ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" As described in more detail in §6,, examining these lines clearly shows that the exact fraction at a given separation is strongly dependent on the choice of mass ranges used for the primary, and hence care must be taken comparing similar samples in other works to ensure they are closely-matched in primary/host properties."," As described in more detail in \ref{sec:comparison}, examining these lines clearly shows that the exact fraction at a given separation is strongly dependent on the choice of mass ranges used for the primary, and hence care must be taken comparing similar samples in other works to ensure they are closely-matched in primary/host properties."3" While there is a discrepancy of ~4% at 250 kpc between the Any Umax,host distribution (black dash-dotted) and the Simulated Clean (green dashed), this is only marginally larger than the scatter over multiple pointings in the mock galaxy catalogs, and is <lo compared to the Poisson errors in the sample."," While there is a discrepancy of $\sim 4\%$ at 250 kpc between the Any $v_{\rm max,host}$ distribution (black dash-dotted) and the Simulated Clean (green dashed), this is only marginally larger than the scatter over multiple pointings in the mock galaxy catalogs, and is $<1\sigma$ compared to the Poisson errors in the sample."4" the mass bin centered around the median Umax,hostAdditionally, for the abundance-matched sample (211 km/s; magenta line) is even closer to the Simulated Clean distribution."," Additionally, the mass bin centered around the median $v_{\rm max,host}$ for the abundance-matched sample (211 km/s; magenta line) is even closer to the Simulated Clean distribution."5" Hence, while the SDSS clean sample at first rather tuned and specific in its parameters, it is inappears fact a fairly general sample that is representative of true satellites of ~LL, hosts."," Hence, while the SDSS clean sample at first appears rather tuned and specific in its parameters, it is in fact a fairly general sample that is representative of true satellites of $\sim L_*$ hosts."6" Specifically, there is no sign that differences in halo assembly time associated with large-scale clustering have given rise to any observable bias in our isolated clean sample compared to the general halo population."," Specifically, there is no sign that differences in halo assembly time associated with large-scale clustering have given rise to any observable bias in our isolated clean sample compared to the general halo population."7 We now turn to an estimate of the 3D distribution of satellites directly from the data themselves., We now turn to an estimate of the 3D distribution of satellites directly from the data themselves.8" We start with the 2D (selection-corrected, clean profile from the right panel of Figure 5,,felean,corr) and determine the on-sky surface density in these annuli."," We start with the 2D (selection-corrected, $f_{\rm clean,corr}$ ) clean profile from the right panel of Figure \ref{fig:fracrad}, and determine the on-sky surface density in these annuli."9" From this surface density, we numerically perform an inverse Abel Transform to approximate the 3D density profile under the assumption of sphericals"," From this surface density, we numerically perform an inverse Abel Transform to approximate the 3D density profile under the assumption of spherical."10ymmetry?.. The 3D number density profile obtained by this prescription is resultingshown in Figure 9 as the (blue) points., The resulting 3D number density profile obtained by this prescription is shown in Figure \ref{fig:threedprof} as the (blue) points.11" This profile is by necessity coarsely binned to reduce numerical noise due to small number statistics, and the missing bins at small radii are due to the declining number of secondaries at radii inside the fiber radius."," This profile is by necessity coarsely binned to reduce numerical noise due to small number statistics, and the missing bins at small radii are due to the declining number of secondaries at radii inside the fiber radius."12 We also show error bars obtained from a combination of Poisson error and bootstrap resampling to simulate other choices of binning., We also show error bars obtained from a combination of Poisson error and bootstrap resampling to simulate other choices of binning.13" We fit a power law to the data (black dotted line), normalized to integrate to from the inner most point to 250 kpc, obtaining a slope of -1.8 (and normalization 6.6x 10-5)."," We fit a power law to the data (black dotted line), normalized to integrate to from the inner most point to 250 kpc, obtaining a slope of -1.8 (and normalization $6.6 \times 10^{-5}$ )."14" Also shown is the 3D of satellites of the simulated clean sample (green densitysolid profileline), normalized to match."," Also shown is the 3D density profile of satellites of the simulated clean sample (green solid line), normalized to match."15 The density profile in the simulations transitions from nearly flat core to a profile falling off as roughly r?., The density profile in the simulations transitions from a nearly flat core to a profile falling off as roughly $r^{-3}$.16" This aprofile is consistent with the Abel inverted observed a fitto a ? profile as an approximation to the profile,observed motivatingprofile."," This profile is consistent with the Abel inverted observed profile, motivating a fit to a \citet{burkert95} profile as an approximation to the observed profile."17" The resulting fit has a core radius Το=68 kpc, or log(ro/kpc)=1.8, and central number density no=1.6x1077kpc?."," The resulting fit has a core radius $r_0=68$ kpc, or $\log(r_0/{\rm kpc})=1.8$, and central number density $n_0 = 1.6 \times 10^{-7} {\rm kpc}^{-3}$."18" These estimates of the profile, however, come with the crucial caveat that the shape (particularly the presence of a core) cannot be truly constrained by the observations without a much larger"," These estimates of the profile, however, come with the crucial caveat that the shape (particularly the presence of a core) cannot be truly constrained by the observations without a much larger"19Type Ia supernovae (SNe LE) are among the most powerful events observed in the universe.,Type Ia supernovae (SNe Ia) are among the most powerful events observed in the universe.20 Their seemingly identical nature has led them to be most useful distance indicators. or standard candles. in cosmology. while their chemical enrichment of the interstellar medium is of paramount importance for the chemical evolution. of galaxies.," Their seemingly identical nature has led them to be most useful distance indicators, or standard candles, in cosmology, while their chemical enrichment of the interstellar medium is of paramount importance for the chemical evolution of galaxies."21 Large amounts of the chemical element iron (Fe) are released during a SN Ia. As an often quoted example. the present mass fraction of this element in the solar neighborhood could not be explained without the inclusion of SNe Ia in chemical evolution models.," Large amounts of the chemical element iron (Fe) are released during a SN Ia. As an often quoted example, the present mass fraction of this element in the solar neighborhood could not be explained without the inclusion of SNe Ia in chemical evolution models."22 The current consensus is that SNe la originate from the thermonuclear disruption of à white dwarf (WD) which is no longer able to support its own mass through degenerate electron pressure. as a result of approaching or exceeding the Chandrasekhar limit (seee.g.Livio2001).," The current consensus is that SNe Ia originate from the thermonuclear disruption of a white dwarf (WD) which is no longer able to support its own mass through degenerate electron pressure, as a result of approaching or exceeding the Chandrasekhar limit \citep[see e.g.][]{livio2001}."23. However. many open questions remain: whether only carbon-oxygen (C-O) WDs are involved. whether the disruption is a detonation or a deflagration. whether the event takes place at the Chandrasekhar mass or at a sub-Chandrasekhar mass. etc. (seee.g.Branchetal. 1995).," However, many open questions remain: whether only carbon-oxygen (C-O) WDs are involved, whether the disruption is a detonation or a deflagration, whether the event takes place at the Chandrasekhar mass or at a sub-Chandrasekhar mass, etc. \citep[see e.g.][]{branch1995}."24. Perhaps most importantly. even the exact progenitor system of a SN Ia has not been unambiguously established.," Perhaps most importantly, even the exact progenitor system of a SN Ia has not been unambiguously established."25 There exist different scenarios. some of them involving one degenerate object accreting from a less evolved companion imn a multiple star system. others assuming that SNe Ia are caused by the merger of two WDs.," There exist different scenarios, some of them involving one degenerate object accreting from a less evolved companion in a multiple star system, others assuming that SNe Ia are caused by the merger of two WDs."26 All of these elements can have important consequences for the applications of SNe Ia. especially for their use as standard candles.," All of these elements can have important consequences for the applications of SNe Ia, especially for their use as standard candles."27 In this work. we differentiate between the two most invoked formation scenarios for SNe Ia: the single degenerate (SD) and double degenerate (DD) model.," In this work, we differentiate between the two most invoked formation scenarios for SNe Ia: the single degenerate (SD) and double degenerate (DD) model."28 In the SD model (seee.g.Nomoto1982) a WD aceretes matter through mass transfer from a companion in a close binary system., In the SD model \citep[see e.g.][]{nomoto1982} a WD accretes matter through mass transfer from a companion in a close binary system.29 The companion can be either a late main sequence (MS) star or a red giant (RG)., The companion can be either a late main sequence (MS) star or a red giant (RG).30 In the DD model (seee.g.Iben&Tutukov1984;bink1984) the SN Ia is caused by the merger of two WDs. the combined mass of which equals or exceeds the Chandrasekhar mass.," In the DD model \citep[see e.g.][]{iben1984,webbink1984} the SN Ia is caused by the merger of two WDs, the combined mass of which equals or exceeds the Chandrasekhar mass."31 Their merger is the result of a spiral-in caused by the emission of gravitational wave radiation (GWR)., Their merger is the result of a spiral-in caused by the emission of gravitational wave radiation (GWR).32 The validity of this scenario has often been questioned. since the exact detonation mechanism is unclear.," The validity of this scenario has often been questioned, since the exact detonation mechanism is unclear."33 It has been argued that a merger may instead result in an off-center carbon ignition and the formation of a oxygen-neon-magnesium WD or a neutron star (seee.g.Saito&Nomoto1998)., It has been argued that a merger may instead result in an off-center carbon ignition and the formation of a oxygen-neon-magnesium WD or a neutron star \citep[see e.g.][]{saio1998}.34. However. by including rotation Piersantietal.(2003) have shown that the aceretor star can cool down. causing a greater expansion of its outer layers and a lowering of the critical angular velocity.," However, by including rotation \citet{piersanti2003} have shown that the accretor star can cool down, causing a greater expansion of its outer layers and a lowering of the critical angular velocity."35 This limits the mass accretion rate and prevents the occurrence of a gravitational instability. allowing mass accumulation up to the explosive central ignition of carbon. leading to à SN Ia. The question that will be addressed in this work is which of these two scenarios Is the main contributor to the SN Ia explosions observed in nature.," This limits the mass accretion rate and prevents the occurrence of a gravitational instability, allowing mass accumulation up to the explosive central ignition of carbon, leading to a SN Ia. The question that will be addressed in this work is which of these two scenarios is the main contributor to the SN Ia explosions observed in nature."36 In order to do this. a comparison with observations ts obviously necessary.," In order to do this, a comparison with observations is obviously necessary."37 Observational studies of the distribution of delay times of SNe la can be used to constrain theoretical models for their progenitors and formation scenarios (seee.g.Mannuecietal.2006)., Observational studies of the distribution of delay times of SNe Ia can be used to constrain theoretical models for their progenitors and formation scenarios \citep[see e.g.][]{mannucci2006}.38. Totantetal.(2008). selected 65 supernova candidates at redshifts from 0.4 to 1.2 (corresponding to a light travel time of 0.1 to 8.0 Gyr). of which they demonstrate that at least must be SNe la. These events were selected from old galaxies of the elliptical type. in which star formation has long ceased almost completely.," \citet{totani2008} selected 65 supernova candidates at redshifts from 0.4 to 1.2 (corresponding to a light travel time of 0.1 to 8.0 Gyr), of which they demonstrate that at least must be SNe Ia. These events were selected from old galaxies of the elliptical type, in which star formation has long ceased almost completely."39 Hence. the selected samples are equivalent to (passively evolving) starburst galaxies for the determination of the delay time of SNe Ia. and can be used for that purpose.," Hence, the selected samples are equivalent to (passively evolving) starburst galaxies for the determination of the delay time of SNe Ia, and can be used for that purpose."40 The thus obtained observational delay time distribution (DTD) can then be directly compared to the theoretically predicted DTDs for starbursts., The thus obtained observational delay time distribution (DTD) can then be directly compared to the theoretically predicted DTDs for starbursts.41 While Totanietal.(2008) make the implicit assumption that the DTDs are independent of metallicity. the samples are expected to be contained within the range 1.0 to 2.5 times solar metallicity. so any metallicity effect should be limited and certainly less than an order of magnitude (as will be shown later).," While \citet{totani2008} make the implicit assumption that the DTDs are independent of metallicity, the samples are expected to be contained within the range 1.0 to 2.5 times solar metallicity, so any metallicity effect should be limited and certainly less than an order of magnitude (as will be shown later)."42 Also. it is assumed that the average age of local elliptical galaxies is 11 Gyr. and for those the authors adopt the SN Ia rate observed for such galaxies by Mannuceietal. (2005)..," Also, it is assumed that the average age of local elliptical galaxies is 11 Gyr, and for those the authors adopt the SN Ia rate observed for such galaxies by \citet{mannucci2005}. ."43 A striking feature of the thus obtained observational, A striking feature of the thus obtained observational44mentioned above. duriug which the flux drops bv754.,"mentioned above, during which the flux drops by."45. We also computed the ratio of counts iu the 26 aud 6 keV euergv bands. which is displaved iu the bottom panel of Figure 3..," We also computed the ratio of counts in the 2–6 and 6--8 keV energy bands, which is displayed in the bottom panel of Figure \ref{fig:prof}."46 This dip appears to be accompanied by a slieht softening of the spectrum. although a \? test ouly allows us to reject the hypothesis that the harduess is coustant at the confidence level.," This dip appears to be accompanied by a slight softening of the spectrum, although a $\chi^2$ test only allows us to reject the hypothesis that the hardness is constant at the confidence level."47 As we discuss iu LL. the dips in the light curve of pprobablv result frou structures in the outer accretion disk that obscure the ceutral N-rav cluitting reeion.," As we discuss in 4, the dips in the light curve of probably result from structures in the outer accretion disk that obscure the central X-ray emitting region."48 Next. we extracted and modeled the spectrum of290031.," Next, we extracted and modeled the spectrum of."49.. We produced source aud background spectra from the respective ονο lists by computing the histogram over pulse height (euergv)., We produced source and background spectra from the respective event lists by computing the histogram over pulse height (energy).50 We, We51of a detailed sticking and destruction model [ον collisions the extra complication involved wilh using a spectrum does nol guarantee exira precision for the present caleulation.,of a detailed sticking and destruction model for collisions the extra complication involved with using a spectrum does not guarantee extra precision for the present calculation.52 To encapsulate (he unknown phvsies of dust-dust interactions. we presume that a collision between two dust eras has a probability. p to result in sticking.," To encapsulate the unknown physics of dust-dust interactions, we presume that a collision between two dust grains has a probability $p$ to result in sticking."53 If such a collision does not result in sticking the grains ave presumed to be unchanged., If such a collision does not result in sticking the grains are presumed to be unchanged.54 Accordingly we can see that. 2 iN Tods the dust-dust collisionM rate then 74Í=ping- and so using. the equation. for. mara).4 As dust grain size is a Κον parameter whose change as a function of the distance from the star we investigate. we will require that dust grains do not significantly migrate radially.," Accordingly we can see that, if $N$ is the dust-dust collision rate then $\frac {dm_d}{dt}=pNm_d$ and so using the equation for $m_d(r_d)$, As dust grain size is a key parameter whose change as a function of the distance from the star we investigate, we will require that dust grains do not significantly migrate radially."55" A simple ""particle-in-a-box collision model implies that where {1 is the dust dise scale height. p and X, are the dust dise volume and surface densities. Q is the orbital angular velocity and οὓς is the dust-dust collisional velocity."," A simple “particle-in-a-box” collision model implies that where $H_d$ is the dust disc scale height, $\rho$ and $\Sigma_d$ are the dust disc volume and surface densities, $\Omega$ is the orbital angular velocity and $v_c$ is the dust-dust collisional velocity."56" The dust and gas scale heights need not be equal. the latter being given by /7,—cQ.!. where c; is (he gas thermal speed."," The dust and gas scale heights need not be equal, the latter being given by $H_g=c_s \Omega^{-1}$, where $c_s$ is the gas thermal speed."57 We can also define a velocity 0;=H4; and wrile Eq., We can also define a velocity $v_h=H_d \Omega$ and write Eq.58 2 in terms of a non-«dimensional ratio c./04., \ref{2} in terms of a non-dimensional ratio $v_c/v_h$.59 Our method of handling turbulence lends itself more readily to Eq., Our method of handling turbulence lends itself more readily to Eq.60 2. however., \ref{2} however.61 If the velocities of the dust grains are uncorrelated. (hen their collisional velocity ο is also their random: velocity dispersion ancl so. akin to the formula for the eas scale heieht Hy=¢./Q. we have that dust scale height My—0/0.," If the velocities of the dust grains are uncorrelated, then their collisional velocity $v_c$ is also their random velocity dispersion and so, akin to the formula for the gas scale height $H_g = c_s/\Omega$, we have that dust scale height $H_d = v_c/\Omega$."62 If the ratio οΗμ in Eq., If the ratio $v_c/H_d$ in Eq.63" 2. is independent of grain size ry. then NVer,Fo"," \ref{2} is independent of grain size $r_d$, then $N \sim r_d^{-1}$."64" For e.=QU, and pa=loom7? the growth rate from Eq. 1.."," For $v_c=\Omega H_d$ and $\rho_d= 1 \rm {gcm}^{-3}$ the growth rate from Eq. \ref{1},"65 oucLOTCan)͵ “is independent of dust size and the formation of meter sized bodies will occur in ~1 vear., $\frac {dr_d}{dt} \simeq 107 \left( \frac {R}{\rm {1AU}} \right)^{-3} \frac {\rm cm}{\rm yr}$ is independent of dust size and the formation of meter sized bodies will occur in $\sim 1$ year.66 As without. turbulence. gravitational instabilitv of the dise will occur for sub-centimeter sized erains (Eq. 74)):," As without turbulence, gravitational instability of the disc will occur for sub-centimeter sized grains (Eq. \ref{R33End}) );"67 Uis process occurs well within the {ime scales required by existing constraints (e.g. D'Alessioetal. (2005))) even considering seltling limes., this process occurs well within the time scales required by existing constraints (e.g. \citet{d'Alessio05}) ) even considering settling times.68" If, however we allow the velocities of the dust. grains to be correlated. as would occur for grains in the same eddy. (here is no reason to presume (hat e,=Off, or that ο. aud Ly are even closely related."," If, however we allow the velocities of the dust grains to be correlated, as would occur for grains in the same eddy, there is no reason to presume that $v_c=\Omega H_d$ or that $v_c$ and $H_d$ are even closely related."69 If the dust couples stronely to the gas and the turbulence causes, If the dust couples strongly to the gas and the turbulence causes70of this distribution. and we consider a fit values more than one standard deviation away from the best fit to be sienificautly worse.,"of this distribution, and we consider a fit values more than one standard deviation away from the best fit to be significantly worse."71 However. this technique was biased against time bius that may truly contain no star formation. since such bins can never have an impact on the CMD regardless of their duration.," However, this technique was biased against time bins that may truly contain no star formation, since such bins can never have an impact on the CMD regardless of their duration."72 Therefore if we found a time biu (or set of adjacent time bins) whose exclusion from the fit did not significantly chauge the fit quality. but that was simrounded by time bins whose exclusion from the fit did sienificautly change the fit quality. we allowed the time yn to remain incependcut. as a possible quiescent period in the SFI.," Therefore if we found a time bin (or set of adjacent time bins) whose exclusion from the fit did not significantly change the fit quality, but that was surrounded by time bins whose exclusion from the fit did significantly change the fit quality, we allowed the time bin to remain independent, as a possible quiescent period in the SFH."73 For example. consider 3 adjacent time bius A.B. and €. and asstmue the exclusion of time bin B had 10 Significant impact on the fit.," For example, consider 3 adjacent time bins A, B, and C, and assume the exclusion of time bin B had no significant impact on the fit."74 If the exclusiou of bin A jegativelv affected the fit aud the exclusion of bin € also deeraded the fit. then we infer that Bois within a time xeriod that is well-sampled iu the €CMD.," If the exclusion of bin A negatively affected the fit and the exclusion of bin C also degraded the fit, then we infer that B is within a time period that is well-sampled in the CMD."75 In such a case. we do not merge bin D with bin A or biu C. even though D inav uot contain any star formation.," In such a case, we do not merge bin B with bin A or bin C, even though B may not contain any star formation."76 In this wav. we allow bins to contain no star formation.," In this way, we allow bins to contain no star formation."77 The results of our time bin determination tests were qualitatively what would be expected., The results of our time bin determination tests were qualitatively what would be expected.78 For the shallowest photometry of the INNER-1 region. we have ouly two statistically mcanimeful age bius for all stars 22300 My.," For the shallowest photometry of the INNER-1 region, we have only two statistically meaningful age bins for all stars $>$ 300 Myr."79 With the dust and crowding problems in this portion of the galaxy. the IIe-burning sequences bleud with the RGD at εκτ~0X which corresponds toages of ~200 Myr.," With the dust and crowding problems in this portion of the galaxy, the He-burning sequences blend with the RGB at $M_{F814W}\sim-3$, which corresponds toages of $\sim$ 200 Myr."80 Furthermore. with the overlapping features and spread in ROB color from both the large photometiy errors from crowding and siguificaut internal extinction. the detailed age distribution of older stars from the RGB should uot be reliable. as indeed our time bin tests reveal.," Furthermore, with the overlapping features and spread in RGB color from both the large photometry errors from crowding and significant internal extinction, the detailed age distribution of older stars from the RGB should not be reliable, as indeed our time bin tests reveal."81 For the less crowded and less dusty regions of the INNER field. we found that we could use 2 age bius for ages 22 Gyr (210 Gyr aud 1011 Car).," For the less crowded and less dusty regions of the INNER field, we found that we could use 2 age bins for ages $>$ 2 Gyr (2–10 Gyr and 10–14 Gyr)."82 The independence of these two bins may be due to variations iu the ratio of ACB to RGB stars aud the slope of the RGB., The independence of these two bins may be due to variations in the ratio of AGB to RGB stars and the slope of the RGB.83 A vounger ROB (<10 Cx) is slightly bluer. las a slightly steeper slope aud a higher ACB/RGB ratio than zu older ROB (210 Cx).," A younger RGB $<$ 10 Gyr) is slightly bluer, has a slightly steeper slope and a higher AGB/RGB ratio than an older RGB $>$ 10 Gyr)."84 For the deep OUTER photometiv. there is more information encoded iu the CAID due to the presence of the older stellar populations that dominate the τος chunp.," For the deep OUTER photometry, there is more information encoded in the CMD due to the presence of the older stellar populations that dominate the red clump."85 These features provide additional coustraiuts ou the SER aud allow shorter biu divisious at ages 71 Cor., These features provide additional constraints on the SFR and allow shorter bin divisions at ages $>$ 1 Gyr.86 The uncertainties in the derived inetallicities fei to be largest at voung ages (100 Myr). where the ouly iuectallicitv iuforiuation comes from the short-livec IIe-burnius sequences.," The uncertainties in the derived metallicities tend to be largest at young ages $<$ 100 Myr), where the only metallicity information comes from the short-lived He-burning sequences."87 These features tend to contain a relatively small nunuber of stars. and the effects of ietallicitv on these features is not well uuderstood iu stellar evolution models2009).," These features tend to contain a relatively small number of stars, and the effects of metallicity on these features is not well understood in stellar evolution models."88. Overall we are able to obtain very reliable estimates of the relative coutributions of stars of old (10 ο). intermediate (2LO Cir). aud vouneg (1 Cwr) ages despite unavoidable sources of uncertainty.," Overall we are able to obtain very reliable estimates of the relative contributions of stars of old $>$ 10 Gyr), intermediate (2–10 Gyr), and young $<$ 1 Gyr) ages despite unavoidable sources of uncertainty."89 We likewise have reliable metallicities covering all but the vouugest ages and high time resolution at voune ages LL 300 Aba), We likewise have reliable metallicities covering all but the youngest ages and high time resolution at young ages $\lap$ 300 Myr).90 The cumulative age distribution is particularly stable against the uncertainties at intermediate ages. because the star formation rates in adjacent tine bius are typically auti-correlated such that some fraction of the star formation will move back and forth between adjacent bius cepeuding ou simall chauges in the overall solution.," The cumulative age distribution is particularly stable against the uncertainties at intermediate ages, because the star formation rates in adjacent time bins are typically anti-correlated such that some fraction of the star formation will move back and forth between adjacent bins depending on small changes in the overall solution."91 Therefore we plot the cumulative distribution at the full resolution of the CMD fit., Therefore we plot the cumulative distribution at the full resolution of the CMD fit.92 The SFIIs of all of our regions are shown in Figures -1U.., The SFHs of all of our regions are shown in Figures \ref{sfr}- \ref{cum}.93 We first describe the most notable features of the results for cach region. before discussing the integrated evolution of the galaxy iu ??..," We first describe the most notable features of the results for each region, before discussing the integrated evolution of the galaxy in \ref{discussion}."94 The outer disk of NGC 2976 appears to he dominated by an old (6Z 8 Cr). intermecdiate-etallicity -1-0.5)) population. much like other outer disks.αι thick disks. aud iuner halos of ellipticals2009).," The outer disk of NGC 2976 appears to be dominated by an old $\gap$ 8 Gyr), intermediate-metallicity ) population, much like other outer disks, thick disks, and inner halos of ellipticals."95. About of its outer disk stars were formed bv :~L1 (see Figure 101)., About of its outer disk stars were formed by $z\sim1$ (see Figure \ref{cum}) ).96" This age is consistent with the mean age of the M33 outer disk2007).. which has a similar mass (V,c9110 kins tows. Vo85 kins | for NGC 2976),"," This age is consistent with the mean age of the M33 outer disk, which has a similar mass $_c\sim110$ km $^{-1}$ vs. $_c\sim85$ km $^{-1}$ for NGC 2976)."97 While the SEFII of the outer disk of NGC 2976 is consistent with roughly constant star formation over much of the age of the universe. in the last Car there has been a significant decline.," While the SFH of the outer disk of NGC 2976 is consistent with roughly constant star formation over much of the age of the universe, in the last Gyr there has been a significant decline."98 Indeed. its recent star formation rate has been more than a factor of 5 lower than average for the past συ Myr and more than a factor of 50 lower than average over the past ~300 Myr.," Indeed, its recent star formation rate has been more than a factor of 5 lower than average for the past $\sim$ 800 Myr and more than a factor of 50 lower than average over the past $\sim$ 300 Myr."99 No areas of current star formation are apparent in the GALEN UV image or in deep Πα images from SINGS2003).. which is consistent with our measurements.," No areas of current star formation are apparent in the GALEX UV image or in deep $\alpha$ images from SINGS, which is consistent with our measurements."100 Iu fact. the mean age of the stars formed im the past Cr is 4104150 Myr. aud 10 stars vounger than 130 Myr are required to produce an acceptable fit to the observed CMD (as determined w the statistical time bin tests described in 2.1.2).," In fact, the mean age of the stars formed in the past Gyr is $\pm$ 150 Myr, and no stars younger than 130 Myr are required to produce an acceptable fit to the observed CMD (as determined by the statistical time bin tests described in 2.4.2)."101 Although there are few young stars present in the outer disk. there is some question as to their origin.," Although there are few young stars present in the outer disk, there is some question as to their origin."102 These stars uav have formedsite. or they may have scattered rom the ier disk.," These stars may have formed, or they may have scattered from the inner disk."103 If they formed iu the outer disk. hey may show some sigus of clustering.," If they formed in the outer disk, they may show some signs of clustering."104 However. as we show in Figure 11.. where we plot the spatial distribution of upper nain-sequence stars in this field (cefined as 2]«FSIIW<26 and 0.25<FOOOITΕδιι« 0.05. or equivalently 5M.S&SM&12 ALL). these voung y.ars are not found in clusters outside of the iuuer disk (seen in the lower-left edge of Figure 113).," However, as we show in Figure \ref{xy}, where we plot the spatial distribution of upper main-sequence stars in this field (defined as $24<F814W<26$ and $-0.25<F606W-F814W<0.05$ , or equivalently $5\,M_{\odot}\lap\,M\,\lap12\,M_{\odot}$ ), these young stars are not found in clusters outside of the inner disk (seen in the lower-left edge of Figure \ref{xy}) )."105 The voungest stars appear smeothlv distributed., The youngest stars appear smoothly distributed.106 A 2-d Nolinoeorov-Suiüruov docs not show a significant difference between je distributions of the upper main sequence stars and jo red eiauts in the OUTER field (onlv probability at the parent distributions are different, A 2-d Kolmogorov-Smirnov does not show a significant difference between the distributions of the upper main sequence stars and the red giants in the OUTER field (only probability that the parent distributions are different).107 We beleve that the most plausible ).origin for the voungest stars we observe in these outer regious is that rev were born m very small clusters that dissolved ou short timescales., We believe that the most plausible origin for the youngest stars we observe in these outer regions is that they were born in very small clusters that dissolved on short timescales.108 Typical small clusters with low star oration efficiency dissolve on timescales «100 Myr 2003). casily short enough to accouut or the few voung stars we observe.," Typical small clusters with low star formation efficiency dissolve on timescales $\ll$ 100 Myr , easily short enough to account for the few young stars we observe."109 However. we caunot conclusively determine if their birth clusters were within he outer disk.," However, we cannot conclusively determine if their birth clusters were within the outer disk."110 Loweranass stars formed iu the same, Lower-mass stars formed in the same111"denoted as pr,qp. are the sanie iu all cases.","denoted as $\mpklrcp$, are the same in all cases."112 This also happens with the values of προς aud the standard deviations of PL: denoted as DE," This also happens with the values of $\smpklclassp$ and the standard deviations of $\mpklrcp$ , denoted as $\smpklrcp$."113 This indicates that the ML. method docs not iutroduce systematic effects ou the results., This indicates that the ML method does not introduce systematic effects on the results.114" We now exauine how well the ML aud classical iicthods recover the input probabilities p,;,, wheu non-uull experimental errors are included im the svuthetic catalogs.", We now examine how well the ML and classical methods recover the input probabilities $\pklrp$ when non-null experimental errors are included in the synthetic catalogs.115 We use the W=1000 source catalogs as an example. which is representative of the general trouds," We use the $N=1000$ source catalogs as an example, which is representative of the general trends."116 The results are shown iu Figure 1l. and are tabulated iu Table 5.," The results are shown in Figure 1, and are tabulated in Table 5."117" It is clear frou Figure 1 that pj, (erosses). recover the η probabilitk⋅5 abilities»Pn jj,sode circles)eaveloe) im41) all cases,yep iptincluding those in which the (blackinserted errors are as large as the bin size (panels e)."," It is clear from Figure 1 that $\pklrcp$ (crosses), recover the input probabilities $\pklrp$ (black circles) in all cases, including those in which the inserted errors are as large as the bin size (panels $c$ )."118" From Table 5 we see that the values of 55,4, always lay. within the confidence interval of the AIL method. defined bv. [aarpSeaPe|Prud: "," From Table 5 we see that the values of $\pklrp$ always lay within the confidence interval of the ML method, defined by $[\mpklrcp - \smpklrcp, \mpklrcp + \smpklrcp]$."119This shows that the ML method ds reliable., This shows that the ML method is reliable.120 lu contrast. the probabilities Pls derived from the classical histogram (gray triangles in Figure 1) systematically deviate from the iuput ↻↥⋅∪⋝⋜∏⋝∐↕↑↕↸∖," In contrast, the probabilities $\pklclassp$ derived from the classical histogram (gray triangles in Figure 1) systematically deviate from the input probabilities."121↴∖↴∙↕⋟↥⋅∪↴⋝⋜∏⋝∐↕↑↕↸∖↴∖↴⋜∐⋅↸∖↴∖↴⋅↖↽↴∖↴↑↸∖⋯⋜↧↑↕↸⊳⋜↧∐⋅↖⇁ nnderestimatedoverestimated im the low/high-axviuuuetry bius (upper/lower panels}. due to a spill-over from the most populated bius (low axviunetries) to the least populated. hielhi-asviunietry bins.," Probabilities are systematically underestimated/overestimated in the low/high-asymmetry bins (upper/lower panels), due to a spill-over from the most populated bins (low asymmetries) to the least populated, high-asymmetry bins."122 Such deviatiousincrease for larger experimental errors., Such deviations increase for larger experimental errors.123 When the errors are as large as the bin size. spil-over is so pronouuced that the probabilities in the hieli-asvaumietry sample (ower rielit panel) are nearly equal for the three redshift bius. aud all information ou the redshitt variation of the galaxy inergor fractions is lost.," When the errors are as large as the bin size, spill-over is so pronounced that the probabilities in the high-asymmetry sample (lower right panel) are nearly equal for the three redshift bins, and all information on the redshift variation of the galaxy merger fractions is lost."124 We couclude that the AIL method is au uubiased. estimator. of. the iuput. distribution., We conclude that the ML method is an unbiased estimator of the input distribution.125. To: put this statement iia more quautitative basis. we carry out a Studeut’s t-test," To put this statement ina more quantitative basis, we carry out a Student's t-test"126 which grows algebraically for Ri<0.,", which grows algebraically for ${\rm Ri} < 0$."127 The disturbance grows exponentially only for Ri«—3/I., The disturbance grows exponentially only for ${\rm Ri} < -3/4$.128 For a semi-iufinite flow. the power-law behavior in time holds for —2<Ri1/1. with exponential erowth for Ri<—2.," For a semi-infinite flow, the power-law behavior in time holds for $-2 < {\rm Ri} < 1/4$, with exponential growth for ${\rm Ri} < -2$."129 These results illustrate the importance of boundary coucitious in determining stability., These results illustrate the importance of boundary conditions in determining stability.130 In the &.=0 limit that we are concerned with here. the correspondence between the clisk and atmospheric inodels turus out to be exact in the sliwave formalisin.," In the $k_z = 0$ limit that we are concerned with here, the correspondence between the disk and atmospheric models turns out to be exact in the shwave formalism."131 This is because the Coriolis ] ↕∐↩∏⊔≺↵≺↵∖⊽∩↥⋯↕∩∐∩↥∎⊳∖∐∖∖↽⋜↕∖⊽≺↵⊳∖↥∐∣≻∩↕∐⋜↕↕⋅⋜∥∐⋜↕∐⊽∖⇁−⊳∖↕↓⋅⋜↕↕∐↕≺↵≺⇂≼∐⊳∖↕⊆⋜↕∐≺⇂⋜↕⊳∖∐≺↵⋜⋃⋅↕∐∑≟⋅⊳∖⋃⋅⋜↕↕," This is because the Coriolis force only appears in equation \ref{BOUSSVX}) ) via $\tilde{\kappa}^2$, which disappears when $k_z = 0$."132"∐∎∐↵≺⇂⋜↕⋃∐∩⊳∖↥↽≻∐≺↵⋅≺↲ . . pe ⋅ ⋅ ⋅ ⋅ ⋅⋅ ↥∩⊓∙≺↵∩∐↥⊽∖⊽⋜↕↥↽≻↥↽≻↩⋜⋃⋅⊳∖↓∐≺↵≺↽↓⋃⋜↕⊔∩∐⋖↜∙↗∙↗⊔∖⊽↓⋜↕↾∙⋅−⋅∖∖↽⇂⊔∢∙↥⊔↥⊳∖⋜↕↥↽≻↥↽≻≺↲⋜⋃⋅⊳∖∖∖↽∐≺↵∐∣⋅⋮↼∙∶∪⋅⊺∐≺↵≺↵≺↽↓⋃⋜↕⋃∩∐≺⇂≺↲⊳∖∢∙⊔∣∐∑≟ is thus ου, Lj a2/ ; PIER ο} δή"," The equation describing the time evolution of shwaves in both a radially-stratified disk and a shearing, stratified atmosphere is thus ^2 _x + 4 _x k_y _x + (N_x^2 + ^2 v_x = 0."133μο We analyze the solutious to this equation iu the following section., We analyze the solutions to this equation in the following section.134" Changing time variables in equation (72)) to 7=&y/hy,. the differential equation governing ov, becomes (1 | | (Ri| 2)8r, = 0."," Changing time variables in equation \ref{BOUSSVX2D}) ) to $\tilde{\tau} \equiv \tilde{k}_x/k_y$ , the differential equation governing $\delta v_x$ becomes (1 + + 4 + + v_x = 0."135(63) ⊺∐≺↵⊳∖∩∐⊔↥∩∐⊳∖↕∩≺↵≺↽↓⋯↕∏∩∐⋖∫⋅∙↗⋅∙≱⋝⋝⋜↕↓⋅≺↵∐⊽∖⊽↥↽≻≺↵↕⋅∑∸≺↵∩⋯≺↵↕∏∢, The solutions to equation \ref{ODE}) ) are hypergeometric functions.136∙↥∎⋃∐∢∙⋃∩∐⊳∖⋅∖↾∖⊽∐∐↕∐≺↵∢∙∐⋜↕∐∑∸↩∩↥∎∖⊽⋜⋃⋅↥⋜↕∣≻↥≺↵⊳∖ m=- —7-. equation. fe (?2)) becomes 2Q(6I) ," With the change of variables $z \equiv137-\tilde{\tau}^2$ , equation \ref{ODE}) ) becomes + - v_x = 0."138"The hypergeometric equation(Abramowitz&Stegun1972) abde, 0(62) has as its two linearly independentsolutions F(a.b:e::) and 2!F(a—e41.6—6e41:2—6:z "," The hypergeometric equation\citep{as72}139 + - v_x = 0 has as its two linearly independentsolutions $F(a,b;c;z)$ and $z^{1-c}140F(a-c+1,b-c+1;2-c;z)$ ."141Comparison of equations (?2)) and (??)) shows that a=(3 αι. b—(3a)/IE aud e—1/: where a is defiued in equation (??)).," Comparison of equations \ref{ODEZ}) ) and \ref{HGEQ}) ) shows that $a = (3 - \alpha)/4$ , $b = (3 + \alpha)/4$ and $c = 1/2$ , where $\alpha$ is defined in equation \ref{ALPHA}))."142rom the host galaxy assuming that the hosts lie on. the A oz relation for 3€ radio galaxies determined by SRL.,from the host galaxy assuming that the hosts lie on the $K$ $z$ relation for 3C radio galaxies determined by SRL.143 We assume the colours of a αν old. stellar. population rom the GISSEL9G6 models of Bruzual Charlot (1993. 1990). and. fine that the hosts typically contribute of the measured Hux.," We assume the colours of a 4-Gyr old stellar population from the GISSEL96 models of Bruzual Charlot (1993, 1999), and find that the hosts typically contribute of the measured flux."144 We also remove the contribution to he photometry from the Ha. emission. line assuming an equivalent width of 448+142 for la. determined. from the 0.1Hocld quasars of Ixapahi et ((1998) ancl Baker et (1999).," We also remove the contribution to the photometry from the $\alpha$ emission line assuming an equivalent width of $448145\pm 142$ for $\alpha$, determined from the $0.1 \leq R < 1$ quasars of Kapahi et (1998) and Baker et (1999)."146 This range of racio core dominance is appropriate for our stecp-speetrum sample., This range of radio core dominance is appropriate for our steep-spectrum sample.147 Following the usual procedure (e.g... Neugebauer ct 11987). we fit the SED of each. quasar as two power-laws which meet at Lym. We denote the spectral index of the power-law in the rest-[rame optical as api. and that in the infrared as ayy.," Following the usual procedure (e.g., Neugebauer et 1987), we fit the SED of each quasar as two power-laws which meet at $1\,\mu$ m. We denote the spectral index of the power-law in the rest-frame optical as $\alo$, and that in the infrared as $\ahi$."148 To the new data presented in this paper. we add SlL's photometry of 3€ 22 and 3C 41 which. as those authors showed. are more correctly classified: as quasars than radio galaxies.," To the new data presented in this paper, we add SRL's photometry of 3C 22 and 3C 41 which, as those authors showed, are more correctly classified as quasars than radio galaxies."149" Le is of course important to remember that the distinction between “quasars” ancl ""racio galaxies” is not clear-cut and objects such as 3€ 65 and ος 265 could also be considered as quasars.", It is of course important to remember that the distinction between “quasars” and “radio galaxies” is not clear-cut and objects such as 3C 65 and 3C 265 could also be considered as quasars.150" As the qualiE of available data improves. perhaps probing dust. columns larger than chy&15 mmae. more 7radio galaxies"" are likely to be reclassified as quasars."," As the quality of available data improves, perhaps probing dust columns larger than $A_V \approx15115$ mag, more “radio galaxies” are likely to be reclassified as quasars."152 For the purposes of this study. however. we are interested. in sources whose continua at Avoc9dl gam are predominantly. non-stellar.," For the purposes of this study, however, we are interested in sources whose continua at $\lambda_{\rm rest} \sim 1\,\mu$ m are predominantly non-stellar."153 The results of our fitting are listed in Table 2) and shown eraphically in Fig. 1.., The results of our fitting are listed in Table \ref{tab:fits} and shown graphically in Fig. \ref{fig:fits}.154 Since 3€ 68.1 is not a member of the complete sample. we exclude it [rom the following analyses. although we continue to indicate iis location on plots.," Since 3C 68.1 is not a member of the complete sample, we exclude it from the following analyses, although we continue to indicate its location on plots."155 We likewise exclude 3€ 22 and 3€ 41. since their observed: properties are highly influenced by significant internal extinction.," We likewise exclude 3C 22 and 3C 41, since their observed properties are highly influenced by significant internal extinction."156 In Lis., In Fig.157 2 we show the distribution of spectral indices., \ref{fig:alpha} we show the distribution of spectral indices.158 Analysis reveals no significanto correlation between a...1 aud au Clable 3))., Analysis reveals no significant correlation between $\alo$ and $\ahi$ (Table \ref{tab:correl}) ).159 Of. particular note are the six objects with, Of particular note are the six objects with160The determination of the stellar Initial Mass Function (AIF) has been a prominent goal of astronomy for over 50 vears.,The determination of the stellar Initial Mass Function (IMF) has been a prominent goal of astronomy for over 50 years.161 The IME. YCAL). describes the number of stars born per unit mass per unit volume.," The IMF, ${\Psi}(M)$, describes the number of stars born per unit mass per unit volume."162 The pioneering study by Salpeter(1955) was limited to stars wilh masses greater (han 0.3M..., The pioneering study by \citet{salp} was limited to stars with masses greater than $0.3~M_{\odot}$.163 Salpeter lound (hat the results were well represented bv a power law. VOW)xM.. with a=2.35.," Salpeter found that the results were well represented by a power law, $\Psi(M) \propto M^{-\alpha}$, with $\alpha = 2.35$."164 Two decades later. Miller&Sealo(1979) used improved observations of lower luminosity stars to show that the IAIF deviates from a simple power law below 1M..," Two decades later, \citet{ms79} used improved observations of lower luminosity stars to show that the IMF deviates from a simple power law below $1~M_{\odot}$."165 Thev derived a better fit. with a log-normal distribution. V(M)xexp(SRTesyo with Ady~0.15M... 60~0.6. and a distribution close to the Salpeter power-law al masses exceeding 1.M..," They derived a better fit with a log-normal distribution, $\Psi(M) \propto \exp{(\frac{\log(M) - \log(M_0)}{\sqrt{2}\sigma})^{2}}$, with $M_0 \sim 0.15~M_\odot$, $\sigma \sim 0.6$, and a distribution close to the Salpeter power-law at masses exceeding $1~M_{\odot}$."166 The change in slope at lower masses is evident both in field-star survevs and in observations of voung open clusters (e.g.. Scalo(1998))).," The change in slope at lower masses is evident both in field-star surveys and in observations of young open clusters (e.g., \citet{scalo98}) )."167 More recent studies (Reid&Gizis1997:INroupa2001:Reid.Gizis.Lawley2003). [avor modeling the field-star INIF using multiple power-laws. wilh à~2.3 al M>1M. and αc1 αἱ lower masses.," More recent studies \citep{rg97,kru,inr03} favor modeling the field-star IMF using multiple power-laws, with $\alpha \sim 2.3$ at $M> 1~M_\odot$ and $\alpha \sim 1$ at lower masses."168 Extending coverage to masses close (ο and below the hvdrogen-burning limit has only become possible within the last decade. as improvements in detector and computational technologies have permitted the first high-sensitivity. wide-field near-infrared sky surveys.," Extending coverage to masses close to and below the hydrogen-burning limit has only become possible within the last decade, as improvements in detector and computational technologies have permitted the first high-sensitivity, wide-field near-infrared sky surveys."169 Analvsis of those surveys has led to the discovery of a host of very low-mass ultracool dwarfs (IXxirkpatricketal.2000:Durgasser2002:Geballe2002) and the first estimate of the brown dwarf mass function in the field (Reidetal.1999).," Analysis of those surveys has led to the discovery of a host of very low-mass ultracool dwarfs \citep{kp00,burg02,geb02} and the first estimate of the brown dwarf mass function in the field \citep{inr99}."170. There are a munber of complications in deriving V(AM) [or substellar mass objects., There are a number of complications in deriving $\Psi(M)$ for substellar mass objects.171 Mass is generally not observed directly. but is estimated from the measured. luminosity.," Mass is generally not observed directly, but is estimated from the measured luminosity."172 In (he case of main-sequence stars this caleulation is relatively s(raighUorwarel. since hydrogen fusion leads to a well defined mass-Inminositv relation.," In the case of main-sequence stars this calculation is relatively straightforward, since hydrogen fusion leads to a well defined mass-luminosity relation."173 Brown dwarls. however. lack a stable. long-term energv source. and. as a result. evolve rapidly (o lower temperatures and lower luminosities.," Brown dwarfs, however, lack a stable, long-term energy source, and, as a result, evolve rapidly to lower temperatures and lower luminosities."174 Thus. the substellar Iuminosity. function depends strongly on both mass and age.," Thus, the substellar luminosity function depends strongly on both mass and age."175 Moreover. the presence of broad spectral absorption features stemmune Irom (he onset ol molecule and dust eloud formation ean lead to significant changes in broadband. absolute magnitudes over small ranges of effective temperature.," Moreover, the presence of broad spectral absorption features stemming from the onset of molecule and dust cloud formation can lead to significant changes in broadband absolute magnitudes over small ranges of effective temperature."176 Finally. short periods of deuterium fusion occur in objects with masses greater than 13M. leading to further transient effects in the huminosity. funetion.," Finally, short periods of deuterium fusion occur in objects with masses greater than $13~M_J$, leading to further transient effects in the luminosity function."177 We invert the problem., We invert the problem.178 Starling with an assumed mass function aud age distribution. we combine theoretical predictions of the evolution of very low-mass dwarfs from the models computed by Burrowsetal.(2001). with empirical estimates of bolometric corrections from Dahnetal.(2002). and Reid&Cruz(2002) to predict laminosity functions for voung (5 Myr to | Gyr) elusters.," Starting with an assumed mass function and age distribution, we combine theoretical predictions of the evolution of very low-mass dwarfs from the models computed by \citet{bur} with empirical estimates of bolometric corrections from \citet{dahn} and \citet{rc} to predict luminosity functions for young (5 Myr to 1 Gyr) clusters."179 Young clusters are convenient for mass function studies because they, Young clusters are convenient for mass function studies because they180"elements (Martin,Livi,&Wang1985).",elements \citep{Martin1985}.181". This flux cancellation is essential to the process of replacement of old magnetic flux with newly emerging flux in the quiet Sun on a timescale of a few days (Schrijveretal.1997;Hagenaar2001),, and also to the process of removal of sunspot magnetic flux from the photosphere (Kuboetal.2008)."," This flux cancellation is essential to the process of replacement of old magnetic flux with newly emerging flux in the quiet Sun on a timescale of a few days \citep{Schrijver1997, Hagenaar2001}, and also to the process of removal of sunspot magnetic flux from the photosphere \citep{Kubo2008}."182". Various possible processes have been proposed to explain the observed flux cancellation (e.g.Zwaan1987;Ryutovaetal.2003),, involving submergence (retract) of Q-shaped loops or emergence of U-shaped loops across the photosphere."," Various possible processes have been proposed to explain the observed flux cancellation \citep[e.g.][]{Zwaan1987, Ryutova2003}, involving submergence (retract) of $\Omega$ -shaped loops or emergence of U-shaped loops across the photosphere."183" In both cases, the canceling magnetic elements correspond to the two intersections of such loops with the photospheric layer."," In both cases, the canceling opposite-polarity magnetic elements correspond to the two intersections of such loops with the photospheric layer."184 The opposite-polarity magnetic elements disappear when the top of a submerging (- has passed through the photospheric layer (seeFig.2inZwaan1987)., The opposite-polarity magnetic elements disappear when the top of a submerging $\Omega$ -loop has passed through the photospheric layer \citep[see Fig.2 in][]{Zwaan1987}.185". Alternatively, these elements disappear when the bottom of a rising U-loop has passed clear through the photospheric layer."," Alternatively, these elements disappear when the bottom of a rising U-loop has passed clear through the photospheric layer."186" When magnetic field lines have emerged into the chromosphere and corona, they can hardly submerge back below the photosphere because of magnetic buoyancy."," When magnetic field lines have emerged into the chromosphere and corona, they can hardly submerge back below the photosphere because of magnetic buoyancy."187 Magnetic reconnection taking place within several scale heights above the solar surface is probably needed to create low-lying Q-loops whose magnetic tension force can then overcome the magnetic buoyancy force (Parker1975)., Magnetic reconnection taking place within several scale heights above the solar surface is probably needed to create low-lying $\Omega$ -loops whose magnetic tension force can then overcome the magnetic buoyancy force \citep{Parker1975}.188". In the photospheric magnetic reconnection cases, reconnection should be most efficient around the temperature minimum region: about 600 km above the solar surface (Litvinenko1999;Takeuchi&Shibata2001)."," In the photospheric magnetic reconnection cases, reconnection should be most efficient around the temperature minimum region: about 600 km above the solar surface \citep{Litvinenko1999, Takeuchi2001}."189". In contrast, both magnetic tension and buoyancy forces are directed upward in the case of a U-loop rising through the photosphere."," In contrast, both magnetic tension and buoyancy forces are directed upward in the case of a U-loop rising through the photosphere."190 Magnetic reconnection is therefore not crucial for the emerging U-loops., Magnetic reconnection is therefore not crucial for the emerging U-loops.191 An important observable signature for understanding flux cancellation is the motion of the horizontal magnetic field connecting the canceling magnetic elements., An important observable signature for understanding flux cancellation is the motion of the horizontal magnetic field connecting the canceling magnetic elements.192 Horizontal magnetic fields have been observed between the opposite-polarity magnetic elements during the cancellations of moving magnetic features around a sunspot (Chaeetal.2004)., Horizontal magnetic fields have been observed between the opposite-polarity magnetic elements during the cancellations of moving magnetic features around a sunspot \citep{Chae2004}.193. Similar horizontal fields have also been observed in events of cancellations of pores and sunspots (Kubo&Shimizu2007)., Similar horizontal fields have also been observed in events of cancellations of pores and sunspots \citep{Kubo2007}.194. A flux cancellation without increase of the horizontal field has also been reported for the moving magnetic features (BellotRubio&Beck2005)., A flux cancellation without increase of the horizontal field has also been reported for the moving magnetic features \citep{Bellot2005}.195". Knowledge of the full vector field permits one to determine whether the field geometry has Q-loop topology or U-loop topology, but in the case of cancellation of small, isolated flux elements, such a determination is often compromised by usual difficulty of resolving the 180° azimuth ambiguity."," Knowledge of the full vector field permits one to determine whether the field geometry has $\Omega$ -loop topology or U-loop topology, but in the case of cancellation of small, isolated flux elements, such a determination is often compromised by usual difficulty of resolving the $\degr$ azimuth ambiguity."196" Regarding the motions at such a cancellation site, Harveyetal.(1999) show that the magnetic flux disappears in the chromosphere before it does in the photosphere for at least about half of the cancellation events."," Regarding the motions at such a cancellation site, \citet{Harvey1999}197 show that the magnetic flux disappears in the chromosphere before it does in the photosphere for at least about half of the cancellation events."198" They suggest that magnetic flux is submerging in most, if not all, of the cancellation sites."," They suggest that magnetic flux is submerging in most, if not all, of the cancellation sites."199" On the other hand, both Doppler red shift (Chaeet and Doppler blue shift (Yurchyshyn&Wang2001) are reported in the cancellation sites."," On the other hand, both Doppler red shift \citep{Chae2004} and Doppler blue shift \citep{Yurchyshyn2001} are reported in the cancellation sites."200 The center-to-limb variations of the Doppler velocities at the polarity inversion lines, The center-to-limb variations of the Doppler velocities at the polarity inversion lines201EWHAL~2000 n typical of accreting binaries (21).,$FWHM\sim2000$ ) typical of accreting binaries \citealt{deUgartePostigo2010b}) ).202 The source was detected in radio with a linear polarization level of ~23% (2). submillimetres (20) and near infrared (?)) wavelengths.," The source was detected in radio with a linear polarization level of $\sim 23\%$ \citealt{vanderHorst2010}) ), submillimetres \citealt{deUgartePostigo2010a}) ) and near infrared \citealt{D'Avanzo2010}) ) wavelengths."203 At high energies MAXI J1659-152 was also observed by the (RXTE) and the XMM and INTEGRAL observatories (2:: 2))., At high energies MAXI J1659-152 was also observed by the (RXTE) and the XMM and INTEGRAL observatories \citealt{Kuulkers2010a}; \citealt{Vovk2010}) ).204 RATE observations performed 3 days after the discovery revealed strong similarities with the typical timing properties of BHT during the HIMS ¢?)) indicating that MAXI J1659-152 is a black hole candidate., RXTE observations performed 3 days after the discovery revealed strong similarities with the typical timing properties of BHT during the HIMS \citealt{Kalamkar2010}) ) indicating that MAXI J1659-152 is a black hole candidate.205 This was confirmed by the subsequent transitions to the SIMS and HSS observed on October 12 (2)) and October 17 (2)). respectively.," This was confirmed by the subsequent transitions to the SIMS and HSS observed on October 12 \citealt{Belloni2010b}) ) and October 17 \citealt{Shaposhnikov2010}) ), respectively."206 After a short (15 days) stay in soft states. a new transition to the HIMS was observed (3).," After a short (15 days) stay in soft states, a new transition to the HIMS was observed \citealt{tmd2010b}) )."207 X-ray dips with a recurrent period of 2.41 hours have been detected in MAXI J16S9-152. pointing to a high orbital inclination and suggesting that MAXI 11659-1532 is the black hole binary with the shortest orbital period (2:: 2:: 25).," X-ray dips with a recurrent period of 2.41 hours have been detected in MAXI J1659-152, pointing to a high orbital inclination and suggesting that MAXI J1659-152 is the black hole binary with the shortest orbital period \citealt{Kuulkers2010b}; \citealt{Belloni2010c}; \citealt{Kuulkers2011}) )."208 Here. we study in detail the evolution of the spectral and timing properties of the source along the 2010 outburst until observations were interrupted due to Sun constraints.," Here, we study in detail the evolution of the spectral and timing properties of the source along the 2010 outburst until observations were interrupted due to Sun constraints."209 We focus on the evolution of the variability during the hard-to-soft and soft-to-hard transitions and how it is related to the relative contribution of the various components present in the energy spectra., We focus on the evolution of the variability during the hard-to-soft and soft-to-hard transitions and how it is related to the relative contribution of the various components present in the energy spectra.210 We analyse 65 RXTE observations of MAXI J1659-152 performed within September 28. 2010 and November 11. The variability study presented in this paper is based on data from the (PCA).," We analyse 65 RXTE observations of MAXI J1659-152 performed within September 28, 2010 and November 11, The variability study presented in this paper is based on data from the (PCA)."211 For some observations the mode GoodXenon!_22s was used but most of the data are in the mode LIs. which covers the PCA effective energy range (2-60 keV)060 with 64 bands.," For some observations the mode 2s was used but most of the data are in the mode 1s, which covers the PCA effective energy range (2-60 keV) with 64 bands."212 Power density spectra (PDS) for each observation were computed following the procedure outlined in ?.., Power density spectra (PDS) for each observation were computed following the procedure outlined in \cite{Belloni2006}.213 We used stretches 16 s long and PCA channels 0—35 (2-15 keV)., We used stretches 16 s long and PCA channels 0–35 (2–15 keV).214 The PCA Standard 2 mode (STD2) was used for the spectra analysis., The PCA Standard 2 mode (STD2) was used for the spectral analysis.215 It covers the 2-60 keV energy range with 129 channels., It covers the 2–60 keV energy range with 129 channels.216 From the data. we extracted hardness (C/). defined as the ratio of counts in STD2 channels 11—20 (6.1—10.2 keV) and 4-10 (3.3—6.1 keV).," From the data, we extracted hardness $h$ ), defined as the ratio of counts in STD2 channels 11–20 (6.1–10.2 keV) and 4-10 (3.3–6.1 keV)."217 Energy spectra from the PCA (background and dead-time corrected) were extracted for each observation using the standard RXTE software within V. 6.7., Energy spectra from the PCA (background and dead-time corrected) were extracted for each observation using the standard RXTE software within V. 6.7.218 For the spectral fitting. Proportional Counter Unit 2 was solely used.," For the spectral fitting, Proportional Counter Unit 2 was solely used."219 In order to accoun for residual uncertainties in the instrument calibration a systematic error of 0.6% was added to thespectra!., In order to account for residual uncertainties in the instrument calibration a systematic error of $0.6\%$ was added to the.220. We computed the fundamental diagrams commonly used for the study of BHT and performed fits to the energy spectra and PDS., We computed the fundamental diagrams commonly used for the study of BHT and performed fits to the energy spectra and PDS.221 The QPOs present in the PDS have been classified following ?.., The QPOs present in the PDS have been classified following \cite{Casella2005}.222 Finally. we have also measured time-lags between soft and hard variability for the only observation long enough to perform this analysis.," Finally, we have also measured time-lags between soft and hard variability for the only observation long enough to perform this analysis."223 As a first step of the analysis. we computed the hardness-intensity and the hardness-rms diagrams (HID and HRD}. which are presented in the upper and middle panels of Fig.].. respectively.," As a first step of the analysis, we computed the hardness-intensity and the hardness-rms diagrams (HID and HRD), which are presented in the upper and middle panels of \ref{hid}, respectively."224 The fractional rms was computed within the frequency band 0.1-64 Hz following ?.., The fractional rms was computed within the frequency band 0.1–64 Hz following \cite{Belloni1990}.225 We have also computed the rms-intensity diagram (RID) presented in Fig., We have also computed the rms-intensity diagram (RID) presented in Fig.226 2. following ?.., \ref{rid} following \cite{tmd2011}.227 Rms values obtained by using a soft (2-6 keV) and a hard (6-15 keV) band are shown in the upper panel of Fig., Rms values obtained by using a soft (2–6 keV) and a hard (6–15 keV) band are shown in the upper panel of Fig.228 3. as open and filled circles. respectively.," \ref{rmsc} as open and filled circles, respectively."229 The comparison between the rms observed in these two bands is effectively à rms spectrum of two energy bins., The comparison between the rms observed in these two bands is effectively a rms spectrum of two energy bins.230 This is enough to get a reliable estimation of the energy spectrum of the variability even when the count rate is low., This is enough to get a reliable estimation of the energy spectrum of the variability even when the count rate is low.231 The latter results in large error bars if using narrow energy bands., The latter results in large error bars if using narrow energy bands.232 This method allows us to infer whether the rms spectrum is flat. hard or inverted (1.9. more variability at low energies) for each observation.," This method allows us to infer whether the rms spectrum is flat, hard or inverted (i.e. more variability at low energies) for each observation."233 For a more detailed comparison. we show in Fig.," For a more detailed comparison, we show in Fig."234 4. three rms spectra corresponding to observations taken along the hard-to-soft transition., \ref{rmss} three rms spectra corresponding to observations taken along the hard-to-soft transition.235 They are obtained using six energy bands and give results consistent with those that can be extracted from the upper panel of Fig. 3.., They are obtained using six energy bands and give results consistent with those that can be extracted from the upper panel of Fig. \ref{rmsc}.236 The source describes in the HID the standard q-shaped pattern moving from observation £11 (open. big circle in Fig. 15 ," The source describes in the HID the standard q-shaped pattern moving from observation 1 (open, big circle in Fig. \ref{hid}) )"237in the counter clockwise direction., in the counter clockwise direction.238 However. the initial flux rise was not observed by RXTE and. as pointed out by ?.. the first RXTE observation already correspond to the HIMS.," However, the initial flux rise was not observed by RXTE and, as pointed out by \citet{Kalamkar2010}, the first RXTE observation already correspond to the HIMS."239 This is confirmed by the fact that no hard line (i.e. sharp. linear rms-flux relation: ?)) is observed in the RID.," This is confirmed by the fact that no hard line (i.e. sharp, linear rms-flux relation; \citealt{tmd2011}) ) is observed in the RID."240 After ~16 days in the HIMS. where the count rate peak is observed. type-B QPOs are seen in the PDS. indicating the system is in the SIMS.," After $\sim 16$ days in the HIMS, where the count rate peak is observed, type-B QPOs are seen in the PDS, indicating the system is in the SIMS."241 Once this state is reached. fast transitions are observed between the SIMS and the HSS.," Once this state is reached, fast transitions are observed between the SIMS and the HSS."242 A hard excursion to the HIMS between two soft excursions is observed., A hard excursion to the HIMS between two soft excursions is observed.243 After an important decrease in count rate the system reaches the softest tobserved) point of the outburst and a soft-to-hard transition is seen., After an important decrease in count rate the system reaches the softest (observed) point of the outburst and a soft-to-hard transition is seen.244 The following can be outlined after a detailed study of the fundamental diagrams:, The following can be outlined after a detailed study of the fundamental diagrams:245]t has been suggested. that brown dwarf-brown: dwarf rinaries. or. more generally. very low mass binaries (VLMDs) with svstem masses <0.2 MM. form in a different way to stellar binaries.,"It has been suggested that brown dwarf-brown dwarf binaries, or, more generally, very low mass binaries (VLMBs) with system masses $< 0.2$ $_\odot$ form in a different way to stellar binaries."246 Phe main argument for this scenario is that he binary fraction and separation distributions of VLMDs are very dillerent to those of stars., The main argument for this scenario is that the binary fraction and separation distributions of VLMBs are very different to those of stars.247 7. point out that the παν fraction of verv-Iow mass systems is only 15. 25 per cent. compared to 42 per cent for highcr-mass Al-dwarls.," \citet{Thies07} point out that the binary fraction of very-low mass systems is only 15 – 25 per cent, compared to 42 per cent for higher-mass M-dwarfs."248 Also. the separation distribution for most stellar. binaries (hieher-mass M-. We. and. Ci-dwarfs) has the same mean aau) and variance (toeweea= 1.53. where e is the seni-major axis in au). and diflers only in the multiplicity. of he primary in the particular mass range (??)..," Also, the separation distribution for most stellar binaries (higher-mass M-, K-, and G-dwarfs) has the same mean au) and variance $\sigma_{\rm log_{10}\,a} = 1.53$ , where $a$ is the semi-major axis in au), and differs only in the multiplicity of the primary in the particular mass range \citep{Duquennoy91,Fischer92}. ."249 Llowever. he observed separation distribution of VLMDs (see show the data (when fitted with a logju-normal) to have a mean of 4.6aau with a much smaller variance.," However, the observed separation distribution of VLMBs \citep[see e.g.][]{Burgasser07} show the data (when fitted with a $_{10}$ -normal) to have a mean of au with a much smaller variance."250 In addition. 77 argue that the observations of VLMDs are not consistent with a continuous IME over the hydrogen-burning limit.," In addition, \citet{Thies07,Thies08} argue that the observations of VLMBs are not consistent with a continuous IMF over the hydrogen-burning limit."251 ? interpreted this as evidence that VLALBs form through a different mechanism to stellar binaries., \citet{Thies07} interpreted this as evidence that VLMBs form through a different mechanism to stellar binaries.252 l]lowever. it is known that binary populations can undergo significant dynamical processing. with many. especially wider systems. being destroved. (222: 7: ?7))," However, it is known that binary populations can undergo significant dynamical processing, with many, especially wider systems, being destroyed \citealp{Heggie75, Kroupa95a, Kroupa95b}; \citealp*{Kroupa99}; \citealp{Kroupa03, Parker09}) )."253 Therefore. the currently observed binary population. especially in the field. is not the same as the birth population (?)..," Therefore, the currently observed binary population, especially in the field, is not the same as the birth population \citep{Goodwin10}."254 In this paper. we examine to what extent an initial VLMD population can be altered hy dynamical processing and so how cillerent the initial VLMD ancl stellar binary populations can be at birth.," In this paper, we examine to what extent an initial VLMB population can be altered by dynamical processing and so how different the initial VLMB and stellar binary populations can be at birth."255 We extend. the work of 7 who examine the evolution of a mixed population of star ancl very low-mass object. (VLAIO) binaries and. find that. dynamically at. least. VELMBDs must form. à. separate population (seealso?7)..," We extend the work of \citet{Kroupa03} who examine the evolution of a mixed population of star and very low-mass object (VLMO) binaries and find that, dynamically at least, VLMBs must form a separate population \citep[see also][]{Thies07, Thies08}."256 Llere we assume that VLMBDs are a separate population and examine what range of initial binary [ractions and separations can reproduce the current observations., Here we assume that VLMBs are a separate population and examine what range of initial binary fractions and separations can reproduce the current observations.257 In Section 2. we review the available VEM data. in Section 3.we describethe set-up of our simulations.," In Section \ref{observe} we review the available VLMB data, in Section \ref{method} we describethe set-up of our simulations,"258The maximum-entropy fits we obtain in this context for each of our 2 data sets are shown on Fig. 43..,"The maximum-entropy fits we obtain in this context for each of our 2 data sets are shown on Fig. \ref{fig:fit},"259 while the corresponding maps (assuming a magnetic field featuring both poloidal and toroidal components) are shown on Fig. 3.., while the corresponding maps (assuming a magnetic field featuring both poloidal and toroidal components) are shown on Fig. \ref{fig:map}.260 Both data sets are fitted down to the noise level and correspond to a reduced oof order unity., Both data sets are fitted down to the noise level and correspond to a reduced of order unity.261 Note that in both cases. the data set is only fragmentary. covering no more than and of the rotation cycle for the June and August sets respectively.," Note that in both cases, the data set is only fragmentary, covering no more than and of the rotation cycle for the June and August sets respectively."262 It explains in. particular why only little magnetic flux. ts reconstructed at the stellar surface in regions not (or only marginally) constrained by observations., It explains in particular why only little magnetic flux is reconstructed at the stellar surface in regions not (or only marginally) constrained by observations.263 This is due to the fact that the imaging code is tailored to produce the simplest surface magnetic topology compatible with the data: it therefore spontaneously biases the solution towards topologies featuring little magnetic flux on poorly observed regions of the stellar surface. provided that (1) this is compatible with observations at other rotational phases and that (11) the assumed field topology is complex enough to allow a mixture of non-magnetic and magnetic regions (re.. the spherical harmonics expansion describing the field topology includes orders significantly larger than 1).," This is due to the fact that the imaging code is tailored to produce the simplest surface magnetic topology compatible with the data; it therefore spontaneously biases the solution towards topologies featuring little magnetic flux on poorly observed regions of the stellar surface, provided that (i) this is compatible with observations at other rotational phases and that (ii) the assumed field topology is complex enough to allow a mixture of non-magnetic and magnetic regions (i.e., the spherical harmonics expansion describing the field topology includes orders significantly larger than 1)."264 For this reason. we emphasise that the nodeling we carry out in this paper is only preliminary and deserves further confirmation and assessment through more complete data sets.," For this reason, we emphasise that the modeling we carry out in this paper is only preliminary and deserves further confirmation and assessment through more complete data sets."265 However. a number of reliable conclusions can be derived already from the present data.," However, a number of reliable conclusions can be derived already from the present data."266 The first point we can address concerns the topology of the field., The first point we can address concerns the topology of the field.267 By trying to fit the data with different field configurations (eg a poloidal field only. or a general poloidal plus toroidal field combination). one can check which topology ts more likely to be present at the surface of the star.," By trying to fit the data with different field configurations (eg a poloidal field only, or a general poloidal plus toroidal field combination), one can check which topology is more likely to be present at the surface of the star."268 In the present case. we find that the field of HD 189733 most probably features both a poloidal and a toroidal component at the surface of the star.," In the present case, we find that the field of HD 189733 most probably features both a poloidal and a toroidal component at the surface of the star."269 Although both options give equivalent likelihoods in terms of the quality of fit to the data. the inclusion of a toroidal field component produces a magnetic configuration with significantly lower contrast (hence greater entropy and higher prior probability). yielding a higher posterior probability.," Although both options give equivalent likelihoods in terms of the quality of fit to the data, the inclusion of a toroidal field component produces a magnetic configuration with significantly lower contrast (hence greater entropy and higher prior probability), yielding a higher posterior probability."270 This is particularly obvious for the August data set. for which the poloidal plus toroidal field configuration that fits the data at the noise level is almost twice as weak on average as that obtained when assuming that the star hosts a purely poloidal field (not shown here).," This is particularly obvious for the August data set, for which the poloidal plus toroidal field configuration that fits the data at the noise level is almost twice as weak on average as that obtained when assuming that the star hosts a purely poloidal field (not shown here)."271 This conclusion can be inferred straightforwardly from the corresponding Stokes V data set (see Fig. 3))., This conclusion can be inferred straightforwardly from the corresponding Stokes $V$ data set (see Fig. \ref{fig:fit}) ).272 At this epoch. the mean Stokes V profile averaged over the whole series. as well as more than half of the individual profiles (eg that at phase 0.620). are clearly more-or-less symmetric about the line center.," At this epoch, the mean Stokes $V$ profile averaged over the whole series, as well as more than half of the individual profiles (eg that at phase 0.620), are clearly more-or-less symmetric about the line center."273 This is the characteristic signature of an azimuthal field ring encircling most of the star (eg.2)..," This is the characteristic signature of an azimuthal field ring encircling most of the star \citep[eg, ][]{petit05}."274 The same conclusion may be deduced from the June data set. although the evidence is weaker than for the other (more complete) data set.," The same conclusion may be deduced from the June data set, although the evidence is weaker than for the other (more complete) data set."275 In particular. the portions of the azimuthal field ring reconstructed at both epochs feature the same (1e clockwise or negative) polarity (see Fig. 3)).," In particular, the portions of the azimuthal field ring reconstructed at both epochs feature the same (ie clockwise or negative) polarity (see Fig. \ref{fig:map}) ),"276 strengthening the evidence that this toroidal field ring is indeed a real component of the magnetic topology of HD 189733., strengthening the evidence that this toroidal field ring is indeed a real component of the magnetic topology of HD 189733.277 We can also be fairly confident that the magnetic field at the surface of the star is significantly more complex than that, We can also be fairly confident that the magnetic field at the surface of the star is significantly more complex than that278model with inner truncation SC3 collapses toward the jet axis leading to knots in the density maps.,model with inner truncation SC3 collapses toward the jet axis leading to knots in the density maps.279 In paper I and also in Fig., In paper I and also in Fig.280" 2 (bottom), we find in the corresponding synthetic emission map in [OI] two areas of enhanced emission whose position, however, is not the same as that of the density knots."," \ref{Fig_emissmaps} (bottom), we find in the corresponding synthetic emission map in [OI] two areas of enhanced emission whose position, however, is not the same as that of the density knots."281 Furthermore the extracted jet width is almost constant despite of these areas., Furthermore the extracted jet width is almost constant despite of these areas.282" In order to find an physical origin of the variations, it is useful not to focus on the first maximum but on the minimum directly behind it."," In order to find an physical origin of the variations, it is useful not to focus on the first maximum but on the minimum directly behind it."283" One common feature in all our MHD simulations is the fast magnetosonic separatrix surface (FMSS,Stuteetal. 2008)."," One common feature in all our MHD simulations is the fast magnetosonic separatrix surface \citep[FMSS,][]{STV08}."284. This surface is a weak shock causally disconnecting the sub-fast flow from the super-fast one., This surface is a weak shock causally disconnecting the sub-fast flow from the super-fast one.285 Its position in Z direction increases monotonically with increasing R value., Its position in $Z$ direction increases monotonically with increasing $R$ value.286 Both density and pressure along the flow line show a jump at the FMSS., Both density and pressure along the flow line show a jump at the FMSS.287" As mentioned above, we convolve our map with a Gaussian of 15 AU and modify the density inside 15 AU from the jet axis."," As mentioned above, we convolve our map with a Gaussian of 15 AU and modify the density inside 15 AU from the jet axis."288" We find that the minimum in the extracted jet width is at the same position, where the FMSS has a radius of 15 AU and enters this region."," We find that the minimum in the extracted jet width is at the same position, where the FMSS has a radius of 15 AU and enters this region."289" For inclinations different to 90°, the two crossing points of FMSS with the Gaussian both in front of the jet and behind the jet are visible as local minima in the extracted jet widths."," For inclinations different to $^\circ$, the two crossing points of FMSS with the Gaussian both in front of the jet and behind the jet are visible as local minima in the extracted jet widths."290" Beyond physical origins of the maxima, another origin is the geometry of the system, ie. the finiteness of our computational domain."," Beyond physical origins of the maxima, another origin is the geometry of the system, i.e. the finiteness of our computational domain."291" In order to quantify this aspect, we calculated the emission maps and extracted jet width for a domain with constant density and temperature."," In order to quantify this aspect, we calculated the emission maps and extracted jet width for a domain with constant density and temperature."292 Thus also the emission is constant across the domain., Thus also the emission is constant across the domain.293" If seen with an inclination of 90°, the extracted jet width is constant as expected; if the inclination is 40°, however, the extracted jet width is almost constant only between about 15 and 68 Ro (Fig. 7))."," If seen with an inclination of $^\circ$, the extracted jet width is constant as expected; if the inclination is $^\circ$, however, the extracted jet width is almost constant only between about 15 and 68 $R_0$ (Fig. \ref{Fig_constant_box}) )."294 These values are dependent on the aspect ratio of the computational domain and the tangent of the inclination., These values are dependent on the aspect ratio of the computational domain and the tangent of the inclination.295" In our models, this geometrical effect leads to another maximum in extracted jet widths whose position moves to smaller distances with decreasing inclination (Fig. 5))"," In our models, this geometrical effect leads to another maximum in extracted jet widths whose position moves to smaller distances with decreasing inclination (Fig. \ref{Fig_inclination_SC1c}) )"296 and has to be corrected when comparing our models to observations., and has to be corrected when comparing our models to observations.297 We used this test case with constant emission for quantifying the area in which our extracted jet widths are not affected by this effect., We used this test case with constant emission for quantifying the area in which our extracted jet widths are not affected by this effect.298" In paper I, we found best-fit models for the jets in the observed sample."," In paper I, we found best-fit models for the jets in the observed sample."299 Note that we always ignored there the first maximum in the synthetic jet widths and focussed on larger distances from the source., Note that we always ignored there the first maximum in the synthetic jet widths and focussed on larger distances from the source.300" Now we can include the effects of inclination, use the position of the maxima in our synthetical jet width variations for estimating the inclination and compare the derived inclination with values from the literature."," Now we can include the effects of inclination, use the position of the maxima in our synthetical jet width variations for estimating the inclination and compare the derived inclination with values from the literature."301 The observed mass of DG Tau (diamonds in Fig. 1)), The observed mass of DG Tau (diamonds in Fig. \ref{Fig_observations}) )302" is 0.67 Μο (Hartiganetal.1995),, therefore we have to focus on the runs (500,1000,0.8), and perhaps also runs (500,600,0.5) and (500,1000,0.5)."," is 0.67 $M_\odot$ \citep{HEG95}, therefore we have to focus on the runs (500,1000,0.8), and perhaps also runs (500,600,0.5) and (500,1000,0.5)."303" The best-fit model is between ADO and SCla, thus the truncation radius is larger than 0.22 AU."," The best-fit model is between ADO and SC1a, thus the truncation radius is larger than 0.22 AU."304" DG Tau can be quite well reproduced with the model SCla, the run (500,1000,0.8) and an inclination of 40° (Fig. 8))."," DG Tau can be quite well reproduced with the model SC1a, the run (500,1000,0.8) and an inclination of $^\circ$ (Fig. \ref{Fig_DG_Tau}) )."305 This inclination is in excellent agreement with the literature values of 32-52? (Eislóffel&Mundt1998;Bacciottietetal. 2003).," This inclination is in excellent agreement with the literature values of $^\circ$ \citep{EiM98,BRM02,PKH03}."306". The mass of CW Tau (squares) is the highest in our sample, 1.03 Me (Hartiganetal.1995)."," The mass of CW Tau (squares) is the highest in our sample, 1.03 $M_\odot$ \citep{HEG95}."307". Using the runs (500,1000,0.8), the best-fit model was SC1b or SClc."," Using the runs (500,1000,0.8), the best-fit model was SC1b or SC1c."308 The truncation radius is thus between 0.25 — 0.3 AU., The truncation radius is thus between 0.25 – 0.3 AU.309" CW Tau may be best-modeled with simulation SClc, run (500,1000,0.8) and an inclination of 60° (Fig. 9))."," CW Tau may be best-modeled with simulation SC1c, run (500,1000,0.8) and an inclination of $^\circ$ (Fig. \ref{Fig_CW_Tau}) )."310" The literature value, however, is about 41° (Coffeyetal. 2007).."," The literature value, however, is about $^\circ$ \citep{CBR07}. ."311Having a supercritical flow that collides with plana which is at rest initially has to result in a shock frout.,Having a supercritical flow that collides with plasma which is at rest initially has to result in a shock front.312 As this shock-trout accelerates the plasma. it mügrates outwards anc leaves the computational domain after [2200 x. Iu the preseut contribution we do not make uv attempt to realistically describe shock waves.," As this shock-front accelerates the plasma, it migrates outwards and leaves the computational domain after 200 s. In the present contribution we do not make any attempt to realistically describe shock waves."313 But it is clear that the shock does no influence the cdyvuauics lappening near ie peuunbral photosphere for several reasons., But it is clear that the shock does not influence the dynamics happening near the penumbral photosphere for several reasons.314 First. the shock frout is àconsequence of the acceleration of plasma within the peuuubra. rather than he cause of the longitudinalC» flow.," First, the shock front is a of the acceleration of plasma within the penumbra, rather than the cause of the longitudinal flow."315 Secoud. the density decreases exponentiallv with height. aud therefore the inertia within the photospheric pemmuibra is much to large o be affected. by the dynwics happening huudreds of slometers above the photosphere.," Second, the density decreases exponentially with height, and therefore the inertia within the photospheric penumbra is much to large to be affected by the dynamics happening hundreds of kilometers above the photosphere."316 Aud after all. the flow velocity upstream of the shock is supercritical. ie.. the oumnbral photosphere doesu't know about the shock rout.," And after all, the flow velocity upstream of the shock is supercritical, i.e., the penumbral photosphere doesn't know about the shock front."317 The flow is decelerated within the shock aud the eas oressure increases there., The flow is decelerated within the shock and the gas pressure increases there.318 That leads to a local expansio- of the tube at the shock front., That leads to a local expansion of the tube at the shock front.319 Such an expiusiou should ο counteracted by magnetic tension forces inside the ube., Such an expansion should be counteracted by magnetic tension forces inside the tube.320 However. within the thin flux tube approxinati- such forces are neglected aud. nothing preveuts the tube roni infinite expansion at the shock frout.," However, within the thin flux tube approximation such forces are neglected and nothing prevents the tube from infinite expansion at the shock front."321 Therefore. we rave meluded the magnetic tension forces inside the tube fictitiously by changing the background pressure. >: At he location of expansion we cnhance the backerouud oessure.," Therefore, we have included the magnetic tension forces inside the tube fictitiously by changing the background pressure, $P_{\rm b}$: At the location of expansion we enhance the background pressure."322 The stronger the expansion. the larecr the vackeroundl pressure.," The stronger the expansion, the larger the background pressure."323 As discussed in Sect. 3.2.3..," As discussed in Sect. \ref{sec_surplus},"324 plasma within the tube expands as it rises throueh the convection zone., plasma within the tube expands as it rises through the convection zone.325 Thereby. je magnetic field streneth. D. ecreascs.," Thereby, the magnetic field strength, $B$, decreases."326 The magnetic cheld streneth of plasma reachingc» the footpoiut is the «παλιο. the larecr is the height difference it traveled woueh the convection zouc.," The magnetic field strength of plasma reaching the footpoint is the smaller, the larger is the height difference it traveled through the convection zone."327" That προς, that ον=Divlzp at the footpoiut decreases continuously. while je flow velocity stays constant in time at the footpoiut."," That implies, that $v_{\rm A}=B/\sqrt{4\pi\rho}$ at the footpoint decreases continuously, while the flow velocity stays constant in time at the footpoint."328 Hence. at some point Gn our sinmlation at fzzT000 x) 1e flow becomes superalfvéóunic aud the centrifugal force exceeds the magnetic tension force at the turuiug point. i.c. the flow overshoots the turmming point.," Hence, at some point (in our simulation at $t\approx 7\,000$ s) the flow becomes superalfvénnic and the centrifugal force exceeds the magnetic tension force at the turning point, i.e. the flow overshoots the turning point."329 Due to radiative osses in the atinosphere. the plasima that overshoots ects chser aud decelerates.," Due to radiative losses in the atmosphere, the plasma that overshoots gets denser and decelerates."330" The amplitude of the overshoot exadually increases iu iue as eyfe, tuercases,", The amplitude of the overshoot gradually increases in time as $v_\|/v_{\rm A}$ increases.331 Once the flax tube dives back iuto the couvectively uustable subplotospheric peuuubra. uti-buovaucy drags the tube down. aud maguctic tension is too weak to prevent the tube from sinking.," Once the flux tube dives back into the convectively unstable subphotospheric penumbra, anti-buoyancy drags the tube down, and magnetic tension is too weak to prevent the tube from sinking."332 Fig., Fig.333 6bb shows a snapshot of the tube in the vicinity of the turning point after 93300 s. The inertia of the upflow at the footpoiut prevents the turuing poit from sinking., \ref{abbcrash}b b shows a snapshot of the tube in the vicinity of the turning point after 300 s. The inertia of the upflow at the footpoint prevents the turning point from sinking.334 The part ofthe tube that dives back beneath the plotosplere sinks down., The part of the tube that dives back beneath the photosphere sinks down.335 Since the radi of curvature at the turning point Gezδι. Mau) aud ate z10.2 Mai become very sxiiall. the thin ux tube approximation is no longer valid.," Since the radii of curvature at the turning point $x\approx 8.4$ Mm) and at $x\approx 10.2$ Mm become very small, the thin flux tube approximation is no longer valid."336 For that reason. we stop the simulation here.," For that reason, we stop the simulation here."337 Iu order to discuss the observational consequences of our model. we concentrate ou the evolution of the tube iu and above the photosphere. since only here is the tube observable.," In order to discuss the observational consequences of our model, we concentrate on the evolution of the tube in and above the photosphere, since only here is the tube observable."338 Fig., Fig.339 7 shows the proper inward velocity of the nuerating footpoiunt as a function of the radial distance s from sunspot center., \ref{footpoint} shows the proper inward velocity of the migrating footpoint as a function of the radial distance $x$ from sunspot center.340 It illustrates the migration of the tube’s footpoiut which will be compared with the observed dwar uueration of bright peuunibral erains., It illustrates the migration of the tube's footpoint which will be compared with the observed inward migration of bright penumbral grains.341 Further. we use Fig.," Further, we use Fig."342 5 to discuss the features of our siuulations iu he context of he observed peuuiibral fine structure such as bright and dark fluneuts aud he Evershed effect., \ref{snapshot} to discuss the features of our simulations in the context of the observed penumbral fine structure such as bright and dark filaments and the Evershed effect.343 It shows an intermediate stage of evolution of the tube near the surface lavers., It shows an intermediate stage of evolution of the tube near the surface layers.344 Fromm. left o right. one can see the uubra. the pemmubra. aud the quiet sium being separated w the peripatopause and the naguetopause. respectively.," From left to right, one can see the umbra, the penumbra, and the quiet sun being separated by the peripatopause and the magnetopause, respectively."345 Iu Fie., In Fig.346 Nass Sec. and Sdd he erav coding represents he temperature variation. the eas pressure variation. and the variation of the magnetic field streugth. respectively.," \ref{snapshot}a a, \ref{snapshot}c c, and \ref{snapshot}d d the gray coding represents the temperature variation, the gas pressure variation, and the variation of the magnetic field strength, respectively."347 Note. that in each background stratification the temperature and the pressure vary ouly," Note, that in each background stratification the temperature and the pressure vary only"348uPhe compact radio. sources consist. of. two population. of objects:. the gigahertz-peaked. spectrum (GPS)bo and compact steep Polspectrum (CSS) sources.,The compact radio sources consist of two population of objects: the gigahertz-peaked spectrum (GPS) and compact steep spectrum (CSS) sources.349 These are considered to be voung and evolve into large radio objects. ILL," These are considered to be young and evolve into large radio objects, II ."350 The GPSUt sources :are considered to be entirely contained within the extent of the narrow-line region (< 1 kpe)., The GPS sources are considered to be entirely contained within the extent of the narrow-line region $\leq$ 1 kpc).351 .Unbeamed. symmetric. GPSbc sources have been classified.n as .Compact Symmetrie.: Objects. by(1994).," Unbeamed, symmetric GPS sources have been classified as Compact Symmetric Objects by."352.. uu:CSS sources are thought to extend to the size. of the host galaxy (x; ∙20 kpe)., CSS sources are thought to extend to the size of the host galaxy $\leq$ 20 kpc).353 .Compact radio. sources are the ideal for learning more about the relation between formation and evolution of the host galaxy. the trigger of the activity and its ellect on the nuclear regions and. ISAT of the host galaxy.," Compact radio sources are the ideal for learning more about the relation between formation and evolution of the host galaxy, the trigger of the activity and its effect on the nuclear regions and ISM of the host galaxy."354 Once the nuclear activity and radio source are triggered. the small-scalejets expand through the natal cocoon. driving outllows in the emission line gas (fast outllows and jet-cloud interactions).," Once the nuclear activity and radio source are triggered, the small-scale jets expand through the natal cocoon, driving outflows in the emission line gas (fast outflows and jet-cloud interactions)."355: In some cases the interaction: of the radio Loijets with. the ISAT. can clisrupt. the jet. and change the morphology and luminosity. of. the source2007)., In some cases the interaction of the radio jets with the ISM can disrupt the jet and change the morphology and luminosity of the source.356. In large radio sources. the emission line activity is connected with black hole mass. fuelling mechanism. and type of the accreating. gas2010).," In large radio sources, the emission line activity is connected with black hole mass, fuelling mechanism and type of the accreating gas."357. However the morphological. division.Ds of⋅ large radio. objects. into. FRU and UE does not. correspond to low/high: excitation⊀⊀ division:MN Us show typically. faintM optical. nuclei. and low excitation⊀⊀ spectra. while⊀ among PRIUS we have both low and high. excitation⊀⊀ galaxies.," However the morphological division of large radio objects into I and II does not correspond to low/high excitation division: Is show typically faint optical nuclei and low excitation spectra, while among IIs we have both low and high excitation galaxies."358. MThe spectroscopic analysis of GPS/CSS sources - progenitors of [aree ETIUIL/ETUILE objects - can allow to derive their accretion properties at times close to the jet launching., The spectroscopic analysis of GPS/CSS sources - progenitors of large II objects - can allow to derive their accretion properties at times close to the jet launching.359 In GPS/CSS sources. the jet is still crossing the 18M and the interaction with the ISM is stronger than in large radio sources.," In GPS/CSS sources, the jet is still crossing the ISM and the interaction with the ISM is stronger than in large radio sources."360 Observations of the ionized gas in GPS and CSS sources show the presence of such interactions, Observations of the ionized gas in GPS and CSS sources show the presence of such interactions361"evaluated al O=O,.",evaluated at ${\bf\Theta}={\bf\Theta}_o$.362 Having an estimator that is unbiased ancl whose variances are characterized in terms of the Fisher matrix simplifies our analysis considerably., Having an estimator that is unbiased and whose variances are characterized in terms of the Fisher matrix simplifies our analysis considerably.363 For the remainder of (his paper we shall assume that the large NV limit applies., For the remainder of this paper we shall assume that the large $N$ limit applies.364" The result that the maximum likelihood estimator O,;, is unbiased. however. also assumes that the velocity fiekl is Gaussian and that (he power spectrum can be well described bv the given paranmeterization. usually one derived from linear theory."," The result that the maximum likelihood estimator ${\bf\Theta}_{ML}$ is unbiased, however, also assumes that the velocity field is Gaussian and that the power spectrum can be well described by the given parameterization, usually one derived from linear theory."365 The collapse of nonlinear densitv perturbations ean cause both of these assumptions to be violated. and can result in Οι being biased in an unpredictable wav (Croft&Elstathion1994).," The collapse of small--scale, nonlinear density perturbations can cause both of these assumptions to be violated, and can result in ${\bf\Theta}_{ML}$ being biased in an unpredictable way \citep{C&E}."366. In order to recover an unbiased estimator. we shall utilize methods of data compression {ο filter out information about smallscale nonlinear velocities and retaining information about arge scales where (he linear and Gaussian approximations should remain valid.," In order to recover an unbiased estimator, we shall utilize methods of data compression to filter out information about small–scale nonlinear velocities and retaining information about large scales where the linear and Gaussian approximations should remain valid."367 While these nelhods are (vpically used to reduce (he size of an unwieldy data set without the loss of information. here we are instead interested in using data compression as a filler of unwanted information.," While these methods are typically used to reduce the size of an unwieldy data set without the loss of information, here we are instead interested in using data compression as a filter of unwanted information."368 Given the diffieuliv in treating (he general case. in the following we retain the model of a Gaussian velocity field.," Given the difficulty in treating the general case, in the following we retain the model of a Gaussian velocity field."369 The assumption here is (hat the primary effect of the collapse of 1ohlinear perturbations is the modification of the power spectrum on small scales ancl (hat departures from: Gaussianily are small enough not to effect our analvsis., The assumption here is that the primary effect of the collapse of nonlinear perturbations is the modification of the power spectrum on small scales and that departures from Gaussianity are small enough not to effect our analysis.370 We will return to this issue in Sec., We will return to this issue in Sec.371 7 and Sec. 5.., \ref{results} and Sec. \ref{sec-pow}.372 For a given set of velocity data. the simplest form of data compression involves replacing A original lineofsight velocities (@y.....va). with AN’ moments. (Qu...ar). where (for a more detailed discussion of cata compression see (1997))).," For a given set of velocity data, the simplest form of data compression involves replacing $N$ original line–of–sight velocities $(v_{1},\ldots,v_{N})$, with $N^{\prime}$ moments, $(u_{1},\ldots,u_{N^{\prime}})$, where $N^{\prime}\le N$ (for a more detailed discussion of data compression see \citet{TTH}) )."373 In this paper we will concentrate onfinear data compression. where the moments can. in general. be written as linear combinations of the velocities: where B;; is a constant |!xNo matrix.," In this paper we will concentrate on data compression, where the moments can, in general, be written as linear combinations of the velocities; where $B_{ij}$ is a constant $N^{\prime}\times N$ matrix."374 If the number of moments NW is less than .V. then replacing the v; with the u; will necessarily lead (ο a loss of information.," If the number of moments $N^{\prime}$ is less than $N$, then replacing the $v_{i}$ with the $u_{i}$ will necessarily lead to a loss of information."375 However. bv a proper choice of the matrix D;;. we can arrange it so that the information lost is primarily associated wilh scales where nonlinear effects are likely to have caused deviations from linear theory.," However, by a proper choice of the matrix $B_{ij}$, we can arrange it so that the information lost is primarily associated with scales where nonlinear effects are likely to have caused deviations from linear theory."376 Thus the process of data compression can be used to produce a set of moments which are much less sensitive to nonlinear effects than the original lineofsight velocities but that still retain the desired information about large scale power., Thus the process of data compression can be used to produce a set of moments which are much less sensitive to nonlinear effects than the original line–of–sight velocities but that still retain the desired information about large scale power.377" For simplicity. consider a model for the power spectrum in which the power on nonlinear scales is proportional to a single parameter 8, (we will discuss a specilic model of a power spectrum of this type below)."," For simplicity, consider a model for the power spectrum in which the power on nonlinear scales is proportional to a single parameter $\theta_{q}$ (we will discuss a specific model of a power spectrum of this type below)."378" Given aset of lineofsight velocities. rp...ta. we can determine the value of 6, within a mininun variance of A= l]/Fj.where Fy, is the qqih element of the Fisher Matrix (Eq. 5))"," Given a set of line–of–sight velocities, $v_{1}\ldots v_{N}$, we can determine the value of $\theta_{q}$ within a minimum variance of $\Delta\theta_{q}^{2} = 1/F_{qq}$, where $F_{qq}$ is the $qq$ th element of the Fisher Matrix (Eq. \ref{fishermat}) )"379 as discussed above., as discussed above.380" The variance AG, is (hus a measure of how sensitive the data set is to nonlinear scales: the larger the variance. the less smallscale inlormation the data contains."," The variance $\Delta\theta_{q}$ is thus a measure of how sensitive the data set is to nonlinear scales; the larger the variance, the less small–scale information the data contains."381Iu cosinological and shearing box ποσο ιοdependent boundary conditious create relative particle volocities that are inverse to gravitational acceleration aud increase with particle distance. ¢Xr.,"In cosmological and shearing box models time-dependent boundary conditions create relative particle velocities that are inverse to gravitational acceleration and increase with particle distance, $v\propto r$."382 In the shearing box model. the relative azimuthal particle velocity duc to the shear flow is. egXr. Where +. is the radial particle distance iu cvliuder coordinates.," In the shearing box model, the relative azimuthal particle velocity due to the shear flow is, $v_{\theta}\propto r_c$, where $r_c$ is the radial particle distance in cylinder coordinates."383" Ta cosimological models. the relative particle velocity iuduced by the ITubble flow Is, ονκF2 OWrere rs d8 the relative particle distance in Cartesian coorcinates,"," In cosmological models, the relative particle velocity induced by the Hubble flow is, $v_r \propto r$, where $r$ is the relative particle distance in Cartesian coordinates."384" These rela1ος and consequeutlv the correspondiug flows are scale“οσο,", These relations and consequently the corresponding flows are scale-free.385 The fact that the shear flow affects ouly the azimnthal velocity componcut may then accomut for the characcristic spiral aria like structures found iu, The fact that the shear flow affects only the azimuthal velocity component may then account for the characteristic spiral arm like structures found in386state. with a  of 1.6.,"state, with a $\gamma$ of 1.6."387 All the initial velocities were set to zero aud the blast was followed for 10 ms., All the initial velocities were set to zero and the blast was followed for 10 ms.388 The calculation was compared to an analvtical solution with a poiut-source cherey producing the blast. evaluated at times from 0.5 ms to LO 1s in 0.5 aus intervals.," The calculation was compared to an analytical solution with a point-source energy producing the blast, evaluated at times from 0.5 ms to 10 ms in 0.5 ms intervals."389 When comparing the exteuded-source to the point-source solution one would expect that at early tines (when the shock is closer to the source). and at later times closer to the initial location of the source. the discrepancies between the computed and analytical solutions should be larger.," When comparing the extended-source to the point-source solution one would expect that at early times (when the shock is closer to the source), and at later times closer to the initial location of the source, the discrepancies between the computed and analytical solutions should be larger."390 This is because the differences between a non-point source calculation aud the point source analytic solution will diminish as the disturbance moves outward., This is because the differences between a non-point source calculation and the point source analytic solution will diminish as the disturbance moves outward.391 The blast radii computed by SPHERLS matched those form the analytic solution to within 7.5 cim at all times., The blast radii computed by SPHERLS matched those form the analytic solution to within 7.5 cm at all times.392 The best match of shock radi (within 1.7 cni) occurred later in the calculation at a time of 10 ms. While the worst match (7.3 011 ) occurred much earlier iu the calculation at 3.5 ms.," The best match of shock radii (within 1.7 cm) occurred later in the calculation at a time of 10 ms, while the worst match (7.3 cm ) occurred much earlier in the calculation at 3.5 ms."393 The computed velocity. deusitv. aud pressure profiles were also compared to the analytic solution. but because of the extended source. only the zones outside the -initial explosion source were conrpared.," The computed velocity, density, and pressure profiles were also compared to the analytic solution, but because of the extended source, only the zones outside the initial explosion source were compared."394 The root niea square of the fractional error in velocity. density. and pressure was less thanSNC. and respectively in the last half of the calculation (5 mis to 10 13).," The root mean square of the fractional error in velocity, density, and pressure was less than, and respectively in the last half of the calculation (5 ms to 10 ms)."395" In the first half of the calculation (0.5 ms to 5 ms) the root mean square of the fractional errors are a bit larger. mostly due to the iffereuce between usine an extended source in the calculation versus a poiut source in the analytic solution aud are witlinGC and for the velocity. ensitv. and pressure respectively,"," In the first half of the calculation (0.5 ms to 5 ms) the root mean square of the fractional errors are a bit larger, mostly due to the difference between using an extended source in the calculation versus a point source in the analytic solution and are within, and for the velocity, density, and pressure respectively."396 The radial profiles of the velocity. density. and pressure fit quite well without any outlying poiuts.," The radial profiles of the velocity, density, and pressure fit quite well without any outlying points."397 Because the calculations are adiabatic. we expect the pulsation to neither erow nor decay and to be reproducible from one period to the rest.," Because the calculations are adiabatic, we expect the pulsation to neither grow nor decay and to be reproducible from one period to the next."398 This should provide a good test to verity hat our nunerical aleorithi fuuctious as desired over iuauv periods., This should provide a good test to verify that our numerical algorithm functions as desired over many periods.399" Both the low amplitude ndeanuenutal aud first overtone pulsation (C'alIII and CallV respectively) had a horizontal velocity ooerturbation imposed on them to break spherical sviunetry. by setting specific values of eg and ο, at a ceutral horizoutal zone located at of he total radius (18 zones iu from the surface of he 107 radial zone models}."," Both the low amplitude fundamental and first overtone pulsation (CalIII and CalIV respectively) had a horizontal velocity perturbation imposed on them to break spherical symmetry, by setting specific values of $v_\theta$ and $v_\phi$ at a central horizontal zone located at of the total radius (18 zones in from the surface of the 107 radial zone models)."400 The velocities were cirected lorizoutally out of the zone through sides deas and idars (see figure 1) )., The velocities were directed horizontally out of the zone through sides $A_{j\pm 1/2}$ and $A_{k\pm 1/2}$ (see figure \ref{fig:cell}) ).401 The maenituce of these horizontal velocities was taken to be half of the initial racial velocity at this radial location (0.3 kins +and 0.03 kins + for CallII and CallV respectively)., The magnitude of these horizontal velocities was taken to be half of the initial radial velocity at this radial location (0.3 km $^{-1}$and 0.03 km $^{-1}$ for CalIII and CalIV respectively).402 Figure 2. shows a two-dimensional slice at constant o of CallII slightly after the mitial couditious., Figure \ref{fig:r-theta-slice-horizontal} shows a two-dimensional slice at constant $\phi$ of CalIII slightly after the initial conditions.403 The slice is at 7225 s iuto the calculation (velatively carly iu the 1.10: s calculation) aud shows the cisturbance resulting from the horizoutal velocity perturbation as well as it’s location and geometry with respect to the rest of the inodel., The slice is at 7225 s into the calculation (relatively early in the $1 \times 10^7$ s calculation) and shows the disturbance resulting from the horizontal velocity perturbation as well as it's location and geometry with respect to the rest of the model.404 The period of the fuudameual mode is 561758 s for the low amplitude calculaion (CalIID). aud compares well with the perioc calculated from. LNA of 5611Ls. There is less than 0.124 difference between the periods of the two codes.," The period of the fundamental mode is 56178 s for the low amplitude calculation (CalIII), and compares well with the period calculated from LNA of 56114 s. There is less than $0.12$ difference between the periods of the two codes."405 The first overtoue model (CalIV). was ound to have a period of 38911 s aud comparewowith the LNA period of 39522 s. procducine ess than a differeuce.," The first overtone model (CalIV) was found to have a period of 38911 s and compares with the LNA period of 39522 s, producing less than a difference."406 Iu addition to the horizontal velocity perturbation we explored in CalllT and CalIV we also explored a velocity perturbation that is lore structured over a larger scale (CalV)., In addition to the horizontal velocity perturbation we explored in CalIII and CalIV we also explored a velocity perturbation that is more structured over a larger scale (CalV).407 To create this model we started with the same struc‘tural model aud radial velocity profile as Cal IIT. this tine however. using a surface amplitude of 10 luis |.," To create this model we started with the same structural model and radial velocity profile as Cal III, this time however, using a surface amplitude of 10 km $^{-1}$."408 On top of the radial velocity profile we added a velocity perturbation in the shape of a torus (see figure 3 for torus egcometiv)., On top of the radial velocity profile we added a velocity perturbation in the shape of a torus (see figure \ref{fig:torus-geo} for torus geometry).409 The velocitv perturbations were taken to be constaut on tιο surface of the torus (the two circles in the lower halfof fSgure 3)) aud parallel to the surface of the torus., The velocity perturbations were taken to be constant on the surface of the torus (the two circles in the lower halfof figure \ref{fig:torus-geo}) ) and parallel to the surface of the torus.410 Dx locating the closest point (defired bv angles a and 2) on the surface of the &xus to the point 15. the distance d in figure 3. cau be calculated.," By locating the closest point (defined by angles $\alpha$ and $\beta$ ) on the surface of the torus to the point $P$, the distance $d$ in figure \ref{fig:torus-geo} can be calculated."411 Then a Coussin centered on tjio surface of the orus with a maxim aupltule of 5 kms1 is evaluated at 4 providing the velocity magnitude., Then a Gaussian centered on the surface of the torus with a maximum amplitude of 5 km $^{-1}$ is evaluated at $d$ providing the velocity magnitude.412 The FWIIM of the Gaussian 1s chosen so that he velocity. perturbations do uot overlap the other parts of the torus. and πο that the velocity oerturbatious are still reasonably strong a zone or two away from the surface «X the torus.," The FWHM of the Gaussian is chosen so that the velocity perturbations do not overlap the other parts of the torus, and so that the velocity perturbations are still reasonably strong a zone or two away from the surface of the torus."413 The direction of the velocityis taken to be parallel to he surface of the torus at the locaiton closest to P., The direction of the velocityis taken to be parallel to the surface of the torus at the locaiton closest to $P$ .414 The velocity maguitudeOo is then broken iuto r. Ó. aud o components.," The velocity magnitude is then broken into $r$ , $\theta$ , and $\phi$ components."415 The result of applying this, The result of applying this416Warren et al.,Warren et al.417 2008. Berger et al.," 2008, Berger et al."418 2011. Mulu-Moore 2011) show that the loops are not always in hydrostatic equilibrium nor isothermal.," 2011, Mulu-Moore 2011) show that the loops are not always in hydrostatic equilibrium nor isothermal."419 Here we supposed the idealistic situation of a static background. however recent analysis by Ruderman (2011) showed that the the temporal dependence of density through flow and cooling can also influence the ratio of the two periods.," Here we supposed the idealistic situation of a static background, however recent analysis by Ruderman (2011) showed that the the temporal dependence of density through flow and cooling can also influence the ratio of the two periods."420 In the Appendix we estimate the corrections to the chosen eigenfunctions due to the density stratification., In the Appendix we estimate the corrections to the chosen eigenfunctions due to the density stratification.421 Analytical progress can be made in the small v/y limit., Analytical progress can be made in the small $y/\chi$ limit.422 Since y Is a value smaller than one. this condition would automatically mean that," Since $\chi$ is a value smaller than one, this condition would automatically mean that"423To show the properties of the distribution of high-density reeious we plot in Figure 7 correlation fuuctious of clusters in verv rich superclusters. samples ACO.AS. ACO.Ra. APALAS and APALRS.,"To show the properties of the distribution of high-density regions we plot in Figure 7 correlation functions of clusters in very rich superclusters, samples ACO.A8, ACO.R8, APM.A8 and APM.R8."424 To generate comparison Poisson salples we used selection functions described iu section 5.1L below. with parameters given in Table 1.," To generate comparison Poisson samples we used selection functions described in section 5.1 below, with parameters given in Table 1."425 For samples ACO.RS and APALRS we plot values of the correlatio- fiction with error bars. for samples ACO.AS iud APALAS we show correlation functious smoothed with Gaussian window of dispersion 10Mpc.," For samples ACO.R8 and APM.R8 we plot values of the correlation function with error bars, for samples ACO.A8 and APM.A8 we show correlation functions smoothed with Gaussian window of dispersion 10."426. Abell clusters occupy a double-conical volume with fuLB depth of τοῦAlpe. thus it is possible to calculate the correlation function for huge separations.," Abell clusters occupy a double-conical volume with full depth of 700, thus it is possible to calculate the correlation function for large separations."427 The APM sample is defined in a simaller volume. aud the correlation function can be found for smaller separations.," The APM sample is defined in a smaller volume, and the correlation function can be found for smaller separations."428 We see that correlation factions. derived for Abell clusters iu very rich superchisters. are oscillating.," We see that correlation functions, derived for Abell clusters in very rich superclusters, are oscillating."429 We can recognize 5 secondary 1iaxina aud 6 imiuina., We can recognize 5 secondary maxima and 6 minima.430 The mean separation of maxima and of minima is 116+21Mpc..., The mean separation of maxima and of minima is $116 \pm 21$.431 The differences between correlation functions derived for all clusters aud for clusters with measured redshifts (samples ACO.AS and ACO.Rs. respectively) are sinall.," The differences between correlation functions derived for all clusters and for clusters with measured redshifts (samples ACO.A8 and ACO.R8, respectively) are small."432 The correlation function of APAL clusters has a more colmplicated behavior., The correlation function of APM clusters has a more complicated behavior.433 If we use alb clusters (sample APALAS). then the first and the secoud secondary maxima have locations close the locations of respective maxima found for Abell cluster samples.," If we use all clusters (sample APM.A8), then the first and the second secondary maxima have locations close the locations of respective maxima found for Abell cluster samples."434 Similarly we cau identity the first and the third minima with minima in the Abell cluster correlation function., Similarly we can identify the first and the third minima with minima in the Abell cluster correlation function.435 But instead of the second luvin near separations of r~200AIpe.. the APAI sample has a inaxinuna at this separation. nof present in the Abell sample.," But instead of the second minimum near separations of $r \approx 200$, the APM sample has a maximum at this separation, not present in the Abell sample."436 If we use only clusters with measured redshifts (sample APALRS). then the first secoudary maxiuun of the correlationfuuction atf 130 dadisappears. and the peculiar inaxiuun ator Ish hhas au enhanced amplitude.," If we use only clusters with measured redshifts (sample APM.R8), then the first secondary maximum of the correlationfunction at $r \approx 130$ disappears, and the peculiar maximum at $r \approx 185$ has an enhanced amplitude."437 The reason for such peculiar behavior can be understood when we cousider the distribution of verv rich superclusters in the APAL samples., The reason for such peculiar behavior can be understood when we consider the distribution of very rich superclusters in the APM samples.438 The sample with all clusters (ΑΡΑAS) is dominated by nmnuuerous very rich superclusters located iu the more distant shell (see right-haud upper pancl of Figure 6)., The sample with all clusters (APM.A8) is dominated by numerous very rich superclusters located in the more distant shell (see right-hand upper panel of Figure 6).439 These superclusters are distributed fürlv regululv aud form a supercluster-void network with a step around 120 ((se6 previous Section)., These superclusters are distributed fairly regularly and form a supercluster-void network with a step around 120 (see previous Section).440 I£ sve use the sample with measured redshifts ouly (APALRS) instead. then the uuuber of verv rich superclusters in the sample decreases: the sample is dominated by two very rich superclusters that border the Sculptor void. oue of the largest voids known (see the laree circles iu the right panels of Figure 6 aud a jump at 200 oof distance distribution of APALR&® clusters in Figure 9).," If we use the sample with measured redshifts only (APM.R8) instead, then the number of very rich superclusters in the sample decreases; the sample is dominated by two very rich superclusters that border the Sculptor void, one of the largest voids known (see the extra-large circles in the right panels of Figure 6 and a jump at 200 of distance distribution of APM.R8 clusters in Figure 9)."441 The secondary ιαπται of the correlation function of the sample APALR®& is determined by mutual separations of clusters belonging to these superclusters., The secondary maximum of the correlation function of the sample APM.R8 is determined by mutual separations of clusters belonging to these superclusters.442 We shall discuss this behavior of the APM sample below., We shall discuss this behavior of the APM sample below.443 We also calculated the correlation length(ie., We also calculated the correlation length(i.e.444 the separation at which the correlation fiction equals unity). ry. for all samples.," the separation at which the correlation function equals unity), $r_0$, for all samples."445 The results. eiven in Table 1. show that there are ouly miner differences between Abell aud APAI cluster samples.," The results, given in Table 1, show that there are only minor differences between Abell and APM cluster samples."446 In both cases the correlation leneth. determined for all clusters. is ry=18353Mpezs for clusters in rich superclusters it is 5j=3945Ape... aud for clusters iu very rich superchuisters. ry=52470 ((the mean aud scatter are determined from all Abell aud APAI samples with respective Nv).," In both cases the correlation length, determined for all clusters, is $r_0 = 18 \pm4473$; for clusters in rich superclusters it is $r_0 = 39 \pm4485$, and for clusters in very rich superclusters, $r_0 = 52 \pm4497$ (the mean and scatter are determined from all Abell and APM samples with respective $N_{cl}$ )."450 Similar values have been found by E97b., Similar values have been found by E97b.451 The power spectrum. P(A). is the the Fourier transform of the correlation fiction. Cr). aud vice versa:," The power spectrum, $P(k)$ , is the the Fourier transform of the correlation function, $\xi(r)$ , and vice versa:"452cluster sources (see Sect.,cluster sources (see Sect.453 2.2 and Table 1) makes the source subtraction at. 1.4 11 more critical than at. lower frequencies., 2.2 and Table 1) makes the source subtraction at 1.4 GHz more critical than at lower frequencies.454 Hence we simply compared the sum of the (ux clensity of the individual sources S4. S6 and the relic to the total Dux density of the Lband images integrating over the whole area encompassing them.," Hence we simply compared the sum of the flux density of the individual sources S4, S6 and the relic to the total flux density of the L–band images integrating over the whole area encompassing them."455 No difference is detected in either images. and in both cases the values agree within =flee," No difference is detected in either images, and in both cases the values agree within $\ltsim$."456 The results of our analysis disagree with Govoni et al. (2011).," The results of our analysis disagree with Govoni et al. \cite{govoni11},"457. who recently claimed the detection of a radio halo (with flux 2030 mJv at 14 Gllz) using the same VLA archival data., who recently claimed the detection of a radio halo (with flux 20–30 mJy at 1.4 GHz) using the same VLA archival data.458 They. also derived an upper limit to the fux clensity of the radio halo at 330 MlIS (x:135 my) using an archive VLA observation. pointed 1.5° away from the cluster centre. and give an upper limit of athedhGH«13 to its spectral slope.," They also derived an upper limit to the flux density of the radio halo at 330 MHz $\leq 135$ mJy) using an archive VLA observation, pointed $^{\circ}$ away from the cluster centre, and give an upper limit of $\alpha_{\rm VLA~330~MHz}^{\rm VLA~1.4~GHz} \leq 1.3$ to its spectral slope."459 Our 325 MlIz observations are about 5 times more sensitive than those in Govoni οἱ al.," Our 325 MHz observations are about 5 times more sensitive than those in Govoni et al.,"460 ancl rule out the presence of a halo in 7781 with [lux density of 2030 mJv at 1.4 Cillz., and rule out the presence of a halo in 781 with flux density of 20–30 mJy at 1.4 GHz.461" Phe resulting spectral index. with our improved. value of the 325. MllIz residual flux density. would be adhd""Lb.vlMian:€Hz0.5 (using à conservative limit. ΟΔΙΕ} my) which is definitely unplausible for diffuse cluster sources."," The resulting spectral index, with our improved value of the 325 MHz residual flux density, would be $\alpha_{\rm GMRT~325~MHz}^{\rm VLA~1.4~GHz} \leq 0.5$ (using a conservative limit, $_{\rm 325 MHz}$$\leq$ 40 mJy) which is definitely unplausible for diffuse cluster sources."462 We point out that one feature in the Govoni et al., We point out that one feature in the Govoni et al.463 residual image is the discrete source 83. which has an optical counterpart. as clear from the left panel of Fig.," residual image is the discrete source S3, which has an optical counterpart, as clear from the left panel of Fig."464 1 and in VOS: moreover. the sources labelled € and D in their paper are clearly extended in the direction of the residual emission.," \ref{fig:a781_tot} and in V08; moreover, the sources labelled C and D in their paper are clearly extended in the direction of the residual emission."465 A statistical connection between the dynamical state of massive clusters in the GMIE sample (WOT ancl VOS) and the presence of radio halos has been derived by CLO. confirming the picture where mergers switchon radio halos in galaxy clusters.," A statistical connection between the dynamical state of massive clusters in the GMRT sample (V07 and V08) and the presence of radio halos has been derived by C10, confirming the picture where mergers switch–on radio halos in galaxy clusters."466 ΤΙ is one of the few outliers in the Cassano et al., 781 is one of the few outliers in the Cassano et al.467 diagrams. Iving in the region of dvnamicallv clisturbecl clusters. but with no detected radio halo at 610 MlIZ (VOS).," diagrams, lying in the region of dynamically disturbed clusters, but with no detected radio halo at 610 MHz (V08)."468 The observations at 325 MIIz. presented in this Letter do not allow a firm detection of a radio halo in the central region ( 1.5 Alpe) of ATTSL., The observations at 325 MHz presented in this Letter do not allow a firm detection of a radio halo in the central region $\sim$ 1.5 Mpc) of 781.469 LE we consider a spectral index à~1.3 between 3251400 MlIz. the residual cilfuse emission measured in our images. 9525Ardy 20 my. puts a conservative limit to the 1.4 Giz luminosity of a halo in ACUSD Piaons€62(994/20) 1077W (where σος is the Dus at 325 MlIZ in mJy).," If we consider a spectral index $\alpha \sim 1.3$ between 325–1400 MHz, the residual diffuse emission measured in our images, $_{\rm 325~MHz}\sim$ 20 mJy, puts a conservative limit to the 1.4 GHz luminosity of a halo in 781 $_{\rm 1.4~GHz} \leq 6 \times (S_{0.3}/20)$$\times$ $^{23}$ W $^{-1}$ (where $S_{0.3}$ is the flux at 325 MHz in mJy)."470 Our results. do not challenge the cluster. mergerradio halo connection., Our results do not challenge the cluster merger--radio halo connection.471" On the basis of the Diaou, Lx correlation. the expected 14 Gilz radio luminosity of the halo is still consistent with our upper limit."," On the basis of the $_{\rm 1.4~GHz}$ $_{\rm X}$ correlation, the expected 1.4 GHz radio luminosity of the halo is still consistent with our upper limit."472 As a matter of fact. the four known radio halos with radio power 107! WO + hosted in clusters with Xray luminosity. Ly5. JOH erg s.+ (ie. 22255. 22256. Coma and 7754) are only detected at low redshift. z<0.1.," As a matter of fact, the four known radio halos with radio power $\sim 10^{24}$ W $^{-1}$ hosted in clusters with X–ray luminosity $_{\rm X} \leq 5$$\times$ $^{44}$ erg $^{-1}$ (i.e. 2255, 2256, Coma and 754) are only detected at low redshift, $\leq$ 0.1."473 On the other hand. if we assume the 1.4 Gllz luminosity recently claimed by Ciovoni et al. (2011).," On the other hand, if we assume the 1.4 GHz luminosity recently claimed by Govoni et al. \cite{govoni11},"474 the halo would lic about an order of magnitude above the racdio/Nrav correlation., the halo would lie about an order of magnitude above the radio/X–ray correlation.475 Incidentallv. in their paper the halo is found. consistent with that correlation simply. because the authors use the old. overestimated. luminosity [or 7781. as given in the eDCS catalogue (see Sect.," Incidentally, in their paper the halo is found consistent with that correlation simply because the authors use the old overestimated luminosity for 781, as given in the eBCS catalogue (see Sect."476 2)., 2).477 Assuming that the residual emission at the centre of ATT7S1 does reveal the presence of an underline very. low brightness radio halo. the combination of 325 anc 610 MlIZ provide further hints on its spectral properties.," Assuming that the residual emission at the centre of 781 does reveal the presence of an underlying very low brightness radio halo, the combination of 325 and 610 MHz provide further hints on its spectral properties."478 The 610 MlIz upper limit and the residual emission. at 325 MIlIz imply a spectral index of the emission steeper than a 2.5., The 610 MHz upper limit and the residual emission at 325 MHz imply a spectral index of the emission steeper than $\alpha \geq$ 2.5.479 Even accounting for the uncertainty in the 610. MlIz upper limit. whieh depends on the assumptions made on 16 unknown brightness distribution. (see Brunetti ct al.," Even accounting for the uncertainty in the 610 MHz upper limit, which depends on the assumptions made on the unknown brightness distribution (see Brunetti et al."480 2007 and VOS). our experience shows that radio halos with SoloMay =l020 mJy are well imaged in the GAIRT Iacdio llalo Survey (ie. AGGOT at a similar τον. VOS).," 2007 and V08), our experience shows that radio halos with $_{\rm 610~MHz}$ =10–20 mJy are well imaged in the GMRT Radio Halo Survey (i.e. 697 at a similar redshift, V08)."481 This sugeests a conservative upper limit of S510Ην<10 mJy. =vhich would still imply à steep spectrum halo. ie. 021.5.," This suggests a conservative upper limit of $_{\rm 610~MHz}<10$ mJy, which would still imply a steep spectrum halo, i.e. $\alpha$$>$ 1.5."482 Lt is noteworthy that statistical expectations based on the turbulent reacceleration model show that radio halos with steep spectra should be quite common in merging clusters with masses 1057 AL.. similar to that of 7781 (Cassano et al.," It is noteworthy that statistical expectations based on the turbulent re–acceleration model show that radio halos with steep spectra should be quite common in merging clusters with masses $\sim 10^{15}$ $_{\odot}$, similar to that of 781 (Cassano et al."483 2006)., 2006).484 We have presented deep GALRP 325 MIIz observations of the unrelaxed ancl luminous cluster 7781. which is a noticeable outlier in the quantitative correlations connecting cluster mergers ancl the presence of a radio halo (C10).," We have presented deep GMRT 325 MHz observations of the unrelaxed and luminous cluster 781, which is a noticeable outlier in the quantitative correlations connecting cluster mergers and the presence of a radio halo (C10)."485 Our images show that the peripheral dilfuse source is the dominant radio feature of the cluster. and. only residual emission at the level of SasΗλ 1520 mv is found in a region of 1.5 \Ipe around the cluster centre (implying a conservative Dux density limit of 9325stgs; 9040 mJy).," Our images show that the peripheral diffuse source is the dominant radio feature of the cluster, and only residual emission at the level of $_{\rm 325~MHz}$$\sim$ 15–20 mJy is found in a region of $\sim 1.5$ Mpc around the cluster centre (implying a conservative flux density limit of $_{\rm 325~MHz}$$\sim$ 30–40 mJy)."486 This value improves the upper limit given in Covoni ct al., This value improves the upper limit given in Govoni et al.487 (2011) by almost a factor of 5. and rules out the claim of a detection of a radio halo at 1.4 Gilg (Govoni et al.," \cite{govoni11}488 by almost a factor of 5, and rules out the claim of a detection of a radio halo at 1.4 GHz (Govoni et al."489 2011) on the basis of simple spectral considerations., 2011) on the basis of simple spectral considerations.490 With our data we cannot confirm the presence of a radio halo at the centre of AT7S1., With our data we cannot confirm the presence of a radio halo at the centre of 781.491 I£ the 325 MlIZ residual emission is real. then it might trace an underlying halo with steep spectrum.," If the 325 MHz residual emission is real, then it might trace an underlying halo with steep spectrum."492 Future high sensitivity observations at lower frequencies combined with deeper observations at GLO MlIz will allow us to clarify the nature of the residual emission., Future high sensitivity observations at lower frequencies combined with deeper observations at 610 MHz will allow us to clarify the nature of the residual emission.493 We thank S. σον for his help in the Xray checks., We thank S. Ettori for his help in the X–ray checks.494 GMRBE is run by the National Centre for Radio Astrophysics of the ‘Tata Institute of Fundamental. Research., GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research.495 Partial support was provicled by the Chandra erant ARO-11017X. NASA contract NASS-39073 and the Smithsonian Institution.," Partial support was provided by the Chandra grant AR0-11017X, NASA contract NAS8-39073 and the Smithsonian Institution."496 S.C. acknowledges support by NASA through Einstein Postdoctoral Fellowship PEO110071. awarded by the Chandra XNray Center which is operated. by the Smithsonian Astrophysical Observatory uncer contract NASS03060., S.G. acknowledges support by NASA through Einstein Postdoctoral Fellowship PF0–110071 awarded by the Chandra X–ray Center which is operated by the Smithsonian Astrophysical Observatory under contract NAS8–03060.497 This work is partially supported. by. INAL and ASIINAF under. grants. PRININAP2007. anclL/088/06/0.," This work is partially supported by INAF and ASI–INAF under grants PRIN–INAF2007, PRIN--INAF2008 and I/088/06/0."498 | qx ,(1 + + 2 + _x = 0.499"The Wrouskian of this equation is -(feOr vs We further simplily the analysis by setting the initial displacement £4, to zero.", The Wronskian of this equation is - = ) = We further simplify the analysis by setting the initial displacement $\xi_{x0}$ to zero.500" With these stinplificatious. the solution given by equations (?2)) and (??)) becomes As in section 3.3. the energy integral for the incompressive perturbations is given by (E)fey — iw,9L? hudky P ο”. for initial perturbatious perpeudicular toaud isotropic in Ay."," With these simplifications, the solution given by equations \ref{SOLVX}) ) and \ref{SOLX}) ) becomes As in section 3.3, the energy integral for the incompressive perturbations is given by E_i = _0 L^2 k_0 dk_0 ) )^2 + N_x^2 ( ], for initial perturbations perpendicular toand isotropic in $\bk_0$."501 Changiug integration variables to 7(ο+cot0. the angular integral becomes where we have used the relation sind=(14-75). !.," Changing integration variables to $\tilde{\tau} = \qe\Omega t + 502\cot\theta$, the angular integral becomes where we have used the relation $\sin\theta = (1 + \tilde{\tau}_0^2)503^{-1}$ ."504 In the limit of large gQ/. the dominant contribution to the angular integral comes from the region 0ESoτσ GqQl.," In the limit of large $\qe \Omega t$, the dominant contribution to the angular integral comes from the region $0 \lesssim 505\tilde{\tau} \lesssim \qe \Omega t$ ."506 This can beseen from the, This can beseen from the507"lines in the UVES solar spectrum and found the resulting value of 5784+152 K to agree well with the literature (?,p.341)..",lines in the UVES solar spectrum and found the resulting value of $5784\pm152$ K to agree well with the literature \citep[][p.~341]{AllenEd4}.508" As an alternative to the modeling of line EWs, the stellar parameters can also be obtained by directly fitting the profile of spectral lines using synthetic spectra."," As an alternative to the modeling of line EWs, the stellar parameters can also be obtained by directly fitting the profile of spectral lines using synthetic spectra."509 This approach is implemented in the “Spectroscopy Made Easy” (SME) package (version2.1;?).., This approach is implemented in the “Spectroscopy Made Easy” (SME) package \citep[version 2.1;][]{ValentiPiskunov1996}.510 This interpolates on a Kurucz grid of stellar atmospheres and employs a (?) line list to compute a synthesized spectrum for each set of stellar parameters., This interpolates on a Kurucz grid of stellar atmospheres and employs a \citep{Piskunov1995} line list to compute a synthesized spectrum for each set of stellar parameters.511 The observed spectrum is fitted by minimizing the residuals via a non-linear least-squares algorithm., The observed spectrum is fitted by minimizing the residuals via a non-linear least-squares algorithm.512 We used SME to determine the stellar parameters first in a global fit and second by fitting individual lines sensitive to aand logg., We used SME to determine the stellar parameters first in a global fit and second by fitting individual lines sensitive to and $\log{g}$.513" Currently, it is not feasible to compute a reliable error estimate for a global fit due to the large computational effort of calculating synthetic spectra."," Currently, it is not feasible to compute a reliable error estimate for a global fit due to the large computational effort of calculating synthetic spectra."514" From the analysis of a set of 1040 FGK stars, however, ? derived typical errors of 44 K inΤεῃ,, 0.06 dex in logg, and 0.03 dex in metallicity, which we adopt below."," From the analysis of a set of 1040 FGK stars, however, \citet{ValentiFischer2005} derived typical errors of 44 K in, 0.06 dex in $\log{g}$, and 0.03 dex in metallicity, which we adopt below."515" For the analysis of single line profiles, we usually fixed all parameters at their best-fit values and obtained the error by computing the An approximation of the effective temperature can be obtained by investigating the Ho line profile."," For the analysis of single line profiles, we usually fixed all parameters at their best-fit values and obtained the error by computing the An approximation of the effective temperature can be obtained by investigating the $\alpha$ line profile."516" The wings of the prominent Ha line at a nominal wavelength of 6563 aare sensitive to a wide range of effective temperatures of G- and F- stars (e.g.?),, while remaining reasonably unaffected by the surface gravity, logg, and the metallicity."," The wings of the prominent $\alpha$ line at a nominal wavelength of $6563$ are sensitive to a wide range of effective temperatures of G- and F-type stars \citep[e.g.][]{Fuhrmann2004}, while remaining reasonably unaffected by the surface gravity, $\log{g}$, and the metallicity."517" However, active late-type stars are known to show strong contributions of chromospheric emission in the Balmer lines, which can even extend into the wings of the line profiles (e.g., ?).."," However, active late-type stars are known to show strong contributions of chromospheric emission in the Balmer lines, which can even extend into the wings of the line profiles \citep[e.g.,][]{Montes1997}."518 Thiscan interfere with the determination of the effective temperature., Thiscan interfere with the determination of the effective temperature.519 We independently analyzed the line wings of Ha and Hf., We independently analyzed the line wings of $\alpha$ and $\beta$.520 Consistent results for the temperatures deduced from both Balmer lines indicate that the wings of Ha are not strongly affected by chromospheric activity (??)..," Consistent results for the temperatures deduced from both Balmer lines indicate that the wings of $\alpha$ are not strongly affected by chromospheric activity \citep{Fuhrmann2004, Koenig2005}."521" A visual inspection of the symmetry of the Ha line profile suggested that the UVES pipeline, in this respect, provided a superior result, so that we rely on the pipeline spectra during this analysis."," A visual inspection of the symmetry of the $\alpha$ line profile suggested that the UVES pipeline, in this respect, provided a superior result, so that we rely on the pipeline spectra during this analysis."522" We note, however, that in any case a manual rectification of the spectrum is necessary."," We note, however, that in any case a manual rectification of the spectrum is necessary."523" Hence, this method is prone to considerable uncertainties."," Hence, this method is prone to considerable uncertainties."524" We used SME to fit synthetic spectra to the observed Ha and Hf line profiles excluding the line cores and found an effective temperature Te of 551030 K and 5520/50 K, respectively."," We used SME to fit synthetic spectra to the observed $\alpha$ and $\beta$ line profiles excluding the line cores and found an effective temperature $T_\mathrm{eff}$ of $5510^{+90}_{-70}$ K and $5520^{+80}_{-90}$ K, respectively."525 This is consistent with the result of 5450+120 K derived from the analysis of the Ha line observed with HARPS (?).., This is consistent with the result of $5450\pm120$ K derived from the analysis of the $\alpha$ line observed with HARPS \citep{Bouchy2008}.526 The good agreement between the Balmer line estimates indicates that the chromospheric contribution remains small., The good agreement between the Balmer line estimates indicates that the chromospheric contribution remains small.527 Several pressure-broadened spectral lines can be used to determine the surface gravity of late-type stars., Several pressure-broadened spectral lines can be used to determine the surface gravity of late-type stars.528" Examples of these lines are the ib triplet (?),, the D doublet, and the lines at 6122, 6162, and 6439 citep[e.g.,][]Bruntt2010.."," Examples of these lines are the b triplet \citep{Fuhrmann1998}, the D doublet, and the lines at 6122, 6162, and 6439 \\citep[e.g.,][]{Bruntt2010}."529" Because of the gap between the two detectors, the spectrum does not contain any Mgib lines."," Because of the gap between the two detectors, the spectrum does not contain any b lines."530 We therefore concentrated on the Na and Ca lines., We therefore concentrated on the Na and Ca lines.531" With SME, we iteratively fitted synthetic spectra to the three lines and the Na D line, leaving only logg as a free parameter."," With SME, we iteratively fitted synthetic spectra to the three lines and the Na D line, leaving only $\log{g}$ as a free parameter."532 The resulting value from the lines (4.49+0.14) was found to be consistent with the value derived from Na D (4.53+0.18)., The resulting value from the lines $4.49\pm0.14$ ) was found to be consistent with the value derived from Na D $4.53\pm0.18$ ).533 The abundance of lithium is a valuable indicator of the stellar age., The abundance of lithium is a valuable indicator of the stellar age.534" The element is depleted by lithium burning primarily during the early phases of stellar evolution, when the existence of deep convection zones allows for the interchange of material between the stellar interior and the surface (e.g.,?).."," The element is depleted by lithium burning primarily during the early phases of stellar evolution, when the existence of deep convection zones allows for the interchange of material between the stellar interior and the surface \citep[e.g.,][]{Pinsonneault1994}."535" sshows a strong Li line at 6708A,, for which wedetermined an EW of 139+1mA.."," shows a strong Li line at $\approx 6708$, for which wedetermined an EW of $139\pm1$."536 We used SME to fit synthetic spectra with all remaining stellar parameters kept fixed and derived an abundance of Aj;=42.6€0.3., We used SME to fit synthetic spectra with all remaining stellar parameters kept fixed and derived an abundance of $A_{\mathrm{Li}}=+2.6\pm0.3$.537" This value confirms the result of ?,, who found Αι;= +2.8."," This value confirms the result of \cite{Gillon2010}, who found $A_{\mathrm{Li}}=+2.8$ ."538" According to ?,, this a Li content is typically found in G-type stars of T«g—5600 KatanagebetweenlOOand250 Ma."," According to \cite{SestitoRandich2005}, this a Li content is typically found in G-type stars of $=5600$ K at an age between 100 and 250 Ma."539 In Fig., In Fig.540" | we show effective temperature versus line EW for the open stellar clusters Orion IC (10 Ma), NGC 2264 (10 Ma), Pleiades (100 Ma), Ursa Major (300 Ma), Hyades location of iis marked in the diagram."," \ref{fig:LiCluster} we show effective temperature versus line EW for the open stellar clusters Orion IC $10$ Ma), NGC 2264 $10$ Ma), Pleiades $100$ Ma), Ursa Major $300$ Ma), Hyades $660$ Ma), and Praesepe $660$ Ma) \citep{King1993, Soderblom1999, Soderblom1993, Soderblom1993b, Soderblom1990, Soderblom1993c}, additionally, the location of is marked in the diagram."541" The clusters are of different age, so that putting iin the context of the cluster properties provides an indication of its age."," The clusters are of different age, so that putting in the context of the cluster properties provides an indication of its age."542" The EW of iis best compatible with those in the Pleiades, indicating an age of about 100 Ma."," The EW of is best compatible with those in the Pleiades, indicating an age of about $100$ Ma."543" This findingis consistent with the numbers derived by ? from evolutionary modeling and also the age estimates given by ?,, who derive an age between 30 and 316 Ma."," This findingis consistent with the numbers derived by \citet{GuillotHavel2011} from evolutionary modeling and also the age estimates given by \citet{Gillon2010}, , who derive an age between $30$ and $316$ Ma."544Since the first Πας]ie of a debris disk around ο) Pictoris (?).. aid the remarkable successes of the radial velocity techlinicpue for exoplauet discovery heralded nearly a decade later by a companion fo solar-lke 51 Peeasi (?).tjo nudistanding of planctary svstenis formation aud evolution has |ecole one of astrononiv«s ercatest challeueos.,"Since the first imaging of a debris disk around $\beta$ Pictoris \citep{1984Sci...226.1421S}, and the remarkable successes of the radial velocity technique for exoplanet discovery heralded nearly a decade later by a companion to solar-like 51 Pegasi \citep{1995Natur.378..355M}, the understanding of planetary systems formation and evolution has become one of astronomy's greatest challenges."545 Today. at least 22 debris disks lave lecu liae at optical. iuyared. or submillimeter wavelengths.," Today, at least 22 debris disks have been imaged at optical, infrared, or submillimeter wavelengths."546 Such «isks are thought to be the cradle where plauctary SvstenuirS have recently formed., Such disks are thought to be the cradle where planetary systems have recently formed.547 The observed dust COMPOrent ds not primordial but instead produced by collisions among largero rocky bodies., The observed dust component is not primordial but instead produced by collisions among larger rocky bodies.548 This makes debris disks ovious places o search for planets. and many show possible iudirect sigus of their preseuce. such as dust structiPOS OF ¢lisk asviuuetries.," This makes debris disks obvious places to search for planets, and many show possible indirect signs of their presence, such as dust structures or disk asymmetries."549 Tlic| receut. detection and coufirmation of a 9 pplane within the disk of (se1uad-niajor axis between 8 aud 15 4v)) usine direct deep inagine validates the Luk between structures in debris disks aud the preseuce of planets (??)..," The recent detection and confirmation of a $\sim9$ planet within the disk of (semi-major axis between 8 and 15 ) using direct deep imaging validates the link between structures in debris disks and the presence of planets \citep{2009A&A...493L..21L,2010Sci...329...57L}."550 Beside:μα this pinet. «mnl a couple of planetarvanuass objects have heen detected around stars with a debris disk.," Besides this planet, only a couple of planetary-mass objects have been detected around stars with a debris disk."551 Iu fact. most debris disks have been naage ALOUid young A- or F-type stars. whic rare either rapi rotators and/or active stars.," In fact, most debris disks have been imaged around young bright A- or F-type stars, which are either rapid rotators and/or active stars."552 The search for conpanious with radial velocity tecliniques. aroun these stars Is therefore extremely difficult., The search for companions with radial velocity techniques around these stars is therefore extremely difficult.553 Kev breakthroughs have recetly beeu iade with high-contrast dmagine: a <3-\ pplanctary companion was detected in f16 ouskirts of Fomalhaut’s debris disk (119AUfromthestar:7).. while four planetary companions of 7. 10. 10. and 10 wwere dnaged at GS. 38. 2[. and LLAU. res)ectivelv. from UR 58799 (??)..," Key breakthroughs have recently been made with high-contrast imaging: a $<3$ planetary companion was detected in the outskirts of Fomalhaut's debris disk \citep[119~\au\ from the554 star;][]{2008Sci...322.1345K}, while four planetary companions of 7, 10, 10, and 10 were imaged at 68, 38, 24, and 14, respectively, from HR 8799 \citep{2008Sci...322.1348M,2010Natur.468.1080M}."555 It is not οear whether these objects could have formed through core accretion and not from eravitational mstabilitios — the foremost theory of plauct formation. although bis as erous candidate for this formation scenario (?)..," It is not clear whether these objects could have formed through core accretion – and not from gravitational instabilities – the foremost theory of planet formation, although b is a serious candidate for this formation scenario \citep{2010Sci...329...57L}."556 Most compauious detected with high-contrast inaeiug. such as AB Pic b (7) or 2MI207 b (2). are believed to be either too far or too massive to have formed through core accretion.," Most companions detected with high-contrast imaging, such as AB Pic b \citep{2005A&A...438L..29C} or 2M1207 b \citep{2004A&A...425L..29C}, are believed to be either too far or too massive to have formed through core accretion."557 An alternate pathway gaining widespread luterest is a stellar formation iuechiuuisni. Le.. formation diving the fragmentation and c‘ollapse of a iiolecular cloud.," An alternate pathway gaining widespread interest is a stellar formation mechanism, i.e., formation during the fragmentation and collapse of a molecular cloud."558 There are many unanswered questious raised by these models., There are many unanswered questions raised by these models.559 Do these two proceses for forming planets and brown dwarts/low-iass stars operate exclusively (does one inhibit the other)?, Do these two processes for forming planets and brown dwarfs/low-mass stars operate exclusively (does one inhibit the other)?560 Can core accretion from a disk operate when a brown-dwarf companion exists at large separation?, Can core accretion from a disk operate when a brown-dwarf companion exists at large separation?561 Iu contrast. can disks aud planets exist around tight binary svstenis. composed of the primary star and a very close low-iass star or brown dwart?," In contrast, can disks and planets exist around tight binary systems, composed of the primary star and a very close low-mass star or brown dwarf?"562 Tow do massive conipauions mapact t1ο dyiauice evolution of planets aud disks?, How do massive companions impact the dynamic evolution of planets and disks?563 To answer these questions. i Is necessary to probe the innenuost regions of debris «isks when searchius for substellar companions.," To answer these questions, it is necessary to probe the innermost regions of debris disks when searching for substellar companions."564 For the closest debris disk. direct Huaging proved to be a successtul technique. as shown for > Pic or Fomalhaut.," For the closest debris disk, direct imaging proved to be a successful technique, as shown for $\beta$ Pic or Fomalhaut."565 But most o the vouueg associations (as well as stellar fornüung regions) lie at more than a iundred parsecs., But most of the young associations (as well as stellar forming regions) lie at more than a hundred parsecs.566 At such a distance. LO lis equivalent to LOQuumas. less than twice the diffraction init of an B-nueter telescope iu he near-infrared.," At such a distance, 10 is equivalent to mas, less than twice the diffraction limit of an 8-meter telescope in the near-infrared."567 This observational domain is not filled by differeutial imagine echuiques. whose iuner working angle is typically of (wo resolution elements.," This observational domain is not filled by differential imaging techniques, whose inner working angle is typically of few resolution elements."568 It is wither filled by long vascline interferometry: the field of view of a single node interferometer is too s1uall. equal to the resolution clement of oue of its telescopes.," It is neither filled by long baseline interferometry: the field of view of a single mode interferometer is too small, equal to the resolution element of one of its telescopes."569 The effectiveness of both, The effectiveness of both570There has recently been some concern raised over the possibiliv that (he slope οἱ Cepheid Period-Luminositv (PL) relation is not universal.,There has recently been some concern raised over the possibility that the slope of Cepheid Period-Luminosity $PL$ ) relation is not universal.571 Ngeow οἱ al. (, Ngeow et al. (5722005). Παπ et al. (,"2005), Kanbur et al. ("5732007). IXoen Siluvele (2007) and other studies cited (herein suggest that the optical,"2007), Koen Siluyele (2007) and other studies cited therein suggest that the optical"574first is (he cluster initial mass function slope.,first is the cluster initial mass function slope.575 Because the huminosity function of a population of coeval clusters is nearly (he same as its mass function. aud because (he sum of many power laws with identical slopes is another power law with that slope. the luminosity function of a cluster population is a power law with the same slope as its mass function.," Because the luminosity function of a population of coeval clusters is nearly the same as its mass function, and because the sum of many power laws with identical slopes is another power law with that slope, the luminosity function of a cluster population is a power law with the same slope as its mass function."576 Two factors complicate Chis shehtly., Two factors complicate this slightly.577 First. the random division of a clusters mass into stars will cause the mass-to-light ratios of coeval clusters to be slightly different.," First, the random division of a cluster's mass into stars will cause the mass-to-light ratios of coeval clusters to be slightly different."578 As the scatter is larger lor clusters. and such clusters are more common. the luminosity [uncetion is svstematically flattened slightly.," As the scatter is larger for low-mass clusters, and such clusters are more common, the luminosity function is systematically flattened slightly."579 The second complication comes [rom incompleteness. which is a function of magnitude. color. anc cluster size.," The second complication comes from incompleteness, which is a function of magnitude, color, and cluster size."580 Since completeness is lower at fainter magnitudes. this again flattens the luminosity function.," Since completeness is lower at fainter magnitudes, this again flattens the luminosity function."581 Both of these are second-order effects. however: the relationship between the mass Bfuiction ancl luminosity function is verv strong and thus it is the best-constrained of (he free parameters.," Both of these are second-order effects, however; the relationship between the mass function and luminosity function is very strong and thus it is the best-constrained of the free parameters."582 Using a (rialanc-error approach (creating a variety of model CAIRDs ancl determining which fits (he best). we measure a mass function slope of a=—1.50+0.07.," Using a trial-and-error approach (creating a variety of model CMRDs and determining which fits the best), we measure a mass function slope of $\alpha = -1.50 \pm 0.07$."583 This is slightly sleeper (han (he observed Iuninosity finelion slopes of —1.43250.12 (all clusters) and (blue clusters) caleulatecl in Paper E this was expected since those values did not incorporate completeness corrections., This is slightly steeper than the observed luminosity function slopes of $-1.43 \pm 0.12$ (all clusters) and $-1.22 \pm 0.23$ (blue clusters) calculated in Paper I; this was expected since those values did not incorporate completeness corrections.584 The second well-constrained input parameter is the distribution of cluster radii., The second well-constrained input parameter is the distribution of cluster radii.585 As shown in Figure 3.. the sharpness value measured by ISTphot is an extremely accurate measurement of the clusters radius.," As shown in Figure \ref{fig_sharp_rc}, the sharpness value measured by HSTphot is an extremely accurate measurement of the cluster's radius."586 While there is some scatter in the diagram. the relation is üght in all chips. with sharpness proportional to the square root of the radius.," While there is some scatter in the diagram, the relation is tight in all chips, with sharpness proportional to the square root of the radius."587 While the scatter in the sharpness vs. core radius relation and the strong influence of radius on completeness prevent one [rom determining the intrinsic radius distribution from ihe CAIRD in the way that one can determine a luminosity function. it is not diffieult to constrain the radius distribution bv comparing the observed and svnthetic CMBRDs.," While the scatter in the sharpness vs. core radius relation and the strong influence of radius on completeness prevent one from determining the intrinsic radius distribution from the CMRD in the way that one can determine a luminosity function, it is not difficult to constrain the radius distribution by comparing the observed and synthetic CMRDs."588 Figure shows the distribution of observed sharpuess values. as well as (hose created by (wo different models.," Figure \ref{fig_sharp_dist} shows the distribution of observed sharpness values, as well as those created by two different models."589" Because the middle panel (computed using a flat distribution of core radii) fits the observed data poorly, we can conclude that the shape of the observed distribution is nol solely caused. by. selection effects aud incompleteness."," Because the middle panel (computed using a flat distribution of core radii) fits the observed data poorly, we can conclude that the shape of the observed distribution is not solely caused by selection effects and incompleteness."590 Instead. we are able {ο solve for the raclius distribution.," Instead, we are able to solve for the radius distribution."591" The best-fittàng sharpness distribution is shown in the bottom panel of Figure 1.. aud was created will a Lorentzian distribution of core radii centered at. 7,=1.5320.15 pe and"," The best-fitting sharpness distribution is shown in the bottom panel of Figure \ref{fig_sharp_dist}, and was created with a Lorentzian distribution of core radii centered at $r_c = 1.53 \pm 0.15$ pc and"592? analyzed a subsample of 24 elliptical ancl lenticular galaxies of the SAURON survey which were biased against triaxialitv and consistent with being axisvmmetrie stellar svstens.,\citet{2007MNRAS.379..418C} analyzed a subsample of 24 elliptical and lenticular galaxies of the SAURON survey which were biased against triaxiality and consistent with being axisymmetric stellar systems.593 Axisvmmetrie (hree-integral. Schwarzschild models (Schwarzschild 1979: Cappellari et al., Axisymmetric three-integral Schwarzschild models (Schwarzschild 1979; Cappellari et al.594 2005) were used to determine the distribution of stellar orbits., 2005) were used to determine the distribution of stellar orbits.595 For an investigation of the validity and accuracy of axisvnunelric Schwarzschild models in reproducing the intrinsic properties of simulated merger remnants. see ?2..," For an investigation of the validity and accuracy of axisymmetric Schwarzschild models in reproducing the intrinsic properties of simulated merger remnants, see \citet{2007arXiv0708.2205T}."596 As SAURON integral-field kinematics was only taken within the effective radius. the Schwarzschild ealeulations were restricted (ο a determination of the orbital parameters for the most bound stus in each galaxy.," As SAURON integral-field kinematics was only taken within the effective radius, the Schwarzschild calculations were restricted to a determination of the orbital parameters for the most bound stars in each galaxy."597 From this. elobal galactic parameters were derived.," From this, global galactic parameters were derived."598 The authors found. two classes olf galaxies. one with and one without signilicant amount of specific augular momentum (Eumsellem et al.," The authors found two classes of spheroid-dominated galaxies, one with and one without significant amount of specific angular momentum (Emsellem et al."599 2007)., 2007).600 They called these groups slow ancl [ast rotators. respectivelv.," They called these groups slow and fast rotators, respectively."601 Following Binnev (1978). lor each galaxy. (he anisotropy parameter was determined.," Following Binney (1978), for each galaxy the anisotropy parameter was determined."602 Ilere. the z axis coincides with the svmuimetry and rotation axis of the anisvininelric galaxy. is the diagonal element of the velocity dispersion tensor in the i-th direction (?).. is the local mean velocity dispersion in the i-th direction and p is the local stellar density.," Here, the z axis coincides with the symmetry and rotation axis of the axisymmetric galaxy, is the diagonal element of the velocity dispersion tensor in the i-th direction \citep{1987gady.book.....B}, $\sigma^2_i=\langle v_i^2 \rangle - \langle v_i \rangle^2$ is the local mean velocity dispersion in the i-th direction and $\rho$ is the local stellar density."603" For axisvinmetric svstenis IT,=IL.", For axisymmetric systems $\Pi_{xx} = \Pi_{yy}$.604" In addition. the so called intrinsic ellipticity €j,, Was determined as the edge-on ellipticity of the projected earlv-tvpe galaxy. corrected for inclination elfects."," In addition, the so called intrinsic ellipticity $\epsilon_{int}$ was determined as the edge-on ellipticity of the projected early-type galaxy, corrected for inclination effects."605 The red and evan filled circles in Fig., The red and cyan filled circles in Fig.606" 1 show 9 versus ej; of the slow and fast rotating ellipticals of the SAURON sample. respectively,"," 1 show $\delta$ versus $\epsilon_{int}$ of the slow and fast rotating ellipticals of the SAURON sample, respectively."607 The population of slow rotators is intrinsically quite round (e;;< 0.25) and characterized by an almost isotropic velocity dispersion with 6<0.15., The population of slow rotators is intrinsically quite round $\epsilon_{int} \leq 0.25$ ) and characterized by an almost isotropic velocity dispersion with $\delta \leq 0.15$.608" In contrast. the [ast rotators are in general much flatter (e;,,> 0.3) and more anisotropic with 6>0.15."," In contrast, the fast rotators are in general much flatter $\epsilon_{int} \geq 0.3$ ) and more anisotropic with $\delta \geq 0.15$."609" This result is in conflict with the standard. paradigm that fast. rotating, ellipticals are nearly isotropic svstems while slowly rotating ellipticals are slronely anisotropic (7)..", This result is in conflict with the standard paradigm that fast rotating ellipticals are nearly isotropic systems while slowly rotating ellipticals are strongly anisotropic \citep{1978MNRAS.183..501B}.610 2? showed that projection effects play an important role for [ast rotators and (hat even strongly anisotropic stellar svstems would appear isotropic when viewed under random projection., \citet{2005MNRAS.363..597B} showed that projection effects play an important role for fast rotators and that even strongly anisotropic stellar systems would appear isotropic when viewed under random projection.611 The origin of the isotropic. slowly rotating population is," The origin of the isotropic, slowly rotating population is"612collapses evavitationally and virializes. the barvouic matter in the object is heated by shock waves up to the virial temperature.,"collapses gravitationally and virializes, the baryonic matter in the object is heated by shock waves up to the virial temperature."613 Particles are expected to be accelerated to high cuerey by shock acceleration. aud accelerated electrous scatter the photons of the cosmic microwave backerouud radiation (CMD) to high euergv ganunia-raxy bands bv the iuverse-Conipton mnechanisu.," Particles are expected to be accelerated to high energy by shock acceleration, and accelerated electrons scatter the photons of the cosmic microwave background radiation (CMB) to high energy gamma-ray bands by the inverse-Compton mechanism."614 Existence of such nouthermal electrons is inferred from radio and hare x-crav observations for some clusters of galaxies (ce... Fusco-Feniano et al.," Existence of such nonthermal electrons is inferred from radio and hard x-ray observations for some clusters of galaxies (e.g., Fusco-Femiano et al."615 1999). although the origin of the nouthermal clectrous is not vet clear.," 1999), although the origin of the nonthermal electrons is not yet clear."616 It has also recently been argued that this radiation process iu the intergalactic medi may explain the diffuse extragalactic gamma-ray backeround radiation (ECRB) observed in the EGRET range (Loeb Wasiman 2000)., It has also recently been argued that this radiation process in the intergalactic medium may explain the diffuse extragalactic gamma-ray background radiation (EGRB) observed in the EGRET range (Loeb Waxman 2000).617 However. it is still lighly speculative aud difficult to test whether this process is really the origin of the ECRB. since the coutribution by unresolved active galactic nuclei is also of the same order of magnitudes (see. e.g.. Müccke Pohl 2000 aud references therein).," However, it is still highly speculative and difficult to test whether this process is really the origin of the EGRB, since the contribution by unresolved active galactic nuclei is also of the same order of magnitudes (see, e.g., Müccke Pohl 2000 and references therein)."618 On the other haud. if the structure formation is actually an cficicut radiation process of ganuna-ravs. clusters of ealaxies should be stroug euutters of ganunma-ravs when hey dynamically form. aud the detectabilitv of such ormiue clusters as discrete sources is of ereat interest as a jew probe of structure formation in the universe as well as a test for the scejuio proposed by Loeb Waxman (2000) or EGRD.," On the other hand, if the structure formation is actually an efficient radiation process of gamma-rays, clusters of galaxies should be strong emitters of gamma-rays when they dynamically form, and the detectability of such forming clusters as discrete sources is of great interest as a new probe of structure formation in the universe as well as a test for the scenario proposed by Loeb Waxman (2000) for EGRB."619 Iu thIs paper we make a theoretical estimate of ie umber and augular size of such gamma-ray ciittineg lusters detectable bv ECRET. based on the standard icorv of structure formation in the CDM universe.," In this paper we make a theoretical estimate of the number and angular size of such gamma-ray emitting clusters detectable by EGRET, based on the standard theory of structure formation in the CDM universe."620 We fud a few tens of such forming clusters should have already con. detected by EGRET., We find a few tens of such forming clusters should have already been detected by EGRET.621 Detectability of such forming clusters iu other wavebands such as optical or x-ray bands will be discussed. iu comparison with the conventional clusters of galaxies identified in these wavebands.," Detectability of such forming clusters in other wavebands such as optical or x-ray bands will be discussed, in comparison with the conventional clusters of galaxies identified in these wavebands."622 We will also calculate the EGRB spectimm from structure formation and derive a quantitative relation between the lugher cut-off photon cucrey aud magnetic field streneth., We will also calculate the EGRB spectrum from structure formation and derive a quantitative relation between the higher cut-off photon energy and magnetic field strength.623 Throughout this paper. we assume a CDM universe with the density paraicter O4=0.3. the cosmological constaut Q4=0.7. the ITubble constant f=fyΕΕΓΕ= 0.7. the barvon density paramcter O5=0115)7. aud the deusitv fluctuation amplitude σς=1.," Throughout this paper, we assume a CDM universe with the density parameter $\Omega_0=0.3$, the cosmological constant $\Omega_\Lambda=0.7$, the Hubble constant $h = H_0/(100624\mbox{km/s/Mpc})=0.7$ , the baryon density parameter $\Omega_B = 0.015625h^{-2}$, and the density fluctuation amplitude $\sigma_8=1$."626 These cosmological paraineters are consistent with various observations iucludiug those of the CMD fluctuations (c.g. de Bernardis et al., These cosmological parameters are consistent with various observations including those of the CMB fluctuations (e.g. de Bernardis et al.627 2000) aud the abuudauce of x-ray clusters of galaxies (0.8. Eke. Cole Freuk 1996: Iütaviuna Suto 19965).," 2000) and the abundance of x-ray clusters of galaxies (e.g. Eke, Cole Frenk 1996; Kitayama Suto 1996b)."628 We first estimate the eamunatrav fux ofa eravitationally bound object of total mass AZ that virializes atredshift :., We first estimate the gamma-ray flux of a gravitationally bound object of total mass $M$ that virializes atredshift $z$.629" The typical radius rq. density js circular velocity V. and temperature Z4, of the object can be computed from the spherical collapse model (Peebles 1980: INitavanua Suto 1996b). that is widely used iu study of structure orlmation."," The typical radius $r_{\rm vir}$, density $\rho_{\rm vir}$, circular velocity $V_c$, and temperature $T_{\rm vir}$ of the object can be computed from the spherical collapse model (Peebles 1980; Kitayama Suto 1996b), that is widely used in study of structure formation."630 The total gravitational enerewv given to the xuvon eas in the formine cluster is eiven bv £aQI(Op/OU)JAZVZ.," The total gravitational energy given to the baryon gas in the forming cluster is given by $E_{\rm baryon} \sim (3/4)(\Omega_B/\Omega_0) M631V_c^2$ ."632 Tt is reasonable to expect that a action £.~0.05 of this energw goes iuto accelerated electrons. since such a fraction is interred for acceleration of cosmic rav electrons in a supernova remiunant SN 1006 roni x-ray and Τον observations (Ikoviua et al.," It is reasonable to expect that a fraction $\xi_e \sim 0.05$ of this energy goes into accelerated electrons, since such a fraction is inferred for acceleration of cosmic ray electrons in a supernova remnant SN 1006 from x-ray and TeV observations (Koyama et al."633 1995: Tanimori ct al., 1995; Tanimori et al.634 1998) and conusisteut with the energetics «λος cosuuc-ravs. turbulent inotions. and superuova rate in our Galaxy.," 1998) and consistent with the energetics among cosmic-rays, turbulent motions, and supernova rate in our Galaxy."635 It has also been suggested that the diffuse radio and hard x-ray euiissious observed iu the Coma cluster (aud possibly other several clusters) cau © attributed to nouthenual electrous with the electron enerev fraction of the same order (e.g. Eusco-Foniauo et al.," It has also been suggested that the diffuse radio and hard x-ray emissions observed in the Coma cluster (and possibly other several clusters) can be attributed to nonthermal electrons with the electron energy fraction of the same order (e.g., Fusco-Femiano et al."636 1999)., 1999).637 Therefore. we use ἐν=0.05 to determine the jormalization of electrou eucergy spectru throughout this oper.," Therefore, we use $\xi_e = 0.05$ to determine the normalization of electron energy spectrum throughout this paper."638 The maxinuun Loreutz factor of electrons is coustrained w the competition of the Ferma acceleration time aud cooling time by iuverse-Compton (IC) scattering of CMD shotous., The maximum Lorentz factor of electrons is constrained by the competition of the Fermi acceleration time and cooling time by inverse-Compton (IC) scattering of CMB photons.639" The acceleration time is given by where rp=ant,(eB) is the Larmor radius of electrons. . the electron Loreutz factor. e the electron charge. Bye;=JBD/(luG) the magnetic field. and VWs=VL/OO!Ίσακ] the shock velocity that is of the same order of magnitudes with the circular velocity of a halo. V..."," The acceleration time is given by where $r_L=m_e \gamma_e / (eB)$ is the Larmor radius of electrons, $\gamma_e$ the electron Lorentz factor, $e$ the electron charge, $B_{\mu G} = B/(1\mu G)$ the magnetic field, and $V_{s, 3} = V_s/(10^3 \rm \ km/s)$ the shock velocity that is of the same order of magnitudes with the circular velocity of a halo, $V_c$."640 Ou the other haud. the IC cooling tune is where or is the Thonisou cross section and (ear=£32.10P11)ergean? is the CMB cuerey density.," On the other hand, the IC cooling time is where $\sigma_T$ is the Thomson cross section and $U_{\rm CMB} = 4.32 \times 10^{-13} (1+z)^4 \ \rm erg \ cm^{-3}$ is the CMB energy density."641" Equating these expressions oftac. and fre. we lave the maxiuun value of 5, as oeauax1.2«10741|:)2p1/2D V3."," Equating these expressions of$t_{\rm acc}$ and $t_{\rm IC}$, we have the maximum value of $\gamma_e$ as $\gamma_{e, \max} = 1.2 \times 10^8 (1+z)^{-2}642B_{\mu G}^{1/2} \ V_{s, 3}$ ."643" We asstune the energy distribution of accelerated electrons as a power-law with au exponcutial cut-off at ορµια DO. UN,fda,X>6‘|expt...- with the standard particle acceleration index of a~2."," We assume the energy distribution of accelerated electrons as a power-law with an exponential cut-off at $\gamma_{e, \max}$ , i.e., $dN_e/d\gamma_e \propto \gamma_e^{-\alpha}644\exp(-\gamma_e/\gamma_{e, \max})$, with the standard particle acceleration index of $\alpha \sim 2$."645 As mentioned above. the normalization of this spectrum is set by the equation with the parameter £.=0.05.," As mentioned above, the normalization of this spectrum is set by the equation with the parameter $\xi_e = 0.05$."646" The observed photon energv e; scattered by electrons is related to 2, as ε-= o. where ευδι⋅εν410.1 eV Tis the mean photon eucrev of the CAIB at 2= 0."," The observed photon energy $\epsilon_\gamma$ scattered by electrons is related to $\gamma_e$ as $\epsilon_\gamma = (4/3)\gamma_e^2 \epsilon_{\rm CMB, 0}$ , where $\epsilon_{\rm CMB, 0} = 6.4 \times 10^{-4}$ eV is the mean photon energy of the CMB at $z=0$ ."647 The cooling time ofclectrous corresponding Το photon enerev €. can be written as ty:=2.1« . ια. conrpared," The cooling time ofelectrons corresponding to photon energy $\epsilon_\gamma$ can be written as $t_{\rm IC} = 2.1 \times 10^{6} (\epsilon_\gamma/ {\rm GeV})^{-1/2} 648(1+z)^{-4}$ yr, and this should be compared"649dividing cosmological data into several pieces so that new models can be consistently explored.,dividing cosmological data into several pieces so that new models can be consistently explored.650 We take a Bavesian outlook on hypothesis testing. as we xdieve (and show below) that this closely reflects the way we think about mocels.," We take a Bayesian outlook on hypothesis testing, as we believe (and show below) that this closely reflects the way we think about models."651 Another reason for being wary of he usual (frequentist) practice of reporting p-values is that he latter arenof probabilities for hypotheses. despite being commonly misinterpreted as such (?2)..," Another reason for being wary of the usual (frequentist) practice of reporting $p$ -values is that the latter are probabilities for hypotheses, despite being commonly misinterpreted as such \citep{Sellke:2001,Gordon:2007xm}."652 Suppose we have a model Ady with parameters 85. that we wish to evaluate in ight of data d.," Suppose we have a model $M_0$ with parameters ${\bf \theta}_0$, that we wish to evaluate in light of data $d$."653 Our updated state of belief in the models xwameters is eiven by the posterior probability clistribution ‘unction (pdf) on 9. obtained via Bayes’ theorem: pld|6y.Mo) .(Iwhere νία]όθο.Alo) is the likelihood. p(869|A4;) the prior on the parameters do. and. p(d|Ao) is the marginal likelihood for Aly.," Our updated state of belief in the model's parameters is given by the posterior probability distribution function (pdf) on ${\bf \theta}_0$ , obtained via Bayes' theorem: _0,M_0) where $p(d|{\bf \theta_0}, M_0)$ is the likelihood, $p({\bf \theta_0}|M_0)$ the prior on the parameters ${\bf \theta_0}$, and $p(d|M_0)$ is the marginal likelihood for $M_0$."654 Now suppose we notice a feature in the data that is not reproduced by model M (for example bycomputing the doubt. as in 2)).," Now suppose we notice a feature in the data that is not reproduced by model $M_0$ (for example bycomputing the doubt, as in \cite{Starkman:2008py}) )."655" We invent a model A, with parameters 6, as an explanation for said feature and compute the evidence for both mocdels 6= 0.1) Each models posterior probability. in. light of. d is given bv pCM;]d)=pdfM;)pCM;/p(d)."," We invent a model $M_1$ with parameters ${\bf \theta}_1$ as an explanation for said feature and compute the evidence for both models $i=0,1$ ) Each model's posterior probability in light of $d$ is given by $p(M_i|d)={p(d|M_i) p(M_i)}\slash{p(d)}$."656 The of our degrees of. belief. in the models. the Daves factor Diu=pit]A4 )/ptd|Ao). penalizes models that are unnecessarily complex. for example because of an excessive number of free parameters. automatically encapsulatingOcean's razor (see c.g. ??7)).," The of our degrees of belief in the models, the Bayes factor $B_{10}={p(d|M_1)}/{p(d|M_0)}$ , penalizes models that are unnecessarily complex, for example because of an excessive number of free parameters, automatically encapsulatingOccam's razor (see e.g. \cite{Trotta:2005ar,Trotta:2008qt}) )."657" In order to increase confidence in the new moclel Aly. all that is required is yy71. be. that A, be a more vellective” description of the available data."," In order to increase confidence in the new model $M_1$, all that is required is $B_{10} > 1$, i.e. that $M_1$ be a more “effective” description of the available data."658 There is no dependence on the models predictivity For observations., There is no dependence on the model's predictivity for observations.659 In practice. a new model probably would not. (and arguably should not) be accepted until it produces a correct prediction for future data d that differs from the old models. thus enabling the models. to be. distinguished.," In practice, a new model probably would not (and arguably should not) be accepted until it produces a correct prediction for future data $d^\prime$ that differs from the old model's, thus enabling the models to be distinguished."660" Formally. the models! relative posterior odds after. sccingboth sets of data are given by Before the data set d came along. model A, was not even on the table: p(AZ,)=0."," Formally, the models' relative posterior odds after seeingboth sets of data are given by Before the data set $d$ came along, model $M_1$ was not even on the table: $p(M_1) = 0$."661" The step of introducing AMcrucial. formally requires the injection of an infinite amount of information to raise pCM,) from 0 to a finite value."," The step of introducing $M_1$, formally requires the injection of an infinite amount of information to raise $p(M_1)$ from 0 to a finite value."662 This prior adjustment is on top of the change in degree of belief coming from d., This prior adjustment is on top of the change in degree of belief coming from $d$.663 lt amounts to using the data d twice. first to introduce Ady by adjusting its prior and then to evaluate the evidence from d.," It amounts to using the data $d$ twice, first to introduce $M_1$ by adjusting its prior and then to evaluate the evidence from $d$."664 The duplicate use of the data d leads to posterior odds which can seriously. overstate the statistical significance of a new elfect., The duplicate use of the data $d$ leads to posterior odds which can seriously overstate the statistical significance of a new effect.665" We suggest to ""forget"" about the details of d. compress its information into a new non-zero (ancl still subjective) prior ΑΛ). and then compute the posterior odds arising solely [rom d. i.e. 1£ an unlimited. amount of data is accessible ancl the anomaly is correctly. modelled by Adj. it isgueranteecd to become eventually favored by the Bayes factor. independent of the exact choices of priors."," We suggest to “forget” about the details of $d$, compress its information into a new non-zero (and still subjective) prior $p(M_1)$, and then compute the posterior odds arising solely from $d^\prime$, i.e. If an unlimited amount of data is accessible and the anomaly is correctly modelled by $M_1$, it is to become eventually favored by the Bayes factor, independent of the exact choices of priors."666" Using a finite. cosmic-variance-limited. data set. only that AL, is confirmed before the data is exhausted. the more the bigger the fraction of unused data in d."," Using a finite, cosmic-variance-limited data set only that $M_1$ is confirmed before the data is exhausted, the more the bigger the fraction of unused data in $d^\prime$."667 Two notable examples in cosmology of devising new models and then adjusting their priors are the cliscovery of dark energy and the realization that inflation can easilv accommodate ο<1., Two notable examples in cosmology of devising new models and then adjusting their priors are the discovery of dark energy and the realization that inflation can easily accommodate $\Omega<1$.668 The discovery of a non-zero. vet tiny cosmological constant X was in stark contradiction to prior expectations.," The discovery of a non-zero, yet tiny cosmological constant $\Lambda$ was in stark contradiction to prior expectations."669" Particle-physics considerations suggested: that A) should either be 0 (model M4.) or have a uniform. prior between +AL} (model Me}. pCXLA4,)=δα)ρανα)OFA]AH) PAL). where AM, is the reduced. Planck mass. O(.r) is a step function and Gr) is a Dirac delta. distribution."," Particle-physics considerations suggested that $\Lambda$ should either be $0$ (model $\mc{M}_1$ ) or have a uniform prior between $\pm M_p^4$ (model $\mc{M}_2$ ), $p(\Lambda|\mc{M}_1)=\delta(\Lambda),670p(\Lambda|\mc{M}_2)=\Theta(|\Lambda|-M_p^4)\slash{2M_p^4}$ , where $M_p$ is the reduced Planck mass, $\Theta(x)$ is a step function and $\delta(x)$ is a Dirac delta distribution."671Oversimplifving history. let us assume these were the only theories at hand. and had equalpriors!:: pM4)=p(Me)L ,"Oversimplifying history, let us assume these were the only theories at hand, and had equal: $p(\mc{M}_1)=p(\mc{M}_2)=\frac{1}{2}$ ."672"Along came supernova (SN) redshift measurements (?).. sugeesting a late time acceleration of the universe driven by (in. the simplest. models) a small ay;=10DUC4°"") q"," Along came supernova (SN) redshift measurements \citep{Perlmutter:1998np}, suggesting a late time acceleration of the universe driven by (in the simplest models) a small $\frac{\Lambda_0}{M_p^4}\approx 10^{-120}$."673sLo simplify..ap let us assume that the available SN data. presented. a Sa deviation from A=0.," To simplify, let us assume that the available SN data presented a $5\sigma$ deviation from $\Lambda=0$."674 Computing the Bayes factor using the Savage-Dickey density ratio (2). gives Due to the strong Occam's razor ellect of the prior on Me. a vanishing cosmological constant should: halve still been yasthy preferred. with odds of order 1010:1. over a model including a hugely fine-tuned A.," Computing the Bayes factor using the Savage-Dickey density ratio \citep{Trotta:2007hy} gives Due to the strong Occam's razor effect of the prior on $\mc{M}_2$, a vanishing cosmological constant should hafve still been vastly preferred, with odds of order $10^{115} : 1$, over a model including a hugely fine-tuned $\Lambda$."675 A ~236 detection of a non-zero cosmological constant would have been required to override the Occam's razor of the prior., A $\sim 23\sigma$ detection of a non-zero cosmological constant would have been required to override the Occam's razor of the prior.676 l]lowever. the particle physics community started reconsidering priors and developed. a new model. Vf involving anthropie reasoning which gave more weight to small values of AL Αλή)=O(I0NoA)/10Xo. with model priors now plMi)=—pCMVS)νο)," However, the particle physics community started reconsidering priors and developed a new model $\mc{M}_3$ involving anthropic reasoning which gave more weight to small values of $\Lambda$, $p(\Lambda|\mc{M}_3)=\Theta(10 \Lambda_0 -677\Lambda)\slash{10\Lambda_0}$, with model priors now $p(\mc{M}_1)=p(\mc{M}_2)=p(\mc{M}_3)=\frac{1}{3}$."678 Under the new anthropie prior. the clleet of Occam's razor3 is vastly reduced. giving a Baves factor By;c10 +. now favoring model νι.," Under the new anthropic prior, the effect of Occam's razor is vastly reduced, giving a Bayes factor $B_{13} \approx 10^{-4}$ , now favoring model $\mc{M}_3$ ."679 The parameter value that was considered. unnatural under the original model. for a cosmological constant (small non-zero (X) described. the data better than the prevailing model of A= 0. but not sulliciently well to be preferred.," The parameter value that was considered unnatural under the original model for a cosmological constant (small non-zero $\Lambda$ ) described the data better than the prevailing model of $\Lambda=0$ , but not sufficiently well to be preferred."680 Introducing an anthropic model based. on the landscape picture. in string theory (2227277) allowed a small. non-zero cosmological constant," Introducing an anthropic model based on the landscape picture in string theory \citep{Bousso:2000xa,Giddings:2001yu,Douglas:2003um,Susskind:2003kw,Starkman:2006at}681 allowed a small, non-zero cosmological constant"682The clearest way to determine directly the presence of a cluster of galaxies is to detect thermal X-ray emission from its hot intracluster medium.,The clearest way to determine directly the presence of a cluster of galaxies is to detect thermal X-ray emission from its hot intracluster medium.683 A certain degree of success has been achieved in detecting and spatially resolving the X-ray emission around clistant (0.5<z« 2) radio galaxies using ROSAT (Crawford Fabian 1993: Worrall 1994: Crawford Fabian 1995a. 1996a.b: Crawford 1997: Dickinson 1997: Llardeastle. Lawrence Worrall 1998: Carillict al 1998).," A certain degree of success has been achieved in detecting and spatially resolving the X-ray emission around distant $0.5<z<2$ ) radio galaxies using ROSAT (Crawford Fabian 1993; Worrall 1994; Crawford Fabian 1995a, 1996a,b; Crawford 1997; Dickinson 1997; Hardcastle, Lawrence Worrall 1998; Carilli et al 1998)."684 Any X-rays emitted by the central bright nucleus of radio galaxies are assumed to be absorbed along the line of sight. as observed. for the powerful low-redshilt radio galaxy Cvgnus-X (Ueno et al 1994).," Any X-rays emitted by the central bright nucleus of radio galaxies are assumed to be absorbed along the line of sight, as observed for the powerful low-redshift radio galaxy Cygnus-A (Ueno et al 1994)."685 The. inferred bolometric Iuminosity of the X-ray sources associated with the radio galaxies is ~0.715l05. easily compatible with that expected from mocerately rich clusters of galaxies around the radio sources.," The inferred bolometric luminosity of the X-ray sources associated with the radio galaxies is $\sim0.7-18\times10^{44}$, easily compatible with that expected from moderately rich clusters of galaxies around the radio sources."686 There could also be a contribution to the extended: X-ray emission from. inverse Compton scattering of the hidden: quasar radiation (eg Arunetti. Setti Comastri LOOT).," There could also be a contribution to the extended X-ray emission from inverse Compton scattering of the hidden quasar radiation (eg Brunetti, Setti Comastri 1997)."687 In the case of radio quasars. however. the X- detection of the spatially extended: environment is complicated. by the presence of bright. spatiallv-unresolvec X-ray emission from the active nucleus.," In the case of radio quasars, however, the X-ray detection of the spatially extended environment is complicated by the presence of bright spatially-unresolved X-ray emission from the active nucleus."688 The ROSAT PSPC did not combine the necessary sensitivity with a sullicientlv σου point-response function. needed. to both detect. ane resolve any cluster emission around quasars.," The ROSAT PSPC did not combine the necessary sensitivity with a sufficiently good point-response function, needed to both detect and resolve any cluster emission around quasars."689 Upper limits of 1635.I0 (in the rrest-[rame band) to X-ray emission from the environmen of three racio-Ioud quasars have been derived from ROSAT HIE cata (all ct al 1995. 1997) assuming the cluster emission profile is modelled by a Wing law.," Upper limits of $1.6-3.5\times10^{44}$ (in the rest-frame band) to X-ray emission from the environment of three radio-loud quasars have been derived from ROSAT HRI data (Hall et al 1995, 1997) assuming the cluster emission profile is modelled by a King law."690 We have also obtained ROSAT LR data to spatially resolve ancl detect the extended. emission from the intracluster medium. around. cach of a small sample of intermediate-redshift: racio-loucl quasars., We have also obtained ROSAT HRI data to spatially resolve and detect the extended emission from the intracluster medium around each of a small sample of intermediate-redshift radio-loud quasars.691 Ehe detection of such a Component is. however. complicated by the wobble of the spacecraft. during the observation.," The detection of such a component is, however, complicated by the wobble of the spacecraft during the observation."692 This occurs on a 402 s period. and when the attitude of the spacecraft is not well reconstructed. leads to smearing of the point-spread function (PSE).," This occurs on a $\sim402$ s period, and when the attitude of the spacecraft is not well reconstructed, leads to smearing of the point-spread function (PSF)."693 The bright emission from the quasar nucleus can then contaminate the outer regions where we hope to detect emission from any surrounding cluster. and this has so far hindered our progress in interpreting the data.," The bright emission from the quasar nucleus can then contaminate the outer regions where we hope to detect emission from any surrounding cluster, and this has so far hindered our progress in interpreting the data."694 In this paper. however. we present an analysis of our ROSAT IUE data taken of seven intermecdiate-recshift (0.12 «0.8) raclio-loud quasars. which employs a new correction for the Esyvacecrall wobble clerivecl by Harris ct al. (," In this paper, however, we present an analysis of our ROSAT HRI data taken of seven intermediate-redshift $<z<$ 0.8) radio-loud quasars, which employs a new correction for the spacecraft wobble derived by Harris et al. ("6951998).,1998).696 A contemporaneous and independent analysis of an overlapping dataset using this technique has been carried out by Lardcastle Worrall (1999). who obtain similar results.," A contemporaneous and independent analysis of an overlapping dataset using this technique has been carried out by Hardcastle Worrall (1999), who obtain similar results."697 We use the ROSAT cata of intermeciate-redshilt. raclio-loucl quasars for which there is prior evidence from other wavebands for a cluster environment (see notes on individual quasars for details).," We use the ROSAT data of intermediate-redshift, radio-loud quasars for which there is prior evidence from other wavebands for a cluster environment (see notes on individual quasars for details)."698 We preferentially selected: quasars of only moderate X-ray luminosity in order to minimise the contrast between the nuclear emission. ancl any cluster emission., We preferentially selected quasars of only moderate X-ray luminosity in order to minimise the contrast between the nuclear emission and any cluster emission.699 These targets were supplemented by data available from the ROSAT public archive on 3C and 3C215., These targets were supplemented by data available from the ROSAT public archive on 3C273 and 3C215.700 We also include the observations of H118211643 to form a comparison to the results. of Hall. etal (1097)., We also include the observations of H1821+643 to form a comparison to the results of Hall etal (1997).701 The observations used. and. details of the quasars are listed in ‘Table L..," The observations used, and details of the quasars are listed in Table \ref{tab:obslog}. ."702For subgiauts. where the tracks converge for differeut nesses. the positionnnl of: the star could larecly. depeud onu inetalliitv.,"For subgiants, where the tracks converge for different masses, the position of the star could largely depend on metallicity."703 ILowever. the presence of mixed !OF=2 modes can affect the measured small separation.," However, the presence of mixed $l=2$ modes can affect the measured small separation."704 Furthernore. the expected shift in the «πα. separation due to metallicity differences is similar in magnitude to the present measurement unucertaiuties iu the small separation. linitiue the usefuluess of tle small separation as a proxy for metallicitv in subeiauts.," Furthermore, the expected shift in the small separation due to metallicity differences is similar in magnitude to the present measurement uncertainties in the small separation, limiting the usefulness of the small separation as a proxy for metallicity in subgiants."705 Having extended the C-D diagrain bevoud the main sequence. we have found that the evolutionary tracks converee for stars of differcut masses during the subeiaut and red-giant phases.," Having extended the C-D diagram beyond the main sequence, we have found that the evolutionary tracks converge for stars of different masses during the subgiant and red-giant phases."706 We now discuss the € diagram. which breaks this degeneracy to soie extent.," We now discuss the $\epsilon$ diagram, which breaks this degeneracy to some extent."707 Fieve 10 shows the € diagram with evolutionary tracks for models of mass 0.72.0 AL. and Zi0.011., Figure \ref{fig10} shows the $\epsilon$ diagram with evolutionary tracks for models of mass 0.7–2.0 $_\odot$ and $Z_0=0.017$.708 Stars evolve from the top to the bottom iu this diagram., Stars evolve from the top to the bottom in this diagram.709 Unlike in the C-D claegraim. the evolutionary tracks iu the e diagram remain well separated for subeiauts.," Unlike in the C-D diagram, the evolutionary tracks in the $\epsilon$ diagram remain well separated for subgiants."710 This raises the possibility of using this diagram to constrain mass and age., This raises the possibility of using this diagram to constrain mass and age.711 However. some difficultics arise that male this challenging. as we now cdiseuss.," However, some difficulties arise that make this challenging, as we now discuss."712 There can be a large uucertaiuty in the measurement of e. as is apparent for several stars shown in Figure 10..," There can be a large uncertainty in the measurement of $\epsilon$, as is apparent for several stars shown in Figure \ref{fig10}."713 This cannot be readily overcome by obtaining higher quality data because it is often due to the jutrinsic curvature of the 7=0 ridee in the écchelle diagram., This cannot be readily overcome by obtaining higher quality data because it is often due to the intrinsic curvature of the $l=0$ ridge in the écchelle diagram.714 To resolve this. if inv be necessary to fit to this curvature. although it may be difficult to do this consistently between models aud observations iu which oulv a few radial orders are observed.," To resolve this, it may be necessary to fit to this curvature, although it may be difficult to do this consistently between models and observations in which only a few radial orders are observed."715 The value of € from observations nav also he aüubieuous bv c1 since the radial order. à». of the modes is unknown (unlike for models).," The value of $\epsilon$ from observations may also be ambiguous by $\pm1$ since the radial order, $n$, of the modes is unknown (unlike for models)."716" For the stars considered iere, if seems that only Scenario A of Procvon has au aubignous value of e."," For the stars considered here, it seems that only Scenario A of Procyon has an ambiguous value of $\epsilon$."717 An important feature of the e diagram is the well- offset between observed aud computed oscillation ryequencies. as mentioned earlier. which manifests itself as an offset in e.," An important feature of the $\epsilon$ diagram is the well-known offset between observed and computed oscillation frequencies, as mentioned earlier, which manifests itself as an offset in $\epsilon$."718 This is the reason that the observed values of ε in Figure 10 are systematically offset roni the models., This is the reason that the observed values of $\epsilon$ in Figure \ref{fig10} are systematically offset from the models.719" One wav —to address this issue is to correct the model frequencies. curpirically, as suggested w EKjeldseuetal.(2008)."," One way to address this issue is to correct the model frequencies empirically, as suggested by \citet{Kjeldsen08}."720.. A more satisfactory approach would naturally be to improve the modcling of the ucar-surface lavers., A more satisfactory approach would naturally be to improve the modeling of the near-surface layers.721 As in the C-D diagram. metallicity has an impact ou the evolutionary tracks in the ε diagram.," As in the C-D diagram, metallicity has an impact on the evolutionary tracks in the $\epsilon$ diagram."722 Diagrams for metal-poor stars (Zy= 0.011) aud imoetalenrich stars (Zy= 0.028) are shown iu Fieure 11.., Diagrams for metal-poor stars $Z_0=0.011$ ) and metal-rich stars $Z_0=0.028$ ) are shown in Figure \ref{fig11}.723 The variation in the position of tracks due to ioetallicitv further emphasizes the inportauce of supporting spectroscopic micasureents., The variation in the position of tracks due to metallicity further emphasizes the importance of supporting spectroscopic measurements.724 For red giauts the οσο]tionary tracks are seen to converge and become iudependeut of mass and metallicity., For red giants the evolutionary tracks are seen to converge and become independent of mass and metallicity.725 It has previously been suggested that the near-surtace offset is negligibe dn red eiauts (Cüllilandetal.2010:DiMauroct2011:Jiang 2011).," It has previously been suggested that the near-surface offset is negligible in red giants \citep{Gilliland10,DiMauro11,Jiang11}."726. This was based upou Πιοιο urodel frequencies that were a close fit to observed freqeucies without anv uecd for a correction., This was based upon finding model frequencies that were a close fit to observed frequencies without any need for a correction.727 However. Fieures 10. and Ll clearly show au offset between the models and observations.," However, Figures \ref{fig10} and \ref{fig11} clearly show an offset between the models and observations."728 We suggest that the published models referenced above do not agree with observations as well as first thought., We suggest that the published models referenced above do not agree with observations as well as first thought.729 While the frequencies iiiv appear to agree. the models iav have a large separation slightly ereater than than the observations.," While the frequencies may appear to agree, the models may have a large separation slightly greater than than the observations."730 Due to the low frequencies of red eiat oscillatious and the few orders observed this effect is subtle. but if wore orders were observed the discrepancy would become clear.," Due to the low frequencies of red giant oscillations and the few orders observed this effect is subtle, but if more orders were observed the discrepancy would become clear."731 We have measured Av and € consistently in models and observatious aud couchide hat the near-surface offset is significant for red eiauts., We have measured $\Delta\nu$ and $\epsilon$ consistently in models and observations and conclude that the near-surface offset is significant for red giants.732 Finally. we address whether € really does discrininate vetween different stellar masses.," Finally, we address whether $\epsilon$ really does discriminate between different stellar masses."733 Models indicate that it does. but eiven the sieuificant contribution to e from jear-xurface lavers. which are preseutly poorly modeled. it is not vet known how the near-surface offset varics with mass. age or metallieitv.," Models indicate that it does, but given the significant contribution to $\epsilon$ from near-surface layers, which are presently poorly modeled, it is not yet known how the near-surface offset varies with mass, age or metallicity."734 It is therefore important 6 verify that stars of higher mass really do have lower values of e. as the moclels predict.," It is therefore important to verify that stars of higher mass really do have lower values of $\epsilon$ , as the models predict."735 To do this. we consider he relative positions of stars with known masses in the € diagran.," To do this, we consider the relative positions of stars with known masses in the $\epsilon$ diagram."736 Let us consider.) Ii. 4j Boo and the fiveNepler subelauts. since it is for subeiants that e is potentially most useful.," Let us consider $\beta$ Hyi, $\eta$ Boo and the five subgiants, since it is for subgiants that $\epsilon$ is potentially most useful."737 Masses for Hài aud 1 Boo have been estimated from models by Braudaoctal.(2011) and DiMauroetal.(2003).. respectively.," Masses for $\beta$ Hyi and $\eta$ Boo have been estimated from models by \citet{Brandao11} and \citet{DiMauro03}, respectively."738 The metallicities adopted for this modeclug were —0.10+0.07 for Πνι (Bruuttetal.2010). aud |0.3040.05 for 5 Boo (Taylor 1996)., The metallicities adopted for this modeling were $-0.10\pm0.07$ for $\beta$ Hyi \citep{Bruntt10} and $+0.30\pm0.05$ for $\eta$ Boo \citep{Taylor96}.739. 111026761 (Cea). was modeled using the individual mode frequencies as constraints by Motcalfeetal. (2010).," 11026764 (Gemma), was modeled using the individual mode frequencies as constraints by \citet{Metcalfe10}."740.. The four otherAepler subgiauts were nodeled by Creeveyetal.(2011) using. Av iud Gua as scisuuic constraiuts., The four other subgiants were modeled by \citet{Creevey11} using $\Delta\nu$ and $\nu_\mathrm{max}$ as seismic constraints.741 The masses determined from the uodeling aud the spectroscopic metallicities are given iu Table 2.. along with the the measured values of e.," The masses determined from the modeling and the spectroscopic metallicities are given in Table \ref{tbl-2}, along with the the measured values of $\epsilon$."742 How do hese masses aud inoetalliities compare with the observed values of e?, How do these masses and metallicities compare with the observed values of $\epsilon$?743 Iu general. we do see a trend of decreasing e with Increasing lass. as expected from the evolutionary tracks in Figure 10.," In general, we do see a trend of decreasing $\epsilon$ with increasing mass, as expected from the evolutionary tracks in Figure \ref{fig10}."744 The only deviations frou this trond are 111395018 and (4 Boo. both of which are substantially iore meta-vich than the other subeiauts.," The only deviations from this trend are 11395018 and $\eta$ Boo, both of which are substantially more metal-rich than the other subgiants."745 lucreased mietalicity results in a larger € for a star of a given inass (Figure 11)). so it is no surprise that111395018. ane η Boo have a slightly larger € than 111026761. despite being more massive.," Increased metalicity results in a larger $\epsilon$ for a star of a given mass (Figure \ref{fig11}) ), so it is no surprise that11395018 and $\eta$ Boo have a slightly larger $\epsilon$ than 11026764, despite being more massive."746" This qualitative comparison shows that € does depend on fundamental stellar parameters. such as mass acd moetallicitv aud coufiris that εἰς useful as an additional asteroseisnic αταοΤο,"," This qualitative comparison shows that $\epsilon$ does depend on fundamental stellar parameters, such as mass and metallicity and confirms that $\epsilon$ is useful as an additional asteroseismic parameter."747We transformed the photon arrival times fo Barveeutric Dynamical Time. and did colereut searches of the full data set usine the discrete. Fourier ransform) technique. also known as the Rayleigh or Zi test. (Buecherietal.1983).,"We transformed the photon arrival times to Barycentric Dynamical Time, and did coherent searches of the full data set using the discrete Fourier transform technique, also known as the Rayleigh or $Z^2_1$ test \citep{buc83}."748.. We searched the entire. rauge of (f.f) parameter space for a pulsar hat has 0.1<f1000 Tz. characteristic age τοf/2fo20 kvr.ns wellas Eg8?Iff«107 eres D.," We searched the entire range of $f,\dot f$ ) parameter space for a pulsar that has $0.1 \leq f \leq 1000$ Hz, characteristic age $\tau_c \equiv -f/2\dot f > 20$ kyr, as well as $\dot E = -4\pi^2If\dot f\leq 10^{37}$ ergs $^{-1}$."749 Tn practice. we found it simplest— to confine he search to the region shaded in Figure 1.. bouuded wf€Ldν1οH8 Is or fA17.9 IIz. aud fox25.loPf3! Te or fQIV17.9 Iz.," In practice, we found it simplest to confine the search to the region shaded in Figure \ref{search}, , bounded by $\dot f \leq 1.4 \times 10^{-11}$ Hz $^{-1}$ for $f < 17.9$ Hz, and $\dot f \leq 2.5 \times 10^{-10}f^{-1}$ Hz $^{-1}$ for $f \geq 17.9$ Hz."750" The otal nmuuber of trials thus defined is 1.6«1017, an oversampling of the independent trials bv a factor of Tmod."," The total number of trials thus defined is $\approx 1.6 \times 10^{10}$, an oversampling of the independent trials by a factor of $\approx 7$."751 This i$ a liberal search auge that is justified as follows: wwould have a blackbody. temperature ereater than its observed ~3.5«10? K if it were younger than 20 kyr: an incdependcut argument for an olderage is eiven in Ll., This is a liberal search range that is justified as follows: would have a blackbody temperature greater than its observed $\sim 3.5 \times 10^5$ K if it were younger than 20 kyr; an independent argument for an olderage is given in 4.752 It would have a wind nebula or stronger uouthermal ταν compoucut if E>109 eres 1., It would have a wind nebula or stronger nonthermal X-ray component if $\dot E > 10^{37}$ ergs $^{-1}$.753" Iu view of the distance unit d<800 pe. the ratio L,/E<10 if E=10% eres 1. a sualler ratio than all other pulsars. which ypically have 10.|<£,E«102,"," In view of the distance limit $d < 800$ pc, the ratio $L_x/\dot E \leq 10^{-6}$ if $\dot E = 10^{37}$ ergs $^{-1}$, a smaller ratio than all other pulsars, which typically have $10^{-4} < L_x/\dot E < 10^{-2}$."754" So it is uniτον hat E is as large as 10%"" ores ο,", So it is unlikely that $\dot E$ is as large as $10^{37}$ ergs $^{-1}$.755 The range of parameters searched also includes all of he known millisecond (recveled) pulsus. aud is effective as loug as the pulsar does not have a neutron star ünarv conipanion.," The range of parameters searched also includes all of the known millisecond (recycled) pulsars, and is effective as long as the pulsar does not have a neutron star binary companion."756 The deep lit. correspondiug o absolute magnitudeMy:219 at d=500 pc. rules out he more common white dwarf companions.," The deep limit, corresponding to absolute magnitude$M_V > 19$ at $d=800$ pc, rules out the more common white dwarf companions."757 No significant pulsed signal was detected., No significant pulsed signal was detected.758 The largest values of ZZ fond were =LL , The largest values of $Z^2_1$ found were $\approx 44$.759The theoretical distribution of follows that of 4? with 2n degrees of freedom., The theoretical distribution of $Z^2_n$ follows that of $\chi^2$ with $2n$ degrees of freedom.760 For 5Z2=1. the distribution is au exponential with a mean of 2. so the sinele-trial probability that ?>Lb by chance is 2.8&1019.," For $n=1$, the distribution is an exponential with a mean of 2, so the single-trial probability that $Z^2_1 \geq 44$ by chance is $2.8 \times 10^{-10}$."761 This is expected to arise randomly iu z101? independent trials., This is expected to arise randomly in $\approx 10^{10}$ independent trials.762" Lealivctal.(1983) showed that to detect sinusoidal pulsation with amplitude (pulsed fraction) f, at a power level S=Zi with probability. the uuuber of photons needed is: No-=qr»2SFF."," \citet{lea83} showed that to detect sinusoidal pulsation with amplitude (pulsed fraction) $f_p$ at a power level $S = Z^2_1$ with probability, the number of photons needed is $N=2S/f_p^2$."763" lu our case, NO-=—.729 (709- corrected for backerouud).o so we fud Jjf,x0.35 correspoudineo to ZpxIL "," In our case, $N = 729$ (709 corrected for background), so we find $f_p \le 0.35$ corresponding to $Z^2_1 \le 44$."764We verified this analytic expression bw exanuning folded light curves at the periods associated with the maximum values of ZZ., We verified this analytic expression by examining folded light curves at the periods associated with the maximum values of $Z^2_1$.765 It is not surprising that the pulsed fraction of a οταν pulsar iu X-ravs should be less than 35%., It is not surprising that the pulsed fraction of a $\gamma$ -ray pulsar in X-rays should be less than $35\%$.766 This is not a very sensitive linut consdermg that other 5-ray pulsars whose soft N-ravs are predonuuautly thermal (Ceominga. PSR BlOd5552. possibly PSR D0656]|11) have even smaller pulsed fractions (30%.21%.and12%.respec-tively.DeLucactal. 2005).," This is not a very sensitive limit consdering that other $\gamma$ -ray pulsars whose soft X-rays are predominantly thermal (Geminga, PSR B1055–52, possibly PSR B0656+14) have even smaller pulsed fractions \citep[30\%, 21\%, and 12\%, respectively,][]{del05}."767. In these cases. the pulse profiles are quasi-sinmsoidal.," In these cases, the pulse profiles are quasi-sinusoidal."768" The Z? test is therefore a eood one for5925.. whose N-ravs are also doninated bv a soft thermal source within the response of the WRC. although the result is not very restrictive in this case,"," The $Z^2_1$ test is therefore a good one for, whose X-rays are also dominated by a soft thermal source within the response of the HRC, although the result is not very restrictive in this case."769 We also note that the Vela pulsar has a more conlicated pulse shape. while its pulsed fraction is ouly (Aanzalictal.2007).," We also note that the Vela pulsar has a more complicated pulse shape, while its pulsed fraction is only \citep{man07}."770. Iu order to test for proper motion of the ueutron star. we compared the position of oon the TRC with the ACIS position obtained 3 vears earlier (Halpernctal.2002).," In order to test for proper motion of the neutron star, we compared the position of on the HRC with the ACIS position obtained 3 years earlier \citep{hal02}."771 First. we updated the ACTS position to the USNO-DBI.O svsteii using optically identified sources in the ACIS imaee.," First, we updated the ACIS position to the USNO-B1.0 system using optically identified sources in the ACIS image."772" The result is RA. = L836""132685. decl."," The result is R.A. = $18^{\rm h}36^{\rm m}13.\!^{\rm s}685$ , decl."773" = |59725/29""95 (J2000.0), and. differs from the previously used USNO-A2.0 system by 073,"," = $+59^{\circ}25^{\prime}29.\!^{\prime\prime}95$ (J2000.0), and differs from the previously used USNO-A2.0 system by $0.\!^{\prime\prime}3$."774 Then we registered the IIRC image to the ACTS nuage using seven X-rav sources in the vicinity of5925.. which required a zero-point slift of the TRC image of |07052 in R.A. and |0/89 in decl. The resulting IRC position of tis RAL = qsB369132671. decl," Then we registered the HRC image to the ACIS image using seven X-ray sources in the vicinity of, which required a zero-point shift of the HRC image of $+0.\!^{\rm s}052$ in R.A. and $+0.\!^{\prime\prime}89$ in decl.. The resulting HRC position of is R.A. = $18^{\rm h}36^{\rm m}13.\!^{\rm s}674$, decl."775 = 459725/30/15 (.J2000.0)., = $+59^{\circ}25^{\prime}30.\!^{\prime\prime}15$ (J2000.0).776 The difference between τις positions of in 2002 and 2005 is therefore oulv 0721. which is conrparable to their comibiued statistical errors.," The difference between the positions of in 2002 and 2005 is therefore only $0.\!^{\prime\prime}21$, which is comparable to their combined statistical errors."777" Tn order o bound the possible proper motion. we adopt au upper init that is twice this difference. or 0712, corresponding o p<O]LL vrt."," In order to bound the possible proper motion, we adopt an upper limit that is twice this difference, or $0.\!^{\prime\prime}42$, corresponding to $\mu < 0.\!^{\prime\prime}14$ $^{-1}$."778" This allows the neutron star to je traveled frou, a birth iu the Galactic plane to its xeseut position iu 6.1«10° vr or longer. which is uot an unreasonable age for its N-vay temperature."," This allows the neutron star to have traveled from a birth in the Galactic plane to its present position in $6.4 \times 10^5$ yr or longer, which is not an unreasonable age for its X-ray temperature."779 At the uaxinmu distance of 800 pe. the limit on j( corresponds o a tangential velocity limit e;«530 kins 7. which is ypical for radio pulsars.," At the maximum distance of 800 pc, the limit on $\mu$ corresponds to a tangential velocity limit $v_t<530$ km $^{-1}$, which is typical for radio pulsars."780 Even iu the absence of detectable pulsations. wemains the leading (αμα onlv) candidate for identification with J1835|5918.," Even in the absence of detectable pulsations, remains the leading (and only) candidate for identification with."781. Its soft X-rav spectrum. and abseuce of optical aud radio emission. support the hypothesis that it is an older aud possibly more distant cousin of the Conüuga pulsar.," Its soft X-ray spectrum, and absence of optical and radio emission, support the hypothesis that it is an older and possibly more distant cousin of the Geminga pulsar."782 The upper lit ou proper motion that we derived is a significant new observational constraint. allowing an age of at least 6.1«10 vr for Hf it was born iu the Galactic plane.," The upper limit on proper motion that we derived is a significant new observational constraint, allowing an age of at least $6.4 \times 10^5$ yr for if it was born in the Galactic plane."783 This compares favorably with the characteristic age 7.—3.1«LO? vr of Cenunea. aud is consistent with a surface temperature of only ~3.5«LO? KI. compared with Ls«10* I& for Cenunea (Caraveoctal.20014:Jackson&Halper2005:INarealtsevetal. 2005).," This compares favorably with the characteristic age $\tau_c = 3.4 \times 10^5$ yr of Geminga, and is consistent with a surface temperature of only $\sim 3.5 \times 10^5$ K, compared with $4.8 \times 10^5$ K for Geminga \citep{car04,jac05,kar05}."784.. Asstuuing that the age and distance of aare both larger than those of Ceminga. it is likely that lis a mnaxinallv efficieut 5-rav pulsar close toits death lue (Chen&Ruderman 1993).. following the treud of -rav effücienev iucreasing with decreasing spin-down power (Thompsonetal.1997. 1999)...," Assuming that the age and distance of are both larger than those of Geminga, it is likely that is a maximally efficient $\gamma$ -ray pulsar close toits death line \citep{che93}, , following the trend of $\gamma$ -ray efficiency increasing with decreasing spin-down power \citep{tho97,tho99}. ."785 Alternatively. we cannot rule out that ls a nullisecoud pulsar with simular spin-down power and inagnetospherie gap voltage as CGonüuga.," Alternatively, we cannot rule out that is a millisecond pulsar with similar spin-down power and magnetospheric gap voltage as Geminga."786 [f so. itsthermal N-rav enüssiou nav be due to surface reheating by a imagnetosphleric accelerator.," If so, itsthermal X-ray emission may be due to surface reheating by a magnetospheric accelerator."787 It is not now possible to make a significantly more sensitive search for A-ray pulsations frou, It is not now possible to make a significantly more sensitive search for X-ray pulsations from788result on the fraction of obseurecl quasars in the local universe.,result on the fraction of obscured quasars in the local universe.789" The work was supported by Chinese NSF through NSECTO413009. NSEC10533050 and ihe CAS ""Dai Ren"" project at University of Science and Technology of China."," The work was supported by Chinese NSF through NSFC10473009, NSFC10533050 and the CAS ""Bai Ren"" project at University of Science and Technology of China."790"therefore possibly flaring M-dwarfs, but optical spectra are needed to confirm this.","therefore possibly flaring M-dwarfs, but optical spectra are needed to confirm this."791" The spectral luminosity of our transients is L,~10'°(Di/1kpc)?ergs!Hz !, where Dr is the luminosity distance."," The spectral luminosity of our transients is $L_{\nu} \simeq 10^{19} (D_{L}/1\unit{kpc})^2 \unit{erg ~s^{-1}Hz^{-1}}$ , where $D_{L}$ is the luminosity distance."792" This spectral luminosity is an order of magnitude more luminous than those found by ? at 5 and 8 GHz, but roughly consistent assuming a spectral index of a=—0.7."," This spectral luminosity is an order of magnitude more luminous than those found by \citet{bower2007sta} at 5 and 8 GHz, but roughly consistent assuming a spectral index of $\alpha=-0.7$."793" The sampling interval of our light curves is typically much longer than those discussed by ? (typically years as opposed to weeks) and we have not yet obtained dedicated optical follow-up of our sources, so our limits on optical counterparts are not very strong."," The sampling interval of our light curves is typically much longer than those discussed by \citet{bower2007sta} (typically years as opposed to weeks) and we have not yet obtained dedicated optical follow-up of our sources, so our limits on optical counterparts are not very strong."794 The scarcity of data means we are unable to robustly classify a large fraction of our transient sources., The scarcity of data means we are unable to robustly classify a large fraction of our transient sources.795" Of the unidentified transients, none have X-Ray counterparts in the X-ray All-Sky Survey Bright Source Catalogue (?).."," Of the unidentified transients, none have X-Ray counterparts in the X-ray All-Sky Survey Bright Source Catalogue \citep{ROSAT}."796 GRB afterglows without a gamma ray trigger (the so-called orphan GRB afterglows) are a possibility and might explain the higher average luminosity., GRB afterglows without a gamma ray trigger (the so-called orphan GRB afterglows) are a possibility and might explain the higher average luminosity.797" Radio supernovae are also a possibility as long as the hosts are nearby and intrinsically faint, but distant RSN would appear to be ruled out by the high luminosity."," Radio supernovae are also a possibility as long as the hosts are nearby and intrinsically faint, but distant RSN would appear to be ruled out by the high luminosity."798" Stellar events are less likely, but flares from nearby late type stars are not ruled out."," Stellar events are less likely, but flares from nearby late type stars are not ruled out."799" Soft gamma repeaters and X-Ray binaries are also possibilities, although the rarity of such objects and our measured transient rate are incompatible."," Soft gamma repeaters and X-Ray binaries are also possibilities, although the rarity of such objects and our measured transient rate are incompatible."800 'The most likely source of variability from extragalactic sources at 843 MHz is refractive Interstellar Scintillation (ISS) of the compact components of AGN., The most likely source of variability from extragalactic sources at 843 MHz is refractive Interstellar Scintillation (ISS) of the compact components of AGN.801" By our definition, our transients could well be such scintillating sources occasionally appearing above our flux threshold, although the light curves of the transient sources have Y>0.6, which would make them the among most extremely variable sources in our sample (c.f."," By our definition, our transients could well be such scintillating sources occasionally appearing above our flux threshold, although the light curves of the transient sources have $\mathcal{V} > 0.6$, which would make them the among most extremely variable sources in our sample (c.f."802 Figure 20) )., Figure \ref{fig:v_histogram}) ).803" Star-forming galaxies, whose radio flux is from widespread star formation and diffuse synchrotron emission in the disk, are unlikely to be intrinsically variable on our time-scales (due to light travel time constraints), or extrinsically variable (due to larger angular size quenching the interstellar scintillation)."," Star-forming galaxies, whose radio flux is from widespread star formation and diffuse synchrotron emission in the disk, are unlikely to be intrinsically variable on our time-scales (due to light travel time constraints), or extrinsically variable (due to larger angular size quenching the interstellar scintillation)."804 Another explanation for the transient sources is time-integrated emission from pulsars with on-times of greater than ~ 12h., Another explanation for the transient sources is time-integrated emission from pulsars with on-times of greater than $\sim~12\unit{h}$ .805" ? proposed pulsars as the source of the transients discovered by ? and ? based on population arguments, and there is some observational evidence for this."," \citet{Ofek10} proposed pulsars as the source of the transients discovered by \citet{bower2007sta} and \citet{Niinuma07} based on population arguments, and there is some observational evidence for this."806" Intermittent pulsars such as PSR B1931+24 (?),, have active periods of a few days and then turn completely off."," Intermittent pulsars such as PSR $+$ 24 \citep{Kramer06}, have active periods of a few days and then turn completely off."807" PSR J0941—39, which was discovered as a Rotating Radio Transient (RRAT) with 5 single pulses in one observation, exhibited standard pulsar emission during another observation (?).."," PSR $-$ 39, which was discovered as a Rotating Radio Transient (RRAT) with 5 single pulses in one observation, exhibited standard pulsar emission during another observation \citep{BurkeSpolaor10}."808" Such objects might appear as transients in our survey if the time between mode-changes had a time-scale of 12 h or longer, and the time-integrated flux densities in both modes were compatible with our non-detection thresholds."," Such objects might appear as transients in our survey if the time between mode-changes had a time-scale of 12 h or longer, and the time-integrated flux densities in both modes were compatible with our non-detection thresholds."809" Pulsars are also not likely to be optically detected at the SuperCOSMOS plate limits, which would explain the Finally, microlensing is an unlikely explanation for our unknown transients, as the implied number of sources to explain our sample is far too high (?).."," Pulsars are also not likely to be optically detected at the SuperCOSMOS plate limits, which would explain the Finally, microlensing is an unlikely explanation for our unknown transients, as the implied number of sources to explain our sample is far too high \citep{bower2007sta}."810" Reflected solar flares are unlikely, as a 1 MJy solar flare would need toreflect of a 1000 km object at a distance of only 7000km to be detected above our threshold."," Reflected solar flares are unlikely, as a 1 MJy solar flare would need toreflect of a 1000 km object at a distance of only 7000km to be detected above our threshold."811forma We can now verity that this mieration is due to the density waves by studving the behavior of wave action.,form We can now verify that this migration is due to the density waves by studying the behavior of wave action.812 The change in the augular momentum coutent of the fluid on account of the presence of the vortex is where subscripts ¢ denote the initial conditious. aud he integral is taken over the whole vortex surface arca.," The change in the angular momentum content of the fluid on account of the presence of the vortex is where subscripts $i$ denote the initial conditions, and the integral is taken over the whole vortex surface area."813 We expect οΓον= Ack. with AA the difference in wave action defined above evaluated for the outer aud he inner wave.," We expect $dL_\mathrm{vort}/dt=\Delta A$ , with $\Delta A$ the difference in wave action defined above evaluated for the outer and the inner wave."814 We show the wave action for three resolutious in Fie. 3.., We show the wave action for three resolutions in Fig. \ref{figwaveaction}.815 Equation 9 only has meaning in the wave region. at distances of at least 2/7/3 from the vortex.," Equation \ref{eqwaveaction} only has meaning in the wave region, at distances of at least $2H/3$ from the vortex."816 Although our owest resolution run clearly docs uot resolve the waves well cnough to ect the correct wave action on both sides. AA is very similar to the higher resolution runs.," Although our lowest resolution run clearly does not resolve the waves well enough to get the correct wave action on both sides, $\Delta A$ is very similar to the higher resolution runs."817 In Sect. 7..," In Sect. \ref{secGlob},"818 we make sure our resolution is at least as high as that of the dashed Lue in Fie. 3.., we make sure our resolution is at least as high as that of the dashed line in Fig. \ref{figwaveaction}.819 The similarity of the wave action for the highest resolution ruus translates mto a simular müeratiou rate after 10 orbits (sce Fig. 2))., The similarity of the wave action for the highest resolution runs translates into a similar migration rate after 10 orbits (see Fig. \ref{figvortmig}) ).820 We have measured the change in angular momentum of the vortex between 5 aud 10 orbits. aud compared this to what is expected from the wave action.," We have measured the change in angular momentum of the vortex between 5 and 10 orbits, and compared this to what is expected from the wave action."821 The results are sunuuuized in Table 1.., The results are summarized in Table \ref{tabwave}.822 We point out that there is a large uncertainty iu the measured AL., We point out that there is a large uncertainty in the measured $\Delta L$ .823 This is because Ljü444 can onlv be 1ueasured to au accuracy of ~5% because of aabienitics in definine the vortex as a separate entitv from the background flow. aud AL results from a subtraction of two almost equal ummbers (typically ALz0.1Lua).," This is because $L_\mathrm{vort}$ can only be measured to an accuracy of $\sim 5\%$ because of ambiguities in defining the vortex as a separate entity from the background flow, and $\Delta L$ results from a subtraction of two almost equal numbers (typically $\Delta L \approx 0.1L_\mathrm{vort}$ )."824 We therefore estimate that there is an uncertainty of at least 50% in the measured values of AL. which makes the agreement between AAA? and AL reasonable (see Table 1)).," We therefore estimate that there is an uncertainty of at least $50\%$ in the measured values of $\Delta L$, which makes the agreement between $\Delta A\Delta t$ and $\Delta L$ reasonable (see Table \ref{tabwave}) )."825 Therefore. the iuvard mieration of the vortex is consistent with the wave torque.," Therefore, the inward migration of the vortex is consistent with the wave torque."826 We show the time evolution of the wave action difference. or wave torque. in Fie. L.," We show the time evolution of the wave action difference, or wave torque, in Fig. \ref{figdAdt},"827 for the same three resolutious as iu Fie. 2.., for the same three resolutions as in Fig. \ref{figvortmig}.828 Tn all cases. a steady torque is set up after 3 orbits. at which time the vortex has reached its equilibrium with the backeround shear.," In all cases, a steady torque is set up after 3 orbits, at which time the vortex has reached its equilibrium with the background shear."829 After the equilibrimm has been set up. the slow time evolution of the torque is due to umumerical diffusion (the decline iu the low resolution case) aud slowly varving backgrouud disk properties due to the changing radial location of the vortex (the slow increase in the highest resolution cases).," After the equilibrium has been set up, the slow time evolution of the torque is due to numerical diffusion (the decline in the low resolution case) and slowly varying background disk properties due to the changing radial location of the vortex (the slow increase in the highest resolution cases)."830 Tn order to understand the origin of the waves eitted bv accretiou disk vortices. let us introduce the local shearing box model (7). ," In order to understand the origin of the waves emitted by accretion disk vortices, let us introduce the local shearing box model \citep{hawley95}. ."831Du this model. we ucelect curvature effects im equations (13)-(2)) aud introduce a local cartesian frame corotating with the disk at ry bv defining.=rory aud y=rog.," In this model, we neglect curvature effects in equations \ref{eqCont}) \ref{eqMom}) ) and introduce a local cartesian frame corotating with the disk at $r_0$ by defining $x=r-r_0$ and $y=r_0\varphi$."832 In this model. equatious (1)) and (2)) read: where O9=Ory) is the Weplerian frequency at ry. g=3/2 for a Ikeplerian rotation profile and we have assunied an isothermal sas.," In this model, equations \ref{eqCont}) ) and \ref{eqMom}) ) read: where $\Omega=\Omega(r_0)$ is the Keplerian frequency at $r_0$, $q=3/2$ for a Keplerian rotation profile and we have assumed an isothermal gas."833 In the following. we consider a vortex located at r=ry and perturbing the surrounding flow.," In the following, we consider a vortex located at $r=r_0$ and perturbing the surrounding flow."834 The vortex core is a non-lincar solution to the above equations (see e.g. 7]). aud we consider theperturbations produced by the vortex core at longdistance.," The vortex core is a non-linear solution to the above equations (see e.g. \citealt{lesur09})), and we consider theperturbations produced by the vortex core at longdistance."835 Since the vortex is. in first approxination. a quasisteadyv structure. we consider stationary perturbations of the EKepleriau flow iutroducing," Since the vortex is, in first approximation, a quasi-steady structure, we consider stationary perturbations of the Keplerian flow $\bm{v}_0=-q\Omega\bm{e_y}$ introducing"836evenis is tentatively marked with a colored strip.,events is tentatively marked with a colored strip.837 We take the appearance of (his sequence as further evidence for a common physical mechanism behind these transients (although not all ILOTs are necessarily powered by accretion)., We take the appearance of this sequence as further evidence for a common physical mechanism behind these transients (although not all ILOTs are necessarily powered by accretion).838 As for P Cvgni. which is not vel proven to be a binary svstem. we preclict that a binary companion exists in (hat svstem. or thal a common envelope occurred in the recent past.).," As for P Cygni, which is not yet proven to be a binary system, we predict that a binary companion exists in that system, or that a common envelope occurred in the recent past.)."839 To sunuuarize. we suggest that most (but probably not all) of the ILOTs are events.," To summarize, we suggest that most (but probably not all) of the ILOTs are accretion-powered events."840 Based on the common energy source they should be grouped in one class together with stellar merger (dal. disruption flares. and large eruptions in LBV binary svslenms.," Based on the common energy source they should be grouped in one class together with stellar merger tidal, disruption flares, and large eruptions in LBV binary systems."841 The shape of the lisht curve (Fig. 1)).," The shape of the light curve (Fig. \ref{fig:lightcurves1}) ),"842 related to the accretion as the energy source. is an important distinguishing feature of many svstenms in (his group.," related to the accretion as the energy source, is an important distinguishing feature of many systems in this group."843 We also that. because of the geometry. of the accretion process the ejecta in (his class of Wansients should svstematically exhibit bipolar structure. as suggested by Soker (2004).," We also that because of the geometry of the accretion process the ejecta in this class of transients should systematically exhibit bipolar structure, as suggested by Soker (2004)."844 We note that in some sinele star models circumstellar material can also posses bipolar structure2009)., We note that in some single star models circumstellar material can also posses bipolar structure.845 We thank Avishay Gal-Yam. Andrea Pastorello. Nathan Suith. Todd Thompson. Romuald Tylenda and an anonvmous referee for helpfulcomments.," We thank Avishay Gal-Yam, Andrea Pastorello, Nathan Smith, Todd Thompson, Romuald Tylenda and an anonymous referee for helpful."846 A. EF. was supported in part at the Technion by a fellowship from the Lady. Davis Foundation., A. F. was supported in part at the Technion by a fellowship from the Lady Davis Foundation.847 This research was supported by ihe Asher Fund lor Space Research at the Technion. and the Israel Science Foundation.," This research was supported by the Asher Fund for Space Research at the Technion, and the Israel Science Foundation."848window cut at 6c=30.,window cut at $\theta_\mathrm{C}=3\sigma$.849 An interesting point now is that the Gabor window is decreasing from the centre and outwards. which is opposite of the noise pattern.," An interesting point now is that the Gabor window is decreasing from the centre and outwards, which is opposite of the noise pattern."850 This gives the pixels with low noise high significant in the analysis ancl the pixels with high noise low significance., This gives the pixels with low noise high significant in the analysis and the pixels with high noise low significance.851 One sees from the expressions for the signal and noise pseudo power spectra that the Gabor window will work cilferentlvy on both., One sees from the expressions for the signal and noise pseudo power spectra that the Gabor window will work differently on both.852 This means that S/N is different depending on the Gabor window., This means that $S/N$ is different depending on the Gabor window.853 For this case. we have plotted the average pseudo power spectrum for signal ancl noise separately in Fig. 15..," For this case, we have plotted the average pseudo power spectrum for signal and noise separately in Fig. \ref{fig:sngaussth}."854 Phis shows the described cllect., This shows the described effect.855 The ratio is much higher for the Gaussian Gabor window in this case. favouring the use of this window for the For. this. example we used again. NeMn=.20 and INT:=100.," The ratio is much higher for the Gaussian Gabor window in this case, favouring the use of this window for the For this example we used again $N^\mathrm{bin}=20$ and $N^\mathrm{in}=100$."856" sThe result is. shown in. Fig."" -17.", The result is shown in Fig. \ref{fig:cdm1}.857. In Fig., In Fig.858""" I8. the average over 5000 simulations and estimations is shown.", \ref{fig:cdm2} the average over 5000 simulations and estimations is shown.859 One can see that the estimate also does well bevond (/=520 which is where the ellective S/N=1., One can see that the estimate also does well beyond $\ell=520$ which is where the effective $S/N=1$.860 The method is still unbiased., The method is still unbiased.861 Phe error bars in the part where noise dominates are here lower than the theoretical approximation (28)) shown as the dark shaded area., The error bars in the part where noise dominates are here lower than the theoretical approximation \ref{eq:uninoiseerror}) ) shown as the dark shaded area.862 The dashed lines show the theoretical lo variance taken from the inverse Fisher matrix which here gives a very good agreement with Monte In Fig., The dashed lines show the theoretical $1\sigma$ variance taken from the inverse Fisher matrix which here gives a very good agreement with Monte In Fig.863" 19. we show the average (over 5000 estimations) of the correlation between the estimates 2, between cillerent bins.", \ref{fig:estcor} we show the average (over 5000 estimations) of the correlation between the estimates $D_b$ between different bins.864 The figure shows that the correlations between estimates are low and in fact in cach line all olf-cliagonal elements are more than an order of magnitude lower than the diagonal clement of that line., The figure shows that the correlations between estimates are low and in fact in each line all off-diagonal elements are more than an order of magnitude lower than the diagonal element of that line.865 In Fig., In Fig.866 20. we show that the probability clistribution of the estimates in Fig., \ref{fig:estprob} we show that the probability distribution of the estimates in Fig.867 15. is almost To test the method at higher multipoles we also did one estimation up to multipole (=2048., \ref{fig:cdm2} is almost To test the method at higher multipoles we also did one estimation up to multipole $\ell=2048$.868 We used LEALPix resolution Αμ=1024 and simulated a sky with as’ Gaussian beam and added noise from a strongly varving non-uniform: noise mocel., We used HEALPix resolution $N_\mathrm{side}=1024$ and simulated a sky with a $8'$ Gaussian beam and added noise from a strongly varying non-uniform noise model.869 3oth the beam and noise level were adjusted according to the specifications for the Planck LPL 161112 detector 1996).., Both the beam and noise level were adjusted according to the specifications for the Planck HFI $143 \mathrm{GHz}$ detector \cite{plancka}. .870 We used again a 15° PWIHIAT Gaussian Gabor window cut 30 away from the centre., We used again a $15^\circ$ FWHM Gaussian Gabor window cut $3\sigma$ away from the centre.871 In the estimation we used AU—40 bins and IN?=200 input C; between =7 and (=2048., In the estimation we used $N^\mathrm{bin}=40$ bins and $N^\mathrm{in}=200$ input $\tilde C_\ell$ between $\ell=7$ and $\ell=2048$.872 The average of 100 such simulations is shown in Lig. 21.., The average of 100 such simulations is shown in Fig. \ref{fig:l2048}.873 Each complete likelihood estimation (which includes a total of about 25 likelihood evaluations) took about S minutes on a single processor on a 500MIIz DEC Alpha work station., Each complete likelihood estimation (which includes a total of about $25$ likelihood evaluations) took about $8$ minutes on a single processor on a $500 \mathrm{MHz}$ DEC Alpha work station.874 In Fig. 22..," In Fig. \ref{fig:onerea},"875 we have plotted the average of 300 estimations where the input data was the C; from simulations with a fixed CAMB realisation and. varying noise realisation.," we have plotted the average of 300 estimations where the input data was the $\tilde876C_\ell$ from simulations with a fixed CMB realisation and varying noise realisation."877" The dotted line shows the NW"" C's (without noise) used as input tothe likelihood.", The dotted line shows the $N^\mathrm{in}$ $\tilde C_\ell$ s (without noise) used as input tothe likelihood.878". EEPhe histogram. is. as before⋅ the input. pseudo spectrum without. noise. binned. in. INdh"" bins.. pus", The histogram is as before the input pseudo spectrum without noise binned in $N^\mathrm{bin}$ bins.879This means that cach, This means that each880propagation in either the lateral or racial clirections.,propagation in either the lateral or radial directions.881 For comparison with the turbulent dellag‘ation case. we calculated the structure of planar helium detonatious uncer the ZND theory (Fickett Davis L979).," For comparison with the turbulent deflagration case, we calculated the structure of planar helium detonations under the ZND theory (Fickett Davis 1979)."882 Our results for the self-sustained detonation speeds and thermocdyuamic couditious at the Chapman-Jouguet poiut are agree with the values obtained by Mazurek (1973) aud Iheykhlov (1988. 1989).," Our results for the self-sustained detonation speeds and thermodynamic conditions at the Chapman-Jouguet point are agree with the values obtained by Mazurek (1973) and Khokhlov (1988, 1989)."883 There :'e several possible cdelfiuitions fo‘the width ofa planar ZND cdetouation., There are several possible definitions for the width of a planar ZND detonation.884 Tese include the distance from the shock front to tlie polit where the nuclear energy generation rate attalus its anim value Worredot- the distatce from the shock frout to the point where the principle [uel has fallen to 1/10 of its initial ναιe eonsition. CIxhokhlov. 1989). the clistance from the shock front to the point where of tle total niclear energy. las beeu leases. ος Gxhokhllov 1989). and the distance from the shock. [rout to where the composition reaches its final nuclear statistical equilibrium state War.," These include the distance from the shock front to the point where the nuclear energy generation rate attains its maximum value $_{{\rm nucdot}}$, the distance from the shock front to the point where the principle fuel has fallen to 1/10 of its initial value $_{{\rm composition}}$ (Khokhlov 1989), the distance from the shock front to the point where of the total nuclear energy has been releases $_{{\rm nuclear}}$ (Khokhlov 1989), and the distance from the shock front to where the composition reaches its final nuclear statistical equilibrium state $_{{\rm NSE}}$."885 For planar ieliuiu deflagrations. tle widths defined by the energy veneration rate maximum αρα are the siiallest widtlis.," For planar helium deflagrations, the widths defined by the energy generation rate maximum $_{{\rm nucdot}}$ are the smallest widths."886 Depeudiug[n] on t upstream ceusity. the composition widths. Weomposition energy. deposition widths Wouelear. ald nuclear statistical equilibrium widths Wye may be larger than the energy. gene‘ation rate maxinuum widths by [actors of 1-15.," Depending on the upstream density, the composition widths $_{{\rm composition}}$, energy deposition widths $_{{\rm nuclear}}$, and nuclear statistical equilibrium widths $_{{\rm NSE}}$ may be larger than the energy generation rate maximum widths by factors of 1–15."887 We will use the WoW lu our analysis. bu qualitatively similar results are obtained if the differences in the various widths are taken into acCount.," We will use the $_{{\rm nucdot}}$ in our analysis, but qualitatively similar results are obtained if the differences in the various widths are taken into account."888 The cetonation widths are shown by he purple curve in Figure L.. ancl t etonation speeds are shown by the purple curve iu Figure 3..," The detonation widths are shown by the purple curve in Figure \ref{lengths}, and the detonation speeds are shown by the purple curve in Figure \ref{speeds}."889 The speeds of self-sustained detonuatiOlls. as expected. are much larger than any other speed in Figues 3..," The speeds of self-sustained detonations, as expected, are much larger than any other speed in Figures \ref{speeds}."890 Perhaps suprisitely. the widh of a sel(-sustained detouatious is larger than the widh of :| purely laiinar deflagration for auy given density iu Figure 1..," Perhaps suprisingly, the width of a self-sustained detonations is larger than the width of a purely laminar deflagration for any given density in Figure \ref{lengths}."891 For detonatious. there is a relatively loug tije betwee when inateri is first heated by the passing shock wave. aud wheu that material begis to burn significantly (the iuduction time scale of detonations).," For detonations, there is a relatively long time between when material is first heated by the passing shock wave, and when that material begins to burn significantly (the induction time scale of detonations)."892 For deflagrations. tlere is a relaively short time betwee when mate‘jal Is first heated by conduction aud begius to burn significatly.," For deflagrations, there is a relatively short time between when material is first heated by conduction and begins to burn significantly."893 These time scales. wlen combinec with the fact the speed of a self-sustained detouation is supersonic while tle speed o. a purely laninar dellagration is very subsonic. explain why the cetonajon widths are arger tha1 the delflag‘allou widths in Figure 1..," These time scales, when combined with the fact the speed of a self-sustained detonation is supersonic while the speed of a purely laminar deflagration is very subsonic, explain why the detonation widths are larger than the deflagration widths in Figure \ref{lengths}."894" For the X-ray burst case. Figure 1 inclicates that the detouatioi width becomes large ‘that the the pressure scale lieiglit at a deisity of p10* ο ""."," For the X-ray burst case, Figure \ref{lengths} indicates that the detonation width becomes larger that the the pressure scale height at a density of $\rho \sim 10^7$ g $^{-3}$."895 The steacy state width is larger than the radial “box” size coutainiug the detonatiou., The steady state width is larger than the radial “box” size containing the detonation.896 This suggests that a steady-state. sel[-sustaiued detonatious cannot come into existaice in the radial direction at deisities sinaller than p10! ecm”.," This suggests that a steady-state, self-sustained detonations cannot come into existance in the radial direction at densities smaller than $\rho897\sim 10^7$ g $^{-3}$."898 If the nuclear statistical eqtülibrium widths are used instead of the reactive widths. the density at which the the width becoijes larger than the radial “box” size is increased to 6x 10' [n]ecm 4 ," If the nuclear statistical equilibrium widths are used instead of the reactive widths, the density at which the the width becomes larger than the radial “box” size is increased to $\sim$$\times$ $^7$ g $^{-3}$."899For the thin shell case. the platar ZND detouation width becomes larger tliau tlie pressure scale height at ~5x10! ο em 7.," For the thin shell case, the planar ZND detonation width becomes larger than the pressure scale height at $\sim 5\times10^4$ g $^{-3}$ ."900 Steady-state. sell-sustained detonations travelling in the racial," Steady-state, self-sustained detonations travelling in the radial"901the principal cause of the modeled bounce is seen ou retfiietempvpost.. in the 1100 second panel. the time of the bounce peak.,"the principal cause of the modeled bounce is seen on \\ref{figtempvpost}, in the 1400 second panel, the time of the bounce peak."902 As noted in rofsseciursse.. the collapse of the vanguard leaves a low-pressure wake which is accentuated by the radial expansion of the pluue.," As noted in \\ref{ssecmrsse}, the collapse of the vanguard leaves a low-pressure wake which is accentuated by the radial expansion of the plume."903 Matter rushes into this wake from the zones having τοLOO kin., Matter rushes into this wake from the zones having $z\ge 400$ km.904 As this matter hits regions of iucreased density near 5~300 kin. it is also shocked aud moderately heated.," As this matter hits regions of increased density near $z\sim 300$ km, it is also shocked and moderately heated."905 Ifa reservoir of jovian air were available above the collapsing plume. this mechanism would explain not ouly the helt curve bounces. but also the relative prominence of methane aud molecular hydrogen quadrupole cussion in the bounce phase(?).," If a reservoir of jovian air were available above the collapsing plume, this mechanism would explain not only the light curve bounces, but also the relative prominence of methane and molecular hydrogen quadrupole emission in the bounce phase."906. However. the initial expansion of the fireball may sweep aside. or eutraiu. much of the overlving jovian atiuosphere.," However, the initial expansion of the fireball may sweep aside, or entrain, much of the overlying jovian atmosphere."907 Our current model cannot determine whether sufficient jovian air remains above the pluue to promptly All the wake of the vanguard collapse. since the answer depeuds on the plysics of the fireball/phune expansion.," Our current model cannot determine whether sufficient jovian air remains above the plume to promptly fill the wake of the vanguard collapse, since the answer depends on the physics of the fireball/plume expansion."908" Yet another ""bounce mecliauisii derives frou the reaction of the underlying atinosphere to the plume infall.", Yet another `bounce mechanism' derives from the reaction of the underlying atmosphere to the plume infall.909 As noted in discussion of reffietcmpypre.. the varving pressure of the overlying plume induces an oscillation iu the underlying atmosphere at the acoustic cutoff period.," As noted in discussion of \\ref{figtempvpre}, the varying pressure of the overlying plume induces an oscillation in the underlying atmosphere at the acoustic cutoff period."910 This is a natural resonance of a stratified atinosphiere i pressure equilibrium(2)., This is a natural resonance of a stratified atmosphere in pressure equilibrium.911. For a constant scale height (£2) the acoustic cutoff period is Ez/Z/e. proportional to P727. where eis the sound speed aud T. is temperature.," For a constant scale height $H$ ) the acoustic cutoff period is $4\pi H /c$ , proportional to $T^{1/2}$, where $c$ is the sound speed and $T$ is temperature."912 We ran a series of computations using several isothermal joviau atimospheric models. with different temperatures.," We ran a series of computations using several isothermal jovian atmospheric models, with different temperatures."913 We verified that the oscillation period im the model varies in proportion to £77., We verified that the oscillation period in the model varies in proportion to $T^{1/2}$.914 For our empirical model the resonance occurs at 150 seconds;, For our empirical model the resonance occurs at $\sim 450$ seconds.915 The acoustic mechanisin contributes to the modeled bounce. but deteriiues the bounce period oulv after the first or second muaxinmnu.," The acoustic mechanism contributes to the modeled bounce, but determines the bounce period only after the first or second maximum."916 Since the initial portion of the bouuce phenomenon has a somewhat longer period (500GOO sec). we expect that the period of the bounce in observed Πο curves should shorten slightly with time.," Since the initial portion of the bounce phenomenon has a somewhat longer period (500–600 sec), we expect that the period of the bounce in observed light curves should shorten slightly with time."917 observed multiple bounces. but their observations contain gaps which make it difficult to discern variations iu the bounce period.," observed multiple bounces, but their observations contain gaps which make it difficult to discern variations in the bounce period."918 The fact that the splashbacks were bright in infrared radiation sugeests that radiative emission may be au important. even dominant. cooling mechanisiu.," The fact that the splashbacks were bright in infrared radiation suggests that radiative emission may be an important, even dominant, cooling mechanism."919 Is the overall uorphology of the light. curves determined by radiative cooling of the splashhack regions?, Is the overall morphology of the light curves determined by radiative cooling of the splashback regions?920 Figure 8. shows the effect on the light curve of turning off the radiative damping term in the model., Figure \ref{figradamp} shows the effect on the light curve of turning off the radiative damping term in the model.921 In. the absence of radiative damping. the peak fux is larger by a factor of 6 (0.8 in log flux).," In the absence of radiative damping, the peak flux is larger by a factor of 6 (0.8 in log flux)."922 Igeuoriug the obvious contradiction (that the radiated flux is greater when we turi off radiation). we use this comparison to evaluate the effects of radiative damping on the splashhack energy budget.," Ignoring the obvious contradiction (that the radiated flux is greater when we turn off radiation), we use this comparison to evaluate the effects of radiative damping on the splashback energy budget."923 At 2000 seconds post impact. the flux in the nominal model has fallen by wo orders of magnitude. whereas the undamped model shows a decrease of 0.6 in log flux (this beiug due to radial expansion).," At 2000 seconds post impact, the flux in the nominal model has fallen by two orders of magnitude, whereas the undamped model shows a decrease of 0.6 in log flux (this being due to radial expansion)."924 In the case of the light curve (not illustrated). the nominal wodel falls by ouly 0.6 in log flux at 2000 sec. versus 0.3 for the uudamped model.," In the case of the light curve (not illustrated), the nominal model falls by only 0.6 in log flux at 2000 sec, versus 0.3 for the undamped model."925 So the effect of radiative damping. relative to cooling by expansion. is ercatest at he shortest waveleneths.," So the effect of radiative damping, relative to cooling by expansion, is greatest at the shortest wavelengths."926 ZM95 invoked an iustautaucous balance between the kinetic energy of the intalling plume aud radiative losses., ZM95 invoked an instantaneous balance between the kinetic energy of the infalling plume and radiative losses.927 Our calculations coufirm that this is a reasonable approximation., Our calculations confirm that this is a reasonable approximation.928 However. the opposite approximation. where radiation is cutirely ueglected aud cooling occurs only by radial expansion. also produces ght curves whosesfapes natch the observations fairly well (c.¢.. reffieradamp.. dashed line). especially for the longer thermal wavelenethls.," However, the opposite approximation, where radiation is entirely neglected and cooling occurs only by radial expansion, also produces light curves whose match the observations fairly well (e.g., \\ref{figradamp}, dashed line), especially for the longer thermal wavelengths."929 Radiative damping affects the time of iiixinmun in the helt curves by a small. vet significant. amount.," Radiative damping affects the time of maximum in the light curves by a small, yet significant, amount."930 Αα of he nominal light curve shifts slightly earlier than in the wadamped case., Maximum of the nominal light curve shifts slightly earlier than in the undamped case.931 This is due to the ercater radiative losses from he hottest shocks. which occur after 720 seconds.," This is due to the greater radiative losses from the hottest shocks, which occur after 720 seconds."932 We monitored the modeled temperature profile of the atinosphliere below the depth of shock heating., We monitored the modeled temperature profile of the atmosphere below the depth of shock heating.933 For the largest impacts (b. CG. K) this depth correspouds to p0.5 mbar. while for the moderate R impact it is p0.1 mbar.," For the largest impacts (L, G, K) this depth corresponds to $p\sim 0.5$ mbar, while for the moderate R impact it is $p\sim 0.1$ mbar."934 Atmospheric cluperatures at ereater pressures did not vary significantly (< LIS). indicating that heating of the lower atinosphere by radiation from the overlving shocks was uceligihle.," Atmospheric temperatures at greater pressures did not vary significantly $< 1$ K), indicating that heating of the lower atmosphere by radiation from the overlying shocks was negligible."935 The of SLO shocks contrasts with the larger terrestrial I.fT npact. where radiation from the splashback is believed to have iguited global terrestrial fires(?).," The of SL9 shocks contrasts with the larger terrestrial K/T impact, where radiation from the splashback is believed to have ignited global terrestrial fires."936. Figure 8 also shows the light curve which results from a plume wherein the vanguard is climinated., Figure \ref{figradamp} also shows the light curve which results from a plume wherein the vanguard is eliminated.937 This causes the main event to be more rounded! aud syiuuaetric. Whereas observations of the C and Is impact show main events which decline more steeply than they ascend(??).," This causes the main event to be more `rounded' and symmetric, whereas observations of the G and K impact show main events which decline more steeply than they ascend."938. The bounce is broadened aud delayed without the vanguard. aud as noted in refssecü)lc.. the vanenard is needed to match the flare seen at 0.9gan.," The bounce is broadened and delayed without the vanguard, and as noted in \\ref{ssec09lc}, , the vanguard is needed to match the flare seen at 0.9."939 Quite a few of the smaller fragments show sviuncetric main events2). and were not observed at 0.9422. so nou-vanguard models might be preferred in those instances.," Quite a few of the smaller fragments show symmetric main events, and were not observed at 0.9, so non-vanguard models might be preferred in those instances."940 describe the expausion of a large ring secu at 31422. but nof at shorter or longer wavelengths., describe the expansion of a large ring seen at 3–4 but not at shorter or longer wavelengths.941" Observations of the rug ~L700 and 7100 sec post-inipact show radii of 11.000 and 18.000 kin. respectively,"," Observations of the ring $\sim 4700$ and 7400 sec post-impact show radii of $\sim 14,000$ and 18,000 km, respectively."942 The ceuter of the ring is offset from the iapact location in the approximate direction of the iucomine fragment by 3600 km., The center of the ring is offset from the impact location in the approximate direction of the incoming fragment by 3600 km.943 Extrapolating the ring radius at the two observed timesback to £—0 sugeests an origin near kc=8000 kin fro the impact site., Extrapolating the ring radius at the two observed timesback to $t=0$ suggests an origin near $r=8000$ km from the impact site.944 Our model explains these effects. as discussed below.," Our model explains these effects, as discussed below."945The measured angular cross-correlations between the various foreground. and. background. samples are shown in Fie. 2..,The measured angular cross-correlations between the various foreground and background samples are shown in Fig. \ref{fig:lensing}.946 X set of logarithmically spaced angular separation bins are used. ranging from ~1 to 50 arcmins.," A set of logarithmically spaced angular separation bins are used, ranging from $\sim1$ to 50 arcmins."947 The green dashed line is the expected Iensing-induced cross-correlation (μι(0). the red. dashed. line is the expected. clustering-induced: eross-correlation ος(0) and the blue dashed. line is the sum of the two.," The green dashed line is the expected lensing-induced cross-correlation $w_{\rm fb}(\theta)$, the red dashed line is the expected clustering-induced cross-correlation $w_{\rm cc}(\theta)$ and the blue dashed line is the sum of the two."948 In the left column ofFig. 2..," In the left column ofFig. \ref{fig:lensing},"949 the expected elustering-induced eross-correlat toe is non-zero because the tail of the background Ns)ion overlaps slightly with that of the foreground. Ας)., the expected clustering-induced cross-correlation $w_{\rm cc}$ is non-zero because the tail of the background $N(z)$ overlaps slightly with that of the foreground $N(z)$.950 Although «v is much smaller than wi. we should bear in mind that wo. could be underestimated if a higher than expected fraction of SMCs reside at low redshifts 21.," Although $w_{\rm cc}$ is much smaller than $w_{\rm fb}$, we should bear in mind that $w_{\rm cc}$ could be underestimated if a higher than expected fraction of SMGs reside at low redshifts $z\lesssim1$."951 In the right column of Fig. 2..," In the right column of Fig. \ref{fig:lensing},"952 the predicted: wee vanishes. as B2 does not overlap with FL or F2.," the predicted $w_{\rm cc}$ vanishes, as B2 does not overlap with F1 or F2."953 To assess the significance of the lensing-induced ceross-correlation signal. eiven the covariance matrix obtained from bootstrap realisations. we derive the Baves factor where {ΑΠων) is the probability of the data given the lensing model and. PCGD|Mya) is the probability of the data assuming there is no cross-correlation.," To assess the significance of the lensing-induced cross-correlation signal, given the covariance matrix obtained from bootstrap realisations, we derive the Bayes factor where $P(D|M_{\textrm{lensing}})$ is the probability of the data given the lensing model and $P(D|M_{\textrm{null}})$ is the probability of the data assuming there is no cross-correlation."954 We find. that ἐν=64 for the cross-corrclation between Fl and B2 and dy=132.6 between F2 and B2., We find that $K=6.3$ for the cross-correlation between F1 and B2 and $K=132.6$ between F2 and B2.955 On Jellrevs’ seale (Jelfrevs 1961). A>3 means that there is substantial evidence that Afeusing Is more strongly supported. by the data than the null hypothesis anc fyOO means that there is decisive evidence that Minus is the favoured model compared. to the null.," On Jeffreys' scale (Jeffreys 1961), $K>3$ means that there is substantial evidence that $M_{\textrm{lensing}}$ is more strongly supported by the data than the null hypothesis and $K>100$ means that there is decisive evidence that $M_{\textrm{lensing}}$ is the favoured model compared to the null."956 Note that there is almost a factor of two increase in the source density in the foreground sample E2 compared to Fl: increasing the number of tracers of the foreground structure increases the strength of the lensing signal., Note that there is almost a factor of two increase in the source density in the foreground sample F2 compared to F1; increasing the number of tracers of the foreground structure increases the strength of the lensing signal.957 The effect of lensing on the number count of the sub-nim sources is expressed in equation (2). under the assumption that the lens plane is at a much. lower redshift) than the source plane.," The effect of lensing on the number count of the sub-mm sources is expressed in equation (2), under the assumption that the lens plane is at a much lower redshift than the source plane."958 Phe power-law slope of the intrinsic unlensecl number count AOS) is not allectecd because the lensing magnification yr is independent. of the flux density., The power-law slope of the intrinsic / unlensed number count $N_{{\rm u}}(S)$ is not affected because the lensing magnification $\mu$ is independent of the flux density.959 Llowever. the overall normalisation of the number count can be πιοΠο by a factor of yr’ where yp=1|opl1]2& in the weak lensing limit.," However, the overall normalisation of the number count can be modified by a factor of $\mu^{\beta-1}$, where $\mu=1+\delta \mu=1+2\kappa$ in the weak lensing limit."960 Weak lensing by large- structure causes aye to follow a Gaussian. function with mean magnification 10/0=0 and its dispersion σι dependent on the redshift of the sub-nim population (DS01)., Weak lensing by large-scale structure causes $\delta \mu$ to follow a Gaussian function with mean magnification $\langle \delta\mu \rangle=0$ and its dispersion $\sigma_{\mu}$ dependent on the redshift of the sub-mm population (BS01).961 Therefore. when averaged over a statistically representative area. the elfect of weak lensing on the number count should be negligible.," Therefore, when averaged over a statistically representative area, the effect of weak lensing on the number count should be negligible."962 The elfect of weak lensing on the local number density of the sub-mnir sources along a certain direction can be estimated [rom the measured. cross-correlation between the foreground ancl the background. populations., The effect of weak lensing on the local number density of the sub-mm sources along a certain direction can be estimated from the measured cross-correlation between the foreground and the background populations.963 In the right panel of Fig., In the right panel of Fig.964 2 where the measured signal is expected to be due to lensing only. we can see that the probability of finding a background sub-mm source close to a foreground galaxy is increased by a few percent above random on angular scales between ~I and 50 aremin.," 2 where the measured signal is expected to be due to lensing only, we can see that the probability of finding a background sub-mm source close to a foreground galaxy is increased by a few percent above random on angular scales between $\sim1$ and 50 arcmin."965 Therefore. the lensing induced change in the number density along a certain direction is expected to be at the level of à few. percent.," Therefore, the lensing induced change in the number density along a certain direction is expected to be at the level of a few percent."966 We can also estimate the cllect of lensing on the local number density through the auto-correlation function of the background sub-nim sources. μπω(0)=(On(oó)an(o') ," We can also estimate the effect of lensing on the local number density through the auto-correlation function of the background sub-mm sources, $w_{\rm auto}(\theta)=\langle \delta n (\hat{ \phi }) \delta n( \hat{\phi'} ) \rangle $."967Using equation. (4). we can decompose μπω). into three components. on(oon(0!) on(Ojon(a)| and dnl(ajan!(os. which represent. the ealaxv-galaxy. galaxv-lensing and lensing-lensing correlation functions respectively.," Using equation (4), we can decompose $w_{\rm auto}(\theta)$ into three components, $\langle \delta n^c(\hat{\phi}) \delta n^c(\hat{\phi'}) \rangle$, $\langle \delta n^c(\hat{\phi}) \delta n^{\mu}(\hat{\phi'})\rangle + \langle \delta n^c(\hat{\phi'}) \delta n^{\mu}(\hat{\phi})\rangle$ and $\langle \delta n^{\mu}(\hat{\phi}) \delta n^{\mu}(\hat{\phi'}) \rangle$, which represent the galaxy-galaxy, galaxy-lensing and lensing-lensing correlation functions respectively."968 Ehe Iensing-lensing term is given by (Aloessner Jain 1998) At zero lag. ie(ü)Eieiislonsius lonsinseiusc(On!)73 is the variance of the number density Ductuatuation due to lensing and thus the rms fluctuation is de!=(ie(0ο...fusαναyl2 which is ab a few percent level.," The lensing-lensing term is given by (Moessner Jain 1998) At zero lag, $w(0)_{\rm auto}^{\rm lensing-lensing}=\langle (\delta n^{\mu})^2 \rangle$ is the variance of the number density fluctuatuation due to lensing and thus the rms fluctuation is $\delta n^{\mu} = (w(0)_{\rm auto}^{\rm lensing-lensing})^{1/2}$ which is at a few percent level."969 The unusually steep number count in the bright sub-mm regime leads to an enhanced cross-correlation signal that is due to weak. gravitational lensing., The unusually steep number count in the bright sub-mm regime leads to an enhanced cross-correlation signal that is due to weak gravitational lensing.970 In this paper. we have measured the angular cross-correlations between sub-num sources detected by cSPIE in Lockman-SWIRE ancl foreground: sources selected. in the optical or near-infrared.," In this paper, we have measured the angular cross-correlations between sub-mm sources detected by -SPIRE in Lockman-SWIRE and foreground sources selected in the optical or near-infrared."971" We have also derived theoretical expectations of the weak lensing-induced. cross-correlation wy, ancl the clustering-induced: eross-correlation wee which are in. good agreement with our measurements.", We have also derived theoretical expectations of the weak lensing-induced cross-correlation $w_{\rm fb}$ and the clustering-induced cross-correlation $w_{\rm cc}$ which are in good agreement with our measurements.972 We find clear evidence or à lensine-inducecl cross-correlation between: sub-mum sources at high redshifts and galaxies at low recdshifts., We find clear evidence for a lensing-induced cross-correlation between sub-mm sources at high redshifts and galaxies at low redshifts.973 The redshift distribution of the sub-nini sources. is he biggest source of uncertainty in our analysis because most of the sources do not have spectroscopic redshifts., The redshift distribution of the sub-mm sources is the biggest source of uncertainty in our analysis because most of the sources do not have spectroscopic redshifts.974" In xinciple. the elustering-induced cross-correlation woo could contaminate the lensing-induced: eross-correlation wg, if a ügher than expected fraction. of sub-nim sources reside in he low-redshift Universe."," In principle, the clustering-induced cross-correlation $w_{\rm cc}$ could contaminate the lensing-induced cross-correlation $w_{\rm fb}$ if a higher than expected fraction of sub-mm sources reside in the low-redshift Universe."975" As the amplitude of wp, is mainly sensitive to the mean redshift of the background population rather than the exact shape of the Ας) (Ménnard. Dartelmann 2002). we have carried out a simple calculation of the expected a and woo amplitude by varving the mean redshift (25 (from 0.3 to 4.0) and the width o (from 0.2 o 2.5) assuming the Ας) of the sub-mnmr sources can »' approximated by a Caussian function."," As the amplitude of $w_{\rm fb}$ is mainly sensitive to the mean redshift of the background population rather than the exact shape of the $N(z)$ (Ménnard Bartelmann 2002), we have carried out a simple calculation of the expected $w_{\rm fb}$ and $w_{\rm cc}$ amplitude by varying the mean redshift $\langle z \rangle$ (from 0.3 to 4.0) and the width $\sigma_z$ (from 0.2 to 2.5), assuming the $N(z)$ of the sub-mm sources can be approximated by a Gaussian function."976" In all cases. to reproduce the measured. cross-correlation signal. wee is at most comparable to wp, when (£z)3.5.0,~1.5. (2)ον or l5.e.~ 0.5."," In all cases, to reproduce the measured cross-correlation signal, $w_{\rm cc}$ is at most comparable to $w_{\rm fb}$ when $\langle z \rangle \sim 3.5, \sigma_z \sim 1.5$, $\langle z \rangle \sim 2.5, \sigma_z \sim 1.0$ or $\langle z \rangle \sim 1.5, \sigma_z \sim 0.5$ ."977 So the detection of the weak Iensing-induced cross-correlation should be robust., So the detection of the weak lensing-induced cross-correlation should be robust.978 Lt should. be possible to acurately determine Ας) in the future when the infrared spectral energy. distributions are well understood and/or. more spectroscopic redshifts are acquired for sub-nin sources., It should be possible to acurately determine $N(z)$ in the future when the infrared spectral energy distributions are well understood and/or more spectroscopic redshifts are acquired for sub-mm sources.979 Limitations in our mocdelling of the cross-correlation include: using a scale- and time-independent bias factor [or the ealaxy-dark matter power spectrum: assuming a, Limitations in our modelling of the cross-correlation include: using a scale- and time-independent bias factor for the galaxy-dark matter power spectrum; assuming a980or both.,or both.981 wee have investigated two different pathways to the planetary radius. relvine ou different assuniptious. aud found them fo eive Incousistcut results.," e have investigated two different pathways to the planetary radius, relying on different assumptions, and found them to give inconsistent results."982 The results of both of these methods.| including a umber of derived stella aud plauctary paralucters. are given in Table 2.," The results of both of these methods, including a number of derived stellar and planetary parameters, are given in Table 2."983 This consistency. had already been noted by Charbouneau et al. (, This inconsistency had already been noted by Charbonneau et al. (9842009). but here we delve further iuto the details aud discuss possible resolutions.,"2009), but here we delve further into the details and discuss possible resolutions."985 Iu the first method. the stellar mass is estimated based ou its observed Iuninositv (parallax. aud appareut magnitude).," In the first method, the stellar mass is estimated based on its observed luminosity (parallax, and apparent magnitude)."986" Then. the stellar radius is found by combining the stellar mass with the mean stellar density p. derived frou the transit light curve. which. for Af,«Af. is only a function of the photometrically-cetermuned parameters a/R, aud P."," Then, the stellar radius is found by combining the stellar mass with the mean stellar density $\rho_\star$ derived from the transit light curve, which, for $M_p \ll M_\star$, is only a function of the photometrically-determined parameters $a/R_\star$ and $P$."987 We begin with the A-baud mass-Inuinositv function of Delfosse et (2000)., We begin with the $K$ -band mass-luminosity function of Delfosse et (2000).988 For CJ 1211. with a parallax," For GJ 1214, with a parallax"989"In order to study the effect of small scale spots additional simulations were run for the model L2, where small poloidal field loops were randomly added into the convection zone once per day (laws L2a and L2b).","In order to study the effect of small scale spots additional simulations were run for the model L2, where small poloidal field loops were randomly added into the convection zone once per day (laws L2a and L2b)."990 The magnetic energy due to the additional field injection in model L2a is about half of the energy of the axisymmetric field component in the quasi-stationary regime., The magnetic energy due to the additional field injection in model L2a is about half of the energy of the axisymmetric field component in the quasi-stationary regime.991" The fields appear as localised spots on the surface, which move with the surface rotation."," The fields appear as localised spots on the surface, which move with the surface rotation."992 With that strong field injection (L2a) the field structure of the global dynamo mode is nearly hidden by the small scale spots., With that strong field injection (L2a) the field structure of the global dynamo mode is nearly hidden by the small scale spots.993" Therefore in a second run 10 times weaker field loops (model L2b) were added, which led to a final energy of the small scale component of only 1/100th of the axisymmetric field."," Therefore in a second run 10 times weaker field loops (model L2b) were added, which led to a final energy of the small scale component of only 1/100th of the axisymmetric field."994 Here the global field again dominates the surface spot structure., Here the global field again dominates the surface spot structure.995" One could also correlate the small scale field injection with the large scale magnetic field, but for simplicity a totally uncorrelated field injection was chosen."," One could also correlate the small scale field injection with the large scale magnetic field, but for simplicity a totally uncorrelated field injection was chosen."996" When using the dynamo models to study the surface differential rotation, the temporal resolution can be chosen high enough that standard cross-correlation methods can be used."," When using the dynamo models to study the surface differential rotation, the temporal resolution can be chosen high enough that standard cross-correlation methods can be used."997 Snapshot maps of the surface magnetic pressure are taken from the dynamo calculations and treated as representations of the magnetic structures at that time point., Snapshot maps of the surface magnetic pressure are taken from the dynamo calculations and treated as representations of the magnetic structures at that time point.998" These maps can be treated the same way as the temperature maps obtained from Doppler imaging, therefore the same techniques as in the case of the real observations can be used to analyse the model snapshots."," These maps can be treated the same way as the temperature maps obtained from Doppler imaging, therefore the same techniques as in the case of the real observations can be used to analyse the model snapshots."999 Magnetic pressure maps have been taken from 36 time points over the activity cycle., Magnetic pressure maps have been taken from 36 time points over the activity cycle.1000" These time points are relatively close to each other: separated by about 50 days in the L1, and by about 18 days with the L2."," These time points are relatively close to each other: separated by about 50 days in the L1, and by about 18 days with the L2."1001 Examples of snapshots for L1 and L2 are shown in on-line Figs., Examples of snapshots for L1 and L2 are shown in on-line Figs.1002" 3 4,, respectively."," \ref{snap_law1} \ref{snap_law2}, respectively."1003 In the analysis each time point is cross-correlated with the following one and the behaviour is studied from equator to the visible pole., In the analysis each time point is cross-correlated with the following one and the behaviour is studied from equator to the visible pole.1004 The dynamo model has a grid of 43x surface points., The dynamo model has a grid of $43\times 43$ surface points.1005 This makes the longitudinal resolution of aand latitudinal of4., This makes the longitudinal resolution of and latitudinal of.10062°.. The equator is going through in the middle of the 22nd latitude strip., The equator is going through in the middle of the 22nd latitude strip.1007 The cross-correlations are obtained for each latitude between the latitudes centred at aand83., The cross-correlations are obtained for each latitude between the latitudes centred at and.10087°.. The last latitude strip closest to the pole is not used due to the lack of signal., The last latitude strip closest to the pole is not used due to the lack of signal.1009 The measured shift in degrees/day at each latitude is compared to the expected shift obtained from the rotation law used in the dynamo model., The measured shift in degrees/day at each latitude is compared to the expected shift obtained from the rotation law used in the dynamo model.1010" The spots are migrating in the dynamo simulation, to remove this field migration all the measured shifts are normalised to the shift at the lowest latitude used in the investigation."," The spots are migrating in the dynamo simulation, to remove this field migration all the measured shifts are normalised to the shift at the lowest latitude used in the investigation."1011 Examples of results from cross-correlating the 36 maps for L1 are shown in Fig. 5.., Examples of results from cross-correlating the 36 maps for L1 are shown in Fig. \ref{CC_solar}.1012 The plots give the shift in degrees/day for each latitude on the visible hemisphere (crosses)., The plots give the shift in degrees/day for each latitude on the visible hemisphere (crosses).1013" The last plot shows the average of the measurements from all the cross-correlations, with standard deviation of the measurements as the error."," The last plot shows the average of the measurements from all the cross-correlations, with standard deviation of the measurements as the error."1014 In the plots the dashed line is the input rotation at the stellar surface., In the plots the dashed line is the input rotation at the stellar surface.1015" The behaviour of the measured spot rotation clearly changes from cross-correlation to cross-correlation, indicating that the appearing surface rotation pattern changes during the activity cycle."," The behaviour of the measured spot rotation clearly changes from cross-correlation to cross-correlation, indicating that the appearing surface rotation pattern changes during the activity cycle."1016" Furthermore, the measured surface rotation can take numerous different forms: typical solar-type rotation law (e.g., cross-correlation 11), almost no difference between the latitudes (e.g., cross-correlation 01) and even completely solar rotation law with the pole rotating faster (e.g., correlation 25)."," Furthermore, the measured surface rotation can take numerous different forms: typical solar-type rotation law (e.g., cross-correlation 11), almost no difference between the latitudes (e.g., cross-correlation 01) and even completely anti-solar rotation law with the pole rotating faster (e.g., cross-correlation 25)."1017" In general it is evident that in the case of L1 the measured surface differential rotation at the low latitudes often is what one would expect from the models, but at higher latitudes the correlation is very poor."," In general it is evident that in the case of L1 the measured surface differential rotation at the low latitudes often is what one would expect from the models, but at higher latitudes the correlation is very poor."1018" The examples of cross-correlation results from L2, shown in Fig. 6,,"," The examples of cross-correlation results from L2, shown in Fig. \ref{CC_axis},"1019 also exhibit large variations in the surface rotation patterns over the activity cycle., also exhibit large variations in the surface rotation patterns over the activity cycle.1020" In some cases the measured surface rotation at the lower latitudes is similar to the input rotation (e.g., cross-correlation 14), at times the surface rotation at the equator and at the polar region is similar to"," In some cases the measured surface rotation at the lower latitudes is similar to the input rotation (e.g., cross-correlation 14), at times the surface rotation at the equator and at the polar region is similar to"1021"Skew-symmetric. broadened Fe Ko emission lines are seen in many Active Galactic Nuclei (AGN) such as 15 (222... 495.(2). and. others(2)... Galactic black hole binaries suchas Cygnus X-1(22)... GX 4(022), or GRS 19154105(22).. and neutron star systems(2222).","Skew-symmetric, broadened Fe $\alpha$ emission lines are seen in many Active Galactic Nuclei (AGN) such as $-$ 6-30-15 , $-$ 495, and others, Galactic black hole binaries suchas Cygnus X-1, GX $-$ 4, or GRS 1915+105, and neutron star systems."1022. These lines are generally interpreted as being caused by the relativistic motion of the line emitting material close to the central compact object., These lines are generally interpreted as being caused by the relativistic motion of the line emitting material close to the central compact object.1023 Since the line shape depends on the spin of the black hole. a. and the emissivity and inclination of the surrounding accretion disc. the diagnostic power of relativistic lines is very high. as they provide one of the most direct ways to probe the physics of the region of strong gravity close to the black holereview).," Since the line shape depends on the spin of the black hole, $a$, and the emissivity and inclination of the surrounding accretion disc, the diagnostic power of relativistic lines is very high, as they provide one of the most direct ways to probe the physics of the region of strong gravity close to the black hole."1024 High signal-to-noise observations of AGN and Galactic black holes have already resulted in several measurements of e with formally small error bars(2222). with systematic effects due to the high count rate of Galactic sources and due to the uncertainty of the parameters of the underlying continuum currently dominating the uncertainty of the measurements.," High signal-to-noise observations of AGN and Galactic black holes have already resulted in several measurements of $a$ with formally small error bars, with systematic effects due to the high count rate of Galactic sources and due to the uncertainty of the parameters of the underlying continuum currently dominating the uncertainty of the measurements."1025 Observations of AGN in the and deep fields prove that broadened iron lines already occured oat high redshifts. ον3}comastri:O+astreblyanska2005a.," Observations of AGN in the and deep fields prove that broadened iron lines already occured at high redshifts, $z$,."1026 Although recent studies seem to exclude that these broad lines are a common feature(2).. observations of such lines could therefore be used to study the expected evolution of black hole spin with 2.," Although recent studies seem to exclude that these broad lines are a common feature, observations of such lines could therefore be used to study the expected evolution of black hole spin with $z$."1027 For example. strong changes in amplitude and direction for the central black hole are predicted in stochastic evolution models(22).," For example, strong changes in amplitude and direction for the central black hole are predicted in stochastic evolution models."1028. Observations of cavities in nearby galaxy clusters are also evidence for spin evolution(22)., Observations of cavities in nearby galaxy clusters are also evidence for spin evolution.1029 In galactic binary systems. the initial Kick during the formation of a stellar-mass black hole in a supernova ean lead to a strong misalignment between the dise and the black hole(2).," In galactic binary systems, the initial kick during the formation of a stellar-mass black hole in a supernova can lead to a strong misalignment between the disc and the black hole."1030". Depending on the mode of accretion. in all of these scenarios it is possible that the angular momenta of black hole and accretion dise become antiparallel. i.e.. the black hole has ""negative spin”."," Depending on the mode of accretion, in all of these scenarios it is possible that the angular momenta of black hole and accretion disc become antiparallel, i.e., the black hole has “negative spin”."1031 As shown by?.. both parallel and antiparallel alignments of the dise and black hole angular momenta are stable configurations: misaligned dises will evolve to one of them.," As shown by, both parallel and antiparallel alignments of the disc and black hole angular momenta are stable configurations; misaligned discs will evolve to one of them."1032 It is therefore not unlikely that a configuration with antiparallel spins exists in nature., It is therefore not unlikely that a configuration with antiparallel spins exists in nature.1033 In fact. accretion onto rapidly-spinning retrograde black holes may be of some importance for understanding the properties of powerful radio-loud AGN.," In fact, accretion onto rapidly-spinning retrograde black holes may be of some importance for understanding the properties of powerful radio-loud AGN."1034 Employing the flux-trapping model of?.. argues that an accretion disk around a retrograde black hole is a particularly potent configuration for generating powerful jets.," Employing the flux-trapping model of, argues that an accretion disk around a retrograde black hole is a particularly potent configuration for generating powerful jets."1035 loreover this might also explain the lack of radio-loud AGN in observations(2)., Moreover this might also explain the lack of radio-loud AGN in observations.1036. It is tantalizing that the broad iron line in the ;xowerful radio-loud AGN 3CI20 implies a truncation at (—10CAL/C7. (09. very close to the innermost stable circular orbit (SCO) for a rapidly-rotating retrograde black hole.," It is tantalizing that the broad iron line in the powerful radio-loud AGN 3C120 implies a truncation at $r\sim103710\,GM/c^2$ , very close to the innermost stable circular orbit (ISCO) for a rapidly-rotating retrograde black hole."1038 However. a urther exploration of this line of thought requires fully-relativistic iron line models that are valid for retrograde black holes.," However, a further exploration of this line of thought requires fully-relativistic iron line models that are valid for retrograde black holes."1039 Although first caleulations of line profiles for a negatively spinning black hole were already performed. e.g. by and ?.. none of the currently available models for relativistic lines such as(2).(2).(2. or the zv--family of models are valid for black holes with retrograde accretion discs.," Although first calculations of line profiles for a negatively spinning black hole were already performed, e.g., by and , none of the currently available models for relativistic lines such as, or the -family of models are valid for black holes with retrograde accretion discs."1040 In this we therefore extend the formalism of employed by many of these models to the ease of 0.098 0.995., In this we therefore extend the formalism of employed by many of these models to the case of $-0.998\le a \le +0.998$ .1041 Section 2. presents an overview of the scheme used for the, Section \ref{sec:theory} presents an overview of the scheme used for the1042photoionization equilibrium as it has low optical depth to the quasar radiation. and the increased densities imply short recombination times.,"photoionization equilibrium as it has low optical depth to the quasar radiation, and the increased densities imply short recombination times."1043 The mass conservation equation (9)) and ionizationparameter (10)) combine to give in this region., The mass conservation equation \ref{mass}) ) and ionizationparameter \ref{ion}) ) combine to give in this region.1044 Vhe rapid cooling in this region implies a rapid transition between the immediate postshock regime (eft. keV excitation) and the much slower and. cooler compressed state.," The rapid cooling in this region implies a rapid transition between the immediate postshock regime $\sim v/4$, keV excitation) and the much slower and cooler compressed state."1045 Phere is direct observational evidence for this cooling shock in NGC 4051 (Pounds et al.," There is direct observational evidence for this cooling shock in NGC 4051 (Pounds et al.,"1046 in. prep)., in prep).1047 Pounds et al (2004) Πας alreacky noted. a correlation. of outllow velocity with ionization in this source., Pounds et al (2004) had already noted a correlation of outflow velocity with ionization in this source.1048 Given the basic structure sketched in the last Section. we can investigate how the shock pattern moves through the interstellar medium of the host galaxy.," Given the basic structure sketched in the last Section, we can investigate how the shock pattern moves through the interstellar medium of the host galaxy."1049 The cooled postshock gas exerts the ram pressure (14)) on the undisturbed interstellar medium. of the galaxy. driving an outer shock into it and sweeping it up into a relatively dense shell of increasing mass.," The cooled postshock gas exerts the ram pressure \ref{ram}) ) on the undisturbed interstellar medium of the galaxy, driving an outer shock into it and sweeping it up into a relatively dense shell of increasing mass."1050" The equation of motion of the shell in the momentum.driven limit is where is the sweptup interstellar gas mass. AZ is the black hole mass. Adin=MGR)f, is the total mass within radius /? (including any dark matter). and fy is the gas fraction (note that in eqn (2) of Wine. 2005 the sullix ‘tot’ was inadvertently missed. olf the relevant. quantity)."," The equation of motion of the shell in the momentum–driven limit is where is the swept–up interstellar gas mass, $M$ is the black hole mass, $M_{\rm tot}= M(R)/f_g$ is the total mass within radius $R$ (including any dark matter), and $f_g$ is the gas fraction (note that in eqn (2) of King, 2005 the suffix `tot' was inadvertently missed off the relevant quantity)."1051 This equation takes different forms depending on which part of the host galaxy the shell has reached., This equation takes different forms depending on which part of the host galaxy the shell has reached.1052 Close to the black hole. ic. within its sphere of influence. of raclius the black hole dominates the gravitational potential. and there is essentially no dark matter.," Close to the black hole, i.e. within its sphere of influence, of radius the black hole dominates the gravitational potential, and there is essentially no dark matter."1053" Phen (16)) becomes Alultiplving through by ALGSRGAL we lind the first integral This equation shows that for any reasonable distribution of matter AZCR).. the shell cannot move outwards unless where we have parametrized the radius in units of the Schwarzschild radius A7, of the black hole. with Als=AI/ÁIUM.."," Then \ref{motion}) ) becomes Multiplying through by $M(R)\dot R/GM$ we find the first integral This equation shows that for any reasonable distribution of matter $M(R)$, the shell cannot move outwards unless where we have parametrized the radius in units of the Schwarzschild radius $R_s$ of the black hole, with $M_8 = M/10^8\msun$ ."1054 The physical content of (21)) is that. the I5ddington thrust cannot lift the weight of a more massive shell at the radius 2., The physical content of \ref{limit}) ) is that the Eddington thrust cannot lift the weight of a more massive shell at the radius $R$.1055 An equivalent formulation is i. that the maximum shell mass at a given radius has Thomson depth ~1., An equivalent formulation is i.e. that the maximum shell mass at a given radius has Thomson depth $\sim 1$.1056 We see that even relatively small amounts of gas sullicienthy close to the black hole can stall the outllow., We see that even relatively small amounts of gas sufficiently close to the black hole can stall the outflow.1057 llowever in this case. the gas from the central Ecelington wind would. accumulate at. the stalled shock until its own mass violated. the limit (21)).," However in this case, the gas from the central Eddington wind would accumulate at the stalled shock until its own mass violated the limit \ref{limit}) )."1058 The equivalent. (22)) shows that the inner wind shock would become optically thick to the quasar radiation. causing multiple scattering and enhancing the momentum deposition.," The equivalent \ref{limit2}) ) shows that the inner wind shock would become optically thick to the quasar radiation, causing multiple scattering and enhancing the momentum deposition."1059" The postshock pressure would begin to exceed Pug, by large factors.", The postshock pressure would begin to exceed $P_{\rm ram}$ by large factors.1060 Unless 16 black hole had a very low mass. this enhanced pressure would cause the shell to move out again.," Unless the black hole had a very low mass, this enhanced pressure would cause the shell to move out again."1061" This argument garows that the shell moves so as to keep the optical depth of the Eddington wind =1. ie. so that and ""his implies that the shell would reach a radius 10542, in no more than à vear."," This argument shows that the shell moves so as to keep the optical depth of the Eddington wind $\la 1$, i.e. so that and This implies that the shell would reach a radius $\sim 10^3R_s$ in no more than a year."1062 At this point the sweptup mass (from (21)) could be as large as 200miM.. which would imply an emission measure comparable with an ACN broad region.," At this point the swept–up mass (from \ref{limit}) ) could be as large as $200m_8\msun$, which would imply an emission measure comparable with an AGN broad--line region."1063" The shell would reach ~Zh in. Z310"" vr. with a velocity A272kms.|l"," The shell would reach $\sim R_{\rm inf}$ in $\la 3\times 10^5$ yr, with a velocity $\dot R1064\ga 2~{\rm km\, s^{-1}}$."1065 Thus even a whose progress is blocked by an unfavourable matter “Shelldistribution. reaches Z5; in about wv vr. assuming that the quasar wind continues to drive .," Thus even a shell whose progress is blocked by an unfavourable matter distribution reaches $R_{\rm inf}$ in about $10^5$ yr, assuming that the quasar wind continues to drive it."1066" In the opposite extreme. where the mass of the wepup matter is low. the time to emerge decreases as |~AL. and is limited. only by the wind.travel time 1042/6~500 vr for arbitrarily low AZ,."," In the opposite extreme, where the mass of the swept–up matter is low, the time to emerge decreases as $t \sim M_g^{1/2}$, and is limited only by the wind–travel time $\sim 10R/c \sim 500$ yr for arbitrarily low $M_g$."1067 This mechanism is clearly limited to the inner parts of a galaxy bulge. as a shell driven in this way can typically only reach radii S200 pe in à Salpeter time. and. 2 kpe even alter a Hubble time.," This mechanism is clearly limited to the inner parts of a galaxy bulge, as a shell driven in this way can typically only reach radii $\la 200$ pc in a Salpeter time, and $\la 2$ kpc even after a Hubble time."1068 Accordingly we do not consider. this mechanism in the next subsection. which treats outllows at radii cmf.," Accordingly we do not consider this mechanism in the next subsection, which treats outflows at radii $>\rinf$."1069 Far from the black hole(ιο. for Iz Bap) the dark matter term Adj becomes dominant in the equation of motion (16)). ancl we can drop the black hole mass term involving A.," Far from the black hole (i.e. for $R > R_{\rm inf}$ ) the dark matter term $M_{\rm tot}$ becomes dominant in the equation of motion \ref{motion}) ), and we can drop the black hole mass term involving $M$ ."1070 The condition that the shell shouldjust be able to escape, The condition that the shell should just be able to escape1071We also calculate the lags with the cross correlation function (CCE) method.,We also calculate the lags with the cross correlation function (CCF) method.1072 The errors of lags are evaluated by simulations., The errors of lags are evaluated by simulations.1073 The results are also reported in Table 1, The results are also reported in Table 1.1074 The lag derived by the CCF ολους (recep) is stronely correlated with Teak. but is svsteiatically than Toeak [Fig. ί," The lag derived by the CCF method $\tau_{\rm CCF}$ ) is strongly correlated with $\tau_{\rm1075peak}$, but is systematically than $\tau_{\rm peak}$ [Fig. \ref{Liso_lag}( ("1076α).,a)].1077 A best fit gives rocgp—€.100217)|(0.01dc(LOS) rial: , A best fit gives $\tau_{\rm CCF}=(-100\pm 17)+(0.91\pm 0.08)\tau_{\rm peak}$ .1078"The Zi,7 relation was discovered with six bright BATSE CRBs (Norris ct al.", The $L_{\rm iso}-\tau$ relation was discovered with six bright BATSE GRBs (Norris et al.1079 2000) aud the spectral lag was defined by the light curves in the 25-50 keV. and 100- keV bands., 2000) and the spectral lag was defined by the light curves in the 25-50 keV and 100-300 keV bands.1080 We investigate whether the lag behavior of NRF 060218 is consistent with the Ly.T relation.," We investigate whether the lag behavior of XRF 060218 is consistent with the $L_{\rm1081iso}-\tau$ relation."1082" Since NRF 060218 is a soft NRF aud the euission in the 100-300 keV baud is too weak to derive a lieht curve. we asmnie that thea, of the light curve iu the 100-300 keV baud follows the ΈνανE relation (Eq.2)) aud perform the extrapolation."," Since XRF 060218 is a soft XRF and the emission in the 100-300 keV band is too weak to derive a light curve, we assume that $t_{peak}$ of the light curve in the 100-300 keV band follows the $t_{peak}-E$ relation \ref{T_E}) ) and perform the extrapolation."1083 With the extrapolated τρωω we then estimate Treas for the light curves in the 25-50 keV (average enerev 30 keV) aud 100-300 keV (average energy 200 keV) bands., With the extrapolated $t_{peak}$ we then estimate $\tau_{peak}$ for the light curves in the 25-50 keV (average energy 30 keV) and 100-300 keV (average energy 200 keV) bands.1084 We obtaiu τσ17716 seconds., We obtain $\tau_{peak}=177\pm 16$ seconds.1085 Siuce Toop is more reliable. we use the teakTeer relation [Fig. ," Since $\tau_{\rm CCF}$ is more reliable, we use the $\tau_{\rm peak}1086- \tau_{\rm CCF}$ relation [Fig. \ref{Liso_lag}( ("1087ία] to derive troop=61426 seconds.,a)] to derive $\tau_{\rm CCF}=61\pm 26$ seconds.1088 This lag is used inthe L r relation analysis., This lag is used in the $L-\tau$ relation analysis.1089 Using the peak fluxes in the BAT and NRT baud. we estimate Lj.=1.2«lol Cres Ἱ.," Using the peak fluxes in the BAT and XRT band, we estimate $L_{iso}=1.2\times 10^{47}$ ergs $^{-1}$."1090" Figure Hb) shows the £j..,7 relation derived by Norris et al. (", Figure \ref{Liso_lag}( (b) shows the $L_{iso}-\tau$ relation derived by Norris et al. (10912000) compared agaius NRF 060218 as well as two other nearby CRBs. 980125 and 031203.,"2000) compared against XRF 060218 as well as two other nearby GRBs, 980425 and 031203."1092" The data of the previous GRBs are taken frou, Norris et al. (", The data of the previous GRBs are taken from Norris et al. (10932000) aud Sazonov et al.,2000) and Sazonov et al.1094"113. The erev. baud and the two dashed lines mark the best fits at the 1o aud 260 confidence level. respectively. aud the solid line is the regression line for the 6 CRBs that were used to draw the £7 correlation. 1.0. logLin,(50.22+0.32)(1.2140.21)«7. (errors are at the lo level)."," The grey band and the two dashed lines mark the best fits at the $1\sigma$ and $2\sigma$ confidence level, respectively, and the solid line is the regression line for the 6 GRBs that were used to draw the $L-\tau$ correlation, i.e. $\log L_{\rm1095iso}=(50.22\pm 0.32)-(1.21\pm 0.21)\times \log \tau$ (errors are at the $1\sigma$ level)."1096 We cau see that NRF 060218 is definitely inside the 26 region aud is mareinally at the lo region boundary., We can see that XRF 060218 is definitely inside the $2\sigma$ region and is marginally at the $1\sigma$ region boundary.1097 Therefore. the hypothesis that NRF 060218 follows the £7 relation cannot be ruled out at the 20 significance level.," Therefore, the hypothesis that XRF 060218 follows the $L-\tau$ relation cannot be ruled out at the $2\sigma$ significance level."1098 We caution that the 7 is inferred frou the extrapolation of the theak£ relation., We caution that the $\tau$ is inferred from the extrapolation of the $t_{\rm peak}-E$ relation.1099 This iutroduces uucertaimtics in deriving the lag., This introduces uncertainties in deriving the lag.1100 The other two uearby GRBs. 980125 aud 031203. are out of the 260 region. which are identified as slgsieificaut. outlicrs of this relation (6.8. Sazonov ot al.," The other two nearby GRBs, 980425 and 031203, are out of the $2 \sigma$ region, which are identified as significant outliers of this relation (e.g. Sazonov et al."1101 2001)., 2004).1102 We have investigated the non-therual emission of NRE 060218., We have investigated the non-thermal emission of XRF 060218.1103 The carly SED of this event from 0.3-150. keV observedby BAT and NRT sugecsts that the non-thermal enüssion detectedby the two iustruinents are the same component., The early SED of this event from 0.3-150 keV observed by BAT and XRT suggests that the non-thermal emission detected by the two instruments are the same component.1104 By subtracting the contribution of the thermal enüsson we derive the lieht curves of the uou-thermal cluission., By subtracting the contribution of the thermal emission we derive the light curves of the non-thermal emission.1105 They are composed of a broad single pulse. aud the enerey dependences of the widths aud the risine-to-decavine-time ratio of the pulses are roughly consisteut with those derived in typical CRBs.," They are composed of a broad single pulse, and the energy dependences of the widths and the rising-to-decaying-time ratio of the pulses are roughly consistent with those derived in typical GRBs."1106 The ligat curves show sjeuificaut spectral lacs. with a well-defined peak. time sequence fron high euerev band) to low energv bands. Le.τα PocalsNE2U.2»-cU.°that.," The light curves show significant spectral lags, with a well-defined peak time sequence from high energy band to low energy bands, i.e. $t_{\rm peak}\propto1107E^{-0.25\pm0.05}$."1108" We inter the specral lag in the BATSE hands and find the hypothesis hat this event complies with the Zi,τ relation with typical GREy. cannot be ruled out at the 20 siguificauce level.", We infer the spectral lag in the BATSE bands and find that the hypothesis that this event complies with the $L_{\rm iso}-\tau$ relation with typical GRBs cannot be ruled out at the $2\sigma$ significance level.1109 These intriguing facts. along with its compliance with the Aimativelation. strongly sugees that CRB 060218 is a “standard” burst at the very faint. long. and soft cucl of the CRB distribution.," These intriguing facts, along with its compliance with the Amati-relation, strongly suggest that GRB 060218 is a “standard” burst at the very faint, long, and soft end of the GRB distribution."1110 Since all these relations concern the temporal aud spectral proerties of emission. they are likely related to the raciatioi mechanisus.," Since all these relations concern the temporal and spectral properties of emission, they are likely related to the radiation mechanisms."1111 The results therefore imply that NRF 06IS and other NRFs may share the simular radiation pwsics (e.g. svuchrotron or Inverse Compton scattering in internal shocks. Mésszárros. 095: Zhang Mésszárros 20FE: Piran 2005: Mésszárros 06) with harder CRBs.," The results therefore imply that XRF 060218 and other XRFs may share the similar radiation physics (e.g. synchrotron or inverse Compton scattering in internal shocks, Mésszárros, 2002; Zhang Mésszárros 2004; Piran 2005; Mésszárros 2006) with harder GRBs."1112 As discovered 1w Norris (2032). the proportion of One-lag bursts within long-duration bursts increases fro neeligible among bright BATSE 1nursts to —50 at the trigeerao threshold. and their peak fluxes are ~2 orders of magnitude lower than those of the brightest bursts.," As discovered by Norris (2002), the proportion of long-lag bursts within long-duration bursts increases from negligible among bright BATSE bursts to $\sim 50\%$ at the trigger threshold, and their peak fluxes are $\sim 2$ orders of magnitude lower than those of the brightest bursts."1113" This arenesOo that they are intrinsically ποοποτ»,", This argues that they are intrinsically under-luminous.1114 Taken together with the fact that three nearby CRBs. 980125. 031203. and 060218. Hare lone-lageed and under-huninous. an intuitive speculation is hat oueg-lag bursts are probably relatively nearby (6.9.. Norris et al.," Taken together with the fact that three nearby GRBs, 980425, 031203, and 060218, are long-lagged and under-luminous, an intuitive speculation is that long-lag bursts are probably relatively nearby (e.g., Norris et al."1115 2005)., 2005).1116 The local CRB rate of these GRBs thus should be uuch lugher than that expered from the high huninosity CRBs (Liang ct al., The local GRB rate of these GRBs thus should be much higher than that expected from the high luminosity GRBs (Liang et al.1117 2006: see also Cobb ct al., 2006; see also Cobb et al.1118 2006: Pian et al., 2006; Pian et al.1119 2006: Soderberethei et al., 2006; Soderberg et al.1120 2006)., 2006).1121 A JOSS]dle scenario to explain ir wide-pulsc. loue-lag. andl Πο catures is the off-axis viewing augle effect {e.g.Yo Nalkuuura 1999: Saliuiousonu. 2000: loka Nakamura 2001).," A possible scenario to explain their wide-pulse, long-lag, and under-luminous features is the off-axis viewing angle effect (e.g. Nakamura 1999; Salmonson 2000; Ioka Nakamura 2001)."1122 Another scenario is that these catures are lutriusic. being due to heir lower Lorentz facOrs (Ixullzumi et al.," Another scenario is that these features are intrinsic, being due to their lower Lorentz factors (Kulkarni et al."1123 1998: Woosley AacFadven 1999: Salinouson 2000: Dui et al., 1998; Woosley MacFadyen 1999; Salmonson 2000; Dai et al.1124 2006: Wane et al., 2006; Wang et al.1125 2006)., 2006).1126 They might be from a unique GRB »»pulatiou (Liane et al., They might be from a unique GRB population (Liang et al.1127" 20066) havingo a different type of central engine (e.g. neutron stars rather than black holes) yourbright CRBs{(ο,ο, Mazzali et a", 2006) having a different type of central engine (e.g. neutron stars rather than black holes) from bright GRBs (e.g. Mazzali et al.1128 2006: Soderbere et al., 2006; Soderberg et al.1129 2006)., 2006).1130" We thank the auouvinous referee for helpful ugeestious.oo and S. Campana. D. Binrows. J. Nousek. Is. Page. T. Sakamoto, X.-Y. Wang. aud Z. Li for discussion."," We thank the anonymous referee for helpful suggestions, and S. Campana, D. Burrows, J. Nousek, K. Page, T. Sakamoto, X.-Y. Wang, and Z. Li for discussion."1131 This work. was supported]w NASA uuder erants NNGOGCGIIG2C: and NNGODCODO7C. aud the? NationalNatural Science Foundation of China uuder grauts 101463001(ENT).," This work was supported by NASA under grants NNG06GH62G and NNG05GB67G, and the National Natural Science Foundation of China under grants 10463001(EWL)."1132of the CoRoT data. fits the ground-based cata very well and the parameters obtained in this way (given in column S of Table 1)) are in good agreement with those obtained rom the ColtoT light curves.,"of the CoRoT data, fits the ground-based data very well and the parameters obtained in this way (given in column 8 of Table \ref{TabAUMon}) ) are in good agreement with those obtained from the CoRoT light curves."1133 We conclude that our mocel describes both data sets adequately., We conclude that our model describes both data sets adequately.1134 The grounc-basecl data and the synthetic lisht-curves roni our model are shown in Figure 4.., The ground-based data and the synthetic light-curves from our model are shown in Figure \ref{fAUMonV}.1135 Phe top panel shows he fit to the light curves in the minimum and maximum of he long evele. the middle panel shows the fit to the entire &rouncd-based. dataset. reduced. for the elfects of the Iong-erm variation. and the bottom panel gives a representation of the model obtained from the entire grouncd-based dataset in the phase of the secondary. eclipse.," The top panel shows the fit to the light curves in the minimum and maximum of the long cycle, the middle panel shows the fit to the entire ground-based dataset, reduced for the effects of the long-term variation, and the bottom panel gives a representation of the model obtained from the entire ground-based dataset in the phase of the secondary eclipse."1136 There are evident short-term variations in the ColtoT light curves of AU Alon., There are evident short-term variations in the CoRoT light curves of AU Mon.1137 The. resicuals after. subtracting the synthetic light curve from the observations (Figure 1.. right panel). also show quasi-periodic variabilitv.," The residuals after subtracting the synthetic light curve from the observations (Figure \ref{fAUMon}, right panel), also show quasi-periodic variability."1138 “Pwo features stand out: a lump in the secondary minimum (around phase 0.5) which is present to some degree in all five residual curves and is partially due to the inability of the model to fit the observations perfectly., Two features stand out: a lump in the secondary minimum (around phase 0.5) which is present to some degree in all five residual curves and is partially due to the inability of the model to fit the observations perfectly.1139 However. the shape and amplitude of the lump change from period to period. sugeesting the presence of intrinsic variability in either the CG type secondary or in the accretion disk or both.," However, the shape and amplitude of the lump change from period to period, suggesting the presence of intrinsic variability in either the G type secondary or in the accretion disk or both."1140 The other notable feature in the residual light curves is the fast and seemingly periodic variation inside the primary minimum. (around. phase 1.0). Desmetctal.(2010).," The other notable feature in the residual light curves is the fast and seemingly periodic variation inside the primary minimum (around phase 1.0). \citet{des10},"1141.. who also noted he fast variation. suggested that its origin is a non-uniform brightness distribution of the accretion disk.," who also noted the fast variation, suggested that its origin is a non-uniform brightness distribution of the accretion disk."1142" There is. however. an alternative interpretation: we relieve that the fast variation during the primary. minimum of AU Mon is caused. by a bicker mode of oscillation of he primary (seeο,ο.Mkrtichianetal.2005)."," There is, however, an alternative interpretation: we believe that the fast variation during the primary minimum of AU Mon is caused by a hidden mode of oscillation of the primary \citep[see e. g.][]{mkrt05}."1143. The origin of the variation is unlikely to be the secondary star or he aceretion disk. because these components are at least xutiallv visible during the entire orbital evele. while the ast variation occurs only in the primary minimum.," The origin of the variation is unlikely to be the secondary star or the accretion disk, because these components are at least partially visible during the entire orbital cycle, while the fast variation occurs only in the primary minimum."1144 If our interpretation is correct. it also represents an indication that he primary star is indeed. producing oscillations.," If our interpretation is correct, it also represents an indication that the primary star is indeed producing oscillations."1145 We performed. a frequency analysis of the residuals remaining alter fitting our model to the observations usingPERIODOL.. a signal analysis program based on Fourier ‘Transform methods (Lenz&Breecr2005).," We performed a frequency analysis of the residuals remaining after fitting our model to the observations using, a signal analysis program based on Fourier Transform methods \citep{lenz05}."1146. A time series of 5000 points was formed. by concatenating the residuals remaining after fitting cach orbital period. allowing the computation of a periodogram in the frequency range from Oto 45 d.+ with a frequency resolution of 0.0001 d. . shown in part in the upper panel of Figure 5..," A time series of 5000 points was formed by concatenating the residuals remaining after fitting each orbital period, allowing the computation of a periodogram in the frequency range from 0 to 45 $d^{-1}$ with a frequency resolution of 0.0001 $d^{-1}$ , shown in part in the upper panel of Figure \ref{periodogram}."1147 The Iow-frequeney range is dominated by the harmonics of the orbital period., The low-frequency range is dominated by the harmonics of the orbital period.1148 Desmetetal.(2010). were laced with the same problem during the frequency analysis of their residual data. and dealt with it first by cutting out the primary minima from their data set. and then by dividing the data with a spline-fit through the highest peaks in the PDA periodogram. with an elfect of a high-pass filter.," \citet{des10} were faced with the same problem during the frequency analysis of their residual data, and dealt with it first by cutting out the primary minima from their data set, and then by dividing the data with a spline-fit through the highest peaks in the PDM periodogram, with an effect of a high-pass filter."1149 Our attempt to remove the harmonics of the orbital [requenev by cutting out regions around the primary and seconcary minima click not result in a significant improvement in theappearance of the periodogram. so we," Our attempt to remove the harmonics of the orbital frequency by cutting out regions around the primary and secondary minima did not result in a significant improvement in theappearance of the periodogram, so we"1150"""ully parametric gas density (or X-ray brightness) and emperature profiles. similar to those commonly used in the iterature. introduces an implicit prior on the form of the mass profile via the hyclrostatie equation.","fully parametric gas density (or X-ray brightness) and temperature profiles, similar to those commonly used in the literature, introduces an implicit prior on the form of the mass profile via the hydrostatic equation."1151 Furthermore. the structure of the prior thus imposed results in an implicit ior on the cluster scaling relations.," Furthermore, the structure of the prior thus imposed results in an implicit prior on the cluster scaling relations."1152 Lf the parametrized models emploved: are insulliciently. exible. or conversely if they are too general to be constrained at the radii of interest. then constraints on the sealing relations will be rlasecl towards having self-similar slopes.," If the parametrized models employed are insufficiently flexible, or conversely if they are too general to be constrained at the radii of interest, then constraints on the scaling relations will be biased towards having self-similar slopes."1153 Alternative techniques for hvedrostatic mass measurement exist which. by construction. do not suller from this bias.," Alternative techniques for hydrostatic mass measurement exist which, by construction, do not suffer from this bias."1154 The most common of these is a semi-parametric approach. in which a parametric prior on the form for the mass profile is explicitly. adopted. with the LOCAL deseribed independently ancl non-parametrically.," The most common of these is a semi-parametric approach, in which a parametric prior on the form for the mass profile is explicitly adopted, with the ICM described independently and non-parametrically."1155 Typically. the priors used. here. are motivated by the results of numerical simulations.," Typically, the priors used here are motivated by the results of numerical simulations."1156 An advantage of the semi-parametric approach is that it requires no a priori assumptions about the potentially complex Form of the IC'M density and temperature profiles. and that the applicability of the mass profile mocdel can be straightforwardly evaluated through the &oodness of fit.," An advantage of the semi-parametric approach is that it requires no a priori assumptions about the potentially complex form of the ICM density and temperature profiles, and that the applicability of the mass profile model can be straightforwardly evaluated through the goodness of fit."1157 We comment further on the relative merits of various methods. and oller general recommendations. inD.," We comment further on the relative merits of various methods, and offer general recommendations, in."1158. In the Literature. results for. the mass.temperature slope obtained by fitting parametric n(r) and Z(r) profiles tend to cluster relatively near the self-similar value.," In the literature, results for the mass–temperature slope obtained by fitting parametric $n(r)$ and $T(r)$ profiles tend to cluster relatively near the self-similar value."1159 Semi-parametric analyses appear to prefer a significantly steeper masstemperature relation. although there are relatively few such works to consider.," Semi-parametric analyses appear to prefer a significantly steeper mass–temperature relation, although there are relatively few such works to consider."1160 While a variety of systematic effects can potentially allect the scaling relations. this segregation of values for the AL T slope suggests that the priors imposed during mass estimation have a significant. inlluence. that needs to be considered. carefully.," While a variety of systematic effects can potentially affect the scaling relations, this segregation of values for the $M$ $T$ slope suggests that the priors imposed during mass estimation have a significant influence that needs to be considered carefully."1161 As cluster survevs at all wavelengths are expanded. to higher and higher redshifts. and are used to investigate more complex cosmological questions. accurate calibration of the relevant scaling relations will only become more important.," As cluster surveys at all wavelengths are expanded to higher and higher redshifts, and are used to investigate more complex cosmological questions, accurate calibration of the relevant scaling relations will only become more important."1162 Gravitational lensing will make a unique contribution to these efforts. particularly in assessing the residual bias in ICM-based: mass. estimates due to the LSE assumption.," Gravitational lensing will make a unique contribution to these efforts, particularly in assessing the residual bias in ICM-based mass estimates due to the HSE assumption."1163 Nevertheless. ICM-based: mass measurements for. relaxed systems will remain an important ingredient in cluster cosmology due to the higher precision and lower svstematic scatter of individual estimates compared. to lensing.," Nevertheless, ICM-based mass measurements for relaxed systems will remain an important ingredient in cluster cosmology due to the higher precision and lower systematic scatter of individual estimates compared to lensing."1164 Lt is therefore eritical. going forward. that the priors emploved in these measurements be minimal. straightforsardly testable. and. well understood.," It is therefore critical, going forward, that the priors employed in these measurements be minimal, straightforwardly testable, and well understood."1165 The authors are grateful. to Mark. Voit) for. interesting and insightful comments., The authors are grateful to Mark Voit for interesting and insightful comments.1166 AM. was. supported by. an appointment to the NASA Postdoctoral Program at. the Goddard Space Flight Center. administered by Oak Riclec Associated Universities through a contract with NASA.," AM was supported by an appointment to the NASA Postdoctoral Program at the Goddard Space Flight Center, administered by Oak Ridge Associated Universities through a contract with NASA."1167 SWA acknowledges supported from the U.S. Department of Enerev under contract number DE-AC02-7T6SP00515., SWA acknowledges supported from the U.S. Department of Energy under contract number DE-AC02-76SF00515.1168"As a consequence of Liouville's theorem, the surface brightness of an astrophysical source is conserved by gravitational lensing.","As a consequence of Liouville's theorem, the surface brightness of an astrophysical source is conserved by gravitational lensing."1169" This means that the observed surface brightness Ijy, at an image-plane position 0 in terms of the source plane surface brightness [εις is where 8(0) is the lensing coordinate transformation.", This means that the observed surface brightness $I_{\text{obs}}$ at an image-plane position $\theta$ in terms of the source plane surface brightness $I_{\text{src}}$ is where $\beta(\theta)$ is the lensing coordinate transformation.1170" If we assume that the intrinsic, unlensed surface brightness profile can be well-described by a set of model parameters {pint}, then the lensed model image is defined to be where Piens is a set of parameters characterizing the lensing transformation."," If we assume that the intrinsic, unlensed surface brightness profile can be well-described by a set of model parameters $\{p_{\text{int}}\}$, then the lensed model image is defined to be where $p_{\text{lens}}$ is a set of parameters characterizing the lensing transformation."1171" For measuring flexion with such an analytic image model, the parameter set pia, defines this transformation."," For measuring flexion with such an analytic image model, the parameter set $p_{\text{lens}}=\{g_1,g_2,\Psi_{11},\Psi_{12},\Psi_{31},\Psi_{32}\}$ defines this transformation."1172" Here σι, Ψτι, and V3, are thereal parts, and go, Ψιο, and V3» are the imaginary parts of g, V4, and Ψα, respectively."," Here $g_1$ , $\Psi_{11}$ , and $\Psi_{31}$ are thereal parts, and $g_2$, $\Psi_{12}$, and $\Psi_{32}$ are the imaginary parts of $g$, $\Psi_{1}$, and $\Psi_{3}$, respectively."1173 The AIM is optimized by minimizing the figure of merit where 0? is the image-plane position of the n™ pixel and 02 is an estimate of the variance in that pixel's value., The AIM is optimized by minimizing the figure of merit where $\theta^{(n)}$ is the image-plane position of the $n^{\text{th}}$ pixel and $\sigma_n^2$ is an estimate of the variance in that pixel's value.1174 The parameter set which minimizes this figure of merit is our estimate of the true set of intrinsic and lensing parameters., The parameter set which minimizes this figure of merit is our estimate of the true set of intrinsic and lensing parameters.1175 We implement the AIM method using a Levenberg-Marquardt minimization algorithmcalled(Markwardt]|2009).., We implement the AIM method using a Levenberg-Marquardt minimization algorithmcalled.1176 is written in the Interactive Data (IDL)., is written in the Interactive Data (IDL).1177 , 1178Cosmic Ray Spallation in Radio-Quiet Active Galactic Nuclei: A Case Study of NGC Recent N-ray data fromNewton. and has led to the discovery of narrow line cussion in the 5 - 6 keV regime in several local Sevfert galaxies (ee.?77)..,"Cosmic Ray Spallation in Radio-Quiet Active Galactic Nuclei: A Case Study of NGC 4051} Recent X-ray data from, and has led to the discovery of narrow line emission in the 5 - 6 keV regime in several local Seyfert galaxies \citep[e.g.][]{turner02a, yaqoob03a}."1179 One popular interpretation of the lines has been as emission from so-called hotspots! ou the accretion disk. ie. enhanced enmuüssiou related to events such as magnetic reconnections on the disk surface.," One popular interpretation of the lines has been as emission from so-called 'hotspots' on the accretion disk, i.e. enhanced emission related to events such as magnetic reconnections on the disk surface."1180 The observed line profile is modified by Doppler aud eravitational effects. depending on the inclination of the svstem to the observers lue-ofsight aud he radial location of the hotspot.," The observed line profile is modified by Doppler and gravitational effects, depending on the inclination of the system to the observers line-of-sight and the radial location of the hotspot."1181 A hotspot that co-otates with the disk should show a periodic ρατοσα of variations in line euergv aud streneth with fiue (so loug as the disk is not observed acc-on)., A hotspot that co-rotates with the disk should show a periodic pattern of variations in line energy and strength with time (so long as the disk is not observed face-on).1182" If the hotspot originates within 207, hen general relativistic effects are predicted to be ucasurable using curreut. N-rav data.", If the hotspot originates within $r_g$ then general relativistic effects are predicted to be measurable using current X-ray data.1183 Superposed ou the periodic shifts. lines should show dowu-shifting in the peak energy of the line with time as he material spirals iuwurd (?)..," Superposed on the periodic shifts, lines should show down-shifting in the peak energy of the line with time as the material spirals inward \citep{dovciak04a}."1184 As disk hotspots are not expected to survive for more than a few orbits at sinall radii (7).. observation of persistent ines apparently originating close to the event iorizon would disfavor the disk hotspot model.," As disk hotspots are not expected to survive for more than a few orbits at small radii \citep{karas01a}, observation of persistent lines apparently originating close to the event horizon would disfavor the disk hotspot model."1185" Alternatively, the shifted lines may arise in ejected blobs of gas (suchascomprisingawind.e.g. 7)."," Alternatively, the shifted lines may arise in ejected blobs of gas \citep[such as comprising a wind, e.g.][]{turner04a}."1186 Iu contrast to the hotspot model. lines originating from ejecta are expected to show nou-periodic evolution with time as the gas moves outwards. and by tracing the line enerev over tine one can potentially constrain the acceleration or deceleration mechiauisin.," In contrast to the hotspot model, lines originating from ejecta are expected to show non-periodic evolution with time as the gas moves outwards, and by tracing the line energy over time one can potentially constrain the acceleration or deceleration mechanism."1187 In principle then. oue could. distinguish disk hotspot aud ejecta origins for line enission iu the 5 - keV baud using time-resolved spectroscopy.," In principle then, one could distinguish disk hotspot and ejecta origins for line emission in the 5 - keV band using time-resolved spectroscopy."1188 However. another model has been sugsested. where observed lines may be iceutified as species of clemenuts such as Cr and Mu that wormally would be too weak to measure usine current data. but whose strength has been euhanced owing to abundance changes in the enüttiug gas from spallation of Fe (e.g.2)..," However, another model has been suggested, where observed lines may be identified as species of elements such as Cr and Mn that normally would be too weak to measure using current data, but whose strength has been enhanced owing to abundance changes in the emitting gas from spallation of Fe \citep[e.g.][]{turner02a}."1189 The interaction of protons having kinetic energy 230 MMeV. with latter can result in spallation of its heavy nuclei. creating chhanced abundances of clemeuts lower in nass than the target nucleus.," The interaction of protons having kinetic energy $\ga 30$ MeV with matter can result in spallation of its heavy nuclei, creating enhanced abundances of elements lower in mass than the target nucleus."1190 In the low energy reenne the protons required for effective spallation need be ouly mildly relativistic. easily. aclievalle iji a nuuber of astrophysical situations and therefore we wight expect to observe spallation under a range of conditions.," In the low energy regime the protons required for effective spallation need be only mildly relativistic, easily achievable in a number of astrophysical situations and therefore we might expect to observe spallation under a range of conditions."1191 Tudecd. spallation is known to significantly affect the abundance ratios in our own Calaxy (77)— where there is approximate cucrey equipartitionbetween cosnmic-rav protous aud the magnetic and radiation fields.," Indeed, spallation is known to significantly affect the abundance ratios in our own Galaxy \citep{reeves74a,lund89a} where there is approximate energy equipartition between cosmic-ray protons and the magnetic and radiation fields."1192 The most noticeable effects of spallation are that abundant uuclei such as C. N. O. Fe are broken down. increasing the fraction of Leltero clements such that the emission or absorption profile of the gas is siguificautlv different than expected for cosnmuüc abundauce material.," The most noticeable effects of spallation are that abundant nuclei such as C, N, O, Fe are broken down, increasing the fraction of lighter elements such that the emission or absorption profile of the gas is significantly different than expected for cosmic abundance material."1193 However. the cross-sections are relatively low (6<I1000muub. ?7?77.. where 100030ub is 102lec0m?). aud sieuificaut abunance changes ina large mass of eas require either hieh proton flux and/or long timescales.," However, the cross-sections are relatively low $\sigma < 1000$ mb, \citealt{letaw83a,silberberg98a,tripathi99a}, where mb is $10^{-24}$ $^{2}$ ), and significant abundance changes in a large mass of gas require either high proton flux and/or long timescales."1194 The conditious for and the cousequences of cosmic ταν production in AGN have been discussed in the past by several authors (7777)..," The conditions for and the consequences of cosmic ray production in AGN have been discussed in the past by several authors \citep{kazanas86a,axford94a,cronin05a,nagano2000a}."1195 While the effects of spallation could be detectable iu any wavebaud. the cross-section for spallatiou increases with atomic mass approximately as A7 (λα this. the high cosmic abundance of Fe aud its observabilitv over a wide range of ionization mca that signatures of spallation may be most casily detected i N-ray spectra of irou group elements.," While the effects of spallation could be detectable in any waveband, the cross-section for spallation increases with atomic mass approximately as $A^{0.7}$ \citep{letaw83a}; this, the high cosmic abundance of Fe and its observability over a wide range of ionization mean that signatures of spallation may be most easily detected in X-ray spectra of iron group elements."1196 At low cosinic rav euergies the primary products from the spallation of Fe. aud their partial cross- for prompt production following collision with a LOOAMIAI¢V proton are Alu uum»). Cr nuub). V anh) aud Ti nub). where the cross-sections have been determuned from code supplied by ?)..," At low cosmic ray energies the primary products from the spallation of Fe, and their partial cross-sections for prompt production following collision with a MeV proton are Mn mb), Cr mb), V mb) and Ti mb), where the cross-sections have been determined from code supplied by \citet{silberberg98a}."1197 Tf we adjust the cross-sections to account for the decay of unstable isotopes. the effective cross-sections become Mu. wah). Cy (5601111b). V τι). and. Ti (1361).," If we adjust the cross-sections to account for the decay of unstable isotopes, the effective cross-sections become Mn mb), Cr mb), V mb) and Ti mb),"1198xoduces more Be aud D relative to ?Li than in Model l. considering that Be aud D are produced by spallation xocesses of C aud O while lithium isotopes are produced uaiulv by α|6 fusion.,"produces more Be and B relative to $^6$ Li than in Model 1, considering that Be and B are produced by spallation processes of C and O while lithium isotopes are produced mainly by $\alpha+\alpha$ fusion."1199 E show the results of calculations of light clement production in the CCR uucleosvuthliesis uodel in Table 1.., I show the results of calculations of light element production in the CCR nucleosynthesis model in Table \ref{tab1}.1200 Iu the secoud coltmun. values of energy yaction of SNRs given to CR acceleration required to xoduce ?Li at the observed level in MPIISs at =3 are shown.," In the second column, values of energy fraction of SNRs given to CR acceleration required to produce $^6$ Li at the observed level in MPHSs at $z=3$ are shown."

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