ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Phe best fit exponential model is shown as a solid line., The best fit exponential model is shown as a solid line.3 νο time scale is clearly much less than the data duration. and the variance in the white noise is greater than that in the red. noise.," The time scale is clearly much less than the data duration, and the variance in the white noise is greater than that in the red noise."4 Ehe OLS spectrum of the residuals whitened using the Cholesky method. is shown in Figure 3(c)., The OLS spectrum of the residuals whitened using the Cholesky method is shown in Figure 3(c).5 It is white within the estimation errors., It is white within the estimation errors.6mosaic.,mosaic.7 Flux calibration was performed. by equating the Hux density of the tip-tilt stars measured. from 2ALASS photometry with the observed OSLRIS spectra., Flux calibration was performed by equating the flux density of the tip-tilt stars measured from 2MASS photometry with the observed OSIRIS spectra.8 We estimate that the uncertainty in Dux calibration is typically, We estimate that the uncertainty in flux calibration is typically.9 1n order to investigate the source plane properties we must irst correct [or the distortion and magnification by the cluster lens., In order to investigate the source plane properties we must first correct for the distortion and magnification by the cluster lens.10 We summarize here the ingredients necessary to construct the relevant cluster mass models., We summarize here the ingredients necessary to construct the relevant cluster mass models.11 We will follow he methodology defined by earlier relevant. articles (7777) within which further details can be found.," We will follow the methodology defined by earlier relevant articles \citep{Kneib93, Kneib96, Smith05, Jullo07} within which further details can be found."12 Our basic approach is to use the code (77) to constrain a parameterizecl model of the dark matter distribution.," Our basic approach is to use the code \citep{Kneib93, Jullo07} to constrain a parameterized model of the dark matter distribution."13 For each cluster. the model comprises wo components: 1 or 2 cluster-scale dark matter halos. xwametrized. with ao dual pseudo-isothermal elliptical massdistribution. (ας. 2)). and ~50 ealaxv-scale. ctLE dark matter halos. centered. on massive cluster members occupying the strong lensing region in order to account for the presence of substructure.," For each cluster, the model comprises two components: 1 or 2 cluster-scale dark matter halos, parametrized with a dual pseudo-isothermal elliptical massdistribution (dPIE, \citealt{Eliasdottir07}) ), and $\sim$ 50 galaxy-scale dPIE dark matter halos, centered on massive cluster members occupying the strong lensing region in order to account for the presence of substructure."14 These galaxy-scale halos are assumed. to have mass properties that follow a scaling relation based on the luminosity of the underlving galaxy. assuming a constant mass-to-lieht ratio (c.g. 2)).," These galaxy-scale halos are assumed to have mass properties that follow a scaling relation based on the luminosity of the underlying galaxy, assuming a constant mass-to-light ratio (e.g. \citealt{Smith05}) )."15 Details on the construction of each. gravitational lens model are given in ? τοῦ MLAC'SJ2135-0102.. 7. [or CI0024|1709 anc ALACS J074413927. and 7? [ος the remaining 3 sources in Table 1.," Details on the construction of each gravitational lens model are given in \cite{Dye07} for J2135-0102, \cite{Limousin09} for Cl0024+1709 and MACS J0744+3927 and \cite{Richard09} for the remaining 3 sources in Table 1."16 Strong lensing constraints originate [rom the identification of 2-5 multiply-imaged systems per cluster within the various ACS images., Strong lensing constraints originate from the identification of 2-5 multiply-imaged systems per cluster within the various ACS images.17 We use the astrometric positions and spectroscopic/photometric redshifts of these as individual constraints to derive best fit parameters on the mass distribution., We use the astrometric positions and spectroscopic/photometric redshifts of these as individual constraints to derive best fit parameters on the mass distribution.18 uses a Markov Chain Monte Carlo (ALCAIC) sampler to derive a family of mass mocels suitably fitting the strong lensing constraints. and we use these to derive the uncertainty on each parameter of the mass distribution.," uses a Markov Chain Monte Carlo (MCMC) sampler to derive a family of mass models suitably fitting the strong lensing constraints, and we use these to derive the uncertainty on each parameter of the mass distribution."19 For each of the sources presented. in. this. paper. the best. model was then used. to derive the geometrical transformation necessary lor mapping the source plane coordinates into the image plane.," For each of the sources presented in this paper, the best model was then used to derive the geometrical transformation necessary for mapping the source plane coordinates into the image plane."20 This transformation enables us to. reconstruct. the4757 morphology and llo emission. lino images in the source plane assuming conservation of surface brightness., This transformation enables us to reconstruct the morphology and $\alpha$ emission line images in the source plane assuming conservation of surface brightness.21 The spot magnification fley AD Ls associated error are computed with at dillerent positions across the object. using the Family of mass models from the ALCALC sampler.," The spot magnification $\mu_{xy}$ and its associated error are computed with at different positions across the object, using the family of mass models from the MCMC sampler."22 We can verify this value by computing the total magnification from the ratio of the sizes (or equivalently. the total Huxes) between the image and its source plane reconstruction.," We can verify this value by computing the total magnification from the ratio of the sizes (or equivalently, the total fluxes) between the image and its source plane reconstruction."23 As the magnification [actor is not isotropic. the angular size of cach image is more highly stretched along a specific orientation (Figure 1)) thus allecting our source plane resolution.," As the magnification factor is not isotropic, the angular size of each image is more highly stretched along a specific orientation (Figure \ref{fig:hst_montage}) ) thus affecting our source plane resolution."24 The linear factors fry and fio of the magnification (with (p=fns qm) together with their associated errors are LHsted in Table 1., The linear factors $\mu_1$ and $\mu_2$ of the magnification (with $\mu=\mu_1\times\mu_2$ ) together with their associated errors are listed in Table 1.25 A detailed illustration of the uncertainties of the mass modeling method for 2135-0102 is given in ?.., A detailed illustration of the uncertainties of the mass modeling method for J2135-0102 is given in \cite{Stark08}.26 A key parameter in our analvsis is the we achieve in the source plane for each target., A key parameter in our analysis is the we achieve in the source plane for each target.27 ‘To measure this. we use observations of the tip-tilt reference stars.," To measure this, we use observations of the tip-tilt reference stars."28 These serve this purpose well as they are point sources observed with conditions and an instrumental configuration identical to those of our distant targets., These serve this purpose well as they are point sources observed with conditions and an instrumental configuration identical to those of our distant targets.29 We “reconstruct” these stars in the source plane as if they were located at the arc position using the same transformation as For the lensed galaxies. and fit a bivariate Gaussian to the point. spread function in order to determine the source plane resolution.," We “reconstruct” these stars in the source plane as if they were located at the arc position using the same transformation as for the lensed galaxies, and fit a bivariate Gaussian to the point spread function in order to determine the source plane resolution."30 The typical ΟΝΝΕΔ of each arc in the direction of highest magnification is listed in Table 1 and. with the exception of CI0024|1709 which is not highlv-magnified. varies [fron ppc with à mean of ppc.," The typical FWHM of each arc in the direction of highest magnification is listed in Table 1 and, with the exception of Cl0024+1709 which is not highly-magnified, varies from pc with a mean of pc."31 First. we reconstruct the reduced. Hux-calibrated: data cubes to the source plane using transformations [rom the eravitational lens mocdels described in 822.3.," First, we reconstruct the reduced, flux-calibrated data cubes to the source plane using transformations from the gravitational lens models described in 2.3."32 The resulting data cubes were binnecl such that each spatial pixel corresponded to 0.5.1 ENIAL resolution elements along the direction of highest magnification (Table 1)., The resulting data cubes were binned such that each spatial pixel corresponded to 0.5–1 FWHM resolution elements along the direction of highest magnification (Table 1).33 We fit Gaussian profiles to the strongest emission line (Hla. or Ομ) at each spatial pixel using a weighted X7 minimization. procedure and determine the two-dimensional intensity. velocity. and velocity dispersion maps.," We fit Gaussian profiles to the strongest emission line $\alpha$ or ]) at each spatial pixel using a weighted $\chi^2$ minimization procedure and determine the two-dimensional intensity, velocity, and velocity dispersion maps."34 To compute the emission line fits we first subtracted the median value at each spatial pixel to remove any source continuum and residual sky background., To compute the emission line fits we first subtracted the median value at each spatial pixel to remove any source continuum and residual sky background.35 A blank region of sky within each data cube was used to determine the sky. variance spectrum V(A)., A blank region of sky within each data cube was used to determine the sky variance spectrum $V(\lambda)$.36 The spectra to be Lit are weighted by w(A)=V.+ appropriate for Gaussian noise. so that regions of higher noise (c.g. strong sky emission lines) do not cause spurious fits.," The spectra to be fit are weighted by $w(\lambda) = V^{-1}$ appropriate for Gaussian noise, so that regions of higher noise (e.g. strong sky emission lines) do not cause spurious fits."37 We compute the x7 statistic for the best-lit. Gaussian as well as a for a [οποίους spectrum (f(A)= 0) and require à minimum improvement over the fit with no line of AY?= 1625 for the various ares (Le. 5o emission line detection)., We compute the $\chi^2$ statistic for the best-fit Gaussian as well as a for a featureless spectrum $f(\lambda) = 0$ ) and require a minimum improvement over the fit with no line of $\Delta \chi^2 = 16$ –25 for the various arcs (i.e. $\sigma$ emission line detection).38 Lf this criterion was not met. we averagedthe surrounding 3.3 spatial pixels o achieve higher signal-to-noise.," If this criterion was not met, we averagedthe surrounding $\times$ 3 spatial pixels to achieve higher signal-to-noise."39 No fit was mace if the 3.3 averaging still Lailed to produce the minimum. N47 improvement., No fit was made if the $\times$ 3 averaging still failed to produce the minimum $\Delta \chi^2$ improvement.40 We caleulated the formal Lo error bounds by »erturbing the Gaussian fit parameters until the X7 increases ον 1 from the best-fit value., We calculated the formal $\sigma$ error bounds by perturbing the Gaussian fit parameters until the $\chi^2$ increases by 1 from the best-fit value.41 In all following sections. we have deconvolved the line widths with the instrumental resolution (I?c 3600) bv subtracting the instrumental resolution in quadrature from the best-fit Gaussian σ.," In all following sections, we have deconvolved the line widths with the instrumental resolution $R\simeq3600$ ) by subtracting the instrumental resolution in quadrature from the best-fit Gaussian $\sigma$."42 The resulting source plane intensity. velocity. ancl dispersion. fields for he entire sample are shown in Figure 2. ancl demonstrate detailed kinematic and morphological properties on scales down to LOO200 pc.," The resulting source plane intensity, velocity, and dispersion fields for the entire sample are shown in Figure \ref{fig:osiris_montage} and demonstrate detailed kinematic and morphological properties on scales down to 100–200 pc."43 From the source plane nebular emission line intensity and dynamics we estimate the size. dispersion. and dynamical mass of cach galaxy.," From the source plane nebular emission line intensity and dynamics we estimate the size, dispersion and dynamical mass of each galaxy."44 The size is calculated. as the maximum cdiameter from pixels with successful emission line. fits. roughly equivalent to a major axis diameter with. limitingM isophote. LO“?16 1 2 3 ," The size is calculated as the maximum diameter from pixels with successful emission line fits, roughly equivalent to a major axis diameter with limiting isophote $\sim10^{-16}$ $^{-1}$ $^{-2}$ $^{-2}$ ."45The uncertainty is dominated. by errors. in the lensing magnification and is <2054 ., The uncertainty is dominated by errors in the lensing magnification and is $\leq20$ .46. We estimate the elobal average, We estimate the global average47"polychromatic sources, only the zero interferometric order will be used as being achromatic.","polychromatic sources, only the zero interferometric order will be used as being achromatic."48 The source characteristics with a 23.75urad separation and a ~20 intensity ratio are correctly recovered in the image., The source characteristics with a $23.75 \mu rad$ separation and a $\sim 20$ intensity ratio are correctly recovered in the image.49 Results are consistent with the theoretical convolution between the point spread function and the object intensity distribution according to eq.23.., Results are consistent with the theoretical convolution between the point spread function and the object intensity distribution according to \ref{equa_PSF}.50" Consequently, over the instrument clear field the instrument imaging capabilities have been demonstrated."," Consequently, over the instrument clear field the instrument imaging capabilities have been demonstrated."51 'This first experimental study was mainly dedicated to the demonstration of the imaging capabilities of a temporal hypertelescope on a one dimensional object., This first experimental study was mainly dedicated to the demonstration of the imaging capabilities of a temporal hypertelescope on a one dimensional object.52" Due to mechanical constraints, the telescope array has been designed in a 2D configuration."," Due to mechanical constraints, the telescope array has been designed in a 2D configuration."53" Even if this array is not absolutely optimized for a two dimensional imaging, it is possible to test the 2D PSF to demonstrate the operation of the 2D imaging process."," Even if this array is not absolutely optimized for a two dimensional imaging, it is possible to test the 2D PSF to demonstrate the operation of the 2D imaging process."54 This picture can be obtained row by row like in a TV raster scan using the phase modulations reported in equation eq.7.., This picture can be obtained row by row like in a TV raster scan using the phase modulations reported in equation \ref{phase_equa_temporal}.55 A set of phase shifts ιο is sent through the driving voltage electronics taking into account the projection of the telescope i baseline along the y direction: This equation describes the phase shift that could be observed for telescope i in the image plane along the vertical axis in a spatial configuration., A set of phase shifts $\varphi_{i0}$ is sent through the driving voltage electronics taking into account the projection of the telescope $i$ baseline along the $y$ direction: This equation describes the phase shift that could be observed for telescope $i$ in the image plane along the vertical axis in a spatial configuration.56 As demonstrated in ref (Reynaud&Delage (2007))) it is possible this way to get a 2D information using a temporal hypertelescope., As demonstrated in ref \citet{RD}) ) it is possible this way to get a 2D information using a temporal hypertelescope.57 We tested this process by recording the 2D PSF using our experimental test bench., We tested this process by recording the 2D PSF using our experimental test bench.58 The theoretical and experimental patterns are reported on Fig.20.., The theoretical and experimental patterns are reported on \ref{psf_2D}.59 The array cophasing was manually achieved during the first scan on the central row (yo= 0)., The array cophasing was manually achieved during the first scan on the central row $y_0=0$ ).60" After this initialization process, it is possible to scan all the field of view taking advantage of the relative stability of the telescope array."," After this initialization process, it is possible to scan all the field of view taking advantage of the relative stability of the telescope array."61 This full operation lasts about 20 seconds to get 50 rows over the 2D PSF., This full operation lasts about 20 seconds to get 50 rows over the 2D PSF.62" In order to quantify the discrepancies between ideal (Figure 20 top) and experimental (Figure 20 middle) 2D PSF, Figure 20 bottom reports the absolute value of the difference between the two images."," In order to quantify the discrepancies between ideal (Figure \ref{psf_2D} top) and experimental (Figure \ref{psf_2D} middle) 2D PSF, Figure \ref{psf_2D} bottom reports the absolute value of the difference between the two images."63 The significant fluctuations are probably due to the lack of an active phase control system during the 2D scan., The significant fluctuations are probably due to the lack of an active phase control system during the 2D scan.64 A fine study of this limitation will be achieved after the implementation of a servo control system of our test bench., A fine study of this limitation will be achieved after the implementation of a servo control system of our test bench.65" Nevertheless, these results are promising and could be enhanced with a convenient cophasing system."," Nevertheless, these results are promising and could be enhanced with a convenient cophasing system."66 The aim of this study was to experimentally demonstrate the operation of a temporal hypertelescope., The aim of this study was to experimentally demonstrate the operation of a temporal hypertelescope.67 This experimental demonstration was achieved by testing the instrument Point Spread Function as a first stage., This experimental demonstration was achieved by testing the instrument Point Spread Function as a first stage.68 The second experiment demonstrated the possibility to observe an unbalanced binary star with a 20 flux ratio., The second experiment demonstrated the possibility to observe an unbalanced binary star with a 20 flux ratio.69" During this first test, the PSF dynamics was limited to 300 due to the lack of servo control system."," During this first test, the PSF dynamics was limited to 300 due to the lack of servo control system."70 The next stage of this study will be the design and implementation of a servo control system to, The next stage of this study will be the design and implementation of a servo control system to71wav oul of the disk.,way out of the disk.72 Indeed. ?./ argue on Che basis of the distinct variability properties of the coronal and thermal components in the soft state. and the correlation between. Iuninosity and coronal power-law slope. that [Inctuations in the accretion rate cannot on their own explain the observed. variability in GDllIs.," Indeed, \cite{Reig06} argue on the basis of the distinct variability properties of the coronal and thermal components in the soft state, and the correlation between luminosity and coronal power-law slope, that fluctuations in the accretion rate cannot on their own explain the observed variability in GBHs."73 More recent work has begun to follow (his path. but twpically has used proxies for the radiation rate rather (han a measure of the Gme-varving huminositv itself.," More recent work has begun to follow this path, but typically has used proxies for the radiation rate rather than a measure of the time-varying luminosity itself."74 ?— took the first step., \cite{HK01} took the first step.75 They computed the power spectra of both the mass accretion rate in the plunging region and the volume-integrated magnetic stress. wilh the thought that one or the other would be a reasonable predictor of the time-«dependence of the light output.," They computed the power spectra of both the mass accretion rate in the plunging region and the volume-integrated magnetic stress, with the thought that one or the other would be a reasonable predictor of the time-dependence of the light output."76 The two power spectra were similar. but not identical. both crudely describable as power-laws with αc—1.5.," The two power spectra were similar, but not identical, both crudely describable as power-laws with $\alpha \simeq -1.5$."77 ?. elaborated this approach., \cite{AR03} elaborated this approach.78 Assuming that thefocal emissivity follows directly rom (he/oeal mass accretion rate (ancl not separating the coronal part from the thermal part). (μον used the verticallv-integrated. ancl azimuthallv-averaged magnetic shear stress rom 3D pseudo-Newtonian MID simulations as à proxy for the local accretion rate.," Assuming that the emissivity follows directly from the mass accretion rate (and not separating the coronal part from the thermal part), they used the vertically-integrated and azimuthally-averaged magnetic shear stress from 3D pseudo-Newtonian MHD simulations as a proxy for the local accretion rate."79 Placing the resulting emissivitv in the disks equatorial plane and assuming further that the Πα ollowed cireular orbits. thev calculated the light curves seen bv distant observers. allowing or general relativistic rav-paths ancl Doppler-shifting.," Placing the resulting emissivity in the disk's equatorial plane and assuming further that the fluid followed circular orbits, they calculated the light curves seen by distant observers, allowing for general relativistic ray-paths and Doppler-shifting."80 Even though the PDSs of individual racial annuli were well described by broken power-laws (04=—1 and ay=—3.5) whose breaks were near the local orbital frequency. (he superposition of these PDSsbecause of (he radial dependence of the emissivityled to à=—2 power-law PDSs in the total output.," Even though the PDSs of individual radial annuli were well described by broken power-laws $\alpha_1 = -1$ and $\alpha_2 = -3.5$ ) whose breaks were near the local orbital frequency, the superposition of these PDSs—because of the radial dependence of the emissivity—led to $\alpha=-2$ power-law PDSs in the total output."81 ? came to similar conclusions based on a Fourier analvsis of the mass accretion rate in the plunging region., \cite{MaMa04} came to similar conclusions based on a Fourier analysis of the mass accretion rate in the plunging region.82 Moving sliehtlv. closer to incorporating radiation mechanism physics. T. used data from 3D MIID simulations in full general relativity (ο predict model light curves and power spectra Irom the/Ahermal component alone.," Moving slightly closer to incorporating radiation mechanism physics, \cite{2006ApJ...651.1031S} used data from 3D MHD simulations in full general relativity to predict model light curves and power spectra from the component alone."83 Most recently. 72. studied the fluctuations in a variety of dvnamical quantities monitored in a 3-cl pseudo-Newtonian MILD simulation. hoping to find an origin flor QPO behavior.," Most recently, \cite{ReynMill09} studied the fluctuations in a variety of dynamical quantities monitored in a 3-d pseudo-Newtonian MHD simulation, hoping to find an origin for QPO behavior."84 In (his paper. we seek to connect dynamical caleulations still more tightly to radiation.," In this paper, we seek to connect dynamical calculations still more tightly to radiation."85 The tool we bring to bear on this problem is a new fully general relativistic 3D MIID simulation code (described in ?))., The tool we bring to bear on this problem is a new fully general relativistic 3D MHD simulation code (described in \cite{Noble09}) ).86 Because this eode intrinsically conserves energy. it can sell- relate cdvnamics to heating.," Because this code intrinsically conserves energy, it can self-consistently relate dynamics to heating."87 ILowever. because inclusion of simultaneous radiation transfer is not vel feasible. we cannot provide a complete account of the radiation output.," However, because inclusion of simultaneous radiation transfer is not yet feasible, we cannot provide a complete account of the radiation output."88 In parücular. photon diffusion times within the disk body are so long (shearing box ealeulations that do include radiation (ransler have shown that they are generally ~10 orbital periods: 7)) that diffusion delavs can substantially affect the time-dependence of the emerging light.," In particular, photon diffusion times within the disk body are so long (shearing box calculations that do include radiation transfer have shown that they are generally $\sim 10$ orbital periods: \cite{HKS06}) ) that diffusion delays can substantially affect the time-dependence of the emerging light."89" Consequently. im (hs paper we locus on the variability of the Iuminosity from the coronal region, where optical depths are likely no more than order unity (see. e.g.. 2))."," Consequently, in this paper we focus on the variability of the luminosity from the coronal region, where optical depths are likely no more than order unity (see, e.g., \cite{Ibrag05}) )."90looking to see if the amount of diffuse substructure in the galaxies correlates with their distance from the center of Virgo (taken to be the position of M87).,looking to see if the amount of diffuse substructure in the galaxies correlates with their distance from the center of Virgo (taken to be the position of M87).91" We quantify the amount of substructure in two ways: the total luminosity in the features (Zsup)), and their fractional luminosity(fsub,, Measured with respect to the total galaxy light)."," We quantify the amount of substructure in two ways: the total luminosity in the features ), and their fractional luminosity, measured with respect to the total galaxy light)."92" In the latter case, the galaxy luminosities are calculated analytically from our Sérrsic surface brightness fits."," In the latter case, the galaxy luminosities are calculated analytically from our Sérrsic surface brightness fits."93 We then calculate each galaxy’s distance from the center of the Virgo Cluster using a combination of their projected distance from M87 on the sky and their line-of-sight distance from Mei (2007)., We then calculate each galaxy's distance from the center of the Virgo Cluster using a combination of their projected distance from M87 on the sky and their line-of-sight distance from Mei (2007).94 These quantities are given in Table 7.., These quantities are given in Table\ref{galprop}. .95to analyze the pulsar aud the PWN cunission separately.,to analyze the pulsar and the PWN emission separately.96 Thauks to the high spatial resolution observatious performed with andXAMAM-Newton. we have been able to satistactorily investigate 27 pulsus aud 21 DWNoe. for which we have deteriuned the uou-thermal N-rav fluxes and spectra in the 2-10 keV baud.," Thanks to the high spatial resolution observations performed with and, we have been able to satisfactorily investigate 27 pulsars and 24 PWNe, for which we have determined the non-thermal X-ray fluxes and spectra in the 2-10 keV band."97 Then we have carried out separated statistic studies of RPPs and PWNe. aud. tested the consistence of their enission properties with current models.," Then we have carried out separated statistic studies of RPPs and PWNe, and tested the consistence of their emission properties with current models."98 The organization of this paper is as following: the sample aud the data processing are presented in section 2: the statistical analyses of the N-rav spectral properties of RPPs aud PWNe are given in section 3: we discuss the plivsical miplicatious of our results iu section [ aud stuumarize our work iu section 5, The organization of this paper is as following: the sample and the data processing are presented in section 2; the statistical analyses of the X-ray spectral properties of RPPs and PWNe are given in section 3; we discuss the physical implications of our results in section 4 and summarize our work in section 5.99" We collect. pulsar aud PAWN samples from the observations by audΝοτίων, which both have high spatial resolutions. Le. ~1” aud ~6"". respectively,"," We collect pulsar and PWN samples from the observations by and, which both have high spatial resolutions, i.e., $\sim1\arcsec$ and $\sim6\arcsec$, respectively."100 We take the data directly from the literatures. and if there are uo published results. we analyzed the data in this paper.," We take the data directly from the literatures, and if there are no published results, we analyzed the data in this paper."101 TheNewton data are adapted ouly if there are no relevant NXMAF-data frou for the same source., The data are adapted only if there are no relevant data from for the same source.102 Allthe results are taken from literatures., All the results are taken from literatures.103 Totally we obtain the X-rav spectra of 27 RPPs aud 21 PWNe., Totally we obtain the X-ray spectra of 27 RPPs and 24 PWNe.104 Iu our samples. mullisecoud pulsars (AISPs) are not iucluded.," In our samples, millisecond pulsars (MSPs) are not included."105 It is eenerallv believed. that AISPs have ever undergone an accreticτdriven spin-up phase aud they are usually old aud regarded as a significantly differeut class., It is generally believed that MSPs have ever undergone an accretion-driven spin-up phase and they are usually old and regarded as a significantly different class.106 Similar study ou the AISPs is also linited by the rare data available., Similar study on the MSPs is also limited by the rare data available.107 Therefore we do uot analyze MSPs here. although we discuss them when conrpare our analysis with the previous work including MSPs.," Therefore we do not analyze MSPs here, although we discuss them when compare our analysis with the previous work including MSPs."108 Iu our samples. there are 15. out of spectra of pulsars obtained from the archived data.," In our samples, there are 15, out of 27, spectra of pulsars obtained from the archived data."109 We select only the pulsars detected by the Advanced CCD hnagine Spectrometer (ACIS) in the Timed Exposure (TE) Mode. in which a pulsar is able to be resolved spatially from ifs surrounding PWN.," We select only the pulsars detected by the Advanced CCD Imaging Spectrometer (ACIS) in the Timed Exposure (TE) Mode, in which a pulsar is able to be resolved spatially from its surrounding PWN."110 We calibrate the data with CIAO (ver 3.1) and CALDD (ver 3.3.0)., We calibrate the data with CIAO (ver 3.4) and CALDB (ver 3.3.0).111 We first reprocess the Level 1 data for the correction of the charge transfer ineficiency (CTI) effects. then clean the backerouud and remove the afterglow.," We first reprocess the Level 1 data for the correction of the charge transfer inefficiency (CTI) effects, then clean the background and remove the afterglow."112 Time intervals with anomalous background rates associated with particle dare events are further rejected in the Level 2 data., Time intervals with anomalous background rates associated with particle flare events are further rejected in the Level 2 data.113 And then the pulsar positions are obtained by thecelldetect tool in CIAO., And then the pulsar positions are obtained by the tool in CIAO.114 Finally. the spectra are extracted from the Level 2 data and then fit withXSPEC.," Finally, the spectra are extracted from the Level 2 data and then fit with."115 We use both the power-law (PL) aud the power-law|blackbody (PL|BB) models to fit the pulsar spectra., We use both the power-law (PL) and the power-law+blackbody (PL+BB) models to fit the pulsar spectra.116 If the resulted spectral iudices are consistent within errors m both models. then the results from the PL model are used. otherwise those from the PLBD model are used.," If the resulted spectral indices are consistent within errors in both models, then the results from the PL model are used, otherwise those from the PL+BB model are used."117 Iu our spectral analysis. we show errors at the confidence level.," In our spectral analysis, we show errors at the confidence level."118 Dileup occurs when more than oue photon are collected in one pixel within a CCD readout frame. since those photous can only be recorded as a single photou eveut whose cucrey is the stm of the collected photons.," Pileup occurs when more than one photon are collected in one pixel within a CCD readout frame, since those photons can only be recorded as a single photon event whose energy is the sum of the collected photons."119 Therefore pileup may affect the results of spectral analysis., Therefore pileup may affect the results of spectral analysis.120 According to section 6.112 in the Proposers Observatory. Codev.7t.. the effect of pileup can be oluitted if the pileup fraction is <10%..," According to section 6.14.2 in the Proposers' Observatory Guide, the effect of pileup can be omitted if the pileup fraction is $\le$."121 However. pileup does affect the spectral analysis even if the pileup fraction is <10%..," However, pileup does affect the spectral analysis even if the pileup fraction is $\le$."122" For exaiuple. since the pileup fraction of PSR J1930]|1852 is estimated fo be ouly it spectral iudex is reported to be 1.09""n|u without pileup conection (Lu ct al."," For example, since the pileup fraction of PSR J1930+1852 is estimated to be only , its spectral index is reported to be $1.09^{+0.08}_{-0.09}$ without pileup correction (Lu et al."123 2002). whileas spectral iudex dis 1.35ionsη fter pileup correction (Camilo et al.," 2002), whileas the spectral index is $1.35^{+0.06}_{-0.10}$ after pileup correction (Camilo et al."124 2002)., 2002).125 Iu spectral analysis. we first estimate the pileup fraction usingPIAIMS®.. aud then add a pileup model iu the spectral fitting of the pulsars if the pileup fraction is higher than3%.," In our spectral analysis, we first estimate the pileup fraction using, and then add a pileup model in the spectral fitting of the pulsars if the pileup fraction is higher than."126.. Totally. there are 8 pulsus iu which the pileup model is included in the spectral fitting. 1.06. PSRs J0205|6119. JO537 6910. LO 69 (and its PWN). 19 τι 2958. 0258. J1930|1852 aud D1951nmed," Totally, there are 8 pulsars in which the pileup model is included in the spectral fitting, i.e., PSRs J0205+6449, $-$ 6910, $-$ 69 (and its PWN), $-$ 45 (Vela), $-$ 2958, $-$ 0258, J1930+1852 and B1951+32."127u The absorption cohuuu deusitv (Nyp) is several wave. (, The absorption column density $N_{\rm H}$ ) is obtained in several ways. (1281) For 6 pulus (PSRs J0205]|6119. Jü537 6910. 2958. JlsI16-0255. J1930|1852 and D1951]32) with bright PWNe. Nj are obtained from the spectral fitting of their PWNe. aud then fixed when fitting the spectra of the pulsus. (,"1) For 6 pulsars (PSRs J0205+6449, $-$ 6910, $-$ 2958, J1846-0258, J1930+1852 and B1951+32) with bright PWNe, $N_{\rm H}$ are obtained from the spectral fitting of their PWNe, and then fixed when fitting the spectra of the pulsars. ("1292) PSRs 69 and 5916 are embedded in SNRs 0510 69.3 aud 292.0|1.5. respectively. aud their PWN spectra below 2.5 keV are stronely affected by the SNRs.,"2) PSRs $-$ 69 and $-$ 5916 are embedded in SNRs $-$ 69.3 and G292.0+1.8, respectively, and their PWN spectra below 2.5 keV are strongly affected by the SNRs."130 At the same iue. conustrainiueg Nyy with cinission above 2.5 keV i difücult because of the small absorption iu this high energv rauge.," At the same time, constraining $N_{\rm H}$ with emission above 2.5 keV is difficult because of the small absorption in this high energy range."131 Therefore their Nyy are obtained by fitting he pulsar spectra that the contamination of the SNR enission is neelieible. aud then Nyy ave fixed iu the spectral fitting of their PWNe. (," Therefore their $N_{\rm H}$ are obtained by fitting the pulsar spectra that the contamination of the SNR emission is negligible, and then $N_{\rm H}$ are fixed in the spectral fitting of their PWNe. ("1323) The PWNe associated. with PSRs B0355|51. 5055. 13. D1929|10 and J2229|6111 are not bright. and Ng ds determined bv jointly fitting the spectra of both the pulsar aud its PWN. ,"3) The PWNe associated with PSRs B0355+54, $-$ 5055, $-$ 13, B1929+10 and J2229+6114 are not bright, and $N_{\rm H}$ is determined by jointly fitting the spectra of both the pulsar and its PWN. ("133"1) PSRs J0633|1716 aud Bos33 15 have been studied extensively, and their Vy values used in our spectral fitting are taken from Caraveo et al. (","4) PSRs J0633+1746 and $-$ 45 have been studied extensively, and their $N_{\rm H}$ values used in our spectral fitting are taken from Caraveo et al. ("1342001) and Pavlov ct al. (,2004) and Pavlov et al. (1352001).,2001).136 The huuinositv uucertaünutv is crucial iu our analysis of correlations. aud should be cousidered carefully.," The luminosity uncertainty is crucial in our analysis of correlations, and should be considered carefully."137 Since the N-ray huninositv is οἴνοι bv Ly=la?fx. where d is he pulsar distance and fx is the 2-10 keV N-rav flux. the Lx uucertiüuntv should be derived from the wucertaimtics of both fx aud 7.," Since the X-ray luminosity is given by $L_{\rm X}=4\pi138d^2f_{\rm X}$, where $d$ is the pulsar distance and $f_{\rm X}$ is the 2-10 keV X-ray flux, the $L_{\rm X}$ uncertainty should be derived from the uncertainties of both $f_{\rm X}$ and $d$."139 The uncertainty of fx is derived. frou hose of the normalization aud the photon iudex iu the spectral fitting., The uncertainty of $f_{\rm X}$ is derived from those of the normalization and the photon index in the spectral fitting.140 For the fiuxes taken from literatures. their uncertainties are extrapolated from the published ones w the ratios of the fluxes in 2-10 keV to those in the corresponding published energy rauges.," For the fluxes taken from literatures, their uncertainties are extrapolated from the published ones by the ratios of the fluxes in 2-10 keV to those in the corresponding published energy ranges."141 The distances are usually not well constrained. thus he distance uncertainty may cominate the bhpuuinositv uncertainty.," The distances are usually not well constrained, thus the distance uncertainty may dominate the luminosity uncertainty."142" There are several cases in our sunuples: (1) the distances of 7 pulsus are derived frou the radio dispersion neasures., and their errors are couscrvatively taken to be as estimated by Cordes Lazio (2001): (2) the distances of LE pulsars are obtained via their associated SNRs. and some ofthem are shown with published distance errors in literatures. while for the others without published errors a conservative error of is taken: (3) PSRs JO537 6910 and 69 are both located in the"," There are several cases in our samples: (1) the distances of 7 pulsars are derived from the radio dispersion measures, and their errors are conservatively taken to be, as estimated by Cordes Lazio (2001); (2) the distances of 14 pulsars are obtained via their associated SNRs, and some ofthem are shown with published distance errors in literatures, while for the others without published errors a conservative error of is taken; (3) PSRs $-$ 6910 and $-$ 69 are both located in the"143shown by the continuous line in Fig. 3..,shown by the continuous line in Fig. \ref{fig:Fig3}.144 This estimate neglects the GC population coming from galaxies fainter than R=18., This estimate neglects the GC population coming from galaxies fainter than R=18.145 However. galaxies just brighter than R=18. and therefore very significantly fainter than M86. also have a lower GC richness compared to this galaxy.," However, galaxies just brighter than R=18, and therefore very significantly fainter than M86, also have a lower GC richness compared to this galaxy."146 This compensates at least partially the first underestimate., This compensates at least partially the first underestimate.147 On the one hand. we show that GCs can explain a large part of the object counts in the western field (Fig. 3)).," On the one hand, we show that GCs can explain a large part of the object counts in the western field (Fig. \ref{fig:Fig3}) )."148 This does not mean that this field is only populated by intergalactic GCs at magnitudes fainter than R=25. but that we can not exclude that a large part of the faint object population in this field could be GCs.," This does not mean that this field is only populated by intergalactic GCs at magnitudes fainter than R=25, but that we can not exclude that a large part of the faint object population in this field could be GCs."149 We have. however. to take into account the fact that at these faint magnitudes. the western field data are becoming incomplete and that the easiest objects to detect are globular clusters because they have a compact shape.," We have, however, to take into account the fact that at these faint magnitudes, the western field data are becoming incomplete and that the easiest objects to detect are globular clusters because they have a compact shape."150 On the other hand. the three other fields have a faint object population that is clearly more numerous than the population of GCs predicted using the M86 data.," On the other hand, the three other fields have a faint object population that is clearly more numerous than the population of GCs predicted using the M86 data."151 This probbaly means that these three fields do not have a high level of GCs compared to their overall very faint galaxy population., This probbaly means that these three fields do not have a high level of GCs compared to their overall very faint galaxy population.152 Subtracting the estimated GC LF to the overall LFs does hot even allow to completely flatten the slope (see dotted lines in Fig. 3))., Subtracting the estimated GC LF to the overall LFs does not even allow to completely flatten the slope (see dotted lines in Fig. \ref{fig:Fig3}) ).153 This is consistent with the results of AO7 who have shown that only the NGC 4874 field has a significant population of objects that could be intergalactie GCs., This is consistent with the results of A07 who have shown that only the NGC 4874 field has a significant population of objects that could be intergalactic GCs.154 Evidence for this last significant population was only given for Bx24.75 and our B and V data are not deep enough to generalize this study down to R=25.5., Evidence for this last significant population was only given for $\leq$ 24.75 and our B and V data are not deep enough to generalize this study down to R=25.5.155 In conclusion. the very faint object population i1 the three eastern fields is probably dominated by galaxies.," In conclusion, the very faint object population in the three eastern fields is probably dominated by galaxies."156 We confirm (compared to A07) that the western part of the Coma cluster is very poorly populated. with less than 30 objects per deg? and per half magnitude bin down to R=25.," We confirm (compared to A07) that the western part of the Coma cluster is very poorly populated, with less than 30 objects per $^2$ and per half magnitude bin down to R=25."157 Even for fainter magnitudes. the level remains lower (around 4000 objects per deg? and per half magnitude) than the populations in the other fields.," Even for fainter magnitudes, the level remains lower (around 4000 objects per $^2$ and per half magnitude) than the populations in the other fields."158 We have previously shown that these objects are unlikely to be galaxies for a large part., We have previously shown that these objects are unlikely to be galaxies for a large part.159 This subfield is included in what we called the South area in AQ7 and it was probably at least partially depopulated in terms of galaxies by major matter infalls coming from the West (see also AQ7)., This subfield is included in what we called the South area in A07 and it was probably at least partially depopulated in terms of galaxies by major matter infalls coming from the West (see also A07).160 LFs in the three other subfields are confirmed (compared to AO7) to be strongly rising with slopes close to —2., LFs in the three other subfields are confirmed (compared to A07) to be strongly rising with slopes close to $-2$.161 This implies the existence of a very large population of dwarf galaxies in these regions and shows that the LF in the central part of the Coma cluster is very significantly different from the field LFs (e.g. [bert et al., This implies the existence of a very large population of dwarf galaxies in these regions and shows that the LF in the central part of the Coma cluster is very significantly different from the field LFs (e.g. Ilbert et al.162 2005)., 2005).163 This also shows that peculiar processes are at work to form or to concentrate at this place such a large amount of faint objects., This also shows that peculiar processes are at work to form or to concentrate at this place such a large amount of faint objects.164 We know that at least part of the faint Coma cluster dwarves (low surface brightness objects. see AO6b) were probably formed in the early stages of the cluster. so at least part of the faint galaxy population is made of old cluster-resident galaxies.," We know that at least part of the faint Coma cluster dwarves (low surface brightness objects, see A06b) were probably formed in the early stages of the cluster, so at least part of the faint galaxy population is made of old cluster-resident galaxies."165 We have also shown in AO6b that another part of these low surface brightness objects does not share the same history and are possibly coming from the field., We have also shown in A06b that another part of these low surface brightness objects does not share the same history and are possibly coming from the field.166 À possible scenario in agreement with the present data could be that debris from brighter disrupted and harassed galaxies are populating the very faint part of the Coma cluster galaxy LFs., A possible scenario in agreement with the present data could be that debris from brighter disrupted and harassed galaxies are populating the very faint part of the Coma cluster galaxy LFs.167 The mass spectrum of these debris would have a slope close to —2., The mass spectrum of these debris would have a slope close to $-2$.168 This could be verified via numerical simulations. testing the mass distribution of debris issued from galaxy close encounters. generalizing for example the results by Bournaud et al. (," This could be verified via numerical simulations, testing the mass distribution of debris issued from galaxy close encounters, generalizing for example the results by Bournaud et al. ("1692003).,2003).170 An example of such candidates is seen in our data around the two possibly interacting galaxies shown in Fig. 4.., An example of such candidates is seen in our data around the two possibly interacting galaxies shown in Fig. \ref{fig:exa}.171 Other concentrations of stars. which are called knots. have also been observed to be ejected from spiral galaxies in clusters by Cortese et al. (," Other concentrations of stars, which are called knots, have also been observed to be ejected from spiral galaxies in clusters by Cortese et al. ("1722007).,2007).173 The faintest knots observed by these authors from HST data have magnitudes Fyys=—11.5 (close to our B band). and are therefore somewhat brighter than the faintest of our objects. but not very far in magnitude. (and therefore mass) range.," The faintest knots observed by these authors from HST data have magnitudes $_{475}=-11.5$ (close to our B band), and are therefore somewhat brighter than the faintest of our objects, but not very far in magnitude (and therefore mass) range."174 They also are very blue. so are still forming stars.," They also are very blue, so are still forming stars."175 Similar blue knots are also observed in our data for example south-west of NGC4858 (see Fig. 4)), Similar blue knots are also observed in our data for example south-west of NGC4858 (see Fig. \ref{fig:exa}) )176 with magnitudes as faint as «24.5. but it is besides the goals of this paper to discuss a precise scenario of what happens around this galaxy.," with magnitudes as faint as $\sim$ 24.5, but it is besides the goals of this paper to discuss a precise scenario of what happens around this galaxy."177 The fact that the three eastern field LFs are very regular (except perhaps around R=22) shows that the general processes proposed in A07 to explain the dips in the LFs detected down to V«22 are not efficient on the Coma very faint galaxy population., The fact that the three eastern field LFs are very regular (except perhaps around R=22) shows that the general processes proposed in A07 to explain the dips in the LFs detected down to $\sim$ 22 are not efficient on the Coma very faint galaxy population.178 Similarly. the two central fields (including the two Coma cluster dominant galaxies NGC 4874 and NGC 4889) are the most populated regions.," Similarly, the two central fields (including the two Coma cluster dominant galaxies NGC 4874 and NGC 4889) are the most populated regions."179 This shows that galaxy disruption sometimes proposed to explain the lack of faint galaxies in the cluster centers does not act too strongly on the faintest existing galaxies (or knots)., This shows that galaxy disruption sometimes proposed to explain the lack of faint galaxies in the cluster centers does not act too strongly on the faintest existing galaxies (or knots).180 The large scale diffuse light sources detected in AOGb around NGC 4874 then probably originate from brighter galaxies., The large scale diffuse light sources detected in A06b around NGC 4874 then probably originate from brighter galaxies.181 Besides the fact that these galaxies could be (at least part of them) debris of larger objects. we investigate here their properties based on colour plots such as B-I versus B-R (see AO7).," Besides the fact that these galaxies could be (at least part of them) debris of larger objects, we investigate here their properties based on colour plots such as B-I versus B-R (see A07)."182 Ideally. we would need B and I data of similar depth as the R data. but this is not the case.," Ideally, we would need B and I data of similar depth as the R data, but this is not the case."183 We will therefore limit our sample to B= level)., We will therefore limit our sample to B=25.25 (the B band conservative completeness level).184 This means that all objects detected in B will also be detected in R and I. assuming typical B-R and B-I colours.," This means that all objects detected in B will also be detected in R and I, assuming typical B-R and B-I colours."185 We then compute galaxy density maps in the B-I/B-R space for the Coma cluster line of sight and for the F02 comparaison field. as already done in. AO7.," We then compute galaxy density maps in the B-I/B-R space for the Coma cluster line of sight and for the F02 comparaison field, as already done in A07."186 The difference between the two maps gives the statistical distribution of objects inside the Coma cluster CS in a B-I versus B-R plot., The difference between the two maps gives the statistical distribution of objects inside the Coma cluster CS in a B-I versus B-R plot.187 In such a plot. we have shown (A07) that early-type. early-spiral and late spiral galaxies were optimally separated in the B-I versus B-R space by the lines: (B-D = -1.2 (B-R) + 1.45 and (B-I) = -1.2 (B-R) + 2.60," In such a plot, we have shown (A07) that early-type, early-spiral and late spiral galaxies were optimally separated in the B-I versus B-R space by the lines: (B-I) = $-1.2$ (B-R) + 1.45 and (B-I) = $-1.2$ (B-R) + 2.60"188"the Gaussian case are of the order of2%,, and at the redshifts considered here and manifest themselves as an overall plateau with slightly more power at the largest scales (a factor two larger than at the smallest scales probed).","the Gaussian case are of the order of, and at the redshifts considered here and manifest themselves as an overall plateau with slightly more power at the largest scales (a factor two larger than at the smallest scales probed)."189" As expected, the effect of primordial non-Gaussianity on the flux power spectrum is small and the effect decreases with time."," As expected, the effect of primordial non-Gaussianity on the flux power spectrum is small and the effect decreases with time."190 In principle this effect on the flux power is degenerate only with a change in the mean flux level (see for example Figure 3 of ? or Figure 13 of ?)): this means that other changes in cosmological parameters and/or astrophysics produce a different k-dependent change in the flux power than the one produced by non-Gaussianities., In principle this effect on the flux power is degenerate only with a change in the mean flux level (see for example Figure 3 of \cite{vielhaehnelt06} or Figure 13 of \cite{mcdonald05}) ): this means that other changes in cosmological parameters and/or astrophysics produce a different $k$ -dependent change in the flux power than the one produced by non-Gaussianities.191" However, the magnitude of this effect is quite small and probably not detectable with present data sets."," However, the magnitude of this effect is quite small and probably not detectable with present data sets."192" Unlike the power spectrum, the bispectrum on large scales is sensitive to the statistical properties of primordial fluctuations like a primordial non-Gaussianity (??7).."," Unlike the power spectrum, the bispectrum on large scales is sensitive to the statistical properties of primordial fluctuations like a primordial non-Gaussianity \citep{fry94,verde02,sefusatti08}."193" Therefore, the 1D flux bispectrum looks like a very promising statistics to search for non-Gaussianities in the IGM."," Therefore, the 1D flux bispectrum looks like a very promising statistics to search for non-Gaussianities in the IGM."194 The flux bispectrum has been calculated for the first time using high-resolution QSO spectra by ?.., The flux bispectrum has been calculated for the first time using high-resolution QSO spectra by \cite{vielbispect}.195" Here, we use the same definition i.e. the real part of the three point function in k—space ,Dr=Re(dr(k1)ór(k2)δε(ka)), for closed triangles ki+koks=0."," Here, we use the same definition i.e. the real part of the three point function in $k-$ space $, D_F= {\rm Re}(\delta_F (k_1)\, \delta_F (k_2) \, \delta_F196(k_3))$, for closed triangles $ k_1 + k_2 + k_3 = 0$."197 óp(k) is the Fourier transform of OF’., $\delta_F(k)$ is the Fourier transform of $\delta F$.198" Dr is related to theflux Br(ki,ko,ka) (Dr) =2 BBr(ki, ko, delta’ (*1+k2+ks)-"," $D_F$ is related to the $B_F(k_1,k_2,k_3)$ D_F = B_F(k_1, k_2, ^D (k_1 + k_2 + k_3)."199 δ3(48) is the one-dimensional Dirac delta function and (-) indicates the ensemble average., $\delta^D(k)$ is the one-dimensional Dirac delta function and $\langle \cdot \rangle$ indicates the ensemble average.200" Since we compute the one- bispectrum our triangles are degenerate and we choose two configurations: i) the flattened configurations for which kj=ko and ks=-2ki; ti) the squeezed configuration for which ki=k—kmin, ko=—k—kmin and ks=2kmin, with kmin=2m/L (L the linear size of the box in km/s)."," Since we compute the one-dimensional bispectrum our triangles are degenerate and we choose two configurations: $i)$ the flattened configurations for which $k_1=k_2$ and $k_3 = -2\,k_1$; $ii)$ the squeezed configuration for which $k_1=k-k_{\rm min}$, $k_2=-k-k_{\rm min}$ and $k_3 =2012\,k_{\rm min}$, with $k_{\rm min}=2\pi/L$ (L the linear size of the box in km/s)."202 In the following we will always show the flux bispectrum as a function of the wavenumber k— ki., In the following we will always show the flux bispectrum as a function of the wavenumber $k=k_1$ .203" In ? à numerical calculation of the flux bispectrum was compared to analytical estimates obtained through an expansion at second order of the fluctuating Gunn-Peterson approximation (?)): while the overall amplitude of the bispectrum was not matched by the theory, the shape, at least at large scales, was well reproduced."," In \cite{vielbispect} a numerical calculation of the flux bispectrum was compared to analytical estimates obtained through an expansion at second order of the fluctuating Gunn-Peterson approximation \cite{FGPA}) ): while the overall amplitude of the bispectrum was not matched by the theory, the shape, at least at large scales, was well reproduced."204" However, the theoretical expression for the flux bispectrum contained only the gravitational terms."," However, the theoretical expression for the flux bispectrum contained only the gravitational terms."205 Here we extend this work by computing the flux bispectrum for NG Gaussian models using the numerical hydrodynamical simulations performed., Here we extend this work by computing the flux bispectrum for NG Gaussian models using the numerical hydrodynamical simulations performed.206 In Figure [6 we plot our findings in terms of ratios between the Gaussian and non-Gaussian models in the squeezed (top panels) and flattened (bottom panels) configurations., In Figure \ref{fig3} we plot our findings in terms of ratios between the Gaussian and non-Gaussian models in the squeezed (top panels) and flattened (bottom panels) configurations.207" Due to the intrinsic noisy nature of the bispectrum, we have binned the values in k—space, in the same way as the flux power of the previous subsection."," Due to the intrinsic noisy nature of the bispectrum, we have binned the values in $k-$ space, in the same way as the flux power of the previous subsection."208" One can see that while at z—3 the differences are very small and usually less than3-4%,, they become much larger and of the order of at z—4."," One can see that while at $z=3$ the differences are very small and usually less than, they become much larger and of the order of at $z=4$."209 At z—5.5 the differences become again smaller and with different wavenumber dependence., At $z=5.5$ the differences become again smaller and with different wavenumber dependence.210 It is possible to interpret this trend in the framework of the second order perturbation theory as done in ?:: the overall amplitude and shape of the flux bispectrum could not be smooth and strongly depend (in a non-trivial way) on the redshift evolution of the coefficients that describe the evolution of the mean flux level and of the IGM temperature-density., It is possible to interpret this trend in the framework of the second order perturbation theory as done in \cite{vielbispect}: the overall amplitude and shape of the flux bispectrum could not be smooth and strongly depend (in a non-trivial way) on the redshift evolution of the coefficients that describe the evolution of the mean flux level and of the IGM temperature-density.211" Among the different flux statistics that we have explored, the flux PDF seems the most promising in order to detect"," Among the different flux statistics that we have explored, the flux PDF seems the most promising in order to detect"212Galactic latitude of the source. its RAL is similar to other known sources in this direction suggesting that intrinsic contribution to the RAL is likely to be less than 20 rad 7.,"Galactic latitude of the source, its RM is similar to other known sources in this direction suggesting that intrinsic contribution to the RM is likely to be less than 20 rad $^{-2}$."213 Llowever these results are preliminary: the RAL clistribution and the inferred magnetic field need to be determined from more detailed multi-frequeney. observations., However these results are preliminary; the RM distribution and the inferred magnetic field need to be determined from more detailed multi-frequency observations.214 The inferred. magnetic field vectors obtained at. present by merely rotating the E-vectors at 4860 MlbIz by 907 shows that the field lines in the relaxed outer northern lobe are nearly cireumferential in the outer periphery., The inferred magnetic field vectors obtained at present by merely rotating the E-vectors at 4860 MHz by $^\circ$ shows that the field lines in the relaxed outer northern lobe are nearly circumferential in the outer periphery.215 The field lines are roughly along the axis of the lobes for both the outer and inner double. although the field lines tend to be orthogonal," The field lines are roughly along the axis of the lobes for both the outer and inner double, although the field lines tend to be orthogonal"216derived value.,derived value.217 To see why this should be true consider the effects of adding a pattern of random noise to the reconstruction of the non-flare photosphere., To see why this should be true consider the effects of adding a pattern of random noise to the reconstruction of the non-flare photosphere.218" The observed intensity of the solar surface with the flare present will not contain this error term, so it will appear that the flare is masking it, suggesting that it is more optically thick."," The observed intensity of the solar surface with the flare present will not contain this error term, so it will appear that the flare is masking it, suggesting that it is more optically thick."219" In order to evaluate the significance of the photospheric noise, we add Gaussian random noise of various (known) amplitude levels to the reconstructed photosphere."," In order to evaluate the significance of the photospheric noise, we add Gaussian random noise of various (known) amplitude levels to the reconstructed photosphere."220 First the RMS error on the photospheric reconstructions was measured for each image frame by comparing the reconstructed photospheric image in a region away from the flare emission to the observed photosphere; results are shown in Table 1.., First the RMS error on the photospheric reconstructions was measured for each image frame by comparing the reconstructed photospheric image in a region away from the flare emission to the observed photosphere; results are shown in Table \ref{tab:results}.221 Normally distributed noise with a range of known standard deviations was then added to the reconstructed photosphere and the calculation of « repeated., Normally distributed noise with a range of known standard deviations was then added to the reconstructed photosphere and the calculation of $\alpha$ repeated.222" This was done multiple times with different random noise for each frame and each value of the noise amplitude, in order to avoid random correlations between added noise and the photosphere."," This was done multiple times with different random noise for each frame and each value of the noise amplitude, in order to avoid random correlations between added noise and the photosphere."223 The variation in the derived value of α versus the total photospheric error for each frame is shown in Figure 7.., The variation in the derived value of $\alpha$ versus the total photospheric error for each frame is shown in Figure \ref{fig:Noise}.224" It can be seen that as the error in the photospheric noise increases, the derived value of a also increases as expected."," It can be seen that as the error in the photospheric noise increases, the derived value of $\alpha$ also increases as expected."225 Note that the values of a determined in image frames where the flare brightness is larger (see Table 1)) are much less sensitive to the effect of the noise., Note that the values of $\alpha$ determined in image frames where the flare brightness is larger (see Table \ref{tab:results}) ) are much less sensitive to the effect of the noise.226 Using this graph it is possible to extrapolate back to a ‘zero error’ value for a., Using this graph it is possible to extrapolate back to a `zero error' value for $\alpha$.227" If this is done for each frame using a simple polynomial extrapolation we get an average value for all the data of a=—0.0001€0.01, so to within the accuracy of these measurements the optical depth is effectively zero."," If this is done for each frame using a simple polynomial extrapolation we get an average value for all the data of $\alpha=-0.0001\pm0.01$, so to within the accuracy of these measurements the optical depth is effectively zero."228" Our direct analysis of the flare emission from seven image frames, comprising a total of 1200 pixels where the flare emission significantly enhanced the surface brightness, has given us the result that the optical depth is 0.0280.01."," Our direct analysis of the flare emission from seven image frames, comprising a total of 1200 pixels where the flare emission significantly enhanced the surface brightness, has given us the result that the optical depth is $0.028\pm0.01$."229" This value however should be regarded as an upper limit on the opacity of the flaring regions; when the effect of photospheric noise is considered the optical depth becomes too small to measure, and certainly less than 0.01."," This value however should be regarded as an upper limit on the opacity of the flaring regions; when the effect of photospheric noise is considered the optical depth becomes too small to measure, and certainly less than 0.01."230" As a result of this the assumption of our heuristic opacity model that τ is depends on the flare source function becomes unimportant, as the optical depth is so close to zero that a more appropriate model for the emission becomes /p=Spolj, where I, is the flare emission."," As a result of this the assumption of our heuristic opacity model that $\tau$ is depends on the flare source function becomes unimportant, as the optical depth is so close to zero that a more appropriate model for the emission becomes $231I_F=S_0+I_1,$ where $_1$ is the flare emission."232 The flare excess simply adds to the photospheric emission., The flare excess simply adds to the photospheric emission.233" 'The optical depth of the white-light flare regions we have studied is very small, indistinguishable from zero in this study, and in any case less than ~0.01."," The optical depth of the white-light flare regions we have studied is very small, indistinguishable from zero in this study, and in any case less than $\sim$ 0.01."234" We infer from this that the flare must be of low density and hot, almost certainly far from LTE."," We infer from this that the flare must be of low density and hot, almost certainly far from LTE."235" The temperature cannot be determined from this but is generally constrained by the new flare bolometric observations (???);; many authors suggest a value near 104 K (e.g., Hudson et al."," The temperature cannot be determined from this but is generally constrained by the new flare bolometric observations \citep{2004GeoRL..3110802W,2008cosp...37.1617K,2010arXiv1003.4194Q}; many authors suggest a value near $^4$ K (e.g., Hudson et al."236 2010)., 2010).237 These results definitely tend to reduce the importance of photospheric backwarming in our understanding of white-light flare emission.," \nocite{2010arXiv1001.1005H}238 These results definitely tend to reduce the importance of photospheric backwarming in our understanding of white-light flare emission."239" First, the low density and high temperature imply an emission source high in the atmosphere, consistent with stopping depths of low-energy electrons but inconsistent with stopping depths of the electrons required for backwarming models (?)."," First, the low density and high temperature imply an emission source high in the atmosphere, consistent with stopping depths of low-energy electrons but inconsistent with stopping depths of the electrons required for backwarming models \citep{2007ASPC..368..423F}."240" Second, the flare image scales (in this case limited by MDI resolution) are of order 1 Mm."," Second, the flare image scales (in this case limited by MDI resolution) are of order 1 Mm."241" If backwarming contributed significantly to the emission then the maximum height of the emission must be around half of the feature size (simple geometric ray model), which would be too low for an optically thin case (seeο"," If backwarming contributed significantly to the emission then the maximum height of the emission must be around half of the feature size (simple geometric ray model), which would be too low for an optically thin case \citep[see][]{2007PASJ...59S.807I}."242" Because the MDI data represent averages over one-minute intervals, and because they represent only a narrow slice of the true continuum, this result should be considered as a preliminary one."," Because the MDI data represent averages over one-minute intervals, and because they represent only a narrow slice of the true continuum, this result should be considered as a preliminary one."243" Newer data with better image cadence and spatial resolution (Hinode or SDO in space, or a variety of ground-based instruments leading up to ATST) should be applied to this interesting problem."," Newer data with better image cadence and spatial resolution (Hinode or SDO in space, or a variety of ground-based instruments leading up to ATST) should be applied to this interesting problem."244" If confirmed, this result suggests that the generally accepted picture of flare energy storage in the corona, with flare effects in the lower atmosphere derived from this energy reservoir, must be correct."," If confirmed, this result suggests that the generally accepted picture of flare energy storage in the corona, with flare effects in the lower atmosphere derived from this energy reservoir, must be correct."245" Note that this is the usual assumption, but that it has not been easy to establish observationally."," Note that this is the usual assumption, but that it has not been easy to establish observationally."246ight evlincer as the representation of the outer gap. they rave calculated the average outer gap size and use it as he representation of the outer gap.,"light cylinder as the representation of the outer gap, they have calculated the average outer gap size and use it as the representation of the outer gap."247 This is very important Or a statistical study., This is very important for a statistical study.248 Cheng et al (2004a) show that in Alonte Carlo simulations even if the inclination. angle of »ulsars is randomly selected from a uniform clistribution. the simulated 5-ray. pulsars detected by EGRET in the galactic plane are vounger and tend to have a larger inclination angle.," Cheng et al (2004a) show that in Monte Carlo simulations even if the inclination angle of pulsars is randomly selected from a uniform distribution, the simulated $\gamma$ -ray pulsars detected by EGRET in the galactic plane are younger and tend to have a larger inclination angle."249 On the otherhand. z-ray. pulsars detected by. EGRET at ueher latitudes are older and have a smaller. inclination anele.," On the otherhand, $\gamma$ -ray pulsars detected by EGRET at higher latitudes are older and have a smaller inclination angle."250 In other words. even if the seed. distribution. has a uniform distribution. a non-uniform cistribution can be generated by the 5-ràav. selection effects.," In other words, even if the seed distribution has a uniform distribution, a non-uniform distribution can be generated by the $\gamma$ -ray selection effects."251 In this paper. we intend to use Monte Carlo methods to study GeV ane Tey 5-rav properties of pulsars. so we adopt the model of Zhang et al. (," In this paper, we intend to use Monte Carlo methods to study GeV and TeV $\gamma$ -ray properties of pulsars, so we adopt the model of Zhang et al. ("2522004) to determine the size of the outer gap.,2004) to determine the size of the outer gap.253 Assuming that the representative region of the outer gap is the average distance to the gap. the mean fractional size of the outer gap can be approximated as ία.P.D)=nla.PBYP.D). where g(o.P.B) is à monotonically increasing function of o.D. and P.," Assuming that the representative region of the outer gap is the average distance to the gap, the mean fractional size of the outer gap can be approximated as $f(\alpha,P,B)254\approx \eta(\alpha,P,B)f(P,B)$, where $\eta(\alpha,P,B)$ is a monotonically increasing function of $\alpha,\ B$, and $P$."255 The value of η roughly decreases hy a factor Lx rom large inclination angles to smaller angles. (Zhang et al., The value of $\eta$ roughly decreases by a factor 3 from large inclination angles to smaller angles (Zhang et al.256 2004)., 2004).257 These 5-rays from the pulsar magnetosphere will contribute to the pulsed GeV. photons in y-ray pulsars detected by EGHIRIZT., These $\gamma$ -rays from the pulsar magnetosphere will contribute to the pulsed GeV photons in $\gamma$ -ray pulsars detected by EGRET.258 In general the differential energy spectrum of 5-ravs for each pulsar is dilferent., In general the differential energy spectrum of $\gamma$ -rays for each pulsar is different.259 In principle we can calculate it if the »ulsar parameters are specified., In principle we can calculate it if the pulsar parameters are specified.260 Llowever. it is very. dillicul o do so in a Monte Carlo simulation. in which we nee o deal with over ten million pulsars.," However, it is very difficult to do so in a Monte Carlo simulation, in which we need to deal with over ten million pulsars."261" EGRET has detecte six *5-rav pulsars and their energy spectra from LOO MeV o a [ew GeV. are all very close to 45,5 ( Hartman et al.", EGRET has detected six $\gamma$ -ray pulsars and their energy spectra from 100 MeV to a few GeV are all very close to $E_\gamma^{-1}$ ( Hartman et al.262 1999)., 1999).263 For thin outer gap pulsars. it has been shown tha he energy spectrum is. proportional. to ££.2d“fogLae-fL-LE. (Cheng. Lo and Ruderman 1986b: Cheng and.Ding 1904).," For thin outer gap pulsars, it has been shown that the energy spectrum is proportional to $E_\gamma^{-1}log(E_{max}/E_\gamma) \propto264E_\gamma^{-1}$ (Cheng, Ho and Ruderman 1986b; Cheng andDing 1994)."265 For simplicity in the Monte Carlo simulation. we wil approximate the expected energy. dilferential 5-ray Dux of thepulsar asa where d is the distance of the pulsar. and AQ is the the solid angle of 5-rav. beaming.," For simplicity in the Monte Carlo simulation, we will approximate the expected energy differential $\gamma$ -ray flux of thepulsar as, where $d$ is the distance of the pulsar, and $\triangle\Omega$ is the the solid angle of $\gamma$ -ray beaming."266 The value of Ονο generally varies with different pulsars., The value of $\triangle\Omega$ generally varies with different pulsars.267 For simplicity. we assume a constant beaming solid angle AO~1 sr in all our analyses.," For simplicity, we assume a constant beaming solid angle $\triangle\Omega\sim 1$ sr in all our analyses."268" In order to compare our model results with observations. we calculate the expected. integral EGRET flux of our model 5-rav pulsars using the formuladl... where Ly, is the maximum -rav energy detected. by EGRET. chosen to be 50 GeV. llere. we have ignored the 5-rav contribution [roni the polar cap. which could be important for Unidentified EGRET Sources (Gonthier et al."," In order to compare our model results with observations, we calculate the expected integral EGRET flux of our model $\gamma$ -ray pulsars using the formula, where $E_{max}$ is the maximum $\gamma$ -ray energy detected by EGRET, chosen to be 50 GeV. Here, we have ignored the $\gamma$ -ray contribution from the polar cap, which could be important for Unidentified EGRET Sources (Gonthier et al."269 2005)., 2002).270 However. the phase-resolved EGRET data of the Crab pulsar (Cheng Ruderman and Zhang 2000). Geminea (Zhang and. Cheng 2001) and the Vela pulsar (Romani 1996) can be explainec very well by the outer gap model and it appears that polar cap emission is unimportant.," However, the phase-resolved EGRET data of the Crab pulsar (Cheng, Ruderman and Zhang 2000), Geminga (Zhang and Cheng 2001) and the Vela pulsar (Romani 1996) can be explained very well by the outer gap model and it appears that polar cap emission is unimportant."271 Most recently. Muslimov Larcline(2004) have suggested that the slot gap mocle could be able to explain the phase-resolved. data as well.," Most recently, Muslimov Harding(2004) have suggested that the slot gap model could be able to explain the phase-resolved data as well."272 Since the distributions of simulated *5-rav. pulsars are mode dependent. in this paper we will ignore the contribution of 5-ravs [rom the polar cap for simplicity.," Since the distributions of simulated $\gamma$ -ray pulsars are model dependent, in this paper we will ignore the contribution of $\gamma$ -rays from the polar cap for simplicity."273 revious models of the pulsar wind. nebulae (e.g.. Ixennel Coroniti 1984: Chevalier 2000) mainly concentrate on he bright nebulae produced by interactions between voung oulsar wind particles and the supernova remnant (SNIU.," Previous models of the pulsar wind nebulae (e.g., Kennel Coroniti 1984; Chevalier 2000) mainly concentrate on the bright nebulae produced by interactions between young pulsar wind particles and the supernova remnant (SNR)."274 On the other hand. while there are no SNR surrounding he mature pulsars. they remain active enough to produce he relatively faint. compact svnchrotron nebulae through interactions between the relativistic wind particles and the interstellar medium.," On the other hand, while there are no SNR surrounding the mature pulsars, they remain active enough to produce the relatively faint, compact synchrotron nebulae through interactions between the relativistic wind particles and the interstellar medium."275 In this work. we use the one-zone moctel o describe high energy raciation from pulsar wind nebulae (Chevalier 2000).," In this work, we use the one-zone model to describe high energy radiation from pulsar wind nebulae (Chevalier 2000)."276 In the mocoel. the relativistic electrons in he shock waves emit X-rays through svnchrotron radiation.," In the model, the relativistic electrons in the shock waves emit X-rays through synchrotron radiation."277 This model can well explain the X-ray luminosity aud spectral properties of pulsar wind nebulae (Cheng ct al., This model can well explain the X-ray luminosity and spectral properties of pulsar wind nebulae (Cheng et al.278 2004b)., 2004b).279 Alature pulsars move at a high proper velocity after their birth. and can form a bow shock structure to produce svnchrotron wind nebulae when the pulsar proper motion velocity is larger than the sound speed in the ambient interstellar medium. (18M).," Mature pulsars move at a high proper velocity after their birth, and can form a bow shock structure to produce synchrotron wind nebulae when the pulsar proper motion velocity is larger than the sound speed in the ambient interstellar medium (ISM)."280" Phe characteristic size of the shock wave produced. by interactions between the pulsar wind particles and the ISM is referred to as the termination radius. 2,. and can be derived from Ho —(Laf2xpete)2Chl. where p—nmy. n=lcm ""is the number density of the ISM. my is the proton rest mass. ey is the pulsar velocity in units of 350 kms + (ef."," The characteristic size of the shock wave produced by interactions between the pulsar wind particles and the ISM is referred to as the termination radius, $R_s$, and can be derived from R_s = v_p^2, where $\rho=nm_p$, $n=1\ {\rm cm^{-3}}$ is the number density of the ISM, $m_p$ is the proton rest mass, $v_p$ is the pulsar velocity in units of 350 km $^{-1}$ (cf."281 5.2). and Lats4 is the spin down power of the pulsar in units of 1075 ere sf.," 5.2), and $L_{\rm sd, 34}$ is the spin down power of the pulsar in units of $10^{34}$ erg $^{-1}$."282 We have assumed the pulsar wind can carry away most of the pulsar spin-down power (L4) and deposit in the shock waves when the wind interacts with the interstellar medium., We have assumed the pulsar wind can carry away most of the pulsar spin-down power $L_{sd}$ ) and deposit in the shock waves when the wind interacts with the interstellar medium.283 In general. the energy in the shock. waves is stored in the magnetic field. the energetic protons (ions) ancl electrons.," In general, the energy in the shock waves is stored in the magnetic field, the energetic protons (ions) and electrons."284 However. the fractional energy. density of the magnetic field ερ is low (typically. egO.00L0.01. Ixennel Coroniti 1984). then by assuming equipartition of energv. between protons and. electrons. we obtain (y~e0.5.," However, the fractional energy density of the magnetic field $\epsilon_B$ is low (typically, $\epsilon_B\sim 0.001-0.01$, Kennel Coroniti 1984), then by assuming equipartition of energy between protons and electrons, we obtain $\epsilon_p \sim \epsilon_e\sim 0.5$."285" For a given cg. the magnetic Field at the termination radius is estimated as D=(6cpL.af"" 3217."," For a given $\epsilon_B$, the magnetic field at the termination radius is estimated as $B =(6\epsilon_B L_{\rm sd}/R_s^2 c)^{1/2}$ ."286" At the shock front. the electron energy distribution is Nis)x5"" for 5,«5X Taux where 5,,=(p|2)(p Desa. and 55 is the Lorentz [actor of the pulsar wind. particles."," At the shock front, the electron energy distribution is $N(\gamma)\propto \gamma^{-p}$ for $\gamma_m <\gamma <\gamma_{\rm287max}$ , where $\gamma_m = [(p-2)/(p-1)] \epsilon_e \gamma_w$ , and $\gamma_w$ is the Lorentz factor of the pulsar wind particles."288" We derive the value of siya, by (wo methods.", We derive the value of $\gamma_ {\rm max}$ by two methods.289 First. an estimate for μμ can be obtained by equating the," First, an estimate for $\gamma_ {\rm max}$ can be obtained by equating the"290node.,mode.291 The main difference between the ος=0 and Op40 cases (Figure 9bb) is that stability in the ο40 case requires a much larger value of the Richardson number. near Ri~5.," The main difference between the $\Omega_F=0$ and $\Omega_F \neq 0$ cases (Figure \ref{us_fig}b b) is that stability in the $\Omega_F \neq 0$ case requires a much larger value of the Richardson number, near $\Ri \sim 5$."292" Il is important (o stress that this threshold value for Ri depends on (he value chosen for the fiducial minimum “unstable” growth rate. since (here is some subjectivity in (he procedure to neastire erowth rates and the slope of wy, as funetion of Ri is quite shallow when Q)40 (see Figure 10))."," It is important to stress that this threshold value for $\Ri$ depends on the value chosen for the fiducial minimum “unstable” growth rate, since there is some subjectivity in the procedure to measure growth rates and the slope of $\omega_I$ as function of $\Ri$ is quite shallow when $\Omega_F \neq 0$ (see Figure \ref{growth_fig}) )."293 Nevertheless. the laver is quite clearly unstable for values of Ri sienilicatively arger that L/4.," Nevertheless, the layer is quite clearly unstable for values of $\Ri$ significatively larger that $1/4$."294 Since Ri can be thought as a proxy for the laver thickness (eq. |42]]).," Since $\Ri$ can be thought as a proxy for the layer thickness (eq. \ref{zmax_eq}] ]),"295 the condition that a larger Ri is requirecl for stability when ο40 is consistent with the results ol 84.2.. in which we found that the final dust distribution is thicker when the Coriolis terms are (urnecl on.," the condition that a larger $\Ri$ is required for stability when $\Omega_F \neq 0$ is consistent with the results of \ref{mu_sec}, in which we found that the final dust distribution is thicker when the Coriolis terms are turned on."296 As a coda [or this section. we comment on the constant Ri distribution adopted here.," As a coda for this section, we comment on the constant $\Ri$ distribution adopted here."297 sekiva(1998). studied the profile determined by a constant-Bài dust distribution and noticed, \citet{sek98} studied the profile determined by a $\Ri$ dust distribution and noticed298ratio for small No?<3.,ratio for small $N \sigma^2<3$.299 So the evidence ratio method is not trivially intuitive., So the evidence ratio method is not trivially intuitive.300 These simple examples show that the odds that we calculate from the evidence ratio may not be useful for making decisions if we take account of statistical variations over an ensemble of datasets., These simple examples show that the odds that we calculate from the evidence ratio may not be useful for making decisions if we take account of statistical variations over an ensemble of datasets.301" A decisive threshold of In£=5 can in many cases be exceeded only a small fraction of the time when Hi is true, even when such a value is effectively impossible under Ho."," A decisive threshold of $\ln{\cal E}=5$ can in many cases be exceeded only a small fraction of the time when $H_1$ is true, even when such a value is effectively impossible under $H_0$."302" In other words, the test is extremely safe (very hard to reject the null hypothesis incorrectly), but lacking in power (little ability to detect the alternative)."," In other words, the test is extremely safe (very hard to reject the null hypothesis incorrectly), but lacking in power (little ability to detect the alternative)."303" This asymmetry between type I and type II performance seems undesirable, particularly because the problem is set up so that there are only two possibilities."," This asymmetry between type I and type II performance seems undesirable, particularly because the problem is set up so that there are only two possibilities."304" If Ho is clearly inconsistent with the data, then /7; must be correct according to the problem as given — even if the Bayesian evidence ratio is only moderate."," If $H_0$ is clearly inconsistent with the data, then $H_1$ must be correct according to the problem as given – even if the Bayesian evidence ratio is only moderate."305" Again, this suggests that we should be free to challenge the statistical formulation and conclude that neither Ho nor Hy are correct."," Again, this suggests that we should be free to challenge the statistical formulation and conclude that neither $H_0$ nor $H_1$ are correct."306" Fisher might have regarded this as the correct (less *wooden"") approach.", Fisher might have regarded this as the correct (less “wooden”) approach.307" We now consider two more complex examples, where we are interested in which of two models is a better fit to spectral line data."," We now consider two more complex examples, where we are interested in which of two models is a better fit to spectral line data."308 We will use Monte Carlo simulation to assess the statistical scatter between different realizations of the data., We will use Monte Carlo simulation to assess the statistical scatter between different realizations of the data.309" We will consider two cases, one ‘nested’ (whether there is an extra component to a spectral line) and one not nested (whether a line has a Gaussian or Lorentzian profile)."," We will consider two cases, one `nested' (whether there is an extra component to a spectral line) and one not nested (whether a line has a Gaussian or Lorentzian profile)."310" Suppose we are trying to decide if a spectral feature is a single Gaussian (the null hypothesis Ho) or two Gaussians, of equal width,known separation, but unknown height ratio (the alternative hypothesis H;)."," Suppose we are trying to decide if a spectral feature is a single Gaussian (the null hypothesis $H_0$ ) or two Gaussians, of equal width,known separation, but unknown height ratio (the alternative hypothesis $H_1$ )."311" This is a nested model because if the height ratio is zero, H; reduces to Ho."," This is a nested model because if the height ratio is zero, $H_1$ reduces to $H_0$."312" The relevant parameters are the baseline; the height, width, and centre of the main line; and the height ratio for the subsidiary line."," The relevant parameters are the baseline; the height, width, and centre of the main line; and the height ratio for the subsidiary line."313 The models are: The extra feature is located a known three standard deviations away from the main one., The models are: The extra feature is located a known three standard deviations away from the main one.314 We also treat the noise levels as free parameters to be determined from the data; this is realistic because we may not know the noise level very well., We also treat the noise levels as free parameters to be determined from the data; this is realistic because we may not know the noise level very well.315" We again assume that each model is a priori equally likely, and that the noise is normally distributed."," We again assume that each model is a priori equally likely, and that the noise is normally distributed."316" The models need priors on the parameters, which we describe later."," The models need priors on the parameters, which we describe later."317" In the Neyman-Pearson framework, our decision rule for this example will be: accept Hj if the evidence exceeds a critical value."," In the Neyman-Pearson framework, our decision rule for this example will be: accept $H_1$ if the evidence exceeds a critical value."318" The Monte Carlo modelling process involves the following steps, some repeated."," The Monte Carlo modelling process involves the following steps, some repeated."319 The use of the Laplace approximation is justified by examining the likelihood functions and finding them to be close to Gaussian — a check that should always be made., The use of the Laplace approximation is justified by examining the likelihood functions and finding them to be close to Gaussian – a check that should always be made.320" The trends of the evidence ratio with signal-to noise ratio are plotted in Fig. 6,,"," The trends of the evidence ratio with signal-to noise ratio are plotted in Fig. \ref{figure5},"321" which shows the median and the interquartile range for the log of the evidence ratio, plotted against the to-noise ratio."," which shows the median and the interquartile range for the log of the evidence ratio, plotted against the signal-to-noise ratio."322" We see that the evidence ratio or odds for Hp, if it is true, do not get very big compared to the odds for Ηι."," We see that the evidence ratio or odds for $H_0$, if it is true, do not get very big compared to the odds for $H_1$ ."323" This is what we expect from a nested model, as H4 can always do just as well as Ho, with only the Ockham penalty for extracomplexity — not"," This is what we expect from a nested model, as $H_1$ can always do just as well as $H_0$ with only the Ockham penalty for extracomplexity – not"324In the local Universe. large scale eas outllows are observed to arise in galaxies exhibiting high surface densities of star formation.,"In the local Universe, large scale gas outflows are observed to arise in galaxies exhibiting high surface densities of star formation."325 While the precise roles of such outllows. including galactic “superwinds”. in galaxy evolution are still being determined. simulations suggest that the balance between outllows and the accretion of cool ogas is one of the primary mechanisms by which star formation is regulated in individual halos (e.g. Oppenheimer et al..," While the precise roles of such outflows, including galactic “superwinds”, in galaxy evolution are still being determined, simulations suggest that the balance between outflows and the accretion of cool gas is one of the primary mechanisms by which star formation is regulated in individual halos (e.g., Oppenheimer et al.,"326 2009: Brooks et eal.," 2009; Brooks et al.,"327 2009)., 2009).328 At the current epoch. the highest star formation rate (SER) surface densities ancl therefore galactic wincds are preferentially found in relatively low-mass halos. such as those hosting dwarl starburst galaxies.," At the current epoch, the highest star formation rate (SFR) surface densities – and therefore galactic winds – are preferentially found in relatively low-mass halos, such as those hosting dwarf starburst galaxies."329 Llowever. the mass," However, the mass"330did take into account.,did take into account.331 Ideally. these electrons would be free to move around. but. grains are observed (o preferentially produce surface charges on (heir collisional partners rather than [ree electrons.," Ideally, these electrons would be free to move around, but grains are observed to preferentially produce surface charges on their collisional partners rather than free electrons."332 We start our investigation with considering multi-electron emission due to dust collisions which may remain on (he grain surface or escape if their energy is large enough., We start our investigation with considering multi-electron emission due to dust collisions which may remain on the grain surface or escape if their energy is large enough.333 We see (his process somewhat in analogy (0 secondary electron. emission where more then one electron could be released curing the collision with an electron or ion., We see this process somewhat in analogy to secondary electron emission where more then one electron could be released during the collision with an electron or ion.334 During such collisions. backward scattering is more efficient in lattices of semi-conductor materials or insulators compared to metals which is of interest because our cloud model predicts parücles made of a mix of materials.," During such collisions, backward scattering is more efficient in lattices of semi-conductor materials or insulators compared to metals which is of interest because our cloud model predicts particles made of a mix of materials."335 The secondary electron enission coefficient ranges from 2.4 for MgOl[s| to 4.6 for AlsOs[s] (NaCH[s]: 6) and is highest for mixed materials (Ae-Cs5O-Cs: 8; Niedrig 1992. p359).," The secondary electron emission coefficient ranges from 2.4 for MgO[s] to 4.6 for $_2$ $_3$ [s] (NaCl[s]: 6) and is highest for mixed materials $_2$ O-Cs: 8; Niedrig 1992, p359)."336 We therefore adopt these secondary. electron emission coelficients. i.e. (he number of free electrons produced per collision. as guidance for mixed materials.," We therefore adopt these secondary electron emission coefficients, i.e. the number of free electrons produced per collision, as guidance for mixed materials."337 We further note in analogy (o the secondary electron emission that an increased collisional energv. will not necessarily cause a continuously increasing number of electron releases because (he impact may affect deeper electrons in the solid which require a larger energy., We further note in analogy to the secondary electron emission that an increased collisional energy will not necessarily cause a continuously increasing number of electron releases because the impact may affect deeper electrons in the solid which require a larger energy.338 We study ionisation events by collisions inside the dust cloud layers that form in Brown Dwarls and planetary. atmospheres., We study ionisation events by collisions inside the dust cloud layers that form in Brown Dwarfs and planetary atmospheres.339 We investigate limiting cases in order to study if grains are charged in substellar clouds ancl hence. if (hey. can act as seeds for other. more powerlul mechanisms like e.g. electron avalanche processes.," We investigate limiting cases in order to study if grains are charged in substellar clouds and hence, if they can act as seeds for other, more powerful mechanisms like e.g. electron avalanche processes."340 We compare the collisional energies to the ionisation energies of the dust grain surface., We compare the collisional energies to the ionisation energies of the dust grain surface.341 Three collision mechanisms are *-0.5cm], Three collision mechanisms are *[-0.5cm]342The best models are obtained by minimizing the 4 function defined as where pr. ;=LN are the values obtained iu the nodels for the observationallv constrained parameters.,"The best models are obtained by minimizing the $\chi^2$ function defined as where $p_i^{\hbox{\rm\tiny mod}}$, $i=1,N$ are the values obtained in the models for the observationally constrained parameters."343 Iu contrast to MOS. we used the Leveuberg-Marquairdt algorithi (as described iu Mielio&Montalbáu 20051) to &ud the minimmin of the 47 function. instead of conpitiug a exid of models.," In contrast to M08, we used the Levenberg-Marquardt algorithm (as described in \cite{2005A&A...441..615M}) ) to find the minimum of the $\chi^2$ function, instead of computing a grid of models."344 This method is an interpolation between he Newton-Raphson algorithia aud the steepest desceut nethod., This method is an interpolation between the Newton-Raphson algorithm and the steepest descent method.345 The steepest desceut imethod is first used. eusurue a rapid approach when the nmiuinauun is far.," The steepest descent method is first used, ensuring a rapid approach when the minimum is far."346 When eotting closer to the ummm. the aleorithin progressively switches to the Newton-Raplson method for a faster convergence tow the mininmiu.," When getting closer to the minimum, the algorithm progressively switches to the Newton-Raphson method for a faster convergence toward the minimum."347 The advantage is that one can find a uinum with oulv a ew iterations., The advantage is that one can find a minimum with only a few iterations.348 This kind of optimization is therefore less πιοσοκΜας thaw computing a erid of models with 5 free parameters aud a fine exid mesh., This kind of optimization is therefore less time-consuming than computing a grid of models with 5 free parameters and a fine grid mesh.349 The uncertainties on the parameters are obtained from the covariance matrix of the standard errors in the free parameters., The uncertainties on the parameters are obtained from the covariance matrix of the standard errors in the free parameters.350 We took the best model found iu ΑΙΟδ as a first guess and performed two miuimuizations: one without overshooting. giving best modelA.. aud oue with overshooting. giving best iiodelB.," We took the best model found in M08 as a first guess and performed two minimizations: one without overshooting, giving best model, and one with overshooting, giving best model."351. Model is. as expected. very close to the one fouud x MOS.," Model is, as expected, very close to the one found by M08."352 The only ifereuce lies in the error bars. which are bigger here.," The only difference lies in the error bars, which are bigger here."353" When usingC» the C»erid-search method. the error bars are obtained by fudiug the change in cach parameter. which increasesM xz,D by E1."," When using the grid-search method, the error bars are obtained by finding the change in each parameter, which increases $\chi^2\ind{min}$ by 1."354 ThisMol approach is. ouly correct if.. we can reelect the correlation between the ciffereut parameters. ws explained iu Bevington&Robinson(2003)..," This approach is only correct if we can neglect the correlation between the different parameters, as explained in \cite{2003drea.book.....B}."355 Several studies have shown tha correlations exist between the xuanmeters (Brownetal.1991.. Ozeletal. 2009)). which aro taken into accotut ij the Leveuberge-Marquardt optimization. since we je access to the nou-diagonal erns in the covariance matrix.," Several studies have shown that correlations exist between the parameters \cite{1994ApJ...427.1013B}, \cite{Ozel2009}) ), which are taken into account in the Levenberg-Marquardt optimization, since we have access to the non-diagonal terms in the covariance matrix."356 This explains why the uucertaiuties were underestimated in MUS., This explains why the uncertainties were underestimated in M08.357 Table 1. gives the physical and scisiaic parameters of both models., Table \ref{fit} gives the physical and seismic parameters of both models.358" For modelA.. parameters ο and 5/4 ave obtaimed at 1.2 6 aud 2.8 6 of the observed values. respectively, causing a high value of πμ29.1 (see Fig. 1))."," For model, parameters $a_1$ and $b_1$ are obtained at 1.2 $\sigma$ and 2.8 $\sigma$ of the observed values, respectively, causing a high value of $\chi^2\ind{min}\simeq 9.1$ (see Fig. \ref{fit_d01}) )."359" Iu coutrast. for modelB..ay aud δι are fitted within 0.5 σ ac 0.2 o. respectively,"," In contrast, for model,$a_1$ and $b_1$ are fitted within 0.8 $\sigma$ and 0.2 $\sigma$, respectively."360" This results in a significant decrease of AZ,=(8 for modelB.", This results in a significant decrease of $\chi^2\ind{min}\simeq0.8$ for model.361. When considering au exteusiou of the nuxed zone associated. to the carly convective core dnedueced hy overshooting. we got a model that fits all the observational constraints better than within 1-0 of the observed values.," When considering an extension of the mixed zone associated to the early convective core induced by overshooting, we get a model that fits all the observational constraints better than within $\sigma$ of the observed values."362 This decrease in the 47 value in fact stems from the survival of the convective core., This decrease in the $\chi^2$ value in fact stems from the survival of the convective core.363 Tudeed. model has a couvective core that extends over about 3 of the stellar amass.," Indeed, model has a convective core that extends over about $3\%$ of the stellar mass."364 The withdrawal of this core generates a discontinuity in the chemical composition eradieut. hence in the sound speed. eradicut (see Fig. 2)).," The withdrawal of this core generates a discontinuity in the chemical composition gradient, hence in the sound speed gradient (see Fig. \ref{sound_speed}) )."365 It has already been established that such ai disconutinutv iuduces an oscillation of the mode frequencies as a function of the radial order (see Cough 1990))., It has already been established that such a discontinuity induces an oscillation of the mode frequencies as a function of the radial order (see \cite{1990LNP...367..283G}) ).366 Provostctal.(1993) derived the expressions of mode frequeucies in the case of a discontinuous sound speed profile nearthe ceuter. in the asviuptotic approximation.," \cite{1993A&A...274..595P} derived the expressions of mode frequencies in the case of a discontinuous sound speed profile nearthe center, in the asymptotic approximation."367 Using the second-order development they propose. we obtained (see Appendix Appendix À:)) the following expression for 014: where a’. AL DB. aud ον} are defined in Appendix AppendixΑν," Using the second-order development they propose, we obtained (see Appendix \ref{app_d01}) ) the following expression for $\zeroun$: where $n'$, $A$, $B$, and $\varphi(\nu)$ are defined in Appendix \ref{app_d01}."368"ν With a discontinuous sound speed profile. the sinall spacing Avy, oscillates with a period P corresponding to the ratio between the acoustic radius of the whole star aud that of the discoutimuity: where raise Is the radius of the discoutiuuitv."," With a discontinuous sound speed profile, the small spacing $\zeroun$ oscillates with a period $\mathcal{P}$ corresponding to the ratio between the acoustic radius of the whole star and that of the discontinuity: where $r\ind{disc}$ is the radius of the discontinuity."369 We can see in Fie., We can see in Fig.370 b. that gj indeed oscillates for model B.. which was not the case for model A., \ref{fit_d01} that $\zeroun$ indeed oscillates for model which was not the case for model .371. When the amount of core overshooting increases. the acoustic radius of the discoutinuityv iu the chemical," When the amount of core overshooting increases, the acoustic radius of the discontinuity in the chemical"372currently under development (Pessemieretal.2010)..,currently under development \citep{Pessemier10}.373" This software is component-based, which means that HERMES could easily be integrated within the global control system by adding components for the detector, the instrument control, and the associated graphical user interfaces (GUI)."," This software is component-based, which means that HERMES could easily be integrated within the global control system by adding components for the detector, the instrument control, and the associated graphical user interfaces (GUI)."374 The instrument control software acts as a bus master for the industrial hardware and implements the low and high level tasks in an way with multiple layers of abstraction., The instrument control software acts as a bus master for the industrial hardware and implements the low and high level tasks in an way with multiple layers of abstraction.375" All relevant data is published to the network, and any interested party (such as the GUIs) can subscribe to it."," All relevant data is published to the network, and any interested party (such as the GUIs) can subscribe to it."376 Integrating HERMES also required extending both the auto-guiding system (to allow target acquisition and centroiding on a fibre image) and the scheduling software., Integrating HERMES also required extending both the auto-guiding system (to allow target acquisition and centroiding on a fibre image) and the scheduling software.377" A GUI is available for the queue scheduling of complete nights of observations, thereby specifying the instrument settings and exposure parameters for each target."," A GUI is available for the queue scheduling of complete nights of observations, thereby specifying the instrument settings and exposure parameters for each target."378" The observer has to supervise the system and intervene whenever needed, while the MOCS software handles the queued observations fully automatically."," The observer has to supervise the system and intervene whenever needed, while the MOCS software handles the queued observations fully automatically."379" The data reduction pipeline performs the traditional corrections for the bias level, the inter-order background level, the fringing on the detector, and the modulation of the intensity in each spectral order (blaze function) and applies a pre-normalisation eliminating the global wavelength-dependency of the flat-field calibration system."," The data reduction pipeline performs the traditional corrections for the bias level, the inter-order background level, the fringing on the detector, and the modulation of the intensity in each spectral order (blaze function) and applies a pre-normalisation eliminating the global wavelength-dependency of the flat-field calibration system."380" It determines in a robust way the dependency of the positions of the spectral orders on time-dependent factors, extracts the flux in each order with the options of estimating the total flux in a cross-cut from the pixels free of cosmic rays and of weighing pixels using a cross-order flux distribution model."," It determines in a robust way the dependency of the positions of the spectral orders on time-dependent factors, extracts the flux in each order with the options of estimating the total flux in a cross-cut from the pixels free of cosmic rays and of weighing pixels using a cross-order flux distribution model."381" Final spectra can be represented order per order in tabular form, assigning a wavelength to each pixel, or resampled to bins with a size of =1.6 km/s (the natural pixel size on average over each order) or with a fixed wavelength step, either over the whole wavelength region, over part of it, or just the ‘natural’ step over each order."," Final spectra can be represented order per order in tabular form, assigning a wavelength to each pixel, or resampled to bins with a size of $\approx 1.6$ km/s (the natural pixel size on average over each order) or with a fixed wavelength step, either over the whole wavelength region, over part of it, or just the `natural' step over each order."382" Depending on the choice, spectra may be merged over several or all orders."," Depending on the choice, spectra may be merged over several or all orders."383 Care is taken not to include parts of orders far out of the free spectral range where the risk is high that systematic bias dominates random noise., Care is taken not to include parts of orders far out of the free spectral range where the risk is high that systematic bias dominates random noise.384 A greatly simplified data reduction option is available for fast first-look purposes., A greatly simplified data reduction option is available for fast first-look purposes.385" Presently, the data reduction pipeline works in a frame-per-frame mode, but the final goal is to execute a number of reduction steps in a differential mode to gain robustness in the temporal model of the spatial and wavelength geometry on the detector (Hensberge2007)."," Presently, the data reduction pipeline works in a frame-per-frame mode, but the final goal is to execute a number of reduction steps in a differential mode to gain robustness in the temporal model of the spatial and wavelength geometry on the detector \citep{Hensberge07}."386. A detailed description of the data reduction procedures will be presented in a forthcoming paper., A detailed description of the data reduction procedures will be presented in a forthcoming paper.387" For the moment, we draw attention to the excellent agreement in the intensity level of the extracted spectra over the common wavelengths in subsequent orders."," For the moment, we draw attention to the excellent agreement in the intensity level of the extracted spectra over the common wavelengths in subsequent orders."388 Fig., Fig.389 16 shows selected regions of the spectrum of a late-B type binary., \ref{fig:overlap} shows selected regions of the spectrum of a late-B type binary.390" For each order, the used wavelength range extends approximately over the range where the intensity of the blaze is higher than one third of its value at maximum."," For each order, the used wavelength range extends approximately over the range where the intensity of the blaze is higher than one third of its value at maximum."391" The extraction is excellent and allows for detailed full spectral reconstruction, even for broad shallow lines at the edges of spectral orders."," The extraction is excellent and allows for detailed full spectral reconstruction, even for broad shallow lines at the edges of spectral orders."392 All raw and reduced frames are archived., All raw and reduced frames are archived.393 A web-based interface for accessing the HERMES database is under development., A web-based interface for accessing the HERMES database is under development.394 The archive also provides input for the scheduler software when composing the observing queues., The archive also provides input for the scheduler software when composing the observing queues.395top be equal to or vary close to the meridional flow speed in that laver.,top be equal to or vary close to the meridional flow speed in that layer.396 We have established both algebraically and numerically that resonance does happen in the bottom most laver of the svstem when the meridional flow satislies that. condition ancl the cross product of the coellicients of ly and By approaches zero., We have established both algebraically and numerically that resonance does happen in the bottom most layer of the system when the meridional flow satisfies that condition and the cross product of the coefficients of $A_L$ and $B_L$ approaches zero.397 In terms of formulas. this resonance occurs in the 2-]aver model in the neighborhood of In both 2 and 3-laver models this implies and The fact that the conditions for resonance are identical in the 2 and 3-laver cases suggests that by induction that this will remain (rue no matter how many lavers the model contains.," In terms of formulas, this resonance occurs in the 2-layer model in the neighborhood of and in the 3-layer model near where In both 2 and 3-layer models this implies and The fact that the conditions for resonance are identical in the 2 and 3-layer cases suggests that by induction that this will remain true no matter how many layers the model contains."398 Therefore it is likely to be a robust general property of (his. [Iux-tranusport. cdvianmo. but we have not attempted to prove this mathematically.," Therefore it is likely to be a robust general property of this flux-transport dynamo, but we have not attempted to prove this mathematically."399 It is evident from equation (44) that the a-elleet in the bottom laver plavs an important role in creating resonance there., It is evident from equation (44) that the $\alpha$ -effect in the bottom layer plays an important role in creating resonance there.400 Some [Iux-transport models applied to the Sun contain no a-ellect there. but Dikpati and Gilman (2001) showed that its presence could be responsible for choosing the correct svinnnetry [or the Sun's toroidal and poloidal fields (see also Bonanno et al 2002. Lotta Yokovama 2010).," Some flux-transport models applied to the Sun contain no $\alpha$ -effect there, but Dikpati and Gilman (2001) showed that its presence could be responsible for choosing the correct symmetry for the Sun's toroidal and poloidal fields (see also Bonanno et al 2002, Hotta Yokoyama 2010)."401 The resonance we demonstrate in (his work gives further importance to knowing what the a-elfect is ab the base of the convection zone., The resonance we demonstrate in this work gives further importance to knowing what the $\alpha$ -effect is at the base of the convection zone.402 The conditions (43) and (44) guarantee an essentially infinitely large resonance (interestingly even though there is diffusion in the problem. which usually bounds (the resonance to a finite value). but to be realized requires a precise combination of values of several parameters of the problem. very unlikely to be realized.," The conditions (43) and (44) guarantee an essentially infinitely large resonance (interestingly even though there is diffusion in the problem, which usually bounds the resonance to a finite value), but to be realized requires a precise combination of values of several parameters of the problem, very unlikely to be realized."403 But just being ‘close’ to resonance is enough to increase (he response of the svstem (o (he same forcing at the top by a factor of 10-100. bevond the range of variation in solar cycle peaks.," But just being 'close' to resonance is enough to increase the response of the system to the same forcing at the top by a factor of 10-100, beyond the range of variation in solar cycle peaks."404 So it is worth mapping out the response, So it is worth mapping out the response405epoch (Yamazakictal.2009:Lianget—2009).,"epoch \citep{Yamazaki09,Liang09}."406". Within such a scenario. a nascent magnetar was bor with au initial period £5—laus at t~5«I0? s, Its intial dipole radiation was trapped by the cuvelope of the xoeenitor and could not escape."," Within such a scenario, a nascent magnetar was born with an initial period $P_0 \sim 1$ ms at $t \sim -5\times 10^3$ s. Its intial dipole radiation was trapped by the envelope of the progenitor and could not escape."407 This spiudown cucrey eives chough impetus to explode the star aud power the euereetie SN 20101011., This spindown energy gives enough impetus to explode the star and power the energetic SN 2010bh.408 After a siguificaut delay (~5«10? s o spin down from T ius to T0 nis for ~31027 C3. the uaenetar wind finally managed to escapeBy as a relativistic Povuting-fiux-dominatec outflow.," After a significant delay $\sim 5\times 10^3$ s to spin down from 1 ms to 10 ms for $B_{\rm p}409\sim 3\times 10^{15}$ G), the magnetar wind finally managed to escape as a relativistic Poynting-flux-dominated outflow."410 An observer noticed he jet emission only around £=0., An observer noticed the jet emission only around $t=0$.411 The above argument also applies to the model of fallback accretion outo a jscen black hole., The above argument also applies to the model of fallback accretion onto a nascent black hole.412 With such a hypothesis one may envision a unified Ποσο το uuderstand the diversity of GRD/SN associations. by invoking a varicty of initial powers and the delay times between the core collapse aud. the emereence of the relativistic jet from the star.," With such a hypothesis, one may envision a unified picture to understand the diversity of GRB/SN associations, by invoking a variety of initial powers and the delay times between the core collapse and the emergence of the relativistic jet from the star."413" The speculation is the followine: Finally. oa straightforward expectation from the speculation that NRF 100316D| outflow is Povutiue-flux-dominated is that the prompt cuussion should be linearly volarized (οσο,OoFanetal.2005)."," The speculation is the following: Finally, a straightforward expectation from the speculation that XRF 100316D outflow is Poynting-flux-dominated is that the prompt emission should be linearly polarized \citep[e.g.,][]{Fan05}."414. The polarimetry lucasurements of events such as NRF 100316D and NRE 060218 would provide a criterion to differentiate this model from the shock breakout model. which does uot predict a strong polarization signal.," The polarimetry measurements of events such as XRF 100316D and XRF 060218 would provide a criterion to differentiate this model from the shock breakout model, which does not predict a strong polarization signal."415 We thank the anouvinous referee for helpful conuneuts. and S. Covino. J. S. Deng aud R. L. €. Starling for conumaimuications.," We thank the anonymous referee for helpful comments, and S. Covino, J. S. Deng and R. L. C. Starling for communications."416 This work was supported in part by the National basic research program of China under eraut 2009CBs?IS00. Gor Y.Z.F. aud E.W.L). aud by NASA NNANOQATGOOC. NNNIOADI8C. and NSF AST-0908362 (for D.Z.).," This work was supported in part by the National basic research program of China under grant 2009CB824800 (for Y.Z.F. and E.W.L), and by NASA NNX09AT66G, NNX10AD48G, and NSF AST-0908362 (for B.Z.)."417"to the model, which also improves the fit from a simple power-law.","to the model, which also improves the fit from a simple power-law."418" However, the column density of this component is poorly constrained, so we fix this to an arbitrary = 24.5."," However, the column density of this component is poorly constrained, so we fix this to an arbitrary $N_{\rm{H}}$ ) = 24.5."419" Estimates of the intrinsic Lyx from the reflection componentNy) predict a Lgoi which agrees well with Lo; estimated from Lyorm], suggesting that NGC 3486 is under-luminous in X-rays due to Compton thick obscuration."," Estimates of the intrinsic $L_{\rm{HX}}$ from the reflection component predict a $L_{\rm{Bol}}$ which agrees well with $L_{\rm{Bol}}$ estimated from $L_{\rm [O\,III]}$, suggesting that NGC 3486 is under-luminous in X-rays due to Compton thick obscuration."420" Finally, there is no evidence for variability of the ray flux in the observation."," Finally, there is no evidence for variability of the X-ray flux in the observation."421" As there have been no observations of NGC 3660 withNewton orChandra, we use the observation and its documentation in the catalogue."," As there have been no observations of NGC 3660 with or, we use the observation and its documentation in the catalogue."422 The spectrum is fitted well by a power-law with no absorption above the Galactic column., The spectrum is fitted well by a power-law with no absorption above the Galactic column.423 Fig., Fig.424 3 shows the light-curve for the 26 ks observation which shows significant variability on short time-scales., \ref{ngc3660lc} shows the light-curve for the 26 ks observation which shows significant variability on short time-scales.425" The spectrum of NGC 3976 is very similar to that of NGC 3486 as it shows no intrinsic absorption, but a hard excess present above the simple power-law fit allows us to add a heavily absorbed power-law component."," The spectrum of NGC 3976 is very similar to that of NGC 3486 as it shows no intrinsic absorption, but a hard excess present above the simple power-law fit allows us to add a heavily absorbed power-law component."426" A strongly absorbed transmission component produces an overall better fit, suggesting that NGC 3976 is also hiding a heavily obscured nucleus beneath its apparently unabsorbed soft X-ray spectrum."," A strongly absorbed transmission component produces an overall better fit, suggesting that NGC 3976 is also hiding a heavily obscured nucleus beneath its apparently unabsorbed soft X-ray spectrum."427" Again, there is also no variability detected in this observation."," Again, there is also no variability detected in this observation."428 TheXMM-Newton spectrum of NGC 4501 reveals another apparently unabsorbed Seyfert 2 galaxy in X-rays., The spectrum of NGC 4501 reveals another apparently unabsorbed Seyfert 2 galaxy in X-rays.429" It is well fitted by a power-law with no intrinsic absorption plus emission from a thermal plasma component, but shows no clear hard excess or other spectral evidence supporting a deeply buried AGN (such as iron Ka emission)."," It is well fitted by a power-law with no intrinsic absorption plus emission from a thermal plasma component, but shows no clear hard excess or other spectral evidence supporting a deeply buried AGN (such as iron $\alpha$ emission)."430" An entirely different picture emerges, however, when one considers the data, which have higher spatial resolution."," An entirely different picture emerges, however, when one considers the data, which have higher spatial resolution."431 The image of NGC 4501 reveals a hard X-ray emission coincident with the optically defined nucleus (Fig. 4)), The image of NGC 4501 reveals a hard X-ray emission coincident with the optically defined nucleus (Fig. \ref{chanimg}) )432 consistent with heavy X-ray absorption., consistent with heavy X-ray absorption.433" It also shows that there are also multiple extra-nuclear sources present, including diffuse soft emission close to the nucleus, whichXMM-Newton could not resolve."," It also shows that there are also multiple extra-nuclear sources present, including diffuse soft emission close to the nucleus, which could not resolve."434" The implication is that the unabsorbed nature of theXMM-Newton spectrum, which has a larger beam size, is due to contamination, and that the true nuclear emission is heavily obscured."," The implication is that the unabsorbed nature of the spectrum, which has a larger beam size, is due to contamination, and that the true nuclear emission is heavily obscured."435" We performed a spectral extraction of the optically defined nucleus using the region identified in Fig 4 which did indeed reveal a hard excess above the unabsorbed power-law, as in NGC 3486 and NGC 3976, which we fit with a Compton reflection component (pexmon)."," We performed a spectral extraction of the optically defined nucleus using the region identified in Fig \ref{chanimg} which did indeed reveal a hard excess above the unabsorbed power-law, as in NGC 3486 and NGC 3976, which we fit with a Compton reflection component )."436 Using the reflection component to estimate the intrinsic Lux shows that the X-ray faintness of NGC 4501 is probably due to heavy absorption (Fig. 2))., Using the reflection component to estimate the intrinsic $L_{\rm{HX}}$ shows that the X-ray faintness of NGC 4501 is probably due to heavy absorption (Fig. \ref{lumfig}) ).437" There is also no evidence for variability of NGC 4501, either between subsequent observations byXMM-Newton andChandra, or during them."," There is also no evidence for variability of NGC 4501, either between subsequent observations by and, or during them."438" We have presented X-ray and multi-waveband data for a sample of bona fide Seyfert 2 galaxies, as defined by their optical line ratios, which appear unabsorbed in the X-ray."," We have presented X-ray and multi-waveband data for a sample of bona fide Seyfert 2 galaxies, as defined by their optical line ratios, which appear unabsorbed in the X-ray."439 Our first key finding, Our first key finding440respective uncorrected rotational diagrams for these species.,respective uncorrected rotational diagrams for these species.441" For each successive iteration, new correction factors (c7) were calculated based on the temperatures derived from the previous iteration."," For each successive iteration, new correction factors $c_\nu^n$ ) were calculated based on the temperatures derived from the previous iteration."442 Converged rotational temperatures and corresponding column densities are given inTable 2.., Converged rotational temperatures and corresponding column densities are given inTable \ref{tab:colds}.443" For molecules for which rotational diagrams could not be plotted, column densities were calculated under the assumption of local thermodynamic equilibrium (LTE), using a gas temperature of 6.1+1.4 K, which is the mean average (34-16). of the excitation temperatures derived from the rotational diagrams."," For molecules for which rotational diagrams could not be plotted, column densities were calculated under the assumption of local thermodynamic equilibrium (LTE), using a gas temperature of $6.1\pm1.4$ K, which is the mean average $\pm1\sigma$ ), of the excitation temperatures derived from the rotational diagrams."444" For molecules in this category with multiple line detections, the weighted-average column densities were calculated based on the individual line signal-to-noise ratios."," For molecules in this category with multiple line detections, the weighted-average column densities were calculated based on the individual line signal-to-noise ratios."445" Where molecular lines were searched for but not detected, column density upper limits were calculated using upper integrated line intensity limits of 3Avx(RMSnoise), for which Av=0.78 wwas used."," Where molecular lines were searched for but not detected, column density upper limits were calculated using upper integrated line intensity limits of $3\Delta v\times({\rm RMS\ noise})$, for which $\Delta v=0.78$ was used."446" For CsH-, the upper limit of 4.79x1019 cm? was derived from the average of the three observed (6Η spectra."," For $_6$ $^-$, the upper limit of $4.79\times10^{10}$ $^{-2}$ was derived from the average of the three observed $_6$ $^-$ spectra."447" For HC3N and c-C3H;», the observed emission lines were subject to radiative transfer modelling using the RADEX code developed by ?.."," For $_3$ N and $c$ $_3$ $_2$, the observed emission lines were subject to radiative transfer modelling using the RADEX code developed by \citet{van07}."448" This routine employs a statistical equilibrium calculation for molecular excitation involving collisional and radiative and accounts for optical depth effects using an escape processes,probability method."," This routine employs a statistical equilibrium calculation for molecular excitation involving collisional and radiative processes, and accounts for optical depth effects using an escape probability method."449" Collisional and radiative (de-)excitation rates were taken from the Leiden Atomic and Molecular Database (LAMDA) (?) which tabulates scaled footnotehttp://www.strw.leidenuniv.nl/~moldata,,versions of the original data published by ? for HC3N and ? for c-C4H;."," Collisional and radiative (de-)excitation rates were taken from the Leiden Atomic and Molecular Database (LAMDA) \citep{sch05}, which tabulates scaled versions of the original data published by \citet{gre78} for $_3$ N and \citet{cha00} for $c$ $_3$ $_2$."450" The RADEX model free parameters (number density of primary collision partner ny,, gas kinetic temperature T and molecular column density N) were optimised using a least-squares algorithm to produce the best fit to the observed integrated line intensities (including the additional higher-frequency line data from ?))."," The RADEX model free parameters (number density of primary collision partner $n_{H_2}$, gas kinetic temperature $T$ and molecular column density $N$ ) were optimised using a least-squares algorithm to produce the best fit to the observed integrated line intensities (including the additional higher-frequency line data from \citealt{kon00}) )."451 The two nuclear-spin species of c-C3H» (ortho and para) were considered separately., The two nuclear-spin species of $c$ $_3$ $_2$ (ortho and para) were considered separately.452" For ortho-c-C3H», the following transitions were included in the fitting: Jg,e,=212—101, 312— and 32;— 32."," For $c$ $_3$ $_2$, the following transitions were included in the fitting: $J_{K_aK_c}=2_{12}-1_{01}$, $3_{12}-2_{21}$ and $3_{21}-3_{12}$ ."453" The best-fitting density was 1.0x106 cm,"," The best-fitting density was $1.0\times10^6$ $^{-3}$ ,"454Acceptable fits were found for most sources. with only three instances of (reduced) Mzoll.,"Acceptable fits were found for most sources, with only three instances of (reduced) $\chi^{2}_{\nu} \geq 1.1$."455 We note that the derived photon indices have a mean value of 2.1 with a standard deviation of 0.3., We note that the derived photon indices have a mean value of 2.1 with a standard deviation of 0.3.456 For nine objects the inclusion of the iron-line component is merited in terms of the resulting improvement in X2 AYO26.2 implying better than 95% confidence in the F-test for two additional parameters)., For nine objects the inclusion of the iron-line component is merited in terms of the resulting improvement in $\chi^{2}$ $\Delta\chi^{2} > 6.2$ implying better than $95$ confidence in the F-test for two additional parameters).457 Also two further sources show at least a marginal improvement in X7 (see ‘Table 2)., Also two further sources show at least a marginal improvement in $\chi^{2}$ (see Table 2).458 There is some evidence for lines originating from fairly highly ionized iron species ΣΕΓΟΝΝ and above) in | Zw 1. Ton S180. PISS 0558-504. PC: 12441026 and Ark 564.," There is some evidence for lines originating from fairly highly ionized iron species $>$ and above) in I Zw 1, Ton S180, PKS 0558-504, PG 1244+026 and Ark 564."459 The measured line equivalent. widths range from 100GOO eV. albeit with Large uncertainties.," The measured line equivalent widths range from 100–600 eV, albeit with large uncertainties."460 Similarly the constraints on the equivalent width of a (neutral) iron line in those sources lacking a signilicant line detection are eencrally rather weak., Similarly the constraints on the equivalent width of a (neutral) iron line in those sources lacking a significant line detection are generally rather weak.461 In general the signal/noise ratio was too poor to meaningfully constrain the intrinsic line widths., In general the signal/noise ratio was too poor to meaningfully constrain the intrinsic line widths.462 Llowever. the second observation of NGC 4051 provides the exception since in this case there is evidence for a broadened iron Wa feature.," However, the second observation of NGC 4051 provides the exception since in this case there is evidence for a broadened iron $\alpha$ feature."463 The best fit parameters for the line are E=6.29+0.09 keV. intrinsic width m=0.360/73 keV and EW24027NU eV. The improvement in the fit upon adding his broad feature is Ay?=76.8.," The best fit parameters for the line are $=6.29\pm0.09$ keV, intrinsic width $\sigma=0.36^{+0.23}_{-0.15}$ keV and $=240^{+90}_{-80}$ eV. The improvement in the fit upon adding this broad feature is $\Delta\chi^{2}=76.8$."464" An attempt has been nace ο Lit the line with the relativistic ""diskline"" profile of Fabian (L989): we find a mildly ionized line (=6.6n keV). with a near to lace-on inclination (7« 17) gives the best it to the data (assuming values for Rj). 5,4; and emissivity index of LOGAL/e7. Mc? ancl 2. respectively)."," An attempt has been made to fit the line with the relativistic “diskline” profile of Fabian (1989); we find a mildly ionized line $=6.6^{+0.1}_{-0.2}$ keV), with a near to face-on inclination $ i < 17^{\circ}$ ) gives the best fit to the data (assuming values for $_{in}$, $_{out}$ and emissivity index of $^{2}$, $^{2}$ and –2, respectively)."465 Note hat Ciuainazzi (1996) discuss the the spectral fitting of this oobservation of NGC 4051 in some cetail., Note that Guainazzi (1996) discuss the the spectral fitting of this observation of NGC 4051 in some detail.466 Extrapolation of the best-fit 2.10 keV spectrum (as defined in Table 2) down to 0.6 keV. in most cases results in a »oor fit of the soft. N-ray spectrum. with the most common residual feature being an excess of soft Dux.," Extrapolation of the best-fit 2–10 keV spectrum (as defined in Table 2) down to 0.6 keV in most cases results in a poor fit of the soft X-ray spectrum, with the most common residual feature being an excess of soft flux."467 In the spectral itting we have attempted. to match this soft. excess. with an additional continuum. component., In the spectral fitting we have attempted to match this soft excess with an additional continuum component.468 Specifically we use a single. blackbody component. although a second power aw often provides an equally good. fit. (," Specifically we use a single blackbody component, although a second power law often provides an equally good fit. ("469In the latter case he second: power-law is typically steeper than the first by ANE20.5 witha break energv in the range 12 keV).,In the latter case the second power-law is typically steeper than the first by $\Delta \Gamma \simeq 0.5$ with a break energy in the range 1–2 keV).470 Table 3 summarises the results of fitting à power law plus blackbocdvy model (note that from here on the iron line parameters are frozen at the values obtained in the earlier 210 keV fits)., Table 3 summarises the results of fitting a power law plus blackbody model (note that from here on the iron line parameters are frozen at the values obtained in the earlier 2–10 keV fits).471 In all but four objects (E Zw 1. PG. 1543]489. Alkn 507 and LIGAS. 20181224) a soft excess component provides a significant improvement in the fit. demonstrating that πο excesses are a very common feature in NLSIs.," In all but four objects (I Zw 1, PG 1543+489, Mkn 507 and IRAS 20181–224) a soft excess component provides a significant improvement in the fit, demonstrating that soft excesses are a very common feature in NLS1s."472 The uncerlving power-Iaw photon indices given in Table 3 have a mean of 2.12 and a standard deviation of 0.26., The underlying power-law photon indices given in Table 3 have a mean of 2.12 and a standard deviation of 0.26.473 Ehe fact the mean is very similar to that obtained. earlier for 210 keV. lits demonstrates that the latter fits are relatively. immune to the presence of the soft excess., The fact the mean is very similar to that obtained earlier for 2–10 keV fits demonstrates that the latter fits are relatively immune to the presence of the soft excess.474 Nine objects show signs of additional spectral complexity. below 2 keV even after the inclusion. of the blackbody component in the fit (Pable 3)., Nine objects show signs of additional spectral complexity below 2 keV even after the inclusion of the blackbody component in the fit (Table 3).475 Unfortunately modelling of the sspectra in terms of additional κο N-rav features. is not particularly straight-forward., Unfortunately modelling of the spectra in terms of additional soft X-ray features is not particularly straight-forward.476 Radiation damage to the CCDs and other factors have meant that there is increasing uncertainty in the calibration of the detectors below 1 keV and. in particular. it has been noted that the two SIS instruments offen give divergent spectra at. the lowest energies (although these calibration uncertainties only dominate over uncertainties in the background subtraction for relatively bright sources).," Radiation damage to the CCDs and other factors have meant that there is increasing uncertainty in the calibration of the detectors below 1 keV and, in particular, it has been noted that the two SIS instruments often give divergent spectra at the lowest energies (although these calibration uncertainties only dominate over uncertainties in the background subtraction for relatively bright sources)."477 Also since most NLS1 galaxies appear to exhibit a solt X-ray excess it is. clillieult to distinguish subtleties in the form of the soft continuum from the clfects of putative broad. emission. and/or absorption features., Also since most NLS1 galaxies appear to exhibit a soft X-ray excess it is difficult to distinguish subtleties in the form of the soft continuum from the effects of putative broad emission and/or absorption features.478 tecent studies of the X-ray spectra of NLSIs (e.g. Leighlv 1997b: Fiore 1998) have established that in addition to classical “warm-absorption” features. NLS1s often show anomalous absorption features in the 12 keV band.," Recent studies of the X-ray spectra of NLS1s (e.g. Leighly 1997b; Fiore 1998) have established that in addition to classical “warm-absorption” features, NLS1s often show anomalous absorption features in the 1–2 keV band."479 Both tvpes of absorption are spectrally complex and will merit. more detailed. analysis using the predictions of appropriate photoionization codes. once high sensitivity X-ray data with e&ood spectral resolution become available from missions such as ANAF. NMM and ASTRO-LE (c.g. Nicastro et al.," Both types of absorption are spectrally complex and will merit more detailed analysis using the predictions of appropriate photoionization codes, once high sensitivity X-ray data with good spectral resolution become available from missions such as AXAF, XMM and ASTRO-E (e.g. Nicastro et al."480 1999)., 1999).481 LLowever. for our present purpose we have taken a very simplistic approach and have attempted to improve Ίο A7 in the spectral fits for nine sources noted above by including just a absorption feature (in the form of a road. Gaussian absorption line) in the spectral model.," However, for our present purpose we have taken a very simplistic approach and have attempted to improve the $\chi^{2}$ in the spectral fits for nine sources noted above by including just a absorption feature (in the form of a broad Gaussian absorption line) in the spectral model."482 ‘Table 4 lists for each of the nine sources the line energy. he equivalent. width and the intrinsic line width obtained when such an absorption feature is added to the power-law xus blackbody continuum model.," Table 4 lists for each of the nine sources the line energy, the equivalent width and the intrinsic line width obtained when such an absorption feature is added to the power-law plus blackbody continuum model."483 The line energies are not consistent with a single value but a bifurcation is suggested. namely absorption either in the 0.70.9 keV. range or in he LdL4 keV range.," The line energies are not consistent with a single value but a bifurcation is suggested, namely absorption either in the 0.7–0.9 keV range or in the 1.1–1.4 keV range."484 Absorption features in the former range are usually interpreted as due to and edges indicative of the presence of ionized material along the line of sight., Absorption features in the former range are usually interpreted as due to and edges indicative of the presence of ionized material along the line of sight.485" The possible origin of the ""anomalous"" absorption features observed at ~12 keV have recently been discussed by Leighly (1997b) and Fiore (1998).", The possible origin of the “anomalous” absorption features observed at $\sim1.2$ keV have recently been discussed by Leighly (1997b) and Fiore (1998).486 As noted above the fitting of a Gaussian absorption feature is necessarily an over simplification of the true picture., As noted above the fitting of a Gaussian absorption feature is necessarily an over simplification of the true picture.487 In. order to investigate the individual sources in somewhat more detail we have refitted the spectra of the nine objects listed in Table 4 including a variety of additional absorption and emission. components., In order to investigate the individual sources in somewhat more detail we have refitted the spectra of the nine objects listed in Table 4 including a variety of additional absorption and emission components.488 For example. we tested for either one or two absorption edges ancl also [or either a single Gaussian emission line or a MERAL--tvpe optically thin thermal spectrum (Ixaastra Alewe 1993).," For example, we tested for either one or two absorption edges and also for either a single Gaussian emission line or a -type optically thin thermal spectrum (Kaastra Mewe 1993)."489 The outcome was that in five of the objects an absorption component gave a significanthy better fit than an emission component. (, The outcome was that in five of the objects an absorption component gave a significantly better fit than an emission component. (490Of course the modelling of the underlving soft excess changes substantially between these. two cases so às to maintain the match to the observed. spectrum in,Of course the modelling of the underlying soft excess changes substantially between these two cases so as to maintain the match to the observed spectrum in491The obvious advantage of solar wind (turbulence is (hat basic plasma physics measurements of vector magnetic field. plasma flow velocity. density. temperatures. and even electron ancl ion distribution funcüons can be measured in situ with spacecralt.,"The obvious advantage of solar wind turbulence is that basic plasma physics measurements of vector magnetic field, plasma flow velocity, density, temperatures, and even electron and ion distribution functions can be measured in situ with spacecraft."492 The fIuctuations in all of these quantities have been extensively studied. a lage literature. written. and major conclusions reached.," The fluctuations in all of these quantities have been extensively studied, a large literature written, and major conclusions reached."493 Among the manv influential articles and reviews of the subject are Bavassanoetal(1982).. (he monograph by TuandMarsch.(1995)... ancl (he review articles by Goldsteinοἱal(1995) and BrunoandCarbone(2005).," Among the many influential articles and reviews of the subject are \cite{Bavassano82}, the monograph by \cite{Tu95}, and the review articles by \cite{Goldstein95} and \cite{Bruno05}."494. Another nearby plasma with extensive diagnostics (although not. as vet. in sit measurements) is (he solar corona.," Another nearby plasma with extensive diagnostics (although not, as yet, in situ measurements) is the solar corona."495 Our knowledge of the corona and its turbulence results from high spatial resolution images. ultraviolet spectroscopy. of numerous (transitions. and radio propagation measurements.," Our knowledge of the corona and its turbulence results from high spatial resolution images, ultraviolet spectroscopy of numerous transitions, and radio propagation measurements."496" In addition. a sort of ""ground (ruth of coronal plasma measurements is provided by spacecraft measurements at heliocentric distances from 0.28 to 1 astronomical units (AU)."," In addition, a sort of “ground truth” of coronal plasma measurements is provided by spacecraft measurements at heliocentric distances from 0.28 to 1 astronomical units (AU)."497 The coronal plasma is convected out into space ancl becomes the solar wind., The coronal plasma is convected out into space and becomes the solar wind.498 Among the many reviews of the coronal plasma. two which are particularly relevant to the present investigation are Cranmer(2002) and DirdanclEdenholer(1990).," Among the many reviews of the coronal plasma, two which are particularly relevant to the present investigation are \cite{Cranmer02} and \cite{Bird90}."499. A list of the main properties of solar wind and coronal turbulence could be extensive., A list of the main properties of solar wind and coronal turbulence could be extensive.500 We list four properties which are particularly relevant {ο (he present investigation., We list four properties which are particularly relevant to the present investigation.501smaller the energy of the initial excitation is more distributed among higher harmonics.,smaller the energy of the initial excitation is more distributed among higher harmonics.502 The results of this Section point out that the time-dependent behavior of standing kink MHD waves of flowing prominence threads is strongly influenced by the form of the initial disturbance., The results of this Section point out that the time-dependent behavior of standing kink MHD waves of flowing prominence threads is strongly influenced by the form of the initial disturbance.503 If the initial disturbance mainly perturbs the dense prominence part of the flux tube. the oscillations are governed by the fundamental kink mode.," If the initial disturbance mainly perturbs the dense prominence part of the flux tube, the oscillations are governed by the fundamental kink mode."504 In such a case. the dependence of both the period and the amplitude with the flow velocity are approximately given by Equations (23)) and (26)). respectively.," In such a case, the dependence of both the period and the amplitude with the flow velocity are approximately given by Equations \ref{eq:period}) ) and \ref{eq:fit}) ), respectively."505 On the contrary. the behavior is more complicated if the initial perturbation takes place in the evacuated part of the fine structure as other harmonies are excited in addition to the fundamental mode.," On the contrary, the behavior is more complicated if the initial perturbation takes place in the evacuated part of the fine structure as other harmonics are excited in addition to the fundamental mode."506 The contribution of the different harmonics depends on both the position and the width of the initial excitation. while the amplitude of the oscillation does not have a simple dependence on the flow velocity.," The contribution of the different harmonics depends on both the position and the width of the initial excitation, while the amplitude of the oscillation does not have a simple dependence on the flow velocity."507 In this paper. we have investigated standing kink MHD waves in the fine structure of solar prominences. modeled as coronal magnetic flux tubes partially filled with flowing threads of prominence material.," In this paper, we have investigated standing kink MHD waves in the fine structure of solar prominences, modeled as coronal magnetic flux tubes partially filled with flowing threads of prominence material."508 The present study extends and complements the previous work by Terradasetal.(2005). who restricted themselves to the numerical investigation of this phenomenon and did not perform an in-depth parametric study.," The present study extends and complements the previous work by \citet{hinode}, who restricted themselves to the numerical investigation of this phenomenon and did not perform an in-depth parametric study."509 Here. we have combined analytical methods based on the WKB approximation with time-dependent numerical simulations to assess the precise effect of the flow on both the period and the amplitude of the fundamental kink mode.," Here, we have combined analytical methods based on the WKB approximation with time-dependent numerical simulations to assess the precise effect of the flow on both the period and the amplitude of the fundamental kink mode."510 As for the effect of the flow on the period. we can distinguish two different situations.," As for the effect of the flow on the period, we can distinguish two different situations."511 On the one hand. we find that the flow has a small effect on the period when the thread is located near the center of the supporting magnetic flux tube.," On the one hand, we find that the flow has a small effect on the period when the thread is located near the center of the supporting magnetic flux tube."512 In this case. the variation of the period with respect to the static case may fall within the error bars of the observations. and so the effect may be undetectable.," In this case, the variation of the period with respect to the static case may fall within the error bars of the observations, and so the effect may be undetectable."513 There our results confirm the qualitative discussion of Terradasetal.(2008) about the effect of the flow on the period., There our results confirm the qualitative discussion of \citet{hinode} about the effect of the flow on the period.514 On the other hand. the variation of the period ts much more important when the thread approaches the footpoint of the magnetic structure.," On the other hand, the variation of the period is much more important when the thread approaches the footpoint of the magnetic structure."515 Then. the decrease of the period ean be larger than with respect to the static case.," Then, the decrease of the period can be larger than with respect to the static case."516 The case in which the thread is near one of the footpoints of the magnetic tube was not analyzed by Terradasetal.(2008)., The case in which the thread is near one of the footpoints of the magnetic tube was not analyzed by \citet{hinode}.517. We have also found that the flow affects the amplitude of the fundamental mode., We have also found that the flow affects the amplitude of the fundamental mode.518 This result was not discussed by Terradasetal.(2008).., This result was not discussed by \citet{hinode}.519 During the motion of the prominence thread along the magnetic structure. we find that the amplitude grows as the thread gets closer to the center of the tube and decreases otherwise.," During the motion of the prominence thread along the magnetic structure, we find that the amplitude grows as the thread gets closer to the center of the tube and decreases otherwise."520 This produces an apparent amplification or damping of the oscillations. respectively.," This produces an apparent amplification or damping of the oscillations, respectively."521 Observations often indicate that thread transverse oscillations are strongly damped (see.e.g..Lin2004.2010:Ningetal.2009).," Observations often indicate that thread transverse oscillations are strongly damped \citep[see, e.g.,][]{lin04,linrev,ning}."522. While several mechanisms have been proposed and investigated to explain the quick attenuation2010).. the process of resonant absorption seems the most likely explanation (e.g..Arreguietal.2008:Soleretal.2009a.b.2010).," While several mechanisms have been proposed and investigated to explain the quick attenuation, the process of resonant absorption seems the most likely explanation \citep[e.g.,][]{arregui08,solerslow,solerRAPI,solerstatic}."523. Our present results indicate that the actual damping rate of the oscillations might be affected by the change of the amplitude due to the flow., Our present results indicate that the actual damping rate of the oscillations might be affected by the change of the amplitude due to the flow.524 This fact should be taken into account when the damping rate is used as a seismological tool to infer physical parameters of prominence threads. because the presence of flow may introduce some uncertainties on these estimations (seedetailsin.Arresur&Ballester2010).," This fact should be taken into account when the damping rate is used as a seismological tool to infer physical parameters of prominence threads, because the presence of flow may introduce some uncertainties on these estimations \citep[see details in][]{arreguiballester}."525. In addition. our numerical simulations have allowed us to determine how different perturbations excite the oscillations of the magnetic structure.," In addition, our numerical simulations have allowed us to determine how different perturbations excite the oscillations of the magnetic structure."526 Based on the cases studied in this paper. we have obtained that the fundamental mode is mostly excited when the perturbation initially disturbs the dense. prominence part of the tube.," Based on the cases studied in this paper, we have obtained that the fundamental mode is mostly excited when the perturbation initially disturbs the dense, prominence part of the tube."527 From the wavelet power spectrum of the radial velocity perturbation. we conclude that the contribution of higher harmonics ts negligible. thus the overall oscillation is governed by the fundamental mode.," From the wavelet power spectrum of the radial velocity perturbation, we conclude that the contribution of higher harmonics is negligible, thus the overall oscillation is governed by the fundamental mode."528" On the contrary. à perturbation located at the evacuated part of the tube excites the fundamental mode and higher harmonies, producing a more complex behavior of the oscillations."," On the contrary, a perturbation located at the evacuated part of the tube excites the fundamental mode and higher harmonics, producing a more complex behavior of the oscillations."529 In this last case. the effect of the flow on the amplitude i5 more complicated and no simple dependence can be extracted from the simulations.," In this last case, the effect of the flow on the amplitude is more complicated and no simple dependence can be extracted from the simulations."530 This paper has explored the properties of MHD waves in à coronal magnetic structure with a changing configuration., This paper has explored the properties of MHD waves in a coronal magnetic structure with a changing configuration.531 Previous similar works m this line are. e.g.. Terradasetal.(2008) in prommences. and Mortonetal.(2010):&Erdélyi(2010a.b) in coronal loops.," Previous similar works in this line are, e.g., \citet{hinode} in prominences, and \citet{morton1,morton2,morton3} in coronal loops."532 During the revision of this paper it also came to our knowledge the recent work by Ruderman(2011)., During the revision of this paper it also came to our knowledge the recent work by \citet{ruderman}.533. In view of the highly dynamic nature of the coronal medium in general. and the prominence plasma in particular. this kind of modeling represents a better description of the actual oscillatory phenomena in the corona and in prominences.," In view of the highly dynamic nature of the coronal medium in general, and the prominence plasma in particular, this kind of modeling represents a better description of the actual oscillatory phenomena in the corona and in prominences."534 The present investigation could be extended in the future by incorporating the effect of the density inhomogeneity in the transverse direction and so investigating the resonant damping of the kink mode., The present investigation could be extended in the future by incorporating the effect of the density inhomogeneity in the transverse direction and so investigating the resonant damping of the kink mode.535and AT=galTt keV du the second. with lvdrogen colunn densities of Ny=5.3!nmκ1ο ?aud Nj=6.7!il«1072 ? respectively.,"and $kT = 53638^{+20}_{-10}$ keV in the second, with hydrogen column densities of $N_{\rm H} = 5.3^{+1.1}_{-1.2} \times 10^{22}$ $^{-2}$ and $N_{\rm H} = 6.7^{+1.4}_{-1.3} \times 10^{22}$ $^{-2}$ respectively."537 The spectra are therefore consisteut with each other., The spectra are therefore consistent with each other.538 The 210 keV flux however. shows a slieht. reduction+ fromBH +1.15«)10H erg eni?P t to 1.32.10H cere cliP Ἐν put there are likely to be systematic uncertainties of up to 5rtA on these values due to background subtraction. judging by the deviations from zero flux at nid eclipse.," The 2–10 keV flux however, shows a slight reduction from $1.45\times10^{-11}$ erg $^{2}$ $^{-1}$ to $1.32\times10^{-11}$ erg $^{2}$ $^{-1}$ , but there are likely to be systematic uncertainties of up to $5\%$ on these values due to background subtraction, judging by the deviations from zero flux at mid eclipse."539 There are two archival observatious of NY Avi. neither of which have previously been published. except in compilation papers examine IP X-ray spectra (Ezuka Ishida 1999: Terada. Ishida AMakishima 2001).," There are two archival observations of XY Ari, neither of which have previously been published, except in compilation papers examining IP X-ray spectra (Ezuka Ishida 1999; Terada, Ishida Makishima 2004)."540 They coluprise an observation from 1995 August 6 with an exposure of around 35 ksec aud another from 1996 Jaunary 28 with ai exposure of around 60 Xsec., They comprise an observation from 1995 August 6 with an exposure of around 35 ksec and another from 1996 January 28 with an exposure of around 60 ksec.541" We extracted lichteurves 1ji each case frou, both the SIS aud. CTS detectors. iu two enerev bands."," We extracted lightcurves in each case from both the SIS and GIS detectors, in two energy bands."542 The low cucrey baud corresponds ο cULT2.0 keV whilst the high band is roughly ~210 keV. Backeround subtracted lightcurves obtained bx stunning the hehltcurves from the two SIS aud two CIS iustruineuts. foded at the white dwarf spin period in cach case are shown in Figure 3.," The low energy band corresponds to $\sim 0.7 - 2.0$ keV whilst the high band is roughly $\sim 2 - 10$ keV. Background subtracted lightcurves obtained by summing the lightcurves from the two SIS and two GIS instruments, folded at the white dwarf spin period in each case are shown in Figure 3."543 As in Figure 1. phase zero is arbitrary in these plots.," As in Figure 1, phase zero is arbitrary in these plots."544 In the August 1995 data there is little evidence for anv modulation above 2 keV. although a possible single-peaked pulse is visible at low energies.," In the August 1995 data there is little evidence for any modulation above 2 keV, although a possible single-peaked pulse is visible at low energies."545" By coutrast. iu January 1996. there is a clear single-peaked. pulse profile in both cucrey lands,"," By contrast, in January 1996, there is a clear single-peaked pulse profile in both energy bands."546 The lightcurves folded at the orbital period are shown iu Figure Ll., The lightcurves folded at the orbital period are shown in Figure 4.547 As in the case of Figure 2. we show the best fit sinusoid to these folded lightcurves (excluding the eclipse) ΩΝΟΥXotted.," As in the case of Figure 2, we show the best fit sinusoid to these folded lightcurves (excluding the eclipse) overplotted."548 Tere the depths of the modulation. listed iu Table 2. are significant at the —10 level iu the low energy baud. with a more mareiial detection in the high energy baud.," Here the depths of the modulation, listed in Table 2, are significant at the $\sim 4 \sigma$ level in the low energy band, with a more marginal detection in the high energy band."549" The spectra of these data are also adequately fit by simple thermal breissrallung models. withB 4zD=0.70— aud TN respectively,"," The spectra of these data are also adequately fit by simple thermal bremsstrahlung models, with $\chi^2_r = 0.70$ and 0.78 respectively."550 The 210 keV fiuxes are consistent across the two oservatious at y=1.79«1011 ere cnaD 1 aud Lal«10E cre wos5 ft. wit.ji likely statisical. uncertaimties of «der ~DI.," The 2–10 keV fluxes are consistent across the two observations at $1.79\times10^{-11}$ erg $^{2}$ $^{-1}$ and $1.84\times10^{-11}$ erg $^{2}$ $^{-1}$, with likely statistical uncertainties of order $\sim 1\%$."551 The fitted coluu densities too are consistent with each other wih values of VyLIS4103«1024022 aud Ny=Lito.x107 respectively., The fitted column densities too are consistent with each other with values of $N_{\rm H} = 4.1^{+0.3}_{-0.2} \times 10^{22}$ $^{-2}$ and $N_{\rm H} = 4.4 \pm 0.1 \times 10^{22}$ $^{-2}$ respectively.552 There are also two archiva observatious of NY Avi. neither of which have previously been published either.," There are also two archival observations of XY Ari, neither of which have previously been published either."553 They comprise au observation from 2000 August 26 with exposures of arouid 16 ksec (ALTOS) and Ls ksec (PN) aud another from 2001 February 5 with exposures of around 29 ksec (MOS) aud 27 ksec (PN)., They comprise an observation from 2000 August 26 with exposures of around 16 ksec (MOS) and 18 ksec (PN) and another from 2001 February 5 with exposures of around 29 ksec (MOS) and 27 ksec (PN).554 We extracted lhehteurves in each case roni both the MOS aud PN detectors. in three energv bands.," We extracted lightcurves in each case from both the MOS and PN detectors, in three energy bands."555 The lowenergv baud corresponds to ~12 keV. the ποπα euergy band is ~2l keV. whilst the high baud is ~110 keV. Iu," The lowenergy band corresponds to $\sim 1 - 2$ keV, the medium energy band is $\sim 2 - 4$ keV, whilst the high band is $\sim 4 - 10$ keV. In"556here (Cnedin&Hui1998). (we discuss this in detail in refsecuünh)).,here \cite{GH98} (we discuss this in detail in \\ref{sec:inh}) ).557 All our simulations have a box size of 205!Alpe (in comoving coordinates) and 2567 particles on a mesh of the same size., All our simulations have a box size of $20h^{-1}\dim{Mpc}$ (in comoving coordinates) and $256^3$ particles on a mesh of the same size.558 The gravitational force is calculated with a Cireen function thatincludes the Optimal Antialising ilter (Ferrell&Bertschinger1994).. by summing over three Drilloun zones.," The gravitational force is calculated with a Green function thatincludes the Optimal Antialising filter \cite{FB94}, by summing over three Brilloun zones."559 Jefore we can test for svstematic errors in the Croft οἱ WDBOL. method. we must first check that we can reproduce their results accurately.," Before we can test for systematic errors in the Croft et \\shortcite{CWB01} method, we must first check that we can reproduce their results accurately."560 In order to reduce the uncertainty in the mean [lux power spectrum. an average of several dillerent: random realizations is usualA used.," In order to reduce the uncertainty in the mean flux power spectrum, an average of several different random realizations is usually used."561 Normally. this procedure requires a large number of realizations. because the variance decreases only as the square του of the number. of realizations.," Normally, this procedure requires a large number of realizations, because the variance decreases only as the square root of the number of realizations."562 Instead. we adopt a slightly cillerent approach.," Instead, we adopt a slightly different approach."563" Out of all random realizations. we first choose ""good"" ones. tthose that give a measured linear power spectrum close to the input linear power spectrum."," Out of all random realizations, we first choose “good” ones, those that give a measured linear power spectrum close to the input linear power spectrum."564 We choose 3 “best” realizations out of 100 random ones. and an average over those three recovers the input power spectrum at least as well as à plain average over LOO truly random realizations.," We choose 3 “best” realizations out of 100 random ones, and an average over those three recovers the input power spectrum at least as well as a plain average over 100 truly random realizations."565 Figure 1. shows the Lux power spectrum 2(4) (shown as AT(h)=KPPOR)/ 287) averaged over 3 and over 12 best realizations (equivalent of 100 and 400 random realizations)., Figure \ref{figRL} shows the flux power spectrum $P_F(k)$ (shown as $\Delta^2(k)\equiv k^3P(k)/2\pi^2$ ) averaged over 3 and over 12 best realizations (equivalent of 100 and 400 random realizations).566 The difference between the two curves provides an estimate of about 2 of the uncertainty in the mean [lux power spectrum (because averaging over 12 realizations gives half the variance of averaging over just 3 realizations)., The difference between the two curves provides an estimate of about 1/2 of the uncertainty in the mean flux power spectrum (because averaging over 12 realizations gives half the variance of averaging over just 3 realizations).567 We notice that this dillerence is significantly smaller than the statistical error-bars of the observational data. indicating that our flux power spectrum is caleulated with sullicient precision.," We notice that this difference is significantly smaller than the statistical error-bars of the observational data, indicating that our flux power spectrum is calculated with sufficient precision."568 llereafter we use. three good” realizations ρα normalization for cach cosmological model., Hereafter we use three “good” realizations per normalization for each cosmological model.569 Thus. each model requires at least six simulations (two clillerent normalizations above ancl below the best-lit value). and more if our initial choice for the two normalizations does not bracket the best-fit value.," Thus, each model requires at least six simulations (two different normalizations above and below the best-fit value), and more if our initial choice for the two normalizations does not bracket the best-fit value."570 As evidence that our method reproduces the Croft. et shortciteC\WBOL results. we show in Figure 2. their fiducial model (courtesy Rupert Croft) and the Dux power spectrum from our simulation of exactly the same cosmological mocel.," As evidence that our method reproduces the Croft et \\shortcite{CWB01}571 results, we show in Figure \ref{figRF} their fiducial model (courtesy Rupert Croft) and the flux power spectrum from our simulation of exactly the same cosmological model."572 Notice that there exist a cillerence on large scales. which is most likely due to the smaller size of our computational box. but that itis smaller than the observational errors and so is unimportant.," Notice that there exist a difference on large scales, which is most likely due to the smaller size of our computational box, but that it is smaller than the observational errors and so is unimportant."573 In this paper our main concern is the clleet that an assumption of a specific cosmological model makes on recovering the linear. power spectrum from the Dux. power spectrum., In this paper our main concern is the effect that an assumption of a specific cosmological model makes on recovering the linear power spectrum from the flux power spectrum.574 Specifically. Croft et shortciteCWBol assume that the Lux power spectrum Pyth) is proportional to the linear power spectrum £7;(4) at the same wavenumber the bias factor b(&) being independent of. or at least insensitive to. the power spectrum PL(A).," Specifically, Croft et \\shortcite{CWB01} assume that the flux power spectrum $P_F(k)$ is proportional to the linear power spectrum $P_L(k)$ at the same wavenumber the bias factor $b(k)$ being independent of, or at least insensitive to, the power spectrum $P_L(k)$."575" Ifthe 7bias factor"" bk) were independent of the linear power spectrum. this would be a direct analogy to the biased galaxy linear. power spectrum."," If the “bias factor” $b(k)$ were independent of the linear power spectrum, this would be a direct analogy to the biased galaxy linear power spectrum."576" However. - the “bias factor"" 6(4) depends on the amplitude of the linear power spectrum Z (A). so that the relation (1)) is"," However, - the “bias factor” $b(k)$ depends on the amplitude of the linear power spectrum $P_L(k)$ , so that the relation \ref{pfl}) ) is"577but with a lower period ratio (0.770) than observed.,but with a lower period ratio (0.770) than observed.578" The best fit solution obtained with these models, for an effective temperature consistent with the spectroscopic determination and assuming solar chemical composition, corresponds to: M= 1.65Mo, logL/Lco= 1.1, Tog=6700 K, logg=3.83."," The best fit solution obtained with these models, for an effective temperature consistent with the spectroscopic determination and assuming solar chemical composition, corresponds to: $M=1.65 M_{\odot}$ , $\log L/{\rm L}_\odot = 1.1$ , $T_{\rm eff}=6700$ K, $\log g = 3.83$."579" We notice that for this combination of stellar parameters, both the fundamental and the first overtone mode are unstable in these models."," We notice that for this combination of stellar parameters, both the fundamental and the first overtone mode are unstable in these models."580" Moreover, looking at the Main Sequence and post-Main Sequence evolutionary tracks in the gravity versus effective temperature plane, as reported in Fig."," Moreover, looking at the Main Sequence and post-Main Sequence evolutionary tracks in the gravity versus effective temperature plane, as reported in Fig."581" 4 of ?,, the solution Τεα = 6700 K, logg=3.83 is consistent with a 1.65Mo stellar mass."," 4 of \citet{c10}, the solution $T_{\rm eff}$ = 6700 K, $\log g = 3.83$ is consistent with a $1.65 M_{\odot}$ stellar mass."582" However, as already noted, the period ratio in our models is lower than the observed value."," However, as already noted, the period ratio in our models is lower than the observed value."583" To resolve this discrepancy, the possibility of low metallicity and rotation effects was examined in more detail with the second modeling package."," To resolve this discrepancy, the possibility of low metallicity and rotation effects was examined in more detail with the second modeling package."584" Models between Tog= 6200KK and 8600K with masses between 1.2 and 1.76Mo, were found to represent a good fit of f; and f» as radial fundamental and first overtone, respectively."," Models between $T_{\rm eff} = 6200$ K and $8600\,$ K with masses between 1.2 and $\msun$, were found to represent a good fit of $f_1$ and $f_2$ as radial fundamental and first overtone, respectively."585" The best fit with the observations was found for M—1.2M models computed with amir=0.5, doy=0.1, and a metallicity of -0.5 dex."," The best fit with the observations was found for $M=1.2\,\msun$ models computed with $\amlt=0.5$, ${\rm d}_{ov}=0.1$, and a metallicity of -0.5 dex."586" Such a low value for the convection efficiency is in- good agreement with the predictions by ? for ó Sct stars, based on their non-adiabatic asteroseismic analysis."," Such a low value for the convection efficiency is in good agreement with the predictions by \citet{Casas06} for $\delta$ Sct stars, based on their non-adiabatic asteroseismic analysis."587" All these parameters roughly match the general characteristics of the ὃ SSct stars with dominant radial modes and large amplitudes, despite being in the limit in metallicity."," All these parameters roughly match the general characteristics of the $\delta$ Sct stars with dominant radial modes and large amplitudes, despite being in the limit in metallicity."588" The P,/Po period ratios predicted by these models (which simultaneously fit Po) are near 0.775, which is lower than the observed ratio, 0.779."," The $P_1/P_0$ period ratios predicted by these models (which simultaneously fit $P_0$ ) are near 0.775, which is lower than the observed ratio, 0.779."589" A period ratio of 0.775 is also obtained by adopting the radial linear nonadiabatic models by ? at Z— 0.006, according to which the best fit solution with effective temperature consistent with the spectroscopic determination, corresponds to Z=0.006, Y=0.25, M= 1.5, logL/Lo=1.04, Τε=6700 K, logg=3.83."," A period ratio of 0.775 is also obtained by adopting the radial linear nonadiabatic models by \citet{m04} at $Z=0.006$ , according to which the best fit solution with effective temperature consistent with the spectroscopic determination, corresponds to $Z=0.006$, $Y=0.25$, $M=1.5$ , $\log L/L_{\odot}=1.04$, $T_e=6700$ K, $\log g = 3.83$."590 Again the fundamental and first overtone modes are predicted to be simultaneoulsy unstable for this parameter combination., Again the fundamental and first overtone modes are predicted to be simultaneoulsy unstable for this parameter combination.591" We explored the possibility that such a discrepancy might be due to rotation effects, particularly second-order distortion effects, as discussed by ? and ?.."," We explored the possibility that such a discrepancy might be due to rotation effects, particularly second-order distortion effects, as discussed by \citet{Sua06pdrotI} and \citet{Sua07pdrotII}."592" These investigations analyze theoretical Petersen Diagrams including rotation effects (Rotational Petersen Diagrams, hereafter RPDs), and show that Pi/P ratios increase as stellar surface rotation increases."," These investigations analyze theoretical Petersen Diagrams including rotation effects (Rotational Petersen Diagrams, hereafter RPDs), and show that $P_1/P_0$ ratios increase as stellar surface rotation increases."593 The rotation rate derived from observations is slightly below! (see refsec:quintuplet))., The rotation rate derived from observations is slightly below$^{-1}$ (see\\ref{sec:quintuplet}) ).594" At such rotation rates near degeneracy effects on the period ratio are small (less than 0.001 in P,/Po).", At such rotation rates near degeneracy effects on the period ratio are small (less than 0.001 in $P_1/P_0$).595" However, when non-spherically symmetric components of the centrifugal force are considered,"," However, when non-spherically symmetric components of the centrifugal force are considered,"596region shows the mean and standard deviation of 10 realisations of the ELFIT model to itself.,region shows the mean and standard deviation of 10 realisations of the ELFIT model to itself.597 The real data appear to have substantially wider distributions of pixel values than these model results., The real data appear to have substantially wider distributions of pixel values than these model results.598 This difference is more apparent as more smoothing is applied., This difference is more apparent as more smoothing is applied.599" The dashed line and green shaded region shows the mean and standard deviation of 10 realisations of the ELFIT model with Gaussian fluctuations added, relative to the ELFIT model."," The dashed line and green shaded region shows the mean and standard deviation of 10 realisations of the ELFIT model with Gaussian fluctuations added, relative to the ELFIT model."600" We generated the Gaussian fluctuations by convolving an image where the pixels were normally distributed, by a Gaussian of the size given, and scaling the size of the resulting fluctuations to have the correct standard deviation."," We generated the Gaussian fluctuations by convolving an image where the pixels were normally distributed, by a Gaussian of the size given, and scaling the size of the resulting fluctuations to have the correct standard deviation."601 The magnitude of these fluctuations is chosen to have a standard deviation of the model pixel values of 4 per cent., The magnitude of these fluctuations is chosen to have a standard deviation of the model pixel values of 4 per cent.602" These distributions better reproduce the width of the data distributions, but the match is not exact."," These distributions better reproduce the width of the data distributions, but the match is not exact."603" If the surface brightness fluctuations are of the order of 4 per cent, these correspond to 2 per cent fluctuations in projected density."," If the surface brightness fluctuations are of the order of 4 per cent, these correspond to 2 per cent fluctuations in projected density."604 We show the distributions for the 3.5 to 7.5 keV band in Fig. 8.., We show the distributions for the 3.5 to 7.5 keV band in Fig. \ref{fig:elldistn3575}.605" The differences between the smooth model and data are less apparent in this band, except when going to larger radii and applying more smoothing."," The differences between the smooth model and data are less apparent in this band, except when going to larger radii and applying more smoothing."606" In this plot we also display the results for a model with Gaussian fluctuations at the 8 per cent level, instead of 4 per cent."," In this plot we also display the results for a model with Gaussian fluctuations at the 8 per cent level, instead of 4 per cent."607 The additional width of the distributions compared to the model confirm the fact that the maps appear to have additional fluctuations in the image above that expected from Poisson noise., The additional width of the distributions compared to the model confirm the fact that the maps appear to have additional fluctuations in the image above that expected from Poisson noise.608 The fluctuations presented above were revealed by the subtraction of an ELFIT cluster model., The fluctuations presented above were revealed by the subtraction of an ELFIT cluster model.609 One potential problem with this approach is that we could be subtracting real signal from the data by including it in the model., One potential problem with this approach is that we could be subtracting real signal from the data by including it in the model.610" The ELFIT model is good at removing features such as edges, which typically follow surface brightness contours."," The ELFIT model is good at removing features such as edges, which typically follow surface brightness contours."611 The method also removes shifts in the centres of isophotes as a function of radius or isophotal twists., The method also removes shifts in the centres of isophotes as a function of radius or isophotal twists.612 In Fig., In Fig.613 9 is shown adaptively smoothed images of the cluster in the 0.6 to 5 keV band using the accumulative smoothing algorithm described in ?.., \ref{fig:contours} is shown adaptively smoothed images of the cluster in the 0.6 to 5 keV band using the accumulative smoothing algorithm described in \cite{SandersBin06}.614 These images were produced using a variable-sized top-hat kernel with a radius chosen to include at least 225 counts at each position., These images were produced using a variable-sized top-hat kernel with a radius chosen to include at least 225 counts at each position.615 Plotted in each image we display the jagged logarithmic-spaced surface brightness contours., Plotted in each image we display the jagged logarithmic-spaced surface brightness contours.616" In the top panel of Fig. 9,,"," In the top panel of Fig. \ref{fig:contours},"617" we also show the contours of an elliptical B model fitted to the surface brightness This model was fitted to the raw data using the package, minimising the 'cstat statistic, which takes account of the Poisson distribution of the counts."," we also show the contours of an elliptical $\beta$ model fitted to the surface brightness This model was fitted to the raw data using the package, minimising the `cstat' statistic, which takes account of the Poisson distribution of the counts."618 We excluded the central arcminute of the cluster from the fit (shown as a bold circle)., We excluded the central arcminute of the cluster from the fit (shown as a bold circle).619" The β model was allowed to have a variable ellipticity, centre, core radius and index."," The $\beta$ model was allowed to have a variable ellipticity, centre, core radius and index."620 The functional form of the surface brightness model used was, The functional form of the surface brightness model used was621"The protostellar disk model we use will be described more fully in a forthcoming publication, Woods&Willacy(2006).","The protostellar disk model we use will be described more fully in a forthcoming publication, \citet{woo06}."622. We use a density and dust temperature profile based on that of D’Alessioetal.(2001) (Fig. 3)).," We use a density and dust temperature profile based on that of \citet{dal01}623 (Fig. \ref{fig:denstemp}) )."624" This is a flared accretion disk model, with a maximum dust grain size of jum, similar to the size of interstellar dust."," This is a flared accretion disk model, with a maximum dust grain size of $\mu$ m, similar to the size of interstellar dust."625" The disk has a mass accretion rate of M—10-5 MM yyr! and a surface density of X—100 cem""? at AAU, whilst the central star has the following properties: M,—0.7 MMo, 7,=4 KK and R,—2 RRo."," The disk has a mass accretion rate of $\dot{M}$ $^{-8}$ $_\odot$ $^{-1}$ and a surface density of $\Sigma$ $^{-2}$ at AU, whilst the central star has the following properties: $M_\star$ $_\odot$, $T_\star$ K and $R_\star$ $_\odot$."626" Using these profiles, we calculate UV photon fluxes throughout the disk with the ray-tracing component of the model of Yorke&Bodenheimer(1999)."," Using these profiles, we calculate UV photon fluxes throughout the disk with the ray-tracing component of the model of \citet{yor99}."627. This calculates the UV field due to the central star and the interstellar radiation field (ISRF) and also includes radiation scattering effects., This calculates the UV field due to the central star and the interstellar radiation field (ISRF) and also includes radiation scattering effects.628" At AAU we assume that the UV field due to the central star is 50,000 times the ISRF, in accordance with the observations of Berginetal.(2003)."," At AU we assume that the UV field due to the central star is 50,000 times the ISRF, in accordance with the observations of \citet{ber03}."629". Despite the differing spectral shapes of the ISRF and a typical T Tauri stellar field, with strong emission lines dominating the T Tauri spectrum (Berginetal.2003),, the formation of benzene in the very dense and well-shielded region we consider is not critically dependent on our choice of stellar UV field."," Despite the differing spectral shapes of the ISRF and a typical T Tauri stellar field, with strong emission lines dominating the T Tauri spectrum \citep{ber03}, the formation of benzene in the very dense and well-shielded region we consider is not critically dependent on our choice of stellar UV field."630" Given gas densities, dust temperatures and UV photon fluxes at each point on ourgrid!,, we are then able to solve the heating and cooling balance of the gas in a similar manner to Kamp&vanZadelhoff(2001),, Kamp&Dullemond(2004) and Gorti&Hollenbach(2004)."," Given gas densities, dust temperatures and UV photon fluxes at each point on our, we are then able to solve the heating and cooling balance of the gas in a similar manner to \citet{kam01}, \citet{kam04} and \citet{gor04}."631" The gas temperature can be underestimated by up to two orders of magnitude if it is assumed to be equal to the dust temperature throughout the disk, although this is less critical for the optically thick midplane region where benzene forms."," The gas temperature can be underestimated by up to two orders of magnitude if it is assumed to be equal to the dust temperature throughout the disk, although this is less critical for the optically thick midplane region where benzene forms."632 Figure 3 shows the range of gas temperatures within the inner AAU of the disk (the benzene formation region)., Figure \ref{fig:denstemp} shows the range of gas temperatures within the inner AU of the disk (the benzene formation region).633" We use a subset of the extensive UMIST Rate99 gas-phase chemical network (LeTeuff 2000),, augmenting it with gas-grain interactions (freezeout, thermal desorption) and grain surface reactions so that our reaction set comprises approximately 2400 reactions amongst 200 species."," We use a subset of the extensive UMIST Rate99 gas-phase chemical network \citep{let00}, augmenting it with gas-grain interactions (freezeout, thermal desorption) and grain surface reactions so that our reaction set comprises approximately 2400 reactions amongst 200 species."634 We include species with more carbon atoms than benzene to ensure that does not result in a spurious build-up of benzene., We include species with more carbon atoms than benzene to ensure that chain-lengthening does not result in a spurious build-up of benzene.635" We have selected reactions which are valid in the region KK; this upper limit is exceeded in the upper regions of the disk where temperatures can reach ~10,000 KK, although at such high temperatures molecules are destroyed."," We have selected reactions which are valid in the region K; this upper limit is exceeded in the upper regions of the disk where temperatures can reach $\sim$ K, although at such high temperatures molecules are destroyed."636" Hence we concentrate on the portions of the disk closer to the midplane, less than 2 scaleheights."," Hence we concentrate on the portions of the disk closer to the midplane, less than 2 scaleheights."637the brown dwarf is « I. the contribution of inverse Compton scattering i5 unlikely to be important.,"the brown dwarf is $\ll$ 1, the contribution of inverse Compton scattering is unlikely to be important."638" For the thermal bremsstrahlung emission of ionized hydrogen and helium dominated source. the detected flux density integrated over frequency is Sx.=4.67x gyRMT. where Z is an ion of charge in units e (here we take Z= 1). gy the Gaunt factor (we take gj=1.2. which gives an accuracy of <20% since 1.1<gy« L5). R, the radius of the source. d distance of the source from us and all quantities are 1n cgs units (2).."," For the thermal bremsstrahlung emission of ionized hydrogen and helium dominated source, the detected flux density integrated over frequency is $S_{\rm X-B}=4.67\times10^{-28}T_{\rm h}^{1/2}n_{\rm h}n_{\rm c}Z^{2}\overline{g}_{\rm B}R_{\rm s}^{3}d^{-2}$ , where $Z$ is an ion of charge in units $e$ (here we take $Z=1$ ), $\overline{g}_{\rm B}$ the Gaunt factor (we take $\overline{g}_{\rm B}=1.2$ , which gives an accuracy of $\lesssim$ since $1.1<\overline{g}_{\rm B}<1.5$ ), $R_{\rm s}$ the radius of the source, $d$ distance of the source from us and all quantities are in $cgs$ units \citep{Rybicki79}."639" In the case of TVLM 513. assuming that the X-ray emission comes from the same region as the radio emission. we can take the parameters as Ty=107 K. m=105 em? ne=3x10° cem. R,=2x105 em. d=10 pex3.1xI0? em. hence we get the Sxp10! erg-em77-s7!. giving an X-ray luminosity of ὧν=5.34x10? ergs!."," In the case of TVLM 513, assuming that the X-ray emission comes from the same region as the radio emission, we can take the parameters as $T_{\rm h}=10^{7}$ K, $n_{\rm h}=10^{8}$ $^{-3}$, $n_{\rm c}=3\times10^{9}$ $^{-3}$, $R_{\rm s}=2\times10^{8}$ cm, $d=10$ $\approx3.1\times10^{19}$ cm, hence we get the $S_{\rm X-B}=4.42\times10^{-21}$ $\cdot$ $^{-2}\cdot$ $^{-1}$, giving an X-ray luminosity of $L_{\rm X-B}\approx5.34\times10^{19}$ $\cdot$ $^{-1}$."640 The X-ray flux density/luminosity could be underestimated significantly as the X-ray emission might be diffuse and from a larger region (perhaps - 10 times) than that of the radio emission. as is the case for the X-ray emission observed from Jupiter by Suzaku (2)...," The X-ray flux density/luminosity could be underestimated significantly as the X-ray emission might be diffuse and from a larger region (perhaps $\sim$ 10 times) than that of the radio emission, as is the case for the X-ray emission observed from Jupiter by $Suzaku$ \citep{Ezoe10}."641 Interestingly. ? obtained a marginal detection in. X-rays suggesting a flux density of 6.3x107!* οσα κ] (luminosity Lx=8.5x 10*ere-s7!) with mean energy at 0.9 keV. This means the temperature of the hot plasma could be slightly lower than 10 K. Further multi-wavelength observations will help to refine our model and its parameters to understand the radio and X-ray emission from these kinds of cool objects.," Interestingly, \citet{Berger08} obtained a marginal detection in X-rays suggesting a flux density of $6.3\times10^{-16}$ $\cdot$ $^{-2}\cdot$ $^{-1}$ (luminosity $L_{\rm X}=8.5\times10^{24}$ $\cdot$ $^{-1}$ ) with mean energy at 0.9 keV. This means the temperature of the hot plasma could be slightly lower than $10^{7}$ K. Further multi-wavelength observations will help to refine our model and its parameters to understand the radio and X-ray emission from these kinds of cool objects."642 An active region model is applied to the radio emission from a cool dwarf. in which the ECMI mechanism is responsible for the radio bursts from the magnetic tubes. while the rotation of the dwarf can modulate the total observed flux with respect to time.," An active region model is applied to the radio emission from a cool dwarf, in which the ECMI mechanism is responsible for the radio bursts from the magnetic tubes, while the rotation of the dwarf can modulate the total observed flux with respect to time."643 The time profile of the radio light curve is in the form of power law in our model., The time profile of the radio light curve is in the form of power law in our model.644 Using this model. we can determine the nature (e.g. size. temperature. density) of the radio-emitting region plus the magnetic topology can be constrained as well.," Using this model, we can determine the nature (e.g. size, temperature, density) of the radio-emitting region plus the magnetic topology can be constrained as well."645" In the case of TVLM 513. our model shows the loss-cone electrons have a density in the range of 1.2510-5x10° em™ and temperature between 10 and 5x10’ K. The brightness temperature is typically ~10 K for pulses. ~5xI0"" κ for the background emission. implying the ECMI mechanism operates in compact region of «0.007 Αιρ if the active region is at 30°."," In the case of TVLM 513, our model shows the loss-cone electrons have a density in the range of $1.25\times10^{5}-5\times10^{5}$ $^{-3}$ and temperature between $10^{7}$ and $5\times10^{7}$ K. The brightness temperature is typically $\sim10^{15}$ K for pulses, $\sim5\times10^{10}$ K for the background emission, implying the ECMI mechanism operates in compact region of $\sim$ 0.007 $R_{\rm Jup}$ if the active region is at $^{\circ}$."646 For an active region closer to the pole. e.g. 70°. the size is ~60% smaller. implying a higher brightness temperature.," For an active region closer to the pole, e.g. $^{\circ}$, the size is $\sim$ smaller, implying a higher brightness temperature."647 The model predicts an enhanced ambient wave energy background and a «7000 G surface magnetic field strength., The model predicts an enhanced ambient wave energy background and a $\approx$ 7000 G surface magnetic field strength.648 The theoretical X-ray flux density in our model is much smaller than a marginal X-ray observation of TVLM 513. which implies a more complicated plasmabehavior or magnetic structure on the dwarf.," The theoretical X-ray flux density in our model is much smaller than a marginal X-ray observation of TVLM 513, which implies a more complicated plasmabehavior or magnetic structure on the dwarf."649 Additional multi-wavelength observations are needed to constrain the tentative conclusions and help us to improve the understanding of the magnetic field on ultracool dwarfs and to test the viability of this model i comparison with others. such as the auroral model.," Additional multi-wavelength observations are needed to constrain the tentative conclusions and help us to improve the understanding of the magnetic field on ultracool dwarfs and to test the viability of this model in comparison with others, such as the auroral model."650c and Mpy—Lpuige relations.,$\sigma$ and $M_\mathrm{BH}$ $L_\mathrm{bulge}$ relations.651" However, we offer an alternative interpretation for why this is so."," However, we offer an alternative interpretation for why this is so."652 We argue here that this is likely a direct consequence of the role of merging dark matter halos that drive SMBH growth., We argue here that this is likely a direct consequence of the role of merging dark matter halos that drive SMBH growth.653" Our view hinges on the fact that the coupling between SMBH growth and dark matter was necessarily strong at high redshifts as merger rates determine the assembly history, and major mergers that trigger accretion episodes are more frequent at high redshift for the most massive halos."," Our view hinges on the fact that the coupling between SMBH growth and dark matter was necessarily strong at high redshifts as merger rates determine the assembly history, and major mergers that trigger accretion episodes are more frequent at high redshift for the most massive halos."654" At late times, however, the SMBH mass itself is more tightly coupled to the properties of the baryonic galactic nucleus, in particular, for low mass galaxies that have experienced practically no major mergers in their entire lifetime."," At late times, however, the SMBH mass itself is more tightly coupled to the properties of the baryonic galactic nucleus, in particular, for low mass galaxies that have experienced practically no major mergers in their entire lifetime."655 The key point here is that major mergers trigger simultaneous SMBH growth and star formation causing a tight coupling between these two components in the galactic nucleus only for massive halos., The key point here is that major mergers trigger simultaneous SMBH growth and star formation causing a tight coupling between these two components in the galactic nucleus only for massive halos.656" To explore this interpretation further, we first re-examine the data from KBC from a purely empirical perspective."," To explore this interpretation further, we first re-examine the data from KBC from a purely empirical perspective."657" The sample is composed of 25 galaxies with dynamical measurements of the black hole mass, Mpu, and high-quality measurements of velocity dispersion, c, and asymptotic circular velocity, V. (Fig. 1))."," The sample is composed of 25 galaxies with dynamical measurements of the black hole mass, $M_\mathrm{BH}$, and high-quality measurements of velocity dispersion, $\sigma$, and asymptotic circular velocity, $V_c$ (Fig. \ref{data}) )."658 Galaxy properties are listed in Table 1 of the Supplementary Information in KBC., Galaxy properties are listed in Table 1 of the Supplementary Information in KBC.659" We fit the data with a functional form of Using a symmetric least-squares fit, we find A=7.240.05 and B=7.603-0.40 with x?/d.o.f.=7.2, indicating that the data are very unlikely to have come from the model used, in strong agreement with KB."," We fit the data with a functional form of Using a symmetric least-squares fit, we find $A = 7.2 \pm 0.05$ and $B660= 7.60 \pm 0.40$ with $\chi^2/\textrm{d.o.f.} = 7.2$, indicating that the data are very unlikely to have come from the model used, in strong agreement with KB."661" We then expand the model to include a log-normal scatter about the relation of standard deviation so, The inclusion of a scatter term of some sort is essential since the deviations from a log-linear relation are in excess of the measurement errors (Hoggetal.2010)."," We then expand the model to include a log-normal scatter about the relation of standard deviation $s_0$, The inclusion of a scatter term of some sort is essential since the deviations from a log-linear relation are in excess of the measurement errors \citep{Hogg2010}."662". We fit using the methods of Gültekinetal. à generalized maximum likelihood method that can (2009),,handle measurement errors in the independent and dependent variables (assumed Gaussian in log space) as well as upper limits."," We fit using the methods of \cite{Gultekin2009}, a generalized maximum likelihood method that can handle measurement errors in the independent and dependent variables (assumed Gaussian in log space) as well as upper limits."663" We find A=7.39€:0.14, B=4.22+0.93, and so=0.534:0.10."," We find $A = 7.39 \pm 0.14$, $B =6644.22 \pm 0.93$, and $s_0 = 0.53 \pm 0.10$."665 So this indicates that a correlation can be inferred from the data., So this indicates that a correlation can be inferred from the data.666" Compared to the rrelation, the scatter in the rrelation is slightly larger for this sample, for which we find A=(i))8.0640.14, B=3.95+ 0.72, and 50=0.50+ 0.09; (ii)) significantly larger than the entire sample in Gültekinetal. (so=0.44+ 0.06) and much larger than the (2009)elliptical-only sample in Gültekin(#é))etal.(2009) (so=0.31+ 0.06)."," Compared to the relation, the scatter in the relation is ) slightly larger for this sample, for which we find $A = 8.06 \pm 0.14$, $B = 3.95 \pm 0.72$ , and $s_0 =6670.50 \pm 0.09$ ; ) significantly larger than the entire sample in \cite{Gultekin2009} $s_0=0.44\pm0.06$ ) and ) much larger than the elliptical-only sample in \cite{Gultekin2009}668 $s_0 = 0.31 \pm 0.06$ )."669" Given that the sample was selected based on the ability to measure V, in each galaxy, the actual scatter in the rrelation may be even larger since those galaxies in which V. is difficult to measure will tend to be outliers."," Given that the sample was selected based on the ability to measure $V_c$ in each galaxy, the actual scatter in the relation may be even larger since those galaxies in which $V_c$ is difficult to measure will tend to be outliers."670 The fact that the inferred scatter in the rrelation is not smaller than the scatter in the iimplies that the halo mass is not driving the correlation at a higher level than the physical process that sets the bulge properties., The fact that the inferred scatter in the relation is not smaller than the scatter in the implies that the halo mass is not driving the correlation at a higher level than the physical process that sets the bulge properties.671" This first assessment corroborates one of the main conclusions of KB, that central black hole’s mass today is notuniquely determined by the mass of the dark matter halo."," This first assessment corroborates one of the main conclusions of KB, that central black hole's mass today is not determined by the mass of the dark matter halo."672" The similar level of scatter in the and ffits, however, confirms that there is a trend in the entire ssample (plus notable outliers; see refdata.."," The similar level of scatter in the and fits, however, confirms that there is a trend in the entire sample (plus notable outliers; see \\ref{data}. ."673" For example, there is only one galaxy with s! and Mgy<10°M, and only one with V.<s! and Mpy>2x10’Mz."," For example, there is only one galaxy with $V_c > 250\kms$ and $\mbh <67410^8\ \msun$ and only one with $V_c < 200\kms$ and $\mbh >6752\times10^7\ \msun$."676 It is also possible to interpret the data as having only a weak correlation below Mpu<5x10’ Με)., It is also possible to interpret the data as having only a weak correlation below $\mbh < 5 \times 10^7\ \msun$ ).677 We show below how this trend is expected to naturally arise in a set of physically well motivated models for the formation of SMBH seeds at the earliest epochs without requiring black holes to partake in exotic nonbaryonic physics., We show below how this trend is expected to naturally arise in a set of physically well motivated models for the formation of SMBH seeds at the earliest epochs without requiring black holes to partake in exotic nonbaryonic physics.678 We focus on a class of SMBH seeding models to illustrate that the observed lack of central black holes in low velocity dispersion bulgeless galaxies today need not imply a lack of correlation between SMBH and dark matter halo properties at earlier epochs (Volonterietal.2008;Volonteri&Natarajan 2009).," We focus on a class of SMBH seeding models to illustrate that the observed lack of central black holes in low velocity dispersion bulgeless galaxies today need not imply a lack of correlation between SMBH and dark matter halo properties at earlier epochs \citep{VLN2008,VN09}."679. We describe below a class of black hole seed formation models where the seed properties are initially correlated to the host dark matter properties at high redshifts., We describe below a class of black hole seed formation models where the seed properties are initially correlated to the host dark matter properties at high redshifts.680" Evolving such models via the merger driven accretion prescription over cosmic time, Volonteri Natarajan (2009) find that a key prediction is thatholes."," Evolving such models via the merger driven accretion prescription over cosmic time, Volonteri Natarajan (2009) find that a key prediction is that."681 The relevant host dark matter halo property in this picture is the spin., The relevant host dark matter halo property in this picture is the spin.682 In a physically motivated model for the formation of heavy SMBH seeds(in contrast to the lowermass remnant seeds from Population III stars) according to the prescription described in Lodato Natarajan (2006; 2007) there is, In a physically motivated model for the formation of heavy SMBH seeds(in contrast to the lowermass remnant seeds from Population III stars) according to the prescription described in Lodato Natarajan (2006; 2007) there is683Any value of X less than this linüt is iuconsisteut with the distribution of the data aud would produce a clear secoudary peal at 3=(p.1)/2. not observed in the data refüe:hist)),"Any value of X less than this limit is inconsistent with the distribution of the data and would produce a clear secondary peak at $\beta = (p-1)/2$, not observed in the data \\ref{fig:hist}) )."684 To avoid this peak. an extremely wide distribution is needed. much wider than the spread of he observed data.," To avoid this peak, an extremely wide distribution is needed, much wider than the spread of the observed data."685 Hence. the upper liuüt on the perceutage of CRBs in our sample where the cooling frequency is greater hau the N-rav frequency (νο27 vx) is approximately 6.5 oerceent. or ~20 out of 301 GRBs.," Hence, the upper limit on the percentage of GRBs in our sample where the cooling frequency is greater than the X-ray frequency $\nu_{\mathrm{c}} > \nu_{\mathrm{X}}$ ) is approximately 6.5 percent, or $\sim20$ out of 301 GRBs."686 This is a discrepancy roni the ratio observed in the multi-baud studies (6.8.. Starlingetal:Curranale: 5 out of 10 and 2 out of 6. respectively) but not seriously so given the extremely low ΠΠΟΙ statistics of those studies.," This is a discrepancy from the ratio observed in the multi-band studies (e.g., \citeauthor{starling2008:ApJ672,curran2009:MNRAS395}: 5 out of 10 and 2 out of 6, respectively) but not seriously so given the extremely low number statistics of those studies."687 If we create a sample of 6 random bursts from our statistical distribution of 301. there would be a nou-neglieible (~ 5 percent) chance hat 2. or more. bursts would have a cooling frequency ercater than the X-ray frequency. consistent with the aforementioned study (Curranet al.)).," If we create a sample of 6 random bursts from our statistical distribution of 301, there would be a non-negligible $\sim$ 5 percent) chance that 2, or more, bursts would have a cooling frequency greater than the X-ray frequency, consistent with the aforementioned study \citeauthor{curran2009:MNRAS395}) )."688" The study of Starlingetal. is based on a sample ofBeppoSANX.. as opposed toSwift., GRBs which may have a different luit on the regime probability. X."," The study of \citeauthor{starling2008:ApJ672} is based on a sample of, as opposed to, GRBs which may have a different limit on the regime probability, $X$."689 An investigation as to why the cooling frequency of afterelows follow this apparent laut. or its nmuplications regarding the distribution of other parameters. is bevoud the scope of this work.," An investigation as to why the cooling frequency of afterglows follow this apparent limit, or its implications regarding the distribution of other parameters, is beyond the scope of this work."690 We use the X-ray spectral iudices of ginuua-rav burst afterelows observed by the XRT aboard to paralucterise the underline distribution of the electron enerev distribution iudex. p. within the framework of the blast wave model.," We use the X-ray spectral indices of gamma-ray burst afterglows observed by the XRT aboard to parameterise the underlying distribution of the electron energy distribution index, $p$, within the framework of the blast wave model."691 The electrou cucrey distribution index is a fundamental paramcter of the svuchrotron enission from a rauge of astronomical sources aud iu this case of the svnchrotrou emission of GRB afterelows., The electron energy distribution index is a fundamental parameter of the synchrotron emission from a range of astronomical sources and in this case of the synchrotron emission of GRB afterglows.692 We use a anit likelihood Monte Carlo analysis to test two Lypotheses. namely that the observed distribution of spectral indices. 9. can be obtained from au uuderlviug distribution of p composed of /) a single discrete value and //) a Gaussian distribution.," We use a maximum likelihood Monte Carlo analysis to test two hypotheses, namely that the observed distribution of spectral indices, $\beta$, can be obtained from an underlying distribution of $p$ composed of $i)$ a single discrete value and $ii)$ a Gaussian distribution."693 We find that the observed distribution of spectral iudices are incousistcut with the first hypothesis but consistent with the secoud. a Gaussian distribution centred at p=2.36 and having a width of 0.59.," We find that the observed distribution of spectral indices are inconsistent with the first hypothesis but consistent with the second, a Gaussian distribution centred at $p = 2.36$ and having a width of $0.59$."694 Furthermore. if we accept that the underlying distribution is a Gaussian. the majority (291 percent) of CRB afterelows in our sample have a cooling break frequency less than the N-rav frequency.," Furthermore, if we accept that the underlying distribution is a Gaussian, the majority $\gtrsim 94$ percent) of GRB afterglows in our sample have a cooling break frequency less than the X-ray frequency."695 We thank the referee for their conunents., We thank the referee for their comments.696 PAC. PAE. ALIP. MdP acknowledge support fou STFC.," PAC, PAE, MJP, MdP acknowledge support from STFC."697 AJwdI was supported by an appoiutiieut to the NASA Postdoctoral Program at the MISFC. adiüuistered by Oak Ridge Associated Universities through a coutract with NASA. Switt.," AJvdH was supported by an appointment to the NASA Postdoctoral Program at the MSFC, administered by Oak Ridge Associated Universities through a contract with NASA. ."698". The probability of spectral iudex. 3. eiven a iieasured value. 3). with asviunetrie crrors. σης (Starlingetal.2008)ls where σι—(o;σι] aud σε=σι(3xdi) where p is the ceutral. or mean. value of the distribution aud o, is the standard deviation of the distribution."," The probability of spectral index, $\beta$, given a measured value, $\beta_i$, with asymmetric errors, $\sigma_{i\pm}$ \citep{starling2008:ApJ672} is where $\overline{\sigma_{i\pm}} = (\sigma_{i-} + \sigma_{i+} )/2$ and $\sigma_{i\pm}= \left\{ 699\begin{array}{ll} 700 \sigma_{i-} & (\beta < \beta_i) \\701 \sigma_{i+} & (\beta \geq \beta_i) 702\end{array} \right. .$ Assume that the distribution of the electron energy distribution index, $p$, can be described by a Gaussian probability: where $\bar{p}$ is the central, or mean, value of the distribution and $\sigma_{p}$ is the standard deviation of the distribution."703 The distribution of the observed. X-ray spectralindices. ἐν eau them be described by a double Cassia:," The distribution of the observed X-ray spectralindices,$\beta$ , can then be described by a double Gaussian:"704(ω< 0.1) scattering off low energy particles (p«OOUd) undergo small angle scattering that can be accurately described by the FP approximation.,$\omega<0.1$ ) scattering off low energy particles $p<0.1$ ) undergo small angle scattering that can be accurately described by the FP approximation.705 As can be seen in Fig., As can be seen in Fig.706 5 aud 6.. the two methods happen ]uckilv to give a correct description of Compton scattering in regions of the (p.i) space that can be complementar.," \ref{fig_photons} and \ref{fig_bdr_part}, the two methods happen luckily to give a correct description of Compton scattering in regions of the $(p,\omega)$ space that can be complementary."707 This sugeests that combining the two methods is a good way to overcome nunerieal accuracy issues im Computing the effects of Comptou scattering., This suggests that combining the two methods is a good way to overcome numerical accuracy issues in computing the effects of Compton scattering.708" However. this can only be done if the validity regions for the two methods cover the cutive simulation domain. that is. for given ep,. ενω aud egp. if: for the equation ou plotous aud particles respectively."," However, this can only be done if the validity regions for the two methods cover the entire simulation domain, that is, for given $\epsilon_{{\rm I},p}$, $\epsilon_{{\rm I},\omega}$ and $\epsilon_{\rm FP }$, if: for the equation on photons and particles respectively."709" Typically. this iuyplies that ενωEegp aud er,€Fp. which sets a constraiut ou the eid resolution: As good accuracy for each methods requires >5 aud épp<< 1l. this puts strong coustraiuts ou the resolution."," Typically, this implies that $\epsilon_{{\rm I},\omega} \le \epsilon_{\rm FP}$ and $\epsilon_{{\rm I},p} \le \epsilon_{\rm FP}$, which sets a constraint on the grid resolution: As good accuracy for each methods requires $n>5$ and $\epsilon_{\rm{FP}}<<1$ , this puts strong constraints on the resolution."710 For example. by setting egp=0.1 and s=5 this leads to A2LO.," For example, by setting $\epsilon_{\rm FP}=0.1$ and $n=5$ this leads to $R>40$."711 For particle grids that typically span 5 orders of magnitude. it implies the need to use 200-bin exids accessible to most desktop computers.," For particle grids that typically span 5 orders of magnitude, it implies the need to use 200-bin grids accessible to most desktop computers."712 However. for photon erids that typically span 15 orders of magnitude. it corresponds to GO0-bin erids. which requires high coluputing power.," However, for photon grids that typically span 15 orders of magnitude, it corresponds to 600-bin grids, which requires high computing power."713" For cach equation (for photous aud for particles). one can define an average boundary when the validity regions of both ucthods overlap: Finally. a combination of the two methods is achieved by solving the following equations: where iutegratious iu the iutegral part are performed oulv above the boundary euergy az, and momentum p, aud where the FP coefficieuts are computed as inteerals of the cross section only below these boundaries: Fig."," For each equation (for photons and for particles), one can define an average boundary when the validity regions of both methods overlap: Finally, a combination of the two methods is achieved by solving the following equations: where integrations in the integral part are performed only above the boundary energy $\omega_c$ and momentum $p_c$ and where the FP coefficients are computed as integrals of the cross section only below these boundaries: Fig."714 5 shows the steady photon and particle distributions for a iore realistic simulation., \ref{fig_steady} shows the steady photon and particle distributions for a more realistic simulation.715 Particles are injected with a mono-cnerectic distribution at Ligh energy (5=10?) at a constant rate (the colpactucss of which is set to inapPinPR)=10. where P is the injected power) and escape at a constant rate with the speed of light to allow for a steady state.," Particles are injected with a mono-energetic distribution at high energy $\gamma=10^2$ ) at a constant rate (the compactness of which is set to $l_{\rm in,e}=\sigma_T P /(m_ec^3R)=10$, where $P$ is the injected power) and escape at a constant rate with the speed of light to allow for a steady state."716 Soft photons are also injected with a black body spectrum of temperature kpT=3<10μωρο and a flix of compactiess {μιαςστfimcR)=1 (scoe.g.Belmontetal.2008.fordetaileddefiuitiousofthecompactuess pariuneters)..," Soft photons are also injected with a black body spectrum of temperature $k_BT=3\times10^{-4} m_ec^2$ and a flux of compactness $l_{{\rm in},\omega}=\sigma_T L_{\rm soft} /(m_ec^3R)=1$ \citep[see e.g.][for detailed definitions of the compactness parameters]{Belmont08}."717 We start with an eniptv svstem aud the code simmltancously evolves both cistributions with time uutil they reach a steady state., We start with an empty system and the code simultaneously evolves both distributions with time until they reach a steady state.718 The only process turned on is Compton scattering., The only process turned on is Compton scattering.719 Fig., Fig.720 δ shows the results of three kinds of rus where the contribution of Compton scattering to he evolution of the particle distribution was forced to be PCeed with the iutegral (several resolutions). the Fokker-Planck aud the combined approaches.," \ref{fig_steady} shows the results of three kinds of runs where the contribution of Compton scattering to the evolution of the particle distribution was forced to be treated with the integral (several resolutions), the Fokker-Planck and the combined approaches."721 The distributions ook very different., The distributions look very different.722 As expected. the integral approach fails to capture cticicntly the particle cooling for low resolution rus: he lower the resolution. the steeper the slope of the Heh euerev tail of the particle distribution.," As expected, the integral approach fails to capture efficiently the particle cooling for low resolution runs: the lower the resolution, the steeper the slope of the high energy tail of the particle distribution."723 These excess Heh euerev particles more effhcieutlv wp-scatter the soft photons aud the resulting spectra are harder., These excess high energy particles more efficiently up-scatter the soft photons and the resulting spectra are harder.724 Tn steady state. the total energy loss ust valance the total injected wer.," In steady state, the total energy loss must balance the total injected power."725" Power is supplied through rtides J,=10 and through photous: Jin=fins|line]l."," Power is supplied through particles $l_{{\rm in},e}=10$ and through photons: $l_{\rm in}=l_{\rm in,e}+l_{{\rm in},\omega}=11$."726 Energw is also lost both through particles aud photons., Energy is also lost both through particles and photons.727 The steady article distribution has ow deusitv 7=στ[ΗΝ2.3«10D so that the energy ost through particle escapes is rather small (ou.c 1) and mios of the CLOYSV escape as radiation.," The steady particle distribution has low density $\tau=\sigma_TR\int dN_e =2.3\times10^{-2}$ so that the energy lost through particle escapes is rather small $l_{\rm out,e}\approx 1$ ) and most of the energy escape as radiation."728 As numerical errors event particles from cooling as they should. the overall svstemi actually ealus energv artificially aud the total cuereyv loses are measured to be larger than the injected power: Jour=lassdlowe= 19.6.11.2.12.2. aud 11.[ from lower to higher erid resolution.," As numerical errors prevent particles from cooling as they should, the overall system actually gains energy artificially and the total energy loses are measured to be larger than the injected power: $l_{\rm out} = l_{\rm out,\omega}+l_{\rm out,e} =19.6, 14.2, 12.2$ , and $11.4$ from lower to higher grid resolution."729 The corresponding effective electron temperatures are Apt.=6.23.68.3.95. and 3.60nie? (seeEq.2.8.Coppi1992).," The corresponding effective electron temperatures are $k_BT_e=6.23, 4.68, 3.95$, and $3.60~m_ec^2$ \citep[see Eq. 2.8, ][]{Coppi92}."730. The Fokker-Plauck equation provides good energv conservation and the dlastua dDuamositv balances the injected power: Jour=11.0., The Fokker-Planck equation provides good energy conservation and the plasma luminosity balances the injected power: $l_{\rm out}=11.0$.731 However. euergy couservation does not guarantee accurate results and. siguificaut deviation is observed in he low energy part of the particle distribution. where theFokker-Plauck approxiuation is expected to fail.," However, energy conservation does not guarantee accurate results and significant deviation is observed in the low energy part of the particle distribution, where theFokker-Planck approximation is expected to fail."732 In the particular case presented. here. this has no effect on he cuiitted spectrum since the spectrun is dominated bv the Couptouisation by high," In the particular case presented here, this has no effect on the emitted spectrum since the spectrum is dominated by the Comptonisation by high"733Iu this case one of the six terms in the decomposed format is not independent owing to the trace-free property.,In this case one of the six terms in the decomposed format is not independent owing to the trace-free property.734 The Doppler patterus of the three waves can then be sumuned to create Doppler patterns for cach tensor element., The Doppler patterns of the three waves can then be summed to create Doppler patterns for each tensor element.735 Thus the full variance of the stochastic background can be sampled., Thus the full variance of the stochastic background can be sampled.736 As in the spherical harmonic case each term will be temporally modulated. and the quantity Jy. is formed by the square root of the sui of the squares of 5 independent terms.," As in the spherical harmonic case each term will be temporally modulated, and the quantity $h_{\rm rms}$ is formed by the square root of the sum of the squares of 5 independent terms."737 While the preceding subsection outlines approaches to detection of the CAW backeround using au array of pulsars. measurenieuts from a single object can establish anMant ou the backerouncd.," While the preceding subsection outlines approaches to detection of the GW background using an array of pulsars, measurements from a single object can establish an on the background."738 ? has stated the best limit at ullz frequencies using precision timing of PSR 01505|09 relative to the world’s best atomic time scale., \citet{Kaspi94} has stated the best limit at nHz frequencies using precision timing of PSR B1855+09 relative to the world's best atomic time scale.739 A second pulsar in their study. PSR B1937|21. was shown to be unstable ou loug time scales. an effect they attribute to internal structure of that ucutron star.," A second pulsar in their study, PSR B1937+21, was shown to be unstable on long time scales, an effect they attribute to internal structure of that neutron star."740 7. improved the limit using further statistical considerations., \citet{Thorsett96} improved the limit using further statistical considerations.741" At a typical frequency of 5 ullz (8 yr period) they couclide that the encrey density in gravitational radiation per logarithiuic frequency interval is less than ©,h?~6«107. where fin this expression is the ratio of IIubble's constant to 100 kin"," At a typical frequency of 5 nHz (8 yr period) they conclude that the energy density in gravitational radiation per logarithmic frequency interval is less than $\Omega_gh^2\sim 6\times 10^{-8}$, where $h$ in this expression is the ratio of Hubble's constant to 100 km $^{-1}$."742 Encrevo deusity scales quadratically with the time derivative of the metric strain., Energy density scales quadratically with the time derivative of the metric strain.743 Therefore the level of Oh?P that can be detected by pulsar timingB scales quadratically. with. the ris timing.+ residual.+ aud as T5 with the duration of the experiment Z. which is the inverse of the minima frequency sampled.," Therefore the level of $\Omega_gh^2$ that can be detected by pulsar timing scales quadratically with the rms timing residual $R$, and as $T^{-5}$ with the duration of the experiment $T$, which is the inverse of the minimum frequency sampled."744 Receutly ? have extended the Naspi study of PSR D1855|09 by more than doubling the experiment duration to l? v. The new upper liit on cherey density is roughly au order of iuagnitude lower at frequencies near 5 ullz., Recently \citet{LommenBackerAAS} have extended the Kaspi study of PSR B1855+09 by more than doubling the experiment duration to 17 y. The new upper limit on energy density is roughly an order of magnitude lower at frequencies near 5 nHz.745 A full report on this work is in preparation., A full report on this work is in preparation.746 An approximate statement of the Kaspi-Louunen limit ou characteristic strain ds given in Fieure 8.. which shows that the measurements are approaching a level of significance given our current model of the Universe.," An approximate statement of the Kaspi-Lommen limit on characteristic strain is given in Figure \ref{fig:strainspec}, which shows that the measurements are approaching a level of significance given our current model of the Universe."747 An alternate wav of stating this is that the measurements are placing useful constraints on the uncertain parameters in our model., An alternate way of stating this is that the measurements are placing useful constraints on the uncertain parameters in our model.748" The ratio of the pulsar detection level to the characteristic strain spectrum level scales as T1,", The ratio of the pulsar detection level to the characteristic strain spectrum level scales as $T^{13/6}$.749" The Pulsar Timing Array experiment. which will use both existing aud new data sets, cai improve ou the ?— result iu three obvious wavs: (a) smaller timune residuals owing to combined data sets; now and uperaced telescopes and better data acquisition techniques (b) more objects which both provide the capability of actual detection as opposed to upper limits aud. if sufficiently numerous. provide a “root N7 advantage: aud (ο) longer experiment duration."," The Pulsar Timing Array experiment, which will use both existing and new data sets, can improve on the \citet{Kaspi94} result in three obvious ways: (a) smaller timing residuals owing to combined data sets, new and upgraded telescopes and better data acquisition techniques; (b) more objects which both provide the capability of actual detection as opposed to upper limits and, if sufficiently numerous, provide a “root N” advantage; and (c) longer experiment duration."750 In Figure δ we show a reasonable goal for the future: 200 us timing precision over cight vears., In Figure \ref{fig:strainspec} we show a reasonable goal for the future: 200 ns timing precision over eight years.751 Current imieasurenment seres are already: achieving this level of precision for a few objects., Current measurement series are already achieving this level of precision for a few objects.752 We have calculated the spectrum of the stochastic background of gravitational radiation from the Universe of coalescing binary black holes iu the centers of galaxies with simple paraieterizatious of the current uncertaiuties., We have calculated the spectrum of the stochastic background of gravitational radiation from the Universe of coalescing binary black holes in the centers of galaxies with simple parameterizations of the current uncertainties.753 This is followed by a discussion of the influence of the stochastic background ou precision ήλιο nieasureinenuts of pulsars which includes upper limits on the backeround and use of au array of pulsars for direct detection., This is followed by a discussion of the influence of the stochastic background on precision timing measurements of pulsars which includes upper limits on the background and use of an array of pulsars for direct detection.754 This work was motivated by improvements both in our knowledge of the preseut-day massive black hole population aud the rate of galaxy merecrs as well as new pulsar lueasurenmoents., This work was motivated by improvements both in our knowledge of the present-day massive black hole population and the rate of galaxy mergers as well as new pulsar measurements.755The solution to the set of nine coupled partial differential equations (11-19) requires nie separate boundary conditions.,The solution to the set of nine coupled partial differential equations (11-19) requires nine separate boundary conditions.756" Eight are applied al the photosphere (svhere the optical depth7,4, = 2/3) and one is applied at (he crust-core interface.", Eight are applied at the photosphere (where the optical depth$\tau_{\mathrm{out}}$ = 2/3) and one is applied at the crust-core interface.757 The outer boundary. conditions for equations (11-13) are r=H. m=AL. and ).," The outer boundary conditions for equations (11-13) are $r = R$, $m = M$, and $\Phi = (c^{2}/2) \ln(1-2 G M / R c^{2})$ ."758 The outer boundary conditions for the hydrogen. helium. and CNO mass Iraction evolution equations (17-19) are given by (he composition of the accreting gas. such that XY=Naa. Y= You. and Zexo=Ζονοωμ. respectively.," The outer boundary conditions for the hydrogen, helium, and CNO mass fraction evolution equations (17-19) are given by the composition of the accreting gas, such that $X = X_{\mathrm{out}}$, $Y = Y_{\mathrm{out}}$ , and $Z_{\mathrm{CNO}} = Z_{\mathrm{CNO, out}}$ , respectively."759 The value for X at the photosphere. X4. is obtained approximately by taking (he opacity at the photosphere to be given by electron scattering.," The value for $\Sigma$ at the photosphere, $\Sigma_{\mathrm{out}}$, is obtained approximately by taking the opacity at the photosphere to be given by electron scattering."760 Thus. X=Tou/(O-2(1+NX44)) gem7.," Thus, $\Sigma_{\mathrm{out}} = 761\tau_{\mathrm{out}}/(0.2 (1 + X_{\mathrm{out}}))$ $\mathrm{g\,cm}^{-2}$."762 The outer boundary condition for equation (14) is then given by The method we use to determine the outer boundary. condition lor equation (15). the outward [lux at the stellar surface. £44. is explained in Paper I. To summarize. we assume a given value of Foy which. when added (o the gravitational energy [hix due to accretion. also delines a surface temperature Toy.," The outer boundary condition for equation (14) is then given by The method we use to determine the outer boundary condition for equation (15), the outward flux at the stellar surface $F_{\mathrm{out}}$, is explained in Paper I. To summarize, we assume a given value of $F_{\mathrm{out}}$ which, when added to the gravitational energy flux due to accretion, also defines a surface temperature $T_{\mathrm{out}}$."763 We then integrate the dillerential equations ancl compare the resulting temperature al the bottom. the crust-core interface. (o the required temperature inner boundary condition.," We then integrate the differential equations and compare the resulting temperature at the bottom, the crust-core interface, to the required temperature inner boundary condition."764 We adjust. Foy and repeat the integration until the temperature boundary condition at (he bottom is satisfied to high accuracy., We adjust $F_{\mathrm{out}}$ and repeat the integration until the temperature boundary condition at the bottom is satisfied to high accuracy.765 What makes our new method superior to that of Paper Lis that we now integrate all (he wav to the stellar core (pjc2x10! gem7. where pj denotes the rest mass density).," What makes our new method superior to that of Paper I is that we now integrate all the way to the stellar core $\rho_{0} \approx 2 \times 10^{14}$ $\mathrm{g\,cm^{-3}}$, where $\rho_{0}$ denotes the rest mass density)."766 Previously. we integrated only a couple of diffusion depths into the star. bul we were unable to integrate past the neutron drip point (pj24x10! ecm 7).," Previously, we integrated only a couple of diffusion depths into the star, but we were unable to integrate past the neutron drip point $\rho_{0} \approx 4 \times 10^{11}$ $\mathrm{g\,cm^{-3}}$ )."767 The long recurrence times of superbursts make the old method inadequate., The long recurrence times of superbursts make the old method inadequate.768 For many caleulations. the thermal diffusion depth is deeper than the crust-core interlace. so integration (o the core is necessary.," For many calculations, the thermal diffusion depth is deeper than the crust-core interface, so integration to the core is necessary."769 For a given calculation. we employ one of (wo methods to determine the temperature inner boundary condition lor equation (16).," For a given calculation, we employ one of two methods to determine the temperature inner boundary condition for equation (16)."770 In our first method. we assume (hat we know (he rate of neutrino emission from (he core; we use (wo prescriptions for this. either mocilied URCA reactions (Friman&Maxwell1979:YakovlevLevenfish1995) or pionic reactions (Maxwelletal. 1971).," In our first method, we assume that we know the rate of neutrino emission from the core; we use two prescriptions for this, either modified URCA reactions \citep{FM79,YL95} or pionic reactions \citep{MBCDM77}."771. Integrating to the crust-core interface gives values for the proper temperature 7. areal radius r. interior gravitational mass m. ancl energy [flux F.," Integrating to the crust-core interface gives values for the proper temperature $T$, areal radius $r$, interior gravitational mass $m$, and energy flux $F$ ."772 The energy flux. which is directedinwardat the interface CF« 0). must be balanced by the neutrino cooling of the core.," The energy flux, which is directedinwardat the interface $F < 0$ ), must be balanced by the neutrino cooling of the core."773"Using the neutrino Iuminosiüies L,(1.T) from","Using the neutrino luminosities $L_{\nu}(m,T)$ from"774moderate and high redshifts.,moderate and high redshifts.775 We expect these to be invaluable probes of large-scale structure., We expect these to be invaluable probes of large-scale structure.776 We thank Emil Lene and Jamie Stevens for their help. the ATLAS team ancl Alark 3irkinshaw for many fruitful discussions. and an anonymous referee whose comments helped improve the manuscript.," We thank Emil Lenc and Jamie Stevens for their help, the ATLAS team and Mark Birkinshaw for many fruitful discussions, and an anonymous referee whose comments helped improve the manuscript."777 ALYAL acknowledges the support of an Australian Postgraduate Award as well as Postgraduate Scholarships from AAO and. ATNE., MYM acknowledges the support of an Australian Postgraduate Award as well as Postgraduate Scholarships from AAO and ATNF.778 We thank the stall at AAO and ATCA for making these observations possible., We thank the staff at AAO and ATCA for making these observations possible.779 The ATCA is part of the Australia Telescope. which is funded by the Commonwealth of Australia [or operation as a National Facility managed by CSIRO.," The ATCA is part of the Australia Telescope, which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO."780 This research has also macle use of NASVs Astrophysics Data System., This research has also made use of NASA's Astrophysics Data System.781radiation.,radiation.782 However. since far-infrared telescopes are relatively insensitive. the m flux density is often used as an imperfect proxy for the FIR flux density (Appletonetal.2004).," However, since far-infrared telescopes are relatively insensitive, the $\mu$ m flux density is often used as an imperfect proxy for the FIR flux density \citep{Appleton2004}."783". While the um flux density 15 subject to other emission mechanisms than warm dust. especially at high redshift. it remains clear (Seymouretal. 2008)) that a high value of the radio-24um flux density ratio indicates the presence of an AGN We note that since. all. our IFRS targets have Siacu, 2lmmJy and are undetected not only at jm but also at 244m. with a 5c limit of Sayan= 2524y. their qoi-log(S»1,44/5204)) Values are lower than pd Jy j2—0.60."," While the $\mu$ m flux density is subject to other emission mechanisms than warm dust, especially at high redshift, it remains clear \citealt{Seymour2008}) ) that a high value of the $\mu$ m flux density ratio indicates the presence of an AGN We note that since all our IFRS targets have $S_{\rm 1.4\,GHz}>$ mJy and are undetected not only at $\mu$ m but also at $\mu$ m, with a $\sigma$ limit of $S_{\rm 24\,\mu m}=252\,\mu$ Jy, their $_{24}$ $S_{\rm 24\,\mu m}$ $S_{\rm 20\,cm}$ ) values are lower than $\mu$ $\mu$ $-0.60$."784" The radio-IR relation for— star forming galaxies has been determined to yield q»,20.84250.28 (Appletonetal. 2004)). so all IFRS have a more than tenfold radio excess over this relation."," The radio-IR relation for star forming galaxies has been determined to yield $_{24}$ $\pm$ 0.28 \citealt{Appleton2004}) ), so all IFRS have a more than tenfold radio excess over this relation."785" The common interpretation of this is that synchrotron radiation is being produced without IR emission, which then is regarded às evidence for non-thermal emission from an AGN."," The common interpretation of this is that synchrotron radiation is being produced without IR emission, which then is regarded as evidence for non-thermal emission from an AGN."786" Therefore. all IFRS can be classified as AGN based on qo, alone."," Therefore, all IFRS can be classified as AGN based on $_{24}$ alone."787 There are two main tools for finding radio galaxies at high redshifts., There are two main tools for finding radio galaxies at high redshifts.788 The so-called z-v relation is derived from. the observation that steep-spectrum radio galaxies tend to have higher redshifts (DeBreucketal.2002:Klamer 2006)).," The so-called $\alpha$ relation is derived from the observation that steep-spectrum radio galaxies tend to have higher redshifts \citealt{DeBreuck2002,Klamer2006}) )."789 Many high-redshift radio galaxies (HzRG) have been found exploiting this relation., Many high-redshift radio galaxies (HzRG) have been found exploiting this relation.790 The other tool is the K-z relation (Lilly&Longair 1984)) which states that the logarithm of an object's redshift is proportional to the near-IR K-band magnitude at um. A combination of these two criteria can be used as an efficient filter for HzRG., The other tool is the K-z relation \citealt{Lilly1984}) ) which states that the logarithm of an object's redshift is proportional to the near-IR K-band magnitude at $\mu$ m. A combination of these two criteria can be used as an efficient filter for HzRG.791 We used the widely-usedSpitzer uim band as a proxy for observations., We used the widely-used $\mu$ m band as a proxy for K-band observations.792 It has been argued previously (Middelberg 2008b.. Garn&Alexander 2008.. Huynhetal. 2010.. Norrisetal. 2010)) that the SEDs of IFRS are compatible with those of high-redshift AGN.," It has been argued previously \citealt{Middelberg2008c}, \citealt{Garn2008}, \citealt{Huynh2010}, \citealt{Norris2010}) ) that the SEDs of IFRS are compatible with those of high-redshift AGN."793 We therefore compiled $20/S3.6 values for the sample of 70 high-redshift radio galaxies (HzRG) by Seymouretal.(2007).. to compare them to the general radio population and the IFRS.," We therefore compiled S20/S3.6 values for the sample of 70 high-redshift radio galaxies (HzRG) by \cite{Seymour2007}, to compare them to the general radio population and the IFRS."794 Seymouretal.(2007) selected from the literature radio galaxies above a redshift of one with a 3GGHz luminosity of more than 10°° WW/Hz. and supplemented their sample with new or archivalSpitzer data.," \cite{Seymour2007} selected from the literature radio galaxies above a redshift of one with a GHz luminosity of more than $^{26}$ W/Hz, and supplemented their sample with new or archival data."795 IFRS are selected based on the ratio of the radio and IR flux densities., IFRS are selected based on the ratio of the radio and IR flux densities.796 Sources in the ATLAS radio catalogues typically have flux densities exceeding 10044Jy. (5.07). whereas the co-spatial 4m observations have | sensitivities of around uJy.," Sources in the ATLAS radio catalogues typically have flux densities exceeding $\mu$ Jy $\sigma$ ), whereas the co-spatial $\mu$ m observations have $\sigma$ sensitivities of around $\mu$ Jy."797" Therefore a detected radio source with no catalogued or visibly identifiable counterpart (Le. S16,<307= 34dy) typically has S20/853.6230."," Therefore a detected radio source with no catalogued or visibly identifiable counterpart (i.e., $S_{\rm 3.6\,\mu798 m}<3\,\sigma=3\,\mu$ Jy) typically has $>$ 30."799 However. the median $20/S3.6 ratio of the IFRS in our sample is 2330. some two orders of magnitude larger than this minimum.," However, the median S20/S3.6 ratio of the IFRS in our sample is 2330, some two orders of magnitude larger than this minimum."800 Hence. while sources with S20/83.6»x50 could be starbursts or AGN-driven. at $20/S3.6 exceeding a few hundred are likely to be similar to the HzRG.," Hence, while sources with $>\approx 50$ could be starbursts or AGN-driven, at S20/S3.6 exceeding a few hundred are likely to be similar to the HzRG."801 The median S20/S3.6 ratio of all sources in. the ATLAS/ELAIS field (with detections in both the radio and IR bands) is 6.12. but the distribution extends over five orders of magnitude.," The median S20/S3.6 ratio of all sources in the ATLAS/ELAIS field (with detections in both the radio and IR bands) is 6.12, but the distribution extends over five orders of magnitude."802 With ratios between approximately 500. and 10000. the IFRS clearly are at and beyond the high tail of the distribution of the general source population.," With ratios between approximately 500 and 10000, the IFRS clearly are at and beyond the high tail of the distribution of the general source population."803 The median S20/S3.6 of the HzRG by Seymouretal.(2007) 1s 6550. significantly larger than in the general source population. and closer to the IFRS median.," The median S20/S3.6 of the HzRG by \cite{Seymour2007} is 6550, significantly larger than in the general source population, and closer to the IFRS median."804 However. HzRG are much brighter — they present high luminosities and have been gathered from surveys covering much larger areas.," However, HzRG are much brighter – they present high luminosities and have been gathered from surveys covering much larger areas."805 In contrast. IFRS are fainter (by a factor of around 50 if they are assumed to be at the same redshifts as HZRG) and have a surface density of around 10ddeg7*. whereas that of HzRG is ddeg7? — approximately four orders of magnitude smaller.," In contrast, IFRS are fainter (by a factor of around 50 if they are assumed to be at the same redshifts as HzRG) and have a surface density of around $^{-2}$, whereas that of HzRG is $^{-2}$ – approximately four orders of magnitude smaller."806 A histogram of $20/S3.6 of the general radio source population. the HzRG and the IFRS is shown in Figure 3..," A histogram of S20/S3.6 of the general radio source population, the HzRG and the IFRS is shown in Figure \ref{fig:radio-ir}."807 We stress that since for IFRS $20/S3.6 has been calculated using upper limits on the 3.6;m flux density. the true ratio is expected to be larger.," We stress that since for IFRS S20/S3.6 has been calculated using upper limits on the $\mu$ m flux density, the true ratio is expected to be larger."808 Given the stacking experiments by Norrisetal.(2010).. who find that the median flux density of IFRS μπι counterparts is less than Jy. we point out that the $20/S3.6 ratios of IFRS could be as much as a factor of 5 higher than estimated here.," Given the stacking experiments by \cite{Norris2010}, who find that the median flux density of IFRS $\mu$ m counterparts is less than $\mu$ Jy, we point out that the S20/S3.6 ratios of IFRS could be as much as a factor of 5 higher than estimated here."809 This would shift the IFRS in Figure to the right by log(5)20.7 (illustrated in the lower panel of Figure 3))., This would shift the IFRS in Figure \ref{fig:radio-ir} to the right by log(5)=0.7 (illustrated in the lower panel of Figure \ref{fig:radio-ir}) ).810 The median $20/S3.6 of the IFRS then increases to 11650. almost two times the HzRG median.," The median S20/S3.6 of the IFRS then increases to 11650, almost two times the HzRG median."811 Norrisetal.(2010). also show that IFRS are consistent with radio-loud AGN at redshifts greater than 3., \cite{Norris2010} also show that IFRS are consistent with radio-loud AGN at redshifts greater than 3.812 They used observations from the Warm Mission (5c limits of uJy. 5 times deeper than theSpitzer SWIRE data) and the published ATLAS radio catalogues.," They used observations from the Warm Mission $\sigma$ limits of $\mu$ Jy, 5 times deeper than the SWIRE data) and the published ATLAS radio catalogues."813 All of their IFRS remain undetected even with these new observations., All of their IFRS remain undetected even with these new observations.814 They argue that. since the $20/S3.6 ratios are of the same order of magnitude as the HzRG by Seymouretal.(2007).. and since the um flux densities of HzRG drop below theSpitzer detection limit when at redshifts larger than 3. IFRS are likely to be at similarly high redshifts.," They argue that, since the S20/S3.6 ratios are of the same order of magnitude as the HzRG by \cite{Seymour2007}, and since the $\mu$ m flux densities of HzRG drop below the detection limit when at redshifts larger than 3, IFRS are likely to be at similarly high redshifts."815 Huynhetal.(2010)— analysed four IFRS in the GOODS/CDFS. which are located in a region for which very deep data had recently become available.," \cite{Huynh2010} analysed four IFRS in the GOODS/CDFS, which are located in a region for which very deep data had recently become available."816 They find counterparts for only two of the IFRS. CS446. and CS5006. yielding S20/83.6 ratios of 51.2 and 30.9. respectively.," They find counterparts for only two of the IFRS, CS446, and CS506, yielding S20/S3.6 ratios of 51.2 and 30.9, respectively."817 The two IFRS still undetected with the newSpitzer data. CS283 and CS415. have $20/S3.6 ratios of > 137 and >2520. respectively.," The two IFRS still undetected with the new data, CS283 and CS415, have S20/S3.6 ratios of $>$ 137 and $>$ 2520, respectively."818 CS415 has a radio spectral index of —1.1 but was not included in our sample because it was deemed too faint for successful GGHz and GGHz observations., CS415 has a radio spectral index of $-1.1$ but was not included in our sample because it was deemed too faint for successful GHz and GHz observations.819 From the histogram of $20/S3.6 it becomes clear that there is more overlap between IFRS and HzRG than between IFRS and the general radio source population., From the histogram of S20/S3.6 it becomes clear that there is more overlap between IFRS and HzRG than between IFRS and the general radio source population.820 IFRS appear to have steep radio spectra and very faint IR flux densities. both of which indicate that they are high-redshift AGN.," IFRS appear to have steep radio spectra and very faint IR flux densities, both of which indicate that they are high-redshift AGN."821"hierarchical models, or at least the one considered here, tend to produce too many compact galaxies.","hierarchical models, or at least the one considered here, tend to produce too many compact galaxies."822" However, we find that such a discrepancy is not as strong as claimed before, and we also add that the difference is morphology-dependent, i.e., significantly reducing with increasing B/T. On the other hand, when moving to more spheroid-dominated galaxies, the model tends to produce an higher fraction of galaxies with R.=3 kpc, predicting up to a factor of ~10 higher number density of super-large galaxies (with Rez30 kpc)."," However, we find that such a discrepancy is not as strong as claimed before, and we also add that the difference is morphology-dependent, i.e., significantly reducing with increasing B/T. On the other hand, when moving to more spheroid-dominated galaxies, the model tends to produce an higher fraction of galaxies with $\gtrsim 3$ kpc, predicting up to a factor of $\sim 10$ higher number density of super-large galaxies (with $\gtrsim 30$ kpc)."823" This overproduction of large galaxies with mass around ~ iis one of the major 1071?causes, together with the overproduction of compact and massive galaxies, for the flattening of the size-mass relation seen in Figure 3.."," This overproduction of large galaxies with mass around $\sim 10^{10}$ is one of the major causes, together with the overproduction of compact and massive galaxies, for the flattening of the size-mass relation seen in Figure \ref{fig|SizeMassRelation}."824 Figures 4 show the corresponding comparison between model predictions and SDSS data on the SMF for the Ον sample (panel b)) and the ? sample (panel d))., Figures \ref{fig|Models} show the corresponding comparison between model predictions and SDSS data on the SMF for the $C_r$ sample (panel ) and the \citet{Hyde09a} sample (panel ).825" It is apparent that the model provides a poorer match to the SMF, irrespective of the sample considered."," It is apparent that the model provides a poorer match to the SMF, irrespective of the sample considered."826" More noticeably, at variance with the data the model predicts a “bump” in the number density of early-type galaxies around Maro1.5x10!°Mo,, and falls short by a factor of ~2 in producing enough galaxies with mass Metar>,10''Mo.."," More noticeably, at variance with the data the model predicts a “bump” in the number density of early-type galaxies around $\sim 1.5\times 10^{10}$, and falls short by a factor of $\sim 2$ in producing enough galaxies with mass $\gtrsim 10^{11}$."827" We have checked that the model by ?,, possibly due to the different treatment of dynamical friction timescales (see, e.g., ??)), indeed produces a flatter"," We have checked that the model by \citet{DeLucia07}, possibly due to the different treatment of dynamical friction timescales (see, e.g., \citealt{Parry08,Seek09}) ), indeed produces a flatter"828of these processes can be straighiforwardly added. (e.g... magnetic fields as in PDO3b. or radiative processes as in Proga 2007).,"of these processes can be straightforwardly added (e.g., magnetic fields as in PB03b, or radiative processes as in Proga 2007)."829 Dherelore. (his work could serve as a good reference point to analvze and interpret more complete ancl complex simulations (e.g.. we already reran some of the models [rom this paper including magnetic fields. Moscibrodzka ancl Proga. in preparation).," Therefore, this work could serve as a good reference point to analyze and interpret more complete and complex simulations (e.g., we already reran some of the models from this paper including magnetic fields, Moscibrodzka and Proga, in preparation)."830 ACKNOWLEDGMENTS: We thank Bozena Czerny and. Marek Abramowicz for very useful commentis., ACKNOWLEDGMENTS: We thank Bozena Czerny and Marek Abramowicz for very useful comments.831 We acknowledge support provided bv the Chandra: award TMT-8008X. issued bv (the Chandra A-Rav Observatory. Center. which is operated by the Smithsonian Astrophysical Observatory [or and on behalf of NASA under contract NÀS8-39073.," We acknowledge support provided by the Chandra award TM7-8008X issued by the Chandra X-Ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-39073."832 M.M also acknowledges supported in part by grant. 1P03D. 003 29 of the Polish State Committee for Scientific Research (XBN)., M.M also acknowledges supported in part by grant 1P03D 008 29 of the Polish State Committee for Scientific Research (KBN).833 While D.P. acknowledges support from NASA under ATP erant NNGOSQDBO6SQG., While D.P. acknowledges support from NASA under ATP grant NNG05GB68G.834adopted for Sagittarius).,adopted for Sagittarius).835 Given that substantial realisation to realisation [luctuations are expected. in the. properties of the more massive subhalos. there is surprisingly &ood agreement between the kinematics of the observed satellites and those predicted by our ACDAL simulation.," Given that substantial realisation to realisation fluctuations are expected in the properties of the more massive subhalos, there is surprisingly good agreement between the kinematics of the observed satellites and those predicted by our $\Lambda$ CDM simulation."836 For Fornax and. Draco. more detailed. kinematic data have been published and allow a closer. comparison.," For Fornax and Draco, more detailed kinematic data have been published and allow a closer comparison."837 In Figure 2 we reproduce velocity dispersion profiles. from Mateo (1997) for Fornax. and from WKlevna (2002) [or Draco. ancl we overplot the predictions of the above equations for a number of our more massive subhalos.," In Figure 2 we reproduce velocity dispersion profiles from Mateo (1997) for Fornax, and from Kleyna (2002) for Draco, and we overplot the predictions of the above equations for a number of our more massive subhalos."838 From this figure it is clear that C:A2 not. only predicts, From this figure it is clear that GA2 not only predicts839A[ultipole expausion is limited by the monopole term.,Multipole expansion is limited by the monopole term.840 A tolerance paraiucter 0 (opening angle”) which controlled the force computation from distant particles was set as Ü.T.," A tolerance parameter $\theta$ (""opening angle"") which controlled the force computation from distant particles was set as 0.7."841 We considered onlv the behavior of the stellar conrponeut of galaxies (elliptical galaxies usually contain a small amount of eas)., We considered only the behavior of the stellar component of galaxies (elliptical galaxies usually contain a small amount of gas).842 The nunber of particles used iu our numerical simulations ranged fromi ος=20000 to Nga=DOOO00 per salaxyv.," The number of particles used in our numerical simulations ranged from $N_{tot} = 20\,000$ to $N_{tot} = 50\,000$ per galaxy."843" In this case we managed to substantially suppress the effects of pair relaxation aud to trace the evolution of iiergiug galaxies ou time scales up to £z0,5<LO years.", In this case we managed to substantially suppress the effects of pair relaxation and to trace the evolution of merging galaxies on time scales up to $t \approx 0.5\times10^9$ years.844 The timestep for the simulations used was as At=10° vears., The timestep for the simulations used was as $\Delta t = 10^6$ years.845 The softening leugth € was taken as <0.1 of the particle distance of the homogoucous state., The softening length $\epsilon$ was taken as $< 0.1$ of the inter-particle distance of the homogoneous state.846 We considered two models for cucounting galaxies., We considered two models for encounting galaxies.847 Oue of them is Plinuner’s spherically-sviuimetric model where M is the galaxy ass aud ap is a scale length., One of them is Plummer's spherically-symmetric model where $M$ is the galaxy mass and $a_{pl}$ is a scale length.848 Iu some experiments galaxies are inodeled dy the potential-density pair proposed by Heruquist (1990) for spherical galaxies It is well known that both models are described by a distribution function in an analytical form and. in the absence of uunierical errors and dvuamical stabilities. remain fine-stationarv.," In some experiments galaxies are modeled by the potential-density pair proposed by Hernquist (1990) for spherical galaxies It is well known that both models are described by a distribution function in an analytical form and, in the absence of numerical errors and dynamical instabilities, remain time-stationary."849" Results are preseuted in the following system of mits: eravitational constaut Go= I. the galaxy mass AM.=1. the tal energy of a sphere E=Lil (b= 3xGAP61a, auda,=37/16 for Plunuucr’s sphere: E=GAPLay and ay,=1/3 for Heoruquist's sphere)."," Results are presented in the following system of units: gravitational constant $G = 1$ , the galaxy mass $M = 1$, the total energy of a sphere $E= -1/4$ $E= - 3 \pi G M^2/ 64 a_{pl}$ and $a_{pl} = 3 \pi / 16$ for Plummer's sphere; $E= - G M^2/ 12 a_{hq}$ and $a_{hq} = 1/3$ for Hernquist's sphere)."850" Scaled to plivsical values appropriate for a typical elliptical galaxy. ie. M=LOM and halfiuass radius (jjjD=3 kpe (37229LBL, - for ον sphere. πο72.lle), - for IHeruquist's ""]iere). units of distance. time and velocity are 3.73 kpc. 10.3 Mya. 315.3 kan 1 respectively."," Scaled to physical values appropriate for a typical elliptical galaxy, i.e. $M = 10^{11}$ and half-mass radius $r_{1/2} = 3$ kpc $r_{1/2}\approx1.31 a_{pl}$ - for Plummer's sphere, $r_{1/2}\approx2.41 a_{hq}$ - for Hernquist's sphere), units of distance, time and velocity are 3.73 kpc, 10.3 Myr, 345.3 km $^{-1}$ respectively."851 We specified the initial distance between two equal-lnass galaxies as R=37.3 kpe aud chose the initial relative velocity in the range V—77.3103.6 kan st., We specified the initial distance between two equal-mass galaxies as $R = 37.3$ kpc and chose the initial relative velocity in the range $V = 77.3-103.6$ km $^{-1}$.852 As a result we had a close eucounter with mereine (the distance of the first closest approach was 5.2 kpc) and a distant eucounter without mereing (nu this case the ninimuiun galaxy separation was 10.3 kpe)., As a result we had a close encounter with merging (the distance of the first closest approach was 5.2 kpc) and a distant encounter without merging (in this case the minimum galaxy separation was 10.3 kpc).853 Fig.3 preseuts some “snapshots” of a close encouuter. showing the initial condition (f= 0). the configuration near the first maxima overlap (£= 30). the configuration shortly before the finalamereer (f= 31). and a merger state (t= 10).," Fig.3 presents some ”snapshots” of a close encounter, showing the initial condition $t=0$ ), the configuration near the first maximum overlap $t=30$ ), the configuration shortly before the final merger $t=34$ ), and a merger state $t=40$ )."854 A contour map of two interacting Plunuuers spheres are plotted in Fie.1., A contour map of two interacting Plummer's spheres are plotted in Fig.4.855 Some changes iu morploloey of model galaxies become noticeable ouly at the final PAages of encouuter (f=30 31)., Some changes in morphology of model galaxies become noticeable only at the final stages of encounter $t=30-34$ ).856 There are real objectswhich are very similar to these interaction stages of model ealaxies. for example NGC 1587/1588. NCC 7236/7237 (Dorue Ioesse 19885).," There are real objectswhich are very similar to these interaction stages of model galaxies, for example NGC 1587/1588, NGC 7236/7237 (Borne Hoessel 1988)."857a Dirac's delta. in agreement with the large—5 limit in Section 2.1.,"a Dirac's delta, in agreement with the $\gamma$ limit in Section 2.1."858 However. the dowustream pitch angle distributions (in their Fig.," However, the downstream pitch angle distributions (in their Fig."859 3b) agree well with mine. but not perfectly.," 3b) agree well with mine, but not perfectly."860 Gallant. Achterberg ancl Wirk (1998) have elaimed that there is a small error in Bednarz aud Ostrowksi's distributions.," Gallant, Achterberg and Kirk (1998) have claimed that there is a small error in Bednarz and Ostrowksi's distributions."861 As a matter of [act. mmy distribution (Fig.," As a matter of fact, my distribution (Fig."862 2) agrees much better with Callaut alLss and Ixirk aud Schneiders (1987) than Beduarz aud Ostrowski's. despite the very sinall shock Lorentz [actors of these two papers (>=2.3 aud >=5. respectively).," 2) agrees much better with Gallant s and Kirk and Schneider's (1987) than Bednarz and Ostrowski's, despite the very small shock Lorentz factors of these two papers $\gamma = 2.3$ and $\gamma = 5$, respectively)."863 Possibly. tle small error in question may even explain the (stall)," Possibly, the small error in question may even explain the (small!)"864 discrepauey between the two values of f., discrepancy between the two values of $k$.865 A limitation applies to the claim of universality of Eqs. δ..," A limitation applies to the claim of universality of Eqs. \ref{up},"866 LL and 23:: | neglected any process altering the particles’ energy during the scattering., \ref{incomplete} and \ref{final}: I neglected any process altering the particles' energy during the scattering.867 Clearly. the results of this paper ouly apply in the limit ap/pS1. where dp is the typical momentum trausfer in each scattering event.," Clearly, the results of this paper only apply in the limit $\delta\!p/p \la 8681$, where $\delta\!p$ is the typical momentum transfer in each scattering event."869 Iu the large momento limit cousklered here. it seems uulikely that this constraint may be violated.," In the large momentum limit considered here, it seems unlikely that this constraint may be violated."870 Lastly. a comment ou tlie assumed depencdence xp* of the distribution fuuctiou upou particle momenta is iu order.," Lastly, a comment on the assumed dependence $\propto p^{-s}$ of the distribution function upon particle momenta is in order."871 It cau be seeu [rom Eq., It can be seen from Eq.872 1. that such a dependeuce is required by this equation., \ref{main} that such a dependence is required by this equation.873 To see this. let us make the usual assumption that D is homogeneous of degree —r in p.Le... DG.p)—q(ii)p .," To see this, let us make the usual assumption that $D$ is homogeneous of degree $-r$ in $p$, $D(\mu, p) = q(\mu) p^{-r}$ ."874 Then by defining a new variable 2=z/p. we see that the form assumed by Eq.," Then by defining a new variable $\hat{z} \equiv z/p^r$, we see that the form assumed by Eq."875 1l alter this change of variable is identical to the original one. except that uow p las altogether disappeared.," \ref{main}876 after this change of variable is identical to the original one, except that now $p$ has altogether disappeared."877 At large 2(£e... far downstream). f—[x= constant. aud there is no p-cepencence.," At large $z$, far downstream), $f 878\rightarrow f_\infty =$ constant, and there is no $p$ –dependence."879 This paradox is solved by noticing that the real problem to be solved involves both scatteriug (= Fermi acceleration) and injection., This paradox is solved by noticing that the real problem to be solved involves both scattering (= Fermi acceleration) and injection.880 Lu this case. a typical injection uiomenutum po arises uaturally. and the dimeusional problem discussed above is naturally solved: we must have f=f(....p/po....) where the clots indicate all other parameters.," In this case, a typical injection momentum $p_0$ arises naturally, and the dimensional problem discussed above is naturally solved: we must have $f = f(...,p/p_0,...)$ where the dots indicate all other parameters."881 In the limit of py—0. f tend to a coustant idependent of py as is always assumed. but tends instead to zero as f—(py/p)>.," In the limit of $p_0 882\rightarrow 0$, $f$ tend to a constant independent of $p_0$ as is always assumed, but tends instead to zero as $f \rightarrow (p_0/p)^s$."883 Problems of this sort. though[un rare iu ΣΕ are common in lycdrocdyuamics. where they are called self-iiinilar 'oblems of the secoud kind (Zeldovich 1956).," Problems of this sort, though rare in astrophysics, are common in hydrodynamics, where they are called self–similar problems of the second kind (Zel'dovich 1956)."884 They rauge from the deceptively simple laminar low of au ideal fluid plast an iufiuite wedge (Laudau aud. Lifshitz 1987) to the illumiuating case ‘the filtration in an elasto-plastic porous imecdiuu (Bareublatt 1996)., They range from the deceptively simple laminar flow of an ideal fluid plast an infinite wedge (Landau and Lifshitz 1987) to the illuminating case of the filtration in an elasto–plastic porous medium (Barenblatt 1996).885 It is remarkable that. iu he problem at hzuxl. no such complication is necessary to fix the all-important index s. vet the »owerful methods of intermediate asyinptotics (Barenblatt 1996) aud the renormalization group (Goldeufekl 1992) cau be brought to bear on the interinediate ~ cases. where no easy limiting solution can be foul.," It is remarkable that, in the problem at hand, no such complication is necessary to fix the all–important index $s$, yet the powerful methods of intermediate asymptotics (Barenblatt 1996) and the renormalization group (Goldenfeld 1992) can be brought to bear on the intermediate $\gamma$ cases, where no easy limiting solution can be found."886 Iu short. what I have done in this paper is to show that the spectrum of non-thermal particlesaccelerated at relativistic shocks is universal. in the seuse that tlie energy spectral index &. aud the angular distributions in both the upstream and. dowustream [rames (Eqs. 8.. LL. 23..," In short, what I have done in this paper is to show that the spectrum of non–thermal particlesaccelerated at relativistic shocks is universal, in the sense that the energy spectral index $k$, and the angular distributions in both the upstream and downstream frames (Eqs. \ref{up}, \ref{incomplete}, \ref{final},"887 and Fig., and Fig.888 2) do not ddepend upon the scattering function. D(p.p). the shock Lorentz factor (provided olf course 5.Z9 1). the magnetic fiekl geometry. and the ratio of cross-lield to parallel diffusiou coellicients.," 2) do not depend upon the scattering function $D(\mu, p)$, the shock Lorentz factor (provided of course $\gamma \gg 1$ ), the magnetic field geometry, and the ratio of cross–field to parallel diffusion coefficients."889Thus we have the result that the cosinie rays! spectra are independent of [low details in both the Newtouiau (Bell 1975) auc the relativistic regimes.,Thus we have the result that the cosmic rays' spectra are independent of flow details in both the Newtonian (Bell 1978) and the relativistic regimes.89022004: Kartaltepe et 22008). and studies of the galaxy content and gas properties of individual clusters (e.g.. Ma et al.,"2004; Kartaltepe et 2008), and studies of the galaxy content and gas properties of individual clusters (e.g., Ma et al."891 2008. 2009).," 2008, 2009)."892 Here we use images of 35 MACS clusters observed with the ACS (GO-09722. GO-10491. GO-10875. PI Ebeling).," Here we use images of 35 MACS clusters observed with the ACS (GO-09722, GO-10491, GO-10875, PI Ebeling)."893 We divide these clusters into two subsamples according to redshift. 0.3sz0.5. and 0.5xz0.7. which consist of 23 and 12 clusters. respectively.," We divide these clusters into two subsamples according to redshift, $0.3 \leq z < 0.5$, and $0.5 \leq z < 0.7$, which consist of 23 and 12 clusters, respectively."894« The low-redshift« sample was observed withAST in Snapshot mode. meaning the telescope schedulers chose a fraction of the targets from the full MACS sample. based solely on their scheduling. convenience.," The low-redshift sample was observed with in Snapshot mode, meaning the telescope schedulers chose a fraction of the targets from the full MACS sample, based solely on their scheduling convenience."895 Thus. the clusters we analyse are an unbiased. representative selection from the entire MACS sample.," Thus, the clusters we analyse are an unbiased, representative selection from the entire MACS sample."896 The medium-redshift sample consists of a complete set of 12 MACS clusters in this redshift range that are visible from Hawaii., The medium-redshift sample consists of a complete set of 12 MACS clusters in this redshift range that are visible from Hawaii.897 Strong-lensing mass reconstructions of the clusters in this subsample have been recently presented by Zitrin et al. (, Strong-lensing mass reconstructions of the clusters in this subsample have been recently presented by Zitrin et al. (8982010).,2010).899 The low-redshift clusters were observed through the Fó06W filter (mean wavelength 6060 A) with exposure times of 1200 s. While the medium-redshift sample was observed through the F8IJ4W filter (mean wavelength 8140. A) with exposure times of 4500 s. Applying the LxMagy of Reiprich Bóhhringer (2002) yields a cluster mass range of (1.4<=Magoo:4.1)x 10M... and (1.6xMagy3.9)10M... for the low- and medium-redshift samples. respectively.," The low-redshift clusters were observed through the ${\rm F}606{\rm W}$ filter (mean wavelength $\sim9006060~{\rm \AA}$ ) with exposure times of $1200$ s, while the medium-redshift sample was observed through the ${\rm F}814{\rm W}$ filter (mean wavelength $\sim 8140~{\rm \AA}$ ) with exposure times of $\sim 4500$ s. Applying the ${\rm901 L_{X}-M_{200}}$ of Reiprich Böhhringer (2002) yields a cluster mass range of $(1.4 \leq902{\rm M}_{200} \leq 4.1)\times 10^{15}{\rm M}_{\odot}$ , and $(1.6 \leq903{\rm M}_{200} \leq 3.9)\times 10^{15}{\rm M}_{\odot}$ for the low- and medium-redshift samples, respectively."904 The cluster properties are listed in Tables | and 2., The cluster properties are listed in Tables 1 and 2.905 The sample of Smith et al. (, The sample of Smith et al. (9062005). as analyzed in HOS. consists of 10 galaxy clusters from the X-ray Brightest Abell-type Clusters of galaxies (XBACS) catalogue (Ebeling et al.,"2005), as analyzed in H05, consists of 10 galaxy clusters from the X-ray Brightest Abell-type Clusters of galaxies (XBACs) catalogue (Ebeling et al."907 1996). with 0.17zx 0.26.," 1996), with $0.17< z <0.26$ ."908 The 0.1].2.4 keV flux limit of fy=5.0xIOE erg 7s applied to this redshift range implies X-ray luminosities Ly»4+1~xT erg |i i.e. similar to the MACS clusters at their higher redshifts.," The $0.1-2.4$ keV flux limit of $f_{X}\geq 5.0\times10^{-12}$ erg $^{-2}$ $^{-1}$ applied to this redshift range implies X-ray luminosities $L_{X}\geq4.1\times10^{44}$ erg $^{-1}$, i.e. similar to the MACS clusters at their higher redshifts."909 Details of this sample and its properties can be found in table | of HOS., Details of this sample and its properties can be found in table 1 of H05.910 The RCS survey was conducted using the Canada-France-Hawati Telescope (CFHT) through the A. and z' filters., The RCS survey was conducted using the Canada-France-Hawaii Telescope (CFHT) through the $R_{c}$ and $z'$ filters.911" Gladders Yee (2005) applied a red-sequencing technique to an area of ~Q0 deg"". and a catalogue of ~1000 clusters at 0.2<z«L4 was compiled."," Gladders Yee (2005) applied a red-sequencing technique to an area of $\sim 100 {\rm912 ~deg}^{2}$ , and a catalogue of $\sim 1000$ clusters at $0.2<z<1.4$ was compiled."913 The survey is complete to 50 magnitude limits of 24.9 and 23.8 in z' and Αι. respectively.," The survey is complete to $5\sigma$ magnitude limits of $24.9$ and $23.8$ in $z'$ and $R_{c}$, respectively."914 Like MACS clusters. RCS clusters have also been used in many applications. e.g. studying the scaling relations between different cluster properties (Hicks et al.," Like MACS clusters, RCS clusters have also been used in many applications, e.g., studying the scaling relations between different cluster properties (Hicks et al."915 2008). and exploring the evolution of the red-sequence galaxy luminosity function (Gilbank et al.," 2008), and exploring the evolution of the red-sequence galaxy luminosity function (Gilbank et al."916 2008)., 2008).917 Among the RCS clusters. a subset of 150 clusters was proposed for HST observation. again in Snapshot mode. out of which 52 were selected by HST schedulers based on scheduling conveneience. and imaged using ACS. (GO-10626. PI Loh.," Among the RCS clusters, a subset of $150$ clusters was proposed for HST observation, again in Snapshot mode, out of which $52$ were selected by HST schedulers based on scheduling conveneience, and imaged using ACS, (GO-10626, PI Loh)."918 Contrary to the MACS and XBACs clusters that we analyse here. which were chosen in an unbiased way from among complete samples. we do not know what were the criteria. if any. for selecting the 150 RCS clusters to be potential HST Snapshot targets.," Contrary to the MACS and XBACs clusters that we analyse here, which were chosen in an unbiased way from among complete samples, we do not know what were the criteria, if any, for selecting the 150 RCS clusters to be potential HST Snapshot targets."919 We suspect that there may have been some bias toward including clusters that already had evidence of strong lensing. based on previous ground-based imaging.," We suspect that there may have been some bias toward including clusters that already had evidence of strong lensing, based on previous ground-based imaging."920 However. it is highly unlikely that the 150 clusters were chosen. intentionally or unintentionally. in a way that wouldavoid systems with strong lensing (and it is also hard to imagine a logical reason for such a choice).," However, it is highly unlikely that the 150 clusters were chosen, intentionally or unintentionally, in a way that would systems with strong lensing (and it is also hard to imagine a logical reason for such a choice)."921 The main result of our study will be that the RCS clusters observed by HST are inefficient as lenses. when compared to the truly unbiased sample of X-ray selected clusters.," The main result of our study will be that the RCS clusters observed by HST are inefficient as lenses, when compared to the truly unbiased sample of X-ray selected clusters."922 This conclusion. applied to the RCS clusters as a whole. will therefore only be strengthened. if the 150 RCS clusters were pre-selected to favor strong lenses.," This conclusion, applied to the RCS clusters as a whole, will therefore only be strengthened, if the 150 RCS clusters were pre-selected to favor strong lenses."923 Our results will thus provide a tirm and useful upper limit on the RCS lensing fraction., Our results will thus provide a firm and useful upper limit on the RCS lensing fraction.924 The clusters were imaged through the FSIJW filter with exposure times of 1440 s. Luminosities and mass estimates of the RCS clusters have not been published to date., The clusters were imaged through the ${\rm F}814{\rm W}$ filter with exposure times of $1440$ s. Luminosities and mass estimates of the RCS clusters have not been published to date.925 In $4 below. we show that the RCS clusters and the X-ray selected clusters above have similar optical luminosities.," In $\S 4$ below, we show that the RCS clusters and the X-ray selected clusters above have similar optical luminosities."926 As with the X-ray selected clusters above. we divide the RCS clusters into redshift bins: the same low (0.3 z« 0.5) and medium (0.5<>< 0.7) redshift subsamples which were defined above. and a third. high-redshift. subsample at 0.7<zx|.," As with the X-ray selected clusters above, we divide the RCS clusters into redshift bins: the same low $0.3 \leq z < 0.5$ ) and medium $0.5927\leq z < 0.7$ ) redshift subsamples which were defined above, and a third, high-redshift, subsample at $0.7 \leq z \leq 1$."928 The three redshift subsamples consist of 18. 18. and 16 clusters. respectively.," The three redshift subsamples consist of $18$, $18$, and $16$ clusters, respectively."929 The properties of the 52 RCS clusters are listed in Tables 3. 4. and 5.," The properties of the $52$ RCS clusters are listed in Tables 3, 4, and 5."930 In HOS. we introduced the use of an automated are detection algorithm to are statistics studies.," In H05, we introduced the use of an automated arc detection algorithm to arc statistics studies."931 Automated are detection is important for an objective. quantitative. and fair comparison of are statistics in observed and simulated data.," Automated arc detection is important for an objective, quantitative, and fair comparison of arc statistics in observed and simulated data."932 In the meantime. a number of other are-detection algorithms have been published. by Lenzen et al. (," In the meantime, a number of other arc-detection algorithms have been published, by Lenzen et al. ("9332004). Alard (2006). and Seidel Bartelmann (2007: SBO07).,"2004), Alard (2006), and Seidel Bartelmann (2007; SB07)."934 In the present work. we subject all of the images to two of these algorithms. HOS and SBOT.," In the present work, we subject all of the images to two of these algorithms, H05 and SB07."935lt is striking that a large proportion of starburst racio galaxies show unusual racio morphologics that place them outside the regular ΕΙERIE morphological classification for extended: radio sources: 7 (33%)) are compact steep spectrum (CSS) or Gigahertz peakecl (GPS) sources whose radio structures are dominated. by structures with a diameter. 2« Ίσκρο (ρθρο. 3€48.. B2 0648|27. PIXS1345|12. 3€305. PINXS1549-79. PINS2135-209): 3 )) show unusually prominent compact steep spectrum core components on a scale 2.κ IOkpc. even if their. radio emission is dominated. by radio lobes and hotspots on a larger scale (30321. 3€433. 3C459): 6 (294)) show inner high surface brightness steep spectrum structures along with lower surface brightness outer haloes or double structures (3€213.1. 90215. 3€236. Con A. PINSIS45|12. 30293): and 15 (71%)) show one or more of these peculiarities.,"It is striking that a large proportion of starburst radio galaxies show unusual radio morphologies that place them outside the regular FRI/FRII morphological classification for extended radio sources: 7 ) are compact steep spectrum (CSS) or Gigahertz peaked (GPS) sources whose radio structures are dominated by structures with a diameter $D < 15$ kpc (PKS0023-26, 3C48, B2 0648+27, PKS1345+12, 3C305, PKS1549-79, PKS2135-209); 3 ) show unusually prominent compact steep spectrum core components on a scale $D < 10$ kpc, even if their radio emission is dominated by radio lobes and hotspots on a larger scale (3C321, 3C433, 3C459); 6 ) show inner high surface brightness steep spectrum structures along with lower surface brightness outer haloes or double structures (3C213.1, 3C218, 3C236, Cen A, PKS1345+12, 3C293); and 15 ) show one or more of these peculiarities."936 For comparison. the rate of detection of such features in. the southern 2Jv sample of radio galaxies with redshifts in the range 0.05<z0.7 (see Dicken ct al.," For comparison, the rate of detection of such features in the southern 2Jy sample of radio galaxies with redshifts in the range $0.05 < z < 0.7$ (see Dicken et al."937 2008 for sample definition) is only28'4., 2008 for sample definition) is only.938. Although our small sample size makes it. dillicult. to, Although our small sample size makes it difficult to939Cepheids is emitted at mil-IR. wavelengths where there is very little or no sensitivity (o temperature.,Cepheids is emitted at mid-IR wavelengths where there is very little or no sensitivity to temperature.940 The slope of the Cail of the distribution is constant. independent of (he temperature of the star.," The slope of the tail of the distribution is constant, independent of the temperature of the star."941 Thus. if a Cepheid approximates a blackbody. the expectation would be that colors based on the IRAC filters (at 3.5. 4.5. 5.8 or 8.0 jun) would be relatively constant as a function of phase and/or period.," Thus, if a Cepheid approximates a blackbody, the expectation would be that colors based on the IRAC filters (at 3.5, 4.5, 5.8 or 8.0 $\mu$ m) would be relatively constant as a function of phase and/or period."942 However. as seen previously in Figure 1l. lor the 4.5 jan band. the presence of broad CO molecular absorption bands between about 4 and 6 jam alfects the 4.5 (and 5.3) san IRAC filters The 3.6 san band lies outside of the CO feature.," However, as seen previously in Figure 1, for the 4.5 $\mu$ m band, the presence of broad CO molecular absorption bands between about 4 and 6 $\mu$ m affects the 4.5 (and 5.8) $\mu$ m IRAC filters The 3.6 $\mu$ m band lies outside of the CO feature."943 The models of Marengo (2010) show Chat these deep CO absorption bands occur in all supergiants of the temperature and gravity of Cephleids. and they also vary. during the Cephleid pulsational evele.," The models of Marengo (2010) show that these deep CO absorption bands occur in all supergiants of the temperature and gravity of Cepheids, and they also vary during the Cepheid pulsational cycle."944 The color variation seen through the evcle results from (he [act that the CO absorption is sensitive to temperature and varies both within a single Cepheid's pulsation evele and between Cepheids of different mean temperatures., The color variation seen through the cycle results from the fact that the CO absorption is sensitive to temperature and varies both within a single Cepheid's pulsation cycle and between Cepheids of different mean temperatures.945 In Figure. 2. we showed 3.6 and 4.5 jim light curves. in addition to |3.6]-4.5] jm color curves lor (wo Cepheids in each of (he Milkv Way. LMC and SAIC.," In Figure 2, we showed 3.6 and 4.5 $\mu$ m light curves, in addition to [3.6]-[4.5] $\mu$ m color curves for two Cepheids in each of the Milky Way, LMC and SMC."946 In general. we find that the [3.6]-[4.5] jam mid-IR color eurves for most of the longer-period (P > 10 day) Cepheids in the LMC and the Galaxy display a signilicant evclieal variability.," In general, we find that the [3.6]-[4.5] $\mu$ m mid-IR color curves for most of the longer-period (P $>$ 10 day) Cepheids in the LMC and the Galaxy display a significant cyclical variability."947 To our knowledge. this effect has never been observed previously since light curves for Cepheids at 4.5 jam have never been obtained before (previous observations have been one or (wo epochs only).," To our knowledge, this effect has never been observed previously since light curves for Cepheids at 4.5 $\mu$ m have never been obtained before (previous observations have been one or two epochs only)."948 Ilowever. V Cen and LIV12452. with P=5.5 and 8.7 days. respectively. show little variability and have colors ol zero.," However, V Cen and HV12452, with P=5.5 and 8.7 days, respectively, show little variability and have colors of zero."949 The light curves for the SMIC. which has à lower metallicity than the Galaxy and the LMC. show very little effect at anv period.," The light curves for the SMC, which has a lower metallicity than the Galaxy and the LMC, show very little effect at any period."950 As we have discussed. this variability occurs as a result of the presence of the CO bandhead falling within the 4.5 jn filter.," As we have discussed, this variability occurs as a result of the presence of the CO bandhead falling within the 4.5 $\mu$ m filter."951 The CO feature strenethens when the stellar atmosphere is more expauded and (therefore cooler., The CO feature strengthens when the stellar atmosphere is more expanded and therefore cooler.952 As seen in Scowcroft the amplitude of the color variability also increases wilh increasing period., As seen in Scowcroft the amplitude of the color variability also increases with increasing period.953 No evelical CO variability is seen for Cepheids with periods less than about. 10 days (the hottest Cepheids)., No cyclical CO variability is seen for Cepheids with periods less than about 10 days (the hottest Cepheids).954 A detailed discussion of the 4.5 san CO feature in our Cepheid sample is presented in Scowerolt et al. (, A detailed discussion of the 4.5 $\mu$ m CO feature in our Cepheid sample is presented in Scowcroft et al. (9552012€).,2012c).956 At (he end of the ev Project. the overall svstematic uncertainty in the value of the IIubble constant was found to be (Freedman οἱ al.," At the end of the Key Project, the overall systematic uncertainty in the value of the Hubble constant was found to be (Freedman et al."957 2001)., 2001).958 Three of the largest sources of svslematic uncertainty listed included (a) involving the distance to the Large Magellanic Cloud. setting the zero point of the Cepheid PL relation. (b) due to the uncertainties involved in making the photometric tie-in between. erounc-based telescopes and the LST photometric svstem(s) and (c) 44% uncertainty due to the difference in metallicity between," Three of the largest sources of systematic uncertainty listed included (a) involving the distance to the Large Magellanic Cloud, setting the zero point of the Cepheid PL relation, (b) due to the uncertainties involved in making the photometric tie-in between ground-based telescopes and the HST photometric system(s) and (c) $\pm$ uncertainty due to the difference in metallicity between"9591n 2001. the neutron star N-rav binaries aand bboth made the transition to quiescence. following accretion episodes of 12.5 and 2.5 vears. respectively 2008).,"In 2001, the neutron star X-ray binaries and both made the transition to quiescence, following accretion episodes of 12.5 and 2.5 years, respectively ."960. More recently. in 200i the ~1.G-vear long outburst of ccame to a halt2010).," More recently, in 2007, the $\sim1.6$ -year long outburst of came to a halt."961.. Al three systems were subsequentLy monitored with aandVALAI-New/on.. which revealed that thermal flux and neutron star temperature were gradually cecreasing over the course of vears (see also Section 2?)).," All three systems were subsequently monitored with and, which revealed that thermal flux and neutron star temperature were gradually decreasing over the course of years (see also Section \ref{sec:discussion}) )."962 This can be interpreted as cooling of the neutron star crust tha has been heated during the prolonged accretion outburst., This can be interpreted as cooling of the neutron star crust that has been heated during the prolonged accretion outburst.963 Successful modelling of the observed. quiescent X-ray lighteurves with neutron star thermal evolution models sup»orts this hypothesis ancl provides important constraints on the crust properties. such as the thermal conductivity2009).," Successful modelling of the observed quiescent X-ray lightcurves with neutron star thermal evolution models supports this hypothesis and provides important constraints on the crust properties, such as the thermal conductivity."964. Along these lines we have pursued an observational campaign of tto study the time evolution of the quicscent X-ray emission Following its long accretion. outburst., Along these lines we have pursued an observational campaign of to study the time evolution of the quiescent X-ray emission following its long accretion outburst.965 In.(2009).. we discussed: aand oobservations obtained. between 2008 September 28 and 2009 January 30.," In, we discussed and observations obtained between 2008 September 28 and 2009 January 30."966 We found a relatively hot and. luminous quiescent system with a temperature of AZ;~O110.13. keV and a thermal 0.01100. keV. luminosity. of ~(S16).10%?(D/T.4kpe)?[UNES +, We found a relatively hot and luminous quiescent system with a temperature of $kT^{\infty}_{\mathrm{eff}}\sim0.11-0.13$ keV and a thermal 0.01–100 keV luminosity of $\sim(8-16)\times10^{33}~(\mathrm{D/7.4~kpc})^2~\lum$ .967 No clear decrease in ellective temperature and thermal bolometric Dux was found over the five-month time span., No clear decrease in effective temperature and thermal bolometric flux was found over the five-month time span.968 In this paper we report on continued aand oobservations of deduring its quiescent state., In this paper we report on continued and observations of during its quiescent state.969 In. addition. we include an archival oobservation »erformed. 2 months after the cessation of the outburst.," In addition, we include an archival observation performed $\sim 2$ months after the cessation of the outburst."970 Previous aand oobservations discussed by were re-analvsed. in this work in order to obtain a homogeneous quicscent [lighteurve., Previous and observations discussed by were re-analysed in this work in order to obtain a homogeneous quiescent lightcurve.971 ‘Table 1 eives an overview of all new observations of cleliscussecl in this paper., Table \ref{tab:obs} gives an overview of all new observations of discussed in this paper.972 A list of earlier. aand oobservations obtained. during the quiescent phase can be found in(2009)., A list of earlier and observations obtained during the quiescent phase can be found in.973. wavas observed with the European Photon Imaging Camera (EPIC) onboard oon 2005 November 6 from 08:30.16:422009)., was observed with the European Photon Imaging Camera (EPIC) onboard on 2008 November 6 from 08:30–16:42.974. Phe EPIC instrument consists of two MOS detectors and one PN camera2001)... which are sensitive in the 0.115 keV energy range and have elfective⋅⋠ areas of⋅ 922 cm⊳↘ and 122i- cnr2 (at 1. keV). respectively.," The EPIC instrument consists of two MOS detectors and one PN camera, which are sensitive in the 0.1–15 keV energy range and have effective areas of 922 $^2$ and 1227 $^2$ (at 1 keV), respectively."975" oth the PN and the two MOS instruments were operated in full window: mode ancl using he medium. optical blocking filter,", Both the PN and the two MOS instruments were operated in full window mode and using the medium optical blocking filter.976 Data reduction. and analysis was carried out with the Science Analysis Software(SAS: v. 9.0.0)., Data reduction and analysis was carried out with the Science Analysis Software; v. 9.0.0).977 We reprocessed. the Original Data Piles (ODE) using the tasks andEPPROC., We reprocessed the Original Data Files (ODF) using the tasks and.978. To identify »xossible periods of high particle background. we extracted ügh-energv lighteurves. 10 keV for the MOS and tween LO12 keV for the PN).," To identify possible periods of high particle background, we extracted high-energy lightcurves $\geq 10$ keV for the MOS and between 10–12 keV for the PN)."979 No strong background [ares occurred. ltduring the observation., No strong background flares occurred during the observation.980 The net exposure times are 29.0 ancl 22.9 ks for the MOS and. PN. respectively.," The net exposure times are 29.0 and 22.9 ks for the MOS and PN, respectively."981We extracted the spectrum for the sources CX] and CX7 whose photon counts 2 200 in 0.3-7 keV energy band.,We extracted the spectrum for the sources CX1 and CX7 whose photon counts $\gtrsim$ 200 in 0.3-7 keV energy band.982 The counts per spectral bin is 15 and we fitted them with a power law model and thermal bremsstrahlung model., The counts per spectral bin is 15 and we fitted them with a power law model and thermal bremsstrahlung model.983 We fixed the Galactic column density Ny at 107 cem derived from optical extinction for the fitting., We fixed the Galactic column density $_\mathrm{H}$ at $10^{21}$ $^{-2}$ derived from optical extinction for the fitting.984 All the models for the two sources can be fitted with a reduced 47 ~ 1.5 and the null hypothesis probability is ~ 0.1., All the models for the two sources can be fitted with a reduced $\chi^{2}$ $\sim$ 1.5 and the null hypothesis probabiility is $\sim$ 0.1.985 The null hypothesis probability is the probability of getting a value of  as large or larger than observed if the model is correct., The null hypothesis probability is the probability of getting a value of $\chi^{2}$ as large or larger than observed if the model is correct.986 If this probability is small then the model is not a good fit., If this probability is small then the model is not a good fit.987 Table 2 summarizes the results of spectral fitting., Table 2 summarizes the results of spectral fitting.988 We also allowed for an additional intrinsic column density to the source beyond the Galactic value. and i each case this fitted intrinsic absorbing ts higher than the (fixed) Galactic value.," We also allowed for an additional intrinsic column density to the source beyond the Galactic value, and in each case this fitted intrinsic absorbing is higher than the (fixed) Galactic value."989 The temperature for thermal bremsstrahlung model is 3 keV for CX1 and 12 keV for CX7., The temperature for thermal bremsstrahlung model is 3 keV for CX1 and 12 keV for CX7.990 The photor index for CXI 15 roughly 2 while for CX7 it is slightly lower than 2., The photon index for CX1 is roughly 2 while for CX7 it is slightly lower than 2.991 Besides. the predicted unabsorbed flux (0.3-7.0 keV) is consistent. with each other in both models.," Besides, the predicted unabsorbed flux (0.3-7.0 keV) is consistent with each other in both models."992 We also extractec the light curve (0.3-7.0 keV) of CXI. with a time resolusior of 2000 seconds.," We also extracted the light curve (0.3-7.0 keV) of CX1, with a time resolusion of 2000 seconds."993 We then performed a Kolmogorov-Smirnov (K-S) test on the light curve of CXI by using LCSTATS in the XRONOS (version 5.21) package., We then performed a Kolmogorov-Smirnov (K-S) test on the light curve of CX1 by using LCSTATS in the XRONOS (version 5.21) package.994 The probability of constancy is 4.79 «107., The probability of constancy is 4.79 $\times$ $10^{-3}$.995 Figure 3 shows the power law fitted spectrum and the light curve of CXI., Figure 3 shows the power law fitted spectrum and the light curve of CX1.996 M12 was observed by AAdvanced Camera for Surveys (ACS) on 2004 June 14 (Proposal ID 10005)., M12 was observed by Advanced Camera for Surveys (ACS) on 2004 June 14 (Proposal ID 10005).997 In this observation. three filters were used: F435W (By35). FO25W (7625). and FOS8W (Hass).," In this observation, three filters were used: F435W $B_\mathrm{435}$ ), F625W $r_\mathrm{625}$ ), and F658W $H\alpha_\mathrm{658}$ )."998 The exposure time for F435W. F658W. and F625W ts 1360 seconds. 1360 seconds. and 200 seconds. respectively.," The exposure time for F435W, F658W, and F625W is 1360 seconds, 1360 seconds, and 200 seconds, respectively."999 The field of view of ACS covers the whole core radius of MI2 but only covers ~75% of the half-mass radius., The field of view of ACS covers the whole core radius of M12 but only covers $\sim$ of the half-mass radius.1000 There are five X-ray sources within the ACS field of view., There are five X-ray sources within the ACS field of view.1001 The five sources are also covered by the WWide Field and Planetary Camera 2 (WFPC2) observation (Proposal ID 8118) (See figure 1)., The five sources are also covered by the Wide Field and Planetary Camera 2 (WFPC2) observation (Proposal ID 8118) (See figure 1).1002 The WFPC2 observation was performed on 2000 August 12., The WFPC2 observation was performed on 2000 August 12.1003 Two filters F439W and F5355W were employed in the observation. and the exposure time for F439W and F555W is 240 seconds and 63 seconds respectively.," Two filters F439W and F555W were employed in the observation, and the exposure time for F439W and F555W is 240 seconds and 63 seconds respectively."1004 We used individual images for photometry and the ACS drizzled images for astrometry and identifying the optical counterparts for X-ray sources., We used individual images for photometry and the ACS drizzled images for astrometry and identifying the optical counterparts for X-ray sources.1005 The drizzled images are combined images which have been calibrated for bias. dark. and flat field.," The drizzled images are combined images which have been calibrated for bias, dark, and flat field."1006 The geometric distortion and cosmic rays are also removed., The geometric distortion and cosmic rays are also removed.1007 The calibrations were performed by ACS calibration pipeline with the toolPyDrizzle!!., The calibrations were performed by ACS calibration pipeline with the tool.1008. As for the WFPC2 images. we used them to perform photometry only.," As for the WFPC2 images, we used them to perform photometry only."1009 The calibrated images were adopted in the data analysis., The calibrated images were adopted in the data analysis.1010 The bias and flatfield corrections were applied on the calibrated images by WFPC2 calibrationpipeline'-., The bias and flatfield corrections were applied on the calibrated images by WFPC2 calibration.1011. For photometry. we used individual images and processed them with the packageDOLPHOT.. à PSF photometry tool adapted from (Dolphin2000)?.," For photometry, we used individual images and processed them with the package, a PSF photometry tool adapted from (Dolphin."1012". can process multiple images at the same field of view for one run and provide the results of combined photometry for each filter,", can process multiple images at the same field of view for one run and provide the results of combined photometry for each filter.1013 We applied the with ACS module in all analysis., We applied the with ACS module in all analysis.1014 First. we run the command on the data quality images provided by Space Telescope Science Institute (STSel) in order to mask bad pixels.," First, we run the command on the data quality images provided by Space Telescope Science Institute (STScI) in order to mask bad pixels."1015 Then we created a sky map by applying the command., Then we created a sky map by applying the command.1016 In the last step. we performed with ACS PSF and Pixel Area Maps provided by the ACS module.," In the last step, we performed with ACS PSF and Pixel Area Maps provided by the ACS module."1017 A master photometry list was given containing the position. magnitude for each bands. signal-to-noise ratio. and other indicators for the detected stars.," A master photometry list was given containing the position, magnitude for each bands, signal-to-noise ratio, and other indicators for the detected stars."1018 We set a criteria to eliminate the cosmic rays. artifacts. and the fake stars located on the diffraction spikes of the saturated stars.," We set a criteria to eliminate the cosmic rays, artifacts, and the fake stars located on the diffraction spikes of the saturated stars."1019 Finally we filtered the output stars and got a “good” star list., Finally we filtered the output stars and got a $\arcsec$ $\arcsec$ star list.1020 Stars were selected if they showed up in all three bands., Stars were selected if they showed up in all three bands.1021 Then we produced the color-magnitude diagrams (CMDs) with the “good” star list (See figure 4. left two diagrams).," Then we produced the color-magnitude diagrams (CMDs) with the $\arcsec$ $\arcsec$ star list (See figure 4, left two diagrams)."1022 We used processes similar to that of AACS data analysis as we performed photometry on the WWEPC?2 data. while we employed the package (version 1.1) instead ofDOLPHOT.," We used processes similar to that of ACS data analysis as we performed photometry on the WFPC2 data, while we employed the package (version 1.1) instead of."1023. We first applied the command to mask bad pixels. and then calculated the sky map by runninggetsky.," We first applied the command to mask bad pixels, and then calculated the sky map by running."1024. The task was employed to filter out the cosmic rays on the images., The task was employed to filter out the cosmic rays on the images.1025 We also removed the hot pixels with the taskhotpixels., We also removed the hot pixels with the task.1026. Finally we combined the image frames for each filter into a single image by the commandcoadd.. and then performed the task on the resultant single image for each filter to calculate the photometry.," Finally we combined the image frames for each filter into a single image by the command, and then performed the task on the resultant single image for each filter to calculate the photometry."1027 can deal with multiple images with different filters simultaneously and produce a master list containing the photometry information. for each filter., can deal with multiple images with different filters simultaneously and produce a master list containing the photometry information for each filter.1028 As a consequence. we produced the CMD of the WFPC2 observation (See figure 4. right diagram).," As a consequence, we produced the CMD of the WFPC2 observation (See figure 4, right diagram)."1029 We further utilized the package (Stetson 1987) in (version | optical counterpart of CX1 from WFEPC2 observation., We further utilized the package (Stetson 1987) in (version 2.12.2a) to extract the photometry information of the possible optical counterpart of CX1 from WFPC2 observation.1030 The CXI counterpart is located on the edge of ΛΕΡΟΣ chip 3 (WFC3). where the image quality might not be as good as that in the central region of the CCD.," The CX1 counterpart is located on the edge of WFPC2 chip 3 (WFC3), where the image quality might not be as good as that in the central region of the CCD."1031 We adopted relative. photometry using the photometry as reference., We adopted relative photometry using the photometry as reference.1032 We then calibrated the photometry by shifting the stars’ magnitudes extracted by to match the same stars? magnitudes extracted byHSTphot., We then calibrated the photometry by shifting the stars' magnitudes extracted by to match the same stars' magnitudes extracted by.1033. Finally. we applied the magnitude shifts on the CXI counterpart and plotted it on the CMD (See figure 4. right diagram).," Finally, we applied the magnitude shifts on the CX1 counterpart and plotted it on the CMD (See figure 4, right diagram)."1034 In order to search for the optical counterparts of the XX-ray sources. we placed the optical and the X-ray images on the same image frame and coordinate system.," In order to search for the optical counterparts of the X-ray sources, we placed the optical and the X-ray images on the same image frame and coordinate system."1035 We took a wide field optical image as the reference image frame and aligned the AACS and images onto it individually., We took a wide field optical image as the reference image frame and aligned the ACS and images onto it individually.1036 The wide field image was retrieved, The wide field image was retrieved1037are divided iuto different magnitude groups with a bin of 0.5 mae.,are divided into different magnitude groups with a bin of 0.5 mag.1038 For photographic B iiagnitudoe. quasars with B magnitude in the range between 16.0 aud 22.0 mag were used.," For photographic $B$ magnitude, quasars with $B$ magnitude in the range between 16.0 and 22.0 mag were used."1039 For SDSS r magnitude. quasars with r magnitude in the range between 16.0 aud 21.0 mag were used.," For SDSS $r$ magnitude, quasars with $r$ magnitude in the range between 16.0 and 21.0 mag were used."1040 For cach magnitude eroup of quasars. a Cassian fiction was used to fit the proper motions in cach component imn that eroup. the mean aud dispersion of the best-fittiug Gaussian fiction correspondiug to the systematic and randoni errors of proper motions of quasars in that eroup are showed as red open circle and error bar in cach paucl of Figure 6..," For each magnitude group of quasars, a Gaussian function was used to fit the proper motions in each component in that group, the mean and dispersion of the best-fitting Gaussian function corresponding to the systematic and random errors of proper motions of quasars in that group are showed as red open circle and error bar in each panel of Figure \ref{fg6}."1041" The left panels of Figure 6 indicate that the systematic errors of i,cos have the similar dependence ou the photographic B magnitude aud on the SDSS ro inaenitude.", The left panels of Figure \ref{fg6} indicate that the systematic errors of $\mu_{\alpha}\cos\delta$ have the similar dependence on the photographic $B$ magnitude and on the SDSS $r$ magnitude.1042" The absolute value of the systematic deviation of jf,cos increases frou the briglitest ος of the quasar magnitude9. eroup to its miuxinmun. then decreases progressively to the faintest cud of the quasar magnitude eroup."," The absolute value of the systematic deviation of $\mu_{\alpha}\cos\delta$ increases from the brightest end of the quasar magnitude group to its maximum, then decreases progressively to the faintest end of the quasar magnitude group."1043" The rus of the svstematic errors of Hacos0 for different quasar magnitude eroups is 0.7 mas for photographic B inaguitude aud 0.5 mas ! for SDSS r inaenitude. respectively,"," The rms of the systematic errors of $\mu_{\alpha}\cos\delta$ for different quasar magnitude groups is $0.7$ mas $^{-1}$ for photographic $B$ magnitude and $0.5$ mas $^{-1}$ for SDSS $r$ magnitude, respectively."1044" But this ruis is smaller than the absolute systematic deviation of 2.0 mas vr in 4,cose for the whole quasar sample by a factor of 3 1.", But this rms is smaller than the absolute systematic deviation of $2.0$ mas $^{-1}$ in $\mu_{\alpha}\cos\delta$ for the whole quasar sample by a factor of 3 – 4.1045 Except the last two points in the faint photographic B magnitude bins. the right panels of Figure 6 indicate that the systematic errors of µε have the similar dependence ou the photographic B magnitude aud ou the SDSS ro inaenitude.," Except the last two points in the faint photographic $B$ magnitude bins, the right panels of Figure \ref{fg6} indicate that the systematic errors of $\mu_{\delta}$ have the similar dependence on the photographic $B$ magnitude and on the SDSS $r$ magnitude."1046 The absolute value of the systematic deviation of jr; decreases progressively frou the brightest cud of the quasar maenitude eroup to the fainter eud of the quasar magnitude eroup., The absolute value of the systematic deviation of $\mu_{\delta}$ decreases progressively from the brightest end of the quasar magnitude group to the fainter end of the quasar magnitude group.1047 The riis of the «ποιατας errors of jpfor different quasar magnitude groups is 0.5 mas Í for photographic D magnitude and 0.1 mas + for SDSS + maguitude. respectively.," The rms of the systematic errors of $\mu_{\delta}$for different quasar magnitude groups is $0.5$ mas $^{-1}$ for photographic $B$ magnitude and $0.4$ mas $^{-1}$ for SDSS $r$ magnitude, respectively."1048 This rins is sunaller than the absolute systematic deviation of 2.1 as tin oe ys for the whole quasar sample by a factor of I., This rms is smaller than the absolute systematic deviation of $2.1$ mas $^{-1}$ in $\mu_{\delta}$ for the whole quasar sample by a factor of 4.1049 The red error bar iu cach panel of Figure 6 shows the rvaudom error of the proper motions in each componcut in cach quasar magnitude eroup., The red error bar in each panel of Figure \ref{fg6} shows the random error of the proper motions in each component in each quasar magnitude group.1050 All of the four paucls of Figure 6 indicate that the random errors of proper notions in cach component increase along with the uaenitude of quasars., All of the four panels of Figure \ref{fg6} indicate that the random errors of proper motions in each component increase along with the magnitude of quasars.1051" The maguitude cdepeudence of the rvaudom error of proper motions in each component can ""d escribed by a funetion 0,4=60|bνexp[nuc] where is the raudoin error of proper iuotions 1n oue conrponeut.τσ0, a. b. and e are the unknown paraneters to © fitted. and ais the B or r magnitude."," The magnitude dependence of the random error of proper motions in each component can be described by a function: $\sigma_{\mu}=a+b\times\exp^{(m-c)}$, where $\sigma_{\mu}$ is the random error of proper motions in one component, $a$, $b$, and $c$ are the unknown parameters to be fitted, and $m$ is the $B$ or $r$ magnitude."1052 Iu cach paucl of Figure 6.. the vellow dash dot line shows the best-fitting function.," In each panel of Figure \ref{fg6}, the yellow dash dot line shows the best-fitting function."1053 Table 1. lists the best-fitting parameters ςτη ifereut proper motions compoucuts and magnitude vpes., Table \ref{tb1} lists the best-fitting parameters for different proper motions components and magnitude types.1054 In ecneral. the random error of proper motions iu one compoucnut ehauges from ~LO mas | to ~8.0 nas + along with the magnitude changing from 16.0 o 21.0 mae.," In general, the random error of proper motions in one component changes from $\sim4.0$ mas $^{-1}$ to $\sim8.0$ mas $^{-1}$ along with the magnitude changing from 16.0 to 21.0 mag."1055 Figure 7 shows the color dependence of the proper motions of quasars in our sauple in each component., Figure \ref{fg7} shows the color dependence of the proper motions of quasars in our sample in each component.1056 The top two panels are based on the photographic BR color. aud the bottom two panels are based on the SDSS gr color.," The top two panels are based on the photographic $B-R$ color, and the bottom two panels are based on the SDSS $g-r$ color."1057 The blue dashed line in cach panel shows the proper motions with value ofzero., The blue dashed line in each panel shows the proper motions with value ofzero.1058 In order to derive the dependence of the proper motions in cach component on the color. quasars are divided iuto differeut color groups with a bin of 0.5 mae for BR aud à biu of 0.2 mae for gre respectively.," In order to derive the dependence of the proper motions in each component on the color, quasars are divided into different color groups with a bin of 0.5 mag for $B-R$ and a bin of 0.2 mag for $g-r$, respectively."1059 For photographic BR color. quasars with BRin the rauge between 1.25 aud 2.75 were used.," For photographic $B-R$ color, quasars with $B-R$ in the range between $-1.25$ and $2.75$ were used."1060 For SDSS gr color. quasars with gr in the range between |0.1 ancl 1.2 were used.," For SDSS $g-r$ color, quasars with $g-r$ in the range between $-0.4$ and $1.2$ were used."1061 For each color eroup of quasars. a Caussian function was used to fif the proper motions in cach compoucut in that eroup. the mean aud dispersion of the best-fitting Gaussian function corresponding to the systematic andrandoni errors of proper mofious of quasars in that eroup are showed as red open circle and error bar iu cach panel of Figur 7..," For each color group of quasars, a Gaussian function was used to fit the proper motions in each component in that group, the mean and dispersion of the best-fitting Gaussian function corresponding to the systematic andrandom errors of proper motions of quasars in that group are showed as red open circle and error bar in each panel of Figure \ref{fg7}."1062" Figure 7 indicate that there is no obvious color dependence of the svstematic errors of fn,cosó aud µη specially in the gor paucl.", Figure \ref{fg7} indicate that there is no obvious color dependence of the systematic errors of $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$ specially in the $g-r$ panel.1063" The nus of the systematic errors in 44,cosd aud jts for different quasar color groups is OON and 0.3 mas | for the photographic BoR color. respectively: and 0.2 and 0.1 mas | for the SDSS gyvr color. respectively."," The rms of the systematic errors in $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$ for different quasar color groups is $0.8$ and $0.3$ mas $^{-1}$ for the photographic $B-R$ color, respectively; and $0.2$ and $0.4$ mas $^{-1}$ for the SDSS $g-r$ color, respectively."1064 In general. the dispersion of svsteni errors of proper motious iun one coniponent for quasars in different color group is smaller than the absolute systematic deviation of the proper motions m that component for all quasars in the sample by a factor of2 |.," In general, the dispersion of system errors of proper motions in one component for quasars in different color group is smaller than the absolute systematic deviation of the proper motions in that component for all quasars in the sample by a factor of 2 – 4."1065 Figure 7T indicates that there is no obvious color dependence of the random erors of proper niofions n cach component both for BRaudg +., Figure \ref{fg7} indicates that there is no obvious color dependence of the random errors of proper motions in each component both for $B-R$ and $g-r$ .1066 But for quasars with verv bluer or redder color. the raucom errors of proper motions of them are bigecr than those for quasars with color iu the range of 0.2<ygor0.7.," But for quasars with very bluer or redder color, the random errors of proper motions of them are bigger than those for quasars with color in the range of $-0.2 < g-r < 0.7$."1067" The ruis ofthe random errors of the proper motions for quasars n different color groups is 0.5 mas tin Hacos and 0.5 nias in fis. respectively,"," The rms of the random errors of the proper motions for quasars in different color groups is $0.8$ mas $^{-1}$ in $\mu_{\alpha}\cos\delta$ and $0.5$ mas $^{-1}$ in $\mu_{\delta}$, respectively."1068 This nusis much sinaller than the raucom error of the proper motions iu cach component for all quasars in our sample by a factor of 5 10., This rmsis much smaller than the random error of the proper motions in each component for all quasars in our sample by a factor of 5 – 10.1069 Figure 8. shows the proper motions of quasars 1u our sample iu each component as a function of right ascension © and declination 9., Figure \ref{fg8} shows the proper motions of quasars in our sample in each component as a function of right ascension $\alpha$ and declination $\delta$.1070 The blue dashed line in each απο shows the proper motions with value of zero., The blue dashed line in each panel shows the proper motions with value of zero.1071 Iu order to derive the dependence of the proper motions in cach component on the position. quasars were divided iuto different position groups with a bin of 35 iu o anda bin of 15° in à. respectively.," In order to derive the dependence of the proper motions in each component on the position, quasars were divided into different position groups with a bin of $35\degr$ in $\alpha$ and a bin of $15\degr$ in $\delta$, respectively."1072 For each position eroup of quasars. a Caussian function was used to fit the proper motions in cach compoucut in that eroup. the mean auddispersion of the best-fitting Gaussian function corresponding to the systematic and randoni errors of proper mofionus of quasars in that eroup are showed as red open circle and error bar iu cach panel of Figure 8..," For each position group of quasars, a Gaussian function was used to fit the proper motions in each component in that group, the mean and dispersion of the best-fitting Gaussian function corresponding to the systematic and random errors of proper motions of quasars in that group are showed as red open circle and error bar in each panel of Figure \ref{fg8}. ."1073 The top two paucls of Figure & shows the distribution of µεcosÓ and pry for quasars in our sample along with a., The top two panels of Figure \ref{fg8} shows the distribution of $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$ for quasars in our sample along with $\alpha$ .1074 These pauels of Figure 8 indicate that. both for BacosÓ and pa. there are svstematic dependence of the systematic errors of the proper motions on a.," These panels of Figure \ref{fg8} indicate that, both for $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$ , there are systematic dependence of the systematic errors of the proper motions on $\alpha$ ."1075 A function of p=a|b«μπαc) was used to fit the a dependence of the proper motions in cach component. where 7 is the systematicerror of the proper motions," A function of $\overline{\mu}=a+b\times\sin(\alpha-c)$ was used to fit the $\alpha$ dependence of the proper motions in each component, where $\overline{\mu}$ is the systematicerror of the proper motions"1076An implicit assumption is that the ring flux contribution is independent of wavelength.,An implicit assumption is that the ring flux contribution is independent of wavelength.1077" For each visibility measurement V(A) of Table 1, the ring flux contribution f;(A) is defined as vO where V, is the modeled visibility of the central ‘star, and V; of the ring."," For each visibility measurement $V(\lambda)$ of Table 1, the ring flux contribution $f_\mathrm{r}(\lambda)$ is defined as $\frac{V(\lambda)-V_\star}{V_\mathrm{r}-V_\star}$, where $V_\star$ is the modeled visibility of the central star, and $V_\mathrm{r}$ of the ring."1078" The values of f, with the same wavelength are averaged.", The values of $f_\mathrm{r}$ with the same wavelength are averaged.1079 Results are presented in Fig. 5.., Results are presented in Fig. \ref{Fig_ratio}.1080" The optical emission in the ring-like gaseous structure is mainly due to Rayleigh diffusion at short wavelength (f.(A) is decreasing), while the Thomson scattering might be dominant for wavelengths longer than A> 510nm (f;(A) is constant)."," The optical emission in the ring-like gaseous structure is mainly due to Rayleigh diffusion at short wavelength $f_\mathrm{r} (\lambda)$ is decreasing), while the Thomson scattering might be dominant for wavelengths longer than $\lambda > 510$ nm $f_\mathrm{r} (\lambda)$ is constant)."1081 We progressively improved our models by exploring several hypothesis., We progressively improved our models by exploring several hypothesis.1082 Models with a large-scale structure of several mas around f Cep have a reduced x? between 15 to 38 times lower than the uniform disk hypothesis., Models with a large-scale structure of several mas around $\beta$ Cep have a reduced $\chi^2$ between 15 to 38 times lower than the uniform disk hypothesis.1083 The mean relative flux contribution of this large-scale structure over all the models presented in this paper is 0.23+ 0.02., The mean relative flux contribution of this large-scale structure over all the models presented in this paper is $0.23 \pm 0.02$ .1084 This is certainly our most important result., This is certainly our most important result.1085 Our best model (reduced x? of 0.9) points toward a peculiar ring geometry as described by Donati et al. (, Our best model (reduced $\chi^2$ of $0.9$ ) points toward a peculiar ring geometry as described by Donati et al. (10862001).,2001).1087" However, such a ring-model is supposed to be thick in the X-ray band, which implies a strong rotational modulation in the X-ray emission, but it is not observed (Favata et al."," However, such a ring-model is supposed to be thick in the X-ray band, which implies a strong rotational modulation in the X-ray emission, but it is not observed (Favata et al."1088 2009)., 2009).1089" Therefore, if the model of Donati et al. ("," Therefore, if the model of Donati et al. ("1090"2001) is valid, the ring should be optically thin even in the X-ray band.","2001) is valid, the ring should be optically thin even in the X-ray band."1091" In addition, the best-fit geometry we obtain for the ring is somewhat greater than the values provided in Donati et al. ("," In addition, the best-fit geometry we obtain for the ring is somewhat greater than the values provided in Donati et al. ("1092"2001): 74+7R, (compared to 2R,) for the inner ring diameter, and 5+6E, (compared to 6R,) for the width.","2001): $74 \pm 7 R_{\star}$ (compared to $2R_{\star}$ ) for the inner ring diameter, and $5 \pm 6 R_{\star}$ (compared to $6R_{\star}$ ) for the width."1093" However, the angular diameter estimate of G Cep we obtain (®,=@yp[V]0.22+0.05 mas) - even if it is indeed model-dependent - is quite preciseof relative precision)."," However, the angular diameter estimate of $\beta$ Cep we obtain $\Phi_\star=\Phi_{\mathrm{UD}}[V]=0.22\pm0.05$ mas) - even if it is indeed model-dependent - is quite preciseof relative precision)."1094 Considering Tog= 26000K and logg=4 for, Considering $T_{\mathrm{eff}}=26000$ K and $\log g=4$ for1095WO6'. ji=cos? =0.96) active region NOAA 9661 as shown in Figure 1..,"$^\circ$ , $\mu= $ $\theta=0.96$ ) active region NOAA 9661 as shown in Figure \ref{FIG:AR}."1096 It contains a 6 sunspot at left. an a sunspot at right. as well as several pores and plages lying in between.," It contains a $\delta$ sunspot at left, an $\alpha$ sunspot at right, as well as several pores and plages lying in between."1097 The obtained spatial sampling is about iin the north-south direction and lin the east-west direction., The obtained spatial sampling is about in the north-south direction and in the east-west direction.1098 Full Stokes 7.Q.U.V. spectra were taken simultaneously in two spectral bands centered at 630.2 nm and 517.27 nm by two ASP cameras.," Full Stokes $I,Q,U,V$ spectra were taken simultaneously in two spectral bands centered at 630.2 nm and 517.27 nm by two ASP cameras."1099 The dispersions for the two spectral bands are 1.27 and 1.02 pm pixel respectively.," The dispersions for the two spectral bands are 1.27 and 1.02 pm $^{-1}$, respectively."1100 Each whole scan took about 25 minutes., Each whole scan took about 25 minutes.1101 A !.total of five whole scans were continuously taken within 2.5 hours. during which no significant evolution of the magnetic structures was found.," A total of five whole scans were continuously taken within 2.5 hours, during which no significant evolution of the magnetic structures was found."1102 Other information about the observation run can be found in Choudhary&Balasubra-maniam(2007 )., Other information about the observation run can be found in \citet{Choudhary+Bala2007}.1103. We applied the standard ASP calibration procedures (Litesetal.199];Skumanich1997) to the data sets.," We applied the standard ASP calibration procedures \citep{Lites+etal1991sopo.work....3L, skumanich+etal1997} to the data sets."1104 The calibrated Stokes 7.Q.U.V spectra were normalized to the quiet Sun continuum intensity 7. that was obtained by fitting the Kitt Peak FTS atlas to the observed Stokes 7 profiles.," The calibrated Stokes $I, Q, U, V$ spectra were normalized to the quiet Sun continuum intensity $I_{c}$ that was obtained by fitting the Kitt Peak FTS atlas to the observed Stokes $I$ profiles."1105 The data sets from the five whole scans were then integrated to increase the signal to noise ratio (S/N)., The data sets from the five whole scans were then integrated to increase the signal to noise ratio (S/N).1106 Furthermore. we calculated the standard deviation c im near continuum wavelength range for each integrated Stokes 7.Q.U.V profile to represent the profile noise level.," Furthermore, we calculated the standard deviation $\sigma$ in near continuum wavelength range for each integrated Stokes $I, Q, U, V$ profile to represent the profile noise level."1107 Only profiles with signal amplitude greater than 77 (an empirical S/N threshold that performs well in our data analysis) were used for this study., Only profiles with signal amplitude greater than $\sigma$ (an empirical S/N threshold that performs well in our data analysis) were used for this study.1108 We extracted the parameters for analyzing the shift and asymmetry of Stokes profiles using the following procedures. (, We extracted the parameters for analyzing the shift and asymmetry of Stokes profiles using the following procedures. (1109I)τη.,1).1110 We employed a Fourier phase method (seeSchmidtetal.1999) to determine the line core wavelength., We employed a Fourier phase method \citep[see][]{schmidt+stix+woehl1999} to determine the line core wavelength.1111 We then converted the wavelength shifts to velocities (67) by using the Doppler formula., We then converted the wavelength shifts to velocities $\nu_i$ ) by using the Doppler formula.1112 As a frame of reference. we use the average velocity of a small area in the nearly motionless umbra. (," As a frame of reference, we use the average velocity of a small area in the nearly motionless umbra. ("11132)i.,2).1114.. Normalized Stokes V profiles were smoothed to remove local noise., Normalized Stokes $V$ profiles were smoothed to remove local noise.1115 They were then divided into two cases: normal profiles that have two opposite lobes and one zero-crossing (ZC) point in between. and abnormal profiles that have no or multiple ZCs within a wavelength range corresponding to £5 ffrom Stokes / line center.," They were then divided into two cases: normal profiles that have two opposite lobes and one zero-crossing (ZC) point in between, and abnormal profiles that have no or multiple ZCs within a wavelength range corresponding to $\pm 5$ from Stokes $I$ line center."1116 Using this method. there is a small chance that we may improperly classify normal profiles into. an abnormal class.," Using this method, there is a small chance that we may improperly classify normal profiles into an abnormal class."1117 For example. strong magneto-optical effects— (see Fig.," For example, strong magneto-optical effects (see Fig."1118 3candtextins; 4.1) — produceStokesV — — fAeéseogensadiyuormal accordin," \ref{FIG:ABVSample}$ $c$ and text in \ref{abnormal}) ) produce Stokes $V$ profiles with 3 ZCs, although the profile is essentially normal."1119gSuchimproperlvclassi fiedeases, Such improperly classified cases only account for a small portion $<$ ) in the data and do not affect the analysis.1120onlyacec in à same manner as ή.," For normal profiles, the ZC shifts are converted to LOS velocities $\nu_{zc}$ ) in a same manner as $\nu_i$."1121 The abnormal profiles will be discussed in 4.1.. (, The abnormal profiles will be discussed in \ref{abnormal}. . (11223)vy.,3).1123" The combination (Q+U7)!"" is a measure of the overall LP magnitude (e.g..Leka&Steiner2001)."," The combination $(Q^2+U^2)^{1/2}$ is a measure of the overall $LP$ magnitude \citep[e.g.,][]{leka+steiner2001}."1124. The LP profiles were smoothed to remove local noise., The $LP$ profiles were smoothed to remove local noise.1125 It is difficult to measure the position of the central 7 component as it is usually small and sometimes even vanishes (see Figure 7))., It is difficult to measure the position of the central $\pi$ component as it is usually small and sometimes even vanishes (see Figure \ref{FIG:AVGPROF}) ).1126 Instead we measure the peak positions of the two σ components and use their mid- as the position of the LP profile., Instead we measure the peak positions of the two $\sigma$ components and use their mid-point as the position of the $LP$ profile.1127" We then converted the LP profile shifts to LOS velocities (7,,) in a same manner as Hi. (", We then converted the $LP$ profile shifts to LOS velocities $\nu_{lp}$ ) in a same manner as $\nu_i$. (11284)dA.,4).1129 The peak amplitudes of the blue (4) and the red (ας) lobes of normal Stokes V profiles and those of the two σ components of LP profiles are determined., The peak amplitudes of the blue $a_b$ ) and the red $a_r$ ) lobes of normal Stokes $V$ profiles and those of the two $\sigma$ components of $LP$ profiles are determined.1130" The areas of blue (Ap) and red (A,) lobes are obtained by integrating over the same wavelength range (0.02 nm) on both sides of the ZC wavelength for Stokes V profiles or the mid-point of the two v components for LP profiles.", The areas of blue $A_b$ ) and red $A_r$ ) lobes are obtained by integrating over the same wavelength range (0.02 nm) on both sides of the ZC wavelength for Stokes $V$ profiles or the mid-point of the two $\sigma$ components for $LP$ profiles.1131 The integrating range not only covers the majority of the Stokes V or LP signal corresponding to Stokes 7 Doppler core. but also rules out the blends from the neighboring telluric lines.," The integrating range not only covers the majority of the Stokes $V$ or $LP$ signal corresponding to Stokes $I$ Doppler core, but also rules out the blends from the neighboring telluric lines."1132 Following Solanki&Stenflo(1984).. the amplitude asymmetry óc and area asymmetry àAÀ are derived using the following formulae: Figure 2. shows the Stokes 7. V and LP images constructed by line core intensity and integrated Stokes V and LP signals. respectively.," Following \citet{Solanki+Stenflo1984A&A...140..185}, the amplitude asymmetry $\delta a$ and area asymmetry $\delta A$ are derived using the following formulae: Figure \ref{FIG:NZC} shows the Stokes $I$, $V$ and $LP$ images constructed by line core intensity and integrated Stokes $V$ and $LP$ signals, respectively."1133 Images of the three spectral lines are arranged following the order of their formation heights (increasing height from bottom to top)., Images of the three spectral lines are arranged following the order of their formation heights (increasing height from bottom to top).1134 The orange points are the locations of noisy profiles with S/N < 7., The orange points are the locations of noisy profiles with S/N $<$ 7.1135 The LP spectra have more noisy profiles than Stokes V. because the Zeeman signals for LP are essentially lower and near the disk center the transverse magnetic fields are weaker than the longitudinal fields for most of the areas in the low atmosphere.," The $LP$ spectra have more noisy profiles than Stokes $V$, because the Zeeman signals for $LP$ are essentially lower and near the disk center the transverse magnetic fields are weaker than the longitudinal fields for most of the areas in the low atmosphere."1136 Compared to the photospheric sspectra. the chromospheric ppolarimetric (Stokes V and LP) spectra generally have lower S/N thus more useless profiles.," Compared to the photospheric spectra, the chromospheric polarimetric (Stokes $V$ and $LP$ ) spectra generally have lower S/N thus more useless profiles."1137 The reasons are mainly due to the larger line width and the lower magnetic field strengths in the chromosphere., The reasons are mainly due to the larger line width and the lower magnetic field strengths in the chromosphere.1138 In the following. we first address the spatial distribution of abnormal Stokes V. profiles. which are important for evaluating the complexity of magnetic and flow fields (e.g..Mickey1985:Sigwarth2001.andreferences therein).," In the following, we first address the spatial distribution of abnormal Stokes $V$ profiles, which are important for evaluating the complexity of magnetic and flow fields \citep[e.g.,][and references therein]{Mickey1985SoPh...97..223M, Sigwarth2001}."1139. We then present the results of Doppler shifts and asymmetric properties of the Stokes profiles. where all the noisy and abnormal profiles are excluded from analysis.," We then present the results of Doppler shifts and asymmetric properties of the Stokes profiles, where all the noisy and abnormal profiles are excluded from analysis."1140 In the middle column of Figure 2.. locations with abnormal Stokes V profiles are marked using colored points.," In the middle column of Figure \ref{FIG:NZC}, locations with abnormal Stokes $V$ profiles are marked using colored points."1141 They are divided into three kinds to the number of ZC profileswith3ZCs.althousialagurg ffrom their Stokes 7 line centers as shown in Figure 3.., They are divided into three kinds according to the number of ZC within a range of $\pm 5$ from their Stokes $I$ line centers as shown in Figure \ref{FIG:ABVSample}.1142 Profiles with two ZCs (green) are most frequently seen. which have three lobes with the central one opposite to the other two (Fig.," Profiles with two ZCs ) are most frequently seen, which have three lobes with the central one opposite to the other two (Fig."1143 3b)., \ref{FIG:ABVSample}$ $b$ ).1144 T heyconcentrateintheregionsof magnetic polaritvinversionline( s, They concentrate in the regions of magnetic polarity inversion line (MPIL) and the outer penumbral boundaries.1145pot there are more location," They are mainly caused by the presence of mixed polarities associated with different velocities \citep[e.g.,][]{Sigwarth2001}, whereby the two polarities can be present beside each other (i.e., within one resolution element) or along the LOS over the line formation region \citep{SanchezAlmeida+Lites1992ApJ...398..359S, Solanki+Montavon1993A&A...275..283S}."1146s with two ," In outer penumbral regions, the number of two ZCs decreases with height, which implies that the mixed polarity effect is weaker at higher atmospheric levels."1147, This is probably due to the fact that the orientation of outer penumbral fields changes from horizontal or even downward to more vertical when they extend from the photosphere to the chromosphere \citep[][and references therein]{Choudhary+Bala2007}.1148ZCs in the image.," However, in the central part of the MPIL of the $\delta$ spot there are more locations with two ZCs in the image."1149 We speculate that this may point to a stronger mixed polarity effect around the highly non-potential MPIL in the chromosphere., We speculate that this may point to a stronger mixed polarity effect around the highly non-potential MPIL in the chromosphere.1150 The central part of the 6 spot's MPIL is also populated by locations without ZC(ved).Such locations may involve magnetic components carrying high speed flows. which cause the ZC to shift far from the line center (seeFig.," The central part of the $\delta$ spot's MPIL is also populated by locations without ZC).Such locations may involve magnetic components carrying high speed flows, which cause the ZC to shift far from the line center (seeFig."1151 3a)., \ref{FIG:ABVSample}$ $a$ ).1152 SincetheZC positiono f StokesV issusceptibletothepresenceo f velo ," Since the ZC position of Stokes $V$ is susceptible to the presence of velocity gradients through the line formation region \citep{LopezAriste2002ApJ...564..379L} or distortion of line profiles by noise, it is also possible that the profiles at these locations are highly asymmetric or distorted."1153There exists another kind of profile with three ZCs (blue)., There exists another kind of profile with three ZCs ).1154 They could be caused by residual noise or mixed, They could be caused by residual noise or mixed1155"10 times less than the Galactic value. and a very [lat spectrum D,214s.","10 times less than the Galactic value, and a very flat spectrum $\Gamma_x\simeq 1.48$."1156 When the column density is fixed at the Galactic value. the fit. becomes much worse with Vifdof.=4.25/11.," When the column density is fixed at the Galactic value, the fit becomes much worse with $\chi^2_\nu/d.o.f. ~=~4.25/11$."1157 In this case the single power law cleseription the UV to X-ray spectral index is 2.30.1. much steeper than for typical radio quiet QSOs with a mean value 1.65 (Yuan οἱ al.," In this case the single power law description the UV to X-ray spectral index is $\pm$ 0.1, much steeper than for typical radio quiet QSOs with a mean value 1.65 (Yuan et al."1158 1998)., 1998).1159 As the photon deficit; around. O.S-1.0 keV. is à tvpical signature of warm. absorption due to edges. more complicated: models were applied.," As the photon deficit around 0.8-1.0 keV is a typical signature of warm absorption due to edges, more complicated models were applied."1160 As a first step. a single absorption edge was added to the model.," As a first step, a single absorption edge was added to the model."1161 A good fit can be obtained with (AZv=LOL/S. Table 3).," A good fit can be obtained with $\chi^2_\nu/\nu=1.01/8$, Table 3)."1162 However. the edge energy of the best fit at 0.5640.03 keV does not correspond o any of the more common ion edges.," However, the edge energy of the best fit at $\pm$ 0.03 keV does not correspond to any of the more common ion edges."1163 This might be caused ον the combination of several edges., This might be caused by the combination of several edges.1164" To evaluate the results μου, we next fitted the spectrum with a warm absorption model using a variable slope power-law ionizing continuum. (sce Zelziarski ct al."," To evaluate the results further, we next fitted the spectrum with a warm absorption model using a variable slope power-law ionizing continuum (see Zdziarski et al."1165 1995)., 1995).1166 Phe free parameters are photon index. column density. absorber temperature and ionization xwameter (£=£Ln IU).," The free parameters are photon index, column density, absorber temperature and ionization parameter $\xi=L/nR^2$ )."1167 We have fixed the temperature a 5.107 Ix and forced the photon index of ionizing continuum o be the same as the N-rav. photon index., We have fixed the temperature at $5\times 10^4$ K and forced the photon index of ionizing continuum to be the same as the X-ray photon index.1168" The best fi »""wameters are. presented in. table 3.", The best fit parameters are presented in table 3.1169 The fit is acceptec αἱ a confidence: level of⋅⋅∣∕ (ify2=EN123/85. Figurem 4).," The fit is accepted at a confidence level of $\chi^2_\nu/\nu=1.23/8$, Figure 4)."1170 A small amount of excess cold absorption is also require withη Ni:=.2.6οLO4—1072U ," A small amount of excess cold absorption is also required with $N_c = 2.6_{-0.9}^{+1.0}\times 117110^{20}$ $^{-2}$."1172"Figure 5 shows £ versus NV, contours for the warm absorption model.", Figure 5 shows $\xi$ versus $N_w$ contours for the warm absorption model.1173" The best. fi column density. IN,:—3.2TEMOoUN10os−− cm7 for the absorbing material is within the range typically for Sevfert L galaxies (ο. Revnolds 1997)."," The best fit column density $N_w=3.2_{-0.8}^{+0.9}\times 10^{22}$ $^{-2}$ for the absorbing material is within the range typically for Seyfert I galaxies ( e.g., Reynolds 1997)."1174 However. the ionization parameter is lower than normally found for other Sevfert | ealaxies.," However, the ionization parameter is lower than normally found for other Seyfert I galaxies."1175" Using the best fit photon index. the X-ray derived. cdimensionless ionization parameter C,—í(densilidensity) (Netzer 1996) is only TUE with Da;£255112."," Using the best fit photon index, the X-ray derived dimensionless ionization parameter $U_x =$ (Netzer 1996) is only $_{-0.010}^{+0.026}$ with $\xi = 55_{-12}^{+16}$."1176 After⋅ correcting. for⋅ the warn absorption. the far UV. to N-rav. spectral slope becomes 1.66«peLOT444. which. is. consistent. with. the X-ray. spectral index. 1.79—U.45L3 and well within+. the range of the mean value for. racio quiet AXGNs.," After correcting for the warm absorption, the far UV to X-ray spectral slope becomes $_{-0.10}^{+0.07}$, which is consistent with the X-ray spectral index $1.79_{-0.19}^{+0.13}$ and well within the range of the mean value for radio quiet AGNs."1177 In figure 6 we show the Spectral Energy. Distribution (SED) of PG. 1126-041 [rom infrared to X-ray energies., In figure 6 we show the Spectral Energy Distribution (SED) of PG 1126-041 from infrared to X-ray energies.1178 The SED peaks around and is fat in the infrared and optical band., The SED peaks around and is flat in the infrared and optical band.1179 As mentioned. in the previous section. the far UV spectrum is steep and consistent with a direct extrapolation of the X-ray spectrum.," As mentioned in the previous section, the far UV spectrum is steep and consistent with a direct extrapolation of the X-ray spectrum."1180 Barvainis (1993) interpreted the Hatness of the infrared. to optical spectrum in this object as contamination of stellar light which fills the gap between the spectral bumps., Barvainis (1993) interpreted the flatness of the infrared to optical spectrum in this object as contamination of stellar light which fills the gap between the spectral bumps.1181 However. the steep UV spectrum cannot be explained in this way since the contribution of stellar light in the far UV is negligible under any reasonable assumption for the stellar population.," However, the steep UV spectrum cannot be explained in this way since the contribution of stellar light in the far UV is negligible under any reasonable assumption for the stellar population."1182 An alternative method to &enerate such steep UV spectra is through significant dust absorption., An alternative method to generate such steep UV spectra is through significant dust absorption.1183 We will show below that this is also an unlikely cause for he steep spectrum., We will show below that this is also an unlikely cause for the steep spectrum.1184 Η the intrinsic UV. spectrum of PGII26-041 is similar o other QSOs a reddening of EQB-V) 20.15. is. required., If the intrinsic UV spectrum of PG1126-041 is similar to other QSOs a reddening of E(B-V) $>$ 0.15 is required.1185 Llowever. the Balmer decrement in this object is normal. with a ratio Ho /11:3 = 2.92 (Miller et al.," However, the Balmer decrement in this object is normal, with a ratio $\alpha$ $\beta$ = 2.92 (Miller et al."1186 1992). very close to hat expected for case B recombination. and it is also similar o the mean value of Hao fll? = 3.0740.56 as determined or a sample of bright QSOs with Z«0.5 bv. Miller οἱ al. (," 1992), very close to that expected for case B recombination, and it is also similar to the mean value of $\alpha$ $\beta$ = $\pm$ 0.56 as determined for a sample of bright QSOs with $<0.5$ by Miller et al. ("11871992).,1992).1188 Using the La tux of 8.92 10.25 erg em7 ft. we ind [rom the να Dux in Table 1. that for P€11126-041 the ratio μαHo is between 2.3 and 3.6. for the two epochs of LUL observations in 1992 and. 1995.," Using the $\alpha$ flux of 8.92 $^{-118913}$ erg $^{-2}$ $^{-1}$, we find from the $Ly\alpha$ flux in Table 1, that for PG1126-041 the ratio $Ly\alpha/H\alpha$ is between 2.3 and 3.6, for the two epochs of IUE observations in 1992 and 1995."1190 As this is alreaciy very close to the photoionization prediction of Lya/ifa 24.0 . it is clear that redeening can not bring the flux at up much more than a factor of two at most. arguing against the existence of large reddening alfecting the emission lines.," As this is already very close to the photoionization prediction of $Ly\alpha/H\alpha$ $\simeq$ 4.0, it is clear that reddening can not bring the flux at up much more than a factor of two at most, arguing against the existence of large reddening affecting the emission lines."1191 As any absorbed UV light must be re-emitted in the infrared. band. the infrared. luminosity due to the dus emission must be a [actor of two larger than the observe luminosity in the UV if the dust covers a larec fraction of the nucleus ancl the reddening is as large as E(DB-V)—0.15.," As any absorbed UV light must be re-emitted in the infrared band, the infrared luminosity due to the dust emission must be a factor of two larger than the observed luminosity in the UV if the dust covers a large fraction of the nucleus and the reddening is as large as E(B-V)=0.15."1192 The observed. integrated infrared Dux in the 1-100722 banc is5.6.10+4 ere 2s +t which is similar to the integratec UV tux [rom to of 5.7.10+4 ere 22s l[or rw 1992 data.," The observed integrated infrared flux in the $\mu m$ band is $\times10^{-11}$ erg $^{-2}$ $^{-11931}$, which is similar to the integrated UV flux from to of $\times10^{-11}$ erg $^{-2}$ $^{-1}$ for the 1992 data."1194 In addition a significant portion of infrarec emission has to originate from the host galaxy., In addition a significant portion of infrared emission has to originate from the host galaxy.1195 Finally. the gaiortage of soft. X-ray photons would even be more severe if the UV. spectrum were highly reddened.," Finally, the shortage of soft X-ray photons would even be more severe if the UV spectrum were highly reddened."1196. With a ECB-V)=0.15 correction applied to the UV. spectrum. the UV lux will increase by a factor of four. bringing ay. back to >2.0. making the object intrinsically very weak in. X-ravs.," With a E(B-V)=0.15 correction applied to the UV spectrum, the UV flux will increase by a factor of four, bringing $\alpha_{uvx}$ back to $>2.0$, making the object intrinsically very weak in X-rays."1197 Also. the absence of a strong feature implies iut the grains must be dillerent from the standard Galactic composition.," Also, the absence of a strong feature implies that the grains must be different from the standard Galactic composition."1198 Although we can not completely rule out the possibility of that reddening is responsible for the steep UV spectrum. it requires a number of rather restrictive constraints: 1) the dust covers only a small fraction of the BLR: (2) the grains are not of Galactic composition. (3) the N-rav emission is intrinsically weak.," Although we can not completely rule out the possibility of that reddening is responsible for the steep UV spectrum, it requires a number of rather restrictive constraints: 1) the dust covers only a small fraction of the BLR; (2) the grains are not of Galactic composition, (3) the X-ray emission is intrinsically weak."1199 On the other hand. the UM. spectrum of an object with UV. absorption lines could. very well be intrinsically steep.," On the other hand, the UV spectrum of an object with UV absorption lines could very well be intrinsically steep."1200 This can be associated. for example. with inclination effects.," This can be associated for example, with inclination effects."

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