ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 This would exclude any foreground solar svstem object. as it would need to be farther than 247.000 AU if orbiting the Sun at ~30 kin Ll which is well bevond the current estimates of the extent of the solar svstem.," This would exclude any foreground solar system object, as it would need to be farther than $247,000$ AU if orbiting the Sun at $\sim30$ km $^{-1}$, which is well beyond the current estimates of the extent of the solar system."3 Slow-moving Galactic stars could also be generally excluded on similar hypothetical grounds., Slow-moving Galactic stars could also be generally excluded on similar hypothetical grounds.4 Variable stars are also easily excluded by their nature of being stars in all epochs of observation. aud by eenerallv appearing unassociated with galaxies in the field.," Variable stars are also easily excluded by their nature of being stars in all epochs of observation, and by generally appearing unassociated with galaxies in the field."5 Variable stars that. on occasion. do appear aligned with field galaxies are (vpically several orders of magnitude brighter (han one would expect for SNe in these ealaxies.," Variable stars that, on occasion, do appear aligned with field galaxies are typically several orders of magnitude brighter than one would expect for SNe in these galaxies."6 What remained in the subtracted images are (rue extragalactic transients (e. g. supernovae and active galactic nuclei) and image artifacts such as misregistrations and variations in the point spread function., What remained in the subtracted images are true extragalactic transients (e. g. supernovae and active galactic nuclei) and image artifacts such as misregistrations and variations in the point spread function.7 As the field is fairly dense with galaxies. and well resolved in the ACS images. there were no sienilicant local nisregistrations in (ae VDF and UDFDP. except for stellar diffraction spikes which rolled with the change in orientation between epochs of the survevs.," As the field is fairly dense with galaxies, and well resolved in the ACS images, there were no significant local misregistrations in the UDF and UDFP, except for stellar diffraction spikes which rolled with the change in orientation between epochs of the surveys."8" The point spread function (PSF) in each median combined image stack was largely stable ancl unallected by short-term. exposure-to-exposure changes in the PSF (e. ο, telescope breathing or focus drift}."," The point spread function (PSF) in each median combined image stack was largely stable and unaffected by short-term, exposure-to-exposure changes in the PSF (e. g. telescope breathing or focus drift)."9 Thus. we are confident that we have identified only extragalactie transients [rom the UDF and UDFP subtraction images.," Thus, we are confident that we have identified only extragalactic transients from the UDF and UDFP subtraction images."10 Variable active galactic nuclei (AGN) were defined as candidates that were within one pixel of their host nuclei., Variable active galactic nuclei (AGN) were defined as candidates that were within one pixel of their host nuclei.11 This is a rather conservative definition. as in principle. we would be capable of identibving transients with centroids a Iraction of a pixel offset [rom the centroid ol light in the nucleus of a galaxy.," This is a rather conservative definition, as in principle, we would be capable of identifying transients with centroids a fraction of a pixel offset from the centroid of light in the nucleus of a galaxy."12" However. there were no detected candidates (down to the 5o threshold) that were <0"".05 [rom the centroid of the host galaxy the UDF and UDFP searches."," However, there were no detected candidates (down to the $\sigma$ threshold) that were $\le0''.05$ from the centroid of the host galaxy the UDF and UDFP searches."13 Other investigations which probe for much smaller optical variations (1 (o 30) in ealaxy nuclei do show evidence for low-level AGN in the UDF target field (Windhorst et al..," Other investigations which probe for much smaller optical variations (1 to $\sigma$ ) in galaxy nuclei do show evidence for low-level AGN in the UDF target field (Windhorst et al.,"14 in preparation). none of which would be undeniably identified with our differencing method.," in preparation), none of which would be undeniably identified with our differencing method."15do not coustrain the τοσο further.,do not constrain the region further.16 Thus. evolutionary syuthesis applied to the 2dFCRS-measured cosmic spectra (2~0.03 0.25) is in concordance with the best-fit results obtained from a variety of rest-frame UV DIunuünositv-density measurements (2~0 1.5).," Thus, evolutionary synthesis applied to the 2dFGRS-measured cosmic spectra $z\sim0.03$ –0.25) is in concordance with the best-fit results obtained from a variety of rest-frame UV luminosity-density measurements $z\sim0$ –4.5)."17 With this technique of primarily using the chigh-frequency” spectral information. there are still siguificaut degeneracies tn deternuning the cosmichistory.," With this technique of primarily using the `high-frequency' spectral information, there are still significant degeneracies in determining the cosmic."18.. Towever. combined with huuinositv-deusitv methods and with further improvements. there is the potential to obtain more accurate star-formation scenarios and to discriminate between IMPEsS aud cosimologies.," However, combined with luminosity-density methods and with further improvements, there is the potential to obtain more accurate star-formation scenarios and to discriminate between IMFs and cosmologies."19 For exaluple. the separation of galaxies into eroups with simulay nunav help break the ceeeneracy. ie. reducing the moreine of features between voung aud old populations.," For example, the separation of galaxies into groups with similar may help break the degeneracy, i.e., reducing the merging of features between young and old populations."20" Iu additiou. it may be possible to improve the fit to the spectra by combining models with different chemical evolution scenarios. οσοι, weighted combinations of spectra with ciffereut f;f.ton."," In addition, it may be possible to improve the fit to the spectra by combining models with different chemical evolution scenarios, e.g., weighted combinations of spectra with different $\tin,\tsf,\zform$."21 Future lavee surveys such as the SDSS iain galaxy siuuple will provide a consistency check with the sspectra (selected with different effective wavoleugtlis. vversus.LTOOA.. magnitude limits and aperture diameters. see Figure 10)).," Future large surveys such as the SDSS main galaxy sample will provide a consistency check with the spectra (selected with different effective wavelengths, versus, magnitude limits and aperture diameters, see Figure \ref{fig:sel-ap}) )."22 With the spectra (resolution 9À)). and especially so with the SDSS spectra LÀ)). it is appareut that higher spectral resolution populatioi svithiesis models (~2A in the optical wavelength range) are needed to maximize the scientific potcutieαἱ ο these data sets;," With the spectra (resolution ), and especially so with the SDSS spectra ), it is apparent that higher spectral resolution population synthesis models $\sim$ in the optical wavelength range) are needed to maximize the scientific potential of these data sets."23" Work is currently underway for this piPpoxc,", Work is currently underway for this purpose.24 Both galaxy surveys can also be used to measure the slope of huninositv density variation with redshift iu the local universe which provides another star formation estimate from the same survey., Both galaxy surveys can also be used to measure the slope of luminosity density variation with redshift in the local universe which provides another star formation estimate from the same survey.25 This can done by either by using k-corrections and determining the bDpuuimositv function in the rest frame or by determining the Iuninositv function in observed wavelength. ie. the extra-ealactic backeround light per unit redshift.," This can done by either by using k-corrections and determining the luminosity function in the rest frame or by determining the luminosity function in observed wavelength, i.e., the extra-galactic background light per unit redshift."26 These measuremeuts can be used to apply further constraints on the cosmic star-formation scenarios and the absolute cosiiic comoving cdeusity., These measurements can be used to apply further constraints on the cosmic star-formation scenarios and the absolute cosmic comoving density.27the proper dependence. and this will be our focus in the rest of this paper.,"the proper dependence, and this will be our focus in the rest of this paper."28 As described by several authors (Gough MelIntyre 1998. Ringot 1998. KTZ99. Kim MacGregor 2001). the most obvious feature of momentum transport by gravity waves is the formation of a double peaked shear layer just below the convection zone (see Fig. 3)).," As described by several authors (Gough McIntyre 1998, Ringot 1998, KTZ99, Kim MacGregor 2001), the most obvious feature of momentum transport by gravity waves is the formation of a double peaked shear layer just below the convection zone (see Fig. \ref{fig:local}) )."29 Gough Melntyre (1998) and Ringot (1998) argued that such a layer would prevent waves from propagating beyond., Gough McIntyre (1998) and Ringot (1998) argued that such a layer would prevent waves from propagating beyond.30 Indeed. local radiative and viscous damping is greatly dependent on the local frequeney and increases when that frequency diminishes (this property leads to the formation of the double peaked shear layer)," Indeed, local radiative and viscous damping is greatly dependent on the local frequency and increases when that frequency diminishes (this property leads to the formation of the double peaked shear layer)."31" The local momentum luminosity integrated over the whole spectrum writes The local amplitude οχρ[--τσ.Ὀ] depends on the integrated damping due to thermal diffusion Ky and (turbulent) VISCOSILY v, where N=Ny.+Nz is the Brunt-Várisállà frequency. IV. is its thermal part and Ni is due to the mean molecular weight stratification (Zahn et al."," The local momentum luminosity integrated over the whole spectrum writes The local amplitude $\exp \left[ -\tau(r, \sigma, \ell)\right]$ depends on the integrated damping due to thermal diffusion $K_T$ and (turbulent) viscosity $\nu_t$ where $N^2 = N_T^2 + N_{\mu}^2$ is the Brunt-Väiisällä frequency, $N_T^2$ is its thermal part and $ N_{\mu}^2$ is due to the mean molecular weight stratification (Zahn et al."32 1997)., 1997).33 The prograde thus filters prograde waves. while the retrograde peak filters retrograde waves.," The prograde thus filters prograde waves, while the retrograde peak filters retrograde waves."34 If the peaks were infinite in height. not a single wave could travel through it.," If the peaks were infinite in height, not a single wave could travel through it."35 This is however not the case. as the magnitude of the shear layer is self regulated by shearturbulence?.," This is however not the case, as the magnitude of the shear layer is self regulated by shear."36. As described by TKZ02. tf no initial differential rotation 18 present. the average wave momentum luminosity that traverses the shear layer is null. and there is no net effect on the interior.," As described by TKZ02, if no initial differential rotation is present, the average wave momentum luminosity that traverses the shear layer is null, and there is no net effect on the interior."37 However. if differential rotation is initially present. as in the case of low mass stars that are braked by a magnetic torque. the average magnitude of the two peaks Is not equal: in the case," However, if differential rotation is initially present, as in the case of low mass stars that are braked by a magnetic torque, the average magnitude of the two peaks is not equal; in the case"38The second recorded nova outburst of CT Aquilae was discovered on 2000 April 28 UT bw Talkamizawa (2000).. 83 vears after the first recorded outburst iu 1917 (Reimuuth1925:Williams2000)..,"The second recorded nova outburst of CI Aquilae was discovered on 2000 April 28 UT by \citet{tak00}, 83 years after the first recorded outburst in 1917 \citep{rei25,wil00db}."39 CT Aql now becomes a iuienmber of the recurrent nova class., CI Aql now becomes a member of the recurrent nova class.40 About 300 davs after the optical παπα. Hachisu&Nato(2001a). estimated various physical parameters of the CI Aql system from tle helt curve fitting aud elucidated its nature.," About 300 days after the optical maximum, \citet{hac01ka} estimated various physical parameters of the CI Aql system from the light curve fitting and elucidated its nature."41 They derived the white chwarf (WWD) mass to be Mp=1240.05AL... the ποια enrichinent of the white dwart cuvelope to IO (I~0.25 by uuuber. aud the mass of the hyvdrogen-rich euvelope ou the white dwarf at the optical maxima to b ΔΑμι75810SAL...," They derived the white dwarf (WD) mass to be $M_{\rm WD}= 1.2 \pm 0.05 ~M_\sun$, the helium enrichment of the white dwarf envelope to be $\sim 0.25$ by number, and the mass of the hydrogen-rich envelope on the white dwarf at the optical maximum to be $\Delta M_{\rm max} \sim 5.8 \times 10^{-6} M_\sun$."42 This envelope mass indicates au average nass accretion rate of MaceMTS10TAL diving the quiescent phase between the 1917 and 200 outbursts., This envelope mass indicates an average mass accretion rate of $\dot M_{\rm acc} \sim 0.7 \times 10^{-7} M_\sun$ $^{-1}$ during the quiescent phase between the 1917 and 2000 outbursts.43 They finally predicted the turn-off time of 2001 August aud. therefore. that the Iunuinous supersoft N-rav source phase lasts until August of 2001.," They finally predicted the turn-off time of 2001 August and, therefore, that the luminous supersoft X-ray source phase lasts until August of 2001."44 After Hachisu&IKato(2001a) has been published. sole new observational indications appeared conceruinug the turn-off time of the 2000 outburst.," After \citet{hac01ka} has been published, some new observational indications appeared concerning the turn-off time of the 2000 outburst."45 The supersoft N-ray fluxes were too weak diving June and August of 2001 (Careimer&DiStefano 2002).. which incicates that the steady hydrogen shell-burning had already vanished.," The supersoft X-ray fluxes were too weak during June and August of 2001 \citep{gre02}, , which indicates that the steady hydrogen shell-burning had already vanished."46 Schaefer(2001) τας optical photometry of CI Aql iu Augus of 200l aud concluded that CI Aql was V—15.3 axd aluxot near its quiesceut phase (Moeunickeut&Toneveutt1995)., \citet{sch01b} made optical photometry of CI Aql in August of 2001 and concluded that CI Aql was $V \sim 15.3$ and almost near its quiescent phase \citep{men95}.47. These results contradict the theoretical preciction that. if the lyvdrogen couteut of the white dwarf euvelope is VY=0.5 bv weight. the steady hydrogen shel-burniitο lasts until August of 2001 (achisu&Ἱναίο2001a).," These results contradict the theoretical prediction that, if the hydrogen content of the white dwarf envelope is $X=0.5$ by weight, the steady hydrogen shell-burning lasts until August of 2001 \citep{hac01ka}."48. Schacter(20010) found on 12 Ikuiux College Obscrvatexv archival photographs the 1911 outburst. the brightuess of which is B—13.8 on Mav 2 of 1911. and suggested that the 1917 discovery could indicate a recumence timescale of about 20 Vis. with missed outbursts arouxl 1960 and 1980.," \citet{sch01c} found on 12 Harvard College Observatory archival photographs the 1941 outburst, the brightness of which is $B \sim 13.8$ on May 2 of 1941, and suggested that the 1917 discovery could indicate a recurrence timescale of about 20 yrs, with missed outbursts around 1960 and 1980."49 Tn this oper. therefore. we reanalyzo the lieht. curves of CT Αι. especially reproducing t1e orbital light. curves newly obtained in April/May auc Atieust of 2001 (seealsoSchac-ey 2001a.b).," In this paper, therefore, we reanalyze the light curves of CI Aql, especially reproducing the orbital light curves newly obtained in April/May and August of 2001 \citep[see also][]{sch01a, sch01b}."50. Additionally. Honeveutt (2X02. private commuiniicatiou) js revised Moenunuickeut Tojeveutt's (1995) photometric data of CT Aql in quiescence.," Additionally, Honeycutt (2002, private communication) has revised Mennickent Honeycutt's (1995) photometric data of CI Aql in quiescence."51 The revised data show about 1.62 mae down in the μοι curve so that the quiesceut evel is as low as V.—16.1. (LN mae fainter than August of 2001.," The revised data show about 0.62 mag down in the $V$ -light curve so that the quiescent level is as low as $V \sim 16.1$, 0.8 mag fainter than August of 2001."52 This value is well cousisteut with Szkody's (1991) V—16.2 in quiescence (seeasoTable2of.Meunickeut&Toueveutt 1995)., This value is well consistent with Szkody's (1994) $V \sim 16.2$ in quiescence \citep[see also Table 2 of ][]{men95}.53. Iu this sease. CT Aq] did not reach its quiescent level but still showed an activity even in August of 2001.," In this sense, CI Aql did not reach its quiescent level but still showed an activity even in August of 2001."54 Therefore. taking these new thines iutoaccount. we have fully recousidered tlie CT ΑΔ model.," Therefore, taking these new things intoaccount, we have fully reconsidered the CI Aql model."55and gnuiv pulses in the BATSE sample with statistically significant values of ¢ less than unity.,and many pulses in the BATSE sample with statistically significant values of $\zeta $ less than unity.56 These GRBs however preceded the afterglow era., These GRBs however preceded the afterglow era.57 For those CRBs which lave measured beaming breaks (see Table d in Bloom.Frail.&Isullsa-rni (2003))). only CRB 9901253 has suffücieutlv bright BATSE data to provide a data point for such a correlation.," For those GRBs which have measured beaming breaks (see Table 1 in \citet{bfk03}) ), only GRB 990123 has sufficiently bright BATSE data to provide a data point for such a correlation."58 CRB 990123 has not vet been analyzed to eive ¢. while analysis of Beppo-SAN data is in progress RRvde. private communication. 2001).," GRB 990123 has not yet been analyzed to give $\zeta$ , while analysis of Beppo-SAX data is in progress Ryde, private communication, 2004)."59" Such a model for the f.,/ej; relationship would explain why ¢ is approximately coustaut for different pulses within a GRB. provided that the opening angle of the GRB jet remains the sale throughout the period of activity of the GRB enuglnuc."," Such a model for the $f_{\e_{pk}}$ $\e_{pk}$ relationship would explain why $\zeta$ is approximately constant for different pulses within a GRB, provided that the opening angle of the GRB jet remains the same throughout the period of activity of the GRB engine."60 The adiabatic/svyuchrotrou uodel would not. however. explain pulses with 2Z5GXX ," The adiabatic/synchrotron model would not, however, explain pulses with $261\lesssim \zeta \lesssim 3$."62There are manyv such pulses in the Boreouovo&Ryde(2001) sample. though eenerally with large error bars.," There are many such pulses in the \citet{br01} sample, though generally with large error bars."63 analysis of Beppo-SAX or Swift data reveal such CRBs. then another explanation is required.," If analysis of Beppo-SAX or Swift data reveal such GRBs, then another explanation is required."64 One possibility is that CRB pulses are due to the interactions of a single impulsive blast wave with inhomogencitics iu the surrounding medium., One possibility is that GRB pulses are due to the interactions of a single impulsive blast wave with inhomogeneities in the surrounding medium.65 This version of the external shock wodel for tle prompt phase can be unich more effiieut than au internal shell model (Dermer&A\Gitmman1999. 2003).. and permits quantitative studies of the statistics of BATSECRBs (Bottcher&Derimer(2000): see Zhang&Moészáros(2001) for a review of the iuternal/exterual controversy).," This version of the external shock model for the prompt phase can be much more efficient than an internal shell model \citep{dm99,dm03}, , and permits quantitative studies of the statistics of BATSEGRBs \citet{bd00}; see \citet{zm04} for a review of the internal/external controversy)."66" Predictions for the f,ey. relatiouship iu an external shock model (Deiner.Chiang.&Bottcher1999) can be derived by adapting the equations for blast wave deceleration in a wuiform iiedium with οο where Py is the initial Lorentz factor. vg is the deceleration distance aud g is the radiative iudex (y=3/2 and 3 for an adiabatie aud fully radiative blast wave. respectively)."," Predictions for the $f_{\e_{pk}}/\e_{pk}$ relationship in an external shock model \citep{dcb99} can be derived by adapting the equations for blast wave deceleration in a uniform medium with $\Gamma67= \Gamma_0/[1+(x/x_d)^g]$, where $\Gamma_0$ is the initial Lorentz factor, $x_d$ is the deceleration distance and $g$ is the radiative index $g = 3/2$ and 3 for an adiabatic and fully radiative blast wave, respectively)."68 Iu the deceleration phase. sowο and therefore Pox£4/9!," In the deceleration phase, $x \propto69t^{1/(2g+1)}$ and therefore $\Gamma \propto t^{-g/(2g+1)}$."70" Ty this model. ερ%TBS). aud fg0DI?nm«?iple where >PHpoxIDixgtet)D inB the slow-cooling- regime,+ and 2,54XCrP)box{ΛΕΣP in+ the fast-cooling reguue."," In this model, $\e_{pk} \propto \Gamma B \gamma_{pk}^2$ and $f_{\e_{pk}}71\propto \Gamma^2 B^2 \gamma_{pk}^2$, where $\gamma_{pk} \propto72\Gamma^4\propto t^{-4g/(2g+1)}$ in the slow-cooling regime, and $\gamma_{pk} \propto (x\Gamma)^{-1}\propto t^{-2/(2g+1)}$ in the fast-cooling regime."73" Thus fL, /e,MDT."," Thus $f_{\e_{pk}}$ $\e_{pk}74\propto B\Gamma$."75 Iu theo slow-coolius regiue. ej;κΓΡ.Εος5 Ὁ gd feummr.," In the slow-cooling regime, $\e_{pk} \propto \Gamma^4\propto76t^{-4g/(2g+1)}$ , and $f_{\e_{pk}}\propto\e_{pk}^{3/2}$."77" Iu. the fast-cooliug. regime,: ejXf.D7ColU2 and fo.xepe1yoly"," In the fast-cooling regime, $\e_{pk} \propto t^{-2/(2g+1)}$ and $f_{\e_{pk}}\propto\e_{pk}^{1+g}$."78 In the slow-coolimg aud fast-cooliug.n+ regimes.H therefore.n values of ον=3/2 aud cy.=1|g. respectively. are predicted.," In the slow-cooling and fast-cooling regimes, therefore, values of $\zeta_{sc} = 3/2$ and $\zeta_{fc} = 1+g$, respectively, are predicted."79 Provided that the surrounding media is uniformi (which can be imferred frou afterglow modchnue. though at a larger distance scale). the slow-cooling result implies a definite value of Q4.=3/2 for fast-rise. smooth decay helt curves when spectral analysis demonstrates that the GRB evolves in the slow-cooling regine.," Provided that the surrounding medium is uniform (which can be inferred from afterglow modeling, though at a larger distance scale), the slow-cooling result implies a definite value of $\zeta_{sc}=3/2$ for fast-rise, smooth decay light curves when spectral analysis demonstrates that the GRB evolves in the slow-cooling regime."80 For CRBs in fast-cooliug regiae. this estimate inplies 5/2<(y.LE. aud in these cases cooling spectra should be apparent.," For GRBs in fast-cooling regime, this estimate implies $5/2 < \zeta_{fc} < 4$, and in these cases cooling spectra should be apparent."81 Further work will be needed to exteud the results to radial deusitv evacients of the eircinuabnurst media. aud to verifv that these relatious hold for deceleration im small density inhomogeneitics that form GRB pulses in the external shock meoclel.," Further work will be needed to extend the results to radial density gradients of the circumburst medium, and to verify that these relations hold for deceleration in small density inhomogeneities that form GRB pulses in the external shock model."82 A simple kinematic model for CRB colliding shells has been constructed. that provides a ramework for analyzing radiative processes du a sinpliBed geometry of a thin or thick shell raveling at relativistic speeds., A simple kinematic model for GRB colliding shells has been constructed that provides a framework for analyzing radiative processes in a simplified geometry of a thin or thick shell traveling at relativistic speeds.83 The relationship vetween observed flux and comoving photon enerev deusity for a given value of P has been studied. showing that the curvature Bit vields he siiallest value of the product 4442.," The relationship between observed flux and comoving photon energy density for a given value of $\Gamma$ has been studied, showing that the curvature limit yields the smallest value of the product $u_0^\prime \Delta \tp$."84 This result can then be used to deduce conservative ower lits ou bulls Loreutz factors derived from. he coudition of +> transparency., This result can then be used to deduce conservative lower limits on bulk Lorentz factors derived from the condition of $\gamma\gamma$ transparency.85 The kinematic model predicts the curvature relationship feXE with ¢=3. at late nies in GRD pulses.," The kinematic model predicts the curvature relationship $f_{\e_{pk}}86\propto \e_{pk}^\zeta$, with $\zeta = 3$, at late times in GRB pulses."87" Equivalenth. curvature effects iauplv that fe(f})xfl"" apnd ενXfl "," Equivalently, curvature effects imply that $f_\e (t)\propto88t^{-3+a}$ and $\epk \propto t^{-1}$."89DATSE data for GRDB pulses do not displav. the curvature relatiouship iu most cases (Dorgouovo&Ryde 2001).. suggesting that the physics of pulse formation is dominated by other effects.," BATSE data for GRB pulses do not display the curvature relationship in most cases \citep{br01}, suggesting that the physics of pulse formation is dominated by other effects."90" A sinple model for joiut evolution of f, aud ey; hat takes iuto account adiabatic aud svuchrotron osses iniplies that 1/2<¢ 2. aud that àzz:0.5 ouly when the shell undergoes three cimensional expansion and the electrous which produce the emission Ucar €,; are rapidly cooling through svuchrotron losses."," A simple model for joint evolution of $f_{\e_{pk}}$ and $\e_{pk}$ that takes into account adiabatic and synchrotron losses implies that $1/2 < \zeta < 2$ , and that $\zeta \approx 0.5$ only when the shell undergoes three dimensional expansion and the electrons which produce the emission near $\e_{pk}$ are rapidly cooling through synchrotron losses."91 Spectral analysis of Swift data. and correlations of ¢ withtimesof the beaming breaks in optical afterglow light curves. can test," Spectral analysis of Swift data, and correlations of $\zeta$ withtimesof the beaming breaks in optical afterglow light curves, can test"92We performed. a stellar. population svnthesis analysis to constrain the ages of the stellar populations of the LRGs.,We performed a stellar population synthesis analysis to constrain the ages of the stellar populations of the LRGs.93 To accomplish this task. we carried out ao likelihood analysis that compares the stacked. spectrum: with mocel expectations for cdilferent stellar age. metallicity ancl star formation history.," To accomplish this task, we carried out a likelihood analysis that compares the stacked spectrum with model expectations for different stellar age, metallicity and star formation history."94 The likelihood function is defined as where / is the age of the stellar populations. No is the number of spectral bins (No= 311). f; is theobserved Iux in the 7th bin. f; is the mocdel prediction. and a; is the corresponding error of the ith element.," The likelihood function is defined as where $t$ is the age of the stellar populations, $N$ is the number of spectral bins $N=311$ ), $f_i$ is theobserved flux in the $i$ th bin, $\bar{f}_i$ is the model prediction, and $\sigma_i$ is the corresponding error of the $i$ th element."95 As described in 22. the Dux calibration became uncertain at A5000AL. corresponding to rest-f[ramoe Az5200 Που these LRGs.," As described in 2, the flux calibration became uncertain at $\lambda\apg 8000$, corresponding to rest-frame $\lambda\apg 5200$ for these LRGs."96 We therefore limited. our analysis to the spectral range 3600.5200 iin the rest-frame of the LRGs (Figure 2).The stellar. population models. were based. on. those described in Bruzual&Charlot(2003). revised. to include a prescription. of the TP-AGB evolution. of low and intermediate mass stars (Alarigo&Girardi2007).., We therefore limited our analysis to the spectral range 3600–5200 in the rest-frame of the LRGs (Figure 2).The stellar population models were based on those described in \citet{bruzual2003a} revised to include a prescription of the TP-AGB evolution of low and intermediate mass stars \citep{marigo2007a}.97 We emploved a Chabricr initial mass function for all models (Chabrier2003).., We employed a Chabrier initial mass function for all models \citep{chabrier2003a}.98 Phe star formation history (SELL) of the model galaxies was parametrized by either a single burst or by an exponentially declining model with an ¢-Lolcing timescale 7., The star formation history (SFH) of the model galaxies was parametrized by either a single burst or by an exponentially declining model with an $e$ -folding timescale $\tau$.99 Phe ages / were equally separated in logarithmic space between 107 vr and S4 Gyr. where the upper-limit corresponds to the age of the Universe at zz0.5.," The ages $t$ were equally separated in logarithmic space between $10^5$ yr and 8.4 Gyr, where the upper-limit corresponds to the age of the Universe at $z \approx 0.5$."100 We also adopted an equal spacing of 50 Myr for 7 from 0.1 to 0.5 Cove and we adopted metallicities of 0.02. 0.2. 1. and 2.5 solar.," We also adopted an equal spacing of 50 Myr for $\tau$ from 0.1 to 0.5 Gyr and we adopted metallicities of 0.02, 0.2, 1, and 2.5 solar."101 To directly compare between data and mocdels. we convolved the model spectra with a top-hat function of width 350 tto mateh the resolution of the data.," To directly compare between data and models, we convolved the model spectra with a top-hat function of width 350 to match the resolution of the data."102 Extinction by the host LAC was not included in. the final model templates., Extinction by the host LRG was not included in the final model templates.103 However. we did generate a library of model spectra with host extinction following the Charlot Fall (2000) prescription.," However, we did generate a library of model spectra with host extinction following the Charlot Fall (2000) prescription."104 We found that the LRG spectra systematically select the models with the least amount of extinction., We found that the LRG spectra systematically select the models with the least amount of extinction.105 For this reason. we did not include extinction bv the host galaxy in the final library of svnthetie spectra.," For this reason, we did not include extinction by the host galaxy in the final library of synthetic spectra."106 ligure 1. shows the stacked. spectra of both samples. of LRGs along with the best-fit stellar population moclel in red., Figure \ref{best} shows the stacked spectra of both samples of LRGs along with the best-fit stellar population model in red.107 The LRGs in both samples exhibit spectral features dominated. by absorption transitions. suggesting an old Ποας stellar population and little star formation in the recent past.," The LRGs in both samples exhibit spectral features dominated by absorption transitions, suggesting an old underlying stellar population and little star formation in the recent past."108 Visual inspections of individual LRG spectra show that three LRGs. (8D85.1H42312.00. 5D85.220703.36. SDS8J232924.13) exhibit traces of OLLI] emission. one of which belongs to the absorbing sample (8DS8S.]220703.36).," Visual inspections of individual LRG spectra show that three LRGs, (SDSSJ142312.00, SDSSJ220703.36, SDSSJ232924.13) exhibit traces of II] emission, one of which belongs to the absorbing sample (SDSSJ220703.36)."109 These three LRGs represent of the absorbing and. non- LRGs combined., These three LRGs represent of the absorbing and non-absorbing LRGs combined.110 The fraction of HI] emitting LRGs is consistent with the finding of Itoseboom et. al. (, The fraction of II] emitting LRGs is consistent with the finding of Roseboom et al. (1112006). who found that —104 of LRGs show LE] emission.,"2006), who found that $\sim$ of LRGs show II] emission."112 The spectra of the LRGs support the previous unclerstancling that these galaxies are primarily quiescent. which is further supported by the results of the population svnthesis analysis presented in Figure 2.," The spectra of the LRGs support the previous understanding that these galaxies are primarily quiescent, which is further supported by the results of the population synthesis analysis presented in Figure 2."113 The relative likelihood functions of the stellar age of these LRGs show that the Mglll absorbing LAC sample is best characterized bv a r model of τς0.15 Car. age /=3.25 Gr. and solar metallicity. while the non-absorbing LRGs are best- by a single burst of age /=8.25 Gyr and metallicity 0.2 solar.," The relative likelihood functions of the stellar age of these LRGs show that the II absorbing LRG sample is best characterized by a $\tau$ model of $\tau=0.15$ Gyr, age $t=3.25$ Gyr, and solar metallicity, while the non-absorbing LRGs are best-characterized by a single burst of age $t=8.25$ Gyr and metallicity $0.2$ solar."114 Our stellar population svnthesis analysis confirms the results of. visual inspections that the LRGs exhibit. little recent (F<1 ον) star formation activities., Our stellar population synthesis analysis confirms the results of visual inspections that the LRGs exhibit little recent $t < 1$ Gyr) star formation activities.115 For both samples. the best-fit models at 6s1.6 Gaver are characterized bv a single burst of 2.5 solar metallicity.," For both samples, the best-fit models at $t \la 1.6$ Gyr are characterized by a single burst of 2.5 solar metallicity."116 Bevond 1.6 Cir. the best-fit models have 7 ranging from τς0.2 to 0.5 Car.," Beyond 1.6 Gyr, the best-fit models have $\tau$ ranging from $\tau=0.2$ to 0.5 Gyr."117 The more extended 7 models are compensated by the corresponding older age., The more extended $\tau$ models are compensated by the corresponding older age.118 At still older ages of/25 Cr. the best-fit models are either single burst of 0.2 solar metallicity or a Ττ model of 7—0.5 Gyr and solar metallicity.," At still older ages of $t>5$ Gyr, the best-fit models are either single burst of 0.2 solar metallicity or a $\tau$ model of $\tau=0.5$ Gyr and solar metallicity."119 Phe corresponding lower metallicity at. older ages is consistent with the well-known age-metallicity degeneracy. (Worthey 1904).. making it dillicult to determine a precise metallicity for the underlying stellar population.," The corresponding lower metallicity at older ages is consistent with the well-known age-metallicity degeneracy \citep{worthey1994a}, , making it difficult to determine a precise metallicity for the underlying stellar population."120 However. the results of our likelihood analysis shows that we can robustly constrain the of the stellar population to be z1 Civr.," However, the results of our likelihood analysis shows that we can robustly constrain the of the stellar population to be $> 1$ Gyr."121 E the vast majority of iutermediate-aged (110 Car). very low-mass stars in the Calactic disk. barring/ a few special cases (e.g. low-mass companions to cooling white chwarts: 2006)) age determinations are difficult to obtain aud highly uncertain.," $\lesssim$ the vast majority of intermediate-aged (1–10 Gyr), very low-mass stars in the Galactic disk, barring a few special cases (e.g., low-mass companions to cooling white dwarfs; ) age determinations are difficult to obtain and highly uncertain."122 Ages are of particular importance for even lower-lmass brown dwarfs (AL © 0.075 M... objects which fail to sustain core hydrogen fusion aud therefore cool aud dim over time1963).," Ages are of particular importance for even lower-mass brown dwarfs (M $\lesssim$ 0.075 ), objects which fail to sustain core hydrogen fusion and therefore cool and dim over time."123. The cooling rate of a brown darf is set by its aec-depeudent Iuimuinositv. while its initial reservoir of thermal cucrey is set by eravitatioual contraction and heuce total mass.," The cooling rate of a brown dwarf is set by its age-dependent luminosity, while its initial reservoir of thermal energy is set by gravitational contraction and hence total mass."124 As such. there is au inherent degeucracy between the mass. age and observable properties of a given brown dwarf in the Galactic field population: one cannot distinguish )etween a vouus. low-mass brown dwiuf sud an old. uassive one from spectral type. πιοαν or effective eniperature alone.," As such, there is an inherent degeneracy between the mass, age and observable properties of a given brown dwarf in the Galactic field population; one cannot distinguish between a young, low-mass brown dwarf and an old, massive one from spectral type, luminosity or effective temperature alone."125 This degeneracy can be resolved for individual sources through measurement of à secondary xuwanieter such as surface gravity. which may theu be compared to predietious from brown dwarf evolutionary uodels (e.g. 2007)).," This degeneracy can be resolved for individual sources through measurement of a secondary parameter such as surface gravity, which may then be compared to predictions from brown dwarf evolutionary models (e.g., )."126 However. surface eravity determünatious are highly depeucent on he accuracy of atinospheric models. which are known o have systematic problems at low temperatures due to incompleteness in nioleculaur opacities (c.e.. 2008)) aud dynamic atmospheric," However, surface gravity determinations are highly dependent on the accuracy of atmospheric models, which are known to have systematic problems at low temperatures due to incompleteness in molecular opacities (e.g., ) and dynamic atmospheric"127higher frequencies were concentrated in the edges of those areas.,higher frequencies were concentrated in the edges of those areas.128 The oscillations were interpreted in terms of magnetoacoustic waves at frequencies less than 8 mHz and fast magnetoacoustic waves at frequencies above that., The oscillations were interpreted in terms of magnetoacoustic waves at frequencies less than 8 mHz and fast magnetoacoustic waves at frequencies above that.129" However, their data did not have information about line profiles. so the identification of MHD waves was not conclusive."," However, their data did not have information about line profiles, so the identification of MHD waves was not conclusive."130" In order to reveal the nature of MHD waves in the corona, we need to take into account the properties of coronal structures such as loops or moss."," 	In order to reveal the nature of MHD waves in the corona, we need to take into account the properties of coronal structures such as loops or moss."131" Recent observations of active region loops with EIS have revealed that coronal loops are not isothermal, and that their filling factors are approximately 10%,, which supports the existence of multi-strands of sub-resolution size 2008)."," 	Recent observations of active region loops with EIS have revealed that coronal loops are not isothermal, 	and that their filling factors are approximately $10$, 	which supports the existence of multi-strands of sub-resolution size \citep{war08}."132". Moss has a bright reticulated pattern, which emits EUV by thermal conduction from overlying hot and relatively high-pressure loops (Bergeretal.1999)."," Moss has a bright reticulated pattern, which emits EUV by thermal conduction from overlying hot and relatively high-pressure loops \citep{ber99}."133". The time scale of moss dynamics is 10—30s, which is due to internal intensity variation, obscuration by chromospheric jets. or mechanical interaction with those jets (DePonticuetal."," The time scale of moss dynamics is $10-30\mspace{3mu} \mathrm{s}$, which is due to internal intensity variation, 	obscuration by chromospheric jets, 	or mechanical interaction with those jets \citep{dep99}."1341999).. (2005) found that filling factors are lower at the footpoints of hot loops than at the footpoints of cool loops., \citet{kat05} found that filling factors are lower at the footpoints of hot loops than at the footpoints of cool loops.135" They concluded that braiding of the coronal magnetic field is more efficient at hot loops than at cool loops, which means there is a larger magnetic energy release at loops with a lower filling factor."," They concluded that braiding of the coronal magnetic field is more efficient at hot loops than at cool loops, 	which means there is a larger magnetic energy release at loops with a lower filling factor."136" Recently, an Fe 195 emission line observed with Hinode//EIS was analyzed to investigate the time variability of intensity, Doppler velocity, and nonthermal velocity in moss (Brooks&Warren2009)."," Recently, an Fe $195\mspace{3mu}$ emission line observed with /EIS was analyzed 	to investigate the time variability of intensity, Doppler velocity, and nonthermal velocity in moss \citep{bro09}."137". There was less than variability in intensity, 3kms7! variability in Doppler velocity, and the average nonthermal velocity was 21.7kms7!."," There was less than variability in intensity, $3 \mspace{3mu} \mathrm{km} \mspace{3mu} {\mathrm{s}}^{-1}$ variability in Doppler velocity, 	and the average nonthermal velocity was $21.7 \mspace{3mu} \mathrm{km} \mspace{3mu} {\mathrm{s}}^{-1}$."138" In this study, we analyzed time series data of intensity and Doppler velocity for loops and moss in an active region using sit-and-stare mode data observed with EIS (Culhaneetal.2007)."," In this study, we analyzed time series data of intensity and Doppler velocity for loops and moss in an active region 	using sit-and-stare mode data observed with EIS \citep{cul07}."139. Our purpose is to identify the modes of detected oscillations in this active region in order to understand which modes of MHD waves contribute to the heating of active regions., Our purpose is to identify the modes of detected oscillations in this active region 	in order to understand which modes of MHD waves contribute to the heating of active regions.140" We compared Fourier amplitudes of intensity and Doppler velocity to determine the modes of the detected oscillatory signals, and then investigated the correspondence between these coronal structures and"," We compared Fourier amplitudes of intensity and Doppler velocity to determine the modes of the detected oscillatory signals, and then investigated the correspondence between these coronal structures and"141oscillator implies 7=2.,oscillator implies $n=2$.142 The final case will be of particular interest chiefly for its analytic simplicity. but we also note that it corresponds to assuming a spatially constant density of matter.," The final case will be of particular interest chiefly for its analytic simplicity, but we also note that it corresponds to assuming a spatially constant density of matter."143 The rate of change of the total energy of a particle orbiting within the potential. dE/d/. is given by thepartial. derivative OV/Otμι Where r(/) denotes the solution to the equations of motion.," The rate of change of the total energy of a particle orbiting within the potential, $\dd E/\dd t$, is given by thepartial derivative $\left. \partial V/\partial t \right|_{r(t)}$, where $r(t)$ denotes the solution to the equations of motion."144 In the limit of an instantaneous change in the potential VΣΥAV occurring at time /. the total energy of the particle therefore changes by AE=AV(r(r))AVoarür.," In the limit of an instantaneous change in the potential $V \to V+\Delta V$ occurring at time $t$, the total energy of the particle therefore changes by $\Delta E = \Delta V(r(t)) = \Delta V_0 \, r(t)^n$."145 Assuming we have no prior knowledge of the phase of the particle. the virial theorem (e.g.2) states that the expected potential energy is where £o is the total energy of the particle and the result is independent of 7.," Assuming we have no prior knowledge of the phase of the particle, the virial theorem \cite[e.g.][]{goldstein2002classical} states that the expected potential energy is where $E_0$ is the total energy of the particle and the result is independent of $j$."146 This and following equations are also therefore valid in the one-dimensional (7= 0) subcase., This and following equations are also therefore valid in the one-dimensional $j=0$ ) subcase.147" If suddenly Vo=VyAWo. the energy after the potential change is Ey AE|. where The fiducial adiabatic limit can be attained from here by assuming AV, and AZ, to be infinitesimal and integrating over a series of such changes taking Vo smoothly to Vj."," If suddenly $V_0 \to V_0 + \Delta V_0$, the energy after the potential change is $E_0 + \Delta E_1$ , where The fiducial adiabatic limit can be attained from here by assuming $\Delta V_0$ and $\Delta E_1$ to be infinitesimal and integrating over a series of such changes taking $V_0$ smoothly to $V_f$."148 This yields a final. finite change in energy: As expected in the adiabatic limit. equation (4)) implies no energy shift. regardless of the intermediate states. if the final potential is the same as the initial.," This yields a final, finite change in energy: As expected in the adiabatic limit, equation \ref{eq:adiabatic-Efinal}) ) implies no energy shift, regardless of the intermediate states, if the final potential is the same as the initial."149 This is the central problem of the adiabatic approximation., This is the central problem of the adiabatic approximation.150 Figure 2 shows that the final distribution of gas will indeed be very similar to the initial. and therefore that the adiabatic prediction will be for no change in the final distribution of dark matter.," Figure \ref{fig:HT-fluctuations} shows that the final distribution of gas will indeed be very similar to the initial, and therefore that the adiabatic prediction will be for no change in the final distribution of dark matter."151 However Section ?? showed that potential changes in the simulations take place —on timescales much shorter than the dynamical time. because the expansion speeds of the supernova-induced bubbles are much larger than the local circular velocity.," However Section \ref{sec:first-sims} showed that potential changes in the simulations take place on timescales much shorter than the dynamical time, because the expansion speeds of the supernova-induced bubbles are much larger than the local circular velocity."152 As the gas expands and leaves the galaxy centre. the potential undergoes a series of large. instantaneous jumps. invalidating the adiabatic result given by equation GE).," As the gas expands and leaves the galaxy centre, the potential undergoes a series of large, instantaneous jumps, invalidating the adiabatic result given by equation \ref{eq:adiabatic-Efinal}) )."153 Instead of integrating. one should therefore recursively apply equation (3)) to each finite change.," Instead of integrating, one should therefore recursively apply equation \ref{eq:deltaE-virial}) ) to each finite change."154 If. for instance. the potential switches immediately back to its original depth. the second shift in energy is given by where the angular brackets indicate averaging over the orbital phase of our chosen trajectory during both the initial and final instantaneous potential jumps.," If, for instance, the potential switches immediately back to its original depth, the second shift in energy is given by where the angular brackets indicate averaging over the orbital phase of our chosen trajectory during both the initial and final instantaneous potential jumps."155 These conditions are justitied because the initial blowout is not causally connected to the location of a single tracer particle. nor is the exaet fractional number of orbits between initial blowout and eventual recollapse predictable (this aperiodieity is illustrated by Figure 259.," These conditions are justified because the initial blowout is not causally connected to the location of a single tracer particle, nor is the exact fractional number of orbits between initial blowout and eventual recollapse predictable (this aperiodicity is illustrated by Figure \ref{fig:HT-fluctuations}) )."156 By Taylor expanding. we find that the expected tinal energy of the orbit is given by which is always an energy gain for bound orbits since Ey«0 for n«0.," By Taylor expanding, we find that the expected final energy of the orbit is given by which is always an energy gain for bound orbits since $E_0<0$ for $n<0$."157 The energy gain is second order in the potential change AV. but linear in the energy.," The energy gain is second order in the potential change $\Delta V_0$, but linear in the energy."158 One may verify that. if the potentially first changes suddenly but then gradually (i.e. adiabatically) relaxes to its original state. we will also see an increase in expected tinal energy of the same magnitude.," One may verify that, if the potentially first changes suddenly but then gradually (i.e. adiabatically) relaxes to its original state, we will also see an increase in expected final energy of the same magnitude."159 The essential point is for the initial change to be rapid: the energy shift will then follow., The essential point is for the initial change to be rapid; the energy shift will then follow.160 The special case of the harmonie oscillator G7=2) is helpful in demonstrating the origin of this energy shift. because its dynamics are especially simple.," The special case of the harmonic oscillator $n=2$ ) is helpful in demonstrating the origin of this energy shift, because its dynamics are especially simple."161 The potential is separable in Cartesian coordinates which means that we can assume the one-dimensional subease without loss of generality., The potential is separable in Cartesian coordinates which means that we can assume the one-dimensional subcase without loss of generality.162 Then. for the case of sudden discrete jumps. the analytic form of the solution is written where @7(f)=2Vg(0) while AU). and wr) specify the amplitude and phase of the oscillation. which change discontinuously with the potential.," Then, for the case of sudden discrete jumps, the analytic form of the solution is written where $\omega^2(t)=2 V_0(t)$ while $A(t)$ and $\psi(t)$ specify the amplitude and phase of the oscillation, which change discontinuously with the potential."163 The new values of A and y after any jump can be determined either through energy arguments as above or by requiring continuity of both x and x., The new values of $A$ and $\psi$ after any jump can be determined either through energy arguments as above or by requiring continuity of both $x$ and $\dot{x}$.164 Without loss of generality. we let @ change from ay to Οι at /=0.," Without loss of generality, we let $\omega$ change from $\omega_0$ to $\omega_1$ at $t=0$."165 The amplitude of the trajectory after the jump. A. is given by the expression which is explicitly dependent onthe orbital phase wo at which the discontinuity occurs.," The amplitude of the trajectory after the jump, $A_1$, is given by the expression which is explicitly dependent onthe orbital phase $\psi_0$ at which the discontinuity occurs."166 The corresponding change of energy is We can now analyze the changes in a single trajectory which lead us to recover the expected gain in orbital energy under a single blowout-recollapse cycle. equation (60).," The corresponding change of energy is We can now analyze the changes in a single trajectory which lead us to recover the expected gain in orbital energy under a single blowout-recollapse cycle, equation \ref{eq:power-potential-energy-change}) )."167 Figure 3. (thick line) shows an example orbit for which a=10@;.," Figure \ref{fig:harmonic-oscillator} (thick line) shows an example orbit for which $\omega_0^2 = 10\, \omega_1^2$."168 The initial amplitude is unity until. at a certain time. the potential flattens out as mass is lost from inside the orbit.," The initial amplitude is unity until, at a certain time, the potential flattens out as mass is lost from inside the orbit."169 Intuitively. or from equation (9)). this must always involve a loss of energy for the particle (since aOp see also panel | at the top of Figure 3..," Intuitively, or from equation \ref{eq:harm-energy-jump}) ), this must always involve a loss of energy for the particle (since $\omega_0^2>\omega_1^2$ ); see also panel 1 at the top of Figure \ref{fig:harmonic-oscillator}. ."170 However. according to equation (8)). the new potential is sufficiently flattened that the orbital amplitude is now larger than unity (panel 2).," However, according to equation \ref{eq:harm-amplitude-jump}) ), the new potential is sufficiently flattened that the orbital amplitude is now larger than unity (panel 2)."171" This is crucial because the energy gain made when the potential change is later reversed (@ returns from @, to ex) will be accordingly larger. sealing with x (panel 3)."," This is crucial because the energy gain made when the potential change is later reversed $\omega$ returns from $\omega_1$ to $\omega_0$ ) will be accordingly larger, scaling with $\langle x^2 \rangle$ (panel 3)."172" Applying equations (8)) and (9)) for the reverse jump (i.e. with e and ex, exchanged) allow this picture to be directly verified.", Applying equations \ref{eq:harm-amplitude-jump}) ) and \ref{eq:harm-energy-jump}) ) for the reverse jump (i.e. with $\omega_1$ and $\omega_0$ exchanged) allow this picture to be directly verified.173 This makes more concrete the assertion of equation (6)) that one always expects to gain energy during a series of potential changes., This makes more concrete the assertion of equation \ref{eq:power-potential-energy-change}) ) that one always expects to gain energy during a series of potential changes.174 Yet seen from another perspective. such a elaim still needs o be reconciled with the underlying dynamics which are fully time-reversible.," Yet seen from another perspective, such a claim still needs to be reconciled with the underlying dynamics which are fully time-reversible."175 For instance. the time-reverse of Figure 3. (viewing the figure from right to left) represents an equally valid trajectory of he forwards dynamies and vet energy.," For instance, the time-reverse of Figure \ref{fig:harmonic-oscillator} (viewing the figure from right to left) represents an equally valid trajectory of the forwards dynamics and yet energy."176 Under time-reversal. the blowout phase maps onto the recollapsephase and vice-versa.," Under time-reversal, the blowout phase maps onto the recollapsephase and vice-versa."177 The irreversibility thus arises not rom dynamical differences but statistical differences between the orwards-blowout and reverse-recollapse pictures., The irreversibility thus arises not from dynamical differences but statistical differences between the forwards-blowout and reverse-recollapse pictures.178 In particular a uniform prior onthe orbital phase before a transition is always assumed. 27p(yo)= I.," In particular a uniform prior onthe orbital phase before a transition is always assumed, $2 \pi\,179p(\psi_0) = 1$ ."180" On the other hand the phase Yh, after the ransition is determined by", On the other hand the phase $\psi_0'$ after the transition is determined by181The apparent variability in (he bband can be described as changes in high-energy. cut-off of the spectrum. while (he count rates in the 0.20.5 keV band changed little.,"The apparent variability in the band can be described as changes in high-energy cut-off of the spectrum, while the count rates in the 0.2–0.5 keV band changed little."182 This cannot be explained by a cold absorber: we also consider a highly ionized absorber to be unlikely. as we do not see warm absorber edges such as due to O VII and OVILL.," This cannot be explained by a cold absorber; we also consider a highly ionized absorber to be unlikely, as we do not see warm absorber edges such as due to O VII and OVIII."183 The variability above 0.8 keV max be due to appearance ancl disappearance of a hot continuum source., The variability above 0.8 keV may be due to appearance and disappearance of a hot continuum source.184 Since such a continuum source also contributes lower energv (0.20.5 keV) flux as well. there must be compensating change in the lower temperature continuum source lo keep the low energv counts unchanged.," Since such a continuum source also contributes lower energy (0.2–0.5 keV) flux as well, there must be compensating change in the lower temperature continuum source to keep the low energy counts unchanged."185 This is exactly what the diskBB fits imply., This is exactly what the diskBB fits imply.186 An alternative interpretation is a simple change of temperature of (he emission region. as parameterized by the blackbody fits.," An alternative interpretation is a simple change of temperature of the emission region, as parameterized by the blackbody fits."187 Therefore. even though neither model provides a statistically. satisfactory. fits lor intervals (b) and (ο). they are likely to reflect the kind of changes taking place in P098.," Therefore, even though neither model provides a statistically satisfactory fits for intervals (b) and (c), they are likely to reflect the kind of changes taking place in P098."188 We therefore consider the implications of the blackbody and diskBB moclel fits., We therefore consider the implications of the blackbody and diskBB model fits.189 In many other ULXs. we have a puzzle in that the black hole mass inferred. [rom the Eddington limit argument is high. while (hat inferred from using the disk blackbody model is low.," In many other ULXs, we have a puzzle in that the black hole mass inferred from the Eddington limit argument is high, while that inferred from using the disk blackbody model is low."190 This is particularly severe if Schwarzschild black hole is assumed: even the assumption of Kerr black holes may not completely solve this puzzle (Ebisawaetal.2001)., This is particularly severe if Schwarzschild black hole is assumed; even the assumption of Kerr black holes may not completely solve this puzzle \citep{E01}.191. In P098. however. the situation is very different.," In P098, however, the situation is very different."192 The low temperature and the large Iuminositv can both be accommodated in the framework of an intermediate mass black hole accreting ad much less (han the Edclington rate., The low temperature and the large luminosity can both be accommodated in the framework of an intermediate mass black hole accreting at much less than the Eddington rate.193 The problem with this picture is the large disk radius changes inferred by the fit (roughly by a [factor of 4) while the inferred bolometric luminosity changes little., The problem with this picture is the large disk radius changes inferred by the fit (roughly by a factor of 4) while the inferred bolometric luminosity changes little.194 It is difficult to understand how a slight change in the mass aceretion rate (as suggested bv the near-constant luninositv) can trigger such a drastic change in inner radius of the accretion disk in such a short timescale., It is difficult to understand how a slight change in the mass accretion rate (as suggested by the near-constant luminosity) can trigger such a drastic change in inner radius of the accretion disk in such a short timescale.195 Looking at Chis from another angle: since a standard accretion disk has an TxR? profile. the temperature at 22=20000 kk should be 0.3 times that at /2=4000 kkin at any given moment. while the ratio of inferred temperatures al the (moving) inner edge of the disk is 0.5.," Looking at this from another angle: since a standard accretion disk has an $T \propto R^{-3/4}$ profile, the temperature at $R=20000$ km should be 0.3 times that at $R=4000$ km at any given moment, while the ratio of inferred temperatures at the (moving) inner edge of the disk is 0.5."196 Thus. if take the diskBB mocel fils al [ace value. POOS must have lost the inner part of the disk. while (he temperature al R=20000 kkin increased by 0.5/0.3~1.67. or the luminosity of the remaining part of the disk by a factor of 23.," Thus, if take the diskBB model fits at face value, P098 must have lost the inner part of the disk, while the temperature at $R=20000$ km increased by $\sim$ 1.67, or the luminosity of the remaining part of the disk by a factor of $\sim$ 8."197 This seems rather contrived for anv potential models in which the blackbody-like component originates in the accretion disk: we therefore prefer an alternative interpretation., This seems rather contrived for any potential models in which the blackbody-like component originates in the accretion disk; we therefore prefer an alternative interpretation.198 The behavior of P093 is reminiscent of the slow evolution of classical novae in the constant bolometric Iuminositv phase (Balmanetal.L998) and of the N-ray. variability of super-soft sources (Southwelletal.1996).," The behavior of P098 is reminiscent of the slow evolution of classical novae in the constant bolometric luminosity phase \citep{B98}199 and of the X-ray variability of super-soft sources \citep{S96}."200. In these svstems. nuclear burning on the surface of an accreting white dwarf keeps the radiative luminosity at or near the Eddineton limit.," In these systems, nuclear burning on the surface of an accreting white dwarf keeps the radiative luminosity at or near the Eddington limit."201 The nuclear enereve. also drives a stronge outflow: this wind is optically thick. hence," The nuclear energy also drives a strong outflow; this wind is optically thick, hence"202algorithm. rejecting values deviating from the mean by >d37 to ensure the removal of any remaining bad pixels and cosmic rays.,"algorithm, rejecting values deviating from the mean by $> \pm 3 \sigma$ to ensure the removal of any remaining bad pixels and cosmic rays."203 To obtain the correct flux measurement for each of the sources the contribution from the sky background also had to be considered., To obtain the correct flux measurement for each of the sources the contribution from the sky background also had to be considered.204 On initial reduction of the ODTS data. significant sky gradients were found across some images which SExtraetor. the adopted source extraction program (2). (see section 4.29). had difficulties correcting. for.," On initial reduction of the ODTS data, significant sky gradients were found across some images which SExtractor, the adopted source extraction program \cite{sex} (see section \ref{sec:sex}) ), had difficulties correcting for."205 These gradients were found to vary between ;xointings. so were thought to be caused by diffuse scattered ligh Tom bright stars in. or just outside. the observed fields. rather than being the result of vignetting within the instrument.," These gradients were found to vary between pointings, so were thought to be caused by diffuse scattered light from bright stars in, or just outside, the observed fields, rather than being the result of vignetting within the instrument."206 An alternative background subtraction algorithm was developed which computed he background value for every pixel in the image by effectively centring a box tof width 15-25 pixels) on each pixel. calculating he modal value of the background within the box surrounding the central pixel and assigning that value to the central pixel.," An alternative background subtraction algorithm was developed which computed the background value for every pixel in the image by effectively centring a box (of width 15-25 pixels) on each pixel, calculating the modal value of the background within the box surrounding the central pixel and assigning that value to the central pixel."207 A bi-cubic spline surface was then fit to the array of modal values in order to create a smoothed sky background map. which was then subtracted from the image.," A bi-cubic spline surface was then fit to the array of modal values in order to create a smoothed sky background map, which was then subtracted from the image."208 Initially. photometric zeropoints were estimated for each frame in every band for each observing run using the standard. star data acquired (see section 4.13).," Initially, photometric zeropoints were estimated for each frame in every band for each observing run using the standard star data acquired (see section \ref{sec:photo}) )."209 Using these zeropoints. SExtractor (7) was then used to perform the photometry.," Using these zeropoints, SExtractor \cite{sex} was then used to perform the photometry."210 After source catalogues had been created for each image (see section 4.23). accurate photometric zeropoints were determined across the 1 band by comparing objects in overlap regions (see section 6.1»). and adjusting their zeropoints relative to a chosen calibrator chip.," After source catalogues had been created for each image (see section \ref{sec:sex}) ), accurate photometric zeropoints were determined across the $V$ band by comparing objects in overlap regions (see section \ref{sec:overlap}) ), and adjusting their zeropoints relative to a chosen calibrator chip."211 Finally. the other bands were adjusted relative to the Y band data by comparing the colours of the stars in the ODTS images with those obtained using the Pickles (1998) library of stellar spectra. and applying zeropoint corrections needed to match these data sets (see section 6.2)).," Finally, the other bands were adjusted relative to the $V$ band data by comparing the colours of the stars in the ODTS images with those obtained using the Pickles (1998) library of stellar spectra, and applying zeropoint corrections needed to match these data sets (see section \ref{sec:stell}) )."212 Extracting source counts from the data at this stage will result in a measure of the instrumental magnitude which must be converted to the apparent magnitude., Extracting source counts from the data at this stage will result in a measure of the instrumental magnitude which must be converted to the apparent magnitude.213 In order to perform this flux calibration. short exposures of various fields containing several standard stars. calibrated by ?.. were observed through the same filters as that night's target fields.," In order to perform this flux calibration, short exposures of various fields containing several standard stars, calibrated by \scite{landolt}, were observed through the same filters as that night's target fields."214 Landolt fields SA92. SA95. SAIO] and SALO4 covered the ODTS fields well. with several standard stars falling in each frame.," Landolt fields SA92, SA95, SA101 and SA104 covered the ODTS fields well, with several standard stars falling in each frame."215 For each observing run. at least two of these standard fields were observed and were chosen to span a large airmass range. enabling us to monitor photometrie quality throughout the night. and allowing for the subsequent estimation ofextinction and colour terms.," For each observing run, at least two of these standard fields were observed and were chosen to span a large airmass range, enabling us to monitor photometric quality throughout the night, and allowing for the subsequent estimation of extinction and colour terms."216 As the survey progressed. the large number of non-photometric nights and the substantial overheads associated with multiple-band observations of standard stars prompted the use of an alternative procedure to establish the multi-band photometry for each survey region (see section 6.1)).," As the survey progressed, the large number of non-photometric nights and the substantial overheads associated with multiple-band observations of standard stars prompted the use of an alternative procedure to establish the multi-band photometry for each survey region (see section \ref{sec:overlap}) )."217 With this method. it is only he zeropointing of the V band calibrator chip that is of importance. as the zeropoints of the rest of the V band data are determinec by overlap matching (see section 6.1..) and the other bands are hen corrected relative to the V band. via stellar locus fitting (see section 6.23).," With this method, it is only the zeropointing of the $V$ band calibrator chip that is of importance, as the zeropoints of the rest of the $V$ band data are determined by overlap matching (see section \ref{sec:overlap}, ,) and the other bands are then corrected relative to the $V$ band, via stellar locus fitting (see section \ref{sec:stell}) )."218 Data for the Andromeda V band calibrator frame and he corresponding standard star observations were obtained during shotometric conditions. and the zeropoint was determined in the usual fashion.," Data for the Andromeda $V$ band calibrator frame and the corresponding standard star observations were obtained during photometric conditions, and the zeropoint was determined in the usual fashion."219 The uncertainty on the zeropoint of the 1 banc calibrator frame was found to be 0.07 magnitudes., The uncertainty on the zeropoint of the $V$ band calibrator frame was found to be $0.07$ magnitudes.220 SExtractor (2).. an. automated. package. was used to perform the image analysis and source extraction.," SExtractor \cite{sex}, an automated package, was used to perform the image analysis and source extraction."221 It is designed for the detection of faint objects in wide-field surveys and so is particularly suited to the ODTS data., It is designed for the detection of faint objects in wide-field surveys and so is particularly suited to the ODTS data.222 It also has the additional advantages of speed. a de-blending algorithm and a neural network. star- classitier.," It also has the additional advantages of speed, a de-blending algorithm and a neural network star-galaxy classifier."223" Due to the afore mentioned problems with the background subtraction, all images were background subtracted"," Due to the afore mentioned problems with the background subtraction, all images were background subtracted"224ο a Hormal maiu-sequeuce star with a specral type of aboti AO.,to a normal main-sequence star with a spectral type of about A9.225 We estimated tlie absolute dimeusious for the binary system from our photometric solion and from Harmauecs (LOSS) ‘elation between the spectral type and stellar mass., We estimated the absolute dimensions for the binary system from our photometric solution and from Harmanec's (1988) relation between the spectral type and stellar mass.226" These are οἱVen in Table L where the luminosity (LJar bolometric magnitudes (35,4) were computed by adopti1ο Tap. =5.780 Ix aud Ay. =+173 or solar values."," These are given in Table 4, where the luminosity $L$ ) and bolometric magnitudes $M_{\rm bol}$ ) were computed by adopting $T_{\rm eff}$$_\odot$ =5,780 K and $M_{\rm bol}$$_\odot$ =+4.73 for solar values."227 For the absolute visual maguitides (My). we used the bolometric correctious (BC's) appropriate for tlie temperature of each component from the exoressiou between logT aud BC given w Torres (2010).," For the absolute visual magnitudes $M_{\rm V}$ ), we used the bolometric corrections (BCs) appropriate for the temperature of each component from the expression between $\log T$ and BC given by Torres (2010)."228 With aLapparent visual magnitude of =+ 10.06 aud the interstelar absorption of Ay —0.11. we calculated the cistarce of the system to be 2€VL pc.," With an apparent visual magnitude of $V$ =+10.06 and the interstellar absorption of $A_{\rm V}$ =0.11, we calculated the distance of the system to be 294 pc."229 This result. is «usistent with 306 pc taken from the trigonometric j»arallax. 2T-E1.09 mas: Perryman et al., This result is consistent with 306 pc taken from the trigonometric parallax $\pm$ 1.09 mas; Perryman et al.230 |907)., 1997).231 A comparison of the SZ Her parameters with the mass-raclits. Inass-Iuiminosity. altμα (AR) «iagrams (Ibbanogllu e al.," A comparison of the SZ Her parameters with the mass-radius, mass-luminosity, and Hertzsprung-Russell (HR) diagrams (İbbanoǧllu et al."232" 2006) clearly demoustrates that the prima""N COMpPOLeL lies in the main-sequence band. while the secondary is slieltly beyond the terminal-age mai sequence aud its radius aud luminosity are about two times cjversized. aud more than four times overlumiuous compared with dwarf stars of the same mass."," 2006) clearly demonstrates that the primary component lies in the main-sequence band, while the secondary is slightly beyond the terminal-age main sequence and its radius and luminosity are about two times oversized and more than four times overluminous compared with dwarf stars of the same mass."233 Iu hese cli:igralus. i1e localious of the two coimnpolielrs conform to the general pattern of classical Aleols.," In these diagrams, the locations of the two components conform to the general pattern of classical Algols."234 ΤΙϱ ass axd temperature of the secondary star correspoud to a spectral type of approximaely W2 o Ix3., The mass and temperature of the secondary star correspond to a spectral type of approximately K2 to K3.235 From the current observatious. six new times of nuinunum light and tlieir errors were cetermiued using the method of Ixwee van Woerden (1956) and with he weighted mean Lor the values in each filter.," From the current observations, six new times of minimum light and their errors were determined using the method of Kwee van Woerden (1956) and with the weighted mean for the values in each filter."236 These are listed in Table 5. wherein 73 additional eclipses were obtained using the data from the WASP (Wide Anele Search [or Planets) public archive (Butters et al.," These are listed in Table 5, wherein 73 additional eclipses were obtained using the data from the WASP (Wide Angle Search for Planets) public archive (Butters et al."237 2010)., 2010).238 For ephemeris computatious. we have collected a total of 1020 timiugs (910 visual. 20 phoographic. 16 photoelectric aud 65 CCD) from the literature (Ixreiuer et al.," For ephemeris computations, we have collected a total of 1050 timings (949 visual, 20 photographic, 16 photoelectric and 65 CCD) from the literature (Kreiner et al."239 2001: Baldwin Samolyx 2002. 200I: Locher 2002a. 2002b: Bakis et al.," 2001; Baldwin Samolyk 2002, 2004; Locher 2002a, 2002b; Bakiş et al."240 2003: Székkely 2003: Dietlelm 2003. 2001: Nelso1 2005: Cook et al.," 2003; Székkely 2003; Diethelm 2003, 2004; Nelson 2005; Cook et al."241 2005: Wim et al., 2005; Kim et al.242 2006: Nagai 2001. 2006: Hübbscher. et al.," 2006; Nagai 2004, 2006; Hübbscher, et al."243 2006. 2009: Senayci el al.," 2006, 2009; Senavci et al."244 2007: Saimolyk 2008a. 2008b: Bratt et al.," 2007; Samolyk 2008a, 2008b; Brátt et al."245 2008: Liakos Niarchos 20(9): Dogrru et al., 2008; Liakos Niarchos 2009; Doğrru et al.246 2009. 2011: Dvorak 2010: Erkan et al.," 2009, 2011; Dvorak 2010; Erkan et al."247 2010: Hübbscher Monniuger 2011) to add to the current 1ueasur'ements., 2010; Hübbscher Monninger 2011) to add to the current measurements.248 Most earlier (imines were extracted [rou tlie «atabase published by Ixreiner et al. (, Most earlier timings were extracted from the database published by Kreiner et al. (2492001).,2001).250 Tie secondary minulna are 1nicl shallower than the pri1a'y ones and the O-C' residuals from the two eclipse types are in phase with each otler., The secondary minima are much shallower than the primary ones and the $O$ $C$ residuals from the two eclipse types are in phase with each other.251 Thus. we did 100 use all secoucary ecipses in the subsedqeut analysis.," Thus, we did not use all secondary eclipses in the subsequent analysis."252 Because mauy tiniugs have been publisllec| witliout errors. the followiug standard deviatioIn were assigued to the timiug residuals based oi 1 observational techliniqie: +£0.0036 ἆ for visual. 20.0020 d for photographic. aud 270.0013 d for p10oelectric aud CCD iniiluna.," Because many timings have been published without errors, the following standard deviations were assigned to the timing residuals based on an observational technique: $\pm$ 0.0036 d for visual, $\pm$ 0.0020 d for photographic, and $\pm$ 0.0013 d for photoelectric and CCD minima."253 Relative weights were then scaled from the inverse scuares of these Vaues (Lee et al., Relative weights were then scaled from the inverse squares of these values (Lee et al.254 2007)., 2007).255 Previous researchers (Székkely 2003: Sovcdugau 2008) have suggestedMOD that the period variatious of SZ Her can be represettec using an LITE caused by the presence of a third body in the system., Previous researchers (Székkely 2003; Soydugan 2008) have suggested that the period variations of SZ Her can be represented using an LITE caused by the presence of a third body in the system.256ceases to be a power law and the perturbations begin to contract and become gravitationally A fundamental assumption of the thinshell mocel is that all fragments evolve independently of one another in an otherwise unperturbed shell.,ceases to be a power law and the perturbations begin to contract and become gravitationally A fundamental assumption of the thin–shell model is that all fragments evolve independently of one another in an otherwise unperturbed shell.257 We used the potential clumpfinding code to verily this assumption., We used the potential clump--finding code to verify this assumption.258 The clumplincing Code is able to follow individual pcores to see how they eain or lose mass and whether they merge or exchange mass with each other as time progresses., The clumpfinding code is able to follow individual p–cores to see how they gain or lose mass and whether they merge or exchange mass with each other as time progresses.259 “To make use of this facility. we arbitrarily clivicle the first 15Myr of the mecitumpressure shells evolution into ten contiguous 1.5 Alvr epochs.," To make use of this facility, we arbitrarily divide the first 15Myr of the medium–pressure shell's evolution into ten contiguous 1.5 Myr epochs."260 In Figure 9 we plot the total number of p.cores extant in cach epoch together with the numbers of clumps formecl and. destroved in the previous epoch. against time.," In Figure \ref{fig:nclumps} we plot the total number of p–cores extant in each epoch together with the numbers of clumps formed and destroyed in the previous epoch, against time."261 Initially. the number of p.cores destroved in the previous epoch is almost equal to the total number of pcores. implying that the objects detected by the elumplinder are," Initially, the number of p–cores destroyed in the previous epoch is almost equal to the total number of p–cores, implying that the objects detected by the clumpfinder are"262Stars: oeidividual:— V615 Cas,Stars: individual:$\equiv$ V615 Cas263"coordinates, (x,y,z), with periodic boundary conditions in the x and y directions and stress-free perfectly conducting boundaries at top and bottom (z= ","coordinates, $(x,y,z)$, with periodic boundary conditions in the $x$ and $y$ directions and stress-free perfectly conducting boundaries at top and bottom $z=\pm L_z/2$ )."264"The volume-averaged density is therefore constant in +L,/2).time and equal to its initial value, po—(p)."," The volume-averaged density is therefore constant in time and equal to its initial value, $\rho_0=\bra{\rho}$."265" We solve the equations for the velocity U, the magnetic vector potential A, and the density p, where v is kinematic viscosity, 7 is magnetic diffusivity, B=Bo+Vx Ais the field, Bo=(0,Bo,0) is the imposed uniform field, magneticJ=VxB/yo is the current density, ug is the vacuum permeability, Sj;=i(Ui;+U;i)−⋛⊂⋝↕⊲∃⋅∇-U is the traceless rate of strain tensor, and commas denote partial differentiation."," We solve the equations for the velocity $\UU$, the magnetic vector potential $\AAA$ , and the density $\rho$, where $\nu$ is kinematic viscosity, $\eta$ is magnetic diffusivity, $\BB=\BB_0+\nab\times\AAA$ is the magnetic field, $\BB_0=(0,B_0,0)$ is the imposed uniform field, $\JJ=\nab\times\BB/\mu_0$ is the current density, $\mu_0$ is the vacuum permeability, ${\sf S}_{ij}=\half(U_{i,j}+U_{j,i})-\onethird\delta_{ij}\nab\cdot\UU$ is the traceless rate of strain tensor, and commas denote partial differentiation."266" The forcing function f consists of random, white-in-time, non-polarized waves with an average wavenumber kpplane=15k;, where ki—2m/L; is the lowest wavenumber in the domain."," The forcing function $\ff$ consists of random, white-in-time, plane non-polarized waves with an average wavenumber $\kf=15\,k_1$, where $k_1=2\pi/L_z$ is the lowest wavenumber in the domain."267" The forcing strength is such that the turbulent rms velocity is approximately independent of z with uj,=(u2)/?zm0.1 ος."," The forcing strength is such that the turbulent rms velocity is approximately independent of $z$ with $\urms=\bra{\uu^2}^{1/2}\approx0.1\,\cs$ ."268" The gravitational acceleration g=(0,0,—g) is chosen such that kj;Πρ--1, which leads to a density contrast between bottom and top of exp(27)αγ535."," The gravitational acceleration $\grav=(0,0,-g)$ is chosen such that $k_1 H_\rho=1$, which leads to a density contrast between bottom and top of $\exp(2\pi)\approx535$."269" Here, H,=c2/g is the density scale height."," Here, $H_\rho=\cs^2/g$ is the density scale height."270" Our simulations are characterized by the fluid Reynolds number Re=us the magnetic Prandtl number ΡΓΛ/= and the magnetic /vkr,Reynolds number Rej=RePry."," Our simulations are characterized by the fluid Reynolds number $\Rey\equiv\urms/\nu\kf$, the magnetic Prandtl number $\Pm=\nu/\eta $ and the magnetic Reynolds number $\Rm\equiv \Rey \, \Pm$."271" Followingν/η earlier work (Brandenburgetal.2011),, we choose Pru=0.5 and Rey in the 0.7—74."," Following earlier work \citep{BKKR11}, we choose $\Pm = 0.5$ and $\Rm$ in the range $0.7$ $74$."272" The magnetic field is expressed in units of the rangelocal equipartition field strength near the Beg=Urms; While Bo is specified in units of the averagedtop, value, \/Ho0PBegg=νµοβοταις."," The magnetic field is expressed in units of the local equipartition field strength near the top, $\Beq=273\sqrt{\mu_0\rho} \, \urms$, while $B_0$ is specified in units of the averaged value, $\Beqz=\sqrt{\mu_0\rho_0} \, \urms$."274" We monitor AB,=B,—Bo, where is an average over y and a certain time interval At."," We monitor $\Delta\meanB_y=\meanB_y-B_0$, where $\meanB_y$ is an average over $y$ and a certain time interval $\Delta t$."275" Time B,is expressed in eddy turnover times, Τιο=(urskg) |."," Time is expressed in eddy turnover times, $\tauto=(\urms\kf)^{-1}$ ."276" Occasionally, we also consider the turbulent-diffusive timescale, τια= (r«ok2)-!, where 0=Urms/ is the estimated turbulent magnetic diffusivity."," Occasionally, we also consider the turbulent-diffusive timescale, $\tautd=(\etatz k_1^2)^{-1}$ , where $\etatz=\urms/3\kf$ is the estimated turbulent magnetic diffusivity."277" Another 3kydiagnostic quantity is the rms magnetic field in the k=A4 Fourier mode, P4, which is here taken as an average over 2<kz3, and is close to the top at kz=m. ("," Another diagnostic quantity is the rms magnetic field in the $k=k_1$ Fourier mode, $B_1$, which is here taken as an average over $2\leq k_1z\leq3$, and is close to the top at $k_1 z=\pi$. ("278Note that B4 does not include the imposed field Bo at k— 0.),Note that $B_1$ does not include the imposed field $B_0$ at $k=0$ .)279 The simulations are performed with the which uses sixth-order explicit finite differences in space and a third-order accurate time stepping method., The simulations are performed with the which uses sixth-order explicit finite differences in space and a third-order accurate time stepping method.280" We use numerical resolutions of 128? and 256? mesh points when L,= L;,and 1024x128? when L,,=8L, 8L,."," We use numerical resolutions of $128^3$ and $256^3$ mesh points when $L_x=L_y=L_z$, and $1024\times128^2$ when $L_x=8L_y=8L_z$ ."281" To capture Lymean-field effects on the slower turbulent-diffusive timescale, which is Tta/Tio=/k2 times slower than the dynamical timescale, we perform31 simulations for several thousand turnover times."," To capture mean-field effects on the slower turbulent-diffusive timescale, which is $\tautd/\tauto=3\kf^2/k_1^2$ times slower than the dynamical timescale, we perform simulations for several thousand turnover times."282" The NEMPI phenomenon is already quite pronounced at intermediate values of ReyZ;3; see1,, where we show averaged over y and Atzz8074, (denoted by B,) at selected B,times during the first 2000 turnover times."," The NEMPI phenomenon is already quite pronounced at intermediate values of $\Rm\ga3$; see, where we show $B_y$ averaged over $y$ and $\Delta t\approx80\tauto$ (denoted by $\meanB_y$ ) at selected times during the first 2000 turnover times."283 The Rej dependence of By/Beg is shown in2., The $\Rm$ dependence of $B_1/\Beq$ is shown in.284". For Rey>3, the Rej; dependence is relatively weak, which suggests that NEMPI is a genuine high Reynolds number effect."," For $\Rm>3$, the $\Rm$ dependence is relatively weak, which suggests that NEMPI is a genuine high Reynolds number effect."285 The results for the case of Rey;=6 show strong similarities to earliermean-field simulations., The results for the case of $\Rm=6$ show strong similarities to earliermean-field simulations.286" the first 500 turnover times, flux concentrations form first Duringnear the surface, but at later times the location of the peak magnetic field moves gradually downward."," During the first 500 turnover times, flux concentrations form first near the surface, but at later times the location of the peak magnetic field moves gradually downward."287" This phenomenon isa directconsequence of the negative effective pressure, making such structures heavier than theirsurroundings."," This phenomenon isa directconsequence of the negative effective magnetic pressure, making such structures heavier than theirsurroundings."288"magnetic Their shape resembles that of a falling “potato sack"" and has been", Their shape resembles that of a falling “potato sack” and has been289much of the observed deficit at that energy may be real (and that our MOS calibration models the neutral Si edge rather well).,much of the observed deficit at that energy may be real (and that our MOS calibration models the neutral Si edge rather well).290" To clarify the comparison with the MOS data in the lower energy band, the upper panel of figure 3 illustrates the photoionised absorber with the Fe abundance set to zero."," To clarify the comparison with the MOS data in the lower energy band, the upper panel of figure 3 illustrates the photoionised absorber with the Fe abundance set to zero."291" Removing Fe from the absorber also shows that potential confusion from Fe-L absorption is limited above ~1.2 keV. The apparent redshift read from the XSTAR model was 4.9+0.3) x 10~?, corresponding to an outflow velocity (in the rest frame of PG1211+143)) of v~0.130+0.003c."," Removing Fe from the absorber also shows that potential confusion from Fe-L absorption is limited above $\sim$ 1.2 keV. The apparent redshift read from the XSTAR model was $\pm$ 0.3) x $^{-2}$, corresponding to an outflow velocity (in the rest frame of ) of $\sim$ $\pm$ 0.003c."292" While this value is consistent with the range of velocities of 0.13-0.15c deduced from the individual line fitting in Xspec, the implied precision is probably not justified given the simplicity of the single absorber XSTAR model."," While this value is consistent with the range of velocities of 0.13-0.15c deduced from the individual line fitting in Xspec, the implied precision is probably not justified given the simplicity of the single absorber XSTAR model."293" Although the addition of a lower ionisation absorber would improve the match to the observed line ratios, in particular in providing stronger absorption for He-like Mg and Ne, we have not included a second absorber in the model, having already achieved our objective of modelling a high velocity outflow across multiple ions."," Although the addition of a lower ionisation absorber would improve the match to the observed line ratios, in particular in providing stronger absorption for He-like Mg and Ne, we have not included a second absorber in the model, having already achieved our objective of modelling a high velocity outflow across multiple ions."294" However, it is interesting to note that the addition of a lower ionisation component would also enhance the ‘red wing’ to the Fe K absorption, already showing up in the XSTAR plot in figure 3 (mid panel), due to increased contributions from ions of FeXX-XXIV, and thereby explain the apparently resolved ~7 keV absorption line (c=168+46 eV) in the pn spectrum."," However, it is interesting to note that the addition of a lower ionisation component would also enhance the `red wing' to the Fe K absorption, already showing up in the XSTAR plot in figure 3 (mid panel), due to increased contributions from ions of FeXX-XXIV, and thereby explain the apparently resolved $\sim$ 7 keV absorption line $\sigma$ $\pm$ 46 eV) in the pn spectrum."295" In summary, modelling the MOS absorption spectrum with a photoionised absorber shows it to be physically compatible with a highly ionised outflow of velocity in the range 0.13-0.15c, as derived from individual line fitting."," In summary, modelling the MOS absorption spectrum with a photoionised absorber shows it to be physically compatible with a highly ionised outflow of velocity in the range 0.13-0.15c, as derived from individual line fitting."296" In their previous analysis of the aabsorption line spectrum P03 showed that, provided the high velocity outflow was not tightly collimated, then the mass loss rate and mechanical energy in the flow would be comparable to the mass accretion rate and ~10 of the bolometric luminosity."," In their previous analysis of the absorption line spectrum P03 showed that, provided the high velocity outflow was not tightly collimated, then the mass loss rate and mechanical energy in the flow would be comparable to the mass accretion rate and $\sim$ 10 of the bolometric luminosity."297 We can now re-estimate those quantities., We can now re-estimate those quantities.298" In doing so we use an estimate of for the covering factor of the fast outflow, calculated by comparing the absorbed and re-emitted power in the highly ionised gas derived from a broad band fit to the full 0.3-10.0 keV spectrum of ((Pounds and Reeves 2006)."," In doing so we use an estimate of for the covering factor of the fast outflow, calculated by comparing the absorbed and re-emitted power in the highly ionised gas derived from a broad band fit to the full 0.3-10.0 keV spectrum of (Pounds and Reeves 2006)."299" Assuming a radial flow, the outflow mass rate is then Mout = 0.37.ni?.v.m,. ~0.27-Lion/€.v.mp where n is the particle density at a radius r, and Lion~1014 erg s! is the ionising luminosity."," Assuming a radial flow, the outflow mass rate is then $\mo$ = $\pi$ $^{2}$ $_{p}$ $\sim$ $\pi$ $_{ion}$ $\xi$ $_{p}$ where n is the particle density at a radius r, and $_{ion}$$\sim~10^{44}$ erg $^{-1}$ is the ionising luminosity."300" With the observed ionisation parameter logé~3, we find Mout ~2.5x107° gm s! (~3.5 Mo νι1)."," With the observed ionisation parameter $\xi$$\sim$ 3, we find $\mo$ $\sim$$2.5\times 10^{26}$ gm $^{-1}$ $\sim$ 3.5 $\msun$ $^{-1}$ )."301" The corresponding mechanical energy in the fast, highly ionised outflow is then ~2x1035 erg s!, compared with an estimated bolometric luminosity for oof ~5x10*° erg s!."," The corresponding mechanical energy in the fast, highly ionised outflow is then $\sim$$2\times 10^{45}$ erg $^{-1}$, compared with an estimated bolometric luminosity for of $\sim$$5\times$$ 10^{45}$ erg $^{-1}$."302 We note this ratio is a factor 3 higher than the ratio v/c expected from a radiation driven wind (King and Pounds 2003)., We note this ratio is a factor $\sim$ 3 higher than the ratio v/c expected from a radiation driven wind (King and Pounds 2003).303" However, given the undoubted simplification of our single-absorber model, and uncertainties in derivation of the covering factor, it is probably premature to adopt the popular appeal to magnetic forces to drive the outflow!"," However, given the undoubted simplification of our single-absorber model, and uncertainties in derivation of the covering factor, it is probably premature to adopt the popular appeal to magnetic forces to drive the outflow!"304" The Black Hole Winds model of King and Pounds (2003) provided a simple physical basis whereby massive, high velocity outflows can be expected in AGN accreting near the Eddington limit."," The Black Hole Winds model of King and Pounds (2003) provided a simple physical basis whereby massive, high velocity outflows can be expected in AGN accreting near the Eddington limit."305" A simultaneous observation of iin 2001 with the OOptical Monitor (Mason 22001) showed the energetically dominant BBB to be at a typical value, indicating a bolometric luminosity of"," A simultaneous observation of in 2001 with the Optical Monitor (Mason 2001) showed the energetically dominant BBB to be at a typical value, indicating a bolometric luminosity of"306is. our results here and that i1 (Zeug&Cao2005) iudicate that. « affects the uuuber density of calaxy clusters exponenutiallv.,"is, our results here and that in \citep{SphereI} indicate that, $w$ affects the number density of galaxy clusters exponentially."307 So we think measuring the nunber density of ealaxy clusers and its evolutions nay be an effective wav to deteThue dw., So we think measuring the number density of galaxy clusters and its evolutions may be an effective way to determine $w$.308 As discussions. we would like to state that. if he xobleuni we pointed out in (Ze1ο&Cao2005) is the act. then we mav have to accept that. we ignored a verv muportant assumption in the usual ACDAL cosmology.," As discussions, we would like to state that, if the problem we pointed out in \citep{SphereI} is the fact, then we may have to accept that, we ignored a very important assumption in the usual $\Lambda$ CDM cosmology."309 That is: the cosmic colmponent denoed w A aud leading to the aceloraion of the universe uoves svuchronouslv with ordinary lmatters., That is: the cosmic component denoted by $\Lambda$ and leading to the accleration of the universe moves synchronously with ordinary matters.310 The reason is very clear. if X docs not move svuchronously with ordinary inatters on Hubble scales. then iu our comoving reference frame mild ou the ordinary matters(such as supernovaes). we should have a A current flowing outside the labde horizon.," The reason is very clear, if $\Lambda$ does not move synchronously with ordinary matters on Hubble scales, then in our comoving reference frame build on the ordinary matters(such as supernovaes), we should have a $\Lambda$ current flowing outside the hubble horizon."311" Ouce that OCCULS, We cannot define an alb universe uniforiulv defined scale factor. so we have no Eriediinaun equation at all."," Once that occurs, we cannot define an all universe uniformly defined scale factor, so we have no Friedmann equation at all."312" Iu that Case, OUP Cl11011 explanation of the acceleration iucicated bv ti6 observation of superuovaes will be very. problematic."," In that case, our current explanation of the acceleration indicated by the observation of supernovaes will be very problematic."313 If A component moves svuchrouously with ονπαν matters. then we will have 10 reason to sav that it is the vacui euergv of quautuni field.," If $\Lambda$ component moves synchronously with ordinary matters, then we will have no reason to say that it is the vacuum energy of quantum field."314 On the coutrary. some kinds of couplings beween A (or dark euergv) aud the ordinary matters 1s a nuust be derivation.," On the contrary, some kinds of couplings between $\Lambda$ (or dark energy) and the ordinary matters is a must be derivation."315 Part of the numerical compitations are performed ou the parallel computers of the Iuter-discipliue C'euter of Theoretical Studies of ITP. CAS. Beijing. China.," Part of the numerical computations are performed on the parallel computers of the Inter-discipline Center of Theoretical Studies of ITP, CAS, Beijing, China."316 Qur results in this paper aud its sibling one (ZeugCao2005) are so different from the previous works that without a concrete comparison aud explicit pointing out the problem iu those works. few peoples will believe our couclusious.," Our results in this paper and its sibling one \citep{SphereI} are so different from the previous works that without a concrete comparison and explicit pointing out the problem in those works, few peoples will believe our conclusions."317" To conipare our basic equatious with the basic equations used by (Waue&Steinhardt1998).. we can differentiate eq(2)) aud use energy conservation law to cot. Iu the right haud side of this equation. if we let aq==a,. 1.0. assume that he dark energy moves svuchnrounouslv with ordinary matters on the galaxy cluster scales. then it reduce to he eq(A2) of (Wang&Steinluudt1998)."," To compare our basic equations with the basic equations used by \citep{WangSteinhardt1}, we can differentiate \ref{ZGEconserve}) ) and use energy conservation law to get, In the right hand side of this equation, if we let $a==a_p$, i.e., assume that the dark energy moves synchronously with ordinary matters on the galaxy cluster scales, then it reduce to the eq(A2) of \citep{WangSteinhardt1}."318. Note. in tie right haud side of eqt59)). o ouly appears in terms where dark cuerev is involved.," Note, in the right hand side of \ref{WSbasicEq1}) ), $a$ only appears in terms where dark energy is involved."319 But (Waug&Stceiihardt1998) docs 10 use this assumption consistenIv. because when it conibine its eq(À2) with the eqwtion describing the dark euergvs evolution eqcA6). i uses the assunuption that ouly on IIubble scales. dark CLOYSV LH1OVCR svuchronouslv with oxluv niaters.," But \citep{WangSteinhardt1} does not use this assumption consistently, because when it combine its eq(A2) with the equation describing the dark energy's evolution eq(A6), it uses the assumption that only on Hubble scales, dark energy moves synchronously with ordinary matters."320 Although we lave pointed out in (Zeng&2005).. we still would ike to point out that. as long as variable separation techuique is used iu solving Limstein equation. then whichever (Ravchanudliawi or Freiduaun) equation we chijose to describe the evolution of the over-deuse regjon. we will iu fact have assumed that dark euergv moves svuchlronously with ordinary matters iu our over-deuse region.," Although we have pointed out in \citep{SphereI}, we still would like to point out that, as long as variable separation technique is used in solving Einstein equation, then whichever (Raychaudhuri or Freidmann) equation we choose to describe the evolution of the over-dense region, we will in fact have assumed that dark energy moves synchronously with ordinary matters in our over-dense region."321 Let us explain this poiut in more details., Let us explain this point in more details.322" For au over-deuse collapsing region. the most eeueral umctric describe its Inside space-time Is Using Eiustein equation G,,=Απτς. we can prove that. only when uo energy current flowing outside the over-deuse region. is the energy momenta tensor T,, diagonal. aud cau the metric function U(t.r) aud V(f.r) be factorized as VVtr)—a?(ty?m(6"," For an over-dense collapsing region, the most general metric describe its inside space-time is Using Einstein equation $G_{\mu\nu}=-8\pi GT_{\mu\nu}$, we can prove that, only when no energy current flowing outside the over-dense region, is the energy momentum tensor $T_{\mu\nu}$ diagonal, and can the metric function $U(t,r)$ and $V(t,r)$ be factorized as V(t,r)=a_p^2(t)r^2."3231) And oulv when the C(f.r) aud V(f.r) functiou is factorized. cau we have," And only when the $U(t,r)$ and $V(t,r)$ function is factorized, can we have"324" Following Cooper Showman (2005), Rauscher Menou (2010) relied on the work of Iro et al. ("," Following Cooper Showman (2005), Rauscher Menou (2010) relied on the work of Iro et al. ("3252005) to implement the detailed profiles of this radiative forcing.,2005) to implement the detailed profiles of this radiative forcing.326" The is divided into actively forced layers, above the 10atmosphere bar level, and ""inert"" layers below."," The atmosphere is divided into actively forced layers, above the 10 bar level, and “inert” layers below."327" The radiative forcing is assumed to be negligible in the inert layers, which corresponds to 7;44—oo."," The radiative forcing is assumed to be negligible in the inert layers, which corresponds to $\tau_{\rm rad}\rightarrow \infty$."328" The active layers, on the other hand, are forced on a finite radiative timescale, Trad(p)."," The active layers, on the other hand, are forced on a finite radiative timescale, $\tau_{\rm329rad}(p)$."330" The local atmospheric temperatures obtained after model relaxation hover at about 1800 K in the deepest levels, while in the upper levels they range from about 500 K on the night side to about 1500 K on the day side (see Rauscher Menou 2010 for details*))."," The local atmospheric temperatures obtained after model relaxation hover at about 1800 K in the deepest levels, while in the upper levels they range from about 500 K on the night side to about 1500 K on the day side (see Rauscher Menou 2010 for )."331" At these temperatures, the primary source of free electrons stems from thermally ionized alkali metals with low first ionization potentials: Na, Al, K. For simplicity here (and consistently with PMRIO), we adopt an approximation to Saha's equation (Balbus Hawley 2000) which assumes potassium to be the dominant contributing species: Here n, and n, are respectively the electron and neutral number densities (in cm?) and ay~107"" is the potassium solar abundance."," At these temperatures, the primary source of free electrons stems from thermally ionized alkali metals with low first ionization potentials: Na, Al, K. For simplicity here (and consistently with PMR10), we adopt an approximation to Saha's equation (Balbus Hawley 2000) which assumes potassium to be the dominant contributing species: Here $n_e$ and $n_n$ are respectively the electron and neutral number densities (in $^{-3}$ ) and $a_K \simeq 10^{-7}$ is the potassium solar abundance."332" As discussed in PMRIO, equation (1)) is a good approximation as long the resulting ionization fraction, Xe, iS «ax; this condition is satisfied in our atmosphere models."," As discussed in PMR10, equation \ref{eq:xe}) ) is a good approximation as long the resulting ionization fraction, $x_e$, is $\ll a_K$; this condition is satisfied in our atmosphere models."333" We assume that the is overall neutral, which an equality between the electrongas number density n, and the impliesionic one n;."," We assume that the gas is overall neutral, which implies an equality between the electron number density $n_e$ and the ionic one $n_i$."334" The electrical conductivity and associated resistivity are given by respectively, with the collision rate between electrons and neutrals approximated as (Draine et al 1983) The first step towards the computation of currents involves an estimate of the importance of various non-ideal MHD terms in the full induction for the weakly-ionized medium."," The electrical conductivity and associated resistivity are given by respectively, with the collision rate between electrons and neutrals approximated as (Draine et al 1983) The first step towards the computation of currents involves an estimate of the importance of various non-ideal MHD terms in the full induction equation for the weakly-ionized medium."335" For the atmospheric equationmodels under consideration here, PMR10 found that, for a surface magnetic field strength of 3 G, the Hall term is completely negligible throughout the flow, while the resistive term largely dominates over the ambipolar diffusion term everywhere except possibly in the"," For the atmospheric models under consideration here, PMR10 found that, for a surface magnetic field strength of 3 G, the Hall term is completely negligible throughout the flow, while the resistive term largely dominates over the ambipolar diffusion term everywhere except possibly in the"336Horizontal branch (HB) stars in Galactic. globular clusters (GCs) are old post- He flash stars of low initial mass M) that. after the exhaustion of hydrogen in the stellar core and their ascension along the red giant branch. eventually ignited heltum(??).,"Horizontal branch (HB) stars in Galactic globular clusters (GCs) are old post- He flash stars of low initial mass (0.7-0.9 $_\odot$ ) that, after the exhaustion of hydrogen in the stellar core and their ascension along the red giant branch, eventually ignited helium."337. GCs display large differences in the HB morphology?)., GCs display large differences in the HB morphology.338 The first parameter responsible for this phenomenon is metallicity. but it alone cannot account for the complex observational picture??).," The first parameter responsible for this phenomenon is metallicity, but it alone cannot account for the complex observational picture."339. While some clusters contain only red HB stars cooler than the RR-Lyrae gap. others host a large population of blue He-burning stars extending even beyond the canonical end of the HB at ~350000 K?).. Even more puzzling. in the color-magnitude diagram (CMD) of some clusters the HB appears continuous in its whole extension?).. while in others it 1s clearly multimodal?).," While some clusters contain only red HB stars cooler than the RR-Lyrae gap, others host a large population of blue He-burning stars extending even beyond the canonical end of the HB at $\sim$ 000 K. Even more puzzling, in the color-magnitude diagram (CMD) of some clusters the HB appears continuous in its whole extension, while in others it is clearly multimodal."340. This observational picture still lacks full comprehension. às a consequence of our poor understanding of the formation mechanism of HB stars in GCs.," This observational picture still lacks full comprehension, as a consequence of our poor understanding of the formation mechanism of HB stars in GCs."341 The HB morphology has been linked. among others. to cluster age(?).. cluster concentration(?).. stellar rotation(2).. cluster mass(?).. helium. and the environment of formation(?).. but none of the proposed second parameters could satisfactorily reproduce the complex observed behaviorreview).," The HB morphology has been linked, among others, to cluster age, cluster concentration, stellar rotation, cluster mass, helium, and the environment of formation, but none of the proposed second parameters could satisfactorily reproduce the complex observed behavior."342. In particular. the most challenging task is to account for the formation of extreme horizontal branch (EHB) stars at. the faint hotter end of HBs (Tay 2200000. K). observed even in high metallicity clusters and old ope clusters?).," In particular, the most challenging task is to account for the formation of extreme horizontal branch (EHB) stars at the faint hotter end of HBs $_\mathrm{eff}\geq$ 000 K), observed even in high metallicity clusters and old open clusters."343. Stars hotter than this eritical temperature do not have an external envelope massive enough to sustain. the shell H-burning. and after the exhaustion of helium in the core they evolve directly to the white dwarf (WD) cooling sequence. without ascending the asymptotic giant branch2).," Stars hotter than this critical temperature do not have an external envelope massive enough to sustain the shell H-burning, and after the exhaustion of helium in the core they evolve directly to the white dwarf (WD) cooling sequence, without ascending the asymptotic giant branch."344. They are extensively observed and studied in the Galactic. field. identified as the so-called subdwarf type (sdB) stars(222).," They are extensively observed and studied in the Galactic field, identified as the so-called subdwarf B-type (sdB) stars."345. However. in GCs they are still poorly studied because of their faintness. and many questions. still await an answerreviews).," However, in GCs they are still poorly studied because of their faintness, and many questions still await an answer."346. Many single-star evolutionary channels have been invoked to explain EHB star formation in GCs. including interactions with a close planet?)mainBodyCitationEnd367|Soker98. helium mixing driven by either internal rotation or stellar encounters(?).. and close encounters with a central intermediate-mass black hole(?).," Many single-star evolutionary channels have been invoked to explain EHB star formation in GCs, including interactions with a close planet, helium mixing driven by either internal rotation or stellar encounters, and close encounters with a central intermediate-mass black hole."347. The dynamical interactions inside binary systems were proposed early on to be responsible for the heavy loss required to form a EHB star(??)., The dynamical interactions inside binary systems were proposed early on to be responsible for the heavy mass-loss required to form a EHB star.348". In the past decade. the ""binary scenario” has achieved many observational and theoretical successes among field sdB stars. and is now widely accepted as the most satisfactory explanation of their formation."," In the past decade, the ”binary scenario"" has achieved many observational and theoretical successes among field sdB stars, and is now widely accepted as the most satisfactory explanation of their formation."349 The binary population synthesis model of could reproduce their observational properties in great detail. although a small fraction of progenies of single stars Is probably required for a perfect match(2).," The binary population synthesis model of could reproduce their observational properties in great detail, although a small fraction of progenies of single stars is probably required for a perfect match."350.. Han's model considers three main. formation channels: the stable Roche Lobe Overflow (RLOF). which produces sdB's in wide binaries: the common envelope (CE) channel. which forms close systems: and the merging of two WDs. whose progenies are single stars.," Han's model considers three main formation channels: the stable Roche Lobe Overflow (RLOF), which produces sdB's in wide binaries; the common envelope (CE) channel, which forms close systems; and the merging of two WDs, whose progenies are single stars."351 On the other hand. many surveys have confirmed that a large fraction of field sdB stars reside in binaries(22222222). and sdB's in close systems with periods shorter than ten days are very common(????).. although the exact close-binary fraction is still uncertain. ranging from to(2).," On the other hand, many surveys have confirmed that a large fraction of field sdB stars reside in binaries, and sdB's in close systems with periods shorter than ten days are very common, although the exact close-binary fraction is still uncertain, ranging from to."352. Observations of EHB stars in GCs have so far presented a challenge to the binary. scenario. at variance with its well-established successes for field stars.," Observations of EHB stars in GCs have so far presented a challenge to the binary scenario, at variance with its well-established successes for field stars."353 The first surveys surprisingly revealed a lack of EHB close systems in GCs(?2)., The first surveys surprisingly revealed a lack of EHB close systems in GCs.354. fixed at the most probable value of the EHB close-binary fraction (fi) in6752.. proposing that a decrease in f. with the age of the stellar population should be a natural expectation of the binary scenario.," fixed at the most probable value of the EHB close-binary fraction $f_\mathrm{c}$ ) in, proposing that a decrease in $f_\mathrm{c}$ with the age of the stellar population should be a natural expectation of the binary scenario."355 The detailed calculations, The detailed calculations356"blue peak of the Paf line profile. but the two local ""maxima"" around the dip do not correspond to any obvious feature in. the emission line.","blue peak of the $\beta$ line profile, but the two local “maxima” around the dip do not correspond to any obvious feature in the emission line."357 Further inspection of the data revealed that the individual traces taken at opposite angles also show this pattern., Further inspection of the data revealed that the individual traces taken at opposite angles also show this pattern.358 Significantly however. the mmima and maxima occur at different wavelengths. and are therefore not reproduceable.," Significantly however, the minima and maxima occur at different wavelengths, and are therefore not reproduceable."359 A similar behaviour ts also found in the data of ¢ Tau. but in this case 1t is cancelled out after combination of the individual traces.," A similar behaviour is also found in the data of $\zeta$ Tau, but in this case it is cancelled out after combination of the individual traces."360" We therefore conclude that the traces in o Col that seem to display a ""periodic"" signal with an amplitude of less than a hundredth of a pixel are artefacts. as they are not reproduceable in otr. redundant. data."," We therefore conclude that the traces in $\alpha$ Col that seem to display a “periodic” signal with an amplitude of less than a hundredth of a pixel are artefacts, as they are not reproduceable in our, redundant, data."361 The reasons for this are unclear and future observations are planned to investigate this issue., The reasons for this are unclear and future observations are planned to investigate this issue.362 In summary. the data have a. statistical. precision of 0.3 mas. while larger scale artefacts of order slightly less than | mas are identified.," In summary, the data have a, statistical, precision of 0.3 mas, while larger scale artefacts of order slightly less than 1 mas are identified."363 The results for α Col and Z Tau are plotted in Fig. 1.., The results for $\alpha$ Col and $\zeta$ Tau are plotted in Fig. \ref{specast}.364 The top panels display the total intensity spectra while the bottom two, The top panels display the total intensity spectra while the bottom two365"The extra factor of e in equation (18)) accounts for a decrease in luminosity interval ο, in the presence of dust.",The extra factor of $e^{\tau}$ in equation \ref{oLFtLF}) ) accounts for a decrease in luminosity interval $dL$ in the presence of dust.366 Equations (17)) and (18)) imply that the true LE can be written and the ratio of observed to true LE normalisation as The observed comoving density of quasars brighter than some absolute maenitucle limit η as a function of recdshilt is computed by integrating the LE: Thus. the true comovinge number density Ny. can be casily calculated by replacing ©. in equation. (21) by (O.fOrJO. leading to the simple result: where the normalisation ratio is defined by equation (20)).," Equations \ref{oLF}) ) and \ref{oLFtLF}) ) imply that the true LF can be written and the ratio of observed to true LF normalisation as The observed comoving density of quasars brighter than some absolute magnitude limit $M_{lim}$ as a function of redshift is computed by integrating the LF: Thus, the true comoving number density $N_{t}$ , can be easily calculated by replacing $\phi_{o}$ in equation \ref{No}) ) by $\phi_{t}\equiv(\phi_{\ast t}/\phi_{\ast o})\phi_{o}$ leading to the simple result: where the normalisation ratio is defined by equation \ref{norm}) )."367 Figure6 shows both the observed and true comoving density of bright quasars (with Mg« 26) as a function of redshift., Figure\ref{comov} shows both the observed and true comoving density of bright quasars (with $M_{B}<-26$ ) as a function of redshift.368 The observed trends are empirical fits deduced by Pei (1995)., The observed trends are empirical fits deduced by Pei (1995).369" The true comoving density in all cases was determined. by assuming relatively ""weak evolution in the dust. properties of intervening galaxies.", The true comoving density in all cases was determined by assuming relatively `weak' evolution in the dust properties of intervening galaxies.370 Two sets of galactic dust. parameters for each qu defined by (rg.ro)=(1.10kpc) (Figs a and c) and (το.ο)=(8.30kpc) (Figs b and d) are assumed.," Two sets of galactic dust parameters for each $q_{0}$ defined by $(\tau_{B},r_{0})=(1,10{\rm kpc})$ (Figs a and c) and $(\tau_{B},r_{0})=(3,30{\rm kpc})$ (Figs b and d) are assumed."371 We shall refer to these as our. “minimal” and “maximal” dust model respectively which bracket the range of parameters observed for local galaxies., We shall refer to these as our “minimal” and “maximal” dust model respectively which bracket the range of parameters observed for local galaxies.372 Comparing the ‘true’ QSO redshift’ distribution with that observed. two features are apparent.," Comparing the `true' QSO redshift distribution with that observed, two features are apparent."373 First. the true number density vs. 2 relation has qualitatively the same behaviour as that observed.," First, the true number density vs. $z$ relation has qualitatively the same behaviour as that observed."374 No I[lattening or increase in true quasar numbers with z is apparent., No flattening or increase in true quasar numbers with $z$ is apparent.375" Second. there appears to be a shift in the redshift. 24,5. where the quasar density peaks."," Second, there appears to be a shift in the redshift, $z_{peak}$, where the quasar density peaks."376 ‘This shift is greatest. for our. maximal cust mocel, This shift is greatest for our maximal dust model377VHS flare of the 1998 outburst in Figure 4)).,VHS flare of the 1998 outburst in Figure \ref{cutoff_vs_index_1998}) ).378" Namely, the black and red data points follow clear non-monotonic curve starting from Efiq 150 keV and the index of 1.4 in LHS, decreasing to the minimum joi of 50 keV for the index of 2.0 at the start of the VHS flare and reaching the of 200 keV and the index of 2.9 at the VHS peak."," Namely, the black and red data points follow clear non-monotonic curve starting from $E_{fold}$ 150 keV and the index of 1.4 in LHS, decreasing to the minimum $E_{fold}$ of 50 keV for the index of 2.0 at the start of the VHS flare and reaching the $E_{fold}$ of 200 keV and the index of 2.9 at the VHS peak."379 Er;Then the source returned back to the values reached at the minimum., Then the source returned back to the values reached at the minimum.380" During the IS which followed after the VHS flare the source took different path marked by smaller index values and transitioneda to the HSS, shown by orange points."," During the IS which followed after the VHS flare the source took a different path marked by smaller index values and transitioned to the HSS, shown by orange points."381 The E’fgiq versus index shows clearly two-parametric behavior in this case., The $E_{fold}$ versus index shows clearly two-parametric behavior in this case.382" One possible explanation for this fact is that the VHS episode was triggered by strong surge of the matter with lower angular momentum, which then serves as a second parameter to define the source behavior."," One possible explanation for this fact is that the VHS episode was triggered by strong surge of the matter with lower angular momentum, which then serves as a second parameter to define the source behavior."383 During the 2000 outburst (Fig. 5)), During the 2000 outburst (Fig. \ref{cutoff_vs_index_2000}) )384 we see only the first part of this Erjj4—I pattern., we see only the first part of this $E_{fold}-\Gamma$ pattern.385" Namely, decreases and reaches down to its minimum value of Ef100-120iq keV while I' does not exceed 2.0 (compare Figs."," Namely, $E_{fold}$ decreases and reaches down to its minimum value of 100-120 keV while $\Gamma$ does not exceed 2.0 (compare Figs."386 4 and 5))., \ref{cutoff_vs_index_1998} and \ref{cutoff_vs_index_2000}) ).387 It is interesting to note that the HSS data (orange points) for the 1998 outburst in Figure 4 lie close to the 2000 outburst data for the HSS in Figure 5 points)., It is interesting to note that the HSS data (orange points) for the 1998 outburst in Figure \ref{cutoff_vs_index_1998} lie close to the 2000 outburst data for the HSS in Figure \ref{cutoff_vs_index_2000} (red points).388" This indicates that during transition to the (redcanonical HSS similar accretion regimes are at work for both outbursts, while during the VHS flare a unique and more rare accretion regime occurred possibly due to a supercritical accretion of matter having significant fraction of the low angular momentum gas."," This indicates that during transition to the canonical HSS similar accretion regimes are at work for both outbursts, while during the VHS flare a unique and more rare accretion regime occurred possibly due to a supercritical accretion of matter having significant fraction of the low angular momentum gas."389" The red VHS track on Figs. 4,,"," The red VHS track on Figs. \ref{cutoff_vs_index_1998},"390 6 and 7 is therefore can be attributed to the higher indexes and fluxes due to strong cooling and higher energy release to unusually high mass accretion rate during this state.," \ref{index_vs_bmc_norm1998} and \ref{cutoff_vs_bmc_norm1998}391 is therefore can be attributed to the higher indexes and fluxes due to strong cooling and higher energy release to unusually high mass accretion rate during this state."392" We see On the other hand, Farinelli&Titarchuk recently show using a number of BeppoSAX observation(2010) of accreting neutron stars that photon index of Comptonization spectra does not show strong evolution and, in fact, stays almost constant around 2.0 from the hard to soft states of neutron star binaries."," We see On the other hand, \cite{ft10} recently show using a number of SAX observation of accreting neutron stars that photon index of Comptonization spectra does not show strong evolution and, in fact, stays almost constant around 2.0 from the hard to soft states of neutron star binaries."393 Laurent&Titarchuk(2010) simulated spectra of the converging flow using Monte Carlo method., \cite{lt10} simulated spectra of the converging flow using Monte Carlo method.394 If was found that the cutoff folding energy Ero of the power law component first decreases and then increases as a function of mass accretion rate 7h., If was found that the cutoff folding energy $E_{fold}$ of the power law component first decreases and then increases as a function of mass accretion rate $\dot m$.395 The cutoff energy reaches its minimum around m~1., The cutoff energy reaches its minimum around $\dot{m}\sim 1$.396" Also they demonstrate that index of the emergent spectrum monotonically increases for 7>0.1 and then saturates in complete agreement with the observed picture shown in Figure 6,, where Np,,. is indicator of the disk mass accretion rate 7n. Because of this monotonic behavior of index vs mass accretion rate up to the saturation level we expect that the same behavior pattern Τ vs  and consequently Ero vs m should be seen in the observations."," Also they demonstrate that index of the emergent spectrum monotonically increases for $\dot m >0.1$ and then saturates in complete agreement with the observed picture shown in Figure \ref{index_vs_bmc_norm1998}, where $N_{bmc}$ is indicator of the disk mass accretion rate $\dot m$ Because of this monotonic behavior of index vs mass accretion rate up to the saturation level we expect that the same behavior pattern $\Gamma$ vs $\dot m$ and consequently $E_{fold}$ vs $\dot m$ should be seen in the observations."397 In Figure 7 we present the observed dependence of Eyoiq as a function of Nome {οςm)., In Figure \ref{cutoff_vs_bmc_norm1998} we present the observed dependence of $E_{fold}$ as a function of $N_{bmc}$ $\propto \dot m$ ).398" As one can see, the observed patterns of Er,j4 and I' versus Nome shown are strikingly similar to the Monte Carlo simulated folding energy and photon index evolution as a function of mass accretion rate [see Fig."," As one can see, the observed patterns of $E_{fold}$ and $\Gamma$ versus $N_{bmc}$ shown are strikingly similar to the Monte Carlo simulated folding energy and photon index evolution as a function of mass accretion rate [see Fig."399 8 and details of these simulations in Laurent&Titarchuk (2, \ref{cutoff_vs_mass_rate_MC} and details of these simulations in \cite{lt10}] ].400"010)]. Groveetal.(1998) reported the results of OSSE observations of seven transient black hole candidates: GRO J0422+32, GX 339-4, GRS 1716-249, GRS 1009-45, 4U 1543-47, GRO J1655-40, and GRS 1915-105."," \cite{grove98} reported the results of OSSE observations of seven transient black hole candidates: GRO J0422+32, GX 339-4, GRS 1716-249, GRS 1009-45, 4U 1543-47, GRO J1655-40, and GRS 1915-105."401" They found that the last four objects exhibit a “power-law gamma-ray state"" with a soft spectral index (T'~2.5—3) and no evidence for a spectral break.", They found that the last four objects exhibit a “power-law gamma-ray state” with a soft spectral index $\Gamma\sim2.5-3$ ) and no evidence for a spectral break.402" For GRO J1655-40, the lower limit on the break energy was found to be 690 keV. Although Groveetal. suggested that the HSS spectra detected by OSSE are (1998)consistent with bulk-motion Comptonization in the convergent accretion flow, Zdziarskietal.(2001) reinterpreted the same data and ruled out the bulk Comptonization as an origin of the HSS spectra because the emergent spectra extended to energies up to 700 keV. Thus, the question is which instrument more accurately describes the phenomenology of the high energy cutoff, OSSE or RXTE/HEXTE."," For GRO J1655-40, the lower limit on the break energy was found to be 690 keV. Although \cite{grove98} suggested that the HSS spectra detected by OSSE are consistent with bulk-motion Comptonization in the convergent accretion flow, \cite{zdz01} reinterpreted the same data and ruled out the bulk Comptonization as an origin of the HSS spectra because the emergent spectra extended to energies up to 700 keV. Thus, the question is which instrument more accurately describes the phenomenology of the high energy cutoff, OSSE or /HEXTE."403 Answer to this question is crucial for understanding and interpretation of the BH spectral signatures., Answer to this question is crucial for understanding and interpretation of the BH spectral signatures.404"In that respect we note that the typical OSSE spectrum require exposure time of about 10° s, i.e more than a day, whereas a typical PCA/HEXTE observation lasts a few kiloseconds, two","In that respect we note that the typical OSSE spectrum require exposure time of about $10^5$ s, i.e more than a day, whereas a typical PCA/HEXTE observation lasts a few kiloseconds, two"405effects which cau introduce spurious ellipticity correlations.Fragimentation:,effects which can introduce spurious ellipticity correlations.:406: A siguificaut fraction of radio sources have a structure. and are broken iuto two components by the object finder.," A significant fraction of radio sources have a double-lobe structure, and are broken into two components by the object finder."407" Because these fraeimienuts tend to be alieued. this produces cllipticity correlations 6n πια angular scales,"," Because these fragments tend to be aligned, this produces ellipticity correlations on small angular scales."408 An analvsis of the excess signal in the correlation unction of FIRST source positions reveals. however. that this effect is uceligible or 0z1’.," An analysis of the excess signal in the correlation function of FIRST source positions reveals, however, that this effect is negligible for $\theta \gtrsim 10'$."409 Because the FIRST survey was derived from uterferoimoetric 6ybservations. the noise iu its nuages is spatially correlated. as is apparent iu ie presence of “stripes” in the noise.," Because the FIRST survey was derived from interferometric observations, the noise in its images is spatially correlated, as is apparent in the presence of “stripes” in the noise."410 The consequence of noise correlation on source cllipticitics was investigated in detais in ref. |l.," The consequence of noise correlation on source ellipticities was investigated in detais in ref. \cite{ref98b},"411 where it was found iat. while the effect is important on small scales. it is neelieible for 0>1’.," where it was found that, while the effect is important on small scales, it is negligible for $\theta \gtrsim 1'$."412 Spurious shape correlations can also be produced by watial variations of the effective couvolution beam., Spurious shape correlations can also be produced by spatial variations of the effective convolution beam.413 The beam shape mostly epeuds onthe orientations of the VLA antennae at the time of the observation. ud can thus be modeled and corrected for. a posteriori.," The beam shape mostly depends on the orientations of the VLA antennae at the time of the observation, and can thus be modeled and corrected for, a posteriori."414 We are currently udving the magnitude of this effect and its consequence for weak leasing lueasurenients., We are currently studying the magnitude of this effect and its consequence for weak lensing measurements.415 If. as we expect. the effect beam distortion can be corrected for. the FIRST survey will allow us to detect. or at least to set a tight upper luit ou. the weak eusing power spectruui on 0.2-20 degree scales.," If, as we expect, the effect beam distortion can be corrected for, the FIRST survey will allow us to detect, or at least to set a tight upper limit on, the weak lensing power spectrum on 0.2-20 degree scales."416 Since these scales correspond o the linear regime. our measurement will be easy to compare to theoretical xedietious.," Since these scales correspond to the linear regime, our measurement will be easy to compare to theoretical predictions."417 Our preliminary measurement of the shear correlation fuuctiou already leads to upper limits that are close to the cluster-normalized CDM xedietious., Our preliminary measurement of the shear correlation function already leads to upper limits that are close to the cluster-normalized CDM predictions.418 Our experiment will complement similar mecasurcients in the 6optical band. which are mostly sensitive to smaller angular scales.," Our experiment will complement similar measurements in the optical band, which are mostly sensitive to smaller angular scales."419Jarvis et al. (,Jarvis et al. (4202001€). investigated the radio luminosity function for the most radio bIuminous low-Lrequeney selected sources.,2001c) investigated the radio luminosity function for the most radio luminous low-frequency selected sources.421 The data used in their analysis were drawn from the complete 3CRR. 6CE and filtered 6C* samples by imposing a lower limit in racio luminosity.," The data used in their analysis were drawn from the complete 3CRR, 6CE and filtered 6C* samples by imposing a lower limit in radio luminosity."422" Only the sources which lie in the top-decade in logy,Lis; wereconsidered""."," Only the sources which lie in the top-decade in $\log_{10}\, L_{151}$ were."423. Focusing on onlv the most luminous sources provided the largest »ossible baseline in redshift for the samples considered. while minimizing the role plaved (in the modelling procedure) by he intrinsic correlations between sample parameters. such as luminosity - spectral index and linear size - spectral index correlations. which are inherent to radio samples (Dluncdell. vwlings Willott 1999).," Focusing on only the most luminous sources provided the largest possible baseline in redshift for the samples considered, while minimizing the role played (in the modelling procedure) by the intrinsic correlations between sample parameters, such as luminosity - spectral index and linear size - spectral index correlations, which are inherent to radio samples (Blundell, Rawlings Willott 1999)."424 The filtered 6C7 sample represented the. greates advanee of this study over earlier work on the high-redshif QLE of. low-frequeney selected: radio sources. (Willott ο al., The filtered 6C* sample represented the greatest advance of this study over earlier work on the high-redshift RLF of low-frequency selected radio sources (Willott et al.425 2001)., 2001).426 However. its use required that the ellects of he selection criteria. namely small angular size ancl steep radio spectral index. and in particular the fraction of sources which were missing from the survey. were taken into consideration in the modelling of the ILE.," However, its use required that the effects of the selection criteria, namely small angular size and steep radio spectral index, and in particular the fraction of sources which were missing from the survey, were taken into consideration in the modelling of the RLF."427 This Led to a parameterisation which was separable in luminosity ane redshift (as in Jarvis Rawlines 2000 and in Willott et al., This led to a parameterisation which was separable in luminosity and redshift (as in Jarvis Rawlings 2000 and in Willott et al.428 2001). and also incorporated distributions in radio spectra shape and linear size. i.e. where p« is the normalising factor and a free parameter measured in units of pe(Lisi). plo). pate.as) and pp(D) are cimensionless distribution. functions in radio luminosity. redshift. spectral shape parameters. aud projected linear size. respectively.," 2001), and also incorporated distributions in radio spectral shape and linear size, i.e. where $\rho_{\circ}$ is the normalising factor and a free parameter measured in units of $^{-3}$ $\rho_{L}(L_{151})$ , $\rho (z)$, $\rho_{a} (a_{1},\,a_{2})$ and $\rho_{D} (D)$ are dimensionless distribution functions in radio luminosity, redshift, spectral shape parameters and projected linear size, respectively."429 The full form of these distributions and their modelling are described. in detail in Jarvis et al. (, The full form of these distributions and their modelling are described in detail in Jarvis et al. (43020010).,2001c).431 We now comment on the shape of the redshift distribution. for which Jarvis ot al. (," We now comment on the shape of the redshift distribution, for which Jarvis et al. ("43220010) tested three cüllerent models.,2001c) tested three different models.433 The mociel favourecl by their maximum likelihood analysis (model €) uses a T-tailed Gaussian to paramoeterise the Ilow-redshift co-moving space density and a power-law distribution at high redshift. ie where z« is the ‘hreak’ redshift where the model switches from the low- to the high-redshift form. zj is the characteristic width of the hall-Gaussian and 7 is the power-law exponent describing the high-redshift co-moving space densitv.," The model favoured by their maximum likelihood analysis (model C) uses a 1-tailed Gaussian to parameterise the low-redshift co-moving space density and a power-law distribution at high redshift, i.e where $z_{\circ}$ is the `break' redshift where the model switches from the low- to the high-redshift form, $z_{1}$ is the characteristic width of the half-Gaussian and $\eta$ is the power-law exponent describing the high-redshift co-moving space density."434 The other models. tested. by Jarvis et al. (, The other models tested by Jarvis et al. (4352001c) were: model X — paramoeterised as a single Gaussian clistribution in redshift: and. model Boa I-12iled. Gaussian which becomes constant and equal to unity bevond the Gaussian peak. Le. the same as model € with 5 fixed at zero.,"2001c) were: model A – parameterised as a single Gaussian distribution in redshift; and, model B – a 1-tailed Gaussian which becomes constant and equal to unity beyond the Gaussian peak, i.e. the same as model C with $\eta$ fixed at zero."436 The advantage of model € over the other models is that: (1) it breaks the svmimetry between low- and high-redshift evolution which is forced by model A (and for which there is no physical basis). and (it) allows for freedom in the evolution at high-redshift which is not possible with mocel D. Model €. is therefore more useful in terms of assessing the form of the evolution of the co-moving space density at high recdshift.," The advantage of model C over the other models is that: (i) it breaks the symmetry between low- and high-redshift evolution which is forced by model A (and for which there is no physical basis), and (ii) allows for freedom in the evolution at high-redshift which is not possible with model B. Model C, is therefore more useful in terms of assessing the form of the evolution of the co-moving space density at high redshift."437 Jarvis et al. (, Jarvis et al. (43820010) found a best-fitting power-law exponent y=0.06 (in their Cosmology. LL). implying a Constant co-moving space density bevond a peak redshift of 2=2.15 to an indeterminable redshift.,"2001c) found a best-fitting power-law exponent $\eta =439-0.06$ (in their Cosmology II), implying a constant co-moving space density beyond a peak redshift of $z_{\circ} = 2.15$ to an indeterminable redshift."440 A steep decline has been ruled out by their analysis at the ~4e level. but the form of the evolution at high redshift remained. unresolved with an uncertainty encompassing both moderate declines and continuing shallow inclines.," A steep decline has been ruled out by their analysis at the $\sim 4 \sigma$ level, but the form of the evolution at high redshift remained unresolved with an uncertainty encompassing both moderate declines and continuing shallow inclines."441 To investigate the co-moving space density. of. high-redshift steep-spectrum radio sources. we now compare the redshift estimates derived. from the GC data. with the ILE of low-frequeney selected radio sources of Jarvis ct al. (," To investigate the co-moving space density of high-redshift steep-spectrum radio sources, we now compare the redshift estimates derived from the 6C** data with the RLF of low-frequency selected radio sources of Jarvis et al. ("44220010).,2001c).443 ‘To be able to compare the 6C data with the RLF model of Jarvis et al. (, To be able to compare the 6C** data with the RLF model of Jarvis et al. (444200160). we must select the most racio Luminous sources in the sample in a fashion that is equivalent to that of Jarvis et al. (,"2001c), we must select the most radio luminous sources in the sample in a fashion that is equivalent to that of Jarvis et al. ("44520016).,2001c).446 For that we use the definition of top- in cosmology HE of Jarvis et al. (, For that we use the definition of top-decade in cosmology II of Jarvis et al. (447"20016) and translate is lower radio luminosity limit to log),Lis,227.61 in the cosmology used in this paper (Qa,=0.3. Ὃν=0.7. iy =70kms+ 1)","2001c) and translate its lower radio luminosity limit to $\log_{10}\, L_{151} \geq 27.61$ in the cosmology used in this paper $\Omega_{M} = 0.3$, $\Omega_{\Lambda} = 0.7$, $H_{0} = 70$ km $^{-1}$ $^{-1}$ )."448" ""Phis means that. based. strictly on the estimated. Lizi> diagram (Lig 9: top-panel). 12 of the 6C** sources are selected."," This means that, based strictly on the estimated $L_{151}-z$ diagram (Fig \ref{fig:pzestimated}: top-panel), 12 of the 6C** sources are selected."449 However. if we consider also the spectroscopic redshifts available. ie. by replacing estimated redshifts with spectroscopic ones where these are available (Fig 9:: bottom-panel). then there are17 sources in the top decade of radio Luminosity.," However, if we consider also the spectroscopic redshifts available, i.e. by replacing estimated redshifts with spectroscopic ones where these are available (Fig \ref{fig:pzestimated}: bottom-panel), then there are17 sources in the top decade of radio luminosity."450 Phese sources are Listed in Table 3.. and. include 6€Y53715618.," These sources are listed in Table \ref{tab:top-decade}, and include 6C**0737+5618."451 Ehe inclusion of this source is cüscussed in more detail in Section 3.., The inclusion of this source is discussed in more detail in Section \ref{sec:pdfdistribution}.452 We note that two of the quasars with under-estimated redshifts (ancl luminosities) are now in the top-decade., We note that two of the quasars with under-estimated redshifts (and luminosities) are now in the top-decade.453 A few of the quasars without spectra are also expected to move into the top-decade once their redshifts are known., A few of the quasars without spectra are also expected to move into the top-decade once their redshifts are known.454 We consider two ways of constructing the binned redshift , We consider two ways of constructing the binned redshift distribution of 6C** sources in the top-decade of luminosity.455In Section. 7.2.2... we use spectroscopic redshifts when available. and otherwise the best-fitting redshift estimates.ic. we consider the sources listed in Table 3 (see also Fig 9: bottom-panel).," In Section \ref{sec:best-fitting}, we use spectroscopic redshifts when available, and otherwise the best-fitting redshift estimates,i.e. we consider the sources listed in Table \ref{tab:top-decade} (see also Fig \ref{fig:pzestimated}: bottom-panel)."456 In Section 7.2.3.. we take into account the redshift) probability distribution of cach source.," In Section \ref{sec:pdfdistribution}, , we take into account the redshift probability distribution of each source."457 Both, Both458"As well as εε and nn correlations themselves, we can cross-correlate the two fields to form the galaxy position-shear, ne, cross-correlation functions as first proposed by ? in the context of dark energy.","As well as $\epsilon\epsilon$ and $nn$ correlations themselves, we can cross-correlate the two fields to form the galaxy position-shear, $n\epsilon$, cross-correlation functions as first proposed by \citet{huj04} in the context of dark energy."459" This is often referred to as galaxy-galaxy lensing, in which the mass of a foreground galaxy distorts the shape of a background galaxy."," This is often referred to as galaxy-galaxy lensing, in which the mass of a foreground galaxy distorts the shape of a background galaxy."460" Here we consider the general cross-correlation which includes contributions from larger dark matter structures, from magnification and also from intrinsic alignments if the correlated galaxies are physically close."," Here we consider the general cross-correlation which includes contributions from larger dark matter structures, from magnification and also from intrinsic alignments if the correlated galaxies are physically close."461 We can write the contributions to the full ne term as (?).., We can write the contributions to the full $n\epsilon$ term as \citep{joachimi_bridle_2009}.462" The individual expressions for the terms in the C""*(I) expansion contain combinations of quantities already considered where we have introduced the additional free functions rg and ΤΙ which appear due to the possible stochastic relation between the galaxy and dark matter distributions (?) as discussed in section below.", The individual expressions for the terms in the $C^{n\epsilon}(l)$ expansion contain combinations of quantities already considered where we have introduced the additional free functions $r_{g}$ and $r_{I}$ which appear due to the possible stochastic relation between the galaxy and dark matter distributions \citep{dekell99} as discussed in section \ref{sec:bias} below.463" As before Pss(k,x)=Προς) x)."," As before $P_{\delta\delta}(k,\chi) \equiv P_{\delta\delta}(\frac{l}{f_{K}(\chi)},\chi)$ ."464" We note that 3|Per(k,x) appears in the C?(1) term because it describes how the dark matter distribution relates to the intrinsic alignments, and we assume the relation between the galaxy distribution and the dark matter distribution can be accounted for by the product bgrg."," We note that $P_{GI}(k,\chi)$ appears in the $C_{ij}^{gI}(l)$ term because it describes how the dark matter distribution relates to the intrinsic alignments, and we assume the relation between the galaxy distribution and the dark matter distribution can be accounted for by the product $b_{g} r_{g}$ ."465 'The observables considered in this paper and the different fields which contribute to each observable are summarised in Table [I]., The observables considered in this paper and the different fields which contribute to each observable are summarised in Table \ref{tab:summary}.466 In Fig., In Fig.467 we plot the angular power spectra of all considered components[I] for a fiducial stage-IV lensing survey., \ref{fig:cls_full} we plot the angular power spectra of all considered components for a fiducial stage-IV lensing survey.468" For our fiducial model in this paper we use the following survey specification: 20,000 deg? with a galaxy number density of 35 arcmin? and a redshift distribution given by the Smail-type n(z), with a=2, 8=1.5, zo.=0.9/2, divided into 10 tomographic bins with equal number density out to redshift 3 and normalised so that n(z)dz— 1."," For our fiducial model in this paper we use the following survey specification: 20,000 $^2$ with a galaxy number density of 35 $^{-2}$ and a redshift distribution given by the Smail-type $n(z)$, with $\alpha=2$, $\beta=1.5$, $z_0=0.9/\sqrt{2}$, divided into 10 tomographic bins with equal number density out to redshift 3 and normalised so that $\int n(z) dz = 1$ ."469 A Gaussian photometric redshift error of c;=f0.05(1+2) is assumed with no catastrophic outliers in redshift., A Gaussian photometric redshift error of $\sigma_z = 0.05(1+z)$ is assumed with no catastrophic outliers in redshift.470" We constrain the set of cosmological parameters {Qm,Wo,wa,h,08,0s,Ms} which take the values Qn=0.25, wo=-—1, wa=O0, h=0.7, σε=0.8, Qh=0.05, n,=1."," We constrain the set of cosmological parameters $\left\{ \Omega_m, w_0, w_a, h, \sigma_8, \Omega_b, n_s \right\}$ which take the values $\Omega_m=0.25$, $w_0=-1$, $w_a=0$, $h=0.7$, $\sigma_8=0.8$, $\Omega_b=0.05$, $n_s=1$."471" All results assume a flat, ACDM cosmology."," All results assume a flat, $\Lambda$ CDM cosmology."472 Linear matter power spectrum is calculated using the ? fitting function and nonlinear corrections are applied where appropriate using the ? formalism., Linear matter power spectrum is calculated using the \citet{eisensteinhu97} fitting function and nonlinear corrections are applied where appropriate using the \citet{smithea03} formalism.473 Fig., Fig.474 [I] is presented and formatted in the same way as Fig., \ref{fig:cls_full} is presented and formatted in the same way as Fig.475 3 in ?.., 3 in \citet{joachimi_bridle_2009}. .476 The purpose is to supply a new reference plot using the most up to date implementation of the LA model for IAs., The purpose is to supply a new reference plot using the most up to date implementation of the LA model for IAs.477 All lines which do not include an “I” term will be identical in both versions of the plot., All lines which do not include an “I” term will be identical in both versions of the plot.478" However, as ? use the original HS04 implementation, from before the publication of the erratum incorporated into ?,, and present lines for the NLA ansatz, there are differences in any lines containing an I contribution."," However, as \citet{joachimi_bridle_2009} use the original HS04 implementation, from before the publication of the erratum incorporated into \citet{hiratas10_posterratum}, and present lines for the NLA ansatz, there are differences in any lines containing an I contribution."479 The NLA version of HS04 is the most widely used in the literature to date; we refer to it subsequently as HSO4NL., The NLA version of HS04 is the most widely used in the literature to date; we refer to it subsequently as HS04NL.480 Note that that we are employing the NLA prescription in HSO4NL even though this was not explicitly discussed in the original ? paper., Note that that we are employing the NLA prescription in HS04NL even though this was not explicitly discussed in the original \citet{hiratas04} paper.481 See the appendix for a more detailed explanation of the evolution of the LA model and the differences between various implementations., See the appendix for a more detailed explanation of the evolution of the LA model and the differences between various implementations.482 The upper triangle of Fig., The upper triangle of Fig.483 [I] shows the contributions to the shear-shear correlation function in black for every other tomographic bin pairing., \ref{fig:cls_full} shows the contributions to the shear-shear correlation function in black for every other tomographic bin pairing.484" As usual the lensing contribution is the largest on all angular scales, but is most dominant in the auto-correlations at high redshift."," As usual the lensing contribution is the largest on all angular scales, but is most dominant in the auto-correlations at high redshift."485 The II intrinsic alignment term is most important in the auto-correlations and negligible for widely spaced bins., The II intrinsic alignment term is most important in the auto-correlations and negligible for widely spaced bins.486 The GI contribution is largest for separated bins (shown as IG for compactness - see caption)., The GI contribution is largest for separated bins (shown as IG for compactness - see caption).487 The intrinsic alignment contributions are typically one to ten per cent of the lensing signal., The intrinsic alignment contributions are typically one to ten per cent of the lensing signal.488" The contributions to the position-position correlation function are shown in pink in the upper triangle and as expected, the auto-correlations are dominated by the intrinsic clustering of galaxies."," The contributions to the position-position correlation function are shown in pink in the upper triangle and as expected, the auto-correlations are dominated by the intrinsic clustering of galaxies."489 The cross-correlations of separated bins can be dominated by the cross-correlation of galaxy clustering and magnification., The cross-correlations of separated bins can be dominated by the cross-correlation of galaxy clustering and magnification.490" As expected, the magnification-only term is most important at high redshift, although it never exceeds the other terms for the redshift ranges we consider."," As expected, the magnification-only term is most important at high redshift, although it never exceeds the other terms for the redshift ranges we consider."491" The lower triangle shows the various contributions to the position-shear cross-correlation function, and shows the effect of reversing the tomographic bin order where relevant (see caption)."," The lower triangle shows the various contributions to the position-shear cross-correlation function, and shows the effect of reversing the tomographic bin order where relevant (see caption)."492 The correlation between lensing shear and galaxy clustering is the strongest of these contributions and is largest when the tomographic bins are separated with the galaxies in the foreground., The correlation between lensing shear and galaxy clustering is the strongest of these contributions and is largest when the tomographic bins are separated with the galaxies in the foreground.493 This is the usual galaxy- lensing contribution., This is the usual galaxy-galaxy lensing contribution.494 Interestingly it is still large in the auto-correlations whichis due to the galaxies inthe nearest part of the redshift bin lensing the galaxiesin the farthest part., Interestingly it is still large in the auto-correlations whichis due to the galaxies inthe nearest part of the redshift bin lensing the galaxiesin the farthest part.495 There is a non-negligible contribution in, There is a non-negligible contribution in496"emerging from the core C and an earlier phase of the jet activity is represented by components A, and B. Because of their symmetry with respect to the radio core, we treated them as jet and counter-jet, respectively.","emerging from the core C and an earlier phase of the jet activity is represented by components $A_{1}$ and B. Because of their symmetry with respect to the radio core, we treated them as jet and counter-jet, respectively."497" Thejet/counter-jet brightness ratio is given by: where f is the speed, ϐ is an angle between the jet axis and the jet/counter-jetline of sight and is the jet average spectral index."," The brightness ratio is given by: where $\beta$ is the jet/counter-jet speed, $\theta$ is an angle between the jet axis and the line of sight and $\alpha_{jet}$ is the jet average spectral index."498" The value of the sidenessoj, parameter is R~13.5.", The value of the sideness parameter is $\rm R\sim13.5$.499 Then assuming a typical value of the spectral index aj=0.75 and jet speed 8=0.9c we obtained the value of the angle thebetween the jet axis and the line of sight to be 0~ 61°.," Then assuming a typical value of the spectral index $\alpha_{jet}=0.75$ and the jet speed $\beta=0.9\,c$ we obtained the value of the angle between the jet axis and the line of sight to be $\theta\sim61\degr$ ."500" However, 0 varies in the range 51°—64? for 8 and aj values in the range 0.7c—0.98c and 0.7—1.1 respectively."," However, $\theta$ varies in the range $\rm50151\degr-64\degr$ for $\beta$ and $\alpha_{jet}$ values in the range $\rm 0.7\,c-0.98\,c$ and $\rm 0.7-1.1$ respectively."502 This may indicate a large change between the orientation of 10454-352 radio structures on the different scales and fits well into the picture of complicated radio morphology., This may indicate a large change between the orientation of 1045+352 radio structures on the different scales and fits well into the picture of complicated radio morphology.503" An assumption of 0—30?61? yields the deprojected linear size of the source of ~5—9 kpc, also indicatinga young radio source."," An assumption of $\theta=30\degr-61\degr$ yields the deprojected linear size of the source of $\sim5-9$ kpc, also indicatinga young radio source."504"the Collect Collapse process tend to be massive (afewhundredMo, and so this process could naturally explain the hierarchical nature of massive stellar clusters (e.g.??)..","the Collect Collapse process tend to be massive \citep[a few hundred M$_{\odot}$ and so this process could naturally explain the hierarchical nature of massive stellar clusters \citep[e.g.][]{bastian2005,oey2005}."505 It should be noted that neither mechanism excludes the other as a means of triggering star formation., It should be noted that neither mechanism excludes the other as a means of triggering star formation.506" Indeed, within a single HII region both RDI and Collect Collapse may operate together (?).."," Indeed, within a single HII region both RDI and Collect Collapse may operate together \citep{deharveng2005}."507" However, recent models of the ionising feedback from massive stars (?) suggest that neither mechanism is responsible and that the UV illumination from these stars simply erodes low density material rather than shaping its evolution and eventual collapse."," However, recent models of the ionising feedback from massive stars \citep{dale2011} suggest that neither mechanism is responsible and that the UV illumination from these stars simply erodes low density material rather than shaping its evolution and eventual collapse."508" In this scenario, the role of triggering in star formation is predicted to be minimal."," In this scenario, the role of triggering in star formation is predicted to be minimal."509 ? find that the location of the dense clumps around the edge of HII regions (such as RCW 120) reflects the pre-existing cloud structure and their formation does not require the Collect Collapse process., \citet{walch2011} find that the location of the dense clumps around the edge of HII regions (such as RCW 120) reflects the pre-existing cloud structure and their formation does not require the Collect Collapse process.510" However, rather than neglecting triggering as in 7, they suggest that stars may form by global implosion of the pre-existing structures (Enhancement of initial Density substructure and simultaneous Global Implosion, or EDGI)."," However, rather than neglecting triggering as in \citet{dale2011}, they suggest that stars may form by global implosion of the pre-existing structures (Enhancement of initial Density substructure and simultaneous Global Implosion, or EDGI)."511" Observational studies of triggered star formation have so far mainly focused on photoionised globules (Bright-RimmedCloudsorBRCs,??) found at the edges of or on the rims of HII regions selected to show relatively simple morphology (???).."," Observational studies of triggered star formation have so far mainly focused on photoionised globules \citep[Bright-Rimmed Clouds or BRCs,][]{sugitani1991,sugitani1994} found at the edges of optically visible HII regions \citep{thompson2004a, urquhart2004,morgan2004, urquhart2006,morgan2008} or on the rims of HII regions selected to show a relatively simple morphology \citep{deharveng2005,zavagno2006,pomares2009}."512 Recent studies of thea latter have been able to take advantage of the large catalogue of infrared bubbles discovered in the GLIMPSE survey (??)..," Recent studies of the latter have been able to take advantage of the large catalogue of infrared bubbles discovered in the GLIMPSE survey \citep{churchwell2006,churchwell2007}. ."513" The properties of these bubbles are consistent with expanding HII regions (??),, although perhaps more consistent with a ring rather than bubble morphology (?).."," The properties of these bubbles are consistent with expanding HII regions \citep{deharveng2010, watson2009}, although perhaps more consistent with a ring rather than bubble morphology \citep{beaumont2010}."514" However, one difficulty with many of these studies is that they are often phenomenological in nature, concentrating upon the visual identification of YSOs or protostars in regions where one might have a prior expectation that they may have been triggered (e.g.???).."," However, one difficulty with many of these studies is that they are often phenomenological in nature, concentrating upon the visual identification of YSOs or protostars in regions where one might have a prior expectation that they may have been triggered \citep[e.g.][]{zavagno2006,zavagno2007,deharveng2010}."515" Such studies cannot attack the central problem in triggered star formation, which is to identify the origin of the discovered star formation (we refer to this as the ""Origin Problem"")."," Such studies cannot attack the central problem in triggered star formation, which is to identify the origin of the discovered star formation (we refer to this as the “Origin Problem”)."516 When trying to identify star formation as being triggered one must first exclude the possibility that the star(s) would have formed spontaneously without the influence of the trigger., When trying to identify star formation as being triggered one must first exclude the possibility that the star(s) would have formed spontaneously without the influence of the trigger.517 The Origin Problem is particularly intractable when considering individual objects — without a good understanding of the initial conditions involved it is almost impossible to categorise an individual star-forming region as being triggered or spontaneous., The Origin Problem is particularly intractable when considering individual objects — without a good understanding of the initial conditions involved it is almost impossible to categorise an individual star-forming region as being triggered or spontaneous.518 In this paper we attempt to move beyond the current phenomenological approach by carrying out a detailed statistical study of star formation around the 322 bubbles of ?.., In this paper we attempt to move beyond the current phenomenological approach by carrying out a detailed statistical study of star formation around the 322 bubbles of \citet{churchwell2006}.519" While the Origin Problem is almost impossible to solve for individual star-forming regions, by considering the global properties of a large sample it may be possible to infer the presence of triggering in a statistical sense."," While the Origin Problem is almost impossible to solve for individual star-forming regions, by considering the global properties of a large sample it may be possible to infer the presence of triggering in a statistical sense."520" These studies are made easier by the existence of large, uniformly selected and well-understood star formation surveys such as the RMS survey (?).."," These studies are made easier by the existence of large, uniformly selected and well-understood star formation surveys such as the RMS survey \citep{urquhart2008}."521 The RMS survey has the goal of identifying every massive young stellar object (YSO) in the Milky Way and comprises an initial infrared selection followed by thorough multi-wavelength follow-up to rigorously classify each object and determine its physical ," The RMS survey has the goal of identifying every massive young stellar object (YSO) in the Milky Way and comprises an initial infrared selection followed by thorough multi-wavelength follow-up to rigorously classify each object and determine its physical properties \citep{urquhart2009b,urquhart2009a,mottram2011a,urquhart2011}."522The RMS survey covers a greater area than the GLIMPSE-I survey region in which the ? bubbles have been identified and is complete to YSOs of luminosity 2104 Lo out to the furthest bubble in the ? catalogue., The RMS survey covers a greater area than the GLIMPSE-I survey region in which the \citet{churchwell2006} bubbles have been identified and is complete to YSOs of luminosity $\ge$ $^{4}$ $_{\odot}$ out to the furthest bubble in the \citet{churchwell2006} catalogue.523 Hence we can conduct a survey for recent massive star formation around of the bubbles (see Fig., Hence we can conduct a survey for recent massive star formation around of the bubbles (see Fig.524 1 for an example)., \ref{fig:bubble} for an example).525 Note that the RMS survey does not include Galactic latitudes [|<10? ffor reasons of cofusion and so we do not consider here the bubble catalogue of ? which is based solely upon the GLIMPSE-II survey region (ie. |||& 10°))., Note that the RMS survey does not include Galactic latitudes $|l|\le10$ for reasons of cofusion and so we do not consider here the bubble catalogue of \citet{churchwell2007} which is based solely upon the GLIMPSE-II survey region (i.e. $|l|\le10$ ).526" On the other hand we must keep in mind the intrinsic subjective biases in the catalogue of bubbles, due to their manual by-eye identification by a number of independent observers (?).."," On the other hand we must keep in mind the intrinsic subjective biases in the catalogue of bubbles, due to their manual by-eye identification by a number of independent observers \citep{churchwell2006}."527 These biases are discussed in detail in Section 2 of ?.., These biases are discussed in detail in Section 2 of \citet{churchwell2006}.528" The current catalogue is likely to be highly incomplete, particularly to small bubbles."," The current catalogue is likely to be highly incomplete, particularly to small bubbles."529" ? estimate a completeness on the order of ~50%,, which is being borne out by early results from the citizen science Milky Way (Simpson et al."," \citet{churchwell2006} estimate a completeness on the order of $\sim$, which is being borne out by early results from the citizen science Milky Way (Simpson et al."530" 2012, in prep)."," 2012, in prep)."531" Nevertheless, the ? catalogue of bubbles currently represents the most complete and well-studied catalogue of HII regions with a simple morphology that lends well to statistical studies of their YSO distribution."," Nevertheless, the \citet{churchwell2006} catalogue of bubbles currently represents the most complete and well-studied catalogue of HII regions with a simple morphology that lends well to statistical studies of their YSO distribution."532" In this paper we present such a study, paying particular attention to the angular distribution of YSOs around the bubbles and potential differences within the YSO population."," In this paper we present such a study, paying particular attention to the angular distribution of YSOs around the bubbles and potential differences within the YSO population."533 Our aims are to providestatistical evidence that the star formation associated with the bubbles may have been triggered and to, Our aims are to providestatistical evidence that the star formation associated with the bubbles may have been triggered and to534working ofa &-mechanism. one would expect a large number of modes to be excited. simultaneously. (,"working of a $\kappa$ -mechanism, one would expect a large number of modes to be excited simultaneously. ("535Phe involved thermal time scale is of the order of a day and the period spacing around an oscillation period of one day is 3«10.7 davs.),The involved thermal time scale is of the order of a day and the period spacing around an oscillation period of one day is $3 \times 10^{-3}$ days.)536 The observed. situation calls for a sharp resonance condition that destabilizes particular modes only., The observed situation calls for a sharp resonance condition that destabilizes particular modes only.537 Since it seems quite certain that we have serencipitously discovered a new class of variable stars. it is important to. produce better models of carly E stars so that we can understand under what conditions these stars show evidence for radial pulsations.," Since it seems quite certain that we have serendipitously discovered a new class of variable stars, it is important to produce better models of early F stars so that we can understand under what conditions these stars show evidence for non-radial pulsations."538 Phe most useful data to obtain in the near future would, The most useful data to obtain in the near future would539that these clusters iav actually consist of nuurelatec overdeusities projected along the same line-of-sight.,that these clusters may actually consist of unrelated overdensities projected along the same line-of-sight.540 We now proceed to a detailed comparison with P96 clusters., We now proceed to a detailed comparison with P96 clusters.541 The original PDCS catalog cousists of 19 clusters detected by the matched filter algorithm both in the Vy) baud aud in the Z; baud (see P96. Table 1).," The original PDCS catalog consists of 19 clusters detected by the matched filter algorithm both in the $V_{4}$ band and in the $I_{4}$ band (see P96, Table 4)."542 Furthermore. the PDCS catalog lists 7 clusters detected only in the Wy band aud. added to the catalog after visual inspection of 5v ! Pun. 5).," Furthermore, the PDCS catalog lists 7 clusters detected only in the $V_{4}$ band and added to the catalog after visual inspection of the CCD images (see P96, Table 5)."543 Tu there are 26 P96 COD1 ud ungeclusters.(ec 18 of Tablewhich are detectedtotal at the 30 level.," In total there are 26 P96 $V_4$ -band clusters, 18 of which are detected at the $\sigma$ level."544 Of onthese last clusters. 13 have estimated redshift withiu the raige Wwhere our VOCE is optimal 2 0.6).," Of these last clusters, 13 have estimated redshift within the range where our VGCF is optimal $0.2 \leq z \leq 0.6$ )."545 In Fie., In Fig.546 swe pot circles correspouding to aIl the P96 clusters deected by the matched filter techuiqie (dotted linc)., 8 we plot circles corresponding to all the P96 clusters detected by the matched filter technique (dotted line).547 We idetity 12 of the 13 clusters detected by P96 at the 3o level aud with estimated redshifts from 7=0.2 to ;Do—0.6., We identify 12 of the 13 clusters detected by P96 at the $\sigma$ level and with estimated redshifts from $z=0.2$ to $z=0.6$.548" The oulv cluster we do not identifv. PSL (2= 0.5). falls just under the limit of our selection criterium with CMY four coincident fuctuations,"," The only cluster we do not identify, P54 $z=0.5$ ), falls just under the limit of our selection criterium with only four coincident fluctuations."549 Beside the above 12 clusters. we detect other 25 galaxy systems.," Beside the above 12 clusters, we detect other 25 galaxy systems."550 Of these 25 systems. 2 are P96 clusters with confidence level less than 30 and redshift 0.6.," Of these 25 systems, 2 are P96 clusters with confidence level less than $\sigma$ and redshift $z \leq 0.6$."551 The remaimine 23 do not have a counterpart in the PDCS catalog., The remaining 23 do not have a counterpart in the PDCS catalog.552 Most of the 23 new clusters have properties comparable o those of P96 clusters as detected by the VOCE., Most of the 23 new clusters have properties comparable to those of P96 clusters as detected by the VGCF.553 At least ut of the jew systems have been detected by the VOCE hauks to its specific properties., At least part of the new systems have been detected by the VGCF thanks to its specific properties.554 For example. because the VOCE does not smooth the data. it is able to separate wo large overdeusities (V2 aud Vis) that are unlikely to ο one system (P19).," For example, because the VGCF does not smooth the data, it is able to separate two large overdensities (V2 and V18) that are unlikely to be one system (P49)."555 Tn fact V2 (vlich we ideutifv as the counterpart of PL9) aud V18 are well separated both on he skv aud in magnitude., In fact V2 (which we identify as the counterpart of P49) and V18 are well separated both on the sky and in magnitude.556The work of JSBW was supported. by the Australian Research Council.,The work of JSBW was supported by the Australian Research Council.557 This work was initiated when one of the authors (VP) was visiting the School. of Physics. University of Melbourne. under the Miegunah Distinguished Fellowship.," This work was initiated when one of the authors (TP) was visiting the School of Physics, University of Melbourne, under the Miegunah Distinguished Fellowship."558We used the images clelivered by the standard. ACS pipeline processing (OPUS 15.a and CALACS code version 4.4.1) which removes cosnmüc-ravs. corrects [or optical distortion. and dither combines the images.,"We used the images delivered by the standard ACS pipeline processing (OPUS 15.a and CALACS code version 4.4.1) which removes cosmic-rays, corrects for optical distortion, and dither combines the images."559 We aligned the F435W image to stars in the USNO D1.0 catalog (Monet.etal.2003) using theànwes tool trom the Smithsonian Astrophysical Observatory Telescope Data Center., We aligned the F435W image to stars in the USNO B1.0 catalog \citep{usnob1} using the tool from the Smithsonian Astrophysical Observatory Telescope Data Center.560 Many of the stars in the USNO 01.0 catalog appear as multiple stars or clusters in the HST image., Many of the stars in the USNO B1.0 catalog appear as multiple stars or clusters in the HST image.561 We selected 10 stars which appear as single stars in the IIST image and have counterparts in the USNO BL.O catalog., We selected 10 stars which appear as single stars in the HST image and have counterparts in the USNO B1.0 catalog.562" The standard deviation of the ollsets ol the stellar positions is 0.37"" which is comparable to the expected accuracy of the USNO DBI.0 posiüons.", The standard deviation of the offsets of the stellar positions is $0.37\arcsec$ which is comparable to the expected accuracy of the USNO B1.0 positions.563 With ten reference stars. (he absolute astrometry of the corrected. IST image should be better than 0.2%," With ten reference stars, the absolute astrometry of the corrected HST image should be better than $0.2\arcsec$."564 The F606W image was aligned to the aspect-correctecdl FASSW image using (heJRAF toolsgeomeap ancl (Τονοἱal.1993)., The F606W image was aligned to the aspect-corrected F435W image using the tools and \citep{tody93}.565 Observations of NGC 1073. were made using the Advanced CCD Imaging Spectrometer spectroscopy array CACIS-S: Bautz οἱ 11998) onboard. the Chandra X-Ray Observatory., Observations of NGC 1073 were made using the Advanced CCD Imaging Spectrometer spectroscopy array (ACIS-S; Bautz et 1998) onboard the Chandra X-Ray Observatory.566 The ACIS-S was used in imaging mode and (he source position for INO 5 as reported by Colbert.&Ptak(2002) was placed at the aimpoint., The ACIS-S was used in imaging mode and the source position for IXO 5 as reported by \citet{colbert02} was placed at the aimpoint.567 The observation (ObsID. 46836: PI lxaaret) began on 9 Feb 2004 03:16:29 UT and had a useful exposure of 5.7 ks., The observation (ObsID 4686; PI Kaaret) began on 9 Feb 2004 08:16:29 UT and had a useful exposure of 5.7 ks.568 The Chandra data were subjected to staudard data processing ancl event screening (ASCDS version 7.1.1 using CALDD version 2.25)., The Chandra data were subjected to standard data processing and event screening (ASCDS version 7.1.1 using CALDB version 2.25).569 The total rate on the $3 chip was below 1.1 c/s for the entire observation indicating that there were no strong background flares., The total rate on the S3 chip was below 1.1 c/s for the entire observation indicating that there were no strong background flares.570 We constructed. an image using all valid events on the S2 and $3 chips and used (he (ool which 1 part of theCAO version 3.1 data analysis package to search [or X-ray sources., We constructed an image using all valid events on the S2 and S3 chips and used the tool which is part of the version 3.1 data analysis package to search for X-ray sources.571 The list of cletected sources with detection significance of 3.50 or higher is given in Table 1.., The list of detected sources with detection significance of $3.5\sigma$ or higher is given in Table \ref{xsources}.572 The Chandra astrometry was aligned to the IST astrometry as described below., The Chandra astrometry was aligned to the HST astrometry as described below.573 We computed an exposure map for an assumed source spectrum of a powerluw wilh photon index of 1.5 absorbed by a column density of 4.2102em72 which is the total Galactic column density along the line of sight (Dickev&Lockman1990).," We computed an exposure map for an assumed source spectrum of a powerlaw with photon index of 1.5 absorbed by a column density of $4.2 \times 10^{20} \rm \,574cm^{-2}$ which is the total Galactic column density along the line of sight \citep{dickey90}."575. In order to eive some indication of the spectral shape of each source. we calculate the the ratio of the Chandra counts in the 17 keV band to counts in (he 0.37 keV band.," In order to give some indication of the spectral shape of each source, we calculate the the ratio of the Chandra counts in the 1–7 keV band to counts in the 0.3–7 keV band."576 We searched for X-rav variability bv comparing the photon arrival times [or each source to the distribution expected for a constant source wilh the same average [lux using à Wolmogorov-Sinimnoll (INS) test., We searched for X-ray variability by comparing the photon arrival times for each source to the distribution expected for a constant source with the same average flux using a Kolmogorov-Smirnoff (KS) test.577 No backeround subtraction was performed., No background subtraction was performed.578 Marginal evidence for variability was found for (wo sources: INO 5 (source #22) which ix variable αἱ a confidence level of and the quasar J024333.6--012222 (source #66) which is variable at a confidence level οἱ95%., Marginal evidence for variability was found for two sources: IXO 5 (source 2) which is variable at a confidence level of and the quasar J024333.6+012222 (source 6) which is variable at a confidence level of.579.. Three quasars ave detected with Chandra., Three quasars are detected with Chandra.580 These are QSO D0240-011 and QSO D0241--011 which were previously detected with ROSAT (Colbert&Ptak2002) and J024333.64-012222, These are QSO B0240+011 and QSO B0241+011 which were previously detected with ROSAT \citep{colbert02} and J024333.6+012222581 These are QSO D0240-011 and QSO D0241--011 which were previously detected with ROSAT (Colbert&Ptak2002) and J024333.64-012222., These are QSO B0240+011 and QSO B0241+011 which were previously detected with ROSAT \citep{colbert02} and J024333.6+012222582and maximum stellar metallicity.,and maximum stellar metallicity.583" In this section, we explore the scaling relations among these properties."," In this section, we explore the scaling relations among these properties."584" We focus in particular on the way in which the formation and evolution of the satellite population is linked to the subhalo mass, and to the influence of the environment."," We focus in particular on the way in which the formation and evolution of the satellite population is linked to the subhalo mass, and to the influence of the environment."585 Figure 8 shows the relationship between present stellar mass and dark matter mass for all satellites that contain stars at z—0., Figure \ref{fig:relation_mdm-ms} shows the relationship between present stellar mass and dark matter mass for all satellites that contain stars at $z=0$.586" In the left panel, the dark matter mass is the current mass of each subhalo, while in the right panel, the dark matter mass is the mass of the satellite at infall, Le. when it first became a subhalo of the host halo (see"," In the left panel, the dark matter mass is the current mass of each subhalo, while in the right panel, the dark matter mass is the mass of the satellite at infall, i.e. when it first became a subhalo of the host halo (see"587"Lyrae gap in MO. they required two different iixiue-leuegthD parameters. one to obtain the observed blue edge location (77IT,z1.5) aud the other to obtain the observed red edge location (jE,~ 2.0).","Lyrae gap in M3, they required two different mixing-length parameters, one to obtain the observed blue edge location $l/H_p\approx 1.5$ ) and the other to obtain the observed red edge location $l/H_p\approx 2.0$ )."588 Tu addition the observed visual auplitude as a function of B-V displavs nonlinear characteristics. while theoretical relatious predict linear relationships.," In addition the observed visual amplitude as a function of B-V displays nonlinear characteristics, while theoretical relations predict linear relationships."589 Marconietal. also mention that a muixine-leneth parameter of 2.0 produces Iuimuinosities for horizoutal-brauch models that are brighter than what is observed by z:0.08+0.05 ae., \citeauthor{Marconi-2003} also mention that a mixing-length parameter of 2.0 produces luminosities for horizontal-branch models that are brighter than what is observed by $\approx0.08\pm0.05$ mag.590 Other models for time-dependent couvection in one dimension have been proposed by I&ulifuss(1986) and Niong (1989).., Other models for time-dependent convection in one dimension have been proposed by \cite{Kuhfuss-1986} and \cite{Xiong-1989}. .591 I&ulhfuss argued that the convective model by Stelliugwerf(198248). docs not use the diffusion approximation consistently throughout the model., \citeauthor{Kuhfuss-1986} argued that the convective model by \cite{Stellingwerf-1982a} does not use the diffusion approximation consistently throughout the model.592 S1iolec&Moskalik developed. their application of the Iuhfuss convective ος. which requies cight free paralcters. and used dt to stucky convection in 2 Cephei stars (Smolec&Aloskalil2007).," \cite{Smolec-2008} developed their application of the \citeauthor{Kuhfuss-1986} convective model, which requires eight free parameters, and used it to study convection in $\beta$ Cephei stars \citep{Smolec-2007}."593. They found that convection is not miportant for calculating pulsation aniplitudes for their models., They found that convection is not important for calculating pulsation amplitudes for their models.594 However. they caution that their convective nodel. while working well for classical pulsators. is at the limits of its applicability in the οςορια nodels they are studving.," However, they caution that their convective model, while working well for classical pulsators, is at the limits of its applicability in the $\beta$ -Cephei models they are studying."595 More receutly. Olivier&Wood(2005) have also developeda code incliding he Επ convective model aud present some est calculations of their program. mentioning that he turbulent viscosity parameter shows potential as an duportant doetermünaut of the pulsation auuplitudes.," More recently, \cite{Olivier-2005} have also developed a code including the \citeauthor{Kuhfuss-1986} convective model and present some test calculations of their program, mentioning that the turbulent viscosity parameter shows potential as an important determinant of the pulsation amplitudes."596 The of distillation1uulti-dinieusional couvective phenomenon to oue dimension is always accompanied by extra equations and/or paraiaeters to approximate the effects of couvective motions of material iu more than oue spatial dimension., The distillation of multi-dimensional convective phenomenon to one dimension is always accompanied by extra equations and/or parameters to approximate the effects of convective motions of material in more than one spatial dimension.597 Deupree(1977a) approached the interaction of convection and stellar pulsation in a fundamentally different way using a two-dimensional hydrodyuauic code directly following the convective flow patterns., \cite{Deupree-1977a} approached the interaction of convection and stellar pulsation in a fundamentally different way using a two-dimensional hydrodynamic code directly following the convective flow patterns.598 While Deupree(1977b.c..1950.1985). was able to successfully determine the observed edees of the RR. Lyrae instability. strip. he was unable to compute full amplitude solutions because lus algorithui for moving the radial coordinate allowed the radial zonine to drift over time.," While \cite{Deupree-1977b,Deupree-1977c,Deupree-1980,Deupree-1985} was able to successfully determine the observed edges of the RR Lyrae instability strip, he was unable to compute full amplitude solutions because his algorithm for moving the radial coordinate allowed the radial zoning to drift over time."599 Consequently at later times. the radial zonine did uot cover the hydrogen ionization zone adequately and the caleulatious were eventually απλοΊσα unreliable.," Consequently at later times, the radial zoning did not cover the hydrogen ionization zone adequately and the calculations were eventually numerically unreliable."600 The algorithui Deupree used for the moving radial coordinate usec the horizoutal average of the radial velocities at a particular radius as the eid velocity., The algorithm \citeauthor{Deupree-1977a} used for the moving radial coordinate used the horizontal average of the radial velocities at a particular radius as the grid velocity.601 Recently Drueunetal.(2010) have used a simular average radial velocity as the exid. velocity to follow the core in fall phase iu supernovac simulations., Recently \cite{Bruenn-2010} have used a similar average radial velocity as the grid velocity to follow the core in fall phase in supernovae simulations.602 Another form of a radial moving grid was by Mundprecht(2009).. where the radial erid velocity at the surface was set as the average of the radial velocities. and the inner grid velocity was held constant.," Another form of a radial moving grid was by \cite{Mundprecht-2009}, where the radial grid velocity at the surface was set as the average of the radial velocities, and the inner grid velocity was held constant."603 Tho iutermediate radial grid velocities were then set using a dilatation factor., The intermediate radial grid velocities were then set using a dilatation factor.604 Recently Stókl(2008) developed au approach for model pulsation somewhere between the 2D model of Deupree and the 1D convective models., Recently \cite{Stokl-2008} developed an approach for model pulsation somewhere between the 2D model of \citeauthor{Deupree-1977a} and the 1D convective models.605 Stokl used two radial columns to model convection., \citeauthor{Stokl-2008} used two radial columns to model convection.606 Oue column represented the sui of all upward couvective flows. and the other colin represcuted the παπι of all downward flows.," One column represented the sum of all upward convective flows, and the other column represented the sum of all downward flows."607 While not includiues auy mining leugth parameter. it does contain free parameters related to the physical size of the couvective cells. aud the fraction of the surface area of a spherical surface which coutaius downdratts.," While not including any mixing length parameter, it does contain free parameters related to the physical size of the convective cells, and the fraction of the surface area of a spherical surface which contains downdrafts."608 These paraiucters do have a plivsical uis. but im practice it would be dificult to determine them as they are probably functions of depth and likely depend on a particular stars xoperties.," These parameters do have a physical basis, but in practice it would be difficult to determine them as they are probably functions of depth and likely depend on a particular star's properties."609 Also. because the model ouly las two radial columus if may iiss some of the more subtle features of convection.," Also, because the model only has two radial columns it may miss some of the more subtle features of convection."610 More recently others rave begun working on directly simulating the interaction of convection. aud pulsation in 2D {Muthsametal.2010:Gastine&Dintrans2010).," More recently others have begun working on directly simulating the interaction of convection and pulsation in 2D \citep{Muthsam-2010b, Gastine-2010}."611 Both Buchler(2009)— and Marcoui(2009) je stressed the importance of iuproviug he couveetive models used din variable stars., Both \cite{Buchler-2009} and \cite{Marconi-2009} have stressed the importance of improving the convective models used in variable stars.612 Duchler— highlights some of the well kuown difüculties facing time-dependent mixing Ieneth iofing that it is an empirical description. rather han a cousisteut physical description.," \citeauthor{Buchler-2009} highlights some of the well known difficulties facing time-dependent mixing length noting that it is an empirical description, rather than a consistent physical description."613 Also. the up to cight or more free parameters used iu ine-depenudeut musing leneth approach cau nof ο chosen based on physics. butiustead ist ο calibrated by comparison with observations.," Also, the up to eight or more free parameters used in time-dependent mixing length approach can not be chosen based on physics, butinstead must be calibrated by comparison with observations."614 Mareoui iuentions some remaining problems for RR Lyrac models. particularly the unsatisfactorv natch between theoretical light curve morphology," \citeauthor{Marconi-2009} mentions some remaining problems for RR Lyrae models, particularly the unsatisfactory match between theoretical light curve morphology"615(section. 11.4) for the case when the swing amplification mechanism is fed by white noise.,(section 11.4) for the case when the swing amplification mechanism is fed by white noise.616 Toonre (1990). cliscusses he source of the noise and argues convincingly that swing amplified white noise explains exactly the behaviour of the star cises in his numerical simulations or that by Selbwood Carlberg (1984)., Toomre (1990) discusses the source of the noise and argues convincingly that swing amplified white noise explains exactly the behaviour of the star discs in his numerical simulations or that by Sellwood Carlberg (1984).617 Phe distribution of amplitudes. which represents the superposition of many short. livecl shearing density waves. is quasistationary and can be modelled. for positive wave numbers Ay empirically as and continued at negative wave numbers fy as od d.," The distribution of amplitudes, which represents the superposition of many short lived shearing density waves, is quasi–stationary and can be modelled for positive wave numbers $k_{\rm y}$ empirically as and continued at negative wave numbers $k_{\rm y}$ as $\delta618\Phi_{\rm {\bf -k}} = \delta \Phi_{\rm {\bf k}}$ ."619" The parameters are estimated as Ayo = 1.5 Ag. Avo = 05 kan. on, = 077 Λο. and σι = 0.1 Aaa Lor the case A=B=40)."," The parameters are estimated as $k_{\rm x0}$ = 1.5 $k_{\rm crit}$ $k_{\rm y0}$ = 0.5 $k_{\rm crit}$, $\sigma_{\rm k_{\rm x}}$ = 0.7 $k_{\rm crit}$, and $\sigma_{\rm k_{\rm y}}$ = 0.1 $k_{\rm crit}$ for the case $A = -B =620\frac{1}{2} \Omega_{\rm 0}$."621 The critical wave number is defined. as hau=(οπές) with C the constant of gravity and X4 the surface density of the disc. respectively.," The critical wave number is defined as $k_{\rm crit} =622\kappa^2/(2 \pi G \Sigma_{\rm d})$ with $G$ the constant of gravity and $\Sigma_{\rm d}$ the surface density of the disc, respectively."623 Using this parametric model the cquacratures in equation (23) can be carried. out explicitely., Using this parametric model the quadratures in equation (23) can be carried out explicitely.624 Each spike in Fie., Each spike in Fig.625 1 represents the superpostion of swing amplified density waves all travelling at à constant wave number Ay along the Ay abscissae at a speed of Ayrj=2.1 with an amplitude which can be mocelled as Inequation (25) AT denotes the original racial wave numbers of the waves and ps the time. when the waves were launched.," 1 represents the superpostion of swing amplified density waves all travelling at a constant wave number $k_{\rm626y}$ along the $k_{\rm x}$ abscissae at a speed of $\dot{k}_{\rm x, eff} = 2 A627k_{\rm y}$ with an amplitude which can be modelled as Inequation (25) $k_{\rm x}^{\rm in}$ denotes the original radial wave numbers of the waves and $t^{\rm in}$ the time, when the waves were launched."628 kitων}Ly parameterizes the excitation rate of the waves and the peak amplification factor of the swinge amplifier (οἱ.," $\tilde{\Phi}_{\rm 629k_{\rm x}^{\rm in}, l_2}(t^{\rm in})$ parameterizes the excitation rate of the waves and the peak amplification factor of the swing amplifier (cf."630 paper D)., paper I).631" Since white noise is à stationary random process. Pus1,07) is evenly distributed over wave number space and ἐν."," Since white noise is a stationary random process, $\tilde{\Phi}_{\rm 632k_{\rm x}^{\rm in}, k_2}(t^{\rm in})$ is evenly distributed over wave number space and $t^{\rm in}$."633 Each of the density waves is only correlated with itself., Each of the density waves is only correlated with itself.634 “Phis implies. if the autocorrelation function in equation (23) is considered. restrictions of the wave numbers and the time intervals to This constraint anc equation (25) lead. to an autocorrelation function in the form of where |P4|? is à normalization constant.," This implies, if the autocorrelation function in equation (23) is considered, restrictions of the wave numbers and the time intervals to This constraint and equation (25) lead to an autocorrelation function in the form of where $|\Phi_0|^2$ is a normalization constant."635 The time integral of the autocorrelation function according to equation (23) is given by (ο>0) ] consider next in equation (23) the integration with respect to wave number Ay. and similarly. In equations (29) and (30) terms of the kind are neglected: as equadraticallv small.," The time integral of the autocorrelation function according to equation (23) is given by $l_2 > 0$ ) I consider next in equation (23) the integration with respect to wave number $k_{\rm x}$, and similarly In equations (29) and (30) terms of the kind are neglected as quadratically small."636 This is justified. because the majority of the stars have epievele sizes smaller than the critical wave length Aca. the twpical spacing between spiral arms (Julian Toomre 1966.cf.," This is justified, because the majority of the stars have epicycle sizes smaller than the critical wave length $\lambda_{\rm crit}$, the typical spacing between spiral arms (Julian Toomre 1966,cf."637 also paper D., also paper I).638" The epievcle size is determined. by VET HB. whereas Ok,OXeri2x/Aogu (el"," The epicycle size is determined by $\sqrt{2 J_{\rm 1}/\kappa}$ , whereas $\sigma_{\rm k_{\rm x}} \propto k_{\rm crit} = 2639\pi / \lambda_{\rm crit}$ (cf."640 Fig., Fig.641 1)., 1).642 Similarly terms of the kind, Similarly terms of the kind643 1095“ore. (sec.eg.Markeviteh&Vikhlinin2007.audreference thereim)..," $10^{64-65} {\rm erg}$ \citep[see, e.g.,][and reference therein]{mar07}."644 The dwuamics of cluster collisions are however dominated by the cluster mass distribution. which caunot be constrained fromi XN-rav observations aloue.," The dynamics of cluster collisions are however dominated by the cluster mass distribution, which cannot be constrained from X-ray observations alone."645" Due to the collisional nature of ICM. cluster mergers are indeed expected to geucrate some transicut decoupling between spatial distributions of the CDM and hot N-ray cutting eas,"," Due to the collisional nature of ICM, cluster mergers are indeed expected to generate some transient decoupling between spatial distributions of the CDM and hot X-ray emitting gas."646 Moreover. mass estimates relving on gas properties may be biased by merecr-induced perturbations of the ICAL hydrostatie equilibrium (ILE.) within iudividual colliding clusters.," Moreover, mass estimates relying on gas properties may be biased by merger-induced perturbations of the ICM hydrostatic equilibrium (H.E.) within individual colliding clusters."647 Weak-leusing distortions of background galaxy images provide us with a unique opportunity to reconstruct the distribution of matter in clusters without any assunption of mass inodel aud dynamical states (e.g...Kaiserctal. and measure cluster masses (e.g...Grayetal.2002:Cavazzi2003:Unietzuetal. 20093.," Weak-lensing distortions of background galaxy images provide us with a unique opportunity to reconstruct the distribution of matter in clusters without any assumption of mass model and dynamical states \citep[e.g., ][]{kai95, bar01, sch06, oka08, oka10b} and measure cluster masses \citep[e.g., ][]{gra02, gav03, bar07, hoe07, oka10b, ume09}."648. Therefore. a wealk-leusine analysis of nereine clusters (6...Cloweetal.2006:MalidaviMertenetal.2011) is an observational breakthrough ii ineasmue mass distribution. thereby providing complementary information to N-vay measurements.," Therefore, a weak-lensing analysis of merging clusters \citep[e.g.,][]{clo06,mah07,oka08,oka10b,mer11}649 is an observational breakthrough in measuring mass distribution, thereby providing complementary information to X-ray measurements."650 Okabe&Uiietsu(2008). conducted a systematic study of seven inereiug clusters. represcuting ος stagesand conditions. based on a joint weak-leusine.," \cite{oka08} conducted a systematic study of seven merging clusters, representing various merging stagesand conditions, based on a joint weak-lensing,"651"In this Appendix. we start with the conservation equations for a fluid. which include contributions from the fluid's enthalpy and from heat flow. and show that the appropriate conserved quantity is the angular momentum per baryon ας, as calculated in $3.","In this Appendix, we start with the conservation equations for a fluid, which include contributions from the fluid's enthalpy and from heat flow, and show that the appropriate conserved quantity is the angular momentum per baryon $u_\phi$ as calculated in 3."652 We begin with the stress tensor for a fluid (see. for example. Mihalas Mihalas 1984).," We begin with the stress tensor for a fluid (see, for example, Mihalas Mihalas 1984)."653 The enthalpy /7 is where the energy density is the sum of rest mass energy. internal energy. and nuclear binding energy.," The enthalpy $h$ is where the energy density is the sum of rest mass energy, internal energy, and nuclear binding energy."654" We write the heat flux as F""'.", We write the heat flux as $F^\alpha$ .655" By setting 0;V,7°""=0. and using baryon number conservation V,,(pu')=0. we obtain the angular momentum conservation law Assuming the azimuthal heat flux F'' may be neglected when compared to the vertical heat flux F=F. we rewrite equation (A4)) as We now simplify this equation using the first law of thermodynamics. which is where s is the entropy per baryon mass. or. using equation (A2)). Substituting for dA/df in equation (A5)). we find The first term in equation (A8)) vanishes. since Zds/dt2—/p)dF/dz is the familiar entropy equation."," By setting $\phi_\beta\nabla_\alpha T^{\alpha\beta}=0$, and using baryon number conservation $\nabla_\alpha (\rho u^\alpha) = 0$, we obtain the angular momentum conservation law Assuming the azimuthal heat flux $F^\phi$ may be neglected when compared to the vertical heat flux $F^r=F$, we rewrite equation \ref{eq:a1}) ) as We now simplify this equation using the first law of thermodynamics, which is where $s$ is the entropy per baryon mass, or, using equation \ref{eq:h}) ), Substituting for $dh/dt$ in equation \ref{eq:a2}) ), we find The first term in equation \ref{eq:a3}) ) vanishes, since $Tds/dt=-(1/\rho)dF/dz$ is the familiar entropy equation."656 The nuclear energy production rate is included in the Tds/dr term. since the nuclear binding energy is included in the enthalpy: equations (A3)) and (A6)) give where /B/dr is the nuclear energy generation rate.," The nuclear energy production rate is included in the $Tds/dt$ term, since the nuclear binding energy is included in the enthalpy: equations \ref{eq:eps}) ) and \ref{eq:firstlaw}) ) give where $dB/dt$ is the nuclear energy generation rate."657" Integrating the second term in equation (A8)) in time. we find it gives a contribution to Au,,/u., of order AP/per=(H/RVP/per)zzGURÁCTXTRV.z1077. where we take the pressure scale height m."," Integrating the second term in equation \ref{eq:a3}) ) in time, we find it gives a contribution to $\Delta u_\phi/u_\phi$ of order $\Delta P/\rho658c^2\approx (H/R)(P/\rho c^2)\approx (gR/c^2)(H/R)^2\approx 10^{-7}$, where we take the pressure scale height $H\approx 10\ {\rm m}$ ."659 The third term in equation (A8)) represents radiative viscosity (see/ Mihalas Mihalas 1984)., The third term in equation \ref{eq:a3}) ) represents radiative viscosity (see Mihalas Mihalas 1984).660" Again integrating in time. we find that this term gives a contribution z(FpceH)(Au,,/u,,)~07(0/IsecyAun,/u,,)."," Again integrating in time, we find that this term gives a contribution $\approx (F/\rho c^2)(t/H)(\Delta661u_\phi/u_\phi)\approx 10^{-4}(t/{\rm sec})(\Delta662u_\phi/u_\phi)$."663 Both the second and third terms are oforder (HRy. or smaller. and may be neglected for our purposes.," Both the second and third terms are oforder $(H/R)^2$ or smaller, and may be neglected for our purposes."664 In summary./ consideration of the conservation law for a fluid gives," In summary, consideration of the conservation law for a fluid gives"665summarized in table 7..,summarized in table \ref{fitd}.666 The reduced 4? is almost the same as that of the model C (partial covering absorption without reflection). and the reflection continuum is not required.," The reduced $\chi^2$ is almost the same as that of the model C (partial covering absorption without reflection), and the reflection continuum is not required."667 This is inconsistent with the existence of the Fe-Ix line., This is inconsistent with the existence of the Fe-K line.668 Another problem is that the powerlaw photon index of 1.7 for the time-averaged spectra in 2009 is different [rom that obtained by the analvsis of the difference spectra. which require the photon index of —2.," Another problem is that the powerlaw photon index of 1.7 for the time-averaged spectra in 2009 is different from that obtained by the analysis of the difference spectra, which require the photon index of $\sim$ 2."669 The powerlaw component is generally thought to be due to thermal Comptonization of disk photons. as well as the low/hard state of black hole binaries.," The powerlaw component is generally thought to be due to thermal Comptonization of disk photons, as well as the low/hard state of black hole binaries."670 For (νο N-1 and GX 339-4. when they. are briehter in the low/hard state. the Compton thickness becomes larger but the Comptonizing electron temperature becomes lower (Makishima et al.," For Cyg X-1 and GX 339-4, when they are brighter in the low/hard state, the Compton thickness becomes larger but the Comptonizing electron temperature becomes lower (Makishima et al."671 2008. Zdziwski et al.," 2008, Zdziarski et al."672 2004. Del Santo 2008).," 2004, Del Santo 2008)."673 As a result. the powerlaw photon index ancl cut-off enerev are larger and lower. respectivelv: in other words. the spectrum becomes solter in the brighter phase.," As a result, the powerlaw photon index and cut-off energy are larger and lower, respectively; in other words, the spectrum becomes softer in the brighter phase."674 A bright Sevfert galaxy. NGC 4151. also exhibited such a trend (Lubiüski el al.," A bright Seyfert galaxy, NGC 4151, also exhibited such a trend ${\rm \acute{n}}$ ski et al."675 2010)., 2010).676 On the other hand. the trend of the Cen A is opposite: the spectrum became harder in the bright phase.," On the other hand, the trend of the Cen A is opposite; the spectrum became harder in the bright phase."677 The Cen A has been found to be a gamma-ray emitter up to the TeV band. while black hole binaries and NGC 4151 are not.," The Cen A has been found to be a gamma-ray emitter up to the TeV band, while black hole binaries and NGC 4151 are not."678 Therefore. (he nonthermal jet component. which connects to the high energy. ganuna-ray band. is expected to exist in the X-ray baud.," Therefore, the nonthermal jet component, which connects to the high energy gamma-ray band, is expected to exist in the X-ray band."679 We included one more powerlaw model in addition to the model D. and multiplied it bv the absorption with a column density of 1x107* 7: In this case. we cannot constrain (he parameters of both powerlaw components well.," We included one more powerlaw model in addition to the model D, and multiplied it by the absorption with a column density of $1\times10^{23}$ $^{-2}$; In this case, we cannot constrain the parameters of both powerlaw components well."680 Ii addition. the intensity of the hard powerlaw component becomes coupled with that of the reflection component.," In addition, the intensity of the hard powerlaw component becomes coupled with that of the reflection component."681 Then. we replaced the model by the model (Nandra et al.," Then, we replaced the model by the model (Nandra et al."682 2007) for the reflection component., 2007) for the reflection component.683 The model, The model684this we mean that the emission is powered by a relativistic outflow created during the core-collapse of a massive star.,this we mean that the emission is powered by a relativistic outflow created during the core-collapse of a massive star.685" Our goal in thisLetter is not to understand all of the observed properties of Sw 1644-57, but rather to assess the zeroth order plausibility of whether it could be associated with the core-collapse of a massive star."," Our goal in this is not to understand all of the observed properties of Sw 1644+57, but rather to assess the zeroth order plausibility of whether it could be associated with the core-collapse of a massive star."686 In §2 we assess (1) the conditions under which neutron star spindown and/or black hole accretion can power a very long timescale high energy transient 2.1)) and (2) whether low-power jets from a central engine can escape their host star or supernovae ejecta ($2.2))., In \ref{sec:grb} we assess (1) the conditions under which neutron star spindown and/or black hole accretion can power a very long timescale high energy transient \ref{sec:energy}) ) and (2) whether low-power jets from a central engine can escape their host star or supernovae ejecta \ref{sec:jet}) ).687 We apply these models to in §3.., We apply these models to in \ref{sec:sw}.688 We conclude by highlighting the many outstanding questions (§4))., We conclude by highlighting the many outstanding questions \ref{sec:discussion}) ).689 Low-power outflows (by GRB standards) during the core-collapse of massive stars can be produced by the spindown of a rapidly rotating neutron star (?) or accretion onto a central black hole., Low-power outflows (by GRB standards) during the core-collapse of massive stars can be produced by the spindown of a rapidly rotating neutron star \citep{metzger07} or accretion onto a central black hole.690" A low power does not imply that the event is sub-energetic relative to canonical GRBs, only that the timescale to extract the energy is much longer."," A low power does not imply that the event is sub-energetic relative to canonical GRBs, only that the timescale to extract the energy is much longer."691" Neutron star-powered activity would be associated with a successful core-collapse explosion while black hole accretion could be powered by the infall of the stellar envelope in a failed explosion, or the fallback of material that remains bound during an otherwise successful explosion (??).."," Neutron star-powered activity would be associated with a successful core-collapse explosion while black hole accretion could be powered by the infall of the stellar envelope in a failed explosion, or the fallback of material that remains bound during an otherwise successful explosion \citep{woosley93,macfadyen99}."692" A neutron star with a spin period of 1P,, ms and a magnetic field strength of 10 G has a rotational energy of Ej~2x10?P2ergs, a relativisticBj4 dipole spindown power of Ε510""B2,P5ergs! and a spindown timescale of fypindown—2Bj2P2, days."," A neutron star with a spin period of $1 \, P_{\rm ms}$ ms and a magnetic field strength of $10^{14} B_{14}$ G has a rotational energy of $E_{{\rm rot}} \simeq 2\times 10^{52}P_{{\rm ms}}^{-2}\,{\rm693 ergs}$, a relativistic dipole spindown power of $ \dot{E} \simeq69410^{47}\, B_{14}^{2} \, P_{{\rm ms}}^{-4} \, \ergs$ and a spindown timescale of $t_{\rm spindown} \simeq 2 \, B_{14}^{-2} \, P_{{\rm ms}}^{2} \, {\rm days}$ ."695" Powering a month-long event with a total energy of 1017? ergs thus requires P~1—3 ms and B~3x10%—1014 G. For vacuum dipole spindown, £ is relatively constant for t< While for f2 Éοςf°."," Powering a month-long event with a total energy of $\sim 10^{51-52}$ ergs thus requires $P \sim 1-3$ ms and $B \sim 3 \times 10^{13} - 10^{14}$ G. For vacuum dipole spindown, $\dot E$ is relatively constant for $t \lesssim t_{\rm spindown}$ while for $t696\gtrsim t_{\rm spindown}$, $\dot E \propto t^{-2}$."697" Note, however, that this tepindownspecific prediction for the fepindown,temporal power-law index for late-time spindown only applies for a braking index of 3, which is not typically observed for pulsars (e.g., ?))."," Note, however, that this specific prediction for the temporal power-law index for late-time spindown only applies for a braking index of 3, which is not typically observed for pulsars (e.g., \citealt{kaspi06}) )."698 The timescale for black hole accretion to power central engine activity depends on the rotation and density profiles of the progenitor star and the energy of the explosion (?) - the latter because it determines how much material remains bound to the black hole., The timescale for black hole accretion to power central engine activity depends on the rotation and density profiles of the progenitor star and the energy of the explosion \citep{kumar08} – the latter because it determines how much material remains bound to the black hole.699" In the simplest case of a failed explosion, the timescale on which infall occurs is set by the free-fall time In order to power a long timescale transient like Sw 1644+57,a weakly bound red supergiant (RSG) progenitor with radius 1019 cm is required."," In the simplest case of a failed explosion, the timescale on which infall occurs is set by the free-fall time In order to power a long timescale transient like Sw 1644+57,a weakly bound red supergiant (RSG) progenitor with radius $R > 10^{13}$ cm is required."700" For a power law density profile, p(r) po(r/R)-”, the enclosed mass M(r)cr"" (for n< 3) and the free fall accretion rate is where tg is the free-fall time evaluated at the outer radius."," For a power law density profile, $\rho(r) = \rho_0 (r/ R)^{-n}$ , the enclosed mass $M(r) \propto r^{3-n}$ (for $n < 3$ ) and the free fall accretion rate is where $t_{\rm ff, R}$ is the free-fall time evaluated at the outer radius."701 The total power available from stellar infall is thus where the stellar envelope mass is scaled to 10Μο and the radius to 1014cm~10°Κο.," The total power available from stellar infall is thus where the stellar envelope mass is scaled to $10 \, M_\odot$ and the radius to $10^{14} \, \cm \simeq 10^3 \, R_\odot$."702" Presumably this energy will be tapped with only fractional efficiency to power jet, but depending upon the collimation the resulting isotropic equivalenta power could be of order equation 3 or greater."," Presumably this energy will be tapped with only fractional efficiency to power a jet, but depending upon the collimation the resulting isotropic equivalent power could be of order equation \ref{eq:lum} or greater."703 The actual accretion rate may deviate from the pure free-fall estimate used here since radial pressure support at small radii can slow the infall (?).., The actual accretion rate may deviate from the pure free-fall estimate used here since radial pressure support at small radii can slow the infall \citep{lindner10}.704" In addition, the accretion energy depends not only on the infall rate, but also on the angular momentum profile of the progenitor, since only the material that circularizes in a disk will be available to power a jet."," In addition, the accretion energy depends not only on the infall rate, but also on the angular momentum profile of the progenitor, since only the material that circularizes in a disk will be available to power a jet."705" As a concrete example, Figure | shows the free fall accretion rate for the non-rotating, solar metallicity pre-supernova progenitor models of ?.."," As a concrete example, Figure \ref{fig:edot} shows the free fall accretion rate for the non-rotating, solar metallicity pre-supernova progenitor models of \cite{woosley02}."706" The models with initial masses x30Μο are RSGs with radii R=0.5—1x104 cm, while the models with higher masses have lost their hydrogen envelope and have much smaller stellar radii (R~10!! cm)."," The models with initial masses $\lesssim 30~\msun$ are RSGs with radii $R = 0.5 -1 \times 10^{14}$ cm, while the models with higher masses have lost their hydrogen envelope and have much smaller stellar radii $R \sim 10^{11}$ cm)."707" The outer density profile for the stars with convective hydrogen layers is shallow and roughly follows a power law with n=2, which gives (eq. 3))"," The outer density profile for the stars with convective hydrogen layers is shallow and roughly follows a power law with $n=2$, which gives (eq. \ref{eq:lum}) )"708 a nearly constant accretion rate over the timescale of 200—300 days., a nearly constant accretion rate over the timescale of $-$ 300 days.709 The power shuts off very rapidly after this point because the stellar photosphere has been accreted., The power shuts off very rapidly after this point because the stellar photosphere has been accreted.710" If the star undergoes a successful supernova explosion, the accretion onto a central black hole at late times depends on how much material remains bound."," If the star undergoes a successful supernova explosion, the accretion onto a central black hole at late times depends on how much material remains bound."711" The escape velocity for a RSG is only v4,(R)=50--100kms; thus even a weak (spherical) explosion can unbind the outer hydrogen envelope and limit the late time accretion.", The escape velocity for a RSG is only $v_{\rm esc}(R) = 50-100~\kms$; thus even a weak (spherical) explosion can unbind the outer hydrogen envelope and limit the late time accretion.712" For the layers that do remain bound, material reaches a turnaround radius r,=r/[1—v?/v2,,], and then falls back on a timescale tg(r;)."," For the layers that do remain bound, material reaches a turnaround radius $r_t = r/ [ 1 - v^2/v_{\rm esc}^2]$, and then falls back on a timescale $\tff(r_t)$."713" In Figure 1,, we show how including linear velocity profile of the form v(r)=v,.(r/R) modifies the late-timeaaccretion For expansion at v,= 2v4(R), the accretion rate remains constant until t~50 days, and then declines as a power law."," In Figure \ref{fig:edot}, we show how including a linear velocity profile of the form $v(r) = v_\star (r/R)$ modifies the late-timeaccretion For expansion at $v_\star = 2 v_{\rm esc}(R)$ the accretion rate remains constant until $t ~\approx 50$ days, and then declines as a power law."714" For expansion velocities much larger than this, the power drops off at yet earlier times «1 day."," For expansion velocities much larger than this, the power drops off at yet earlier times $ < 1$ day."715 Thus to explain the long duration, Thus to explain the long duration716observed.,observed.717 As can be seen from figure 7.. a Lux density limit in the sample of 1 Jv means that all sources. with corrected. luminosities greater than25.4 Wissr| can be detected. out to z=2. and that only source with lower radio power. and Consequently at ο<0.6. have to be corrected. for the fact that they only could have been seen out to a certain redshift.," As can be seen from figure \ref{lumcor}, a flux density limit in the sample of 1 Jy means that all sources with corrected luminosities greater than25.4 $W Hz^{-1}Sr^{-1}$ can be detected out to z=2, and that only source with lower radio power, and consequently at $z<0.6$, have to be corrected for the fact that they only could have been seen out to a certain redshift."718 However. a possible additional redshift limit results from the lower limit in peak frequency at O4 Cllz in the bright Stangellini et al.," However, a possible additional redshift limit results from the lower limit in peak frequency at 0.4 GHz in the bright Stangellini et al."719 sample. and in the faint sample due to the limit in 35-5O00. Mllz spectral index.," sample, and in the faint sample due to the limit in 325-5000 MHz spectral index."720 For these sources à weight-factor is usec equal to the volume of the survey (assuming a redshift limit of 2.0) divided by the maximum. volume over which they could have been in the sample. which is dependen on the maximum observable redshift.," For these sources a weight-factor is used equal to the volume of the survey (assuming a redshift limit of 2.0) divided by the maximum volume over which they could have been in the sample, which is dependent on the maximum observable redshift."721 Phe corrections above are relatively straight-forward., The corrections above are relatively straight-forward.722 However. some additional. more complicated corrections have to be made for the fain GPS sample.," However, some additional, more complicated corrections have to be made for the faint GPS sample."723 Firstly. this sample is originally selected a 325 Mllz frequency. eg.," Firstly, this sample is originally selected at 325 MHz frequency, eg."724 on the optically thick part of their spectrum., on the optically thick part of their spectrum.725 Furthermore. only sources with positive spectra indices between this frequency and 5 Cillz were initially selected.," Furthermore, only sources with positive spectral indices between this frequency and 5 GHz were initially selected."726 Therefore the faint WIZNSS sample is more biasec towards GPS sources with higher peak frequencies than the bright Stanghellini et al., Therefore the faint WENSS sample is more biased towards GPS sources with higher peak frequencies than the bright Stanghellini et al.727 sample., sample.728 To. correct. for. this we assumed that the parent distribution of peak frequencies is independent of [ux density and radio power. and determined what fraction of the Stangellini et al sample would have been included in the sample if it would have been selected as for the faint WENSS sample.," To correct for this we assumed that the parent distribution of peak frequencies is independent of flux density and radio power, and determined what fraction of the Stangellini et al sample would have been included in the sample if it would have been selected as for the faint WENSS sample."729 Ht turns out that 26 of the ealaxies in the bright sample have 325 Mllz Hux densities 1 Jw and positive spectral indices between 325 MIIz and 5 CGllz., It turns out that 26 of the galaxies in the bright sample have 325 MHz flux densities $>$ 1 Jy and positive spectral indices between 325 MHz and 5 GHz.730 In addition. the bright CIPS sample has a limit in optically thin spectral index of 0.5. while several sources in the faint sample have a fatter optically thin spectral index.," In addition, the bright GPS sample has a limit in optically thin spectral index of $-0.5$, while several sources in the faint sample have a flatter optically thin spectral index."731 ‘Taking into account these two cllects. the number densities for the faint sample are multiplied by a factor 3.2.," Taking into account these two effects, the number densities for the faint sample are multiplied by a factor 3.2."732 The resulting local luminosity function of GPS sources is shown in [figure SN., The resulting local luminosity function of GPS sources is shown in figure \ref{llf}. .733 Note that a luminosity bin, Note that a luminosity bin734on original Wipparcos reductions that should assess aud quantifv is auv svsteimiaties affect the Pleiades data.,on original Hipparcos reductions that should assess and quantify is any systematics affect the Pleiades data.735 The question about the distance to the Pleiades has uot vet been firmly solved. aud to tackle it now. robust aux independent approaches (as much geometric as possible) are required.," The question about the distance to the Pleiades has not yet been firmly solved, and to tackle it new, robust and independent approaches (as much geometric as possible) are required."736 A first one. advocated by Paczxuuski (2003). conibines astrometric and spectroscopic observatious of Atlas (ID 23850). one of the briehltest nembers of the Pleiades. which is an astrometric binary with a perio of 291 dax. a senmianajor axis of 12.9 mas and 0.216 eccentricity.," A first one, advocated by Paczýnnski (2003), combines astrometric and spectroscopic observations of Atlas (HD 23850), one of the brightest members of the Pleiades, which is an astrometric binary with a period of 291 day, a semi-major axis of 12.9 mas and 0.246 eccentricity."737 Pan et al. (, Pan et al. (7382001) did not ive the radia velocities. but thev znvwayv derived the distance bv combinius the astrometric orbit with a mass-Iunuinosity relation.,"2004) did not have the radial velocities, but they anyway derived the distance by combining the astrometric orbit with a mass-luminosity relation."739 They derived a distance of 13542 pc. which is iu close agrecinent with the results of main-sequence fitting methods.," They derived a distance of $\pm$ 2 pc, which is in close agreement with the results of main-sequence fitting methods."740 Another method involves douhle-lined eclipsing binaries (SB2 ED). which are the distance indicators now providing the most reliable distances to Magellauic Clouds aud other galaxies iu the Local Croup.," Another method involves double-lined eclipsing binaries (SB2 EB), which are the distance indicators now providing the most reliable distances to Magellanic Clouds and other galaxies in the Local Group."741 The receut discovery by Torres (2003) that ITD 23612 in the Pleiades is an SB2 eclipsing binary (tle oulv one so far known in, The recent discovery by Torres (2003) that HD 23642 in the Pleiades is an SB2 eclipsing binary (the only one so far known in742models without explicitly considering such connections.,models without explicitly considering such connections.743 Consider a set of observed band-powers D; in units of p K. together with their covariance matrix Pj.," Consider a set of observed band-powers $\mathcal{D}_i$ in units of $\mu$ $^2$, together with their covariance matrix $P_{ij}$."744 If the overall fractional calibration uncertainty of the experiment 15 5 we can add this to the covariance matrix as follows: For the purposes of the present analysis we assume s=0.08 which includes both temperature scale and beam uncertainties (the fractional error on the band-powers ts corresponding to in temperature units — see Paper II)., If the overall fractional calibration uncertainty of the experiment is $s$ we can add this to the covariance matrix as follows: For the purposes of the present analysis we assume $s=0.08$ which includes both temperature scale and beam uncertainties (the fractional error on the band-powers is corresponding to in temperature units — see Paper II).745 Now consider a model power spectrum C;., Now consider a model power spectrum $\mathcal{C}_l$.746" The expectation value of the data given the model is obtained through the window function WP/7 ((Knox 1999). The band-power window functions WP// are calculated from the band-power Fisher matrix. F.and the Fisher matrix £ of the bands. 4;. sub-divided into individual multipole moments. ((adapted from 1999, for Fisher matrices. with significant off-diagonal elements)."," The expectation value of the data given the model is obtained through the ``band-power'' window function $W^\mathrm{B}_{il}/l$ \markcite{knox99}( 1999), The band-power window functions $W^\mathrm{B}_{il}/l$ are calculated from the band-power Fisher matrix, $F$,and the Fisher matrix $F^\mathrm{s}$ of the bands, $b_i$, sub-divided into individual multipole moments, \markcite{knox99}( (adapted from 1999, for Fisher matrices with significant off-diagonal elements)."747 The sum of each row of the array WP// is unity. so Equation (2)) simply represents a set of weighted means.," The sum of each row of the array $W^\mathrm{B}_{il}/l$ is unity, so Equation \ref{eqn:wfunc}) ) simply represents a set of weighted means."748 Note that any experiment with less than full sky coverage will always have non top-hat band-power window functions., Note that any experiment with less than full sky coverage will always have non top-hat band-power window functions.749 In practice. we calculate Equation (3)) by subdividing each band into four sub-bands. and interpolate the results.," In practice, we calculate Equation \ref{eqn:wfcalc}) ) by subdividing each band into four sub-bands, and interpolate the results."750 The functions for the bband-powers are plotted in Figure |.. and are available at ourwebsite!.," The functions for the band-powers are plotted in Figure \ref{fig:wfunc}, and are available at our."751. In practice the effect of using the correct window function. versus simply choosing the C; at the nominal band center. is extremely modest.," In practice the effect of using the correct window function, versus simply choosing the $\mathcal{C}_l$ at the nominal band center, is extremely modest."752 The uncertainties of the D; are non-Gaussian so it would not be correct to calculate 47 at this point., The uncertainties of the $\mathcal{D}_i$ are non-Gaussian so it would not be correct to calculate $\chi^2$ at this point.753 However it is possible to make a transformation such that the uncertainties become Gaussian to a very good approximation ((Bond.Jaffe. 2000).," However it is possible to make a transformation such that the uncertainties become Gaussian to a very good approximation \markcite{bond00}(, 2000)."754 An additional set of quantities x; need to be calculated from the data which represent the component of the total uncertainty which ts due to instrument noise., An additional set of quantities $x_i$ need to be calculated from the data which represent the component of the total uncertainty which is due to instrument noise.755 We can then transform each of the variables as follows. and calculate X7 as usual. The inverse covariance matrix. elements Mf. will be approximately independent of the bandpowers 7.," We can then transform each of the variables as follows, and calculate $\chi^2$ as usual, The inverse covariance matrix elements $M^Z_{ij}$ will be approximately independent of the bandpowers $\mathcal{D}_i$."756 This is true even with the added calibration uncertainty term. in Equation. (1)). under the assumption that the band-power uncertainty is sample variance dominated. 1e... D;/v;>| (as is the case with almost all the bband-powers). or that the fractional calibration uncertainty is small compared to the total uncertainty in the band-power. NiiD>. which is the case forDMR.," This is true even with the added calibration uncertainty term in Equation \ref{eqn:varcal}) ), under the assumption that the band-power uncertainty is sample variance dominated, i.e., $\mathcal{D}_i/x_i757\gg 1$ (as is the case with almost all the band-powers), or that the fractional calibration uncertainty is small compared to the total uncertainty in the band-power, $s^2 \ll N_{ii}/\mathcal{D}_i^2$ , which is the case for."758. Use of this transformation is very important as it allows us to use \7. and therefore not only to find the best fitting model. but to determine an absolute goodness of fit.," Use of this transformation is very important as it allows us to use $\chi^2$, and therefore not only to find the best fitting model, but to determine an absolute goodness of fit."759 The ability of smaller angular scale (/>100) CMB data to set constraints on model parameters is much improved when the large angular scale (/<25) information from the unstrument is included., The ability of smaller angular scale $l>100$ ) CMB data to set constraints on model parameters is much improved when the large angular scale $l\leq25$ ) information from the instrument is included.760 We use the bbandpowers deseribed and tabulated in Paper II together with the 24 bband-powers provided in the RADPACK distribution ((Knox 2000: 2000). concatenating the D; and s; vectors and forming a block diagonal covariance matrix.," We use the bandpowers described and tabulated in Paper II together with the 24 band-powers provided in the RADPACK distribution \markcite{knox_radpack,bond00}( (Knox 2000; 2000), concatenating the $\mathcal{D}_i$ and $x_i$ vectors and forming a block diagonal covariance matrix."761 Note that while the effect of the transformation described above is modest for the ppoints. it is very important for those from ((due to the large sample variance at the lower /s).," Note that while the effect of the transformation described above is modest for the points, it is very important for those from (due to the large sample variance at the lower $l$ 's)."762 Figure 2 shows the bband-powers. together with the ddata condensed to a single point for display.," Figure \ref{fig:bestfit} shows the band-powers, together with the data condensed to a single point for display."763 The 47 of the best fit model which falls on our grid is 29.5 for the 9 pplus 24 bband-powers., The $\chi^2$ of the best fit model which falls on our grid is $29.5$ for the 9 plus 24 band-powers.764 Assuming a full 7 degrees of freedom are lost to the fit this is at the point of the cumulative distribution function(cdf).," Assuming a full 7 degrees of freedom are lost to the fit, this is at the point of the cumulative distribution function."765. The parameters of this model are800).. equivalent to(0.," The parameters of this model are, equivalent to."76609.0.64.0.33.0.0.95.0.48).. However. no particular importance should be ascribed to these — the concordance model ((Ostriker 1995; 1995) which is shown has a X7 of 30.8 (76%)) and is also rather a good fit.," However, no particular importance should be ascribed to these — the concordance model \markcite{ostriker95,krauss95}( 1995; 1995) which is shown has a $\chi^2$ of 30.8 ) and is also rather a good fit."767 The message of Figure 2 is simply that there are models within the grid which fit acceptably well. and that we are therefore justified in proceeding to marginalized parameter constraints.," The message of Figure \ref{fig:bestfit} is simply that there are models within the grid which fit acceptably well, and that we are therefore justified in proceeding to marginalized parameter constraints."768 We convert \7 to likelihood. £2€7.," We convert $\chi^2$ to likelihood, $\mathcal{L}=e^{-\chi^2/2}$."769" The extreme degeneracy of CMB data in the (O,,.O4) plane has already been mentioned."," The extreme degeneracy of CMB data in the $(\Om,\Ol)$ plane has already been mentioned."770 This inability to choose betweer models with the same lis in fact weakly broken at very low-/ numbers by the Sachs-Wolfe effect ((Efstathiou 1999)., This inability to choose between models with the same is in fact weakly broken at very $l$ numbers by the Sachs-Wolfe effect \markcite{efstathiou99}( 1999).771" The likelihood contours diverge from the Q,,,=1 line as bbecomes =>|. and the allowed region broadens."," The likelihood contours diverge from the $\Ot=1$ line as becomes $\gg1$, and the allowed region broadens."772 Consequently the marginal likelihood curve of aaequires a high side tail as models with progressively greater aare included., Consequently the marginal likelihood curve of acquires a high side tail as models with progressively greater are included.773 These high mmodels have very low values of /. and are known to be invalid from a wide range of non-CMB data.," These high models have very low values of , and are known to be invalid from a wide range of non-CMB data."774 This being the case it is clearly not sensible to allow them to influence our results., This being the case it is clearly not sensible to allow them to influence our results.775 We are therefore prompted to introduce additional external information., We are therefore prompted to introduce additional external information.776" We could simply restrict aand tto some “reasonable”range: for example requiring O470 and Q,,« 1.", We could simply restrict and to some “reasonable”range; for example requiring $\Ol>0$ and $\Om<1$ .777 Instead we choose to introduce a prior on, Instead we choose to introduce a prior on778media (NGC 3516 I&riss et al 1996: MICC-6-3-15 Otani et al 1996).,media (NGC 3516 Kriss et al 1996; MCG-6-3-15 Otani et al 1996).779 The preseut analysis indicates that PGILOL|226 is another such case of iiultiphase absorbing mediuu (but the non-sumiultaucitv of the observatious has to be kept iu munud)., The present analysis indicates that PG1404+226 is another such case of multiphase absorbing medium (but the non-simultaneity of the observations has to be kept in mind).780 With the detection of N-rav and UV absorption in PCLIOL|226 the statistical association between the presence of UV absorption lines aud N-ray absorption edges becomes stronger (Ulich 1988. Mathur Wilkes Elvis 1998).," With the detection of X-ray and UV absorption in PG1404+226 the statistical association between the presence of UV absorption lines and X-ray absorption edges becomes stronger (Ulrich 1988, Mathur Wilkes Elvis 1998)."781 The two absorbers could be two different eascous phases; partaking iu the same outflow but differing by their pliysical couditious. velocity aud radial distance to the central black hole.," The two absorbers could be two different gaseous phases, partaking in the same outflow but differing by their physical conditions, velocity and radial distance to the central black hole."782Observations of NGC 4151 were made on 7 Max 2001 using the University of Florida mid-infrared camera/spectrometer OSCIR on the Gemini North 8an telescope.,Observations of NGC 4151 were made on 7 May 2001 using the University of Florida mid-infrared camera/spectrometer OSCIR on the Gemini North 8-m telescope.783 OSCR. uses a Rockwell 128 x 128 Si:As Blocked Impurity Band (BIB) detector., OSCIR uses a Rockwell 128 x 128 Si:As Blocked Impurity Band (BIB) detector.784 On Gemini North. OSCIR has a plate scale of 070089 1. corresponding to a field of view of 111744 x 11744.," On Gemini North, OSCIR has a plate scale of 089 $^{-1}$, corresponding to a field of view of 4 x 4."785" Images were obtained in the N (A,=10.8 ja. AA=5.2 n) and HIW18 (A;—18.2 jam. AA=1.7 n) fillers using a standard chop/nod technique to remove skv backeround aud thermal emission from the telescope."," Images were obtained in the N $\lambda _{o}$ =10.8 $\micron$ $\Delta \lambda $ =5.2 $%786\micro n) and IHW18 $\lambda _{o}$ =18.2 $\micron$ $\Delta \lambda $ =1.7 $%787\micro n) filters using a standard chop/nod technique to remove sky background and thermal emission from the telescope."788 The chopper throw was 15¢ in declination at a frequency. of 3 Iz and the telelescope was nocdcdedIded every 230 SOCOLDCGCS.," The chopper throw was $%789\arcse c in declination at a frequency of 3 Hz and the telescope was nodded every 30 seconds."790| NGC 4151 was observed for a total chopped integration (ime of 360 seconds αἱ 10.5 jan and 480 seconds at [8.2 yan., NGC 4151 was observed for a total chopped integration time of 360 seconds at 10.8 $\micron$ and 480 seconds at 18.2 $\micron$.791 Observations of 3 GGem were taken for flux calibration and as a measure of the telescope point spread funcüon (PSF)., Observations of $\beta $ Gem were taken for flux calibration and as a measure of the telescope point spread function (PSF).792 Measurements. of other calibration stars throughout the night showed flux calibration variations of less than ad 10.8 n and less than at 15.2 jam.," Measurements of other calibration stars throughout the night showed flux calibration variations of less than at 10.8 $%793\micro n and less than at 18.2 $\micron$."794 Absolute calibration 3 GGem was achieved using a spectral inracliance model by Cohen (1995) adjusted for filler and atmospheric transmission.," Absolute calibration $%795\beta Gem was achieved using a spectral irradiance model by Cohen (1995) adjusted for filter and atmospheric transmission."796 The calibration value and EWILIM were also color corrected to account [or the cifferent spectral slope of 3 GGem versus NGC 4151 as observed within our N and. IIIWIS filters., The calibration value and FWHM were also color corrected to account for the different spectral slope of $\beta $ Gem versus NGC 4151 as observed within our N and IHW18 filters.797 The measured color corrected EWIIM of 3 GGem was 07553 at 10.5 nand 07553 al 18.2 jan based on a GO second chopped integration.," The measured color corrected FWHM of $\beta $ Gem was 53 at 10.8 $%798\micro nand 58 at 18.2 $\micron$ based on a 60 second chopped integration."799 Short integrations of 6 GGem were sufficient for comparison to NGC 4151 due to the stability of the OSCIR/Gemini PSF., Short integrations of $\beta $ Gem were sufficient for comparison to NGC 4151 due to the stability of the OSCIR/Gemini PSF.800 Observations of several standard stars including 9 GGem. j(/ Uma. and 5. Aq! showed variations in the FEWIIM of < throughout the night.," Observations of several standard stars including $\beta $ Gem, $\mu $ Uma, and $\gamma $ Aql showed variations in the FWHM of $<$ throughout the night."801 Finally. observations of NGC 4151 showed no change in structure when divided into increments of time equal to that of the PSF (605).," Finally, observations of NGC 4151 showed no change in structure when divided into increments of time equal to that of the PSF (60s)."802 wwas mounted on the telescope with the Gemini instrument rotator oriented such (hat north was up and east was left on the detector array., was mounted on the telescope with the Gemini instrument rotator oriented such that north was up and east was left on the detector array.803" In. post-processing. images of the PSF star 2 GGem were ""unrotated ο and -22.9° ἀπ 10.8 jn and 18.2 jum respectively to match the position angle of the Gemini North telescope aas projected on the detector array when NGC 4151 was observed."," In post-processing, images of the PSF star $\beta $ Gem were “unrotated” $\degr$ and $\degr$ at 10.8 $\micron$ and 18.2 $\micron$ respectively to match the position angle of the Gemini North telescope as projected on the detector array when NGC 4151 was observed."804 This is necessary to correctly. account for the rotation of the telescope pupil with respect to OSCIR (during an observation or when changing pointing) due to the all-az mount of the Gemini North telescope., This is necessary to correctly account for the rotation of the telescope pupil with respect to OSCIR (during an observation or when changing pointing) due to the alt-az mount of the Gemini North telescope.805 In addition. PSF images were rotationally “smeared” to account for the slight rotation of the pupil (< 4°) during the exposure times of NGC 4151.," In addition, PSF images were rotationally “smeared” to account for the slight rotation of the pupil $\lesssim $ $\degr$ ) during the exposure times of NGC 4151."806 Flux density maps were created by convolving images al 10.3 jan with the 18.2 jm PSF and vice-versa to attain (he same resolution at both wavelengths., Flux density maps were created by convolving images at 10.8 $\micron$ with the 18.2 $\micron$ PSF and vice-versa to attain the same resolution at both wavelengths.807 Color temperature and enission optical depth maps were calculated based on the ratio of these images., Color temperature and emission optical depth maps were calculated based on the ratio of these images.808 Since no astrometric calibration was perlormed due to the limited field of view of OSCIR. the," Since no astrometric calibration was performed due to the limited field of view of OSCIR, the"809star shows the ἐν line in strong emission. together with li; and ff. lines in clear core emission and. ffs only in a weak wav.,"star shows the $H_{\alpha}$ line in strong emission, together with $H_{\beta}$ and $H_{\gamma}$ lines in clear core emission and $H_{\delta}$ only in a weak way."810 The 27. 37. 38. 42. 48. 49 and 19. 26 multiplets also appear in emission.," The 27, 37, 38, 42, 48, 49 and 19, 26 multiplets also appear in emission."811 Ehe Balmer continuum is in emission. too. but not as strong as Stephenson Sancluleak (1971) claimed.," The Balmer continuum is in emission too, but not as strong as Stephenson Sanduleak (1971) claimed."812" Ehe ££, equivalent width is 76 and the rotation velocity is near οs/ni~210.—300 km/see from lines 4471 and 4026.", The $H_{\alpha}$ equivalent width is $\sim~76$ and the rotation velocity is near $v~sin~i \sim 270-300$ km/sec from lines 4471 and 4026.813 The spectral classilication of LSS 440 was performed using the BCD spectrophotometric svstem (sce Barbier Chalonge 1941. Chalonge Divan 1952. 1973 ancl C'idale et al.," The spectral classification of LSS 440 was performed using the BCD spectrophotometric system (see Barbier Chalonge 1941, Chalonge Divan 1952, 1973 and Cidale et al."814 2001 for the description of the method)., 2001 for the description of the method).815 Briellv. the method is based on the study. of the Balmer discontinuity. which is independent on interstellar ancl circumstellar extinctions.," Briefly, the method is based on the study of the Balmer discontinuity, which is independent on interstellar and circumstellar extinctions."816" Using then the obtained BCD parameters Aj,=50.7 AL D=0.078 dex and calibration tables given by Zorec (1986). we classified this star as DO Ve."," Using then the obtained BCD parameters $\lambda_1 = 59.7$ , $D = 0.078$ dex and calibration tables given by Zorec (1986), we classified this star as B0 Ve."817 Phe carly type and the presence of emission Fell lines could indicate LSS 440 as a member of Group I according to the classification scheme proposed by Jaschek et al. (, The early type and the presence of emission FeII lines could indicate LSS 440 as a member of Group I according to the classification scheme proposed by Jaschek et al. (8181980).,1980).819 The models given by Zoree ct al. (, The models given by Zorec et al. (820"2002) can be used to get the average photospheric properties for this star as well: My=3640.5: εξ30000+1000A: fogg=4.0+0.1 and Ad,—6540.2.","2002) can be used to get the average photospheric properties for this star as well: $M_V =821-3.6 \pm 0.5$; $T_{eff} = 30000 \pm 1000~K$; $log~g = 4.0 \pm 0.1$ and $M_{bol} = -6.5 \pm 0.2$."822 Combining with Cirardi et al. (, Combining with Girardi et al. (823"2000) evolutionary models of solar metallicity. a star with such properties should have a mass near 15 Vf; and an age about 5-6 10"" vr.","2000) evolutionary models of solar metallicity, a star with such properties should have a mass near 15 ${\cal M}_{\sun}$ and an age about 5-6 $10^6$ yr."824 Likewise. based on the slope change of the star spectra from 4000 to 4600 and using the Chalonge Divan (1973) calibration improvements to the BCD method by Cidale ct al. (," Likewise, based on the slope change of the star spectra from 4000 to 4600, and using the Chalonge Divan (1973) calibration improvements to the BCD method by Cidale et al. ("8252001). we can compute the star visual absorption. (Clo). produced. by both the interstellar dust and the circumstellar envelope.,"2001), we can compute the star visual absorption $A_V$ ) produced by both the interstellar dust and the circumstellar envelope."826 Ehe computations vielded ely=1.38 setting the true distance modulus of LSS 440 in VoMy1444c0.5 corresponding to a distance d=7.7 kpe., The computations yielded $A_V = 1.33$ setting the true distance modulus of LSS 440 in $V_O - M_V = 14.44 \pm 0.5$ corresponding to a distance $d=7.7$ kpc.827" Fabregat ""Forrejon. (2000) studied. the abundance of Be stars in open clusters as a function of the cluster ages.", Fabregat Torrejon (2000) studied the abundance of Be stars in open clusters as a function of the cluster ages.828 Following these authors findings De-tvpe stars show a maximum of appearance in clusters the age of NGC 2401., Following these authors findings Be-type stars show a maximum of appearance in clusters the age of NGC 2401.829to the Ne NI flux was taken.,to the Ne XI flux was taken.830 The largest contribution found amounted to15%... but was less than for the great majority of the lines. confirming the assessment of McelIxeuzie that Fe XIX blends are not significant [or these observations.," The largest contribution found amounted to, but was less than for the great majority of the lines, confirming the assessment of \citet{McKenzie.Feldman:92} that Fe XIX blends are not significant for these observations."831 The abundance ratios as a function of temperature for both isothermal and DEM cases are shown in Figure 4.. together with their error-weighted linear best fits.," The abundance ratios as a function of temperature for both isothermal and DEM cases are shown in Figure \ref{f:abuns}, together with their error-weighted linear best fits."832 Best-fits accounted lor errors both in the Ne/O fhix ratios. and in the temperatures derived [rom the Fe XVII and Fe XVIII lines.," Best-fits accounted for errors both in the Ne/O flux ratios, and in the temperatures derived from the Fe XVII and Fe XVIII lines."833 The temperature dependence in (the derived Ne/O abundance ratios is again obvious. wilh both DEM and isothermal cases showing a rise to higher Ne/O with rising temperature.," The temperature dependence in the derived Ne/O abundance ratios is again obvious, with both DEM and isothermal cases showing a rise to higher Ne/O with rising temperature."834 The mean Ne/O ratio is slighth lower than values proposed by Asplundetal.(2005.Ne/O-0.15bynumber.or—0.32in logarithm).. Asplundetal.(2009.Ne/O=0.17bvnun-or—0.76inlog) ancl Grevesse&Sauval(1998.Ne/O=0.18bxnumberor—0.75inlog)..," The mean Ne/O ratio is slightly lower than values proposed by \citet[Ne/O=0.15 by number, or $-0.82$ in logarithm]{Asplund.etal:05}, \citet[Ne/O=0.17 by number, or $-0.76$ in log]{Asplund.etal:09} and \citet[Ne/O=0.18 by number or $-0.75$ in log]{Grevesse.Sauval:98}."835 The data of Schmelzetal.(2005). did not include the Fe f[Iuxes we require here to derive DEM peak temperatures ancl are therefore not shown., The data of \citet{Schmelz.etal:05b} did not include the Fe fluxes we require here to derive DEM peak temperatures and are therefore not shown.836 However. it is clear [from (he overlap ol Schmelzetal.(2005). and MéelIxenzie&Feldman(1992) line intensity ratios shown in Figure 3.. aud comparison of Figures 32. and 4.. that (hose data also correspond (to a mean slightly lower than these values.," However, it is clear from the overlap of \citet{Schmelz.etal:05b} and \citet{McKenzie.Feldman:92} line intensity ratios shown in Figure \ref{f:linerats}, and comparison of Figures \ref{f:linerats} and \ref{f:abuns}, that those data also correspond to a mean slightly lower than these values."837 Can errors in (he underlving atomic data be responsible for the apparent trend of Ne/O with temperature?, Can errors in the underlying atomic data be responsible for the apparent trend of Ne/O with temperature?838 The IIe-like and II-like ions present the simplest cases for computing both ion balances and collisional excitation rates. and atomic data for these species should in general be more accurate than for more complex ions.," The He-like and H-like ions present the simplest cases for computing both ion balances and collisional excitation rates, and atomic data for these species should in general be more accurate than for more complex ions."839 The shape of the theoretical Ne IN/O VIII emissivitv ratio in the temperature range of interest. here is determined primarily by the increasing excitation rate wilh temperature for both species and the of the Ne IX and O VIII ion populations toward higher temperatures., The shape of the theoretical Ne IX/O VIII emissivity ratio in the temperature range of interest here is determined primarily by the increasing excitation rate with temperature for both species and the ramp-down of the Ne IX and O VIII ion populations toward higher temperatures.840 It is difficult to imagine incurring an error of a factor of ~2 in the ratio of the former., It is difficult to imagine incurring an error of a factor of $\sim 2$ in the ratio of the former.841 Revised assessments of {he emissivity ingredients for the Ne IX and O VIII resonance lines were included in version 6 of the CHIANTI database (Dereοἱal.2009) used here., Revised assessments of the emissivity ingredients for the Ne IX and O VIII resonance lines were included in version 6 of the CHIANTI database \citep{Dere.etal:09} used here.842 Dereοἱal.(2009) note that QO VIII line intensities are in close agreement with the previous ones., \citet{Dere.etal:09} note that O VIII line intensities are in close agreement with the previous ones.843 Chenοἱal.(2006) also reported. A-Matrix collision strengths for Ne IX within a lew percent of early data., \citet{Chen.etal:06} also reported $R$ -Matrix collision strengths for Ne IX within a few percent of early data.844 We have nevertheless repeated the calculations reported here for CHIANTI versions 4 and 5. and find only very small differences of less than iin derived abundances.," We have nevertheless repeated the calculations reported here for CHIANTI versions 4 and 5, and find only very small differences of less than in derived abundances."845(404)) near Ly16kpc and increasing bevond that.,) near $R_g\gtrsim16\kpc$ and increasing beyond that.846 This distortion will produce an observably lopsided: disk outer disk (see Figs. 141- 12))., This distortion will produce an observably lopsided disk outer disk (see Figs. \ref{fig:inplane432m1L}- \ref{fig:inplane432m1R}) ).847 Unfortunately. it is cillicult to determine precise distances to gas in the outer galaxy and this signature will be difficult to alfirm.," Unfortunately, it is difficult to determine precise distances to gas in the outer galaxy and this signature will be difficult to affirm."848 The (quacdrupole leads to a measurable oval distortion only for Ry>20kpe of (16%)) and is at the percent level or smaller near the solar circle (see Figs. 13- 14))., The quadrupole leads to a measurable oval distortion only for $R_g\gtrsim20\kpc$ of ) and is at the percent level or smaller near the solar circle (see Figs. \ref{fig:inplane432m2L}- \ref{fig:inplane432m2R}) ).849 This mile oval distortion is much smaller than and. will be swamped by the predicted m=1 signature., This mild oval distortion is much smaller than and will be swamped by the predicted $m=1$ signature.850 There are no. simple. formulae. describing the warp amplitudes in general because of the complexity of the interaction., There are no simple formulae describing the warp amplitudes in general because of the complexity of the interaction.851 Qualitative guidelines are as follows., Qualitative guidelines are as follows.852 Within he range of scenarios explored. here. the most. importan condition is the coincidence of wake pattern speed. anc he disk bending-moce frequency.," Within the range of scenarios explored here, the most important condition is the coincidence of wake pattern speed and the disk bending-mode frequency."853 Exploration suggests the 2:1 resonance between the satellite and. orbital. azimutha requencies and the ILIt-like resonance are most important., Exploration suggests the 2:1 resonance between the satellite and orbital azimuthal frequencies and the ILR-like resonance are most important.854 A secondary consideration is the location and. amplitude of the wake itself which depends on the halo profile ane he existence of low-order resonances in the vicinity of the disk., A secondary consideration is the location and amplitude of the wake itself which depends on the halo profile and the existence of low-order resonances in the vicinity of the disk.855 These two features are not independent., These two features are not independent.856 However. if onecould fix the orbital frequencies of halo stars. the wake amplitude would be proportional to the halo density and if onecould fix the density. the wake location would scale with the orbital frequencies.," However, if one fix the orbital frequencies of halo stars, the wake amplitude would be proportional to the halo density and if one fix the density, the wake location would scale with the orbital frequencies."857 The halos considered here are chosen to have [lat rotation curves between the outer disk. aux satellite pericenter., The halos considered here are chosen to have flat rotation curves between the outer disk and satellite pericenter.858 Because the wake is dominated by the 2:1 resonance. the wake peaks at roughly half the pericenter distance.," Because the wake is dominated by the 2:1 resonance, the wake peaks at roughly half the pericenter distance."859 Pherclore. increasing the mass of the halo will tenc to increase the wake amplitude but can decrease the disk warp if the frequeney match with the global disk mocles is less favorable.," Therefore, increasing the mass of the halo will tend to increase the wake amplitude but can decrease the disk warp if the frequency match with the global disk modes is less favorable."860 Because of this complicated. interplay and. sensitivity to the actual disk ancl halo profiles. E will illustrate the range of possibilities with some examples rather than give an exhaustive set of models.," Because of this complicated interplay and sensitivity to the actual disk and halo profiles, I will illustrate the range of possibilities with some examples rather than give an exhaustive set of models."861 For à standard halo and satellite interaction. the disk warp," For a standard halo and satellite interaction, the disk warp"862Furthermore. we have modelled the 1001 emission as a broken power-law. characterized by two power-law slopes and a breaking poiut.,"Furthermore, we have modelled the IC/3K emission as a broken power-law, characterized by two power-law slopes and a breaking point."863 We could not obtain a robust fit letting the two slopes being free pariuncters., We could not obtain a robust fit letting the two slopes being free parameters.864 Therefore. we fixed the steeper slope. a2. equal to the observed slope of the radio spectrum in the ranec HOO.100] MIIz. i.c.. 1.55 (Bagchi ct al.," Therefore, we fixed the steeper slope, $\alpha_{2}$, equal to the observed slope of the radio spectrum in the range [100–400] MHz, i.e., $\alpha_{2}=1.85$ (Bagchi et al."865 1998) ux fixed the VAhallower slope (04) either to 1.0 (from the radio spectrum) or to 0.1. our best Gt with a singlepower-law (cf.," 1998) and fixed the shallower slope $\alpha_{1}$ ) either to 1.0 (from the radio spectrum) or to 0.4, our best fit with a singlepower-law (cf."866 Table 3))., Table \ref{tbl:2CompCentre}) ).867" Tn the first case. with a,=1l. the fit is only slightly better than those with a single power-law aud the derived IC/31I& fiux is wich smaller than the thermal fux."," In the first case, with $\alpha_{1}=1$, the fit is only slightly better than those with a single power-law and the derived IC/3K flux is much smaller than the thermal flux."868 Uufortunatelv. we cannot obtain a ucaningful value for the breakiug poiut.," Unfortunately, we cannot obtain a meaningful value for the breaking point."869 Iu the second case; ay=0.1 the fit is still better and the breaking point is well determined at eL keV. However. the derived fluxes for the thermal aud the broken power-law components are alinost the same. oexdicatins the confusion in separating the thermal frou the non-thermal cussion.," In the second case, $\alpha_{1}=0.4$ the fit is still better and the breaking point is well determined at 7.4 keV. However, the derived fluxes for the thermal and the broken power-law components are almost the same, indicating the confusion in separating the thermal from the non-thermal emission."870 Sarazin (1999) has computed the LIuverse Compton spectra for a number of models with differcut relativistic electron population., Sarazin (1999) has computed the Inverse Compton spectra for a number of models with different relativistic electron population.871 For the models with steady. particle injection. the IC oeission spectra in the combined MECS aud LECS range would be well represeuted by a siugle power-law with slope àzz(p/2). where p is the logarithiu slope of he relativistic electron distribution (cf.," For the models with steady particle injection, the IC emission spectra in the combined MECS and LECS range would be well represented by a single power-law with slope $\alpha \approx872(p/2)$, where $p$ is the logarithm slope of the relativistic electron distribution (cf."873 Fig., Fig.874 12 of Sarazin 1999)., 12 of Sarazin 1999).875 For the models with no injection of electrons but with au initial population. the IC emission could oulv be detectable if the initial population were injected im the cluster at redshift lower than 0.1 (cf.," For the models with no injection of electrons but with an initial population, the IC emission could only be detectable if the initial population were injected in the cluster at redshift lower than 0.1 (cf."876 Fie., Fig.877 13 of Sarazin 1999)., 13 of Sarazin 1999).878 Iu this case. a broken power-law is needed to reproduce the IC emission with o4z(p.1)/2 and αυτν (actually the cussion has au exponential cut-off aud these slopes ave ouly valid in the range [Q.110.0] keV).," In this case, a broken power-law is needed to reproduce the IC emission with $\alpha_{1} \approx (p-1)/2$ and $\alpha_{2} \approx p$ (actually the emission has an exponential cut-off and these slopes are only valid in the range [0.1–10.0] keV)."879 We lave mace fits iu the regions we called. 1st. 2ud. 3rd Rines and N. VSSRS.," We have made fits in the regions we called 1st, 2nd, 3rd Rings and N. VSSRS."880 Iu the 3rd rine and N. VSSRS regions. the error bars are quite laree due to the simall uunuber of counts and it is difficult to deduce stroug results.," In the 3rd ring and N. VSSRS regions, the error bars are quite large due to the small number of counts and it is difficult to deduce strong results."881 The bydrogen column density aud metallicity decrease from the centre to the 2ud ring. while the temperatures of the 1st and 2ud rugs are quite larger than iu the ceutre.," The hydrogen column density and metallicity decrease from the centre to the 2nd ring, while the temperatures of the 1st and 2nd rings are quite larger than in the centre."882 Iu section ?7.. we have attempted to separate the thermal and uou-thermal X-ray cussion coniponents at the VSSRS aud at the South Blob regions. where radio observations have detected diffuse svuchrotrou radiation. showing the presence of maguetic fields and relativistic electrons.," In section \ref{sec:results}, we have attempted to separate the thermal and non-thermal X-ray emission components at the VSSRS and at the South Blob regions, where radio observations have detected diffuse synchrotron radiation, showing the presence of magnetic fields and relativistic electrons."883 Here. we estimate the volume average D field in these zones. using the nou-thermal fluxes (cf.," Here, we estimate the volume averaged $B$ field in these zones, using the non-thermal fluxes (cf."884 Table 3))., Table \ref{tbl:2CompCentre}) ).885 We wish to inject a cautionary note at this stage: in this section the 2 values are expressed as actual estimates. where we have used the nominal results given in Table 3..," We wish to inject a cautionary note at this stage: in this section the $B$ values are expressed as actual estimates, where we have used the nominal results given in Table \ref{tbl:2CompCentre}."886 Uowever. given the nou-thermal N-rav fluxes errors bars. these fluxes should be regarded as upper limits.," However, given the non-thermal X-ray fluxes errors bars, these fluxes should be regarded as upper limits."887 Therefore all our estimates of the B field intensities should be ideally treated as ouly lower limits., Therefore all our estimates of the $B$ field intensities should be ideally treated as only lower limits.888" lu the first case (MERAL|DPOW). when the spectral indices of non-thermal X-ray aud radio photons are both fixed at a,=I. the IC/3I& flus (fie) is estimated to be 3.3.10Pa) Perg tan 7 in 210 keV range and the radio flux (fa) to be 6.6«10 tere tem 7 in 10100 MIIZ range."," In the first case (MEKAL+POW), when the spectral indices of non-thermal X-ray and radio photons are both fixed at $\alpha_{1} = 1$, the IC/3K flux $f_{\rm889IC}$ ) is estimated to be $3.3 \times 10^{-13}$ erg $^{-1}$ $^{-2}$ in 2–10 keV range and the radio flux $f_{\rm S}$ ) to be $6.6 \times89010^{-14}$ erg $^{-1}$ $^{-2}$ in 10–100 MHz range."891" This leads to a field value of B=1.5212:0.2 Inc. Iu the secoud case. when we have allowed the spectral oeidex to vary. we have obtained the value of a,=0.1. with laree error bars (Table 3))."," This leads to a field value of $B = 1.34\pm 0.24 \mu$ G. In the second case, when we have allowed the spectral index to vary, we have obtained the value of $\alpha_{1} = 0.4$, with large error bars (Table \ref{tbl:2CompCentre}) )."892 This value of spectral neidex seenis roughly consistent with radio spectral shape ithe range 10.15 MIIZz (Baechi. Pislar Lima Neto 1998).," This value of spectral index seems roughly consistent with radio spectral shape in the range 10–45 MHz (Bagchi, Pislar Lima Neto 1998)."893 Tn this case we have fic:1 Mores 1 7 aud fo=LE&I10 teres tem 7.," In this case we have $f_{\rm IC} = 1.2 \times89410^{-12}$ erg $^{-1}$ $^{-2}$ and $f_{\rm S} = 4.4 \times89510^{-14}$ erg $^{-1}$ $^{-2}$."896" From +jose, we then obtain B=0.10x 0.134. Finally. we consider the more complex model where the nou-thermal spectrin is represeuted by two power-law forms with a cspectral break! in-between (MERAL|2POW)."," From these, we then obtain $B = 0.40 \pm 0.13 \mu$ G. Finally, we consider the more complex model where the non-thermal spectrum is represented by two power-law forms with a `spectral break' in-between (MEKAL+2POW)."897 When the low and the high fequency spectral seeimeuts are fixedpriori. with spectral indices ay= land αυ= L.85. we once more obtain the magnetic," When the low and the high frequency spectral segments are fixed, with spectral indices $\alpha_{1} = 1$ and $\alpha_{2} = 1.85$ , we once more obtain the magnetic"898onlv the sources with reliable spectra in (his region (i.e. MIPS464. MIPS15880. MIPS16080. κ MIPS22548).,"only the sources with reliable spectra in this region (i.e. MIPS464, MIPS15880, MIPS16080, MIPS16152, MIPS22548)."899" The aabsorplion and the 6.35 and ΠΑΟ features appear in this as well. although the ""bump is less pronounced (han seen in rellig.lach.."," The absorption and the 6.85 and HAC features appear in this as well, although the `bump' is less pronounced than seen in \\ref{fig_stack}."900 The CCO feature is hinted at but seems (o be driven bv the feature in MIPSA464 as when this source is not inelucled we have the four outlier stacks., The CO feature is hinted at but seems to be driven by the feature in MIPS464 as when this source is not included we have the four outlier stacks.901 This re-inforces the conclusion that. apart from the three sources discussed before. the CO feature is either not present or is extremely weak (τρ jj 00.2)/nthema jorit yof oursample.," This re-inforces the conclusion that, apart from the three sources discussed before, the CO feature is either not present or is extremely weak $\tau_{4.6}$ $<<$ 0.2) in the majority of our sample."902 The silicate feature does not fall within our new deeper data and is discussed in more detail in Sajinaetal.(200728). for the GOL sources ancl Dasvraetal.(2009) [or the GO2 sources., The silicate feature does not fall within our new deeper data and is discussed in more detail in \citet{sajina07} for the GO1 sources and \citet{dasyra09} for the GO2 sources.903 ILowever here we acldress (he measurement and reliability of the silicate feature depths for our 11 targets specilically., However here we address the measurement and reliability of the silicate feature depths for our 11 targets specifically.904 This is necessary because in order to pul our newly detected molecular absorption features in context with local sources we would like to look αἱ the ice-to-silicate and ILAC-to-silieate feature ratios (which we do in the Discussion)., This is necessary because in order to put our newly detected molecular absorption features in context with local sources we would like to look at the ice-to-silicate and HAC-to-silicate feature ratios (which we do in the Discussion).905 Many of our sources have poorly defined continuum bevond rest-Drame ~ aand also tend to have very low signal-to-noise inside the feature itself (see P , Many of our sources have poorly defined continuum beyond rest-frame $\sim$ and also tend to have very low signal-to-noise inside the feature itself (see \\ref{fig_specs}) ).906hesefeaturesiwereoriginallyfitiilhapowerlawplusertinclionlewimodel(see Sajinaetal.20," These features were originally fit with a power law plus extinction law model \citep[see][]{sajina07}, which as discussed earlier relates to the observed silicate feature depth via $\tau_{9.7,model}$ $\tau_{9.7,obs}$."907 For some of the sources this is fairly well determined. but for others the fitted value has large uncertainty (either due to poorly determined continuum. or uncertaintv due to the PAII features [Iankine the feature).," For some of the sources this is fairly well determined, but for others the fitted value has large uncertainty (either due to poorly determined continuum, or uncertainty due to the PAH features flanking the feature)."908" For example. for MIPS464 we derived model 7;i; € 11.6 which translates to observed 79,2hs d 11.1."," For example, for MIPS464 we derived model $\tau_{9.7}$ $\pm$ 1.6 which translates to observed $\tau_{9.7,obs}$ $\pm$ 1.1."909 Dy contrast. MIPS158380 has considerably better defined feature. and we derive model τονi 400.4 which translates to observed Tyrobs d: 00.3.," By contrast, MIPS15880 has considerably better defined feature, and we derive model $\tau_{9.7}$ $\pm$ 0.4 which translates to observed $\tau_{9.7,obs}$ $\pm$ 0.3."910 In the case of the strong-PAIL source. MIPS22530. the silicate feature is saturated and we can only determine (hat it has observed silicate absorption of 795 7.33.7.," In the case of the strong-PAH source, MIPS22530, the silicate feature is saturated and we can only determine that it has observed silicate absorption of $\tau_{9.7}$ $>$ 3.7."911 In order (ο farther test the uncertainty associated with our silicate feature optical depth estimates. we also fit all of them using (lie same procedure as used for the local ULIBRGs in Spoonetal.(2007).," In order to further test the uncertainty associated with our silicate feature optical depth estimates, we also fit all of them using the same procedure as used for the local ULIRGs in \citet{spoon07}."912. We find that for the majority of the sources. the two approaches give consistent results. the values obtained diller most for (hie sources with poor continuum ancl noisy features. but are within the fitted uncertainty (e.g. MIPS464 has 75; 22.5 consistent with our το 11.1).," We find that for the majority of the sources, the two approaches give consistent results, the values obtained differ most for the sources with poor continuum and noisy features, but are within the fitted uncertainty (e.g. MIPS464 has $\tau_{Si}$ 2.5 consistent with our $\tau_{9.7}$ $\pm$ 1.1)."913 The most substantial difference comes lor MIPS22530 where, The most substantial difference comes for MIPS22530 where9142.03 Jy at 60 um and 4.51 Jy at 100 wm. Estimating the TIR using equation 5 from ? we find 3.1x10!°L which yields SFR(IRAS)=3.74Μοντ! using equation 4 from ? converted toa? IMF.,2.03 Jy at 60 $\mu$ m and 4.51 Jy at 100 $\mu$ m. Estimating the TIR using equation 5 from \cite{dale2002a} we find $\mathrm{3.1\times10^{10}~L_\odot}$ which yields $\mathrm{SFR(IRAS)=3.74~M_\odot~yr^{-1}}$ using equation 4 from \cite{kennicutt1998a} converted to a \cite{kroupa2001a} IMF.915 The total SFR that we derived from 24+FUV is 2.89Μοyr!., The total SFR that we derived from 24+FUV is $\mathrm{2.89~M_\odot~yr^{-1}}$.916" This is only slightly lower than the IRAS value, most likely due to missing extended emission."," This is only slightly lower than the IRAS value, most likely due to missing extended emission."917 CO(1-0) and CO(2-1) emission was detected for all pointings except for C2 for which there is a marginal detection in CO(1-0) and no detection in CO(2-1)., CO(1–0) and CO(2–1) emission was detected for all pointings except for C2 for which there is a marginal detection in CO(1–0) and no detection in CO(2–1).918 The quality for the other positions is sufficient to determine the CO(2-1)/CO(1- ratios., The quality for the other positions is sufficient to determine the CO(2--1)/CO(1--0) ratios.919" The line ratios in NC (0.9+0.1) and C3 (0.9+0.1) are consistent with the average value found in nearby galaxies (0.89,?),, if the CO emission comes from a region roughly as large as the CO(1-0) beam."," The line ratios in NC $\pm$ 0.1) and C3 $\pm$ 0.1) are consistent with the average value found in nearby galaxies \citep[0.89,][]{braine1992a}, if the CO emission comes from a region roughly as large as the CO(1–0) beam."920" At these positions, optically thin emission, for which a line ratio »1 would be expected, can be excluded."," At these positions, optically thin emission, for which a line ratio $>1$ would be expected, can be excluded."921" Indeed, at the local thermodynamical equilibrium for a high temperature and high opacity we have CO(2-1)/CO(1-0)=1."," Indeed, at the local thermodynamical equilibrium for a high temperature and high opacity we have CO(2--1)/CO(1--0)=1."922 In the case of optically thin emission we expect line ratios >1 with an asymptotic case of CO(2-1)/CO(1-0) = (21/vio? for optically thin gas in local thermodynamical equilibrium with a sufficiently high temperature (?).., In the case of optically thin emission we expect line ratios $>1$ with an asymptotic case of CO(2–1)/CO(1–0) = $\left(\nu_{21}/\nu_{10}\right)^2$ for optically thin gas in local thermodynamical equilibrium with a sufficiently high temperature \citep{wilson2009a}.923" Both the NE clump and C5 exhibit line ratios above 1 (1.3+0.2 for the NE clump, and 1.5+0.6 for C5)."," Both the NE clump and C5 exhibit line ratios above 1 $1.3\pm0.2$ for the NE clump, and $1.5\pm0.6$ for C5)."924 This could be dueto (i) optically thin emission or (ii) emission concentrated to a region smaller than the CO(1-0) beam., This could be dueto (i) optically thin emission or (ii) emission concentrated to a region smaller than the CO(1-0) beam.925" Since both the 24 um and the CO emission are strong at these positions, we think that option (ii) is more likely."," Since both the 24 $\mu$ m and the CO emission are strong at these positions, we think that option (ii) is more likely."926 Note however that the beam sizes are different which makes strong conclusions difficult., Note however that the beam sizes are different which makes strong conclusions difficult.927" We calculate the molecular masses using equation 1 from ?:: where Ico is the observed line intensity in the beam in units of K km s!, Xco is the conversion factor to estimate the molecular mass from CO taken as 2x1070cm?(Kkms!)7!, D the distance of the system, © the solid angle of the beam (1.1367, @ being the beam FWHM), and my, the mass of a proton."," We calculate the molecular masses using equation 1 from \cite{braine2001a}: where $\mathrm{I_{CO}}$ is the observed line intensity in the beam in units of K km $^{-1}$, $\mathrm{X_{CO}}$ is the conversion factor to estimate the molecular mass from CO taken as $\mathrm{2\times10^{20}~cm^{-2}~(K~km~s^{-1})^{-1}}$, D the distance of the system, $\Omega$ the solid angle of the beam $\mathrm{1.13\theta^2}$, $\theta$ being the beam FWHM), and $\mathrm{m_p}$ the mass of a proton."928" Similarly to ?,, we do not take into account the helium mass to compute the molecular mass."," Similarly to \cite{bigiel2008a}, we do not take into account the helium mass to compute the molecular mass."929" It corresponds to My,=751coD?O, with My, in Mo, Ico in K km s!, D in Mpc, and Q in arcsec?."," It corresponds to $\mathrm{M_{H_2}=75I_{CO}D^2\Omega}$, with $\mathrm{M_{H_2}}$ in $\mathrm{M_\odot}$, $\mathrm{I_{CO}}$ in K km $^{-1}$, D in Mpc, and $\Omega$ in $^2$."930" The low resolution of HI data makes it difficult to determine the HI mass within the CO(1—0) beam, especially in the main bodies of the galaxies."," The low resolution of HI data makes it difficult to determine the HI mass within the CO(1–0) beam, especially in the main bodies of the galaxies."931 As C5 is relatively well isolated from the rest of the interacting system it is easier to measure its HI mass., As C5 is relatively well isolated from the rest of the interacting system it is easier to measure its HI mass.932" However, rather than examining the mass encompassed in the CO(1-0) beam, we look at the column density in the pixel corresponding to the centre of the CO(1-0) beam in order to limit the blending with the HI emission from nearby regions."," However, rather than examining the mass encompassed in the CO(1–0) beam, we look at the column density in the pixel corresponding to the centre of the CO(1–0) beam in order to limit the blending with the HI emission from nearby regions."933 The derived molecular gas mass as well as molecular and atomic gas column densities are presented in Table 6.., The derived molecular gas mass as well as molecular and atomic gas column densities are presented in Table \ref{tab:masses}.934" The system contains large amounts of molecular gas, particularly in the nuclei."," The system contains large amounts of molecular gas, particularly in the nuclei."935" However, the CO—to-H» conversion factor is uncertain in these environments and it is likely that there is more CO emission per unit H» in galactic centres."," However, the $_2$ conversion factor is uncertain in these environments and it is likely that there is more CO emission per unit $_2$ in galactic centres."936" The molecular mass in the tidal features is lower, 5.8x107 Mg in C2 and 6.8x107 Μο in C5."," The molecular mass in the tidal features is lower, $5.8\times10^7$ $_\odot$ in C2 and $6.8\times10^7$ $_\odot$ in C5."937" Comparing to the sample of TDG candidates of ?,, it is in the lower range of observed molecular masses."," Comparing to the sample of TDG candidates of \cite{braine2001a}, it is in the lower range of observed molecular masses."938" Both nuclei are significantly dominated by their molecular phase, which is commonly observed in the centre of spiral galaxies (?).."," Both nuclei are significantly dominated by their molecular phase, which is commonly observed in the centre of spiral galaxies \citep{bigiel2008a}."939" C5, on the other hand, is HI dominated and its molecular to atomic gas mass ratio is typical of what is observed in collision debris (?).."," C5, on the other hand, is HI dominated and its molecular to atomic gas mass ratio is typical of what is observed in collision debris \citep{braine2001a}."940" A comparison of the HI, CO(1-0) and CO(2-1) spectra of the four CO-detected regions is presented in Fig. 3.."," A comparison of the HI, CO(1–0) and CO(2–1) spectra of the four CO–detected regions is presented in Fig. \ref{fig:HI-CO-spectra}."941" The recession velocity of the system that we determined through optical spectroscopy, CO and HI observations is consistent with the value of 4758 km s! mentioned in the introduction."," The recession velocity of the system that we determined through optical spectroscopy, CO and HI observations is consistent with the value of 4758 km $^{-1}$ mentioned in the introduction."942" The system rotates clockwise, the C5 and NE regions having a recession velocity comprised between 4900 km s! and 5000 km s! whereas the western C3 and C2 regions have a smaller velocity between 4500 km s! and 4700 km s'!."," The system rotates clockwise, the C5 and NE regions having a recession velocity comprised between 4900 km $^{-1}$ and 5000 km $^{-1}$ whereas the western C3 and C2 regions have a smaller velocity between 4500 km $^{-1}$ and 4700 km $^{-1}$."943 The NE region presents a double-peaked profile centered around 4950 km s~!., The NE region presents a double–peaked profile centered around 4950 km $^{-1}$.944 It is most prominent in CO(2-1) in which the peaks are separated by a velocity of 70 km s!., It is most prominent in CO(2–1) in which the peaks are separated by a velocity of 70 km $^{-1}$ .945" The peaks are not as strong in CO(1—0) and HI, probably due to additional contamination because of the larger beam."," The peaks are not as strong in CO(1–0) and HI, probably due to additional contamination because of the larger beam."946" This may be the signature of a rotating ring of star formation in the nucleus of the galaxy with blueshifted and redshifted sides, consistent"," This may be the signature of a rotating ring of star formation in the nucleus of the galaxy with blueshifted and redshifted sides, consistent"947with the summation being over the available bands. and denoted here by the index 7.,"with the summation being over the available bands, and denoted here by the index $i$ ."948 D(z) is the redshift prior. m4; are the model magnitudes computed from the templates (see 827)). m; are the measured magnitudes. and dii; ave the photometric errors ancl moclel dispersions summed in euadrature.," $P(z)$ is the redshift prior, $m_{\mathrm{mod},i}$ are the model magnitudes computed from the templates (see \ref{model}) ), $m_i$ are the measured magnitudes, and $dm_i$ are the photometric errors and model dispersions summed in quadrature."949 In order (ο account for the different dispersions in the absolute magnitudes of the model SNe and their colors. we technically do not fit 7 magnitudes in n bands. but rather one magnitude and (7—1) colors.," In order to account for the different dispersions in the absolute magnitudes of the model SNe and their colors, we technically do not fit $n$ magnitudes in $n$ bands, but rather one magnitude and $(n-1)$ colors."950 We marginalize the likelihood function over the three parameters. ο. Ay. and /. and obtain the summed likelihood for each ivpe of SN. commonly referred (ο in Bavesian literature (e.g...Gelmanetal.1995) as theevidence. In order (o classify the SNe. we define a relative evidence to express the probability that an object is à SN Ia. as We also derive for each SN its posterior redshilt. assuming it belongs to a given tvpe of SN. by marginalizing the relevant likelihood function over the nuisance parameters. namely the age and (he extinction.," We marginalize the likelihood function over the three parameters, $z$, $A_V$, and $t$, and obtain the summed likelihood for each type of SN, commonly referred to in Bayesian literature \citep[e.g., ][]{GELMAN_BAYS} as the, In order to classify the SNe, we define a relative evidence to express the probability that an object is a SN Ia, as We also derive for each SN its posterior redshift, assuming it belongs to a given type of SN, by marginalizing the relevant likelihood function over the nuisance parameters, namely the age and the extinction."951 The final output is then the probability for (he SN to be of type la. rather (han being a core-collapse event. and its posterior z-pdf£.," The final output is then the probability for the SN to be of type Ia, rather than being a core-collapse event, and its posterior z-pdf."952 In (the following sections. we consider the adopted type ofa SN to be the (vpe which has a probability higher (han 0.5.," In the following sections, we consider the adopted type of a SN to be the type which has a probability higher than $0.5$."953 Naturally. the higher this probability. the more secure is (he classification.," Naturally, the higher this probability, the more secure is the classification."954 We also examine the \? value for the best fitting template. in order (o ascertain the goodness of fit in an absolute sense. and in order to reject SN impostors. mainiv active galactic nuclei (AGNs).," We also examine the $\chi^2$ value for the best fitting template, in order to ascertain the goodness of fit in an absolute sense, and in order to reject SN impostors, mainly active galactic nuclei (AGNs)."955 We now apply our algorithm to (wo real data sets. SNLS and GOODS. that have photometric data of the (vpe we are considering (e.g.. SNe observed in at least (ree bands). andfollowup spectroscopy based upon which we can evaluate (he performance of our method.," We now apply our algorithm to two real data sets, SNLS and GOODS, that have photometric data of the type we are considering (e.g., SNe observed in at least three bands), andfollowup spectroscopy based upon which we can evaluate the performance of our method."956It is supposed that mass of the Sun mi is greater (han mass of the Earth 9. therefore myomacano and maomacamo.,It is supposed that mass of the Sun $m_1$ is greater than mass of the Earth $m_2$ therefore $m_1\leq m_1+m_2$ and $m_2\leq m_1+m_2$.957" Im otherwords. m, lies in fey.ry+mo] and maolies in leo.my+ma]. where eq>€»0."," In otherwords, $m_1$ lies in $ [\epsilon_1,m_1+m_2]$ and $m_2$lies in $[ \epsilon_2,m_1+m_2]$, where $\epsilon_1\geq \epsilon_2\geq 0$."958" Using relation po=WII the domain of mass parameter can be obtained as: From relation⋅ r2⋅↽—(1oq,⋡⊇∶⋉≱⋡+7. the domain⋅ of. mass reduction. factor. qj is. given. as: And from relation ss "," Using relation $\mu=\frac{m_{2}}{m_{1}+m_{2}}$, the domain of mass parameter can be obtained as: From relation $r_c^2=(1-\mu)q_1^{2/3}+\mu^2$, the domain of mass reduction factor $q_1$ is given as: And from relation $A_{2}=\frac{r^{2}_{e}-r^{2}_{p}}{5r^{2}}$, where $r_e\in[\epsilon_4,r]$ and $r_e\in[\epsilon_5,r]$ , $\epsilon_4\geq \epsilon_5\geq 0$."959"Now- from.relation. n?2=14-ado224aDAL,1 sn€.[0.2]. T—0.1. then the domain. of. 1, is. as⋅ 0. TU—].∶⊾≱⋡∶⊾≱⋡↘∣∣⋡∣∣↓⇁↾⋡"," The domain of oblateness coefficient canbe obtained as: Now fromrelation $n^{2}=1+\frac{3A_{2}}{2}+\frac{2M_b960r_c}{\left(r_c^2+T^2\right)^{3/2}}$, $n\in [0,2]$, $T=0.1$, then the domain of $M_b$ is obtained as $[0,\frac{33(r+0.01)^{3/2}}{20r}]$."961"∶In particular ife;− p =0(/.1.2.3.4.5).""M⊾my ms=1(unit of− mass). obtained r.cro Launit of distance). then itis obtained ji€[0. 1].q4€ [222.22].44€[-+. 1. and Ad,€(0. 1.6748]."," In particular if $\epsilon_i=0(i=1,2,3,4,5)$, $ m_1+m_2=1$ (unit of mass), $r_c=r=1$ (unit of distance), then itis obtained $\mu\in[0,\frac{1}{2}]$ ,$q_1\in[-2\sqrt{2},2\sqrt{2}]$ ,$A_2 \in\left[-\frac{1}{5},\frac{1}{5}\right]$ , and $M_b\in[0,1.6748]$ ."962 But in the present model it is consideredthat 0—Fi< Fy. ro mrysO definitely q lies in [0.1]. ele€[0.1/5] ie Ay=2.4337x10. 1”.," But in the present model it is consideredthat $0\leq F_p\leq F_g$ , $r_e\geq r_p$ , so definitely $q_1$ lies in [0,1], $A_2\in[0,1/5]$ i.e $A_2=2.4337\times10^{-12}$ ."963Observational studies show resonant KBOs to. have inclinations up to 30° (22)..,"Observational studies show resonant KBOs to have inclinations up to $30^{\circ}$ \citep{brown01,gulbis10}."964 They are commonly believed to have been trapped in an MMR with Neptune when the planet was migrating outward. having their eccentricity and inclination raised during the process.," They are commonly believed to have been trapped in an MMR with Neptune when the planet was migrating outward, having their eccentricity and inclination raised during the process."965 This mechanism explains Pluto’s peculiar orbit (2).. and inclinations of up to ~15° in general for bodies outside Neptune's orbit (2)..," This mechanism explains Pluto's peculiar orbit \citep{malhotra93}, and inclinations of up to $\sim15^{\circ}$ in general for bodies outside Neptune's orbit \citep{malhotra95}."966 However. only a small fraction of the resonant KBOs in the simulations have their inclinations raised in excess of (2)..," However, only a small fraction of the resonant KBOs in the simulations have their inclinations raised in excess of \citep{malhotra00}."967 Other mechanisms have been proposed to account for the observed inclinations. including sweeping secular resonances (?).. and stirring by large planetesimals (?).. but no definitive answer has been given.," Other mechanisms have been proposed to account for the observed inclinations, including sweeping secular resonances \citep{li08}, and stirring by large planetesimals \citep{morbidelli97}, but no definitive answer has been given."968 Scattered KBOs show a wider spread in semi-major axes and their inclinations are usually greater than 10° with a peak around 20° (?).., Scattered KBOs show a wider spread in semi-major axes and their inclinations are usually greater than $10^{\circ}$ with a peak around $20^{\circ}$ \citep{gulbis10}.969 It is this broad distribution in orbital parameters that indicates that their orbits are probably the result of a close encounter with Neptune (2).., It is this broad distribution in orbital parameters that indicates that their orbits are probably the result of a close encounter with Neptune \citep{brown01}.970 ? conelude from simulations that about of the KBOs in the scattered disk might not have suffered a close encounter. but rather obtained their orbits from Neptune's resonances during the migration epoch.," \citet{hahn05} conclude from simulations that about of the KBOs in the scattered disk might not have suffered a close encounter, but rather obtained their orbits from Neptune's resonances during the migration epoch."971 Their model is unable to reproduce the observed abundance of KBOs with i>15° however., Their model is unable to reproduce the observed abundance of KBOs with $i>15^{\circ}$ however.972 From studying the Kuiper Belt. it appears there are 2 clear mechanisms that are able to increase an object’s melination drastically; resonance trapping and close encounters.," From studying the Kuiper Belt, it appears there are 2 clear mechanisms that are able to increase an object's inclination drastically; resonance trapping and close encounters."973 The degree of inclination-raising by resonance trapping is determined. and therefore limited by. the migration distance of the planet.," The degree of inclination-raising by resonance trapping is determined, and therefore limited by, the migration distance of the planet."974 ? shows a migration Neptune over a distance of 7 AU to cause an increase in eccentricity of 0.25 and in inclination of about 107., \citet{malhotra95} shows a migration Neptune over a distance of 7 AU to cause an increase in eccentricity of 0.25 and in inclination of about $10^{\circ}$.975 The inclination that can be reached by direct scattering is limited by the relative velocity between the planet and the object and the escape velocity at the planet's surface. as we shall seein section ??..," The inclination that can be reached by direct scattering is limited by the relative velocity between the planet and the object and the escape velocity at the planet's surface, as we shall seein section \ref{sec:scattering}."976 It appears direct scattering is a more promising way to get bodies onto inclined orbits. and it i$ this path that we will pursue in the rest of this work.," It appears direct scattering is a more promising way to get bodies onto highly-inclined orbits, and it is this path that we will pursue in the rest of this work."977" Suppose we have a planet of mass M, and radius Ay orbiting a star of mass M.. on a circular orbit with Keplerian velocity v&=GM,/ay."," Suppose we have a planet of mass $M_{\rm pl}$ and radius $R_{\rm pl}$ orbiting a star of mass $M_{*}$, on a circular orbit with Keplerian velocity $v_{\rm K}=\sqrt{GM_{*}/a_{\rm pl}}$."978 We assume a planetesimal of mass m«My on an orbit with negligible inclination is approaching the planet with an impact parameter 5 and a relative velocity Veiel-, We assume a planetesimal of mass $m\ll M_{\rm pl}$ on an orbit with negligible inclination is approaching the planet with an impact parameter $b$ and a relative velocity $v_{\rm rel}$.979 If 6 is small enough. the close encounter can be treated as a 2 body interaction. without having to consider the central star.," If $b$ is small enough, the close encounter can be treated as a 2 body interaction, without having to consider the central star."980 During this interaction. the magnitude of the velocity is conserved but the direction is changed by a scattering angle of (e.g.?) We normalize distances to the radius of the planet and velocities to the Keplerian velocity This allowsRy us to rewrite eq.," During this interaction, the magnitude of the velocity is conserved but the direction is changed by a scattering angle of \citep[e.g.][]{weidenschilling75}981 We normalize distances to the radius of the planet and velocities to the Keplerian velocity This allows us to rewrite eq."982 | as follows where v.=QGMyRy)!* is the escape velocity at the surface of the planet., \ref{eq:theta1} as follows where $v_{\rm esc} = (2GM_{\rm pl}/R_{\rm pl})^{1/2}$ is the escape velocity at the surface of the planet.983 This equation shows that a scattering angle of 90° is reached for Thus. for velocities v4ov/V2. an impact parameter smaller than the physical size of the planet is required.," This equation shows that a scattering angle of $90^{\circ}$ is reached for Thus, for velocities $v_{\rm rel}>v_{\rm esc}/\sqrt{2}$, an impact parameter smaller than the physical size of the planet is required."984 Such a planetesimal will crash into the planet., Such a planetesimal will crash into the planet.985 Due to gravitational focussing any planetesimal with an impact parameter smaller than will be lost 1n a physical collision with the planet (?).., Due to gravitational focussing any planetesimal with an impact parameter smaller than will be lost in a physical collision with the planet \citep{safronov66}.986 Thus. for a planet to be able to significantly scatter a planetesimal out of the orbital plane. the relative velocity of the encounter needs to be about à factor 2 lower than the escape velocity at the planets surface.," Thus, for a planet to be able to significantly scatter a planetesimal out of the orbital plane, the relative velocity of the encounter needs to be about a factor 2 lower than the escape velocity at the planet's surface."987 Suppose the planet is able to scatter the planetesimal out of the orbital plane by an angle of 907., Suppose the planet is able to scatter the planetesimal out of the orbital plane by an angle of $90^{\circ}$.988 In the frame of the planet. the planetesimal’s total velocity is now pointing perpendicular to the orbital plane.," In the frame of the planet, the planetesimal's total velocity is now pointing perpendicular to the orbital plane."989 In the stellar frame however. the planetesimal is also moving with the planet at the Keplerian velocity. and we can calculate the new inclination using This simple calculation shows that an inclination of 45° can be reached for v4=vk.," In the stellar frame however, the planetesimal is also moving with the planet at the Keplerian velocity, and we can calculate the new inclination using This simple calculation shows that an inclination of $45^{\circ}$ can be reached for $v_{\rm rel}=v_{\rm K}$."990 Summing up. planetesimals can only be scattered into highly-inclined orbits for a particular combination of v4. vse and vy.," Summing up, planetesimals can only be scattered into highly-inclined orbits for a particular combination of $v_{\rm rel}$, $v_{\rm esc}$ and $v_{\rm K}$."991 This condition ean be written as We can write the relative velocity of the collision as a function of orbital parameters of both objects., This condition can be written as We can write the relative velocity of the collision as a function of orbital parameters of both objects.992 Recall that the planet moves on a circular orbit with semi-major axis ey., Recall that the planet moves on a circular orbit with semi-major axis $a_{\rm pl}$.993 We define the orbit of the planetesimal by its eccentricity e. axis e. and inclination / relative to the planet.," We define the orbit of the planetesimal by its eccentricity $e$, semi-major axis $a$, and inclination $i$ relative to the planet."994" The relative velocity is then given by (?) Recalling ¢=0 and taking a=«y. we need an eccentricity of e>(3/4)7x0,87 to get Ver>ovy."," The relative velocity is then given by \citep{weidenschilling75}995 Recalling $i=0$ and taking $a=a_{\rm pl}$, we need an eccentricity of $e\geq(3/4)^{1/2}\approx0.87$ to get $v_{\rm rel}\geq v_{\rm K}$."996 Particles on orbits larger than that of the planet reach similar relative velocities for lower inclinations., Particles on orbits larger than that of the planet reach similar relative velocities for lower inclinations.997 However. if the particle is located inside the planetary orbit. for instance in the 1:2 MMR. it has α/αμι and only reaches vy.)=vy for an eccentricity of 0.97.," However, if the particle is located inside the planetary orbit, for instance in the 1:2 MMR, it has $a/a_{\rm pl}\approx0.63$ and only reaches $v_{\rm rel}=v_{\rm K}$ for an eccentricity of 0.97."998 Since this study focusses on planetary migration. most of the material will have a« «y.," Since this study focusses on planetary migration, most of the material will have $a<a_{\rm pl}$ ."999 It is obvious from eq., It is obvious from eq.1000population and an isotropically-misaligned population.,population and an isotropically-misaligned population.1001 At that time. the spin-orbit misalignment of XO-3b (?) comprised the only evidence of the isotropic. population.," At that time, the spin-orbit misalignment of XO-3b \citep{Hebrard:2008p226} comprised the only evidence of the isotropic population."1002 Since then. the misalignment of XO-3b has been confirmed by ?.. and significant misalignments have been found for HD 80606b (?) and WASP-I4b (?)..," Since then, the misalignment of XO-3b has been confirmed by \citet{Winn:2009p3777}, and significant misalignments have been found for HD 80606b \citep{Moutou:2009p2007} and WASP-14b \citep{Johnson:2009p3754}."1003 Moreover. retrograde orbital motion has been identified in HAT-P-7b (22)..," Moreover, retrograde orbital motion has been identified in HAT-P-7b \citep{Winn:2009p3712, Narita:2009p5188}."1004 Other systems show indications of misalignment but need confirmation., Other systems show indications of misalignment but need confirmation.1005 One such object is WASP-17b (?) which is one of the subjects of the present paper., One such object is WASP-17b \citep{Anderson:2010p5177} which is one of the subjects of the present paper.1006 The Wide Angle Search for Planets (WASP) project aims at finding transiting gas giants (2).., The Wide Angle Search for Planets (WASP) project aims at finding transiting gas giants \citep{Pollacco:2006p1500}.1007 Observing the northern and southern hemispheres with sixteen cem refractive telescopes. the WASP consortium has published more than 20 transiting planets in a large range of period. mass and radius. around stars with apparent magnitudes between 9 and 13.," Observing the northern and southern hemispheres with sixteen cm refractive telescopes, the WASP consortium has published more than 20 transiting planets in a large range of period, mass and radius, around stars with apparent magnitudes between 9 and 13."1008 The planet candidates observable from the South are confirmed by a large radial-velocity follow-up using the CORALIE high resolution écchelle spectrograph. mounted on the 1.2mm Swiss Telescope. at La Silla. Chile.," The planet candidates observable from the South are confirmed by a large radial-velocity follow-up using the CORALIE high resolution écchelle spectrograph, mounted on the m Swiss Telescope, at La Silla, Chile."1009 As part of our efforts to understand the planets that have been discovered. we have initiated à systematic program to measure the Rossiter-MeLaughlin effect in the planets discovered by the WASP survey. in order to measure their projected spin-orbit misalignment angles f.," As part of our efforts to understand the planets that have been discovered, we have initiated a systematic program to measure the Rossiter-McLaughlin effect in the planets discovered by the WASP survey, in order to measure their projected spin-orbit misalignment angles $\beta$."1010 In this paper we report the measurement of f in six southeri transiting planets from the WASP survey. and analyse their long term radial velocity behaviour.," In this paper we report the measurement of $\beta$ in six southern transiting planets from the WASP survey, and analyse their long term radial velocity behaviour."1011 In sections 2 and3 we describe the observations and the methods employed to extract anc analyse the data., In sections 2 and 3 we describe the observations and the methods employed to extract and analyse the data.1012 In section 4 we report in detail on the Rossiter-McLaughlin effects observed during transits of the six systems observed., In section 4 we report in detail on the Rossiter-McLaughlin effects observed during transits of the six systems observed.1013 In sections 5 and 6 we discuss the correlations and trends that emerge from the study and their implications. for planetary migration models., In sections 5 and 6 we discuss the correlations and trends that emerge from the study and their implications for planetary migration models.1014 In order to determine precisely and accurately the angle f. we need to obtain radial velocities during planetary transits at a high cadence and high precision.," In order to determine precisely and accurately the angle $\beta$, we need to obtain radial velocities during planetary transits at a high cadence and high precision."1015 We therefore observed with the high resolution écchelle spectrograph HARPS. mounted at the La Silla 3.6mm ESO telescope.," We therefore observed with the high resolution écchelle spectrograph HARPS, mounted at the La Silla m ESO telescope."1016 The magnitude rangeσα within which planets are found by the SuperWASP instruments allows us to observe each object in adequate conditions., The magnitude range within which planets are found by the SuperWASP instruments allows us to observe each object in adequate conditions.1017 For the main survey proposal 082.C-0040. we selected as targets the entire population of transiting planets known at the time of proposal submission to be observable from La Silla during Period 82. te. WASP-2b. 4b. 5b. 6b. 8b and 15b.," For the main survey proposal 082.C-0040, we selected as targets the entire population of transiting planets known at the time of proposal submission to be observable from La Silla during Period 82, i.e. WASP-2b, 4b, 5b, 6b, 8b and 15b."1018 The results for WASP-6b are presented separately by ? and for WASP-8b by ?.., The results for WASP-6b are presented separately by \citet{Gillon:2009p3869} and for WASP-8b by \citet{Queloz:2010p7085}.1019 Two targets were added in separate proposals., Two targets were added in separate proposals.1020 A transit of WASP-18b was observed during GTO time (072C-0488) of the HARPS consortium allocated to this planet because of its short and eccentric orbit., A transit of WASP-18b was observed during GTO time (072C-0488) of the HARPS consortium allocated to this planet because of its short and eccentric orbit.1021 During the long-term spectroscopic follow-up of WASP-17b undertaken for the discovery.paper (?)..robubls three CORALIE measurements fell during transit showiing a retrograde orbit.," During the long-term spectroscopic follow-up of WASP-17b undertaken for the discovery paper \citep{Anderson:2010p5177}, , three CORALIE measurements fell during transit showing a probably retrograde orbit."1022 Observations of the Rossiter-MeLaughlin with CORALIE confirmed the conclusions of ?.. and a follow-up DDT proposal (283.C-5017) was awarded time on HARPS.," Observations of the Rossiter-McLaughlin with CORALIE confirmed the conclusions of \citet{Anderson:2010p5177}, and a follow-up DDT proposal (283.C-5017) was awarded time on HARPS."1023 The strategy of observations was to take two high precision HARPS points the night before transit and the night after transit., The strategy of observations was to take two high precision HARPS points the night before transit and the night after transit.1024 The radial-velocity curve was sampled densely throughout the transit. beginning 90 minutes before ingress and ending 90 minutes after egress.," The radial-velocity curve was sampled densely throughout the transit, beginning 90 minutes before ingress and ending 90 minutes after egress."1025 The data taken before ingress and after egress allow any activity-related offset in the effective velocity of the system's centre of mass to be determined for the night of observation., The data taken before ingress and after egress allow any activity-related offset in the effective velocity of the system's centre of mass to be determined for the night of observation.1026 In addition. radial velocity data from the high resolution écchelle spectrograph CORALIE mounted on the Swiss 1.2mm Telescope. also at La Silla was acquired to help search for a long term variability in the the periodic radial velocity signal.," In addition, radial velocity data from the high resolution écchelle spectrograph CORALIE mounted on the Swiss m Telescope, also at La Silla was acquired to help search for a long term variability in the the periodic radial velocity signal."1027" All our HARPS observations have been conducted in the OBJO mode. without simultaneous Thorium-Argon spectrum,"," All our HARPS observations have been conducted in the OBJO mode, without simultaneous Thorium-Argon spectrum."1028 The velocities are estimated by a Thorium-Argon calibration at the start of the night., The velocities are estimated by a Thorium-Argon calibration at the start of the night.1029 HARPS is stable within ! across a night., HARPS is stable within $^{-1}$ across a night.1030 This is lower than our individual error bars and leads to no contamination of the Th-Ar lamp onto the stellar spectrum easing spectral analysis., This is lower than our individual error bars and leads to no contamination of the Th-Ar lamp onto the stellar spectrum easing spectral analysis.1031 The spectroscopic data were reduced using the online Data Reduction Software (DRS) which comes with HARPS., The spectroscopic data were reduced using the online Data Reduction Software (DRS) which comes with HARPS.1032 The radial velocity information was obtained by removing the instrumental blaze function and cross-correlating each spectrum with one of two masks., The radial velocity information was obtained by removing the instrumental blaze function and cross-correlating each spectrum with one of two masks.1033 This correlation 1s compared with the Th-Ar spectrum acting as a reference: see 2.. 2 ? for details.," This correlation is compared with the Th-Ar spectrum acting as a reference; see \citet{Baranne:1996p1069}, \citet{Pepe:2002p1068} \citet{Mayor:2003p4493} for details."1034 Recently the DRS was shown to achieve remarkable precision (2). thanks to a revision of the reference linesfor, Recently the DRS was shown to achieve remarkable precision \citep{Mayor:2009p4452} thanks to a revision of the reference linesfor1035The natural shape of an isolated. self-gravitating [uid is axially svimmetric.,The natural shape of an isolated self-gravitating fluid is axially symmetric.1036 For this reason. exact axial svmmetric solutions of Einstein field equations are good. candidates to model astrophysical bodies in General Relativity.," For this reason, exact axial symmetric solutions of Einstein field equations are good candidates to model astrophysical bodies in General Relativity."1037 In the last decades. several exact solutions were studied as possible ealactic models.," In the last decades, several exact solutions were studied as possible galactic models."1038 Static thin disk solutions were first studied bv Bonnor&Sacklicld(1968) and Morgan.&Morgan (1969).. where they considered disks without radial pressure.," Static thin disk solutions were first studied by \cite{bon:sac} and \cite{mor:mor1}, where they considered disks without radial pressure."1039 Disks with racial pressure and with radial tension had been considered by Morgan&(1970). and González&Letelier (1999)... respectively.," Disks with radial pressure and with radial tension had been considered by \cite{mor:mor2} and \cite{gon:let1}, respectively."1040 Self-similar static disks were studied by Lvnden-Dell&Pineault’(L9O78).. ancl Lemos (1989).," Self-similar static disks were studied by \cite{lyn:pin}, and \cite{lem}."1041. Moreover. solutions that involve superpositions of black holes with static disks were analyzed by Lemos&Lete-lier(1993.1994.1996). and Wlein(1997)..," Moreover, solutions that involve superpositions of black holes with static disks were analyzed by \cite{lem:let1, lem:let2, lem:let3} and \cite{kle1}."1042. Also. relativistic counter-rotating thin disks as sources of the Ίος tvpe metrics were found by Biedk&Ledvinka(1993).," Also, relativistic counter-rotating thin disks as sources of the Kerr type metrics were found by \cite{bic:led}."1043. Counter-rotating models with racial pressure and dust disks without racial pressure were studied by González&Espitia(2003).. and Garcia&González(2004)... respectively: while rotating disks with heat [low were studied by González&|Letelier (2000).," Counter-rotating models with radial pressure and dust disks without radial pressure were studied by \cite{gon:esp}, and \cite{gar:gon}, respectively; while rotating disks with heat flow were studied by \cite{gon:let2}."1044. Furthermore. static thin disks as sources of known vacuum spacetimes from the Chazs-Curzon metric 19024:Curzon1924) and Zipoy-Voorhees (Zipov19060:Voorhees1970). metric were obtained by Biédk.Lyacden-Bell&Ixatz (1993).," Furthermore, static thin disks as sources of known vacuum spacetimes from the Chazy-Curzon metric \citep{cha,cur} and Zipoy-Voorhees \citep{zip,voo} metric were obtained by \cite{bic:lyn1}. ."1045. Also. Biéák.Lynden-Dell&Pichon(1993) found an infinite number of new relativistic static solutions that correspond to the classical galactic disk potentials of Ixuzmin Toomre (Ixuzmin1956:Toomre1963) and Alestel Ixalnajs (Alestel1963:WKalnajs1972).," Also, \cite{bic:lyn2} found an infinite number of new relativistic static solutions that correspond to the classical galactic disk potentials of Kuzmin Toomre \citep{kuz,too} and Mestel Kalnajs \citep{mes,kal}."1046. Stationary clisk models including electric fields (Ledvinka.Zolka&Biedk 1999).. magnetic fields (Letclier1999)... and both electric and magnetic Lields (Ixatz.Biedk&Lyouden-Bell1999) hac been studied.," Stationary disk models including electric fields \citep{led:zof}, magnetic fields \citep{let}, and both electric and magnetic fields \citep{kat:bic} had been studied."1047 In the last vears. exact solutions for thin disks mace with single and composite halos of matter (Vogt&Letelier 2003).. charged. dust. (Vogt.&Letelier20042) ancl charged: perfect. Uuicl (Vogt.&Letelier2004b) were obtained.," In the last years, exact solutions for thin disks made with single and composite halos of matter \citep{vog:let1}, charged dust \citep{vog:let2} and charged perfect fluid \citep{vog:let3} were obtained."1048 For a survey on relativistic gravitating clisks. see Semerák(2002) and Ixaras.Lluré&Semerak(2004).," For a survey on relativistic gravitating disks, see \cite{sem} and \cite{kar:hur}."1049. Most ofthe models constructed above were found using the metric to calculate its energv momoentunr-tensor. Le. an inverse problem.," Most of the models constructed above were found using the metric to calculate its energy momentum-tensor, i.e. an inverse problem."1050 Several exact. disk solutions were found. using the direct. method. that consists in computing the metric. for a given energv momentum tensor representing the clisk (Neugebauer&Moeinel1995:WleinRichter1999:Ixlein2001:Erauendiener&IxIeinKlein2002. 2003a.," Several exact disk solutions were found using the direct method that consists in computing the metric for a given energy momentum tensor representing the disk \citep{neu:mei, kle:ric, kle2, fra:kle, kle3, kle4, kle5}."1051b).. In a first approximation. the galaxies can be thought to be thin. what usually simplifies the analysis ancl provides very useful information.," In a first approximation, the galaxies can be thought to be thin, what usually simplifies the analysis and provides very useful information."1052 But. in order to model real physical galaxies the thickness of the disks must be considered.," But, in order to model real physical galaxies the thickness of the disks must be considered."1053 Exact axially svmumetric relativistic thick disks in cdilferent coorcinate systems were studied bv González&Letelier(2004)., Exact axially symmetric relativistic thick disks in different coordinate systems were studied by \cite{gon:let3}.1054.. Also. cilferent thick disks were obtained [rom the Schwarzschilel metric in clillerent coordinates svstems with the “cisplace. cut. fill. and rellect method (Vogt&Letelicr2005a)," Also, different thick disks were obtained from the Schwarzschild metric in different coordinates systems with the “displace, cut, fill, and reflect"" method \citep{vog:let4}."1055 The applicability of these disks models to any structure founcl in Nature lays in its μαability., The applicability of these disks models to any structure found in Nature lays in its stability.1056 “Phe study of the stability. analytically or numerically. is vitalto. the acceptance of particular model.," The study of the stability, analytically or numerically, is vitalto the acceptance of a particular model."1057 Also. the study of dillerent types of perturbations.a when applied to these models. might eive an insight on the formation of bars.rings or cilferent," Also, the study of different types of perturbations, when applied to these models, might give an insight on the formation of bars,rings or different"1058"they did in the full data set, and they were significant up to much higher The frequency analysis of the full data set was therefore only used to find a pulsation and Blazhko period for the data and to determine the overall properties of the modulation components.","they did in the full data set, and they were significant up to much higher The frequency analysis of the full data set was therefore only used to find a pulsation and Blazhko period for the data and to determine the overall properties of the modulation components."1059 Another approach to avoid the residual peaks caused by the changes in the modulation is to subdivide the light curve into small bins which are hardly affected by the Blazhko modulation and to calculate the amplitudes and phases of fo and its harmonics for each of them., Another approach to avoid the residual peaks caused by the changes in the modulation is to subdivide the light curve into small bins which are hardly affected by the Blazhko modulation and to calculate the amplitudes and phases of $f_0$ and its harmonics for each of them.1060" This method is used to investigate the time-dependent behaviour of the star on a time scale of a few days, reflected by the Fourier We divided the data set into 73 bins of 2 d duration each (i.e, about 3.5 pulsation cycles), and calculated the Fourier parameters A; and y, (with k denoting the harmonic order), as well as their amplitude ratios Rei= A&/Aj and epoch-independent phase differences qx1=qx—ky in each bin."," This method is used to investigate the time-dependent behaviour of the star on a time scale of a few days, reflected by the Fourier We divided the data set into 73 bins of 2 d duration each (i.e., about 3.5 pulsation cycles), and calculated the Fourier parameters $A_k$ and $\varphi_k$ (with k denoting the harmonic order), as well as their amplitude ratios $R_{k1}=A_k/A_1$ and epoch-independent phase differences $\varphi_{k1}=\varphi_k-k\varphi_1$ in each bin."1061 These Fourier parameters are useful in many aspects., These Fourier parameters are useful in many aspects.1062" First of all, they describe the shape of the light curve, which for RRab stars is known to change dramatically during the Blazhko cycle."," First of all, they describe the shape of the light curve, which for RRab stars is known to change dramatically during the Blazhko cycle."1063" Furthermore, they are a practical tool to compare the properties of synthetic light curves from hydrodynamical models to real data (e.g.,Dorfi&Feuchtinger1999;Smolecetal.2011), and Kovacs&Zsoldos(1995) showed that - for non-modulated stars - it is possible to derive fundamental stellar parameters like the metallicity from the Fourier parameters of RR Lyrae stars."," Furthermore, they are a practical tool to compare the properties of synthetic light curves from hydrodynamical models to real data \citep[e.g.,][]{dorfi, smo11}, and \citet{kov95} showed that - for non-modulated stars - it is possible to derive fundamental stellar parameters like the metallicity from the Fourier parameters of RR Lyrae stars."1064" Moreover, Jurcsiketal.(2002) used the Fourier parameters and their interrelations to test at which Blazhko phase, if at all, the light curves of Blazhko stars resemble those of non-modulated RR Lyrae stars."," Moreover, \citet{jur02} used the Fourier parameters and their interrelations to test at which Blazhko phase, if at all, the light curves of Blazhko stars resemble those of non-modulated RR Lyrae stars."1065" Also, in the case of a changing Blazhko effect like in CoRoT 105288363, they are useful to compare the different observed cycles in the context of the light curve shape which is given by the The Fourier parameters of CoRoT 105288363 are displayed in Figure 5.."," Also, in the case of a changing Blazhko effect like in CoRoT 105288363, they are useful to compare the different observed cycles in the context of the light curve shape which is given by the The Fourier parameters of CoRoT 105288363 are displayed in Figure \ref{fp}."1066" Some interesting features can immediately be seen: while A; shows a definite decrease of its variation, indicating a weakening of the Blazhko effect during the duration of the observations, the variation of yi is getting stronger and sometimes shows double maxima."," Some interesting features can immediately be seen: while $A_1$ shows a definite decrease of its variation, indicating a weakening of the Blazhko effect during the duration of the observations, the variation of $\varphi_1$ is getting stronger and sometimes shows double maxima."1067" The other phases also show distinct differences from one cycle to the next, with the fourth observed Blazhko cycle being very weak in all of them."," The other phases also show distinct differences from one cycle to the next, with the fourth observed Blazhko cycle being very weak in all of them."1068" The amplitude ratio [οι increases its variation, with flat maxima in the beginning of the observations, and a sharper maximum in the last cycle, and also for the phase differences, none of the Blazhko cycles resembles the other ones exactly."," The amplitude ratio $R_{21}$ increases its variation, with flat maxima in the beginning of the observations, and a sharper maximum in the last cycle, and also for the phase differences, none of the Blazhko cycles resembles the other ones exactly."1069 The O-C analysis is the most classical way to analyse RR Lyrae stars and has nowadays mostly been replaced by Fourier analysis as the preferred method of investigation., The O-C analysis is the most classical way to analyse RR Lyrae stars and has nowadays mostly been replaced by Fourier analysis as the preferred method of investigation.1070" In the case of strong changes of the pulsation behaviour, however, when the Fourier spectrum shows a large number of unresolved peaks that hamper the analysis, an O-C diagram might still be a valuable tool to have a closer look at the Blazhko effect."," In the case of strong changes of the pulsation behaviour, however, when the Fourier spectrum shows a large number of unresolved peaks that hamper the analysis, an O-C diagram might still be a valuable tool to have a closer look at the Blazhko effect."1071" As CoRoT provides continuous time sampling and therefore complete light curves, it is possible to plot an O-C diagram not only for the times of maximum light but also for the minima."," As CoRoT provides continuous time sampling and therefore complete light curves, it is possible to plot an O-C diagram not only for the times of maximum light but also for the minima."1072" As CoRoT 105288363 also shows dramatic changes in the light curve shape, the O-C of minima might hold some additional information."," As CoRoT 105288363 also shows dramatic changes in the light curve shape, the O-C of minima might hold some additional information."1073 The O-C values of both the maxima and minima are shown in Figure 6.., The O-C values of both the maxima and minima are shown in Figure \ref{Maxfigure}.1074" Additionally, the brightness values of the extrema are shown for The first obvious observation is that the O-C of maxima and minima show diametrical behaviour, with the minima occurring latest when the maxima are earliest and vice versa."," Additionally, the brightness values of the extrema are shown for The first obvious observation is that the O-C of maxima and minima show diametrical behaviour, with the minima occurring latest when the maxima are earliest and vice versa."1075 This reflects the fact that CoRoT 105288363 has a skewer light curve during Blazhko maximum than during Blazhko minimum., This reflects the fact that CoRoT 105288363 has a skewer light curve during Blazhko maximum than during Blazhko minimum.1076" The next observation is that the O-C of maxima shows an increase in amplitude from one cycle to the next, starting from a value of 0.011 d (i.e., about 16 minutes) peak-to-peak amplitude in the first observed cycle, then increasing to 0.016 and 0.021 and finally to 0.023 (i.e., 33 minutes) in the fourth cycle, resulting in an increased to about twice"," The next observation is that the O-C of maxima shows an increase in amplitude from one cycle to the next, starting from a value of 0.011 d (i.e., about 16 minutes) peak-to-peak amplitude in the first observed cycle, then increasing to 0.016 and 0.021 and finally to 0.023 d (i.e., 33 minutes) in the fourth cycle, resulting in an increase to about twice"1077Here. 04(0.q) is a special case of the Jacobi elliptic theta function. which is known to satisfy (?.p463ff.) We can then re-obtain the probability density function by differentiation. where 9(0.4)=hy0.,"Here, $\vartheta_4\left(0,q\right)$ is a special case of the Jacobi elliptic theta function, which is known to satisfy \citep[p463 ff.]{Whittaker1963}1078 We can then re-obtain the probability density function by differentiation, where $\vartheta^{\prime}_4\left(0,q\right) = \deriv{\vartheta_4\left(0,q\right)}{q}$."1079A It is. not clear to us yet whether this connection to elliptical functions is a coincidence. for just this special case. or whether it points towards a possible reformulation of the probability distribution for general power spectra.," It is not clear to us yet whether this connection to elliptical functions is a coincidence for just this special case, or whether it points towards a possible reformulation of the probability distribution for general power spectra."1080 However. it allows us to analyse the asymptotic behaviour of the distribution function for large £.," However, it allows us to analyse the asymptotic behaviour of the distribution function for large $\xi$."1081 From Eq. (48)).," From Eq. \ref{eq:univar_special_theta4}) ),"1082 we have for g<|., we have for $q \ll 1$.1083 Then. inserting into Eq. (50)).," Then, inserting into Eq. \ref{eq:univar_special_pxi_dtheta}) ),"1084 we obtain for €>1., we obtain for $\xi \gg 1$.1085 Thus. the distribution function behaves like a single exponential at large & and not like a Gaussian at all.," Thus, the distribution function behaves like a single exponential at large $\xi$, and not like a Gaussian at all."1086 This is in agreement with our general result p(é)«eUo? for large € from Sect. 2.1.., This is in agreement with our general result $p(\xi) \propto \eto{-\xi / \left(2C_{\mathrm{max}}\right)}$ for large $\xi$ from Sect. \ref{sec:univar_derivation}.1087 For the same power spectrum. we can also explicitly calculate the moments.," For the same power spectrum, we can also explicitly calculate the moments."1088" With C,ePUA)ΙΤ. we obtain the i-th (central) moment from the sum Here. ZGün) is the Riemann zeta function and B,, are the Bernoulli numbers (?.p.776) given by For example. the mean of the distribution then is simply given by €=LA/I2 and the standard deviation is cLAJ(o VIO)."," With $C_n \propto P(|k|) \propto |k|^{-2}$, we obtain the $m$ -th (central) moment from the sum Here, $\zeta(m)$ is the Riemann zeta function and $B_m$ are the Bernoulli numbers \citep[p. 776]{Prudnikov1986} given by For example, the mean of the distribution then is simply given by $\overline{\xi} = LA/12$ and the standard deviation is $\sigma_{\xi} = LA/\left(6\sqrt{10}\right) \, $ ."1089 For power law power spectra with a different exponent. Eq. (45))," For power law power spectra with a different exponent, Eq. \ref{eq:univar_special_prudnikov}) )"1090 still allows us to express the product factors explicitly in terms of known (trigonometric and hyperbolic) functions., still allows us to express the product factors explicitly in terms of known (trigonometric and hyperbolic) functions.1091 Regrettably. these do not yield any known functions for the full probability distribution. or for the moments. as far as we are aware.," Regrettably, these do not yield any known functions for the full probability distribution, or for the moments, as far as we are aware."1092 Thus. a really explicit form was found for the special case of P(k)&|K[7 only.," Thus, a really explicit form was found for the special case of $P(k) \propto |k|^{-2}$ only."1093 In this section. we will calculate the bivariate probability distribution function. p(£CGvi£2). which we will mostly abbreviate as p(£j.£:) with £j=£v. &=ἕἔίαν).," In this section, we will calculate the bivariate probability distribution function $p(\xi(x_1),\xi(x_2))$, which we will mostly abbreviate as $p(\xi_1,\xi_2)$ with $\xi_1=\xi(x_1)$, $\xi_2=\xi(x_2)$."1094" All preliminaries carry over from the univariate case. and the starting point of this calculation is The characteristic function is now bivariate as well. In the last step. we have defined a generalised shorthand for the factors Cy,=cq.COS(K,.x4) to allow for the two different lag parameters x,."," All preliminaries carry over from the univariate case, and the starting point of this calculation is The characteristic function is now bivariate as well, In the last step, we have defined a generalised shorthand for the factors $C_{nm} = \sigma_n^2 \cos(k_n x_m)$ to allow for the two different lag parameters $x_m$."1095" It is worth noting at this point that for higher multivariate distributions. say p(é).é2.....&). the only change necessary in the characteristic function will be to add additional terms of sy,Cy,, 1n this factor. resulting in the generally valid expression Next. we will obtain the bivariate probability distribution itself from the characteristic function by Fourier inversion. in analogy to the univariate case."," It is worth noting at this point that for higher multivariate distributions, say $p(\xi_1,\xi_2,\dots,\xi_k)$, the only change necessary in the characteristic function will be to add additional terms of $s_m C_{nm}$ in this factor, resulting in the generally valid expression Next, we will obtain the bivariate probability distribution itself from the characteristic function by Fourier inversion, in analogy to the univariate case."1096 But an important difference arises m this step. since the inversion now contains a double integration.," But an important difference arises in this step, since the inversion now contains a double integration."1097 Thus. we have to calculate the following: Since the pairs of variables (54.53) and (£4.63) each are mutually independent. the result has to be invariant. under exchanging the order of integration.," Thus, we have to calculate the following: Since the pairs of variables $(s_1,s_2)$ and $(\xi_1,\xi_2)$ each are mutually independent, the result has to be invariant under exchanging the order of integration."1098" We choose to first integrate over ds» and after that over ds,.", We choose to first integrate over $\diff{s_2}$ and after that over $\diff{s_1}$.1099 From the resulting formula. the symmetry will not be immediately apparent.," From the resulting formula, the symmetry will not be immediately apparent."1100 However. we have checked the equivalence of both approaches by also explicitly evaluating the other. choice.," However, we have checked the equivalence of both approaches by also explicitly evaluating the other choice."1101" Also. we will assume simple poles in both integrations. and will only briefly comment on the effects of multiple poles at the end of this section,"," Also, we will assume simple poles in both integrations, and will only briefly comment on the effects of multiple poles at the end of this section."1102 The poles for the inner integration are now located at, The poles for the inner integration are now located at1103of the true image using an ideal PSF.,of the true image using an ideal PSF.1104" Over the years several variants have been proposed to overcome various limitations and nuances that are intrinsic to bs,31.", Over the years several variants have been proposed to overcome various limitations and nuances that are intrinsic to .1105".However, therestillremainsabasicassumptionthattheskyiscomposedo fpointsources, whichisadequi a"," However, there still remains a basic assumption that the sky is composed of point sources, which is adequate if the source being observed has limited extent."1106asalargenumbero f pointsourcesandtheiterative procedurebecomesatime —consumingprocessinvolvingaconstantlyincreasingnumbero f poii c, Extended structure is modeled by as a large number of point sources and the iterative procedure becomes a time-consuming process involving a constantly increasing number of point sources.1107"canberestrictedtoonlyworkinregionswherethesourceo f interest isknowntoexist ,t hroughtheuseo f **windows ."," To partly compensate for this problem, can be restricted to only work in regions where the source of interest is known to exist, through the use of `windows'."1108"Suchwindowsrequirepriorknowledgeo fthesourcestructureandextent ,butare f lexibleandmultiplewindowscanbeusedtoboundaco "," Such windows require prior knowledge of the source structure and extent, but are flexible and multiple windows can be used to bound a complicated source."1109An obvious enhancement to wwould be to make it more efficient at modeling extended structures., An obvious enhancement to would be to make it more efficient at modeling extended structures.1110 Many such ‘scale-sensitive’ algorithms have been proposed., Many such `scale-sensitive' algorithms have been proposed.1111" These methods generally assume that the sky is not composed of only point-sources as ddoes, but of sources of many different sizes and scales."," These methods generally assume that the sky is not composed of only point-sources as does, but of sources of many different sizes and scales."1112" One of the first such methods, multi-resolutionCLEAN,, tackles the problem by smoothing and decimating the dirty image and PSF to emphasize the extended emission."," One of the first such methods, multi-resolution, tackles the problem by smoothing and decimating the dirty image and PSF to emphasize the extended emission."1113" The image resulting from cleaning this dirty image is then used as an initial model for cleaning the next higher resolution image, citepws,,rclean."," The image resulting from cleaning this dirty image is then used as an initial model for cleaning the next higher resolution image, ."1114.Waveletclean uusesthewavelettrans f ormintheclean pprocessbutbasicallyoperatesinasimilarmannertomulti —resolutioncl, Wavelet uses the wavelet transform in the process but basically operates in a similar manner to multi-resolution .1115ean hemorerecentlydevelopedAdaptiveScalePixelclean uusesscalesizesthatcan‘adapt' theirsizeduring processing (?)., The more recently developed Adaptive Scale Pixel uses scale sizes that can `adapt' their size during processing .1116".T hereisawealtho f literatureexplainingtheinnerworkingso fmulti aandtheotheral gorithmsmentionedaboveindetail , includingaconsiderableamounto f modelingasw "," There is a wealth of literature explaining the inner workings of multi-resolution and the other algorithms mentioned above in detail, including a considerable amount of modeling as well as some practical tests."1117Multi-scale ((hereafter referred to as MSCLEAN)) is a straight-forward extension of the classical aalgorithm for handling extended sources(?)., Multi-scale (hereafter referred to as ) is a straight-forward extension of the classical algorithm for handling extended sources.1118". Just like the multi-resolution ddefined by?,, it works by assuming the sky is composed of emission at different spatial scales."," Just like the multi-resolution defined by, it works by assuming the sky is composed of emission at different spatial scales."1119" However, whilst the wworks on each scale sequentially, wworks simultaneously on all scales that are being considered."," However, whilst the multi-resolution works on each scale sequentially, works simultaneously on all scales that are being considered."1120 This prevents potential errors made at a previous larger scale from being ‘frozen in’ and requiring many iterations at smaller scales to correct., This prevents potential errors made at a previous larger scale from being `frozen in' and requiring many iterations at smaller scales to correct.1121 hhas been implemented in both (formerly AIPS++) and classical (as part of the multi-resolution options of the IMAGR task)., has been implemented in both (formerly AIPS++) and classical (as part of the multi-resolution options of the IMAGR task).1122" In this paper, we compare the operation of aagainst classical bboth with and without the use of wwindows, using some real-world data and astronomical problems derived from high quality HI data obtained through the THINGS "," In this paper, we compare the operation of against classical both with and without the use of windows, using some real-world data and astronomical problems derived from high quality HI data obtained through the THINGS project."1123"We refer to for a more technical description ofMSCLEAN,, as well as a description of tests involving artificial data."," We refer to for a more technical description of, as well as a description of tests involving artificial data."1124" project.THINGS, The NNearby Galaxy Survey, consists of a sample of 34 nearby galaxies observed with the NRAO Very Large (VLA) B,C and arrays (?)."," THINGS, The Nearby Galaxy Survey, consists of a sample of 34 nearby galaxies observed with the NRAO Very Large (VLA) B,C and D arrays ."1125". The high resolution (~6"", ~5 s-1)) achieved with THINGS pushes the VLA to the limits of its current performanceD for observations of a significant sample of galaxies."," The high resolution $\sim6\arcsec$, $\sim5$ ) achieved with THINGS pushes the VLA to the limits of its current performance for observations of a significant sample of galaxies."1126" The THINGS observations, being combined multi-array data with a large range of spatial scales therefore present one of the most challenging data-sets with which to compare the efficiency of deconvolution algorithms."," The THINGS observations, being combined multi-array data with a large range of spatial scales therefore present one of the most challenging data-sets with which to compare the efficiency of deconvolution algorithms."1127" We emphasize that classical wworks very well on the THINGS data sets, and that with a full knowledge of its intricacies excellent results can be achieved."," We emphasize that classical works very well on the THINGS data sets, and that with a full knowledge of its intricacies excellent results can be achieved."1128" However, iis not perfect, and our goal in this paper is to describe some practical applications of the aalgorithm."," However, is not perfect, and our goal in this paper is to describe some practical applications of the algorithm."1129 sseems to have fewer limitations than ddoes when it comes to handling data of extended sources., seems to have fewer limitations than does when it comes to handling data of extended sources.1130" It is promising enough that it might point the way to an efficient exploration of the high-quality data, similar to the THINGS data set, that will be routinely produced by the next-generation radio and millimeter facilities such asALMA'®,,EVLA!!,, and This paper begins with a brief description of the aand aalgorithms in Section 2.."," It is promising enough that it might point the way to an efficient exploration of the high-quality data, similar to the THINGS data set, that will be routinely produced by the next-generation radio and millimeter facilities such as, and This paper begins with a brief description of the and algorithms in Section \ref{sec:deconv-desc}."1131" In addition to summarizing the procedure each algorithm uses in Sections 2.1 and 2.2,, the paper discusses thelimitations of the aalgorithm and the advantages that"," In addition to summarizing the procedure each algorithm uses in Sections \ref{sec:clean-proc} and \ref{sec:msclean-proc}, the paper discusses thelimitations of the algorithm and the advantages that"1132"The measured event parameters constitute a 4-dimensional data space. in which we have to search for a ""source signature"".","The measured event parameters constitute a 4-dimensional data space, in which we have to search for a ""source signature""."1133" In practice the dimension of the data space is lowered by integrating along the 74, direction between user selected boundaries.", In practice the dimension of the data space is lowered by integrating along the $\etot$ direction between user selected boundaries.1134 The event distribution of a point source (the Point Spread Function. PSF) in this reduced 3-d data space Is concentrated in a cone-shaped structure with its apex at the source position (yo. 09).," The event distribution of a point source (the Point Spread Function, PSF) in this reduced 3-d data space is concentrated in a cone-shaped structure with its apex at the source position $\chi_0,\psi_0$ )."1135 In the spatial or imaging analysis we proceed as follows: We generate a background model from the sparsely filled event dataspace (3d) through sophisticated smoothing techniques (see e.g. 1994)., In the spatial or imaging analysis we proceed as follows: We generate a background model from the sparsely filled event dataspace (3d) through sophisticated smoothing techniques (see e.g. ).1136 Because the measured events in the 3d- are primarily internally generated background events (~90 95%) this background model represents a good approximation of the genuine instrumental background., Because the measured events in the 3d-dataspace are primarily internally generated background events $\sim 90-95\%$ ) this background model represents a good approximation of the genuine instrumental background.1137 The search for point sources in the measured 3d-dataspace is accomplished by a maximum likelihood ratio (MLR) test at scan positions in the selected sky field., The search for point sources in the measured 3d-dataspace is accomplished by a maximum likelihood ratio (MLR) test at scan positions in the selected sky field.1138" In the null hypothesis Hy the measured events are described in terms of a background model alone. while in the alternative hypothesis H, the data are described in terms of a background model and a point source at a given scan position."," In the null hypothesis ${\cal{H}}_0$ the measured events are described in terms of a background model alone, while in the alternative hypothesis ${\cal{H}}_1$ the data are described in terms of a background model and a point source at a given scan position."1139 From the parameter optimizations under Hy we can derive the source flux., From the parameter optimizations under ${\cal{H}}_1$ we can derive the source flux.1140 From the optimized likelihoods under 744 and Hy we can determine the maximum likelihood ratio A at each scan position. giving us information on the detection significance of a source.," From the optimized likelihoods under ${\cal{H}}_1$ and ${\cal{H}}_0$ we can determine the maximum likelihood ratio $\lambda$ at each scan position, giving us information on the detection significance of a source."1141 For more detailed information see(19983)., For more detailed information see.1142" For consistency purposes we have produced MLR maps for the same energy windows (0.75-3 and 3-10 MeV) as used in the timing analysis. and also made selections on pulse phase. the ""pulsed"" and ""unpulsed"" windows introduced in Sect."," For consistency purposes we have produced MLR maps for the same energy windows (0.75-3 and 3-10 MeV) as used in the timing analysis, and also made selections on pulse phase, the “pulsed” and “unpulsed” windows introduced in Sect."1143 3.5. while we also considered the total emission. the sum of both.," 3.5, while we also considered the total emission, the sum of both."1144 In Fig., In Fig.1145" 4. the MLR images are shown for the ""pulsed and ""unpulsed"" phase intervals in the energy windows 0.75-3 and 3-10 MeV. The contours start at an equivalent of 30 in steps of lo for | degree of freedom (1e. at A=9.16.25.36 ete.)."," \ref{fig:comptel_maps_lt_teen} the MLR images are shown for the “pulsed” and “unpulsed” phase intervals in the energy windows 0.75-3 and 3-10 MeV. The contours start at an equivalent of $3\sigma$ in steps of $1\sigma$ for 1 degree of freedom (i.e. at $\lambda=9, 1146 16, 25, 36$ etc.),"1147 representative if the source position 1s known., representative if the source position is known.1148" From these maps it is evident that significant emission at the pulsar position (indicated by à 7x7 mark) is only observed in the ""pulsed"" maps: L.5¢ in the 0.75-3 MeV energy window and Sq in the 3-10 MeV window.", From these maps it is evident that significant emission at the pulsar position (indicated by a ” mark) is only observed in the “pulsed” maps: $4.5\sigma$ in the 0.75-3 MeV energy window and $8\sigma$ in the 3-10 MeV window.1149 From the maximum likelihood fits we can also obtain estimates for the source flux., From the maximum likelihood fits we can also obtain estimates for the source flux.1150 However. in the maps shown in Fig.," However, in the maps shown in Fig."1151 4. the structured galactic diffuse emission is not included in the background model. and may contribute to the source flux.," \ref{fig:comptel_maps_lt_teen} the structured galactic diffuse emission is not included in the background model, and may contribute to the source flux."1152" In addition. any pulsar/nebula DC-emission will contribute equally to the ""pulsed""7 and ""unpulsed maps."," In addition, any pulsar/nebula DC-emission will contribute equally to the “pulsed” and “unpulsed” maps."1153" Since À is not zero at the source position in the ""unpulsed7"" maps. we subtracted the measured fluxes (counts) in the ""unpulsed"" maps from those in the ""pulsed"" maps in order to obtain independent estimates of the ""pulsed"" fluxes."," Since $\lambda$ is not zero at the source position in the “unpulsed” maps, we subtracted the measured fluxes (counts) in the “unpulsed” maps from those in the “pulsed” maps in order to obtain independent estimates of the “pulsed” fluxes."1154" For the 0.75-3 MeV interval we found 7202+1386 counts correlating with a point source at the pulsar position in the ""pulsed"" interval and 2261+1382 n the ""unpulsed"" interval.", For the 0.75-3 MeV interval we found $7202\pm 1386$ counts correlating with a point source at the pulsar position in the “pulsed” interval and $2264\pm 1382$ in the “unpulsed” interval.1155 The difference of 1938+1960 Is consistent with the pulsed excess counts in the timing analysis., The difference of $4938\pm 1960$ is consistent with the pulsed excess counts in the timing analysis.1156" The number of counts found in the ""unpulsed"" window car be fully attributec to contributions of galactic diffuse origin. as has been verified in a simulation of the galactic diffuse emission using the model components and scale factors found by Bloemenetal.(1999)."," The number of counts found in the “unpulsed” window can be fully attributed to contributions of galactic diffuse origin, as has been verified in a simulation of the galactic diffuse emission using the model components and scale factors found by \cite{bloemen}."1157. This means that there is no room for any significant pulsar or nebula DC-component in this energy window., This means that there is no room for any significant pulsar or nebula DC-component in this energy window.1158 For the 3-10 MeV energy interval we obtained a similar picture., For the 3-10 MeV energy interval we obtained a similar picture.1159" In this case we find 5233+593 counts correlating with à point source at the pulsar position in the ""pulsed"" map and 2755+590 in the ""unpulsed"" map.", In this case we find $5233\pm 593$ counts correlating with a point source at the pulsar position in the “pulsed” map and $2755\pm 590$ in the “unpulsed” map.1160 This leaves 2178+8LO counts for the genuinely pulsed emission. consistent with the timing analysis results.," This leaves $2478\pm 840$ counts for the genuinely pulsed emission, consistent with the timing analysis results."1161 The “unpulsed™ value can again be explained with being of galactic diffuse origin., The “unpulsed” value can again be explained with being of galactic diffuse origin.1162 In conclusion. the fluxes derived from the spatial analysis for energies below 10 MeV are consistent with those derived from the timing analysis and there is no evidence for the detection of DC-emission from the pulsar or its nebula.," In conclusion, the fluxes derived from the spatial analysis for energies below 10 MeV are consistent with those derived from the timing analysis and there is no evidence for the detection of DC-emission from the pulsar or its nebula."1163Kin and ky.,$\kapth$ and $\kapv$.1164" As before, HD 209458b is our proxy."," As before, HD 209458b is our proxy."1165" First I rederive the difference in radius between the model radius, the photospheric radius and the transit radius."," First I rederive the difference in radius between the model radius, the photospheric radius and the transit radius."1166" The problem has been discussed before(????),, but is calculated in the context of our analytical atmospheric temperature profile."," The problem has been discussed before, but is calculated in the context of our analytical atmospheric temperature profile."1167 I then compare the evolution of the transit radii for the different boundary conditions to the measured one., I then compare the evolution of the transit radii for the different boundary conditions to the measured one.1168" Our approximation of a planar atmosphere is equivalent to assuming that the pressure scale height in the atmosphere H=—dr[d]nP is infinitely small compared to the planetary radius, ie. H/r«1."," Our approximation of a planar atmosphere is equivalent to assuming that the pressure scale height in the atmosphere $H\equiv -dr/d\ln P$ is infinitely small compared to the planetary radius, i.e. $H/r \ll 1$."1169" In the case of HD209458b, assuming a perfect gas, a mean molecular weight u=2.3 a mean temperature T=1500 KK and gravity g=980cms?, H=RT/ug« 550kkm, for a planetary radius R=94370 km."," In the case of HD209458b, assuming a perfect gas, a mean molecular weight $\mu=2.3$ a mean temperature $T=1500$ K and gravity $g=980\,\rm cm\,s^{-2}$, $H={\cal R}T/\mu g \approx 550$ km, for a planetary radius $R=94370\,$ km."1170 Therefore H/r«6x10? which is very small compared to other sources of uncertainties and justifies the planar approximation., Therefore $H/r\approx 6\times 10^{-3}$ which is very small compared to other sources of uncertainties and justifies the planar approximation.1171 I will therefore consider that g is constant in the atmosphere., I will therefore consider that $g$ is constant in the atmosphere.1172" In what follows, I will use the following notation: X(r) will denote a quantity that is evaluated at level r but that is assumed constant in the atmosphere."," In what follows, I will use the following notation: $X(r)$ will denote a quantity that is evaluated at level $r$ but that is assumed constant in the atmosphere."1173" The independent length variable in the atmosphere will be denoted z, z=0 corresponding to a radius level r as measured from the planet's center (see fig. 8))."," The independent length variable in the atmosphere will be denoted $z$, $z=0$ corresponding to a radius level $r$ as measured from the planet's center (see fig. \ref{fig:chord}) )."1174" By definition of 7 In the context of a plane-parallel, hydrostatic atmosphere, thiscan be integrated to show that or equivalently to relate optical depth and altitude: Note that H is a function of g(r) (assumed constant in the atmosphere), but also for T(z) which can vary significantly."," By definition of $\tau$ In the context of a plane-parallel, hydrostatic atmosphere, thiscan be integrated to show that or equivalently to relate optical depth and altitude: Note that $H$ is a function of $g(r)$ (assumed constant in the atmosphere), but also for $T(z)$ which can vary significantly."1175" The above equation can be integrated to yield where 6(r,z) is a non-isothermal correction that is equal to In the limit of an isothermal atmosphere, 6(7,z)=1."," The above equation can be integrated to yield where $\tht(r,z)$ is a non-isothermal correction that is equal to In the limit of an isothermal atmosphere, $\tht(r,z)=1$."1176" In all cases, eq. (53)) "," In all cases, eq. \ref{eq:z(tau)}) )"1177may be used to evaluate the height difference between a calculated level and e.g. the photospheric level 2/3., may be used to evaluate the height difference between a calculated level and e.g. the photospheric level $\tau=2/3$ .1178" When measuring the size of an exoplanet from a primary transit, the level that is probed is higher than the photospheric level."," When measuring the size of an exoplanet from a primary transit, the level that is probed is higher than the photospheric level."1179" It corresponds instead to the level at which optical rays that are grazing, at the terminator, have an optical depth close to unity(?)."," It corresponds instead to the level at which optical rays that are grazing, at the terminator, have an optical depth close to unity."1180". Neglecting refraction, we thus define a chord optical depth for this grazing incident radiation: As shown by fig. 8,,"," Neglecting refraction, we thus define a chord optical depth for this grazing incident radiation: As shown by fig. \ref{fig:chord},"1181" (r+z=r?s?, hence This equation may be simplified with our plane-parallel assumption (z/r«1)."," $(r+z)^2=r^2+s^2$ , hence This equation may be simplified with our plane-parallel assumption $z/r\ll 1$ )."1182 We further use eqs. (50)), We further use eqs. \ref{eq:dtau}) )1183" and (53)) to yield With a new change of variable Z=—In[r(r+z)/1(r)], we get Using eq. (53)),"," and \ref{eq:z(tau)}) ) to yield With a new change of variable $Z=-\ln[\tau(r+z)/\tau(r)]$, we get Using eq. \ref{eq:z(tau)}) ),"1184 we now rewrite eq. (58)), we now rewrite eq. \ref{eq:tauchord}) )1185" at level r+Az: The height difference between the photospheric level for which r(r)=2/3 and the transit radius for which τεµ(ν,r+Az)2/3 is: In the limit of an isothermal atmosphere, δε,Z)=1, the integral is equal to 1 (the erf function evaluated at infinity) and the expression of the chord optical depth and height difference reduce to the relations proposed by ?."," at level $r+\Delta z$: The height difference between the photospheric level for which $\tau(r)=2/3$ and the transit radius for which $\tauch(\nu,r+\Delta z)=2/3$ is: In the limit of an isothermal atmosphere, $\tht(r,Z)=1$, the integral is equal to 1 (the erf function evaluated at infinity) and the expression of the chord optical depth and height difference reduce to the relations proposed by ."1186". Thus in the isothermal case, In the more general case of a variable atmospheric temperature profile, eq. (60))"," Thus in the isothermal case, In the more general case of a variable atmospheric temperature profile, eq. \ref{eq:deltaz}) )"1187 may be easily resolved by iterations., may be easily resolved by iterations.1188 In the past few years a great deal of attention has become focused on the very rare class of objects known as the “r-process-enhanced metal-poor” stars., In the past few years a great deal of attention has become focused on the very rare class of objects known as the “r-process-enhanced metal-poor” stars.1189 These objects are enormously important as they allow to study. among other things. the nature of the rapid neutron-capture process(es). and possibly identify the site(s) for this nucleosynthesis process.," These objects are enormously important as they allow to study, among other things, the nature of the rapid neutron-capture process(es), and possibly identify the site(s) for this nucleosynthesis process."1190 Furthermore. and perhaps even more importantly. individual age determinations are possible for these stars using long-lived radioactive isotopes. such as (half-life 14.05 GGyr) or (4.468 GGyr).," Furthermore, and perhaps even more importantly, individual age determinations are possible for these stars using long-lived radioactive isotopes, such as (half-life $14.05$ Gyr) or $4.468$ Gyr)."1191 By comparing the abundance ratio of these elements relative to a stable r-process element of similar mass to the production ratio expected from theoretical r-process yields. the time elapsed since the nucleosynthesis event that produced these elements took place (e.g.. in a type-II supernova) can be derived.," By comparing the abundance ratio of these elements relative to a stable r-process element of similar mass to the production ratio expected from theoretical r-process yields, the time elapsed since the nucleosynthesis event that produced these elements took place (e.g., in a type-II supernova) can be derived."1192 The time between this nucleosynthesis event and the birth of stars that formed from gas clouds enriched by this material. including the low-mass. r-process-enhanced stars that we observe today. is considered as neglible compared the age of the star.," The time between this nucleosynthesis event and the birth of stars that formed from gas clouds enriched by this material, including the low-mass, r-process-enhanced stars that we observe today, is considered as neglible compared the age of the star."1193 Therefore. abundance ratios like Th/Eu. U/Eu. or U/Th can be used as chronometers for age determination of r-process-enhanced stars.," Therefore, abundance ratios like Th/Eu, U/Eu, or U/Th can be used as chronometers for age determination of r-process-enhanced stars."1194 For ease of discussion. we divide the r-process enhancement phenomenon in metal-poor stars into two categories: Note that the term “metal-poor is not necessarily refering to the overall metal-content of the star. which might in fact not be significantly below the solar value when the star under consideration also has strong overabundances of C. Ν. and O. We use Eu as reference element for the neutron-capture elements which were mainly produced by the r-process in the solar material. because its abundance is most easily measurable.," For ease of discussion, we divide the r-process enhancement phenomenon in metal-poor stars into two categories: Note that the term 'metal-poor' is not necessarily refering to the overall metal-content of the star, which might in fact not be significantly below the solar value when the star under consideration also has strong overabundances of C, N, and O. We use Eu as reference element for the neutron-capture elements which were mainly produced by the r-process in the solar material, because its abundance is most easily measurable."1195 We include the condition [Ba/Eu|<0 into the above definitions. because Eu be produced by the s-process as well.," We include the condition $\mbox{[Ba/Eu]} < 0$ into the above definitions, because Eu be produced by the s-process as well."1196" Therefore we need to distinguish between ""pure"" r-process-enhanced stars and stars that were enriched by material produced in the r- s-process (like CS 27 and CS 34. and HE 1247; see ? and ?.. respectively). or only by the s-process."," Therefore we need to distinguish between “pure” r-process-enhanced stars and stars that were enriched by material produced in the r- s-process (like CS $-$ 27 and CS $-$ 34, and HE $-$ 1247; see \citealt{Hilletal:2000} and \citealt{Cohenetal:2003}, respectively), or only by the s-process."1197 Adopting the values of ? for the solar Ba and Eu abundances and r- and s-fractions of these elements. it follows that a star purely enriched by," Adopting the values of \citet{Burrisetal:2000} for the solar Ba and Eu abundances and r- and s-fractions of these elements, it follows that a star purely enriched by"1198" Heckman(1980).. Hoetal.(1997),,"," \citet{Heckman80}. \citet{Ho97b},"1199" Kewleyetal.(2006) al.(2010) non-starbursting Ferland(2009);Eracleousetal.(2010),, (Terlevich (Heckman1980;Dopita&Sutherland2001a;Liparietal.2004) Kewley"," \citet{Kewley06} \citet{CidFernandes10} \citet{Ferland83,Halpern83,Ho99,Kewley06,Ho09,Eracleous10}, \citep{Terlevich85,Trinchieri91,Shields92,Binette94,Stasinska08,Sarzi10}, \citep{Heckman80,Dopita96,Kewley01a,Lipari04} \citep{Voit97}."1200(Voit&Donahue1997).. al.2010;Eracleouset2010) neither mechanism provides a wholly satisfactory answer in all cases.," \citep{Sarzi10, Annibali10, Eracleous10} neither mechanism provides a wholly satisfactory answer in all cases."

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