ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 The chanee in relative velocity given by a ecucral gravitational scattering is given by Av=AvyAvy., The change in relative velocity given by a general gravitational scattering is given by $\Delta \vec v = \Delta \vec v_2 - \Delta \vec v_1$.3 The resulting change in the eccentricity vector is The change in i is where vis the uuit normal vector to the biuary orbital plane., The resulting change in the eccentricity vector is The change in $\vec i$ is where $\hat n$ is the unit normal vector to the binary's orbital plane.4 For both the farthest perturbers aud the closest. the dependence of equations 2. aud { on the impact parameters cau be simplified.," For both the farthest perturbers and the closest, the dependence of equations \ref{eqDeltaegeneral} and \ref{eqDeltaigeneral} on the impact parameter can be simplified."5 We discuss these Huts in the following sections., We discuss these limits in the following sections.6" Tuteractious with impact parameters greater than the radius of the primary or secondary but much less than the secnirnmajor axis of the binary belong to what we call the ""close-encouuter regiue.", Interactions with impact parameters greater than the radius of the primary or secondary but much less than the semi-major axis of the binary belong to what we call the “close-encounter regime.”7 By definition the eucouuters iu this regine of iurpact parameter are much closer to oue imoeniber of the binary than the other., By definition the encounters in this regime of impact parameter are much closer to one member of the binary than the other.8 As a result the relative iupulse experienced is dominated by the single impulse deliveredto that body. |Av|z [Avj|.," As a result the relative impulse experienced is dominated by the single impulse deliveredto that body, $|\Delta \vec v| \approx |\Delta \vec v_j|$ ."9 The changes in e and i are then eiven not by the ditfereuce of the impulses on cach body. as iu equations 3. and L.. but by the effects of only the largest impulse.," The changes in $\vec e$ and $\vec i$ are then given not by the difference of the impulses on each body, as in equations \ref{eqDeltaegeneral} and \ref{eqDeltaigeneral}, , but by the effects of only the largest impulse."10 For the change in eccentricity we fud.," For the change in eccentricity we find,"11"dwarf temperature by 2OOOK changes Ze,fa by less than do.",dwarf temperature by 2000K changes $R_{w}/a$ by less than $\sigma$.12 Phe white chwarf distance estimates change by 10-20pc., The white dwarf distance estimates change by 10-20pc.13 We therefore conclude any error in white cwarl temperature that may occur does not alfect our final svstemi parameters bv a significant amount., We therefore conclude any error in white dwarf temperature that may occur does not affect our final system parameters by a significant amount.14 We note here that our moecdelling does not include treatment of any boundary Laver around the white dwarl and assumes all of the white dwarl’s surface is visible.," We note here that our moedelling does not include treatment of any boundary layer around the white dwarf, and assumes all of the white dwarf's surface is visible."15 Either ellect could lead to systematic uncertainty in our white clwarl raclii (?).., Either effect could lead to systematic uncertainty in our white dwarf radii \citep{wood1986}.16 A Markov Chain Monte Carlo (AICAIC) analysis was used to adjust all parameters bar Cy., A Markov Chain Monte Carlo (MCMC) analysis was used to adjust all parameters bar $U_W$.17 AICAIC analysis is an ideal tool as not only does it. provide a robust. method for quantifving the uncertainties in the various svsteni parameters. it is more likely to converge on the global minimum X? rather than a local minimum X7.," MCMC analysis is an ideal tool as not only does it provide a robust method for quantifying the uncertainties in the various system parameters, it is more likely to converge on the global minimum $\chi^{2}$ rather than a local minimum $\chi^{2}$ ."18" We refer the reader to ὃν, 7. and references therein for excellent overviews of ΙΟΝΤΟ chains aid Bayesian statistics and limit ourselves to à simple overview."," We refer the reader to \citet[][]{ford2006}, \citet[][]{gregory2007} and references therein for excellent overviews of MCMC chains and Bayesian statistics and limit ourselves to a simple overview."19 AICMC is a random walk process where at cach step in the chain we draw a set of model parameters from a normal. multi-variate clistribution.," MCMC is a random walk process where at each step in the chain we draw a set of model parameters from a normal, multi-variate distribution."20 This is governed. by a covariance array. which we estimate from the initial stages of the AICAIC chain.," This is governed by a covariance array, which we estimate from the initial stages of the MCMC chain."21 “Phe step is either accepted or rejected based on a transition probability. which is a function of the change in A7.," The step is either accepted or rejected based on a transition probability, which is a function of the change in $\chi^{2}$."22 We adopt a transition probability given by the Aletropolis-Llastings (M-II) rule. that is 22=expA2," We adopt a transition probability given by the Metropolis-Hastings (M-H) rule, that is $P = \exp^{-\Delta\chi^{2}/2}$."23 The sizes of the steps in the ΙΟΝΙΟ chain are multiplied bv à scale factor. tuned to keep the acceptance rate near 3. which is found to be the optimal value for multi-variate chains such as these (?)..," The sizes of the steps in the MCMC chain are multiplied by a scale factor, tuned to keep the acceptance rate near 0.23, which is found to be the optimal value for multi-variate chains such as these \citep{roberts1997}."24 A typical MCMC chain included. some 700.000. steps. split into two. 350.000 step sections.," A typical MCMC chain included some 700,000 steps, split into two, 350,000 step sections."25 The first section is used to convergefowerds the global minimum and estimate the covariance matrix (known as the burn-in phase)., The first section is used to converge the global minimum and estimate the covariance matrix (known as the burn-in phase).26 The second. section fine tunes the solution bv sampling areas of parameter space around the mininium., The second section fine tunes the solution by sampling areas of parameter space around the minimum.27 In doing so. we also produce a robust estimation of our uncertainties.," In doing so, we also produce a robust estimation of our uncertainties."28 Together. these steps are usually sullicient. to enable the model to converge on the statistical best fit. regardless of the initial starting parameters.," Together, these steps are usually sufficient to enable the model to converge on the statistical best fit, regardless of the initial starting parameters."29 While implementing he ALCAIC code. we discovered a bug in our original cocο.," While implementing the MCMC code, we discovered a bug in our original code."30 The re-binning code usec to average several light curves together mistreated the widths of the bins. which in turn afected the trapezoidal integration of the model over these ins.," The re-binning code used to average several light curves together mistreated the widths of the bins, which in turn affected the trapezoidal integration of the model over these bins."31 The direct. result. was that in cases of heavy binninο. such as systems with heavy lickering or where severa light curves had. been averaged ogether (e.g. SDSS 1502). the white dwarl racius. {ρα was underestimated.," The direct result was that in cases of heavy binning, such as systems with heavy flickering or where several light curves had been averaged together (e.g. SDSS 1502), the white dwarf radius, $R_{w}/a$, was underestimated."32 The exact amount depended: on the evel of binning used., The exact amount depended on the level of binning used.33 TPlis consequently resulted. in an overestimate of the white chwarl mass., This consequently resulted in an overestimate of the white dwarf mass.34" Since the mass of he donor star. M, is related to he white cwarl mass M, o» AL,=qM, we were also left with an overestimate of he donor mass."," Since the mass of the donor star, $M_{r}$, is related to the white dwarf mass $M_{w}$ by $M_{r} = qM_{w}$, we were also left with an overestimate of the donor mass."35 “Phis problem alfects all of our previously xublished. eclipsing-CV. papers (Feline et al., This problem affects all of our previously published eclipsing-CV papers (Feline et al.36 2004a. 2004b: Littlefair et al.," 2004a, 2004b; Littlefair et al."37 2006a.. 2006b.. 2007. 2008) bv. differing amounts.," 2006a, 2006b, 2007, 2008) \nocite{feline2004a, feline2004b, littlefair2006a, 38littlefair2006b, littlefair2007, littlefair2008} by differing amounts."39 However. in most cases re-mocdelling provides new system parameters that are within 1.28 of our original results. with only two exceptions (see section 3.4)).," However, in most cases re-modelling provides new system parameters that are within $1-2 \sigma$ of our original results, with only two exceptions (see section \ref{sec:notes}) )."40 The new results are presented in Table 3.., The new results are presented in Table \ref{table:system_params}.41 For cach svstem we ran an AICAIC simulation on cach phase-folded i. q'. i or #d light curve from an arbitrary starting position.," For each system we ran an MCMC simulation on each phase-folded $u'$, $g'$, $r'$ or $i'$ light curve from an arbitrary starting position."42 Exceptions include CPC 1900. where each night of observations was fit. individually. ancl SDSS 1152 and SDSS 1501. for which we only caleulated fits in the g and r bands due to απο data of insullicient quality to constrain the model.," Exceptions include CTCV 1300, where each night of observations was fit individually, and SDSS 1152 and SDSS 1501, for which we only calculated fits in the $g'$ and $r'$ bands due to $u'$ -band data of insufficient quality to constrain the model."43 Where no a’ band MCMC fit could be obtained. we fit and scaled the g band model to the v band light curves without X optimisation.," Where no $u'$ band MCMC fit could be obtained, we fit and scaled the $g'$ band model to the $u'$ band light curves without $\chi^{2}$ optimisation."44 This allows us to estimate the white dwarf [lux in the a band. and thus estimate the white dwarf temperature.," This allows us to estimate the white dwarf flux in the $u'$ band, and thus estimate the white dwarf temperature."45 In the case of SDSS 1501. we also fit a cillerent data set to the 2006 NIIT data of ?7..," In the case of SDSS 1501, we also fit a different data set to the 2006 WHT data of \citet{littlefair2008}."46 We fit our model to the single light curve dated 2004 Alay 17., We fit our model to the single light curve dated 2004 May 17.47 This 2004 data was not fit by Littlefair et al. (, This 2004 data was not fit by Littlefair et al. (482008) as the simplex methods used gave a seemingly &ood fit to the 2006 data.,2008) as the simplex methods used gave a seemingly good fit to the 2006 data.49 Despite appearing to have converged to a eood fit. the AICAIC analysis revealed. that the 2006 data does not constrain the model. most likely due to the very weak bright spot features.," Despite appearing to have converged to a good fit, the MCMC analysis revealed that the 2006 data does not constrain the model, most likely due to the very weak bright spot features."50 Phe 2004 data shows much clearer ancl well-defined bright-spot features than the 2006 data (see Fie of Littlefair et al., The 2004 data shows much clearer and well-defined bright-spot features than the 2006 data (see Fig.1 of Littlefair et al.51 2008). and so despite only having one eclipse (and thus lower signal-to-noise) it is favoured for the fitting process.," 2008), and so despite only having one eclipse (and thus lower signal-to-noise) it is favoured for the fitting process."52 In general our fits to each svstem are in excellent agreement with the light curves (sce Fig. 2)).," In general our fits to each system are in excellent agreement with the light curves (see Fig. \ref{fig:eclipses}) ),"53 giving us confidence that our new moclels accurately describe each svsteor., giving us confidence that our new models accurately describe each system.54 To obtain final svsteni parameters we combine our MCMC. chains with Kepler's 37 law. the orbital period. our derived white chvarl temperature. ancl a series of white dwarl mass-ractius relationships.," To obtain final system parameters we combine our MCMC chains with Kepler's $3^{rd}$ law, the orbital period, our derived white dwarf temperature, and a series of white dwarf mass-radius relationships."55 We favour the relationships of ?.. because they have thicker hydrogen lavers which may be more appropriate for CVs.," We favour the relationships of \citet{wood1995}, because they have thicker hydrogen layers which may be more appropriate for CVs."56 However. they co not reach high enough masses for some of our svstems.," However, they do not reach high enough masses for some of our systems."57" Above Al,=LOAL.. we adopt the mass-racius relationships of ?.."," Above $M_{w} = 1.0 M_{\odot}$, we adopt the mass-radius relationships of \citet{panei2000}. ."58" 1n turn. these models do not extend bevond AZ,=L2Al.: above this mass we use the ? relationship."," In turn, these models do not extend beyond $M_{w} = 1.2 M_{\odot}$; above this mass we use the \citet{hamada1961} relationship."59 No attempt is made to remove discontinuities from the resulting racius relationship., No attempt is made to remove discontinuities from the resulting mass-radius relationship.60" We calculate. the mass ratio g. white dwarf. mass AL,fAL.. white dwarf radius AH.. donor mass AL,/AL.. donor radius £2)/£2.. inclination 7. binary separation ei. ancl radial velocities of the white cwarl anc conor star (IN, and νε respectivelv) for cach step of the MCNMC chain."," We calculate the mass ratio $q$, white dwarf mass $M_{w}/M_{\odot}$, white dwarf radius $R_{w}/R_{\odot}$, donor mass $M_{r}/M_{\odot}$, donor radius $R_{r}/R_{\odot}$, inclination $i$, binary separation $a/R_{\odot}$ and radial velocities of the white dwarf and donor star $K_{w}$ and $K_{r}$, respectively) for each step of the MCMC chain."61 Since each step of the AICAIC has already been accepted or rejected based. upon the Metropolis-Hastings rule. the distribution function for cach parameter gives an estimate of the probability density function (PDE) of that parameter. given the constraints of our eclipse data.," Since each step of the MCMC has already been accepted or rejected based upon the Metropolis-Hastings rule, the distribution function for each parameter gives an estimate of the probability density function (PDF) of that parameter, given the constraints of our eclipse data."62 We can then combine the PDEs obtained in cach band fit into the total PDE for cach system. as shown in Fig. 4..," We can then combine the PDFs obtained in each band fit into the total PDF for each system, as shown in Fig. \ref{fig:pdfs}."63 We note that most systems have system parameters with a Gaussian distribution with very little asymmetry., We note that most systems have system parameters with a Gaussian distribution with very little asymmetry.64 Our adopted value [or à given parameter is taken from the peak of the PDP., Our adopted value for a given parameter is taken from the peak of the PDF.65 Upper and lower error bounds are derived. from the confidence levels., Upper and lower error bounds are derived from the confidence levels.66 For simplicity: since the distributions are mostly svmmoetrical. we take an average of the upper ancl lower error bounds.," For simplicity, since the distributions are mostly symmetrical, we take an average of the upper and lower error bounds."67 The final adopted. svstemi parameters are shown inTable 3..although Fig.," The final adopted system parameters are shown inTable \ref{table:system_params}, ,although Fig."68 7 and 8 show the true confidence levels for the whitedwarf mass and. donor mass respectively.for cach system.," \ref{figure:wd_masses} and \ref{figure:models} show the true confidence levels for the whitedwarf mass and donor mass respectively,for each system."69error circle was refined to the large solid. circle shown in the igure (Imanishi 2001. private communication).,"error circle was refined to the large solid circle shown in the figure (Imanishi 2001, private communication)."70 Within the ROSAT error circle for RX J0050.7-7316 and he revised ASCA circle for AX 0051-733 Lies an obvious optical object that has been proposed as the counterpart to roth of these N-ray. objects (Cowley et al. 1997. Schimidtke Cowley. 1998. Coe Orosz. 2000).," Within the ROSAT error circle for RX J0050.7-7316 and the revised ASCA circle for AX J0051-733 lies an obvious optical object that has been proposed as the counterpart to both of these X-ray objects (Cowley et al, 1997, Schmidtke Cowley, 1998, Coe Orosz, 2000)."71 It is à blue star exhibiting variability which stronely suggests that it is a De star companion to the N-rav pulsar., It is a blue star exhibiting variability which strongly suggests that it is a Be star companion to the X-ray pulsar.72 Fhis object also shows a strong Ü.7d optical modulation (or possibly twice hat value) which could be associated with a binary. period of the svstem (Cook 1998. Coe Orosz 2000).," This object also shows a strong 0.7d optical modulation (or possibly twice that value) which could be associated with a binary period of the system (Cook 1998, Coe Orosz 2000)."73 Llowever. his period is very short for a WAINB and the modulation signature atypical of tha seen [rom such objects.," However, this period is very short for a HMXB and the modulation signature atypical of that seen from such objects."74 Consequently. it was felt necessary to revisit the linking of this optical object wih the ASCA pulsar to make sure that some other candidate was not more appropiate within the X-ray error circle.," Consequently, it was felt necessary to revisit the linking of this optical object with the ASCA pulsar to make sure that some other candidate was not more appropiate within the X-ray error circle."75 Optical photometric observations were taken from. the SAO Lm telescope on 2 October 1900., Optical photometric observations were taken from the SAAO 1.0m telescope on 2 October 1996.76 Phe data were collected using the Teks CCD giving a field. of —6 x 6 arcminutes and a pixel scale of 0.6. aresce/pixel., The data were collected using the Tek8 CCD giving a field of $\sim$ 6 x 6 arcminutes and a pixel scale of 0.6 arcsec/pixel.77 Observations were made through standard Johnson V H filters plus an Ho filter., Observations were made through standard Johnson V R filters plus an $\alpha$ filter.78 Phe standard star L950 was used for photometric calibration., The standard star E950 was used for photometric calibration.79 From these CCD frames a llo colour index was created. and this was plotted. against the V band Dux for 7800 objects., From these CCD frames a $\alpha$ colour index was created and this was plotted against the V band flux for $\sim$ 800 objects.80 On the assumption that our optical counterpart was likely to be a Ho bright system. all the objects in the top third of the colour-magnitude plot were examined and their location in the field identified.," On the assumption that our optical counterpart was likely to be a $\alpha$ bright system, all the objects in the top third of the colour-magnitude plot were examined and their location in the field identified."81 Only four such objects were determined to be in. or close to. the ASC'X error circle.," Only four such objects were determined to be in, or close to, the ASCA error circle."82 These are numbered 476. 499. 512 and 647 in Figure 1. (object no: 512 is the proposed counterpart to the ROSATL sources).," These are numbered 476, 499, 512 and 647 in Figure \ref{optir} (object no: 512 is the proposed counterpart to the ROSAT sources)."83 AI the other objects with an R-Lla index =1.0 Hie well away from the region of interest., All the other objects with an $\alpha$ index $\ge-1.0$ lie well away from the region of interest.84 ‘The average D. V Icoloursofthesefourobjeclswereerel," The average $B$, $V$ $ I$ colours of these four objects were extracted from the OGLE database and are presented in Table 1."85racted fromtheOC LIdalabaseandarepi ," In addition, IR magnitudes for two of the objects are also presented that were extracted from the 2MASS survey data base, the other 2 candidates were too faint to be detected in that survey."86To confirm the nature of Object 512 as a D or Be star. optical spectra were obtained on 3 occasions (1 Nov 999. 15 Sep 2000 and 22 Oct 2000) from the ESO 1.52-m elescope at La Silla Observatory. Chile. equipped with the Boller Chivens spectrograph.," To confirm the nature of Object 512 as a B or Be star, optical spectra were obtained on 3 occasions (1 Nov 1999, 15 Sep 2000 and 22 Oct 2000) from the ESO 1.52-m telescope at La Silla Observatory, Chile, equipped with the Boller Chivens spectrograph."87 Phe no: 33 holographic erating was used. which gives a resolution of ~LA// pixel.," The no: 33 holographic grating was used, which gives a resolution of $\sim$ /pixel."88 Since no obvious variations were seen between the spectra hey were combined to increase the signal-to-noise ratio., Since no obvious variations were seen between the spectra they were combined to increase the signal-to-noise ratio.89 The resulting spectrum is presented in Figure 2.., The resulting spectrum is presented in Figure \ref{os}.90 In this igure our spectrum is compared to that of the DO.5V standard. 40 Per., In this figure our spectrum is compared to that of the B0.5V standard 40 Per.91 Object 512 is obviously a Be star. with 1L2 and H5 in emission and most other lines allectec by emission components.," Object 512 is obviously a Be star, with $\beta$ and $\gamma$ in emission and most other lines affected by emission components."92 The presence of weak A4686 places the object close to BOY (Walborn Fitzpatrick 1990)., The presence of weak $\lambda$ 4686 places the object close to B0V (Walborn Fitzpatrick 1990).93" ""Though several lines are present. A4650 iis surprisingly absent."," Though several lines are present, $\lambda$ 4650 is surprisingly absent."94 The relatively weak and lines seen in 40 Per are not easily detectable in object 512. which is compatible with the lower metallicity of the SMC. but unexpected in view of the rather strong lines.," The relatively weak and lines seen in 40 Per are not easily detectable in object 512, which is compatible with the lower metallicity of the SMC, but unexpected in view of the rather strong lines."95 The field of AX 0051-733 lies within the areas covered by both the OGLE and ALACLIO monitoring progranumes., The field of AX J0051-733 lies within the areas covered by both the OGLE and MACHO monitoring programmes.96 Hence excellent. photometric coverage exists for the xieghter counterparts for à total of nearly 7 vears., Hence excellent photometric coverage exists for the brighter counterparts for a total of nearly 7 years.97 Detailed. £ band. pjiotometrv was obtained from the OGLE cata base for objects numbered. 499 (no significant variability). 647. (some evidence for long term changes comparable to the lenet rol the data set) and 512.," Detailed $I$ band photometry was obtained from the OGLE data base for objects numbered 499 (no significant variability), 647 (some evidence for long term changes comparable to the length of the data set) and 512."98 As Cook (1998) and Coe Orosz (2000) have already. shown from subsets of the OGLIZ/NACLLO data. this object exhibits a," As Cook (1998) and Coe Orosz (2000) have already shown from subsets of the OGLE/MACHO data, this object exhibits a"99 (21017 L ep. ZT. 3 E»=E/1iQU in the production region in the unit of speed of light and the enerev of cosnüe rays. respectively.," $\gtrsim 10^{19}$ $L$ $\epsilon_B$ $Z$ $\Gamma$ $\beta$ $E_{20} = E / 10^{20}$ in the production region in the unit of speed of light and the energy of cosmic rays, respectively."100 Among known caudidates. few steady sources such as Fanaroft-Rilev (FR) II ealasies seeni to satisfy this condition in local Universe for Z=|. which is inconsistent with the observed anisotropy as long as UIECRs are protons2009).," Among known candidates, few steady sources such as Fanaroff-Riley (FR) II galaxies seem to satisfy this condition in local Universe for $Z = 1$, which is inconsistent with the observed anisotropy as long as UHECRs are protons."101. Also. Zaw ct al. (," Also, Zaw et al. ("1022009) argued that the power of AGN correlating with detected UMECRs seenis. iusufiicient to produce CHECR protons.,2009) argued that the power of AGN correlating with detected UHECRs seems insufficient to produce UHECR protons.103 The above luminosity requirement can be satisfied. however. if UITECTS are geucrated by powerful trausieut phenomena like AGN flares. CRBs and newly bor maguetars even if they are protons2009).," The above luminosity requirement can be satisfied, however, if UHECRs are generated by powerful transient phenomena like AGN flares, GRBs and newly born magnetars even if they are protons."104. The other possible astroplivsical solution is to consider that heavy nuclei dominate over protons. where the required luminosity is reduced bv Z? and therefore more objects are allowed to be UITECR sources.," The other possible astrophysical solution is to consider that heavy nuclei dominate over protons, where the required luminosity is reduced by $Z^2$ and therefore more objects are allowed to be UHECR sources."105 Tucleed. the heavs-iou-doninated composition has been implied bv recent results of the Pierre Auger Observatory (DAO)2010a).," Indeed, the heavy-ion-dominated composition has been implied by recent results of the Pierre Auger Observatory (PAO)."106. Π this is the case. ouly a few nearby radio galaxies or even a single ACN such as Cen Α max coutribute to the observed CIECR flux2008).," If this is the case, only a few nearby radio galaxies or even a single AGN such as Cen A may contribute to the observed UHECR flux."107. Other sources. inchiding radio- AGN απ CRBs2008).. are also viable.," Other sources, including radio-quiet AGN and GRBs, are also viable."108 The absence of anisotropy at ~107eV/Z may imply hie[um abundance of nuclei even at thelower cuereies. the origin ofwhich is unelear.," The absence of anisotropy at $\sim {10}^{20}~{\rm eV}/Z$ may imply high abundance of nuclei even at thelower energies, the origin ofwhich is unclear."109 On the other hand. the PAO data on tle fluctuation of X444 seca difficult to be reconciled wit[uum the μιας distribution of the same data2011).. aud proton composition may bepossible with a differeutestimator of primary composition 2011).," On the other hand, the PAO data on the fluctuation of $X_{\rm max}$ seem difficult to be reconciled with the $X_{\rm max}$ distribution of the same data, and proton composition may bepossible with a differentestimator of primary composition ."110. Also. the Tieh Resolution Fly's," Also, the High Resolution Fly's"111 ILj kms.| |OIII]5007/113.«3 ρωLiac1) (e.g.IXomossaοἱal.2006).," $\rm H\beta$ $\rm km112~s^{-1}$ $\rm [O III]1135007/H\beta < 3$ $L_{\rm bol}/L_{\rm114Edd}\sim1$ \cite[e.g.][]{kom06}."115. ~2.5% 22>100).," $\sim2.5\%$ $R>100$ \cite{kom06},"116number of detected counts within cach of the arm polygons. and the overall disc. were calculated.,"number of detected counts within each of the arm polygons, and the overall disc, were calculated."117 GALA then permits he apertures to be imported into the Ho. images. which rad been aligned exactly. such that the apertures lie over he same physical regions of the galaxies at both Ix and Ho.," GAIA then permits the apertures to be imported into the $\alpha$ images, which had been aligned exactly, such that the apertures lie over the same physical regions of the galaxies at both K and $\alpha$."118 hotometry was then obtained for all regions (arms. total disc and nucleus) in the Lo. images in exactly the same wav as for the images.," Photometry was then obtained for all regions (arms, total disc and nucleus) in the $\alpha$ images in exactly the same way as for the images."119 Finally. ratios were calculated of Ha lux divided byA band Εαν for all of the regions.," Finally, ratios were calculated of $\alpha$ flux divided by band flux for all of the regions."120 The test is then to see whether this ratio is larger for the arm regions han for the disc generally. where the latter ratio is taken rom the total disc minus the central region.," The test is then to see whether this ratio is larger for the arm regions than for the disc generally, where the latter ratio is taken from the total disc minus the central region."121 Any obvious Ooreground. stars are removed from. [rom the arm απ disc regions before this comparison is done., Any obvious foreground stars are removed from from the arm and disc regions before this comparison is done.122 If arms represent regions where all disc material is concentrated by an equal factor. then the Ho£A ratio would be the same in arms as in the disc overall.," If arms represent regions where all disc material is concentrated by an equal factor, then the $\alpha$ ratio would be the same in arms as in the disc overall."123 Lo there were no connection between star formation anclA band. structure. then this ratio would be lower in the selected arm regions. since these were chosen to have higher than averageA surface brightnesses.," If there were no connection between star formation and band structure, then this ratio would be lower in the selected arm regions, since these were chosen to have higher than average surface brightnesses."124 However. in the majority of cases. we Found HoA ratios to be significantly hisher in theA band arms than in the disces generally.," However, in the majority of cases, we found $\alpha$ ratios to be significantly higher in the band arms than in the discs generally."125 We measured a total of 49 arm regions in 20 galaxies (see Table 2): 38 (76%)) of these arms had. Ho/Ix ratios greater than that of the disc of the same galaxy., We measured a total of 49 arm regions in 20 galaxies (see Table 2); 38 ) of these arms had $\alpha$ /K ratios greater than that of the disc of the same galaxy.126 Averaging the ratios over all arms observed in a given. galaxy. we find. (Table 2 final column) that 19 of the 2) galaxies show a net enhancement in Hoήν ratio within their arm regions.," Averaging the ratios over all arms observed in a given galaxy, we find (Table 2 final column) that 19 of the 20 galaxies show a net enhancement in $\alpha$ ratio within their arm regions."127 The errors in table 2 were calculated by both adding and subtracting the uncertainty in the sky background from the Hà images ancl performing the same analysis for the original Ho. image. the La image subtracted by the sky background. uncertainty. and the llo image added by the sky. background: uncertainty.," The errors in table 2 were calculated by both adding and subtracting the uncertainty in the sky background from the $\alpha$ images and performing the same analysis for the original $\alpha$ image, the $\alpha$ image subtracted by the sky background uncertainty, and the $\alpha$ image added by the sky background uncertainty."128 The error in the sky background was calculated using both the formal uncertainty from pixel noise. and largerscale systematic variations in the sky structure.," The error in the sky background was calculated using both the formal uncertainty from pixel–pixel noise, and larger–scale systematic variations in the sky structure."129 Combining the results for all 49 arms. the median ratio was 40.11 times higher in the arms than in the corresponding disces.," Combining the results for all 49 arms, the median ratio was $\pm$ 0.11 times higher in the arms than in the corresponding discs."130 We have taken the median ratio in order to give less weight to galaxies which may be alfected by starbursts., We have taken the median ratio in order to give less weight to galaxies which may be affected by starbursts.131 Given the conservative nature of the test. this represents a highly significant finding of triggering of star formation within spiral arms.," Given the conservative nature of the test, this represents a highly significant finding of triggering of star formation within spiral arms."132 We checked that the location of the arms would not have been changed had we usedJ rather thanA images. and thus our results are not alfected by the possibility that hot dust may contribute to galaxy light atA (James mSelgar 1999).," We checked that the location of the arms would not have been changed had we used rather than images, and thus our results are not affected by the possibility that hot dust may contribute to galaxy light at (James Seigar 1999)."133 Two of the galaxies warrant further comment., Two of the galaxies warrant further comment.134 UGC 3053 exhibits 3 welldefined arm segments in itsA band image. but there is little or no Lla luminosity [rom LIL regions associated with these arms.," UGC 3053 exhibits 3 well–defined arm segments in its band image, but there is little or no $\alpha$ luminosity from HII regions associated with these arms."135 This is reflected in the low Ho/A ratios for all three arm regions in this galaxy. which thus appears to have no arm.induced star formation according to this test.," This is reflected in the low $\alpha$ ratios for all three arm regions in this galaxy, which thus appears to have no arm–induced star formation according to this test."136 UGC 6332 has two tightly. wound arms. which could be classified as a single ring. anc which appear highly symmetrical in theA image.," UGC 6332 has two tightly wound arms, which could be classified as a single ring, and which appear highly symmetrical in the image."137 However. this svnunetry breaks down completely in Ho light. since one arm is clearly associated with a string of LILL regions. aud the other with no detectable LLL regions at all.," However, this symmetry breaks down completely in $\alpha$ light, since one arm is clearly associated with a string of HII regions, and the other with no detectable HII regions at all."138 As a result. these two arms give rise respectively to the second.highest. and to easilv the lowest. of the 49 measured Ho/A ratios.," As a result, these two arms give rise respectively to the second–highest, and to easily the lowest, of the 49 measured $\alpha$ ratios."139 This asymmetry. could be an extinction elfect. due to the olfset between the dust lane and the peak of vw induced star formation.," This asymmetry could be an extinction effect, due to the offset between the dust lane and the peak of the induced star formation."140 ln this analysis we have ignored the resu hat theA band light may have a contribution of up to from star formation (James Seigar 1999)., In this analysis we have ignored the result that the band light may have a contribution of up to from star formation (James Seigar 1999).141 An elfect such as this will tend. to increase the amplitude of theA band μαspiral arms. and hence decrease the cllect that we find.," An effect such as this will tend to increase the amplitude of the band spiral arms, and hence decrease the effect that we find."142 Hence our result is conservative and can only be strengthened. by making corrections for this., Hence our result is conservative and can only be strengthened by making corrections for this.143 A further test of arm induced star formation is to see if the enhancement in Ho flux in the arm regions relates to the strength of shocks in the arms., A further test of arm induced star formation is to see if the enhancement in $\alpha$ flux in the arm regions relates to the strength of shocks in the arms.144 Seigar James (1998b) used the ratio between arm equivalent angle (EA) and arm full width half maximum (ENLIM) as measured fromA band images. às à measure of the relative strength of shocks in spiral arms.," Seigar James (1998b) used the ratio between arm equivalent angle (EA) and arm full width half maximum (FWHM) as measured from band images, as a measure of the relative strength of shocks in spiral arms."145" From here on. we refer to this ratio as the ""central arm contrast’."," From here on, we refer to this ratio as the `central arm contrast'."146 Arm EA is defined. as that angle subtended by the disc that contains an amount οἱ light equivalent to that in the spiral armi (sce Scigar James 1998a for a detailed cliscussion) ancl is therefore a measure of the amount of light contained in a spiral arm., Arm EA is defined as that angle subtended by the disc that contains an amount of light equivalent to that in the spiral arm (see Seigar James 1998a for a detailed discussion) and is therefore a measure of the amount of light contained in a spiral arm.147" However. it contains no information about how concentrated the light from the arm is. and this is the justification in dividing this quantity by arm ENWIIM. (measured. from the crosssectional light. profiles ofA. band. arms) to estimate the ""central arm concentration’."," However, it contains no information about how concentrated the light from the arm is, and this is the justification in dividing this quantity by arm FWHM (measured from the cross--sectional light profiles of band arms) to estimate the `central arm concentration'."148 Lf shocks are necessary to crive star formation. it seems reasonable that an arm with a high central arm concentration will be more ellicient at forming stars than an arm with a low central arm concentration.," If shocks are necessary to drive star formation, it seems reasonable that an arm with a high central arm concentration will be more efficient at forming stars than an arm with a low central arm concentration."149satellites around the Milky Wavy within the same radius.,satellites around the Milky Way within the same radius.150 The Local Group data is from the compilation of ?., The Local Group data is from the compilation of .151. The figure clearly shows that the spatial distribution of dwart ealaxies around the Milky. Wav is more compact than the distribution of the DAL population., The figure clearly shows that the spatial distribution of dwarf galaxies around the Milky Way is more compact than the distribution of the DM population.152 The median distauce of observed satellites within 200)+ pe is GOD1 kpe and 85h1 kpe for the MW aud MBL. respectively.," The median distance of observed satellites within $200h^{-1}$ kpc is $60h^{-1}$ kpc and $85h^{-1}$ kpc for the MW and M31, respectively."153" For the DM. satellites the correspouding median distances are 1165! spe. 12143 pe, and 1205.| kpe."," For the DM satellites the corresponding median distances are $116h^{-1}$ kpc, $121h^{-1}$ kpc, and $120h^{-1}$ kpc."154 Althoneh the median or MIBL satellites is znaller than that of the DM satellites. heir radial distributious are formally cousisteut.," Although the median for M31 satellites is smaller than that of the DM satellites, their radial distributions are formally consistent."155 However. he comparison with the M31 satellites is difficult at preseut jecauxe typical distance errors are ~20/050 kpe (and &70 kpe for some galaxies). comparable to the distance o the host," However, the comparison with the M31 satellites is difficult at present because typical distance errors are $\sim15620-50$ kpc (and $\gtrsim 70$ kpc for some galaxies), comparable to the distance to the host."157 For the MW satellites the tvpical distance erors are au order of maguitide sualler and the comparison is cousiderablv nore meaninetful., For the MW satellites the typical distance errors are an order of magnitude smaller and the comparison is considerably more meaningful.158 The IKolinogorov-Suirnov (KS) test eives xobabilitv of (68)«LO1 that the MW satellites are ≼⊔⋅⋜∏↖↽∐↕≯↥⋅∪⋯↑∐↸∖↴∖↴⋜⊔⊔↸∖↥⋅⋜∥↕⋜↕↕≼∐↴∖↴⊓⋅∏⋝∏↑↕∪∐⋜↧↴∖↴↑∐↸∖↕≻⋀∖, The Kolmogorov-Smirnov (KS) test gives probability of $(6-8)\times 10^{-4}$ that the MW satellites are drawn from the same radial distribution as the DM satellites.159↕↴∖↴⋜↧↑↸∖↕∐↑↸∖↴∖↴⋅ This has also been pointedout recently?.. who compared lio spatial distribution of the MW satellitesby to results of heir scii-analytic model of galaxy formation.," This has also been pointed out recently by, who compared the spatial distribution of the MW satellites to results of their semi-analytic model of galaxy formation."160 Thus. in addition to the vastly different of abundancesthe observed and predicted satellites. there is a discrepancy in the radial distribution.," Thus, in addition to the vastly different abundances of the observed and predicted satellites, there is a discrepancy in the radial distribution."161 Models that aim to reproduce the abundance of the LG satellites should therefore be able to reproduce the radial distribution as well., Models that aim to reproduce the abundance of the LG satellites should therefore be able to reproduce the radial distribution as well.162" Tn order to gain insight iuto which halos nüght become and which uot, we nuplement the following simple uousmodel star mightformation."," In order to gain insight into which halos might become luminous and which might not, we implement the following simple model of star formation."163" We use the standard assmition hat the gas of the halos with virial temmperatyre Ty>LOE S withindissipates its ο via theradiative cooling aud σας a disk,", We use the standard assumption that the gas within the halos with the virial temperature $T_{\rm vir} > 10^4$ K dissipates its energy via radiative cooling and forms a disk.164 We apply the enrpirical Schmidt law to calculate the star thenformation rate in radial shells within he disk., We then apply the empirical Schmidt law to calculate the star formation rate in radial shells within the disk.165 The novel features of our model include: (4) use of dass aud history of dwart halos extracted from accretionsimulation. (11) stripping of effectsphotoioniziugthe extragalactic ckeround using the filtering mass. (ii) effects of inefficient ot the gas at Zu~101 I. and (iv) bursts of star dissipationformation duc to strong tidal shocks.," The novel features of our model include: (i) use of mass accretion and stripping history of the dwarf halos extracted from simulation, (ii) effects of photoionizing extragalactic background using the filtering mass, (iii) effects of inefficient dissipation of the gas at $T_{\rm vir} \lesssim 10^4$ K, and (iv) bursts of star formation due to strong tidal shocks."166 The details of he model are as follows. (, The details of the model are as follows. (1671) the amass assembly . ofa ∙∙siven Usinghalo directly from the historysimulation. (MATT)mstead ot a satellitesenmi-aualvtie approach. we able to trace MaJor merecr events as well as the quiescentare accretionof thematerial.,"i) Using the mass assembly history (MAH) of a given satellite halo directly from the simulation, instead of a semi-analytic approach, we are able to trace the major merger events as well as the quiescent accretion of material."168 The halo ass increases ta both regimes. but the star," The halo mass increases in both regimes, but the star"169readout.,readout.170 Iterations of the fitting procedure rejected. outlier values in determining the model parameters d; and b;, Iterations of the fitting procedure rejected outlier values in determining the model parameters $a_i$ and $b_i$.171" Pixels for which no solution converged. or for which the ""1l 0 interquantile width (auedian miuus 16th percentile) of the distribution of residuals from the fit was more than three tines wider than the median residual value for the nuage. were masked as bad pixels."," Pixels for which no solution converged, or for which the “1 $\sigma$ ” interquantile width (median minus 16th percentile) of the distribution of residuals from the fit was more than three times wider than the median residual value for the image, were masked as bad pixels."172 All nuages were then corrected according to their exposure time using the superdark D;., All images were then corrected according to their exposure time using the superdark $D_i$.173 Iu seneral neither twilight nor dome flats were reeularly available. aud nuages taken under dark-skv conditions were often contaminated with stroue fringes.," In general neither twilight nor dome flats were regularly available, and images taken under dark-sky conditions were often contaminated with strong fringes."174 We therefore chose to construct flat fields using science nuages taken both during twilight aud in mooulieht., We therefore chose to construct flat fields using science images taken both during twilight and in moonlight.175 The calculations of ?.. appropriately adapted to Mt. Palomar. suggests that the loss of flatucss due to the nuon-uniforiuitfv of moonlight should be less than over the extent of each chip (0.5 degrees) for nuages taken inore than 20 degrees from) the moon. and we required this of miages used to build the Hat field.," The calculations of \cite{ks91}, appropriately adapted to Mt. Palomar, suggests that the loss of flatness due to the non-uniformity of moonlight should be less than over the extent of each chip (0.5 degrees) for images taken more than 20 degrees from the moon, and we required this of images used to build the flat field."176 We also required that the sky level frou scattered moonlight in these mages be at least five times that typical of dark. sky conditions., We also required that the sky level from scattered moonlight in these images be at least five times that typical of dark sky conditions.177 Tages passing both of these cuts were 1orinalized to a imean sky brightuess of 1.0. and combined w taking the median at cach pixel location to produce a superflat for the month.," Images passing both of these cuts were normalized to a mean sky brightness of 1.0, and combined by taking the median at each pixel location to produce a superflat for the month."178 Pixels with uuusuallv large Huctuations relative to other pixels were masked as bad. ax for superdarks above.," Pixels with unusually large fluctuations relative to other pixels were masked as bad, as for superdarks above."179 All images were then flattened using these superflats., All images were then flattened using these superflats.180 Superfiuges were constructed m an analo@ous niauner o the superflats usine images taken under dark-sky conditions., Superfringes were constructed in an analogous manner to the superflats using images taken under dark-sky conditions.181 The baseline fringe patteru was assumed o be a time-invariant characteristic of cach chip over the month., The baseline fringe pattern was assumed to be a time-invariant characteristic of each chip over the month.182 The fiuge amplitude i each science nage was determined through cross-correlation with the superfiinec. and the fringes in the nuage removed by subtracting the superfüiusge scaled bw this amplitude.," The fringe amplitude in each science image was determined through cross-correlation with the superfringe, and the fringes in the image removed by subtracting the superfringe scaled by this amplitude."183 Changing skv conditions can of course produce time varlatious iu the frinecs. particularly im such a wicle-xad Alter.," Changing sky conditions can of course produce time variations in the fringes, particularly in such a wide-band filter."184 We accept this as a systematic error in the photometry. with a coutribution roughly ou the same order as the sky noise under dark sky. couditious.," We accept this as a systematic error in the photometry, with a contribution roughly on the same order as the sky noise under dark sky conditions."185 Object detection aud aperture photometry were serformed on the detreuded (hias-subtracted. dark-subtracted. flattened aud de-f£iuged) nuages sine (?))," Object detection and aperture photometry were performed on the detrended (bias-subtracted, dark-subtracted, flattened and de-fringed) images using \citealt{sextractor}) )."186 Astrometry was performed on cach yale using the suite (?2))., Astrometry was performed on each frame using the suite \citealt{astronet}) ).187 Magnuitudes were dneasuredo for cach astrometry.netobject using ten aperture diameters raneing from 1 pixel to 16 pixels: this work uses the 3-pixel diameter aperture measurements as the primary flux imieasurenmieutf., Magnitudes were measured for each object using ten aperture diameters ranging from 1 pixel to 16 pixels; this work uses the 3-pixel diameter aperture measurements as the primary flux measurement.188 Aperture corrections were calculated as the clipped mecian of the 12-pixel diameter aperture flux divided by the pixel aperture fis., Aperture corrections were calculated as the clipped median of the 12-pixel diameter aperture flux divided by the 3-pixel aperture flux.189 This correction was calculated using all good-quality lueasurements on a frame. and calculated separately for cach frame.," This correction was calculated using all good-quality measurements on a frame, and calculated separately for each frame."190 A nmuuber of cuts are made on the quality of the data., A number of cuts are made on the quality of the data.191 First. flags are checked for objects that are blended or saturated. close to image boundaries. or for which the measurement failed: these flags. clinunate about of the data.," First, flags are checked for objects that are blended or saturated, close to image boundaries, or for which the measurement failed; these flags eliminate about of the data."192 A further saturation check is made bv comparing object fluxcs to saturation levels determined for each chip. which are more accurate than the single baseline saturation level checked bySExtractor.," A further saturation check is made by comparing object fluxes to saturation levels determined for each chip, which are more accurate than the single baseline saturation level checked by."193. Verv few objects are eliminated by this cut., Very few objects are eliminated by this cut.194 Variations iu the backeround sky level ou the sanall spatial scale of 545 pixels are examined. aud a fraane is discarded if they are typically large enough to contribute a error to the photometry of au object with magnitude I8: this removes about of the inages.," Variations in the background sky level on the small spatial scale of $\times$ 5 pixels are examined, and a frame is discarded if they are typically large enough to contribute a error to the photometry of an object with magnitude 18; this removes about of the images."195 Frames are also rejected for which the mecian full width at half masximan (FWOAD exceeds 5 pixels. eliinatiug about of the data.," Frames are also rejected for which the median full width at half maximum (FWHM) exceeds 5 pixels, eliminating about of the data."196 To ensure that closely spaced detections do not coutaminate the aperture photometry. an object is rejected if it has a neighbor within four arc seconds (23.5 pixels): iost object affected. by this cut are already discarded for beiug blended inSExtractor.," To ensure that closely spaced detections do not contaminate the aperture photometry, an object is rejected if it has a neighbor within four arc seconds $\sim$ 3.5 pixels); most object affected by this cut are already discarded for being blended in."197. Spatial fluctuations of the moon/twilieht fat fields aud variabilitv in night «kv lines during observations nado it difficult to completely remove the frinecs from the data., Spatial fluctuations of the moon/twilight flat fields and variability in night sky lines during observations made it difficult to completely remove the fringes from the data.198 This results iva —2% flux systematic for bright objects. which is added in quadrature to the statistical errors.," This results in a $\sim 2\%$ flux systematic for bright objects, which is added in quadrature to the statistical errors."199 A standard inethod of calibration is simply to determine a iuultiplicativeo constaut zero point which corrects differences in average response (both intrinsic and weather-related) between two images., A standard method of calibration is simply to determine a multiplicative constant zero point which corrects differences in average response (both intrinsic and weather-related) between two images.200 We perform such a frame-based calibration as a first step., We perform such a frame-based calibration as a first step.201 All overlapping images are determined. and the one in which objects have the brightest 1uieasureiments ix assigned as he standard.," All overlapping images are determined, and the one in which objects have the brightest measurements is assigned as the standard."202 A single zero point is determined for cach frame in order to bring it to the level of the standard., A single zero point is determined for each frame in order to bring it to the level of the standard.203 This constant is determined using objects ofall nagnitudes., This constant is determined using objects of all magnitudes.204 The correction is also calculated separately or bius of different maeuitudes: five bius between SDSS r magnitudes of roughly 15 and 20., The correction is also calculated separately for bins of different magnitudes: five bins between SDSS r magnitudes of roughly 15 and 20.205 Ou average. the differeuce in the mean correction between the Iyrightest yn and a fainter one ranges from about to6," On average, the difference in the mean correction between the brightest bin and a fainter one ranges from about to."206%.. Πα arecr variation than this is seen. the frame is assumed ο be non-Inear and is not used.," If a larger variation than this is seen, the frame is assumed to be non-linear and is not used."207 This climinates about of the data: the non-lincaritv is partially due to intrinsic properties of the CCDs. but primarily due to the insuffiicicut quality of the fringe aud flat field calibration data.," This eliminates about of the data; the non-linearity is partially due to intrinsic properties of the CCDs, but primarily due to the insufficient quality of the fringe and flat field calibration data."208 Poor frames are also ideutifiedk by comparing their nieasurenmieuts to the mean measurements of the objects thev hold., Poor frames are also identified by comparing their measurements to the mean measurements of the objects they hold.209 Tf of the flux measurements on a frame disagree with their objects? iieaus by more than 3 times the measurement errors. then the frame is discarded.," If of the flux measurements on a frame disagree with their objects' means by more than 3 times the measurement errors, then the frame is discarded."210 This removes about of the data. for which the systematic effects are catastrophic.," This removes about of the data, for which the systematic effects are catastrophic."211 The systematic residuals in the data make a frame-basecd calibration insufficient for accurate photometry: while a systematic term— describes— the typical uncertainties. the error distribution is nof Gaussian and therefore this procedure ecucrates Waly photometric outhers.," The systematic residuals in the data make a frame-based calibration insufficient for accurate photometry; while a systematic term describes the typical uncertainties, the error distribution is not Gaussian and therefore this procedure generates many photometric outliers."212 Because the spatial scale of the «ποιαας variations is much larger than the size of each object. we can refine the frame-based calibration using an object-based one.," Because the spatial scale of the systematic variations is much larger than the size of each object, we can refine the frame-based calibration using an object-based one."213 This technique involves ecucrating a zero poiut for one object at a time by considering oulv its close neighbors., This technique involves generating a zero point for one object at a time by considering only its close neighbors.214 A large scale systematic variation far awav from an object will affect a fiune-based calibration: ai object-based one will be less seusitive to such features., A large scale systematic variation far away from an object will affect a frame-based calibration; an object-based one will be less sensitive to such features.215 We therefore implement. as a second step. an ohject-based calibration.," We therefore implement, as a second step, an object-based calibration."216 We use the average of at least LO neighbors within 150 arc seconds to caleulate the correction between an objects nicasuremoenuts on two, We use the average of at least 10 neighbors within 150 arc seconds to calculate the correction between an object's measurements on two217The ice abundance in (he disk gas is determined with the thermal equilibrium condition under which (he partial pressure of water vapor is limited by the saturated vapor pressure (Dauera,The ice abundance in the disk gas is determined with the thermal equilibrium condition under which the partial pressure of water vapor is limited by the saturated vapor pressure (Bauer.218"l 1991): The partial pressure of water vapor Z,0 Is approximately given by the product of the water vapor mole fraction Ayo and the total gas pressure: The water vapor mole fraction Nqj,0 is limited by 1.2xLO7. so excess water molecules condense as water ice."," 1997): The partial pressure of water vapor $P_{\mathrm{H_{2}O}} $ is approximately given by the product of the water vapor mole fraction $X_{\mathrm{H_{2}O}}$ and the total gas pressure: The water vapor mole fraction $X_{\mathrm{H_{2}O}}$ is limited by $1.2 \times 10^{-3}$, so excess water molecules condense as water ice."219" Thus. IX4,0 is given by Then. the mass ratio of ice to the total watermolecules in the disk gas. «προ. is given bv Using Όρο, (e absorption aud scattering coellicients of the disk medium. Ay. and Aya. are given as Where Εμμ Reilecas Piceabs:) QC μονο represent the absorption and scattering coellicients of disk medium attributed to silicate ancl ice dust particles. respectively."," Thus, $X_{\mathrm{H_{2}O}}$ is given by Then, the mass ratio of ice to the total watermolecules in the disk gas, $x_{\mathrm{ice}}$, is given by Using $x_{\mathrm{ice}}$, the absorption and scattering coefficients of the disk medium, $\kappa_{\mathrm{abs}}$ and $\kappa_{\mathrm{sca}}$ , are given as where $\kappa_{\mathrm{sil, abs}}$, $\kappa_{\mathrm{sil, sca}}$, $\kappa_{\mathrm{ice, abs}}$, and $\kappa_{\mathrm{ice, sca}}$ represent the absorption and scattering coefficients of disk medium attributed to silicate and ice dust particles, respectively."220 Eqs. (6)), Eqs. \ref{kappa_1}) )221 and (7)) are held for each frequency of the radiative transfer., and \ref{kappa_2}) ) are held for each frequency of the radiative transfer.222 The disk temperature depends on cj. hence the temperature and c; are solved.consistently by iterative calculations.," The disk temperature depends on $x_{\mathrm{ice}}$ , hence the temperature and $x_{\mathrm{ice}}$ are solvedconsistently by iterative calculations."223oL galaxies ancl must be small enough to iguore the evolution.,of galaxies and must be small enough to ignore the evolution.224 We may choose redshift bands of each survey region As;~O.L., We may choose redshift bands of each survey region $\Delta z_i\sim 0.1$.225 Theu the number of galaxies observed Neo las to satisly fo. For SDSS (SloanDi, Then the number of galaxies observed $N_O$ has to satisfy $N_O \geq 10^3 z_G/\Delta z_i/f_G$ .226gitalSkySurvey (2000))). which covers one quarter of the sky aud probes more than oue million galaxies with photometric redshift up to zIL. the requirement No>10? is easily satisfied.," For SDSS \citet{SDSS}) ), which covers one quarter of the sky and probes more than one million galaxies with photometric redshift up to $z\sim 1$, the requirement $N_O \geq 10^5$ is easily satisfied."227 The imeasuremeut of the intergalactic gas at redshift z requires the ealaxy survey at least up to that redshilt (equation 25)). so we need deeper galaxy survey in order to probe the gas beyond 2~1. (," The measurement of the intergalactic gas at redshift z requires the galaxy survey at least up to that redshift (equation \ref{eqn:phim}) ), so we need deeper galaxy survey in order to probe the gas beyond $z\sim1$. ("228b) fiinM>107(2000/1).,b) $f_{cmb} \Delta l \geq 10^2 (2000/l)$.229 For CMB experiments with relatively lower resolution. larger sky coverage is required.," For CMB experiments with relatively lower resolution, larger sky coverage is required."230 For example. though Plauck ouly measures /x2000. i covers the whole sky aud therefore satisfies this condition.," For example, though Planck only measures $l\leq 2000$, it covers the whole sky and therefore satisfies this condition."231 For those with much higher resolution such as AMIBA ancl Subinillimeter Telescope. the required sky coverage can be relaxed to the order ol 15.," For those with much higher resolution such as AMIBA and Submillimeter Telescope, the required sky coverage can be relaxed to the order of $1 \%$."232 This variation method ouly depends ou the assumption that the cross correlation coellicien rk.2) is approximately a coustant. which is the direct result of the hierarchical model aud bas only weak clepeuceuce ou the gas model and cosmologies.," This variation method only depends on the assumption that the cross correlation coefficient $r(k,z)$ is approximately a constant, which is the direct result of the hierarchical model and has only weak dependence on the gas model and cosmologies."233 Furthermore. the hierarchical model is strougly supported by the consistency of the CAIB SZ power spectrum depeudence on ox and the behavior of the gas bias between our model aud simulations.," Furthermore, the hierarchical model is strongly supported by the consistency of the CMB SZ power spectrum dependence on $\sigma_8$ and the behavior of the gas bias between our model and simulations."234 Since the averaged r(&.2) is measurable. our uietliod does uot rely much ou the theoretical value of r(&.z) aud thus observationally cousisteut.," Since the averaged $r(k,z)$ is measurable, our method does not rely much on the theoretical value of $r(k,z)$ and thus observationally consistent."235 Pen (1999) bas shown that the [GM las most likely Όσοι preheated by nou-gravitatioual energy sources with energy injection Exc;1 keV per nucleon., Pen (1999) has shown that the IGM has most likely been preheated by non-gravitational energy sources with energy injection $E_{NG}\sim 1$ keV per nucleon.236 This section is devoted to consider this effect., This section is devoted to consider this effect.237 Because the relation between the gravitational heating and the non-gravitational heatiug is very uncertain. we ouly cousider two extreme cases.," Because the relation between the gravitational heating and the non-gravitational heating is very uncertain, we only consider two extreme cases."238 The first oneis that the uou-gravitational heating is perfectly correlated with the gravitatioual heating. then we can change Eq. (5))," The first oneis that the non-gravitational heating is perfectly correlated with the gravitational heating, then we can change Eq. \ref{eqn:temp}) )"239 to: We will append all former results from gravitational heating with a superscript A (Adiabatic)., to: We will append all former results from gravitational heating with a superscript 'A' (Adiabatic).240 Here. 2=Tye{Ty represents the ratio of the non-gravitational heating aud the gravitational heating. νο=8/3/(38+ON)Eye.," Here, $\beta\equiv T_{NG}/\bar{T_g}^A$ represents the ratio of the non-gravitational heating and the gravitational heating. $kT_{NG}=8/3/(3+5 X) E_{NG}$."241 Exc;~1 keV corresponds το)~1.," $E_{NG}\sim 1$ keV corresponds to $\beta \sim 2421$."243" All former results are not allected by this change except Ty. yxTy. CjxTyE and Osx-1/7, due to the dependence T,4x(E3)."," All former results are not affected by this change except $\bar{T_g}$, $\bar{y} \propto \bar{T_g}$, $C_l \propto \bar{T_g}^2$ and $\Theta_3 \propto 1/\bar{T_g}$ due to the dependence $\bar{T_g} \propto (1+\beta)$."244 FigureoO 1. and L need to be changeded correspondiuelv., Figure \ref{fig:temp} and \ref{fig:cl} need to be changed correspondingly.245o FigureoO 5 and 7 will changee only when 9 is time-cepencent.," Figure \ref{fig:zcon}246 and \ref{fig:Corr} will change only when $\beta$ is time-dependent."247 All other figures remain the same., All other figures remain the same.248 The second case is that nou-gravitational heating is uucorrelated with local density. then. Eq. (51) ," The second case is that non-gravitational heating is uncorrelated with local density, then, Eq. \ref{eqn:temp}) )"249changes to: BT4/ ⊺∙↙∕∶⊺∙↙∕↲↱↕∖⋖∙⊲∶∪↲↱↴≩≼∶∏⊺∫∕⋅⊺∐↩∐⋅↕∐≺↵∢∙≺∐⋅⋅≺," changes to: $\bar{T_g}=\bar{T_g}^A+T_{NG}=[1+\beta(z)]250\bar{T_g}^A$ ."251↵⊳∖↥↽≻∩∐≺∐∐∑≟∐≺↵∖∖↽↕⋅≺↵⊳∖⋃∐⊳∖↥∩∐∩∖∖↽⋯∑∸↕∐≺↵⊳∖⋜⋃∐≺↵ ⋅ ⋅," Then, the corresponding new results following the same"252the non-weak regime: strong lensing can likely tell us more about the clensity profiles of massive Clusters at such small scales.,the non-weak regime; strong lensing can likely tell us more about the density profiles of massive clusters at such small scales.253 Alternatively. other methods. such as the maximum likelihood approach of Schneider&Rix(1997).. might be able to better handle this regime. though at the cost of introducing explicit model dependence.," Alternatively, other methods, such as the maximum likelihood approach of \cite{schneider-rix:max-like}, might be able to better handle this regime, though at the cost of introducing explicit model dependence."254 We can rewrite Equation 7 (aller multiplving by X5) as or in terms of the shear. (multiplving Equation 5. bv Xj) An equation for V'(HR) is useful because of the existence of the Von Zeipel (or sometimes called Abel) inversion formula for the 3D density profile: The inverse of (his equation is just the usual projection where. as before. Apt)=pli)—p. because we do not recover the average mass density of the Universe: lensing is not sensitive {ο mass sheets.," We can rewrite Equation \ref{eq:non-lin-inv} (after multiplying by $\Sigma_{crit}$ ) as or in terms of the shear, (multiplying Equation \ref{eq:kappa-prime} by $\Sigma_{crit}$ ) An equation for $\Sigma^{\prime}(R)$ is useful because of the existence of the Von Zeipel (or sometimes called Abel) inversion formula for the 3D density profile: The inverse of this equation is just the usual projection where, as before, $\Delta\rho(r) \equiv \rho(r)-\bar{\rho}$, because we do not recover the average mass density of the Universe: lensing is not sensitive to mass sheets."255 That is. we have arbitrarily chosen the boundary condition pix)=p or Ap(x:)=0: for further discussion of the mass sheet clegeneracy. see 85.2.," That is, we have arbitrarily chosen the boundary condition $\rho(\infty)=\bar{\rho}$ or $\Delta\rho(\infty)=0$; for further discussion of the mass sheet degeneracy, see 5.2."256 Inversions of this tvpe have a long history in astronomy., Inversions of this type have a long history in astronomy.257 VonZeipel(1908) derived (his inversion formula and used it (to determine the 3D density. profile of elobular clusters from imaging data., \cite{vonzeipel:deproj} derived this inversion formula and used it to determine the 3D density profile of globular clusters from imaging data.258 Von Zeipel's proof of this inversion formula rests on reducing it through substitutions to Abel's formula (Abel1826).. which in turn. is usually proven through the use of the Laplace transform. Plummer(1911)..," Von Zeipel's proof of this inversion formula rests on reducing it through substitutions to Abel's formula \citep{abel:deproj}, which in turn, is usually proven through the use of the Laplace transform. \cite{plummer:deproj},"259 also concerned with globular clusters. derived a similar formula which uses intensities in long parallel strips rather (han circular annuli.," also concerned with globular clusters, derived a similar formula which uses intensities in long parallel strips rather than circular annuli."260 Recently Ixaastra(1989). has shown that Von Zeipels Formula can be derived Irom Plummer5, Recently \cite{kaastra:deproj} has shown that Von Zeipel's formula can be derived from Plummer's261Both operative modes can be active at the same time. but the one relevant to GRB investigation is the BURST mode.,"Both operative modes can be active at the same time, but the one relevant to GRB investigation is the BURST mode."262 BURST data are stored in a circular buffer and analysed by a dedicated trigger logic. described in detail in ?..," BURST data are stored in a circular buffer and analysed by a dedicated trigger logic, described in detail in \citet{Fuschino2008}."263 If à trigger is issued. the data are sent to telemetry on a photon-by-photon basis including. for each event. energy information and a time tag with 2yes accuracy.," If a trigger is issued, the data are sent to telemetry on a photon-by-photon basis including, for each event, energy information and a time tag with $2~\mathrm{\mu s}$ accuracy."264 Without a trigger. or when the trigger logic is off. due to telemetry limitations BURST data are not sent to the ground on a photon-by-photon basis. but are used to build two broad band energy spectra (Scientific Ratemeters. SRM). one for each detection layer. and stored in telemetry with a 1.024 s time bin.," Without a trigger, or when the trigger logic is off, due to telemetry limitations BURST data are not sent to the ground on a photon-by-photon basis, but are used to build two broad band energy spectra (Scientific Ratemeters, SRM), one for each detection layer, and stored in telemetry with a 1.024 s time bin."265 Due to programmatic constraints it was not possible to switch on and configure the on-board trigger logie. prior to the end of November 2007., Due to programmatic constraints it was not possible to switch on and configure the on-board trigger logic prior to the end of November 2007.266 Then it was switched off again during January 2008. and since the 5” of February 2008 it has again been operative.," Then it was switched off again during January 2008, and since the $5^{th}$ of February 2008 it has again been operative."267 When the trigger logic was not active. GRBs were detected by on-ground analysis. scanning the SRM data for rate increases with a dedicated software task.," When the trigger logic was not active, GRBs were detected by on-ground analysis, scanning the SRM data for rate increases with a dedicated software task."268 Despite several GRBs having been detected with this method. the coarse time and energy binning limits the scientific exploitation of the data.," Despite several GRBs having been detected with this method, the coarse time and energy binning limits the scientific exploitation of the data."269 On the contrary. with the onset of the on-board trigger logic. time and energy binnir5 for triggered events is only limited by counting statistics.," On the contrary, with the onset of the on-board trigger logic, time and energy binning for triggered events is only limited by counting statistics."270 The early MCAL GRB detections are reported in ?.., The early MCAL GRB detections are reported in \citet{Marisaldi2008}.271 Several GRB detectors are currently active in space. each with its own specific characteristics.," Several GRB detectors are currently active in space, each with its own specific characteristics."272 Apart from Swift-BAT (?).. INTEGRAL-IBIS (?).. SuperAGILE (?).. GLAST-GBM (?)) and GLAST-LAT (?).. all the other detectors have no or very limited imaging capabilities and rely on triangulation between different spacecraft for GRB localization. through the 304 Inter-Planetary Network(IPN)'.," Apart from Swift-BAT \citep{Barthelmy2000}, INTEGRAL-IBIS \citep{Ubertini2003}, , SuperAGILE \citep{Feroci2007}, GLAST-GBM \citep{Meegan2007} and GLAST-LAT \citep{Michelson2007}, all the other detectors have no or very limited imaging capabilities and rely on triangulation between different spacecraft for GRB localization, through the $3^{rd}$ Inter-Planetary Network."273. Among the current IPN instruments. only three have spectroscopic capabilities at MeV energies. in an energy range partially overlapping with that of MCAL: Konus-Wind (?).. Suzaku-WAM (?) and RHESSI (?)..," Among the current IPN instruments, only three have spectroscopic capabilities at MeV energies, in an energy range partially overlapping with that of MCAL: Konus-Wind \citep{Aptekar1995}, Suzaku-WAM \citep{Yamaoka2006} and RHESSI \citep{Wigger2004}."274 Among these. only the RHESSI spectrometer is capable of photon-by-photon data download.," Among these, only the RHESSI spectrometer is capable of photon-by-photon data download."275 Also GLAST-GBM. expected to join the IPN too. has both spectral capabilities in the MeV range and photon-by-photon data download for triggered events.," Also GLAST-GBM, expected to join the IPN too, has both spectral capabilities in the MeV range and photon-by-photon data download for triggered events."276 GLAST-LAT has both high spectral andtiming capabilities. but in an energy range higher than that of MCAL.," GLAST-LAT has both high spectral andtiming capabilities, but in an energy range higher than that of MCAL."277" Between 22"" June 2007 and 30 June 2008 MCAL detected 5| GRBs. with an average detection rate of about | GRB/week."," Between $22^{nd}$ June 2007 and $30^{th}$ June 2008 MCAL detected 51 GRBs, with an average detection rate of about 1 GRB/week."278 Most of these detections have been independently confirmed by other instruments., Most of these detections have been independently confirmed by other instruments.279 Only 16 events have been localized. either by Swift. SuperAGILE or the IPN. as reported in Table 1..," Only 16 events have been localized, either by Swift, SuperAGILE or the IPN, as reported in Table \ref{table:1}."280 The IPN localizations reported here are those publicly available at the time of writing: since most of the MCAL events have also been detected by other IPN instruments (?) the number of IPN localizations is expected to rise when the IPN catalogues become available., The IPN localizations reported here are those publicly available at the time of writing; since most of the MCAL events have also been detected by other IPN instruments \citep{Hurley2008} the number of IPN localizations is expected to rise when the IPN catalogues become available.281 The detection rate 1s in good agreement with the sensitivity estimations reported in ?.., The detection rate is in good agreement with the sensitivity estimations reported in \citet{Ghirlanda2004}.282 It must also be noted that in the same time period SuperAGILE localized another four GRBs that were not detected by MCAL., It must also be noted that in the same time period SuperAGILE localized another four GRBs that were not detected by MCAL.283 Figure 1 shows the MCAL light curves for a sample of GRBs., Figure \ref{MCAL_lc_various} shows the MCAL light curves for a sample of GRBs.284 Panels (a). (b) anc (c) refer to GRBs triggered on the ground based on SRM ¢ata.," Panels (a), (b) and (c) refer to GRBs triggered on the ground based on SRM data."285 For these events the on-board trigger logic was not active: only the light curves relative to the upper detection layer (the one closer to the silicon tracker) are shown., For these events the on-board trigger logic was not active; only the light curves relative to the upper detection layer (the one closer to the silicon tracker) are shown.286" Panels (d) to (κ) refer to GRBs triggered on-board: the light curves relative to the complete instrument are shown,", Panels (d) to (k) refer to GRBs triggered on-board; the light curves relative to the complete instrument are shown.287 Panels (d) to (f) refer to «5s long GRBs. shown here with a 32ms time bin.," Panels (d) to (f) refer to $<5\mathrm{s}$ long GRBs, shown here with a $32\mathrm{ms}$ time bin."288 Panels (5) to (k) refer to longer GRBs. shown here with a 256ms time bin.," Panels (g) to (k) refer to longer GRBs, shown here with a $256\mathrm{ms}$ time bin."289 For those events with a public localization available the GRB name is reported too., For those events with a public localization available the GRB name is reported too.290 Figure 2. is a polar plot centered at the pointing direction of the AGILE satellite. showing the position of the localized GRBs detected by MCAL tn the considered period.," Figure \ref{FigMCAL_localization_polar} is a polar plot centered at the pointing direction of the AGILE satellite, showing the position of the localized GRBs detected by MCAL in the considered period."291 Coordinates for GRB 070915 and GRB 070825. provided by IPN but not published in GCN. are also included (?)..," Coordinates for GRB 070915 and GRB 070825, provided by IPN but not published in GCN, are also included \citep{Palshin2007}."292 Several GRBs have been detected at off-axis angles greater than 90°. with the highest beingthe bright GRB 071020. localized by Swift (?).. detected at 166° off-axis. 1.e. coming almost from a direction opposite to the AGILE pointing.," Several GRBs have been detected at off-axis angles greater than $90^\circ$, with the highest beingthe bright GRB 071020, localized by Swift \citep{Holland2007GCN6949}, detected at $166^\circ$ off-axis, i.e. coming almost from a direction opposite to the AGILE pointing."293 Despite that for > events it is difficult to provide reliable spectral information. due to the still incomplete modeling of the spacecraft shell with Monte Carlo simulations (??).. it demonstrates the MCAL detection capabilities.," Despite that for $> 90^\circ$ events it is difficult to provide reliable spectral information, due to the still incomplete modeling of the spacecraft shell with Monte Carlo simulations \citep{Longo2002,Cocco2002b}, , it demonstrates the MCAL all-sky detection capabilities."294 The only GRB detected by the GRID detectorabove 50 MeV in the considered period is GRB 080514B (22)... which," The only GRB detected by the GRID detectorabove 50 MeV in the considered period is GRB 080514B \citep{Rapisarda2008,Giuliani2008}, , which"295between SDF and ADF vs CFF does not depend on the window function used.,between SDF and $^2$ vs CFF does not depend on the window function used.296 For wavefront sensing. the quantities that really need to be measured are the average wavefront gradients at the positions corresponding to the subapertures.," For wavefront sensing, the quantities that really need to be measured are the average wavefront gradients at the positions corresponding to the subapertures."297 One assumes that a shift in image position corresponds perfectly to the average gradient of the wavefront across the subaperture., One assumes that a shift in image position corresponds perfectly to the average gradient of the wavefront across the subaperture.298 However. in addition to local gradients. continuous wavefront aberrations across the telescope aperture also result in local wavefront curvature.," However, in addition to local gradients, continuous wavefront aberrations across the telescope aperture also result in local wavefront curvature."299 [s the assumption valid anyway and how good is it for different seeing conditions. as quantified with Fried’s parameter 70?," Is the assumption valid anyway and how good is it for different seeing conditions, as quantified with Fried's parameter $r_0$?"300 Using Kolmogorov statistics for different ro without any assumption of partial correction by an AO system makes the statistics from this experiment relevant to open-loop WES., Using Kolmogorov statistics for different $r_0$ without any assumption of partial correction by an AO system makes the statistics from this experiment relevant to open-loop WFS.301 Le.. systems for measuring seeing statistics (e.g...Scharmer&vanWerkhoven2010) and the capture phase for AO systems. but not necessarily AO systems in closed loop.," I.e., systems for measuring seeing statistics \cite[e.g., ][]{scharmer10s-dimm+} and the capture phase for AO systems, but not necessarily AO systems in closed loop."302 The setup corresponds to a filled 98-cm pupil (like the SST) with 85 subapertures. each 9.55 em edge-to-edge.," The setup corresponds to a filled 98-cm pupil (like the SST) with 85 subapertures, each 9.55 cm edge-to-edge."303 In 5a we show one sample Kolmogorov wavefront phase., In \ref{fig:hexwavefront} we show one sample Kolmogorov wavefront phase.304 The superimposec pattern shows the geometry of 85 hexagonal microlenses circumscribed by a telescope pupil., The superimposed pattern shows the geometry of 85 hexagonal microlenses circumscribed by a telescope pupil.305 Figure 5b demonstrates the local plane approximation implicit in SH wavefront sensing. while 5c. shows just the tilts.," Figure \ref{fig:hexplanes} demonstrates the local plane approximation implicit in SH wavefront sensing, while \ref{fig:hextilts}306 shows just the tilts."307 The exact geometry does not matter for the results reported here. since our tests do not involve the step where wavefronts are reconstructed from the shift measurements.," The exact geometry does not matter for the results reported here, since our tests do not involve the step where wavefronts are reconstructed from the shift measurements."308 However. the geometry discussed is along the lines planned for the next generation SST AO system. and in that respect motivates the particular subaperture size and shape investigated.," However, the geometry discussed is along the lines planned for the next generation SST AO system, and in that respect motivates the particular subaperture size and shape investigated."309 We generated 100 wavefront phases. ¢;. following Kolmogorov. statistics.," We generated 100 wavefront phases, $\phi_i$, following Kolmogorov statistics."310 For making each simulated phase screen. the following procedure was used.," For making each simulated phase screen, the following procedure was used."311 1003 random numbers were drawn from a standard normal distribution. scaled with the square root of the atmospheric variances and used as coefficients for atmospheric Karhunen-Lóeeve (KL) functions 2—1004.," 1003 random numbers were drawn from a standard normal distribution, scaled with the square root of the atmospheric variances and used as coefficients for atmospheric Karhunen–Lòeeve (KL) functions 2–1004."312 We used KL functions based directly on the theory of Fried(1978).. as implemented by Dai(1905).," We used KL functions based directly on the theory of \citet{fried78probability}, as implemented by \citet{dai95modal}."313" These modes are numbered in order of decreasing atmospheric variance. and the exact range of indices is motivated by KL, being piston and KLjoos a circular mode. starting a higher radial order."," These modes are numbered in order of decreasing atmospheric variance, and the exact range of indices is motivated by $_1$ being piston and $_{1005}$ a circular mode, starting a higher radial order."314 Figure 5a shows a sample wavefront masked with the pattern of the 85 hexagonal microlens geometry., Figure \ref{fig:hexwavefront} shows a sample wavefront masked with the pattern of the 85 hexagonal microlens geometry.315 For all simulations. we used a wavelength of 500 nm and a telescope aperture diameter of Dyy=98 cm.," For all simulations, we used a wavelength of 500 nm and a telescope aperture diameter of $D_\text{tel}=98$ cm."316 In order to cover a range of different seeing conditions. we scaled these wavefront phases to different values of Fried’s parameter. ro€15.7.10.15.20] em. by multiplying with (Duro).," In order to cover a range of different seeing conditions, we scaled these wavefront phases to different values of Fried's parameter, $r_0\in\{5,7,10,15,20\}$ cm, by multiplying with $(D_\text{tel}/r_0)^{5/6}$."317 Using the same wavefront shapes scaled differently like this. the performance for different values of ro should be directly comparable.," Using the same wavefront shapes scaled differently like this, the performance for different values of $r_0$ should be directly comparable."318 For each random wavefront. separately scaled to each value of ry. and for each subpupil defined by a microlens. we generated an image by convolving the Gl in la with a PSF based on the subpupil and the local wavefront phase.," For each random wavefront, separately scaled to each value of $r_0$, and for each subpupil defined by a microlens, we generated an image by convolving the GI in \ref{fig:GI} with a PSF based on the subpupil and the local wavefront phase."319 We want to examine the effect of using different subfield sizes., We want to examine the effect of using different subfield sizes.320 Increased subfield size can be used in different ways: Either one can change the image scale. so the same amount of granulation fits in the FOV but in better pixel resolution.," Increased subfield size can be used in different ways: Either one can change the image scale, so the same amount of granulation fits in the FOV but in better pixel resolution."321 Or one can keep the original image scale so more granulation fits in the FOV. (, Or one can keep the original image scale so more granulation fits in the FOV. (322Or something in between.),Or something in between.)323 Therefore we make images at three different image scales by box-car compressing them by three different integer factors. 7. 10. and 13.," Therefore we make images at three different image scales by box-car compressing them by three different integer factors, 7, 10, and 13."324 The resulting image scales are (229/pixel. 441/pixel. and 0553/pixel.," The resulting image scales are 29/pixel, 41/pixel, and 53/pixel."325 To summarize: the images we have generated were downgraded to the resolution of the subpupil. shifted by the local wavefront tilt and also somewhat blurred by the local wavefront curvature. the latter in. particular for data with small ro.," To summarize: the images we have generated were downgraded to the resolution of the subpupil, shifted by the local wavefront tilt and also somewhat blurred by the local wavefront curvature, the latter in particular for data with small $r_0$."326 A bias was then added to make the RMS contrast of the granulation pattern approximately of the mean intensity., A bias was then added to make the RMS contrast of the granulation pattern approximately of the mean intensity.327 For each subfield size. noise. and ry. relative shifts and tilts were calculated for 490.000 randomly selected pairs of subpupil images.," For each subfield size, noise, and $r_0$, relative shifts and tilts were calculated for 490,000 randomly selected pairs of subpupil images."328 We operate on image pairs corresponding to subpupils from different random wavefronts. so results are not influenced systematically by spatial correlations.," We operate on image pairs corresponding to subpupils from different random wavefronts, so results are not influenced systematically by spatial correlations."329 For the shift measurements. we use all the CF methods from Sect.," For the shift measurements, we use all the CF methods from Sect."330 2 except ADF. applied to the two images in a pair.," \ref{sec:algorithms} except ADF, applied to the two images in a pair."331 We use only the 201 method for subpixel interpolation., We use only the 2QI method for subpixel interpolation.332 Shift measurements were calculated twice. with and without noie added to the images.," Shift measurements were calculated twice, with and without noise added to the images."333 We increased the noise level from the used in Sect., We increased the noise level from the used in Sect.334 3.3.3 to make the effect of noise clearer and thus allow better comparison. of different methods., \ref{sec:noisy-data} to make the effect of noise clearer and thus allow better comparison of different methods.335 We do not investigate bias mismatch in this experiment., We do not investigate bias mismatch in this experiment.336 The conclusion from Sect., The conclusion from Sect.337 3. is that bias mismatch should be compensated for before applying the shift measurement methods., \ref{sec:algorithm-accuracy} is that bias mismatch should be compensated for before applying the shift measurement methods.338 For comparison with the shift measurements. Ovqin. We fitted Zermike tip and tilt to each wavefront. within each hexagonal subpupil.," For comparison with the shift measurements, $\delta x_\text{shift}$, we fitted Zernike tip and tilt to each wavefront, within each hexagonal subpupil."339 The relative wavefront tilt for an image par is the difference between the Zernike tilts for the two subpupils in the pair., The relative wavefront tilt for an image pair is the difference between the Zernike tilts for the two subpupils in the pair.340 These relative tip/tilt coefficients in radians. ay. are converted to image shift. where r is the image scale in rad/pixel.," These relative tip/tilt coefficients in radians, $\alpha_x$, are converted to image shift, where $r$ is the image scale in rad/pixel."341 We calculate the robust statistics of the resulting shifts. remove 4c outliers. and fit the data to the relationship where «=27/1 pixel.," We calculate the robust statistics of the resulting shifts, remove $4\sigma$ outliers, and fit the data to the relationship where $a=2\pi/1$ pixel."342 Compare Eq. (5))., Compare Eq. \ref{eq:linesineone}) ).343"alternatives for jj, which in the previous example we had to set case-by-case.","alternatives for $\mu$, which in the previous example we had to set case-by-case."344" The evidence ratio, in the sense H;/Ho, is now The likelihood term depends on µ but not c, which enters through the prior on µ."," The evidence ratio, in the sense $H_1$ $H_0$, is now The likelihood term depends on $\mu$ but not $\sigma$, which enters through the prior on $\mu$."345 The ratio simplifies to where which tends to unity as c becomes large., The ratio simplifies to where which tends to unity as $\sigma$ becomes large.346" Evidently, the distribution of € under repeated trials will be determined by the distribution of »,Xi, which will be Gaussian under either Ho or Hi."," Evidently, the distribution of ${\cal E}$ under repeated trials will be determined by the distribution of $\sum_i X_i$, which will be Gaussian under either $H_0$ or $H_1$ ."347" To calculate this in detail, we define: which becomes Under Ho, the sum is Gaussian of mean zero and variance N, so that y (and hence In £) is a x? variable with one degree of freedom."," To calculate this in detail, we define: which becomes Under $H_0$, the sum is Gaussian of mean zero and variance $N$, so that $y$ (and hence $\ln {\cal E}$ ) is a $\chi^2$ variable with one degree of freedom."348" Its density is This immediately tells us that In€ is a x” variable and so € will have considerable scatter, affecting the power of the test."," Its density is This immediately tells us that $\ln {\cal E}$ is a $\chi^2$ variable and so ${\cal E}$ will have considerable scatter, affecting the power of the test."349 The case of Type II error requires a little more thought., The case of Type II error requires a little more thought.350" In this case, the X; are Gaussian with mean jz, and so equation (16)) can only give us the distribution of € conditional upon jz, which we do not know."," In this case, the $X_i$ are Gaussian with mean $\mu$, and so equation \ref{eqn15}) ) can only give us the distribution of ${\cal E}$ conditional upon $\mu$, which we do not know."351 It is natural however to marginalize over the prior on µ to obtain an unconditional distribution for £., It is natural however to marginalize over the prior on $\mu$ to obtain an unconditional distribution for ${\cal E}$.352" This is an important conceptual step in the analysis, putting the prior spread in a parameter, µ, on the same footing as spread in the data."," This is an important conceptual step in the analysis, putting the prior spread in a parameter, $\mu$, on the same footing as spread in the data."353 The result is that the distribution of € is broadened beyond what would be the case if we considered repeated trials in which only measuring error (the distribution around fixed jy) caused fluctuations in the result., The result is that the distribution of ${\cal E}$ is broadened beyond what would be the case if we considered repeated trials in which only measuring error (the distribution around fixed $\mu$ ) caused fluctuations in the result.354" We see no alternative to this conclusion: the existence of a prior on |, means that it must be treated as a random variable, whose value is undetermined before we perform an experiment."," We see no alternative to this conclusion: the existence of a prior on $\mu$ means that it must be treated as a random variable, whose value is undetermined before we perform an experiment."355" The larger the uncertainty in yu, the larger the scatter in the values of € that we can obtain."," The larger the uncertainty in $\mu$, the larger the scatter in the values of ${\cal E}$ that we can obtain."356 It follows that the distribution of € depends on the distribution of »X; marginalized over the prior., It follows that the distribution of ${\cal E}$ depends on the distribution of $\sum X_i$ marginalized over the prior.357 For Ηι we then find: with z=y/(1+ No?)., For $H_1$ we then find: with $z \equiv y/(1+N\sigma^2)$ .358" Returning to the Neyman-Pearson analysis, since P(£)d£=P(y)dy we can change to our convenient variable y and integrate over Gaussians to obtain and with z;=yc/(1--Na”),"," Returning to the Neyman-Pearson analysis, since $P({\cal E})\, d{\cal359E}=P(y)\, dy$ we can change to our convenient variable $y$ and integrate over Gaussians to obtain and with $z_c \equiv360y_c/(1+N\sigma^2)$."361 The threshold y. is related to our choice of critical ἕε via equation (18))., The threshold $y_c$ is related to our choice of critical ${\cal E}_c$ via equation \ref{eqn18}) ).362 Fig., Fig.363 3 shows curves for the power versus significance level as a function of No?., \ref{figure2} shows curves for the power versus significance level as a function of $N \sigma^2$.364 This parameter expresses the dependence of test performance on the amount of data (V) and the prior degree of difference between the proposed models (o)., This parameter expresses the dependence of test performance on the amount of data $N$ ) and the prior degree of difference between the proposed models $\sigma$ ).365" In this plot, it is remarkable where standard choices of critical evidence ratio lie."," In this plot, it is remarkable where standard choices of critical evidence ratio lie."366" Take In£.= for definiteness: at, say, NVc?—8 we find the significance level5 to be 2x10 and the corresponding power to be 0.19."," Take $\ln {\cal E}_c=5$ for definiteness: at, say, $N \sigma^2=8$ we find the significance level to be $2 \times 10^{-4}$ and the corresponding power to be $0.19$."367" In words, this means that if we require the odds on Ηι to be 148 to 1 or stronger, then we will reject Ho incorrectly only one time out of 5000 trials, and we will pick H; when we should only one time out of 5 trials."," In words, this means that if we require the odds on $H_1$ to be 148 to 1 or stronger, then we will reject $H_0$ incorrectly only one time out of 5000 trials, and we will pick $H_1$ when we should only one time out of 5 trials."368 This is an excessively conservative decision procedure and parallels what we saw in the first example., This is an excessively conservative decision procedure and parallels what we saw in the first example.369" Evidently, we will need much smaller critical odds than 148 to 1 to get reasonable performance from this test."," Evidently, we will need much smaller critical odds than 148 to 1 to get reasonable performance from this test."370" To re-emphasize, this is a function of the chosen critical evidence ratio, not the form of the test, which is intuitive."," To re-emphasize, this is a function of the chosen critical evidence ratio, not the form of the test, which is intuitive."371 The problem is that In£ is noisy for small amounts of data and cannot sustain such decisive tests as are implied by Inδε=5 (for example)., The problem is that $\ln {\cal E}$ is noisy for small amounts of data and cannot sustain such decisive tests as are implied by $\ln {\cal E}_c=5$ (for example).372 Fig., Fig.373 4 illustrates this point., \ref{figure3} illustrates this point.374" This test might intuitively be derived without the evidence ratio, focusing on the test statistic (*,X;), where the square enters to allow for the possibility that the actual, non-zero µ can be be of either sign."," This test might intuitively be derived without the evidence ratio, focusing on the test statistic $(\sum_i X_i)^2$, where the square enters to allow for the possibility that the actual, non-zero $\mu$ can be be of either sign."375" For simplicity, consider the form y we defined before, which is chi-square distributed (see equation 19))."," For simplicity, consider the form $y$ we defined before, which is chi-square distributed (see equation \ref{yeqn}) )."376" A simple test could be, reject Ho if y>Yc, where the critical yc corresponds to some desired significance level or probability p of Type I error."," A simple test could be, reject $H_0$ if $y>y_c$, where the critical $y_c$ corresponds to some desired significance level or probability $p$ of Type I error."377 The power of this proposed test is conditional upon 44., The power of this proposed test is conditional upon $\mu$.378" Marginalizing out jj with the Gaussian prior, as before, the forms of the power and significance level turn out to be identical to those based on the evidence ratio test."," Marginalizing out $\mu$ with the Gaussian prior, as before, the forms of the power and significance level turn out to be identical to those based on the evidence ratio test."379 So the test is natural enough; the difficulty arises in choosing a sensible value for the critical evidence ratio., So the test is natural enough; the difficulty arises in choosing a sensible value for the critical evidence ratio.380 This is exactly the same difficulty that occurs inchoosing the significance level in any classical test., This is exactly the same difficulty that occurs inchoosing the significance level in any classical test.381 It might seem even more ‘natural’ for this problem to choose 3x? as a test statistic., It might seem even more `natural' for this problem to choose $\sum X_i^2$ as a test statistic.382" Working through the Neyman-Pearson analysis in this case is not possible analytically, as non-central chi- distributions arise."," Working through the Neyman-Pearson analysis in this case is not possible analytically, as non-central chi-square distributions arise."383" However, a numerical analysis shows that this ‘natural’ procedure only performsbetter than the evidence"," However, a numerical analysis shows that this `natural' procedure only performsbetter than the evidence"384calibration that could add an additional uncertainty to the determined flux density values.,calibration that could add an additional uncertainty to the determined flux density values.385" Comparisons of the component positions, flux densities and sizes determined from the Gaussian modelfits revealed a new moving emission region, labeled Q9, first detected in the VLBA image from June 16, 2008, followed by detections of another new component on January 24, 2009 (Q10), a third one on July 27, 2009 (Q11), and a fourth on November 28, 2009 (Q12)."," 	Comparisons of the component positions, flux densities and sizes determined from the Gaussian modelfits revealed a new moving emission region, labeled Q9, first detected in the VLBA image from June 16, 2008, followed by detections of another new component on January 24, 2009 (Q10), a third one on July 27, 2009 (Q11), and a fourth on November 28, 2009 (Q12)."386" In the following, components Q9, Q10, Q11 and Q12 (Fig. 1))"," In the following, components Q9, Q10, Q11 and Q12 (Fig. \ref{fig:map}) )"387" observed within a distance of mmas from the core QO are referred to as the ""jet"".", observed within a distance of mas from the core Q0 are referred to as the “jet”.388 We determine the kinematics of individual features from their relative positional offsets with respect to QO., 	We determine the kinematics of individual features from their relative positional offsets with respect to Q0.389 The temporal evolution of the measured offsets is plotted in Fig. 3.., The temporal evolution of the measured offsets is plotted in Fig. \ref{fig:separation}.390" The component Q8, which was first observed in 2007, is also included for the purpose of comparison."," The component Q8, which was first observed in 2007, is also included for the purpose of comparison."391" The motions in the jet of 3345 are investigated using the R.A., Dec. (x, y) positions of a jet component relative to the core component (QO) over the observed periods, fitting them separately using polynomials of different order (cf. ?))"," 	The motions in the jet of 345 are investigated using the R.A., Dec. $x$, $y$ ) positions of a jet component relative to the core component (Q0) over the observed periods, fitting them separately using polynomials of different order (cf. \citealt{1995ApJ...443...35Z}) )"392" and applying the following procedure: Using this approach, we find that it is sufficient to represent the trajectories of components Q8, Q11 and QI2 by linear fits in both the x and y directions."," and applying the following procedure: 	Using this approach, we find that it is sufficient to represent the trajectories of components Q8, Q11 and Q12 by linear fits in both the $x$ and $y$ directions."393" In the case of components Q9 and Q10, a second order polynomial represents the best fit to the observed data in the x direction, implying apparent acceleration."," In the case of components Q9 and Q10, a second order polynomial represents the best fit to the observed data in the $x$ direction, implying apparent acceleration."394 In the y direction a linear fit is sufficient., In the $y$ direction a linear fit is sufficient.395" The resulting fitted radial separations, r(f)=4/x(t?+y(t)’, are drawn in Fig. 3.."," The resulting fitted radial separations, $r(t) = \sqrt{x(t)^2 + y(t)^2}$, are drawn in Fig. \ref{fig:separation}."396" For each component, the fits yield average proper motion and mean angular speed (jz) and the average direction of motion (®)."," For each component, the fits yield average proper motion and mean angular speed $\langle\mu\rangle$ and the average direction of motion $\langle\Phi\rangle$."397 The kinematic properties thus derived for the jet components indicate that Q9 and Q10 underwent a clear phase of apparent acceleration over a period of 1.5 years and over a distance of ~0.3 mmas ppc)., The kinematic properties thus derived for the jet components indicate that Q9 and Q10 underwent a clear phase of apparent acceleration over a period of 1.5 years and over a distance of $\sim$ mas pc).398" No statistically significant acceleration was observed for Q8, Q11 and Q12."," No statistically significant acceleration was observed for Q8, Q11 and Q12."399" The observed values for (u) are in the range of 0.25 - 0.42 year""! and for (®) in the range of —96 to --1205,, also see Table "," The observed values for $\langle\mu\rangle$ are in the range of 0.25 - 0.42 $^{-1}$ and for $\langle\Phi\rangle$ in the range of $-96$ to $-120$, also see Table \ref{tab:kinsummary}."4002.. ? previously reported apparent jet component speeds of 0.29 — 0.69 yyear! and a jet position angle of -66 —95*., \citet{2005AJ....130.1418J} previously reported apparent jet component speeds of 0.29 – 0.69 $^{-1}$ and a jet position angle of -66 –.401". Using (4), the average apparent speed Bapp and the speed in the source frame (deprojected) β are derived through, απά whereBapp Dj, is the luminosity distance, z is the redshift and © is the jet angle to the line of sight (viewing angle)."," Using $\langle\mu\rangle$, the average apparent speed $\overline{\beta}_\mathrm{app}$ and the speed in the source frame (deprojected) $\overline{\beta}$ are derived through, and where $D_\mathrm{L}$ is the luminosity distance, $z$ is the redshift and $\Theta$ is the jet angle to the line of sight (viewing angle)."402" As a final step the physical parameters, Doppler factor ó, Lorentz factor I and viewing angle © of each jet component are derived."," As a final step the physical parameters, Doppler factor $\delta$, Lorentz factor $\Gamma$ and viewing angle $\Theta$ of each jet component are derived."403" For the following calculations, we assume that the jet emission is dominated by radiative losses (seee.g.,?) and consist of optically thin shocked gas, «=-—0.7 (ie. S,ocR-1995.y+? where R is the size of the emitting region in the rest-frame of the jet and v the frequency in the observer's frame, ?))."," For the following calculations, we assume that the jet emission is dominated by radiative losses \citep[see e.g.,][]{2005AJ....130.1418J} and consist of optically thin shocked gas, $\alpha=-0.7$ (i.e. $ S_\nu \propto R^{-1.633}\cdot\nu^{+\alpha}$, where $R$ is the size of the emitting region in the rest-frame of the jet and $\nu$ the frequency in the observer's frame, \citealt{1985ApJ...298..114M}) )."404" The variability Doppler factor is then derived as, where Dj, is the luminosity distance and deg is the effective angular size of a spherical region (i.e. the measured FWHM"," The variability Doppler factor is then derived as, where $D_\mathrm{L}$ is the luminosity distance and $d_\mathrm{eff}$ is the effective angular size of a spherical region (i.e. the measured FWHM"405where fj; is the observed flux of the ‘th image and fiu; is the modeled flux of the ith image.,"where $f_{{\rm obs,} i}$ is the observed flux of the $i$ th image and $f_{{\rm mod,} i}$ is the modeled flux of the $i$ th image."406 The modeled fluxes are related to the modeled magnifications by where So is the unlensed source flux., The modeled fluxes are related to the modeled magnifications by where $S_0$ is the unlensed source flux.407 The unlensed source flux. however. is unknown.," The unlensed source flux, however, is unknown."408 If there were no flux perturbations. the source flux would be equivalent to So=fas;/piou;.," If there were no flux perturbations, the source flux would be equivalent to $S_0 = f_{{\rm obs,} i}/\mu_{{\rm mod,}i}$."409" It can be estimated by where — in order to minimize the biasing due to flux perturbations — we discard the images with the largest and smallest ratios of foi,;/15594; and average over the remaining two We separate the four images of each lens by brightness and parity. denoting positive and negative parity Images by UR and 7-7 signs and brightest and faintest images by U*C and 7 signs."," It can be estimated by where – in order to minimize the biasing due to flux perturbations – we discard the images with the largest and smallest ratios of $f_{{\rm obs,} i}/\mu_{{\rm mod,}i}$ and average over the remaining two We separate the four images of each lens by brightness and parity, denoting positive and negative parity images by $+$ "" and $-$ "" signs and brightest and faintest images by $\bigstar$ "" and $\ast$ "" signs."410" Thus. each lens has a brightest positive parity Image (4. κ). a faintest positive parity image (/_,). a brightest negative parity image (/_,). and a faintest negative parity image (/_.)."," Thus, each lens has a brightest positive parity image $\mathcal I_{+\bigstar}$ ), a faintest positive parity image $\mathcal I_{+\ast}$ ), a brightest negative parity image $\mathcal I_{-\bigstar}$ ), and a faintest negative parity image $\mathcal I_{-\ast}$ )."411 Correspondingly. each image. { has a magnification. 475. and flux perturbation. 6;;. or magnification perturbation. 9;=;/log(uosHiod.i)-," Correspondingly, each image, $\mathcal I_i$, has a magnification, $\mu_i$, and flux perturbation, $\delta_{f,i}$, or magnification perturbation, $\delta_i= {\rm log} (\mu_{{\rm obs,}i}/\mu_{{\rm mod,}i})$."412 The cumulative distribution of flux perturbations. N(«oy)/(totalnumberof lenses). is shown in Figure I..," The cumulative distribution of flux perturbations, $N(< \delta_{f,i})/(\rm total~number~of~lenses)$ , is shown in Figure \ref{fig:data}."413 The results are plotted so that negative (positive) values represent images with fluxes that are dimmer (brighter) than the best-fit modeled fluxes., The results are plotted so that negative (positive) values represent images with fluxes that are dimmer (brighter) than the best-fit modeled fluxes.414 The results do not reproduce the exact relation seen in δν specifically. our results show overall larger magnification perturbations in the faint images (in particular in 7. ).," The results do not reproduce the exact relation seen in \citet{kochanek_dalal04}: specifically, our results show overall larger magnification perturbations in the faint images (in particular in $\mathcal I_{-\ast}$ )."415 In addition. not all of our lenses show that 0;_%«O as is the case in ?..," In addition, not all of our lenses show that $\delta_{f,-\bigstar} < 0$ as is the case in \citet{kochanek_dalal04}."416 This does not constitute a discrepancy since the unlensed source flux has been estimated slightly differently., This does not constitute a discrepancy since the unlensed source flux has been estimated slightly differently.417 Our results generally agree with ? as parity dependence is very clearly seen and is such that δρα.«Ofapona (e.. the brightest negative parity image 1s less magnified or more demagnified relative to its modeled magnification than other images are compared to their modeled magnifications).," Our results generally agree with \citet{kochanek_dalal04} as parity dependence is very clearly seen and is such that $\delta_{f,-\bigstar} < \delta_{f, \rm ~all~ others}$ (i.e., the brightest negative parity image is less magnified or more demagnified relative to its modeled magnification than other images are compared to their modeled magnifications)."418 Our code uses commonly used methods for lens modeling (see.e.g..?) and commonly used lens parameterizations but is independent of the analysis by ?.. suggesting that parity dependence is a generic result of parametric lens modeling.," Our code uses commonly used methods for lens modeling \citep[see, e.g.,][]{keeton01b} and commonly used lens parameterizations but is independent of the analysis by \citet{kochanek_dalal04}, suggesting that parity dependence is a generic result of parametric lens modeling."419 In addition. the errors in the fluxes (from less than one percent to 10%)) are not large enough to obliterate the observed effect.," In addition, the errors in the fluxes (from less than one percent to ) are not large enough to obliterate the observed effect."420" The best-fit parameters for b. q. y. and 4, are shown in Table ].."," The best-fit parameters for $b$, $q$, $\gamma$, and $\theta_{\gamma}$ are shown in Table \ref{tab:DK02}."421 We use these parameters. in addition to the halo orientation and the best-fit source and lens positions to create a set of smooth models on which to test substructure models.," We use these parameters, in addition to the halo orientation and the best-fit source and lens positions to create a set of smooth models on which to test substructure models."422 We test substructure models with mock observations of lens systems., We test substructure models with mock observations of lens systems.423 We begin with a set of models for lens halos and lens environments: the best-fit smooth macromodels of the previous section as summarized in Table |.., We begin with a set of models for lens halos and lens environments: the best-fit smooth macromodels of the previous section as summarized in Table \ref{tab:DK02}.424 To the lens halos we add clumps as discussed in the following section., To the lens halos we add clumps as discussed in the following section.425 For a single mock observation of a lens macromodel and substructure. we choose a source position and find the associated image positions and magnifications by solving the lens equation using a Newton-Raphson method on a grid of possible image positions.," For a single mock observation of a lens macromodel and substructure, we choose a source position and find the associated image positions and magnifications by solving the lens equation using a Newton-Raphson method on a grid of possible image positions."426 Gaussian observational errors are added to image positions and Jens galaxy position: we adopt an observational error of 3 mas., Gaussian observational errors are added to image positions and lens galaxy position: we adopt an observational error of 3 mas.427" Systems that result in 4 ""observed"" images are modeled using our automated lensing code. and the results are used to create a cumulative magnification perturbation distribution."," Systems that result in 4 “observed"" images are modeled using our automated lensing code, and the results are used to create a cumulative magnification perturbation distribution."428 When we choose a source position. we have two options.," When we choose a source position, we have two options."429 We can use the best-fit source positions of the observational sample., We can use the best-fit source positions of the observational sample.430 This results in a lens configuration (e.g.. cusp. fold. or cross) that is similar to that of the observed lenses.," This results in a lens configuration (e.g., cusp, fold, or cross) that is similar to that of the observed lenses."431 Alternately. we can sample the source plane and create a variety of lens configurations.," Alternately, we can sample the source plane and create a variety of lens configurations."432 When sampling the source plane. we account for magnification bras. assigning source positions by sampling the image plane uniformly as described by ?..," When sampling the source plane, we account for magnification bias, assigning source positions by sampling the image plane uniformly as described by \citet{keeton_zabludoff04}."433"? Results where the source plane is sampled with a uniform weighting in the image plane are labeled ""UW/", Results where the source plane is sampled with a uniform weighting in the image plane are labeled `UW.'434 Regardless of how the source positions are assigned. we create and model ~ 1000 realizations for each lens macromodel. for a total of - 5000 realizations.," Regardless of how the source positions are assigned, we create and model $\sim$ 1000 realizations for each lens macromodel, for a total of $\sim$ 5000 realizations."435 In order to approximate the clumpy distributions of matter we expect to find in galaxy halos. we add dark matter substructure to the smooth macromodel.," In order to approximate the clumpy distributions of matter we expect to find in galaxy halos, we add dark matter substructure to the smooth macromodel."436 These clumps are modeled as projected Moore-like profiles (see. for comparison. Moore et al.," These clumps are modeled as projected Moore-like profiles (see, for comparison, Moore et al."437" 1999) with density profile where x=Αη R is the projected separation from the center of the clump. 7, ts the scale radius. and 7, is the tidal radius of the clump."," 1999) with density profile where $x = R/r_{\rm s}$, $R$ is the projected separation from the center of the clump, $r_{\rm s}$ is the scale radius, and $r_{\rm t}$ is the tidal radius of the clump."438 We test substructure models based on simulations and ad hoe substructure models as described in the following sections., We test substructure models based on simulations and ad hoc substructure models as described in the following sections.439Given (hese reasonable assumptions. a strong clustering of Ly makes sense if the physical quantities that are responsible for Ly are clustered.,"Given these reasonable assumptions, a strong clustering of $L_X$ makes sense if the physical quantities that are responsible for $L_X$ are clustered."440 As can be seen from Equation 2.. this would require (hat Ly be linearly related to £i.," As can be seen from Equation \ref{eqn:Lx-Eb}, this would require that $L_X$ be linearly related to $E_b$."441 Such a relation is possible if three conditions are met., Such a relation is possible if three conditions are met.442 First. the afterglow X-ray emission on timescales of 10 hr must be primarily dominated bv svnchrotron emission (which is the basis of Equation 2)).," First, the afterglow X-ray emission on timescales of 10 hr must be primarily dominated by synchrotron emission (which is the basis of Equation \ref{eqn:Lx-Eb}) )."443 Contribution from inverse Compton(1C) emission which depends stronglv on ry and ej (Sari&Esin2001).. is apparently not significant.," Contribution from inverse Compton(IC) emission, which depends strongly on $n_0$ and $\epsilon_B$ \citep{se01}, is apparently not significant."444 A possible exception is 0000926 Clarrisonοἱal.2001).. but even there the IC! contribution is similar to that from svnchrotron emission.," A possible exception is 000926 \citep{hys+01}, but even there the IC contribution is similar to that from synchrotron emission."445 second. the energy radiated bv the afterglow from the time of the explosion to /=10 hr cannot be significant.," Second, the energy radiated by the afterglow from the time of the explosion to $t=10$ hr cannot be significant."446 This constrains the radiative losses at early time to ad most a factor ol lew., This constrains the radiative losses at early time to at most a factor of few.447 Third. p must be relatively constant (as one mav expect in any case [rom insisting that (he microphysics should not be different lor different bursts).," Third, $p$ must be relatively constant (as one may expect in any case from insisting that the microphysics should not be different for different bursts)."448" For example. changing p [rom a value of 1.5 to 3 results in Y"" ranging from 0.003 to 117. a [actor of 39.000!"," For example, changing $p$ from a value of $1.5$ to $3$ results in $Y^\epsilon$ ranging from 0.003 to 117, a factor of 39,000!"449 Even small changes in p. e.g. from p—1.75 (o p=2.25. result in a factor of 8 echange in Y*.," Even small changes in $p$, e.g. from $p=1.75$ to $p=2.25$, result in a factor of 8 change in $Y^\epsilon$."450 In contrast. some afterglow models vield values of p significantly below 2 (e.g. Panaileseu 2002)). while others have p approaching 3 (Chevalier&Li2000).," In contrast, some afterglow models yield values of $p$ significantly below $2$ (e.g. \citealt{pk02}) ), while others have $p$ approaching $3$ \citep{cl00}."451. Our results. on the other hand. indicate (hat one should set pzz2 and attribute apparent deviant. values of p to external environment or energy injection [from the central source.," Our results, on the other hand, indicate that one should set $p\approx 2$ and attribute apparent deviant values of $p$ to external environment or energy injection from the central source."452 We end with an interesting conclusion from (he results presented here., We end with an interesting conclusion from the results presented here.453 Since both the prompti and afterglow emission exhibit a strong correlation with fj. which is determined from late-time observations (hours to weeks alter the burst). the resulting constaney of both Ey and £4. indicates that GRB jets must be relatively homogeneous and maintain a simple conical geometry all the way [rom internal shocks (~107—10!! em) to the epoch of jet break (~LO! em).," Since both the prompt and afterglow emission exhibit a strong correlation with $f_b$, which is determined from late-time observations (hours to weeks after the burst), the resulting constancy of both $E_\gamma$ and $E_b$, indicates that GRB jets must be relatively homogeneous and maintain a simple conical geometry all the way from internal shocks $\sim 10^{13}-10^{14}$ cm) to the epoch of jet break $\sim 10^{17}$ cm)."454 This rules out the idea that brighter bursts are due to bright spots along specilic lines of sight (Ixumar&Piran2000).. or that GRB jets have a strong; energy and/or Lorentz [actor gradient across their surface (Rossi.Lazzati&Rees 2002)..," This rules out the idea that brighter bursts are due to bright spots along specific lines of sight \citep{kp00}, or that GRB jets have a strong energy and/or Lorentz factor gradient across their surface \citep{rlr02}. ."455 It 1s indeed remarkable that the simplest description of jets is fully consistent wilh the observations., It is indeed remarkable that the simplest description of jets is fully consistent with the observations.456 ORIN thanks S. Phinney lor valuable discussions., SRK thanks S. Phinney for valuable discussions.457 We acknowledge support from SNF and NASA grants., We acknowledge support from SNF and NASA grants.458panels: in cts 1 aresee 7) for the position angles 190220 (south of the ACN: left) and. position angles 35020 (north of the ACGN: right).,panels; in cts $^{-1}$ $^{-2}$ ) for the position angles 190--220 (south of the AGN; left) and position angles 350–20 (north of the AGN; right).459 These surface brightness profiles show signatures comumensurate with a weak shock at à radius of r150 arcsec., These surface brightness profiles show signatures commensurate with a weak shock at a radius of $r\sim180$ arcsec.460 Phe relevant features occur at a slightly. smaller radius to the south with respect to the north (r~170 as opposed to r180 aresec)., The relevant features occur at a slightly smaller radius to the south with respect to the north $r\sim170$ as opposed to $r\sim180$ arcsec).461 Overplotted on these profiles are simple shock mocels for a range of Mach numbers: for the northern sector. Mach numbers of 1.30. 1.34 ancl 1.38: for the southern sector. Mach numbers 1.24. 1.29 ancl 1.53.," Overplotted on these profiles are simple shock models for a range of Mach numbers: for the northern sector, Mach numbers of 1.30, 1.34 and 1.38; for the southern sector, Mach numbers 1.24, 1.29 and 1.33."462 The shock models assume a spherically svmametric. hyvdrodynamic model of a point explosion in an initially isothermal. hydrostatic atmosphere.," The shock models assume a spherically symmetric, hydrodynamic model of a point explosion in an initially isothermal, hydrostatic atmosphere."463 The initial gas density profile is assumed to be a power law. which is adjusted to match the observed surface. brightness profile beyond the shock (Nulsen 20052: Simionescu 2009).," The initial gas density profile is assumed to be a power law, which is adjusted to match the observed surface brightness profile beyond the shock (Nulsen 2005a; Simionescu 2009)."464 We have also explored a mioclel that injects a constant amount of encrey per unit time into the system., We have also explored a model that injects a constant amount of energy per unit time into the system.465 This model provides no significant change to the calculated. surface. brightness profile. which is already fit well by the simple point explosion model.," This model provides no significant change to the calculated surface brightness profile, which is already fit well by the simple point explosion model."466 These models show good. overall agreement with the data and the analysis performed by Forman (2007)., These models show good overall agreement with the data and the analysis performed by Forman (2007).467 ‘Table 2 shows the Mach. number and shock radius from + cillerent 30 degree. wedges (from -50. degrees ancl also from 190220 degrees)., Table 2 shows the Mach number and shock radius from 4 different 30 degree wedges (from -40–50 degrees and also from 190–220 degrees).468 Systematic uncertainties dominate the modelling of the surface. brightness in these wedges., Systematic uncertainties dominate the modelling of the surface brightness in these wedges.469 These include any projected: non-sphericity. of the shock due to the likely jet axis alignment. near our line of sight. and the incorrect assumption of an initially isothermal. hvelrostatic atmosphere.," These include any projected non-sphericity of the shock due to the likely jet axis alignment near our line of sight, and the incorrect assumption of an initially isothermal, hydrostatic atmosphere."470 We. therefore. do not. include standard. statistical error bars from the mocels.," We, therefore, do not include standard, statistical error bars from the models."471 Instead. we estimate the uncertainty in the Mach number by finding a Mach number which brackets the observed scatter in the surface brightness profiles (see Fig. 15)).," Instead, we estimate the uncertainty in the Mach number by finding a Mach number which brackets the observed scatter in the surface brightness profiles (see Fig. \ref{fig:vert}) )."472 This represents a conservative estimate of the uncertainty in the Mach number of the shock., This represents a conservative estimate of the uncertainty in the Mach number of the shock.473 The overall shape of the surface brightness constrains the Mach number of the shock to within 5 per cent., The overall shape of the surface brightness constrains the Mach number of the shock to within $\sim5$ per cent.474 The radius and Mach number of the shock vary at the ten per cent level as a function of position angle., The radius and Mach number of the shock vary at the ten per cent level as a function of position angle.475 “Phis is, This is476complex. variability which appeared inconsistent with a simple svnchrotron “bubble” model.,complex variability which appeared inconsistent with a simple synchrotron “bubble” model.477 Instead. the authors concluded that the core emission was produced in a hybrid hermal/non-thermal plasma in order to explain the Faraday rotation observed in this source., Instead the authors concluded that the core emission was produced in a hybrid thermal/non-thermal plasma in order to explain the Faraday rotation observed in this source.478 For a more detailed review of polarisation properties of X-ray binaries. see Lender (2003).," For a more detailed review of polarisation properties of X-ray binaries, see Fender (2003)."479 In the remainder of this section we sununarise the iterature published for NPE J1748 28s., In the remainder of this section we summarise the literature published for XTE $-$ 288.480 In Sections 2 and 3 we present the results of radio monitoring of the 1998 outburst., In Sections 2 and 3 we present the results of radio monitoring of the 1998 outburst.481 We then discuss our results in Section 4 and o)resent our conclusions in Section 5., We then discuss our results in Section 4 and present our conclusions in Section 5.482 NTE 288 was discovered. on 1998 June 4 using the All Sky Monitor (ASAI) on-board the Rossi rav Timing Explorer (ANTE) satellite (Smith. Levine Wood 1998).," XTE $-$ 288 was discovered on 1998 June 4 using the All Sky Monitor (ASM) on-board the Rossi X-ray Timing Explorer ) satellite (Smith, Levine Wood 1998)."483 The source was also detected by the Burst and ‘Transient Source Experiment (B.XESIZ) on-boare the Compton Gamma Ray Observatory (CORO). suggesting that the rise began on June 3 (Llarmon ct al.," The source was also detected by the Burst and Transient Source Experiment (BATSE) on-board the Compton Gamma Ray Observatory ), suggesting that the rise began on June 3 (Harmon et al."484 1998)., 1998).485 The A-ray source was initially hard but. began to soften at BATSE energies (20100 keV) within the first two days of monitoring., The X-ray source was initially hard but began to soften at BATSE energies (20–100 keV) within the first two days of monitoring.486 Phe X-ray source continued to brighten: hy June 6 the X-ray colours and timing properties were still consistent with those expected for a source in the low/hard state. although the timing properties were also reminiscent of GX Lin the very high state (Fox Lewin 1998).," The X-ray source continued to brighten; by June 6 the X-ray colours and timing properties were still consistent with those expected for a source in the low/hard state, although the timing properties were also reminiscent of GX $-$ 4 in the very high state (Fox Lewin 1998)."487 Revnivtsey. πιουνσον Borozdin. (2000) made a more detailed study. of the N-rav.EUNT clata using both ASM and PCA (Proportional Counter Array).," Revnivtsev, Trudolyubov Borozdin (2000) made a more detailed study of the X-ray data using both ASM and PCA (Proportional Counter Array)."488 Based. on X-ray spectral and timing analysis and comparison with GIU 683. these authors suggested that the outburst began in the very high state but. that. there was an unusually dominant. power-law component. present.," Based on X-ray spectral and timing analysis and comparison with GRS $-$ 683, these authors suggested that the outburst began in the very high state but that there was an unusually dominant power-law component present."489 As the X-ray source faded. it passed through the high/soft. and low/hard states. the 1530 keV [lux rising during the latter.," As the X-ray source faded, it passed through the high/soft and low/hard states, the 15–30 keV flux rising during the latter."490 Detection of an iron emission line was reported by Miller et al. (, Detection of an iron emission line was reported by Miller et al. (4912001) and Wotani ct al. (,2001) and Kotani et al. (492"2000) using cata [rom and (Advanced Satellite for Cosmology and Astrophysics) respectively,",2000) using data from and (Advanced Satellite for Cosmology and Astrophysics) respectively.493 An optically thin radio counterpart was discovered. by Ljellming. Rupen Mioduszewski (1998a) on 1998 June 7.," An optically thin radio counterpart was discovered by Hjellming, Rupen Mioduszewski (1998a) on 1998 June 7."494 ὃν June 10 the flux had risen. confirming its association with the A-ray source (Πομίμος et al.," By June 10 the flux had risen, confirming its association with the X-ray source (Hjellming et al."495 1998b: Fender et al., 1998b; Fender et al.496 1998)., 1998).497 Finally on June 1415. the source was resolved by the VLA. indicating proper motions of 2040 mas per day (Itupen. Hjellming Alioduszewski 1998).," Finally on June 14–15, the source was resolved by the VLA, indicating proper motions of 20–40 mas per day (Rupen, Hjellming Mioduszewski 1998)."498 Follow-up work by Hjellming ct al. (, Follow-up work by Hjellming et al. (4991998€) revealed a jet velocity of > making it the third known Galactic source displaving apparent superluminal motion — a distance of >S kpe and the apparent deceleration of the jet as it collided. with the ISM.,1998c) revealed a jet velocity of $> 0.93c$ – making it the third known Galactic source displaying apparent superluminal motion – a distance of $> 8$ kpc and the apparent deceleration of the jet as it collided with the ISM.500 The Australia Telescope Compact Array (APCA) obtained observations of NTE 288 on seven davs curing 1908 June and July. while the X-ray. source was in. outburst.," The Australia Telescope Compact Array (ATCA) obtained observations of XTE $-$ 288 on seven days during 1998 June and July, while the X-ray source was in outburst."501 The source was observed at 4.800 Gllz ancl 8.640. Cillz ab all seven epochs. plus 1.384 and 2.496 Cllz on four occasions.," The source was observed at 4.800 GHz and 8.640 GHz at all seven epochs, plus 1.384 and 2.496 GHz on four occasions."502 The array was in the 7501 configuration with a xuxcbwidth of 128 MIIz., The array was in the 750E configuration with a bandwidth of 128 MHz.503 The lux and polarisation calibrator was PINS 638 and the phase calibrator was one of νο BIT30-130 or PINS B1921-293. depending on the epoch.," The flux and polarisation calibrator was PKS $-$ 638 and the phase calibrator was one of PKS B1730-130 or PKS B1921-293, depending on the epoch."504 The data were reduced. using standard Uageine. calibration and imaging routines [rom the package.," The data were reduced using standard flagging, calibration and imaging routines from the package."505 Due to contamination bv emission from a nearby supernova remnant. ib was necessary to reject the short baselines at all wavelengths: we excluded baselines at ve radii smaller han 3. 5. 10 and 20 FA at 1.4. 24. LS and 8.7 Cillz respectively.," Due to contamination by emission from a nearby supernova remnant, it was necessary to reject the short baselines at all wavelengths; we excluded baselines at $uv$ radii smaller than 3, 5, 10 and 20 $k\lambda$ at 1.4, 2.4, 4.8 and 8.7 GHz respectively."506 Ehe routine.GPCAL. was used to solve or both instrumental ancl source polarisation. parameters.," The routine, was used to solve for both instrumental and source polarisation parameters."507 ‘Thus images were obtained (using natural weighting) in 1. Q and U Stokes parameters. from which LP and fractional LP images could be constructed.," Thus images were obtained (using natural weighting) in I, Q and U Stokes parameters, from which LP and fractional LP images could be constructed."508 Flux densities were obtained from the Stokes L images and are listed in Table 1., Flux densities were obtained from the Stokes I images and are listed in Table 1.509 We note that it was not. possible to obtain information regarding circular polarisation: with the linear feeds of ATO. unless the leakage terms can be determined very accurately. intrinsic circular polarisation cannot be distinguished from a small leakage of total intensity into the circular polarisation signal (Sault. Ixilleen Ixesteven 1991).," We note that it was not possible to obtain information regarding circular polarisation; with the linear feeds of ATCA, unless the leakage terms can be determined very accurately, intrinsic circular polarisation cannot be distinguished from a small leakage of total intensity into the circular polarisation signal (Sault, Killeen Kesteven 1991)."510 Additional racio images were obtained from the archives of the Very Large. Array for comparison with the ATCA data., Additional radio images were obtained from the archives of the Very Large Array for comparison with the ATCA data.511 Data were taken at 1.425. 4.86. 8.46. 14.94. and 22.46 Cllz.," Data were taken at 1.425, 4.86, 8.46, 14.94, and 22.46 GHz."512 Phe array was in its BoA configuration prior to 1998 July 3. after which it moved to D configuration.," The array was in its BnA configuration prior to 1998 July 3, after which it moved to B configuration."513 Calibration, Calibration514accretion disks and their associated outflows have not been well characterized yet.,accretion disks and their associated outflows have not been well characterized yet.515" Hence, the formation process of massive stars remains an open issue."," Hence, the formation process of massive stars remains an open issue."516 There are several problems that hamper the analysis of massive star formation regions (MSFRs)., There are several problems that hamper the analysis of massive star formation regions (MSFRs).517" First, massive protostars form in clusters, which together with projection effects, make these regions difficult to interpret."," First, massive protostars form in clusters, which together with projection effects, make these regions difficult to interpret."518" Moreover, the MSFRs are found at larger distances than low-mass star formation regions, with typical distances of 5 kpc."," Moreover, the MSFRs are found at larger distances than low-mass star formation regions, with typical distances of 2-5 kpc."519" Thus, to get an insight of the closest regions to the protostars, where accretion disks are expected, the highest angular resolution of the current telescopes is needed."," Thus, to get an insight of the closest regions to the protostars, where accretion disks are expected, the highest angular resolution of the current telescopes is needed."520" Even so, most of the dust and gas structures detected around high-mass protostars are ~1000 AU."," Even so, most of the dust and gas structures detected around high-mass protostars are $\sim1000$ AU."521" 'This is the smallest diameter that an interferometer can resolve with a 1"" angular resolution at those distances.", This is the smallest diameter that an interferometer can resolve with a $\arcsec$ angular resolution at those distances.522" At these scales, such structures could harbour systems of several protostars, that could be forming high mass stars by other mechanisms such as mergers."," At these scales, such structures could harbour systems of several protostars, that could be forming high mass stars by other mechanisms such as mergers."523" In fact, the nearest massive protostars (Orion BN/KL and Cepheus A HW2), show complex scenarios, with a possible merger of protostars (Orion BN/KL, ?)), or close passages between protostars (Cep A HW2, ?))."," In fact, the nearest massive protostars (Orion BN/KL and Cepheus A HW2), show complex scenarios, with a possible merger of protostars (Orion BN/KL, \citealt{2009Zapata}) ), or close passages between protostars (Cep A HW2, \citealt{2009Cunningham}) )."524" Therefore, with the current interferometers, only a few MSFRs may be studied with adequately high angular resolution."," Therefore, with the current interferometers, only a few MSFRs may be studied with adequately high angular resolution."525" To demonstrate the existence of a disk around a massive protostar, it is not enough to detect its dust continuum emission; its kinematics must also be (sub)millimetermeasured via the molecular line emission associated with the gas-phase chemistry developed after the evaporation of the molecules from the ice mantles (??))."," To demonstrate the existence of a disk around a massive protostar, it is not enough to detect its (sub)millimeter dust continuum emission; its kinematics must also be measured via the molecular line emission associated with the gas–phase chemistry developed after the evaporation of the molecules from the ice mantles \citealt{1998Hatchell,2007Cesaroni}) )."526" However, searching for molecular tracers of disks in MSFRs is a complex task."," However, searching for molecular tracers of disks in MSFRs is a complex task."527 There are molecules that show emission from the envelope and the disk simultaneously., There are molecules that show emission from the envelope and the disk simultaneously.528" Other molecules show optically thick emission, thus complicating the kinematic study of the disk."," Other molecules show optically thick emission, thus complicating the kinematic study of the disk."529" On the other hand, S-bearing species (such as Πο», SO, SO», CS, OCS...) could be intimately linked with the evaporation process of the disk surface becoming good tracers of the dynamics of the (????)),innermost parts of the high mass protostars."," On the other hand, S-bearing species (such as $_2$ S, SO, $_2$, CS, OCS...) could be intimately linked with the evaporation process of the disk surface \citealt{1997Charnley,1998Hatchell,2003VanderTak,2005MartinPintado}) ), becoming good tracers of the dynamics of the innermost parts of the high mass protostars."530" Recently, several papers have been published on the detection of S-bearing species in disks "," Recently, several papers have been published on the detection of S-bearing species in disks and other warm gas-structures of MSFRs \citealt{2006VanderTak,2007JimenezSerra,2009Klaassen,2009Franco-Hernandez,5312009Zapata}) )."532"In particular, SO2 transitions, ubiquitous within the (sub)millimeter range, show à very compact nature,"," In particular, $_2$ transitions, ubiquitous within the (sub)millimeter range, show a very compact nature,"533"From Ho, and LIo,, it is possible to recover the rms amplitude Ao, of a mode.","From $H_{0,n}$ and $\Gamma_{0,n}$, it is possible to recover the rms amplitude $A_{0,n}$ of a mode."534 Amplitudes are always better determined than heights and widths themselves., Amplitudes are always better determined than heights and widths themselves.535" This is true regardless of the values of i and v, (?)..", This is true regardless of the values of $i$ and $\nu_\mathrm{s}$ \citep{Ballot08}.536 The amplitudes follow the relation The mode amplitudes are listed in Table 5 and plotted in Fig. 14.., The amplitudes follow the relation The mode amplitudes are listed in Table \ref{tab:fwhmamp} and plotted in Fig. \ref{fig:amp}.537" The errors take the correlations between the determinations of Ho,, and Io, into account."," The errors take the correlations between the determinations of $H_{0,n}$ and $\Gamma_{0,n}$ into account."538 The amplitudes increase almost regularly until reaching a maximum (3.86 ppm) around the frequency2100µΗ7., The amplitudes increase almost regularly until reaching a maximum (3.86 ppm) around the frequency.539". Then, the mode amplitudes remain close to this maximum before sharply dropping aboveuHz."," Then, the mode amplitudes remain close to this maximum before sharply dropping above."540". It is also possible to derive the amplitude of radial modes from the smoothed power spectrum after subtracting the background (see?),, or, similarly, by using the fitted Gaussian profile B,(v) of the p-mode power excess derived in Sect. ??.."," It is also possible to derive the amplitude of radial modes from the smoothed power spectrum after subtracting the background \citep[see][]{Kjeldsen08}, or, similarly, by using the fitted Gaussian profile $B_\mathrm{p}(\nu)$ of the p-mode power excess derived in Sect. \ref{sec:bg}."541" By using ?,, we recover the amplitude of radial modes through a relation where Rjzo and Roseare the CoRoT response functions for |=0 modes and for the sum of all modes of degree 1=0 to 4 (seedefinitionsin?,notice R)-oisidenticaltothegranulationresponseRg defined in thatarticle)."," By using \citet{Michel09}, we recover the amplitude of radial modes through a relation where $R_{l=0}$ and $R_\mathrm{osc}$are the CoRoT response functions for $l=0$ modes and for the sum of all modes of degree $l=0$ to 4 \citep[see definitions in][notice that $R_{l=0}$ is identical to the granulation response$R_g$ defined in that."542" We used the approximated formulations of the responses they derived, and find ΚΙ:=3.89 and Κο=6.86, by considering Teg~6100 K for52265."," We used the approximated formulations of the responses they derived, and find $R_{l=0}=3.89$ and $R_\mathrm{osc}=6.86$, by considering $\teff\approx6100$ K for."543". When the spectrum is barely resolved, this procedure is a common way to extract the mode amplitudes."," When the spectrum is barely resolved, this procedure is a common way to extract the mode amplitudes."544" In the present situation, we are thus able to compare these estimates to the individually fitted mode amplitudes."," In the present situation, we are thus able to compare these estimates to the individually fitted mode amplitudes."545" In Fig. 14,,"," In Fig. \ref{fig:amp},"546 we have also plotted the radial mode amplitudes deduced from the smoothed spectrum and from the profile By., we have also plotted the radial mode amplitudes deduced from the smoothed spectrum and from the profile $B_\mathrm{p}$.547" Although the amplitudes of radial modes do not follow a perfect Gaussian profile, the Gaussian profile is a reasonable fit to the smoothed spectrum."," Although the amplitudes of radial modes do not follow a perfect Gaussian profile, the Gaussian profile is a reasonable fit to the smoothed spectrum."548 The Gaussian profile reaches the maximum value AQ)=fHAy3.7 ppm., The Gaussian profile reaches the maximum value $\displaystyle A^\mathrm{(max)}=\frac{R_{l=0}}{R_\mathrm{osc}}\sqrt{H_\mathrm{p}^\mathrm{(max)}\Dnu}\approx 3.7$ ppm.549 This is consistent with the maximum fitted amplitude (ame)=3.86+0.24 ppm)., This is consistent with the maximum fitted amplitude $A_{l=0}^{(\mathrm{max})}=3.86\pm0.24$ ppm).550" We get very good agreement at high frequency, but there is a clear departure at low frequency between the amplitudes obtained from the smoothed spectrum and from the fitted modes."," We get very good agreement at high frequency, but there is a clear departure at low frequency between the amplitudes obtained from the smoothed spectrum and from the fitted modes."551 The fitted background is probably underestimated around -1200--uHz., The fitted background is probably underestimated around $\sim$.552". This could come from a component missing in our model, like a contribution of faculae or from an excess of power due to leakage effects."," This could come from a component missing in our model, like a contribution of faculae or from an excess of power due to leakage effects."553" Thus, when the granulation is fitted in Sect. ??,,"," Thus, when the granulation is fitted in Sect. \ref{sec:bg},"554" the extra power increases the apparent contribution from p modes; however, when we fit p modes, in a restricted range (Sect. ??)),"," the extra power increases the apparent contribution from p modes; however, when we fit p modes, in a restricted range (Sect. \ref{ssec:fit}) ),"555 the extra power excess is included in the background., the extra power excess is included in the background.556 The amplitudes are measured in the CoRoT spectral band and must be converted into bolometric amplitudes., The amplitudes are measured in the CoRoT spectral band and must be converted into bolometric amplitudes.557" According to ?,, the bolometric correction factor is Cpo.=4/Rj-9 and iS Cp)=1.03 for 52265."," According to \citet{Michel09}, the bolometric correction factor is $c_\mathrm{bol}=4/R_{l=0}$ and is $c_\mathrm{bol}=1.03$ for ."558". The maximum bolometric amplitude of radial mode is then By combining the adiabatic relation proposed by ? to relate mode amplitudes in intensity to mode amplitudes in velocity and the scaling law proposed by ?,, we get the relation Moreover, if we assume that thefrequency of maximum p-mode amplitude y”) scales with the acoustic cut-off frequency (e.g.,see?),, we obtain the relation (?):: By using ADAL=2.53+0.11ppm (?),, Tag=5777 K, and να)=3050,Hz for the Sun and by considering for oour estimations Teg=6100+60 K, and νὰ)=2090+ 20uHz, we obtain Du=3.7+0.2 ppm."," The maximum bolometric amplitude of radial mode is then By combining the adiabatic relation proposed by \citet{Kjeldsen95} to relate mode amplitudes in intensity to mode amplitudes in velocity and the scaling law proposed by \citet{Samadi07}, we get the relation Moreover, if we assume that thefrequency of maximum p-mode amplitude $\nu^{(\mathrm{max})}$ scales with the acoustic cut-off frequency \citep[e.g., see][]{Bedding03}, we obtain the relation \citep{Deheuvels10}: By using $A_{l=0,\mathrm{bol},\sun}^{(\mathrm{max})}=2.53\pm0.11\unit{ppm}$ \citep{Michel09}, $T_{\mathrm{eff},\sun}=5777$ K, and $\nu^{(\mathrm{max})}_{\sun}=3050\muHz$ for the Sun and by considering for our estimations $\teff=6100\pm60$ K, and $\nu^{(\mathrm{max})}=2090\pm20\muHz$ , we obtain $A_{l=0,\mathrm{bol}}^{(\mathrm{max})}=3.7\pm0.2\unit{ppm}$ ."559" This predicted value is slightly lower than the value measured for 52265,, but still consistent within the error bars."," This predicted value is slightly lower than the value measured for , but still consistent within the error bars."560 In contrast to previous observationsof F stars (e.g.?) which have smaller amplitudes, In contrast to previous observationsof F stars \citep[e.g.][]{Michel08} which have smaller amplitudes561" E2 Ge |:Eatfaa 02(25,,4 fion] andl nal fllTE2011we12 2 ?(2 Douai Top, freed} | where wenote forjustice fj»=fuenp(s}) aud foa» fusis). with V, Wey,=VS. from (33))-036))."," = ^2 ) - _2^2 ] + 2 ^2 ) - _2^2 ) ] + ^2} - _2^2 ) ] , and = ^2 } - _1^2 ) ] + 2 ^2 ) - _1^2 ) ] + ^2 ) - _1^2 ], where wenote forinstance $f_{1;22}=f_{a;bb}(s)$ and $f_{2;12}=f_{b;ab}(s)$ , with $V_a=V_1$ , $V_b=V_2$, from \ref{fabb})\ref{fbab}) )."562 Next. the Gaussian weight Ty=(Cpt)2 yoads at order zero aud at first order. --= (02...1 | | 2 | 2À (2 fons) | 2An (2 Jio) | 2X," Next, the Gaussian weight $\Gam_{12}=(\chi.C_L^{-1}.\chi)/2$ reads at order zero = , and at first order, = ( _1^2 + ) + ( + _2^2 ) + 2 + 2 (2 ) + 2 (2 ) + 2 ."563" Therefore. ii the rare-event linüt the tail⋅ of. the bivariate distribution (87)) reads as796)290: with —-V, DT, ] where Py. is eiven by Eqxs.(111))-(112)). and Ty and Do by Eqs.(65))-(66)) for each sphere Vi aud 15."," Therefore, in the rare-event limit the tail of the bivariate distribution \ref{rareP12}) ) reads as, with = - _1 - _2, where $\Gam_{12}$ is given by \ref{Gam0_12}) \ref{Gam1_12}) ), and $\Gam_1$ and $\Gam_2$ by \ref{Gam0}) \ref{Gam1}) ) for each sphere $V_1$ and $V_2$."564 Next. following Valageas (2009b). we write the halo two-point correlation as where the factor (1|Ópar(Cs)) inodels the effects associated with the mapping from Laeraneian to Evlerian space.," Next, following Valageas (2009b), we write the halo two-point correlation as = , where the factor $(1+\delta_{LM}(s))$ models the effects associated with the mapping from Lagrangian to Eulerian space."565" This is the local linear density contrast at radius v4 ch‘oun à halo of mass ALmax(Ay.Ma) (to keep the SVIviuuetrv AL,<>AM») ax given by Eqs.(62))-(63))."," This is the local linear density contrast at radius $s$ from a halo of mass $M=\max(M_1,M_2)$ (to keep the symmetry $M_1\leftrightarrow M_2$ ), as given by \ref{deltap0}) \ref{deltap1}) )."566 A sutiicicutly accurate approximation wolld be to use only he zeroth-order term (62)). as shown bv Fig. l..," A sufficiently accurate approximation would be to use only the zeroth-order term \ref{deltap0}) ), as shown by Fig. \ref{figdeltaLq},"567 bu aking iutoaccount the correction (63)) brings no further difficulty., but taking intoaccount the correction \ref{deltap1}) ) brings no further difficulty.568" Here we approximated the jionlinear ceusity COtrast da, bv the linear density contrast 6,ay. since a aree clistance where dayl] we have 342ὄρλι."," Here we approximated the nonlinear density contrast $\delta_M$ by the linear density contrast $\delta_{LM}$, since at large distance where $\delta_M\ll 1$ we have $\delta_M \simeq \delta_{LM}$."569" Next. we dust express the Lagrangian seuuaion s in terius of he Euler distance 0,"," Next, we must express the Lagrangian separation $s$ in terms of the Eulerian distance $x$."570 Following Valageas (2009b). a owest order where we consider cach halo as a test particle hat falls iuto the potential well dnit bv the other halo. we obtain s as the solution of the implicit equation : ία 4 . where dpa;(5) is the linear density contrast within radius s of the halo of mass A;. given by Eqs.(59))-(60)).," Following Valageas (2009b), at lowest order where we consider each halo as a test particle that falls into the potential well built by the other halo, we obtain $s$ as the solution of the implicit equation x= s ( 1 - - ), where $\delta_{LM_i}(s)$ is the linear density contrast within radius $s$ of the halo of mass $M_i$, given by \ref{delta0}) \ref{delta1}) )."571 At laree separation. this relation canbe inverted as x ία . pease )» which provides an explicit expressionfor s.," At large separation, this relation canbe inverted as s= x ( 1 + + ), which provides an explicit expressionfor $s$."572 Finally. we define the real-space halo bias as the ratio of the halo aud matter two-point correlations. UU ," Finally, we define the real-space halo bias as the ratio of the halo and matter two-point correlations, (x) =."573Since at large distance the matter correlation is within the linear regime. f(r)xo5act). we also write in this μαι UC which fullydetermines the halo bias from (115)).," Since at large distance the matter correlation is within the linear regime, $\xi(x) \simeq \sigma^2_{0,0}(x)$, we also write in this limit (x) , which fullydetermines the halo bias from \ref{xiM1M2}) )."574 For equal-iiass halos of radius 4. defiued by the same threshold dp. the two Lagrauge multipliers are equal. Ay ae Nyhd )-9 (109))-(110)). simplify as and fis). Suppl yuwe note o?⋅= a.," For equal-mass halos of radius $q$ , defined by the same threshold $\delta_L$ , the two Lagrange multipliers are equal, $\lambda_1=\lambda_2=\lambda$ , and \ref{lambda0_1}) \ref{lambda0_2}) ), \ref{lambda1_1}) \ref{lambda1_2}) ), simplify as = , and = ) , where we note $\sigma^2=\sigma_q^2$ ."575 This. vields. for. the Gaussian4. weight P4». 52122;," This yields for the Gaussian weight $\Gam_{12}$ , = ,"576excitation temperature higher than the lowest temperature case which likely shrinks the T range in Fig.,excitation temperature higher than the lowest temperature case which likely shrinks the T range in Fig.577 4., 4.578 Our results may suggest that carriers of some DIBs. especiallyAA.. could be centrosymmetric molecules. whose spectral features become broader üs their rotational temperatures increase.," Our results may suggest that carriers of some DIBs, especially, could be centrosymmetric molecules, whose spectral features become broader as their rotational temperatures increase."579 This means that conditions of excitation of C» and the DIB carrier should be similar., This means that conditions of excitation of $C_2$ and the DIB carrier should be similar.580ACDAL ff He an!SOQQA. ⊺↸∖∶↴∙⊾⋯⋜∐⋅↨↘↽↸∖⋜↧↕∙∐≝↭⊤⋟↴∖↴∐∪↖↖⇁↸∖≼⊔↕⋜↧↑↑∐↸∖∐↥⋅↴∖↴↑↕↿∐∏∪∏↴∖↴ ~30inside A£..halo cLOOOA).which &Norman(2007)aud etal.(2007).,$\Lambda CDM$ \citet{Barkana 2001}) $H$ $He$ $8000K$ \citet{Tegmark 1997} $z\sim 30$ $10^{6}M_{\odot}$ $T_{vir}\sim 1000K$ \citet{O'Shea 2007} \citet{Gao 2007}.581.Teemark etal.(1997)also 1003.(Abel otal.2002)., \citet{Tegmark 1997} $\sim 100M_{\odot}$ \citep{Abel2002}.582". recombination. Lf. ~ (Pallaetprimordialal.1983). amieutalSOOQA.temperatures If, iu this context were Saslaw&Zipov(1967) andl Peebles&Dicke"," $H_{2}$ $\sim 10^{-3}-10^{-4}n_{H}$ \citep{Palla et al. 1983}, $8000K$ $H_{2}$ in this context were \citet{Saslaw} and \citet{Peebles 1968}."583" Sasha Zipoy (1961) showed the nuportauce of (1968).the charge transfer reaction and II to form II. aud Peebles Dickebetweeu (1968) IL,suggested a mecha to formi IT» frou IT 7"," Saslaw Zipoy (1967) showed the importance of the charge transfer reaction between $H_{2}^{+}$ and $H$ to form $H_{2}$, and Peebles Dicke (1968) suggested a mechanism to form $H_{2}$ from $H^{-}$ ."584" The Il» molecule forms by theff and I7. chauncls mainly,", The $H_{2}$ molecule forms by the$H^{-}$ and $H_{2}^{+}$ channels mainly.585 The reactions are followed by Due to its zero dipolar moment only quadrupolar rotational trausifious are allowed. /> x2. where J is the quantmn umuber for angular momentum: Aberalletal. (1982).," The reactions are followed by Due to its zero dipolar moment only quadrupolar rotational transitions are allowed, $J\rightarrow J \pm 2$ , where $J$ is the quantum number for angular momentum; \citet{Abgrall}."586. Furthermore. due to its σπα moet of inertia (the smallest oue. between all molecules) the energy gap between itsrotational quautium states. AL. is large compared with other iiolecules (AE)i449XlI. where Z is themomentofinertia).," Furthermore, due to its small moment of inertia (the smallest one between all molecules) the energy gap between itsrotational quantum states, $\Delta E$, is large compared with other molecules $\Delta E_{J\rightarrow J\pm 2}\propto 1/I$, where $I$ is themomentofinertia)."587" Thesmallest energy eapis AE,ayzm HOOK.Withthis enerev. differeuce it is very diffucult toreachtemperatures below ον 100A. (see Palla(1999).D and refereuces therein)."," Thesmallest energy gapis $\Delta E_{2\rightarrow 0}\approx 500 K$ .Withthis energy difference it is very diffucult toreachtemperatures below $\sim 100K$ , (see \citet{Palla 1999} and references therein)."588 The IL molecule forms throushDaud D chaunel mainly (see Dalearuoctal. (1973): (20023)), The $HD$ molecule forms through$D^{+}$and $D$ channel mainly (see \citet{Dalgarno 1973}; ; \citet{Galli 2002}) )589"To calculate the dark energy results presented in Table 4,, we employ a redshift distribution of clusters drawn from a simulated X-ray luminosity function for both a given fiducial cosmology and a future, planned X-ray cluster survey.","To calculate the dark energy results presented in Table \ref{tab:models}, we employ a redshift distribution of clusters drawn from a simulated X-ray luminosity function for both a given fiducial cosmology and a future, planned X-ray cluster survey."590" As discussed in Section 3.2.2,, we select clusters from this distribution using the same criterion (kT> 5keV) than we use for current data(?)."," As discussed in Section \ref{sec:selec}, we select clusters from this distribution using the same criterion $kT>5$ keV) than we use for current data."591. To apply this selection criterion to the simulated data set we use a luminosity-temperature relation obtained from present-day data(?)., To apply this selection criterion to the simulated data set we use a luminosity-temperature relation obtained from present-day data.592". Note that in this relation the temperatures are emission weighted instead of mass weighted, as they are in?,, which makes our selection even more conservative."," Note that in this relation the temperatures are emission weighted instead of mass weighted, as they are in, which makes our selection even more conservative."593" Finally, we select only relaxed clusters by scaling the distribution with a factor 1/8 (or 1/16 for the half sample scenario)."," Finally, we select only relaxed clusters by scaling the distribution with a factor $1/8$ (or $1/16$ for the half sample scenario)."594" This factor is especially conservative at low redshifts (2< 0.5), where the MACS survey has shown that 1/4 clusters are sufficiently relaxed for feas work."," This factor is especially conservative at low redshifts $z\lsim 0.5$ ), where the MACS survey has shown that $1/4$ clusters are sufficiently relaxed for $f_{\rm gas}$ work."595 This suggests that selecting a distribution with more clusters at low redshifts is a plausible alternative., This suggests that selecting a distribution with more clusters at low redshifts is a plausible alternative.596" Furthermore, after all these conservative cuts we obtain a total number of clusters suitable for [κας work larger than 500."," Furthermore, after all these conservative cuts we obtain a total number of clusters suitable for $f_{\rm gas}$ work larger than $500$."597 This offers us additional freedom to build an alternative redshift distribution., This offers us additional freedom to build an alternative redshift distribution.598" In this section, we use two alternative distributions to assess the impact that choosing a particular distribution has on the dark energy constraints."," In this section, we use two alternative distributions to assess the impact that choosing a particular distribution has on the dark energy constraints."599" Within the limits of the analysis described above, we design two test distributions such that their peaks are at a lower redshift, z~0.5, than that of the original distribution, z~ 0.65."," Within the limits of the analysis described above, we design two test distributions such that their peaks are at a lower redshift, $z \sim6000.5$, than that of the original distribution, $z \sim 0.65$ ."601" From each test distribution we form an [κας sample of ~500 clusters, and ~5 per cent feas measurement errors per cluster, as we did for the original distribution."," From each test distribution we form an $f_{\rm gas}$ sample of $\sim 500$ clusters, and $\sim 5$ per cent $f_{\rm gas}$ measurement errors per cluster, as we did for the original distribution."602" The first test distribution is approximately gaussian, with a large number of clusters at low redshift, a small tail at high redshifts, and very few clusters beyond redshift 1."," The first test distribution is approximately gaussian, with a large number of clusters at low redshift, a small tail at high redshifts, and very few clusters beyond redshift $1$."603" The second test distribution is similar to the original, but shifted towards lower redshifts."," The second test distribution is similar to the original, but shifted towards lower redshifts."604 At high redshifts this distribution has less clusters than the originalbut significantly more clusters than the first test distribution., At high redshifts this distribution has less clusters than the originalbut significantly more clusters than the first test distribution.605" Using our default dark energy model, and the 2 per cent set of systematic allowances, the first test distribution provides an increase in the FoM of ~10 per cent with respect to the original distribution."," Using our default dark energy model, and the $2$ per cent set of systematic allowances, the first test distribution provides an increase in the FoM of $\sim 10$ per cent with respect to the original distribution."606" As mentioned in Section 3.2.3,, the pivot redshift, zp, is important for the DETF FoM criterion."," As mentioned in Section \ref{sec:fgas_distr}, the pivot redshift, $z_{\rm p}$, is important for the DETF FoM criterion."607" Figure 5 shows that for the [κας experiment, zp~0.25."," Figure \ref{fig:evol} shows that for the $f_{\rm gas}$ experiment, $z_{\rm p}\sim 0.25$ ."608" Interestingly, the second test distribution provides an increase in the FoM of ~40 per cent, which suggests that having enough high redshift clusters is also important for the DETF FoM. Note also that to obtain the fgas measurements for each of the test samples, we will require a shorter total exposure time than that estimated for the original sample (c15Ms)."," Interestingly, the second test distribution provides an increase in the FoM of $\sim 40$ per cent, which suggests that having enough high redshift clusters is also important for the DETF FoM. Note also that to obtain the $f_{\rm gas}$ measurements for each of the test samples, we will require a shorter total exposure time than that estimated for the original sample $\sim60915$ Ms)."610" Thus, using the same exposure time, an even larger increase in the FoM should be achievable with such samples."," Thus, using the same exposure time, an even larger increase in the FoM should be achievable with such samples."611 These results indicate that a further analysis is required to determine the optimal redshift distribution of clusters with which to carry out future κας experiments., These results indicate that a further analysis is required to determine the optimal redshift distribution of clusters with which to carry out future $f_{\rm gas}$ experiments.612" Such analysis is beyond the scope of this paper, but we will pursue it in a forthcoming publication."," Such analysis is beyond the scope of this paper, but we will pursue it in a forthcoming publication."613" Figure 5 shows the evolution of the dark energy equation of state as a function of scale factor, w(a)."," Figure \ref{fig:evol} shows the evolution of the dark energy equation of state as a function of scale factor, $w(a)$."614" The pivot scale factor, ap, is the scale factor at which we obtain the tightest constraint on w [that measurement being o(wp)]."," The pivot scale factor, $a_{\rm p}$ , is the scale factor at which we obtain the tightest constraint on $w$ [that measurement being $\sigma(w_{\rm615 p})]$."616" As shown in Figure 5,, for the [κας experiment we measure a pivot scale factor of ap~0.8, which corresponds to a pivot redshift z,~0.25."," As shown in Figure \ref{fig:evol}, for the $f_{\rm gas}$ experiment we measure a pivot scale factor of $a_{\rm p}\sim 0.8$, which corresponds to a pivot redshift $z_{\rm p}\sim 0.25$."617" Interestingly, these values lie between the pivot scale factors/redshifts reported by the DETF for SNIa experiments (ap~ 0.93/z,~ 0.075) and galaxy cluster number counts, weak lensing and BAO experiments (ap~ 0.65/z,y~ 0.54)."," Interestingly, these values lie between the pivot scale factors/redshifts reported by the DETF for SNIa experiments $a_{\rm618 p}\sim 0.93$ $z_{\rm p}\sim 0.075$ ) and galaxy cluster number counts, weak lensing and BAO experiments $a_{\rm p}\sim 0.65$ $z_{\rm619 p}\sim 0.54$ )."620 Pinning down the evolution of w over a wide redshift range will be a crucial for unraveling the nature of dark energy., Pinning down the evolution of $w$ over a wide redshift range will be a crucial for unraveling the nature of dark energy.621" Our results argue that a combination of feas, CMB, BAO, SNIa, weak lensing and galaxy cluster number count experiments is likely to prove powerful in this regard."," Our results argue that a combination of $f_{\rm gas}$, CMB, BAO, SNIa, weak lensing and galaxy cluster number count experiments is likely to prove powerful in this regard."622" The acoustic scale at last scattering, /4, is tightly constrained by CMB data and is highly sensitive to the amount of dark energy at recombination."," The acoustic scale at last scattering, $l_{\rm a}$, is tightly constrained by CMB data and is highly sensitive to the amount of dark energy at recombination."623 /4 changes drastically if the early dark energy density exceeds the matter plusradiation density (?)., $l_{\rm a}$ changes drastically if the early dark energy density exceeds the matter plusradiation density .624" CMB constraints on /4 provide a strong constraint on dark energy parameters atearly times(?),,defining a well-known boundary in the wo—wa plane At late times, for our experiment, dark energy"," CMB constraints on $l_{\rm a}$ provide a strong constraint on dark energy parameters atearly times,defining a well-known boundary in the $w_{\rm625 0}-w_{\rm a}$ plane At late times, for our experiment, dark energy"626The results from the central column densities are borne out by the azimuthally averaged column density profiles.,The results from the central column densities are borne out by the azimuthally averaged column density profiles.627" As before, the and Flat energy produce quantitatively similar Kolmogorovresults."," As before, the Kolmogorov and Flat energy spectra produce quantitatively similar results."628 The probability spectradistributions of are shown in the leftmost two panels in Figures 3-—5.. YX(R)/Xei, The probability distributions of $\Sigma(R)/\Sc$ are shown in the leftmost two panels in Figures \ref{fig:KetoCasellids}- \ref{fig:fcds}.629"Over-plotted in red within the bottom left panels are a number of static isothermal core profiles, for a number of C."," Over-plotted in red within the bottom left panels are a number of static isothermal core profiles, for a number of $\zeta$."630" XR) for the critical case is shown by the solid line, with moving and downward in increments of 4."," $\Sigma(R)$ for the critical case is shown by the solid line, with profiles moving upward and downward in $\zeta$ increments of $4$."631" In profilesparticular, the upward¢=18 and 22 profiles ¢do a fair job of fitting the averaged column density profiles, while those with significantly smaller ¢ do not."," In particular, the $\zeta=18$ and $22$ profiles do a fair job of fitting the averaged column density profiles, while those with significantly smaller $\zeta$ do not."632" For reference, profiles associated with randomly chosen examples with central densities at the5%,,35%,, and cumulative probabilities are shown by the green dotted lines (in each Figure, these are associated with the maps shown on the right)."," For reference, profiles associated with randomly chosen examples with central densities at the, and cumulative probabilities are shown by the green dotted lines (in each Figure, these are associated with the maps shown on the right)."633 The produces similar column density profiles., The fundamental-Kolmogorov energyspectrum produces similar column density profiles.634" fundamental-KolmogorovAs energyanticipated by spectrumthe X./Xi distribution, these are centered the critical profile, with both low and high-¢ profiles represented."," As anticipated by the $\Sigma_c/\Sc$ distribution, these are centered upon the critical profile, with both low and $\zeta$ profiles represented."635"upon In this case the to fit the static-core more averagedaccurately, profilesthough this appearmay be due to the decreased profilesdeviation from the critical core "," In this case the averaged profiles appear to fit the static-core profiles more accurately, though this may be due to the decreased deviation from the critical core profile."636"This suggests that if profile.observations of pulsating cores are to a static BE model, the observed cores will quite comparedcommonly appear strongly super-critical with ¢>(4; even though the cores are in no imminent danger of collapse."," This suggests that if observations of pulsating cores are compared to a static BE model, the observed cores will quite commonly appear strongly super-critical with $\zeta > \zeta_{crit}$ even though the cores are in no imminent danger of collapse."637" Despite the approximate equivalence between the average column density profiles of stable pulsating cores and static super-critical cores, the full two-dimensional maps of pulsating cores can be dramatically asymmetric."," Despite the approximate equivalence between the average column density profiles of stable pulsating cores and static super-critical cores, the full two-dimensional maps of pulsating cores can be dramatically asymmetric."638" Example column density maps, randomly chosen, are shown in the center and columns of Figures 3-—5,, corresponding to the same rightconfigurations for which the azimuthally averaged distributions are shown in the bottom left of each Figure."," Example column density maps, randomly chosen, are shown in the center and right columns of Figures \ref{fig:KetoCasellids}- \ref{fig:fcds}, corresponding to the same configurations for which the azimuthally averaged distributions are shown in the bottom left panel of each Figure."639" These are representative of the configurations panelappearing at the5%,,35%,, and cumulative probabilities, giving some idea of how typical and, perhaps, rare cores appear."," These are representative of the configurations appearing at the, and cumulative probabilities, giving some idea of how typical and, perhaps, rare cores appear."640" the column density maps associated with the KolmogorovAgain and Flat energy spectra are similar, though associated with the former are typically more centrally mapsconcentrated."," Again the column density maps associated with the Kolmogorov and Flat energy spectra are similar, though maps associated with the former are typically more centrally concentrated."641" In roughly and of cases, for the and Flat spectra, respectively, the column density maps are Kolmogorovdouble-peaked."," In roughly and of cases, for the Kolmogorov and Flat spectra, respectively, the column density maps are double-peaked."642" With fewer degrees of freedom, and smaller net density variations for the same Es, it is not surprising that the fundamental-Kolmogorov spectrum shows less small-scale structure."," With fewer degrees of freedom, and smaller net density variations for the same $\Eo$, it is not surprising that the fundamental-Kolmogorov spectrum shows less small-scale structure."643 In most cases the column density maps are only weakly non-circular., In most cases the column density maps are only weakly non-circular.644" Driving Eo; up to 0.6E produces roughly comparable variations in and correspondingly larger deviations from cylindrical 3/3,symmetry, typically with aspect"," Driving $\Eo$ up to $0.6\Eb$ produces roughly comparable variations in $\Sigma_c/\Sc$ , and correspondingly larger deviations from cylindrical symmetry, typically with aspect"645"As for the case with no pre-heating (upper left panel), a satisfactory agreement with data is obtained at rs0o, while simulated groups have a too low level of entropy at T2500.","As for the case with no pre–heating (upper left panel), a satisfactory agreement with data is obtained at $r_{500}$, while simulated groups have a too low level of entropy at $r_{2500}$."646 This result is in line with the comparison performed by ? between their observational results and the best—fit relation from the hydrodynamical simulations by ?.., This result is in line with the comparison performed by \cite{sun08} between their observational results and the best--fit relation from the hydrodynamical simulations by \cite{nagai07}.647" These simulations include radiative cooling, star formation and a rather inefficient form of feedback, and therefore are expected to provide similar results to the reference (non pre-heated) run."," These simulations include radiative cooling, star formation and a rather inefficient form of feedback, and therefore are expected to provide similar results to the reference (non pre–heated) run."648" Clearly, the enntropy level at r2500 is not the only problem suffered by a radiative run without extra heating."," Clearly, the enntropy level at $r_{2500}$ is not the only problem suffered by a radiative run without extra heating."649" Indeed, in this simulation overcooling causes about 40-50 per cent of the baryons within rsoo to be converted in stars, with a decreasing trend with the system temperature."," Indeed, in this simulation overcooling causes about 40–50 per cent of the baryons within $r_{500}$ to be converted in stars, with a decreasing trend with the system temperature."650" This fraction, which is a lower limit owing to the resolution dependence of the cooling efficiency (e.g. ??),, is in excess with respect to observational estimates (e.g.?).."," This fraction, which is a lower limit owing to the resolution dependence of the cooling efficiency \citep[e.g.][]{balogh01,borgani06}, , is in excess with respect to observational estimates \citep[e.g.][]{gonzalez07}."651" Therefore, while cooling plays the role of establishing the level of entropy (?),, a form of non-gravitational heating is required to regulate the amount of lower-entropy gas which is destined to cool and form stars."," Therefore, while cooling plays the role of establishing the level of entropy \citep{voit2001b}, a form of non–gravitational heating is required to regulate the amount of lower–entropy gas which is destined to cool and form stars."652 As for heating with Ka—100 keV cm? (upper right panel of Fig. i," As for heating with $K_{\rm fl}=100$ keV $^2$ (upper right panel of Fig. \ref{fig3}) ),"653"t has a rather small effect on the gas entropy, while it By.does have a significant effect on the fraction of stellar mass, which drops to 10-20 per cent."," it has a rather small effect on the gas entropy, while it does have a significant effect on the fraction of stellar mass, which drops to 10–20 per cent."654" This result implies that, with this level of Ka, radiative cooling is still the main responsible for setting the entropy level, while extra heating regulate the amount of cooled gas."," This result implies that, with this level of $K_{\rm fl}$, radiative cooling is still the main responsible for setting the entropy level, while extra heating regulate the amount of cooled gas."655 A further increase of Kg is then required to alleviate the tension between the observed and the measured levels of entropy in galaxy groups., A further increase of $K_{\rm fl}$ is then required to alleviate the tension between the observed and the measured levels of entropy in galaxy groups.656" Indeed, using Ka=300 keV cm? (bottom panels of Fig. B» "," Indeed, using $K_{\rm657 fl}=300$ keV $^2$ (bottom panels of Fig. \ref{fig3}) )"658brings the entropy level in the simulated groups to better match the observed one., brings the entropy level in the simulated groups to better match the observed one.659" However, as discussed in the previous section imposing an entropy floor generates too large voids in the forest, an effect that can be compensated by increasing the heating overdensity threshold, δι."," However, as discussed in the previous section imposing an entropy floor generates too large voids in the forest, an effect that can be compensated by increasing the heating overdensity threshold, $\delta_{\rm h}$."660" However, increasing the latter from ὃν=10 (bottom left panel) to 30 (bottom right panel) induces a slight but sizable decrease of Ka, especially for A—2500, as a consequence of the smaller number of gas particles heated at z—4."," However, increasing the latter from $\delta_{\rm h}=10$ (bottom left panel) to 30 (bottom right panel) induces a slight but sizable decrease of $K_\Delta$, especially for $\Delta=2500$, as a consequence of the smaller number of gas particles heated at $z=4$."661" Therefore, while heating at relatively high overdensity is required by the void statistics of the forest, it goes in the wrong direction to reproduce the thermodynamical properties of intra-group medium at small radii."," Therefore, while heating at relatively high overdensity is required by the void statistics of the forest, it goes in the wrong direction to reproduce the thermodynamical properties of intra–group medium at small radii."662 This demonstrate how effective is combining observations of the high-z IGM and low—z intra-group medium to constrain the thermal history of the cosmic baryons., This demonstrate how effective is combining observations of the $z$ IGM and $z$ intra–group medium to constrain the thermal history of the cosmic baryons.663" We presented an analysis of cosmological hydrodynamical simulations, including radiative cooling and pre-heating, aimed at characterising both the properties of the high-redshift forest and the thermodynamical properties of the diffuse gas within nearby galaxy groups."," We presented an analysis of cosmological hydrodynamical simulations, including radiative cooling and pre–heating, aimed at characterising both the properties of the high–redshift forest and the thermodynamical properties of the diffuse gas within nearby galaxy groups."664" We use a simple phenomenological recipe for pre-heating, in which at z=4 all the gas particles lying at an overdensity above ὃν are brought to a minimum entropy level of Ka."," We use a simple phenomenological recipe for pre–heating, in which at $z=4$ all the gas particles lying at an overdensity above $\delta_{\rm h}$ are brought to a minimum entropy level of $K_{\rm665 fl}$."666" At z=2.2 mock QSO spectra were extracted and their properties compared to the observed distribution of voids in the flux (?), while at z=0 the entropy-temperature relation of galaxy groups is compared with recent results from X-ray observations (?).."," At $z=2.2$ mock QSO spectra were extracted and their properties compared to the observed distribution of voids in the flux \citep{viel08voids}, while at $z=0$ the entropy–temperature relation of galaxy groups is compared with recent results from X–ray observations \citep{sun08}. ."667" The main results of our analysis can be summarised as follows: i) pre-heating all the gas, irrespective of its density, produces voids in the forest, which are toolarge if compared to observations; i)imposing a modest overdensity threshold"," The main results of our analysis can be summarised as follows: $i)$ pre–heating all the gas, irrespective of its density, produces voids in the forest, which are toolarge if compared to observations; $ii)$imposing a modest overdensity threshold"668propagation of CATEs in the corona.,propagation of CMEs in the corona.669 The (SECCLII) (Llowarelοἱal.2005) suite of instruments on the STEREO spacecraft carries (wo white-light coronagraphs. CORLL and COR2. with fields of view 1.4—-4.0R. and 2.0—15.0R.. respectively. and Extreme UltraViolet Imager (EUVI) imaging the Sun at four wavelengths in the extreme ultraviolet band.," The (SECCHI) \citep{Howard.etal2008} suite of instruments on the STEREO spacecraft carries two white-light coronagraphs, COR1 and COR2, with fields of view $1.4-4.0\Rsun$ and $2.0-15.0\Rsun$ respectively, and Extreme UltraViolet Imager (EUVI) imaging the Sun at four wavelengths in the extreme ultraviolet band."670 We have used images obtained [rom the two coronagrapls to study six CAIEs that occurred on 2007 November 16. 2007 December 31. 2008 April 9. 2009 December 16. 2010 April 13. and 2010 August I.," We have used images obtained from the two coronagraphs to study six CMEs that occurred on 2007 November 16, 2007 December 31, 2008 April 9, 2009 December 16, 2010 April 13, and 2010 August 1."671 The cadence of images for the cases analvsed was at best 5 minutes for COR and 15 minutes lor CODB2., The cadence of images for the cases analysed was at best 5 minutes for COR1 and 15 minutes for COR2.672 In addition. three EPs that were associated with the CMEs on 2008 April 9. 2010 April 13. and 2010 August 1 were also analvsed using images from the EUVI instrument. having a cadence of 10 minutes.," In addition, three EPs that were associated with the CMEs on 2008 April 9, 2010 April 13, and 2010 August 1 were also analysed using images from the EUVI instrument having a cadence of 10 minutes."673 A sample image of each event observed. [from coronagraphs CORL and COR2. and EUVI for the three EPs. are shown in Figures 1- 6..," A sample image of each event observed from coronagraphs COR1 and COR2, and EUVI for the three EPs, are shown in Figures \ref{F:img16nov}- \ref{F:img01aug}."674 The soft N-ray flux data from Geostationary Operational Environmental Satellite (GOES) satellite was used to determine start ancl peak (ime of the flare associated with the CAIEs on 2007 December 31 and 2009 December 16., The soft X-ray flux data from Geostationary Operational Environmental Satellite (GOES) satellite was used to determine start and peak time of the flare associated with the CMEs on 2007 December 31 and 2009 December 16.675 A feature that could be identified and tracked in all the simultaneous pairs of images from the spacecralt was used [or stereoscopic reconstruction., A feature that could be identified and tracked in all the simultaneous pairs of images from the spacecraft was used for stereoscopic reconstruction.676 To be able to unambiguously identify the feature in fields of view of both the STEREO coronagraphs. we had to select a leature in the inner part of the LE. and not the outermost feature in the LE.," To be able to unambiguously identify the feature in fields of view of both the STEREO coronagraphs, we had to select a feature in the inner part of the LE, and not the outermost feature in the LE."677 The reconstruction technique involves rotating the heliocentric Earth ecliptic coordinate svstem, The reconstruction technique involves rotating the heliocentric Earth ecliptic coordinate system678"WTTS or CTTS we use the accuracy. clefined as where Nyp and γρ are the number of true positives and false positives. respectively,","WTTS or CTTS we use the accuracy, defined as where $N_{TP}$ and $N_{FP}$ are the number of true positives and false positives, respectively."679 We also look at computed CTTS fraction. given bv In Figure 20. we plot both of these selection metrics against the threshold value of oy.," We also look at computed CTTS fraction, given by In Figure \ref{fig-metric} we plot both of these selection metrics against the threshold value of $\sigma_V$."680 We find that the peak accuracy of 720.4 is found for a threshold value of 0.1 magnitudes and that the computed CTTS fraction is close to the actual CTTS fraction for σι. thresholds between 0.1 and 0.15 magnitudes., We find that the peak accuracy of $\sim$ 0.4 is found for a threshold value of 0.1 magnitudes and that the computed CTTS fraction is close to the actual CTTS fraction for $\sigma_V$ thresholds between 0.1 and 0.15 magnitudes.681 Since the variability aunplitude in CTTS increases sharply al shorter wavelengths. with tvpical values of ap/ay~1.3 (Ilerbstetal.1994).. we mieht expect that the optimal threshold lor WTTS/CTTS differentiation using the SDSS g band. which has a similar effective wavelength as D. may be in the range of 0.13 to 0.2 magnitudes.," Since the variability amplitude in CTTS increases sharply at shorter wavelengths, with typical values of $\sigma_B/\sigma_V \sim 1.3$ \citep{her94}, we might expect that the optimal threshold for WTTS/CTTS differentiation using the SDSS $g$ band, which has a similar effective wavelength as $B$, may be in the range of 0.13 to 0.2 magnitudes."682" This suggests that the computed CTTS fraction in our work. which is based on a o, threshold ol 0.2 magnitudes. may not be unreasonable."," This suggests that the computed CTTS fraction in our work, which is based on a $\sigma_g$ threshold of 0.2 magnitudes, may not be unreasonable."683" The 25 Orionis group is evident in a surface densitv plot of candidate PMS stars that are identified on the basis of o,>0.05.", The 25 Orionis group is evident in a surface density plot of candidate PMS stars that are identified on the basis of $\sigma_g > 0.05$.684 In Figure 21. there are three obvious groupings ol PAIS stars which. in order of increasing R.A... are the 25 Ori group. the Orion OBIb subassociation. and the NGC 2068/NGC 2071 star formation site in the L1630 cloud.," In Figure \ref{fig-radec}685 there are three obvious groupings of PMS stars which, in order of increasing R.A., are the 25 Ori group, the Orion OB1b subassociation, and the NGC 2068/NGC 2071 star formation site in the L1630 cloud."686 The surface densities are computed on a 1.0* by 0.257 grid in RA. and Dec. with the peak value of 68 stars ? found at the center of the Ori ODIb subassociation., The surface densities are computed on a $1.0\degr$ by $0.25\degr$ grid in R.A. and Dec. with the peak value of 68 stars $^{-2}$ found at the center of the Ori OB1b subassociation.687 We look for the southern extent of the 25 Ori group by computing the surface density ol the PAIS candidates as a function of radial distance from the Be star 25 Orionis., We look for the southern extent of the 25 Ori group by computing the surface density of the PMS candidates as a function of radial distance from the Be star 25 Orionis.688" Due to the center of the group being outside of the SDSS imaging area we compute the areas lor each radial bin as INOreos“d/rdr where the radial bin size Ar=0.4°. the distance between 25 Ori and the SDSS imaging area d—0.6"". and r>d."," Due to the center of the group being outside of the SDSS imaging area we compute the areas for each radial bin as $\int_{r}^{r+{\Delta}r} 2r cos^{-1}(d/r) dr$ where the radial bin size ${\Delta}r = 0.4\degr$, the distance between 25 Ori and the SDSS imaging area $d = 0.6\degr$, and $r \ge d$."689 In Figure 22. we see (hat the 25 Ori group blends into the surrounding dispersed PAIS population of Ori OBla at distances greater than 1.4 from the Be star 24 Orionis., In Figure \ref{fig-density} we see that the 25 Ori group blends into the surrounding dispersed PMS population of Ori OB1a at distances greater than $\degr$ from the Be star 24 Orionis.690 In, In691thus to determine at which frequcney the spectral break occurs.,thus to determine at which frequency the spectral break occurs.692" The break [requeney i, is strictly related to the radiative Lifetime of the svnchrotron. emitting electrons Haa.", The break frequency $\nu_{\rm br}$ is strictly related to the radiative lifetime of the synchrotron emitting electrons $t_{\rm syn}$.693 Once the magnetic field. is known. for example assuming minimum total energy content corresponding to equipartition between particles anc magnetic field (11) energies (Pacholezek|1970)... anc following some assumptions (Murgia2003).. the radiative age can be easilv estimated by means Several studies aimed at estimating the radiative age in compact radio objects indicate ages between 107 - 107 vears (Ασίαetal.1999:ALurgia2003) in excellent. agreenicnt with the kinematic Given all the assumptions mentioned. earlier. these methods do not provide the accurate source age. that can be improved either. by increasing the time interval spanned by the observations or through a better sampling of the frequeney coverage used to derive the radio Among all the CSOs studied. in this framework. the radio source 0050|6001 represents à peculiar case.," Once the magnetic field is known, for example assuming minimum total energy content corresponding to equipartition between particles and magnetic field $H$ ) energies \citep{pacho70}, and following some assumptions \citep{mm03}, the radiative age can be easily estimated by means Several studies aimed at estimating the radiative age in compact radio objects indicate ages between $^{3}$ - $^{4}$ years \citep{mm99,mm03}, in excellent agreement with the kinematic Given all the assumptions mentioned earlier, these methods do not provide the accurate source age, that can be improved either by increasing the time interval spanned by the observations or through a better sampling of the frequency coverage used to derive the radio Among all the CSOs studied in this framework, the radio source J0650+6001 represents a peculiar case."694 “This source is identified with a quasar at redshift +=0.455. and its optical spectrum is characterized. by very weak. broad lines and prominent narrow lines (Stickel&Ixühr1993).," This source is identified with a quasar at redshift $z = 0.455$, and its optical spectrum is characterized by very weak broad lines and prominent narrow lines \citep{stickel93}."695. It has a non-aligned triple radio structure with a total angular size of 7 mas (40 pc). and its total radio spectrum turns over around 5.5 GlLlz (Orientietal.2007)..," It has a non-aligned triple radio structure with a total angular size of 7 mas $\sim$ 40 pc), and its total radio spectrum turns over around 5.5 GHz \citep{mo07}."696 From a previous study no evidence of proper motion has been found (Orienti&Dallacasa 2008).. although the resolution at 5 Cillz (i.e. the frequeney at which several observations spanning almost a decade have been performed) was not adequate to reliably estimate small changes in the component positions.," From a previous study no evidence of proper motion has been found \citep{mo08}, although the resolution at 5 GHz (i.e. the frequency at which several observations spanning almost a decade have been performed) was not adequate to reliably estimate small changes in the component positions."697 llowever. another analvsis of the position of the source components based on global VLBI observations (Akujoretal. 1996).. indicated. an apparent contraction between. the central and the southern components.," However, another analysis of the position of the source components based on global VLBI observations \citep{akujor96}, indicated an apparent contraction between the central and the southern components."698" In this paper we report on the results on multi-epoch VLBI and 5-Gllz VLA data of the compact. symmetric object’ 0050|6001. and we present an interpretation to explain the radio properties of this ""Throughout this paper. we assume the following cosmologv: Jj)=Tlkms‘Alpe DOO=027. and f. in à flat. Universe."," In this paper we report on the results on multi-epoch VLBI and 5-GHz VLA data of the compact symmetric object J0650+6001, and we present an interpretation to explain the radio properties of this Throughout this paper, we assume the following cosmology: $H_{0} =69971\, {\rm km\, s^{-1}\, Mpc^{-1}}$, $\Omega_{\rm M} = 0.27$, and $\Omega_{\Lambda} = 0.73$, in a flat Universe."700 At the redshift of the target =5.773 kpe., At the redshift of the target $^{''} = 5.773$ kpc.701 The spectral index is defined as ον)κmm To determine a possible source growth. we complemented the information available in the literature for the target source JO0650|6001. with archival VLBA data. obtained in November 1909 at 5.0 Cllz. and VLBA|Ellelsberg observations at 5.0 and S.4 CGllz carried out in. December 2004 (see Table 1)).," The spectral index is defined as $S {\rm (\nu)} \propto \nu^{- \alpha}$ To determine a possible source growth, we complemented the information available in the literature for the target source J0650+6001 with archival VLBA data obtained in November 1999 at 5.0 GHz, and VLBA+Effelsberg observations at 5.0 and 8.4 GHz carried out in December 2004 (see Table \ref{vlba}) )."702 The data reduction was carried out by means of the NRAOQ ALPS package., The data reduction was carried out by means of the NRAO AIPS package.703 The accuracy of the, The accuracy of the704hot spot (Meisenheimer&Réser1986).,hot spot \citep{mei86}.705. The proximity of 3C 33 permits us to resolve spatially the emission features at the highest possible linear resolution., The proximity of 3C 33 permits us to resolve spatially the emission features at the highest possible linear resolution.706" In addition, since this source has a narrow-line nucleus, relativistic beaming is not likely to be important in modifying the spectral or morphological properties of the hot spots."," In addition, since this source has a narrow-line nucleus, relativistic beaming is not likely to be important in modifying the spectral or morphological properties of the hot spots."707 This paper is organized as follows., This paper is organized as follows.708" Section 2 contains à summary of the observations, the results of the data analysis are presented in section 3, and we discuss the implications of our results in section 4."," Section 2 contains a summary of the observations, the results of the data analysis are presented in section 3, and we discuss the implications of our results in section 4."709 Section 5 contains a brief summary and conclusions., Section 5 contains a brief summary and conclusions.710" We assume WMAP cosmology throughout this paper (Spergeletaf, 2003)..", We assume WMAP Year-1 cosmology throughout this paper \citep{spe03}. .711" The observed redshift (220.0597) of the host galaxy of 3C 33 corresponds to a luminosity distance of 263.9 Mpc, and one aresecond is 1.14 kpe."," The observed redshift $z$ =0.0597) of the host galaxy of 3C 33 corresponds to a luminosity distance of 263.9 Mpc, and one arcsecond is 1.14 kpc."712" All uncertainties are at confidence for one parameter of interest unless otherwise stated, and all coordinates are J2000."," All uncertainties are at confidence for one parameter of interest unless otherwise stated, and all coordinates are J2000."713" Absorption by gas in our Galaxy CVjj24.0x 107"" 7) (Dickey&Lockman1990) is included in all spectral fits and count rate to flux density conversions.", Absorption by gas in our Galaxy $N_H$ $\times$ $^{20}$ $^{-2}$ ) \citep{dic90} is included in all spectral fits and count rate to flux density conversions.714" The radio galaxy 3C 33 was observed with Chandra/ACIS-S in two observations (OBSID 6190 and 7200) on November 8, 2005 and November 12, 2005 (PI: Stephen Murray)."," The radio galaxy 3C 33 was observed with /ACIS-S in two observations (OBSID 6190 and 7200) on November 8, 2005 and November 12, 2005 (PI: Stephen Murray)."715 The total observing time was ~40.3 ks., The total observing time was $\sim$ 40.3 ks.716" The observation was pointed so that the SHS was near the best focus. but all regions of the radio galaxy, including the northern hot spot (NHS) and nucleus, were contained on the S3 chip."," The observation was pointed so that the SHS was near the best focus, but all regions of the radio galaxy, including the northern hot spot (NHS) and nucleus, were contained on the S3 chip."717" We made light curves for the S3 CCD in the 5.0 to 10.0 keV band. excluding the nucleus, to search for background flares, and removed intervals where the background rate was more than 30 above the mean, leaving 39831.6 s of good data."," We made light curves for the S3 CCD in the 5.0 to 10.0 keV band, excluding the nucleus, to search for background flares, and removed intervals where the background rate was more than $\sigma$ above the mean, leaving 39831.6 s of good data."718" Bad pixels, hot columns, and events along node boundaries also were removed, and standard ASCA grade filtering (0,2.3.4.6) was applied to the events file."," Bad pixels, hot columns, and events along node boundaries also were removed, and standard ASCA grade filtering (0,2,3,4,6) was applied to the events file."719 Emission from 3C 33 fills only à small traction of the field of view of the S3 chip. so local background was used in all spectral analysis.," Emission from 3C 33 fills only a small fraction of the field of view of the S3 chip, so local background was used in all spectral analysis."720" The core is aligned to —0.1"" with the radio core. so no adjustment of the X-ray coordinates was necessary."," The X-ray core is aligned to $\sim$ $''$ with the radio core, so no adjustment of the X-ray coordinates was necessary."721 All X-ray images presented in this paper were generated from theChandra data., All X-ray images presented in this paper were generated from the data.722 observed 3C 33 for a total of 17 ks in two separate observations on 2004 January 4 and 2004 January 21 (PI: Martin Hardeastle)., observed 3C 33 for a total of 17 ks in two separate observations on 2004 January 4 and 2004 January 21 (PI: Martin Hardcastle).723 The data were processed with the Scientific Analysis Software (SAS) using the standard pipeline tasks and and filtered for patterns <=4 (MOS) or <=12 (pn) and using the bit-mask flags 0x766a0600 for MOS and Oxfa000c for pn. which are equivalent to the standard flagset #XXMMEA_EEM/EP but include out of field-of-view events and exclude bad columns and rows.," The data were processed with the Scientific Analysis Software (SAS) using the standard pipeline tasks and and filtered for patterns $<= 4$ (MOS) or $<=12$ (pn) and using the bit-mask flags 0x766a0600 for MOS and 0xfa000c for pn, which are equivalent to the standard flagset EM/EP but include out of field-of-view events and exclude bad columns and rows."724" In the first of the two observations, thebackground count rate was low (~0.2 counts ! for MOS and ~0.4 counts ! for pn) so that no"," In the first of the two observations, thebackground count rate was low $\sim$ 0.2 counts $^{-1}$ for MOS and $\sim$ 0.4 counts $^{-1}$ for pn) so that no"725with a central cusp of slope 2.,with a central cusp of slope $-2$.726 They did not πα any dependence of the hardening rate on the uunuber of stars., They did not find any dependence of the hardening rate on the number of stars.727 To stummarize. there is no single accepted view for the evolution of massive black hole binaries in the center of galaxies.," To summarize, there is no single accepted view for the evolution of massive black hole binaries in the center of galaxies."728 The simple analytic theory (BBR) predicts that the hardening timescale should be determined bx the timescale for refilhug the loss-cone. and therefore should be proportional to the relaxation time. or roughly speaking. the umuber of stars in the system.," The simple analytic theory (BBR) predicts that the hardening timescale should be determined by the timescale for refilling the loss-cone, and therefore should be proportional to the relaxation time, or roughly speaking, the number of stars in the system."729 The results of uunerical studies range from no depeudenuce (Milosavljovió&.Mexitt.2001) to a dependence ATP Taking1997)., The results of numerical studies range from no dependence \citep{MilosavljevicMerritt2001} to a dependence $\propto N^{1/3}$ \citep{Makino1997}.730. Iu this paper. we eive a clear and decisive answer to the question whether the hardenimg timescale depeucds ou the number of particles used in the simulation. aud if so. du what wav.," In this paper, we give a clear and decisive answer to the question whether the hardening timescale depends on the number of particles used in the simulation, and if so, in what way."731 In section 2 we describe the initial model aud the uumerical method used., In section 2 we describe the initial model and the numerical method used.732 Iu section 3 we eive the result., In section 3 we give the result.733 Section { coutaius the discussion., Section 4 contains the discussion.734 We performed N-body simulations of galaxies with massive black holes., We performed $N$ -body simulations of galaxies with massive black holes.735 For alb caleulatiouns. we used a programm with direct force calculation and fourth-order Ucrmite integrator with individual (block) timestep (Alakino&Aarseth1992).," For all calculations, we used a program with direct force calculation and fourth-order Hermite integrator with individual (block) timestep \citep{MakinoAarseth1992}."736. For eravitational interaction between field stars. we apply the usual Pluuunuer softening.," For gravitational interaction between field stars, we apply the usual Plummer softening."737 The size of the softening is described in section 2.2.., The size of the softening is described in section \ref{sect:initialmodels}.738 The gravitational interactions between black holes and that between black holes and field particles are calculated with very simall softening. ερ=109.," The gravitational interactions between black holes and that between black holes and field particles are calculated with very small softening, $\epsilon_{BH} = 10^{-6}$."739 Since we do not apply auy regularization technique. we need to euarautee that the gravitational force does not diveree.," Since we do not apply any regularization technique, we need to guarantee that the gravitational force does not diverge."740 For calculation of gravitational forces from field articles (to both the field particles and black holes). we used thle special-purpose hardware GRAPE-6(Makiuoetal. 2002).," For calculation of gravitational forces from field particles (to both the field particles and black holes), we used the special-purpose hardware \citep{Makinoetal2002}."741. The calculation of the forces from black roles was done on the host computer to maintain sufficient accuracy. In a way shular to Makino&Ebisuzaki (1996).," The calculation of the forces from black holes was done on the host computer to maintain sufficient accuracy, in a way similar to \cite{MakinoEbisuzaki1996}."742". The relative accuracy of the pairwise orco calculated with ""οι. accuracy” versions of GRAPE hardwares (GBAPE-2. Laud 6) is roughly single xecisiou (21-bit mantissa)."," The relative accuracy of the pairwise force calculated with “High accuracy” versions of GRAPE hardwares (GRAPE-2, 4 and 6) is roughly single precision (24-bit mantissa)."743 This accuracy is usually sufficient. since the errors of the forces from many articles partially cancel each other.," This accuracy is usually sufficient, since the errors of the forces from many particles partially cancel each other."744 However. sinele-swrecision is not quite chough for forces froii black hole articles.," However, single-precision is not quite enough for forces from black hole particles."745 The reason is that some particles. and most rotably the black hole particles themselves after they ormed a binary. orbit around a black hole particle a πο of times. csscutially fecling ouly the force from oue black hole particle.," The reason is that some particles, and most notably the black hole particles themselves after they formed a binary, orbit around a black hole particle a number of times, essentially feeling only the force from one black hole particle."746 In this case. the rouud-off eror acetates. aud the error iu the total euergy. becomes alarnunely large.," In this case, the round-off error accumulates, and the error in the total energy becomes alarmingly large."747 Moreover. all the errors are generated from the black hole binary aud stars which are close to them. the behavior of which we are interested in.," Moreover, all the errors are generated from the black hole binary and stars which are close to them, the behavior of which we are interested in."748 Iu order to euarantee sufficient accuracy. we chose to calculate all eravitational forces from black hole particles ou the host computer. usiug full dowhle-precision (53-bit mantissa) niunubers.," In order to guarantee sufficient accuracy, we chose to calculate all gravitational forces from black hole particles on the host computer, using full double-precision (53-bit mantissa) numbers."749 No relativistic effect was taken into account., No relativistic effect was taken into account.750 Our calculation is purely Newtonian., Our calculation is purely Newtonian.751 We do not model the accretion to black holes or collisions between stars. since their cross sections are sinall.," We do not model the accretion to black holes or collisions between stars, since their cross sections are small."752 Tn this paper. we consider a simple model. where we place two iassive poiutauass particles im a spherical ealaxy.," In this paper, we consider a simple model, where we place two massive point-mass particles in a spherical galaxy."753 For our standard set of runs. the initial galaxy model is a Wine model with nonduneusional central potential Wy=7.," For our standard set of runs, the initial galaxy model is a King model with nondimensional central potential $W_0=7$."754 We use Iegeie units. where the mass Af and the virial radius δρ of the initial galaxy model and gravitational constant G are all unity.," We use Heggie units, where the mass $M$ and the virial radius $R_v$ of the initial galaxy model and gravitational constant $G$ are all unity."755 In these units. the binding eucrev of the initial ealaxv is E=L/L.," In these units, the binding energy of the initial galaxy is $E = -1/4$."756 The mass of the black hole particles is Mp;=0.01., The mass of the black hole particles is $M_{BH}=0.01$.757 Thev are initially placed at (40.5.0.0) with velocity (0.40.1.0).," They are initially placed at $(\pm 0.5,0,0)$ with velocity $(0,\pm 0.1,0)$."758 Thus. they are initially outside the core. at the apoceuter of nearly racial orbits.," Thus, they are initially outside the core, at the apocenter of nearly radial orbits."759 We varied the number of particles Α΄ from 2.000to 1.000.000.," We varied the number of particles $N$ from 2,000to 1,000,000."760 To investigate the possible depeudenuce of the results on the softeniug Ieneth. we tried three differeut choices for the softeniug leugth: (a) e=0.01. (b) (6) e=20/N.," To investigate the possible dependence of the results on the softening length, we tried three different choices for the softening length: (a) $\epsilon=0.01$, (b) $\epsilon=0.01/(N/2000)^{1/3}$ , (c) $\epsilon=20/N$."761 All give the same e=0.01 for Vo—2000. but they have a differeut depeudeuce on AN.," All give the same $\epsilon=0.01$ for $N=2000$, but they have a different dependence on $N$."762 The largest calculation (1 nulliou particles for up to f=300) took about one month on a sinele-host. Lbsrocessor-hoard GRAPE-G system with a peak speed of | Tfüops.," The largest calculation (1 million particles for up to $t=300$ ) took about one month on a single-host, 4-processor-board GRAPE-6 system with a peak speed of 4 Tflops."763 The total number of individual timesteps was L2«101., The total number of individual timesteps was $1.2\times 10^{11}$.764 In other words. the (harmonic) average inestep is around 2.5«LO2.," In other words, the (harmonic) average timestep is around $2.5\times 10^{-3}$."765 In comparison. the total muuber of block timesteps is 2.1«105.," In comparison, the total number of block timesteps is $2.1\times 10^8$."766 Thus. the typical iuestep size of the particle with the sinallest timestep (generally the black hole particles themselves or particles close to them) is 1.£10.9. more than 1000 times sinaller hau the average stepsize.," Thus, the typical timestep size of the particle with the smallest timestep (generally the black hole particles themselves or particles close to them) is $1.4 \times76710^{-6}$, more than 1000 times smaller than the average stepsize."768 Without the use of individual inesteps. this calculation would have required a fraction of a Petaflops-vear. rather than 1/3 Teratlops-vear.," Without the use of individual timesteps, this calculation would have required a fraction of a Petaflops-year, rather than 1/3 Teraflops-year."769 For all calculations. the total cucrey is conserved to etter than or better than of the binding enerev ofthe DII binary.," For all calculations, the total energy is conserved to better than, or better than of the binding energy of the BH binary."770 We did several test calculations with both higher aud lower accuracy criteria. but fouud 10 svstenmatic difference in the final results.," We did several test calculations with both higher and lower accuracy criteria, but found no systematic difference in the final results."771 Figure 1l. shows the time evolution of the specific binding energv (per uuit of reduced mass) of the black hole binary., Figure \ref{fig:ebfign} shows the time evolution of the specific binding energy (per unit of reduced mass) of the black hole binary.772 The relation between the sciai-major axis a and the binding cucrev is The relation between the orbital velocity of the black holes aud £j is given simaply by where eds the three-dimenusional velocity dispersion of the field stars. iu a central region of the galaxy. chosen to be large enough not to be affected significantly by the black holes.," The relation between the semi-major axis $a$ and the binding energy is The relation between the orbital velocity of the black holes and $E_b$ is given simply by where $v_c$ is the three-dimensional velocity dispersion of the field stars, in a central region of the galaxy, chosen to be large enough not to be affected significantly by the black holes."773" Thus. if we interpret the host galaxy as a ealaxy with a velocity dispersion of 300 kms. the black hole biuarv with £;,=1 has an orbital velocity of 300 lius. Frou. figure 1.. it is clear that the evolution timescale continues to depend on NV for the entire range of /N for which we performed our simulations. with no indication whatsoever of even an onset toward convergence."," Thus, if we interpret the host galaxy as a galaxy with a velocity dispersion of 300 km/s, the black hole binary with $E_b=-1$ has an orbital velocity of 300 km/s. From figure \ref{fig:ebfign}, , it is clear that the evolution timescale continues to depend on $N$ for the entire range of $N$ for which we performed our simulations, with no indication whatsoever of even an onset toward convergence."774Current and upcoming survevs ina variely of wavelengt(l bands will increase (le number of wellobserved clusters of galaxies bv at least an order of magnitude. while probing to much hieher redshilts (han before.,"Current and upcoming surveys in a variety of wavelength bands will increase the number of well–observed clusters of galaxies by at least an order of magnitude, while probing to much higher redshifts than before."775 Understanding the physical state of the intra-cluster medium (ICAL) will be essential to exploiting this new data., Understanding the physical state of the intra-cluster medium (ICM) will be essential to exploiting this new data.776 In. particular. it is necessary {ο develop methods of accurately. modeling the thermal state of the gas in clusters before one can ex(ract cosmological information Irom large surveys. which measure quantities arising from that state.," In particular, it is necessary to develop methods of accurately modeling the thermal state of the gas in clusters before one can extract cosmological information from large surveys, which measure quantities arising from that state."777 For cluster-sizecl halos in a cosmological setting. the theoretical final distribution expected [rom the gravitational collapse of the dark matter (DM) is well understood (Navarro2006:Luetal. 2006)..," For cluster-sized halos in a cosmological setting, the theoretical final distribution expected from the gravitational collapse of the dark matter (DM) is well understood \citep{NavarroFW97,BullockKSSKKPD01,JingSuto02,PowerNJFWSSQ03,778ZhaoJMB03,NavarroHPJFWSSQ04,TasitsiomiKGK04,ReedGVGQSML05,779BartelmannDPBMMT05,DiemandZMSC05,ShawWOB06,LuMKW06}."780 Measurements of the DM density. profile in galaxy eroups and clusters agree well with this theoretical expectation (Lewisetal.2003:Dahleetal.2006:Schmidt&Allen20060:Saha 2006).," Measurements of the DM density profile in galaxy groups and clusters agree well with this theoretical expectation \citep{LewisBS03,DahleHS03,PrattArnaud05,PointecouteauAP05,781ComerfordMBS06,LokasWGMP06,RinesDiaferio06,ZekserWBBFIBPJC06,782MandelbaumSCBHB06,GastaldelloBHZBBM06,SchmidtAllen06z,SahaRW06}."783. Llowever. the hot intracluster gas in these svstems does not parallel the DM in either densitv or temperature distribution.," However, the hot intracluster gas in these systems does not parallel the DM in either density or temperature distribution."784 Aluch progress has been made in understanding the expected ICM distribution inside a standard DM halo (viththedensitv.prolileshowingapowerlawcuspasinNavarroelal.1997:Mooreetal.1999.," Much progress has been made in understanding the expected ICM distribution inside a standard DM halo \citep[with the density profile showing a power law785cusp as in][or similar]{NavarroFW97,MooreQGSL99}."786or similar).. Makinoetal.(1998) gave an analvlic expression [or the density of isothermal gas in hwdrostatic equilibrium with a NEW potential: (his was soon extended (o non-isothermal gas will a polvtiropic equation of state (SutoWiretal.2000:LoewensteinAÁscasibarοἱ 2003).. and to triaxial halos (LeeWang&Fan 2006).," \citet{MakinoSS98} gave an analytic expression for the density of isothermal gas in hydrostatic equilibrium with a NFW potential; this was soon extended to non-isothermal gas with a polytropic equation of state \citep{SuotSM98,WuFN00,Loewenstein00,AscasibarYMS03}, and to triaxial halos \citep{LeeSuto03,WangFan06}."787. The resulüng σας profiles possess a finite density core. and not a cusp as seen in the DM.," The resulting gas profiles possess a finite density core, and not a cusp as seen in the DM."788 The gross energetics of the gas do not parallel (hat of the DM either., The gross energetics of the gas do not parallel that of the DM either.789 Assuming that the eas energv comes solely ου gravitational collapse gives the sell-similar scalings between mass M. luminosity L. and temperature T of ALxT7 and LxT? 1993).," Assuming that the gas energy comes solely from gravitational collapse gives the self-similar scalings between mass $M$, luminosity $L$, and temperature $T$ of $M\propto T^{3/2}$ and $L\propto T^2$ \citep{Kaiser86,EkeNF98}."790. IIowever. these scalings do not agree with the observed relations. leading to propose (hat non-gravitational energy injection is important.," However, these scalings do not agree with the observed relations, leading \citet{Kaiser91} to propose that non-gravitational energy injection is important."791 This idea has gained support [from a number of analvüc investigations into polvtropic ICM. in DAI potentials (Baloghetal.1999:Suto1998:Wuοἱ2000:Loewenstein2000;Tozzi&Norman2004;Lapietal.2005;Afshordi2005:Solanesοἱ 2005).," This idea has gained support from a number of analytic investigations into polytropic ICM in DM potentials \citep{BaloghBP99,SuotSM98,WuFN00,Loewenstein00,792TozziNorman01,KomatsuSeljak01,BabulBLP02,VoitBBB02,793DosSantosDore02,ShimizuKSS04,LapiCM05,AfshordiLS05,794SolanesMGS05}."795.. An additional departure [rom self-similarity can come from star formation. which selectively removes gas with short cooling times. low entropy. and low total energyv. leaving behind higher entropy," An additional departure from self-similarity can come from star formation, which selectively removes gas with short cooling times, low entropy, and low total energy, leaving behind higher entropy"796aud the couvolution operators along (Gc.gy) aud: do not conumuute. even though the Πο bauk satisfies the exact reconstmetiou formula.,"and the convolution operators along $(x,y)$ and $z$ do not commute, even though the filter bank satisfies the exact reconstruction formula."797 by defining the unltivesolution support from the stabilized cocfiicicuts. and by using au iterative reconstruction scheme.," by defining the multiresolution support from the stabilized coefficients, and by using an iterative reconstruction scheme."798 Ax the roise ou the stabilized coefficients is Gaussian.1.. we consider that a wavelet coefficient Wolkehy.ke] is significaut. Le.. not due to noise. if its absolute value is larger than5.," As the noise on the stabilized coefficients is Gaussian, we consider that a wavelet coefficient $w_{j_1,j_2}[k_x,k_y,k_z]$ is significant, i.e., not due to noise, if its absolute value is larger than."799. The multiresolution support will be obtained by detecting at cach scale the significant coefficieuts., The multiresolution support will be obtained by detecting at each scale the significant coefficients.800 The niultiresohttion support for is defined as Tn words. the unItiresolution support AL indicates at which scales (spaial and time/enerev)) aud which positions. we have significant signal.," The multiresolution support for is defined as In words, the multiresolution support $M$ indicates at which scales (spatial and ) and which positions, we have significant signal."801 We YV the 2D-1Dabove.. R the inverse wavele transforma aud Y the input data cube.," We ${\cal W}$ the 2D-1D, $\JF{{\cal R}}$ the inverse wavelet transform and $Y$ the input data cube."802 We want our solition Y exactly the same coefficients as the wavele cocfiicicnts of the input data Y. but oulv at scales axd positions where sjeuifüicaut signal has been detected (1.0. ADV AJYVY).," We want our solution $X$ exactly the same coefficients as the wavelet coefficients of the input data $Y$, but only at scales and positions where significant signal has been detected (i.e. $ M {\cal W} X = M {\cal W} Y$ )."803 At other scales and posilous. we want the smoothest solutionsolution.," At other scales and positions, we want the smoothest solution."804.. It is clear that there are many solutions satisfviug the )osifivitv. aud multiresolution support consistency requirements. e.g. Y itself.," It is clear that there are many solutions satisfying the positivity and multiresolution support consistency requirements, e.g. $Y$ itself."805 Thus. our reconstruction problem based solely ο1 these coustraiuts is an il-posed inverse problem that must be regularized.," Thus, our reconstruction problem based solely on these constraints is an ill-posed inverse problem that must be regularized."806 Typicalv. the solution iu which we are interested must be sparse by involving he lowest budget of wavelet coefficients.," Typically, the solution in which we are interested must be sparse by involving the lowest budget of wavelet coefficients."807 Therefore The final 2D-1D wavelet denoising algoritlin is the followine: 2.2..., Therefore The final 2D-1D wavelet denoising algorithm is the following: \ref{subsec:latsimudata}.808 , 809"The theoretical interpretation of the ""second solar spectrum"". namely the linearly polarized spectrum of the solar radiatio coming from quiet regions close to the limb. ts presently one of the most intriguing challenges in the field of solar physics.","The theoretical interpretation of the “second solar spectrum”, namely the linearly polarized spectrum of the solar radiation coming from quiet regions close to the limb, is presently one of the most intriguing challenges in the field of solar physics."810 Although the basic physical process at the origi of this spectrum is clear (scattering line polarization). anc although several of its properties and peculiarities have bee interpreted through the theoretical approaches that have bee proposed so far. our understanding of this spectrum remains rather fragmentary. and several features still elude any attempt of interpretation.," Although the basic physical process at the origin of this spectrum is clear (scattering line polarization), and although several of its properties and peculiarities have been interpreted through the theoretical approaches that have been proposed so far, our understanding of this spectrum remains rather fragmentary, and several features still elude any attempt of interpretation."811 The main difficulty in the interpretation of the second solar spectrum is that many physical mechanisms are capable of generating or modifying the polarization of the solar radiation. and it is an extremely complicated task to properly quantify their effects 1n such a complex environment as the solar atmosphere.," The main difficulty in the interpretation of the second solar spectrum is that many physical mechanisms are capable of generating or modifying the polarization of the solar radiation, and it is an extremely complicated task to properly quantify their effects in such a complex environment as the solar atmosphere."812 On the other hand. our knowledge of some of these mechanisms is still rather poor. since they have received. attention only recently. both from a theoretical and experimental point of view (e.g.. evaluation of the depolarizing collisional rates. development of theoretical frameworks able to account for partial redistribution effects m a self-consistent way. ete.).," On the other hand, our knowledge of some of these mechanisms is still rather poor, since they have received attention only recently, both from a theoretical and experimental point of view (e.g., evaluation of the depolarizing collisional rates, development of theoretical frameworks able to account for partial redistribution effects in a self-consistent way, etc.)."813 Nevertheless. the efforts that have been made in this sense are fully justified. because a complete and correct understanding and modeling of the physics underlying the formation of the second solar spectrum will allow us to fully exploit its enormous diagnostic potential. mainly for the investigation of the magnetic fields present in the solar atmosphere (seeTrujilloBueno.2009.forarecentreview)..," Nevertheless, the efforts that have been made in this sense are fully justified, because a complete and correct understanding and modeling of the physics underlying the formation of the second solar spectrum will allow us to fully exploit its enormous diagnostic potential, mainly for the investigation of the magnetic fields present in the solar atmosphere \citep[see][for a recent review]{JTB09}."814 Observations performed with instruments having sensitivities on the order of 107-107 have shown in great detail the spectral richness and complexity of the second solar spectrum (seeStenflo&Keller.1996.1997).," Observations performed with instruments having sensitivities on the order of $^{-3}$ $^{-4}$ have shown in great detail the spectral richness and complexity of the second solar spectrum \citep[see][]{Ste96,Ste97}."815. Among the profiles observed. those with à three-peak structure have particularly excited the interest and curiosity of the scientific community.," Among the profiles observed, those with a three-peak structure have particularly excited the interest and curiosity of the scientific community."816 Remarkable examples are the three-peak Q// profiles of the Cat line at 4226 A. of the Nat D> line at 5889A. and of the Ba D» line at 4554A., Remarkable examples are the three-peak $Q/I$ profiles of the Ca line at 4226 of the Na $_2$ line at 5889 and of the Ba $_2$ line at 4554.817 The intensity spectrum and the second solar spectrum of the Na and Ba D» lines areshown in the first two panels of Fig. |. , The intensity spectrum and the second solar spectrum of the Na and Ba $_2$ lines areshown in the first two panels of Fig. \ref{fig:3-peak}. .818The three-peak structure shown by the Ba D» line has been explained in terms of the presence of barium isotopes both with and without hyperfine structure (HFS) (seeStenflo.1997;Belluzzietal.. 2007).," The three-peak structure shown by the Ba $_2$ line has been explained in terms of the presence of barium isotopes both with and without hyperfine structure (HFS) \citep[see][]{Ste97a,Bel07}."819. In particular. it has been shown that the two secondary peaks in the wings of the Q// profile are due to the isotopes with HFS (= in abundance). while the central. higher peak is produced by the isotopes without HFS (= in abundance).," In particular, it has been shown that the two secondary peaks in the wings of the $Q/I$ profile are due to the isotopes with HFS $\approx$ in abundance), while the central, higher peak is produced by the isotopes without HFS $\approx$ in abundance)."820 Taking into account the effect of the HFS shown by this rather small fraction of barium isotopes. the observed three-peak profile could be reproduced to very high accuracy. even within the simplifying modeling assumption of the so-called optically thin slab model (1.e.. neglecting radiative transfer effects).," Taking into account the effect of the HFS shown by this rather small fraction of barium isotopes, the observed three-peak profile could be reproduced to very high accuracy, even within the simplifying modeling assumption of the so-called optically thin slab model (i.e., neglecting radiative transfer effects)."821 As can be observed in the right panel of Fig. ..," As can be observed in the right panel of Fig. \ref{fig:3-peak},"822 also the Se line at 4247 shows in the second solar spectrum a three-peak Q/I profile., also the Sc line at 4247 shows in the second solar spectrum a three-peak $Q/I$ profile.823 In contrast to the O// profile produced by the Ba D> line. which shows a central peak (due to the isotopes without HFS) of amplitude much larger than that of the lateral peaks. the three peaks exhibited by this scandium signal have approximately the same amplitude.," In contrast to the $Q/I$ profile produced by the Ba $_2$ line, which shows a central peak (due to the isotopes without HFS) of amplitude much larger than that of the lateral peaks, the three peaks exhibited by this scandium signal have approximately the same amplitude."824 This peculiarity strongly suggests that also the three-peak structure of this signal might be due to HFS. since scandium has a single stable isotope. which shows HFS (see Sect.," This peculiarity strongly suggests that also the three-peak structure of this signal might be due to HFS, since scandium has a single stable isotope, which shows HFS (see Sect."825 2.2)., 2.2).826 This possibility is strengthened by the wavelength separation between the lateral peaks being very similar to that observed in the Q/T profile of the Ba D» line. and by this scandium line in the intensity spectrum being very similar to the Ba D» line.," This possibility is strengthened by the wavelength separation between the lateral peaks being very similar to that observed in the $Q/I$ profile of the Ba $_2$ line, and by this scandium line in the intensity spectrum being very similar to the Ba $_2$ line."827 We note that these latter circumstances do not hold in the case of the Na D» line: the sodium line ts much stronger and broader in the intensity spectrum. and the wavelength separation between the lateral peaks shown by the Q// profile is much larger than for either barium or scandium.," We note that these latter circumstances do not hold in the case of the Na $_2$ line: the sodium line is much stronger and broader in the intensity spectrum, and the wavelength separation between the lateral peaks shown by the $Q/I$ profile is much larger than for either barium or scandium."828 Indeed. it has already been observed that the three-peak structure of the Na D» line cannot be explained only in terms of the HFS exhibited by the single stable isotope of sodium. but that its interpretation seems to require the inclusion of other physical “Ingredients” such as “super-interferences” and lower level polarization (seeLandiDegl'Innocenti.. 1998)... and/or the effects of partial redistribution in frequency (seeHolzreuteretal..2005)..and/or theenhancement of the line-center scattering polarization peak by vertical magnetic fields (seeTrujilloBuenoetal.. 2002)..," Indeed, it has already been observed that the three-peak structure of the Na $_2$ line cannot be explained only in terms of the HFS exhibited by the single stable isotope of sodium, but that its interpretation seems to require the inclusion of other physical “ingredients” such as “super-interferences” and lower level polarization \citep[see][]{Lan98}, and/or the effects of partial redistribution in frequency \citep[see][]{Hol05},,and/or theenhancement of the line-center scattering polarization peak by vertical magnetic fields \citep[see][]{JTB02}. ."829 For the reasons explained above. we considered 1t worthwhile," For the reasons explained above, we considered it worthwhile"830(FR D. (ER ID. (ER ID. (FR I) and (FR TI) (see Paper I for images of the radio sources): We note tha reactivation. as we consider at hore. is a more general phenouenon than the ~double-«louble” norplology (escribed. by Schocuaalkers et al. (20000).,"(FR I), (FR II), (FR II), (FR I) and (FR I) (see Paper I for images of the radio sources): We note that reactivation, as we consider it here, is a more general phenomenon than the “double-double” morphology described by Schoenmakers et al. \cite{arno3}) ),"831" which eau be cousiderec las a particular cas within which onlv tre radio source 1i our sample J1835|620 properly fits,", which can be considered as a particular case within which only the radio source in our sample J1835+620 properly fits.832 The physical conditions under wich aradio source eal experinent a process o yeactivatioji are not kuown., The physical conditions under which a radio source can experiment a process of reactivation are not known.833 It is )clieved that interaction and mereiueSo with ucighboring ealaxies can be critical for this. xovidiug an oeffücieut nechaism fo remove angular ΠΟΙΟΤΗ anne directing eas towards the active center of fje galaxy {D.Locicall et al. 1997)).," It is believed that interaction and merging with neighboring galaxies can be critical for this, providing an efficient mechanism to remove angular momentum and directing gas towards the active center of the galaxy (Bahcall et al. \cite{bahcall}) )."834" ILowever. we only fiud jecarby c""Oll»udlons iu wo of the previously mentioned galaxies (J0317|769 and J1535|620. see Paper ID."," However, we only find nearby companions in two of the previously mentioned galaxies (J0317+769 and J1835+620, see Paper II)."835 A auch more detaied optical study of the lost galaxies with high augular resolution is recessary to reach definite conclusions about t1ο relation οποσα mereme and reactivation of the radio enission., A much more detailed optical study of the host galaxies with high angular resolution is necessary to reach definite conclusions about the relation between merging and reactivation of the radio emission.836 Tn this section we address the question raised by several authors (e.g. Batu ct al. 1905...," In this section we address the question raised by several authors (e.g. Baum et al. \cite{baum},"837 Chiselini Colotti 2001)) about the possibility o: au FR II tvpe radio galaxy evolving iuto au FR I tvpe source., Ghisellini Celotti \cite{ghisellini}) ) about the possibility of an FR II type radio galaxy evolving into an FR I type source.838 For that. we compare the predictions derived from tre racio Innuimosiv fiction (RLF) with our observations.," For that, we compare the predictions derived from the radio luminosity function (RLF) with our observations."839 Civeu that our sample consists of large size objects aud for that reaso1 probally older than objects in other sauples (from whic ithe RLF is determined). we expect that if such evolution exists it will manifest itself iu an evolved sample like ours. in the sense of having an over-populatiou of FR Is iux fewer FR Ts than expected from the RLF.," Given that our sample consists of large size objects, and for that reason probably older than objects in other samples (from which the RLF is determined), we expect that if such evolution exists it will manifest itself in an evolved sample like ours, in the sense of having an over-population of FR Is and fewer FR IIs than expected from the RLF."840 We have used the Dunlop Peacock (1990)) RLF at 2.7 CdIz., We have used the Dunlop Peacock \cite{dunlop1}) ) RLF at 2.7 GHz.841 To choose one among the several models preseuted by these authors is relevant at the redshifts involved dn our sample. sinee all inodels are well coustrained bv the local RLF.," To choose one among the several models presented by these authors is irrelevant at the redshifts involved in our sample, since all models are well constrained by the local RLF."842 We have used heir free-form model 5. which providess the best resuls for the LBDS Hercules sample of 12Jy radio sources (Waddington et al. 200111.," We have used their free-form model 5, which provides the best results for the LBDS Hercules sample of mJy radio sources (Waddington et al. \cite{waddington}) )."843 In the RLF. we have introduce the area of our survey and the fiux density limit of the sample transformed to 2.7 GIIz assuming a spectral ixlex a=0.75.," In the RLF, we have introduced the area of our survey and the flux density limit of the sample transformed to 2.7 GHz assuming a spectral index $\alpha = -0.75$ ."844 We have also comparesLthe results with he receut RLF determuned by Willott et al. (2001)), We have also compared the results with the recent RLF determined by Willott et al. \cite{willott}) )845 at 151 MIIz., at 151 MHz.846 As expected for radio sources with redshift below 1. both RLFs provide simular results.," As expected for radio sources with redshift below 1, both RLFs provide similar results."847 We define he parameter psoas the difference in the uuuber of FR II and ER Iz: «lio sources divided by the total umber o| yacdio sources ver redshift iuterval of 0.05., We define the parameter $x$ as the difference in the number of FR II and FR I radio sources divided by the total number of radio sources per redshift interval of 0.05.848 This parameter illustrates the relative abundance of FR Is aud FR IIs in t1e sample. aud row this relative abuuda1ος varies with the redshift.," This parameter illustrates the relative abundance of FR Is and FR IIs in the sample, and how this relative abundance varies with the redshift."849" If all ποιαον ALC of FR II tvIC, then.e =1: itt rere are only FR I type racic) ealaxies. then C=1."," If all sources are of FR II type, then $x=1$; if there are only FR I type radio galaxies, then $x=-1$."850 Iu Fig., In Fig.851" 19 we dispav the parameter c in the redshift rane0 το 0.35,", \ref{abund} we display the parameter $x$ in the redshift range 0 to 0.35.852 At higher redshifts .=1. since we do not deect FR Is.," At higher redshifts $x=1$, since we do not detect FR Is."853 From he RLF we have computed. for each redsni interval. the nuuuber of sotrees with radio power below axl above the weak power that separates neatly the two families of racio ealaxies (Section 2.1)). aud obtained the value of . iud its dependence with redshift.," From the RLF we have computed, for each redshift interval, the number of sources with radio power below and above the break power that separates neatly the two families of radio galaxies (Section \ref{fr12}) ), and obtained the value of $x$ and its dependence with redshift."854 It is not possible to introduce in the RLF the aneular size Iuuit o “our sanuple. so we assuie that οὐ does not depexd ou the source augulur size (sec! pote of caution below).," It is not possible to introduce in the RLF the angular size limit of our sample, so we assume that $x$ does not depend on the source angular size (see note of caution below)."855 We obtain that t16 RLF predicts well the ack of FR Ils at ow redshift. aud the abseuce of FR 1 type rac10 ealaxies at redshifts above 0.25.," We obtain that the RLF predicts well the lack of FR IIs at low redshift, and the absence of FR I type radio galaxies at redshifts above 0.25."856 However. from our data we find a larger number of FR II type radio galaxies than predicted by the RLF.," However, from our data we find a larger number of FR II type radio galaxies than predicted by the RLF."857 This 1esult is not cousisteut with all CVOutio1 of iucividial racio eaaxies frou FR II to FR I type since in that case we should obtain the opposite result in an evolved sauple lise ours: a larger anmudauce of FR Is., This result is not consistent with an evolution of individual radio galaxies from FR II to FR I type since in that case we should obtain the opposite result in an evolved sample like ours: a larger abundance of FR Is.858" This result. tiat ds. he lack of evieuce of a FR II to FR I evolution. might lc' iufiueuced by at least two factors: firs Jit is not possible to ¢iscard a dependence of the parameter ο with the raclo sonrce size. which might be partially masking the concUSIOUS! SCCOLL. but related. the overaludance of FR IL x""dio galaxies nuelt be the result of a bias in the selectiμα1 of FR I radio galaxies due to seusitivitv Iuaitation 1- he detectio1 of extended CLUISSIOL."," This result, that is, the lack of evidence of a FR II to FR I evolution, might be influenced by at least two factors: first, it is not possible to discard a dependence of the parameter $x$ with the radio source size, which might be partially masking the conclusions; second, but related, the overabundance of FR II radio galaxies might be the result of a bias in the selection of FR I radio galaxies due to sensitivity limitation in the detection of extended emission."859 Tn Fie., In Fig.860 LL we «isplav the uuuber of radio galaxies per redshift bin of 0.05. and coupsue the observational resuts with the predictions of the RLF.," \ref{rlf} we display the number of radio galaxies per redshift bin of 0.05, and compare the observational results with the predictions of the RLF."861 As inentioned previously. he RLF cannot deal with an aigular size limit of I but we try here to estimate which is the Yactiou of radio ealaxies with aneular sizes above this value. compariis he RLF with our observations.," As mentioned previously, the RLF cannot deal with an angular size limit of $4'$ but we try here to estimate which is the fraction of radio galaxies with angular sizes above this value, comparing the RLF with our observations."862 In Fie., In Fig.863 1 tbh. we show the nuuber of FR I radio galaxies per redsuft biu.," \ref{rlf}b b, we show the number of FR I radio galaxies per redshift bin."864 We fiud hat the RLF. restricted to FR Ts and scaled by a factor of LOL? predicts well the observed umber of FR I objects at a redshift 7— O.1.where we do uo expect to have," We find that the RLF, restricted to FR Is and scaled by a factor of 0.047 predicts well the observed number of FR I objects at a redshift $z\sim 0.1$ where we do not expect to have"865Two models will have statistically incistinguishable empoerature. polarisation and cross-correlation linear power spectra as a result of the geometrical clegencracy if they lve: If the above conditions are satisfied. the CAIB power spectra of the two models will be indistinguishable on small angular scales. but will diller at large. angles because of eeometrical effects on near curvature scales and. in the case of temperature anisotropies. through the integrated Sachs-Wolfe elect.,"Two models will have statistically indistinguishable temperature, polarisation and cross-correlation linear power spectra as a result of the geometrical degeneracy if they have: If the above conditions are satisfied, the CMB power spectra of the two models will be indistinguishable on small angular scales, but will differ at large angles because of geometrical effects on near curvature scales and, in the case of temperature anisotropies, through the integrated Sachs-Wolfe effect."866 Llowever. jose elleets are weak discriminators of models.," However, these effects are weak discriminators of models."867 In the analvsis that. follows. when we compare two models. we normalise them so that the root. mean square mass deviation computed within à top hat window of radius R=Sh !Mpe denoted. hereafter. ae (/)] is the samescallering (@= lps).," In the analysis that follows, when we compare two models, we normalise them so that the root mean square mass deviation computed within a top hat window of radius $R=8h^{-1}$ Mpc [denoted hereafter $\sigma_R(t)$ ] is the same $t=t_{LS}$ )."868 This. prescription determines the relative normalisations of any two moclels that we wish to compare. but does not determine the absolute normalisation.," This prescription determines the relative normalisations of any two models that we wish to compare, but does not determine the absolute normalisation."869 The etfects of gravitational lensing depend. of course. on the absolute normalisation of the matter fluctuations.," The effects of gravitational lensing depend, of course, on the absolute normalisation of the matter fluctuations."870 We therefore normalise a given target model so that the rnis nias Huetuations within a sphere of SfI Mpe at the present day (f= fy) reproduces the abundances of rich clusters of galaxies., We therefore normalise a given target model so that the rms mass fluctuations within a sphere of $8h^{-1}$ Mpc at the present day $t=t_0$ ) reproduces the abundances of rich clusters of galaxies.871 We therefore impose the constraint. from the recent analvsis of Eke. Cole FErenk (1996).," We therefore impose the constraint, from the recent analysis of Eke, Cole Frenk (1996)."872 The normalisation of scale-invariant moclels derived. from (2)) is usually lower than that inferred. from the 4 vear COBE-DAIR data (c.g. Gorrski 1998)., The normalisation of scale-invariant models derived from \ref{cluster}) ) is usually lower than that inferred from the 4 year COBE-DMR data (e.g. Górrski 1998).873 Llowever. equation (2)) provides a more clirect measure of the amplitude of the mass fluctuations which generate eravitational lensing elfects at recent epochs.," However, equation \ref{cluster}) ) provides a more direct measure of the amplitude of the mass fluctuations which generate gravitational lensing effects at recent epochs."874 We eive the la uncertainty in equation (2)). though this is sullicicntly small that it has no significant ellect on results described below.," We give the $1\sigma$ uncertainty in equation \ref{cluster}) ), though this is sufficiently small that it has no significant effect on results described below."875 Some authors. e.g. Viana LLiddle (1996) deduce. slightly larger. values of ax(ty) for low density models. in which case our analysis will underestimate the cllects of gravitational lensing on the CMB.," Some authors, e.g. Viana Liddle (1996) deduce slightly larger values of $\sigma_8(t_0)$ for low density models, in which case our analysis will underestimate the effects of gravitational lensing on the CMB."876 In summary. we pick a specific set of cosmological parameters to define a target model anc we use equation (2)) to set the absolute normalisation of the fluctuation spectrum.," In summary, we pick a specific set of cosmological parameters to define a target model and we use equation \ref{cluster}) ) to set the absolute normalisation of the fluctuation spectrum."877 When we compare models with a different set of cosmological parameters. we choose a normalisation so that the uctuation spectra have the same amplitude at the time of recombination. so preserving the ecometrical degeneracy.," When we compare models with a different set of cosmological parameters, we choose a normalisation so that the fluctuation spectra have the same amplitude at the time of recombination, so preserving the geometrical degeneracy."878 These points are illustrated in Figures 1 and 2.., These points are illustrated in Figures \ref{fig1} and \ref{fig2a}.879" Figure l shows degenerate loci in the wy. wy plane (res=constant) for models with wy0.1] and ay,=0.0125."," Figure \ref{fig1} shows degenerate loci in the $\omega_K$, $\omega_\Lambda$ plane $r_{LS}= {\rm constant}$ ) for models with $\omega_{\rm m}=0.1$ and $\omega_{\rm b} = 0.0125$."880 Figures 2a.b show the lincar CAIB power spectra for. two sets of models satisfving the geometrical degeneracy plotted as filled cireles in Figure 1..," Figures 2a,b show the linear CMB power spectra for two sets of models satisfying the geometrical degeneracy plotted as filled circles in Figure \ref{fig1}."881 These have been computed using a version of the CAIBFAS'T code developed by Seljak ZZLalcdarriaga (1996) which we have modified to gain an improvement in accuracy (see Section 4.2)., These have been computed using a version of the CMBFAST code developed by Seljak Zaldarriaga (1996) which we have modified to gain an improvement in accuracy (see Section 4.2).882 Clearly. the spectra for cach set of models are almost indistinguishable.," Clearly, the spectra for each set of models are almost indistinguishable."883" The only significant deviations are. at. low multipoles (6X, 100) and are a consequence of the integrated. Sachs-Wolfe. elect described above.", The only significant deviations are at low multipoles $\ell\simlt 100$ ) and are a consequence of the integrated Sachs-Wolfe effect described above.884 In. fact. the numerically computed spectra in Figures 2a.b also show some residual cillerenees at high. ¢ (illustrated by the dashed. line in the middle panels of Figure 2a.b).," In fact, the numerically computed spectra in Figures 2a,b also show some residual differences at high $\ell$ (illustrated by the dashed line in the middle panels of Figure 2a,b)."885 However. these cilferenees are dominated by residual numerical inaccuracies in CMDLEAST (see the discussion. in Section 4.2).," However, these differences are dominated by residual numerical inaccuracies in CMBFAST (see the discussion in Section 4.2)."886 bor models with reasonable normalisations reproducing cluster abundances as inferred. from equation. (2))] these numerical errors are much smaller than cdillerences arising [rom gravitational lensing., For models with reasonable normalisations reproducing cluster abundances as inferred from equation \ref{cluster}) )] these numerical errors are much smaller than differences arising from gravitational lensing.887 Η we keep all of the parameters of a target model fixed but vary wy and wy. the geometrical degeneracy will be satisfied if where the subscript 0 on any quantity denotes that it is computed. assuming the parameters of the target. moclel.," If we keep all of the parameters of a target model fixed but vary $\omega_K$ and $\omega_\Lambda$, the geometrical degeneracy will be satisfied if where the subscript $0$ on any quantity denotes that it is computed assuming the parameters of the target model."888 We can define two new parameters qj and gj. where ó—arctanOres is. the angle between a degenerate curve plotted in Figure 1. and the wy axis.," We can define two new parameters $\omega_\parallel$ and $\omega_\perp$, where $\displaystyle{\phi\equiv -\arctan\l[\l({\partial r_{LS}\over889\partial \omega_\Lambda}\r)_{0}^{-1}\l({\partial r_{LS}\over \partial890\omega_K}\r)_{0}\r]}$ is the angle between a degenerate curve plotted in Figure \ref{fig1} and the $\omega_K$ axis."891 Models satisfving wy=0 thus have the same value of ros lor small variations of parameters and therefore satisfy the eeometrical degeneracy., Models satisfying $\omega_\perp=0$ thus have the same value of $r_{LS}$ for small variations of parameters and therefore satisfy the geometrical degeneracy.892" Hereafter we call any direction with wp,=0 a degeneracy. direction.", Hereafter we call any direction with $\omega_\perp=0$ a degeneracy direction.893 ΙΓ the geometrical degeneracy were perfect. the derivative of the CAIB power spectrum along a degeneraey. direction should be exactly equal to zero.," If the geometrical degeneracy were perfect, the derivative of the CMB power spectrum along a degeneracy direction should be exactly equal to zero."894 The numerical derivatives of lincar power spectra are discussed in section 4.2 (see also Efstathiou DBDBond 1998) and shown in Figures 4 oo., The numerical derivatives of linear power spectra are discussed in section 4.2 (see also Efstathiou Bond 1998) and shown in Figures 4 8.895the gray one Fig. 6..,the gray one Fig. \ref{avg_profiles}.896 A shallow mean thermal gradient weakens the contrast between strong and weak lines and this is visible in the molecular band strength which is much stronger for the non-gray model., A shallow mean thermal gradient weakens the contrast between strong and weak lines and this is visible in the molecular band strength which is much stronger for the non-gray model.897 Top right panel of Fig., Top right panel of Fig.898" 10 shows also that the TiO band strength of non-gray model is more similar to the cool 1D MARCS model at 3430K than the hot one at 3700K. This reflects the fact that the 3D mean thermal structure in the outer layers is very similar to 1D-3430K model (Fig. 5,,"," \ref{tio_band} shows also that the TiO band strength of non-gray model is more similar to the cool 1D MARCS model at 3430K than the hot one at 3700K. This reflects the fact that the 3D mean thermal structure in the outer layers is very similar to 1D-3430K model (Fig. \ref{temperature_profile},"899 top right The approximation of gray radiative transfer is justified only in the stellar interior and it is inaccurate in the optically thin layers., top right The approximation of gray radiative transfer is justified only in the stellar interior and it is inaccurate in the optically thin layers.900" So far, this approximation has been due to the fact that the RHD simulations have been constrained by execution time."," So far, this approximation has been due to the fact that the RHD simulations have been constrained by execution time."901" However, with the advent of more powerful computers, the frequency-dependent treatment of radiative transfer is now possible and, on a wavelength scale of one or more molecular bands, the use of this method is big step forward for a quantitative analysis of The shape of the spectral energy distribution (SED) reflects the mean thermal gradient of the simulations."," However, with the advent of more powerful computers, the frequency-dependent treatment of radiative transfer is now possible and, on a wavelength scale of one or more molecular bands, the use of this method is big step forward for a quantitative analysis of The shape of the spectral energy distribution (SED) reflects the mean thermal gradient of the simulations."902 The absolute flux plots in the bottom row of Fig., The absolute flux plots in the bottom row of Fig.903" 10 display that at lower resolution two important conclusions can be retrieved: (i) the spectrum based on the gray model is largely different from the 1D spectra; (ii) the non-gray model shows that the SED, compared to the ID MARCS model with the hot temperature (3700K), displays almost no distinction in infrared region, and weaker in molecular bands in the visible region and in the near-ultraviolet region."," \ref{tio_band} display that at lower resolution two important conclusions can be retrieved: (i) the spectrum based on the gray model is largely different from the 1D spectra; (ii) the non-gray model shows that the SED, compared to the 1D MARCS model with the hot temperature (3700K), displays almost no distinction in infrared region, and weaker in molecular bands in the visible region and in the near-ultraviolet region."904" Using the prescriptionsby ? for the filters BVRJHK, we computed expected colors for the gray and non-gray models as well as the corresponding MARCS models (Table 5))."," Using the prescriptionsby \cite{1998A&A...333..231B} for the filters $BVRJHK$, we computed expected colors for the gray and non-gray models as well as the corresponding MARCS models (Table \ref{tablecolors}) )."905 The non-gray 3D model shows smaller differences to the 1D model than the gray one., The non-gray 3D model shows smaller differences to the 1D model than the gray one.906" The stronger radiative efficiency in the non-gray case forces the temperature stratification to be closer to the radiative equilibrium than in the gray case, where convection and waves have a larger impact on ? probed the usefulness of the index V—K as a temperature indicator for Galactic RSGs, but ?,, fitting TiO band depths, showed that V—K and V—R provides systematic"," The stronger radiative efficiency in the non-gray case forces the temperature stratification to be closer to the radiative equilibrium than in the gray case, where convection and waves have a larger impact on \cite{2000A&A...357..225J} probed the usefulness of the index $V-K$ as a temperature indicator for Galactic RSGs, but \cite{2006ApJ...645.1102L}, , fitting TiO band depths, showed that $V-K$ and $V-R$ provides systematic"907"Wes (€6.41-0.1) is an old-age (>10 vvr: WKaspietal. 1903)). mixed morphology supernova remnant (SNR) spanning ,45° RNwith a distance.. estimated. to be in. the rangeLS to 3.3kkpe (e.g. Goudis1976:Lozinskava 19811).","W28 (G6.4-0.1) is an old-age $> 10^{4}$ yr; \citealt{kaspi}) ), mixed morphology supernova remnant (SNR) spanning $^\prime \times 45^\prime$ with a distance estimated to be in the range1.8 to kpc (e.g. \citealt{goudis,lozinskaya}) )."908 The SNR exhibits non-thermal racio emission and thermal X-rays (Dubnerctal.2000:Rho&Borkowski 2002).. and more recently. ganmua-rav sources at Γον (1077 ceV) (Abaronianetal.200Sb) and GeV (10° ecV) (Ciuhanietal.2010:Abdo2010). energies have been discovered. by LASS.S...ACIEE. and. FermiLONE telescopes respectively. pointing to high energy. particles in the region.," The SNR exhibits non-thermal radio emission and thermal X-rays \citep{dubner,rho2002}, , and more recently, gamma-ray sources at TeV $^{12}$ eV) \citep{hess_w28} and GeV $^{9}$ eV) \citep{agile,fermi_w28} energies have been discovered by H.E.S.S., and -LAT telescopes respectively, pointing to high energy particles in the region."909 “οσοα0). 7CO((21) and 7CO((32) surveys reveal massive molecular clouds to the north cast (NIE) and to the south (8) of the SNR (Arikawaetal.1999:Reachal. 2008)..," $^{12}$ (1–0), $^{12}$ (2–1) and $^{12}$ (3–2) surveys reveal massive molecular clouds to the north east (NE) and to the south (S) of the SNR \citep{arikawa,reach,torres,hess_w28,nanten21}."910 Most. of the CO emission appears centred at a local standard of rest velocity similar to that inferred for W28 T (or  2kkpc) based on LHüstudies (Velázquezctal., Most of the CO emission appears centred at a local standard of rest velocity similar to that inferred for W28 $\sim$ (or $\sim 2$ kpc) based on studies \citep{velazquez}.911 2010).. Torresetal.(2003). has argued that W28 has disrupted much of this CO gas. giving rise to its relatively broad. velocity distribution.," \citet{torres} has argued that W28 has disrupted much of this CO gas, giving rise to its relatively broad velocity distribution."912 Notably. the NIE region contains a rich concentration of MMLIz OLI masers (Frailοἱal. (with inthe range 5 to lknmis)). and near-IR rovibrational Ls emission (Reachetal. 2010).. all indicating shocked gas which likely results froma SNR. shock," Notably, the NE region contains a rich concentration of MHz OH masers \citep{frail,claussen} (with inthe range 5 to ), and near-IR rovibrational $_2$ emission \citep{reach2000,neufeld,marquez-lugo}, , all indicating shocked gas which likely results from a SNR shock"913"The resulting magnetic field has then ouly a radial compoucut D, in direction of r. with the surface field streneth By=$9/:94.","The resulting magnetic field has then only a radial component $B_r$ in direction of ${\bf r}$, with the surface field strength $B_0=\Phi_0/z_0$."914 This unipolar poteutial field ful&ülls the divergeucce-free condition. as it can be caleulated from the Laplacian operator of the potential function. The fulfillment of the divergence-free condition cau also be verified from the couservation of the magnetic flux theorem (Eq.," This unipolar potential field fulfills the divergence-free condition, as it can be calculated from the Laplacian operator of the potential function, The fulfillment of the divergence-free condition can also be verified from the conservation of the magnetic flux theorem (Eq."915 3). if the envelope of a fixtube is defined by radial field les. so that the cross-sectional areaAG)xBis)D7 relmains constant for s—r.," 3), if the envelope of a fluxtube is defined by radial field lines, so that the cross-sectional area$A(s) \propto B(s)^{-2}$ remains constant for $s=r$."916 In our first model we euiploy: a superposition of JN inultiple uuipolar charges. in terms of the vector ry=[Cecry)(yyy).f2lj.," In our first model we employ a superposition of $N$ multiple unipolar charges, in terms of the vector ${\bf r}_j = [(x-x_j), (y-y_j), (z-z_j)]$."917 For a single uuipolu charge. the Sold lines will all be straight lines in racial direction away from the buried charge. which cau approximate opeu-field regions.," For a single unipolar charge, the field lines will all be straight lines in radial direction away from the buried charge, which can approximate open-field regions."918 Birving multiple magnetic charges of opposite maguectic polarity. however. ean mimic closed-field regions.," Burying multiple magnetic charges of opposite magnetic polarity, however, can mimic closed-field regions."919 Au exiuuple is given in Fig., An example is given in Fig.920 1l. where we compare the magnetic field of a dipole with that of a combination of two unipolar charges with opposite maeuctic polarity.," 1, where we compare the magnetic field of a dipole with that of a combination of two unipolar charges with opposite magnetic polarity."921 Actually. the two magnetic field models become identical when the two unipolar charecs are moved close together at the location of the dipole moment. as it can be shown mathematically.," Actually, the two magnetic field models become identical when the two unipolar charges are moved close together at the location of the dipole moment, as it can be shown mathematically."922 Although the two models are equivalent in the far-field approximation. a conibination of two unipolar charges GQvith 2«|=8 free parameters) allows more general solutions than a suele dipole (with 6 free parameters). especially in the case of stronely asvuuuetric fields (suuspots) or opeu-field regions. as they exist is most active regions.," Although the two models are equivalent in the far-field approximation, a combination of two unipolar charges (with $2 \times 4 = 8$ free parameters) allows more general solutions than a single dipole (with 6 free parameters), especially in the case of strongly asymmetric fields (sunspots) or open-field regions, as they exist is most active regions."923 The forward-fitting of our analytical maenetic field model to a set of observed maeuctic field vectors b=BiB (e.e.. using stercoscopically triangulated loop coordinates}. is the task of optimizing the free parameters of the analytical model until the best match with the observed field lines is obtained.," The forward-fitting of our analytical magnetic field model to a set of observed magnetic field vectors ${\bf b}={\bf B}/B$ (e.g., using stereoscopically triangulated loop coordinates), is the task of optimizing the free parameters of the analytical model until the best match with the observed field lines is obtained."924" For the evaluation of the gooduess or cousisteney of the analytical maguetic ficld models BY’? with the observed field liue model B. we define the 3-D misaligument anele 0,,;;. which is defined by the scalar product between the twofield vectors BY’?(x) and B"" (x). or equivalently. between the uuity field vectors b""(x) aud be’ (x)."," For the evaluation of the goodness or consistency of the analytical magnetic field models ${\bf B}^{theo}$ with the observed field line model ${\bf B}^{obs}$, we define the 3-D misalignment angle $\alpha_{mis}$, which is defined by the scalar product between the twofield vectors ${\bf B}^{theo}({\bf x})$ and ${\bf B}^{obs}({\bf x})$ , or equivalently, between the unity field vectors ${\bf b}^{theo}({\bf x})$ and ${\bf b}^{obs}({\bf x})$ ,"925in the same orieutation as the SDSS exteuded PSF.,in the same orientation as the SDSS extended PSF.926 Four 20 s dithered exposures were obtained at an aiviass of 1.31 iu each of the J.T. aud A filters.," Four 20 s dithered exposures were obtained at an airmass of 1.31 in each of the $J$ , $H$ , and $K$ filters."927" We also obtained two 20 s dithered images of the nearby (p~ 9.1) point source 2ALASS J15501059|1500305 (N, = L3ALEO03 mae. JA, = OT3E0.01b mae) in each of the JIDLI filters iuuuediatelv after the observation to serve as a PSF calibrator."," We also obtained two 20 s dithered images of the nearby $\rho \sim$ $\arcmin$ ) point source 2MASS J15504059+1500305 $K_s$ = $\pm$ 0.03 mag, $J-K_s$ = $\pm$ 0.04 mag) in each of the $JHK$ filters immediately after the observation to serve as a PSF calibrator."928 huagmg data were reduced in a standard nuuner using custom Iuteractive Data Lauguage (IDL) routines., Imaging data were reduced in a standard manner using custom Interactive Data Language (IDL) routines.929 After mirror-fippiug the raw imaging data alone the v-axis to reproduce the sky oricutation (J. RRavuer. 2009. private conuuunication). sky images for each filter were produced by imediau-combining all of the and PSF calibrator images.," After mirror-flipping the raw imaging data along the y-axis to reproduce the sky orientation (J. Rayner, 2009, private communication), sky images for each filter were produced by median-combining all of the and PSF calibrator images."930 These were subtracted from the raw imaecing data. aud cach skv image was also normalized aud used as a flat-field frame to correct for pixel-to-pixel response variations.," These were subtracted from the raw imaging data, and each sky image was also normalized and used as a flat-field frame to correct for pixel-to-pixel response variations."931 Subsectious of cach image. 51 pixels (6712) on a side and centered on the target source. were extracted. from these calibrated frames.," Subsections of each image, 51 pixels $\farcs$ 12) on a side and centered on the target source, were extracted from these calibrated frames."932 A final image for cach flter/target pair was produced by averaging the registered subtrames together. rejecting Ὁσ pixcl outliers for the observatious.," A final image for each filter/target pair was produced by averaging the registered subframes together, rejecting $\sigma$ pixel outliers for the observations."933 These colmbined Πππασος are shown in Figure 3.., These combined images are shown in Figure \ref{fig_image}.934 The two colmponcnts of are clearly resolved. separated by roughly 17 along a nearly northi-soutli axis. the southern component appearing to be slightly brightcr in all three filter bands.," The two components of are clearly resolved, separated by roughly $\arcsec$ along a nearly north-south axis, the southern component appearing to be slightly brighter in all three filter bands."935 EHereafter. we refer to this component as LISSA and the northern component as 1155D. Component magnitudes and the aneular separation of the paix were determined by PSF fits to the reduced iuagiue data. following the prescription described in MeEhwaiu&Durgasser(2006)..," Hereafter, we refer to this component as A and the northern component as B. Component magnitudes and the angular separation of the pair were determined by PSF fits to the reduced imaging data, following the prescription described in \citet{2006AJ....132.2074M}."936 Fits were made to cach individual image frame usine both PSFcalibrator images in a given filter band. for a total of cight incependeut measures of the relative JLTIv coluponent magnitudes aud 21 independent measures of the separation aud oricutation of the pair.," Fits were made to each individual image frame using both PSFcalibrator images in a given filter band, for a total of eight independent measures of the relative $JHK$ component magnitudes and 24 independent measures of the separation and orientation of the pair."937 \Leasuremicuts of the latter were converted frou pixels to arcseconds ase a plate seale of 07120207002. pixel| RRavuer. 2005. private conuuuuication) and no distortion.," Measurements of the latter were converted from pixels to arcseconds assuming a plate scale of $\farcs$ $\pm$ $\farcs$ 002 $^{-1}$ Rayner, 2005, private communication) and no distortion."938 The position angle was assed to be accurate to within (0725 (ibid.)., The position angle was assumed to be accurate to within $\fdg$ 25 (ibid.).939 To test for systematic effects in the derived relative magnitudes. we performed the same fits on svuthetic binary Huages constructed frou the PSF frames.," To test for systematic effects in the derived relative magnitudes, we performed the same fits on synthetic binary images constructed from the PSF frames."940" For cach filter, svuthetic images were made by combining two randouly selected calibrator images. one shifted according to the measured separations (with an additional random shift based on the separation uncertainties) and scaled by flux ratios spanning 0.2 to 1.0 Gnaguitude differences of 1.75 to 0 mag)."," For each filter, synthetic images were made by combining two randomly selected calibrator images, one shifted according to the measured separations (with an additional random shift based on the separation uncertainties) and scaled by flux ratios spanning 0.2 to 1.0 (magnitude differences of 1.75 to 0 mag)."941 A linear fit between input and output fux ratios for 200 trials inclicates systematic shiftsof depeuding ou the filter baud (largest at A). which were3-7% incorporated iuto the reported photometry and uncertainties.," A linear fit between input and output flux ratios for 200 trials indicates systematic shifts of depending on the filter band (largest at $K$ ), which were incorporated into the reported photometry and uncertainties."942 Results are listed in Table 1.., Results are listed in Table \ref{tab_psf}.943 The augular separation of the pair is interred to be 079120703 at a position angle of 1676-4171 (feast of north. vector pointing from primary to secondary).," The angular separation of the pair is inferred to be $\farcs$ $\pm$ $\farcs$ 03 at a position angle of $\fdg$ $\pm$ $\fdg$ 1 (east of north, vector pointing from primary to secondary)."944 The magnitude differeuces of the two components decrease from J to Iv. indicating a secondary that is siguificautly redder than the primary. JWye = 1L.6340.06 mae versus 1340.06 As described below. this is consistent with the sleltly later spectral classification inferred for this componcut.," The magnitude differences of the two components decrease from $J$ to $K$, indicating a secondary that is significantly redder than the primary, $J-K_s$ = $\pm$ 0.06 mag versus $\pm$ 0.06 As described below, this is consistent with the slightly later spectral classification inferred for this component."945 We performed the same analysis on the epoch 2005 March 10 (UT) SDSS / and + mages. using three nearby point sources as PSF calibrators.," We performed the same analysis on the epoch 2005 March 10 (UT) SDSS $i$ and $z$ images, using three nearby point sources as PSF calibrators."946" The coarser plate seale of the SDSS images (07396. pixel3: Pieretal. 2003)) aud larger PSFs result iu both larger astrometric""uncertaintiesand larger svstematic offsets in the relative photometry (up to 30%... based on simulations equivalent to those described above)."," The coarser plate scale of the SDSS images $\farcs$ 396 $^{-1}$; \citealt{2003AJ....125.1559P}) ) and larger PSFs result in both larger astrometricuncertaintiesand larger systematic offsets in the relative photometry (up to , based on simulations equivalent to those described above)."947 Nevertheless. the interrect separation and orientation of the compoucuts formally aeree with the SpeX results.," Nevertheless, the inferred separation and orientation of the components formally agree with the SpeX results."948 There is also an imdication, There is also an indication949sotween these competing models for 1121tb would waive important consequences because they each imply a very different formation and evolutionary history for he planet.,between these competing models for 1214b would have important consequences because they each imply a very different formation and evolutionary history for the planet.950 Coustraining the formation aud evolutionary ustory for this planet would be an nuportaut step iu our quest to obtain a general understaudiug of the intermediate-size planets for which this object appears ο be an archetype., Constraining the formation and evolutionary history for this planet would be an important step in our quest to obtain a general understanding of the intermediate-size planets for which this object appears to be an archetype.951 The most interesting characteristic of 11211b is hat it orbits a verv siall M dwarf. aud thus the system has a planet-to-star radius ratio comparable to a Jupiter-size planct transiting a Suu-like star.," The most interesting characteristic of 1214b is that it orbits a very small M dwarf, and thus the system has a planet-to-star radius ratio comparable to a Jupiter-size planet transiting a Sun-like star."952 This quality uakes it the most feasible known intermediate-size lancet for atinosphieric studies using transit spectroscopy echuiques., This quality makes it the most feasible known intermediate-size planet for atmospheric studies using transit spectroscopy techniques.953 The three models proposed for the plauct would also exhibit very different transmission spoectruii eatures;, The three models proposed for the planet would also exhibit very different transmission spectrum features.954 Mini-Neptune and true Super-Earth planets with thei hwdrogeu-donmünated. and thus large scale weight. atimospheres would exhibit relatively large spectral features in transmission owing to absorption by race gases like water and methane. and scattering by nolecular hydrogen and cloud or haze particles.," Mini-Neptune and true Super-Earth planets with their hydrogen-dominated, and thus large scale height, atmospheres would exhibit relatively large spectral features in transmission owing to absorption by trace gases like water and methane, and scattering by molecular hydrogen and cloud or haze particles."955 Ou the other haud. a Water World planet with a primarily water vapor atinosphere. aud thus small scale height. would exhibit relatively siunall spectral features im transmission.," On the other hand, a Water World planet with a primarily water vapor atmosphere, and thus small scale height, would exhibit relatively small spectral features in transmission."956 We recently obtained measurements of I1211bx ransiuission spectimm in the red optical (0.75 1.00;0u0) with the FORS instrument on the VLT ming a new eround-based technique to constrain the lancet atinospheric composition (?).., We recently obtained measurements of 1214b's transmission spectrum in the red optical (0.78 -- $\mu$ m) with the FORS instrument on the VLT using a new ground-based technique to constrain the planet's atmospheric composition \citep{bean10}.957 This remarkably caturelesss spectruni is consistent with a model Or a inetalyich atimosphere with αᾱ small scale weight. and iuconsistent with a model for cloud-frec wdrogen-dominated atmospheres. which would have a luge scale height.," This remarkably featureless spectrum is consistent with a model for a metal-rich atmosphere with a small scale height, and inconsistent with a model for cloud-free hydrogen-dominated atmospheres, which would have a large scale height."958 Clouds or haze in a lydrogeu-dominated atinosphere could conceivably also vield a fat spectrum consistent with the observations., Clouds or haze in a hydrogen-dominated atmosphere could conceivably also yield a flat spectrum consistent with the observations.959 Subsequeutly. we presented broadband. photometric mieasuremients obtained at 3.6 and yan with that provided additional constraints on the composition of the atmosphere €2)..," Subsequently, we presented broadband photometric measurements obtained at 3.6 and $\mu$ m with that provided additional constraints on the composition of the atmosphere \citep{desert11}."960" These data were also consistent with a featureless transimission spectruni when analyzed iu isolation and iu combination with the FORS data. but the overall interpretation of the flat spectrum remained nucertain due to the possibility of clouds or haze providing a erav opacity source. and nou-equilibrimui abuudances of methane. which is the primary expected opacity source at jn. Iu contrast to the results showing a featureless spectrum. 7? prescuted erouucd-basec ncar-intrarce, photometry observations that incicated 1121μυς ransiuission spectrum has a large feature in the A.-ud (bandpass approximately 2.0 — 2.3420) based ou 1ο nieasureineut of a substantially deeper transit in rat band as compared to the observations at other wavelengths."," These data were also consistent with a featureless transmission spectrum when analyzed in isolation and in combination with the FORS data, but the overall interpretation of the flat spectrum remained uncertain due to the possibility of clouds or haze providing a gray opacity source, and non-equilibrium abundances of methane, which is the primary expected opacity source at $\mu$ m. In contrast to the results showing a featureless spectrum, \citet{croll11a} presented ground-based near-infrared photometry observations that indicated 1214b's transmission spectrum has a large feature in the $K_{s}$ -band (bandpass approximately 2.0 – $\mu$ m) based on the measurement of a substantially deeper transit in that band as compared to the observations at other wavelengths."961 The main interpretation of the observations in this case is unanubieuous: the large scale height of a ivdroseu-donmiünated atmosphere is required for such a eature to be observed., The main interpretation of the observations in this case is unambiguous; the large scale height of a hydrogen-dominated atmosphere is required for such a feature to be observed.962 ? presented hiel-vesolition spectroscopy of 1121Lb οπου 2.10 jnu. They detected no spectral features. mt could not comunent on the absolute depth of the ransit at these wavelengths due to the purely ciffereutial ature of their data.," \citet{crossfield11} presented high-resolution spectroscopy of 1214b between 2.1 – $\mu$ m. They detected no spectral features, but could not comment on the absolute depth of the transit at these wavelengths due to the purely differential nature of their data."963 7. came to similar conclusions as did based on the data because methane is also he expected source of waveleneth-depeudent opacity in he their observational window., \citet{crossfield11} came to similar conclusions as did based on the data because methane is also the expected source of wavelength-dependent opacity in the their observational window.964 The observational results showing a featureless rausluission spectrum for (1121tb aud the result rom ? indicating lavee spectral features in the rearintrared are not strictly in conflict because they either were obtained at differcut wavelengths [i.c.. the ? and ? studies} or have different sensitivities ie. the ? duvestigation].," The observational results showing a featureless transmission spectrum for 1214b and the result from \citet{croll11a} indicating large spectral features in the near-infrared are not strictly in conflict because they either were obtained at different wavelengths [i.e., the \citet{bean10} and \citet{desert11} studies] or have different sensitivities [i.e., the \citet{crossfield11} investigation]."965 Also. there is a plausible qualitative explanation for all the obscrvatious: a wrodecn-domunated atmosphere depleted im methane and with clouds or haze opaque at optical wavelengths.," Also, there is a plausible qualitative explanation for all the observations: a hyrodgen-dominated atmosphere depleted in methane and with clouds or haze opaque at optical wavelengths."966 However. there is some tension because. for all the dlausibility of the qualitative model. it is not supported * physical calculations at this point. aud it has to be finely tuned to match the observations.," However, there is some tension because, for all the plausibility of the qualitative model, it is not supported by physical calculations at this point, and it has to be finely tuned to match the observations."967 Given the outstanding issues iu our uuderstauding of 1121b's atinosphere. we were motivated to conduct ither observational studies of its transmission spectrum o improve our wuderstancding of this important world.," Given the outstanding issues in our understanding of 1214b's atmosphere, we were motivated to conduct further observational studies of its transmission spectrum to improve our understanding of this important world."968" Iu articular. we aimed to male independent measurements of the planet's trausudsson spectrun in the A-baud region using a different techuique than ? used, and also to make measurements further in the blue part of the optical to search for the signature of scattering from cloud. haze. or gas particles."," In particular, we aimed to make independent measurements of the planet's transmission spectrum in the $K$ -band region using a different technique than \citet{croll11a} used, and also to make measurements further in the blue part of the optical to search for the signature of scattering from cloud, haze, or gas particles."969 We present here the results of these investieatious., We present here the results of these investigations.970 In 822 we describe our observations and data reduction., In 2 we describe our observations and data reduction.971 Iu 833 we describe our analysis of the data., In 3 we describe our analysis of the data.972 We compare our new nieasurenients of the planct’s transnüssion spectrum to previous imeasurenients and theoretical models in 811., We compare our new measurements of the planet's transmission spectrum to previous measurements and theoretical models in 4.973 We conclude in 855 with a sununary of the results., We conclude in 5 with a summary of the results.974 We observed transits of 112115 on 2011 May. 15 and 18 using the MMIRS iustiumeut (7?) on the Magellan (Clay) telescope at Las Campanas Observatory., We observed transits of 1214b on 2011 May 15 and 18 using the MMIRS instrument \citep{mcleod04} on the Magellan (Clay) telescope at Las Campanas Observatory.975 We used the same multi-object. spectroscopy approach for the MMIBS observations as was used for the FORS observations of 1121tb that we presented previously (2).., We used the same multi-object spectroscopy approach for the MMIRS observations as was used for the FORS observations of 1214b that we presented previously \citep{bean10}.976 We gathered time-series spectra for 1121tb aud three other refereuce stars of similar brielituess withiu musing slits with leueths of aad widths of12”., We gathered time-series spectra for 1214b and three other reference stars of similar brightness within using slits with lengths of and widths of.977". The offaxis euide aud wavefrout sensor of the mstrumnent. which is seusitive to wavelengths between 0.6 aud 22. was usec to feed corrections to the telescope control aud active optics systenis,"," The off-axis guide and wavefront sensor of the instrument, which is sensitive to wavelengths between 0.6 and $\mu$ m, was used to feed corrections to the telescope control and active optics systems."978 We used an ITI erii as the dispersive clement and an Ty filter to isolate the first order spectra., We used an HK grism as the dispersive element and an HK filter to isolate the first order spectra.979 Complete spectra from 1.23 to jaa with a dispersion of 1 were obtained for all the objects., Complete spectra from 1.23 to $\mu$ m with a dispersion of $^{-1}$ were obtained for all the objects.980 As described below. only the data obtained on the second night are reliable.," As described below, only the data obtained on the second night are reliable."981 The observatious for this transit spanned Lh from UT 06:15 to 05:53., The observations for this transit spanned h from UT 06:15 to 08:53.982 Exposure tinies were sx. aud the overlead per exposure inchicding the read and reset time of the detector was Liss. A total of 239 exposures were obtained. 79 of which were in transit.," Exposure times were s, and the overhead per exposure including the read and reset time of the detector was s. A total of 239 exposures were obtained, 79 of which were in transit."983 The observations began when the field was at an airmass, The observations began when the field was at an airmass984to the band. isophotes. using a custom-written package for galactic surface photometry (“GALPHOL™).,"to the -band isophotes, using a custom-written package for galactic surface photometry ”)."985" In each case. conservative estimates of the onset of the truncation region and of the region near the galactic plane most allectecl by extinction. were mace based on detailed visual examinations of the radial ancl vertical luminosity distributions. respectively,"," In each case, conservative estimates of the onset of the truncation region and of the region near the galactic plane most affected by extinction were made based on detailed visual examinations of the radial and vertical luminosity distributions, respectively."986 The inner boundaries used. for the radial fitting were chosen to minimize possible bulge ellects ane will be ciseussec incliviclually below., The inner boundaries used for the radial fitting were chosen to minimize possible bulge effects and will be discussed individually below.987 Table 2 summarizes the racial ranges adopted for the disc fits. as well as the vertical ranges excluded to avoid extinction effects.," Table \ref{boundaries.tab} summarizes the radial ranges adopted for the disc fits, as well as the vertical ranges excluded to avoid extinction effects."988 Fig., Fig.989 2 shows the £-band images and residual emission (disc model subtracted from the observations) for ESO 201-22 and ESO 416-625., \ref{2D.fig} shows the -band images and residual emission (disc model subtracted from the observations) for ESO 201-G22 and ESO 416-G25.990 Table 1. contains the resulting global scale parameters., Table \ref{pilot.tab} contains the resulting global scale parameters.991 The associated uncertainties are the observational errors. estimated by comparing results [rom several similar fits in which we adjusted the boundaries of the radial fitting range by2050: the formal errors. were in general less than1%...," The associated uncertainties are the observational errors, estimated by comparing results from several similar fits in which we adjusted the boundaries of the radial fitting range by; the formal errors were in general less than. –"992 Figs., Figs.993 2aa and b clearly show the bulge component and. just outside the masked region. the effects of either residual extinction near the galactic plane or. more likely. an additional disc component.," \ref{2D.fig}a a and b clearly show the bulge component and, just outside the masked region, the effects of either residual extinction near the galactic plane or, more likely, an additional disc component."994 The residuals in the fitted region do not show large systematic effects: the bulge contribution to the disc-dominated fitting range is negligible., The residuals in the fitted region do not show large systematic effects; the bulge contribution to the disc-dominated fitting range is negligible.995 ‘The negative residuals extending to the edges of these figures clearly show the presence ofa truncation in the galactic light clistribution. , The negative residuals extending to the edges of these figures clearly show the presence of a truncation in the galactic light distribution. –996Εμίν is the earliest-tvpe galaxy in our pilot sample., This is the earliest-type galaxy in our pilot sample.997 The residuals after subtracting the disc-onlv fit (Fig., The residuals after subtracting the disc-only fit (Fig.998 2dd) do not appear to be systematic in the region where the fit was done. and their amplitude is small (rns.," \ref{2D.fig}d d) do not appear to be systematic in the region where the fit was done, and their amplitude is small (r.m.s."999 residual zlY muassenna).," residual $\approx10001.7\ \sigma_{\rm background}$ )."1001 Although we included a bulge component. the6-parameter fit proved to be very unstable. ," Although we included a bulge component, the6-parameter fit proved to be very unstable. –"1002Figs., Figs.1003 lee and - show that this galaxy. is not exactly. edge-on.," \ref{contours.fig}c c and \ref{bgcheck.fig}1004 show that this galaxy is not exactly edge-on."1005 Extinetion predominantly: allects the eastern side., Extinction predominantly affects the eastern side.1006 A dust mask placed svimametrically with respect to the major axis is therefore not appropriate., A dust mask placed symmetrically with respect to the major axis is therefore not appropriate.1007 The residuals are relatively large (res., The residuals are relatively large (r.m.s.1008 residual 23.3(esed) but do not appear to be svstematic in the region where the fit was done.," residual $\approx 3.3\ \sigma_{\rm1009background}$ ) but do not appear to be systematic in the region where the fit was done."1010 A fit including an exponential bulge did not converge. , A fit including an exponential bulge did not converge. –1011Surface brightness profiles of ESO 446- do not reveal any bulge component., Surface brightness profiles of ESO 446-G44 do not reveal any bulge component.1012 They. cdo show. however. that ESO 446-C44 may not be exactly edegc-on.," They do show, however, that ESO 446-G44 may not be exactly edge-on."1013 Again. the residuals in the region. where we applied our fitting routine are large (rns.," Again, the residuals in the region where we applied our fitting routine are large (r.m.s."1014 residual 25.39(0s ) but do not appear to be systematic.," residual $\approx 5.3\1015\sigma_{\rm background}$ ) but do not appear to be systematic."1016 Lavine just obtained reliable global scale parameters [or our sample galaxies. we are now ready to quantify the disc truncations occurring in these galaxies.," Having just obtained reliable global scale parameters for our sample galaxies, we are now ready to quantify the disc truncations occurring in these galaxies."1017 In the analvsis of cclegc-on galaxies. the inner disc region closest to the plane often needs to be avoided because of the presence of either a prominent dust lane. or a patchy dust distribution with its highest. density towards the galactic plane.," In the analysis of edge-on galaxies, the inner disc region closest to the plane often needs to be avoided because of the presence of either a prominent dust lane, or a patchy dust distribution with its highest density towards the galactic plane."1018 In many cases. the dust component extends. all the way to the οσο of the disc. thus making the luminosity distribution near the galactic planes useless for our study.," In many cases, the dust component extends all the way to the edge of the disc, thus making the luminosity distribution near the galactic planes useless for our study."1019 The exponential scale/rezgh! of galactic disces is to first, The exponential of galactic discs is – to first1020"This letter demonstrates that flux tube shortening is a powertul, inevitable mechanism for heating post-flare loops, which has not been previously investigated.","This letter demonstrates that flux tube shortening is a powerful, inevitable mechanism for heating post-flare loops, which has not been previously investigated."1021" The magnetic forces responsible for shortening, also drive compressive parallel flows at the Alfvénn speed."," The magnetic forces responsible for shortening, also drive compressive parallel flows at the Alfvénn speed."1022" At very low 9, these are high-Mach number flows whose collision naturally generates very strong shocks."," At very low $\beta$, these are high-Mach number flows whose collision naturally generates very strong shocks."1023" The shocks are distinct trom the SMSs of Petschek reconnection and are driven by reconnection-initiated, perpendicular dynamics."," The shocks are distinct from the SMSs of Petschek reconnection and are driven by reconnection-initiated, perpendicular dynamics."1024 This is in contrast to previous investigations of flux tube shocks wherein acoustic wave-steepening or pressure differences were considered as drivers1991)., This is in contrast to previous investigations of flux tube shocks wherein acoustic wave-steepening or pressure differences were considered as drivers.1025" We begin by assuming that localized. transient. fast magnetic reconnection has occurred, by an unspecified physical mechanism, within an otherwise static current sheet."," We begin by assuming that localized, transient, fast magnetic reconnection has occurred, by an unspecified physical mechanism, within an otherwise static current sheet."1026" This will, as just discussed, leave a A-shaped flux tube, initially at rest."," This will, as just discussed, leave a $\Lambda$ -shaped flux tube, initially at rest."1027" Due to its sharp bend it is out of equilibrium, and magnetic forces start it sliding downward between the magnetic layers separated by the current sheet."," Due to its sharp bend it is out of equilibrium, and magnetic forces start it sliding downward between the magnetic layers separated by the current sheet."1028" The tube's retraction, unhindered by the external flux layers. can be modeled using thetube equations of and subsequent authors2000)."," The tube's retraction, unhindered by the external flux layers, can be modeled using the equations of and subsequent authors."1029". While the flux tubes in those previous investigations are confined by the pressure of the unmagnetized convection zone, our post-reconnection tube has very low 7 and is confined by the magnetic pressure of the flux layers outside the current sheet."," While the $\beta$ flux tubes in those previous investigations are confined by the pressure of the unmagnetized convection zone, our post-reconnection tube has very low $\beta$ and is confined by the magnetic pressure of the flux layers outside the current sheet."1030 The tube is an isolated entity distinguished from its surroundings by its connectivity2008)., The tube is an isolated entity distinguished from its surroundings by its connectivity.1031. We assume sufficient collisionality to justify the use of MHD equations throughout., We assume sufficient collisionality to justify the use of MHD equations throughout.1032 The tube is assumed thin enough to be described only by its axis., The tube is assumed thin enough to be described only by its axis.1033" Internal properties such as the magnetic field strength, 2), pressure, p;. and mass density οι. are function only of axial position."," Internal properties such as the magnetic field strength, $B_i$, pressure, $p_i$, and mass density $\rho_i$, are function only of axial position."1034 The tube is also thin enough for fast magnetosonie waves to establish pressure balance across its diameter virtually instantancously., The tube is also thin enough for fast magnetosonic waves to establish pressure balance across its diameter virtually instantaneously.1035 This assumption constrains the internal properties to match those outside the flux tube: B?/87+p;=D?/85p. assumed to be uniform and constant.," This assumption constrains the internal properties to match those outside the flux tube: $B_i^2/8\pi+p_i=B_e^2/8\pi+p_e$, assumed to be uniform and constant."1036 We will also assume the plasma ? to be always small., We will also assume the plasma $\beta$ to be always small.1037 The main force on a section of tube is therefore the magnetic tension due to curvature of the axis Bat/Ol)/4x. where f£ is are-length and &=Ox/Of is the unit tangent vector.," The main force on a section of tube is therefore the magnetic tension due to curvature of the axis $B_i^2(\partial\that/\partial\ell)/4\pi$, where $\ell$ is arc-length and $\that=\partial\xvec/\partial\ell$ is the unit tangent vector."1038" Since it is ultimately the Lorentz force, it is natural that this force is strictly perpendicular to the axis (6-06/0(= 0)."," Since it is ultimately the Lorentz force, it is natural that this force is strictly perpendicular to the axis $\that\cdot\partial\that/\partial\ell=0$ )."1039" The pressure gradient. —tορ,Οἱ, is formally smaller. by a factor of ο. than the magnetic tension."," The pressure gradient, $-\that\,\partial p_i/\partial\ell$, is formally smaller, by a factor of $\beta$, than the magnetic tension."1040" It is, however, the only force parallel to the axis, and is essential to arresting internal"," It is, however, the only force parallel to the axis, and is essential to arresting internal"1041passage. the patch is presumably completely transmitted to the star and so no further Haring behaviour is scen.,"passage, the patch is presumably completely transmitted to the star and so no further flaring behaviour is seen."1042 If AZ variations are a significant [actor in the evolution of the Hare. we might see other indications in the Hare shape.," If ${\dot M}$ variations are a significant factor in the evolution of the flare, we might see other indications in the flare shape."1043 If the polar region cools much more slowly than the Hare timescale an asvmnmetric Dare might be observed., If the polar region cools much more slowly than the flare timescale an asymmetric flare might be observed.1044 Spectral model fits might also indicate. cooling of the emission Component originating from the pole., Spectral model fits might also indicate cooling of the emission component originating from the pole.1045 However. the [are appears almost completely symmetric. and. spectral fits to the rising and falling parts of the [are do not exhibit cooling al any statistically significant level.," However, the flare appears almost completely symmetric, and spectral fits to the rising and falling parts of the flare do not exhibit cooling at any statistically significant level."1046 We would. like to thank Dr. WK. Wu for many helpful discussions ancl suggestions during the preparation of this paper., We would like to thank Dr. K. Wu for many helpful discussions and suggestions during the preparation of this paper.1047 TheRXTE GOK provided timely and vital help and information. as well as the archival observations from 1996 and 1997.," The GOF provided timely and vital help and information, as well as the archival observations from 1996 and 1997."1048 We would also like to thank the BATSE pulsar eroup for providing the timing data., We would also like to thank the BATSE pulsar group for providing the timing data.1049 , 1050" ~5&«10.ασ7. V~9 >1.6 >1.6.10?!eres ""a1.1«Qqn10dbaerecl2.1s ↕∙↴∖∖⊽⋠∐∖∉⋈↕∖⊽∖∖⊽↕↾∐↕∐⋠∐∖↸∩≓↕↕⇁⊧⋂∙≩⋠↕∖↽∏∐⋯↕↕∙↕∐⋠∖↾∙↕↕et7alcloνο)» dave MORE»m"" ∪∐⋜⋯∪↑↕∐∖↥⋅↻∪↖↖↽↸∖↥⋅↕⋜↧↖↖⇁↖↖⇁↕↑∐↕∐≼∐∖↘∩⋅≻∫⋣⊳∶⊓⋝⋅↱≻∶∶∩∙∩⊓ L54LLOALH(CCastro-Tirado[2n (Fruchter ↕⋜∥∐∖↴∖↴≼↧∪↖↖⇁∐∙≼↧∪⋯∐↕⋜↕⊓∐∶↴⋁⋜↧↑∐∖↴⋝↸∖∶↴∙⊾∐∐∐∐∶↴∙⊾↕∐⊸∖≓↥⋅⋜↧⋅↖↽↴∖↴⋜⋯≼↧ ⋖↸∖∙∶↴∙⊾∙∙↕⋟⋜⋯⋜⊔↑↸∖↴∖↴↸⊳∏∙⋀∖↕↸∖↴∖↴↴∖↴∑⋜∐⋅↥⋅∪↴∖↴∙∖↽↕⊰↸∖↸∖↴∖↴↓∩∩≺∖∶∐∏⋜⋯∶↴∙⊾↸∖↑ "," $\sim 5\times 10^{-4}\,{\rm erg}\,{\rm cm}^{-2}$ $V\sim 9$ $z\ge 1.6$ $\ge 1.6\times 10^{54}\,1051{\rm ergs}$ $1.1\times105210^{-11}\,{\rm erg}\,{\rm cm}^{-2}\,{\rm s}^{-1}$ $\alpha_X=-1.44\pm 0.07$ $\alpha_{1R}=-1.1\pm 0.03$ $2.04\pm 0.46$ $\alpha_{2R}=-1.65\pm 0.06$ $-1.75\pm 0.11$ $-1.8$ "1053PZightly decreasing luminosity after the flash. and the mean density of the stars is enhanced.,"slightly decreasing luminosity after the flash, and the mean density of the stars is enhanced."1054 The increase in the mean density leads tostars., The increase in the mean density leads to.1055. However. the change in the mean density is different from star to star.," However, the change in the mean density is different from star to star."1056 The mass of the stars evolved into CHeB at the same age is approximate. but the extent of central helium burning is different.," The mass of the stars evolved into CHeB at the same age is approximate, but the extent of central helium burning is different."1057 The stars around the ZAHB have a smaller radius than approaching the AGB., The stars around the ZAHB have a smaller radius than approaching the AGB.1058 The fractional change caused by mass loss in the radius of the stars around the ZAHB is larger. and the change in the mean density of these stars is also larger than approaching the AGB.," The fractional change caused by mass loss in the radius of the stars around the ZAHB is larger, and the change in the mean density of these stars is also larger than approaching the AGB."1059 stars which are close to the ZAHB are located around the upper boundary of the distributions of λα and Av with age. while approaching the AGB are located around the lower boundary.," stars which are close to the ZAHB are located around the upper boundary of the distributions of $\nu_{max}$ and $\Delta\nu$ with age, while approaching the AGB are located around the lower boundary."1060 the changes of the upper and lower boundary shown in Fig., the changes of the upper and lower boundary shown in Fig.1061 5 are different., \ref{faged} are different.1062 However. for the middle age population. the stars lose only a little amount of mass from their surface before the helium flash. which affect the radius and luminosity of the stars after the flash.," However, for the middle age population, the stars lose only a little amount of mass from their surface before the helium flash, which affect the radius and luminosity of the stars after the flash."1063 Because the mass decrease slightly but the radius is almost not changed. the mass loss results in that the ρα and Av of these stars decrease slightly.," Because the mass decrease slightly but the radius is almost not changed, the mass loss results in that the $\nu_{max}$ and $\Delta\nu$ of these stars decrease slightly."1064 The Reimers mass loss mainly affects the old population., The Reimers mass loss mainly affects the old population.1065 The mass loss leads to an increase in the μα and Av of old population., The mass loss leads to an increase in the $\nu_{max}$ and $\Delta\nu$ of old population.1066 a high mass-loss rate can impede the low-mass low-metal stars evolving into CHeB stage., a high mass-loss rate can impede the low-mass low-metal stars evolving into CHeB stage.1067 If the Reimers mass loss is very efficient during the red-giant branch. the £5 and Av of CHeB stars would not be observed in old clusters.," If the Reimers mass loss is very efficient during the red-giant branch, the $\nu_{max}$ and $\Delta\nu$ of CHeB stars would not be observed in old clusters."1068 The asteroseismical observation on old clusters may provide a help to constrain the mass-loss rate., The asteroseismical observation on old clusters may provide a help to constrain the mass-loss rate.1069 For 4 = 0.5. the value of ρα and Av of population with age 7 2 Gyr is almost located in the range of 10-30 (/;Hz and 1-4 pz. and gathers about25 (/ Hz and 3 (/ Hz. respectively.," For $\eta$ = 0.5, the value of $\nu_{max}$ and $\Delta\nu$ of population with age $>$ 2 Gyr is almost located in the range of 10-30 $\mu$ Hz and 1-4 $\mu$ Hz, and gathers about25 $\mu$ Hz and 3 $\mu$ Hz, respectively."1070 increasing or decreasing the number of stars at a certain age > 2 Gyr affect the peak locations of the 7... and Av., increasing or decreasing the number of stars at a certain age $>$ 2 Gyr affect the peak locations of the $\nu_{max}$ and $\Delta\nu$.1071 So the peak locations are not sensitive to the SFR and whether population contains old stars., So the peak locations are not sensitive to the SFR and whether population contains old stars.1072 For η = 1.10. increasing the SFR of stars with age between 7-9.5 Gyr can increase the stars with VasZ7 25 plz and Av 3 Hz.," For $\eta$ = 1.0, increasing the SFR of stars with age between 7-9.5 Gyr can increase the stars with $\nu_{max} >$ 25 $\mu$ Hz and $\Delta\nu1073>$ 3 $\mu$ Hz."1074 But even enhancing the SFR to several times. the peak locations are not affected.," But even enhancing the SFR to several times, the peak locations are not affected."1075 In BSP. some CHeB stars can lose a little mass. but some stars can accrete a little mass by the weak binary interactions.," In BSP, some CHeB stars can lose a little mass, but some stars can accrete a little mass by the weak binary interactions."1076 The effect of before the helium flash on the uminosity and radius of CHeB stars after the flash is negligible., The effect of before the helium flash on the luminosity and radius of CHeB stars after the flash is negligible.1077" the v,,,.,.. and Av of the CHeB stars which lost a little bit of mass decrease: whereas those of the CHeB stars which accreted a little mass increase.", the $\nu_{max}$ and $\Delta\nu$ of the CHeB stars which lost a little bit of mass decrease; whereas those of the CHeB stars which accreted a little mass increase.1078 the distributions of αν and Av of CHeB stars be affected., the distributions of $\nu_{max}$ and $\Delta\nu$ of CHeB stars be affected.1079 However. for the strong binary interactions. on the one hand. some stars which have lost an appreciable amount of mass from their surface would move to he left of the H-R diagram with slightly decreasing luminosity. at the same time. the mean density of these stars would increase.," However, for the strong binary interactions, on the one hand, some stars which have lost an appreciable amount of mass from their surface would move to the left of the H-R diagram with slightly decreasing luminosity, at the same time, the mean density of these stars would increase."1080 the ων and Av of these stars increase., the $\nu_{max}$ and $\Delta\nu$ of these stars increase.1081 the other hand. some stars with age > 2 Gyr which have accreted a considerable amount of mass would become like the stars with age « 2 Gyr. their ρω and Av can increase obviously too.," the other hand, some stars with age $>$ 2 Gyr which have accreted a considerable amount of mass would become like the stars with age $<$ 2 Gyr, their $\nu_{max}$ and $\Delta\nu$ can increase obviously too."1082 However. the fraction of these interactive binary stars appearing in our simulated CHeB stars is very small.T," However, the fraction of these interactive binary stars appearing in our simulated CHeB stars is very small.,"1083herefore.. although the binary interactions such as mass transfer and mass accretion ean affect the ρω and Av of CHeB stars undergoing a mass accretion or mass loss. the effect of binary interactions on the distributions of ως and Av of CHeB stars is not significant.," although the binary interactions such as mass transfer and mass accretion can affect the $\nu_{max}$ and $\Delta\nu$ of CHeB stars undergoing a mass accretion or mass loss, the effect of binary interactions on the distributions of $\nu_{max}$ and $\Delta\nu$ of CHeB stars is not significant."1084 An increase in the mixing-length parameter o. mainly leads to a decrease in the radius of all CHeB stars after the helium flash., An increase in the mixing-length parameter $\alpha$ mainly leads to a decrease in the radius of all CHeB stars after the helium flash.1085" Thus the /,,,"" and Av of CHeB stars increase with a.", Thus the $\nu_{max}$ and $\Delta\nu$ of CHeB stars increase with $\alpha$.1086 Consequently. the peak locations of the ρω and Av can be affected by the a.," Consequently, the peak locations of the $\nu_{max}$ and $\Delta\nu$ can be affected by the $\alpha$."1087 For the middle-age populationGyr.. the peak locations are more sensitive to the à than mass-loss rate. SFR and metal abundance.," For the middle-age population, the peak locations are more sensitive to the $\alpha$ than mass-loss rate, SFR and metal abundance."1088 Thus the asteroseismical observation on the middle age clusters may provide a help to constrain the mixing-length parameter., Thus the asteroseismical observation on the middle age clusters may provide a help to constrain the mixing-length parameter.1089 The mass of simulated CHeB stars is mainly located in 1-2 M.., The mass of simulated CHeB stars is mainly located in 1-2 $M_{\odot}$.1090 For the CHeB stars with the mixing-length parameter à = 2.0. have a radius [1-14 /?..," For the CHeB stars with the mixing-length parameter $\alpha$ = 2.0, have a radius 11-14 $R_{\odot}$."1091 even the mass distribution is uniform. the stars have an approximate mean density.," even the mass distribution is uniform, the stars have an approximate mean density."1092 they have an approximate {ας and Av., they have an approximate $\nu_{max}$ and $\Delta\nu$.1093 Consequently. there is a dominant peak in the distributions of the {όν απ Av.," Consequently, there is a dominant peak in the distributions of the $\nu_{max}$ and $\Delta\nu$."1094 A high Reimers mass loss can lead to an increase in the Mine and Av of old population. and impedes thelow-mass low-metal stars evolving into CHeB stage.," A high Reimers mass loss can lead to an increase in the $\nu_{max}$ and $\Delta\nu$ of old population, and impedes thelow-mass low-metal stars evolving into CHeB stage."1095population... However. the mass loss affect the ρα and Av of young population.," However, the mass loss affect the $\nu_{max}$ and $\Delta\nu$ of young population."1096 The effect of the Reimers mass loss on the peak locations of Mu. and Av of the CHeB stars is not significant unless the mass-loss rate is very high., The effect of the Reimers mass loss on the peak locations of $\nu_{max}$ and $\Delta\nu$ of the CHeB stars is not significant unless the mass-loss rate is very high.1097 The effect of star formation rate and binary interactions on the peak locations of ρα and Av of the CHeB stars is also not significant., The effect of star formation rate and binary interactions on the peak locations of $\nu_{max}$ and $\Delta\nu$ of the CHeB stars is also not significant.1098 The dominant peak Of Vy and Av is due to the fact that most of CHeB stars have an approximate radius., The dominant peak of $\nu_{max}$ and $\Delta\nu$ is due to the fact that most of CHeB stars have an approximate radius.1099 The radius can be affected by the mixing- parameter., The radius can be affected by the mixing-length parameter.1100 peak location also can. thus.. be affected by the mixing-length parameter.," peak location also can, , be affected by the mixing-length parameter."1101 We thank the anonymous referee for his/her helpful comments., We thank the anonymous referee for his/her helpful comments.1102 This work was supported by the Ministry of Science and Technology of the People; republic of China through grant 2007CB815406. the NSFC thoughs grants 10773003. 10933002. 10963001. 102300410223.. and the high-performance grid computing platform of Henan Polytechnic University.," This work was supported by the Ministry of Science and Technology of the People¡¯s republic of China through grant 2007CB815406, the NSFC though grants 10773003, 10933002, 10963001, , and the high-performance grid computing platform of Henan Polytechnic University."1103Examples of the full range of possible meridional flow structures found with our moclel is displaved in Figure 8: the turbulent viscosity increases [rom top to bottom. over the range 102—10!*em?s.1.,"Examples of the full range of possible meridional flow structures found with our model is displayed in Figure 8; the turbulent viscosity increases from top to bottom, over the range $10^{12}-10^{17} {\rm cm}^2\,{\rm s}^{-1}$."1104 The examples shown range from having three nodes in the streamfunction (frames a.b) down to zero nodes (frames oli).," The examples shown range from having three nodes in the streamfunction (frames a,b) down to zero nodes (frames g,h)."1105 This evolution is accomplished first by the countercell expanding to ever higher latitudes. followed by the primary cell doing the same.," This evolution is accomplished first by the countercell expanding to ever higher latitudes, followed by the primary cell doing the same."1106 In all cases. the amplitude of each cell peaks near its low latitude boundary. auc each cell successively closer to the poles is weaker (han its neighbor on the low latitude side.," In all cases, the amplitude of each cell peaks near its low latitude boundary and each cell successively closer to the poles is weaker than its neighbor on the low latitude side."1107 The color contours are logarithmic to allow one to see (he weaker cells better: [rom the right hand. column of frames. it is clear that no matter how many nodes there are. on a linear velocity scale. al most only the countercell is detectable. ancl it is always substantially smaller (han the primary cell (hat is imposed from low latitudes.," The color contours are logarithmic to allow one to see the weaker cells better; from the right hand column of frames, it is clear that no matter how many nodes there are, on a linear velocity scale, at most only the countercell is detectable, and it is always substantially smaller than the primary cell that is imposed from low latitudes."1108 These results imply that on the Sun. for all viscosity values. it should be possible to detect the countercell. but perhaps none of the smaller cells. if anv. occurring poleward of it.," These results imply that on the Sun, for all viscosity values, it should be possible to detect the countercell, but perhaps none of the smaller cells, if any, occurring poleward of it."1109Initially the method produces halos of mass 1 and S cell units. but as blocks begin to merge so they produce halos of a wide variety of shapes and a continuous spectrum. of masses.,"Initially the method produces halos of mass 1 and 8 cell units, but as blocks begin to merge so they produce halos of a wide variety of shapes and a continuous spectrum of masses."1110 The two most common methods of sudden change in halo mass are creation by the merger of several sub-units 2bb) or accretion of a new block of approximately equal mass which overlaps with the halo 2ec)., The two most common methods of sudden change in halo mass are creation by the merger of several sub-units \ref{fig:halo}b b) or accretion of a new block of approximately equal mass which overlaps with the halo \ref{fig:halo}c c).1111 These produce approximately cubie structures. or triaxial with axial ratios ranging from 3:2 to 11 8)).," These produce approximately cubic structures, or triaxial with axial ratios ranging from 3:2 to 1:1 \ref{fig:axes}) )."1112 Contrast this with the wwhere the halo masses always increase by à factor of two at each merger event., Contrast this with the where the halo masses always increase by a factor of two at each merger event.1113 We have tested. our algorithm on power-law density Huctuation spectra. whieh should give self-similar scaling on scales much smaller than the box-size.," We have tested our algorithm on power-law density fluctuation spectra, which should give self-similar scaling on scales much smaller than the box-size."1114 We take a power-law μαectrum L(A)xAY where n2.2 or 0 to span the range of solutions expected. in the real Universe.," We take a power-law spectrum $P(k)\propto k^n$, where $n=-2$ or 0 to span the range of solutions expected in the real Universe."1115 In an infinite box these would. translate to a root-mean-square density lluctuation spectrum a(n)xm where a=(3|n)/6.," In an infinite box these would translate to a root-mean-square density fluctuation spectrum $\sigma(m)\propto1116m^{-\alpha}$ where $\alpha=(3+n)/6$."1117 —Oowever. in. practice we are missing a lot of power outside the box and so the decline is steeper than this at high masses. specially for η=2.," However, in practice we are missing a lot of power outside the box and so the decline is steeper than this at high masses, especially for $n=-2$."1118 This is illustrated in 3aa where re spectrum is Clearly not a power-Iaw. but is well-it bv the solid line which shows e(m) caleulatecd bv direct summation of waves inside the box with a window function associated with a cubical filter.," This is illustrated in \ref{figps}a a where the spectrum is clearly not a power-law, but is well-fit by the solid line which shows $\sigma(m)$ calculated by direct summation of waves inside the box with a window function associated with a cubical filter."1119 For η=0 the effect is not so severe. so we fit the data with the functional formi of a(n) for an infinite box.," For $n=0$ the effect is not so severe, so we fit the data with the functional form of $\sigma(m)$ for an infinite box."1120 Note that. because we are using a cubical filter. the normalization is dillerent than it would be for a spherical top-hat.," Note that, because we are using a cubical filter, the normalization is different than it would be for a spherical top-hat."1121 Fhis difference is irrelevant for the purposes of this paper because the normalization we use is arbitrary. however it could be important i£ we were to compare our predictions with the results of N-body simulations.," This difference is irrelevant for the purposes of this paper because the normalization we use is arbitrary, however it could be important if we were to compare our predictions with the results of N-body simulations."1122 The results presented. here were mostly obtained using boxes of side £=128., The results presented here were mostly obtained using boxes of side $L=128$.1123 We tried a range of box-sizes. [rom L=32 to 256. to test the effect. of variable resolution on our results.," We tried a range of box-sizes, from $L=32$ to 256, to test the effect of variable resolution on our results."1124 The code needs about 257 words of memory so L=256 is the largest practical size on a workstation., The code needs about $2L^3$ words of memory so $L=256$ is the largest practical size on a workstation.1125 Lf the merger tree is to be used as the basis of galaxy formation models. however. then much more storage is required. and L=128 would be the largest simulation we can allow for.," If the merger tree is to be used as the basis of galaxy formation models, however, then much more storage is required and $L=128$ would be the largest simulation we can allow for."1126 4 shows the cumulative mass function. £(AL.2). [or L=128. averaged. over four realizations.," \ref{fig:cummf} shows the cumulative mass function, $F(M,z)$ for $L=128$, averaged over four realizations."1127" The output is shown for four redshifts corresponding to fractions is i1Lol and =L of the box contained in collapsed regions [or p—2 and fractions i5. ""5. $ and io[or p=ϐ (these choices were made simply to get well-spacecl curves in the ligure: we can reconstruct the curves at anv intermediate time)."," The output is shown for four redshifts corresponding to fractions ${1\over16}$, ${1\over8}$, ${1\over4}$ and ${1\over2}$ of the box contained in collapsed regions for $n=-2$ and fractions ${3\over16}$, ${1\over4}$, ${3\over8}$ and ${1\over2}$ for $n=0$ (these choices were made simply to get well-spaced curves in the figure: we can reconstruct the curves at any intermediate time)."1128 The dashed lines show the corrected. Press-Schechter prediction where a(n) is obtained from fits to the points shown in 3.., The dashed lines show the corrected Press-Schechter prediction where $\sigma(m)$ is obtained from fits to the points shown in \ref{figps}.1129 In both cases the evolution is approximately self-similar., In both cases the evolution is approximately self-similar.1130" This can be seen more clearly in 5 which shows a differential plot. οαν. where 7=9,f0CM.z) is the ordinate (9p=(MM? for n= 0)."," This can be seen more clearly in \ref{figdifmf} which shows a differential plot, $-\partial F/\partial\ln\nu$, where $\nu=\delta_c/\sigma(M,z)$ is the ordinate $\nu=(M/M_*)^{1/2}$ for $n=0$ )."1131 Also shown is the corrected PS prediction. When expressed in this way the functional form of the mass distribution is absolutely universal. it does. not depend on any parameter of the simulation.," Also shown is the corrected PS prediction, When expressed in this way the functional form of the mass distribution is absolutely universal, it does not depend on any parameter of the simulation."1132 Consider first the n—0 case., Consider first the $n=0$ case.1133" Here the dillerential mass curves seem to have the same shape as the PS prediction.but with a higher normalization (alternatively one could sav that 9, should be reduced slightly so as to shift the predicted"," Here the differential mass curves seem to have the same shape as the PS prediction,but with a higher normalization (alternatively one could say that $\delta_c$ should be reduced slightly so as to shift the predicted"1134"range of ary, For which halos at that scale will be significantly evolved due to collisions.",range of $\sigma_1v_{100}^a$ for which halos at that scale will be significantly evolved due to collisions.1135 Or [or fixed ory). 1t indicates the range of scales that will have undergone the desired amount of evolution.," Or for fixed $\sigma_1v_{100}^a$, it indicates the range of scales that will have undergone the desired amount of evolution."1136 From the curves in Figure 4. [or α—0. a clear but somewhat surprising result emerges: (he quantity n is nearly a constant over three orders of magnitude in circular velocity.," 	From the curves in Figure \ref{sigvcirc} for $a=0$, a clear but somewhat surprising result emerges: the quantity $\frac{t_{rel}}{t_H-t_f}$ is nearly a constant over three orders of magnitude in circular velocity."1137 A constant cross section thus implies cwarl galaxies will be just as relaxed as clusters., A constant cross section thus implies dwarf galaxies will be just as relaxed as clusters.1138 llowever. observations indicate that cbwarf galaxies have larger cores in proportion to (heir characteristic size than do clusters.," However, observations indicate that dwarf galaxies have larger cores in proportion to their characteristic size than do clusters."1139 There is thus a scaling problem for a constant cross section as pointed out by Dave et al. (, There is thus a scaling problem for a constant cross section as pointed out by Davé et al. (11402000) ancl Yoshida et al. (,2000) and Yoshida et al. (11412000b).,2000b).1142 A velocity dependent cross section obviously remedies this problem since collisions will be more frequent in lower velocity environments and smaller svstems will (hus be more evolved., A velocity dependent cross section obviously remedies this problem since collisions will be more frequent in lower velocity environments and smaller systems will thus be more evolved.1143 However it is apparent from Figure 4. that if the velocity dependence is too steep (« is too large) only a narrow window of scales will have evolved significantly ancl all larger scales will be identical to CDM halos., However it is apparent from Figure \ref{sigvcirc} that if the velocity dependence is too steep $a$ is too large) only a narrow window of scales will have evolved significantly and all larger scales will be identical to CDM halos.1144 We can obtain a rough estimate of the value of @ that will reproduce observations of core sizes on both dwarl galaxy ancl cluster scales as follows., We can obtain a rough estimate of the value of $a$ that will reproduce observations of core sizes on both dwarf galaxy and cluster scales as follows.1145" Kochanek White's (2000) simulations indicate that the core radius grows linearly during the expansion phase of halo that. r. x (η""4)."," Kochanek White's (2000) simulations indicate that the core radius grows linearly during the expansion phase of halo evolution, so that $r_{c} \propto \left(r_s\frac{t_H-t_f}{t_{rel}}\right)$."1146/Thenlythe :ratio of cluster⋅ to⋅⋅ clwarl core radii ruf roue.so will depend only on e. or solving lor a -," Then the ratio of cluster to dwarf core radii, $r_{c,cl}/r_{c,dw}$, will depend only on $a$, or solving for $a$ ."1147"-- Consider DDO 154. a dwairl galaxy which has a core radius r4,22.5 kpe and maximum rotational velocity 0,,,,24rkms! (Carnigan Purton 1993). which can be identified with the circular velocity of the dark halo."," Consider DDO 154, a dwarf galaxy which has a core radius $r_{c,dw} \approx 2.5$ kpc and maximum rotational velocity $v_{max}\approx 47 \ \mathrm{km} \ \mathrm{s}^{-1}$ (Carnigan Purton 1998), which can be identified with the circular velocity of the dark halo."1148 The lensing cluster EEMSS 13582-6245 has a core radius reaE40 kpe and an inferred halo mass of Mj&4x10!M. (Arabadjis. Dautz. Garmire).," The lensing cluster EMSS 1358+6245 has a core radius $r_{c,cl} \lesssim 40$ kpc and an inferred halo mass of $M_{halo} \approx 4\times 10^{14} \ M_{\odot}$ (Arabadjis, Bautz, Garmire)."1149 Using the scaling relations in Appendix A to calculate py. ry. and ey. equ. (7.1))," Using the scaling relations in Appendix A to calculate $\rho_s$, $r_s$, and $v_s$, eqn. \ref{core}) )"1150 gives «q70.6., gives $a\approx 0.6$.1151 The curves in Figure 4. can be translated into constraints on the dark matter interaction bv fixing c; and thus specibving a physical scale., 	The curves in Figure \ref{sigvcirc} can be translated into constraints on the dark matter interaction by fixing $v_{circ}$ and thus specifying a physical scale.1152 For example. since smaller mass halos will always be more evolved relative to larger halos. an upper limit can be obtained in the σι—@ plane by requiring that the smallest. dark halos observed today.have vet io undergo core collapse.," For example, since smaller mass halos will always be more evolved relative to larger halos, an upper limit can be obtained in the $\sigma_1v_{100}^a-a$ plane by requiring that the smallest dark halos observed todayhave yet to undergo core collapse."1153 We designate (4=20kms! halos as the smallest observed, We designate $v_{circ}= 20 \ \mathrm{km} \ \mathrm{s}^{-1}$ halos as the smallest observed1154included dominate the signal-to-noise.,included dominate the signal-to-noise.1155 These biases are already at the level of current statistical errors., These biases are already at the level of current statistical errors.1156 While our simulations cannot reach halos with &~1. our analysis can shed some light on what behaviour to expect for bx0.8-1.2 halos of relevance to the WigeleZ survey and more closely related to the perturbation theory studies or matter.," While our simulations cannot reach halos with $b \sim 1$, our analysis can shed some light on what behaviour to expect for $b \approx 0.8 - 1.2$ halos of relevance to the WiggleZ survey and more closely related to the perturbation theory studies for matter."1157 Fig., Fig.1158 + shows that the non-linear mapping should be a small correction for r>304 ‘Mpc. but that it still amplifies € on smaller scales.," \ref{fig:streaminglin} shows that the non-linear mapping should be a small correction for $r \gtrsim 30\,h^{-1}$ Mpc, but that it still amplifies $\xi_2$ on smaller scales."1159" If we evaluate our perturbation theory predictions or b=|. we find that the total correction to Πο) can be well-approximated by only the P, term: however. the higher order erms still dominate the corrections to the velocity dispersions."," If we evaluate our perturbation theory predictions for $b=1$, we find that the total correction to $v_{12}(r)$ can be well-approximated by only the $P_{\delta \theta}$ term; however, the higher order terms still dominate the corrections to the velocity dispersions."1160 Therefore. while the bispectrum terms should not be negligible. fitting formulae based on Eq.," Therefore, while the bispectrum terms should not be negligible, fitting formulae based on Eq."1161" 24 with o treated as a free parameter capture at least some of the relevant non-linear corrections and can absorb the rest into σε: even while providing a good fit to the data. we are not guaranteed that the underlying peculiar velocity field amplitude will be recovered at the few per cent level. especially when fitting down to Kyo,=0.3A ! tie. sui,10 'Mpe)."," \ref{scoccPT} with $\sigma_v^2$ treated as a free parameter capture at least some of the relevant non-linear corrections and can absorb the rest into $\sigma_v^2$; even while providing a good fit to the data, we are not guaranteed that the underlying peculiar velocity field amplitude will be recovered at the few per cent level, especially when fitting down to $k_{max} = 0.3 \; h$ $^{-1}$ (i.e., $s_{min} \approx 10\,h^{-1}$ Mpc)."1162" In contrast to many recent theoretical investigations of redshift space distortions. which have focused on the matter density tield and/or performed analyses in Fourier space. in this paper we focus on the redshift space clustering of dark matter halos in configuration space. and use 67:54*Gpe* of N-body simulations o make precise Measurements of £j», as a function of halo bias."," In contrast to many recent theoretical investigations of redshift space distortions, which have focused on the matter density field and/or performed analyses in Fourier space, in this paper we focus on the redshift space clustering of dark matter halos in configuration space, and use $67.5\,h^{-3}\,{\rm Gpc}^3$ of $N$ -body simulations to make precise measurements of $\xi_{0,2,4}$ as a function of halo bias."1163 In our modelling we focus on two distinct corrections to the inear theory predictions: the non-linear mapping between real and redshift space. and the non-linearity of the halo pairwise velocities.," In our modelling we focus on two distinct corrections to the linear theory predictions: the non-linear mapping between real and redshift space, and the non-linearity of the halo pairwise velocities."1164 We find both corrections to be important on the quasilinear scales of interest to this work (~30—807 'Mpe).," We find both corrections to be important on the quasilinear scales of interest to this work $\sim 30-80\,h^{-1}$ Mpc)."1165 To model the non-linear real to redshift space mapping of pairs. we take a non-perturbative approach and employ the scale-dependent Gaussian streaming model. Eq. 25.," To model the non-linear real to redshift space mapping of pairs, we take a non-perturbative approach and employ the scale-dependent Gaussian streaming model, Eq. \ref{streamingeqn},"1166 in which the pairwise velocity probability distribution function (PDF) is assumed to be Gaussian. but where the pairwise velocities have a mean and dispersion that depend on the pair separation distance r und the angle of the pair separation vector with the LOS.," in which the pairwise velocity probability distribution function (PDF) is assumed to be Gaussian, but where the pairwise velocities have a mean and dispersion that depend on the pair separation distance $r$ and the angle of the pair separation vector with the LOS."1167 A similar model has been used with some success on somewhat smaller scales in the context of the halo model., A similar model has been used with some success on somewhat smaller scales in the context of the halo model.1168 Fig., Fig.1169" 4. shows that this model significantly enhances both &», on quasilinear scales for real space statistics expected in linear theory."," \ref{fig:streaminglin} shows that this model significantly enhances both $\xi_{2,4}$ on quasilinear scales for real space statistics expected in linear theory."1170 When we know perfectly the real space clustering and velocity statistics. Fig.," When we know perfectly the real space clustering and velocity statistics, Fig."1171 @ shows that this model is accurate at the <2 per cent level for s>25/1' Mpc. i.e. at about the level demanded by ongoing experiments like BOSS.," \ref{fig:streaming1} shows that this model is accurate at the $\lesssim 2$ per cent level for $s > 25\,h^{-1}$ Mpc, i.e., at about the level demanded by ongoing experiments like BOSS."1172 For the first time (to our knowledge). we have computed the next-to-leading order corrections to pairwise mean infall velocities and dispersions for linearly biased halos as a function of real space separation in standard perturbation theory.," For the first time (to our knowledge), we have computed the next-to-leading order corrections to pairwise mean infall velocities and dispersions for linearly biased halos as a function of real space separation in standard perturbation theory."1173 While we find relatively good agreement between our calculations and halo samples drawn from a large volume of N-body simulations (see Fig. 9).," While we find relatively good agreement between our calculations and halo samples drawn from a large volume of N-body simulations (see Fig. \ref{fig:vstats}) ),"1174 when used as input into the streaming model. there remain offsets at the several percent level for s.&40/4 'Mpc.," when used as input into the streaming model, there remain offsets at the several percent level for $s \leq 40\,h^{-1}$ Mpc."1175 We are able to trace the discrepancy to the scale-dependent inaccuracy of the perturbation theory prediction for halo infall velocities: note that even in linear theory. the redshift space quadrupole & depends on the derivative dvistr)/dr.," We are able to trace the discrepancy to the scale-dependent inaccuracy of the perturbation theory prediction for halo infall velocities; note that even in linear theory, the redshift space quadrupole $\xi_2$ depends on the derivative $dv_{12}(r)/dr$."1176 In future work we hope to explore other perturbation theory schemes as a means to improve the level of accuracy of the mean pairwise velocity perturbation theory prediction: more complex biasing schemes may also improve agreement2010)., In future work we hope to explore other perturbation theory schemes as a means to improve the level of accuracy of the mean pairwise velocity perturbation theory prediction; more complex biasing schemes may also improve agreement.1177. Both of the corrections we described above have signiticant higher order contributions that depend on the halo bias., Both of the corrections we described above have significant higher order contributions that depend on the halo bias.1178 In Section 8.. we show that while the bias dependence is detectable but weak for the non-linear velocity corrections. the dominant correction for the non-linear mapping from real and redshift space scales as 5.," In Section \ref{biasdep}, we show that while the bias dependence is detectable but weak for the non-linear velocity corrections, the dominant correction for the non-linear mapping from real and redshift space scales as $b^3$."1179 These effects have opposite signs in the halo bias range we have studied. so that for some limited range of halo bias and scale. they approximately cancel.," These effects have opposite signs in the halo bias range we have studied, so that for some limited range of halo bias and scale, they approximately cancel."1180 Our findings demonstrate. in line with other recent works. that a model of the form in Eq.," Our findings demonstrate, in line with other recent works, that a model of the form in Eq."1181 24. that only includes two-point corrections cannot accurately deseribe the dependence of redshift space halo clustering on bias., \ref{scoccPT} that only includes two-point corrections cannot accurately describe the dependence of redshift space halo clustering on bias.1182" Finally. we note that in order to infer for, from redshift space distortions in halo clustering. one must make the assumption that the bias inferred from real space clustering is the same one that determines the halo pairwise infall velocity amplitude."," Finally, we note that in order to infer $f\sigma_8$ from redshift space distortions in halo clustering, one must make the assumption that the bias inferred from real space clustering is the same one that determines the halo pairwise infall velocity amplitude."1183 Our large volume of N-body simulations allows us to confirm this assumption at the per cent level on large seales. once we incorporate the effects of non-linear growth using perturbation theory.," Our large volume of $N$ -body simulations allows us to confirm this assumption at the per cent level on large scales, once we incorporate the effects of non-linear growth using perturbation theory."1184 Before our model ean be applied to analysing real galaxy surveys. the large velocity dispersions ofsatellite galaxies must be accounted for separately in the model.," Before our model can be applied to analysing real galaxy surveys, the large velocity dispersions ofsatellite galaxies must be accounted for separately in the model."1185 We are cautiously optimistic that these additional corrections. at least for &:. will be relatively small.," We are cautiously optimistic that these additional corrections, at least for $\xi_2$, will be relatively small."1186 In a preliminary study. we found that (s=307'Mpo) is damped by <2 per cent when satellites from the best fit HOD of are included.," In a preliminary study, we found that $\xi_2(s=30\,h^{-1}{\rm Mpc})$ is damped by $\lesssim 2$ per cent when satellites from the best fit HOD of are included."1187" However. our model prediction for £, is worse than for the halo-only samples."," However, our model prediction for $\xi_4$ is worse than for the halo-only samples."1188 We reserve this line of research for a future work., We reserve this line of research for a future work.1189 BAR thanks Jeremy Tinker and Ravi Sheth for insightful discussions., BAR thanks Jeremy Tinker and Ravi Sheth for insightful discussions.1190 Support for this work was provided by NASA through Hubble Fellowship grant 51280 awarded by the Space Telescope Science Institute. which is operated by the Association of Universities for Research in Astronomy. Inc... for NASA. under contract NAS 5-26555.," Support for this work was provided by NASA through Hubble Fellowship grant 51280 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555."1191 MW is supported by the NSF and NASA., MW is supported by the NSF and NASA.1192 The simulations used in this paper were analysed at the National Energy Research Scientific Computing Center. the Shared Research Computing Services Pilot of the University of California and the Laboratory Research Computing project at Lawrence Berkeley National Laboratory.," The simulations used in this paper were analysed at the National Energy Research Scientific Computing Center, the Shared Research Computing Services Pilot of the University of California and the Laboratory Research Computing project at Lawrence Berkeley National Laboratory."1193 We refer the reader to for an introduction to standard perturbation theory., We refer the reader to for an introduction to standard perturbation theory.1194 In this appendix we provide explicit expressions for all terms contributing up to fourth order in the linear density field o4(KR) to pairwise mean velocities and dispersions for linearly biased tracers., In this appendix we provide explicit expressions for all terms contributing up to fourth order in the linear density field $\delta_1({\bf k})$ to pairwise mean velocities and dispersions for linearly biased tracers.1195 Our results are presented using the Fourier convention given in Eq. 12.., Our results are presented using the Fourier convention given in Eq. \ref{eq:fourier}. .1196 Terms in Eq., Terms in Eq.1197 26 that depend on only one ó can be written in terms, \ref{eq:vinfall} that depend on only one $\delta$ can be written in terms1198where m; and £D are in units of MM. and kkpc. respectively. and Nis the initial number of stars in. the cluster.,"where $m_i$ and $D$ are in units of $_{\odot}$ and kpc, respectively, and $N$ is the initial number of stars in the cluster."1199 To take into account disc shocking. the factor ho is merely replaced by A as defined by equation (3) of Vesperini (1998).," To take into account disc shocking, the factor $F_{cw}$ is merely replaced by $\lambda$ as defined by equation (3) of Vesperini (1998)."1200 We have distributed 20.000 clusters following various radial ane mass distributions.," We have distributed 20,000 clusters following various radial and mass distributions."

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