ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 For completeness. we present here the solution inside the external mecium.," For completeness, we present here the solution inside the external medium."3 By assumption. the external medium has a uniform temperature and density. and a uniform rate of cooling.," By assumption, the external medium has a uniform temperature and density, and a uniform rate of cooling."4 To maintain equilibrium. there has to be some constant source of heat that exactly. compensates for the cooling.," To maintain equilibrium, there has to be some constant source of heat that exactly compensates for the cooling."5 We assume that such a source of heat exists (c.g. cosmic ravs).," We assume that such a source of heat exists (e.g., cosmic rays)."6 The rotation @ is non-zero. but it clecays rapidly outward.," The rotation $\Omega$ is non-zero, but it decays rapidly outward."7 “Phe small amount of rotation helps to transport the angular momentum [lux from the star out into the external medium., The small amount of rotation helps to transport the angular momentum flux from the star out into the external medium.8" Solving the angular momentunir conservation law (3). we obtain the following solution Latin. Omega, ‘Uprttlicted Has QUSS and post=2&8ο"," Solving the angular momentum conservation law (3), we obtain the following solution , _3 where _3 = (k , and $p_{\rm ext}=2kT_{\rm9ext}\rho_{\rm ext}/m_p$."10 For i=O. the velocity scales as 2," For $\dot m\not=0$, the velocity scales as $r^{-2}$."11 The three self-similar solutions written above are special solutions of the basie dilferential equations (2). (3) and (5). which are valid. under specific conditions.," The three self-similar solutions written above are special solutions of the basic differential equations (2), (3) and (5), which are valid under specific conditions."12 To check the validity of these analytical solutions. we have computed numerical solutions of the basic dilferential equations.," To check the validity of these analytical solutions, we have computed numerical solutions of the basic differential equations."13 We use the same code as in ΜΙΝΟΣ with two changes.," We use the same code as in MN01, with two changes."14 First. we switched to the viscosity prescription given in equation (4)). rather than the prescription vo=oclíOg used in AINOL.," First, we switched to the viscosity prescription given in equation \ref{nu}) ), rather than the prescription $\nu = \alpha15c_s^2/\Omega_K$ used in MN01."16 Second. in addition to viscous heating. we included a constant heating rate which we adjusted so as to balance the radiative cooling in the homogeneous external medium (see 822.3).," Second, in addition to viscous heating, we included a constant heating rate which we adjusted so as to balance the radiative cooling in the homogeneous external medium (see 2.3)."17 The code uses a relaxation method to solve the onc-dimensional hyelrodvnamic equations. with specified inner and outer boundary conditions., The code uses a relaxation method to solve the one-dimensional hydrodynamic equations with specified inner and outer boundary conditions.18" Although it. employs the full equations of a two-tempoerature plasma. the results are essentially equivalent to those of a one-tempoerature plasma in the region of interest for this paper. namely the region at large radius where the flow matches onto the external mecdium In the calculations. the How was taken to extend from. an inner radius Ain=3Ry, to Raw=10*Hg."," Although it employs the full equations of a two-temperature plasma, the results are essentially equivalent to those of a one-temperature plasma in the region of interest for this paper, namely the region at large radius where the flow matches onto the external medium In the calculations, the flow was taken to extend from an inner radius $R_{\rm in}=3~R_g$ to $R_{\rm out}=10^7~R_g$."19 Lhe mass accretion rate was taken to be low. ii—2«10.7. in order hat the Low should. correspond to the regime of the hot settling Low solution.," The mass accretion rate was taken to be low, $\dot m=2\times 10^{-5}$, in order that the flow should correspond to the regime of the hot settling flow solution."20 We took the viscosity. parameter to »' à=OL and set the spin of the star to be s=0.3 (i.c... of the Ixeplerian rotation at the stellar surface).," We took the viscosity parameter to be $\alpha=0.1$ and set the spin of the star to be $s=0.3$ (i.e., of the Keplerian rotation at the stellar surface)."21 We took the other inner boundary conditions to be the same as in MNOI., We took the other inner boundary conditions to be the same as in MN01.22 At the outer boundary. we specified the emperature and. density of the external medium.," At the outer boundary, we specified the temperature and density of the external medium."23 Figure 4 shows four solutions.," Figure \ref{f:prof}24 shows four solutions."25" Phe external temperature is kept ixecl αἱ T(Rox)=10 lx in all the solutions. but. the external density varies by. a decade and a halt: pCoxi)=202185(,23ο2.510.&1-I0 em7."," The external temperature is kept fixed at $T(R_{\rm ext})=10^8$ K in all the solutions, but the external density varies by a decade and a half: $\rho(R_{\rm ext})= 2.5\times10^9,\268.1\times10^8,\ 2.5\times10^8,\ 8.1\times10^7$ $^{-3}$."27 We have also clonemE other cuedlations in which we kept post fixed and varied Lis)., We have also done other calculations in which we kept $\rho_{\rm ext}$ fixed and varied $T_{\rm ext}$.28 These give very similar results., These give very similar results.29 lis., Fig.30 4 shows that. right next to the star. there is a boundary. laver. where the density rises sharply as one gocs into the star and the temperature drops. suddenly.," \ref{f:prof} shows that, right next to the star, there is a boundary layer, where the density rises sharply as one goes into the star and the temperature drops suddenly."31 We do not analyze this region., We do not analyze this region.32 Once we are outside the boundary laver. the eas behaves very much according to the analytical solutions discussed in 822.," Once we are outside the boundary layer, the gas behaves very much according to the analytical solutions discussed in 2."33 Starting just outside the boundary laver and extending over a wicle range of radius. the numerical solution exhibits a selsimilar behavior with power-law dependences of the density. emperature and angular velocity.," Starting just outside the boundary layer and extending over a wide range of radius, the numerical solution exhibits a self-similar behavior with power-law dependences of the density, temperature and angular velocity."34 This region corresponds o the self-similar solution of AINOL., This region corresponds to the self-similar solution of MN01.35 There are. in fact. wo zones. an inner lwo-tempoeratiure Zone. and an outer one-temperature zone (ALNOL).," There are, in fact, two zones, an inner two-temperature zone, and an outer one-temperature zone (MN01)."36 The latter corresponds to solution 1 (eq. 6)), The latter corresponds to solution 1 (eq. \ref{1st-sol}) )37 discussed in 822.1., discussed in 2.1.38 The most notable eature of this region is that the density. temperature and angular velocity of the numerical solutions are completeA independent of the outer temperature ancl density. as by the analytical solution.," The most notable feature of this region is that the density, temperature and angular velocity of the numerical solutions are completely independent of the outer temperature and density, as predicted by the analytical solution."39 The slopes of the numerical curves also agree well with the analytical scalings., The slopes of the numerical curves also agree well with the analytical scalings.40" At a radius sas,~5105.2«107I, 9depending on the outer pressure. see eq. 13))."," At a radius $R_{\rm match}\sim5\times10^4 ... 2\times10^5~R_g$ 9depending on the outer pressure, see eq. \ref{R12}) ),"41 solution 1 merges with solution 2 (eq. 11)), solution 1 merges with solution 2 (eq. \ref{2nd-sol}) )42 described in 822.2., described in 2.2.43" Here. the solution does depend on the outer boundary conditions. and it scales roughly according to the slopes derived analytically,"," Here, the solution does depend on the outer boundary conditions, and it scales roughly according to the slopes derived analytically."44" At even larger racii /?>Ros~Bo107.2210""A (see eq. 142)."," At even larger radii $R > R_{\rm ext}\sim3\times10^5 ... 2\times10^6~R_g$ (see eq. \ref{R23}) ),"45 the Dow matches onto the ambient external medium., the flow matches onto the ambient external medium.46 In this region we have solution 3 (eq. 15)), In this region we have solution 3 (eq. \ref{3rd-sol}) )47 described. in 822.3., described in 2.3.48 As expected. out here only the angular velocity and the racial velocity vary with radius.," As expected, out here only the angular velocity and the radial velocity vary with radius."49 Both have the scalings predicted for solution 3., Both have the scalings predicted for solution 3.50 In this paper. we have removecl one piece of mystery surrounding the self-similar “hot settling [low or “hot brake” solution discovered. by ALNOL.," In this paper, we have removed one piece of mystery surrounding the self-similar “hot settling flow” or “hot brake” solution discovered by MN01."51 Specifically. we have shown that. the remarkable insensitivity. of the AINOL solution to external boundary. conditions is a consequence of the fact that the solution is insulated. from the outer boundary by the presence ofa second solution. which bridges the gap between the first solution and the external medium.," Specifically, we have shown that the remarkable insensitivity of the MN01 solution to external boundary conditions is a consequence of the fact that the solution is insulated from the outer boundary by the presence of a second solution, which bridges the gap between the first solution and the external medium."52 We derived the form of the second. solution analytically in 822.2 and showed via numerical computations (833. Fig.," We derived the form of the second solution analytically in 2.2 and showed via numerical computations 3, Fig."53 1) that the two solutions together are able to match a wide range of outer boundary. conditions., 1) that the two solutions together are able to match a wide range of outer boundary conditions.54 This solves one of the nivsteries associated with the hot settling Dow solution., This solves one of the mysteries associated with the hot settling flow solution.55 There are. however. two other problems that still need o be addressed.," There are, however, two other problems that still need to be addressed."56 First. the solution we have derived. treats he mass accretion rate 5)» as a free parameter. (," First, the solution we have derived treats the mass accretion rate $\dot m$ as a free parameter. ("57Indeed. he analvtical solutions were obtained for the limit ) be. for a hot atmosphere.),"Indeed, the analytical solutions were obtained for the limit $\dot m\to0$ , i.e. for a hot atmosphere.)"58 What determines ri?, What determines $\dot m$?59 Lt is certainly not the outer boundary. since we have obtained the complete outer solution.," It is certainly not the outer boundary, since we have obtained the complete outer solution."60 The accretion rate must therefore xf determined by an innerboundary condition., The accretion rate must therefore be determined by an innerboundary condition.61 This is not unexpected., This is not unexpected.62 In the case of spherical accretion. one recalls hat. while the accretion rate for the transonic solution is determined by the outer boundary conditions. the accretion," In the case of spherical accretion, one recalls that, while the accretion rate for the transonic solution is determined by the outer boundary conditions, the accretion"63"The solution is so that. uxiug οαοσα1.020,47. The divergence as C approaches unity is not real. as our ueglect of adiabatic losses and of acctuuulation within the shell are incorrect when the holes close up.","The solution is so that, using $(1-C_f)(1-1.045 C_f)\simeq (1-1.02 C_f)^2$, The divergence as $C_f$ approaches unity is not real, as our neglect of adiabatic losses and of accumulation within the shell are incorrect when the holes close up."64" Likewise values of füapae less than fi, are not realistic. because the wind force is always present: our error in this unit is to assume that the wind energy is thermalizecl when iu fact it remains mostly kinetic if the shell is mostly holes."," Likewise values of $f_{\rm trap,w}$ less than $f_w$ are not realistic, because the wind force is always present; our error in this limit is to assume that the wind energy is thermalized, when in fact it remains mostly kinetic if the shell is mostly holes."65" since f,&0.5. this iuplies that faa&0.22/(1Cy)~1l unless we are cousidering the case of an embedded: region with an extremely non-porous shell Lo€1l."," Since $f_w\simeq 0.5$, this implies that $f_{\rm trap,w}\simeq 0.22/(1-C_f) \sim 1$ unless we are considering the case of an embedded region with an extremely non-porous shell, $1-C_f \ll 1$."66 Such low porosity is imuplausible eiven the turbulent. chuupy nature of the interstellar medi and the fact that pressure-driven shocks tend to run down density eracdieuts and “blow out”.," Such low porosity is implausible given the turbulent, clumpy nature of the interstellar medium and the fact that pressure-driven shocks tend to run down density gradients and “blow out”."67 Even if one started with a perfectly uniforii ISM. the expanding shell is subject to? instability of a pressure-driven slab: moreover if the wind caused the expanding shell to accelerate then the Ravleigh-Tavlor instability would spontaneously create holes iu the shell. reducing C below τητν.," Even if one started with a perfectly uniform ISM, the expanding shell is subject to \citet{Vishniac83a} instability of a pressure-driven slab; moreover if the wind caused the expanding shell to accelerate then the Rayleigh-Taylor instability would spontaneously create holes in the shell, reducing $C_f$ below unity."68" Thus we couclude that fija, is at most a few. and is likely to be small than order uuitv."," Thus we conclude that $f_{\rm trap,w}$ is at most a few, and is likely to be small than order unity."69 Our conchision is cousistent with the numerical simulations of ?.. who also flud that. in a non-uuifori medi. the bulk of the mass around a youug star is not swept up into the thermal wind drveu by ~LO! K clustereas.," Our conclusion is consistent with the numerical simulations of \citet{tenorio-tagle06a}, who also find that, in a non-uniform medium, the bulk of the mass around a young star cluster is not swept up into the thermal wind driven by $\sim 10^7$ K gas."70 Iustead. that gas escapes rapidly through the porous shell. while the bulk of the mass expands more slowly (see their Figure 9).," Instead, that gas escapes rapidly through the porous shell, while the bulk of the mass expands more slowly (see their Figure 9)."71 The above calculation depends somewhat ou our estimate of the term Mag. which is uncertain for several reasons: because the phivsies of ablation is uot well understood. because the ablating area could be very different from for instance if the shells structure is amore interestingπμ. than a broken sphere. and because other mechiauisuis like thermal evaporation. photoevaporation. aud cloud disruption can all imject mass.," The above calculation depends somewhat on our estimate of the term $\dot{M}_{\rm abl}$, which is uncertain for several reasons: because the physics of ablation is not well understood, because the ablating area could be very different from $4\pi C_f \rii^2$, for instance if the shell's structure is more interesting than a broken sphere, and because other mechanisms like thermal evaporation, photoevaporation, and cloud disruption can all inject mass."72 Similarly. the deusitv of the ablating gas could be lugher than indicated by our pressurc-balauce areument. since photocvaporation nüght compress the gas (0.8.?)..," Similarly, the density of the ablating gas could be higher than indicated by our pressure-balance argument, since photoevaporation might compress the gas \citep[e.g.][]{bertoldi90}."73 Given these uncertainties. one might consider ey better constrained than Maji for mstance. au upper limit ou the N-rav huuinosity implies a lower limit oun ex.," Given these uncertainties, one might consider $c_X$ better constrained than $\dot{M}_{\rm abl}$ – for instance, an upper limit on the X-ray luminosity implies a lower limit on $c_X$ ."74" Takine ον as given aud solving equations (21)) aud (25)) for Py. we find so trapping is muportant when (1CyyeyCpfafd~ OA, "," Taking $c_X$ as given and solving equations \ref{HotGasConservation1}) ) and \ref{HotGasConservation2}) ) for $P_X$, we find so trapping is important when $(1-C_f) c_X/v_w < f_w/5 \simeq 0.1$ ."75Protostellar winds represeut a separate. brief. but very intense phase which deserve separate mention.," Protostellar winds represent a separate, brief, but very intense phase which deserve separate mention."76 Bene magnetically launched. they axe strougly collimated aud may far exceed the photon momentum: moreover the entire stellar population generates them.," Being magnetically launched, they are strongly collimated and may far exceed the photon momentum; moreover the entire stellar population generates them."77 Rather than assess them directly we appeal to the treatinent by ?.. who found that protostellar winds are very significant in the formation of the Pleiades and Orion Nebula clusters. but quite insignificant iu the formation of the Arches or more Inassive clusters.," Rather than assess them directly we appeal to the treatment by \citet{matzner07}, who found that protostellar winds are very significant in the formation of the Pleiades and Orion Nebula clusters, but quite insignificant in the formation of the Arches or more massive clusters."78 If the expanding shell traps the iutrared light eiuitted within if. then ifs momentum will exceed. that of the diivius starlighit by a factor where Pug is the pressure of the trapped IR radiation field inside the shell.," If the expanding shell traps the infrared light emitted within it, then its momentum will exceed that of the driving starlight by a factor where $P_{\rm IR}$ is the pressure of the trapped IR radiation field inside the shell."79 We first cousider the highly idealized case of a uniform. non-porous shell C;=1. which provides an upper Tit on fap. before treating leakage through holes.," We first consider the highly idealized case of a uniform, non-porous shell, $C_f = 1$, which provides an upper limit on $\ftrapIR$, before treating leakage through holes."80 When a uniform shell is optically thick to its own thermal enüssiou. it radiates from a photosphere above which the dus-averaged optical depth is 2/3.," When a uniform shell is optically thick to its own thermal emission, it radiates from a photosphere above which the flux-averaged optical depth is 2/3."81 The enmüssion is characterized by the shells effective temperature. which satisfies InroupTil.=L. and the fiux-averaged nass opacity above the photospliere is approximately the Plauck mean #p(Tug). implviug a colunu Syn2ΑΜνι) above the photosphere.," The emission is characterized by the shell's effective temperature, which satisfies $4\pi \rii^2 \sigma_{\rm SB} \Teffsh^4 = L$, and the flux-averaged mass opacity above the photosphere is approximately the Planck mean $\kappa_P(\Teffsh)$, implying a column $\Sigma_{\rm ph}\simeq2/[3\kappa_P(\Teffsh)]$ above the photosphere."82" Shells with “yj,=Mi,< are optically thin to reprocessed light.", Shells with $\Sigma_{\rm sh} = \msh/(4\pi \rii^2)<\Sigma_{\rm ph}$ are optically thin to reprocessed light.83"(Liv?) Thick shells.δα with Xa,>> Man can be treated du the diffusion approximation (Pir) ιο and sg the Rosselaud mean mass opacity). below the photosphere."," Thick shells, with $\Sigma_{\rm sh}\gg \Sigma_{\rm ph}$ , can be treated in the diffusion approximation $d P_{\rm IR}/\kappa_R(T) = - \sigma_{\rm SB} \Teffsh^4 d\Sigma$ with $P_{\rm IR}=a T(\Sigma)^4/3$ and $\kappa_R$ the Rosseland mean mass opacity), below the photosphere."84 The solution for the pressurewithin au optically thick shell is where JP)—fyPirUPigiT). aud Fo+) is. the inverse function of JF.," The solution for the pressurewithin an optically thick shell is where ${\cal F}(P_{\rm IR}) = \int_0^{P_{\rm IR}} dP_{\rm IR}'/\kappa_R(T')$, and ${\cal F}^{(-1)}$ is the inverse function of $\cal F$."85" Evaluating equation (33)) for the To staucdare dust model ""A7 for Ry=5.5. we fiud that to good accuracy. where Mayuai is understood to be in gea7."," Evaluating equation \ref{Prad}) ) for the \citet{weingartner01} standard dust model “A” for $R_V=5.5$, we find that to good accuracy, where $\Sigma_{\rm shell}$ is understood to be in $^{-2}$."86 This result shows that radiation trapping can be quite significant. for instance when XaZl aud Ditech>GO TN. as is expected around a Iuuiuous vouug cluster: however this estimate is unrealistically igh wheu radiation can leak away.," This result shows that radiation trapping can be quite significant, for instance when $\Sigma_{\rm shell} \gtsim 1$ and $\Teffsh > 60$ K, as is expected around a luminous young cluster; however this estimate is unrealistically high when radiation can leak away."87 Iu the more realistic case where leakage is important. we can compute Pip dm a manner analogous to our calculation of Py. by balancing the rate at which energy the stars inside the shell add cucrey against the rate at which it leaks out.," In the more realistic case where leakage is important, we can compute $P_{\rm IR}$ in a manner analogous to our calculation of $P_X$, by balancing the rate at which energy the stars inside the shell add energy against the rate at which it leaks out."88 Our treatment here is a simplified version of that given in Appendix D of ?.., Our treatment here is a simplified version of that given in Appendix D of \citet{mckee08a}.89" We limit our attention to the case where the shell is optically thick (Sopa9 Myn(Toarun)) ou average: in this limit we cau conipute the energy density of the trapped radiation field when the shell is porous. C,« I. siniply by treating the shell as a perfectly opaque sphere with holes iu it."," We limit our attention to the case where the shell is optically thick $\Sigma_{\rm shell}\gg \Sigma_{\rm ph}(\Teffsh)$ ) on average: in this limit we can compute the energy density of the trapped radiation field when the shell is porous, $C_f < 1$ , simply by treating the shell as a perfectly opaque sphere with holes in it."90 Tn this case enerevbalance requires that, In this case energybalance requires that91moments.,moments.92 For more details the reader is referred to the review article by Stergioulas (2003)., For more details the reader is referred to the review article by Stergioulas (2003).93 The interior and exterior spacetime of a stationary. axisymmetric star is described by a metric in the following form: ολαBre Qut)7 rugduh where v.B.@ and @ are four metric functions to be determined by solving four field equations.," The interior and exterior spacetime of a stationary, axisymmetric star is described by a metric in the following form: dt^2+B^2 dt)^2 ^2), where $\nu,~B, ~\alpha$ and $\omega$ are four metric functions to be determined by solving four field equations."94 In the numerical method of Komatsu (1989. henceforth ΚΕΠ) one defines two auxiliary functions p. Y through the relations v—(yp)/2 and B—οἳ.," In the numerical method of Komatsu (1989, henceforth KEH) one defines two auxiliary functions $\bar \rho$, $\bar \gamma$ through the relations $\nu=(\bar \gamma + \bar \rho)/2$ and $B=e^{\bar \gamma}$."95" Then. three out of the four field equations are written in the following integral forms where rr. ryr. rr. rjr. and S5. Sy and 5, are lengthy source terms. whose expressions can be found in KEH."," Then, three out of the four field equations are written in the following integral forms _0^1 r'^2 ^2(r,r') ) ), _0^1 r'^2 ) _0^1 r'^3 ) ), where r, r'>r, r, r'>r, and $S_{\bar \rho}$, $S_{\bar \gamma}$ and $S_\omega$ are lengthy source terms, whose expressions can be found in KEH."96" In the equations above. 4=cos. while P,(44) denotes the Legendre polynomials and P7'(u) the associated Legendre functions."," In the equations above, $\mu=\cos\theta$, while $P_n(\mu)$ denotes the Legendre polynomials and $P_n^m(\mu)$ the associated Legendre functions."97 The metric function & is determined by an ordinary differential equation., The metric function $\alpha$ is determined by an ordinary differential equation.98 We compute numerical equilibrium models using the code by Stergioulas and Friedman (1995) (see Nozawa 1998 and Stergioulas 2003 for extensive accuracy tests)., We compute numerical equilibrium models using the code by Stergioulas and Friedman (1995) (see Nozawa 1998 and Stergioulas 2003 for extensive accuracy tests).99 The numerical code uses the CST formulation. in which the KEH equations are written in terms of a compactified coordinate s detined through the relation where rp is the (coordinate) radius of the stellar equator.," The numerical code uses the CST formulation, in which the KEH equations are written in terms of a compactified coordinate $s$ defined through the relation ), where $r_e$ is the (coordinate) radius of the stellar equator."100 This allows the computation of the whole exterior spacetime out to infinity. which is important in detailed comparisons of the numerical metric to the analytic metric.," This allows the computation of the whole exterior spacetime out to infinity, which is important in detailed comparisons of the numerical metric to the analytic metric."101 For a configuration that 1s stationary. axisymmetric. symmetric with respect to reflections in the equatorial plane and asymptotically flat. the spacetime can be characterized by twosets of scalar multipole moments: the even-valued mass moments (Mo.Mo. M4...) and the odd-valued current moments (51.δὲ. Ss...," For a configuration that is stationary, axisymmetric, symmetric with respect to reflections in the equatorial plane and asymptotically flat, the spacetime can be characterized by twosets of scalar multipole moments: the even-valued mass moments $M_0,~M_2,~M_4\dots$ ) and the odd-valued current moments $S_1,~S_3,~S_5\dots$ )."102) Ryan (1997) presented a method for extracting the multipole moments from the asymptotic formof the metric functions., Ryan (1997) presented a method for extracting the multipole moments from the asymptotic formof the metric functions.103 The lowest-order appearance of each moment in terms of a power series in |/r is determined by the expansions |. )and," The lowest-order appearance of each moment in terms of a power series in $1/r$ is determined by the expansions ), and ."104LS/LIS transition.,LS/HS transition.105 Since the accretion rate during the LS is very close to the critical value. a slight. increase in the accretion rate by a small factor would produce a stable disc.," Since the accretion rate during the LS is very close to the critical value, a slight increase in the accretion rate by a small factor would produce a stable disc."106 As a result. a shorter interval to the next state transition would be expected.," As a result, a shorter interval to the next state transition would be expected."107 Unlike the SN'Ts in which the outburst timescale is normally longer than ten vears. 3339.4 has much more frequent state transitions. às seen in e.g. the AASAI data (see Fig. 2)).," Unlike the SXTs in which the outburst timescale is normally longer than ten years, 339–4 has much more frequent state transitions, as seen in e.g. the ASM data (see Fig. \ref{fig:ginga}) )."108 In fact. the 232-d variability seen in the aand data has already hinted at such behaviour.," In fact, the 232-d variability seen in the and data has already hinted at such behaviour."109 The most interesting behaviour of the 1998 LIS is tha he observed. [lat-topped: X-ray. light: curve of 3339.4 »ears Characteristics of Z Cam-type DN in which standstills (i.c. the brightness remains constant) occasionally interrup he recurrent outbursts., The most interesting behaviour of the 1998 HS is that the observed flat-topped X-ray light curve of 339–4 bears characteristics of Z Cam-type DN in which standstills (i.e. the brightness remains constant) occasionally interrupt the recurrent outbursts.110 Such a scenario can be explainec wv the DIM (Meyer&Alever-Lolmeister1983:WineCan-nizzo1998) in which the accretion rate before standstil is very close to a critical value and a sudden increase in he accretion rate (c.g. bx a starspot or irradiation induce mass overllow) triggers the standstill state.," Such a scenario can be explained by the DIM \cite{meyer83,king98} in which the accretion rate before standstill is very close to a critical value and a sudden increase in the accretion rate (e.g. by a starspot or irradiation induced mass overflow) triggers the standstill state."111 Phe light curve of 33394 is even more similar to the model proposed by Ixing&Cannizzo(1998) in which the stancdstill is at a higher luminosity than the normal outbursts., The light curve of 339–4 is even more similar to the model proposed by \scite{king98} in which the standstill is at a higher luminosity than the normal outbursts.112 For Z Cam systems. the intensity of the standstills is lower than the maximum of the outbursts (Alever&Mever-Llofmeister 1983)). but we should note that the models for explaining the Z Cam systems are used to account for optical light curves.," For Z Cam systems, the intensity of the standstills is lower than the maximum of the outbursts \pcite{meyer83}) ), but we should note that the models for explaining the Z Cam systems are used to account for optical light curves."113 The second. similarity between 3339.4 and Z Com systems concerns the recurrence of outbursts between stancdstills., The second similarity between 339–4 and Z Cam systems concerns the recurrence of outbursts between standstills.114 From our earlier period. analysis of the archival 33394 data over 30 vears. we find a variability timescale of 7190240 d and we suggest this to be the recurrent outbursting behaviour seen in Z Cam systems.," From our earlier period analysis of the archival 339–4 data over 30 years, we find a variability timescale of $\sim$ 190–240 d and we suggest this to be the recurrent outbursting behaviour seen in Z Cam systems."115 As pointed out by Dubus et al. (, As pointed out by Dubus et al. (116in preparation). the accretion rate can vary on timescales of 10.100 cavs when a viscously unstable disce is irracliatecl by a constant N-rav. flux.,"in preparation), the accretion rate can vary on timescales of 10–100 days when a viscously unstable disc is irradiated by a constant X-ray flux."117" HU irradiation is crucial for determining the acerction rate of 3339.4. this mav explain the variability of the ""mini-outbursts observed during the LS."," If irradiation is crucial for determining the accretion rate of 339–4, this may explain the variability of the `mini'-outbursts observed during the LS."118 Phere is also an indication that the accretion rate of 33394 was building up before the LES in 1998 as 1ο average intensity level of both AASM and BATSE data has a slight. increasing trend especially after ALJD 50000 (see Fig. 3))., There is also an indication that the accretion rate of 339–4 was building up before the HS in 1998 as the average intensity level of both ASM and BATSE data has a slight increasing trend especially after MJD 50000 (see Fig. \ref{fig:batse}) ).119 In addition. the LS occurring at NLJD 48550 and 49450 (see refsec:ibatse)) were just after a strong X-ray outburst in the LS (see Fig. 3)).," In addition, the HS occurring at MJD 48550 and 49450 (see \\ref{sec:batse}) ) were just after a strong X-ray outburst in the LS (see Fig. \ref{fig:batse}) )."120 Perhaps this takes the accretion rate in the LS to be close to the critical value and finally triggers the state transition., Perhaps this takes the accretion rate in the LS to be close to the critical value and finally triggers the state transition.121 As a result. this LIS may be simply a garong. prolonged outburst in an otherwise LS.," As a result, this HS may be simply a strong, prolonged outburst in an otherwise LS."122 In fact. from 10 period analysis of the2D ancl ddata for which state transitions are included. in the calculation. the timescale of variability resembles that found in the AASM data in the LS.," In fact, from the period analysis of the and data for which state transitions are included in the calculation, the timescale of variability resembles that found in the ASM data in the LS."123 Perhaps the LS outbursts may be excursions towards the LES but which they do not. quite reach., Perhaps the LS outbursts may be excursions towards the HS but which they do not quite reach.124 Lf this is the case. we would expect similar spectral evolution during the LS outhurst. just like during a state transition.," If this is the case, we would expect similar spectral evolution during the LS outburst, just like during a state transition."125 Lowever. such outbursts are usually short and therefore. observations are clillicult to arrange.," However, such outbursts are usually short and therefore observations are difficult to arrange."126 The most likely observations available are from Wilmsetal.(1999).. in which an ppointecl observation. of 3339.4. was mace near the outburst (AIJD 50710) just. before the LS/IS transition.," The most likely observations available are from \scite{wilms99}, in which an pointed observation of 339–4 was made near the outburst (MJD 50710) just before the LS/HS transition."127 Although the energy spectrum appeared to be slightly softer. it is still consistent with other LS observations within the uncertainties.," Although the energy spectrum appeared to be slightly softer, it is still consistent with other LS observations within the uncertainties."128 Lt is worth noting that XX1 also shows LS/LS transitions occasionally ancl it has Daring activities during the LS., It is worth noting that X–1 also shows LS/HS transitions occasionally and it has flaring activities during the LS.129 Moreover. the long LIS of XX.1 between 1996 Alay ancl August resembles that seen in 3339.4. but with more Lares during the LIS (Zhangetal.1997).," Moreover, the long HS of X–1 between 1996 May and August resembles that seen in 339–4, but with more flares during the HS \cite{zhang97}."130. Therefore. it is possible that the state transition of NNl is due to a similar mechanism to that. discussed. here (sce however Zhangetal.1997:Esin1998)).," Therefore, it is possible that the state transition of X--1 is due to a similar mechanism to that discussed here (see however \pcite{zhang97,esin98}) )."131 More recently. XX.3 was also shown to have recurring state transitions but the driving force is very likely to be due to other mechanisms (Boveetal.2000:Wilms2001).," More recently, X–3 was also shown to have recurring state transitions but the driving force is very likely to be due to other mechanisms \cite{boyd00,wilms00}."132. Given that the accretion rate in the LS is close to the critical value. similar LS/LIS transitions would be expected in the near future and multi-waveleneth observations of such transitions. particularly the correlation between the N-ray. optical and radio emissions will constrain the accretion disc structure and behaviour of the secondary star.," Given that the accretion rate in the LS is close to the critical value, similar LS/HS transitions would be expected in the near future and multi-wavelength observations of such transitions, particularly the correlation between the X-ray, optical and radio emissions will constrain the accretion disc structure and behaviour of the secondary star."133 We are grateful to Colleen Wilson-Llodge and Ken Watanabe [or providing the updated: BATSE data., We are grateful to Colleen Wilson-Hodge and Ken Watanabe for providing the updated BATSE data.134 We also thank Christine Done for the red-noise generator code., We also thank Christine Done for the red-noise generator code.135 Alytis is supported by a Hong Kong Oxford Scholarship., AKHK is supported by a Hong Kong Oxford Scholarship.136 This paper utilizies quick-look results provided. by the ASM/IUCNTIEE team and data obtained. through the WEASARC Online Services of NASA/GSEC., This paper utilizies quick-look results provided by the ASM/RXTE team and data obtained through the HEASARC Online Services of NASA/GSFC.137 33394 has been observed by several X-ray satellites in the past 30 vears and the results [rom those pointed observations are crucial to determine the ‘state of. the source., 339–4 has been observed by several X-ray satellites in the past 30 years and the results from those pointed observations are crucial to determine the `state' of the source.138 We compile here a list. of pointed. observations of 33394 from the literature (see Table AL)., We compile here a list of pointed observations of 339–4 from the literature (see Table A1).139 Note that the “state? quoted is determined. by spectral and temporal analysis., Note that the `state' quoted is determined by spectral and temporal analysis.140 Although the X-ray llux level can more or less reflect the ‘state’ of the source. on several occasions the ray [lux in the LS is actually higher than the LIS (e.g. 1981 May ancl 1984 Mas).," Although the X-ray flux level can more or less reflect the `state' of the source, on several occasions the X-ray flux in the LS is actually higher than the HS (e.g. 1981 May and 1984 May)."141 Hence the X-ray intensity itself is not an accurate indicator of X-ray ‘state’., Hence the X-ray intensity itself is not an accurate indicator of X-ray `state'.142distributions. while data allow us to probe a regionlarger than these radii. which permits us to investigate the core radius phenomenon at large clistances ancl consequently to constrain the size of the core radii (note. however. the case of NGC 7339 discussed in Appendix A).,"distributions, while data allow us to probe a region than these radii, which permits us to investigate the core radius phenomenon at large distances and consequently to constrain the size of the core radii (note, however, the case of NGC 7339 discussed in Appendix A)."143 The rotation curves used. here consist of the Lla data for the inner parts and the data for the outer parts., The rotation curves used here consist of the $\alpha$ data for the inner parts and the data for the outer parts.144 The claim of unreliability of observed kinematics put forward by lthee.IXIvpin&Valenzuela(2003). does not apply here: a) the derivation of the rotation curve was performed in a more thorough and. reliable way than the standard. tiltecd-ring analvsis on the velocity field: b) the galaxies studied here were at an inclination optimal to minimise projection elfects: c) in the regions were they coexist. the Ho and data (emerging from cillerent. physical processes) do agree. iniplving a high quality of thedatat.," The claim of unreliability of observed kinematics put forward by \citet*{Rh:03} does not apply here: a) the derivation of the rotation curve was performed in a more thorough and reliable way than the standard tilted-ring analysis on the velocity field; b) the galaxies studied here were at an inclination optimal to minimise projection effects; c) in the regions were they coexist, the $\alpha$ and data (emerging from different physical processes) do agree, implying a high quality of the."145. The small internal scatter inside the cach radial bin indicates that. for the galaxies of our sample. the ellects of non-circular motions are negligible (even though a more thorough investigation should involve 2-dimensional Ho cata). cillerently from the case shown by Swatersetal.(2003b).," The small internal scatter inside the each radial bin indicates that, for the galaxies of our sample, the effects of non-circular motions are negligible (even though a more thorough investigation should involve 2-dimensional $\alpha$ data), differently from the case shown by \citet{Sw:03}."146. Moreover. it can be shown (see e.g. deBlok.MeGaugh&Dosma 2003)) that the bias towards lower velocity gracients in the rotation curve due to a misalignment between the slit with the kinematical axis is likely to be small.," Moreover, it can be shown (see e.g. \citealt{dB:03}) ) that the bias towards lower velocity gradients in the rotation curve due to a misalignment between the slit with the kinematical axis is likely to be small."147" The five galaxies of this sample were chosen from the sample of 967 galaxies with optical rotation curves presented by Persic&Salucei(1995).. according to the following criteria: a) they belong to the ""exeellent subsample (i.e. the two sides are svmmetric. the cata are extended out to at. least ro and the number of data points is z 30): b) they have a reasonably high total flux: ο) they have a relatively low I-band luminosity (AZ;7 21.8). d) they have a large angular size. and e) they have an inclination / suitable forLIL studies (50°r<7< 857)."," The five galaxies of this sample were chosen from the sample of 967 galaxies with optical rotation curves presented by \citet{PS:95}, according to the following criteria: a) they belong to the “excellent” subsample (i.e. the two sides are symmetric, the data are extended out to at least $r_{opt}$ and the number of data points is $\geq$ 30); b) they have a reasonably high total flux; c) they have a relatively low I-band luminosity $M_{\rm I} > -21.8$ ), d) they have a large angular size, and e) they have an inclination $i$ suitable for studies $50^{\circ} < i < 85 ^{\circ}$ )."148 For each galaxy. the raw Lla data were binned in groups of 4 to 6 (Persic&Salucei1995).. and the given error is the uncertainty on the average value inside the radial bin.," For each galaxy, the raw $\alpha$ data were binned in groups of 4 to 6 \citep{PS:95}, and the given error is the uncertainty on the average value inside the radial bin."149" We took a ""minimum error equal to half the average error in order to avoid data points. with unrealistically low errors that could bias the rotation curves decompositions: for the same reason. when a data point was Clearly inconsistent with the two neighbouring points and the general trend of the rotation curve. the value of its error was increased."," We took a “minimum error” equal to half the average error in order to avoid data points with unrealistically low errors that could bias the rotation curves decompositions; for the same reason, when a data point was clearly inconsistent with the two neighbouring points and the general trend of the rotation curve, the value of its error was increased."150 The complete description. of the optical observations (spectroscopic and photometric) can be found in Mathewson.Ford&Buchhorn(1992) and Persic&Salucci (1995)., The complete description of the optical observations (spectroscopic and photometric) can be found in \citet*{Ma:92} and \citet{PS:95}.151. We observed ESO 116-G12. ESO 287-G13 and ESO 79-Ci14 with the Australia “Telescope Compact Array in the 750 m. and 1.5 km configurations: the resulting baselines range from 31 mto 1500 m. The galaxies were observed for 12 hrs in cach configuration.," We observed ESO 116-G12, ESO 287-G13 and ESO 79-G14 with the Australia Telescope Compact Array in the 750 m and 1.5 km configurations; the resulting baselines range from 31 m to 1500 m. The galaxies were observed for 12 hrs in each configuration."152 The correlator setup vielded 512 channels of, The correlator setup yielded 512 channels of153Lt is welbestablished that rotation is a function of object mass (see?.forareview)...,It is well-established that rotation is a function of object mass \citep[see][for a review]{2007prpl.conf..297H}.154 Specifically. there is accumulating evidence that in the very low mass regime the average period drops steadily with decreasing mass.," Specifically, there is accumulating evidence that in the very low mass regime the average period drops steadily with decreasing mass."155 This positive period-mass correlation at masses <0.8O44. has been found in the ONC (?).. ©OOrt (7).. and the Pleiacles (?).. clusters with ages between 1 and MMwyr.," This positive period-mass correlation at masses $<0.3-0.4\,M_{\odot}$ has been found in the ONC \citep{2001ApJ...554L.197H}, $\epsilon$ Ori \citep{2005A&A...429.1007S}, and the Pleiades \citep{2004A&A...421..259S}, clusters with ages between 1 and Myr."156 Similarly. in the clusters Νάς25160 ancl M34 (22)... which roughly mark the ZAMS for very low mass objects at ages of 150 and 200Myr. there seems to be a general decline of the upper envelopeM of the periods with decreasing mass (7.seetheirFig.17)..," Similarly, in the clusters NGC2516 and M34 \citep{2006MNRAS.370..954I,2007MNRAS.tmp..276I}, which roughly mark the ZAMS for very low mass objects at ages of 150 and Myr, there seems to be a general decline of the upper envelope of the periods with decreasing mass \citep[][see their Fig. 17]{2007MNRAS.tmp..276I}."157 ]t has been pointed. out that this trend. is consistent. with constant angular momentum for all object masses (e.g.?).. and thus might just reflect the drop in stellar radius.," It has been pointed out that this trend is consistent with constant angular momentum for all object masses \citep[e.g.][]{2001ApJ...554L.197H}, and thus might just reflect the drop in stellar radius."158 Since it is already. established at very voung ages. it may be related to the initial distribution of angular momentum.," Since it is already established at very young ages, it may be related to the initial distribution of angular momentum."159 Llere we probe if our small period sample in. Praesepe older than all other clusters with rotation periods in this mass range allows us to see a similar trend., Here we probe if our small period sample in Praesepe – older than all other clusters with rotation periods in this mass range – allows us to see a similar trend.160 We derived masses for the five objects in Table 2. by comparing the available photometry in the Lhand from the literature with evolutionary tracks from ? for an age of GiCivr.," We derived masses for the five objects in Table \ref{periods} by comparing the available photometry in the I-band from the literature with evolutionary tracks from \citet{1998A&A...337..403B}161 for an age of Gyr."162 According to these estimates. all five objects are in the very low mass regime with masses 0.4AL...," According to these estimates, all five objects are in the very low mass regime with masses $\le 0.4\,M_{\odot}$."163 Due to age uncertainties. photometric band inconsistencies. ancl mocel shortcomüngs. the uncertainties in the derived. masses. are considerable (probably on the order of )).," Due to age uncertainties, photometric band inconsistencies, and model shortcomings, the uncertainties in the derived masses are considerable (probably on the order of )."164 However. most of this uncertainty is svstematic. thus we expect that in a relative sense our masses are realistic.," However, most of this uncertainty is systematic, thus we expect that in a relative sense our masses are realistic."165 We caution against comparing these values with masses derived using a dilferent approach., We caution against comparing these values with masses derived using a different approach.166 Using the same model isochrone. we determined ellective temperatures for our five targets.," Using the same model isochrone, we determined effective temperatures for our five targets."167 Comparing with the Zi scale from ? gives an estimate for the spectral types (sce “Table 2))., Comparing with the $T_{\mathrm{eff}}$ scale from \citet{2003ApJ...593.1093L} gives an estimate for the spectral types (see Table \ref{periods}) ).168 The uncertainties in these “photometric? spectral tvpes are probably +12 subclasses., The uncertainties in these 'photometric' spectral types are probably $\pm 1-2$ subclasses.169 In Fig. 2..," In Fig. \ref{f2},"170 upper panel. we plot periods vs. masses for 16 five objects in Table 2..," upper panel, we plot periods vs. masses for the five objects in Table \ref{periods}."171 Lt is immediately obvious that 10 periods appear to increase with mass in a roughly linear wav., It is immediately obvious that the periods appear to increase with mass in a roughly linear way.172 A linear least-square fit (shown as dotted line) gives: P=(24040)(ΑΛ(21x10)h.," A linear least-square fit (shown as dotted line) gives: $P = (240 \pm 40)\,(M/M_{\odot}) - (21\pm10)\,h$."173 The correlation is significant with a false alarm probability of4., The correlation is significant with a false alarm probability of.174. The slope in the relationship is clearly steeper than in the Pleiades (105€GLCAZI/AL.). 2)). maybe indicating that rotational braking on the main-sequence is a function of object mass.," The slope in the relationship is clearly steeper than in the Pleiades $105 \pm 61\,(M/M_{\odot})$, \citet{2004A&A...421..259S}) ), maybe indicating that rotational braking on the main-sequence is a function of object mass."175 Based on only five datapoints. however. this finding is of somewhat limited value.," Based on only five datapoints, however, this finding is of somewhat limited value."176 Clearly. more datapoints are needed to solidifv the main-sequence P-M correlation in the VEM Lt is more instructive to look on the VLM periods in comparison with rotation measurements obtained for more massive stars.," Clearly, more datapoints are needed to solidify the main-sequence P-M correlation in the VLM It is more instructive to look on the VLM periods in comparison with rotation measurements obtained for more massive stars."177 To our knowledge. such data is not available [or Praesepe. but for the ELEvades. with 600Myr a roughly coeval cluster (22)...," To our knowledge, such data is not available for Praesepe, but for the Hyades, with Myr a roughly coeval cluster \citep{1981A&A....97..235M,1998A&A...331...81P}."178 For this comparison. we prefer to use spectral types instead. of masses. in order not to be biased » model inconsistencies in the mass estimates. which are illieult to avoid when covering a mass range of more than one order of magnitude.," For this comparison, we prefer to use spectral types instead of masses, in order not to be biased by model inconsistencies in the mass estimates, which are difficult to avoid when covering a mass range of more than one order of magnitude."179 Since we use only coeval objects. Ίο spectral type is a valid. indicator for stellar mass.," Since we use only coeval objects, the spectral type is a valid indicator for stellar mass."180 We ‘olleetecl a sample of 25 periods for Hades members from 16 photometric monitoring campaigns published by 7? and S, We collected a sample of 25 periods for Hyades members from the photometric monitoring campaigns published by \citet{1987ApJ...321..459R} and \citet{1995PASP..107..211P}.181pectral types for. these objects have originally been rublished by 2? and. ον., Spectral types for these objects have originally been published by \cite{1952BAN....11..385V} and \citet{1969AJ.....74....2V}.182 Combined. with our sample. the spectral range from late Foto late M is covered. roughly corresponding to a mass range from 0.1 to 2AL..," Combined with our sample, the spectral range from late F to late M is covered, roughly corresponding to a mass range from 0.1 to $M_{\odot}$."183 The period/spectral type relation is shown in Fig. 2..," The period/spectral type relation is shown in Fig. \ref{f2},"184 lower panel., lower panel.185 Lt clearly demonstrates that for. E-Ix. stars the periods increase towards later spectral types., It clearly demonstrates that for F-K stars the periods increase towards later spectral types.186 According to ?.. these periods can be explained in terms of the correlation between magnetic activity and the inverse Rossby number Ro. the ratio between rotation period and convective turnover timescale το (e.g.οι.," According to \citet{1987ApJ...321..459R}, these periods can be explained in terms of the correlation between magnetic activity and the inverse Rossby number $Ro$, the ratio between rotation period and convective turnover timescale $\tau_C$ \citep[e.g.][]{1984ApJ...279..763N}."187 This relation basically implies that the magnetic field amplification mainly depencls on convection properties and rotation supporting the idea of an aw dyvnamo operating in F-Ix stars., This relation basically implies that the magnetic field amplification mainly depends on convection properties and rotation – supporting the idea of an $\alpha\omega$ dynamo operating in F-K stars.188 We note that the Ilvades periods for E-Ix stars represent what ο called the, We note that the Hyades periods for F-K stars represent what \cite{2003ApJ...586..464B} called the189with Az=x—rg and Ay=y—yo.,with $\Dx \equiv x - x_0$ and $\Dy \equiv y - y_0$.190" Note forp=0 (uncorrelated x and y), the x? looks familiar."," Note for $\rho = 0$ (uncorrelated $x$ and $y$ ), the $\chi^2$ formula looks familiar."191" For correlated x and y (p> 0), x? is formulareduced."," For correlated $x$ and $y$ $\rho > 0$ ), $\chi^2$ is reduced."192" Consider a Fisher matrix provided by the DETF (Table for optimistic Stage IV BAO observations for the []))following variables: Qa, Ωμ), where Wm=Qh? and OQ,--Q4Q0;=1."," Consider a Fisher matrix provided by the DETF (Table \ref{tab:fish}) ) for optimistic Stage IV BAO observations for the following variables: $\om, \OL, \Ok$ ), where $\om \equiv \Om h^2$ and $\Om + \OL + \Ok = 1$."193" The (Wm,covariance matrix (inverse of the Fisher matrix) is given in Table ", The covariance matrix (inverse of the Fisher matrix) is given in Table \ref{tab:cov}.194"For example, the top- element tells us that Aw,,5”Bl.0.00566z3.20E—5."," For example, the top-left element tells us that $\Delta \om \approx 0.00566 \approx \sqrt{3.20E-5}$."195" When quoting these uncertainties on Ww», the other variables (Q4, Ωκ) have automatically been marginalized over."," When quoting these uncertainties on $\om$, the other variables $\OL, \Ok$ ) have automatically been marginalized over."196" That is, their probabilities have been integrated over: they have been set free to hold any values while we calculate the range of acceptable wy."," That is, their probabilities have been integrated over: they have been set free to hold any values while we calculate the range of acceptable $\om$."197" To calculate a new Fisher matrix marginalized over any variable, simply remove that variable's row and column from the covariance matrix, and take the inverse of that to yield the new Fisher matrix."," To calculate a new Fisher matrix marginalized over any variable, simply remove that variable's row and column from the covariance matrix, and take the inverse of that to yield the new Fisher matrix."198 Suppose instead want the opposite: perfect knowledge of a parameter., Suppose instead want the opposite: perfect knowledge of a parameter.199" For example, we want to consider a flat universe with a fixed value of Ωμ=0."," For example, we want to consider a flat universe with a fixed value of $\Ok = 0$."200" To do this, simply remove Ωμ from the Fisher matrix ))."," To do this, simply remove $\Ok$ from the Fisher matrix (Table \ref{tab:fishflat}) )."201 The new covariance matrix and parameter uncertainties(Table are calculated from the revised Fisher matrix., The new covariance matrix and parameter uncertainties are calculated from the revised Fisher matrix.202" Alternatively, the on-diagonal element corresponding to that parameter can be set to a very large value."," Alternatively, the on-diagonal element corresponding to that parameter can be set to a very large value."203" For example, if we set the bottom-right element in Table to 1013, that would correspond to a 1079 uncertainty in Wm, or nearly fixed."," For example, if we set the bottom-right element in Table \ref{tab:fish} to $10^{12}$, that would correspond to a $10^{-6}$ uncertainty in $\om$, or nearly fixed."204 Note that higher values in the Fisher matrix correspond to higher certainty., Note that higher values in the Fisher matrix correspond to higher certainty.205" Rather than fixing a parameter to an exact value,(1- we may want to place a prior such as AQ,=0.01 e)."," Rather than fixing a parameter to an exact value, we may want to place a prior such as $\Delta \Ok = 0.01$ $\sigma$ )."206" In this case,corresponding simply add 1/σ3=103 to the on-diagonal element to that variable (in this case, the bottom left element)."," In this case, simply add $1 / \sigma^2 = 10^4$ to the on-diagonal element corresponding to that variable (in this case, the bottom left element)."207" To combine constraints from multiple experiments, simply add their Fisher matrices: F=ΕΙ+F5."," To combine constraints from multiple experiments, simply add their Fisher matrices: $F = F_1 + F_2$."208" Strictly speaking, anymarginalization should be performed after the addition."," Strictly speaking, anymarginalization should be performed after the addition."209" But if the nuisance parameters"" are uncorrelated between the two data sets, then marginalization may be performed before the addition."," But if the “nuisance parameters” are uncorrelated between the two data sets, then marginalization may be performed before the addition."210" Given the badness of fit x?(x,y), your 2-D Fisher matrix can be calculated as follows: In other words,Fj;=21dx?0püpy "," Given the badness of fit $\chi^2(x,y)$, your 2-D Fisher matrix can be calculated as follows: In other words, $F_{ij} = \displaystyle \frac{1}{2} \frac{\p \chi^2}{\p p_i \p p_j}$."211"'These derivatives are simple to calculate numerically: Suppose we are given a Fisher matrix in terms of variables p=(x,y,z) but we are interested in constraints on related variables p'= (a,b,c)."," These derivatives are simple to calculate numerically: Suppose we are given a Fisher matrix in terms of variables $p = (x,y,z)$ but we are interested in constraints on related variables $p^\prime = (a,b,c)$ ."212 We can obtain a new Fisher matrix as follows:, We can obtain a new Fisher matrix as follows:213galaxies.,galaxies.214 Currently methods are being developed in order to relate galaxy luminosities to cark matter halocs in a statistical wav (e.@2?77)..," Currently methods are being developed in order to relate galaxy luminosities to dark matter haloes in a statistical way \cite[e.~g.~][]{Yang2004a, Vale2004a,215 Cooray2005a, Conroy2006a}."216 Here we follow this idea and associate luminosities to the (sub-)haloes in the group., Here we follow this idea and associate luminosities to the (sub-)haloes in the group.217 We assume simply that the most luminous galaxy is the central galaxy of the group host halo with circular velocity voici.," We assume simply that the most luminous galaxy is the central galaxy of the group host halo with circular velocity ${\rm v_{\rm circ,1}}$."218 Consequently. the halo with the second. highest circular velocity voies. will host the second brightest group galaxy.," Consequently, the halo with the second highest circular velocity ${\rm v_{\rm circ,2}}$ will host the second brightest group galaxy."219 llere the circular. velocity vere is always taken at. the maximum of the rotation curve., Here the circular velocity ${\rm v_{circ}}$ is always taken at the maximum of the rotation curve.220 To model the magnitude-gap we adopt a similar approach as ? where we relate the the halo circular velocity to the luminosity of the central galaxy using an empirically measured mean I-band mass-to-light ratio (2).., To model the magnitude-gap we adopt a similar approach as \citet[][]{Milosavljevic2006a} where we relate the the halo circular velocity to the luminosity of the central galaxy using an empirically measured mean R-band mass-to-light ratio \cite[][]{Cooray2005a}.221 Assuming a Sheth-Thormen (7) mass distribution function for the dark matter haloes and a functional form as in Equation 1. that expresses the halo mass in luminosity for the central ealaxies. ? [it the measured H-band luminosity function of 7..," Assuming a Sheth-Thormen \cite[][]{Sheth1999a} mass distribution function for the dark matter haloes and a functional form as in Equation 1, that expresses the halo mass in luminosity for the central galaxies, \citet[][]{Cooray2005a} fit the measured R-band luminosity function of \citet[][]{Seljak2005a}."222" We convert our circular velocities to luminosities by the relation with Luη10L.. Mo22«103M. a 4.6=0.57. ο= 3.78. d= 0.23. where we substitute circular velocities for masses using the relation found by 7:: AL(hHAL.)-10""vus(kns1j “with a—43 and 3=3.4."," We convert our circular velocities to luminosities by the relation with $L_{0} = 5.7\times10^{9} L_{\odot}$, $M_{0} = 2\times10^{11}223{\rm M_{\odot}}$, $a = 4$, $b = 0.57$, $c = 3.78$ $d = 0.23$ , where we substitute circular velocities for masses using the relation found by \citet[][]{Bullock2001a}: $M/\left(h^{-1}\;{\rm M_{\odot}}\right) =22410^{\alpha}\cdot \left[{\rm v_{circ}}\right/\left({\rm km225 \;s^{-1}}\right)]^{\beta}$ , with $\alpha = 4.3$ and $\beta = 3.4$."226 We then define fossil eroups as having masses in the range of 105Loyh1M. and a magnitucde-gap Ane mae in the It-band.," We then define fossil groups as having masses in the range of $(1\times 10^{13} -2275 \times 10^{13}) h^{-1}{\rm M}_{\odot}$ and a magnitude-gap $\mgap \ge 2$ mag in the R-band."228 Alass accretion onto haloes stops at the time when they become sub-halos of a more massive object like a group., Mass accretion onto haloes stops at the time when they become sub-halos of a more massive object like a group.229 After infall they start to lose matter clue to tidal interactions., After infall they start to lose matter due to tidal interactions.230 Since barvons tend to lic deeper in the potential well. they will be less prone to get tically stripped.," Since baryons tend to lie deeper in the potential well, they will be less prone to get tidally stripped."231 Fherefore. the total uminositv is more likely to be related to the mass at infall (scec.ο.ο).," Therefore, the total luminosity is more likely to be related to the mass at infall \cite[see232e.~g.~][]{Kravtsov2004a}."233 Following this idea we characterize the sub-ialoes of the groups by their masses and. circular velocities onto the group., Following this idea we characterize the sub-haloes of the groups by their masses and circular velocities onto the group.234 Phe choice of. relating uminosities to the circular velocities of halos at infall time las been motivated by recent successes in matching the data » mocdeling the two- and three-point correlation functions (??7)..," The choice of relating luminosities to the circular velocities of halos at infall time has been motivated by recent successes in matching the data by modeling the two- and three-point correlation functions \cite[][]{Conroy2006a, Berrier2006a, Marin2007a}."235 In this section our main aim is to characterize the properties of the fossil groups of our group sample in order to guide the interpretation of future observational constraints., In this section our main aim is to characterize the properties of the fossil groups of our group sample in order to guide the interpretation of future observational constraints.236 We begin by computing the abundance of fossil systems in our catalog., We begin by computing the abundance of fossil systems in our catalog.237" Assuming a magnitude-gap of Anny.2 (see dashed line in Figure 1) 24 per cent of the groups of our catalog ave classified as fossil.X corresponding to a number density of 5.5«ο7. ""Ph"," Assuming a magnitude-gap of $\mgap \ge 2$ (see dashed line in Figure 1) 24 per cent of the groups of our catalog are classified as fossil,  corresponding to a number density of $5.5 \times 10^{-5} h^{3}{\rm Mpc}^{-3}$."238is rate is higher than previous estimates based on IN-body. simulations (?).. semi-analytic models (??).. ancl observational estimates (2277)... which all ect a fraction of around 10. per cent for groups in the mass range considered ποι," This rate is higher than previous estimates based on $N$ -body simulations \cite[][]{dOnghia2007a}, semi-analytic models \cite[][]{Sales2007a,239 Dariush2007a}, and observational estimates \cite[][]{ Vikhlinin1999a,240 Romer2000a, Jones2003a, vandenBosch2007a}, which all get a fraction of around 10 per cent for groups in the mass range considered here."241ο— However. only 15 well stucied fossil groups are known at present with X-ray data.,"  However, only 15 well studied fossil groups are known at present with X-ray data."242 Therefore these abunclances present large uncertainties andA nueht be well underestimated., Therefore these  abundances present large uncertainties and  might be well underestimated.243 We believe that the over-estimate comes from our adopted scheme for relating circular. velocities to luminosities of the central galaxies in eroups. where we followed 2? and. 2..," We believe that the over-estimate comes from our adopted scheme for relating circular velocities to luminosities of the central galaxies in groups, where we followed \citet[][]{Milosavljevic2006a} and \citet[][]{Bullock2001a}."244 We are interested mainty in the formation process of systems with a large magnitude-gap. which clearly corresponds to systems with a large eap in circular velocities even if the related magnitudes are uncertain.," We are interested mainly in the formation process of systems with a large magnitude-gap, which clearly corresponds to systems with a large gap in circular velocities even if the related magnitudes are uncertain."245 We therefore stick to our adopted method. and study how our selected. fossil population dillers from the normal group population., We therefore stick to our adopted method and study how our selected fossil population differs from the normal group population.246 Fossil groups are systems with many. properties tvpical for ealaxy clusters., Fossil groups are systems with many properties typical for galaxy clusters.247 Hence. a further interesting test. concerns the question whether fossil groups are. isolated: svstenis that populate the low density regions or tend to reside in higher density regions of the Universe like galaxy. clusters.," Hence, a further interesting test concerns the question whether fossil groups are isolated systems that populate the low density regions or tend to reside in higher density regions of the Universe like galaxy clusters."248 A good test would be the cross-correlate the X-ray emitting fossil groups with galaxies in the nearby universe. c.g with SDSS data.," A good test would be the cross-correlate the X-ray emitting fossil groups with galaxies in the nearby universe, e.g with SDSS data."249 However the limited. number of fossil groups actually known makes an estimate of such correlations extremely dillicult., However the limited number of fossil groups actually known makes an estimate of such correlations extremely difficult.250 Some observational indications. though still uncertain. would suggest that fossil groups could. be fairly isolated systems (e.g.2??)..," Some observational indications, though still uncertain, would suggest that fossil groups could be fairly isolated systems \cite[e.g.][]{Jones2000a, Jones2003a, Adami2007a}."251 We check in our simulated: sample of groups whether fossil systems populate preferentially low density. regions in the universe., We check in our simulated sample of groups whether fossil systems populate preferentially low density regions in the universe.252 We estimate the environmental density on a scale of 4., We estimate the environmental density on a scale of 4.253. To this end. we determine. the environmental over-density AL=paffial. where pj is the dark matter density within 4 from the group center of mass. with the inner one virial radius is subtractect. and pus is the background. matter density.," To this end we determine the environmental over-density $\Delta_{4} = \rho_{4}/\rho_{\rm bg} - 1$, where $\rho_4$ is the dark matter density within 4 from the group center of mass, with the inner one virial radius is subtracted, and $\rho_{\rm bg}$ is the background matter density."254 Figure 2 shows the distribution of the over-clensity Ay for fossil and normal groups., Figure \ref{density} shows the distribution of the over-density $\Delta_{4}$ for fossil and normal groups.255 Alost of the groups.in the range of mass considered here. independent of being fossil or not. populate," Most of the groups,in the range of mass considered here, independent of being fossil or not, populate"256effeclive radius 5ni are plotted in fig.2..,effective radius $5 ~nm$ are plotted in \ref{fig2}.257 The exünction efficiency for nanociamonds of all shapes and the sizes is similar being negligible in the Ilt. visible aud increasing steeply in the UV., The extinction efficiency for nanodiamonds of all shapes and the sizes is similar being negligible in the IR – visible and increasing steeply in the UV.258 The extinction from 7.1 to 7.6 yam+ (1400 to 1300 A)) becomes constant and even decreases slightly., The extinction from 7.1 to 7.6 $\mu m^{-1}$ (1400 to 1300 ) becomes constant and even decreases slightly.259 This shape and size independent pause in extinction at 14100 is also seen in figure 1 of Binetteetal.(2005) lor spherical nanodiamonds., This shape and size independent pause in extinction at 1400 is also seen in figure 1 of \citet{binette05} for spherical nanodiamonds.260 The exünction efficiency is more for non-spherical shapes and the pause al 1400 is more prominent for particles departing more from (he spherical., The extinction efficiency is more for non-spherical shapes and the pause at 1400 is more prominent for particles departing more from the spherical.261 Mathis(1996) observed that extinction cross-section for spheroids are larger than those of spheres of same volume but. Voschonnikov(2004) points out that this is (rue for small particles and in the forward direction only., \citet{mathis96} observed that extinction cross-section for spheroids are larger than those of spheres of same volume but \citet{voshchinnikov04} points out that this is true for small particles and in the forward direction only.262 This is also true for graphitie particles (Guptaetal.2005)., This is also true for graphitic particles \citep{rgupta05}.263. The exünction efficiency. for ellipsoid of shape 432 for the four effective sizes is plotted in fie. 3((A). which shows increase in extinction with particle size.," The extinction efficiency for ellipsoid of shape 432 for the four effective sizes is plotted in \ref{fig3}( (A), which shows increase in extinction with particle size."264 The scattering and absorption efficiencies for shape 432 of effective radius 5 nm is shown in fig.3((D)., The scattering and absorption efficiencies for shape 432 of effective radius 5 nm is shown in \ref{fig3}( (B).265 The total extinction is almost all cue to absorption even in prolile., The total extinction is almost all due to absorption even in profile.266 The scattering efficiency is much smaller in comparison., The scattering efficiency is much smaller in comparison.267 The extinction increases almost linearly. with size for different wavelengths aud is shown in fig.4 for two extreme wavelengths 5 jan (IR) and 0.1. pam (far-UV)., The extinction increases almost linearly with size for different wavelengths and is shown in \ref{fig4} for two extreme wavelengths 5 $\mu $ m (IR) and 0.1 $\mu $ m (far-UV).268 This is πιο in general [or nanosized particles Draine&Malhotra(1993) ancl extinction [rom any in-between particle size can be extrapolated., This is true in general for nanosized particles \citet{draine93} and extinction from any in-between particle size can be extrapolated.269" The polarization efficiency is defined as differenGal extinction cross-section in (wo orthogonal polarizations as Qy4={Qeer|e)—(Q,,Le} where e is unit vector perpendicular to the direction of propagation.", The polarization efficiency is defined as differential extinction cross-section in two orthogonal polarizations as $ Q_{pol}=\{Q_{ext}\parallel \textbf{e}\}- \{ Q_{ext}\perp \textbf{e} \} $ where $\textbf{e}$ is unit vector perpendicular to the direction of propagation.270 The polarization efficiency for shape 432 and size 5nim is shownin fig.5.., The polarization efficiency for shape 432 and size $5 ~nm$ is shownin \ref{fig5}.271" Q, follows the same trend as total extinction and decreases with increasing erain orientation angle 9%. as defined in DDSCAT (Draine2004)."," $Q_{pol}$ follows the same trend as total extinction and decreases with increasing grain orientation angle $\beta$, as defined in DDSCAT \citep{draine04}."272". For 9=45"". (Q,,||] and (Q,,,L] are equal ancl polarization efficiency is nearly negligible."," For $\beta = 45^0 $, $\{Q_{ext}\parallel \}$ and $\{Q_{ext}\perp \}$ are equal and polarization efficiency is nearly negligible."273 Small grains are hard to orient in a particular direction (Whittet 2003).. thus nanocdiamonds have negligible contribution in polarization.," Small grains are hard to orient in a particular direction \citep{whittet}, , thus nanodiamonds have negligible contribution in polarization."274" In case of bulk diamond (he energy band-gap £j is nearly 5.47 eV and For nanocdiamonds ana? gap size dependence gives 2,=Ey-0.38(a/nm)? (Li2004).", In case of bulk diamond the energy band-gap $E_0$ is nearly 5.47 eV and for nanodiamonds an $a^{-2}$ gap size dependence gives $E_g = E_0 + 0.38(a/nm)^{-2}$ \citep{li04}.275. Variation in band-gap for nanocdiamoncds is observable only below 2ΠΠ size (Ratyοἱal.2003) and [ον smaller size cHiamoneloicds it is reported to be close to bulk diamond (Landtοἱal.2009)., Variation in band-gap for nanodiamonds is observable only below $2~nm$ size \citep{raty03} and for smaller size diamondoids it is reported to be close to bulk diamond \citep{landt09}.276". The absorption of EM waves in nanodiamonds can be related to this band-gap as it starts [rom e 4.7 pant, ", The absorption of EM waves in nanodiamonds can be related to this band-gap as it starts from $\sim$ 4.7 $\mu m^{-1}$ .277The rise in extinction dueto nanodiamond in [αςδν) region is abrupt and with increasing steepness., The rise in extinction dueto nanodiamond in far-UV region is abrupt and with increasing steepness.278 This huge extinction explains the Lu-UV quasar break (Dinetteοἱal.2005) , This large extinction explains the far-UV quasar break \citep{binette05} 279increasing number of low-mass X-rav. binaries. and systems exhibiting black-hole LLEXTDPOs are likely to have mass ratios q0.3 and therefore to have eccentric disces during at least some phases of their outbursts.,"increasing number of low-mass X-ray binaries, and systems exhibiting black-hole HFQPOs are likely to have mass ratios $q\la0.3$ and therefore to have eccentric discs during at least some phases of their outbursts."280 ltecentlv. Kato(2007) argued that one-armed global oscillations. svmmetric with respect to the z=Q0 plane. can excite trapped oscillations.," Recently, \cite{kato2007} argued that one-armed global oscillations, symmetric with respect to the $z=0$ plane, can excite trapped oscillations."281 His conclusions are based on analvtical. Lagrangian calculations and are too crude to allow for more than simple estimates for the growth rates.," His conclusions are based on analytical, Lagrangian calculations and are too crude to allow for more than simple estimates for the growth rates."282 In this section we describe an excitation mechanism similar to the one reported. previously. but where an (m=lon0) eccentric mode has the role that. previously belonged to the (i=low1) warp wave.," In this section we describe an excitation mechanism similar to the one reported previously, but where an $(m=1,n=0)$ eccentric mode has the role that previously belonged to the $(m=1,n=1)$ warp wave."283 Using the same numerical method as before. we calculate the trapped r mode growth rales.," Using the same numerical method as before, we calculate the trapped r mode growth rates."284 As before. consider the set of equations (10)) (13)).," As before, consider the set of equations \ref{free1}) \ref{free2}) )."285 A global eccentric mode corresponds to à zero-frequency. wave with mΞ land n=0. (, A global eccentric mode corresponds to a zero-frequency wave with $m=1$ and $n=0$. (286Lf the global eccentric mocde precesses freely. the frequency. is not exactly zero but is completely neeligible compared to the characteristic frequencies in the,"If the global eccentric mode precesses freely, the frequency is not exactly zero but is completely negligible compared to the characteristic frequencies in the"287lis producing an intrinsically one-sided outflow. or that a counter-jet is present but cannot be seen.,"is producing an intrinsically one-sided outflow, or that a counter-jet is present but cannot be seen."288" While multipole components to the neutron star magnetic field could indeed produce a one-sided jet (Chagelishvili.Bodo.&Trussoni 1996)). there is strong circumstantial evidence that the pulsar generates a collimated outflow to its north through which it is interacting with the RCW 89 region (Manchester&Dur-din 1983: Tamuraetal. 1996:; Brazier&Becker 1997:, G99)."," While multipole components to the neutron star magnetic field could indeed produce a one-sided jet \cite{cbt96b}) ), there is strong circumstantial evidence that the pulsar generates a collimated outflow to its north through which it is interacting with the RCW 89 region \cite{md83}; \cite{tkyb96}; \cite{bb97}; G99)."289 This conclusion is further bolstered by feature D in Figure 2.. which is significantly elongated along the main axis of the system and widens with increasing distance from the pulsar.," This conclusion is further bolstered by feature D in Figure \ref{fig_g320_acisi}, which is significantly elongated along the main axis of the system and widens with increasing distance from the pulsar."290 We propose that this feature represents a jet which produces no directly detectable emission. but for which we observe enhanced emission in a cylindrical sheath along the interface between the jet and its surroundings.," We propose that this feature represents a jet which produces no directly detectable emission, but for which we observe enhanced emission in a cylindrical sheath along the interface between the jet and its surroundings."291 Assuming that feature C and its unseen counterpart have similar intrinsic surface brightnesses and outflow velocities. relativistic Doppler boosting can account for the observed brightness contrast provided that 1;cos¢~0.28c. where ¢ is the inclination of the outflow to the line-of-sight.," Assuming that feature C and its unseen counterpart have similar intrinsic surface brightnesses and outflow velocities, relativistic Doppler boosting can account for the observed brightness contrast provided that $v_j \cos \zeta \sim 0.28c$, where $\zeta$ is the inclination of the outflow to the line-of-sight."292 Since cos¢<| for any inclination. we can infer a lower limit v;>0.28c. consistent with the estimate v;>0.2¢ determined above from the energetics of the system.," Since $\cos \zeta < 1$ for any inclination, we can infer a lower limit $v_j >2930.28c$, consistent with the estimate $v_j > 0.2c$ determined above from the energetics of the system."294" Brazier Becker (1997)) estimated ¢>70° on the basis of HHRI data. in which the PWN appears to have a ""eross-shaped morphology suggestive of an edge-on torus."," Brazier Becker \nocite{bb97}) ) estimated $\zeta > 70^\circ$ on the basis of HRI data, in which the PWN appears to have a “cross”-shaped morphology suggestive of an edge-on torus."295 However. this inclination then results in an uncomfortably high velocity. v;>0.8c.," However, this inclination then results in an uncomfortably high velocity, $v_j >2960.8c$."297" In our oobservation, this eross-shaped morphology is not apparent: it presumably resulted from imaging of the inner and outer ares (features E and 5 respectively) at the lower spatial resolution and sensitivity of the HHRI."," In our observation, this cross-shaped morphology is not apparent; it presumably resulted from imaging of the inner and outer arcs (features E and 5 respectively) at the lower spatial resolution and sensitivity of the HRI."298 A more reasonable shock flow speed vj2c/3 citekeSda)) corresponds to à smaller inclination angle 307., A more reasonable post-shock flow speed $v_j \approx c/3$ \\cite{kc84a}) ) corresponds to a smaller inclination angle $\zeta \sim 30^\circ$ .299 This low value of ¢ has additional support from radio polarization observations of PSRB1509—58.. which exclude the larger values of argued by Brazier Becker (1997)) at the ~3¢ level (Crawford.¢Manchester.&Kaspi 2001)).," This low value of $\zeta$ has additional support from radio polarization observations of PSR, which exclude the larger values of $\zeta$ argued by Brazier Becker \nocite{bb97}) ) at the $\sim3\sigma$ level \cite{cmk01}) )."300 Models 1n which the pulsar's high-energy emission originates in. outer gaps of the magnetosphere result in à viewing angle ¢45° (Romani&Yadigaroglu 1995)). while those in which the +-ray emission is produced in a polar cap generally require small values of (Kuiperetal. 1999)).," Models in which the pulsar's high-energy emission originates in outer gaps of the magnetosphere result in a viewing angle $\zeta \sim30145^\circ$ \cite{ry95}) ), while those in which the $\gamma$ -ray emission is produced in a polar cap generally require small values of $\zeta$ \cite{khk+99}) )."302 We are thus unable to distinguish between¢ these models from the available data., We are thus unable to distinguish between these models from the available data.303 Feature E. the bright semi-circular are to the north of the pulsar. demarcates a clear transition between the collection of compact bright features within I’ of the pulsar and the diffuse nebula which extends to much larger scales.," Feature E, the bright semi-circular arc to the north of the pulsar, demarcates a clear transition between the collection of compact bright features within $1'$ of the pulsar and the diffuse nebula which extends to much larger scales."304 The arc-like morphology of this feature is suggestive of a bow-shock. as would result where the ram-pressure from a fast-moving pulsar balances the outflow from the relativistic pulsar wind.," The arc-like morphology of this feature is suggestive of a bow-shock, as would result where the ram-pressure from a fast-moving pulsar balances the outflow from the relativistic pulsar wind."305 For a bow-shock to result. the pulsar's motion must be supersonic with respect to the sound speed in the surrounding medium.," For a bow-shock to result, the pulsar's motion must be supersonic with respect to the sound speed in the surrounding medium."306 Since the PWN itself has a sound speed ον. this condition can only be met if the reverse shock from the surrounding SNR has collided with the PWN. bringing thermal material to the center of the system (Chevalier1998::," Since the PWN itself has a sound speed $c/\sqrt{3}$, this condition can only be met if the reverse shock from the surrounding SNR has collided with the PWN, bringing thermal material to the center of the system \cite{che98}; \cite{vagt01}; \cite{bcf01}) )."307 vanderSwaluwetal.," However, it is unlikely that this stage in PWN evolution has yet occurred in this system, since the resulting PWN would be brighter and more compact than is observed, and would occupy only a small fraction of the SNR's interior volume."308 2001:: Blondin., An alternative interpretation is suggested by the fact that the dominant features seen in X-ray emission from both the Crab and Vela PWNe are bright toroidal arcs surrounding the pulsar \cite{hss+95}; \cite{hgh01}) ).309Chevalier.," In these cases, it is thought that these tori correspond to synchrotron-emitting particles from a pulsar wind focused into the equatorial plane of the system."310&Frierson 2001)). However. it ," Furthermore, in the case of the Crab, data show a ring of emission situated interior to the torus \cite{wht+00}) ), which may represent the point where the free-flowing pulsar wind first shocks."311ts unlikely that this stage in PWN," In the case of PSR, features E and 5 both show an arc-like morphology which is bisected by the symmetry axis of the nebula, similar to what is seen in these other PWNe."312 evolution has ," The orientation inferred from the outflow being along the spin axis implies that features E and 5 are closer to the observer than is the pulsar, and are produced by a wind whose line-of-sight velocity component is directed towards us."313yet occurred in this," The upper limit on any departure from circularity in the projected appearance of feature E implies $\zeta \la 30^\circ$, in agreement with the estimate of the inclination angle determined in \\ref{sec_discuss_orient}."314 system. since the resulting PWN would be ," Correcting for this inclination angle, we can infer a separation $r_5 = 0.4-0.5$ pc between the pulsar and feature 5, and $r_E = 0.75-0.85$ pc between the pulsar and feature E. In interpreting this emission, we first note that there are two characteristic time-scales associated with such features: $t_{flow}$, the time taken for particles to flow from the pulsar to this position, and $t_{synch}$, the synchrotron lifetime for these particles."315brighter a," We parametrize the upstream relativistic wind by the ratio, $\sigma_1$, of the energy in electromagnetic fields to that carried in particles \cite{rg74}) )."316nd more compa," This implies that $\sigma_1 = B_1^2/4\pi\rho_1 \gamma_1317c^2$, where $B_1$ is the toroidal magnetic field, $\rho_1$ is the lab frame total rest mass density, and $c\gamma_1 \gg c$ is the four-velocity of the wind, all just upstream of the termination shock in the pairs."318ct than is o," We assume $\sigma_1 \ll 1$, and will show in \\ref{sec_wisps_struc} that this assumption is self-consistent."319bser," In this case, the bulk velocity in the post-shock flow at a distance $r$ from the pulsar is \cite{kc84a}) ): where $r_s$ is the distance from the pulsar to the termination shock."320ved. and ," We then find that: For pairs emitting at energy $\varepsilon$ keV in a magnetic field $B$ $\mu$ G, the synchrotron lifetime is For the Crab Nebula, we adopt $r_s \approx 0.15$ pc and $B \sim 100$ $\mu$ G, and consider the Crab's X-ray torus at $r \approx 0.4$ pc."321wo," At an energy $\varepsilon=5$ keV, we find $t_{flow} \sim 30$ yr and $t_{synch} \sim 20$ yr, so that these time scales are comparable."322uld oc," In the case of PSR, we assume that the location of the termination shock corresponds approximately to that of feature 5 (the inner arc), and so adopt $r_s \approx r_5$."323cu," For a magnetic field $B \sim B_n = 8$ $\mu$ G, we then find that in feature E, $t_{flow} \sim 25$ yr $\ll324t_{synch} \sim 800$ yr."325py only a smal," Since the post-shock magnetic field in the inner nebula is generally weaker than the mean value for the PWN \cite{kc84a}) ), this value of $t_{synch}$ is likely to be a lower limit, further widening the discrepancy between the two time-scales."326l fraction of the SNR's," Thus while the bright torus seen in the Crab simply corresponds to the region in which most of the X-ray emitting particles radiate their energy, synchrotron cooling is not significant at this distance from PSR even at X-ray energies, and the brightness enhancement in feature E cannot be due to rapid dumping of pairs' energy into X-ray photons."327 in," The long synchrotron lifetimes require that most of the X-ray emission comes from a much larger volume, as is indeed observed."328terior , It is therefore not valid to argue that feature E is the analog of the X-ray torus seen in the Crab; the much lower nebular magnetic field in the case of PSR demands a different interpretation.329volu," This conclusion is supported by the fact that feature E has a distinctly harder photon index than the overall nebula and also shows a clear radio counterpart (see Fig. \ref{fig_g320_pol}) ),"330me., neither of which would be expected if this feature were primarily due to radiative losses.331ofa | wavepacket separated in 2 by 2Ay.,of a $+$ wavepacket separated in $z$ by $\ga\Lambda^-_\lambda$.332 Thus they inupriut their parallel scales ou the | ve waves. aud IHeuceforth we denote the common parallel scales by Ay. Thisdisc," Thus they imprint their parallel scales on the $+$ ve waves, and Henceforth we denote the common parallel scales by $\Lambda_\lambda\,$."333overy that the parallel scales are similar iu au inbalanuced cascadeis a nont, This that the parallel scales are similar in an imbalanced cascadeis a result.334rivial result. Equatious (1)) aud (5)) vield that the cascade of νο waves ds critically valance., Equations \ref{eq:Lambdaminus}) ) and \ref{eq:equal}) ) yield that the cascade of $-$ ve waves is critically balanced.335 Tt remains to calculate the | ve waves’ cascade time., It remains to calculate the $+$ ve waves' cascade time.336 All of the following material up to equation (9)). as well as he material in the Appendix. is devoted to the result: 7~Afi.," All of the following material up to equation \ref{eq:fluxplus2}) ), as well as the material in the Appendix, is devoted to the result: $\tau_\lambda^+\sim\lambda/w_\lambda^-$."337 This result is remarkable., This result is remarkable.338" It shows hat the straining rate imposed bv the ve waves on | ve ones. iyfA. is Iniposed coliereutly over a time Aft,."," It shows that the straining rate imposed by the $-$ ve waves on $+$ ve ones, $w_\lambda^-/\lambda$, is imposed coherently over a time $\lambda/w_\lambda^-$."339" Yet he waveperiod of νο waves is mich shorter than this. by he factor since yy 1. one nüght be tempted to conclude, erroneously. that | ve waves undergo a weal cascade. 1.6.. that νο waves impose on them small. short uncorrelated strains of amplitude ὧνover time intervals ~Αλτι resulting in τν~(yy)Αν)Αλ ων)."," Yet the waveperiod of $-$ ve waves is much shorter than this, by the factor Since $\chi_\lambda^-\ll 1$ , one might be tempted to conclude, erroneously, that $+$ ve waves undergo a weak cascade, i.e., that $-$ ve waves impose on them small, short uncorrelated strains of amplitude $\chi_\lambda^-$over time intervals $\sim340\Lambda_\lambda/\va$ resulting in $\tau_\lambda^+\sim341(\chi_\lambda^-)^{-2}(\Lambda_\lambda/\va)\sim342(\chi_\lambda^-)^{-1}(\lambda/w_\lambda^-)$ ."343 Tusteack. the correct couclusion is that a (NAcolierent strain is inposed over tine interval ," Instead, the correct conclusion is that a coherent strain is imposed over time interval $\lambda/w_\lambda^-$ ."344Tow cau the cobhereuce time Aaexceed X4/V47?, How can the coherence time exceed $\Lambda_\lambda/\va$?345 The kevpoint is that the straining of the| ve waves is duc to the νν field as seen from the | ve waves’ rest frame (which has 4jurea!myeiDOVt.4= of)," The keypoint is that the straining of the$+$ ve waves is due to the ${\bf346w}^-$ field as seen from the $+$ ve waves' rest frame (which has $x'=x, \;y'=y, \;z' = z - \va t, \;t'=t$ )."347" In this frame. the MIID equations (1)) transform to To appreciate that the correlation time of w— iu the primed frame can exceed Ayτε, consider the limiting case in which w— ds πο stall that backreaction outo the | ve waves can be neglected."," In this frame, the MHD equations \ref{eq:mhd}) ) transform to To appreciate that the correlation time of ${\bf w}^-$ in the primed frame can exceed $\Lambda_\lambda/\va$, consider the limiting case in which ${\bf w}^-$ is so small that backreaction onto the $+$ ve waves can be neglected."348 Then w! is iudepeudent of £. aud is a function oulv of r/. so ν satisfies a linear (integrodifferential) equation. whose coefficients are iudependoeut of #.," Then ${\bf w}^+$ is independent of $t'$, and is a function only of ${\bf r}'$, so ${\bf w}^-$ satisfies a linear (integro--differential) equation, whose coefficients are independent of $t'$."349 Tf ve waves are injected ou a leugthliscale nich larecr than the scale of iterest. with a long coherence time T. then as they cascade down to snaller scales their colercuce time remains fixed. 7...=T. where !corr. yas defined as the correlation time ofthe ve waves in the frame of the | ve waves.," If $-$ ve waves are injected on a lengthscale much larger than the scale of interest, with a long coherence time $T$, then as they cascade down to smaller scales their coherence time remains fixed, $\tau_{\rm corr,\lambda}^-=T$, where $\tau_{\rm corr,\lambda}^-$ is defined as the correlation time ofthe $-$ ve waves in the frame of the $+$ ve waves."350" In the lamiting case that wis held fixed at the injection scale (Fo— x). then on smaller scales wo ds independeut of £ (£z, x). even though it is nuderegoineg an active cascade to small scales."," In the limiting case that ${\bf w^-}$ is held fixed at the injection scale $T=\infty$ ), then on smaller scales ${\bf w}^-$ is independent of $t'$ $\tau_{\rm corr,\lambda}^-=\infty$ ), even though it is undergoing an active cascade to small scales."351 To estimate 7... When w is not imfuutesimally sux. it is necessary to account for backreaction: ve waves alter | ve waves. which react back on the νο ones," To estimate $\tau_{\rm corr,\lambda}^-$ when ${\bf352w}^-$ is not infinitesimally small, it is necessary to account for backreaction: $-$ ve waves alter $+$ ve waves, which react back on the $-$ ve ones."353 Ax ve waves cross a plane atfixed z/. the | ve waves at that plane are changing on their cascade time scale 7 . Hence. over times separated by ry. the ve waves crossing z are cascaded by eutirelv different. |ve waves.," As $-$ ve waves cross a plane atfixed $z'$, the $+$ ve waves at that plane are changing on their cascade time scale $\tau_\lambda^+$ Hence, over times separated by $\tau_\lambda^+$, the $-$ ve waves crossing $z^\prime$ are cascaded by entirely different $+$ ve waves."354" This inplies that T,corr.À~r8A Because the | voe waves are strained at rate wyfA. dt follows that AΑν."," This implies that $\tau_{\rm355corr,\lambda}^-\sim \tau_\lambda^+$ Because the $+$ ve waves are strained at rate $w_\lambda^-/\lambda$, it follows that $\tau_\lambda^+\sim\lambda/w_\lambda^-$."356 Thus Tuvoking Kohnosorov's lypothesis of the scale (ic. A} independence of the cucrey fluxes eiven by equations (3)) and (9)). we obtain the inertialrange scalings. The [ve wave cascade shares some characteristics with both weak aud strong balanced) MIID. cascades.," Thus Invoking Kolmogorov's hypothesis of the scale (i.e. $\lambda$ ) independence of the energy fluxes given by equations \ref{eq:fluxminus}) ) and \ref{eq:fluxplus2}) ), we obtain the inertial–range scalings, The $+$ ve wave cascade shares some characteristics with both weak and strong balanced MHD cascades."357 Iu the weak cascades. the cascade time is longer than the waveperiod. aud a wave experiences multiple. raudonilv-phased perturbations during its cascade time.," In the weak cascades, the cascade time is longer than the waveperiod, and a wave experiences multiple, randomly-phased perturbations during its cascade time."358 In the strong cascades. the cascade time is comparable to (or shorter than) the waveperiod. aud a wave suffers a coherent strain as it cascades.," In the strong cascades, the cascade time is comparable to (or shorter than) the waveperiod, and a wave suffers a coherent strain as it cascades."359 Furthermore. weak turbulence subunits to perturbation theory but strong turbulence does not.," Furthermore, weak turbulence submits to perturbation theory but strong turbulence does not."360 Iu the | ve wave cascade: We contend that the [ve wave cascade is strong because the second aud third items have dynamical sjeuificauce whereas the first does not., In the $+$ ve wave cascade: We contend that the $+$ ve wave cascade is strong because the second and third items have dynamical significance whereas the first does not.361 The cimensiouless paralmcter that iudicates whether the |ve waves are strouely cascaded. is and not ὧν., The dimensionless parameter that indicates whether the $+$ ve waves are strongly cascaded is and not $\chi_\lambda^-$.362" Strong cascades. corresponi toy, ~EH. and weals ones to ὧν<1."," Strong cascades correspond to $\hat{\chi}_\lambda^{-}\sim 1$, and weak ones to $\hat{\chi}_\lambda^{-}<1$."363 For the νο wave cascade. W=l. since the correlation time of | vo waves iu the frame of the ve ones is A/Va.," For the $-$ ve wave cascade, $\hat{\chi}_\lambda^+={\chi}_\lambda^+\sim 1$, since the correlation time of $+$ ve waves in the frame of the $-$ ve ones is $\Lambda_\lambda/\va$."364" We call the criterion WI] ""modified critical balance; to distinguish it frou critical balance (which would incorrectly imply WI~ i)."," We call the criterion $\hat{\chi}_\lambda^\pm\sim 1$ “modified critical balance,” to distinguish it from critical balance (which would incorrectly imply $\chi_\lambda^\pm\sim 1$ )."365 We lave deduced the behavior of mibalauced. strong ΑΠΟ turbulence., We have deduced the behavior of imbalanced strong MHD turbulence.366" Its salicut properties are: 1,", Its salient properties are: 1.367 The | ve aud ve waves carry unequalenergy fluxes. el #2. whilethey bothundergo cascades.," The $+$ ve and $-$ ve waves carry unequalenergy fluxes, $\varepsilon^+\neq \varepsilon^-\,$ , whilethey bothundergo cascades."368 2., 2.369 In the inertialrange. the rans.," In the inertial–range, the r.m.s."370 Elsasser amplitudes are proportional to the one.third power of the transverse scale: TNx AU].," Elsasser amplitudes are proportional to the one–third power of the transverse scale: $w^{\pm}_\lambda\propto371\lambda^{1/3}\,$ ."372 This is similar to the balanced. strong cascade.," This is similar to the balanced, strong cascade."373 Moreover. their ratio. uuTSalfs is independent of A.," Moreover, their ratio, $\wpluslam/\wminuslam \sim374\varepsilon^+/\varepsilon^-$ is independent of $\lambda$ ."375 3.The parallel scales of the | ve aud νο waves are equal., 3.The parallel scales of the $+$ ve and $-$ ve waves are equal.376 The conunon parallel scale of eddies of transverse seale AL isAyxATO μή] to the balanced. strong cascade.," The common parallel scale of eddies of transverse scale $\lambda$ , is$\Lambda_\lambda \propto\lambda^{2/3}$ , similar to the balanced, strong cascade."377phase.,phase.378 This 1iechauisui should also produce shorter more svuuuetrie bursts than in crustal fracture., This mechanism should also produce shorter more symmetric bursts than in crustal fracture.379 2? states that the harduess-fuence anticorrclation found in SCGRs is consistent with magnetic reconnection., \citet{lyu03} states that the hardness-fluence anticorrelation found in SGRs is consistent with magnetic reconnection.380 For the surtace-cooling model. the opposite is expected.," For the surface-cooling model, the opposite is expected."381" As diseussed by δν, both miechliuisius could easily be at work."," As discussed by \citet{lyu03}, both mechanisms could easily be at work."382 ? suggested that observationallv. there are two types of magnetar bursts.," \citet{wkg+05} suggested that observationally, there are two types of magnetar bursts."383 Type A bursts are nearly sviunetric and are typical of SCR bursts., Type A bursts are nearly symmetric and are typical of SGR bursts.384 Type D bursts have cen observed in ANPs aud are characterized by a short spike followed by a long tail. typically much longer hau the rotational period of the pulsar.," Type B bursts have been observed in AXPs and are characterized by a short spike followed by a long tail, typically much longer than the rotational period of the pulsar."385 Pulsatious have οσα observed iu these tails., Pulsations have been observed in these tails.386 Since the Type B bursts observed in ANPs occur prefercutially in phase and exhibit a harduess-fiueuce correlation. and the Type A musts in SGBs are distributed raucomly m phase aud je a harduess-flucuce auti-correlation. 7? suggest the naenetic reconnection mcchanisin for tvpe A bursts aud he surtace-cooling model for Type D bursts.," Since the Type B bursts observed in AXPs occur preferentially in phase and exhibit a hardness-fluence correlation, and the Type A bursts in SGRs are distributed randomly in phase and have a hardness-fluence anti-correlation, \citet{wkg+05} suggest the magnetic reconnection mechanism for type A bursts and the surface-cooling model for Type B bursts."387 For LE 51058. none of the bursts detected bySwift NRT could be classified as Type D. However. the two nursts with lone pulsating tails found in data by 2 and ? have typical Type B morphology.," For 1E $-$ 5408, none of the bursts detected by XRT could be classified as Type B. However, the two bursts with long pulsating tails found in data by \citet{snb+10} and \citet{mgw+09} have typical Type B morphology."388 For the bursts in this work. over half of the bursts were classified as svuuuetric. which nonünallv corresponds o Type A (see topaight pauecl of Figure 13. for example).," For the bursts in this work, over half of the bursts were classified as symmetric, which nominally corresponds to Type A (see top-right panel of Figure \ref{fig:burstex} for example)."389 About of the bursts were classified as slow-fall bursts. which are actually closer to Type A in norpholoey than Type B. although they are not very svuuuetne.," About of the bursts were classified as slow-fall bursts, which are actually closer to Type A in morphology than Type B, although they are not very symmetric."390 Thus. the bursts from 1E 5108 are rot easilv classified into Types A and D as described o Y.," Thus, the bursts from 1E $-$ 5408 are not easily classified into Types A and B as described by \citet{wkg+05}."391" Moreover. for both the svuuuetric aud slow-fall musts. the folded photon arrival times exhibited a clear phase dependence. although for the slow-fall bursts this ""pulse is auch strouger."," Moreover, for both the symmetric and slow-fall bursts, the folded photon arrival times exhibited a clear phase dependence, although for the slow-fall bursts this `pulse' is much stronger."392 That the svuumetric bursts slow sole pulse nodulation is sueecstive of a difference with ‘classical’ Type A bursts. or that pulse phase analyses of he latter should be attempted using all burst couuts. as hey too may be pulsed.," That the symmetric bursts show some pulse modulation is suggestive of a difference with `classical' Type A bursts, or that pulse phase analyses of the latter should be attempted using all burst counts, as they too may be pulsed."393 That the burst counts are pulsed indicates that burst enussion comes from a preferred region in rotational phase. be it on or near the surface or high in the magnetosphere. even if the burst peaks arrive randomly iu phase.," That the burst counts are pulsed indicates that burst emission comes from a preferred region in rotational phase, be it on or near the surface or high in the magnetosphere, even if the burst peaks arrive randomly in phase."394 The offset between the burst counts pulse peak aud the persistent pulse peak secu when comparing Figures Th aud το denmoustrates that the preferred burst cinissiou region has location and ecolctry similar to. but distinct from. that producimg the persistent pulsations.," The offset between the burst counts pulse peak and the persistent pulse peak seen when comparing Figures 7b and 7e demonstrates that the preferred burst emission region has location and geometry similar to, but distinct from, that producing the persistent pulsations."395 The total οποιον released iu the Suiff-detected bursts was ~τν10/9 ore in the 1-10 keV range.," The total energy released in the -detected bursts was $\sim3961 \times 10^{40}$ erg in the 1-10 keV range."397 This is much lower than the 1-10 keV energv released frou the persistent enission between 2009 January 22 and 2009 September 30 of ~9«10! ore., This is much lower than the 1-10 keV energy released from the persistent emission between 2009 January 22 and 2009 September 30 of $\sim 9 \times 10^{41}$ erg.398 For reference. the energv released frou the spin-down in that same period is ~ὃν10! ore.," For reference, the energy released from the spin-down in that same period is $\sim 5 \times 10^{40}$ erg."399 2 find that for SCRs. the enerev released in the bursts is higher than that released in the persistent cussion. but for LE 2259|586. the opposite is true.," \citet{wkt+04} find that for SGRs, the energy released in the bursts is higher than that released in the persistent emission, but for 1E 2259+586, the opposite is true."400 Iu this regard. the 2009 outburst of LE 1517. 5108 is more like that of ANP 1E 2259|586.," In this regard, the 2009 outburst of 1E $-$ 5408 is more like that of AXP 1E 2259+586."401 We have presented an analysis of the persistent radiative evolution of the 2009 January outburst of 1E 5108 from NRT observations., We have presented an analysis of the persistent radiative evolution of the 2009 January outburst of 1E $-$ 5408 from XRT observations.402 We found that —6 hr after the 2009 DAT trigger the observed persisteut 110 keV unabsorbed fux reached a peak of —S10P? eres 72 1; au increase of more than 500 times the quiesceut flux leadiug up to the outburst.," We found that $\sim6$ hr after the 2009 BAT trigger the observed persistent 1–10 keV unabsorbed flux reached a peak of $\sim8 \times 10^{-9}$ ergs $^{-2}$ $^{-1}$, an increase of more than 500 times the quiescent flux leading up to the outburst."403 This flux evolution is not due solely to the source: in the first dav. there is also emission from dust scattering rues that is delaved eiission from an energtie event near the ousct of the outburst.," This flux evolution is not due solely to the source; in the first day, there is also emission from dust scattering rings that is delayed emission from an energtic event near the onset of the outburst."404 There was significant spectral hardening at the outburst as secu in other maguctar outbursts., There was significant spectral hardening at the outburst as seen in other magnetar outbursts.405 Note that the absence of spectral variation reported by ? is consistent with our results. as thev uissed the bulk of the spectal changes which occured iu the first dav of the outburst aud their observations did not beein until the next day.," Note that the absence of spectral variation reported by \citet{nkd+10} is consistent with our results, as they missed the bulk of the spectal changes which occured in the first day of the outburst and their observations did not begin until the next day."406 The pulsed fraction showed au auti-correlatiou with the phase-averaged fux for both the previous 2008 aud 2009 outbursts. with both sets of data following the same trend. ?..," The pulsed fraction showed an anti-correlation with the phase-averaged flux for both the previous 2008 and 2009 outbursts, with both sets of data following the same trend. \citet{wkg+05}."407 ? , \citet{bis+11} 408sky are expected to be confusiou-limited by these sources.,sky are expected to be confusion-limited by these sources.409 The anisotropies are the result of variations in the nuuber of verv fait sources with fluxes around 0.5 12Js., The anisotropies are the result of variations in the number of very faint sources with fluxes around 0.5 mJy.410 À linJw point source will produce an increment of 20 pl in the APEN-SZ map., A 1 mJy point source will produce an increment of 20 $\mu$ K in the APEX-SZ map.411 The APEN-SZ map of the AMALLSS field is too shallow to pick out these sub-niJv sources. and we see no evidence of reaching the confusion-limüt iu the current observations.," The APEX-SZ map of the XMM-LSS field is too shallow to pick out these sub-mJy sources, and we see no evidence of reaching the confusion-limit in the current observations."412" The dusty ealaxy coutribution to the APEN-SZ baud powers is predicted by the model presented in? to be C, = 1.1 «1ο pS? (LT Jy? sy 4) iu the absence of clustering. which is in good aerecment with the measured poiut source power in Table 2.."," The dusty galaxy contribution to the APEX-SZ band powers is predicted by the model presented in \citet{negrello2007} to be $C_\ell$ = 1.1 $\times 10^{-5}$ $\mu$ $^2$ (1.7 $^2$ $^{-1}$ ) in the absence of clustering, which is in good agreement with the measured point source power in Table \ref{tab:params}."413 The predicted power from dusty ealaxies is nearly indepeudent of the flux cut level above liuJs., The predicted power from dusty galaxies is nearly independent of the flux cut level above 1 mJy.414 Dusty galaxies are expected to account for most of the power in the APEX-SZ maps., Dusty galaxies are expected to account for most of the power in the APEX-SZ maps.415 The BLAST collaboration veceutly released measurements of the power spectrum of the— cosmic farunfrared background at frequencies of 600 CIIz to 1.2 THz (?).., The BLAST collaboration recently released measurements of the power spectrum of the cosmic far-infrared background at frequencies of 600 GHz to 1.2 THz \citep{viero2009}.416 BLAST incasured a Poisson contribution frou star-forming galaxies with an amplitude of 2.68340.1«10° Ίντα | at 600 ο., BLAST measured a Poisson contribution from star-forming galaxies with an amplitude of $2.63 \pm 0.1 \times 10^3$ $^2$ $^{-1}$ at 600 GHz.417 A clustering term is detected as well on aneular scales larger than those probed by APEX-SZ., A clustering term is detected as well on angular scales larger than those probed by APEX-SZ.418 Expressing the frequency dependence of the source fuses as οί)xrÜ. we can derive an effective spectral iudex. a. by comparing the power measured by BLAST at 600 GIIz to the point source power likelihooc function of the APEN-SZ maps at 150 CGIIz.," Expressing the frequency dependence of the source fluxes as $S(\nu) \propto \nu^\alpha$, we can derive an effective spectral index, $\alpha$, by comparing the power measured by BLAST at 600 GHz to the point source power likelihood function of the APEX-SZ maps at 150 GHz."419 This iudex will depend ou the the spectra of the iudividual galaxies and their redshift distribution., This index will depend on the the spectra of the individual galaxies and their redshift distribution.420" We find that a spectra index. of à=2.61105 scales the BLAST power to match the best-fit C, = «107 pK? (7S Jv? sv !) of the APEN-SZ data.", We find that a spectral index of $\alpha=2.64^{+0.4}_{-0.2}$ scales the BLAST power to match the best-fit $C_\ell$ = $^{+0.9}_{-0.8} \times 10^{-5}$ $\mu$ $^2$ $^{+1.4}_{-1.3}$ $^2$ $^{-1}$ ) of the APEX-SZ data.421 This inferred spectra index agrees well with previous estinates for sub-uuu bright ealaxics., This inferred spectral index agrees well with previous estimates for sub-mm bright galaxies.422" 2 examined nearby galaxy data a found 5,xp29*9?.Iu an alternative approach. ? conrpared the flux of sources in overlapping regions observed by MAMBO (1.2 nimi) and SCUBA (850 jan) and fouud the fuxes scaled as 5,xv2."," \citet{knox2004} examined nearby galaxy data and found $S_\nu \propto \nu^{2.6 \pm 0.3}$.In an alternative approach, \citet{greve2004} compared the flux of sources in overlapping regions observed by MAMBO (1.2 mm) and SCUBA (850 $\mu$ m) and found the fluxes scaled as $S_\nu \propto \nu^{2.65}$."423 The poiut source power in the APEN-SZ data set at 150 GIIz is consistent with beiug eutirelv. due to a population of dusty subnmuu-hbresht galaxies such as those observed by BLAST., The point source power in the APEX-SZ data set at 150 GHz is consistent with being entirely due to a population of dusty submm-bright galaxies such as those observed by BLAST.424 We also consider radio sources as a potential foreground. in the APEN-SZ maps., We also consider radio sources as a potential foreground in the APEX-SZ maps.425 ? and ?/— have modeled the uuuber counts of several classes of racio sources at tens of GIIz., \cite{granato2004} and \cite{zotti2005} have modeled the number counts of several classes of radio sources at tens of GHz.426 We derive Cio frou their modeled παο counts at 150 GIIz., We derive ${\it C}_\ell^{\rm radio}$ from their modeled number counts at 150 GHz.427 The radio source power is dependent on the brightest objects and is expected to scale approximately lincarly with the source cut threshold., The radio source power is dependent on the brightest objects and is expected to scale approximately linearly with the source cut threshold.428 At the 2 mJy source cut threshold of APEN-SZ. CP should be X5% of the dusty ealaxy contribution.," At the 2 mJy source cut threshold of APEX-SZ, ${\it C}_\ell^{\rm radio}$ should be $\lesssim 5\%$ of the dusty galaxy contribution."429 We find 27 point sources above 3 0 (~2 mJ) in the APEX-SZ maps using the approach outlined in refSUDSEC:psestinate.., We find 27 point sources above 3 $\sigma$ $\sim$ 2 mJy) in the APEX-SZ maps using the approach outlined in \\ref{SUBSEC:psestimate}.430 Eight of these sources are within 1/of à NVSS source aud are likely radio sources., Eight of these sources are within $^\prime$ of a NVSS source and are likely radio sources.431 We expect four false detections based on Cassia statistics and the number of beamrsized pixels iu the APEN-SZ imap., We expect four false detections based on Gaussian statistics and the number of beam-sized pixels in the APEX-SZ map.432 The remaining sources are tentativelv identified as dusty galaxies., The remaining sources are tentatively identified as dusty galaxies.433 We cun compare the observed nunber counts in the APENX-SZ maps with other experiments at 150 GIIz. however most previous experiments were tarecting larger angular scales aud are relatively iuseusitive to dini point sources;," We can compare the observed number counts in the APEX-SZ maps with other experiments at 150 GHz, however most previous experiments were targeting larger angular scales and are relatively insensitive to dim point sources."434 QUaD (?) and ACBAR (?) both report —0.1 radio sources per square degree with a flux detection threshold of may tens of indy., QUaD \citep{friedman2009} and ACBAR \citep{reichardt2008} both report $\sim$ 0.1 radio sources per square degree with a flux detection threshold of many tens of mJy.435 The deepest previously published map at 150 CIIz is from Bolocai (2). which reports no sources above LO mJy in a 1 deg? patch., The deepest previously published map at 150 GHz is from Bolocam \citep{sayers09} which reports no sources above 10 mJy in a 1 $^2$ patch.436 As dN(2S)/dS is expected to fall steeply above 1 12Jy for dusty ealaxies. the scarcity of detected sources in these maps is nof particularly surprising.," As $>$ S)/dS is expected to fall steeply above 1 mJy for dusty galaxies, the scarcity of detected sources in these maps is not particularly surprising."437 The BLAST source catalogue (1) of 351 sources detected at 250. 350 or 500 μπι allows a more interesting cross-colparison.," The BLAST source catalogue \citep{dye2009} of 351 sources detected at 250, 350 or 500 $\mu$ m allows a more interesting cross-comparison."438 The BLAST catalogue has 291 sources per square degree in the deep coverage region and 15 sources per square degree in the shallow coverage regiou., The BLAST catalogue has 294 sources per square degree in the deep coverage region and 15 sources per square degree in the shallow coverage region.439 At 500 jou. the detection threshold of the BLAST catalogue is 30 µι]ν and 100 indy respectively.," At 500 $\mu$ m, the detection threshold of the BLAST catalogue is 30 mJy and 100 mJy respectively."440 For the best-fit effective spectral iudex of a=2.61 derived earlier. this correspouds to a source detection threshold at 150 Ον of 0.5 aud 2.6 mJy respectively.," For the best-fit effective spectral index of $\alpha=2.64$ derived earlier, this corresponds to a source detection threshold at 150 GHz of 0.8 and 2.6 mJy respectively."441 These two detection thresholds bracket the average APEN-SZ 36 detection threshold of 2 παν. aud the observed APEN-SZ nou-racdio source unuber density of 19 sources/deg? falls between these two source densities as we would expect.," These two detection thresholds bracket the average APEX-SZ $\,\sigma$ detection threshold of 2 mJy, and the observed APEX-SZ non-radio source number density of 19 $^2$ falls between these two source densities as we would expect."442 The source uunber counts in the APEN-SZ maps appear cousisteut with the wuubers expected for dusty galaxies., The source number counts in the APEX-SZ maps appear consistent with the numbers expected for dusty galaxies.443 Observations with the APEN-SZ instrument have beeu used to constrain the power m excess of the primary CXMB temperature aulsotropies at 150 CGIIz.," Observations with the APEX-SZ instrument have been used to constrain the power in excess of the primary CMB temperature anisotropies at $150\,$ GHz."444 This power is expected to be dominated by cussion from sub-una bright. dusty galaxies and the APEN-SZ baud powers are cousistent with this hvpothesis.," This power is expected to be dominated by emission from sub-mm bright, dusty galaxies and the APEX-SZ band powers are consistent with this hypothesis."445 We find excelleu agreement between the point source power iu the APEX-SZ maps aud model predictions based ou observations a other frequencics., We find excellent agreement between the point source power in the APEX-SZ maps and model predictions based on observations at other frequencies.446" We estimate that the fiux of these sub-unm bright galaxies scales with frequency as S,~778 * ColNparing the power measured by BLAST at 600 CGIIz to the best-fit point source power in the APEX-SZ maps at 150 GIIz.", We estimate that the flux of these sub-mm bright galaxies scales with frequency as $S_\nu \sim \nu^{2.64}$ by comparing the power measured by BLAST at 600 GHz to the best-fit point source power in the APEX-SZ maps at 150 GHz.447 Determining the contribution of hese foreground sources not only constrains models for he population of dusty galaxies. but is important for annus current aud future observations of secondary ΑΠΟ anisotropies at these waveleneths.," Determining the contribution of these foreground sources not only constrains models for the population of dusty galaxies, but is important for planning current and future observations of secondary CMB anisotropies at these wavelengths."448 We also place upper limits on c4 from fits to he amplitude of the SZE power spectrum while nareinalizinge over a Poisson point source coutribution., We also place upper limits on $\sigma_8$ from fits to the amplitude of the SZE power spectrum while marginalizing over a Poisson point source contribution.449 We assume a template for the SZE power spectim derived from simulations by ? with the amplitude of the SZE power spectrum scaling as og., We assume a template for the SZE power spectrum derived from simulations by \cite{shaw2009} with the amplitude of the SZE power spectrum scaling as $\sigma_8^7$ .450 We find an upper luit of ex<L.18 at confidence., We find an upper limit of $\sigma_8< 1.18$ at confidence.451 This result is similar to the constraints from the CBI aud BIMA interferometers operating at 30 GIIz.," This result is similar to the constraints from the CBI and BIMA interferometers operating at $30\,$ GHz."452 The Bits frou SZA. QUaD. or ACBAR would likely be slightly lower. but they did not express their results iu terms of upper limits ou oy.," The limits from SZA, QUaD, or ACBAR would likely be slightly lower, but they did not express their results in terms of upper limits on $\sigma_8$."453 At these frequeucies aud angular scales. the previous best luit comes frou ?.. who used observations with the Bolocai iustruieut to coustrain ey«1.57 at 90% confidence.," At these frequencies and angular scales, the previous best limit comes from \citet{sayers09}, , who used observations with the Bolocam instrument to constrain $\sigma_8<1.57$ at $90\%$ confidence."454 A third of the APEN-SZ instrument was recentlv uperaded to more sensitive detectors with iuproved optical efficicucies., A third of the APEX-SZ instrument was recently upgraded to more sensitive detectors with improved optical efficiencies.455 Iu the next vear. the reminderof the focal plane will be upgraded resulting in siguificaut," In the next year, the remainderof the focal plane will be upgraded resulting in significant"456population of clectrous with power-law index p as ys”.,population of electrons with power-law index $p$ as $n_0\gam^{-p}$.457" The total wuuber of relativistic electrons in one blob is The fraction of the relativistic electrons to the total iuuber of the initial blob is about «ΤΟgn= for p>2. where ©»τμ=£/0.01 and 5,44,=50."," The total number of relativistic electrons in one blob is The fraction of the relativistic electrons to the total number of the initial blob is about $\xi k\tss/\gmin m_ec^2=0.012\xi_{-2}$ for $p>2$, where $\xi_{-2}=\xi/0.01$ and $\gmin=50$."458 This stronely προς that the αμα electrons may originate from the present mechanism which may be a proposing nechanisuni responsible for the acceleration of relativistic olectrous in some of radio-loud quasars.," This strongly implies that the radiating electrons may originate from the present mechanism, which may be a proposing mechanism responsible for the acceleration of relativistic electrons in some of radio-loud quasars."459 It is expected the nouthermal emission spectra and light curves should be similar to some properties predicted by Li I&usunose (2000) ancl I&usunose et al. (, It is expected the nonthermal emission spectrum and light curves should be similar to some properties predicted by Li Kusunose (2000) and Kusunose et al. (4602000).,2000).461 It is thus inevitable for the ejected blob that the lugh-temperature drops due to the strong interaction between the blob aud its surroundings. aud as a natural consequence there is a eroup of clectrous to be accelerated to relativistic eucrev responsible for the coutimmim aud sole recombination lines from the cooled blob," It is thus inevitable for the ejected blob that the high-temperature drops due to the strong interaction between the blob and its surroundings, and as a natural consequence there is a group of electrons to be accelerated to relativistic energy responsible for the continuum and some recombination lines from the cooled blob."462 It has been generally accepted that accretion onto super massive black holes leads to the release of gravitational οποιον in active galactic nuclei (Rees 1981)., It has been generally accepted that accretion onto super massive black holes leads to the release of gravitational energy in active galactic nuclei (Rees 1984).463 However. the status of the accretion disk im differeut kinds of ACNs remains uncertain.," However, the status of the accretion disk in different kinds of AGNs remains uncertain."464 Iou-supported tori may power the central cneiue iu radio-loud quasars (Rees et al., Ion-supported tori may power the central engine in radio-loud quasars (Rees et al.465 1982)., 1982).466 A famous low luminosity ACN NCC 1258 is cenerally thought as representative of ADAFs (Camunie et al., A famous low luminosity AGN NGC 4258 is generally thought as representative of ADAFs (Gammie et al.467 1999)., 1999).468 However. receut observatious of bv show the origination is not from an accretion disk (Reynolds ct al.," However, recent observations of by show the origination is not from an accretion disk (Reynolds et al."469 Ww00)., 2000).470 Yaqoob et al. (, Yaqoob et al. (4711999) detected a highly Dopplerbhic-shifted Ik-eiissiou line iu PISS 2119306.,1999) detected a highly Doppler blue-shifted K-emission line in PKS 2149–306.472 We thus apply our model to the two objects., We thus apply our model to the two objects.473"4255: The ass the central black hole is well determiued tobe sovationAL,or«10AZ, by. Mivoshi et al. (", The mass of the central black hole is well determined to be $\mbh=3.6\times 10^7\sunm$ by Miyoshi et al. (4741995).,1995).475" Radio ol set the transition radius frou the standard disk to the ADAF to be 10072, (Herrustein et al.", Radio observation set the transition radius from the standard disk to the ADAF to be $R_g$ (Herrnstein et al.476 1999). and the accretion rate is ~LO«10.PMg (Camuunie et al.," 1999), and the accretion rate is $\sim 1.0\times 10^{-3}\dot{M}_{\rm Edd}$ (Gammie et al."477 1999)., 1999).478" Taking the typical value of a=0.) we have T4LT& 10K and s4=7.2«Loan 7. if the ejection takes place at LOR,. where the viscous heating rate is lighest."," Taking the typical value of $\alpha=0.1$, we have $T_1=4.7\times 10^{10}$ K and $n_1=7.2\times 10^{10}$ $^{-3}$, if the ejection takes place at $R_g$, where the viscous heating rate is highest."479" The initial dimension of the ejected blob is taken to be Ry=108,104! cm.", The initial dimension of the ejected blob is taken to be $R_0=10R_g=10^{14}$ cm.480 The additional componcut with huninostv £4=2.0«10Ü cres/s idu N-ray shows that the teuuous plasma is of temperature 0.5 keV (Revnolds et al., The additional component with luminosity $L_X^A=2.0\times 10^{40}$ ergs/s in X-ray shows that the tenuous plasma is of temperature 0.5 keV (Reynolds et al.481 2000)., 2000).482" This sets constraints on the density of the environment iu the vicinity of the uucleus via the Thomson scattering depth Ty=Oy,Nef. where σι, is the Thomson scattering cross section and f is the dimension of its surroundings."," This sets constraints on the density of the environment in the vicinity of the nucleus via the Thomson scattering depth $\tau_{_{\rm Th}} = \st n_2 \ell$, where $\st$ is the Thomson scattering cross section and $\ell$ is the dimension of its surroundings."483" Using the N-rav. luminosity of the additional componcut contributed. from. the teimous plasma L4=απ1mAn3T,yal/2 (A=3.1s10 25, we have the umuber density of the surroundings to be ny=TOy "," Using the X-ray luminosity of the additional component contributed from the tenuous plasma $L_X^A=\frac{4}{3}\pi\ell^3 \Lambda n_2^2T_e^{1/2}$ $\Lambda=3.4\times 10^{-27}$ ), we have the number density of the surroundings to be $n_2=10^8(\tau_{_{\rm Th}}/0.1)^3$ $^{-3}$."484From equation (1) we have the Mach munuber Moο=97., From equation (4) we have the Mach number ${\cal M} = 97$.485 The timescale of cooling duc to expansion is then given bv τ2.36« 1078. which is much shorter than that of free cooling.," The timescale of cooling due to expansion is then given by $\tau=2.36\times 10^5$ s, which is much shorter than that of free-free cooling."486 The expanded radius of the blob is cu., The expanded radius of the blob is cm.487 The temperature will drop from L7«1019. to T=Tj£M?x5.0«08h. Dining the cooling sole recombination lines will be produced (Ravinoud Sinith 1977). such as FeNNVIAL7SA.. FoNNVAI.85À.. FOXNVALAGA.. audRR line OVITTALS.97. aud silicou Si NIVAG.ISÁ.. ete.," The temperature will drop from $4.7\times 10^{10}$ K to $T=T_1/{\cal M}^2\approx 5.0\times 10^6$ K. During the cooling some recombination lines will be produced (Raymond Smith 1977), such as $\lambda1.78$, $\lambda1.85$ , $\lambda1.86$ , and oxygen line $\lambda18.97$, and silicon Si $\lambda 6.18$, etc."488 mIf the blob moves with Doppler factor of10 (Ganuuie et al., If the blob moves with Doppler factor of10 (Gammie et al.489 we expect to observe the highly Doppler bluc-shifted line at GLPyy keV. where D=LODiy is the Doppler factor.," 1999), we expect to observe the highly Doppler blue-shifted line at $\cd_{10}$ keV, where $\cd=10\cd_{10}$ is the Doppler factor."490 Such lines should be detected by future observations ofINTEGRAL., Such lines should be detected by future observations of.491306: The lighly Doppler shifted iron EK-cussion line has been detected by in this hieh redshift (222.315) radio-loud quasar (Yaqoob et al., The highly Doppler shifted iron K-emission line has been detected by in this high redshift $z$ =2.345) radio-loud quasar (Yaqoob et al.492" 1999). although the curent data does not allow to determine its ""uenbiguous profile."," 1999), although the current data does not allow to determine its unambiguous profile."493 We attempt to apply our prescut uodel to this source., We attempt to apply our present model to this source.494 The central mass can be obtained roni the full-width-at-half-1naxiununmni CEWIIM) and the ununmositv of emission line CIV (Peterson 1998)., The central mass can be obtained from the full-width-at-half-maximum (FWHM) and the luminosity of emission line CIV (Peterson 1998).495 With the neasurements of Ον=6100kim/s (Wilkes 1986). aud L(CTV)=1.2xs10 eres (Wilkes et al.," With the measurements of $v_{_{\rm FWHM}}=6400$ km/s (Wilkes 1986), and $L({\rm CIV})=1.2\times 10^{46}$ erg/s (Wilkes et al."496" 1983) (which we neasured from the spectrum). we have the mass of the central black hole. M=3.1«109AZ... which corresponds Eddinston huninositv =L3«10!ere/s. If we ollow the mean spectrum L,,,of radio-loud quasars (Elvis et al."," 1983) (which we measured from the spectrum), we have the mass of the central black hole, $\mbh=3.4\times 10^9\sunm$, which corresponds to Eddington luminosity $L_{_{\rm Edd}}=4.3\times 10^{47}$ erg/s. If we follow the mean spectrum of radio-loud quasars (Elvis et al."497" 1991). we ect the bolometric Iuniuositv Lj,%οςLOM ere/s based ou the coutimmun (Siebert et al."," 1994), we get the bolometric luminosity $L_{\rm bol}\approx 5.0\times 10^{47}$ erg/s based on the continuum (Siebert et al."498 1996)., 1996).499" Then the accretion rate is roughlya=μμad7A2.010. 2, where Doppler factor D=2.65: here(DIL, we directly used the Doppler factor of the iron [& cinission line as jets."," Then the accretion rate is roughly$ \dot{m} = L_{\rm bol}/(\cd^4L_{_{\rm Edd}}) \approx 2.0\times 10^{-2}$ , where Doppler factor $\cd=2.65$; here we directly used the Doppler factor of the iron K emission line as jet's."500 It sugeests that this object may be powered bv au ADAF., It suggests that this object may be powered by an ADAF.501 The trausition radius from the standard disk to the ADAF can be obtained by the approximate formula ry©2.6<Late7 for the case that half the released energy is advected [their eq. , The transition radius from the standard disk to the ADAF can be obtained by the approximate formula $r_{\rm tr}\approx 2.6\times 10^3 \alpha^4\dot{m}^{-2}$ for the case that half the released energy is advected [their eq. (502£L1) of Narayan Yi 1995].,4.1) of Narayan Yi 1995].503 We get rgzmLOO for a=0.1., We get $r_{\rm tr}\approx 400$ for $\alpha=0.1$.504" Tf the ejection takes place at LOR, with initial radius Ry= 100. then the deusity is ay=1.95«L0Scun Ὁ LOR,and the temperature is T,=2.3« 10M. Taking the typical values of the parameters. πο=5.0&L0°cm 7 aud T2=5.0& I0""K. for ICAL in the BLR (Netzer 1991). we have the typical expansion timescale ττε2.8 θα, aud the temperature will drop to 10777 K. where Mach uuuber WM?L7«10° from equationCI)."," If the ejection takes place at $10R_g$ with initial radius $R_0=10R_g\approx 10^{16}$ cm, then the density is $n_1=1.7\times 10^8$ $^{-3}$ and the temperature is $T_1=2.3\times 10^{11}$ K. Taking the typical values of the parameters, $n_2=5.0\times 10^6$ $^{-3}$ and $T_2=5.0\times 10^7$ K, for ICM in the BLR (Netzer 1991), we have the typical expansion timescale $\tau \approx 2.8\times 10^6$ s, and the temperature will drop to $10^{7\sim 8}$ K, where Mach number ${\cal M}^2=4.7\times 10^3$ from equation (4)."505 Theblob's distance from the= center is about JerzS&L«10! ome (3zm 1)., The blob's distance from the center is about $\beta c\tau \approx 8.4\times 10^{16}$ $\approx 80R_g$ $\beta\approx 1$ ).506" It is thus expected that some high cnerev SOR,recombination ues will appear in 2.8< δν since the ejection of a blob", It is thus expected that some high energy recombination lines will appear in $2.8\times 10^6$ s since the ejection of a blob.507 There should be two steps to eject a blob., There should be two steps to eject a blob.508" The first is the blob formation with the timescale of which is approximate to the viscous timescale (timescale to accumulate matter). namely zzmatr. |r.=1/0,(Ryce)?= 10s at r= Μη."," The first is the blob formation with the timescale of $\tau_{\rm f}$, which is approximate to the viscous timescale (timescale to accumulate matter), namely $\tau_{\rm f} \approx \alpha^{-1}\tau_{_{\rm K}}$ $\tau_{_{\rm K}}=1/\ok=(R_g/c)r^{3/2}=10^6$ s at $r=10$ ]."509 Iu the more accurate global solutiou the radial velocity is higher than the above onc., In the more accurate global solution the radial velocity is higher than the above one.510 The second is the relativistic ejection with timescale 7., The second is the relativistic ejection with timescale $\tau_{\rm e}$.511 It seclus reasonable to assume that the timescale of ejection is much shorter than the timescale of blob formation., It seems reasonable to assume that the timescale of ejection is much shorter than the timescale of blob formation.512" The duration for a blob to produce the iron recombination lines is approximately ty=6.6vrfor T,= 1091 aud n,1.0s10m 3.", The duration for a blob to produce the iron recombination lines is approximately $\tau_{\rm ff}=6.6$yrfor $T_e=10^8$ K and $n_e=1.0\times 10^7$ $^{-3}$ .513" Therefore the uuniber of the blobs producing the recombination line of won I-eumission would be Ny,zmrgí(T|T)€ates.c20 if the ejectionnube takes place at LOR,(It shouldbe noted that this is not the total of the ejected blobs)."," Therefore the number of the blobs producing the recombination line of iron K-emission would be $N_b\approx \tau_{\rm ff}/(\tau_{\rm e}+\tau_{\rm f}) 514\approx \alpha \tau_{\rm ff}/\tau_{_{\rm K}} \approx 20$ if the ejection takes place at $R_g$ (It should be noted that this number is the total of the ejected blobs)."515 We assume the, We assume the516"spatial and velocity resolutions, respectively.","spatial and velocity resolutions, respectively."517" We identified 123 cores and estimated the beam-deconvolved radiusReore, velocity width in FWHM corrected for the spectrometer resolutiondu4,, LTE massMoore, virial massM,;,, and mean density of the cores."," We identified 123 cores and estimated the beam-deconvolved radius, velocity width in FWHM corrected for the spectrometer resolution, LTE mass, virial mass, and mean density of the cores."518 Table 2 shows the physical properties of the cores in S140., Table \ref{propertyTable} shows the physical properties of the cores in S140.519 The definitions of these parameters are the same as those in (2009).., The definitions of these parameters are the same as those in \citet{ike09b}.520 Here we briefly summarize the parameters specific to this study., Here we briefly summarize the parameters specific to this study.521" We adopted=22"".0 as described in §2,, the antenna efficiency η of 0.4, and the fractional abundance of C180 relative to H5, Xciso of 1.7x1077 (Frerkingetal.1982)."," We adopted$= 22''.0$ as described in \ref{observation}, the antenna efficiency $\eta$ of 0.4, and the fractional abundance of $^{18}$ O relative to $_{2}$, $X_{\rm C^{18}O}$ of $1.7\times10^{-7}$ \citep{fre82}."522". The optical depth of the line in the $140 region has been estimated to be smaller than 1; derived the upper limit of the optical depth of 0.5, from the intensity ratio of the(J—1-0) to C!""O(J—1-0) lines."," The optical depth of the line in the S140 region has been estimated to be smaller than 1; \citet{hig09} derived the upper limit of the optical depth of 0.5, from the intensity ratio of the to $^{17}$ O lines."523" We assumed that the excitation temperature Tex is uniform over the $140 region and is equal to the rotational temperature of 24 K in the NH3 (1, 1) and (2, 2) observations by Higuchietal.(2009)."," We assumed that the excitation temperature $T_{\rm ex}$ is uniform over the S140 region and is equal to the rotational temperature of 24 K in the $_{3}$ (1, 1) and (2, 2) observations by \citet{hig09}."524". In the head clump, the temperature of > 20 K is reasonable because the clump faces the Sh 2-140 H region and numerous young stellar objects have been found (Megeathetal.2004),, as well as the OMC-1 cloud."," In the head clump, the temperature of $>$ 20 K is reasonable because the clump faces the Sh 2-140 H region and numerous young stellar objects have been found \citep{meg04}, as well as the OMC-1 cloud."525" On the other hand, the other two clumps have not been well studied compared to the head clump."," On the other hand, the other two clumps have not been well studied compared to the head clump."526" In the filamentary clump, two IRAS point sources 221924-6302 and 221964-6302 are detected, but the nature of the sources is unknown."," In the filamentary clump, two IRAS point sources 22192+6302 and 22196+6302 are detected, but the nature of the sources is unknown."527" Toward the tail clump, no signature of star formation has been found."," Toward the tail clump, no signature of star formation has been found."528" Although our assumption of the uniform temperature cannot be validated for the two clumps, we found that a low Τε value of 10 K does not seriously affect our discussion, and therefore we adopted the assumption of the uniform Τος in this study."," Although our assumption of the uniform temperature cannot be validated for the two clumps, we found that a low $T_{\rm ex}$ value of 10 K does not seriously affect our discussion, and therefore we adopted the assumption of the uniform $T_{\rm ex}$ in this study."529 We discuss the physical properties of the cores on the basis of comparison with, We discuss the physical properties of the cores on the basis of comparison with530"we can model the secular evolution at this location (Fig. 11,","we can model the secular evolution at this location (Fig. \ref{fig:dampmig},"531 top two rows)., top two rows).532" When this ratio is small (“fast” migration), Neptune effectively damps at its final position and we can model the secular evolution there (Fig. 11,,"," When this ratio is small (“fast"" migration), Neptune effectively damps at its final position and we can model the secular evolution there (Fig. \ref{fig:dampmig},"533 bottom two rows)., bottom two rows).534" When the ratio is order unity modeling the secular evolution at the location Neptune reaches after half a damping time is a decent approximation (Fig. 11,,"," When the ratio is order unity, modeling the secular evolution at the location Neptune reaches after half a damping time is a decent approximation (Fig. \ref{fig:dampmig},"535 middle row)., middle row).536" However, we have not explored the regime in which ΤαΤε Or Τα~Τι in detail."," However, we have not explored the regime in which $\tau_a \sim \tau_e$ or $\tau_a \sim \tau_i$ in detail."537" Typically, we expect the damping and migration to occur in either the fast or slow regime, for reasons we will now state."," Typically, we expect the damping and migration to occur in either the fast or slow regime, for reasons we will now state."538 The models in which Neptune is scattered from its location of formation to close to its current location (e.g.?) can be considered fast migration., The models in which Neptune is scattered from its location of formation to close to its current location \citep[e.g.][]{2008L} can be considered fast migration.539" For extensive migration in a planetesimal disk, we expect the migration timescale to be significantly longer than the"," For extensive migration in a planetesimal disk, we expect the migration timescale to be significantly longer than the"540These seven facts can be used to consider the time evolution in the twisted geometry of KDJ that results in the type I field line topology in Figure 1.,These seven facts can be used to consider the time evolution in the twisted geometry of KDJ that results in the type I field line topology in Figure 1.541 Figure 2 simulates the most plausible scenario based on these seven results above which is used as a surrogate for actual fine time scale data sampling., Figure 2 simulates the most plausible scenario based on these seven results above which is used as a surrogate for actual fine time scale data sampling.542 The left hand frame shows a typical twisted accretion disk coil in white being approached by a coronal hairpin in red near the black hole., The left hand frame shows a typical twisted accretion disk coil in white being approached by a coronal hairpin in red near the black hole.543 Notice that the coronal hairpin is azimuthally twisted in KDJ., Notice that the coronal hairpin is azimuthally twisted in KDJ.544 Reconnection is very complicated in a twisted 3-D environment and is not well understood (Pontinetal2011)., Reconnection is very complicated in a twisted 3-D environment and is not well understood \citep{pon11}.545". However, the configuration as drawn forms a natural reconnection site (an X-point)."," However, the configuration as drawn forms a natural reconnection site (an X-point)."546" We expect both types of field lines in Figure 2 to exist from points 1, 4 and 5 above."," We expect both types of field lines in Figure 2 to exist from points 1, 4 and 5 above."547" The elements required for the pre-reconnection geometry in the left hand frame of Figure 2, commonly occur in this family of simulations."," The elements required for the pre-reconnection geometry in the left hand frame of Figure 2, commonly occur in this family of simulations."548" Thus, it is reasonable to expect that these field configurations coexist in proximity at various times and these potential reconnection sites should not be rare."," Thus, it is reasonable to expect that these field configurations coexist in proximity at various times and these potential reconnection sites should not be rare."549" However, the reconnection rate in such a complicated geometry that does not proceed by a physical mechanism, but through numerical diffusion, is very uncertain."," However, the reconnection rate in such a complicated geometry that does not proceed by a physical mechanism, but through numerical diffusion, is very uncertain."550" By points 2, 3 and 6 above, reconnection must have occurred in KDJ as depicted in the right hand frame of Figure 2."," By points 2, 3 and 6 above, reconnection must have occurred in KDJ as depicted in the right hand frame of Figure 2."551 The white curve in the right hand frame is poloidal flux through the equatorial plane of the ergosphere in one hemisphere in analogy to the left hand frame of Figure 1 and the red curve would be a buoyant hairpin field line that moves out in the corona consistent with point 7., The white curve in the right hand frame is poloidal flux through the equatorial plane of the ergosphere in one hemisphere in analogy to the left hand frame of Figure 1 and the red curve would be a buoyant hairpin field line that moves out in the corona consistent with point 7.552" A significant difference between the topology resulting from the reconnection in Figure 2 compared to that in Figure 11 of Beckwithetal(2009),, is that in Figure 2 the reconnection is happening before the hairpin penetrates the event horizon and in Figure 11 of Beckwithetal(2009) it occurs after the hairpin penetrates the horizon."," A significant difference between the topology resulting from the reconnection in Figure 2 compared to that in Figure 11 of \citet{bec09}, is that in Figure 2 the reconnection is happening before the hairpin penetrates the event horizon and in Figure 11 of \citet{bec09} it occurs after the hairpin penetrates the horizon."553 This indicates that the coherent flux transport rate combined with the reconnection rate and twisted 3-D field line geometry (which affects the reconnection rate) might determine if a field line penetrates the event horizon or the inner accretion flow when and if reconnection occurs., This indicates that the coherent flux transport rate combined with the reconnection rate and twisted 3-D field line geometry (which affects the reconnection rate) might determine if a field line penetrates the event horizon or the inner accretion flow when and if reconnection occurs.554 The final field line topology depends on the balancing of reaction rates (reconnection and transport) as well as internal dynamics (that affect field line shape) that are determined by the numerical simulation., The final field line topology depends on the balancing of reaction rates (reconnection and transport) as well as internal dynamics (that affect field line shape) that are determined by the numerical simulation.555" The Letter shows that the ""coronal mechanism” for flux transport in simulations of black hole accretion provides a plausible explanation for the one sided ergospheric disk field lines in the high spin 3-D simulation KDJ."," The Letter shows that the ""coronal mechanism"" for flux transport in simulations of black hole accretion provides a plausible explanation for the one sided ergospheric disk field lines in the high spin 3-D simulation KDJ."556" It therefore explains the strange phenomenon observed in KDJ that the black hole driven jet Poynting flux was very one sided, jumping from side to side and emanating primarily from the ergospheric disk."," It therefore explains the strange phenomenon observed in KDJ that the black hole driven jet Poynting flux was very one sided, jumping from side to side and emanating primarily from the ergospheric disk."557" An otherwise almost identical simulation to KDJ that includes additional artificial diffusion terms in the equations of continuity, energy conservation, and momentum conservation (as described in DeVilliers (2006))) do not show these one sided ergospheric disk structures Punsly(2011)."," An otherwise almost identical simulation to KDJ that includes additional artificial diffusion terms in the equations of continuity, energy conservation, and momentum conservation (as described in \citet{dev07}) ) do not show these one sided ergospheric disk structures \citet{pun11}."558. This is seems to indicate a change in the the reconnection process that is driven either directly or indirectly by the numerical diffusion., This is seems to indicate a change in the the reconnection process that is driven either directly or indirectly by the numerical diffusion.559" In support of this interpretation, the force-free simulations of an initially uniform field in Komissarov(2004) show magnetic flux threading the ergospheric equatorial plane near the black hole, yet the same initial state that is time evolved in a different force-free code with a slower ansatz for the reconnection rate shows no magnetic flux threading the equatorial plane near the black hole (McKinney2006a).."," In support of this interpretation, the force-free simulations of an initially uniform field in \citet{kom04} show magnetic flux threading the ergospheric equatorial plane near the black hole, yet the same initial state that is time evolved in a different force-free code with a slower ansatz for the reconnection rate shows no magnetic flux threading the equatorial plane near the black hole \citep{mck05}."560 The implication is that the global topology of the black hole, The implication is that the global topology of the black hole561a given X-ray spectral index. the Compton parameter. v=47.7. is approximately constant.,"a given X-ray spectral index, the Compton parameter, $y=4 T_{\rm e}\tau_{\rm T}$, is approximately constant."562 Also. A7. is anticorrelated with τι for a given local dissipation rate in a hot flow. reflecting the varying power per electron.," Also, $kT_{\rm e}$ is anticorrelated with $\tau_{\rm T}$ for a given local dissipation rate in a hot flow, reflecting the varying power per electron."563" Fits of the one-zone thermal-Compton model yield ry~| (e.g. Yuan Zdziarski 2004) whereas the vertical optical depths of the flow are ry«I. see reffig:OSedd((b). which expresses the same discrepancy as 7, of the flow being too high."," Fits of the one-zone thermal-Compton model yield $\tau_{\rm T}\sim 1$ (e.g., Yuan Zdziarski 2004) whereas the vertical optical depths of the flow are $\tau_{\rm T}\ll 1$, see \\ref{fig:05edd}( (b), which expresses the same discrepancy as $T_{\rm e}$ of the flow being too high."564 As stated above. taking into account the GR effects in the global-Compton model improves the agreement significantly (pointing to the inadequacy of Comptonization models neglecting GR). but not sutficientlv.," As stated above, taking into account the GR effects in the global-Compton model improves the agreement significantly (pointing to the inadequacy of Comptonization models neglecting GR), but not sufficiently."565 On the face of it. this discrepancy might indicate that the hot flow model is not applicable to the hard state of black hole binaries and Seyfert galaxies.," On the face of it, this discrepancy might indicate that the hot flow model is not applicable to the hard state of black hole binaries and Seyfert galaxies."566 However. we note that the present calculations assume a very strong outflow. equation (3)) with s= 0.3. motivated by the modelling of the Galactic Centre. (Yuan et 22003).," However, we note that the present calculations assume a very strong outflow, equation \ref{eq:outflow}) ) with $s=0.3$ , motivated by the modelling of the Galactic Centre (Yuan et 2003)."567 On the other hand. our assumed. dimensionless accretion rate is >> that of the Galactic Centre source. whereas the relative strength of outflows appears to decrease with the increasing accretion rate (Gallo. Fender Pooley 2003: Fender. Belloni Gallo 2004). as also indicated by a relatively small change of the X-ray bolometric luminosity during hard/soft state transitions (e.g Zadziarski et 22004).," On the other hand, our assumed dimensionless accretion rate is $\gg$ that of the Galactic Centre source, whereas the relative strength of outflows appears to decrease with the increasing accretion rate (Gallo, Fender Pooley 2003; Fender, Belloni Gallo 2004), as also indicated by a relatively small change of the X-ray bolometric luminosity during hard/soft state transitions (e.g., Zdziarski et 2004)."568" This is plausible from a theoretical point of view because the Bernoulli parameter becomes smaller with the increasing accretion rates (Yuan, Cui Narayan 2005: Bu Yuan in preparation)."," This is plausible from a theoretical point of view because the Bernoulli parameter becomes smaller with the increasing accretion rates (Yuan, Cui Narayan 2005; Bu Yuan in preparation)."569 Thus. it is likely that the fractional strength of the outflow. 82 per cent for our assumed s. οι and Mo (with 18 per cent of My crossing the horizon). may in reality be much weaker.," Thus, it is likely that the fractional strength of the outflow, 82 per cent for our assumed $s$, $R_{\rm out}$ and $\dot M_0$ (with 18 per cent of $\dot M_0$ crossing the horizon), may in reality be much weaker."570 Setting s=0 leads to τι being a few times higher and 7. about a factor of two lower. see reftig:outflow..," Setting $s=0$ leads to $\tau_{\rm T}$ being a few times higher and $T_{\rm e}$ about a factor of two lower, see \\ref{fig:outflow}."571 Although the calculations in reffigcoutflow are done with the local analytical treatment of Comptonization. and are thus not self-consistent. they correctly predict the direction of the changes of the flow parameter.," Although the calculations in \\ref{fig:outflow} are done with the local analytical treatment of Comptonization, and are thus not self-consistent, they correctly predict the direction of the changes of the flow parameter."572" If the characteristic 7, of the self-consistent flow were reduced by the same factor of two with respect the model with s=0.3. the peak of the EdL/dE spectrum would also go down by a similar factor. bringing it to the observed range and resolving the discrepancy with the data."," If the characteristic $T_{\rm e}$ of the self-consistent flow were reduced by the same factor of two with respect the model with $s=0.3$, the peak of the $E {\rm d}L/{\rm d}E$ spectrum would also go down by a similar factor, bringing it to the observed range and resolving the discrepancy with the data."573 Our second assumption has been of a strong viscous heating of electrons. 6=0.5.," Our second assumption has been of a strong viscous heating of electrons, $\delta=0.5$."574 As seen in reftig:outflow.. this has a relatively minor effect on 7. and τι.," As seen in \\ref{fig:outflow}, this has a relatively minor effect on $T_{\rm e}$ and $\tau_{\rm T}$."575 We ulso note that the half-depth Thomson optical depth of a slab is the quantity closest to that of the half-depth of the flow. and should preferably be used when comparing accretion flow models with one-zone thermal Comptonization models.," We also note that the half-depth Thomson optical depth of a slab is the quantity closest to that of the half-depth of the flow, and should preferably be used when comparing accretion flow models with one-zone thermal Comptonization models."576 For a given. spectral index. the optical depth is somewhat lower for a slab geometry than for spherical one.," For a given X-ray spectral index, the optical depth is somewhat lower for a slab geometry than for spherical one."577 We note that there is à number of additional effects that can further reduce 7. and increase r4. possibly allowing the hot flow model to be in agreement with the full range of the observed hard- spectra.," We note that there is a number of additional effects that can further reduce $T_{\rm e}$ and increase $\tau_{\rm T}$, possibly allowing the hot flow model to be in agreement with the full range of the observed hard-state spectra."578 First. an increase of the black-hole spin reduces the radial velocity and increases the density of the flow.," First, an increase of the black-hole spin reduces the radial velocity and increases the density of the flow."579 The effect is rather strong. as can be seen. e.g.. in 55 of Gammie Popham (1998).," The effect is rather strong, as can be seen, e.g., in 5 of Gammie Popham (1998)."580 Global Comptonization in the Kerr metric will be studied in detail in our forthcoming work., Global Comptonization in the Kerr metric will be studied in detail in our forthcoming work.581 Second. the presence of moderate large-scale toroidal magnetic fields in the accretion flow significantly reduces 7... as shown by Bu. Yuan Xie (2009).," Second, the presence of moderate large-scale toroidal magnetic fields in the accretion flow significantly reduces $T_{\rm e}$, as shown by Bu, Yuan Xie (2009)."582" Third. electron cooling will also be significantly enhanced in either a two-phase flow. with cold clouds mixed with the hot flow. or. fourth. at presence of an inner collapsed dise. with both effects wppening above some critical accretion rate (Section ὃς, see also YOI. Yuan 2003)."," Third, electron cooling will also be significantly enhanced in either a two-phase flow, with cold clouds mixed with the hot flow, or, fourth, at presence of an inner collapsed disc, with both effects happening above some critical accretion rate (Section \ref{results}, see also Y01, Yuan 2003)."583 Furthermore. the cut-off energy in the hard state of black- binaries is observed to decrease with the increasing luminosity (Wardzinsski et 22002: Yamaoka et 22006: Yuan et 22007: Miyakawa et22008)!.," Furthermore, the cut-off energy in the hard state of black-hole binaries is observed to decrease with the increasing luminosity (Wardzińsski et 2002; Yamaoka et 2006; Yuan et 2007; Miyakawa et."584. Also. the hot-flow characteristic emperature goes down with the increasing accretion rate. in agreement with the observations.," Also, the hot-flow characteristic temperature goes down with the increasing accretion rate, in agreement with the observations."585" In our case. the bolometric uminosity is only 0.0077, (Section 59). and. thus our model spectrum should. be compared with the hard state at the correspondingly low £ (which is somewhat below. e.g.. the state range of L of Cyg X-I of =0.01-0.02£,.. Zdziarski et 22002). which spectra are likely to have the cut-off energies 100 keV. This would be in agreement with our results. after the correction for the outflow discussed above."," In our case, the bolometric luminosity is only $0.007 L_{\rm E}$ (Section \ref{results}) ), and thus our model spectrum should be compared with the hard state at the correspondingly low $L$ (which is somewhat below, e.g., the hard-state range of $L$ of Cyg X-1 of $\simeq 0.01$ $0.02L_{\rm E}$, Zdziarski et 2002), which spectra are likely to have the cut-off energies $>100$ keV. This would be in agreement with our results, after the correction for the outflow discussed above."586 Malzae Belmont (2009) have also pointed out that the ion temperatures implied by observations of the hard state are much lower than those typical for ADAF models., Malzac Belmont (2009) have also pointed out that the ion temperatures implied by observations of the hard state are much lower than those typical for ADAF models.587 However. the ratio of Ti/T.. calculated by Malzac Belmont (2009) directly from the formula for Coulomb energy transfer from ions to electrons. is approximately οτp and the discrepancy pointed out by those authors occurs at Tp.|.," However, the ratio of $T_{\rm i}/T_{\rm e}$, calculated by Malzac Belmont (2009) directly from the formula for Coulomb energy transfer from ions to electrons, is approximately $\propto \tau_{\rm T}^{-2}$, and the discrepancy pointed out by those authors occurs at $\tau_{\rm T}\sim 1$."588 Tf we take instead the low values of τι obtained in ADAF models. there is an agreement between their estimate and the hot flow models.," If we take instead the low values of $\tau_{\rm T}$ obtained in ADAF models, there is an agreement between their estimate and the hot flow models."589 On the other hand. we stress that using equation (3)) with does not weaken our conclusions related to the role of globa Comptonization.," On the other hand, we stress that using equation \ref{eq:outflow}) ) with $s=0.3$ does not weaken our conclusions related to the role of global Comptonization."590 Instead. if the outflow is weaker for à given M. the radiation generated at small radii and subsequently received a large radii will be stronger. thus the global Comptonization effec will become even more important than for our chosen assumption.," Instead, if the outflow is weaker for a given $\dot M_0$, the radiation generated at small radii and subsequently received at large radii will be stronger, thus the global Comptonization effect will become even more important than for our chosen assumption."591" This would further reduce the average photon energy of the emitted spectrum,", This would further reduce the average photon energy of the emitted spectrum.592 Another related issue is our determination of the value of the critical aceretion rate. at which an inner part of the hot flow collapses.," Another related issue is our determination of the value of the critical accretion rate, at which an inner part of the hot flow collapses."593 We tind it corresponds to a relatively low £L=0.011.," We find it corresponds to a relatively low $L\simeq5940.01\ledd$."595 Luminosities of the hard state of black-hole binaries are commonly above this £L (e.g. Done et 22007: Zdziarski et 22002).," Luminosities of the hard state of black-hole binaries are commonly above this $L$ (e.g, Done et 2007; Zdziarski et 2002)."596 Again. our determination is for the assumed strong outflow. and relaxing this assumption may increase that critical luminosity.," Again, our determination is for the assumed strong outflow, and relaxing this assumption may increase that critical luminosity."597 On the other hand. the presence of a collapsed geometrically thin dise close to the horizon would explain the tinding of relativistically broaden Fe Κα line in the hard state of black-hole binaries (e.g.. Miller et 22006: Miller 2007: but see Done Diaz Trigo 2009 for a critical view). whose origin would have otherwise been in conflict with the hot accretion flow model of the hard state.," On the other hand, the presence of a collapsed geometrically thin disc close to the horizon would explain the finding of relativistically broaden Fe $\alpha$ line in the hard state of black-hole binaries (e.g., Miller et 2006; Miller 2007; but see Done Diaz Trigo 2009 for a critical view), whose origin would have otherwise been in conflict with the hot accretion flow model of the hard state."598 Finally. we note that alternative models for the hard state have been proposed.," Finally, we note that alternative models for the hard state have been proposed."599" A very interesting recent model is non-thermal. in which the power supplied to electrons (with the optical depth of T,7 1) goes into their acceleration into a power-law distribution (Poutanen Vurm 2009: Malzac Belmont 2009)."," A very interesting recent model is non-thermal, in which the power supplied to electrons (with the optical depth of $\tau_{\rm T}\ga 1$ ) goes into their acceleration into a power-law distribution (Poutanen Vurm 2009; Malzac Belmont 2009)."600 Then. synchrotron self-absorption and Coulomb interactions efficiently thermalize the electrons provided any blackbody emission 1s weak.," Then, synchrotron self-absorption and Coulomb interactions efficiently thermalize the electrons provided any blackbody emission is weak."601 This radiative one-zone model fits the hard-state data. e.g. of Cyg X-l. very well.," This radiative one-zone model fits the hard-state data, e.g., of Cyg X-1, very well."602 An important issue here is the location of the non- plasma., An important issue here is the location of the non-thermal plasma.603 It cannot be a corona as the model constrains any dise blackbody emission irradiating the plasma to be very weak., It cannot be a corona as the model constrains any disc blackbody emission irradiating the plasma to be very weak.604 If, If605we require a shapelet model of the relevant. kernel.,we require a shapelet model of the relevant kernel.606 1n the radio image the restoring beam is exactly known. so the deconvolution process is relatively straightforward.," In the radio image the restoring beam is exactly known, so the deconvolution process is relatively straightforward."607 As mentioned above. the restoring beam is a 0.4 arcsec circular Gaussian.," As mentioned above, the restoring beam is a 0.4 arcsec circular Gaussian."608 Massey&Relreeicr(2005). describe the ensuing deconvolution step in detail: briellv.. the shapelets: are convolved with the PSE model. and the resulting Functions are least-squares fit to the data.," \citet{2005MNRAS.363..197M} describe the ensuing deconvolution step in detail; briefly, the shapelets are convolved with the PSF model, and the resulting functions are least-squares fit to the data."609 The coellicients of the fit correspond to the deconvolvect model., The coefficients of the fit correspond to the deconvolved model.610 To estimate the ACS PSE. we also use SlExtractor to create a catalogue of stars using the SExtractor star/galaxy classifier index (see Bertin&Arnouts(1996). for details).," To estimate the ACS PSF, we also use SExtractor to create a catalogue of stars using the SExtractor star/galaxy classifier index (see \citet{1996A&AS..117..393B} for details)."611 We decompose cach stellar image into shapelet coefficients: for each shapelet mode. the mean cocllicient is used for the PSE model.," We decompose each stellar image into shapelet coefficients; for each shapelet mode, the mean coefficient is used for the PSF model."612 Again. the methodology of Massey(2005) is used to deconvolve all galaxy images.," Again, the methodology of \citet{2005MNRAS.363..197M} is used to deconvolve all galaxy images."613 3efore arriving at a final shear catalogue. various necessary cuts were applicd to the datasets.," Before arriving at a final shear catalogue, various necessary cuts were applied to the datasets."614 Galaxies with failures in the shapelet modelling. due to poor 7 fits. have been removed.," Galaxies with failures in the shapelet modelling, due to poor $\chi^2$ fits, have been removed."615 In the radio case we also removed all objects that were not resolved. ic. ΕΛΛΗΝΙΚΟ0.4. and. also applied. a Hux cut of Sy254yrJy to remove low level noise peaks.," In the radio case we also removed all objects that were not resolved, i.e. $<0.4''$, and also applied a flux cut of $S_{1.4}>54\mu\mbox{Jy}$ to remove low level noise peaks."616 In the optical case we applied a magnitude cut of m.<25 in order to only work with objects with S/N6: this cut also removed all unresolved objects., In the optical case we applied a magnitude cut of $m_{z}<25$ in order to only work with objects with $>6$; this cut also removed all unresolved objects.617 We now nee to combine the shapelet coefficients of each object to estimate the weak shear they have experienced., We now need to combine the shapelet coefficients of each object to estimate the weak shear they have experienced.618We use the simple Gaussian-weightecd shear estimator given by Masseyctal.(2007). Noteote that tlthe averageσ on the ddenominator[ is taktaken over the objects once the cuts described above have been mace.,"We use the simple Gaussian-weighted shear estimator given by \citet{2007MNRAS.380..229M}, Note that the average on the denominator is taken over the objects once the cuts described above have been made."619 La this fashion we calculate a two-component shear estimator for each useable galaxy in the survey., In this fashion we calculate a two-component shear estimator for each useable galaxy in the survey.620 We are now ready to examine the properties of weak lensing in the radio at current Dux limits., We are now ready to examine the properties of weak lensing in the radio at current flux limits.621 1n our final shear catalogue constructed as described above. we obtain number densities of 7=0.75aremin for the eold radio dataset. 7=3.76aremin for the silver racio dataset. and n=40.66arcmin7 for the optical data.," In our final shear catalogue constructed as described above, we obtain number densities of $n=0.75\mbox{ arcmin}^{-2}$ for the gold radio dataset, $n=3.76 \mbox{ arcmin}^{-2}$ for the silver radio dataset, and $n=40.66\mbox{ arcmin}^{-2}$ for the optical data."622 lt can immediately be seen that currently. racio number densities are substantially lower than those available at optical wavelengths.," It can immediately be seen that currently, radio number densities are substantially lower than those available at optical wavelengths."623 Llowever. it should also be noted how much » has increased in relation to Changetal.(2004).. where there were only &20 objects per square degree.," However, it should also be noted how much $n$ has increased in relation to \citet{2004ApJ...617..794C}, where there were only $\simeq20$ objects per square degree."624 With the imminent arrival of e-\LERLIN and LOLFAR. racio number densities will begin to compare well with optical number densities: this is crucial for weak lensing 2-point statistics. where the noise is inversely proportional to the number clonsity.," With the imminent arrival of -MERLIN and LOFAR, radio number densities will begin to compare well with optical number densities; this is crucial for weak lensing 2-point statistics, where the noise is inversely proportional to the number density."625" In addition. the noise on weak lensingin] 2-point statistics is proportional to the shear estimator variance. στ, so this is"," In addition, the noise on weak lensing 2-point statistics is proportional to the shear estimator variance, $\sigma_\gamma^2$ , so this is"626width of the last scattering laver aud the distortion of the CAIB spect.,width of the last scattering layer and the distortion of the CMB spectrum.627 Though the amount of the residual ionization is uportaut for the further evolution of the Universe (Peebles 1995. Lepp Shull 1981). it cai not be measured directly.," Though the amount of the residual ionization is important for the further evolution of the Universe (Peebles 1993, Lepp Shull 1984), it can not be measured directly."628 A possible observable consequence of the hydrogen recombination m the carly Universe is the distortion of the mucrowave backerotnd radiaion spectrüun., A possible observable consequence of the hydrogen recombination in the early Universe is the distortion of the microwave background radiation spectrum.629 [t was first calculated for the flat cosmological model by Peebles (196i., It was first calculated for the flat cosmological model by Peebles (1968).630 In this work we concentrate on the deernünnuation o[o this: distortiou for different cosmological models., In this work we concentrate on the determination of this distortion for different cosmological models.631 Recently there Las been a considerable observational aud theoretical activity to determine the spectrau of the COSuic backeround radiatiojio and carving out ealaxy counts in the far infrared‘submillimeter range (Puget et al., Recently there has been a considerable observational and theoretical activity to determine the spectrum of the cosmic background radiation and carrying out galaxy counts in the far infrared/submillimeter range (Puget et al.632 1996. Schlegel et al.," 1996, Schlegel et al."633 1997. Ctuxeroni et al.," 1997, Guideroni et al."634 1997)., 1997).635 Bocase the wdrogen recolubiration chawes the CBAL specruni in he same spectral rauge a detailed exact recalculation of the frequency distribujon of the recoubiation phoous Is Muportait., Because the hydrogen recombination changes the CBM spectrum in the same spectral range a detailed exact recalculation of the frequency distribution of the recombination photons is important.636 In this paper we calculate he recombination CYOSS SOClonis exaclv bv using a coitinnous. plysical cut off for tie hiehlv excited states o| hydrogen. tzse into account he induced recombination ale explain. why the tine¢epeudenuce of the recoubination process 1s 80 haradly effected x different techlues aux by different effective uzatio) curves.," In this paper we calculate the recombination cross sections exactly by using a continuous, physical cut off for the highly excited states of hydrogen, take into account the induced recombination and explain, why the time dependence of the recombination process is so hardly effected by different techniques and by different effective ionization curves."637 The outliue of the paper ds as follows., The outline of the paper is as follows.638 In 82 we cisctss the recolubinaion process and ¢erive the τοςΟΙüuatiou equation., In 2 we discuss the recombination process and derive the recombination equation.639 We eive a new paranuetrization of the effective recolubinalon coefficients. taking iuto account the induced recolbination as well.," We give a new parametrization of the effective recombination coefficients, taking into account the induced recombination as well."640 Iu the third section we solve the recolbination equation., In the third section we solve the recombination equation.641 The spectrum) of the recombination photons aud its dependence on the cosmological parameters is even πι the fourth8. and in the fifth closing section we discuss our results.," The spectrum of the recombination photons and its dependence on the cosmological parameters is given in the fourth, and in the fifth closing section we discuss our results."642 The umber of recombinations in unit tie can be calculated from the recombination equation as a functiou of the density of free electrous Εν teuuperature T. aud cosinological. and atomic coustants.," The number of recombinations in unit time can be calculated from the recombination equation as a function of the density of free electrons $n_e\,$, temperature $T\,$, and cosmological, and atomic constants."643 Iu this section we derive this equation following Peebles (1965)., In this section we derive this equation following Peebles (1968).644 At the beeinnine of the Lwdrogen recombination the helium is already: completely recombined., At the beginning of the hydrogen recombination the helium is already completely recombined.645 The mass fraction of the helium is 25 of he total baryonic mass., The mass fraction of the helium is 25 of the total baryonic mass.646 As was remarked by Novikov aud Ze‘dovich (1967) the direct recombinations to the eround state are inhibited. while the new born enerectic phoons ionize again almost nunediatelv when there are alreacv sone hydrogen atoms.," As was remarked by Novikov and Zel'dovich (1967) the direct recombinations to the ground state are inhibited, while the new born energetic photons ionize again almost immediately when there are already some hydrogen atoms."647 In the following we neglect coupletelv the direct recombinations to the ground sta5, In the following we neglect completely the direct recombinations to the ground state.648" The states with principal quautuu number n2 plav a kev role in the recombination Xrocesses,"," The states with principal quantum number $n = 2 \,$ play a key role in the recombination processes."649 First we calculate the raeof recombinations tov 2 for given free electron umber deusitv ο. temperature T aud ος.," First we calculate the rate of recombinations to $ n \geq 2\,$ for given free electron number density $n_e$, temperature T and $n_{2s}$."650 Tere Dar 19 the cleIs]vof atoms in the state with the principal quant number 3) ancl aueular moment quanti munber /., Here $n_{nl}$ is the density of atoms in the state with the principal quantum number $n$ and angular momentum quantum number $l$.651" Second. we determine thenet umuber of 5>1 transitions in unit tine bv given no, and1e"," Second, we determine thenet number of $2 \rightarrow 1$ transitions in unit time by given $n_{2s} $ and$n_{1s}$."652 The two rates nmt be equal. so we can eliminate 1o. from the calculations.," The two rates must be equal, so we can eliminate $n_{2s}$ from the calculations."653 The loincΠιο cherey of the η=2 state is By=Byflw=X1ceV.," The binding energy of the $n = 2 \,$ state is $_2 = {\rm B}_1/4 \approx 6543.4\, eV$ ."655 During the recombination process there are a large nuniber of photons with euergv less than D». therefore the excited states of the hivdrogeu atomis are in thermodynamical equilibrium above the second level. ic. Iu the case of gaseous uebulae the mean free path of low energetic photons is larger than the cdimensious of the ionized region. the svsteu is far from being in equilibrium above the η=2 level in contrast to the recombining Universe.," During the recombination process there are a large number of photons with energy less than $B_{2}$, therefore the excited states of the hydrogen atoms are in thermodynamical equilibrium above the second level, i.e. In the case of gaseous nebulae the mean free path of low energetic photons is larger than the dimensions of the ionized region, the system is far from being in equilibrium above the $ n = 2\,$ level in contrast to the recombining Universe."656" The partiion. stun $5,,7,|4Lip(Boltzmann 1s divereeut."," The partition sum $\sum_{nl} (2 l + 1) n_{nl}^{({\rm Boltzmann})} \,$ is divergent."657 As analysed w Πιο aud \Ghalas (1988) à uber of effects μπιτ the rauge of sununation., As analysed by Hummer and Mihalas (1988) a number of effects limit the range of summation.658 In the considered telpcrature and deusitv range the action of free protous turus out to be the most important. the action of neutral atoms are nch sinaller.," In the considered temperature and density range the action of free protons turns out to be the most important, the action of neutral atoms are much smaller."659" The free protons «estrov the state n witha proability 1w,, where w,,=exp|{mylis2}|t with wv.=1075.9πο.15 (i, oerem ο)."," The free protons destroy the state $n\,$ with a probability $ 1 - w_n\,$, where $w_n = \exp[\,-({n \over n_*})^{15/2}\,]\,$, with $n_* = 1075.9 \,{\rm cm}^{-2/5}\, n^{-2/15}_e\,$ $_e$ in $^{-3}$ )."660" This means that the recombined electrons become uubouud with 1te, probability. before they would beein to move towards the state. corresponding to tfrerimal equilibria."," This means that the recombined electrons become unbound with $1- w_n$ probability, before they would begin to move towards the state, corresponding to thermal equilibrium."661 The highly excited (7 larger than ~ ni) states are practically completely destroved., The highly excited $n$ larger than $\sim n_*$ ) states are practically completely destroyed.662 The occuation nmuubers of the excited states in thermal equilibrium are: Owing to lis fact. the uuuber of electrons in bouud states is finite. axd thermia equilibrium between the »z2 bound states aud the contiuuua is possible.," The occupation numbers of the excited states in thermal equilibrium are: Owing to this fact, the number of electrons in bound states is finite, and thermal equilibrium between the $n \geq 2$ bound states and the continuum is possible."663 This approximation is good down to z z 300.," This approximation is good down to z $\approx \,$ 300."664 The »=2 levels freeze out between fre redshifts 300 aud 250.," The $n = 2 \,$ levels freeze out between the redshifts 300 and 250."665 The ground state of the lydrogen atom ds about 10.2 eV deeper thai the»)=2 level., The ground state of the hydrogen atom is about 10.2 eV deeper than the $n = 2$ level.666" Cousequeutly. it’s occupatio ids ereater than the occupation of the excited states together:[ mi,29awitoHg."," Consequently, it's occupation is greater than the occupation of the excited states together: $ n_{1s} \gg \sum_{n \geq 2} n_n$."667 This meaus. that the density o: free. electrons plus the density of lydrogen atonis in ground state can be taken as equal to the total proton umber sa.|ys p.," This means, that the density of free electrons plus the density of hydrogen atoms in ground state can be taken as equal to the total proton number : $ n_e + n_{1s} = p\,$ ."668 The totalbarvon number (determined by 05) is the sum of p aud the nuuuber of barvous iu the hela nuclei., The totalbaryon number (determined by $\Omega_b$ ) is the sum of p and the number of baryons in the helium nuclei.669of this part of work we really look for severe. departure from nonnormality and keep our discussion brief.,of this part of work we really look for severe departure from non–normality and keep our discussion brief.670 The assembly maps appear to have slightly more than expected points beyond the confidence region., The assembly maps appear to have slightly more than expected points beyond the confidence region.671 Moreover. the two noncosmological [requeney maps show clear signs of normality.," Moreover, the two non–cosmological frequency maps show clear signs of non--normality."672 The two CALBonly maps also show signs of nonnormalitv- the POLL map result appearing to have departed furthest [rom normality., The two CMB–only maps also show signs of non--normality- the TOH map result appearing to have departed furthest from normality.673 Our bivariate analysis results are shown in Figures 9--14.., Our bivariate analysis results are shown in Figures \ref{fig:multi_skew1}- \ref{fig:multi_trans2}.674 The bivariate skewness statistics (0615/6) calculated. from he 16 maps are shown in Figures 9 ane 10.., The bivariate skewness statistics $nb_{12}/6$ ) calculated from the 16 maps are shown in Figures \ref{fig:multi_skew1} and \ref{fig:multi_skew2}.675 The statistic appears to be abnormal for three of the assembly. maps- (QI. M2 and WM 4.," The statistic appears to be abnormal for three of the assembly maps- $Q$ 1, $W$ 2 and $W$ 4."676 Some of the other assembly maps have wo or three points outside the confidence region but visually the results do not look too unusual., Some of the other assembly maps have two or three points outside the confidence region but visually the results do not look too unusual.677 Once again. the wo noncosmological frequencies have results that strongly indicate nonnormality.," Once again, the two non–cosmological frequencies have results that strongly indicate non–normality."678 Phis non.normality is still evident inthe Q and V band., This non–normality is still evident in the $Q$ and $V$ band.679 The two CALB maps also have a higher han expected number of points above the confidence region., The two CMB maps also have a higher than expected number of points above the confidence region.680 It. would appear that the bivariate skewness results ΠΟ their univariate counterparts., It would appear that the bivariate skewness results mimic their univariate counterparts.681 The bivariate kurtosis results are cisplaved in Figures 1l and 12.., The bivariate kurtosis results are displayed in Figures \ref{fig:multi_kurtosis1} and \ref{fig:multi_kurtosis2}.682 2s with the skewness results. bivariate kurtosis seem similar to their univariate equivalent.," As with the skewness results, bivariate kurtosis seem similar to their univariate equivalent."683 Nevertheless. in the case of the assembly maps. the shift. away from the expected value is even greater than for the univariate results.," Nevertheless, in the case of the assembly maps, the shift away from the expected value is even greater than for the univariate results."684 As before. the Galactic frequency maps are clearly found to be nonnormal.," As before, the Galactic frequency maps are clearly found to be non–normal."685 The higher value than expected. value of the bivariate kurtosis persists in the foreground:cleaned CMD maps The bivariate power transformation is shown in Figures 13. and l14.., The higher value than expected value of the bivariate kurtosis persists in the foreground–cleaned CMB maps The bivariate power transformation is shown in Figures \ref{fig:multi_trans1} and \ref{fig:multi_trans2}.686 The assembly results do not look entirely consistent with being drawn [rom a X3 distribution., The assembly results do not look entirely consistent with being drawn from a $\chi^2_2$ distribution.687 Five of the assembly maps produce. results with 5 or more points outside the confidence region., Five of the assembly maps produce results with 5 or more points outside the confidence region.688 Saving that. our Gaussian MC map has four points outside this region. which makes it hard to draw definite conclusions.," Saying that, our Gaussian MC map has four points outside this region, which makes it hard to draw definite conclusions."689 This is certainly. not true for the two Galactic frequency bands that are clearly inconsistent. with normality., This is certainly not true for the two Galactic frequency bands that are clearly inconsistent with normality.690 The two CAIBonly maps also appear to have an extremely high number. of volnts bevond the confidence region., The two CMB–only maps also appear to have an extremely high number of points beyond the confidence region.691o Lastly. in this subsection. we assess the linearity of the data.," Lastly, in this subsection, we assess the linearity of the data."692 We tried. adding separately three nonlinear terms to our linear model of the data (as described in 5))., We tried adding separately three non–linear terms to our linear model of the data (as described in \ref{sec:implementation}) ).693 However. all," However, all"694satisfies equation (16)) with €z0.911.,satisfies equation \ref{pwnexp}) ) with $\bar C\simeq 0.911$.695 This derivation based on (vai) pressure balance at the immer aud outer edees of the pulsar wind nebula coufiiiis our earlier result obtained from overall energy. couservation., This derivation based on (ram) pressure balance at the inner and outer edges of the pulsar wind nebula confirms our earlier result obtained from overall energy conservation.696 The conustaut wind Lhuuinositv assuniptfion is nof very realistic bv the time the effects of the reverse shock iud its associated reverberations have vanished., The constant wind luminosity assumption is not very realistic by the time the effects of the reverse shock and its associated reverberations have vanished.697 The spin-down huninosity of the pulsar is more realistically described by the huninosity evolution frou a rotating magnetic dipole model:, The spin-down luminosity of the pulsar is more realistically described by the luminosity evolution from a rotating magnetic dipole model:.698 Therefore we now consider the more realistic case of a timce-dependeut huinositv given by (31))., Therefore we now consider the more realistic case of a time-dependent luminosity given by \ref{pulsarlum}) ).699 The energy balance equation for the PWN reads: We solve this equation uunercallhv using a fourth-order Ruusc-Iutta method (e.g. Press et al.," The energy balance equation for the PWN reads: We solve this equation numerically using a fourth-order Runge-Kutta method (e.g. Press et al.,"700 1992)., 1992).701 As an initial condition we take the radius of the PWN equal to zero at the start of the evolution. neglecting the initial stage when the PWN is expanding supersonicallv.," As an initial condition we take the radius of the PWN equal to zero at the start of the evolution, neglecting the initial stage when the PWN is expanding supersonically."702 For the pressure f. we use the pressure at the center of the Sedov SNR (23)).," For the pressure $P_{\rm i}$, we use the pressure at the center of the Sedov SNR \ref{Shurel}) )."703 We fiud that the solution for Riya converges to Tax$85 on a time scale unich larger than the tvpical time scale for the reverse shock to hit the edee of the PWN., We find that the solution for $R_{\rm pwn}$ converges to $R_{\rm pwn}\propto t^{0.3}$ on a time scale much larger than the typical time scale for the reverse shock to hit the edge of the PWN.704 Figure 9 shows his seuni-analvtical result together with results from lyvdrodvuamical simulations., Figure 9 shows this semi-analytical result together with results from hydrodynamical simulations.705 For the senu-analytical equation woe Use 54=5/3. because the lvdrodvuanues code also uses this value (see section L1 below).," For the semi-analytical equation we use $\gamma_{\rm pwn} =5/3$, because the hydrodynamics code also uses this value (see section 4.1 below)."706 Our simulations were performed using the Versatile Advection Code (VAC. Tótth 1996) which can inteerate the equations of gas dynaudes in a conservative fori in 1l. 2 or 3 climeusions.," Our simulations were performed using the Versatile Advection Code (VAC, Tótth 1996) which can integrate the equations of gas dynamics in a conservative form in 1, 2 or 3 dimensions."707 We used the TVD-MUSCL scheme with a Roc-tvpe approximate Riemiaun solver from the nunerical aleorithins available in VAC (Totth aud Odstréil. 1996): a discussion of this aud other schemes for merical wdrodvuamucs can be found in LeVeque (1998).," We used the TVD-MUSCL scheme with a Roe-type approximate Riemann solver from the numerical algorithms available in VAC (Tótth and Odstrčiil, 1996); a discussion of this and other schemes for numerical hydrodynamics can be found in LeVeque (1998)."708 Iu this paper our caleulatiouns are limited to spherically sviunietric flows., In this paper our calculations are limited to spherically symmetric flows.709 We use a uniform grid with a erid spacing chosen sufficiently fine to resolve both the shocks inside the PWN aud the larecr-scale shocks associated with the SNR., We use a uniform grid with a grid spacing chosen sufficiently fine to resolve both the shocks inside the PWN and the larger-scale shocks associated with the SNR.710 Table 1 gives the plivsical scale associated with the erid size for the simulations prescutec here., Table 1 gives the physical scale associated with the grid size for the simulations presented here.711 An expanding SNR is created by impulsively releasing the mechanical enerev of he SN explosion in the first few erid cells., An expanding SNR is created by impulsively releasing the mechanical energy of the SN explosion in the first few grid cells.712 The thermal energy aud mass deposited. there lead to freely expanding ejecta with a nearly uniforii density. aud a huear velocity profile as a function of radius.," The thermal energy and mass deposited there lead to freely expanding ejecta with a nearly uniform density, and a linear velocity profile as a function of radius."713"single integer index i that labels the specific splitting (i=l,-,N.= 14).","single integer index $i$ that labels the specific splitting $i= 1,714\cdots, N_{\rm s}\equiv 14$ )."715" Each term of the sum is weighted with the inverse square of the standard uncertainty (c;) of the observed splittings, which are derived from the uncertainties in the frequencies given in Fu et al. ("," Each term of the sum is weighted with the inverse square of the standard uncertainty $\sigma_i$ ) of the observed splittings, which are derived from the uncertainties in the frequencies given in Fu et al. ("7162007) and are shown in the last column of Table 2..,2007) and are shown in the last column of Table \ref{table2}.717" This is at variance with the preliminar study of Córrsico Althaus (2010), in which the fits of the rotational splitting were made without weighting the terms of the sum, and so, the impact of the different uncertainties of the observational data on the final result was neglected."," This is at variance with the preliminar study of Córrsico Althaus (2010), in which the fits of the rotational splitting were made without weighting the terms of the sum, and so, the impact of the different uncertainties of the observational data on the final result was neglected."718" The lower the value of x?, the better the match between the theoretical and the observed frequency splittings."," The lower the value of $\chi^2$, the better the match between the theoretical and the observed frequency splittings."719 'The theoretical rotational splittings are computed using the expressions resulting from the perturbative theory to first order in €) (the rotation rate) that assumes that the pulsating star rotates with a period (P= 1/Q) much longer than any of its pulsation periods (Unno et al., The theoretical rotational splittings are computed using the expressions resulting from the perturbative theory to first order in $\Omega$ (the rotation rate) that assumes that the pulsating star rotates with a period $P \equiv 1/\Omega$ ) much longer than any of its pulsation periods (Unno et al.720 1989)., 1989).721" Under the assumption of rigid rotation (Q constant), the theoretical frequency splittings are given by: with m=0,+1,...,+¢, and Cy, being coefficients that depend on the eigenfunctions of the pulsation mode obtained in the non-rotating case."," Under the assumption of rigid rotation $\Omega$ constant), the theoretical frequency splittings are given by: with $m= 0, \pm 1, \ldots, \pm \ell$, and $C_{k \ell}$ being coefficients that depend on the eigenfunctions of the pulsation mode obtained in the non-rotating case."722 Such coefficients are computed as (Unno et al., Such coefficients are computed as (Unno et al.723" 1989): where £, and & are the unperturbed radial and tangential eigenfunctions, respectively."," 1989): where $\xi_r$ and $\xi_t$ are the unperturbed radial and tangential eigenfunctions, respectively."724" In the case of g-modes, when k is large then £,.<&, in such a way that Cy;>1/£(£+1) (Brickhill 1975)."," In the case of $g$ -modes, when $k$ is large then $\xi_r \ll \xi_t$, in such a way that $C_{k725 \ell} \rightarrow 1 / \ell(\ell+1)$ (Brickhill 1975)."726" If the condition of rigid body rotation is relaxed and (spherically symmetric) differential rotation is assumed, 2= Q(r), the frequency splittings are given by (Unno et al."," If the condition of rigid body rotation is relaxed and (spherically symmetric) differential rotation is assumed, $\Omega= \Omega(r)$ , the frequency splittings are given by (Unno et al."727 1989): Γκι) being the first-order rotation kernels computed from the rotationally unperturbed eigenfunctions as (Unno et al., 1989): $K_{k\ell}(r)$ being the first-order rotation kernels computed from the rotationally unperturbed eigenfunctions as (Unno et al.728 1989): From Eq. (4)), 1989): From Eq. \ref{rota-diff}) )729" it is clear that the frequency splitting for a given mode is just a weighted average of the rotation rate Q(r) throughout the star, being the rotation kernel Kxe¢(r) precisely the weighting function."," it is clear that the frequency splitting for a given mode is just a weighted average of the rotation rate $\Omega(r)$ throughout the star, being the rotation kernel $K_{k730\ell}(r)$ precisely the weighting function."731 Note that the perturbative theory to first order in Ω predicts symmetric separations of the m40 components within each multiplet with respect to the central one 0) (see Eqs. (2)), Note that the perturbative theory to first order in $\Omega$ predicts symmetric separations of the $m \neq 0$ components within each multiplet with respect to the central one $m= 0$ ) (see Eqs. \ref{rota-rigid}) )732 and (4)))., and \ref{rota-diff}) )).733" Therefore, in this work we are neglecting the departures from symmetric frequency splitting within the triplets centered at II~560 s and II~610 s exhibited by"," Therefore, in this work we are neglecting the departures from symmetric frequency splitting within the triplets centered at $\Pi \sim 560$ s and $\Pi734\sim 610$ s exhibited by"735operated by these agencies in co-operation with ESA and NSC (Norway).,operated by these agencies in co-operation with ESA and NSC (Norway).736 We thank the referee for valuable comments that helped us to improve the paper., We thank the referee for valuable comments that helped us to improve the paper.737" S.W., C.L., R.L., and H.W. were supported by NSF grants AGS 08-19662, AGS 08-49453, and AGS 09-36665, and NASA grants NNX 08AQ90G, NNX 08AJ23G, and NNX 11AC05G. N.D. was supported by NASA grant NNX 08AQ32G."," S.W., C.L., R.L., and H.W. were supported by NSF grants AGS 08-19662, AGS 08-49453, and AGS 09-36665, and NASA grants NNX 08AQ90G, NNX 08AJ23G, and NNX 11AC05G. N.D. was supported by NASA grant NNX 08AQ32G."738It will be instructive to look briefly at Wari Dark Matter (WDMD). both to see that some variants of CDAD have less success than others iu fitting cosmological observations. and also because there is renewed interest in WDAL,"It will be instructive to look briefly at Warm Dark Matter (WDM), both to see that some variants of CDM have less success than others in fitting cosmological observations, and also because there is renewed interest in WDM."739 Although CIIDM and WDALI ave similar in the seuse that doth are intermediate models between CDAL aud TIDAL CITDM aud WDAL are quite different in their implications.," Although CHDM and WDM are similar in the sense that both are intermediate models between CDM and HDM, CHDM and WDM are quite different in their implications."740 The problems with a pure Hot Dark Matter (IIDMD) adiabatic cosmology are well known: frec-streaming of the hot dark matter completely estrovs scale fluctuations. so that the first structures that can form are on the mass scale of clusters or superclusters. and galaxies nuust formi by fragmentation of these burger structures: but observations show that galaxies are much older than superchisters. which have low overdensity aud are still forming.," The problems with a pure Hot Dark Matter (HDM) adiabatic cosmology are well known: free-streaming of the hot dark matter completely destroys small-scale fluctuations, so that the first structures that can form are on the mass scale of clusters or superclusters, and galaxies must form by fragmentation of these larger structures; but observations show that galaxies are much older than superclusters, which have low overdensity and are still forming."741 Moreover. with the CODE upper limit to the normalization of IDF. hardly αν structure at all will form even by the preseut epoch.," Moreover, with the COBE upper limit to the normalization of HDF, hardly any structure at all will form even by the present epoch."742 WODAL is a simple modification of DAL obtained by changing the assumed average tuber deusitv » of the particles.," WDM is a simple modification of HDM, obtained by changing the assumed average number density $n$ of the particles."743" In the usual TIDAL. the dark matter particles are ucutrinos. cach species of which has 5,=108 7"". with a corresponding mass of ny—QO,pg/n,0,9257 cV. with lL."," In the usual HDM, the dark matter particles are neutrinos, each species of which has $n_\nu=108$ $^{-3}$, with a corresponding mass of $m_0 =744\Omega_\nu \rho_0/n_\nu = \Omega_\nu 92 h^2$ eV, with $\Omega_\nu = 7451- \Omega_b \approx 1$ ."746" In WDAML there is a new parameter. m/m. the ratio of the mass of the warn particl to the above neutrino mass: correspoudinely. the ή, of the wari particles is reduced bv the inverse of this factor. so that thei otal contribution to the cosmological density is unchanged."," In WDM, there is a new parameter, $m/m_0$, the ratio of the mass of the warm particle to the above neutrino mass; correspondingly, the number density of the warm particles is reduced by the inverse of this factor, so that their total contribution to the cosmological density is unchanged."747 Pagels and I [55] xoposed perhaps the first WDAL particle candidate. a light exaxitiuo. which was ie lightest supersvuuuetric particle (LSP) in the earliest version of Πο phenomenoloey Gvhich was subsequeutly larecly abaudoned m favor of a hidden-sector gsvpeorsvnuuuetry breaking scheme. but which is now being reconsidered: 0).," Pagels and I \cite{PP82} proposed perhaps the first WDM particle candidate, a light gravitino, which was the lightest supersymmetric particle (LSP) in the earliest version of supersymmetric phenomenology (which was subsequently largely abandoned in favor of a hidden-sector sypersymmetry breaking scheme, but which is now being reconsidered: cf. \cite{Dine96}) )."748 Olive Turner [60] proposed left-handed ucutrinos as ΤΟΝΙ, Olive Turner \cite{OT82} proposed left-handed neutrinos as WDM.749", In tli cases. these particles iuteract much more weakly than neutrinos. decouple earlier from the hot big bane. aud thus have diluted uuuber density compared o neutrinos since they do not share iu the entropy rekased by the subsequent aunihilation of species such as quarks."," In both cases, these particles interact much more weakly than neutrinos, decouple earlier from the hot big bang, and thus have diluted number density compared to neutrinos since they do not share in the entropy released by the subsequent annihilation of species such as quarks."750 This is analogous to (but more extreme han) the neutrinos themselves. which have lower uuuber deusitv today than photous because the neutrinos decouple before | annihilation (aud also vecause they are fermiouxs).," This is analogous to (but more extreme than) the neutrinos themselves, which have lower number density today than photons because the neutrinos decouple before $^+$ $^-$ annihilation (and also because they are fermions)."751" Iu order to investigate the cosmnological duplications of any dark matter candidate, it is necessary to work out the gravitational clustering of these warticles. first in linear theory. and then after the amplitude of the fluctuations grows iuto the nonlinear regime."," In order to investigate the cosmological implications of any dark matter candidate, it is necessary to work out the gravitational clustering of these particles, first in linear theory, and then after the amplitude of the fluctuations grows into the nonlinear regime."752 Colombi. Dodelson. Widrow [61] recently did this for WDML aud Figure lin their paper compares the square of the lear vauster functions for WDM aud CIIDM.," Colombi, Dodelson, Widrow \cite{WDM} recently did this for WDM, and Figure 1 in their paper compares the square of the linear transfer functions for WDM and CHDM."753 One often can study huge scale structure just on the basis of such linear calculations. without the need to do computationally expensive sinulatious of he nou-lnear gravitational clusterimg.," One often can study large scale structure just on the basis of such linear calculations, without the need to do computationally expensive simulations of the non-linear gravitational clustering."754 Such studies have shown that matchinghe observed cluster aud ealaxy correlations on scales of about 20-30 72.1 Mpe, Such studies have shown that matchingthe observed cluster and galaxy correlations on scales of about 20-30 $h^{-1}$ Mpc755system ds close to zero velocity in the source frame while the blue svsteià originates from immaterial which has an outflow velocity of ~L900 aus + (towards us with respect to the quasar).,system is close to zero velocity in the source frame while the blue system originates from material which has an outflow velocity of $\sim 1900$ km $^{-1}$ (towards us with respect to the quasar).756 Several factors the measurement of the absorption lines: iiodest. ο...S/N. thelimited resolution of FOS and uncertainties affecting profile of the eissiou lines.," Several factors hamper the measurement of the absorption lines: modest S/N, limited resolution of FOS and uncertainties affecting the profile of the emission lines."757 The absorption lues were measured assunius a plausible reconstruction of the top of the ομοι Ines., The absorption lines were measured assuming a plausible reconstruction of the top of the emission lines.758 Still it is not possible to obtain sufficieutlv accurate Lya absorption profile. aid NW aud CTV doublet ratios to ascertain whether these lines are optically thin or thick and to estimate the covering factor (some of the galactic lines do not reach zero either).," Still it is not possible to obtain sufficiently accurate $\alpha$ absorption profile, and NV and CIV doublet ratios to ascertain whether these lines are optically thin or thick and to estimate the covering factor (some of the galactic lines do not reach zero either)."759 Hieher spectral resolution is needed to elucidate these important points., Higher spectral resolution is needed to elucidate these important points.760 With this caveat. the measures are eiven in Table |," With this caveat, the measures are given in Table 4."761 Particularly interesting is theabsorption line at 1282.5 (CEWIIM of and EW of z 0.7 Aj. which could be 1175 in the 2 = 0.091 system.," Particularly interesting is the absorption line at 1282.5 (FWHM of and EW of $\approx$ 0.7 ), which could be $^*$ 1175 in the $z$ = 0.091 system."762 The agreement in redshift is good., The agreement in redshift is good.763 This line is preseut in the IUE aud, This line is present in the IUE and764clouds where they formed. while as they become older. they progressively. eiierge from them.,"clouds where they formed, while as they become older, they progressively emerge from them."765 In this picture. the spectra of SSPs of differcut ages are supposed to be dust-reddened by different amounts: dust is assunued to he distributed so to simulate a uuiforiui laver in frout of the stars. and the Calactic extinction curve (Cardellictal..1989) is adopted.," In this picture, the spectra of SSPs of different ages are supposed to be dust-reddened by different amounts; dust is assumed to be distributed so to simulate a uniform layer in front of the stars, and the Galactic extinction curve \citep{cardelli89}766 is adopted."767 Building a selt£-cousisteut. clemical model. that svouk ake iuto account changes in the metal coutent of a ealaxy and its cliemical evolution as a fiction of mass and star formation history. was far bevoud the scope of lis work.," Building a self-consistent chemical model, that would take into account changes in the metal content of a galaxy and its chemical evolution as a function of mass and star formation history, was far beyond the scope of this work."768 Tlis is why we adopted a homogencous value or the metallicitv. for our theoretical spectra. aud lef it to the model free to choose between. three differeu sets of metallicity. namely Z=0.05. Z=0.02 aud Z=0.0 (super-solar. solar and sub-solar. respectively).," This is why we adopted a homogeneous value for the metallicity for our theoretical spectra, and left it to the model free to choose between three different sets of metallicity, namely Z=0.05, Z=0.02 and Z=0.004 (super-solar, solar and sub-solar, respectively)."769 Fitting au observed spectrum with a single value of the metallicity ix equivalent to assuming that this value belongs to the stellar population that is dominating its light., Fitting an observed spectrum with a single value of the metallicity is equivalent to assuming that this value belongs to the stellar population that is dominating its light.770 However. as described in F07. acceptable fits are obtained for most of he spectra adopting different metallicities. which means hat this kiud of analysis is often not able to provide a unique value for the metallicity.," However, as described in F07, acceptable fits are obtained for most of the spectra adopting different metallicities, which means that this kind of analysis is often not able to provide a unique value for the metallicity."771 It is clear lat. assuninueg a unique value for the SSP'« netallicity when reproducing an observed spectruni is a sinplifiug assumption since. iu practice. the stellar o»pulatious of a galaxy span a rauge iu metallicity values.," It is clear that, assuming a unique value for the SSP's metallicity when reproducing an observed spectrum is a simplifying assumption since, in practice, the stellar populations of a galaxy span a range in metallicity values."772 One could hence question the reliability of the nass aud of the SEIT determination done Ww usns one single metallicity value., One could hence question the reliability of the mass and of the SFH determination done by using one single metallicity value.773 To etter undoerstaiu this possible das due to the mix of uctallicities that is expected in galaxies. we repeated the check already performed in FOF: we built template svuthetic spectra with 26 differen SFUs as in FU. but with values ofthe metallicity varving as a function of stellar age. to roughly simulate a chenucal evolution. and we analyzed them by means of our spectroplotometric fitting code.," To better understand this possible bias due to the mix of metallicities that is expected in galaxies, we repeated the check already performed in F07: we built template synthetic spectra with 26 different SFHs as in F07, but with values of the metallicity varying as a function of stellar age, to roughly simulate a chemical evolution, and we analyzed them by means of our spectrophotometric fitting code."774 The results clearly show that the wav we deal with the metallicity docs not introduce any bias in the recovered total stellar mass or SFU., The results clearly show that the way we deal with the metallicity does not introduce any bias in the recovered total stellar mass or SFH.775 All of the stellar population properties that are derived are strictly related to the theoretical mocels that we use in our fitting aleorithlun., All of the stellar population properties that are derived are strictly related to the theoretical models that we use in our fitting algorithm.776 It is hence of fouudamental Huportance to eive all the details of the plivsies aud of the paraueters that were used to build the., It is hence of foundamental importance to give all the details of the physics and of the parameters that were used to build them.777 First of all. WE make use of he Padova evolutionary tracks (Bertellietal...1991) and use a standard Salpeter(1955). initial mass function (IATF). with masses in the range 0.15-120 AL...," First of all, WE make use of the Padova evolutionary tracks \citep{bertelli94} and use a standard \cite{salpeter55} initial mass function (IMF), with masses in the range 0.15-120 $_\odot$."778 Our optical spectra were obtained using two different sets of observed stellar atinosplieres: for ages vouuger than LO? vears we used Jacobyetal.(198L).. while for older SSPs we used spectra from the MILES library (Sauchez-Blazquez.2001:Sánchez-Dlázquezetal.Ww106) and both sets were degraded in spectral resolution. oeoi order to match that of our observed spectra (namely 3. 6 and 9 oof FWIAL see Sect.?? for details).," Our optical spectra were obtained using two different sets of observed stellar atmospheres: for ages younger than $10^9$ years we used \cite{jacoby84}, while for older SSPs we used spectra from the MILES library \citep{Psanchez04,Psanchez06} and both sets were degraded in spectral resolution, in order to match that of our observed spectra (namely 3, 6 and 9 of FWHM, see \ref{sec:data} for details)."779 Using the theoretical libraries of I&urucz. the SSP spectra were extended to the ultra-violet aud iutrared. widening. iu this wav. the waveleneth range down to 90 am up to ~10? ((note that in hese intervals the spectral resolution is much lower. being ~20Α.. but im auv case outside the range of interest or the spectra used for our analysis).," Using the theoretical libraries of Kurucz, the SSP spectra were extended to the ultra-violet and infrared, widening, in this way, the wavelength range down to 90 and up to $\sim 10^9$ (note that in these intervals the spectral resolution is much lower, being $\sim 20$, but in any case outside the range of interest for the spectra used for our analysis)."780" Cas enission. whose effect is visible through emission lines, was also computed and included in the theoretical spectra by ineans of the plhotoiouisation code (Ferlaud.1996)."," Gas emission, whose effect is visible through emission lines, was also computed –and included in the theoretical spectra– by means of the photoionisation code \citep{ferland96}."781.. The optical spectra of SSPs Vounecr than ~ὃς10° display. in this way. both permitted forbidden lines (typically. hydrogen. [On].Ομ. and ΓΗ).," The optical spectra of SSPs younger than $\sim 2\times 10^7$ display, in this way, both permitted and forbidden lines (typically, hydrogen, , and )."782 This nebular component was computed asstunine (seeOsterbrock.-150).. an electron teixperatine of 104 IS. aud an electron density of 100 cix7.," This nebular component was computed assuming \citep[see][]{osterbrock89}, an electron temperature of $10^4$ K, and an electron density of $100$ $^{-3}$."783 The radius of the ioniziug star cluster was asstuned to be 15 pe. and its mass 105 M.," The radius of the ionizing star cluster was assumed to be 15 pc, and its mass $10^4$ $_\odot$."784 Finally. cuuission from the circmusteclar euvelopes of ACB stars was computed aud added as described iu Bressan(1995).," Finally, emission from the circumstellar envelopes of AGB stars was computed and added as described in \cite{bressan98}."785. The initial set of SSPs was composed of 105 theoretical spectra referring to stella ages ranging from LO? to 20«10? years. for each one of the three aforeaneutioned values of the metallicity.," The initial set of SSPs was composed of 108 theoretical spectra referring to stellar ages ranging from $10^5$ to $20\times 10^9$ years, for each one of the three afore-mentioned values of the metallicity."786 Determining the age of stellar »opulatious from an iuteerated optical spectrum with such a ligh temporal resolution is well bevoud the capabilities of auy spectral analysis., Determining the age of stellar populations from an integrated optical spectrum with such a high temporal resolution is well beyond the capabilities of any spectral analysis.787 Weuce. as a first step. we reduced he stellar age resolution by binning the spectra.," Hence, as a first step, we reduced the stellar age resolution by binning the spectra."788 This was done by taking into account both the characteristics of the evolutionary plases of stars. aud the trends im spectral catures as a function of the SSP age (see both sectiou 2.1.1 and Fie.," This was done by taking into account both the characteristics of the evolutionary phases of stars, and the trends in spectral features as a function of the SSP age (see both section 2.1.1 and Fig."789 | in ΕΟΤ)., 1 in F07).790 After combining the spectra at lis first stage. we euded up with 13 stellar age bius.," After combining the spectra at this first stage, we ended up with 13 stellar age bins."791 As we describe in FO7. this set of theoretica Spectra originally included also a SSP whose age. namely ~17.5 Cyr. is older than the universe age.," As we describe in F07, this set of theoretical spectra originally included also a SSP whose age, namely $\sim 17.5$ Gyr, is older than the universe age."792 The use of his SSP was nierelv statistical: since the ouly appreciable difference between the three oldest SSPs of our set is. actually. the niass-to-hunuinositv ratio. using such an ok SSP would prevent our random search of the best fit model to be systematically biased towards the vounges of the old SSPs.," The use of this SSP was merely statistical: since the only appreciable difference between the three oldest SSPs of our set is, actually, the mass-to-luminosity ratio, using such an old SSP would prevent our random search of the best fit model to be systematically biased towards the youngest of the old SSPs."793 Nevertheless. the adoption of such an approach can lead some models to be dominated by lis verv old stellar population vielding. in this way. mass values that are too high. due to the higher mass-to-lieht ratio.," Nevertheless, the adoption of such an approach can lead some models to be dominated by this very old stellar population yielding, in this way, mass values that are too high, due to the higher mass-to-light ratio."794 To overcome this issue we decide to avoid the use of the oldest stellar populations. linütiug ourselves tostellar populations whose ages are consistent with that of the universe.," To overcome this issue we decide to avoid the use of the oldest stellar populations, limiting ourselves tostellar populations whose ages are consistent with that of the universe."795 We will hence refer. from now on. to these 12 SSP«.," We will hence refer, from now on, to these 12 SSPs."796the reference lor the oxvgen abundances.,the reference for the oxygen abundances.797 If we examine the clusters with nominal ages corresponding to the progenitors of the three PN Types. namely. in the age intervals of (<1. 1<t<5. and (25 Gyr. we can compare directly the PN results with those age-appropriate clusters whose oxvgen abundances are available.," If we examine the clusters with nominal ages corresponding to the progenitors of the three PN Types, namely, in the age intervals of $\leq$ 1, $<$ $<$ 5, and $\geq$ 5 Gyr, we can compare directly the PN results with those age-appropriate clusters whose oxygen abundances are available."798 We have caleulated the absolute oxvgen abundances for the clusters by using the same solar oxvgen ratio used in the original papers., We have calculated the absolute oxygen abundances for the clusters by using the same solar oxygen ratio used in the original papers.799 In cases where we could not find the solar oxvgen ratio used by the authors. we do not use the datum in the gradient determination. given that adopted values can differ bv large amounts.," In cases where we could not find the solar oxygen ratio used by the authors, we do not use the datum in the gradient determination, given that adopted values can differ by large amounts."800 Oxveen abundances are available [or a few very voung clusters (<1 Gyr) within a very limited. galactocentric distance range. (hus an estimate of the gradient. would not be meaningful (allhough the abundance distribution would be compatible. within the uncertainties. with that of Tvpe I PNe).," Oxygen abundances are available for a few very young clusters $\leq$ 1 Gyr) within a very limited galactocentric distance range, thus an estimate of the gradient would not be meaningful (although the abundance distribution would be compatible, within the uncertainties, with that of Type I PNe)."801 A better comparison sample is available for the intermediate age clusters. corresponding approximatelv to (the ages of Type II PNe progenitors. where (he data span a range of ealactocentrie distances. ancl a gradient estimate is sensible.," A better comparison sample is available for the intermediate age clusters, corresponding approximately to the ages of Type II PNe progenitors, where the data span a range of galactocentric distances, and a gradient estimate is sensible."802 We find that the oxveen eradient in open clusters of ages between |. and 5 Gyr is Mog(O/ID) /.NAB;—-0.023 dex +., We find that the oxygen gradient in open clusters of ages between 1 and 5 Gyr is $\Delta$ $\Delta$ $_{\rm G}$ =-0.028 dex $^{-1}$.803 As discussed further in the next section. NGC 6253 and NGC 6791 can be suspected of having an origin in (he inner disk. therefore not being truly representative ol the metallicity at the radius where Chev are observed today.," As discussed further in the next section, NGC 6253 and NGC 6791 can be suspected of having an origin in the inner disk, therefore not being truly representative of the metallicity at the radius where they are observed today."804 Only NGC 6253 [alls in the age interval considered here., Only NGC 6253 falls in the age interval considered here.805 Lit is removed from the sample. (the gradient decreases to -0.022 dex 4.," If it is removed from the sample, the gradient decreases to -0.022 dex $^{-1}$."806 The two estimates of metallicity gradient for open clusters of ages corresponding to Type IL PN progenitors well encompass those derived directly from these PNe., The two estimates of metallicity gradient for open clusters of ages corresponding to Type II PN progenitors well encompass those derived directly from these PNe.807 As shown in Figure 8. oxveen gradients from open clusters and PNe of intermediate ages are fully consistent. with one another.," As shown in Figure 8, oxygen gradients from open clusters and PNe of intermediate ages are fully consistent with one another."808 Finally. for clusters older (han 5 Gyr we have only three possible data points and," Finally, for clusters older than 5 Gyr we have only three possible data points and"809redshift 2. the maximum value of A.,"redshift $z$, the maximum value of $K$."810 Similar to stars. non- disces have a maximum mass Al/p4 which increases with central redshift.," Similar to stars, non-rotating discs have a maximum mass $M/\rho\subscr{d}$ which increases with central redshift."811 In Fie., In Fig.812 3 the total gravitational mass is plotted versus central redshift for the two dillerent equations of state., 3 the total gravitational mass is plotted versus central redshift for the two different equations of state.813 The higher total masses are reached in the case of the simple equation (20)). dashed line. while the polvtropic relation (23)) has a maximum at a finite redshift οτε3.25.," The higher total masses are reached in the case of the simple equation \ref{eos0}) ), dashed line, while the polytropic relation \ref{eos1}) ) has a maximum at a finite redshift $z \approx 3.25$."814 The stronger relativistic cases have been caleulatecl here using a higher grid resolution of 256. 256., The stronger relativistic cases have been calculated here using a higher grid resolution of $256 \times 256$ .815 Llowever. the last part of the curves for z/(1|]2)20.9 may nevertheless still be unreliable.," However, the last part of the curves for $z/(1+z) \ga 0.9$ may nevertheless still be unreliable."816 Phe problem arises from the strong central concentration of the surface density (Fig., The problem arises from the strong central concentration of the surface density (Fig.817 4)., 4).818 Due to this problem AZ reaches its maximum for the first equation of state (20)) most likely at infinite central redshift., Due to this problem $M$ reaches its maximum for the first equation of state \ref{eos0}) ) most likely at infinite central redshift.819 At larger and larger redshifts. the density increasingly peakes at the origin. (refer to the model with z= 17.0).," At larger and larger redshifts, the density increasingly peakes at the origin (refer to the model with $z=17.0$ )."820 The sequence terminates eventually at a black hole configuration. with all the mass located at the origin.," The sequence terminates eventually at a black hole configuration, with all the mass located at the origin."821 The strong increase of internal pressure with z leads also to a central drop in the metric potential D whieh is plotted. in Fig., The strong increase of internal pressure with $z$ leads also to a central drop in the metric potential $B$ which is plotted in Fig.822 5., 5.823 Por the pressure-free dust. disc. Bo=l everywhere: however. in the case of non-zero pressure. equation (28)) ereates a deviation from this simple relation.," For the pressure-free dust disc, $B=1$ everywhere; however, in the case of non-zero pressure, equation \ref{bjmp}) ) creates a deviation from this simple relation."824 With increasing z. the metric potential D decreases. (in all space) and its central value approaches zero in the extreme relativistic limit (2= 1).," With increasing $z$ , the metric potential $B$ decreases (in all space) and its central value approaches zero in the extreme relativistic limit $z=1$ )."825 The variation of the polvtropic constant AN with redshift is displaved in Fig., The variation of the polytropic constant $K$ with redshift is displayed in Fig.826 6., 6.827 With increasing redshift. A drops from the Newtonian limit and increases again for stronger relativistic disces.," With increasing redshift, $K$ drops from the Newtonian limit and increases again for stronger relativistic discs."828 Adding rotation (£2 0) will lower the value of A. In the following diagrams ἐν will be normalized. to this maximum value uas, Adding rotation $\Omega>0$ ) will lower the value of $K$ In the following diagrams $K$ will be normalized to this maximum value $K\subscr{max}$.829 Rotating clises were studied for the isentropic second equation of state only (23)). and the primary results are displaved in Fig.," Rotating discs were studied for the isentropic second equation of state only \ref{eos1}) ), and the primary results are displayed in Fig."830 7 in the A9 diagram., 7 in the $K-\Omega$ diagram.831 The curves are labeled: with the corresponding central redshifts of the sequences., The curves are labeled with the corresponding central redshifts of the sequences.832 Weaker relativistic disces (solid line. 2=0.025) follow the Newtonian curve (thin dotted Line. eq. 24))," Weaker relativistic discs (solid line, $z=0.025$ ) follow the Newtonian curve (thin dotted line, eq. \ref{newtok}) )"833" closely up to a finite ο«O, and then biftweate continuously into a ring-like structure at οος20.84.", closely up to a finite $\Omega < \Omega\subscr{c}$ and then bifurcate continuously into a ring-like structure at $\Omega/\Omega_c \approx 0.84$.834 This continuous transition [rom disc to ring occurs only lor z&0.01., This continuous transition from disc to ring occurs only for $z \la 0.01$.835 The details of the bifurcation process will be explained. below., The details of the bifurcation process will be explained below.836 Lor intermediate central recshifts 0.01<z0.22 (dashed-dotted. line). the dises and rings coexist. with no apparent connecting branch between them.," For intermediate central redshifts $0.01 < z < 0.22$ (dashed-dotted line), the discs and rings coexist with no apparent connecting branch between them."837 Stronger relativistic. zc 0.22. (dashed. Lines) disces terminate in a mass shed limit. where at the outer edge of the disc (p= pa) gravity is balanced exactly by centrifugal forces.," Stronger relativistic, $z \ga 0.22$ , (dashed lines) discs terminate in a mass shed limit, where at the outer edge of the disc $\rho =\rho\subscr{d}$ ) gravity is balanced exactly by centrifugal forces."838 From the hydrostatic equation we obtain the criterion for reaching the mass-shed limit The end points of the dashed curves and the thick otted line mark the loci where the edge of the disc reaches is limit., From the hydrostatic equation we obtain the criterion for reaching the mass-shed limit The end points of the dashed curves and the thick dotted line mark the loci where the edge of the disc reaches this limit.839 In case of the dust disc. all raclii are at this limit gaimultaneously. since eq. (39))," In case of the dust disc, all radii are at this limit simultaneously, since eq. \ref{mslimit}) )"840 is exactly the hydrostatic quation for a pressure-less disc., is exactly the hydrostatic equation for a pressure-less disc.841" It should. be noted. that 1e angular velocity reached in these strongerrelativistic cases exceeds the value of thepressure-Free case (Q= O,) or the same central redshift.", It should be noted that the angular velocity reached in these strongerrelativistic cases exceeds the value of thepressure-free case $\Omega=\Omega_c$ ) for the same central redshift.842 This effect. is caused by 1f non-linearity of the Einstein-equations., This effect is caused by the non-linearity of the Einstein-equations.843Through. the eravitational action of the internal pressure. the potential,"Through the gravitational action of the internal pressure, the potential"844ideal MHD. they evolve according to corresponding to the advection of magnetic field lines by Lagrangian particles (2)..,"ideal MHD, they evolve according to corresponding to the advection of magnetic field lines by Lagrangian particles \citep{stern66}."845 We extend the Euler potentials method to non-ideal MHD by incorporating shock-capturing dissipation terms. the form of which is given. using a simple generalisation of the terms derived in ?.. by where the summation is over neighbouring particles. e. is a maximum signal velocity between the particle pair as in PMOS. the mean density p=0.5(p;|pj). VM refers to the magnitude of the mean kernel gradient VM;;|=0.5;j|(hi)VWithj)] and a? is a time-variable co-efficient for each particle that is evolved as described in PMOS.," We extend the Euler potentials method to non-ideal MHD by incorporating shock-capturing dissipation terms, the form of which is given, using a simple generalisation of the terms derived in \citet{pm04b}, by where the summation is over neighbouring particles, $v_{\rm sig}$ is a maximum signal velocity between the particle pair as in PM05, the mean density $\bar{\rho} = 0.5(\rho_i + \rho_{j})$, $\vert \overline{\nabla W_{ij}} \vert$ refers to the magnitude of the mean kernel gradient $\overline{\nabla W_{ij}} = 0.5[\nabla W_{ij}(h_{i}) + \nabla W_{ij}(h_{j})]$ and $\alpha^{\rm B}$ is a time-variable co-efficient for each particle that is evolved as described in PM05."846 The magnetic force is computed using the ?— formalism discussed in PMOS (using the B computed from equation 51) which ensures stability of the SPMHD formalism against particle-clumping instabilities in the regime where gas pressure is dominant over magnetic pressure., The magnetic force is computed using the \citet{morris96} formalism discussed in PM05 (using the ${\bf B}$ computed from equation \ref{eq:eulerpots}) ) which ensures stability of the SPMHD formalism against particle-clumping instabilities in the regime where gas pressure is dominant over magnetic pressure.847 The MHD part of the force equation (that is. apart from the gravitational and artificial viscosity forces) reads where ¢;.p;.P; and D; refer to the density. pressure and magnetic field of particle { and O is a normalisation term related to the gradient of the smoothing length (as in. e.g. 22»).," The MHD part of the force equation (that is, apart from the gravitational and artificial viscosity forces) reads where $v_{i}, \rho_{i}, P_{i}$ and $B_{i}$ refer to the density, pressure and magnetic field of particle $i$ and $\Omega$ is a normalisation term related to the gradient of the smoothing length (as in, e.g. \citealt{monaghan02,pm06}) )."848 The first term in (I2)) is the isotropic hydrodynamic + magnetic pressure force and the second term is the magnetic tension force., The first term in \ref{eq:morrisforce}) ) is the isotropic hydrodynamic + magnetic pressure force and the second term is the magnetic tension force.849 For simulations “without magnetic tension” we do not include the latter term., For simulations “without magnetic tension” we do not include the latter term.850" A detailed summary of the recent changes to the hydrodynamic method (including details of the implementation of the variable smoothing length SPH formalisms in both the pressure and gravity terms) and the implementation of the Euler potentials into the numerical code (including test problems comparing the use of them to the ""standard SPMHD formalism of PMOS) are discussed in detail in 2. and we refer the reader to this paper for an up-to-date summary of the present numerical code (the specitic code described differs fromthat used here but the algorithms implemented in each are identical).", A detailed summary of the recent changes to the hydrodynamic method (including details of the implementation of the variable smoothing length SPH formalisms in both the pressure and gravity terms) and the implementation of the Euler potentials into the numerical code (including test problems comparing the use of them to the `standard' SPMHD formalism of PM05) are discussed in detail in \citet{pr07} and we refer the reader to this paper for an up-to-date summary of the present numerical code (the specific code described differs fromthat used here but the algorithms implemented in each are identical).851 The initial cloud is a sphere of radius 2=4«107 em (0.013 pe) and mass AJ=LAZ. with mean density 10 ο ., The initial cloud is a sphere of radius $R= 4\times 10^{16}$ cm (0.013 pc) and mass $M= 1M_{\odot}$ with mean density $\rho_{0} = 7.43\times 10^{-18}$ g $^{-3}$.852 The free-fall time of the cloud is --2.4107 years., The free-fall time of the cloud is $t_{\rm ff} = 2.4\times 10^{4}$ years.853 We assume. for simplicity. that an initially uniform magnetic flux threads the cloud and connects it to the surrounding interstellar medium.," We assume, for simplicity, that an initially uniform magnetic flux threads the cloud and connects it to the surrounding interstellar medium."854 However. a key factor in the problems studied here is the angular momentum transfer introduced by the magnetic field in the form of magnetic braking of the rotating core.," However, a key factor in the problems studied here is the angular momentum transfer introduced by the magnetic field in the form of magnetic braking of the rotating core."855 Thus careful attention must be paid to the boundary condition at r= 11., Thus careful attention must be paid to the boundary condition at $r=R$ .856 Experiments with simple boundary conditions for SPH (for example. using pressure boundaries Or ghost partices) proved somewhat constantunsatisfactory. particularly because. in the higher magnetic field strength runs. significant material is flung outwards (12hy the cloud along the magnetic field lines into the surrounding medium.," Experiments with simple boundary conditions for SPH (for example, using constant pressure boundaries or ghost particles) proved somewhat unsatisfactory, particularly because, in the higher magnetic field strength runs, significant material is flung outwards by the cloud along the magnetic field lines into the surrounding medium."857Toa: Weτ thereforeM model the boundaries: self-consistently: by placing the eloud within a uniform. low density box of surrounding material in pressure equilibrium with the cloud (seealso.27)..," We therefore model the boundaries self-consistently by placing the cloud within a uniform, low density box of surrounding material in pressure equilibrium with the cloud \citep[see also ][]{hosking02,bp06}."858" To ensure regularity of the particle distributions at the box boundaries. we use quasi-periodic boundary conditions at the box edge (that is. particles within 2 smoothing lengths of the boundary are ""ghosted' to the opposite boundary. with no self gravity between SPH particles and ghost particles)."," To ensure regularity of the particle distributions at the box boundaries, we use quasi-periodic boundary conditions at the box edge (that is, particles within $2$ smoothing lengths of the boundary are `ghosted' to the opposite boundary, with no self gravity between SPH particles and ghost particles)."859 Since a uniform magnetic field necessarily implies a linear gradient in the Euler potentials. continuity of the magnetic field across the box boundary is ensured by adding an offset to the values of à and «2 copied to the ghosted particles corresponding to an extrapolation of the linear gradients outside the box boundaries.," Since a uniform magnetic field necessarily implies a linear gradient in the Euler potentials, continuity of the magnetic field across the box boundary is ensured by adding an offset to the values of $\alpha$ and $\beta$ copied to the ghosted particles corresponding to an extrapolation of the linear gradients outside the box boundaries."860" We tind that satisfactory results are obtained using a box size of 8.IO ""em «c.g.zSI0! em (that is. twice the cloud radius in each direction) and a density ratio of 30:1 between the cloud and the surrounding medium."," We find that satisfactory results are obtained using a box size of $-8 \times 10^{16}$ cm $< x,y,z < 8 \times 10^{16} $ cm (that is, twice the cloud radius in each direction) and a density ratio of $30:1$ between the cloud and the surrounding medium."861 This density ratio was chosen simply to ensure that the surrounding medium is sufficiently hot so as not to contribute significantly to the self-gravity of the cloud (that is c22GAL/ 2).," This density ratio was chosen simply to ensure that the surrounding medium is sufficiently hot so as not to contribute significantly to the self-gravity of the cloud (that is, $c_{\rm s}^{2} > GM/R$ )."862 The initial setup is shown in Figure I. showing a cross-section slice of density at y=0 with overlaid magnetic field lines for a field initially oriented in the : direction.," The initial setup is shown in Figure \ref{fig:setup}, showing a cross-section slice of density at $y=0$ with overlaid magnetic field lines for a field initially oriented in the $z-$ direction."863 Both the spherical cloud and the surrounding medium are set up by placing the particles in a regular close-packed lattice arrangement (e.g.2?) which is a stable arrangement for the particles (2).., Both the spherical cloud and the surrounding medium are set up by placing the particles in a regular close-packed lattice arrangement \citep[e.g.][]{hosking02} which is a stable arrangement for the particles \citep{morrisphd}. .864 Whilst such> regularity introduces some undesirable side effects due to the lattice regularity in the initial collapse phase. these small and transient effects are largely eliminated by the time," Whilst such regularity introduces some undesirable side effects due to the lattice regularity in the initial collapse phase, these small and transient effects are largely eliminated by the time"865colour band excess on LLJD 3524 and in the carly phase of the secondary outburst at JD. 3546.,colour band excess on HJD 3524 and in the early phase of the secondary outburst at HJD 3546.866 On the night of 2005. June 5 the band measurement at 1LJD 37.1449. revealed a ~0.45 magnitude excess above the trend. from. previous and succeeding nights.," On the night of 2005, June 5 the band measurement at HJD 3527.1449 revealed a $\sim 0.45$ magnitude excess above the trend from previous and succeeding nights."867 Phere was no evidence of any excess above the trend-lines for any of the other colours all of which were measured within ~2 hrs of the band., There was no evidence of any excess above the trend-lines for any of the other colours all of which were measured within $\sim 2$ hrs of the band.868 The existence of an band: excess is also obvious in the broadband spectrum for the night as shown in bie., The existence of an band excess is also obvious in the broadband spectrum for the night as shown in Fig.869 4., 4.870 The absence of any perceptible increase in or indicates that the enhanced radiation in was sharply cut-olf in waveleneth or was of cluration less than 32 minutes when the next measurement (in V) was mace., The absence of any perceptible increase in or indicates that the enhanced radiation in was sharply cut-off in wavelength or was of duration less than 32 minutes when the next measurement (in ) was made.871 An enhanced orbital modulation can be ruled. out since there was no increase in or measured one orbital evele alter4., An enhanced orbital modulation can be ruled out since there was no increase in or measured one orbital cycle after.872RATE Proportional Counter Array (PCA) measurements show that a typical Type L N-ray burst occurred. almost in the micelle of our 300 see band integration (private communication. Wijnands Ixlein-Wolt).," Proportional Counter Array (PCA) measurements show that a typical Type I X-ray burst occurred almost in the middle of our 300 sec band integration (private communication, Wijnands Klein-Wolt)."873 The peak amplitude was 40 times the baseline flux and the duration (to 5% of baseline) was 35 s. The associated. optical burst. generated. by reprocessing of the burst X-rays undoubtedly contributed to the increase in4., The peak amplitude was $\sim 40$ times the baseline flux and the duration (to $ 5\% $ of baseline) was $\sim 35$ s. The associated optical burst generated by reprocessing of the burst X-rays undoubtedly contributed to the increase in.874 Type PE X-ray bursts have been observed. from. many neutron star binaries and typically last LO20 sec although a few have lasted. up to 150 seconds ( Wong et al., Type I X-ray bursts have been observed from many neutron star binaries and typically last 10–20 sec although a few have lasted up to 150 seconds ( Kong et al.875 2000)., 2000).876 For the fe examples available with simultaneous X-ray and optical data. mostly from 4U 163653 (Pedersen et al.," For the few examples available with simultaneous X-ray and optical data, mostly from 4U 1636–53 (Pedersen et al."877 1982: Lawrence et al., 1982; Lawrence et al.878 1983: Matsuoka ct al., 1983; Matsuoka et al.879 1984) and GS 182624 ( Ίνοις et al., 1984) and GS 1826--24 ( Kong et al.880 2000). the optical and X-ray. profiles are similar in shape and duration “Phere is usually evidence for an optical lag of a few seconds corresponding to the leh travel time to the reprocessing site.," 2000), the optical and X-ray profiles are similar in shape and duration There is usually evidence for an optical lag of a few seconds corresponding to the light travel time to the reprocessing site."881 Preliminary calculations suggest that reprocesscc radiation contributed only a small fraction of the increase seen in the banc., Preliminary calculations suggest that reprocessed radiation contributed only a small fraction of the increase seen in the band.882 A paper on this event. combining the A-ray. optical and radio data. is in preparation.," A paper on this event, combining the X-ray, optical and radio data, is in preparation."883 This wil include detailed: calculations setting limits on the optica Hux expected. from reprocessed radiation., This will include detailed calculations setting limits on the optical flux expected from reprocessed radiation.884 For now we rely on nsoximate approximateestimates based on scaling areargumentsnts using published: simultaneous optical ancl X-ray. observations of the A-rav burst source 4U. 1636.53., For now we rely on approximate estimates based on scaling arguments using published simultaneous optical and X-ray observations of the X-ray burst source 4U 1636–53.885" Phe peak amplitudes of the bursts were 40 times the baseline N-rav. lux. in both svstems although the duration of the SAX JISOS.43658 burst was about twice as long as typical bursts seen in 4U 163653,", The peak amplitudes of the bursts were $\sim 40 $ times the baseline X-ray flux in both systems although the duration of the SAX J1808.4--3658 burst was about twice as long as typical bursts seen in 4U 1636–53.886 Optical bursts are generated by reprocessing of burst X-ravs incident on the disc and the companion., Optical bursts are generated by reprocessing of burst X-rays incident on the disc and the companion.887 The fraction observed from the disc is expected to be strongly dependent on the inclination of the svstem., The fraction observed from the disc is expected to be strongly dependent on the inclination of the system.888 The component coming [rom the companion star will also be dependent on on the inclination (though not so strongly) and will be proportional to the solid angle subtended by the companion Roche lobe ab the burst source., The component coming from the companion star will also be dependent on on the inclination (though not so strongly) and will be proportional to the solid angle subtended by the companion Roche lobe at the burst source.889 Lts amplitude. will depend. on the orbital phase at which the burst occurred., Its amplitude will depend on the orbital phase at which the burst occurred.890 We assume in the calculations below that the fraction. arising from the companion is equal to the fractional. orbital modulation observed during transient outbursts., We assume in the calculations below that the fraction arising from the companion is equal to the fractional orbital modulation observed during transient outbursts.891 The inclination angles are poorly known in both SAX JIsO0S.43658 and 4U 163653 but are believed to be ~60! in both systems (Chakrabarty Morgan. 1998: Homer et al., The inclination angles are poorly known in both SAX J1808.4–3658 and 4U 1636–53 but are believed to be $\sim 60 \degr $ in both systems (Chakrabarty Morgan 1998; Homer et al.892 2002: Frank. Wine Lasota LOST).," 2002; Frank, King Lasota 1987)."893 The X-ray burst occurred at binary phase ©=0.08 (phase zero corresponds to the time when the companion star is at its maximum distance from the observer). almost optimum time for observing reprocessed radiation from the companion.," The X-ray burst occurred at binary phase $\phi = 0.08$ (phase zero corresponds to the time when the companion star is at its maximum distance from the observer), almost optimum time for observing reprocessed radiation from the companion."894 Using the estimated dimensions of the two systems (Frank. lxing Lasota LOST: Chakrabarty Morgan 1998) we find that the solid angle of the Roche lobe in the 4U 163653 system is 4times that in SAX JISOS4.3658.," Using the estimated dimensions of the two systems (Frank, King Lasota 1987; Chakrabarty Morgan 1998) we find that the solid angle of the Roche lobe in the 4U 1636–53 system is $\sim 4$ times that in SAX J1808.4–3658."895 Hence the peak optical burst [ux from the companion in 4U 163653 will be 4 times that in SAN JLSOS.43658 assuming that the X-ray bursts are similar in peak llux., Hence the peak optical burst flux from the companion in 4U 1636–53 will be 4 times that in SAX J1808.4–3658 assuming that the X-ray bursts are similar in peak flux.896 Orbital modulation measurements show. however. that the fraction of radiation reprocessed on the companion to 4U 163653 is ~25 per cent (Giles et al.," Orbital modulation measurements show, however, that the fraction of radiation reprocessed on the companion to 4U 1636–53 is $ \sim 25$ per cent (Giles et al."897 2002) which is only twice that in SAN JISOS.43658 (Giles et al., 2002) which is only twice that in SAX J1808.4–3658 (Giles et al.898 1999)., 1999).899 Llenee. for the same peak X-ray. burst flux. the observed. reprocessed. radiation from the disc is also larger in 4U 163653 than in S.XX JISOS.43658.," Hence, for the same peak X-ray burst flux, the observed reprocessed radiation from the disc is also larger in 4U 1636–53 than in SAX J1808.4–3658."900 This mav be a consequence of a larger disc size or perhaps of a smaller inclination angle for 4U 163653., This may be a consequence of a larger disc size or perhaps of a smaller inclination angle for 4U 1636–53.901 The two conditions above are satisfied if we assume that. for the same peak A-ray burst Hux. optical bursts in 4U 163653 are twice as large as those in SAN JLSOSA3658.," The two conditions above are satisfied if we assume that, for the same peak X-ray burst flux, optical bursts in 4U 1636–53 are twice as large as those in SAX J1808.4–3658."902 The typical peak optical burst. Εαν to baseline. ratio in 4U 163653 is ~1.5 (Pedersen ct al., The typical peak optical burst flux to baseline ratio in 4U 1636–53 is $\sim 1.5$ (Pedersen et al.903 1982: Lawrence et al., 1982; Lawrence et al.904 1983)., 1983).905 Bursts in GS 182624 are much longer in duration but the ratio of optical to X-ray burst. height. is less (Ixong et al., Bursts in GS 1826–24 are much longer in duration but the ratio of optical to X-ray burst height is less (Kong et al.906 2000)., 2000).907 Given that the X-ray bursts in SAX JISQS.43658 and 4U 163653 are of similar peak amplitude we expect the optical burst in SAX JISQOS.43658 to have half the relative amplitude (~0.75r times baseline)., Given that the X-ray bursts in SAX J1808.4–3658 and 4U 1636–53 are of similar peak amplitude we expect the optical burst in SAX J1808.4–3658 to have half the relative amplitude $\sim 0.75$ times baseline).908" The total band integration time (300 s) was much longer than the burst duration and this will reduce the amplitude of the reprocessing signal bv the ratio of the integrated optical burst flux to the ""normal. optical flux.", The total band integration time (300 s) was much longer than the burst duration and this will reduce the amplitude of the reprocessing signal by the ratio of the integrated optical burst flux to the 'normal' optical flux.909 ‘Vhis ratio is ~0.5«|20/300 assuming the optical burst. profile was triangular with effective duration 20 s. Hence the increase in the integrated. band Lux due to reprocessing would be 2.5 per cont above baseline., This ratio is $\sim 0.5\times20/300$ assuming the optical burst profile was triangular with effective duration $ \sim 20$ s. Hence the increase in the integrated band flux due to reprocessing would be $\sim 2.5$ per cent above baseline.910 This is a factor 20 less than the observed. ~50 per cent increase in7., This is a factor 20 less than the observed $\sim 50 $ per cent increase in.911 There are many uncertainties in the above argument but it seems. unlikely that all the band excess can be due to reprocessed) X-ray burst emission., There are many uncertainties in the above argument but it seems unlikely that all the band excess can be due to reprocessed X-ray burst emission.912 The burst may have been the trigger for an on-going svnchrotron emission event., The burst may have been the trigger for an on-going synchrotron emission event.913 ltupen et al. (, Rupen et al. (9142005) detected: weak 4.86 and 8.46 Ciz radio emission [rom SAN JISOS.4.3658 on 2005 June 7. 11 &116 (LLJD 3529. 3533. 538) and suggested it was due to svnchrotron emission.,"2005) detected weak 4.86 and 8.46 GHz radio emission from SAX J1808.4–3658 on 2005 June 7, 11 16 (HJD 3529, 3533 3538) and suggested it was due to synchrotron emission."915 Rea et al. (, Rea et al. (9162005) measured magnitudes on 2005 June 5 (LID — 3526.5) and. set ade upper limit of 16.5 on band LR emission.,2005) measured magnitudes on 2005 June 5 (HJD $ \sim 3526.5 $ ) and set a $5\sigma$ upper limit of 16.5 on band IR emission.917 Their measurements of the optical magnitudes are of low precision but are more consistent with our normal. spectrum of June 3 than with the anomalous. data of June 5., Their measurements of the optical magnitudes are of low precision but are more consistent with our 'normal' spectrum of June 3 than with the 'anomalous' data of June 5.918" Their band upper Limit is slightly above an extrapolation of the ‘normal’ spectrum but is more consistent with it than with the ""anomalous! one.", Their band upper limit is slightly above an extrapolation of the 'normal' spectrum but is more consistent with it than with the 'anomalous' one.919 The measurements by Rea et al. (, The measurements by Rea et al. (9202005) were made 12 hrs before our observations of June 5.,2005) were made $\sim 12$ hrs before our observations of June 5.921 It seems likely that the LR excess was not present at that time ancl we note also that no radio emission was detected on 2005, It seems likely that the IR excess was not present at that time and we note also that no radio emission was detected on 2005922models in the M-Rin plane.,models in the $\dot{M}$ $R_{in}$ plane.923 The symbols represent a sample of observations of solar-type objects classified as ‘transition’ discs by Espaillat et al. (, The symbols represent a sample of observations of solar-type objects classified as `transition' discs by Espaillat et al. (924"2007a,b,2008,2010) - Red Circles, Hughes et al. (","2007a,b,2008,2010) - Red Circles, Hughes et al. ("925"2009,2010) - Red Squares, Kim et al. (","2009,2010) - Red Squares, Kim et al. ("926"2009) - Red Diamonds, Calvet et al. (","2009) - Red Diamonds, Calvet et al. ("927"2005) - Black Diamonds, Merin et al. (","2005) - Black Diamonds, n et al. ("9282010) - Black Squares and Cieza et al. (,2010) - Black Squares and Cieza et al. (9292010) - Black Triangles (Although Cieza et al.,2010) - Black Triangles (Although Cieza et al.930 2010 do not fit for the inner-hole radius they list as transitional sources those discs that have a deficit of emission in theSpitzer IRAC bands; therefore we conservatively estimate an inner hole radius of « 10AU for all their sources)., 2010 do not fit for the inner-hole radius they list as transitional sources those discs that have a deficit of emission in the IRAC bands; therefore we conservatively estimate an inner hole radius of $<10$ AU for all their sources).931" It is immediately clear from the figure that there is a population of large inner hole, strongly accreting transition discs that cannot have been created by XPE."," It is immediately clear from the figure that there is a population of large inner hole, strongly accreting transition discs that cannot have been created by XPE."932 Gap opening by a giant planet or grain growth is perhaps the most plausible explanation for these objects., Gap opening by a giant planet or grain growth is perhaps the most plausible explanation for these objects.933" However, there is a significant number of discs with inner holes that are consistent with an XPE origin."," However, there is a significant number of discs with inner holes that are consistent with an XPE origin."934" Furthermore we note the lack of observations of non-accreting ‘transition’ discs with holes at radii greater than 20AU, where our model predicts a significant populations (although several non-accreting discs with large holes have been detected in different mass ranges e.g. Merín et al."," Furthermore we note the lack of observations of non-accreting `transition' discs with holes at radii greater than 20AU, where our model predicts a significant populations (although several non-accreting discs with large holes have been detected in different mass ranges e.g. n et al."935" 2010, where the observations probe different radial scales)."," 2010, where the observations probe different radial scales)."936 The observations are still rather sparse and it is currently not possible to say whether the observed population of transition discs is a true representation or an artifact of observational selection effects., The observations are still rather sparse and it is currently not possible to say whether the observed population of transition discs is a true representation or an artifact of observational selection effects.937" One obvious consequence of an X-ray photoevaporation mechanism is that the properties of transition discs should be correlated with the X-ray luminosity, something no other model of photoevaporation or ‘transition’ disc origin would predict."," One obvious consequence of an X-ray photoevaporation mechanism is that the properties of transition discs should be correlated with the X-ray luminosity, something no other model of photoevaporation or `transition' disc origin would predict."938" In Figure 14,, we show two such correlations namely the inner hole radius (left panel) and accretion rate (right panel) against X-ray luminosity, considering only accreting ‘transition’ discs (i.e. those with an accretion rate >1x10!'Ms !))"," In Figure \ref{fig:inner_corr}, we show two such correlations namely the inner hole radius (left panel) and accretion rate (right panel) against X-ray luminosity, considering only accreting `transition' discs (i.e. those with an accretion rate $>1\times939 10^{-11}$ )."940" The plots have been generated by randomly sampling (in time) the accreting transition phase of each disc model several times, and should therefore provide a reasonable estimate of both the general form of the correlation plus the associated scatter."," The plots have been generated by randomly sampling (in time) the accreting transition phase of each disc model several times, and should therefore provide a reasonable estimate of both the general form of the correlation plus the associated scatter."941" Clearly, since discs with higher X-ray luminosities open gaps earlier and at higher accretion rates a strong positive correlation between"," Clearly, since discs with higher X-ray luminosities open gaps earlier and at higher accretion rates a strong positive correlation between"942population. with the Se being widely dominant in the 100 bband.,"population, with the Sc being widely dominant in the 100 band."943 Despite their high luminosities. we predict that starburst galaxies do not provide a significant contribution to the IR emission. due to their low expected number.," Despite their high luminosities, we predict that starburst galaxies do not provide a significant contribution to the IR emission, due to their low expected number."944 We obtain a contribution of 15.4 Jy at 60 aand 12.1 Jy at 100 corresponding respectively to about and of total predicted signal., We obtain a contribution of 15.4 Jy at 60 and 12.1 Jy at 100 corresponding respectively to about and of total predicted signal.945 Only in our extreme scenario. their contribution becomes non-negligible in the 60 bband. reaching the of the total predicted flux.," Only in our extreme scenario their contribution becomes non-negligible in the 60 band, reaching the of the total predicted flux."946 This low contribution agrees with the low rate of starburst galaxies as found in the field by LeFloc'hetal.(2005). at the redshift range of the SDSS-maxBCG catalogue (1.6. 0.]<z« 0.3)., This low contribution agrees with the low rate of starburst galaxies as found in the field by \citet{lefloch05} at the redshift range of the SDSS-maxBCG catalogue (i.e. $0.1<z<0.3$ ).947 The total fluxes associated to the galactic emission predicted by our reference model are 684.5|546.5.895.8] Jy at 60 and 1904.8|1475.7.2521.9] Jy at 100 ((the bracketed interval indicate the values derived from our conservative and extreme models. see Sect. 3.4)).," The total fluxes associated to the galactic emission predicted by our reference model are $684.5 \ [546.5,895.8]$ Jy at 60 and $1904.8 \ [1475.7,2521.9]$ Jy at 100 (the bracketed interval indicate the values derived from our conservative and extreme models, see Sect. \ref{ssec:unc}) )."948 It appears that the reconstructed IR emission due to the galactic dust emission of the cluster members can explain the entire signal measured by Giardetal.(2008)... with an indication that our reference model overestimates the total flux. particularly. at 100um.," It appears that the reconstructed IR emission due to the galactic dust emission of the cluster members can explain the entire signal measured by \cite{giard08}, with an indication that our reference model overestimates the total flux, particularly at 100."949. Indeed. these authors obtained 570.1+36.1 Jy and 1359.9+249.1 Jy at 60 aand 100üum.. respectively.," Indeed, these authors obtained $570.1\pm36.1$ Jy and $1359.9\pm249.1$ Jy at 60 and 100, respectively."950 We will propose an explanation of this discrepancy in the next sections., We will propose an explanation of this discrepancy in the next sections.951 However. when considering our conservative scenario. the predicted emission is in good agreement with the total measured signal in. both bands.," However, when considering our conservative scenario, the predicted emission is in good agreement with the total measured signal in both bands."952 Given these results. modulo the uncertainties. of our modelisation. we obtain that the IR emission of the galaxy members is consistent with the total observed emission of our clusters sample. leaving little space to the possible presence of other components like intracluster dust.," Given these results, modulo the uncertainties of our modelisation, we obtain that the IR emission of the galaxy members is consistent with the total observed emission of our clusters sample, leaving little space to the possible presence of other components like intracluster dust."953inviscid.,inviscid.954 In this work we examine low Mach. number Lows which. taken in concert with the isothermal assumption. means that features in the Low such as shocks are unlikely to create regions of high ionisation.," In this work we examine low Mach number flows which, taken in concert with the isothermal assumption, means that features in the flow such as shocks are unlikely to create regions of high ionisation."955 The HYDILA code solves the following equations for a system of NV Πα»., The HYDRA code solves the following equations for a system of $N$ fluids.956 Phe simulations described in this paper consist of three Duids. indexed. by 7=0 for the neutral Iluid and ;=1 and ;=2 for the electron. anc ion fluids respectively.," The simulations described in this paper consist of three fluids, indexed by $i=0$ for the neutral fluid and $i=1$ and $i=2$ for the electron and ion fluids respectively."957 The equations to be solved are where p;. ο. B. and J are the mass. densities. velocities. magnetic field ancl current. density. respectively.," The equations to be solved are where $\rho_i$, $\mathbf{q}_i$, $\mathbf{B}$, and $\mathbf{J}$ are the mass 	densities, velocities, magnetic field and current density, respectively."958 e denotes the sound speed. anc a; and. Ajo) are the charge-to-mass ratios and the collision coellicients. between the charged species and the neutral Duid. respectively.," $a$ denotes the sound speed, and $\alpha_i$ and $K_{i0}$ are the charge-to-mass ratios and the collision coefficients between the charged species and the neutral fluid, respectively."959" These equations lead to an expression for the electric ficld in the frame of the Εις. E/. given by the generalised Ohm's Lawwhere the components of the field are given by using the definitions ay=foB. ay=fuB. ay=f/,B. where foVrofD. fuΓΗ and fy— "," These equations lead to an expression for the electric field in the frame of the fluid, $\mathbf{E}^\prime$, given by the generalised Ohm's Lawwhere the components of the field are given by using the definitions $\mathbf{a}_{\rm O} \equiv f_{\rm O}\mathbf{B}$, $\mathbf{a}_{\rm H} \equiv f_{\rm H}\mathbf{B}$, $\mathbf{a}_{\rm A} \equiv f_{\rm A}\mathbf{B}$, where $f_{\rm O} \equiv \sqrt{r_{\rm O}}/B$, $f_{\rm H} \equiv r_{\rm H}/B$ and $f_{\rm A} \equiv \sqrt{r_{\rm A}}/B$."960The pesistivities given here are the Ohmic. Hall ancl VrxX/D.ambipolar resistivities. respectively. and are defined by where the conductivities are given hy where the Hall parameter 3; for a charged. species is eiven by To solve these equations numerically we use three diferent operators: These operators are applied. using Strangoperator splitting in order to maintain the second order accuracy of the overall scheme.," The resistivities given here are the Ohmic, Hall and ambipolar resistivities, respectively, and are defined by where the conductivities are given by where the Hall parameter $\beta_i$ for a charged species is given by To solve these equations numerically we use three different operators: These operators are applied using Strangoperator splitting in order to maintain the second order accuracy of the overall scheme."961 We refer the reader to O'SullivanDownes(2006.2007) for à more detailed description.," We refer the reader to \cite{osd06, osd07} for a more detailed description."962 The simulations are carried out on a DD slab grid in the Àày-plane., The simulations are carried out on a D slab grid in the $xy$ -plane.963 The grid consists of 6400.«2001 cells. in the .r. jy. and 2 directions respectively.," The grid consists of $6400 \times 200 \times 1$ cells, in the $x$, $y$, and $z$ directions respectively."964 This resolution was chosen on the basis that it reproduces the initial linear. growth. of the ideal MED system in Ixeppensetal.(1999)., This resolution was chosen on the basis that it reproduces the initial linear growth of the ideal MHD system in \cite{keppens99}.965.. Resolution stucies were performed to confirm the resolution as being appropriate (see and 4.3.1))., Resolution studies were performed to confirm the resolution as being appropriate (see \\ref{sec:ambi-res-study} and \ref{sec:hall-res-study}) ).966 The initial set-up used was that of two plasmas Ilowing anti-parallel side-by-side on a grid of size μι0.32£] and y=0.1).," The initial set-up used was that of two plasmas flowing anti-parallel side-by-side on a grid of size $x = [0, 32L]$ and $y = [0, L]$."967 The plasma velocities are given by. |i and m in the g-direction. with a tangential shear laver of width 2« at the interface at c=16L.," The plasma velocities are given by $+ \frac{V_0}{2}$ and $-\frac{V_0}{2}$ in the $y$ -direction, with a tangential shear layer of width $2a$ at the interface at $x = 16L$."968 This velocity profile is described by The width of the shear layer is chosen to be.=0.05. or approximately 20 erid zones.," This velocity profile is described by The width of the shear layer is chosen to be $\frac{a}{L} =9690.05$, or approximately 20 grid zones."970 Ehe magnetic field is initially set to be uniform and aligned with the plasma flow., The magnetic field is initially set to be uniform and aligned with the plasma flow.971 The initial background for all three IEuids in the svsteni is now an exact equilibrium., The initial background for all three fluids in the system is now an exact equilibrium.972 Phe initial neutral velocity field. Vo is then augmented with a perturbation given by where 8l; is set to 10LY.," The initial neutral velocity field, $V_0$ is then augmented with a perturbation given by where $\delta V_0$ is set to $10^{-4}\,V_0$."973 The wavelength of the perturbation is set equal to the characteristic length scale. A=5= L. so that a single wavelength fits exactly into the computational domain.," The wavelength of the perturbation is set equal to the characteristic length scale, $\lambda974= \frac{2 \pi}{k_y} = L$ , so that a single wavelength fits exactly into the computational domain."975 This maximises the possibility of resolving structures that are small relative to. the initial perturbecl wavelength. (Frankctal. 1996)...," This maximises the possibility of resolving structures that are small relative to the initial perturbed wavelength, \citep{frank96}. ."976 “Lhe, The977was the first millisceone pulsar (AISP1)) discovered in the ongoing Arecibo L-band Feed Array (ALFA) pulsar survey 7..,was the first millisecond pulsar ) discovered in the ongoing Arecibo L-band Feed Array (ALFA) pulsar survey \cite{cfl+06}.978" In the discovery. paper ὃν, we presented the results of shase-coherent radio timing of this pulsar carried out with he Green Bank and Arecibo radio telescopes."," In the discovery paper \cite{crl+08}, we presented the results of phase-coherent radio timing of this pulsar carried out with the Green Bank and Arecibo radio telescopes."979 These quickly revealed that the pulsar was in a 05-day orbit around. a 1 solar mass CM.) companion., These quickly revealed that the pulsar was in a 95-day orbit around a 1 solar mass $M_{\odot}$ ) companion.980 This object is remarkable for ing the first (and thus Far. the only) disk. MSP known o have an eccentric (e= 0.44) orbit.," This object is remarkable for being the first (and thus far, the only) disk MSP known to have an eccentric $e = 0.44$ ) orbit."981 In globular. clusters (GCs) there are several binary AISPs with eccentric orbits: rut those are thought to be caused by perturbations of the unarv svstemis by occasional close interactions with other stars., In globular clusters (GCs) there are several binary MSPs with eccentric orbits; but those are thought to be caused by perturbations of the binary systems by occasional close interactions with other stars.982 Coincident with the pulsar position derived. from the iming. a star was found. whose near-infrared) magnitudes were consistent with a 14. main-sequence star at the distance and reddening estimated for PSR. 1903]0327.," Coincident with the pulsar position derived from the timing, a star was found whose near-infrared magnitudes were consistent with a $1\,M_{\odot}$ main-sequence star at the distance and reddening estimated for PSR J1903+0327."983 1 was not known then whether this was just an unlikely. (~ 2.6%)) chance alignment or whether the star is genuinely associated withis and if so whether i is the binary companion responsible for the 95-day orbi of the pulsar.," It was not known then whether this was just an unlikely $\sim$ ) chance alignment or whether the star is genuinely associated with, and if so whether it is the binary companion responsible for the 95-day orbit of the pulsar."984 Such a finding would be surprising. as the conventional understanding of AISP evolution posits tha such a neutron star (NS) is spun up to high spin frequencies bv aceretion of matter and angular momentum from a Companion star while the companion passes through a gian phase ?:: this circularises the system. and a recycled. MSP is left orbiting a low-mass white dwarl (the remnant core of the donor) in a low-ceecentricity orbit (ο<10.7: Phinney 992)).," Such a finding would be surprising, as the conventional understanding of MSP evolution posits that such a neutron star (NS) is spun up to high spin frequencies by accretion of matter and angular momentum from a companion star while the companion passes through a giant phase \cite{bv91}; this circularises the system, and a recycled MSP is left orbiting a low-mass white dwarf (the remnant core of the donor) in a low-eccentricity orbit $e < 10^{-3}$; Phinney \nocite{phi92}) )."985 Until the discovery of all known AISPs in the Galactic disk hac such low-eccentricitvy orbits., Until the discovery of all known MSPs in the Galactic disk had such low-eccentricity orbits.986 Lor Leviews. see Phinney Wulkarni (1904)... Stairs. (2004)... Tauris van cen Lleuvel (2006).," For reviews, see Phinney Kulkarni \nocite{pk94}, Stairs \nocite{sta04}, Tauris van den Heuvel \nocite{th06}."987. For these reasons. Champion ct al.," For these reasons, Champion et al."988 proposed hat ⊳⊔↓⋜↧∙∖⇁∣⋈⋅↓≻⋜⊔⋅↥∪⇂⋅⋜↧⇂↓⋅⊲↓↓≻↓∢⊾⊳∖∙∖⇁⊳∖∩⊾⊔↓∖∖⊽⇂↥∢⋅↓⋅⋖⋅↥⇂↥∢⋅≤⋗⋅∏−∠⇂⋜↧∙∖⇁⋖⋟↓⋅∣⋡↕↿∪⇂∎ he pulsar is caused by a massive unseen WD and the third member is the star detected in the near-infrared.," \nocite{crl+08}989 proposed that may be part of a triple system where the 95-day orbit of the pulsar is caused by a massive unseen WD and the third member is the star detected in the near-infrared."990 The latter is in à long-period orbit and. drives the eccentricity of the inner pair through the Ixozai mechanism ?.., The latter is in a long-period orbit and drives the eccentricity of the inner pair through the Kozai mechanism \cite{koz62}.991 An alternative possibility. also discussed in ? is that the companion to .in the 95-dav orbit is the star detected in the near-infrared. but that this eccentric. unusual svstem originated in an exchange interaction in a dense stellar environment. like a elobular cluster.," An alternative possibility, also discussed in \cite{crl+08} is that the companion to in the 95-day orbit is the star detected in the near-infrared, but that this eccentric, unusual system originated in an exchange interaction in a dense stellar environment, like a globular cluster."992 In this paper. we present new optical measuremoents and further radio timing of obtained with the aim of testing these scenarios.," In this paper, we present new optical measurements and further radio timing of obtained with the aim of testing these scenarios."993 The plan for the rest of this paper is as follows., The plan for the rest of this paper is as follows.994 The optical and racio observations are described 2.., The optical and radio observations are described \ref{sec:observations}.995 Phe immediate results from. these observations are described in 3.., The immediate results from these observations are described in \ref{sec:results}.996 In +4 we discuss the implications of these results regarding the formation and evolution of this svstem., In \ref{sec:discussion} we discuss the implications of these results regarding the formation and evolution of this system.997 In 5 we discuss how this svstenm might have formed., In \ref{sec:formation} we discuss how this system might have formed.998 We sumnmarise our main conclusions in ETT., We summarise our main conclusions in \ref{sec:conclusions}.999 Long-slit spectroscopy of the suspected. counterpart to was obtained. with FORS2 7.. the low dispersion spectrograph of ESO's Very. Large Telescope.," Long-slit spectroscopy of the suspected counterpart to was obtained with FORS2 \cite{aff+98}, the low dispersion spectrograph of ESO's Very Large Telescope."1000 Four spectra were obtained on 2008 June 21. three on 2008 August 23 and one a day Later. on August 24.," Four spectra were obtained on 2008 June 21, three on 2008 August 23 and one a day later, on August 24."1001 All spectra had exposure times of mminutes. and used a 17 slit combined. with the 10254 holographic grism. providing wavelength coverage over ttoAA.," All spectra had exposure times of minutes, and used a $1\asec$ slit combined with the 1028Z holographic grism, providing wavelength coverage over to."1002.. The detectors were read out with 2.2 binning. vielding a resolution ofAA.. sampled at 0.86 ppix+.," The detectors were read out with $2\times2$ binning, yielding a resolution of, sampled at $0.86$ $^{-1}$."1003 The slit was placed such that both the pulsar companion and a bright nearby star were centred on the slit., The slit was placed such that both the pulsar companion and a bright nearby star were centred on the slit.1004 The observations were taken during clear and photometric nights. with the seeing between 0748 and 0772.," The observations were taken during clear and photometric nights, with the seeing between $0\farcs48$ and $0\farcs72$."1005 Phe spectral observations were corrected. for bias and. Uat-Llicldecl using lamp fats., The spectral observations were corrected for bias and flat-fielded using lamp flats.1006 Spectral extraction is complicated by the bright star. henceforth star A. located 273 from the pulsar counterpart (sce Lig. 2.1).," Spectral extraction is complicated by the bright star, henceforth star A, located $2\farcs3$ from the pulsar counterpart (see Fig. \ref{fig:finder}) )."1007 The star is brighter by about manag in the {ρα and as a result. about of the detected counts at the spatial position of the pulsar counterpart are, The star is brighter by about mag in the $I$ -band and as a result about of the detected counts at the spatial position of the pulsar counterpart are1008and the mass fraction i4.=0.3.,and the mass fraction $m_1 = 0.3$.1009" For the smaller source radii (p,=0.05 and p,= 0.1. the source transits the caustic and moves completely inside. so that separated fold-caustic passages produce distinct characteristic peaks that can be described by a generic profile function (e.g.?).."," For the smaller source radii $\rho_\star = 0.05$ and $\rho_\star = 0.1$ ), the source transits the caustic and moves completely inside, so that separated fold-caustic passages produce distinct characteristic peaks that can be described by a generic profile function \citep*[e.g.][]{Do:fold}."1010 In these cases. he insertion of a seed image mapping to a local minimum of he distance of the source centre from the caustic was essential.," In these cases, the insertion of a seed image mapping to a local minimum of the distance of the source centre from the caustic was essential."1011" In contrast. the source never moves completely inside the caustic for p,=0.2 or f=0.5."," In contrast, the source never moves completely inside the caustic for $\rho_\star = 0.2$ or $\rho_\star = 0.5$."1012" For p,=0.2. there are epochs for which the source crosses the same fold line (as for the smaller racii) or different adjoining fold lines. with or without the cusp in between."," For $\rho_\star = 0.2$, there are epochs for which the source crosses the same fold line (as for the smaller radii) or different adjoining fold lines, with or without the cusp in between."1013" Moreover. or p,=0.5 there are epochs for which a various number of up to hree cusps are enclosed by the source."," Moreover, for $\rho_\star = 0.5$ there are epochs for which a various number of up to three cusps are enclosed by the source."1014" For p,=05. a light curve for a brightness profile corresponding to maximal limb darkening. is shown along with that for a uniformly bright source."," For $\rho_\star = 0.5$, a light curve for a brightness profile corresponding to maximal limb darkening, is shown along with that for a uniformly bright source."1015 With a smaller fraction of the total brightness in the outer parts for the imb-darkened source. the source magnification shows a smaller rise as the source enters or exits the caustic but is larger in between.," With a smaller fraction of the total brightness in the outer parts for the limb-darkened source, the source magnification shows a smaller rise as the source enters or exits the caustic but is larger in between."1016 The application of Green's theorem to replace the integration over the image area by an integration along its boundary is a very efficient approach if the images are moderately distorted. so that a large area for the given boundary length is enclosed (a circle is optimal).," The application of Green's theorem to replace the integration over the image area by an integration along its boundary is a very efficient approach if the images are moderately distorted, so that a large area for the given boundary length is enclosed (a circle is optimal)."1017 There is signiticantly less gain. however. for extremely strong distortions leading to the enclosed area resembling a line.," There is significantly less gain, however, for extremely strong distortions leading to the enclosed area resembling a line."1018 This case is indeed approached if a source star gets very closely aligned with a lens star that is only associated with much less massive companions such as orbiting planets., This case is indeed approached if a source star gets very closely aligned with a lens star that is only associated with much less massive companions such as orbiting planets.1019 Resulting in large oak magnifications. such configurations. are of some specific interest due to their planet-detection potential (22)..," Resulting in large peak magnifications, such configurations are of some specific interest due to their planet-detection potential \citep{GS:HME,Ratt:high}."1020 For modelling he event with the largest peak magnification recorded so far. OGLE 2004-BLG-343 with 244~3000. 2. have derived a more efficient variant of the ray-shooting technique.," For modelling the event with the largest peak magnification recorded so far, OGLE 2004-BLG-343 with $A_0 \sim 3000$, \citet{Dong:ray} have derived a more efficient variant of the ray-shooting technique."1021 In fact. the current version of he adaptive contouring algorithm is significantly slowed down for very small impact angles between source and planet-surrounded ens star. but. for uniformly bright sources. the computation of a single magnification with a relative uncertainty of 5107 can still be carriedout in ~200 ms on a 600 MFlops machine for magnifications in the range ef~ 100—1000. while a result is," In fact, the current version of the adaptive contouring algorithm is significantly slowed down for very small impact angles between source and planet-surrounded lens star, but, for uniformly bright sources, the computation of a single magnification with a relative uncertainty of $5\times 10^{-4}$ can still be carriedout in $\sim 200$ ms on a 600 MFlops machine for magnifications in the range $A \sim 100$ $1000$ , while a result is"1022in a given virtual detector is given by summing over all those trajectories whose velocity vector lies within the acceptance cone of that detector.,in a given virtual detector is given by summing over all those trajectories whose velocity vector lies within the acceptance cone of that detector.1023" Formally, ,t) ,t) ,PP(Q,,c,,t) = ,t) ,t) and the integrations over x and p reduce in the PIC case to summations over all trajectories that illuminate the specified detector."," Formally, ,t) ,t) ,t) = ,t) ,t) and the integrations over $\bm{x}$ and $p$ reduce in the PIC case to summations over all trajectories that illuminate the specified detector."1024" For the high-energy emission of particles accelerated at a relativistic shock front, the restriction imposed by this procedure is not important, because the anisotropy of the particle distribution is expected to be on a scale larger than the beaming angle."," For the high-energy emission of particles accelerated at a relativistic shock front, the restriction imposed by this procedure is not important, because the anisotropy of the particle distribution is expected to be on a scale larger than the beaming angle."1025" Thus, the angular dependence of the emitted radiation found by Sironi&Spitkovsky and Frederiksenetal. should just reflect the(2009b) angular dependence of the(2010) distribution function at the relevant particle energy, and would be preserved in this approach."," Thus, the angular dependence of the emitted radiation found by \citet{sironispitkovsky09b} and \citet{frederiksenetal10} should just reflect the angular dependence of the distribution function at the relevant particle energy, and would be preserved in this approach."1026 As pointed out by Hededal(2005) the computation of synthetic spectra from trajectories taken from PIC simulations inevitably involves interpolation.," As pointed out by \citet{hededalphd}1027 the computation of synthetic spectra from trajectories taken from PIC simulations inevitably involves interpolation."1028" Specifically, the algorithm presented in (18))-(26)) transforms the integration variable from time to phase."," Specifically, the algorithm presented in \ref{ptotal}) \ref{p2}) ) transforms the integration variable from time to phase."1029" In order to split the contributions to the integral into an alternating series (59)), the discrete trajectory must be interpolated."," In order to split the contributions to the integral into an alternating series \ref{instpower2}) ), the discrete trajectory must be interpolated."1030" Interpolation is not a sensitive procedure provided many points are contained within a photon formation time, a constraint that will be made more precise below."," Interpolation is not a sensitive procedure provided many points are contained within a photon formation time, a constraint that will be made more precise below."1031" An accurate evaluation of the instantaneous power at any time step can, for example, be obtained simply by linearly interpolating the functions g, y, 6, g, 6B and 6A, which are known at all neighboring grid points."," An accurate evaluation of the instantaneous power at any time step can, for example, be obtained simply by linearly interpolating the functions $g$, $\gamma$, $\beta$, $\dot{g}$, $\delta\bm{\beta}$ and $\delta\Delta$, which are known at all neighboring grid points."1032" When the photon formation length drops to only a few time steps, this procedure fails."," When the photon formation length drops to only a few time steps, this procedure fails."1033" However, the validity of the PIC simulation requires that the electromagnetic fields vary slowly between time steps, which is precisely the condition for applicability of the generalized synchrotron formula (56))."," However, the validity of the PIC simulation requires that the electromagnetic fields vary slowly between time steps, which is precisely the condition for applicability of the generalized synchrotron formula \ref{instsyncheq}) )."1034" Therefore, in a valid simulation, the instantaneous power can safely be evaluated using this method, if the formation time is not long compared to the time step."," Therefore, in a valid simulation, the instantaneous power can safely be evaluated using this method, if the formation time is not long compared to the time step."1035" It follows that, for a given frequency, the method of evaluating the instantaneous power at each of the discrete set of particle positions a(t,), depends on the value of the photon formation time at that point."," It follows that, for a given frequency, the method of evaluating the instantaneous power at each of the discrete set of particle positions $\bm{x}(t_n)$, depends on the value of the photon formation time at that point."1036" At high frequencies, the formation time is short, and can be much shorter than the typical time-step used in PIC simulations, which is a fraction of a plasma cycle."," At high frequencies, the formation time is short, and can be much shorter than the typical time-step used in PIC simulations, which is a fraction of a plasma cycle."1037 It is straightforward to find for each time-step (labeled by n) the values JA of the deviation of the displacement at the neighboring points n+ 1., It is straightforward to find for each time-step (labeled by $n$ ) the values $\delta\Delta^\pm_n$ of the deviation of the displacement at the neighboring points $n\pm1$ .1038" For a given frequency, the photon formation lengths in the forward and backward directions follow."," For a given frequency, the photon formation lengths in the forward and backward directions follow."1039" Alternatively, two critical frequencies wzTL can be found such that atthese frequencies the neighboring points lie precisely one"," Alternatively, two critical frequencies $\omega^\pm_n$ can be found such that atthese frequencies the neighboring points lie precisely one"1040Under the influence of gravity. disk galaxies are expected o assemble in an “inside-out” fashion: stars form first from uigh-density gas in the central region of the galaxy where the yotential is deepest. and subsequently at increasing galacto- radii (e.g.Larson1976).,"Under the influence of gravity, disk galaxies are expected to assemble in an “inside-out” fashion: stars form first from high-density gas in the central region of the galaxy where the potential is deepest, and subsequently at increasing galacto-centric radii \citep[\eg][]{Larson76}."1041. An immediate consequence of his formation scenario is that stars born at the same time and in the same region of a galaxy should have similar chemical compositions., An immediate consequence of this formation scenario is that stars born at the same time and in the same region of a galaxy should have similar chemical compositions.1042 However. observations in our Galaxy suggest that hese initial conditions are not maintained.," However, observations in our Galaxy suggest that these initial conditions are not maintained."1043 Wielenetal.(1996) argued that the Sun was substantially more metal rich than nearby solar age stars and the local interstellar medium (ISM)., \citet{Wielen96} argued that the Sun was substantially more metal rich than nearby solar age stars and the local interstellar medium (ISM).1044 A recent recalibration of the Geneva Copenhagen Survey (GCS) using the infrared flux method finds no discrepancy with solar age stars (Casagrandeetal.2011). but even modern. studies contirm that the age-metallicity relationships (AMRs) of field and solar neighborhood stars are characterized by higher dispersions than expected (Edvardssonetal.1993:Nordstróm2004:Holmbergetal.2007:Casagrande 2011..," A recent recalibration of the Geneva Copenhagen Survey (GCS) using the infrared flux method finds no discrepancy with solar age stars \citep{Casagrande11}, but even modern studies confirm that the age-metallicity relationships (AMRs) of field and solar neighborhood stars are characterized by higher dispersions than expected \citep{Edvardsson93,Nordstrom04, Holmberg07,1045Casagrande11}."1046. In. addition. simple chemical evolution models that divide the Galaxy into independently evolving concentric annuli predict many more low metallicity G-dwarfs in our region of the disk compared to those observed. a discrepancy known as “the local G-dwarf problem” (vandenBergh1962:Schmidt1963).," In addition, simple chemical evolution models that divide the Galaxy into independently evolving concentric annuli predict many more low metallicity G-dwarfs in our region of the disk compared to those observed, a discrepancy known as “the local G-dwarf problem” \citep[][]{vandenbergh62, Schmidt63}."1047 Evidence seemingly in contradiction to standard galaxy chemical evolution theory is not limited to our own Galaxy., Evidence seemingly in contradiction to standard galaxy chemical evolution theory is not limited to our own Galaxy.1048 Metallicity gradients in disk galaxies are shallower than predicted by classical models (e.g..Magrinietal.," Metallicity gradients in disk galaxies are shallower than predicted by classical models \citep[\eg,][]{Magrini07}."1049 2007)... Ferguson&Johnson(2001). and Fergusonetal.(2007) find unexpectedly old stellar populations on nearly circular orbits in the outskirts of M31 and M33. respectively.," \citet{Ferguson01} and \citet{Ferguson07}1050 find unexpectedly old stellar populations on nearly circular orbits in the outskirts of M31 and M33, respectively."1051 The outermost regions of NGC300 and NGC7739 show flattened or positive abundance gradients with radius (Vlajiéetal.2009.2011).," The outermost regions of NGC300 and NGC7739 show flattened or positive abundance gradients with radius \citep{Vlajic09,Vlajic11}."1052. These perplexing observations cannot be readily explained within the contines of classic galaxy formation models., These perplexing observations cannot be readily explained within the confines of classic galaxy formation models.1053 A natural explanation for the observational challenges above arises if the present day radii of many stars could be signiticantly different from their birth radii., A natural explanation for the observational challenges above arises if the present day radii of many stars could be significantly different from their birth radii.1054 One difficulty in establishing radial migration as a common phenomenon. from a dynamical standpoint.," One difficulty in establishing radial migration as a common phenomenon, from a dynamical standpoint,"1055that incorporation of type-I migration without auy conditions causes severe inconsistency with observed data of extrasolar planets aud our Solar System.,that incorporation of type-I migration without any conditions causes severe inconsistency with observed data of extrasolar planets and our Solar System.1056 If we rely ou type-I migration moclel. we ueed to clarify the condition for the occurrence of type-[ inigration at the same time.," If we rely on type-I migration model, we need to clarify the condition for the occurrence of type-I migration at the same time."1057 The high deusity of the close-in ext‘asolar elaut planet HD119026b recently discovered by Cialleuges theories of plaiet. formation., The high density of the close-in extrasolar giant planet HD149026b recently discovered by \citet{Sato05} challenges theories of planet formation.1058 Iu this paper. we have attempted to «lerive robust constraiits on the planet's compositio1 auc iufer possible routes to explain its formation.," In this paper, we have attempted to derive robust constraints on the planet's composition and infer possible routes to explain its formation."1059 We have fi‘st sinlated the evolution of HD119026) more exteusively than previous w«kers (Satoetal.2005xFortiey2006) aid corfirmed that the planet coutaius a sustantla alnot ol heavy eeluerts.," We have first simulated the evolution of HD149026b more extensively than previous workers \citep{Sato05,Fortney06} and confirmed that the planet contains a substantial amount of heavy elements."1060 Preerred values of t1 elota| mass of heavy elements are 50-80 ÀLl (secTOl 2.1 which is €OUSISent wihi the previous calculaious.," Preferred values of the total mass of heavy elements are 50–80 $\mearth$ (section \ref{sec:standard_model}) ), which is consistent with the previous calculations."1061 We showed that the results a| unciauged or heavy eleijens locatec Lin the central core. or distributed iuside the euvelope. provided they remain deeper thiui the exterial radiative zone.," We showed that the results are unchanged for heavy elements located in the central core, or distributed inside the envelope, provided they remain deeper than the external radiative zone."1062 In the event of a significant enrichment of tlie outer layers. slightly hieher values of heavy elements coutent are possible (section 2.3)).," In the event of a significant enrichment of the outer layers, slightly higher values of heavy elements content are possible (section \ref{sec:core_or_envelope}) )."1063 Iu. order ο €lerive luΠΕΙ values of the mass of heavy eements. we have explored tle possibility that tle planet Was slOpec ina relatively cold euviroumeu for sotje time before mierating near to tlie pinet.," In order to derive minimum values of the mass of heavy elements, we have explored the possibility that the planet was stored in a relatively cold environment for some time before migrating near to the planet."1064 This strict miniΕΜΠ is ~35M.. but is regarced as unlikely because it reques a late migrat1 and no yeieating of the planet by tidal circulizajon (section 2.3)).," This strict minimum is $\sim 35 \mearth$, but is regarded as unlikely because it requires a late migration and no reheating of the planet by tidal circulization (section \ref{sec:cold_storage_hypothesis}) )."1065 We have then investigated the possillity of subcritical core accreion as envisioned. OotU rantS d Neptune to account for the small eivelope lass as well as the arge core mass., We have then investigated the possibility of subcritical core accretion as envisioned for Uranus and Neptune to account for the small envelope mass as well as the large core mass.1066 D1 incipe arge Cor eo. 90-80 M Ca1 be formed by sul(critical Core accretion., In principle a large core of 50–80 $\mearth$ can be formed by subcritical core accretion.1067 However we |ave found very unlikelv for at least two reasons: (i) A σιberitical core accreion results in a ratio of te ο bass d Ol1ο total mass a)ove ~OQ.T (section 3.1)). whereas ot revolutio1 calculaious slowed ‘th a hiei ratio to be possible in a very limited range of paraneers (see Table l1) (ii) Te )critical forration of a 50-80 M core requires au extremely massive or meal-rich clisk with dust ‘face deisity 30-50 times tlie vates obtained for the mai ninilass solar uebula (section :3.," However we have found it very unlikely for at least two reasons: (i) A subcritical core accretion results in a ratio of the core mass to the total mass above $\sim 0.7$ (section \ref{sec:critical_mass}) ), whereas our evolution calculations showed such a high ratio to be possible in a very limited range of parameters (see Table \ref{tab:constraints}) ); (ii) The subcritical formation of a 50–80 $\mearth$ core requires an extremely massive or metal-rich disk with dust surface density 30-50 times the values obtained for the minimum mass solar nebula (section \ref{sec:subcritical}) )."10682 'easonably jassive and/or metaI-yich disk eau fori cores of at most ~30K [ar [rom the parent a5, A reasonably massive and/or metal-rich disk can form cores of at most $\sim 30 \mearth$ far from the parent star.1069" Those facts require us to coSidler (i) the migration ol the planet. (ii) the supy of 1eavy ements to tle planet during or alte ""the gas accretion pliase. aud (11) a limited suppvy of cis&e Bas0 oss of the envelope gas to acco1 for the properties o. HD119026b."," Those facts require us to consider (i) the migration of the planet, (ii) the supply of heavy elements to the planet during or after the gas accretion phase, and (iii) a limited supply of disk gas or loss of the envelope gas to account for the properties of HD149026b."1070 h seclior L.1.. we have discusse how the heavy elements cau be delivered to the planet dWing Or alter the gas accretion pliase according to hese scenarios.," In section \ref{sec:Z_supply}, we have discussed how the heavy elements can be delivered to the planet during or after the gas accretion phase according to these scenarios."1071 An efficieit delivery. durius tle gas accretlon piase ueeds to be re-invesigated in much more details. becaise the shepherdiug eucs to prevent he planet from accreting plauetesinals (section [.1.1)).," An efficient delivery during the gas accretion phase needs to be re-investigated in much more details, because the shepherding tends to prevent the planet from accreting planetesimals (section \ref{sec:concurrent_Z_supply}) )."1072 Ou he other hand. scatteriug oL plajetes]tals/planets by one or several outer giant. planets was shown to lead to au elicient accrelion by a close-in giaut. planet. and is a p'omisiug explanation for tje formation of meta|-rich," On the other hand, scattering of planetesimals/planets by one or several outer giant planets was shown to lead to an efficient accretion by a close-in giant planet, and is a promising explanation for the formation of metal-rich"1073"Mi.=Vie/G r=GAL,⋉/2cz""EE,La Myr.)=1. (Vs(rs)>1). (Maier)1). CAEGn)uw1) ParkerUs laa-b: see1909)). Parker ‘acceler (Lamers&Wintersetal.2000) n(f-:|: ACIE=0) Lee) 7. f. Parker {1 p,Cr). η).ei(r) Vy pw. àV dp ®,i M,1 r,1 Ἐν. ","$\mach_w=V_w/\cs$ $r_c=GM_\ast/2\cs^2$ $\mach_w(r_c)=1$ $\mach_w(r_c)>1$ $\mach_w(r_c)=1$ $\mach_w(r_c)<1$ \citeauthor{par58}' \ref{fig:init}a \citealp[see also Figure~3.1 of][]{lam99}) \citeauthor{par58}' \citep{lam99,win00} $f=1$ $M_\ast^{\rm eff}=0$ \ref{fig:init}c $r_\ast$ $f$ \citeauthor{par58}' $f=1$ $\rho_w(r)$ $V_w(r)$$\cs(r)$ $\vct{V_w}$ $\rho_w$ $\delta\vct{V}$ $\delta\rho$ $\Phi_p$ $M_p$ $r_p$ $V_p$ "1074 , 1075tidal torques and infall episodes.,tidal torques and infall episodes.1076 These questions can likely be addressed: using the Millennium Simulation which has already been used to explore properties of BC'Gs (seec.g.?) Recent surveys such as the SDSS Stripe S2 and future surveys such as LSS (?.LSSTScience.Book)— and PanSTARRS (7?) with deeper photometry will allow us to probe clusters at higher redshifts to study the evolution of alignment over a larger range of cosmic time.," These questions can likely be addressed using the Millennium Simulation which has already been used to explore properties of BCGs \citep[see e.g.][]{2009ApJ...696.1094R}1077 Recent surveys such as the SDSS Stripe 82 and future surveys such as LSST \citep[][LSST Science Book]{2009arXiv0912.0201L} and PanSTARRS \citep{2002SPIE.4836..154K} with deeper photometry will allow us to probe clusters at higher redshifts to study the evolution of alignment over a larger range of cosmic time."1078 Deeper surveys will also increase the number of galaxies in low-redshift clusters. reducing Poisson noise in our samples.," Deeper surveys will also increase the number of galaxies in low-redshift clusters, reducing Poisson noise in our samples."1079 This will allow us to study cluster shapes and. alignments for galaxies of dillerent luminosities. a diagnostic of dillerent accretion and dynamical histories.," This will allow us to study cluster shapes and alignments for galaxies of different luminosities, a diagnostic of different accretion and dynamical histories."1080 Simulations addressing the connection between BCC dominance and alignment will be important in discovering which mechanisms cause the distinct. physical. properties of the BCGs and their relation to their parent cluster., Simulations addressing the connection between BCG dominance and alignment will be important in discovering which mechanisms cause the distinct physical properties of the BCGs and their relation to their parent cluster.1081 AMINO is funded. by the Gates Cambridge Trust. the Isaac Newton Studentship fund and the Science and ‘Technology Facilities Council (SPEC).," MNO is funded by the Gates Cambridge Trust, the Isaac Newton Studentship fund and the Science and Technology Facilities Council (STFC)."1082 ALAS was supported in part by NSE grant .AST-0707266., MAS was supported in part by NSF grant AST-0707266.1083. We thank James LE. Gunn and Michael D. Claceders for valuable discussions aud eedback and the anonymous referee for help in clarifying he text., We thank James E. Gunn and Michael D. Gladders for valuable discussions and feedback and the anonymous referee for help in clarifying the text.1084 Funding for the SDSS and SDSS-LE has been provided w the Alfred. D. Sloan Foundation. the Participating Institutions. the National Science. Foundation. the U.S. Department of Energy. the National Aeronautics and Space Administration. the Japanese Monbukagakusho. the Max λαο Society. and the Higher Education Funding Council or England.," Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England."1085 The SDSS Web Site is http:wav.sclss.0re, The SDSS Web Site is http://www.sdss.org/.1086"is (he consequence of an increase in (he radial component of the pressure gradients of the eas,",is the consequence of an increase in the radial component of the pressure gradients of the gas.1087 Figure 8 shows (is concept in more detail., Figure 8 shows this concept in more detail.1088 In (his figure. we have plotted the density of the gas as a [unction of r on a plane parallel to the midplane at 2=0.2 AU.," In this figure, we have plotted the density of the gas as a function of $r$ on a plane parallel to the midplane at $z=0.2$ AU."1089 As a result of increasing the temperature of (he gas from 50 Ix to 1000 Ix. the maximum value of the gas density on this plane is increased by (three orders of magnitude.," As a result of increasing the temperature of the gas from 50 K to 1000 K, the maximum value of the gas density on this plane is increased by three orders of magnitude."1090 Such an increase implies an increase in the radial component of the pressure gradients of the eas which in turn results in more rapid radial migration., Such an increase implies an increase in the radial component of the pressure gradients of the gas which in turn results in more rapid radial migration.1091 From equation (5). the radial position of the maxinuun of the gas density al a certain j1ejeht z approaches smaller values bv increasing the gas temperature.," From equation (5), the radial position of the maximum of the gas density at a certain height $z$ approaches smaller values by increasing the gas temperature."1092 Figure ὃ shows (his or z —0.2 AU., Figure 8 shows this for $z=$ 0.2 AU.1093 For an object at this height and at an initial radial position of r=2 AU. such a decrease in the radius of the local density enhancement causes the distance of the initial outward migration of the object to become smaller (Figure 7).," For an object at this height and at an initial radial position of $r=2$ AU, such a decrease in the radius of the local density enhancement causes the distance of the initial outward migration of the object to become smaller (Figure 7)."1094 For the temperature of 1000 Ix. the radial location of the maximum gas density αἱ 2=0.2 AU becomes smaller than 2 AU and as a result. an object at (2.0.2) AU does not undergo an initial outward migration.," For the temperature of 1000 K, the radial location of the maximum gas density at $z=0.2$ AU becomes smaller than 2 AU and as a result, an object at (2,0.2) AU does not undergo an initial outward migration."1095 While the combined effect of pressure gradients and (he drag force of the gas causes solids to racially migrate toward the location of local densitv enhancement. the vertical component of the gravitational force of the central star attracts solids toward the midplane of the nebula.," While the combined effect of pressure gradients and the drag force of the gas causes solids to radially migrate toward the location of local density enhancement, the vertical component of the gravitational force of the central star attracts solids toward the midplane of the nebula."1096 Figure 9 shows the vertical motion of solids with different sizes., Figure 9 shows the vertical motion of solids with different sizes.1097 The dependence ol the rate of vertical migration on the size of an object can clearly be seen [rom this figure., The dependence of the rate of vertical migration on the size of an object can clearly be seen from this figure.1098 As shown here. except for when the objects are in the vicinitv of the midplane. the rates of (heir vertical migrations increase by increasing (their radii.," As shown here, except for when the objects are in the vicinity of the midplane, the rates of their vertical migrations increase by increasing their radii."1099 Ili (he vicinity of the midplane. however. while I0 centimeter-sized and smaller objects continue their smooth descent. the 1 meter-sized object undergoes an overshoot.," In the vicinity of the midplane, however, while 10 centimeter-sized and smaller objects continue their smooth descent, the 1 meter-sized object undergoes an overshoot."1100 Such an overshoot aud its corresponding damped oscillatory motion are more pronounced when (he density of (he object is increased., Such an overshoot and its corresponding damped oscillatory motion are more pronounced when the density of the object is increased.1101 Figure 10 shows the vertical migrations of a 1 centimeter-sized and a 1 meter-sized object for different values of their densities., Figure 10 shows the vertical migrations of a 1 centimeter-sized and a 1 meter-sized object for different values of their densities.1102 As shown here. the rates of vertical descent of both objects increase bv increasing their densities.," As shown here, the rates of vertical descent of both objects increase by increasing their densities."1103 Once in (he vicinity of the midplane. the meter-sized object undergoes a damped oscillatory motion whose amplitude increases by increasing (he solid's density.," Once in the vicinity of the midplane, the meter-sized object undergoes a damped oscillatory motion whose amplitude increases by increasing the solid's density."1104 Figure 11 shows the thiree-dimensional paths of these (wo objects., Figure 11 shows the three-dimensional paths of these two objects.1105 The clvnamical behavior ofan object along the z-axis and in the vicinity of the midplane can be explainecl bv studying equation (13) in more detail., The dynamical behavior of an object along the $z$ -axis and in the vicinity of the midplane can be explained by studying equation (18) in more detail.1106 In this equation. the crag coellicient C5 is Che factor that determines the funetional form of D.," In this equation, the drag coefficient $C_{\rm D}$ is the factor that determines the functional form of ${{\dot {\hat P}}_z}$."1107 substituting for the drag force of the eas lrom equation (8) and lor the z-component of the relative velocity of, Substituting for the drag force of the gas from equation (8) and for the $z$ -component of the relative velocity of1108absorption).,absorption).1109 The coluun deusitv Nyy is between 1.0 and 1.1107? ?., The column density $N_{\rm H}$ is between 1.0 and $\times10^{22}$ $^{-2}$.1110 This range is consistent with the value resulting from the interstellar reddening to Terzan 6: for Epvy=2.21 (Barbuy et al., This range is consistent with the value resulting from the interstellar reddening to Terzan 6: for $E_{\rm B-V}=2.24$ (Barbuy et al.1111 1997) with an estimated error of 0.1. ely=6.9L40.31 and Ny=(7940.1)«10214 3 (according to the conversion of Av to Nyy by Predehl Scluuitt 1995).," 1997) with an estimated error of 0.1, $A_{\rm V}=6.94\pm0.31$ and $N_{\rm H}=(1.79\pm0.1)\times10^{21}A_{\rm V}=(1.2\pm0.1)\times10^{22}$ $^{-2}$ (according to the conversion of $A_{\rm V}$ to $N_{\rm H}$ by Predehl Schmitt 1995)."1112 The xoad component at 1.6-2.0 keV. which we moceled by black body radiation. affects the determination of Nyy somewha but we estimate that this is limited to 0.2«1072 cu?.," The broad component at 1.6-2.0 keV, which we modeled by black body radiation, affects the determination of $N_{\rm H}$ somewhat but we estimate that this is limited to $0.2\times10^{22}$ $^{-2}$."1113 Ouly the LECS aud MECS provide data curing the eclipse that are of sufficient quality to allow a meaninetul analvsis., Only the LECS and MECS provide data during the eclipse that are of sufficient quality to allow a meaningful analysis.1114 Formally. the spectrunn is consistent iu shape with that outside the eclipse (A2=1.18 for 28 dof).," Formally, the spectrum is consistent in shape with that outside the eclipse $\chi^2_{\rm r}=1.18$ for 28 dof)."1115 Nevertheless.the spectiiun has the appearance of bene somewhat softer.," Nevertheless,the spectrum has the appearance of being somewhat softer."1116 If. iu the Comptonized model. ki. is allowed to vary during the fit. it converges to a value of 1.54£0.9 keV (42=0.90 for 27 dof).," If, in the Comptonized model, $T_{\rm e}$ is allowed to vary during the fit, it converges to a value of $1.5\pm0.9$ keV $\chi^2_{\rm r}=0.90$ for 27 dof)."1117 The F-est predicts a probability of less than 0.02 for a chance occurrence of the fuprovement in 47., The F-test predicts a probability of less than 0.02 for a chance occurrence of the improvement in $\chi^2$.1118 The same kind of improvement can be obtained when leaving free the optical depth instead of the plasma temperature. so we conclude that the nature of the softening is unclear.," The same kind of improvement can be obtained when leaving free the optical depth instead of the plasma temperature, so we conclude that the nature of the softening is unclear."1119 The 2-10 keV. fiux i 2.34101 Cres ley 2 (2-10 keV) or of that outside the eclipse., The 2-10 keV flux is $2.3\times10^{-11}$ erg $^{-1}$ $^{-2}$ (2-10 keV) or of that outside the eclipse.1120 Figs., Figs.1121 Loo aud 5. show that there appear to be two different stages of ceress: the fast 35 s rie and a shoulder of a few luudred seconds., \ref{fignfilc} and \ref{figlczoom} show that there appear to be two different stages of egress: the fast 35 s rise and a shoulder of a few hundred seconds.1122 We generated separate spectra for these two time intervals aud fitted them with the Comptouization model while keeping all parameters values fixed to those found for the out-of-eclipse spectra (Table 1)) except Ap., We generated separate spectra for these two time intervals and fitted them with the Comptonization model while keeping all parameters values fixed to those found for the out-of-eclipse spectrum (Table \ref{tabnfifit}) ) except $N_{\rm H}$.1123 We used only LECS and MECS data because we are primarily interested i whether Ny changes during ceress., We used only LECS and MECS data because we are primarily interested in whether $N_{\rm H}$ changes during egress.1124 Frou this we fiud that during the quick rie [Ng=(10+3)<1072 7 and during the shoulder (1.27x0.07)νE1077OD P 7., From this we find that during the quick rise $N_{\rm H}=(10\pm3)\times10^{22}$ $^{-2}$ and during the shoulder $(1.27\pm0.07)\times10^{22}$ $^{-2}$ .1125 However. iftq we leave free in addition the nornalizations of the Comptonized spectrum. the scusitivity to measuring Vy ," However, if we leave free in addition the normalizations of the Comptonized spectrum, the sensitivity to measuring $N_{\rm H}$ "1126Estimations show that VLP is possibly resulted from the standing slow sausage modes coupling and resonating with the underlying photospheric 5-min p-mode oscillations.,Estimations show that VLP is possibly resulted from the standing slow sausage modes coupling and resonating with the underlying photospheric 5-min p-mode oscillations.1127 It may be associated with evolutive behaviors of the solar internal structures., It may be associated with evolutive behaviors of the solar internal structures.1128" As VLPs have the largest magnitude of emission fluxes, we suggest that the modulations are amplified and form the main framework of the whole flare/CME eruptive processes."," As VLPs have the largest magnitude of emission fluxes, we suggest that the modulations are amplified and form the main framework of the whole flare/CME eruptive processes."1129" From Equ.(2) and (3), we can estimate the radius of the emission source region: Here, the period (P), radio central frequency (/) and radio emission intensity (F) can be obtained from radio observations, the loop length (L) can be estimated from the optical or other imaging observations approximately."," From Equ.(2) and (3), we can estimate the radius of the emission source region: Here, the period $P$ ), radio central frequency $f$ ) and radio emission intensity $F$ ) can be obtained from radio observations, the loop length $L$ ) can be estimated from the optical or other imaging observations approximately."1130 Then we may obtain the radius of the radio emission source region (r) by adopting Equ.(7) even if we have no radio imaging observations., Then we may obtain the radius of the radio emission source region $r$ ) by adopting Equ.(7) even if we have no radio imaging observations.1131" By substituting the parameters obtained in the above sections, we may get the radius of the emission source region from VLP paragraph A, B, C to D is from 2.04x10° km, 2.06x10° km, 1.62x10° km to 0.92x10? km, ie., the source region is undergoing an evolutive process of expanding at first, and then shrinking."," By substituting the parameters obtained in the above sections, we may get the radius of the emission source region from VLP paragraph A, B, C to D is from $2.04\times10^{5}$ km, $2.06\times10^{5}$ km, $1.62\times10^{5}$ km to $0.92\times10^{5}$ km, i.e., the source region is undergoing an evolutive process of expanding at first, and then shrinking."1132" However, as we have no radio imaging observations at the corresponding frequencies, we do not know the exact cites of the emission source region, the only thing we can do is to adopt the averaged loop length in our above estimations, which may have much uncertainties."," However, as we have no radio imaging observations at the corresponding frequencies, we do not know the exact cites of the emission source region, the only thing we can do is to adopt the averaged loop length in our above estimations, which may have much uncertainties."1133" Similar to VLP, LPP and SPP (may include part of slow-VSP) are also caused by MHD oscillations."," Similar to VLP, LPP and SPP (may include part of slow-VSP) are also caused by MHD oscillations."1134" However, their MHD modes may have some differences."," However, their MHD modes may have some differences."1135 They may be related with the standing fast sausage or kink modes., They may be related with the standing fast sausage or kink modes.1136 The propagating MHD modes and the LRC-circuit resonation of current-carrying plasma loops are also the possible candidates of the generating mechanism., The propagating MHD modes and the LRC-circuit resonation of current-carrying plasma loops are also the possible candidates of the generating mechanism.1137 Fast-VSP and most part of slow-VSP are generated by a completely different mechanism: the modulation of the resistive tearing-mode oscillations in electric current-carrying flare loops., Fast-VSP and most part of slow-VSP are generated by a completely different mechanism: the modulation of the resistive tearing-mode oscillations in electric current-carrying flare loops.1138" In this mechanism, both, the period and duration of QPP are coupled with the magnetic field, plasma density, electric current, and the loop parameters."," In this mechanism, both, the period and duration of QPP are coupled with the magnetic field, plasma density, electric current, and the loop parameters."1139" By using their relation, we may deduce the physical conditions of the emission source region."," By using their relation, we may deduce the physical conditions of the emission source region."1140 The timescale of periods of QPPs implies a limit on the pulsating emission source size., The timescale of periods of QPPs implies a limit on the pulsating emission source size.1141 Regardless of generating mechanism the pulsating source must be smaller than that given by the product of speed of light and period (P)., Regardless of generating mechanism the pulsating source must be smaller than that given by the product of speed of light and period $P$ ).1142" If not, the pulsating structure would be smeared out (Elgardy, 1986)."," If not, the pulsating structure would be smeared out $\phi$ y, 1986)."1143" So, it is reasonable to suppose that the short periodic QPP may come from a smaller source region."," So, it is reasonable to suppose that the short periodic QPP may come from a smaller source region."1144" The broad hierarchy of timescales of QPPs occurred in a flare event may imply that there is a multi-scale hierarchy of sizes of the magnetic configurations in the flaring region, and timescales of the dynamic processes."," The broad hierarchy of timescales of QPPs occurred in a flare event may imply that there is a multi-scale hierarchy of sizes of the magnetic configurations in the flaring region, and timescales of the dynamic processes."1145" The frequency drift rate and the bandwidth of the pulsating emission are dominated by the emission mechanism which is always related to the magnetic field strength, plasma density, and possibly to the plasma temperature."," The frequency drift rate and the bandwidth of the pulsating emission are dominated by the emission mechanism which is always related to the magnetic field strength, plasma density, and possibly to the plasma temperature."1146" It may be reasonable to suppose that the frequency drift features of QPPs implies the motion of the pulsating source regions, and the bandwidth of the pulsating emission are related to the dimensional size of the pulsating source regions."," It may be reasonable to suppose that the frequency drift features of QPPs implies the motion of the pulsating source regions, and the bandwidth of the pulsating emission are related to the dimensional size of the pulsating source regions."1147 The period ratio between different classes of QPP have no obvious trend., The period ratio between different classes of QPP have no obvious trend.1148" This fact may imply that there is no originated link between different classes of QPP, even if they are occurred simultaneous in the same frequency range."," This fact may imply that there is no originated link between different classes of QPP, even if they are occurred simultaneous in the same frequency range."1149" Actually, it is possible that the short periodic QPP (e.g. fast-VSP, etc) is a small quasi-periodic perturbation which superposed on the longer periodic QPPs (e.g. VLP, etc), and the latter may dominate the whole evolution of the flaring processes."," Actually, it is possible that the short periodic QPP (e.g. fast-VSP, etc) is a small quasi-periodic perturbation which superposed on the longer periodic QPPs (e.g. VLP, etc), and the latter may dominate the whole evolution of the flaring processes."1150" However, so far, because of the lack of imaging observations with spatial resolutions in the corresponding"," However, so far, because of the lack of imaging observations with spatial resolutions in the corresponding"1151with three Gaussians. each characterised by centroid and a width parameter taken as the standard deviation of the Gaussian. c.,"with three Gaussians, each characterised by centroid and a width parameter taken as the standard deviation of the Gaussian, $\sigma$."1152 Two were narrow. having c of only a few A.," Two were narrow, having $\sigma$ of only a few $\AA$."1153 The third component was much broader. with σ up to 20 A.," The third component was much broader, with $\sigma$ up to 20 $\AA$."1154 This third component was identified with an origin in the wind above the accretion disk. and it is the subject of the present paper.," This third component was identified with an origin in the wind above the accretion disk, and it is the subject of the present paper."1155 Fig.l] of Blundell. Bowler Schmidtobreick (2008) displays the centroids of these fitted Gaussians as a function of time. in the same sequence as the montage in Fig.2 of Schmidtobreick Blundell (2006).," Fig.1 of Blundell, Bowler Schmidtobreick (2008) displays the centroids of these fitted Gaussians as a function of time, in the same sequence as the montage in Fig.2 of Schmidtobreick Blundell (2006)."1156 Because of their importance. | have reproduced these data in Fig.1.," Because of their importance, I have reproduced these data in Fig.1."1157 This figure shows that the two narrow Gaussian components of Ha have centroids that scarcely move over more than two orbits. and the broad component oscillates in Doppler shift with a period of 13 days.," This figure shows that the two narrow Gaussian components of $\alpha$ have centroids that scarcely move over more than two orbits, and the broad component oscillates in Doppler shift with a period of 13 days."1158 It is most redshifted close to orbital phase 0. at primary eclipse.," It is most redshifted close to orbital phase 0, at primary eclipse."1159 This might suggest that this component ts formed in an aceretion stream rather than in the wind., This might suggest that this component is formed in an accretion stream rather than in the wind.1160 The two narrow components were identified with the inner rim of a cireumbinary disk in Blundell. Bowler Schmidtobreick (2008).," The two narrow components were identified with the inner rim of a circumbinary disk in Blundell, Bowler Schmidtobreick (2008)."1161 A very similar plot has been obtained from a set of Ha spectra taken between 2004 and 2008 at the Purple Mountain Observatory., A very similar plot has been obtained from a set of $\alpha$ spectra taken between 2004 and 2008 at the Purple Mountain Observatory.1162 The original data are to be found in Fig.2 of Li Yan (2010) and the motions of fitted centroids as a function of orbital phase are displayed in Fig.2 of Bowler (2011a)., The original data are to be found in Fig.2 of Li Yan (2010) and the motions of fitted centroids as a function of orbital phase are displayed in Fig.2 of Bowler (2011a).1163 The same features are apparent., The same features are apparent.1164 In Fig.2 I show the variation of Doppler speed for the centre of the He broad component (Blundell. Bowler Schmidtobreick 2008) and above it the same for the broader component of the He I 6678 lline. obtained from my fits reported in Bowler (201Ib).," In Fig.2 I show the variation of Doppler speed for the centre of the $\alpha$ broad component (Blundell, Bowler Schmidtobreick 2008) and above it the same for the broader component of the He I 6678 line, obtained from my fits reported in Bowler (2011b)."1165 These broad components have centroids that oscillate with a day period and with velocity amplitude ~110 km s7!., These broad components have centroids that oscillate with a 13-day period and with velocity amplitude $\sim$ 110 km $^{-1}$.1166 They are most redshifted a little before orbital phase O and most blueshifted a little before 0.5., They are most redshifted a little before orbital phase 0 and most blueshifted a little before 0.5.1167 Lines produced in an atmosphere co-moving with the compact object would be most redshifted at orbital phase 0.75 and most blueshifted at 0.25 - the broad lines associated with the wind lag the motion of the compact object by ~ 0.2 of a period and have a reduced orbital Doppler amplitude., Lines produced in an atmosphere co-moving with the compact object would be most redshifted at orbital phase 0.75 and most blueshifted at 0.25 - the broad lines associated with the wind lag the motion of the compact object by $\sim$ 0.2 of a period and have a reduced orbital Doppler amplitude.1168 The identification of the broad component of the Haw emission line with an origin in the wind from the disk is discussed in Blundell. Bowler Schmidtobreick (2008).," The identification of the broad component of the $\alpha$ emission line with an origin in the wind from the disk is discussed in Blundell, Bowler Schmidtobreick (2008)."1169 In brief. the width parameter ο drops smoothly from approximately 20 nnear JD +245 (precession phase approximately 0; accretion disk wide open) to 10 nnear JD +274 as the accretion disk comes closer to edge on.," In brief, the width parameter $\sigma$ drops smoothly from approximately 20 near JD +245 (precession phase approximately 0; accretion disk wide open) to 10 near JD +274 as the accretion disk comes closer to edge on."1170 In addition. this measure of the line of sight wind speed follows the nodding motion of the accretion disk. as inferred from the Doppler shifts of the relativistic jets (Blundell. Bowler Schmidtobreick 2007).," In addition, this measure of the line of sight wind speed follows the nodding motion of the accretion disk, as inferred from the Doppler shifts of the relativistic jets (Blundell, Bowler Schmidtobreick 2007)."1171" The synthesis of absorption line studies of the wind (Fabrika 1997, 2004) shows that the line of sight expansion speed varies as approximately the square of the cosine of the angle between the jet axis and the line of sight. reaching 1600 km s! for 60°."," The synthesis of absorption line studies of the wind (Fabrika 1997, 2004) shows that the line of sight expansion speed varies as approximately the square of the cosine of the angle between the jet axis and the line of sight, reaching 1600 km $^{-1}$ for $^{\circ}$."1172 Thus these observations have established that the source of this wind line ts rooted 1n the accretion disk., Thus these observations have established that the source of this wind line is rooted in the accretion disk.1173 In Blundell. Bowler and Schmidtobreick (2008) the authors cautiously observed that despite this. the motion of the centroid of the wind should not be taken as a measure of the orbital velocity of the compact object.," In Blundell, Bowler and Schmidtobreick (2008) the authors cautiously observed that despite this, the motion of the centroid of the wind should not be taken as a measure of the orbital velocity of the compact object."1174 Ifà given parcel of wind continues emitting Ha over a period of several days. the data displayed in Fig.2 are reconciled with an origin in the tilting and nodding aceretion disk. according to the scenario sketched in the introduction.," If a given parcel of wind continues emitting $\alpha$ over a period of several days, the data displayed in Fig.2 are reconciled with an origin in the tilting and nodding accretion disk, according to the scenario sketched in the introduction."1175 Absorption line studies have shown that the wind from SS 433 is slow in the plane of the accretion disk. but that the speed increases rapidly as the angle to the jet axis decreases.," Absorption line studies have shown that the wind from SS 433 is slow in the plane of the accretion disk, but that the speed increases rapidly as the angle to the jet axis decreases."1176" The results are summarised in Fabrika (1997. 2004) in the form where V,. is the velocity (in km s) of the gas flowing out from the disk as a function of the polar angle a."," The results are summarised in Fabrika (1997, 2004) in the form where $V_w$ is the velocity (in km $^{-1}$ ) of the gas flowing out from the disk as a function of the polar angle $\alpha$."1177 The width c of the broad H« component in the data of Blundell. Bowler Schmidtobreick (2008) has a value of ~20 eearly on. when the angle y between the Jet axis and the line of," The width $\sigma$ of the broad $\alpha$ component in the data of Blundell, Bowler Schmidtobreick (2008) has a value of $\sim$ 20 early on, when the angle $\chi$ between the jet axis and the line of"1178 +).,$^{-1}$ ).1179 lOcQsPECTRUAL shows the results of a spectra svnthesis of the continuum emission., \\ref{FIG:QSPECTRUM} shows the results of a spectral synthesis of the continuum emission.1180 We find that the accretion discs light has a power-law index of 0.60250.3 ane contributes 37-18 percent to the observed continuum ligh atAA., We find that the accretion disc's light has a power-law index of $\pm$ 0.3 and contributes $\pm$ 13 percent to the observed continuum light at.1181 From the residual of the fit it can be seen that a power-law model for the cise predicts more fux short-ware ofSOOOA.. so a power-Iaw. function does not best describe the disc's light.," From the residual of the fit it can be seen that a power-law model for the disc predicts more flux short-ward of, so a power-law function does not best describe the disc's light."1182 LE we moclel the spectrum of the disc with a blackbody function. we obtain a sienificantly better fi (at the 99 percent level). where the dise contributes 5843:16 percent to the continuum [ux at aancd the disc has a blackbody temperature of 4600+ Why and a radius of 0.502£0.," If we model the spectrum of the disc with a blackbody function, we obtain a significantly better fit (at the 99 percent level), where the disc contributes $\pm$ 16 percent to the continuum flux at and the disc has a blackbody temperature of $\pm$ K and a radius of $\pm$."1183061... Using a WS star in order to match the blue end of the spectrum does not give a better fit (at the 99.99 percent confidence level.), Using a K3 star in order to match the blue end of the spectrum does not give a better fit (at the 99.99 percent confidence level.)1184 ALL the uncertainties quoted are 1-0 and have been rescaled so that the 42 ofthe fit is 1., All the uncertainties quoted are $\sigma$ and have been rescaled so that the $\chi_{\nu}^{2}$ of the fit is 1.1185 Although our determination of the fractional contribution of the accretion disc's light to that observed is consistent with the findings of Oke(1077).. 7? and MeClintocketal.(1995). the form of power-law description of the clise’s light is not.," Although our determination of the fractional contribution of the accretion disc's light to that observed is consistent with the findings of \citet{Oke77}, \citet{MR86} and \citet{MHR95}, the form of power-law description of the disc's light is not."1186 However. it should. be noted that the non-variable accretion disc light is à composite of light from the steady-state accretion disc plus the excess light from star-spots or a late-superhump. which most probably have very dilferent spectral shapes.," However, it should be noted that the non-variable accretion disc light is a composite of light from the steady-state accretion disc plus the excess light from star-spots or a late-superhump, which most probably have very different spectral shapes."1187 For the case where the excess light is due to a late-superhump. the late-superhump modulation may have its origin in the outer regions of the disc in the changing streame-cdisc interaction (Rolle. Laswell Pattterson 2001). the spectrum. of the [ate-superhump is expected. to. be different compared to the steady-state disc.," For the case where the excess light is due to a late-superhump, the late-superhump modulation may have its origin in the outer regions of the disc in the changing stream-disc interaction (Rolfe, Haswell Pattterson 2001), the spectrum of the late-superhump is expected to be different compared to the steady-state disc."1188 Although the tically heated streame-disc impact region will be hotter than the rest of the outer disc. it is not obvious how much hotter this will be compared. to. the inner regions of the disc. where viscous stresses due to dillerential rotation are much higher.," Although the tidally heated stream-disc impact region will be hotter than the rest of the outer disc, it is not obvious how much hotter this will be compared to the inner regions of the disc, where viscous stresses due to differential rotation are much higher."1189 Thus it is. cillicult to estimate the spectrum. of the late-superhump without detailed computations., Thus it is difficult to estimate the spectrum of the late-superhump without detailed computations.1190 Therefore. it is no surprise that the discs light and spectrum are observed to change with time. as it just reflects the variable behaviour of the accretion disc.," Therefore, it is no surprise that the disc's light and spectrum are observed to change with time, as it just reflects the variable behaviour of the accretion disc."1191 Assuming that the light produced by the Lares is simply added) t0. the quiescent spectrum. which contains the secondary star and light from the accretion disc (assumed to be non-variable). the dillerence between Hare-state spectra and the quict-state spectra. vields an estimate. for. the spectrum of the Dares.," Assuming that the light produced by the flares is simply added to the quiescent spectrum which contains the secondary star and light from the accretion disc (assumed to be non-variable), the difference between flare-state spectra and the quiet-state spectra yields an estimate for the spectrum of the flares."1192 Phe actual portions of the lighteurves used to determine the Dare-state and (quiet-state spectra are marked in retIG:PLAIUEPOS and were selected after subtracting the secondary star's ellipsoidal modulation., The actual portions of the lightcurves used to determine the flare-state and quiet-state spectra are marked in \\ref{FIG:FLAREPOS} and were selected after subtracting the secondary star's ellipsoidal modulation.1193 retICESPECTTRUSM shows the resulting spectrum. which has been binned for clarity.," \\ref{FIG:FSPECTRUM} shows the resulting spectrum, which has been binned for clarity."1194 We compared the average Hare spectrum taken during the beginning and end of the night., We compared the average flare spectrum taken during the beginning and end of the night.1195 Fhey. were found to be the same to within 1.5 percent., They were found to be the same to within 1.5 percent.1196 Before the subtraction we shift the spectra into the rest. frame of the secondary. star. so that the features from the secondary are removed cleanly.," Before the subtraction we shift the spectra into the rest frame of the secondary star, so that the features from the secondary are removed cleanly."1197 The I-band mag varies on a timescale of a few hundred cays with an amplitude of 0.3 mag (LeibowitzLemar&Orio908)., The R-band mag varies on a timescale of a few hundred days with an amplitude of 0.3 mag \citep{Leibowitz98}.1198. However. since this timescale is much longer than he orbital period it is safe to assume that the lighteurve of he superhump of excess light does not change shape over he length of the orbital period.," However, since this timescale is much longer than the orbital period it is safe to assume that the lightcurve of the superhump of excess light does not change shape over the length of the orbital period."1199 The Hare spectrum has a relatively fat continuum sugeesting that a high temperature model is needed. to it the data., The flare spectrum has a relatively flat continuum suggesting that a high temperature model is needed to fit the data.1200 We attempt to fit the [lare spectrum. with iWerent models., We attempt to fit the flare spectrum with different models.

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