the early stages of galaxy formation."192" Whatever the origin of the enhancement. the persistence of the gradients to the current epoch suggests that this population has not been disturbed by ""dry"" mergers. whieh would tend to smooth out the gradient."," Whatever the origin of the enhancement, the persistence of the gradients to the current epoch suggests that this population has not been disturbed by “dry” mergers, which would tend to smooth out the gradient."193 Simulations of the effect of mergers on the persistence of metallicity gradients have been carried out by Kobayashi (2004) and Di Matteo et al. (, Simulations of the effect of mergers on the persistence of metallicity gradients have been carried out by Kobayashi (2004) and Di Matteo et al. (1942009).,2009).195 The effect of mergers on a helium gradient is a somewhat simpler case. as there is no clear mechanism for regenerating such a gradient if it is disturbed.," The effect of mergers on a helium gradient is a somewhat simpler case, as there is no clear mechanism for regenerating such a gradient if it is disturbed."196 Di Matteo et al. (, Di Matteo et al. (1972009) consider dry mergers of galaxies of equal mass galaxies with a range of initial metallicity slopes.,2009) consider dry mergers of galaxies of equal mass galaxies with a range of initial metallicity slopes.198 Although theyfind that, Although theyfind that199In this section we discuss the properties of LAE and comment on the significance in the application (to pulsars.,In this section we discuss the properties of LAE and comment on the significance in the application to pulsars.200 Our results suggest the following interpretation of LAE., Our results suggest the following interpretation of LAE.201 As a charge is accelerated. over the first half phase of the LAEW it emits a pulse of radiation in the forward direction ol duration Mage7/O.," As a charge is accelerated, over the first half phase of the LAEW it emits a pulse of radiation in the forward direction of duration $\Delta t_{\rm emit}\sim\pi/\Omega$."202 The radiation received by a distant observer has a shorter time scale «λίγο=(1—9) Magi. where oc is the speed at which the particle is approaching the observer.," The radiation received by a distant observer has a shorter time scale $\Delta t_{\rm rec}=(1-\beta)\Delta t_{\rm emit}$ , where $\beta c$ is the speed at which the particle is approaching the observer."203 The shortest time scale on which structure can be observed in the pulse is ∆∕↓⋅≺⋅⋅⊲≈∆∕≺⋅⋯⊔∕∕∕−≻↰≟≈⊤∕∕∕−≻≤≥↰−↕⋅⊳↔⊲∏≺∢∐≀↧↴↕↽≻∏↥⋟∖⇁≼↲∪↓↕⋅≀↧↴≼∐≀↧↴⊔∪∐∐≀↧↪∖⊽⊟∏∐⋅↕≼↲↕⋅≺∢∪∐↓↕, The shortest time scale on which structure can be observed in the pulse is $\Delta t_{\rm rec}\approx\Delta t_{\rm emit}/2\gamma_\pm^2\approx\pi/2\Omega\gamma_\pm^2$.204↽≻∪∐≼↲↕∐⋟∖⊽↕∏↽≻↥∪≀↧↴MP ⋅⋅ ⋅ ↓≯↕⋅≼↲≺⇂⋯↲∐≺↕∖↽⊔∩∾⊥∕∕∕∆∕↓−≺⋅∙⊲≈⋅−≤≥↴≩∕∕∕⊼⋅↴∏∐⊳∖⊽↕⋅≀↧↴≼∐≀↧↴∐∪∐↕⊳∖⇁≺∢∐≀↧↴↕⋅≀↧↴≺∢∥↲↕⋅↥⊳∖⊽∐≺∢∪↓⋟≼↲∐↓↕⊳∖⊽⊳∖⇁↕∪∐∣↽≻⋡∖↽, Such a pulse of radiation has Fourier components up to a frequency $\omega\sim1/\Delta t_{\rm rec}\approx2\Omega\gamma_\pm^2/\pi$.205≀↧↴↕↽≻≀↧↴↕⋅∐≺∢↥≼↲ ∖∖↽↕⊔↥∟∪↕⋅≼↲∐↥∠↓⋟≀↧↴≺∢↥∪↕⋅↷⇌↴∶≀↧↴∐≼⊔⊳∖⊽≺∢∪↕∐∎↓∐≼↲≼⇂↥∪≀↧↴≺∢∪∐≼↲∪↓⋟∐≀↧↴∐≯≀↧↴∐≸≟↥≼↲↴∿↴⊥∕∕∕↷⇩↴∶≀↧↴∣↽≻∪∏↥⊔∐↲≼∐↕⋅≼↲≺∢∐∪∐∪↓⋟ ∐↓∪∐∪∐⋅↴∏↥↕⋟∖⊽⋟∖⇁↕∐↓↕↽≻↥≼↲∐↓⋯⇂≼↲↥↕⋅≼↲↕↽≻↕⋅⋯⇂∏≺∢≼↲, This radiation is characteristic of emission by a particle with Lorentz factor $\gamma_\pm$ and is confined to a cone of half angle $\sim1/\gamma_\pm$ about the direction of motion.206⋟∖⊽⊔∐↲≺∢∐≀↧↴↕⋅≀↧↴≺∢∩↲↕⋅↕⋟∖⊽∐≺∢∐⋅≼↲≺⇂⋯↲∐≺↕∖↽≀↧↴∐≼⇂≀↧↴∐≸↽↔↴∏↥≀↕↴↕⋅≺∐⋟∖⊽⊔⋅↕∣↽≻∏∐∪∐ ∐∐↕↽≻∐≼↲≼⊓↽≻∡∖⇁⊔∐↲≼↲∐∐⋟∖∷∖⇁↕∖↽∐⋡∖↽≼⋝⊑↽⊰⋅⊥⇄⋝⇄⋝, This simple model reproduces the characteristic frequency and angular distribution implied by the emissivity \ref{eta2a}) ).207⋅ ↴∏∐↲≺∢∐≀↕↴↕⋅≀↕↴≺∢∩↲↕⋅↕⋟∖⊽∐≺∢∐↓≀↕↴⇀↸↕∐∐∐⊔↓≯↕⋅≼↲≺⇂⋯↲∐≺∶∖↽↕⋟∖⊽∟≮∖⊏↕⋟∖⊽↓⋟∪∏∐≼⇂↥∪∣↽≻≼↲≤≥↴≟⋅∖∖⇁↥∐↲↕⋅≼↲≤≥↕⋟∖⊽⊔∐↲ [requeney of the LAEW.," The characteristic maximum frequency is LAE is found to be $\Omega\gamma_\pm^2$, where $\Omega$ is the frequency of the LAEW."208" This result is derived assuming that the initial Lorentz factor. 5. is much smaller than 5,447ep/OQ. wp=οJie, which is the maximum Lorentz [actor that a background. particle reaches in the LAEW. with 55=g;co."," This result is derived assuming that the initial Lorentz factor, $\gamma_0$, is much smaller than $\gamma_{\rm max}\sim\omega_E/\Omega$, $\omega_E=|qE_0|/mc$, which is the maximum Lorentz factor that a background particle reaches in the LAEW, with $\gamma_\pm=\gamma_{\rm max}\pm\gamma_0$."209 In the opposite limit. 5o29y. the elfect of the LAEW may be treated using perturbation theory. and the characteristic frequency of LAE in O52 (Melrose1978).," In the opposite limit, $\gamma_0\gg\gamma_{\rm max}$, the effect of the LAEW may be treated using perturbation theory, and the characteristic frequency of LAE in $\Omega\gamma_0^2$ \citep{m78}."210. In the case where LAEmay be treated usingperturbation theory. it may be regarded as a Form of [ree-electron maser enussion (Fung&Ixuijpers 2004)..," In the case where LAEmay be treated usingperturbation theory, it may be regarded as a form of free-electron maser emission \citep{fk04}. ."211of the NEW profile have recently come frou further lnieh resolution dark matter sinuulations (c.e..Tavlor&Navarro 2001. the issue is far from beine settled.,"of the NFW profile have recently come from further high resolution dark matter simulations \citep[e.g.,][]{taylor01}, the issue is far from being settled."212" Moreover. even if these cosmological simulations are very successful on large scale. at galactic scale there are nusolved issues. like the ""augular momentum problem” (Somuner-Larsen.Gelato&Vedel1999:Souuner-Larseu&Doleov2001:BurkertD'Onghia2001) or the ""Unadssng satellite problemi (Klvpiuetal.(al. 1999)... which are vet to be addressed."," Moreover, even if these cosmological simulations are very successful on large scale, at galactic scale there are unsolved issues, like the “angular momentum problem” \citep{sl99,sl01,burk04} or the “missing satellite problem” \citep{klypin99,moore99}, which are yet to be addressed."213 Here. we have developed a selt£cousisteut model of the dark matter halo substructure distribution atf ealactic scale to explain observed NEW-like rotation curves.," Here, we have developed a self-consistent model of the dark matter halo substructure distribution at galactic scale to explain observed NFW-like rotation curves."214 Support for the existence of dark matter substructures has medulv come from wumerical siuulatious (CüocoliLElahictal.200948:Ludlowet 2009).," Support for the existence of dark matter substructures has mainly come from numerical simulations \citep{gc08,mdk08,vs08,etws09,lad09}."215. But. there are strong observational hiuts like flux anomalies aud time delavs in gravitational leusius (Chen2009:Ikeeton& 2009).. or cruhanced eanunua ravs aud leptonie cosmic ravs (Elahietal.2009):Piuzke2009).. iudicatiug the presence of substructures.," But, there are strong observational hints like flux anomalies and time delays in gravitational lensing \citep{chen09,km09,vk09,xu09}, or enhanced gamma rays and leptonic cosmic rays \citep{ep09,pinz09}, indicating the presence of substructures."216 The preseut model is based ou the assuniptiou of a scale free nature of the dark matter clustering that leads to a statistically scltsimilar distribution of the halo substructures at ealactic scale., The present model is based on the assumption of a scale free nature of the dark matter clustering that leads to a statistically self-similar distribution of the halo substructures at galactic scale.217 It is shown that a simple fractal model of the dark matter halo substructure predicts an NFW-like rotation curve., It is shown that a simple fractal model of the dark matter halo substructure predicts an NFW-like rotation curve.218 Such a iodel also predicts a scale free power spectrum of the rotation velocity fluctuations., Such a model also predicts a scale free power spectrum of the rotation velocity fluctuations.219 The model is described iu Section 2.. and the results are preseuted in Section 3..," The model is described in Section \ref{sec:model}, and the results are presented in Section \ref{sec:result}."220 Possible limitations of our analysis are discussed. iu Section L., Possible limitations of our analysis are discussed in Section \ref{sec:disc}.221 Finally. we sunmuuize aud preseut our couclusions in Section 5..," Finally, we summarize and present our conclusions in Section \ref{sec:concl}."222 Assunmiug that the dark matter clustering has a scale free nature (i.c.. there exist halo substructures of a wide range of nass). the density profile can be described as a combination of a smooth radial profile prr.) and a stochastic part dp.," Assuming that the dark matter clustering has a scale free nature (i.e., there exist halo substructures of a wide range of mass), the density profile can be described as a combination of a smooth radial profile $\overline{\rho(r/r_c)}$ and a stochastic part $\delta\rho$."223 Tere r5. is a characteristic vcore” radius and p coutains information of the deusitv variation at scales larger than or comparable to r.., Here $r_c$ is a characteristic “core” radius and $\overline{\rho}$ contains information of the density variation at scales larger than or comparable to $r_c$.224 For the purpose of this work. we have used a simpler model of this deusity distribution which. however. retains all relevant kev features.," For the purpose of this work, we have used a simpler model of this density distribution which, however, retains all relevant key features."225 Iu this simplified model. we have asstuned that cach dark matter chuup las a number of smaller chuups around it.," In this simplified model, we have assumed that each dark matter clump has a number of smaller clumps around it."226 Each of these smaller chumps are in turn just a scaled down version with even sinaller chumps around them., Each of these smaller clumps are in turn just a scaled down version with even smaller clumps around them.227 As a result. the whole structure has an approximate spherical svaunucetrv aud a statistical sclfsimularity.," As a result, the whole structure has an approximate spherical symmetry and a statistical self-similarity."228 It is assuued here that all these clumps have non-ingular isothermal deusity profile where the ceutral deusity (pg). the core radius (0s). the cut-off radius (yg) aud the halo to sublialo distance CD) are scaled down accordingly.," It is assumed here that all these clumps have non-singular isothermal density profile where the central density $\rho_0$ ), the core radius $r_c$ ), the cut-off radius $r_{max}$ ) and the halo to subhalo distance $D$ ) are scaled down accordingly."229 Wowever. this specific deusitv profile is not a crucial assunption iu our model and the iudividual substructures may have any non-singular density profile p(rír.) where r. is sole characteristic radius.," However, this specific density profile is not a crucial assumption in our model and the individual substructures may have any non-singular density profile $\rho(r/r_c)$, where $r_c$ is some characteristic radius."230" Esseutiallv. this is a fractal structure with three parameters: (1) p. the number of sanall clumps around auv chuup. Gi) f. spatial scaling factor for core radius. cut-off radius aud distance aud (ii) f,. ceutral deusity scaling factor between au clip and its next snallest chuups."," Essentially, this is a fractal structure with three parameters: (i) $n$, the number of small clumps around any clump, (ii) $f_r$, spatial scaling factor for core radius, cut-off radius and distance and (iii) $f_\rho$, central density scaling factor between any clump and its next smallest clumps."231 A fractal is a fragineuted and imeeular ecometrical shape with exact or stochastic selfsimular structures at all scales (ALaudelbrot1983)., A fractal is a fragmented and irregular geometrical shape with exact or stochastic self-similar structures at all scales \citep{mand83}.232. ludepeudeut of the value of f. aud ». the (Iausdorff) fractal dimension of such a structure is 3 for pf?«l.," Independent of the value of $f_r$ and $n$, the (Hausdorff) fractal dimension of such a structure is $3$ for $nf_r^3<1$ ."233" Tlowever. since at each iteration. the linear size of chuups scales by. a factor f, aud the mass scales by a factor p. the local mass dimension for any substructure level is D,,= logQi)/log(f,) over a certain range of scales."," However, since at each iteration, the linear size of clumps scales by a factor $f_r$ and the mass scales by a factor $n$, the local mass dimension for any substructure level is $D_m = -log(n)/log(f_r)$ over a certain range of scales."234" A nass dimension of D,, for a medium maplies that the mass enclosed iu a sphere of radius r in such a iedimn will be After)=ο", A mass dimension of $D_m$ for a medium implies that the mass enclosed in a sphere of radius $r$ in such a medium will be $M(r) = kr^{D_m}$.235 So. for the N™ substructure level. My(r)=kyr? over a range of scales depending ou V. s. μι D aud rye.," So, for the $N^{\rm th}$ substructure level, $M_N(r) = k_Nr^{D_m}$ over a range of scales depending on $N$, $n$, $f_r$, $D$ and $r_{max}$."236 Note that this range is different for different substructure levels., Note that this range is different for different substructure levels.237 Hence. for the complete structure. the total mass AL(r). which is the stm of Afy(r) of all the substructure levels. will not have a simple power law radial dependence.," Hence, for the complete structure, the total mass $M(r)$, which is the sum of $M_N(r)$ of all the substructure levels, will not have a simple power law radial dependence."238 But. the dark iatter halo mass funetion will still be a power law. Noi)ων where the power law iudex a—log(i)logF2f.) Is a lore plvsically motivated parameter of this model aud cau be constrained from theoretical aud uuuerical analysis of dark matter structure formation (Caoetal.2001:Zenipetal.20093..," But, the dark matter halo mass function will still be a power law, $N(m) \propto m^{-\alpha}$, where the power law index $\alpha = -log(n)/log(f_r^3 f_{\rho})$ is a more physically motivated parameter of this model and can be constrained from theoretical and numerical analysis of dark matter structure formation \citep{gao04,zemp09}. ."239" The deusitv distribution cau be written as where Phe is backeround σαςτν aud PslUPoiFedsVasPj) 8 deusity profile of individual substructure ceutred atf 55; with central density (py.;). core radius (675.,;) aud cut-off radius (705,44)."," The density distribution can be written as where $\rho_{\rm bg}$ is background density and $\rho_s(\rho_{0,i}, r_{c,i}, 240r_{max,i}, \vec{r}_{i,j})$ is density profile of individual substructure centred at $\vec{r}_{i,j}$ with central density $\rho_{0,i}$ ), core radius $r_{c,i}$ ) and cut-off radius $r_{max,i}$ )."241 Considering the selfsinularity of this model. where ko=nf1. d ds a unit leusth vector with random orientation aud the initial set of parameters PoweFesCnet=PoeleeVinge Is for the largest subhalo centered at the origin.," Considering the self-similarity of this model, where $k=n^{i-1}$, $\vec{d}$ is a unit length vector with random orientation and the initial set of parameters $\rho_{0,0}, r_{c,0}, r_{max,0} = \rho_{0}, 242r_{c}, r_{max}$ is for the largest subhalo centered at the origin."243 In principle. pi; may be a smooth function of r.," In principle, $\rho_{\rm bg}$ may be a smooth function of $r$."244 But. since we are assuming it to be a siuall backerouncl density threshold. its effect ou the final rotation curve is not very sigenificaut.," But, since we are assuming it to be a small background density threshold, its effect on the final rotation curve is not very significant."245 So. for simplicity. we have assumed pi; tfo be constaut over the radius of our interest.," So, for simplicity, we have assumed $\rho_{\rm bg}$ to be constant over the radius of our interest."246 This structure is shown schematically (without amv rancdommess for the shake of clarity) im the left panel of Figure 1.., This structure is shown schematically (without any randomness for the shake of clarity) in the left panel of Figure \ref{fig:dmfrac}.247" After introducing randomness iu aneular position of the subhalos. oue realization of such a structure with n=7 and f,=0.33 is shown with two and four substructure levels in the muddle aud right paucl respectively."," After introducing randomness in angular position of the subhalos, one realization of such a structure with $n=7$ and $f_r=0.33$ is shown with two and four substructure levels in the middle and right panel respectively."248 This model can be considered as a simplified represcutation ofthe scale free. clumpy density structure of dark iatter above a small threshold deusitv at theealactic scale.," This model can be considered as a simplified representation of the scale free, clumpy density structure of dark matter above a small threshold density at thegalactic scale."249 We uote that the parameters for this model are constrained to a eood extent by various physical considerations., We note that the parameters for this model are constrained to a good extent by various physical considerations.250 Ássuninue that the structure is extended, Assuming that the structure is extended251"a measured electron density n. = 10"" em on the surface of a neutral disk or cocoon which envelopes the low mass YSO (Aleaburn 988).",a measured electron density $_{e}$ = $\times$ $^{6}$ $^{-3}$ on the surface of a neutral disk or cocoon which envelopes the low mass YSO (Meaburn 1988).252 From L.3-mum interferometric observations Bally ct al. (, From 1.3-mm interferometric observations Bally et al. (2531998b) deduce an upper limit to the mass of molecular hydrogen in this neutral component of —0.015 AL. to give an IL» density of n; € 10° *.,1998b) deduce an upper limit to the mass of molecular hydrogen in this neutral component of $\sim$ 0.015 $_{\odot}$ to give an $_{2}$ density of $_{o}$ $\leq$ $\times$ $^{9}$ $^{-3}$.254" On the other hand. simple pressure balance between the ionised and neutral gas with temperatures of TL. = 107 Ix and T, — 107 LIENIx would give; n,z ? OLI"," On the other hand, simple pressure balance between the ionised and neutral gas with temperatures of $_{e}$ = $^{4}$ K and $_{o}$ = $^{3}$ K would give $_{o}\approx$ $\times$ $^{9}$ $^{-3}$."255 masers have vet to be found in regions of purely low- star-formation., OH masers have yet to be found in regions of purely low-mass star-formation.256 However. it is this dense. circeumstellar molecular gas around proplyels. stimulated by photons from An Ori opuC. that is. the potential. source of⋅ any maser emission.," However, it is this dense, circumstellar molecular gas around proplyds, stimulated by photons from $\theta^{1}$ Ori C, that is the potential source of any maser emission."257s We would expect to find. ΟΙ masers at a distance. of To 104 em from an O6.5 star (ef, We would expect to find OH masers at a distance of $\sim$ $\times$ $^{17}$ cm from an O6.5 star (cf.258 Baart Coben 1985)., Baart Cohen 1985).259 Llowever. if Ixeplerian motion around the YSO occurs in this =πογα] cocoon it will have a rotational velocity of 4 km s.+ ue dts outer edge with higher velocities towards the centre proportional. to Lm )," However, if Keplerian motion around the YSO occurs in this neutral cocoon it will have a rotational velocity of 4 km $^{-1}$ at its outer edge with higher velocities towards the centre (proportional to $^{-1/2}$ )."260 In these circumstances. the Pelocity. coherence required. for strong maser amplification =vill occur over a path length that is much smaller than rw overall racius of the proplyd., In these circumstances the velocity coherence required for strong maser amplification will occur over a path length that is much smaller than the overall radius of the proplyd.261 This. together with possible chemical cllects (Section 3.5)). could explain our non-detection of OLL masers in this region.," This, together with possible chemical effects (Section \ref{proplyds1}) ), could explain our non-detection of OH masers in this region."262 The distribution of ΟΠ masers in the Orion-DN/IXL region is far more extensive than previously realized. covering a region of 30 aresee extent and a racial velocity range [rom 1310 |42 kam |.," The distribution of OH masers in the Orion-BN/KL region is far more extensive than previously realized, covering a region of 30 arcsec extent and a radial velocity range from --13 to +42 km $^{-1}$."263 Phe bulk of the emission can be modelle in terms of a rotating and expanding torus. centred on ιο or radio source Lo with an inner cavity of 1300 au radius.," The bulk of the emission can be modelled in terms of a rotating and expanding torus, centred on IRc2 or radio source I, with an inner cavity of $\sim$ 1300 au radius."264 Phe rotation axis has the same position angle anc inclination to the line-of-sight as the molecular outllow and the Large scale magnetic field. inferred [rom mim- anc submuime-polarization (Section 4.1))., The rotation axis has the same position angle and inclination to the line-of-sight as the molecular outflow and the large scale magnetic field inferred from mm- and submm-polarization (Section \ref{model}) ).265 The dynamical timescale is similar to that of the explosive event. that produce the widespread. shocked. Ll emission., The dynamical timescale is similar to that of the explosive event that produced the widespread shocked $_{2}$ emission.266 Lt is likely that the OLLI masers trace the interaction between the low-velocity molecular outllow and the molecular hot core. and that they acquired their expansional motions in the same event that produced the outflow.," It is likely that the OH masers trace the interaction between the low-velocity molecular outflow and the molecular hot core, and that they acquired their expansional motions in the same event that produced the outflow."267 Of particular interest is a string of masers. Stream A. ab 21 kms +. that extends at position angle ~15° between Iic2 and. BN. in the direction of the radio proper motions of these two dominant sources.," Of particular interest is a string of masers, Stream A, at $\sim$ 21 km $^{-1}$, that extends at position angle $\sim$ between IRc2 and BN, in the direction of the radio proper motions of these two dominant sources."268 We suggest that Stream A may have appeared. like a vapour trail. in the wake of the runaway star DN.," We suggest that Stream A may have appeared, like a vapour trail, in the wake of the runaway star BN."269 ‘Phe proper motions of BN and sources Land n project back to the base of Stream A (Fig. 1).," The proper motions of BN and sources I and n project back to the base of Stream A (Fig. \ref{ra-dec}) ),"270 ο aresec Northwest of the centre of the OLL maser torus. a position that is largely devoid of masers.," $\sim$ 4 arcsec Northwest of the centre of the OH maser torus, a position that is largely devoid of masers."271 The 1612-MlIz. masers have ai more widespread distribution than the other OLL masers. with kinematics that are more like those of the LO masers associated with the outllow.," The 1612-MHz masers have a more widespread distribution than the other OH masers, with kinematics that are more like those of the $_{2}$ O masers associated with the outflow."272 Many of these 1612-MIEIZ masers are spatially associated with fingers of shocked. LH» emission (Fig. 7))., Many of these 1612-MHz masers are spatially associated with fingers of shocked $_{2}$ emission (Fig. \ref{subcore}) ).273 These Oll masers are thought to require relatively. low eas ancl dust. temperatures for their inversion (Section 4.3))., These OH masers are thought to require relatively low gas and dust temperatures for their inversion (Section \ref{1612}) ).274 Apart from the OLL 1612-MIETz masers. the other OLI masers have complementary distributions ancl kinematics to the LO masers (Figs. 1- 4).," Apart from the OH 1612-MHz masers, the other OH masers have complementary distributions and kinematics to the $_{2}$ O masers (Figs. \ref{ra-dec}- \ref{dec-vel}) ),"275 with essentially no overlap., with essentially no overlap.276 OLL is also spatially and kinematically distinct from the class E methanol 25-Gllz masers., OH is also spatially and kinematically distinct from the class I methanol 25-GHz masers.277 A possible correspondence between OLL 1612-MllIz anc class LE methanol 6.7-Cillz masers reported by. Voronkoy ct al. (, A possible correspondence between OH 1612-MHz and class II methanol 6.7-GHz masers reported by Voronkov et al. (2782005) requires further study at higher angular resolution.,2005) requires further study at higher angular resolution.279 The magnetic field strength in the OLL maser regions ranges from 1.8 to 16.3 mG. with a possible field reversal (Section 3.4)).," The magnetic field strength in the OH maser regions ranges from 1.8 to 16.3 mG, with a possible field reversal (Section \ref{zeeman}) )."280" A search. for OLL masers associated. with the proplyds around @n Ori. €"" vielded. only upper limits.M which. may indicate a low OLL abundance in this more evolved region."," A search for OH masers associated with the proplyds around $\theta^{1}$ Ori C yielded only upper limits, which may indicate a low OH abundance in this more evolved region."281 We thank the anouvmous referee for helpful conmmuients and in particular for drawing our attcution to the paper by Cónuuez et al., We thank the anonymous referee for helpful comments and in particular for drawing our attention to the paper by Gómmez et al.282 We thank Busaba Thitawarakorn for assistance with the data reduction. Ralph Shupiug for providing a high resolution version of the Ikeck nuage in Fig.," We thank Busaba Hutawarakorn for assistance with the data reduction, Ralph Shuping for providing a high resolution version of the Keck image in Fig."283 5. aud Masa Iavashi," 5, and Masa Hayashi"284 , 285the heated continuum from very small grains enters the 15 tun band.,the heated continuum from very small grains enters the 15$\umu$ m band.286 But if this were theond elfect one should expect also a break in the 2.2/15] slope. which is not seen.," But if this were the effect one should expect also a break in the $[2.2/15]$ slope, which is not seen."287 And since the strength of PALL emission. would be expected to follow the interstellar raciation field (SRE). the break in 2.2/6.7] could be taken to indicate the depletion of UIDs in galaxies with hottest 60/100] (sce. Cosarsky 1996 for the elfect in localized. intense raciation environments).," And since the strength of PAH emission would be expected to follow the interstellar radiation field (ISRF), the break in $[2.2/6.7]$ could be taken to indicate the depletion of UIBs in galaxies with hottest $[60/100]$ (see Cesarsky 1996 for the effect in localized intense radiation environments)."288 The LISO-LR.AS diagram must then be explained by both the increasing 15 pum emission and decreasing (relative to 191419) 6.7 um emission., The ISO-IRAS diagram must then be explained by both the increasing 15 $\umu$ m emission and decreasing (relative to ISRF) 6.7 $\umu$ m emission.289 Are these elfects driven mainly by dillering amounts of quiescent and active media in the galaxy as a whole (as in the two-component model. Helou 1986. Dale 1999). by different proportions of star-formation happening in the disk tthe central parts Roussel 2001. Vigroux 1999). or something else?," Are these effects driven mainly by differing amounts of quiescent and active media in the galaxy as a whole (as in the two-component model, Helou 1986, Dale 1999), by different proportions of star-formation happening in the disk the central parts Roussel 2001b, Vigroux 1999), or something else?"290 To study this in detail is out of scope of the present paper. and in any case cannot be done only with integrated. global values.," To study this in detail is out of scope of the present paper, and in any case cannot be done only with integrated, global values."291 Llowever. it is interesting to note the trends with the morphologies.," However, it is interesting to note the trends with the morphologies."292 The galaxies with constant 6.7/15]~1 are mainly normal disk galaxies. and. in fact. their spread in. 2.2/15] anc 2.2/6.7] is correlated with their Llubble tvpe as already seen. in Section 4.1..," The galaxies with constant $[6.7/15]\sim1$ are mainly normal disk galaxies, and, in fact, their spread in $[2.2/15]$ and $[2.2/6.7]$ is correlated with their Hubble type as already seen in Section \ref{class}."293 Those with higher 60/100] span all morphological types. but stand out by having been classified as peculiar one wav or another (more actice nuclear regions?).," Those with higher $[60/100]$ span all morphological types, but stand out by having been classified as peculiar one way or another (more actice nuclear regions?)."294 Thus. it appears. xi at lower heating levels (60/100]Z 0.4) the NERYAMIR (and ELI) colours of galaxies are driven. by morphology. by the spatial distribution of ISM.," Thus, it appears, that at lower heating levels $[60/100] \sol 0.4$ ) the NIR/MIR (and FIR) colours of galaxies are driven by morphology, by the spatial distribution of ISM."295 At higher 60/100] 1e trends on the other hand follow closely the increasing radiation field. the warming dust continuum. and (possibly) 1e destruction of PALL carriers.," At higher $[60/100]$ the trends on the other hand follow closely the increasing radiation field, the warming dust continuum, and (possibly) the destruction of PAH carriers."296 This is in agreement with 16 MIUELI. studies of Sauvage Thuan (1994). who find 1e FER. colours along the Llubble sequence to be driven w both star-formation efficiency. and spatial distribution of cust.," This is in agreement with the MIR/FIR studies of Sauvage Thuan (1994), who find the FIR colours along the Hubble sequence to be driven by both star-formation efficiency and spatial distribution of dust."297 As seen in Fig.12.. there are several early type galaxies in the high 60/100] region of the panels.," As seen in \ref{fircols}, there are several early type galaxies in the high $[60/100]$ region of the panels."298 Phese must have strong nuclear star formation since the ALR. and EH colours of the galaxies are totally dominated by a starburst., These must have strong nuclear star formation since the MIR and FIR colours of the galaxies are totally dominated by a starburst.299 However. it is interesting that the inclusion of near-It. photometry distinguishes several galaxies with high NIIU/MILII ratios which otherwise are tighth placed. within the main group of points in the{ή and. LSO-LRAS-plots.," However, it is interesting that the inclusion of near-IR photometry distinguishes several galaxies with high NIR/MIR ratios which otherwise are tightly placed within the main group of points in the and -plots."300 These are also all early types. but apparently not true starbursts.," These are also all early types, but apparently not true starbursts."301 They simultaneously have relatively high heating levels (especially one at 60/100]zz OS. NGC 1266) and high NERYMLR. ratios. typical of more normal lenticulars.," They simultaneously have relatively high heating levels (especially one at $[60/100]\approx0.8$ , NGC 1266) and high NIR/MIR ratios, typical of more normal lenticulars."302 This may suggest. for," This may suggest, for"303previously.,previously.304 To transform the averaged instrumental magnitudes to the standard γκο system we employed the normal transformation equations in Holtzman ((1995)., To transform the averaged instrumental magnitudes to the standard $VI_{KC}$ system we employed the normal transformation equations in Holtzman \nocite{hol95}.305. For the faint objects lacking any /-band measurement. we assumed a (V—7) colour of 0.95. the observed mean color of the brighter clusters (see below).," For the faint objects lacking any $I-$ band measurement, we assumed a $(V-I)$ colour of 0.95, the observed mean color of the brighter clusters (see below)."306 The basic transformation used was to which we then added the individual zero-point terms for each chip as listed in Table 2.., The basic transformation used was to which we then added the individual zero-point terms for each chip as listed in Table \ref{tab:trans}.307" In these equations, we have added the standard value of 0.05 mag to the published zero-points to account for the deferred charge transfer effect that produces an offset between long and short exposures ίο.ο.. Stetson ((1999))."," In these equations, we have added the standard value of 0.05 mag to the published zero-points to account for the deferred charge transfer effect that produces an offset between long and short exposures (e.g., Stetson \nocite{ste99}) )."308" As a direct check on this offset, we intercompared the magnitudes of several of the brightest stars on our long and short exposures, and found That is to say, magnitudes determined using short exposures (like those used for the calibration. of Holtzmanetal. 1995)) tend to be fainter than those determined using long exposures: our internal tests confirm the  0.05—mag offset normally used."," As a direct check on this offset, we intercompared the magnitudes of several of the brightest stars on our long and short exposures, and found That is to say, magnitudes determined using short exposures (like those used for the calibration of \cite{hol95}) ) tend to be fainter than those determined using long exposures; our internal tests confirm the $\simeq 0.05-$ mag offset normally used."309" Our final catalog of objects with deep V—band measurements is still contaminated to some extent by a few foreground stars (nearly negligible) and by faint, extremely small galaxies that might have crept through the image classification procedure described above."," Our final catalog of objects with deep $V-$ band measurements is still contaminated to some extent by a few foreground stars (nearly negligible) and by faint, extremely small galaxies that might have crept through the image classification procedure described above."310" To define a “background” population, we simply use those objects which lie on the radial outskirts of our field. more than 75 arcseconds (corresponding roughly to 40 kpc) from the center of NGC 4874."," To define a “background” population, we simply use those objects which lie on the radial outskirts of our field, more than 75 arcseconds (corresponding roughly to 40 kpc) from the center of NGC 4874."311" At these large radii. we find that the number density of globular clusters is still declining: that 1s, the total extent of the GCS evidently spills well beyond the borders of our single WFPC? field."," At these large radii, we find that the number density of globular clusters is still declining; that is, the total extent of the GCS evidently spills well beyond the borders of our single WFPC2 field."312" However, the object density within the background area is only a small fraction (14%)) of the density in the core region (the area covered by the PCI chip), so we can use the outer corners for background knowing that it will produce only a small over-subtraction of the globular cluster population itself."," However, the object density within the background area is only a small fraction ) of the density in the core region (the area covered by the PC1 chip), so we can use the outer corners for background knowing that it will produce only a small over-subtraction of the globular cluster population itself."313 This raw GCLF must be corrected for detection incompleteness at the faint end., This raw GCLF must be corrected for detection incompleteness at the faint end.314" The detection probability is, in turn, dependent on the local level of background light and thus is a function of the distance from thegalaxy center."," The detection probability is, in turn, dependent on the local level of background light and thus is a function of the distance from thegalaxy center."315" Figure 2 shows the completeness fraction for four radial zones (3<r<13”.13""<r<227.2?""507.50"" 100"")."," Figure \ref{fig:recf} shows the completeness fraction for four radial zones $3\arcsec\le r < 13\arcsec, 13\arcsec\le r < 22\arcsec, 22\arcsec\le r < 50\arcsec, 31650\arcsec\le r < 100\arcsec$ )."317" Clearly, the inner zones — mostly within PCI and within the bright galaxy envelope — have noticeably brighter. but consistent. completeness cutoff levels than in the outer annuli."," Clearly, the inner zones – mostly within PC1 and within the bright galaxy envelope – have noticeably brighter, but consistent, completeness cutoff levels than in the outer annuli."318 This radial dependence was explicitly folded in to the completeness corrections to the raw data., This radial dependence was explicitly folded in to the completeness corrections to the raw data.319 The full completeness-corrected and background-subtracted luminosity functions are shown in Figure 5 and Table 3.., The full completeness-corrected and background-subtracted luminosity functions are shown in Figure \ref{fig:gclf_binned} and Table \ref{tab:gclf_data}.320 The limit of our deep V photometry reaches the turnover point (GCLF peak) or just past it., The limit of our deep $V$ photometry reaches the turnover point (GCLF peak) or just past it.321" The standard candle of the GCLF method is the luminosity level of the turnover or peak point, which we call V."," The standard candle of the GCLF method is the luminosity level of the turnover or peak point, which we call $V^0$."322" The immediate goal for this discussion is therefore to estimate this point as accurately as possible given that we see only the bright half of the GCLF and the turnover region itself, and not the faint half."," The immediate goal for this discussion is therefore to estimate this point as accurately as possible given that we see only the bright half of the GCLF and the turnover region itself, and not the faint half."323" Conventionally, simple interpolation functions such as a Gaussian (e.g.. Jacobyetal. 1992)) or fa (Secker&Harris 1993)), both of which have two free parameters (V"" and the dispersion width), have been used for this purpose since they have repeatedly been shown to match the region near the turnover quite accurately."," Conventionally, simple interpolation functions such as a Gaussian (e.g., \cite{jac92}) ) or $t_5$ \cite{sec93}) ), both of which have two free parameters $V^0$ and the dispersion width), have been used for this purpose since they have repeatedly been shown to match the region near the turnover quite accurately."324" For cases such as ours wherethe photometric limit V(lim) is fairly close to V"". it is important to note that attempts to solve for both the peak V"" and dispersion oy of the interpolation function are problematic, because the two parameters are correlated (sce Secker&Harris1993:; Hanes&Whittaker 1987)) and tend to produce overestimates of both the turnover and dispersion when the fit is constrained by only one side of the GCLF."," For cases such as ours wherethe photometric limit $V(lim)$ is fairly close to $V^0$, it is important to note that attempts to solve for both the peak $V^0$ and dispersion $\sigma_V$ of the interpolation function are problematic, because the two parameters are correlated (see \cite{sec93}; \cite{han87}) ) and tend to produce overestimates of both the turnover and dispersion when the fit is constrained by only one side of the GCLF."325 A systematically more accurate procedure is toadopt a value for cy. and to solve only for the turnover magnitude., A systematically more accurate procedure is to a value for $\sigma_V$ and to solve only for the turnover magnitude.326" Such an approach is expected to work essentially because, for giant ellipticals, the GCLP dispersion in its Gaussian form is observed to be highly consistent from one galaxy to another."," Such an approach is expected to work essentially because, for giant ellipticals, the GCLF dispersion in its Gaussian form is observed to be highly consistent from one galaxy to another."327" For 13 gE galaxies with well measured GCLFs, Whitmore (1996) and Harris (1999) find σν=1.4 with an uncertainty of just £0.05."," For 13 gE galaxies with well measured GCLFs, Whitmore (1996) and Harris (1999) find $\sigma_V = 1.4$ with an uncertainty of just $\pm 0.05$ ."328" In particular, this dispersion value fits the very thoroughly studied Virgo giant M87 quite well (see Harrisetal. 1998b:; Kunduetal. 1999))."," In particular, this dispersion value fits the very thoroughly studied Virgo giant M87 quite well (see \cite{har98b}; ; \cite{kun99}) )."329 A further application, A further application330was detected in the other filters as highlighted in Fig.8.. The photometry of all sources is reported in Table 4..,was detected in the other filters as highlighted in Fig.\ref{ima_optnir}. The photometry of all sources is reported in Table \ref{tab_photom}.331" The source possesses a long orbital period of (185.5+1.1)/f d where f=1,2,3,or4 and a spin period of ~66 s. At the likely periastron passage, the source goes through an outburst whose duration is estimated to ~12 d (withan upper-limit of <18 d)"," The source possesses a long orbital period of $(185.5\pm1.1)/f$ d where $f=1,2,3,\ \mathrm{or}\ 4$ and a spin period of $\sim 66$ s. At the likely periastron passage, the source goes through an outburst whose duration is estimated to $\sim 12$ d (withan upper-limit of $\lesssim 18$ d)."332" With such orbital period (f=1) and outburst duration, the source is bright «10% of its time."," With such orbital period $f=1$ ) and outburst duration, the source is bright $<10$ of its time."333 The recurrence of such long outbursts related to the binary motion corresponds to type I outbursts observed in other BeXB (??)..," The recurrence of such long outbursts related to the binary motion corresponds to type I outbursts observed in other BeXB \citep{Coe00, Negueruela07}."334" Furthermore, combining the observed pulsation and orbital period, ffalls well in the BeXB arm of the Corbet diagram (i.e. Pspin vs Pow; strengthening its identification as a BeXB."," Furthermore, combining the observed pulsation and orbital period, falls well in the BeXB arm of the Corbet diagram \citep[{\it i.e.} $P_{\mathrm{spin}}$ vs $P_{\mathrm{orb}}$ strengthening its identification as a BeXB."335 The large orbital period rules out the possibility to associate this source with a low-mass X-ray binary whose companion is a star of the main sequence., The large orbital period rules out the possibility to associate this source with a low-mass X-ray binary whose companion is a star of the main sequence.336" Flaring activity in BeXB has never been observed except in EXO 2030--375 and recently in SWIFT J1626.6—5156 (?,andreferencestherein).", Flaring activity in BeXB has never been observed except in EXO $+$ 375 and recently in SWIFT $-$ 5156 \citep[][and references therein]{Reigal08}.337" For SWIFT J1626.6—5156, the intensity varied by a factor 4 on a timescale of 450 s with sharp rise/decay of the count rate."," For SWIFT $-$ 5156, the intensity varied by a factor 4 on a timescale of 450 s with sharp rise/decay of the count rate."338" This behaviour differs from the bright flare of ddetected with ISGRI in revolution118, which shows a smooth rate's rise/decay, a variability factor of 8, and a duration of 0.5 d. This bright flare in revolution is likely to be due to a sensitivity bias where only the peak flux of the outburst is significantly detected in individual pointings."," This behaviour differs from the bright flare of detected with ISGRI in revolution, which shows a smooth rate's rise/decay, a variability factor of 8, and a duration of 0.5 d. This bright flare in revolution is likely to be due to a sensitivity bias where only the peak flux of the outburst is significantly detected in individual pointings."339" However, flaring activity cannot be discarded for bbecause of the detections in pointings and01730024, where the rate varies by a factor 3-4 on a timescale of 1 h in comparison to the average rates during the outbursts."," However, flaring activity cannot be discarded for because of the detections in pointings and, where the rate varies by a factor 3–4 on a timescale of 1 h in comparison to the average rates during the outbursts."340" Still, these detections may also be due to a sensitivity bias, because the count rates are similar to the 5.lo detection threshold."," Still, these detections may also be due to a sensitivity bias, because the count rates are similar to the $\sigma$ detection threshold."341 A spin-downof iis observed between the 2 observations of the bright flare with aand the oobservation., A spin-downof is observed between the 2 observations of the bright flare with and the observation.342 We derived a spin-down of P=0.080.02syr7! Y=(—6.2+1.4)x107Hz s-!).," We derived a spin-down of $\dot{P}=0.08\pm0.02\ \mathrm{s}\,\unit{yr}{-1}$ $\dot{\nu}=(-6.2\pm1.4)\times 10^{-13}\ \mathrm{Hz}\,\unit{s}{-1}$ )."343" Such spin-down episodes have already been observed in other accreting pulsars, some examples being EXO 2030-375 with v=—3.4x107Hzs! and A0535426 with y=—2.2x10?Hzs! (?,andreferences therein).."," Such spin-down episodes have already been observed in other accreting pulsars, some examples being EXO $+$ 375 with $\dot{\nu}=-3.4\times 10^{-14}\ \mathrm{Hz}\,\unit{s}{-1}$ and $+$ 26 with $\dot{\nu}=-2.2\times 10^{-13}\ \mathrm{Hz}\,\unit{s}{-1}$ \citep[][and references therein]{Bildstenal97}. ."344" To have accretion onto an NS, the magnetic radius Rmag must be lower than the co-rotation radius R;4,."," To have accretion onto an NS, the magnetic radius $R_{\mathrm{mag}}$ must be lower than the co-rotation radius $R_{\mathrm{cor}}$."345" Otherwise, the infalling matter is centrifugally expelled by the magnetic field (thepropellerregime,?).."," Otherwise, the infalling matter is centrifugally expelled by the magnetic field \citep[the propeller regime,][]{Illarionoval75}."346" For an NS (M=1.4Mo, R=10 km) with a spin period of 66 s, at the equilibrium point Rmag= Recor, one estimates the magnetic field to be B26.5x10P?Gx(M/107!°Mo yr!)!/”."," For an NS $M=1.4\ \Ms$, $R=10$ km) with a spin period of 66 s, at the equilibrium point $R_{\mathrm{mag}}=R_{\mathrm{cor}}$ , one estimates the magnetic field to be $B=6.5\times10^{12}\ \mathrm{G}\times (\dot{M}/10^{-10}\,\Ms\,\unit{yr}{-1})^{1/2}$ ."347" The magnetic radius depends on the accreted matter flow as Rmagος M~?/’. Thus, the magnetic radius mayexceed the co-rotation radius ifthe"," The magnetic radius depends on the accreted matter flow as $R_{\mathrm{mag}}\propto \dot{M}^{-2/7}$ Thus, the magnetic radius mayexceed the co-rotation radius ifthe"348 (OOOr)== (71) VR? /Δ0. (Or. iür)y= (72) 1aud «= 1/2: exceotfor variatic1sin scalethere are no qualitative,"Despite the complexity of the coordinate transformations linking them to the familiar Boyer-Lindquist coordinates, the quasi-spherical coordinates $\rb$ , $\thetab$ introduced in this paper and the light cones associated with them provide new and useful insights into the structure of the Kerr geometry and wave propagation in Kerr spacetime."349 differencesin the shape, We anticipate that they will find increasing use as their special advantages become apparent.350sof thecurves, This work was supported by NSERC of Canada and by the Canadian Institute for Advanced Research.351normalized to the Milky Way value. with a loss time of tugXEM2.,"normalized to the Milky Way value, with a loss time of $t_{\rm diff} \propto E^{-1/2}$."352 We also consider variauts with advective escape. as in starburst superwinds.," We also consider variants with advective escape, as in starburst super-winds."353 We assune that cosuuic rays travel through gas withdensity foi). where (1j dS the mean ISM nuuber deusity aud 1.0xf2.0.," We assume that cosmic rays travel through gas withdensity $f\mean{n}$ , where $\mean{n}$ is the mean ISM number density and $1.0 \le f \le 2.0$."354 The magnetic field is parametrized as BoxX or Bxp. normalized by the Milkv Way magnetic field strength.," The magnetic field is parametrized as $B \propto \Sigma_g^a$ or $B \propto \rho^a$, normalized by the Milky Way magnetic field strength."355 We searched for models that satisfv the local 50 FRC for normal galaxies aud compact starbursts., We searched for models that satisfy the local $z \approx 0$ FRC for normal galaxies and compact starbursts.356 The CR proton spectrum is then normalized by Milkv. Wax CR proton coustraints., The CR proton spectrum is then normalized by Milky Way CR proton constraints.357 The parameters chosen for cach variant are used to predict the FRC for putty starbursts and at high :., The parameters chosen for each variant are used to predict the FRC for puffy starbursts and at high $z$.358 Iu this paper. we consider several variauts to ect a seuse of how the FRC varies with redshift: We show in Table À2. that we can reproduce an acceptably lincar local FRC for cach variaut.," In this paper, we consider several variants to get a sense of how the FRC varies with redshift: We show in Table \ref{table:Models} that we can reproduce an acceptably linear local FRC for each variant."359" We are able to adopt parameters consistent with Alls. Wavy-derived CR proton coustraimts such that Ley/Lyra, Varies by a factor of 1.7 - 2.2 from normal galaxies to compact starbursts.", We are able to adopt parameters consistent with Milky Way-derived CR proton constraints such that $L_{\rm TIR}/L_{\rm radio}$ varies by a factor of 1.7 - 2.2 from normal galaxies to compact starbursts.360" This variation is consistent with the factor of 2 scatter in the (οσοι,Yunetal.2001)."," This variation is consistent with the factor of $\sim 2$ scatter in the \citep[e.g.,][]{Yun01}."361. As in LTQ. the need for a near local FRC strongly constrains the magnetic field iu. &alaxies to scale as either Xt9 or p?96 (see 2)).," As in LTQ, the need for a linear local FRC strongly constrains the magnetic field in galaxies to scale as either $\Sigma_g^{0.7 - 0.8}$ or $\rho^{0.5 - 0.6}$ (see \ref{sec:Theory}) )."362 The dependence§ of the FIR. cinission at a given wavelength is bevond the scope of this paper. since it depends on the exact SED of the FIR. cussion iu the ealaxy.," The dependence of the FIR emission at a given wavelength is beyond the scope of this paper, since it depends on the exact SED of the FIR emission in the galaxy."363" Instead. we simply use the Total Infrared (TTR) cnussion. assuming it is all of the UV light reprocessed by the dust. and use £5), asa proxy for Lgjg."," Instead, we simply use the Total Infrared (TIR) emission, assuming it is all of the UV light reprocessed by the dust, and use $L_{\rm TIR}^{\prime}$ asa proxy for $L_{\rm FIR}^{\prime}$."364" Calzettiet estimate that Loy,%Lb a correction we apply to the local value of Lpyp/Ley.Ly, frou Yunetal.(2001) to find the normalization of £4),/L'radio at 2&(0 (see We assune that the total TIR cluissivity (defined here as buuinositv per volume) has been measured and corrected for redshift to its rest-frame value. ετῃν."," \citet{Calzetti00} estimate that $L_{\rm TIR}^{\prime} \approx 1.75 L_{\rm FIR}^{\prime}$, a correction we apply to the local value of $L_{\rm FIR}^{\prime}/L_{\rm radio}^{\prime}$ from \citet{Yun01} to find the normalization of $L_{\rm TIR}^{\prime}/L_{\rm radio}^{\prime}$ at $z \approx 0$ (see We assume that the total TIR emissivity (defined here as luminosity per volume) has been measured and corrected for redshift to its rest-frame value, $\epsilon_{\rm TIR}^{\prime}$."365 We can also calculate the observable quantity dein as 3.07 (Ilelouctal.L985). For thelogyy(Ltig/Leadic), We can also calculate the observable quantity $q_{\rm FIR}$ as $\log_{10}(L_{\rm TIR}/L_{\rm radio}) - 3.67$ \citep{Helou85}.366" radio cussion. we calculate both the iine radio cluissivity 6por=776,07) where p)=1.1CUIIz. aud the rest-frame racio enissivityv as estimated o» an observer use a k-correction."," For the radio emission, we calculate both the rest-frame radio emissivity $\epsilon_{\rm radio, rest}^{\prime} = \nu^{\prime} \epsilon_{\nu}^{\prime} (\nu^{\prime})$ where $\nu^{\prime} = 1.4~\GHz$ , and the rest-frame radio emissivity as estimated by an observer using a k-correction."367" Note that we are actually trvine to calculate the specific ux in the observer παλιο, but instead what an observer will infer or the fux after using ak-correctiou?:: the rest-frame flux is what matters when we are considering je true. intrinsic evolution of the FRC."," Note that we are actually trying to calculate the specific flux in the observer frame, but instead what an observer will infer for the flux after using a: the rest-frame flux is what matters when we are considering the true, intrinsic evolution of the FRC."368 ence. although i6 specific fluxiu the observer-trame will have a vandwidth compression factor. we assume the observer will take it back out to ect the iuferred rest-frame specific flux.," Hence, although the specific fluxin the observer-frame will have a bandwidth compression factor, we assume the observer will take it back out to get the inferred rest-frame specific flux."369 To calculate the obscerver-interred rest-frame chuissivity at rest-frame frequency vo=d.dGIL we staat with νεήν) where vu=(11jv and po=i!=1.1GIIEz.," To calculate the observer-inferred rest-frame emissivity at rest-frame frequency $\nu^{\prime} = 1.4~\GHz$, we start with $\nu^{\prime} \epsilon_{\nu}^{\prime}(\nu^{\prime}_{\rm obs})$, where $\nu^{\prime}_{\rm obs} = (1 + z) \nu$ and $\nu = \nu^{\prime} = 1.4~\GHz$ ."370" Since the svuchrotron spectra are typically expected to fall off as ενx8 frou observations of local star-forming galaxies. the radio hDuninositv cau be k-corrected bw imultipbhiuge bv (1|23%""."," Since the synchrotron spectra are typically expected to fall off as $\epsilon_{\nu}^{\prime} \propto \nu^{\prime -0.7}$ from observations of local star-forming galaxies, the radio luminosity can be k-corrected by multiplying by $(1 + z)^{0.7}$."371 We therefore ⋈⋡⋏∖↽∕ -.../+~\O.7 ⇁⋅⊳ ⋯↕∏∏∡⋔←↕⋯⊔⋅↳↕↕↓↕≓↗∕←⊼∕⊔∕⋅⋔∖⋈↓↖∙⋝∙↖↖↕∐↸∐↖↖↸↖∏∐," We therefore calculate $\epsilon_{\rm radio, inf}^{\prime} = \nu^{\prime} \epsilon_{\nu}^{\prime}(\nu^{\prime}_{\rm obs}) (1 + z)^{0.7}$, which we will refer to as the “inferred” radio emissivity."372 ↥⋅↸∖↕⋟↸∖↥⋅↑∪⋜↧↴∖↴↑↕∐∖−⇁↕∐↕≯↸∖↥⋅↥⋅↸∖≼↧∥↥⋅⋜∥∐∪↸∖⋯↕↴∖∷∖↴↕↖↽↕↑⋅↖↽∙↽∕∏∐∖⋯↑↕∪ ∪↕⋟↑∐↸∖⊺∐⊰⋜⋯≼↧↥⋅⋜∥∐∪↕∏∐∐↕⋯↴∖↴↕↑↕↸∖↴∖↴⊉∣⊺∐⊰↕⋤↕≖∐⋂↕↴∖↴↑↕∐∖∐ ←↽∣⊺∐∖≯←↽↕⋯∐⋂≱↕↖⋅∖⊺↕∐↑∐↸∖↥⋅↸∖↴∖↴↑↕≯↥⋅⋜⋯∐∖∙⋜⋯≼↧↖↖↽∪∏↕≺∏⋝↸∖↕∐↕⋟↸∖∐⋅↸∖≼↧ ↑∪↴⋝↸∖←↽∣⊺∐∖⋡←↽↕⋯∐⋂⊳↕↕↓↕↕∐↑∐↸∖↥⋅↸∖↴∖↴↑≓↕⋟↥⋅⋜∐⊔↸∖↴⋝∙↖↽∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖↥⋅↴∖↴∙," The ratio of the TIR and radio luminosities $L_{\rm TIR}^{\prime} / L_{\rm radio}^{\prime}$ is then $\epsilon_{\rm TIR}^{\prime} / \epsilon_{\rm radio,rest}^{\prime}$ in the rest frame, and would be inferred to be $\epsilon_{\rm TIR}^{\prime} / \epsilon_{\rm radio, inf}^{\prime}$ in the rest-frame by observers."373 We show the rest-frame FRC for our model with BxXU. the DU? star-formation law. aud no winds. in Fieure d. panel)) as an example.," We show the rest-frame FRC for our model with $B \propto \Sigma_g^{0.7}$, the B07 star-formation law, and no winds, in Figure \ref{fig:LFIRRadioRest} ) as an example."374 The solid dark red line is the τ=0 FRC., The solid dark red line is the $z = 0$ FRC.375 All solid lines asse that starbursts are compact. with f=100pe.," All solid lines assume that starbursts are compact, with $h = 100~\pc$."376 It is clear frou Figure d that compact starbursts show little evolutio in the FRC. while low surface density galaxies have lower radio huuinosities at high redshift.," It is clear from Figure \ref{fig:LFIRRadioRest} that compact starbursts show little evolution in the FRC, while low surface density galaxies have lower radio luminosities at high redshift."377 This behavior is robust iu all of the variants., This behavior is robust in all of the variants.378 The cause of evolution iu the FRC is Inverse Compton losses off the CMD for CR clectrous aud positrous., The cause of evolution in the FRC is Inverse Compton losses off the CMB for CR electrons and positrons.379 Figure 2. pancl)) shows that the FRC should display relatively little evolution out to 2 l. except for thelowest surface briglituess galaxies.," Figure \ref{fig:FRCEvolution} ) shows that the FRC should display relatively little evolution out to $z \approx 1$ , except for thelowest surface brightness galaxies."380" ILlowever. normal galaxies have suppressed svuchrotron radio emission at :z2. a factor of ~2 for X,=LOlοcm (Magac0.06AL.kpe?wo 1) and of order 10 for X,=0.001οcm7 (Seppc0.001 1j "," However, normal galaxies have suppressed synchrotron radio emission at $z \approx 2$, a factor of $\sim 2$ for $\Sigma_g = 0.01~\gcm2$ $\Sigma_{\rm SFR} \approx 0.06~\Msun~\kpc^{-2}~\yr^{-1}$ ) and of order 10 for $\Sigma_g = 0.001~\gcm2$ $\Sigma_{\rm SFR} \approx 0.001 - 0.002~\Msun~\kpc^{-2}~\yr^{-1}$ )."381The radio. huninositios+eye continue+ o fall with redshitt., The radio luminosities continue to fall with redshift.382" At 2z 5. ICoff the CMD starts to natter even for. the weaker starbursts (X,=0.1+@cuP 7: MarrτνLAL...okpe3yr 1)."," At $z \approx 5$ , ICoff the CMB starts to matter even for the weaker starbursts $\Sigma_g = 0.1~\gcm2$ ; $\Sigma_{\rm SFR} \approx 2 - 4~\Msun~\kpc^{-2}~\yr^{-1}$ )."383 Dense starbursts (y= 7: Xaggz900AL.kpe3yrο for the K98 law or 9000AL.kpe?yr! for the BOT law) remain ona linear FRC even at 210., Dense starbursts $\Sigma_g = 10~\gcm2$ ; $\Sigma_{\rm SFR} \approx 900~\Msun~\kpc^{-2}~\yr^{-1}$ for the K98 law or $9000~\Msun~\kpc^{-2}~\yr^{-1}$ for the B07 law) remain on a linear FRC even at $z \approx 10$.384" The strong cooling from broimisstralluug. iouization. aud IC off starlight iuplied by the high-X, conspiracy 2)) acts as a buffer against IC losses off the CMD."," The strong cooling from bremsstrahlung, ionization, and IC off starlight implied by the $\Sigma_g$ conspiracy \ref{sec:Theory}) ) acts as a buffer against IC losses off the CMB."385analysis. then the azimuthal average taken over an isophotal contour wrt.,"analysis, then the azimuthal average taken over an isophotal contour w.r.t."386 the isophotal centre would give a zero average lopsidedness since the average of cos ó would be zero., the isophotal centre would give a zero average lopsidedness since the average of cos $\phi$ would be zero.387 Thus. for measuring the non-axisvmumetric mass distribution we need to keep the centre constant ancl then measure the Fourier amplitudes over annular. radial bins. for this a special procedure was adopted which is described below.," Thus, for measuring the non-axisymmetric mass distribution we need to keep the centre constant and then measure the Fourier amplitudes over annular radial bins, for this a special procedure was adopted which is described below."388 First. the x and v. co-ordinates of the centre of. the ealaxy (or the stellar centre) were determined using the task “imexam” in LRA and plotting the radial profile.," First, the x and y co-ordinates of the centre of the galaxy (or the stellar centre) were determined using the task ""imexam"" in IRAF and plotting the radial profile."389 Once this pixel value was found in terms of the x and ν co-ordinates of the frame. we designated the rest of the image pixels in terms of the distance r and the angle 8 from the centre.," Once this pixel value was found in terms of the x and y co-ordinates of the frame, we designated the rest of the image pixels in terms of the distance $r$ and the angle $\theta$ from the centre."390 The image was then eut into annular regions., The image was then cut into annular regions.391 A polar coordinate erid was centered on the galaxy. nucleus with 36 azimuthal bins with 10 degrees per bin. and the number of radial bins depended on the size of the galaxy.," A polar coordinate grid was centered on the galaxy nucleus with 36 azimuthal bins with 10 degrees per bin, and the number of radial bins depended on the size of the galaxy."392 In each case. we took the radial width of the annular ring to be at least 2 times the resolution of the image.," In each case, we took the radial width of the annular ring to be at least 2 times the resolution of the image."393 The pixel intensity. values in each bin were summed to give an average value per bin., The pixel intensity values in each bin were summed to give an average value per bin.394" Using the task ""nfitld within STSDAS. we fit the following function. f 10 each annular region: where the οτιο ete denote the fractional Fourier amplitudes anc the py.po ete denote the phases of the various Fourier components."," Using the task ""nfit1d"" within STSDAS, we fit the following function, $f$ to each annular region: where the $A_1, A_2$ etc denote the fractional Fourier amplitudes and the $p_1,p_2$ etc denote the phases of the various Fourier components."395 Each annular region in the image gives one set of values for the above fitting., Each annular region in the image gives one set of values for the above fitting.396" The number of points we get in the final plot are the same as the number of annular regions that were made in the origina Image,", The number of points we get in the final plot are the same as the number of annular regions that were made in the original image.397 In Figure 3. we plot the fractional amplituces zi.24 and the phases pi.pe. versus radius rk (in. 7) for m=! ane 2 respectively.," In Figure 3, we plot the fractional amplitudes $A_1, A_2$ and the phases $p_1, p_2$ versus radius $r$ (in $\arcsec$ ) for m=1 and 2 respectively."398 The m=3 anc 4 amplitudes are generally smaller. and m=3 is important. only when m-l is large.," The m=3 and 4 amplitudes are generally smaller, and m=3 is important only when m=1 is large."399 For the sake of brevity. we do not show the amplitudes anc phases for m=3 and 4 for the sample.," For the sake of brevity, we do not show the amplitudes and phases for m=3 and 4 for the sample."400 However. in the notes on individual galaxies (Appendix A) we also add comments about As and Ay when relevant.," However, in the notes on individual galaxies (Appendix A) we also add comments about $_3$ and $_4$ when relevant."401 Figure 3 shows that all the mergers studied show a high value of lopsidedness CX). the values are generally. higher for the class LLL galaxies - see Table 2 for the detailed values including the averages over the classes.," Figure 3 shows that all the mergers studied show a high value of lopsidedness $_1$ ), the values are generally higher for the class III galaxies - see Table 2 for the detailed values including the averages over the classes."402 Phe average values for Ay and X» are given over the central 5 kpe in each merger since it represents a tvpical central region. and also this allows a comparison between dilferent. galaxies.," The average values for $_1$ and $_2$ are given over the central 5 kpc in each merger since it represents a typical central region, and also this allows a comparison between different galaxies."403 In order to avoid any spurious variation with class introduced. due to the dependence on the band. chosen. we have taken homogeneous data (in J-band from 2NLASS) for all the galaxies for the above non-axisvmametric. analysis (Fie.," In order to avoid any spurious variation with class introduced due to the dependence on the band chosen, we have taken homogeneous data (in J-band from 2MASS) for all the galaxies for the above non-axisymmetric analysis (Fig."404 3). and the WKy-banc cata from 2ALASS for the isophotal analvsis (rig.," 3), and the $_s$ -band data from 2MASS for the isophotal analysis (Fig."405 2)., 2).406 Figure 3 shows that the values of As in mergers are also large., Figure 3 shows that the values of $_2$ in mergers are also large.407 Normally. the values of A» are taken to denote bars or spirals or disc ellipticity (Rix Zaritskv 1995. Buta ct al.," Normally, the values of $_2$ are taken to denote bars or spirals or disc ellipticity (Rix Zaritsky 1995, Buta et al."408 2005. Bournaud ct al.," 2005, Bournaud et al."409 2005 a)., 2005 a).410 Ht is hard to see how spiral features can survive the strong disturbance in a merger., It is hard to see how spiral features can survive the strong disturbance in a merger.411 We add the evidence from the isophotal analysis and. find that the characteristic feature of bars. namely increasing ellipticity ancl a nearly constant position angle (PA) (e.g. Wozniak et al.," We add the evidence from the isophotal analysis and find that the characteristic feature of bars, namely increasing ellipticity and a nearly constant position angle (PA) (e.g. Wozniak et al."412 1995) is seen in only three cases. which we conclude have well-defined. bars.," 1995) is seen in only three cases, which we conclude have well-defined bars."413 “hese are: Arp 100. Arp 162. and Arp 163.," These are: Arp 160, Arp 162, and Arp 163."414 CGrosbol et al. (, Grosbol et al. (4152004) state that a circular cise will appear elliptical when projected and this could. give rise to an artificial bisymmetric component with a constant. phase.,2004) state that a circular disc will appear elliptical when projected and this could give rise to an artificial bisymmetric component with a constant phase.416 This could. be used to explain the high. values of As seen in many galaxies in our sample., This could be used to explain the high values of $_2$ seen in many galaxies in our sample.417 In. fact this effect is seen in all the galaxies except Arp 221 (Class D). Arp 212 (Class LL). and Arp 209 (Class HD).," In fact this effect is seen in all the galaxies except Arp 221 (Class I), Arp 212 (Class II), and Arp 209 (Class III)."418 Thus. in most cases stιοτος. 10 merger remnants seem to indicate a preferred disc plane.," Thus, in most cases studied, the merger remnants seem to indicate a preferred disc plane."419 ‘This is seen even in three of the class E galaxies with an outer liptical-like profile (Arp 222. Arp 225. AMOG612-:3). which is unexpected.," This is seen even in three of the class I galaxies with an outer elliptical-like profile (Arp 222, Arp 225, AM0612-373), which is unexpected."420 We note. however. that the previous work on deriving 10 Fourier cocllicicnts to ect the asvmmetry. has been one for spiral galaxies.," We note, however, that the previous work on deriving the Fourier coefficients to get the asymmetry has been done for spiral galaxies."421 These galaxies were deprojected by estimating their inclinations assuming that the clises are intrinsically round., These galaxies were deprojected by estimating their inclinations assuming that the discs are intrinsically round.422 Le is reasonable to talk about projection ellects in the case of spirals and also comparatively easy to deproject these galaxies., It is reasonable to talk about projection effects in the case of spirals and also comparatively easy to deproject these galaxies.423 HLowever. here we are looking at systems completely or partially distorted by the interaction or à merger and hence it is not. possible to estimate the inclination of the disc component and correct for inclination ellects.," However, here we are looking at systems completely or partially distorted by the interaction or a merger and hence it is not possible to estimate the inclination of the disc component and correct for inclination effects."424 X further discussion. on the variation of Fourier amplitudes with class types in our sample is given in Section 4.2., A further discussion on the variation of Fourier amplitudes with class types in our sample is given in Section 4.2.425 So [ar we have studied the mergers and we have shown these to have significant central non-axisvmmetry., So far we have studied the mergers and we have shown these to have significant central non-axisymmetry.426 In. order to check that the origin of this is related to the merger history. we next carry out a similar analysis for a control sample of non-merging. normal spiral galaxies and show that these incecd. have lower central asymmetry.," In order to check that the origin of this is related to the merger history, we next carry out a similar analysis for a control sample of non-merging, normal spiral galaxies and show that these indeed have lower central asymmetry."427 The selection. of a sample of non-merger galaxies is » no means a trivial issue., The selection of a sample of non-merger galaxies is by no means a trivial issue.428 We do not include any carly-ype galaxies which are now believed to evolve from. [ate-vpe galaxies via secular evolution or galaxy mergers., We do not include any early-type galaxies which are now believed to evolve from late-type galaxies via secular evolution or galaxy mergers.429 The ealaxies selected are nearly face-on (for easier analysis). and are late-tvpe and not strongly. barred and not active - so as o increase the chance of their having had. no interactions in he recent. past.," The galaxies selected are nearly face-on (for easier analysis), and are late-type and not strongly barred and not active - so as to increase the chance of their having had no interactions in the recent past."430 The set of eight such normal or non-merecr ealaxies which are also large enough in angular size to allow he non-axisvmmetric analysis in J-band (see Section 2) were chosen from the 2\LASS Large Galaxy Catalog (Jarrett et al., The set of eight such normal or non-merger galaxies which are also large enough in angular size to allow the non-axisymmetric analysis in J-band (see Section 2) were chosen from the 2MASS Large Galaxy Catalog (Jarrett et al.431 2003). and these are: NGC 628 (AIT4). NGC 3147. Νας 4254 (MIOQO). NGC 4321 (M99). NGC 4540. NGC 4689. Νας 5248. NGC 5311.," 2003), and these are: NGC 628 (M74), NGC 3147, NGC 4254 (M100), NGC 4321 (M99), NGC 4540, NGC 4689, NGC 5248, NGC 5377."432close to the accreting star for model M-3 is shown.,close to the accreting star for model M-3 is shown.433 The density decreases exponentially up to 5 AU in a slightly eccentric disk and is to be thick., The density decreases exponentially up to 5 AU in a slightly eccentric disk and is likely to be optically thick.434 This is consistent with the size of likelythe disk around opticallyMira B estimated by ?.., This is consistent with the size of the disk around Mira B estimated by \citet{2007ApJ...662..651I}.435 We show the flowlines after 1 orbital period in Fig.[I4]., We show the flowlines after 1 orbital period in Fig. \ref{fig:stream}.436 The flowlines are calculated integrating the equation of motion from the line joining the stars using positive and negative time-steps., The flowlines are calculated integrating the equation of motion from the line joining the stars using positive and negative time-steps.437 When the wind speed is of the order of the escape velocity from the AGB star the flow is focused by the gravitational pull from the secondary and the accretion rate is enhanced factor of a few with respect to standard Bondi-Hoyle accretion., When the wind speed is of the order of the escape velocity from the AGB star the flow is focused by the gravitational pull from the secondary and the accretion rate is enhanced by a factor of a few with respect to standard Bondi-Hoyle accretion.438bya We show the radial velocity map for a model with wind temperature 10? K and inner boundary at 20 AU with, We show the radial velocity map for a model with wind temperature $10^3$ K and inner boundary at 20 AU with439t: the first tevin σοος to zero and the secoud terii dominates so that we have XxRot? (if n21). which distiuguislies it from the selfsimulavity solution.,"t; the first term goes to zero and the second term dominates so that we have $\Sigma\propto R^{-1.5}$ (if n=1), which distinguishes it from the self-similarity solution."440 Next. we consider the late stage when Ry is independent of time analytically by the Creeu's function method.," Next, we consider the late stage when $_{D}$ is independent of time analytically by the Green's function method."441 If the viscosity vis a function of radius. equation ALT is a linear equation for X aud can be solved by a Crecu's function (Lust 1952: Lvuden-Dell Pringle 1971).," If the viscosity $\nu$ is a function of radius, equation \ref{eq:evolve} is a linear equation for $\Sigma$ and can be solved by a Green's function (Lust 1952; Lynden-Bell Pringle 1974)."442" If ££=AR"". the above equation becomes ⋜⋯≼↧↑∐↸∖↥⋅⋜∥∐⋜↧↕≼∐∖↻↸∖∐≼∐∖∐↸⊳↸∖∪↕∑↕↴∖↴⋜↧↕∐∐∖⋜∐⋅↸⊳∪∐∐⋝∐↕⋜↧⊓∪↕↕∪↕↑∐↸∖↕≧↸∖↴∖↴↴∖↴↸∖⊔⋯∐⊳↑↕∪∐↴∖↴⋅∫⊔∣⋜⋯≼↧⋅∫∕∣∙↖↖↽↕∐∖↥⋅↸∖∕∣−∶↓⊓−≽∣∣⋟− ∏⇀⋅↖↽∐≼∐∖∐≓↕≧↸∖∐∙∖↽↕⋟∏∐∶↴∙⊾↕↸∖↕∩⊤⊔⋅∐∪↖↖↽↸∖↖"," If $\nu=k R^{n}$, the above equation becomes and the radial dependence of $\Sigma$ is a linear combination of the Bessel functions $J_{+\mu}$ and $J_{-\mu}$ , where $\mu^{2}=1/4(2-n)^{2}$ (Lynden-Bell Pringle 1974)."443↽↸∖↥⋅↕≯∪↥⋅⋜↧∐⊼⋯⇂∑↕∐∐↸∖↥⋅↴⋝≺∏⋯≺↧⋜∐⋅⋅↖↽↸⊳∪∐≼∐↑↕∪∐⋜↧↑∫⊽↿⋟∠≻∙ we can substitute X with X so that equation ALO aud the boundary condition A20 changes to and which becomes a normal disk evolution equation of X with a zero surface density boundary condition.," However for a fixed $\Sigma$ inner boundary condition at $R_{D}$ , we can substitute $\Sigma$ with $\Sigma'$ so that equation \ref{eq:evolve2} and the boundary condition \ref{eq:bound} changes to and which becomes a normal disk evolution equation of $\Sigma'$ with a zero surface density boundary condition."444"The solution of δν is well studied aud this disk expands with limit tf>oc. M.>0. thus from equation À21.. we derive f>x. XΣΠΠο)""V7.","The solution of $\Sigma'$ is well studied and this disk expands with limit $t\rightarrow\infty$, $\Sigma'\rightarrow 0$, thus from equation \ref{eq:sigmaprime2}, we derive $t\rightarrow\infty$, $\Sigma\rightarrow \Sigma_{A}(R/R_{D})^{-n-1/2}$."445" Thus aslong as the disk evolves long enough the impact of auy initial condition will be washed out. and the boundary term dominates the surface density distribution with XxR""(7,"," Thus as long as the disk evolves long enough the impact of any initial condition will be washed out, and the boundary term dominates the surface density distribution with $\Sigma\propto R^{-n-1/2}$."446 In the nadiation dominated case. n=l. we transform equation A22 by writing «=RY? aud s=X'R7 (Pringle 1991) to get with the boundary condition στ0 atcSap=n.," In the irradiation dominated case, n=1, we transform equation \ref{eq:evolve3} by writing $x=R^{1/2}$ and $\sigma=\Sigma'R^{3/2}$ (Pringle 1991) to get with the boundary condition $\sigma=0$ at $x=x_{D}=R_{D}^{1/2}$."447 The eeucral solution is then where e?=Bh/ 1., The general solution is then where $c^{2}=3k/4$ .448 Ay is determined by the initial conditions., $A_{\lambda}$ is determined by the initial conditions.449 Following Pringle(1991). in order to obtain the Creeu's function. we set the initial coudition with With the delta function Fourier traustori. {evcp(2zeA)dA=6e) and i62orp. we derive Thus the solution for the mitial condition À26 is Finally. the solution σα.f£) for auv initial coudition oGre.f=0)σα) isand where the first term ds the disk evolution with a zero boundary condition aud the secoud terimis the fixed X boundary effect.," Following Pringle(1991), in order to obtain the Green's function, we set the initial condition with With the delta function Fourier transform $\int exp(2\pi x\lambda450i)d\lambda=\delta(x)$ and $x>x_{D}$, we derive Thus the solution for the initial condition \ref{eq:ini} is Finally, the solution $\sigma(x,t)$ for any initial condition $\sigma(x,t=0)=\sigma'(x)$ isand where the first term is the disk evolution with a zero boundary condition and the second termis the fixed $\Sigma$ boundary effect."451" Astsx. NMoNA(R/Rp})ay ""7."," As $t\rightarrow\infty$, $\Sigma\rightarrow452\Sigma_{A}(R/R_{D})^{-3/2}$ ."453"field structures, is required to resolve this issue.","field structures, is required to resolve this issue."454" The structure of the underlying magnetic field is intricately linked to the fragmentation process of filamentary clouds (e.g. Fiege Pudritz (2000)., Falgarone et al. (2001))),"," The structure of the underlying magnetic field is intricately linked to the fragmentation process of filamentary clouds (e.g. Fiege Pudritz \cite{2000MNRAS.311..105F}, Falgarone et al. \cite{2001ApJ...555..178F}) ),"455 and consequently to outflow orientation., and consequently to outflow orientation.456 The outflow sample obtained by our survey will be an outstanding and unique opportunity to perform this analysis., The outflow sample obtained by our survey will be an outstanding and unique opportunity to perform this analysis.457 We expect that the majority of outflow sources will be at distances of kkpc., We expect that the majority of outflow sources will be at distances of kpc.458 The Galactic Plane magnetic field structure within 2 or kkpc is revealed by stellar polarization surveys (e.g. Heiles (2000))) and out to larger distances by other techniques such as Faraday rotation of pulsars and extra-galactic radio sources (e.g. Han (2009)))., The Galactic Plane magnetic field structure within 2 or kpc is revealed by stellar polarization surveys (e.g. Heiles \cite{2000AJ....119..923H}) ) and out to larger distances by other techniques such as Faraday rotation of pulsars and extra-galactic radio sources (e.g. Han \cite{2009IAUS..259..455H}) ).459 Recently the relation of outflow direction and magnetic field structure has been investigated in individual clouds (e.g. in 221 by Kirby (2009))., Recently the relation of outflow direction and magnetic field structure has been investigated in individual clouds (e.g. in 21 by Kirby \cite{2009ApJ...694.1056K}) ).460" When such magnetic field studies become available for other regions, the UWISH2 data will be helpful to support or negate the relative orientation of outflows with magnetic fields, thus constraining an important aspect of star formation."," When such magnetic field studies become available for other regions, the UWISH2 data will be helpful to support or negate the relative orientation of outflows with magnetic fields, thus constraining an important aspect of star formation."461" There are of course many other outflow parameters that can be measured in a large infrared study: What fraction are collimated, and what fraction are parsec-scale in length?"," There are of course many other outflow parameters that can be measured in a large infrared study: What fraction are collimated, and what fraction are parsec-scale in length?"462" Does the mean flow length correlate with the median age of the embedded population, derived from colour analysis or the mean mid-IR spectral index"," Does the mean flow length correlate with the median age of the embedded population, derived from colour analysis or the mean mid-IR spectral index"463This indicates that /«4245/2 because m>—1.,This indicates that $k<4+n/2$ because $m>-1$.464 In addition. the pressure equilibrium vields a relation of constants (hat have been introduced in (he preceding sections as This relation will be used to discuss the propagation of the outer shock in (he ambient mecdiun.," In addition, the pressure equilibrium yields a relation of constants that have been introduced in the preceding sections as This relation will be used to discuss the propagation of the outer shock in the ambient medium."465 A blast wave in a uniform ambient medium with power supply was treated by (1976)., A blast wave in a uniform ambient medium with power supply was treated by \citet{Blandford76}.466. They assumed that the power is supplied by a stationary source located abr=0 and varies with (ime as a power law. L=Lol.," They assumed that the power is supplied by a stationary source located at $r=0$ and varies with time as a power law, $L=L_0t^s$."467 If s=(2n—8)/(n+2). then the flow in the shocked ambient medium evolves exactly in the same way as described in (1976).," If $s = (2n-8)/(n+2)$, then the flow in the shocked ambient medium evolves exactly in the same way as described in \citet{Blandford76}."468.. Thev also argued that the adiabatic impulsive solution is appropriate for the flow with m in the range of i23 or i<-1., They also argued that the adiabatic impulsive solution is appropriate for the flow with $m$ in the range of $m>3$ or $m<-1$.469 Since m>—1 in our problem. the condition m>3 restricts the value of » to be less than —2//3 through equation (39)).," Since $m>-1$ in our problem, the condition $m>3$ restricts the value of $n$ to be less than $-2k/3$ through equation \ref{tev}) )."470 Thus the values of η= 1.1 and 2.6 indicate a continuous supply of energy., Thus the values of $n=$ 1.1 and 2.6 indicate a continuous supply of energy.471 When (7.4)=(1.1.2). equation (39)) vieldsm=2/(n+2)~0.65 and then. from equation (14)). q~1.06.," When $(n,k) = (1.1,\,2)$, equation \ref{tev}) ) yields$m=2/(n+2)\sim0.65$ and then, from equation \ref{eq-q}) ), $q\sim1.06$."472 Performing numerical integration of equations (25)) (27)) and (34)) (36)) with these parameters. boundary conditions (eqs. (28))," Performing numerical integration of equations \ref{Ge}) \ref{He}) ) and \ref{fa}) \ref{ha}) ) with these parameters, boundary conditions (Eqs. \ref{bce}) )"473 and (37))). aud 5=5/3 in (he shocked ejecta. we find £.~0.95 and (f...go.Fo.Ge)~(0.18.0.47.2.1. 0.93).," and \ref{bca}) )), and $\hat{\gamma}=5/3$ in the shocked ejecta, we find $\xi_{\rm c}\sim0.95$ and $(f_{\rm c}, \,g_{\rm c}, \, F_{\rm c},\, G_{\rm c}) \sim (0.18,\, 0.47,\, 2.1,\, 0.98)$ ."474 Here the subseript ¢ of each variable indicates that the value is taken at the contact surface., Here the subscript c of each variable indicates that the value is taken at the contact surface.475 Results ave shown in Figure la., Results are shown in Figure 1a.476 When (7.4)=(2.6.2). the same procedure leads to 1»= 0.43. qe1.05. ἐν~ 0.91. and (fi.ge.FeeGe)~(0.32.0.70.2.0.0.93).," When $(n,k) = (2.6,\,2)$, the same procedure leads to $m=2/(n+2)\sim0.43$ , $q\sim1.05$, $\xi_{\rm c}\sim0.97$ , and $(f_{\rm c}, \,g_{\rm c}, \, F_{\rm c},\, G_{\rm c}) \sim (0.32,\, 0.70,\, 2.0,\, 0.98)$."477 Results are shown in Figure 1b., Results are shown in Figure 1b.478 Nakavama&Shigevama(2005) investigated the evolution of an ultra-relativistic shock wave In a plane-parallel atinosphere and derived sell-similar solutions., \citet{Nakayama05} investigated the evolution of an ultra-relativistic shock wave in a plane-parallel atmosphere and derived self-similar solutions.479" The resultant energy spectrum of the ejected matter with an explosion energy Ey, and an ejected mass M for a raciative stellar envelope can be expressed as where AM(22)denotes the ejectedmass that have particle enerev per nucleon greater than ©=my(5.— 1).", The resultant energy spectrum of the ejected matter with an explosion energy $E_{\rm ex}$ and an ejected mass $M_{\rm ej}$ for a radiative stellar envelope can be expressed as where $M(>\varepsilon)$denotes the ejectedmass that have particle energy per nucleon greater than $\varepsilon = m_p (\gamma_{\rm e} -1)$ .480 Here the proportionality constant is not specified by, Here the proportionality constant is not specified by481to the dise thickness.,to the disc thickness.482 We define dL as the net mechanical wind huminosity emanating from (his volume element. and ¢ as (he associated mean outflow speed at the chosen radius.," We define $dL$ as the net mechanical wind luminosity emanating from this volume element, and $v$ as the associated mean outflow speed at the chosen radius."483 We posit that the winds emanating from either side of (hin annulus are not exactly in momentum balance al all times due to turbulent [Inctuations., We posit that the winds emanating from either side of thin annulus are not exactly in momentum balance at all times due to turbulent fluctuations.484" We denote wind mechanical Iuminosities Lor a given eddy emanating from the top and bottom of the disc as dL,4, and dL, respectively. such that dL=dL,4,+dLy."," We denote wind mechanical luminosities for a given eddy emanating from the top and bottom of the disc as $dL_{top}$ and $dL_{bot}$ respectively, such that $dL = dL_{top} + dL_{bot}$."485" Let €),) and ενω denote unit vectors in the direction of wind flow on the top and bottom.", Let $\boldsymbol\epsilon_{top}$ and $\boldsymbol\epsilon_{bot}$ denote unit vectors in the direction of wind flow on the top and bottom.486 The net force on the volume element from the two winds is where €=(eidLio+€iuidLi)/dL. and characterizes (he direction of wind imbalance.," The net force on the volume element from the two winds is where $\boldsymbol\epsilon' \equiv (\boldsymbol\epsilon_{top}487 dL_{top}488+ \boldsymbol489\epsilon_{bot}dL_{bot}490)/dL$, and characterizes the direction of wind imbalance."491 Since we have assumed that the origin of the force imbalance (turbulence) is intrinsically random. €e' will be a random vector dependent on both time and position.," Since we have assumed that the origin of the force imbalance (turbulence) is intrinsically random, $\boldsymbol\epsilon'$ will be a random vector dependent on both time and position."492 FlIuctuations around both the mean outflow speed and mass outflow rate can be incorporated into e' given ils definition: (he explicitly presence of the mean velocity in (7)) does not preclude (his., Fluctuations around both the mean outflow speed and mass outflow rate can be incorporated into $\epsilon'$ given its definition; the explicitly presence of the mean velocity in \ref{6}) ) does not preclude this.493 The force on a disc volume element results from a “rocket effect created. by last term in (7)).," The force on a disc volume element results from a “rocket effect"" created by non-vanishing last term in \ref{6}) )."494 To ealeulate the associated torque. we assume that €' is a poloidal vector (€-O= 0) lor every volume element.," To calculate the associated torque, we assume that $\boldsymbol\epsilon'$ is a poloidal vector $\boldsymbol\epsilon' \cdot \hat{\phi} = 0$ ) for every volume element."495 The associated toreue then lies in the initial disc plane and is given by summine the torques for all volume elements at radius r leaves a net torque on an annulus of radial thickness dr al radius r given bv where we have delined E(r)={allvolumeelementsatradiusr}. and €=So(rx€).," The associated torque then lies in the initial disc plane and is given by Summing the torques for all volume elements at radius $r$ leaves a net torque on an annulus of radial thickness $dr$ at radius $r$ given by where we have defined $E(r) \equiv \{\mbox{all volume elements at radius r}\}$, and $\boldsymbol\epsilon\equiv \sum (\hat{\mathbf{r}} \times \boldsymbol\epsilon')496$."497 Note that since €' is poloidal. rκε’ lies in the plane of the disc. and therefore so does e. being a sum of such vectors.," Note that since $\boldsymbol\epsilon'$ is poloidal, $\hat{\mathbf{r}} \times \boldsymbol\epsilon'$ lies in the plane of the disc, and therefore so does $\boldsymbol\epsilon$, being a sum of such vectors."498" Since dr lies in the plane of the disc. so does dT,,4."," Since $d{\boldsymbol\tau}$ lies in the plane of the disc, so does $d\boldsymbol\tau_{net}$."499 By summing over all (he volume elements in the annulus we have removed the azimuthal dependence. providing what is needed to characterize the response of an axisvinmetric mean field annulus.," By summing over all the volume elements in the annulus we have removed the azimuthal dependence, providing what is needed to characterize the response of an axisymmetric mean field annulus."500 This is an annulus of a “standard” axisvimietric radially dependent accretion disc (which itself is axisvimnmnetrie precisely because of (he azimuthal average over turbulent. [lnctuations)., This is an annulus of a “standard” axisymmetric radially dependent accretion disc (which itself is axisymmetric precisely because of the azimuthal average over turbulent fluctuations).501 We can now calculate the rate of change of angular momentum of this annulus associated with tilling from its initial disc symmetry plane., We can now calculate the rate of change of angular momentum of this annulus associated with tilting from its initial disc symmetry plane.502 This tilt introduces an angular momentum, This tilt introduces an angular momentum503with multiple repoiutiugs cach day to periit study of transient sources and rare states of known sources.,with multiple repointings each day to permit study of transient sources and rare states of known sources.504 The goal for the large area x-ray detector is to provide au order of magnitude increase mn x-ray tinue capabilities relative to RNTE., The goal for the large area x-ray detector is to provide an order of magnitude increase in x-ray timing capabilities relative to RXTE.505 The design goals are: a useful detector area of at least G m7. sensitivitv from 2 keV to 30 keV. absolute timing better than 10ys. minimal dead time effects for sources 10 times as bright as the Crab nebula. an energy resolution of 1.2 keV (preferably 300 eV) at 6 keV. no inaenme. aud a field of view of 1° or simaller.," The design goals are: a useful detector area of at least 6 $^2$, sensitivity from 2 keV to 30 keV, absolute timing better than $10 \, \rm \mu s$, minimal dead time effects for sources 10 times as bright as the Crab nebula, an energy resolution of 1.2 keV (preferably 300 eV) at 6 keV, no imaging, and a field of view of $1^{\circ}$ or smaller."506 Albsky x-ray monitoring is needed for several reasons., All-sky x-ray monitoring is needed for several reasons.507 First. the x-ray. imonitor provides continual long-term lielit curves.," First, the x-ray monitor provides continual long-term light curves."508 As may x-ray sources are Liehly variable. knowledge of the long term behavior in important m unuderstaudiug the plivsical nature of the sources and in placing pointed observations iu the context of the source state.," As many x-ray sources are highly variable, knowledge of the long term behavior in important in understanding the physical nature of the sources and in placing pointed observations in the context of the source state."509 Second. au xav nionitor provides a means to trigecrao pointed observations when a selected source reaches a state of particular interest.," Second, an x-ray monitor provides a means to trigger pointed observations when a selected source reaches a state of particular interest."510" Finally. an x-ray mouitor allows discovery of now sources or new. uupredicted. outbursts of known sources,"," Finally, an x-ray monitor allows discovery of new sources or new, unpredicted, outbursts of known sources."511 Manv of the sources of interest are transieuts with uuknown or mreeular recurrence intervals., Many of the sources of interest are transients with unknown or irregular recurrence intervals.512 Au x-ray moniter is essential to detect trausicut events., An x-ray monitor is essential to detect transient events.513 The design goal for the x-ray monitor is a sensitivity of several Cra for daily observations. sufficient to moniter a large sample of AGNs (~ LO) on a daily basis.," The design goal for the x-ray monitor is a sensitivity of several mCrab for daily observations, sufficient to monitor a large sample of AGNs $\sim 40$ ) on a daily basis."514 An effective area of 6 un? will require a total geometric detector area near 10 1r., An effective area of 6 $^2$ will require a total geometric detector area near 10 $^2$.515 A detector with a cross sectional area of 10 107. aud a thickness of 0.75 ni? fits within the 3m diameter fairing of a two-stage Delta IL, A detector with a cross sectional area of 10 $^2$ and a thickness of 0.75 $^2$ fits within the 3 m diameter fairing of a two-stage Delta II.516 Thus. a 6 mi? detector can be accommodated in a “medium-sized” mission without a deploviment mechaisi.," Thus, a 6 $^2$ detector can be accommodated in a “medium-sized” mission without a deployment mechanism."517. The s-rav detector must have low mass per unit effective area. reasonable cost. lughly reliable and stable operation. efficient rejection of particle backerouuds. aud eood energy resolution.," The x-ray detector must have low mass per unit effective area, reasonable cost, highly reliable and stable operation, efficient rejection of particle backgrounds, and good energy resolution."518 After extensive review of tle available detector teclinologies. we have selected silicon detectors as the most promising candidate for laree format x-ray astrononuv detectors.," After extensive review of the available detector technologies, we have selected silicon detectors as the most promising candidate for large format x-ray astronomy detectors."519 A 2 nuu thick silicon detector provides effücienev up to 30 keV at a mass of 0.5 eii/en: this compares favorably aa ↑∪↕⋟≼⊲⊀≚∪∐⊸∖↽∏⋮⋜↧↑⋜↧⊔⋜↧↴∖↴↴∖↴∪↕≝, A 2 mm thick silicon detector provides efficiency up to 30 keV at a mass of 0.5 $^2$; this compares favorably to PCA on XTE at a mass of 90 $^2$.520⋊∣∶↴⋁⋯↸⊳⋯−∙∺∏↕↸⊳∪∐↕↴∖↴↖↖⇁↕≼∐∖↕⋅↖↽∏↴∖↴↸∖≼↧⋜⋯≼↧↸⊳⋜⋯↴⋝↸∖ . ∣⋅≻ ⋅ ⋅ ∪↴⋝↑⋜⊔∐↸∖≺⋜↧↑↕∪↖↖↽↸⊳∪↴∖↴↑≺⊔↸∖∪↕⋜∐⋅∶↴⋁↸∖↸∖↸⊳∪∐∪∐∐↸∖↴∖↴∪↕↴∖↴↸⊳⋜↧↕↸∖∶∩⋯−∪↸⊳∪⋯⋯↸∖↥⋅↸⊳↕⋜↕∐⋅↖⇁⋜↧↖↽⋜⊔↕⋜∏⋝↕↸∖ ↴∖↴∐↕↸⊳∪∐↴∖↴⊓⋅∏≻≼∐∖↑↸∖↸⊳↑∪↥⋅↴∖↴≺↴∖↴↸∖↸∖↴⋝↸∖↕∪∖↖↽⋟⋯⊔⋝↸∖↻↥⋅≺⋉⊳↿∐⋅↸∖≺⇂↕≯∪↥⋅↕↸∖↴∖↴↴∖↴↑∐⋜⋯↕↸≋⋅≊⊔⋀∖↕∙≋∐↕⋯∐ has a low ionization potential which leads to good cuerey resolution and allows silicon detectors to be operated without internal amplification., Silicon is widely used and can be obtained at low cost due to large economies of scale; 10 $^2$ of commercially available silicon strip detectors (see below) can be procured for less than 4M. Silicon has a low ionization potential which leads to good energy resolution and allows silicon detectors to be operated without internal amplification.521 While the lack of internal amplification mandates the use of low capacitance detectors aud low noise electrouies for good performance. it also climinates the need for high voltage aud facilitates reliable aud stable operation.," While the lack of internal amplification mandates the use of low capacitance detectors and low noise electronics for good performance, it also eliminates the need for high voltage and facilitates reliable and stable operation."522 Silicon detectors can be configured im differeut geometries includiug PIN diodes. slieon strip detectors. aud silicon dift chambers.," Silicon detectors can be configured in different geometries including PIN diodes, silicon strip detectors, and silicon drift chambers."523 Silicon strip detectors (SSDs) are widely used in particle physics., Silicon strip detectors (SSDs) are widely used in particle physics.524 SSDs offer ouc-dimenusional inagiug which iav provide a means of effective discrimination against particle backerouuds., SSDs offer one-dimensional imaging which may provide a means of effective discrimination against particle backgrounds.525 However. SSDs eiiploy charge collection strips which run the leugth of a water aud. thus. have relatively high capacitance which leads to high electronic noise and poor energv," However, SSDs employ charge collection strips which run the length of a wafer and, thus, have relatively high capacitance which leads to high electronic noise and poor energy"526other hand. (he stars of the first generation were likely formed together with the central O star.,"other hand, the stars of the first generation were likely formed together with the central O star."527 An age οἱ 0.3 Myrs is estimated for the III] region by considering its spatial extent (Cernicharoetal.1998) and the age of the first generation stars is thought to be less than 1 Mvrs (seereviewbyRhoοἱal.2008)., An age of 0.3 Myrs is estimated for the HII region by considering its spatial extent \citep{cer1998} and the age of the first generation stars is thought to be less than 1 Myrs \citep[see review by][]{rho2008}.528. The distribution of the URAS emission shown in Figures 2ee 31 is centered on the O star. and the boundary at the half peak intensity level shows an extension similar to that of ihe HI] region (Cernicharoetal. 1998)..," The distribution of the IRAS emission shown in Figures \ref{iimap}g \ref{iimap}i i is centered on the O star, and the boundary at the half peak intensity level shows an extension similar to that of the HII region \citep{cer1998}. ."529 The total infrared luminosity 7; is given bv the following equations (Dale&Helou2002):: llere fy is the lux in each of the 3 IILAS bands and D is the distance to the object., The total infrared luminosity $L_{\rm ir}$ is given by the following equations \citep{dal2002}; Here $f_\lambda$ is the flux in each of the 3 IRAS bands and $D$ is the distance to the object.530 Ly for M20 is hence estimated to be ~2.4x10° L. and 6.1x10 L. for distances of 1.7 kpe and 2.7 kpe. respectively.," $L_{\rm ir}$ for M20 is hence estimated to be $\sim2.4\times10^5$ $L_\odot$ and $6.1\times10^5$ $L_\odot$ for distances of 1.7 kpc and 2.7 kpc, respectively."531 Draine&Li(2007) pointed out Chat the above equations eiven by Dale&Helou(2002) underestimate Li bv up to within a radiation intensity U range of LO100. and applving this correction increases our estimates of Li. to 3.4x10? L. and 8.6x10 L. [or the two distances.," \cite{dra2007} pointed out that the above equations given by \cite{dal2002} underestimate $_{\rm ir}$ by up to within a radiation intensity $U$ range of 10–100, and applying this correction increases our estimates of $L_{\rm ir}$ to $3.4\times10^5$ $L_\odot$ and $8.6\times10^5$ $L_\odot$ for the two distances."532 The bolometric luminosity of the O star is 13 4.2x10 L. (Conti&Alschuler1971:Walborn1973).. corresponding to 40.120 and 2050 of the above estimates for (wo distances. respectively.," The bolometric luminosity of the O star is $1.3$ $4.2\times10^5$ $L_\odot$ \citep{con1971,wal1973}, corresponding to 40–120 and 20–50 of the above estimates for two distances, respectively."533 These figures indicate that the dust luminosity is dominated by the energy of the O star. which accounts for most οἱ the radiative energy in M20.," These figures indicate that the dust luminosity is dominated by the energy of the O star, which accounts for most of the radiative energy in M20."534 We therefore argue that the first generation stars. including the O star. dominate the total energv release in (he region aud probably also make up the majority of the stellar mass contained within it.," We therefore argue that the first generation stars, including the O star, dominate the total energy release in the region and probably also make up the majority of the stellar mass contained within it."535 On the other hand. the stars formed in the other outer clouds NW. 5$ and NE are much less dominant in huminosity andperhaps also in terms of the masses of individual stars.," On the other hand, the stars formed in the other outer clouds NW, S and NE are much less dominant in luminosity andperhaps also in terms of the masses of individual stars."536 We here discuss the heating mechanism of the warm gas in the 2 km 1 and clouds, We here discuss the heating mechanism of the warm gas in the 2 km $^{-1}$ and clouds537planets increases steeply with stellar metallicity. that. Jupiter-like enhancement over solar abundances are standard for gas giants. and that more massive planets tend to have lower enrichment. could be enhanced or refuted by additional detections of transiting planets with equilibrium temperatures less (han 1000. Ix... These longer-period systems will continue to be detected [rom the ground and recently NASA's. spacecraft. identified dozens of candidates for a potentially dramatically larger sample of these less-irracdliiated: (ransiline eijant planets (Doruckietal.2011).,"planets increases steeply with stellar metallicity, that Jupiter-like enhancement over solar abundances are standard for gas giants, and that more massive planets tend to have lower enrichment, could be enhanced or refuted by additional detections of transiting planets with equilibrium temperatures less than 1000 K. These longer-period systems will continue to be detected from the ground and recently NASA's spacecraft identified dozens of candidates for a potentially dramatically larger sample of these less-irradiated transiting giant planets \citep{Borucki11}."538. We thank Mark Marley. Nevin Sehlaufinan. James Guillochon. Philip Nutzman. ancl Eliza Ixempton for providing feedback and encouragement.," We thank Mark Marley, Kevin Schlaufman, James Guillochon, Philip Nutzman, and Eliza Kempton for providing feedback and encouragement."539 JJE acknowledges the support of NSF erant. AST-1010017 and an Alfred P. Sloan Research Fellowship., JJF acknowledges the support of NSF grant AST-1010017 and an Alfred P. Sloan Research Fellowship.540"run with Hpz=2.3H exhibits a higher positive bump at r~0.89 and a smaller negative bump at r~1.04, which therefore corresponds to a slightly smaller differential Lindblad torque.","run with $\hdz=2.3H$ exhibits a higher positive bump at $r\sim 0.89$ and a smaller negative bump at $r\sim 1.04$, which therefore corresponds to a slightly smaller differential Lindblad torque."541" For the run with Hpz=2.3H, the positive torque excess for 0.9<r0.94 can be explained by looking at the vertical torque distribution Γ(2) exerted by the disk region located between a—x, and a+x, and which is displayed in the lower panel of Fig. 7.."," For the run with $\hdz=2.3H$, the positive torque excess for $0.9<r<0.94$ can be explained by looking at the vertical torque distribution $\Gamma(z)$ exerted by the disk region located between $a-x_s$ and $a+x_s$ and which is displayed in the lower panel of Fig. \ref{torquedistrib}. ."542" For this simulation, the torque becomes positive beyond Z>1.7H, which is clearly not the case for the run with Hpz=H."," For this simulation, the torque becomes positive beyond $Z > 1.7H$, which is clearly not the case for the run with $\hdz=H$."543 This unambiguously confirms that the corotation torque exerted by the viscously-evolving layers is unsaturated in the run with Hpz=2.3H and tends to slow down migration., This unambiguously confirms that the corotation torque exerted by the viscously-evolving layers is unsaturated in the run with $\hdz=2.3H$ and tends to slow down migration.544 We now turn to the question of how the orbit of a Jupiter-mass planet evolves in a dead-zone., We now turn to the question of how the orbit of a Jupiter-mass planet evolves in a dead-zone.545" Here again, to address this issue, we restarted the simulations presented in Sect."," Here again, to address this issue, we restarted the simulations presented in Sect."546" 4.1 once the mass of the accreting protoplanet has reached m,=1Mj, but we now let the planet evolve under the influence of the disk for 500 The time evolution of Jupiter's semi-major axis is shown in the upper panel of Fig. 9.."," \ref{part1} once the mass of the accreting protoplanet has reached $m_p=1\;M_J$, but we now let the planet evolve under the influence of the disk for $\sim 500$ The time evolution of Jupiter's semi-major axis is shown in the upper panel of Fig. \ref{jupiter}."547" As expected, the planet migrates on a timescale corresponding to Type II migration in the case where Hpz/H=0."," As expected, the planet migrates on a timescale corresponding to Type II migration in the case where $\hdz/H=0$."548" For models with Hpz#0 however, wesee here that, compared with the Saturn case, the dependency of the migration rate upon the value for Hpz is stronger, with a clear tendency for the semi-major axis to decrease more slowly as the size of the dead-zone increases."," For models with $\hdz\ne 0$ however, wesee here that, compared with the Saturn case, the dependency of the migration rate upon the value for $\hdz$ is stronger, with a clear tendency for the semi-major axis to decrease more slowly as the size of the dead-zone increases."549" Examination of the total disk torques, which are represented in the lower panel of Fig. 9,,"," Examination of the total disk torques, which are represented in the lower panel of Fig. \ref{jupiter},"550 clearly reveals that these decrease in magnitude with increasing the size of the dead-zone., clearly reveals that these decrease in magnitude with increasing the size of the dead-zone.551" The outer and inner torques exerted on the planet are displayed in the upper and lower panels of Fig. 10,,"," The outer and inner torques exerted on the planet are displayed in the upper and lower panels of Fig. \ref{torques-jupiter},"552 respectively., respectively.553" Interestingly, and despite a weak dependency on the value for Hpz, the presence of a dead-zone reduces the effects of the outer torques exerted on the planet."," Interestingly, and despite a weak dependency on the value for $\hdz$, the presence of a dead-zone reduces the effects of the outer torques exerted on the planet."554" As illustrated in Fig. 11,,"," As illustrated in Fig. \ref{surface-density},"555" which shows the disk surface density as a function of radius (at an azimuthal position corresponding to that of the planet), this arises because the surface density at the outer edge of the gap is greater in the case where Hpz=0 compared to cases where Hpz>0, increasing the magnitude of the outer torques."," which shows the disk surface density as a function of radius (at an azimuthal position corresponding to that of the planet), this arises because the surface density at the outer edge of the gap is greater in the case where $\hdz=0$ compared to cases where $\hdz>0$, increasing the magnitude of the outer torques."556" Moreover, Fig."," Moreover, Fig."557" 11 reveals that the density in the inner disk is much more higher for the simulation with Hpz=2.3H, which consequently favours the higher positive torque exerted on the planet in this case (see the lower panel of Fig. 10))."," \ref{surface-density} reveals that the density in the inner disk is much more higher for the simulation with $\hdz=2.3H$, which consequently favours the higher positive torque exerted on the planet in this case (see the lower panel of Fig. \ref{torques-jupiter}) )."558" It should benoted that for models with Hpz# 0, and provided that the viscosity is high enough in the live-zone, a migration"," It should benoted that for models with $\hdz\ne 0$ , and provided that the viscosity is high enough in the live-zone, a migration"559ascent red giant that underwent dredge-up only 50 Myr ago: its anomalously low ο ος has appeared imumediatelv. after clredge-up.,ascent red giant that underwent dredge-up only $\sim 50$ Myr ago; its anomalously low $^{12}$ $^{13}$ C has appeared immediately after dredge-up.560 We echo the conclusions of Tautvaisiené(2010a) that extra mixing on the RGB in magneticallv-active low-mass stars like A Ànd and 29 Dra appears to act below the luminosity function bump. in contradiction with current thermohaline mixing models.," We echo the conclusions of \citet{Tautvaisiene.etal:10} that extra mixing on the RGB in magnetically-active low-mass stars like $\lambda$ And and 29 Dra appears to act below the luminosity function bump, in contradiction with current thermohaline mixing models."561 Magnetic flux tube buovant mixing (Bussoetal.2007) would appear to warrant more detailed investigation., Magnetic flux tube buoyant mixing \citep{Busso.etal:07} would appear to warrant more detailed investigation.562" Evolutionary models of tidally-interacting binaries by Denissenkovetal.(2006) (hat. predict large luminosity excursions at the bump might also allow A And to be a 7post-bump"" giant aud alleviate its otherwise precociouslv diminished C isotope ratio.", Evolutionary models of tidally-interacting binaries by \citet{Denissenkov.etal:06b} that predict large luminosity excursions at the bump might also allow $\lambda$ And to be a “post-bump” giant and alleviate its otherwise precociously diminished C isotope ratio.563 Such a mechanism would appear {ο be less promising for wider binaries such as 29 Dra., Such a mechanism would appear to be less promising for wider binaries such as 29 Dra.564 We thank the NASA AISRP for providing financial assistance for the development of the PINTofALE package., We thank the NASA AISRP for providing financial assistance for the development of the PINTofALE package.565 JJD was supported by NASA contract NASS-39073 to theCenter durng the course of this research., JJD was supported by NASA contract NAS8-39073 to the during the course of this research.566 WD was supported by award number AR45002% issued by the X-ray. Center., WB was supported by award number AR4-5002X issued by the X-ray Center.567 JJD thanks LL. Tananbaum and the CXC science team for advice and support., JJD thanks H. Tananbaum and the CXC science team for advice and support.568"Tjo velocity «Ispersion. σε, provides a measure of the total kinetic enerev in the cloud inclusive of thermal. turbulent. rotational. aud expanding motions.","The velocity dispersion, $\sigma_v$, provides a measure of the total kinetic energy in the cloud inclusive of thermal, turbulent, rotational, and expanding motions."569 A scaling relationship between the velocity dispersion aud tle size1 of a clo| was initialv identified by Larson (1981) using data taken from the dierature., A scaling relationship between the velocity dispersion and the size of a cloud was initially identified by Larson (1981) using data taken from the literature.570 A recent compilation ο [data from luaiv studies using several differeut molecular line tracers demonstrates this correlation of velocity. disΟΡΙΟ. With size within [| orders of magnitude in size scale (Falearone 1996)., A recent compilation of data from many studies using several different molecular line tracers demonstrates this correlation of velocity dispersion with size within 4 orders of magnitude in size scale (Falgarone 1996).571 The origin of this relationship has heen attributed to turbulence (Larson 1981: Myers 1983). or simply. a COLSCQUCLICC o: eravitation: decvilibriuni aud constant eas cohmin density which are Imaitedxd by observational selection effects (Scalo 1990).," The origin of this relationship has been attributed to turbulence (Larson 1981; Myers 1983), or simply, a consequence of gravitational equilibrium and constant gas column density which are limited by observational selection effects (Scalo 1990)."572 It isiuportant to distiieui«sli he relationship derived using multitracer observations frou that determined from a siele gas tracer (Cioodnan L998)., It is important to distinguish the relationship derived using multitracer observations from that determined from a single gas tracer (Goodman 1998).573 The excitatio1 requirenits for a given molecule determine the angular exteit over Wwich any object can be identified., The excitation requirements for a given molecule determine the angular extent over which any object can be identified.574 M1]titracer olservations sample different density reeinies which οςX0YOspo to distinct. but neste. volumes of material.," Multitracer observations sample different density regimes which correspond to distinct, but nested, volumes of material."575 Iu this wax. a larger dynamic raiege of sizes is prolIOC than c1 be suuple« Dy ay siiele gas tracer.," In this way, a larger dynamic range of sizes is probed than can be sampled by any single gas tracer."576 The correlation between veocity dispersiou aud size las bee restablired for sinele eas tracers but over a nore limited rauge of sizes aud larger iutriusic scater (Larson 1981: Dine 195τι Solomon 1987)., The correlation between velocity dispersion and size has been established for single gas tracers but over a more limited range of sizes and larger intrinsic scatter (Larson 1981; Dame 1987; Solomon 1987).577 These sugle tracer relatiouships exaiuiue he varkution of the velocity (lspersk nwlilh size witim a more limited range of density., These single tracer relationships examine the variation of the velocity dispersion with size within a more limited range of density.578 Fieure 6 presenS he varlation ¢X velcity disversion with the effective radius. à. for the ensemble of clotids intus studs.," Figure \ref{vw-r} presents the variation of velocity dispersion with the effective radius, $r_e$, for the ensemble of clouds in this study."579 EK nore effectivev cousolidate t1ο infornation. the mean veocity dispersion is calculated within binned cd radi.," To more effectively consolidate the information, the mean velocity dispersion is calculated within binned cloud radii."580 For objecs withsizes €reater than ~7 pc. there is a teucency for iucreasus velocity dispersion Wihn size.," For objects withsizes greater than $\sim$ 7 pc, there is a tendency for increasing velocity dispersion with size."581 T1ο slope oft16 power aw fit to objecs with radi ereater than 9 pc is 70.5 and simular te| that derived by Solomon {198n, The slope of the power law fit to objects with radii greater than 9 pc is $\sim$ 0.5 and similar to that derived by Solomon (1987).582 However. the biuned vales show little svsenc variation of the veocitv dispersion with size OY ry i pc.," However, the binned values show little systemic variation of the velocity dispersion with size for $r_e <$ 7 pc."583 The appareit flatening of the relationship for s1uall clouds is not zu artifact of our cloud deuitio slwee df occurs at a velcity dispersion. for which our luehock is reasonadv accurate (see Appendix D)., The apparent flattening of the relationship for small clouds is not an artifact of our cloud definition since it occurs at a velocity dispersion for which our method is reasonably accurate (see Appendix B).584 A liied uber o: followup observations with much ligicr spectral resoluion of narrow line width clods ideutified in the catalog show comparable velocity dis)ersions (see Appexlix D)., A limited number of followup observations with much higher spectral resolution of narrow line width clouds identified in the catalog show comparable velocity dispersions (see Appendix B).585 A population of sal cloucs with line widths below our threshold for cloud idetification which do follow the standard relationship cau not be exclued., A population of small clouds with line widths below our threshold for cloud identification which do follow the standard relationship can not be excluded.586 However. our observations have ideified nuu stall clouds with line widths in exCONS ο the extrapolated size line-widthli relationship of Sokmuon (1987).," However, our observations have identified many small clouds with line widths in excess of the extrapolated size line-width relationship of Solomon (1987)."587 This result does not dismiss t1e velocity dispersiosize relatiouship determined from nuutitracer observa1015., This result does not dismiss the velocity dispersion-size relationship determined from multitracer observations.588 Narrow line width reeious witli1 molecular οouds are identified from tracers of lig1 density gas Πο CS. IICN) aud these often ollow he couveutiowl scaling law (Myers 1983).," Narrow line width regions within molecular clouds are identified from tracers of high density gas $_3$, CS, HCN) and these often follow the conventional scaling law (Myers 1983)."589 Such PC@IOUS are nof reacily identified by OOr eolussion., Such regions are not readily identified by or emission.590 Previous CO studies which have ideutifi« a size line width scaling law have been limited to large. self eravitatiug clotd complexes with masses ercater than 101 ((Solomon 1987. Scoville 1987).," Previous CO studies which have identified a size line width scaling law have been limited to large, self gravitating cloud complexes with masses greater than $^4$ (Solomon 1987, Scoville 1987)."591 The ucar coustaut velocity dispersion with size for the small cloud or clunip populatio iluav reflect a different dynamical state than the larger giant iiolecular cloud complexes (seo ] [INH2)., The near constant velocity dispersion with size for the small cloud or clump population may reflect a different dynamical state than the larger giant molecular cloud complexes (see $\S$ 3.2).592 To evaluate the role of self eravitv iu the equilibriun of the ideutified molecular regions. we determine the iuaenitude of the virial mass with respect to the measured mass of the object derived from the CO luminosity.," To evaluate the role of self gravity in the equilibrium of the identified molecular regions, we determine the magnitude of the virial mass with respect to the measured mass of the object derived from the CO luminosity."593 Following Bertoldi MelIxee (1992). the virial mass. Mj. Is calculated from the measured cloud parameters.," Following Bertoldi McKee (1992), the virial mass, $M_{vir}$ , is calculated from the measured cloud parameters,"594Following Tremaine Weinbere (198D). the radial part of the perturbing potential is expanded im terms of the basis function ut and each resulting term is expressed in the form HOVyO.0) asa Fourier series iu the angle variables w.,"Following Tremaine Weinberg (1984), the radial part of the perturbing potential is expanded in terms of the basis function $u^l_i$ and each resulting term is expressed in the form $u^l_{i}(r)Y_{lm}(\theta,\phi)$ as a Fourier series in the angle variables ${\bf w}$."595 We finally obtain: where aud 9, We finally obtain: where and .596445) The angle 3 is the inclination of the orbital plane to the equatorial plane aud έν(3)j are the compoucuts of tle rotation matrices (see e.g. Γαμος 196;, The angle $\beta$ is the inclination of the orbital plane to the equatorial plane and $r^l_{\g_2\g_3}(\beta)$ are the components of the rotation matrices (see e.g. Edmonds 1960).597 Sinilulv. we can express the perturbing aud the response potential iu the form yew For the perturbing potential. each cocfiicicut Ta(f£) can be expressed asthe product of a time-indepeudent coefficient. bi und a fiction of time depending oulv on 7 aud 353. g(t).," Similarly, we can express the perturbing and the response potential in the form _j. For the perturbing potential, each coefficient $a^j_{l\g_3}(t)$ can be expressed asthe product of a time-independent coefficient, $b^j_{l\g_3}$, and a function of time depending only on $l$ and $\g_3$, $g_{l\g_3}(t)$."598" The functional fori of gj4,(f) can be easily derived for any value of / and 553 using. equation. . (À2)).", The functional form of $g_{l\g_3}(t)$ can be easily derived for any value of $l$ and $\g_3$ using equation \ref{eq3}) ).599 For example. for. r«R. 1=.2 and 55=.2. one finds. go»=cos’aO(f)ojZO) Equation (A)) now takes the form For self-cousisteucv. the response density. which is obtained by intcerating equation (À7)) over the velocity coordinates. pi77. aust be equal to the density pi determined by the Poissou's equation with $4=917.," For example, for $r<R$, $l=2$ and $\g_3=2$, one finds $600g_{22}=\cos^3\Theta(t)e^{-2i\Theta(t)}.601$ Equation \ref{lftr}) ) now takes the form For self-consistency, the response density, which is obtained by integrating equation \ref{lftr1}) ) over the velocity coordinates, $\rho_1^{resp}$, must be equal to the density $\rho_1^{P}$ determined by the Poisson's equation with $\Phi_1=\Phi_1^{resp}$."602 huposiug the couditionpiresp. uuiltiplving both sides of equatiou(A.2)) by 1)dl and iuteeratius over the spatial coordinates. we obtain the following equation forthe coefficieuts )," Imposing the condition, multiplying both sides of \ref{cons}) ) by $Y_{l\g_3}^*u^l_i$ and integrating over the spatial coordinates, we obtain the following equation forthe coefficients ."603]- Equivaleutly. this way be written as a matrix equation: where the eleineuts of the matrix ΝΕ(5) are defined as," Equivalently, this may be written as a matrix equation: where the elements of the matrix ${\bf M}_{l\g_3}(s)$ are defined as"604We refer to (he term in equation (4)) proportional to m as the dipole field. and the terms in equations (3)) and (4)) proportional to m and m as the inductive and radiative terms. respectively.,"We refer to the term in equation \ref{Eind4}) ) proportional to ${\bi m}$ as the dipole field, and the terms in equations \ref{Eind3}) ) and \ref{Eind4}) ) proportional to ${\dot{\bi m}}$ and ${\ddot{\bi m}}$ as the inductive and radiative terms, respectively."605 In the following discussion. (he radiative ternis are ignored. except where stated otherwise: for most purposes thev can be combined with the inductive ternis.," In the following discussion, the radiative terms are ignored, except where stated otherwise; for most purposes they can be combined with the inductive terms."606 The magnetic field depends on (ime. with —aulE(.x)-—. |. and it has a nonzero curl: r?c].," The magnetic field depends on time, with ) ], and it has a nonzero curl: ]."607 For a dipole rotating with angular velocity w. one has-—-uwlimesm.. wlimest(wlimesm)). m)).," For a dipole rotating with angular velocity $\bomega$, one has, ), )]."608 Of particular interest in the following are the parallel ancl perpendicular components of the inductive field. where by ‘parallel’ we mean along the dipolar field lines.," Of particular interest in the following are the parallel and perpendicular components of the inductive field, where by `parallel' we mean along the dipolar field lines."609 The parallel component is, The parallel component is610"Following this adopted intrinsic distribution we inject 20000 sources in each of the images, for 60 equal redshift steps between z=0.0 and z=6.0.","Following this adopted intrinsic distribution we inject $20\,000$ sources in each of the images, for 60 equal redshift steps between $z=0.0$ and $z=6.0$."611" To verify that the injected sources do not significantly influence each other by blending, nor that the background is influenced significantly, we perform the following tests."," To verify that the injected sources do not significantly influence each other by blending, nor that the background is influenced significantly, we perform the following tests."612" We inject the same 20000 sources in 4 stages, 5000 sources each, and do a third analysis where we inject 100000 sources in total."," We inject the same $20\,000$ sources in 4 stages, 5000 sources each, and do a third analysis where we inject $100\,000$ sources in total."613 In Fig., In Fig.614" 5 the recovered fractions of sources that also satisfy our g-dropout criteria are shown as a function of magnitude, for one particular redshift step."," \ref{fig:consistencycheck2} the recovered fractions of sources that also satisfy our $g$ -dropout criteria are shown as a function of magnitude, for one particular redshift step."615" Only for faint magnitudes does the 100000 curve deviate from the other ones, which are identical in this regime."," Only for faint magnitudes does the $100\,000$ curve deviate from the other ones, which are identical in this regime."616 In Fig., In Fig.617 6 the distribution of recovered with an intrinsic magnitude of m=25.0 is shown as a function of recovered magnitude., \ref{fig:consistencycheck3} the distribution of recovered with an intrinsic magnitude of $m=25.0$ is shown as a function of recovered magnitude.618 We conclude that the injection of 20000 sources does not influence the images such that the photometry would be perturbed significantly.," We conclude that the injection of $20\,000$ sources does not influence the images such that the photometry would be perturbed significantly."619 A similar behaviour is expected for the u- and r-dropout samples., A similar behaviour is expected for the $u$ - and $r$ -dropout samples.620 The clustering of LBGs is not taken into account., The clustering of LBGs is not taken into account.621" We assume this effect to be insignificant for estimating completeness, as the correlation length, which is typically around 5 Mpc (?), is very small compared to the survey volume."," We assume this effect to be insignificant for estimating completeness, as the correlation length, which is typically around 5 Mpc \citep{hildebrandt09a}, is very small compared to the survey volume."622 Therefore we spread our simulated sources uniformly over the images., Therefore we spread our simulated sources uniformly over the images.623" Next we define the function p(m,z) to be the number of sources recovered with an observed magnitude in the interval [m;m+Am], and are selected as dropouts, divided by the number of injected sources with an intrinsic magnitude in the same interval [m;m+Am] and a redshift in the interval [z;z+Az]."," Next we define the function $p(m,z)$ to be the number of sources recovered with an observed magnitude in the interval $[m;m+\Delta m]$, and are selected as dropouts, divided by the number of injected sources with an intrinsic magnitude in the same interval $[m;m+\Delta m]$ and a redshift in the interval $[z;z+\Delta z]$."624" Note that the definition of p(m,z) is slightly different compared to the one used in e.g. ?,, as they do not take Eddington bias into account."," Note that the definition of $p(m,z)$ is slightly different compared to the one used in e.g. \citet{st2}, as they do not take Eddington bias into account."625" In our definition, p(m,z) could potentially be > 1 as a result of this bias correction."," In our definition, $p(m,z)$ could potentially be $>$ 1 as a result of this bias correction."626" The effective volumes (Vg) of our survey are given by where A; is. the field area in. square arcminutes,. and 777dVc is; the comoving volume per square arcminute, which depends on the adopted cosmology."," The effective volumes $V_{\rm{eff}}$ ) of our survey are given by where $A_{f}$ is the field area in square arcminutes, and $\frac{dV_{\rm{C}}}{dz}$ is the comoving volume per square arcminute, which depends on the adopted cosmology."627"contribution from the shielded cold dust component is in agreement with the analysis by Gallianoetal.(2005),, there is quantitative difference between our results and theirs.","contribution from the shielded cold dust component is in agreement with the analysis by \citet{galliano05}, there is quantitative difference between our results and theirs."628" Gallianoetal.(2005) adopted QabsοςA? at A>100 jum. If the absorption efficiency is normalized to the value at λ=100 jum, the absorption efficiency adopted in this paper (equation 3)) is 2 times larger than that used in Gallianoetal.(2005) at A=850 yum. Therefore, we require less very cold dust component than Gallianoetal.(2005) by a factor of 2."," \citet{galliano05} adopted $Q_\mathrm{abs}\propto\lambda^{-2}$ at $\lambda >100~\mu$ m. If the absorption efficiency is normalized to the value at $\lambda =100~\mu$ m, the absorption efficiency adopted in this paper (equation \ref{eq:reach}) ) is 2 times larger than that used in \citet{galliano05} at $\lambda =850~\mu$ m. Therefore, we require less very cold dust component than \citet{galliano05} by a factor of 2."629" In this paper, we have adopted a common FIR dust optical properties; that is, we have applied the same absorption efficiency Qabs and grain size distribution as adopted in our previous model for the Milky Way and the Magellanic Clouds (HHS07)."," In this paper, we have adopted a common FIR dust optical properties; that is, we have applied the same absorption efficiency $Q_\mathrm{abs}$ and grain size distribution as adopted in our previous model for the Milky Way and the Magellanic Clouds (HHS07)."630 The same dust optical properties are also consistent with the FIR colours of BCDs., The same dust optical properties are also consistent with the FIR colours of BCDs.631 Hibietal.(2006) and HHS07 also argue that those dust optical properties also provide a good statistical fit to the FIR colours of nearby galaxies., \cite{hibi06} and HHS07 also argue that those dust optical properties also provide a good statistical fit to the FIR colours of nearby galaxies.632" Therefore, we suggest that the absorption efficiency in the form of equation (3)), which Reachal.(1995) adopted to fit the dust emission spectra in the Milky Way, is generally applicable in galactic environments."," Therefore, we suggest that the absorption efficiency in the form of equation \ref{eq:reach}) ), which \citet{reach95} adopted to fit the dust emission spectra in the Milky Way, is generally applicable in galactic environments."633" As shown above, the submm emission from nearby galaxies can also be explained by the same dust emissivity."," As shown above, the submm emission from nearby galaxies can also be explained by the same dust emissivity."634 It is also important to stress that the classical dust emissivity model by Draine&Lee(1984) cannot explain the FIR colour-colour relation of the nearby galaxies (Hibietal.2006;; HHS07)., It is also important to stress that the classical dust emissivity model by \citet{draine84} cannot explain the FIR colour--colour relation of the nearby galaxies \citealt{hibi06}; HHS07).635" As indicated by the emissivity assumed by Reachetal.(1995), it is better to adopt 8~1 for 100wmSAA1~200 um rather than to assume 3~2 in the entire FIR wavelength range longer than 100 jum. Some amorphous materials indeed show 3« (e.g.Agladzeetal. 1996)."," As indicated by the emissivity assumed by \citet{reach95}, it is better to adopt $\beta\sim 1$ for $100~\mu\mathrm{m}\la\lambda\la\lambda_1\sim 200~\mu$ m rather than to assume $\beta\sim 2$ in the entire FIR wavelength range longer than 100 $\mu$ m. Some amorphous materials indeed show $\beta <2$ \citep[e.g.][]{agladze96}."636. Amorphous grains are expected to form2 by the irradiation of cosmic rays (Jageretal.2003)., Amorphous grains are expected to form by the irradiation of cosmic rays \citep{jager03}.637. Theoretically the break of the dust emissivity at ; might be associated with the energy splitting of the ground state because of irregular amorphous structure., Theoretically the break of the dust emissivity at $\lambda_1$ might be associated with the energy splitting of the ground state because of irregular amorphous structure.638" Menyetal.(2007) show that the absorption coefficient of amorphous dust has a break at À~Am, which corresponds to the cut-off energy hwm of the energy splitting due to the amorphous structure (wm= 27c/Am)."," \citet{meny07} show that the absorption coefficient of amorphous dust has a break at $\lambda\sim\lambda_\mathrm{m}$, which corresponds to the cut-off energy $\hbar\omega_\mathrm{m}$ of the energy splitting due to the amorphous structure $\omega_\mathrm{m}\equiv 2\pi c/\lambda_\mathrm{m}$ )."639" Therefore, a possible interpretation is that Am~A1."," Therefore, a possible interpretation is that $\lambda_\mathrm{m}\sim\lambda_1$."640" Since Menyetal.(2007) suggest Am~700 µπι based on experimental data, the cut-off energy corresponding to Am200 um may be too high."," Since \citet{meny07} suggest $\lambda_\mathrm{m}\sim 700~\mu$ m based on experimental data, the cut-off energy corresponding to $\lambda_\mathrm{m}\sim 200~\mu$ m may be too high."641 Nevertheless it is still worth investigating amorphous materials with higher cut-off energy as a candidate of cosmic dust., Nevertheless it is still worth investigating amorphous materials with higher cut-off energy as a candidate of cosmic dust.642" We have investigated the properties of FIR emission of a sample of BCDs observed byAKARL, especially focusing on FIR colours and dust temperature."," We have investigated the properties of FIR emission of a sample of BCDs observed by, especially focusing on FIR colours and dust temperature."643" We have utilized the data at A=65 uum, 90 um, and 140 jum, and have examined the relation between 60 µπι--100 jum colour, (60/100), and 140 µπι--100 um colour (140/100)4."," We have utilized the data at $\lambda =65~\mu$ m, 90 $\mu$ m, and 140 $\mu$ m, and have examined the relation between 60 $\mu$ m–100 $\mu$ m colour, $(60/100)_\mathrm{cl}$, and 140 $\mu$ m–100 $\mu$ m colour $(140/100)_\mathrm{cl}$."644" Then, we have found that the FIR colours of the BCDs are located at a natural high-temperature extension of the DIRBE data of the Milky Way, the LMC and the SMC on the colour-colour diagram."," Then, we have found that the FIR colours of the BCDs are located at a natural high-temperature extension of the DIRBE data of the Milky Way, the LMC and the SMC on the colour–colour diagram."645" We have explained the FIR colours also theoretically by assuming the same absorption efficiency, which may be appropriate for amorphous dust grains, and the same grain size distribution as the Milky Way dust."," We have explained the FIR colours also theoretically by assuming the same absorption efficiency, which may be appropriate for amorphous dust grains, and the same grain size distribution as the Milky Way dust."646 We have also shown that it is not easy to distinguish between a large dust optical depth and a low dust temperature only with FIR colours although addition of submillimetre data relax this degeneracy., We have also shown that it is not easy to distinguish between a large dust optical depth and a low dust temperature only with FIR colours although addition of submillimetre data relax this degeneracy.647" In order to examine if the dust optical depth plays an important role in determining the dust temperature, we have investigated the correlation between FIR colour (dust temperature) and dust-to-gas ratio."," In order to examine if the dust optical depth plays an important role in determining the dust temperature, we have investigated the correlation between FIR colour (dust temperature) and dust-to-gas ratio."648 We have found that the dust temperature tends to become high as the dust-to-gas ratio decreases as would be expected from, We have found that the dust temperature tends to become high as the dust-to-gas ratio decreases as would be expected from649Iower than the two highest frequencies of the observed peaks.,lower than the two highest frequencies of the observed peaks.650 A more realistic atmosphere might have a higher value than this. which itself is higher than the value for the Ecelington erev atmosphere quoted in Table 2 ancl used by ((2000).," A more realistic atmosphere might have a higher value than this, which itself is higher than the value for the Eddington grey atmosphere quoted in Table 2 and used by (2000)."651 The amplitudes: of stochastically excited nonraclial modes. including those that are most ellicientIy. trapped in the acoustic cavity. are expected to have values much lower than those of corresponding radial modes.," The amplitudes of stochastically excited nonradial modes, including those that are most efficiently trapped in the acoustic cavity, are expected to have values much lower than those of corresponding radial modes."652 Equation (20) applies to nonracdial moces if the contributions to fy and 1 from the e-mocde propagation zone are included., Equation (20) applies to nonradial modes if the contributions to $I_{\rm n}$ and $D$ from the g-mode propagation zone are included.653" The values ofboth Jy and 2, are substantially larger than those plotted in the lower panels of Fig.", The values of both $I_{\rm n}$ and $D_{\rm g}$ are substantially larger than those plotted in the lower panels of Fig.654 2 and 3. owing to the damping elfect in the outer lavers.," 2 and 3, owing to the damping effect in the outer layers."655 The results of the stability analvsis presented in Section 4.1 seem to exclude an interpretation of the low-frequency part of the a UMa oscillation spectrum in terms of self-excited modes.," The results of the stability analysis presented in Section 4.1 seem to exclude an interpretation of the low-frequency part of the $\alpha\,$ UMa oscillation spectrum in terms of self-excited modes."656 Indeed. the damping effect of convection exceeds by a large margin the driving ellect of the opacity perturbation.," Indeed, the damping effect of convection exceeds by a large margin the driving effect of the opacity perturbation."657 However. there still seems to be a greater chance for an interpretation in ternis of Mira-like excitation than in terms of solar-like excitation.," However, there still seems to be a greater chance for an interpretation in terms of Mira-like excitation than in terms of solar-like excitation."658 “Phe trend of calculated. amplitudes is determined mainly by the factor Z4 Haa equation (21). which is the most. reliably calculated quantity in. the expression.," The trend of calculated amplitudes is determined mainly by the factor $I_{\rm n}^{-1/2}$ in equation (21), which is the most reliably calculated quantity in the expression."659" One may contemplate that for the first three modes 0), is really much lower than what we calculated. but this option would require near cancellation of damping and driving ellects: it is more plausible that the quantity is less than zero and that the modes are unstable."," One may contemplate that for the first three modes $D_{\rm p}$ is really much lower than what we calculated, but this option would require near cancellation of damping and driving effects; it is more plausible that the quantity is less than zero and that the modes are unstable."660 Ehe option that remains is an increase of A747 by [our to six orders ο maenitucle., The option that remains is an increase of $\lambda^2E$ by four to six orders of magnitude.661 Whatever is the correct. answer. the required. changes are bound to be related to the way in which we trea 16 interaction between pulsation ancl convection.," Whatever is the correct answer, the required changes are bound to be related to the way in which we treat the interaction between pulsation and convection."662 Our reatment. like most of those that have been used. is based on the mixine-leneth formalism. and we know tha it is an inadequate tool for describing the mean properties of convection.," Our treatment, like most of those that have been used, is based on the mixing-length formalism, and we know that it is an inadequate tool for describing the mean properties of convection."663 In studies of acoustic mode damping: au excitation we have to consider more detailed aspects of the vnamies of convection., In studies of acoustic mode damping and excitation we have to consider more detailed aspects of the dynamics of convection.664 The alternative is a hvedrodynamica simulation., The alternative is a hydrodynamical simulation.665 This has already. been applied. to solar raclia oscillations by c.g. Stein ancl Nordlund (2001)., This has already been applied to solar radial oscillations by e.g. Stein and Nordlund (2001).666 Lt is to be roped that before long this approach will become applicable ο red-giant oscillations too., It is to be hoped that before long this approach will become applicable to red-giant oscillations too.667 Low could. future observational work on recl-giant variability help us?, How could future observational work on red-giant variability help us?668 One possibility is the disproof of genuine »ulsations in a WAla and in other red giants.," One possibility is the disproof of genuine pulsations in $\alpha\,$ UMa and in other red giants."669 Short-term variability could be a cireet manifestation of convection. like arge-scale eranulation.," Short-term variability could be a direct manifestation of convection, like large-scale granulation."670 This would result in progress being slow: compare how much we have learned in the past. from he Sun's eranulation with what we have learned [rom its oscillations., This would result in progress being slow: compare how much we have learned in the past from the Sun's granulation with what we have learned from its oscillations.671 One very promising observational approach to the solar- Mira-like. alternatives is repeating the analvsis of ((1997) NLACTIO data with a much longer time base or of extensive data from another microlensing projects such as OGLE 11997)., One very promising observational approach to the solar-like Mira-like alternatives is repeating the analysis of (1997) MACHO data with a much longer time base or of extensive data from another microlensing projects such as OGLE 1997).672 Much. improved frequeney and. amplitude resolution is expected., Much improved frequency and amplitude resolution is expected.673 Showing that the ridges extend from a few days to hundreds of davs with a continuous zumplitude increase might strengthen the Mira-like interpretation., Showing that the ridges extend from a few days to hundreds of days with a continuous amplitude increase might strengthen the Mira-like interpretation.674 Other observational evidence supporting a Alira-like interpretation would be the identification of nonracial modes., Other observational evidence supporting a Mira-like interpretation would be the identification of nonradial modes.675 We have seen in Section 3 that if radial modes are unstable some (=1 and 2 modes should be unstable too., We have seen in Section 3 that if radial modes are unstable some $\ell=1$ and 2 modes should be unstable too.676 Η the modes are stable. then. as we cliseussed at the end of Section 4.2. nonradial modes will be excited stochastically. but their amplitudes will be much lower than those of their racial counterparts.," If the modes are stable, then, as we discussed at the end of Section 4.2, nonradial modes will be excited stochastically, but their amplitudes will be much lower than those of their radial counterparts."677 Lt could be possible that low-order modes in à UMa are Mira-like whilst those of higher order are solar-like.," It could be possible that low-order modes in $\alpha\,$ UMa are Mira-like whilst those of higher order are solar-like."678 This could also be the case for the multiperiodic M-type giants found. by Koen and. Laney (2000)., This could also be the case for the multiperiodic M-type giants found by Koen and Laney (2000).679 In. some of these stars the frequency ratio exceeds 10. and there is no doubt that the highest frequencies exceed the acoustic eut-olf frequeney.," In some of these stars the frequency ratio exceeds 10, and there is no doubt that the highest frequencies exceed the acoustic cut-off frequency."680 Two of the peaks in a UM as we have already. noted. are also above the acoustic cut-olf frequency. but that does not necessarily produce pulsational stability (ef.," Two of the peaks in $\alpha\,$ UMa, as we have already noted, are also above the acoustic cut-off frequency, but that does not necessarily produce pulsational stability (cf."681 22001) Reearcdless of what the excitation. mechanism is. the data on normal-mocdoe frequencies will be very useful as a constraint on stellar. parameters and. models.," 2001) Regardless of what the excitation mechanism is, the data on normal-mode frequencies will be very useful as a constraint on stellar parameters and models."682 Prospects of detecting nonradial modes is particularly interesting in this Context., Prospects of detecting nonradial modes is particularly interesting in this context.683 Alost of this work was carried out while WAD was a lawvmond anc Beverly Sackler Foundation Astronomer at the Institute of Astronomy. Cambridge.," Most of this work was carried out while WAD was a Raymond and Beverly Sackler Foundation Astronomer at the Institute of Astronomy, Cambridge."684 Research of WAD ancl RS is supported in part by the Polish grant IKRBN 5PO3D 030 20., Research of WAD and RS is supported in part by the Polish grant KBN 5P03D 030 20.685 GILL is grateful for the support of the Ulx Particle Physics and Astronomy Research Council., GH is grateful for the support of the UK Particle Physics and Astronomy Research Council.686is a predefined accretion radius that is set independently from the initial sink particle radius.,is a predefined accretion radius that is set independently from the initial sink particle radius.687" In practice, only ~200 mesh-generating points are removed during this step, since the spatial resolution around the sink particle decreases at larger radii."," In practice, only $\simeq 200$ mesh-generating points are removed during this step, since the spatial resolution around the sink particle decreases at larger radii."688" The sink particle is placed at the center of mass of the removed cells with a velocity determined by linear momentum conservation, while the angular momentum and internal energy of the gas are discarded."," The sink particle is placed at the center of mass of the removed cells with a velocity determined by linear momentum conservation, while the angular momentum and internal energy of the gas are discarded."689" The additional factor 1/3 in the gravitational softening is used to avoid artificial fragmentation, which might occur if gravitational forces on the gas are reduced on the scale of the accretion radius."," The additional factor $1/3$ in the gravitational softening is used to avoid artificial fragmentation, which might occur if gravitational forces on the gas are reduced on the scale of the accretion radius."690 Accretion onto existing sink particles occurs if the mesh-generating point associated with a candidate cell falls within the accretion radius racc of the sink particle it is most bound to., Accretion onto existing sink particles occurs if the mesh-generating point associated with a candidate cell falls within the accretion radius $r_{\rm acc}$ of the sink particle it is most bound to.691" This method exploits the Lagrangian nature of the mesh-generating points, and yields the (incremental) rate at which mass flows onto sink particles."," This method exploits the Lagrangian nature of the mesh-generating points, and yields the (incremental) rate at which mass flows onto sink particles."692" We have also tested an implementation with a more stringent criterion, where in addition to being bound to the sink particle, the semimajor axis of the respective two-body system must fall below the accretion"," We have also tested an implementation with a more stringent criterion, where in addition to being bound to the sink particle, the semimajor axis of the respective two-body system must fall below the accretion"693acceleration of the shock wave through the exponentially decaying density profile of the progenitor star.,acceleration of the shock wave through the exponentially decaying density profile of the progenitor star.694 These layers in mass) (0.01-0.1are set into high-velocity and are not homologously expanding (seealsoUtrobin2004;Woosley," These layers (0.01-0.1 in mass) are set into high-velocity and are not homologously expanding \citep[see also][]{utrobin04,woosley88}."695" During the first ~10-20 days after the explosion, the 1988)..photosphere is located in this shell, which is then cooler and has a higher velocity than the bulk of the ejecta."," During the first $\sim$ 10-20 days after the explosion, the photosphere is located in this shell, which is then cooler and has a higher velocity than the bulk of the ejecta."696 This results in a different evolution of the photospheric temperature and velocity., This results in a different evolution of the photospheric temperature and velocity.697" A better agreement during this phase is found with the semi-analytic code, that adopts a uniform density distribution."," A better agreement during this phase is found with the semi-analytic code, that adopts a uniform density distribution."698" Some disagreement is present also at late-times (> 80-110 that is probably related to differences in the treatmentdays), of ionization balance and in the adopted opacities (including the opacity floor)."," Some disagreement is present also at late-times $\gtrsim$ 80-110 days), that is probably related to differences in the treatment of ionization balance and in the adopted opacities (including the opacity floor)."699" Despite the limitations of our simplified initial conditions, also the comparison with the bolometric light curve of SN 19874 is satisfactory."," Despite the limitations of our simplified initial conditions, also the comparison with the bolometric light curve of SN 1987A is satisfactory."700" We are able to reproduce its main features (peak luminosity and phase at maximum) with models having initial radius of 3x1013 cm, total initial energy of 1 foe, amount of equal to 0.07Mo,, and envelope mass ranging between 16 and 18 (models (1) and (2) in Figures 10 and 11))."," We are able to reproduce its main features (peak luminosity and phase at maximum) with models having initial radius of $3\times10^{12}$ cm, total initial energy of $1$ foe, amount of equal to $0.07$, and envelope mass ranging between 16 and 18 (models (1) and (2) in Figures \ref{fig:LC87A} and \ref{fig:VT87A}) )."701 The agreement can be considered satisfactory also because we did not perform any “fine-tuning” of the initial composition which is typically needed in order to accurately reproduce the observed shape (width and rise to peak) of the bolometric light curve of SN 1987A Woosley1988;Utrobin2004).," The agreement can be considered satisfactory also because we did not perform any “fine-tuning” of the initial composition which is typically needed in order to accurately reproduce the observed shape (width and rise to peak) of the bolometric light curve of SN 1987A \citep[e.g.][]{woosley88,utrobin04}."702. Further residual differences(e.g. may also be caused by the absence of non-thermal ionization from gamma rays in our models., Further residual differences may also be caused by the absence of non-thermal ionization from gamma rays in our models.703" The time evolution of the photospheric velocity and temperature of SN 1987A is also well reproduced by models (1) and (2), apart from the differences in the early and the late-time evolution due to the same reasons mentioned above."," The time evolution of the photospheric velocity and temperature of SN 1987A is also well reproduced by models (1) and (2), apart from the differences in the early and the late-time evolution due to the same reasons mentioned above."704" Moreover, as can be seen from Figure 10,, the luminosity in the radioactive tail predicted by the model is lower than the observed one."," Moreover, as can be seen from Figure \ref{fig:LC87A}, the luminosity in the radioactive tail predicted by the model is lower than the observed one."705 This is a consequence of fallback occurring during the evolution., This is a consequence of fallback occurring during the evolution.706" We found that the innermost 0.01 of the envelope, containing ~2.4x10? of9Ni, have been accreted onto the central remnant."," We found that the innermost $\sim0.01$ of the envelope, containing $\sim 2.4\times10^{-3}$ of, have been accreted onto the central remnant."707" To give a general overview of the post-explosion evolution of a “typical” CC-SN, we focus on the properties of our model (13) that has rather common initial parameters."," To give a general overview of the post-explosion evolution of a “typical” CC-SN, we focus on the properties of our model (13) that has rather common initial parameters."708 The evolution is determined by the thermodynamics of the expanding ejecta., The evolution is determined by the thermodynamics of the expanding ejecta.709 The internal energy deposited by the shock wave and that released by gamma-ray radioactive decays are used to expand the ejecta and power light curve., The internal energy deposited by the shock wave and that released by gamma-ray radioactive decays are used to expand the ejecta and power light curve.710 The evolution is characterized by three phases in which different heating and emission mechanisms dominate., The evolution is characterized by three phases in which different heating and emission mechanisms dominate.711" During the first phase (diffusive phase), the envelope is completely ionized and optically thick, and the emission is due to the release of internal energy on a diffusion timescale."," During the first phase (diffusive phase), the envelope is completely ionized and optically thick, and the emission is due to the release of internal energy on a diffusion timescale."712" In the second phase (recombination phase), the ejecta are recombining and the emission is dominated by the sudden release of energy caused by the receding motion of the wavefront through the envelope."," In the second phase (recombination phase), the ejecta are recombining and the emission is dominated by the sudden release of energy caused by the receding motion of the wavefront through the envelope."713" During the last phase (radioactive-decay phase or radioactive tail, the envelope is recombined and optically thin to optical photons, and the emission comes from the thermalization of the energy deposited by gamma-ray photons."," During the last phase (radioactive-decay phase or radioactive tail), the envelope is recombined and optically thin to optical photons, and the emission comes from the thermalization of the energy deposited by gamma-ray photons."714" Observationally, the first two phases coincide with what is usually defined the plateau or photopheric phase, while the last phase is referred to as nebular phase."," Observationally, the first two phases coincide with what is usually defined the plateau or photopheric phase, while the last phase is referred to as nebular phase."715" Figures 12 through 14 showthe physical properties of model (13) at three different times, taken to be representative of the aforementioned three phases."," Figures \ref{fig:modB_18d} through \ref{fig:modB_130d} showthe physical properties of model (13) at three different times, taken to be representative of the aforementioned three phases."716" Moreover Figures 15 through 18 show the evolution of the photopheric radius, and the radial profiles of the photospheric velocity and temperature in more detail."," Moreover Figures \ref{fig:modB_TvsR} through \ref{fig:modB_radius} show the evolution of the photopheric radius, and the radial profiles of the photospheric velocity and temperature in more detail."717" During the first phase (<35 days), the radiation diffusion time-scale is much longer than the expansion time-scale, and the cooling induced by photon diffusion is negligible."," During the first phase $\la 35$ days), the radiation diffusion time-scale is much longer than the expansion time-scale, and the cooling induced by photon diffusion is negligible."718" Although the internal energy decreases because of expansion, the temperature and the density are sufficiently high that the envelope remains completely ionized and optically thick (Figures 12,, 15 and 16))."," Although the internal energy decreases because of expansion, the temperature and the density are sufficiently high that the envelope remains completely ionized and optically thick (Figures \ref{fig:modB_18d}, , \ref{fig:modB_TvsR} and \ref{fig:modB_TvsM}) )."719" The photopheric radius, which is located in the outermost"," The photopheric radius, which is located in the outermost"720&reat value to any study involving the evolution of the substructure population of cold dark matter halos.,great value to any study involving the evolution of the substructure population of cold dark matter halos.721 To facilitate their use in this way we provide a simple fitting function which describes he two-dimensional clistribution of orbital velocities., To facilitate their use in this way we provide a simple fitting function which describes the two-dimensional distribution of orbital velocities.722 Through simple variable transformations this function also describes the distributions of substructure energies. angular momenta. eccentricities etc.," Through simple variable transformations this function also describes the distributions of substructure energies, angular momenta, eccentricities etc."723 We find that our measured. two-climmensional distributions o£ orbital velocities can be reasonably well fit with the following fitting function: where Note that this has a form similar to a two-dimensional Alaxwell-Boltzmann distribution for the tangential velocity and a Ciaussian for the raclial velocity. as might be expected rom the results of Vitvitskactal.(2002).," We find that our measured two-dimensional distributions of orbital velocities can be reasonably well fit with the following fitting function: where Note that this has a form similar to a two-dimensional Maxwell-Boltzmann distribution for the tangential velocity and a Gaussian for the radial velocity, as might be expected from the results of \scite{vitvit02}."724.. However. the mean and clispersion of the radial velociv distribution are à 'unction of the tangential velocity. as is necessary to account or the correlation between these two veocities found in our clistributions.," However, the mean and dispersion of the radial velocity distribution are a function of the tangential velocity, as is necessary to account for the correlation between these two velocities found in our distributions."725 We have fit this function to clistribuions of orbits taken rom the combined VLS and VIRGO ACDAL simulations (the VLS simulation is the only one whic1 provides sullicient signal to noise to make fitting worthwhile)., We have fit this function to distributions of orbits taken from the combined VLS and VIRGO $\Lambda$ CDM simulations (the VLS simulation is the only one which provides sufficient signal to noise to make fitting worthwhile).726 Figures 7 hrough 9. show distributions of orbita velocities together with the fitting Function. while Table 2 lists the parameter values used in the fits.," Figures \ref{fig:fit0} through \ref{fig:fit1} show distributions of orbital velocities together with the fitting function, while Table \ref{tb:fitpar} lists the parameter values used in the fits."727the test runs.,the test runs.728 In the top panel we show the results for the case with ra.=3., In the top panel we show the results for the case with $r_{\rm gas} = 3$.729 Time is measured dimensionlessly where we have taken the gravitational constant G=|: the crossing time of the sink cluster is 2., Time is measured dimensionlessly where we have taken the gravitational constant $G = 1$; the crossing time of the sink cluster is $\sim 2$.730 In this setup. the gus free-fall time is ~6 and the gas accretes quickly compared to the time for the N-body dynamics to dissolve the small-N sink system.," In this setup, the gas free-fall time is $\sim 6$ and the gas accretes quickly compared to the time for the $N$ -body dynamics to dissolve the $N$ sink system."731 The agreement between all the test runs is excellent., The agreement between all the test runs is excellent.732 The bottom panel shows the r4.=10 cases. and the gas falls onto the sink system over a longer time scale. with a free-fall time 35.," The bottom panel shows the $r_{\rm gas} = 10$ cases, and the gas falls onto the sink system over a longer time scale, with a free-fall time $\sim 35$."733 At early times the agreement is quite good. with some disagreement between the runs appearing after t.~20.," At early times the agreement is quite good, with some disagreement between the runs appearing after $t \sim 20$."734 We attribute this to the fact that at this point the N- dynamics of the different runs have set the clusters on clearly divergent paths: recall that the gravitational smoothing length of the sinks is proportional to their sink radius., We attribute this to the fact that at this point the $N$ -body dynamics of the different runs have set the clusters on clearly divergent paths; recall that the gravitational smoothing length of the sinks is proportional to their sink radius.735 By t=80 , By $t = 80$ 736à better spatial coverage of the cluster. but at a somewhat compromised energy resolution. which is sufficient. for the broad-band imaging.,"a better spatial coverage of the cluster, but at a somewhat compromised energy resolution, which is sufficient for the broad-band imaging."737 When an X-ray photon produces an electron cloud centered on a problematic region. such as a gap or a bad pixel. most of the energy of the photon will be lost.," When an X-ray photon produces an electron cloud centered on a problematic region, such as a gap or a bad pixel, most of the energy of the photon will be lost."738 Instead of an event occupying two pixels (a double). we will detect an event occupying one pixel (a single). but of much lower energy.," Instead of an event occupying two pixels (a double), we will detect an event occupying one pixel (a single), but of much lower energy."739 We found experimentally that the above process was important in the 0.2—0.4 keV band. producing bright columns near gaps.," We found experimentally that the above process was important in the 0.2–0.4 keV band, producing bright columns near gaps."740 Given our choice to include these columns in the image. we had to avoid energies below 0.4 keV. We employed the wavelet image reconstruction technique (Vikhlinin et al.," Given our choice to include these columns in the image, we had to avoid energies below 0.4 keV. We employed the wavelet image reconstruction technique (Vikhlinin et al."741 1998) in order to begin separating the small-scale X-ray structure. possibly associated with individual galaxies. from the large-scale structure originating from the hot cluster gas.," 1998) in order to begin separating the small-scale X-ray structure, possibly associated with individual galaxies, from the large-scale structure originating from the hot cluster gas."742 We set the wavelet peak detection threshold to dor. accepted flux down to 1.7c and performed ten iterations at wavelet scales of4 and 8 areseconds.," We set the wavelet peak detection threshold to $4\sigma$, accepted flux down to $1.7\sigma$ and performed ten iterations at wavelet scales of 4 and 8 arcseconds."743 The DSS? B-band image of Coma is overlaid in Figs.1--5. with contours of the X-ray emission detected on small scales using the 0.5—2.0 keV energy band., The DSS2 B-band image of Coma is overlaid in \ref{f:imh}- \ref{f:imhsw} with contours of the X-ray emission detected on small scales using the 0.5–2.0 keV energy band.744 Except for the Coma center. the identification of X-ray sources with galaxies is unambiguous.," Except for the Coma center, the identification of X-ray sources with galaxies is unambiguous."745 The nominal uncertainty in the astrometry of XMM-Newton is I., The nominal uncertainty in the astrometry of XMM-Newton is $1^{\prime\prime}$.746 Our source detection method is subject to an additional positional uncertainty of 2 (1/2 of the pn pixel)., Our source detection method is subject to an additional positional uncertainty of $2^{\prime\prime}$ (1/2 of the pn pixel).747 These small errors make the identification of the point-like and nearly point-like sources obvious., These small errors make the identification of the point-like and nearly point-like sources obvious.748 Contrary to point sources. the identification of extended features is non-trivial.," Contrary to point sources, the identification of extended features is non-trivial."749 In. particular near the cluster center. the X-ray map exhibits numerous extended fluctuations. which might be associated with individual galaxies or be local enhancements of the ICM.," In particular near the cluster center, the X-ray map exhibits numerous extended fluctuations, which might be associated with individual galaxies or be local enhancements of the ICM."750 A strictly positional criterion would cause us to reject the identification of those X-ray sources that are slightly displaced from the optical galaxy position by the action of ram-pressure stripping., A strictly positional criterion would cause us to reject the identification of those X-ray sources that are slightly displaced from the optical galaxy position by the action of ram-pressure stripping.751 Thermodynamics helps us: since stripping implies a gaseous origin for the offset emission. we expect it to have a typical entropy of galactic gas. which is much lower than the entropy of the cluster ICM.," Thermodynamics helps us: since stripping implies a gaseous origin for the offset emission, we expect it to have a typical entropy of galactic gas, which is much lower than the entropy of the cluster ICM."752 The two giant galaxies at the center of Coma provide a good illustration of the problem., The two giant galaxies at the center of Coma provide a good illustration of the problem.753 Vikhlinin et al. (, Vikhlinin et al. (7541994) using ROSAT data. found an emission enhancement on scales of | areminute.,"1994) using ROSAT data, found an emission enhancement on scales of 1 arcminute."755 Using Chandra observations Vikhlinin et a. (2001) showed that the gas associated with this scale has a temperature of 10 keV. while there is à much more compact emission at ~| keV temperature centered on both the galaxies.," Using Chandra observations Vikhlinin et a. (2001) showed that the gas associated with this scale has a temperature of 10 keV, while there is a much more compact emission at $\sim7561$ keV temperature centered on both the galaxies."757 Based on the, Based on the758displayed in Figure (3).,displayed in Figure (3).759 A very. clear trend is apparent with a linear regression Lit giving The variance in the slope is of 0.17. and of 0.05 in the intercept.," A very clear trend is apparent with a linear regression fit giving The variance in the slope is of 0.17, and of 0.05 in the intercept."760 This relation is assumed to hold for all the LSB galaxies and provides the fourth observational constraint on the typical LSB we want to model., This relation is assumed to hold for all the LSB galaxies and provides the fourth observational constraint on the typical LSB we want to model.761" Notice that the slopes of the T-E. relation ancl the AZíes.A, relation almost exactly satisfy equation (2). 5=2.33 which was derived merely on dimensional grounds. ancl under the hypothesis of self similar halos having à constant barvon fraction and constan A."," Notice that the slopes of the T-F relation and the $M_d vs. R_d $ relation almost exactly satisfy equation (2), $ {3.5 \over 3.5-2} =2.33 $ which was derived merely on dimensional grounds, and under the hypothesis of self similar halos having a constant baryon fraction and constant $\lambda$."762 This result shows that as we are assuming self similar halos. requiring that our final galaxies should satisfy the two observational relations presented above will probably viel ealaxies with a constant £. and a constant A. which is wha one might imagine would hold for a given class of galaxies.," This result shows that as we are assuming self similar halos, requiring that our final galaxies should satisfy the two observational relations presented above will probably yield galaxies with a constant $F$ , and a constant $\lambda$, which is what one might imagine would hold for a given class of galaxies."763 At this point we have used. all available observationa constraints. and have to introduce a filth condition in order to fullv fix our. typical LSB galaxy.," At this point we have used all available observational constraints, and have to introduce a fifth condition in order to fully fix our typical LSB galaxy."764 The low surface brightness of these svstems ancl the consequent large seale radii imply ai large angular momentum., The low surface brightness of these systems and the consequent large scale radii imply a large angular momentum.765 Analytical (e.g. Peebles 1000. Catelan Theuns 1996) and numerical (c.g. Barnes Efstathiou LOST. Warren οἱ al.," Analytical (e.g. Peebles 1969, Catelan Theuns 1996) and numerical (e.g. Barnes Efstathiou 1987, Warren et al."766 1992) studies of the way tidal interactions between forming protogalactic Huctuations transfer orbital. angular momentum to rotational angular momentum in these systems coincide in predicting values of A for galaxies in the range 0.01 - 0.2. with à mean value around 0.05.," 1992) studies of the way tidal interactions between forming protogalactic fluctuations transfer orbital angular momentum to rotational angular momentum in these systems coincide in predicting values of $\lambda$ for galaxies in the range 0.01 - 0.2, with a mean value around 0.05."767 As cliscussecl above. it is plausible to expect that LSB galaxies are clrawn rom the high A region of the distribution. so for our last restriction. we shall impose that this typical LSB galaxy ws à À—Q.1.," As discussed above, it is plausible to expect that LSB galaxies are drawn from the high $\lambda$ region of the distribution, so for our last restriction, we shall impose that this typical LSB galaxy has a $\lambda=0.1$."768 In choosing a value for this parameter we are estimating the typical A of a high A system. there can be ittle uncertainty in this number. perhaps of around a factor of less than 1.5.," In choosing a value for this parameter we are estimating the typical $\lambda$ of a high $\lambda$ system, there can be little uncertainty in this number, perhaps of around a factor of less than 1.5."769 This value will be our only [free parameter. as [rom this tvpical LSB we shall calibrate relations to use or other galaxies.," This value will be our only free parameter, as from this typical LSB we shall calibrate relations to use for other galaxies."770 Now that we have as many restrictions on our tvpical LSB as initial conditions required. for a. model. we can search the initial conditions space for the values ofthe five parameters that result in the specified LSB.," Now that we have as many restrictions on our typical LSB as initial conditions required for a model, we can search the initial conditions space for the values of the five parameters that result in the specified LSB."771 Given the shape of the restrictions introduced. it is easy to see that. this point will be unique.," Given the shape of the restrictions introduced, it is easy to see that this point will be unique."772 The full rotation curve of this typical LSB is shown in Figure (4) by the solid line., The full rotation curve of this typical LSB is shown in Figure (4) by the solid line.773 It can be seen that it resembles those of de Blok et al. (, It can be seen that it resembles those of de Blok et al. (7741996) rather well. which is natural. as this is what was required of it.,"1996) rather well, which is natural, as this is what was required of it."775 Figure (4) also shows the final halo rotation curve (dotted line) which is seen to form the dominant component in all but the extreme innermost regions., Figure (4) also shows the final halo rotation curve (dotted line) which is seen to form the dominant component in all but the extreme innermost regions.776 The thin line in Figur (4) shows the rotation curve of the initial Wing halo. whic= clearly did suller some inward pull (rom the formation of the disk.," The thin line in Figure (4) shows the rotation curve of the initial King halo, which clearly did suffer some inward pull from the formation of the disk."777 Figure (5) is analogous to Figure (4). but shows the ealaxy out to a much larger radial distance. where the drop in the rotation curve is apparent. and an almost Weplerian region appears outward of 30 kpc.," Figure (5) is analogous to Figure (4), but shows the galaxy out to a much larger radial distance, where the drop in the rotation curve is apparent, and an almost Keplerian region appears outward of 30 kpc."778 Lt can also be seen that the aciabatic response ofthe halo was confined to the inner regions., It can also be seen that the adiabatic response ofthe halo was confined to the inner regions.779 Outside of z25Epe. only the subtraction of the barvon fraction from the original halo is seen.," Outside of $\approx 25 kpc$, only the subtraction of the baryon fraction from the original halo is seen."780 We now look at the initial conditions which this model required., We now look at the initial conditions which this model required.781 The shape parameter ofthe typical LSB is {πι= 4. the," The shape parameter ofthe typical LSB is $P_0=4$ , the"782The algorithm discussed above is quite simplified because it assumes that all sources detected in the same redshift bin have the same color S4/S4.,The algorithm discussed above is quite simplified because it assumes that all sources detected in the same redshift bin have the same color $S_{\lambda}/S_{\alpha}$.783 In contrast we would expect there to be a continuous variation of S/S with both δα and z., In contrast we would expect there to be a continuous variation of $S_{\lambda}/S_{\alpha}$ with both $S_{\alpha}$ and $z$.784 Following this assumption allows us to interpolate values between detections at different δα for each redshift slice., Following this assumption allows us to interpolate values between detections at different $S_{\alpha}$ for each redshift slice.785" A more complicated means of correction is to smooth our predictions by interpolating S, through the grid formed by the set of points S5—25t—S** found with the stacking algorithm described above for the whole S,—z plane.", A more complicated means of correction is to smooth our predictions by interpolating $S_{\lambda}$ through the grid formed by the set of points $S_{\alpha}^{St}-z^{St}-S_{\lambda}^{St}$ found with the stacking algorithm described above for the whole $S_{\alpha}-z$ plane.786" We do this with the IDL function TRIGRID, which given data points defined by the parameters S5*—25* and a triangulation of the planar set of points determined by S3/ and z?' returns a regular grid of interpolated S) values."," We do this with the IDL function TRIGRID, which given data points defined by the parameters $S_{\alpha}^{St}-z^{St}-S_{\lambda}^{St}$ and a triangulation of the planar set of points determined by $S_{24}^{St}$ and $z^{St}$ returns a regular grid of interpolated $S_{\lambda}$ values."787 We tried both approaches and found that the differences between the results for the two different smoothings is very small so from now on we use only the “S) smoothing”., We tried both approaches and found that the differences between the results for the two different smoothings is very small so from now on we use only the $S_{\lambda}$ smoothing”.788 Figure 1., Figure \ref{fig:Smoothing Cut}.789.α shows the fluxes at 350 um (with 1.5«z 1.6) before and after the two dimensional smoothing., .a shows the fluxes at 350 $\mu$ m (with $1.5<z<1.6$ ) before and after the two dimensional smoothing.790" It shows the real fluxes of the sources (known from the simulations), the recovered fluxes using the smoothing technique, and the recovered fluxes without smoothing."," It shows the real fluxes of the sources (known from the simulations), the recovered fluxes using the smoothing technique, and the recovered fluxes without smoothing."791 We can see that the smoothing greatly improves the accuracy of the fluxes., We can see that the smoothing greatly improves the accuracy of the fluxes.792" After this correction, the results are in very good agreement with the input fluxes."," After this correction, the results are in very good agreement with the input fluxes."793" We now test the limitations of the method related to the difficulties we expect to face when real data are analyzed (e.g., intrinsic dispersion in the colors of the sources, errors in the measurement of the fluxes and in redshifts,clustering)""."," We now test the limitations of the method related to the difficulties we expect to face when real data are analyzed (e.g., intrinsic dispersion in the colors of the sources, errors in the measurement of the fluxes and in redshifts,."794". To illustrate the limitations, in this section we use the simulations at 350 jum. We reached the same conclusions using other far-infrared and submillimeter wavelengths."," To illustrate the limitations, in this section we use the simulations at 350 $\mu$ m. We reached the same conclusions using other far-infrared and submillimeter wavelengths."795" The size of the redshift slices that divide the $24—z space was chosen to be dz=0.1; wider redshift slices would stack together sources with very different fluxes; smaller redshift slices led to too low signal-to-noise Two different Spitzer surveys are used, COSMOS and SWIRE."," The size of the redshift slices that divide the $S_{24}-z$ space was chosen to be $dz=0.1$; wider redshift slices would stack together sources with very different fluxes; smaller redshift slices led to too low signal-to-noise Two different Spitzer surveys are used, COSMOS and SWIRE."796 COSMOS is a deep observation with a completeness of ~100% up to $54=80 Jy (?)..," COSMOS is a deep observation with a completeness of $\sim$ up to $S_{24}=80\,\mu$ Jy \citep{2007ApJS..172...86S}."797 It allows us to test the stacking of faint sources., It allows us to test the stacking of faint sources.798 COSMOS covers a smaller field than SWIRE (2 sq., COSMOS covers a smaller field than SWIRE (2 sq.799 deg., deg.800 versus 50 sq., versus 50 sq.801 deg.), deg.)802 hence its stacking measurements are less accurate for bright sources., hence its stacking measurements are less accurate for bright sources.803" Thus we also use the much larger SWIRE survey (?),, which is less deep ($34>270 Jy) but covers ~25 times morearea?."," Thus we also use the much larger SWIRE survey \citep {2004ApJS..154...54L}, which is less deep $S_{24}>270\,\mu$ Jy) but covers $\sim$ 25 times more."804". We analyze the stacking of 24 wm sources for two study cases: observations in the far-infrared with Herschel at um and (in the next section) observations in the submillimeter with Planck and SCUBA-2 at jum. The characteristics of the Herschel/SPIRE, Planck/HFI, and SCUBA-2 observations are the following:"," We analyze the stacking of 24 $\mu$ m sources for two study cases: observations in the far-infrared with Herschel at $\,\mu$ m and (in the next section) observations in the submillimeter with Planck and SCUBA-2 at $\,\mu$ m. The characteristics of the Herschel/SPIRE, Planck/HFI, and SCUBA-2 observations are the following:"805The lline has[O beenIv] shown to be an accurate tracer of AGN intrinsic luminosity 2009).,The line has been shown to be an accurate tracer of AGN intrinsic luminosity .806. The line is dominated by the AGN unless the IR luminosity associated with SF exceeds the AGN intrinsic luminosity by an order of magnitude 2010)., The line is dominated by the AGN unless the IR luminosity associated with SF exceeds the AGN intrinsic luminosity by an order of magnitude .807". We use the calibration of to convert between lluminosity[O1v] and AGN intrinsic luminosity, LAGN=Ίοιν]X 2550, which has an rms scatter of 0.4 dex."," We use the calibration of to convert between luminosity and AGN intrinsic luminosity, $L_{\textnormal{\scriptsize{AGN}}}=L_{\scriptsize{\oiv}}\times2550$ , which has an rms scatter of 0.4 dex."808" Assuming a radiative efficiency —0.1 nMpg c), this is equivalent to the following: We note that there are theoretical expectations that the radiative efficiency may drop at both high >1l, and low <0.01, accretion rates due to advection of matter onto the 1995)black hole."," Assuming a radiative efficiency $\eta=0.1$ $L_{\textnormal{\scriptsize{AGN}}}=\eta\dot{M}_{BH}c^2$ ), this is equivalent to the following: We note that there are theoretical expectations that the radiative efficiency may drop at both high >1, and low <0.01, accretion rates due to advection of matter onto the black hole."809" The latter regime is relevant for our sample, such that equation 1 may underestimate the true mass accretion rate for sources with small values."," The latter regime is relevant for our sample, such that equation \ref{eq:oiv} may underestimate the true mass accretion rate for sources with small $L/L_{Edd}$ values."810" To assess the L/Lgagqdemographics of the sample in terms of the ratio of the AGN intrinsic luminosity to the Eddington luminosity, Lgpp=1.3x10706(Mpj/105Mc) erg s!, we gathered estimates of black hole mass from the literature based on high-resolution gas, stellar, or maser dynamics (5 objects), reverberation mapping (10 objects), and bulge velocity dispersion (46 objects)."," To assess the demographics of the sample in terms of the ratio of the AGN intrinsic luminosity to the Eddington luminosity, $_{\textnormal{\scriptsize{EDD}}}=1.3\times10^{46}(M_{BH}/10^{8}M_{\odot})$ erg $^{-1}$, we gathered estimates of black hole mass from the literature based on high-resolution gas, stellar, or maser dynamics (5 objects), reverberation mapping (10 objects), and bulge velocity dispersion (46 objects)."811" The values of AGN intrinsic Iuminosity, black hole mass, and Eddington ratio for the sample are shown in Figure 1 and compiled in Table 3.."," The values of AGN intrinsic luminosity, black hole mass, and Eddington ratio for the sample are shown in Figure \ref{fig:ml}812 and compiled in Table \ref{tab:data}."813" Most objects fall in the range LAGN=1042-1099 erg s-!, Mgg=106 1085Mo, and L/Leaa=1074-1."," Most objects fall in the range $L_{AGN}=10^{42}$ $10^{45}$ erg $^{-1}$ , $M_{BH}=10^6$ $10^{8}~M_{\odot}$, and $L/L_{Edd}=10^{-4}$ –1."814" The mid-IR aromatic features2007),, the lline2010),, and the 24 wm continuum luminosity can all be used as tracers of the SFR for normal2009) star-forming galaxies."," The mid-IR aromatic features, the line, and the 24 $\mu$ m continuum luminosity can all be used as tracers of the SFR for normal star-forming galaxies."815" However, when a galaxy contains a central AGN, dust heated by the AGN will likely dominate the 24 wm continuum2006),, ionizing photons from the AGN(e.g., can contribute significantly to and high-energy photons or citep[e.g.,][Jgro06,per10,,shocks associated with the AGN may destroy or modify the molecules that produce the mid-IR aromatic features"," However, when a galaxy contains a central AGN, dust heated by the AGN will likely dominate the 24 $\mu$ m continuum, ionizing photons from the AGN can contribute significantly to, and high-energy photons or shocks associated with the AGN may destroy or modify the molecules that produce the mid-IR aromatic features."816" Nonetheless, showed2010).. that the 11.3 zm aromatic feature is robust to the effects of AGN- and shock-processing, and outlined a method to determine the star-formation (2008b)contribution to ffor AGNs."," Nonetheless, showed that the 11.3 $\mu$ m aromatic feature is robust to the effects of AGN- and shock-processing, and outlined a method to determine the star-formation contribution to for AGNs."817" In this section, we evaluate[Neτῇ the merit of the 11.3 um aromatic feature and the eemission line for estimating nuclear SFRs of AGN host galaxies."," In this section, we evaluate the merit of the 11.3 $\mu$ m aromatic feature and the emission line for estimating nuclear SFRs of AGN host galaxies."818 We used the star-forming galaxy templates to convert the 11.3 (2009)um aromatic feature and eemission-line strengths into SFRs., We used the star-forming galaxy templates to convert the 11.3 $\mu$ m aromatic feature and emission-line strengths into SFRs.819" Based on spectral decompositions with PAHFIT, we determined the strength of these features for the templates in the Lrg= 101015Lo range, which are appropriate for the nuclear SFRs in thesample (<10 yr7!)."," Based on spectral decompositions with PAHFIT, we determined the strength of these features for the templates in the $L_{IR}=10^{9.75}$ $10^{10.75}~L_{\odot}$ range, which are appropriate for the nuclear SFRs in thesample $<10$ $_{\odot}$ $^{-1}$ )."820" For these templates, the 11.3 jum aromatic Mefeature contributes 1.2%+0.196 of the IR luminosity, while ccontributes 0.1396+0.01% (above Liz=1011Lo these fractions drop to ~0.5% and ~0.07%, respectively)."," For these templates, the 11.3 $\mu$ m aromatic feature contributes $1.2\%\pm0.1\%$ of the IR luminosity, while contributes $0.13\%\pm0.01\%$ (above $L_{IR}=10^{11}~L_{\odot}$ these fractions drop to $\sim0.5\%$ and $\sim0.07\%$, respectively)."821" Using the calibration between Lrr and SFR$,, we find for this luminosity range: We note that equation 2 of implies that"," Using the calibration between $L_{IR}$ and , we find for this luminosity range: We note that equation 2 of implies that"822| for the radii. 15 for the luminosity. and 34 for the degree of contact.,"1 for the radii, 15 for the luminosity, and 34 for the degree of contact."823 Since no mean temperature has been reported by Kaluzny Rucinski. a temperature somewhat smaller than the primary's polar temperature (5980 K) has been adopted. as 1t is the case in BV Dra.," Since no mean temperature has been reported by Kaluzny Rucinski, a temperature somewhat smaller than the primary's polar temperature $5980$ K) has been adopted, as it is the case in BV Dra."824 The models are again stable., The models are again stable.825 This has been checked in evolutionary. calculations., This has been checked in evolutionary calculations.826 The temperature suggests a metallicity Z=0.005...0.006 which is very similar to the metallicity of BV. Dra., The temperature suggests a metallicity $Z=0.005\ldots 0.006$ which is very similar to the metallicity of BV Dra.827 This is as expected., This is as expected.828 The degree of contact suggests again the efficiency fe~10., The degree of contact suggests again the efficiency $f_{\rm E}\simeq 10^{-3}$.829 Adopting these values and a temperature difference AT;.=200 K. the agreement between theory and observations is very close.," Adopting these values and a temperature difference $\Delta T_{\rm e}=200$ K, the agreement between theory and observations is very close."830 The system OO Agl. observed by Hrivnak (1989)). has a very large mass ratio (¢= 0.813).," The system OO Aql, observed by Hrivnak \cite{hri89}) ), has a very large mass ratio $q=0.843$ )."831 Other constraints are AL—1.92M;. P=0.506789 day.," Other constraints are $M=1.92 M_{\sun}$, $P=0.506789$ day."832 The observed temperature difference AT;.=65 K has been added as a constraint., The observed temperature difference $\Delta T_{\rm e}=65$ K has been added as a constraint.833 Other observed properties are listed in the first line of Table 7.., Other observed properties are listed in the first line of Table \ref{OO}.834 Since q is large. evolutionary effects in the secondary are important. (," Since $q$ is large, evolutionary effects in the secondary are important. ("835If they are ignored. the constraints require a negative amplitude f.),"If they are ignored, the constraints require a negative amplitude $f$ .)"836" Table 7 contains properties of configurations for different combinations of Vo, and δω.", Table \ref{OO} contains properties of configurations for different combinations of $X_{{\rm c}1}$ and $X_{{\rm c}2}$.837 These combinations are approximately determined by the condition that f is positive and small., These combinations are approximately determined by the condition that $f$ is positive and small.838" Note that .|V,» is only slightly larger than [X4 and that these values depend on the choice of ο.", Note that $X_{{\rm c}2}$ is only slightly larger than $X_{{\rm c}1}$ and that these values depend on the choice of $x_{\rm c}$.839 Evolutionary effects are large i this system. in accordance with the result of Hrivnak.," Evolutionary effects are large in this system, in accordance with the result of Hrivnak."840 The configurations in the last two lines are in excellent agreement with the observations., The configurations in the last two lines are in excellent agreement with the observations.841 The radit are slightly smaller than those given by Hrivnak., The radii are slightly smaller than those given by Hrivnak.842 The agreement is nevertheless perfect., The agreement is nevertheless perfect.843 Hrivnak’s radii are volume radii (c.f., Hrivnak's radii are volume radii (c.f.844 Mochnacki 1984)) and thus larger (in the present case by about 1.4 percent) than the radit in a spherically averaged treatment of the components (c.f., Mochnacki \cite{moch}) ) and thus larger (in the present case by about 1.4 percent) than the radii in a spherically averaged treatment of the components (c.f.845 Kahhler 1986)). (, Kähhler \cite{k86}) ). (846A similar difference in radit occurs in the systems discussed above).,A similar difference in radii occurs in the systems discussed above).847 The metallicity (Z=0.013...0.01£) turns out to be larger than estimated by Hrivnak., The metallicity $Z=0.013\ldots0.014$ ) turns out to be larger than estimated by Hrivnak.848 The efficiency ts extremely small (ff~10. ?). and the amplitude is rather large CF~ 0.09).," The efficiency is extremely small $f_{\rm E}\simeq 10^{-5}$ ), and the amplitude is rather large $f\simeq 0.09$ )."849 Again the stability was tested in evolutionary calculations., Again the stability was tested in evolutionary calculations.850 The two best models (in the last two lines of Table 7)) are stable. but the other models are unstable.," The two best models (in the last two lines of Table \ref{OO}) ) are stable, but the other models are unstable."851 Apparently an extremely low efficiency (or a rather large degree of contact) is necessary for stability., Apparently an extremely low efficiency (or a rather large degree of contact) is necessary for stability.852 This ts suggested also by other models not listed in Table 7.., This is suggested also by other models not listed in Table \ref{OO}.853 Several observed systems with well-determined parameters have been used as tests of the theory., Several observed systems with well-determined parameters have been used as tests of the theory.854 In all cases an excellent agreement between theory and observations is obtained., In all cases an excellent agreement between theory and observations is obtained.855 This is as expected from the number of free parameters., This is as expected from the number of free parameters.856 In all systems evolutionary effects are important., In all systems evolutionary effects are important.857 All systems turned out to be stable., All systems turned out to be stable.858 This lends support not only to the transport equation used in the present model but also to the assumption of thermal equilibrium and to the treatment of the stability problem., This lends support not only to the transport equation used in the present model but also to the assumption of thermal equilibrium and to the treatment of the stability problem.859 The efficiency was determined to be very small (fr.-5...10 ), The efficiency was determined to be very small $f_{\rm E}\simeq 10^{-3}\ldots 10^{-5}$ ).860 This shows that the velocities of the internal mass motions in the neighbourhood of the inner Lagrangian point are much smaller than the sound velocity., This shows that the velocities of the internal mass motions in the neighbourhood of the inner Lagrangian point are much smaller than the sound velocity.861 So far Roche geometry has been assumed and the effects of internal mass motions on the equation of hydrostatic equilibrium have been neglected., So far Roche geometry has been assumed and the effects of internal mass motions on the equation of hydrostatic equilibrium have been neglected.862 This is justified as a close approximation to real systems. but a closer look into the layers in the common envelope reveals an inconsistency.," This is justified as a close approximation to real systems, but a closer look into the layers in the common envelope reveals an inconsistency."863 This, This864Bolatto at the Berkeley Racio Astronomy Laboratory for his preliminary results.,Bolatto at the Berkeley Radio Astronomy Laboratory for his preliminary results.865 Steve Curran acknowledges receipt of a UNSW NS Global Fellowship., Steve Curran acknowledges receipt of a UNSW NS Global Fellowship.866 This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated. by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Acronautics and Space Administration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."867agreement with the negative slope of the last oscillation in the O-C curve.,agreement with the negative slope of the last oscillation in the O-C curve.868 Some scatter in the cata. especially on the descending branch. does indeed suggest variations that could be due to Blazhko effect.V29:," Some scatter in the data, especially on the descending branch, does indeed suggest variations that could be due to Blazhko effect.:"869 this star has no previous period determination., this star has no previous period determination.870 It is very ckvse to the center. and the quality of the photometry is quite 00D.V30:," It is very close to the center, and the quality of the photometry is quite poor.:"871 this variable was included in the study by S73., this variable was included in the study by S73.872 The bes period we have found is slightly longer than the value given by 573 and SII73. in agreement with the O-C trend. clesrivecl by 873.," The best period we have found is slightly longer than the value given by S73 and SH73, in agreement with the O-C trend derived by S73."873 The star is near the cluster center, The star is near the cluster center874PSR 63 was discovered. in. a large-scale high frequeney survey of the Galactic plane (Johnston 1992a).,PSR $-$ 63 was discovered in a large-scale high frequency survey of the Galactic plane \cite{jlm+92}.875. It is unique because it is the only known radio pulsar in orbit about à massive. main-sequence. D2e star (Johnstonetal. 1992b).," It is unique because it is the only known radio pulsar in orbit about a massive, main-sequence, B2e star \cite{jml+92}."876. PSR 63 has a short spin period of ~48 ms and moderate. period derivative of 2.28101. implving a characteristic age of only 330 Kvr from spin-down » magnetic dipole radiation.," PSR $-$ 63 has a short spin period of $\sim$ 48 ms and moderate period derivative of $2.28\times10^{-15}$, implying a characteristic age of only 330 kyr from spin-down by magnetic dipole radiation."877 I has an orbital period of ~ 1287 days. and an eccentricity of 0.87. the longest orbita »eriod and largest eccentricity of any of the known binary racio pulsars.," It has an orbital period of $\sim$ 1237 days, and an eccentricity of 0.87, the longest orbital period and largest eccentricity of any of the known binary radio pulsars."878 “Lhe inclination of the orbit to the plane of he sky is 7~36°, The inclination of the orbit to the plane of the sky is $i\sim36\arcdeg$.879 The companion. SS 2883. is a IOth magnitude star with amass of about LO AL. ancl a radius of 6 R..," The companion, SS 2883, is a 10th magnitude star with a mass of about 10 $\msolar$ and a radius of 6 $\rsolar$."880 Typical of De stars as a class. it has a hot. tenuous polar wind and a cooler. high density. equatorial disk.," Typical of Be stars as a class, it has a hot, tenuous polar wind and a cooler, high density, equatorial disk."881" The mass loss rate of he Bee star is ~10."" M..."," The mass loss rate of the B2e star is $\sim88210^{-6}$ $\msolar$ ."883 Johnston et al., Johnston et al.884 observed Llea emission lines from the disk at 20 stellar radii (1t; ). just inside the pulsar orbit of 24 It; at periastron.," \nocite{jml+94} observed $\alpha$ emission lines from the disk at 20 stellar radii $_{*}$ ), just inside the pulsar orbit of 24 $_{*}$ at periastron."885" The density of the disk material is high near the stellar surface (10°107"" *y and falls olf as a power-law with distance from he star."," The density of the disk material is high near the stellar surface $10^{8}-10^{10}$ $^{-3}$ ), and falls off as a power-law with distance from the star."886 The disk is ikelv to be highly. tilted with respect o the pulsar orbital xdane. andPSR. B1259 63 is eclipsed or about 40 davs as it goes behind the disk.," The disk is likely to be highly tilted with respect to the pulsar orbital plane, andPSR $-$ 63 is eclipsed for about 40 days as it goes behind the disk."887 Agasuming the Bee star is rotating αἲ ντ per cent of its break up velocity (Porter2001).. SS 2883 hen has an equatorial velocity. οσο ," Assuming the B2e star is rotating at $\sim$ 70 per cent of its break up velocity \cite{por96}, SS 2883 then has an equatorial velocity $\sim$ 280 $^{-1}$."888The spin-inclucecl oblateness of the star implies an additional 1/r3 gravitational potential term. in the interaction with the oulsar. known as quaclrupole eravitational moment in vpical binary system.," The spin-induced oblateness of the star implies an additional $1/r^3$ gravitational potential term in the interaction with the pulsar, known as quadrupole gravitational moment in typical binary system."889 This etfec introduces an apsidal motion and recession of the orbital plane if the spin of the companion is not aligned with the orbit angular momentum. characterised by a@ and vt respectively. where w is the longitude of periastron passage ancl.r is the projected pulsarsemi-major axis (Lai.Bilelsten&Ixaspi 1995)..," This effect introduces an apsidal motion and precession of the orbital plane if the spin of the companion is not aligned with the orbit angular momentum, characterised by $\dot \omega$ and $\dot890x$ respectively, where $\omega$ is the longitude of periastron passage and $x$ is the projected pulsarsemi-major axis \cite{lbk95}. ."891 In an eccentric binary system. the passage of the pulsar through periastron excites tidal motions on the companion," In an eccentric binary system, the passage of the pulsar through periastron excites tidal motions on the companion"892The rate at which cosmic structures grow is set by a competition between gravitational instability ancl the rate of expansion of the Universe.,The rate at which cosmic structures grow is set by a competition between gravitational instability and the rate of expansion of the Universe.893 Phe growth of structure can be measured by analvsing the distortions in the galaxy clustering pattern. when viewed in redshift space (ic. when a galaxys redshift is used to infer its radial position).," The growth of structure can be measured by analysing the distortions in the galaxy clustering pattern, when viewed in redshift space (i.e. when a galaxy's redshift is used to infer its radial position)."894 Proof of concept of this approach came recently fron? who used spectroscopic data for 10.000 galaxies from the VIMOS-VLT Deep Survey (2). to measure the growth rate of structure at redshift 2=0.77 toan accuracy of ~40% (seealso 7)..," Proof of concept of this approach came recently from \citet{Guzzo:2008ac} who used spectroscopic data for 10,000 galaxies from the VIMOS-VLT Deep Survey \citep{LeFevre:2004hv} to measure the growth rate of structure at redshift $z=0.77$ toan accuracy of $\sim 40\%$ \citep[see also][]{2001Natur.410..169P}."895 To distinguish between competing explanations for the accelerating expansion of the Universe. we need to measure the growth of structure to an accuracy ofa few percent over a wide redshift interval.," To distinguish between competing explanations for the accelerating expansion of the Universe, we need to measure the growth of structure to an accuracy of a few percent over a wide redshift interval."896 The next generation of galaxy recishift surveys. such as LESA’s Euclid. mission (2).. will be able o achieve this precision.," The next generation of galaxy redshift surveys, such as ESA's Euclid mission \citep{2009ExA....23...39C}, will be able to achieve this precision."897 These redshift: space distortions are commonly modelled using a linear perturbation theory expression., These redshift space distortions are commonly modelled using a linear perturbation theory expression.898 We test the validity of this approximation using arge volume N-bocky simulations to model the redshift space distortions in CDM and quintessence dark energy mocels. o see if it works at the level required to take advantage of he information in forthcoming surveys.," We test the validity of this approximation using large volume N-body simulations to model the redshift space distortions in $\Lambda$ CDM and quintessence dark energy models, to see if it works at the level required to take advantage of the information in forthcoming surveys."899 The large volume of our simulations means that we are able to find the limits of perturbation theory models., The large volume of our simulations means that we are able to find the limits of perturbation theory models.900 We can also study the impact of non-linearities on large scales in cosmologies with cillerent expansion histories from ΑςΕΟΝ. such as quintessence dark CDCPEV.," We can also study the impact of non-linearities on large scales in cosmologies with different expansion histories from $\Lambda$ CDM, such as quintessence dark energy."901 One explanation of the accelerating expansion. of the Universe is that a negative pressure dark energy component makes up approximately of the present density of the Universe (22)...," One explanation of the accelerating expansion of the Universe is that a negative pressure dark energy component makes up approximately of the present density of the Universe \citep{Komatsu:2008hk, 2009MNRAS.400.1643S}."902 examples of4 dark energy. models include the cosmological constant ancl a dynamical scalar field such as quintessence (seec.g.2.fora review)..., Examples of dark energy models include the cosmological constant and a dynamical scalar field such as quintessence \citep[ see e.g.][for a review]{Copeland:2006wr}. .903 Other possible solutions require modifications to general relativity and, Other possible solutions require modifications to general relativity and904In our analysis. we found two different effects biasing the statistics related to the HI and CIV absorption lines: the choice of the UV background and theVPFIT lines fitting procedure.,"In our analysis, we found two different effects biasing the statistics related to the HI and CIV absorption lines: the choice of the UV background and the lines fitting procedure."905 In the future we will try to improve these statistics by using a more physically motivated UV background that takes into account Hell reionization at >~3., In the future we will try to improve these statistics by using a more physically motivated UV background that takes into account HeII reionization at $z\sim 3$.906" Furthermore. we will try to improve our automatic line-titting analysis by removing numerical artifacts introduced byVPFIT. since the automatic fitting procedure is not ikely to be as accurate as a “by eye"" fitting made by an observer. and introduce spurious lines especially in the continuum region."," Furthermore, we will try to improve our automatic line-fitting analysis by removing numerical artifacts introduced by, since the automatic fitting procedure is not likely to be as accurate as a “by eye” fitting made by an observer, and introduce spurious lines especially in the continuum region."907 Our results can also be tested by using other statistics based on jixel-optical depths techniques., Our results can also be tested by using other statistics based on pixel-optical depths techniques.908 A second possible improvement of the results presented in his paper is the refinement of the feedback models and the inclusion of new physical processes like turbulence. metal diffusion and radiative transfer. that can help in polluting with metals the ow-density IGM.," A second possible improvement of the results presented in this paper is the refinement of the feedback models and the inclusion of new physical processes like turbulence, metal diffusion and radiative transfer, that can help in polluting with metals the low-density IGM."909 So far we explored feedback preseriptions in he form of energy-driven galactic winds (EDW). momentum-driven galactic winds (MDW) and black holes accretion (AGN feedback).," So far we explored feedback prescriptions in the form of energy-driven galactic winds (EDW), momentum-driven galactic winds (MDW) and black holes accretion (AGN feedback)."910" Exploring the combined effect of these models seems to be promising: for example the “energy coupled momentum driven winds"" model by ?. succeeds in enriching the gas (like the EDW model) without heating too much the IGM (like the MDW model).", Exploring the combined effect of these models seems to be promising: for example the “energy coupled momentum driven winds” model by \citet{choi2010} succeeds in enriching the gas (like the EDW model) without heating too much the IGM (like the MDW model).911 The modelization inside the hydrodynamie simulations of the radiative transfer is fundamental and could also impact on the metal mixing., The modelization inside the hydrodynamic simulations of the radiative transfer is fundamental and could also impact on the metal mixing.912 Finally. it will be crucial to incorporate in the code the small-scale turbulence and its impact on the metal diffusion at large scales.," Finally, it will be crucial to incorporate in the code the small-scale turbulence and its impact on the metal diffusion at large scales."913 With physical mixing. fluid elements on a fixed (resolved) physical scale do exchange energy/entropy due to unresolved (turbulent) motions: diffusion allows some ejecta gus to mix while exiting the galaxies (?)..," With physical mixing, fluid elements on a fixed (resolved) physical scale do exchange energy/entropy due to unresolved (turbulent) motions: diffusion allows some ejecta gas to mix while exiting the galaxies \citep{shenetal09}."914 All the previous effects. once included in simulations. could help in improving our understanding of the chemical and physical evolution of the IGM and provide a more comprehensive framework of the high-redshift galaxy/IGM interplay.," All the previous effects, once included in simulations, could help in improving our understanding of the chemical and physical evolution of the IGM and provide a more comprehensive framework of the high-redshift galaxy/IGM interplay."915 Numerical computations were done on the COSMOS (SGI Altix 3700) supercomputer at DAMTP and at High Performance Computer Cluster (HPCP) in Cambridge (UK) and at CINECA (Italy)., Numerical computations were done on the COSMOS (SGI Altix 3700) supercomputer at DAMTP and at High Performance Computer Cluster (HPCF) in Cambridge (UK) and at CINECA (Italy).916 COSMOS is a UK-CCC facility which is supported by HEFCE. PPARC and Silicon Graphics/Cray Research.," COSMOS is a UK-CCC facility which is supported by HEFCE, PPARC and Silicon Graphics/Cray Research."917" The CINECA (""Centro Interuniversitario del Nord Est per il Calcolo Elettronico"") CPU time has been assigned thanks to an INAF-CINECA grant.", The CINECA (“Centro Interuniversitario del Nord Est per il Calcolo Elettronico”) CPU time has been assigned thanks to an INAF-CINECA grant.918 This work has been partially supported by the INFN-PD$31 grant. an ASI-AAE Theory grant and a PRIN-MIUR.," This work has been partially supported by the INFN-PD51 grant, an ASI-AAE Theory grant and a PRIN-MIUR."919" 2m J|K>2.3 darkAf>inyplicsΤΟΝΙ,lindos matter clustering."," $z \gtrsim9202$ $J-K > 2.3$ $M \gtrsim 10^{13} \rm{M_\odot}$ matter clustering."921 Tere we use a 0. G5dee? field from the UKIRT Iufrared Deep Sky Survey (UKIDSS). which is —5 times larger than the area used by but with siular NIR depth. to determine whether the strong observed clustering of DRGs found in previous studies was an artifact due to limited field sizes or whether some other explanation must be found.," Here we use a $\sim$ $\rm{deg}^2$ field from the UKIRT Infrared Deep Sky Survey (UKIDSS), which is $\sim$ 8 times larger than the area used by but with similar NIR depth, to determine whether the strong observed clustering of DRGs found in previous studies was an artifact due to limited field sizes or whether some other explanation must be found."922 We use (Qay.Ox(0.3.0.7.0.9.0.7).," We use $(\Omega_M, \Omega_\Lambda, \sigma_8, h) = (0.3, 0.7, 0.9,9230.7)$."924 Sinall changes in these parametersos.D) do not affect our basic conclusions., Small changes in these parameters do not affect our basic conclusions.925 Maguitudes are given in the Vega svsteni. except where noted.," Magnitudes are given in the Vega system, except where noted."926 The UKIDSS projec covers differeut areas to differeut deptls: here we makese of the deepest UKIDSS dataset. known as the Ultra Deep Survey (UDS).," The UKIDSS project covers different areas to different depths; here we make use of the deepest UKIDSS dataset, known as the Ultra Deep Survey (UDS)."927 We use the UDS DataRelease 1 images 2007).. which reach 5 σ point-source depths of 7~23 ux Iv~21.6.," We use the UDS DataRelease 1 images , which reach 5 $\sigma$ point-source depths of $J \sim 23$ and $K \sim 21.6$."928 We note that used. the UDS Early Data Release to study the clustering of DRGs down to A~19. however such bright DRGs lie primarily at : and may not be directly relevant to the galaxies that are the subject of this work.," We note that used the UDS Early Data Release to study the clustering of DRGs down to $K \sim 19$, however such bright DRGs lie primarily at $z < 2$ and may not be directly relevant to the galaxies that are the subject of this work."929 Most of the UDS field has coverage in the optical bands frou the Subaru-NMM deep Survey , Most of the UDS field has coverage in the optical bands from the Subaru-XMM deep Survey .930We use the beta-release of the DBR!:Z4 images. which reach depths of ~25.327.5 7(AB magnitudes).," We use the beta-release of the $BRi'z'$ images, which reach depths of $\sim$ 25.3–27.5 (AB magnitudes)."931 Finally. we combine these data with Gu and 554 imagine from theWide-Area Iufrared Extragalactic Survey 2003).," Finally, we combine these data with $3.6\mu$ and $4.5\mu$ imaging from theWide-Area Infrared Extragalactic Survey ."932. Theprocedures used to create amulticolor A-selected, Theprocedures used to create amulticolor $K$ -selected933that of dust. in a galaxy on the scale of the PSF using only one image in one filter.,"that of dust, in a galaxy on the scale of the PSF using only one image in one filter."934 The structure map is mathematically defined as where S is the structure map. / is the image. P is the point- function (PSF). P' is the transform of the PSF. and & is the convolution operator (Pogge&Martini 2002)).," The structure map is mathematically defined as where $S$ is the structure map, $I$ is the image, $P$ is the point-spread function (PSF), $P^{\rm t}$ is the transform of the PSF, and $\otimes$ is the convolution operator \cite{PO02}) )."935 We used synthetic PSFswhich were created with the Tiny Tim software (Krist&Hook 1999))., We used synthetic PSFswhich were created with the Tiny Tim software \cite{KR99}) ).936 We used images taken through green or red optical filters to apply the structure map operator. namely F547M.F606W.F791W. and F814W for ΜΕΡΟΣ images. and F625W and F814W for ACS images.," We used images taken through green or red optical filters to apply the structure map operator, namely $F547M, F606W, F791W$, and $F814W$ for WFPC2 images, and $F625W$ and $F814W$ for ACS images."937 The resulting images are shown in Appendices A (for the c-drop sample) and B (for the control sample. the appendices are online-only).," The resulting images are shown in Appendices A (for the $\sigma$ -drop sample) and B (for the control sample, the appendices are online-only)."938 For 10 of the 20 galaxies in our c-drop sample and for ten more in our control sample we could retrieve nnarrow-band imaging from the archive., For 10 of the 20 galaxies in our $\sigma$ -drop sample and for ten more in our control sample we could retrieve narrow-band imaging from the archive.939 We used images taken through the narrow filters F656N or F658N. and a continuum image taken through a red broad-band filter.," We used images taken through the narrow filters $F656N$ or $F658N$, and a continuum image taken through a red broad-band filter."940 In the few cases where images taken through both filters were available in the archive. we chose the F658N image. because the lline of our sample galaxies was better centred in its passband.," In the few cases where images taken through both filters were available in the archive, we chose the $F658N$ image, because the line of our sample galaxies was better centred in its passband."941 The images used for the continuum subtraction were those from which we derived the structure maps., The images used for the continuum subtraction were those from which we derived the structure maps.942 After selecting the images from the archive. the continuum and narrow-band images were aligned using standard [RAF software.," After selecting the images from the archive, the continuum and narrow-band images were aligned using standard IRAF software."943 We then plotted for each pixel in the whole image the number of counts in the narrow-band filter versus that in the continuum filter., We then plotted for each pixel in the whole image the number of counts in the narrow-band filter versus that in the continuum filter.944 In the absence of line emission. the number of counts in the narrow-band filter will be proportional to the number of counts in the continuum. and the constant of proportionality is the factor by which the continuum has to be scaled before subtracting from the narrow-band image.," In the absence of line emission, the number of counts in the narrow-band filter will be proportional to the number of counts in the continuum, and the constant of proportionality is the factor by which the continuum has to be scaled before subtracting from the narrow-band image."945 Since even for a star-forming galaxy most pixels trace only continuum emission. those pixels without emission can easily be recognised in the graph. and a fit to them yields the continuum sealing factor (see Knapen et al.," Since even for a star-forming galaxy most pixels trace only continuum emission, those pixels without emission can easily be recognised in the graph, and a fit to them yields the continuum scaling factor (see Knapen et al."946 2005. 2006 for details and a graphic illustration).," 2005, 2006 for details and a graphic illustration)."947 In most cases. there is a contribution from the [Nu]] line in the images but this is not a problem because we do not use the limages for photometry. and [Nu]] emission is unlikely to affect the morphology on the scales we are interested in here.," In most cases, there is a contribution from the ] line in the images but this is not a problem because we do not use the images for photometry, and ] emission is unlikely to affect the morphology on the scales we are interested in here."948 The resulting continuum-subtracted images are shown in Appendices A and B (for the c-drop and control samples. respectively: on-line only).," The resulting continuum-subtracted images are shown in Appendices A and B (for the $\sigma$ -drop and control samples, respectively; on-line only)."949 We have searched for correlations between size of the c-drop region and other properties of their host galaxies. such as differences in morphology or in radio emission from gas (see further sections for details on how we study those properties).," We have searched for correlations between size of the $\sigma$ -drop region and other properties of their host galaxies, such as differences in morphology or in radio emission from gas (see further sections for details on how we study those properties)."950 We have found no correlation between any of these properties and the size of the «drops., We have found no correlation between any of these properties and the size of the $\sigma$ -drops.951 We have also made a comparison between the radius of the c-drop Gua) and ος. a measure of radius which is directly related to the visible size of the galaxy and which we define as is half of Das as taken from the RC3).," We have also made a comparison between the radius of the $\sigma$ -drop $r_{\sigma\rm{-drop}}$ ) and $r_{\rm{c}}$ , a measure of radius which is directly related to the visible size of the galaxy and which we define as is half of $D_{25}$ as taken from the RC3)."952 We use the definition for r. because it is similar to the effective radius of the bulge of a spiral galaxy (Laurikainenetal. 2004))—1t thus provides an objective but simple and effective working definition of the central region., We use the definition for $r_{\rm{c}}$ because it is similar to the effective radius of the bulge of a spiral galaxy \cite{LA04}) )—it thus provides an objective but simple and effective working definition of the central region.953 The data used appear in Table 5 and the plots are in Fig. 2.., The data used appear in Table \ref{size} and the plots are in Fig. \ref{sigmasizes}.954 The radii of the o-drops were taken from the velocity dispersion plots in the papers cited in Section 2., The radii of the $\sigma$ -drops were taken from the velocity dispersion plots in the papers cited in Section 2.955 These dispersions are not always very well defined because in several papers the spectra are taken only along one axis of the galaxy (usually the major axis) and this does not provide as good a measure of the o-drop radius as JFL spectroscopy., These dispersions are not always very well defined because in several papers the spectra are taken only along one axis of the galaxy (usually the major axis) and this does not provide as good a measure of the $\sigma$ -drop radius as $IFU$ spectroscopy.956 We note," We notethat the highest value of the ratio $r_{\sigma\rm{-drop}}/r_{\rm{c}}$ , NGC 3593, is"957starts falling back in (for a more complete description. readers are encouraged to see MBH06).,"starts falling back in (for a more complete description, readers are encouraged to see MBH06)."958" Quantitatively. we concluded that the net impact of a transient UVB on star-formation could be understood simply in terms of the molecular hydrogen cooling time-scale: Here. Ae is the Boltzmann constant. 7 isthe temperature. pg, is the H» cooling function. ας, is the free electron number fraction. n. ng. and ng, are the number densities of all baryons and electrons. neutral hydrogen. and He. respectively. and the second equality is accurate shortly after ziως Since the recombination times at ugh redshifts and inside halos are very short."," Quantitatively, we concluded that the net impact of a transient UVB on star-formation could be understood simply in terms of the molecular hydrogen cooling time-scale: Here, $k_B$ is the Boltzmann constant, $T$ isthe temperature, $\Lambda_{\rm H_2}$ is the $_2$ cooling function, $x_e$ is the free electron number fraction, $n_g$, $n_{\rm HI}$, and $n_{\rm H_2}$ are the number densities of all baryons and electrons, neutral hydrogen, and $_2$, respectively, and the second equality is accurate shortly after $\zuvboff$, since the recombination times at high redshifts and inside halos are very short."959 We found that the netdelay in star-formation caused by the ransient UVB is simply the ratio of the H» cooling time in the run with the UVB. to the H» cooling time in the run without UV jeating.," We found that the net in star-formation caused by the transient UVB is simply the ratio of the $_2$ cooling time in the run with the UVB, to the $_2$ cooling time in the run without UV heating."960 This ratio is calculated near the halo core. shortly after the UVB disappears (when the shock first starts to dissipate and the gas behind it starts infalling again).," This ratio is calculated near the halo core, shortly after the UVB disappears (when the shock first starts to dissipate and the gas behind it starts infalling again)."961 For example. the delay in ormation of a halo in the rrun with respect to the same halo in the run is: We will now demonstrate that eq. (3))," For example, the delay in star-formation of a halo in the run with respect to the same halo in the run is: We will now demonstrate that eq. \ref{eq:delay}) )"962 is equally adept at quantifying feedback in our new simulations., is equally adept at quantifying feedback in our new simulations.963 First. we show the spherically averaged radial profiles of the same (typical) halo in the lines). lines) and lines) simulation runs in our Figure [..," First, we show the spherically averaged radial profiles of the same (typical) halo in the ), ) and ) simulation runs in our Figure \ref{fig:early_profiles}."964 This halo. which has a mass of4.107AZ. at +=24.62. was first able to form CD gus at >= 20. 21. 19 in theNoUVB..Heat0.08.. and rruns. respectively.," This halo, which has a mass of $4\times10^5 \Msun$ at $z=24.62$, was first able to form CD gas at $z=$ 20, 21, 19 in the, and runs, respectively."965 The top and bottom pairs of figures are snapshots at 2= 24.62. 23. 21. and 19 right).," The top and bottom pairs of figures are snapshots at $z =$ 24.62, 23, 21, and 19 )."966 The show the hydrogen density. mass-weighted gas temperature. gas cooling time. and radial velocity left).," The show the hydrogen density, mass-weighted gas temperature, gas cooling time, and radial velocity )."967 The show mass fractions of HI. ΠΠ. He. and the number fraction of ¢ left).," The show mass fractions of HI, HII, $_2$, and the number fraction of $e^-$ )."968 The profiles confirm the qualitative story line from the beginning of this section., The profiles confirm the qualitative story line from the beginning of this section.969 The outward-moving pressure shock is evident in both UVB runs from the density and velocity panels at 2=σινι. Just before the UVB was turned off.," The outward-moving pressure shock is evident in both UVB runs from the density and velocity panels at $z=\zuvboff$, just before the UVB was turned off."970 This gas has already cooled to 7=10° K and started to collapse back onto the halo only a few Myr afterward at 2.=23., This gas has already cooled to $T=10^3$ K and started to collapse back onto the halo only a few Myr afterward at $z=23$.971 Note that the outflow and the resulting suppression of gas near the core is stronger in the run with a stronger UVB., Note that the outflow and the resulting suppression of gas near the core is stronger in the run with a stronger UVB.972 Halos in the runs with a UVB also experience a strong boost in the H» fraction following σι νι]. with the increase being insensitive to the strength of the UVB.," Halos in the runs with a UVB also experience a strong boost in the $_2$ fraction following $\zuvboff$ , with the increase being insensitive to the strength of the UVB."973 Formation of CD gas in this halo is notably delayed until 2=19 in the, Formation of CD gas in this halo is notably delayed until $z=19$ in the974DX Mon was discovered. on à. Harvard. objective prism plate by Alawall (1940).,BX Mon was discovered on a Harvard objective prism plate by Mayall (1940).975 Hs. classification às à symbiotic system (SS) was based on its optical spectrum. showing a combinationDEN of. strong hydrogen emissionD. lines: ancl sTiO absorption. bands of. a late-type star (lijima.. 1985. aeIxenvon 1986. Viotti et al.," Its classification as a symbiotic system (SS) was based on its optical spectrum, showing a combination of strong hydrogen emission lines and TiO absorption bands of a late-type star (Iijima 1985, Kenyon 1986, Viotti et al."976 LOSG)., 1986).977 Its. identification as S68 has been questioned (Allen 1982). until medium. ionization lines have been identified in LUE (International Ultraviolet Explorer spectra) (Michalitianos 1982).," Its identification as SS has been questioned (Allen 1982), until medium ionization lines have been identified in IUE (International Ultraviolet Explorer spectra) (Michalitianos 1982)."978 Its infrared: colors and spectral energy distribution are that of à normal M5 LLL star and exclude the presence of Mira variable (Whitclock Cathpole 1983. Viotti et al.," Its infrared colors and spectral energy distribution are that of a normal M5 III star and exclude the presence of a Mira variable (Whitelock Cathpole 1983, Viotti et al."979 1986.a Dunn οἱ al.," 1986, Dumm et al."980 1998)., 1998).981 No nova-like eruption event has been recorded for this system., No nova-like eruption event has been recorded for this system.982 DX Mon large photometric variability had already been discovered in L940 by Mavall (L940) anc a period of 1380 α was suggested. with ephemeris JD(max)- 2412490 d. Its optical and ultraviolet spectrum. is also strongly variable.," BX Mon large photometric variability had already been discovered in 1940 by Mayall (1940) and a period of 1380 d was suggested, with ephemeris JD(max)= 2412490 d. Its optical and ultraviolet spectrum is also strongly variable."983 Llowever. the spectroscopic variability is hardly. explained bv the Mavall’s period. (ijima 1985. Viotti et al.," However, the spectroscopic variability is hardly explained by the Mayall's period (Iijima 1985, Viotti et al."984 1986)., 1986).985 lijima (1985) noted that two epochs of low excitation states seem to occur at phases near the photometric. maximum. of⋅ Mavall's. ephemeris.. suggestingD that the Alavall’s lieht curve representation may contain a mistake or that a change occurred in the variations phase.," Iijima (1985) noted that two epochs of low excitation states seem to occur at phases near the photometric maximum of Mayall's ephemeris, suggesting that the Mayall's light curve representation may contain a mistake or that a change occurred in the variations phase."986 Dumm et al. (, Dumm et al. (9871998). analvzed. the Alavall’s cata and he cata of the RASNZ (Roval Astronomical Society of row Zealand) obtained between the vears 1959 ancl 1995. covering/ less than two cycles.,"1998) analyzed the Mayall's data and the data of the RASNZ (Royal Astronomical Society of New Zealand) obtained between the years 1989 and 1995, covering less than two cycles."988 :“Pwo possible.ἳ periodicitneaies rave been suggested. 338+s8 d and P=l4ol+s d. The xwiod P= 1401 d seems to explain the LUE: spectra variationsIU (Dumm et al.," Two possible periodicities have been suggested, $\pm$ 8 d and $\pm$ 8 d. The period P= 1401 d seems to explain the IUE spectra variations (Dumm et al."989 1998) and in: particular. the USI lux attenuation as due to eclipses of the hot component by he cool one., 1998) and in particular the UV flux attenuation as due to eclipses of the hot component by the cool one.990 Fekel et al. (, Fekel et al. (9912000). combining their own radial velocity measurements and a few old data by Dumm ct al. (,"2000), combining their own radial velocity measurements and a few old data by Dumm et al. ("9921998) established an orbital period. of 1259 +416 d. A period. of P= 1262 £32 d was determined from the RASNZ cata,1998) established an orbital period of 1259 $\pm$ 16 d. A period of P= 1262 $\pm$ 32 d was determined from the RASNZ data993al ~5 MMyr given by Rebulletal.(2004)..,at $\sim 5$ Myr given by \citet{2004AJ....127.1029R}.994 To take into account (he pre-2nain-sequence contraction. we use radii from Chabrier&Daraffe(1997). for a stellar mass of MM... which is (vpical for our sample.," To take into account the pre-main-sequence contraction, we use radii from \citet{1997A&A...327.1039C} for a stellar mass of $_{\odot}$, which is typical for our sample."995 In the upper panel of Fie. 6..," In the upper panel of Fig. \ref{f7},"996" we plot the expected rotational evolution for (vo extreme cases, constant angular momentum with a solid line (model A) and constant angular velocity with a dashed line (model D)."," we plot the expected rotational evolution for two extreme cases, constant angular momentum with a solid line (model A) and constant angular velocity with a dashed line (model B)."997 In (his approach. we follow Rebulletal.(2004). who have done a similar comparison for stars with ages frou MMvyr.," In this approach, we follow \citet{2004AJ....127.1029R}998 who have done a similar comparison for stars with ages from Myr."999 In model D. the period is constant. as expected in a scenario with ideal 'disk-locking. and thus sin?xAR.," In model B, the period is constant, as expected in a scenario with ideal `disk-locking', and thus $v\sin i \propto R$."1000" Model A. on the other hand. shows purely the spin-up due to contraction and thus sin?xRt, "," Model A, on the other hand, shows purely the spin-up due to contraction and thus $v\sin i \propto R^{-1}$."1001While both models are in good agreement wilh observations until ages of ~10 MMvr. only model A is clearly consistent with the median esin; at MMwyr.," While both models are in good agreement with observations until ages of $\sim 10$ Myr, only model A is clearly consistent with the median $v\sin i$ at Myr."1002 Model D. however. gives too low values for ages 210 MMvyr: it tàuneates the esin/ distribution at the quartile in DPMCG and at the quartile in TII.," Model B, however, gives too low values for ages $>$ Myr; it truncates the $v\sin i$ distribution at the quartile in BPMG and at the quartile in TH."1003 Thus. from 10 to MMvr the objects show rotation rates rather consistent with conservation of angular momentum than with constant rotation period.," Thus, from 10 to Myr the objects show rotation rates rather consistent with conservation of angular momentum than with constant rotation period."1004 Thus. the dominating effect for the rotational evolution in this time window is due to the pre-main-sequence contraction.," Thus, the dominating effect for the rotational evolution in this time window is spin-up due to the pre-main-sequence contraction."1005 This result is robust against uncertainties in the stellar radii. because only the ratio of radii is used in the calculation.," This result is robust against uncertainties in the stellar radii, because only the ratio of radii is used in the calculation."1006 In strong contrast to our finding. lor ages <5 MMvr the rotational evolution closely follows the track for constant angular velocity. as concluded by Rebulletal.(2004)..," In strong contrast to our finding, for ages $<5$ Myr the rotational evolution closely follows the track for constant angular velocity, as concluded by \citet{2004AJ....127.1029R}."1007 There is growing evidence for a strong rotational braking in the first few Myr. most likely produced by interaction with accretion disks (e.g.Herbstetal.2002:Rebull2006) aud preventing (he stars [rom spinning up by essentially locking the rotation period (e.g.Rebulletal.2002:Tinkeretal.2002:Herbst&Mundi 2005)... ," There is growing evidence for a strong rotational braking in the first few Myr, most likely produced by interaction with accretion disks \citep[e.g.][]{2002A&A...396..513H,2006ApJ...646..297R} and preventing the stars from spinning up by essentially locking the rotation period \citep[e.g.][]{2002AJ....124..546R,2002ApJ...564..877T,2005ApJ...633..967H}. ."1008Our results now demonstrate that while the period max be locked until ages of ~5—10 MMvr. in the following ~20 MMwyr the stus spin up without clear evidence for rotational braking.," Our results now demonstrate that while the period may be locked until ages of $\sim 5-10$ Myr, in the following $\sim 20$ Myr the stars spin up without clear evidence for rotational braking."1009 Thus. rotational acceleration (measured in period) becomes significant al ages of LOMA | which is consistent with the (vpical iletime of circumstellar disks (laischetal.2001)..," Thus, rotational acceleration (measured in period) becomes significant at ages of Myr – which is consistent with the typical lifetime of circumstellar disks \citep{2001ApJ...553L.153H}."1010 Specifically. it has been shown that many of the voungest stars in our sample (n 7 Cha and TWA) are affected by innerdisk clearing neasured [rom mid-inlrared excess (Ilaischetal.2005:Javawarchana1999)... while the oldest objects Gu TII) do not show any evidence for disks at mid-infrared wavelengths (\lamajeketal.2004)..," Specifically, it has been shown that many of the youngest stars in our sample (in $\eta$ Cha and TWA) are affected by innerdisk clearing measured from mid-infrared excess \citep{2005ApJ...627L..57H,1999ApJ...521L.129J}, while the oldest objects (in TH) do not show any evidence for disks at mid-infrared wavelengths \citep{2004ApJ...612..496M}."1011 Thus. the change of the rotational regulation at MMvr coincides with the disappearance of the inner disks.," Thus, the change of the rotational regulation at Myr coincides with the disappearance of the inner disks."1012 It has to be emphasized. however. that all these considerations onlv apply to thefypiea! evolution.," It has to be emphasized, however, that all these considerations only apply to the evolution."1013 For individual objects. (he period-locking limescale can vary by alot possibly due to different disk liletimes.," For individual objects, the period-locking timescale can vary by a lot – possibly due to different disk lifetimes."1014 To follow the evolution to the main sequence. we compared our dataset with the rotational velocity datain the Pleiades.," To follow the evolution to the main sequence, we compared our dataset with the rotational velocity datain the Pleiades."1015 In (he lower panel of Fig. 6..," In the lower panel of Fig. \ref{f7}, ,"1016 we plot the median, we plot the median1017possible to compare wwith other sites of high mass star formation within G333.,possible to compare with other sites of high mass star formation within G333.1018" Models of high mass star formation emphasise the role of turbulence (?),, so quantifying the variation in the properties of turbulence throughout G333 is important to the testing of such models."," Models of high mass star formation emphasise the role of turbulence \citep{McKee2007}, so quantifying the variation in the properties of turbulence throughout G333 is important to the testing of such models."1019 Turbulent velocities in aare highly supersonic and large by low mass star formation standards., Turbulent velocities in are highly supersonic and large by low mass star formation standards.1020" However, they are significantly less than those measured in the three most massive star forming regions in G333 (~6; Bains et al, in prep.)."," However, they are significantly less than those measured in the three most massive star forming regions in G333 $\sim 6$; Bains et al, in prep.)."1021" The core has a lower mass and a lower turbulent (and infall) velocity that might be expected simply from virial theorem arguments, where the mass of the cold core is 2.2x10? citepGaray2004,, an order of magnitude lower than the three most massive sources in G333."," The core has a lower mass and a lower turbulent (and infall) velocity that might be expected simply from virial theorem arguments, where the mass of the cold core is $2.2 \times 10^3$ \\citep{Garay2004}, an order of magnitude lower than the three most massive sources in G333."1022" The coincidence of the continuum sources at four different wavelengths (3 and 7 mm, 24 and 70 um)) further confirms that the internal heating source is deeply embedded in the cold core."," The coincidence of the continuum sources at four different wavelengths (3 and 7 mm, 24 and 70 ) further confirms that the internal heating source is deeply embedded in the cold core."1023 Whether the continuum emission is due to warm dust or free-free emission from a deeply embedded region can be examined using the spectral index α (see Section 3))., Whether the continuum emission is due to warm dust or free-free emission from a deeply embedded region can be examined using the spectral index $\alpha$ (see Section \ref{sec:results}) ).1024" The three millimetre wavelength (1.2, 3 and 7 mm) data points yield a spectral index a of 4.2+0.07 and dust emissivity 8 of 2.2, which is comparable to the dust emissivity of 8—2 found by ? for cold cores."," The three millimetre wavelength (1.2, 3 and 7 mm) data points yield a spectral index $\alpha$ of $4.2 \pm 0.07$ and dust emissivity $\beta$ of 2.2, which is comparable to the dust emissivity of $\beta = 2$ found by \citet{Hill2006} for cold cores."1025" Thus, to at least 7-mm wavelength, the continuum emission is due to thermal dust emission rather than free-free emission."," Thus, to at least 7-mm wavelength, the continuum emission is due to thermal dust emission rather than free-free emission."1026" At longer wavelengths, there is no detectable (free-free) continuum emission from the core, thus it is possible that anΗΠ region still has not yet developed at this stage."," At longer wavelengths, there is no detectable (free-free) continuum emission from the core, thus it is possible that an region still has not yet developed at this stage."1027" The secondary molecular source (denoted ‘B’ in Figure 3)) has no detectable millimetre, 24 nor 70 ccontinuum emission, thus no indication of an internal heating source."," The secondary molecular source (denoted `B' in Figure \ref{fig:intensity}) ) has no detectable millimetre, 24 nor 70 continuum emission, thus no indication of an internal heating source."1028 We speculate this source could be an even less evolved object., We speculate this source could be an even less evolved object.1029 Contrary to the Mopra, Contrary to the Mopra1030"where5 can be either 54, or 5». and el and D are properties of a galaxy. such as those defined. in eq.(42)).","where$\gamma$ can be either $\gamma_1$ or $\gamma_2$ , and $A$ and $B$ are properties of a galaxy, such as those defined in \ref{shear12PSF2}) )."1031" Similar to eq.(47)). eq.(48)) implies1 the following:8 where C' satislies (C5,,,=0."," Similar to \ref{assume_wr2}) ), \ref{symbol}) ) implies the following: where $C$ satisfies $\langle C\rangle_{en}=0$."1032" Lowe assume that the C' of any galaxy does not correlate with the 2's and C's of otherealaxies"".. the n-point correlation functions of the shear field can be probed. using the following relation: The ensemble averagesD are taken over a large5 number of galaxies whose relative positions À;—6; (ij=1.2..... n) ave fixed."," If we assume that the $C$ of any galaxy does not correlate with the $B$ 's and $C$ 's of other, the n-point correlation functions of the shear field can be probed using the following relation: The ensemble averages are taken over a large number of galaxies whose relative positions $\vec{x}_i-\vec{x}_j$ $i,j=1,2,\ldots,n$ ) are fixed."1033 In practice. the n-point shear correlation functions can be measured using: where the sum is taken over all the galaxy groups that satisfy the positional constraints.," In practice, the n-point shear correlation functions can be measured using: where the sum is taken over all the galaxy groups that satisfy the positional constraints."1034 Note thatsuimamalions., Note that.1035 The standard deviation (o) of the correlation function in such a measurement can be calculated as follows: where Nis the total number of galaxy groups(e.g... the number of galaxy pairs for 2-point correlations) used.," The standard deviation $\sigma$ ) of the correlation function in such a measurement can be calculated as follows: where $N$ is the total number of galaxy groups, the number of galaxy pairs for 2-point correlations) used."1036 To summarize. in the new type of shear measurement. the shear correlation function should be measured. using the ratio of two ensemble averages. as shown in eq.(50)).," To summarize, in the new type of shear measurement, the shear correlation function should be measured using the ratio of two ensemble averages, as shown in \ref{symbol3}) )."1037 Lo 2B in eq.(48)) is viewed as a multiplicative bias. we need to measure thecorrelations of these multiplicative biases as well in order to ect the correct shear correlation functions.," If $B$ in \ref{symbol}) ) is viewed as a multiplicative bias, we need to measure the of these multiplicative biases as well in order to get the correct shear correlation functions."1038 In this section. we show how accurately one can recover the cosmic shears and their 2-point correlation functions with the method proposed in refalternatives and refstatistics..," In this section, we show how accurately one can recover the cosmic shears and their 2-point correlation functions with the method proposed in \\ref{alternatives} and \\ref{statistics}."1039" For a comparison. wealso show the results using the method of ZOS in the “conventional” (fut wrong) wav.ie... eq(41). but without taking into account the biases. ὃν and 35."" Since our locus is to demonstrate principles. we do not include photon noise or the pixelation οσο in this paper. and we approximate the PSE as an isotropic Gaussian."," For a comparison, wealso show the results using the method of Z08 in the “conventional” (but wrong) way, \ref{shear12PSF_wrong}) ), but without taking into account the biases, $\delta_1$ and $\delta_2$ Since our focus is to demonstrate principles, we do not include photon noise or the pixelation effect in this paper, and we approximate the PSF as an isotropic Gaussian."1040 Including these cllects is straightforward. (, Including these effects is straightforward. (1041Note also that the conventional estimators vielcL biased results even in this iclealizecl case.),Note also that the conventional estimators yield biased results even in this idealized case.)1042 Alore comprehensive tests of the method. of ZOS have been presented in Zhang(2010b).. which further improves the accuracy of shear measurement by including the second order shear/convergence terms.," More comprehensive tests of the method of Z08 have been presented in \cite{zhang10b}, which further improves the accuracy of shear measurement by including the second order shear/convergence terms."1043 As shown in that paper. the second. order correction is proportional to the convergence 5B.," As shown in that paper, the second order correction is proportional to the convergence $\kappa$."1044 We simply set &=0 in thenumerical simulations here., We simply set $\kappa=0$ in thenumerical simulations here.1045 The residual svstematic error on the recovered. shear (54 Or 52) therefore shouldbe expected. to have à magnitude comparable to the third order terms in shear(e.g... 51.51 2153.E 2).," The residual systematic error on the recovered shear $\gamma_1$ or $\gamma_2$ ) therefore shouldbe expected to have a magnitude comparable to the third order terms in shear, $\gamma_1^3$, $\gamma_1^2\gamma_2$, $\gamma_1\gamma_2^2$, $\gamma_2^3$ )."1046 Phe errors shown in the rest of this section are all at the Lo confidence level., The errors shown in the rest of this section are all at the $1\sigma$ confidence level.1047 The mock galaxy images we use in our numerical tests are ecncrated by the algorithms introduced in ZOS ancl Zhang (2010a).4c... cach galaxy is generated as a collection of point sources.," The mock galaxy images we use in our numerical tests are generated by the algorithms introduced in Z08 and Zhang (2010a), each galaxy is generated as a collection of point sources."1048 The reason is simple: one can accurately and casily mimic the lensing effect by clisplacing the points., The reason is simple: one can accurately and easily mimic the lensing effect by displacing the points.1049 It also allows us to generate galaxies of complex morphologies., It also allows us to generate galaxies of complex morphologies.1050 There are two types of galaxies we use in this paper: 1., There are two types of galaxies we use in this paper: 1.1051 randomly oriented regular galaxies. cach of which contains an exponential disk in the galactic plane (no bulge): 2.," randomly oriented regular galaxies, each of which contains an exponential disk in the galactic plane (no bulge); 2."1052 irregular galaxies being mace of points generated by the trajectories of 2D random walks., irregular galaxies being made of points generated by the trajectories of 2D random walks.1053 For simplicity. the PSE is always an isotropic Gaussian function. whose scale radius is four times the grid size to avoid the pixelation problem.," For simplicity, the PSF is always an isotropic Gaussian function, whose scale radius is four times the grid size to avoid the pixelation problem."1054 AI the lengths in our simulations are in units of the grid size in the rest of this section., All the lengths in our simulations are in units of the grid size in the rest of this section.1055 The dimension of the grid is G4.64., The dimension of the grid is $64\times 64$ .1056 As our first example. we study how accurately a single input cosmic shear can be recovered by a large number of mock ealaxies.ie... the l-point statistics.," As our first example, we study how accurately a single input cosmic shear can be recovered by a large number of mock galaxies, the 1-point statistics."1057 We use the regular tvpe mock galaxies as introduced in refimage.., We use the regular type mock galaxies as introduced in \\ref{image}.1058 Each disk galaxy is composed of ten point sources which are randomly distributed within a radius of 7., Each disk galaxy is composed of ten point sources which are randomly distributed within a radius of 7.1059 The intensity of à point is an exponentially decaving function of its distance to the center of the disk with a decay. length equal to 7., The intensity of a point is an exponentially decaying function of its distance to the center of the disk with a decay length equal to 7.1060 The galactic disk is then projected. onto the source plane in a randomcirection., The galactic disk is then projected onto the source plane in a randomdirection.1061 For each input shear value. we use LOT mock galaxies to recover the shear.," For each input shear value, we use $10^7$ mock galaxies to recover the shear."1062" To quantify the accuracyof shear recovery. weadopt the standard techniquein the weak lensing community by using the “multiplicative bias” m; and the ""additive bias? c;. which are defined as:Our simulations use six sets of input shear values (σα. so)."," To quantify the accuracyof shear recovery, weadopt the standard techniquein the weak lensing community by using the “multiplicative bias” $m_i$ and the “additive bias” $c_i$ , which are defined as:Our simulations use six sets of input shear values $\gamma_1$ , $\gamma_2$ )."1063 They are: (0.05. 0.05). (0.038. 0.03). (0.01. 0.01). (0.01. 0.01). 0.03. 0.03). 0.05. 0.05).," They are: $0.05$ , $-0.05$ ), $0.03$ , $-0.03$ ), $0.01$ , $-0.01$ ), $-0.01$ , $0.01$ ), $-0.03$ , $0.03$ ), $-0.05$ , $0.05$ )."1064" The recovered shear values as well as the linear fitting results for 5, and", The recovered shear values as well as the linear fitting results for $\gamma_1$ and1065" The recovered shear values as well as the linear fitting results for 5, and", The recovered shear values as well as the linear fitting results for $\gamma_1$ and$1066" The recovered shear values as well as the linear fitting results for 5, and", The recovered shear values as well as the linear fitting results for $\gamma_1$ and$\1067" The recovered shear values as well as the linear fitting results for 5, and", The recovered shear values as well as the linear fitting results for $\gamma_1$ and$\g1068" The recovered shear values as well as the linear fitting results for 5, and", The recovered shear values as well as the linear fitting results for $\gamma_1$ and$\ga1069" The recovered shear values as well as the linear fitting results for 5, and", The recovered shear values as well as the linear fitting results for $\gamma_1$ and$\gam1070" The recovered shear values as well as the linear fitting results for 5, and", The recovered shear values as well as the linear fitting results for $\gamma_1$ and$\gamm1071" The recovered shear values as well as the linear fitting results for 5, and", The recovered shear values as well as the linear fitting results for $\gamma_1$ and$\gamma1072" The recovered shear values as well as the linear fitting results for 5, and", The recovered shear values as well as the linear fitting results for $\gamma_1$ and$\gamma_1073" The recovered shear values as well as the linear fitting results for 5, and5", The recovered shear values as well as the linear fitting results for $\gamma_1$ and$\gamma_21074" The recovered shear values as well as the linear fitting results for 5, and5»", The recovered shear values as well as the linear fitting results for $\gamma_1$ and$\gamma_2$1075"many bulges have characteristics that indicate that they were formed secularly by processes within the disc itself, rather than being related to merging or cold dark matter structure formation (?7)..","many bulges have characteristics that indicate that they were formed secularly by processes within the disc itself, rather than being related to merging or cold dark matter structure formation \citep{kormendy04,kormendy10}."1076" The most recent simulations of massive disc galaxies continue to form classical bulges, (B/T=0.19in ?,, and B/T=0.25 in ?,, see also ???))."," The most recent simulations of massive disc galaxies continue to form classical bulges, (B/T=0.19in \citealt{agertz10}, and B/T=0.25 in \citealt{guedes11}, , see also \citealt{scannapieco10,stinson10,brooks11}) )."1077" We note that in the ? paper, the authors claim that their bulge is secular in nature, based on the low Sérrsic index of the bulge in their two component bulge+disc decomposition."," We note that in the \cite{guedes11} paper, the authors claim that their bulge is secular in nature, based on the low Sérrsic index of the bulge in their two component bulge+disc decomposition."1078" However, they also state that their B/T has doubled since z=3, indicating that their bulge is at least partially classical."," However, they also state that their B/T has doubled since $z=3$, indicating that their bulge is at least partially classical."1079 These latest simulations have nevertheless formed significantly improved realisations of L. disc galaxies., These latest simulations have nevertheless formed significantly improved realisations of $_*$ disc galaxies.1080" Yet the angular momentum problem, and the associated problem of forming disc galaxies which do not have classical bulges, remains a serious challenge for the cold dark matter paradigm."," Yet the angular momentum problem, and the associated problem of forming disc galaxies which do not have classical bulges, remains a serious challenge for the cold dark matter paradigm."1081" Assuming the verity of the cold dark matter paradigm, it would seem that the resolution of the angular momentum problem requires either the orredistribution of low angular momentum material."," Assuming the verity of the cold dark matter paradigm, it would seem that the resolution of the angular momentum problem requires either the or of low angular momentum material."1082 Ejection of low angular momentum material has certainly been proposed (???)..," Ejection of low angular momentum material has certainly been proposed \citep{binney01,maller02,dutton09}."1083" Indeed, the ejection of low angular momentum gas by supernova explosions was shown to be key to the success of the first simulated bulgeless dwarf galaxies, which share many characteristics with observed dwarf galaxies (??).."," Indeed, the ejection of low angular momentum gas by supernova explosions was shown to be key to the success of the first simulated bulgeless dwarf galaxies, which share many characteristics with observed dwarf galaxies \citep{governato10,oh11}."1084" The processes which result in the ejection of low angular momentum gas from low mass galaxies, and the key role this has in suppressing bulge formation, were outlined in Brook et al. ("," The processes which result in the ejection of low angular momentum gas from low mass galaxies, and the key role this has in suppressing bulge formation, were outlined in Brook et al. ("1085"2011, Paper I).","2011, Paper I)."1086" The large scale ejection of low angular momentum gas meshes well with the need to enrich the IGM (??7),, and also with the observed low baryonic mass fraction of low mass galaxies (e.g. ?????))."," The large scale ejection of low angular momentum gas meshes well with the need to enrich the IGM \citep{maclow99,oppenheimer06,shen10}, and also with the observed low baryonic mass fraction of low mass galaxies (e.g. \citealt{klypin99,mandelbaum06,koposov08,guo10,moster10}) )."1087" However, in the absence of AGN feedback, more massive galaxies with larger potential wells will have greater difficulty ejecting their gas."," However, in the absence of AGN feedback, more massive galaxies with larger potential wells will have greater difficulty ejecting their gas."1088" This is reflected in the strength of the relationship between total mass and the baryonic mass fraction; higher mass disc galaxies have significantly higher baryonic mass fractions, retaining a far larger proportion of the cosmic baryon fraction."," This is reflected in the strength of the relationship between total mass and the baryonic mass fraction; higher mass disc galaxies have significantly higher baryonic mass fractions, retaining a far larger proportion of the cosmic baryon fraction."1089 This means that the large scale outflow of low angular momentum gas is not likely to explain the fact that many massive disc galaxies do not have classical bulges (?).., This means that the large scale outflow of low angular momentum gas is not likely to explain the fact that many massive disc galaxies do not have classical bulges \citep{kormendy10}.1090" Thus, processes which low angular momentum material may be necessary in higher mass disc galaxies."," Thus, processes which low angular momentum material may be necessary in higher mass disc galaxies."1091" In this paper, we propose that galactic fountains are an effective mechanism for such redistribution."," In this paper, we propose that galactic fountains are an effective mechanism for such redistribution."1092 It is generally accepted that supernova-powered bubbles drive gas out of the galactic disc and through the halo., It is generally accepted that supernova-powered bubbles drive gas out of the galactic disc and through the halo.1093" The expelled gas eventually falls back onto the disc, a mechanism known as galactic fountain (?7).."," The expelled gas eventually falls back onto the disc, a mechanism known as a galactic fountain \citep{shapiro76, bregman80}."1094" Here, we examine galactic fountainsa on larger scales, both spatially and temporally, by examining the fate of gas expelled from the inner regions of galaxies as they are assembling their mass at high redshift."," Here, we examine galactic fountains on larger scales, both spatially and temporally, by examining the fate of gas expelled from the inner regions of galaxies as they are assembling their mass at high redshift."1095" It is well established that supernova-driven winds can result in gas outflows (??) and that starbursts trigger strong outflows from the central regions, particularly during merger events (????).."," It is well established that supernova-driven winds can result in gas outflows \citep{matthews71,veilleux05} and that starbursts trigger strong outflows from the central regions, particularly during merger events \citep{cc85,heckman90,strickland07,tremonti07}."1096" Outflows are expected, and indeed observed to be more common at high redshift where star formation is more active, and potential wells shallower (??7???7).."," Outflows are expected, and indeed observed to be more common at high redshift where star formation is more active, and potential wells shallower \citep{madau96,pettini98, pettini00,simcoe02, shapley03,adelberger05}. ."1097 The bipolarstructure at the Galactic centre (27) lends support for galactic scale," The bipolarstructure at the Galactic centre \citep{joss03,su10} lends support for galactic scale"1098assuming it is ou the birthline.,assuming it is on the birthline.1099" Likewise. they calculate that the maximum likely mass of WLO is approximately O.1 ML.: this increases somewhat if he Lig, = 2.4 L. of WLY is adopted."," Likewise, they calculate that the maximum likely mass of WL6 is approximately 0.4 $_{\odot}$; this increases somewhat if the $_{\rm bol}$ = 2.4 $_{\odot}$ of WLY is adopted."1100 These maxim calculated masses assume that esseutially all luminosity is due to photospheric thermal radiation (L=Ix oT!) aud esseitially none is cdie to aceretion (L=GALAL/R).," These maximum calculated masses assume that essentially all luminosity is due to photospheric thermal radiation $L = 4\pi 1101R^{2}\sigma T^{4}$ ) and essentially none is due to accretion $L = G 1102M\dot{M}/R$ )."1103 These soIces are discussed further in §3., These sources are discussed further in $\S 4.3$.1104 We estimate that Elias 29 aix IRS 51 have veΝ high veilines if they are late-type low-lass stars. rg>LL-3L.," We estimate that Elias 29 and IRS 54 have very high veilings if they are late-type low-mass stars, $r_{k} > 14 - 34$."1105 The bolometric luminosity of IRS 2511s estimated to ye only 12 L. (WLY). also consistent. with this object beiug a low-niass p‘olostar which is accreting is envelope at the ate prescribed by the p Oph clotds gas temperaure.," The bolometric luminosity of IRS 54 is estimated to be only 12 $_{\odot}$ (WLY), also consistent with this object being a low-mass protostar which is accreting its envelope at the rate prescribed by the $\rho$ Oph cloud's gas temperature."1106 However. Hs conutinuun veiling must be ry>14—20 if it has spectral type MO aud is rotating rapidly.," However, its continuum veiling must be $r_{k} > 14 - 20$ if it has spectral type M0 and is rotating rapidly."1107 This is alxout a factor of 2 higher han the model precictious of Calvet et ab.," This is about a factor of 2 higher than the model predictions of Calvet et al.,"1108 but those calculations were cloje for z| hypohetical p Oph Class I YSO with L — 5 L.., but those calculations were done for a hypothetical $\rho$ Oph Class I YSO with L = 5 $_{\odot}$.1109 The i1odel may predict greater veiling or IRS ot if its hieler uminosity is taker iuto consideration., The model may predict greater veiling for IRS 54 if its higher luminosity is taken into consideration.1110 It is also possible that this source may be a sonew!at earlier ype protostar whichcl is less veiled., It is also possible that this source may be a somewhat earlier type protostar which is less veiled.1111 Elias 29 has tle highest derived. veiliug of the sample. ry25—31. assutulig aun ltrinsic 10 photosphere aix a hieh rotation rate.," Elias 29 has the highest derived veiling of the sample, $r_{k} > 25 - 111234$, assuming an intrinsic M0 photosphere and a high rotation rate."1113 WLY estimate its luminosity to be Lp — ISL... aud ALS have modele as a 1l M. protostar which is accreting its circumstellar euveloye.," WLY estimate its luminosity to be $_{\rm bol}$ = 48 $_{\odot}$, and ALS have modeled it as a 1 $_{\odot}$ protostar which is accreting its circumstellar envelope."1114 Such a star would have a spectral type of Ix3-4 iL o1 the birhline (seeD'Antona& 1988).. with an intrinsic CO absorption approxiujutely as strong as that of a1 MO star (see 83.2).," Such a star would have a spectral type of K3–4 if on the birthline \citep[see][]{DM97, S88}, with an intrinsic CO absorption approximately as strong as that of an M0 star (see 3.2)."1115 Thus we revise our estimate of the likely veiliug of this YSO to rj>15—20 if it is Indeed a LAL. protostar., Thus we revise our estimate of the likely veiling of this YSO to $r_{k} > 15 - 20$ if it is indeed a 1 $_{\odot}$ protostar.1116 In Paper I we analyzed t1e ALS model for Elias 29 aud showed ta the predicted emission from the inuer protostellar euveope of his source would produce a veiliig of rgcAv20. assunmiug that its disk Duiinosity is 0.75 Ly.," In Paper I we analyzed the ALS model for Elias 29 and showed that the predicted emission from the inner protostellar envelope of this source would produce a veiling of $r_{k} \approx 20$, assuming that its disk luminosity is 0.75 $_{\rm bol}$."1117 TIus OUF new neasureiment is COsistent with our earlier prediction based o the ALS moclel., Thus our new measurement is consistent with our earlier prediction based on the ALS model.1118 The hieh |uuluosity [9] “Elias 29 also allows for it being a more massive. earjer spectral type YSO that las ugher stellar luminosity ail less accretion lumüuosity than assujed by the ALS model.," The high luminosity of Elias 29 also allows for it being a more massive, earlier spectral type YSO that has higher stellar luminosity and less accretion luminosity than assumed by the ALS model."1119 HoyΜΟΝΟΙ. Hois unlsely to be very dillerent. because the observed. uear-to-lar IR energy distribution ai the 10 pi1 silicate absorpion of Elias 29 are fit well by the ALS model aud there are no clues wuieh inclicate hat Elias 29 is ὶur early-type object.," However, it is unlikely to be very different because the observed near-to-far IR energy distribution and the 10 $\micron$ silicate absorption of Elias 29 are fit well by the ALS model, and there are no clues which indicate that Elias 29 is an early-type object."1120 For example. WL 16. which is likely an early A tyye star (BiscayaHolzbacheal. 2000).. bas mid-IR aromatic hydrocarbou emissiou features whieh indicate a UV radiation fied (Hauuer.Tokunuaga.&Geballe1992).," For example, WL 16, which is likely an early A type star \citep{BHCRL00}, , has mid-IR aromatic hydrocarbon emission features which indicate a UV radiation field \citep{HTG92}."1121. However. Elias 29 shows uo evidence for IR. hydrocarbou euission (Hauner.1999) and thus no evidence for a UV radiatiou field.," However, Elias 29 shows no evidence for IR hydrocarbon emission \citep{HBT95,B99} and thus no evidence for a UV radiation field."1122 Our observatious. specifically the broad baud head shapes of IRS 51 and IRS 63. strengthen the earlier fiudiugs of Paper ΠΠ which si18800ested that flat-spectrum. protostars rotate morerapidly," Our observations, specifically the broad band head shapes of IRS 51 and IRS 63, strengthen the earlier findings of Paper II which suggested that flat-spectrum protostars rotate morerapidly"1123"The frequency of a photon with wavevector k as measured by an observer (or source) with 4-velocity U is—k""U,.",The frequency of a photon with wavevector $k^\mu$ as measured by an observer (or source) with 4-velocity $U^\mu$ is.1124".(14) If both the observer and the source are comoving in the LTB metric, then the photon redshift is given by loc z-k(tere)Το), where the subscripts e and o denote the event of emission and that of observation, respectively, and kt=k*(te,re)=1 is set arbitrarily as the initial condition."," If both the observer and the source are comoving in the LTB metric, then the photon redshift is given by 1 + z =, where the subscripts e and o denote the event of emission and that of observation, respectively, and $k_\rme^t \equiv k^t(t_\rme, r_\rme) = 1$ is set arbitrarily as the initial condition."1125" In actual calculations, we propagate photons backward from the observer to the source surface by setting —v k""— —k"") and the initial condition kf=kí(to,r9)(hence= —1."," In actual calculations, we propagate photons backward from the observer to the source surface by setting $v\to -v$ (hence $k^\mu \to -k^\mu$ ) and the initial condition $k_\rmo^t \equiv k^t(t_\rmo, r_\rmo) = -1$ ."1126" While Equations (3--3)) remain the same under the reversal of v, others may change sign."," While Equations \ref{eq:geo}- \ref{eq:z}) ) remain the same under the reversal of $v$, others may change sign."1127" 'To avoid confusion, we only refer to the forward case in all the equations and discussions below."," To avoid confusion, we only refer to the forward case in all the equations and discussions below."1128" The RS effect under investigation is of the order |AT|/T=|Az|/(1+z)~ 1079-1075, so one must ensure that numerical errors in k’ is much less than one part in a million."," The RS effect under investigation is of the order $|\Delta T|/T=|\Delta z|/(1+z) \sim 10^{-6}$ $10^{-5}$, so one must ensure that numerical errors in $k^t$ is much less than one part in a million."1129 Numerical results can be easily checked in uniform regions where alternative solutions exist., Numerical results can be easily checked in uniform regions where alternative solutions exist.1130" In addition, we perform several general tests that may detect numerical errors, which are described as follows."," In addition, we perform several general tests that may detect numerical errors, which are described as follows."1131" By definition, null geodesics obey k,k""=0."," By definition, null geodesics obey $k_\mu k^\mu = 0$."1132" This is a redundant constraint once the initial condition is set, as in principle the geodesic equation does not induce violation of the condition."," This is a redundant constraint once the initial condition is set, as in principle the geodesic equation does not induce violation of the condition."1133" However, numerical errors could be accumulated."," However, numerical errors could be accumulated."1134" While enforcing redundant constraints numerically is a subject of research itself, we simply adjust the time steps so that |k,k/k,k'|<10-8 when the photons exit the systems."," While enforcing redundant constraints numerically is a subject of research itself, we simply adjust the time steps so that $|k_\mu k^\mu / k_t k^t| \lesssim 10^{-8}$ when the photons exit the systems."1135" This condition is not sufficient to validate the results, but violation of it indicates significant numerical errors."," This condition is not sufficient to validate the results, but violation of it indicates significant numerical errors."1136" In spherically symmetric systems, each geodesic remains in a plane."," In spherically symmetric systems, each geodesic remains in a plane."1137" One can always rotate the coordinates to place the geodesic in the equatorial plane, in which case R?k? is conserved."," One can always rotate the coordinates to place the geodesic in the equatorial plane, in which case $R^2 k^\phi$ is conserved."1138" Similarly, R?k° is conserved if k?—0."," Similarly, $R^2 k^\theta$ is conserved if $k^\phi=0$."1139 We do not apply the known solution to reduce the dimensions of the system., We do not apply the known solution to reduce the dimensions of the system.1140" Rather, we use them to check the precision of the numerical solutions."," Rather, we use them to check the precision of the numerical solutions."1141 The maximum fractional error of the conserved quantity along off-center geodesics is found to be ~107°., The maximum fractional error of the conserved quantity along off-center geodesics is found to be $\sim 10^{-9}$.1142" Finally, radial geodesics can be calculated directly from the LTB metric dr=+,.,(16) where outward (inward) geodesics take the positive (negative) sign."," Finally, radial geodesics can be calculated directly from the LTB metric =, where outward (inward) geodesics take the positive (negative) sign."1143" By differentiating with respect to r(v), one gets the evolution of redshift where the sign on the far right side is the sameas that in Mustaphaetal.1998;Célérier2000,foranalternative(seederivation).."," By differentiating with respect to $r(v)$, one gets the evolution of redshift where the sign on the far right side is the sameas that in \citep[see][for an alternative derivation]{mustapha98,celerier00}."1144 Fractional differences between numerical solutions of z(r) and t(r) using Equations -11)) and those using Equations (3)) and (17)) are when photons exit the model structures., Fractional differences between numerical solutions of $z(r)$ and $t(r)$ using Equations \ref{eq:tdd}- \ref{eq:rdd}) ) and those using Equations \ref{eq:dtdr}) ) and \ref{eq:dzdr}) ) are $\lesssim 10^{-8}$ when photons exit the model structures.1145" 'The clusters studied in Granettetal.2008 have radii of roughly 100-!Mpc and a mean galaxy overdensity of 0.72 within the overdense region, corresponding to a matter overdensity of 0.36 with a galaxy clustering bias of roughly 2 for luminous red galaxies (Padmanabhanetal.2007;Blake2008)."," The clusters studied in \citealt{granett08} have radii of roughly $100\Mpch$ and a mean galaxy overdensity of 0.72 within the overdense region, corresponding to a matter overdensity of 0.36 with a galaxy clustering bias of roughly 2 for luminous red galaxies \citep{padmanabhan07,blake08}."1146". Thus, our simple LTB models of these clusters have an inner radius ri= an outer radius rg;=280Mpc (205 Mpc) for the compensated (uncompensated) profile, and a uniform overdensity 6;=0.36 in region I at z=0.5."," Thus, our simple LTB models of these clusters have an inner radius $\rI=140 \Mpc$ , an outer radius $\rII = 280 \Mpc$ (205 Mpc) for the compensated (uncompensated) profile, and a uniform overdensity $\dI=0.36$ in region I at $z=0.5$."1147" For voids, the only difference is 6;=—0.19."," For voids, the only difference is $\dI=-0.19$."1148 provides more details about these profiles and their corresponding metric quantity R., provides more details about these profiles and their corresponding metric quantity $R$.1149" To calculate the RS effect, we place a model structure between an observer and a source surface and propagate photons from the latter to the former (as mentioned in3,, they are actually propagated backwards)."," To calculate the RS effect, we place a model structure between an observer and a source surface and propagate photons from the latter to the former (as mentioned in, they are actually propagated backwards)."1150" The source surface is spherical around the observer in coordinate space, so that in absence of the structure, photons originated from the surface at the same time would reach the observer at the same time with the same redshift."," The source surface is spherical around the observer in coordinate space, so that in absence of the structure, photons originated from the surface at the same time would reach the observer at the same time with the same redshift."1151" With the intervening structure though, the photons received at the same time would have started from the source surface at different times because of gravitational time delay, and their redshifts would have to compensate for the time delay plus additional changes because of nonlinear evolution of the structure."," With the intervening structure though, the photons received at the same time would have started from the source surface at different times because of gravitational time delay, and their redshifts would have to compensate for the time delay plus additional changes because of nonlinear evolution of the structure."1152" The net change in temperature is a sum of the two components: AT= + where Tomp=],=2.73K is the present CMB temperature, At, is the time difference at the source, H,=H(zs) is the Hubble parameter at the source redshift z,, and Az, is the redshift difference “measured” by an observer at present."," The net change in temperature is a sum of the two components: T = + ], where $T_\mathrm{CMB}=2.73\,\mathrm{K}$ is the present CMB temperature, $\Delta t_\mathrm{s}$ is the time difference at the source, $H_\mathrm{s} \equiv H(z_\mathrm{s})$ is the Hubble parameter at the source redshift $z_\mathrm{s}$, and $\Delta z_\mathrm{s}$ is the redshift difference “measured” by an observer at present."1153 Note that the two components in cannot be measured separately in the case of the CMB., Note that the two components in cannot be measured separately in the case of the CMB.1154"(4) The time component accounts for the decrease of the CMB temperature with time, and Az, bears the subscript s because it varies with the source location."," The time component accounts for the decrease of the CMB temperature with time, and $\Delta z_\mathrm{s}$ bears the subscript s because it varies with the source location."1155" In the uniform background universe, a small time difference of At translates to a redshift difference of Hence, in region III of compensated models, one can separate 2ς into a time-compensation term and an evolution term z=Az,— 2t."," In the uniform background universe, a small time difference of $\Delta t$ translates to a redshift difference of Hence, in region III of compensated models, one can separate $z_\mathrm{s}$ into a time-compensation term and an evolution term $z_\mathrm{s}^{e} = \Delta z_\mathrm{s} - z_\mathrm{s}^{t}$ ."1156" Since zi exactly cancels H,At, in region III, becomes"," Since $z_\mathrm{s}^{t}$ exactly cancels $H_\mathrm{s}\Delta t_\mathrm{s}$ in region III, becomes"1157After scaling the fluxes. we compiled a SED and fit a single grey-body to the l60um Lo mmweavelengthdata(seeFigs.,"After scaling the fluxes, we compiled a SED and fit a single grey-body to the $\micron$ -1 mm wavelength data (see Figs."1158 2??aa— candllaa eytoderivethemassandtheaveragedusttemperatureo feachdensecore., \ref{fig:SEDex}a a-c and \ref{fig:SEDex2}a a-e) to derive the mass and the average dust temperature of each dense core.1159"Wec with ky=0.1gem"" and a dust emissivity index MofB22.", We assumed a dust opacity law $\kappa_\lambda=\kappa_{0}\times\left( \frac{\lambda}{300~\mu\mbox{\tiny m}} \right)^{-\beta}$ with $\kappa_{0}=0.1~\gcm$ and a dust emissivity index of $\beta=2$.1160 EUMOur limited knowledge ot dust emissivity makes masses systematically uncertain by a thefactor of ~2., Our limited knowledge of the dust emissivity makes masses systematically uncertain by a factor of $\sim$ 2.1161 The mass and dust temperature uncertainties quoted in Table | reflect SED fits to fluxes varying by with a constant emissivity., The mass and dust temperature uncertainties quoted in Table \ref{table:MDC} reflect those of SED fits to fluxes varying by with a constant emissivity.1162those.of We successfully counterchecked our results obtained with single grey-body fits to the long wavelength (2160 4m) component of SEDs by fitting two-temperature grey-body models to the data (see Fig. ??)).," We successfully counterchecked our results obtained with single grey-body fits to the long wavelength $>$$160\,\mu$ m) component of SEDs by fitting two-temperature grey-body models to the data (see Fig. \ref{fig:SEDex}) )."1163" We also derived the bolometric luminosity &,,, and submillimeter luminosity L.,, by integrating fluxes below the measurement points Le. from 3.6jmrol.l mmandfrom350pm to 1.1 mm. respectively."," We also derived the bolometric luminosity $\lbol$ and submillimeter luminosity $\lsubmm$ by integrating fluxes below the measurement points i.e., from $\micron$ to 1.1 mm and from $\micron$ to 1.1 mm, respectively."1164 When sources were not detected at mid-infrared wavelengths.," When sources were not detected at mid-infrared wavelengths,"1165reason why Yegn is because the bulk of the Me is not near the photosphere. but rather deep in the envelope.,"reason why $y_{\rm He} \gg y_{\rm ph}$ is because the bulk of the He is not near the photosphere, but rather deep in the envelope."1166 We show this in the top pancls of Figures 2. and 3 where we plot gg (short-dashed lines) as a function of y.," We show this in the top panels of Figures \ref{fig:he1167 burning profile 1} and \ref{fig:he burning profile 2} where we plot $y_{\rm He}$ (short-dashed lines) as a function of $y$."1168 Note that the bulk of the Te docs not reside near the surface. but increases substantially until is asviuptotes at a column of 47Your.," Note that the bulk of the He does not reside near the surface, but increases substantially until is asymptotes at a column of $y\approx1169y_{\rm cut}$."1170 We now explain why the bulk of We resides near gag., We now explain why the bulk of He resides near $y_{\rm cut}$.1171 Iu paper L we showed that the total lifetime of IT ou a proton capturing substrate is dominated by the time it takes to remove a photospheric IT column.," In paper I, we showed that the total lifetime of H on a proton capturing substrate is dominated by the time it takes to remove a photospheric H column."1172 Namely. we fouud that the II lifetime. τμ. scales with the IT column as πικud. where 6=ASA|feyZo|. where 1 aud 2 denote the background and trace ion species respectively. ie. D]80=5/12<0 for a II ou C envelope (paper D.," Namely, we found that the H lifetime, $\tau_{\rm H}$, scales with the H column as $\tau_{\rm H} \propto y_{\rm H}^{1+\delta}$, where $\delta = A_2(Z_1 + 1)/A_1 - Z_2 - 1$, where $1$ and $2$ denote the background and trace ion species respectively, i.e., $1+\delta=-5/12 < 0$ for a H on C envelope (paper I)."1173 As we discussed in 85.2 of paper L this scaling arises from the power-law falloff of II abundance in a nondegeuerate atmosphere. which is Επxamap12 (soc eq. [," As we discussed in 5.2 of paper I, this scaling arises from the power-law falloff of H abundance in a nondegenerate atmosphere, which is $n_{\rm H}/n_{\rm1174 tot} \propto y^{\delta} = y^{-17/12}$ (see eq. ["11751] of paper D).,31] of paper I).1176 For Πο on C. the Ie abundance follows μαWwgτμD5m The ," For He on C, the He abundance follows $n_{\rm He}/n_{\rm tot} \propto1177y^{\delta} = y^{-2/3}$."1178IT abundance ou a C substrate falls off steeper than yLo whereas the Te abundance on a C substrate falls off shallower than y+.," The H abundance on a C substrate falls off steeper than $y^{-1}$, whereas the He abundance on a C substrate falls off shallower than $y^{-1}$."1179 Thus. the IL cohuun is capped at the T/C boundary. the colin where the umber deusitv of IT and C are equal. but the We column coutinucs to increase substantially below the Πο/C boundary.," Thus, the H column is capped at the H/C boundary, the column where the number density of H and C are equal, but the He column continues to increase substantially below the He/C boundary."1180 Indeed. one can show that the Ile column always increases below the Te/substrate boundary for auv substrate with A/Z~2.," Indeed, one can show that the He column always increases below the He/substrate boundary for any substrate with $A/Z \approx 2$."1181 This increasing Πο column carries through to the Coulomb case as discussed earlier im refsecicoulonib.., This increasing He column carries through to the Coulomb case as discussed earlier in \\ref{sec:coulomb}. .1182 Indeed. the We column coutinues to rise uutil it is capped at a column of fag as we argued iu retsec:theriait.," Indeed, the He column continues to rise until it is capped at a column of $y_{\rm cut}$ as we argued in \\ref{sec:thermal}."1183. We now uote that the burning laver is close to the reeion where He beeius to get cut off. vinevYeur (800 for instance. Figures 2 and 3)).," We now note that the burning layer is close to the region where He begins to get cut off, $y_{\rm burn} \sim y_{\rm cut}$ (see for instance, Figures \ref{fig:he burning profile 1} and \ref{fig:he1184 burning profile 2}) )."1185 I£sve sav that they are the sale. we are left with the result that the Πο abundance in the burning laver aud the total Πο column axelinearly related to each over.," If we say that they are the same, we are left with the result that the He abundance in the burning layer and the total He column are related to each over."1186 Since the rate of Πο DNB (via captures outo €) is linearly related to the He abundance (and hence p.X sue). we find that the lifetime of the Ile laver. τις=πιωte Is Independent of gui as demonstrated in Table 1.. explaining the indepcudence of Tile axd tlle.," Since the rate of He DNB (via captures onto C) is linearly related to the He abundance (and hence $\dot{y}_{\rm He} \propto y_{\rm He}$ ), we find that the lifetime of the He layer, $\tau_{\rm He} = y_{\rm1187 He}/\dot{y}_{\rm He}$ is independent of $y_{\rm He}$ as demonstrated in Table \ref{table:tau}, explaining the independence of $\tau_{\rm1188 He}$ and $y_{\rm He}$."1189 Iu Figure L. we show the He lifetinie. 7j. for a ange of a-capturnug material as a function of base temperature. Ji (left). effective temperature. Z5. aud B=0 (solid lues).," In Figure \ref{fig:He burning lifetime col}, we show the He lifetime, $\tau_{\rm He}$ , for a range of $\alpha$ -capturing material as a function of base temperature, $T_b$ (left), effective temperature, $T_e$, and $B=0$ (solid lines)."1190 We also plot (dotted lines) the same case but for a radial B-ficld of B=LOY €. Magnetic fields up to pulsar strengths do not make a siguificaut difference., We also plot (dotted lines) the same case but for a radial B-field of $B=10^{12}$ G. Magnetic fields up to pulsar strengths do not make a significant difference.1191 For sufficeutlv. large base teuiperatures. the lifetime to deplete the atmosphere of He is a few weeks.," For sufficently large base temperatures, the lifetime to deplete the atmosphere of He is a few weeks."1192 To compare the lifetime of a Te laver with the typical cooling history of a NS. we plot in Figure 5. a few representative cooling tracks (loug-dashed dines) aud overlay the τι relation shown iu Figure L.," To compare the lifetime of a He layer with the typical cooling history of a NS, we plot in Figure \ref{fig:He burning lifetime} a few representative cooling tracks (long-dashed lines) and overlay the $\tau_{\rm He}$ $T_b$ relation shown in Figure \ref{fig:He burning1193 lifetime col}."1194 Here. we have plotted Z5. which during the very carly history (age X100 vrs) of the NS zT...," Here, we have plotted $T_b$, which during the very early history (age $\lesssim 100$ yrs) of the NS $\neq T_c$."1195" Only after the cooling wave sweeps through the star. which cau be seen by the sudden drop in Z5, at ~LOO vrs. is the NS in thermal equilibrimm."," Only after the cooling wave sweeps through the star, which can be seen by the sudden drop in $T_b$ at $\sim 100$ yrs, is the NS in thermal equilibrium."1196 As we have done in paper IL. we include a standard cooling track which prestunes modified URCA cooling ona 1.3 NNS. another with core proton superfiuiditv (Potelshin et al.," As we have done in paper II, we include a standard cooling track which presumes modified URCA cooling on a 1.3 NS, another with core proton superfluidity (Potekhin et al."1197 2003). and one with triplet-state neutron superfuidity in the core with a mnaxuuuni critical temperature of δν10°IS (ealeulated by D. €. Yakovlev previously for paper ID.," 2003), and one with triplet-state neutron superfluidity in the core with a maximum critical temperature of $8\times 10^8 \ {\rm K}$ (calculated by D. G. Yakovlev previously for paper II)."1198 The remarkable aspect of this plot is that independent of the cooling model assuned (where we have taken a few representative models that span the range frou standard cooling to fast cooling). the lifetime of a ο atmosphere is short compared to the cooling age (duriug its carly history}.," The remarkable aspect of this plot is that independent of the cooling model assumed (where we have taken a few representative models that span the range from standard cooling to fast cooling), the lifetime of a He atmosphere is short compared to the cooling age (during its early history)."1199 For iustauce. Ho on a € envelope will be depleted even in the fast cooling case. if it was deposited up to 1000 vrs after formation.," For instance, He on a C envelope will be depleted even in the fast cooling case, if it was deposited up to 1000 yrs after formation."1200 For slowly cooling models. this can extend up to almost 1 Myr.," For slowly cooling models, this can extend up to almost 1 Myr."

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