ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 A LU? dependence gives a reasonable Π το typical densities through the PPN and PN stages (as observed by. e.g. Martin-Pintadoetal.1995: Aleaburnctal.1998)).," A $t^{-3/2}$ dependence gives a reasonable fit to typical densities through the PPN and PN stages (as observed by, e.g. \citealt{martin-pintando.et.al95}; \citealt{meaburn.et.al98b}) )."3" Therefore we adopt for times />£4. where /,=100vr."," Therefore we adopt n(t)=10^7 ( , for times $t > t_1$, where $t_1 = 100~{\rm yr}$."4 On the assumption of constant clump mass throughout the expansion. this gives ," On the assumption of constant clump mass throughout the expansion, this gives (."5The visual extinction associated with a clump must therefore⋅ vary as /17. and we write. (G," The visual extinction associated with a clump must therefore vary as $t^{-1}$, and we write (."6-p The distance of the clump from the star is d. which in a steady [ow must increase lincarly with time: = (ο)cm.," The distance of the clump from the star is $d$, which in a steady flow must increase linearly with time: d(t) = (."7 We adopt the following dependence of temperature on time. as it gives values for the PN clump temperatures comparable to the typical measured. values (Martin-Pintadoetal.1995:Meaburnct 1998): ο...," We adopt the following dependence of temperature on time, as it gives values for the PN clump temperatures comparable to the typical measured values \citep{martin-pintando.et.al95,meaburn.et.al98b}: T(t) = (."8 The radiation field experienced. by the parcel of gas is initially dominated by the contribution from the central star. and later by that of the interstellar radiation field.," The radiation field experienced by the parcel of gas is initially dominated by the contribution from the central star, and later by that of the interstellar radiation field."9 We adopt the following expression. similar to that used by (1994).. for the radiation field intensity Y.," We adopt the following expression, similar to that used by \citet{howe.et.al94}, , for the radiation field intensity $\chi$ ,"10The merger of (wo supermassive black holes has been a topic of lively astrophysical speculation for many vears (7)..,The merger of two supermassive black holes has been a topic of lively astrophysical speculation for many years \citep{BBR80}.11 Recent developments in galaxy formation theory have made the prospect more plausible and suggest an environment for such events: the centers of ealaxies (hat underwent major mergers a lew hundred million vears in the past (??)..," Recent developments in galaxy formation theory have made the prospect more plausible and suggest an environment for such events: the centers of galaxies that underwent major mergers a few hundred million years in the past \citep{HaehKauff02,Volont03}."12 Mergers mav be particularly likely when the galaxy. contains a relatively rich supply of interstellar eas. which may help binary black holes overcome the “last parsec problem” and approach each other close enough for gravitational wave emission (o compress the orbit to merger," Mergers may be particularly likely when the galaxy contains a relatively rich supply of interstellar gas, which may help binary black holes overcome the “last parsec problem"" and approach each other close enough for gravitational wave emission to compress the orbit to merger"13P=1.69 PER =0.5Po and Ny inthe rauge (9.1d0.6 to 31.0.T.5) x107 ? (4?=193.L: d.o.f.=296: see Table 5)).,"$\Gamma = 1.69^{+0.07}_{-0.07}$ , $\cal R$ $= 0.5^{+0.2}_{-0.1}$ and $N_{\rm H}$ inthe range $9.1 \pm 0.6$ to $31.9^{+5.4}_{-4.3}$ ) $\times 10^{22}$ $^{-2}$ $\chi^{2} = 193.4$; $d.o.f. = 296$; see Table \ref{tbl-3}) )."14 This model provides a significantly (>99% «)) etter fit to the data (on the basis ofa F-test for oue additional (ree parameter). than our earler preferred model (1uodel 2).," This model provides a significantly $> 99$ ) better fit to the data (on the basis of a F-test for one additional free parameter), than our earlier preferred model (model 2)."15 The iron. Iva emission. line. flux was 1.6àOLS52xE10?5 photons tem >?. Which yields an equivalent width iu the rauge 10-120 eV. compared with tle 50 eV equivalent width expected from the rellectiou continuum (George&Fabian1991:Mattetal.Chusellini199D.," The iron $\alpha$ emission line flux was $1.6^{+0.8}_{-0.7} \times 10^{-5}$ photons $^{-1}$ $^{-2}$, which yields an equivalent width in the range 40–120 eV, compared with the $\sim 50$ eV equivalent width expected from the reflection continuum \citep{gf91,mat91,ghi94}."16. Thus. for the brighter source states. reflection could »rocice all of the observed line emission.," Thus, for the brighter source states, reflection could produce all of the observed line emission."17 When the relative strength of the reflection coutinuuui is alowed to vary between the observations. there is a strong correlation between its strength an the intensity of the source. with a strouger reflection continuum beiug preferred for the weaker sotrces ales.," When the relative strength of the reflection continuum is allowed to vary between the observations, there is a strong correlation between its strength and the intensity of the source, with a stronger reflection continuum being preferred for the weaker source states."18 However. the 'eduction. iu. 47> of. NA>z5- is insignificant (on tlie basis of a F-test for six additional free parametes) aud. therefore. we cannol draw auy firm conclusions.," However, the reduction in $\chi^{2}$ of $\Delta \chi^{2} \approx 5$ is insignificant (on the basis of a F-test for six additional free parameters) and, therefore, we cannot draw any firm conclusions."19 If the molecular torus is optically thick. then Compton rellec101 originating at the (far-side inner walls of the torus may be seen directly. rather than througl the gas column responsible for he low energy absorption (dependiug. of cou‘se. on the torus οeoljetry and view augle).," If the molecular torus is optically thick, then Compton reflection originating at the (far-side) inner walls of the torus may be seen directly, rather than through the gas column responsible for the low energy absorption (depending, of course, on the torus geometry and view angle)."20 Sucl ‘eflection would not be expected to vary on timescales shorter tlal about a year. aud could in srinciple lead to a uet softening of tle spectrun as the source inteusity increases.," Such reflection would not be expected to vary on timescales shorter than about a year, and could in principle lead to a net softening of the spectrum as the source intensity increases."21 Such reflection could also contribute siguilicautly Oa μοι-varying component of tje iron Ia emission line., Such reflection could also contribute significantly to a non-varying component of the iron $\alpha$ emission line.22 To test his possibility. the cata were fitted o a model including au absorbed power-law continuum. ar Comj»ton relleci¢1 component. aud a narrow Craussian emission line (inodel 5).," To test this possibility, the data were fitted to a model including an absorbed power-law continuum, an Compton reflection component, and a narrow Gaussian emission line (model 5)."23 The Compton reflectionspectrum was tlie sane as that wed for model {., The Compton reflectionspectrum was the same as that used for model 4.24 The best-fit values are D—1.65+0.05 atd Nyjin the ange (0.8(QuU9ας to 32.1i6» 2) x1077 cm7 (4?=188.5: d.o.[=296: see Table 5 D.," The best-fit values are $\Gamma = 1.65 \pm 0.05$ and $N_{\rm H}$in the range $9.8^{+0.9}_{-0.7}$ to $32.4^{+6.8}_{-6.2}$ ) $\times2510^{22}$ $^{-2}$ $\chi^{2} = 188.5$; $d.o.f = 296$; see Table \ref{tbl-3}) )."26 Tle improvenielul in X? over that [or the variable absorber model is significant at >99% (on the basis of a F-tes for one additional term)., The improvement in $\chi^{2}$ over that for the variable absorber model is significant at $> 99$ (on the basis of a F-test for one additional term).27" The relative normalization between the direct aud 'elleced contiuua var]es from A, zz0.3 to R x0.8 as the level of the fe‘er changes.", The relative normalization between the direct and reflected continua varies from $\cal R$ $\approx 0.3$ to $\cal R$ $\approx 0.8$ as the level of the former changes.28" The iron Ίνα emission liue flix was 1.6dE0.7x10? photons 1 >7. aud yields"" an equivalent width in tle ra1ge 20-120 eV. comparable to the 30—100 eV rauge expected from reflection continuum aloie."," The iron $\alpha$ emission line flux was $1.6 \pm 0.7 \times 10^{-5}$ photons $^{-1}$ $^{-2}$, and yields an equivalent width in the range 30–120 eV, comparable to the 30–100 eV range expected from reflection continuum alone."29 Recently. evidence liz15 emerge for Comptou-thick material which partially. or fully covers the central nucleus in severa Seyert 2 [n]ealaxies (NGC 1915. Iwasawa et al.," Recently, evidence has emerged for Compton-thick material which partially, or fully covers the central nucleus in several Seyfert 2 galaxies (NGC 4945, Iwasawa et al."30 1993. Done. Macejski Sumith 1996: IAS 01575-7537. Vigjiali οἱ al.," 1993, Done, Madejski Smith 1996; IRAS 04575-7537, Vignali et al."31 1998: Mrk 3. Turner et al.," 1998; Mrk 3, Turner et al."32 1997. Cappi et al.," 1997b, Cappi et al."33 1999. Georgantopoulos et al.," 1999, Georgantopoulos et al."34 1999: GC 1582. Turner et al.," 1999; NGC 7582, Turner et al."35 2000)., 2000).36 In order to test for the presence of Comptou-thick material obscu‘ine tje nucleus in Mrk 318. (1e data were fitted to a model cousistiug of a power-law continuum. which is »artially covered by a coistant columu (ΝΕΤ). aud fully covered by a variable absorber (Νις). dlus a uarrow Craussian emission liue (model 6).," In order to test for the presence of Compton-thick material obscuring the nucleus in Mrk 348, the data were fitted to a model consisting of a power-law continuum, which is partially covered by a constant column $N_{\rm H1}$ ), and fully covered by a variable absorber $N_{\rm H2}$ ), plus a narrow Gaussian emission line (model 6)."37 This model provides the best fit so far to thedata. with D=1.77040 jus: Mu4:=OlMEE35)xLO? ? covering 0.21n of the source. aud Nyy iu the range (9.7We to 319 21) x107 2 (4?= 1819: d.o.J.= 295: see Table 6)).," This model provides the best fit so far to thedata, with $\Gamma38= 1.77^{+0.10}_{-0.05}$ , $N_{\rm H1} = (111^{+52}_{-32}) \times3910^{22}$ $^{-2}$ covering $0.24^{+0.03}_{-0.07}$ of the source, and $N_{\rm H2}$ in the range $9.7^{+0.8}_{-0.6}$ to $31.9^{+5.4}_{-5.1}$ ) $\times 10^{22}$ $^{-2}$ $\chi^{2} = 184.9$ ; $d.o.f. = 295$ ; see Table \ref{tbl-4}) )."40 The iron Wa line equivalent width expected from an obscuring column of ΝΤ~107! 7? would be ~500 eV (Leal&Creighton1993) with respect to the absorbed continuum. but," The iron $\alpha$ line equivalent width expected from an obscuring column of $N_{\rm H} \sim4110^{24}$ $^{-2}$ would be $\sim 500$ eV \citep{lc93} with respect to the absorbed continuum, but"42obtained in the latest years have confirmed such time scales: PKS 1454-354 (Abdo et al.,obtained in the latest years have confirmed such time scales: PKS $-$ 354 (Abdo et al.43" 2009), PKS 1502+106 (Abdo et al."," 2009), PKS $+$ 106 (Abdo et al."44" 2010a), PKS B1510—089 (Tavecchio et al."," 2010a), PKS $-$ 089 (Tavecchio et al."45" 2010), 3C 454.3 (Foschini et al."," 2010), 3C 454.3 (Foschini et al."46" 2010, Tavecchio et al."," 2010, Tavecchio et al."47" 2010, Ackermann et al."," 2010, Ackermann et al."48 2010) and 3C 273 (Abdo et al., 2010) and 3C 273 (Abdo et al.49 2010b)., 2010b).50 The availability of the satellite provides a plethora of y-ray data where to search for short variability events., The availability of the satellite provides a plethora of $\gamma$ -ray data where to search for short variability events.51" The Large Area Telescope (LAT, Atwood et al."," The Large Area Telescope (LAT, Atwood et al."52" 2009) onboard represents the state of the art of y-ray space instruments, with an increase of sensitivity of a factor ~20—30 with respect to its predecessors."," 2009) onboard represents the state of the art of $\gamma$ -ray space instruments, with an increase of sensitivity of a factor $\sim 20-30$ with respect to its predecessors."53" operates in scanning mode, i.e. it performs an all-sky survey every 3 hours (two orbits)."," operates in scanning mode, i.e. it performs an all-sky survey every 3 hours (two orbits)."54" This is the first continuous monitoring of the high-energy y- ray sky and offers the unique possibility to study the blazar population, the duty cycle of individual sources, and to catch the most powerful outbursts."," This is the first continuous monitoring of the high-energy $\gamma$ -ray sky and offers the unique possibility to study the blazar population, the duty cycle of individual sources, and to catch the most powerful outbursts."55" The bad side of the thing is that the scanning mode hampers the probing of subhour variability, because the source is not always at the LAT’s boresight, where the instrument has its best performance."," The bad side of the thing is that the scanning mode hampers the probing of subhour variability, because the source is not always at the LAT's boresight, where the instrument has its best performance."56" A tentative to get over this obstacle out has been done in 2010 April, when 3C 454.3 underwent an intense ourburst with flux above 100 MeV in excess of 10? ph cm""? s-!."," A tentative to get over this obstacle out has been done in 2010 April, when 3C 454.3 underwent an intense ourburst with flux above 100 MeV in excess of $10^{-5}$ ph $^{-2}$ $^{-1}$."57" During this episode, Fermi//LAT performed a pointed observation staring at the FSRQ (2010 April 5-8)."," During this episode, /LAT performed a pointed observation staring at the FSRQ (2010 April $-$ 8)."58" The latter, however, did not collaborate and remained almost constant with poorly significant variations (3 hours) and began to be variable only toward the end of the special observation (Foschini et al."," The latter, however, did not collaborate and remained almost constant with poorly significant variations $\sim 3$ hours) and began to be variable only toward the end of the special observation (Foschini et al."59" 2010, Ackermann et al."," 2010, Ackermann et al."60 2010)., 2010).61" Therefore, we decided to expand our search to other — possibly more active — periods and sources."," Therefore, we decided to expand our search to other – possibly more active – periods and sources."62" We searched for other cases of FSRQ with high-energy y-ray flux exceeding 107? ph cm? s! for at least one day, in order to have the best available statistics."," We searched for other cases of FSRQ with high-energy $\gamma$ -ray flux exceeding $10^{-5}$ ph $^{-2}$ $^{-1}$ for at least one day, in order to have the best available statistics."63" We found three FSRQs fulfilling this criterion, which were 3C 454.3 (z= 0.859), 3C 273 (z= 0.158), and PKS B12224216 (z= 0.432)."," We found three FSRQs fulfilling this criterion, which were 3C 454.3 $z=0.859$ ), 3C 273 $z=0.158$ ), and PKS $+$ 216 $z=0.432$ )."64 We report here the results of this analysis., We report here the results of this analysis.65" There were two more cases that could have been of interest, but they were discarded."," There were two more cases that could have been of interest, but they were discarded."66 PKS B1510—-089 and PKS 1830-211 have exceeded the threshold flux for a few hours (Ciprini et al., PKS $-$ 089 and PKS $-$ 211 have exceeded the threshold flux for a few hours (Ciprini et al.67" 2010, Tavecchio et al."," 2010, Tavecchio et al."68" 2010), but not for at least one day, and therefore we did not consider them."," 2010), but not for at least one day, and therefore we did not consider them."69" Moreover, at the time of writing this work (Christmas 2010), 3C 454.3 exceeded again the threshold, but we limited our data set at the end of 2010 November."," Moreover, at the time of writing this work (Christmas 2010), 3C 454.3 exceeded again the threshold, but we limited our data set at the end of 2010 November."70" As stated above, we have searched for very high fluxes sources (Fy>10? ph cm? s! averaged over one day; E»100 MeV)."," As stated above, we have searched for very high fluxes sources $F_{\gamma} > 10^{-5}$ ph $^{-2}$ $^{-1}$ averaged over one day; $E>100$ MeV)."71" We have identified three candidates: 3C 454.3, which has exceeded the flux threshold three times to date (2009 December, 2010 April and November), PKS B1222+216 (2010 May-June) and 3C 273 (2009 September)."," We have identified three candidates: 3C 454.3, which has exceeded the flux threshold three times to date (2009 December, 2010 April and November), PKS B1222+216 (2010 May-June) and 3C 273 (2009 September)."72 Fermi//LAT data for the above mentioned sources and time periods were downloaded from the atHEASARC!., /LAT data for the above mentioned sources and time periods were downloaded from the at.73". The selected data were screened, filtered, and analyzed as described in greater detail in Foschini et al. ("," The selected data were screened, filtered, and analyzed as described in greater detail in Foschini et al. ("74"2010), but with a more recent version of the 9.18.6)) and the corresponding calibration files.","2010), but with a more recent version of the ) and the corresponding calibration files."75" Moreover, while in Foschini et al. ("," Moreover, while in Foschini et al. ("76"2010) we could build time bins smaller than the good-time intervals (GTI) because of the better LAT performance during pointed observations (the collected counts are greater than in survey mode by a factor  3.5, see also Ackermann et al.","2010) we could build time bins smaller than the good-time intervals (GTI) because of the better LAT performance during pointed observations (the collected counts are greater than in survey mode by a factor $\sim$ 3.5, see also Ackermann et al."77" 2010), this is no more possible when analyzing LAT data from scanning mode observations, which in turn constitute the majority of the data analyzed in the present work."," 2010), this is no more possible when analyzing LAT data from scanning mode observations, which in turn constitute the majority of the data analyzed in the present work."78" Searching for the best trade off between a small time bin and the need of significant statistics in each bin, we have found that the best option is to have time bins equal to the GTI, which generally are of the order of a few kiloseconds (a bit less than one orbit)."," Searching for the best trade off between a small time bin and the need of significant statistics in each bin, we have found that the best option is to have time bins equal to the GTI, which generally are of the order of a few kiloseconds (a bit less than one orbit)."79 Shorter bins could suffer of artifacts as indicated in the caveats listed in the web pages at HEASARC; larger bins would wash out the variability., Shorter bins could suffer of artifacts as indicated in the caveats listed in the web pages at HEASARC; larger bins would wash out the variability.80" Last, but not least, we have required that the flux in each bin was at least a factor 2 greater than its error, i.e. that there were sufficient events to correctly and significantly reconstruct the source flux."," Last, but not least, we have required that the flux in each bin was at least a factor 2 greater than its error, i.e. that there were sufficient events to correctly and significantly reconstruct the source flux."81 The extracted light curves are displayed in Figs. (1--3))., The extracted light curves are displayed in Figs. \ref{fig:curva3c273}- \ref{fig:curva3c454}) ).82" We have noted that 3C 454.3 reached its peak flux of (1.0+ ph cm? s! (E>100 MeV, corresponding to a luminosity of about ~3x10°° erg s!) on 2010 November 20 between 01:45 and 03:03 UTC (source ontime ~4.7 ks)."," We have noted that 3C 454.3 reached its peak flux of $(1.0\pm0.1)\times 10^{-4}$ ph $^{-2}$ $^{-1}$ $E>100$ MeV, corresponding to a luminosity of about $\sim 3\times 10^{50}$ erg $^{-1}$ ) on 2010 November 20 between 01:45 and 03:03 UTC (source ontime $\sim 4.7$ ks)."83" During this time, LAT detected 110 events from the blazar (22σ detection)."," During this time, LAT detected 110 events from the blazar $22\sigma$ detection)."84 This is the greatest y-ray flux ever detected to date from an AGN., This is the greatest $\gamma$ -ray flux ever detected to date from an AGN.85" It is worth noting that, contrary to previous observations at high-energy y rays, this time 3C 454.3 displayed significant spectral changes in the y-ray energy band (Abdo et al."," It is worth noting that, contrary to previous observations at high-energy $\gamma$ rays, this time 3C 454.3 displayed significant spectral changes in the $\gamma$ -ray energy band (Abdo et al."86 2011)., 2011).87" Once prepared, we have scanned all the light curves searching for the minimum time of doubling/halving flux:"," Once prepared, we have scanned all the light curves searching for the minimum time of doubling/halving flux:"88"The best fits of both components are shown in ptiand fit,pts.",The best fits of both components are shown in \\ref{fit_opt_1} and \\ref{fit_opt_2}.89.ThefitoftheUV spectrumoftheprimarvisshowninF, The fit of the UV spectrum of the primary is shown in \\ref{fit_UV_1}.90 ThederivedparametersaregatheredinTable2 (bottom part), The derived parameters are gathered in Table \ref{tab_orb} (bottom part).91Th lead, The quality of the fit is on average very good.92 sto, Only a few features are not reproduced.93a, This is the case of the lines around 4550.94better Fit. butinthatcasetheotherdiagnosticsarelesswellre," Increasing leads to a better fit, but in that case the other diagnostics are less well reproduced."95 produ ," This problem is frequently observed in our models, and the origin is not known at present."96," Hence, we decided not to rely on these lines in the present study."97better understand the binary system LZCCep. and in particular. its geometry. we also performed an analysis of the Hipparcos light curve.," To better understand the binary system Cep, and in particular, its geometry, we also performed an analysis of the Hipparcos light curve."98" This investigation was made with the NIGHTFALLprogramme"".", This investigation was made with the NIGHTFALL.99 This software is based on a generalized Wilson-Devinney method assuming à standard Roche. geometry., This software is based on a generalized Wilson-Devinney method assuming a standard Roche geometry.100 We performed a Π of the light curve by minimizing the free parameters., We performed a fit of the light curve by minimizing the free parameters.101 We fixed the effective temperatures to 32000 K and 28000 K. for the primary and the secondary star. respectively. as determined by the CMFGEN analysis (see refs pec).," We fixed the effective temperatures to 32000 K and 28000 K, for the primary and the secondary star, respectively, as determined by the CMFGEN analysis (see \\ref{s_spec}) )."102 Themassratioandtheorbitalperiodarethoseobtained fromtheo ) , The mass ratio and the orbital period are those obtained from the orbital solution (see \\ref{tab_orb}) ).103Westressthatthezero phaseof thelightcurve fitcorrespond sto , We stress that the zero phase of the light curve fit corresponds to the zero phase of the orbital solution.104The light curve (Fig. 7)), The light curve (Fig. \ref{fit_lc}) )105 does not exhibit any eclipses but ellipsoidal variations are clearly visible., does not exhibit any eclipses but ellipsoidal variations are clearly visible.106 The depth of the secondary minimum ts very similar to that of the primary minimum., The depth of the secondary minimum is very similar to that of the primary minimum.107 ? considered two different models to explain the geometry of this binary system: a first one where both stars fill Roche lobe. and a second Wwith a »emi-detached configuration.," \citet{howarth91} considered two different models to explain the geometry of this binary system: a first one where both stars fill their Roche lobe, and a second one with a semi-detached configuration."108their The emphasis of their oneanalysis was put on the second model with the secondary star filling its Roche lobe., The emphasis of their analysis was put on the second model with the secondary star filling its Roche lobe.109 In our analysis. the NIGHTFALL programme also gives us two situations but. at each time. converges towards a semi-detached system.," In our analysis, the NIGHTFALL programme also gives us two situations but, at each time, converges towards a semi-detached system."110 The first possibility is a situation in which the primary component fills up its Roche lobe(Sol | in Table3), The first possibility is a situation in which the primary component fills up its Roche lobe (Sol 1 in Table \ref{tab_lc}) ).111 , 112"and the scan direction, respectively.","and the scan direction, respectively."113 The spatial resolution was ~1.3” and the noise level in the polarization profiles is of about after the denoising using the procedure described by MartínezGonzálezetal.(2008b)., The spatial resolution was $\sim 1.3''$ and the noise level in the polarization profiles is of about after the denoising using the procedure described by \cite{marian_08}.114. We investigate how the distribution of polarization amplitudes changes with the spatial resolution following two approaches., We investigate how the distribution of polarization amplitudes changes with the spatial resolution following two approaches.115" First, we compare the Hinode data set degraded to different spatial resolutions by adding adjacent pixels."," First, we compare the Hinode data set degraded to different spatial resolutions by adding adjacent pixels."116 This allows us to study the very same quiet Sun region at different spatial resolutions., This allows us to study the very same quiet Sun region at different spatial resolutions.117" In spite of the lower spatial resolution, POLIS and ZIMPOL Observations present a better signal-to-noise ratio, thus allowing the detection of fainter signals."," In spite of the lower spatial resolution, POLIS and ZIMPOL observations present a better signal-to-noise ratio, thus allowing the detection of fainter signals."118" In order to complete the picture, we compare all data sets, although it is fundamental to remind that"," In order to complete the picture, we compare all data sets, although it is fundamental to remind that"119The detection of over 400 planets orbiting Sun-like stars has revolutionised our knowledge of our local neighbourhood and our position therein.,The detection of over 400 planets orbiting Sun-like stars has revolutionised our knowledge of our local neighbourhood and our position therein.120 Yet planets are not the sole close companions to solar-type stars., Yet planets are not the sole close companions to solar-type stars.121 For instance. ?? and ? have examined stellar multiplicity in. a series of papers.," For instance, \citet{duquennoy,duquennoy91} and \citet{duquennoy92} have examined stellar multiplicity in a series of papers."122" Radial-velocity surveys have revealed few brown dwarfs orbiting solar-type stars (e.g. ?:; 2)) leading to the phrase ""brown dwarf desert being coined to describe this paucity (2).", Radial-velocity surveys have revealed few brown dwarfs orbiting solar-type stars (e.g. \citealp{wittenmyer09}; \citealp{jenkins09a}) ) leading to the phrase `brown dwarf desert' being coined to describe this paucity \citealp{marcy}) ).123 However. beyond -4AU one would expect few radial-velocity planetary or brown dwarf companions to be known due to the limited temporal coverage at the required precision levels necessary to fully sample such companions.," However, beyond $\sim$ 4AU one would expect few radial-velocity planetary or brown dwarf companions to be known due to the limited temporal coverage at the required precision levels necessary to fully sample such companions."124 In addition. radial-velocity surveys also have strong biases against the detection of long-period companions. as the radial-velocity amplitude is a strong function of orbital period and also since this technique requires the observation of at least half an orbit (e.g. ?)) to constrain companion properties.," In addition, radial-velocity surveys also have strong biases against the detection of long-period companions, as the radial-velocity amplitude is a strong function of orbital period and also since this technique requires the observation of at least half an orbit (e.g. \citealp{wright07}) ) to constrain companion properties."125 Only now are we sensitive enough to detect solar system-like gas giant planets in solar system-like orbits (e.g. 2))., Only now are we sensitive enough to detect solar system-like gas giant planets in solar system-like orbits (e.g. \citealp{jones10}) ).126 Conversely. direct and coronographic imaging techniques can probe much wider separations than current radial-velocity programs can reach.," Conversely, direct and coronographic imaging techniques can probe much wider separations than current radial-velocity programs can reach."127" For example. ? and ? have directly imaged planetary mass companions to the stars Fomalhaut and HR 8799. located at angular separations of 14.9"" and 1.73”. or H15AU and 68AU. respectively."," For example, \citet{kalas08} and \citet{marois08} have directly imaged planetary mass companions to the stars Fomalhaut and HR 8799, located at angular separations of $''$ and $''$ , or 115AU and 68AU, respectively."128 ? found another deficit of brown dwarf companions between 75-1200 AU., \citet{mccarthy04} found another deficit of brown dwarf companions between 75-1200 AU.129 ? used the Gemini-North and Keck Adaptive Optics (AQ) systems to obtain three epochs of images of the brown dwarf companion to HR 7672. which had initially been detected by its signature.," \citet{liu02} used the Gemini-North and Keck Adaptive Optics (AO) systems to obtain three epochs of images of the brown dwarf companion to HR 7672, which had initially been detected by its signature."130" The flux ratio at 2.16//m was found to be 8.6 magnitudes at a separation of 0.79"".", The flux ratio at $\mu$ m was found to be 8.6 magnitudes at a separation of $''$.131 This level of contrast pushed the instrumentation used 1n this detection to its very limits., This level of contrast pushed the instrumentation used in this detection to its very limits.132 However the introduction of Simultaneous Differential Imaging (SDI) on the VLT's NACO facility permits the achievement of higher contrasts. at smaller separations. for the coolest stellar companions.," However the introduction of Simultaneous Differential Imaging (SDI) on the VLT's NACO facility permits the achievement of higher contrasts, at smaller separations, for the coolest stellar companions."133 For example. contrasts on the order of AH~13 have been demonstrated at ~0.5” by ? and ?..," For example, contrasts on the order of $\Delta$ $\sim$ 13 have been demonstrated at $\sim$ $''$ by \citet{mugrauer} and \citet{biller07}."134 In order to guide the selection of target host stars for adaptive optics imaging of brown dwarfs and exoplanets. we have performed simulations which take the best currently available companion parameters from radial-velocity data sets. combined with host-star age estimates and brown dwarf and exoplanetary interior models. to derive predicted magnitude differences and angular separations on sky.," In order to guide the selection of target host stars for adaptive optics imaging of brown dwarfs and exoplanets, we have performed simulations which take the best currently available companion parameters from radial-velocity data sets, combined with host-star age estimates and brown dwarf and exoplanetary interior models, to derive predicted magnitude differences and angular separations on sky."135 These simulations were performed for all stars in the Anglo-Australian and Keck Planet Searches (for samples see ?.. ?.. ? and references therein). which show a long term radial-velocity profile consistent with an orbiting low-mass companion.," These simulations were performed for all stars in the Anglo-Australian and Keck Planet Searches (for samples see \citealp{jones02a}, \citealp{marcy05a}, \citealp{butler06} and references therein), which show a long term radial-velocity profile consistent with an orbiting low-mass companion."136 Hippareos distance data (?)) 1s available for all these objects (which all lie at distances of less than 100pc)., Hipparcos distance data \citealp{vanleeuwen05}) ) is available for all these objects (which all lie at distances of less than 100pc).137 It should be noted that in most cases. the radial-velocity orbital solutions are not well constrained.," It should be noted that in most cases, the radial-velocity orbital solutions are not well constrained."138 This is largely because the companion orbits are much longer than the monitoring baselines of the surveys. and in some cases because the companion properties have been derived with no inflection in the radial-velocity curve (often referred to in the planet searches as a “liner”).," This is largely because the companion orbits are much longer than the monitoring baselines of the surveys, and in some cases because the companion properties have been derived with no inflection in the radial-velocity curve (often referred to in the planet searches as a “liner”)."139 The fits to both these classes of data produce only semi-major axis lower limits., The fits to both these classes of data produce only semi-major axis lower limits.140 Inaddition. the eccentricities of most of the companions are so," Inaddition, the eccentricities of most of the companions are so"141LISA.,LISA.142 Henee. there may be two classes of EAIRI: the high eecentricity inspiral of a single star. and the zero eccentricity inspiral of a lidally separated binary.," Hence, there may be two classes of EMRI: the high eccentricity inspiral of a single star, and the zero eccentricity inspiral of a tidally separated binary."143 Comparing the ratio of the signals can probe the structure. stellar content. and recent. kinematic history. of the central regions of galaxies.," Comparing the ratio of the signals can probe the structure, stellar content, and recent kinematic history of the central regions of galaxies."144 We would like to acknowledge the support of the Center for Gravitational Wave Physics. which is hiidecd by the National Science Foundation under the cooperative agreement PIIY 01-14375.," We would like to acknowledge the support of the Center for Gravitational Wave Physics, which is funded by the National Science Foundation under the cooperative agreement PHY 01-14375."145 This work was completed with the support of a grant from the NSF. PIIY and.from NASA. ATP NNGO4GU99G. This manuscript was written at the Aspen Center for Physics and KIB would also like to thank the Center and the other participants for their hospitality.," This work was completed with the support of a grant from the NSF, PHY 02-03046, and,from NASA, ATP NNG04GU99G. This manuscript was written at the Aspen Center for Physics and KHB would also like to thank the Center and the other participants for their hospitality."146Two interacting binary stars have been discovered which appear to have orbital periods shorter than teu uinutes: V[07 Vul. with a period of 9.5 πέος (Motchetal.1996:Cropper 1998).. and TAL Cuc. with a xeriod of 5.1 minutes (Ixraeletal.2002).,"Two interacting binary stars have been discovered which appear to have orbital periods shorter than ten minutes: V407 Vul, with a period of 9.5 minutes \citep{Mot96,Cro98}, and HM Cnc, with a period of 5.4 minutes \citep{Isr02}."147. The uniquely short period of 5.1 minutes. if it is the orbital period. inuplies that unmst have formed frou two white dwarts. driven ogether as a result of eravitationalawave radiation.," The uniquely short period of 5.4 minutes, if it is the orbital period, implies that must have formed from two white dwarfs, driven together as a result of gravitational-wave radiation."148 It mav curently be expericucing stable mass transfer hrough Roche-lohe overflow., It may currently be experiencing stable mass transfer through Roche-lobe overflow.149 Because it is potentially so extreme and unique. substantial effort has been put iuto unveiliue ss true nature. but as vot without conclusive results.," Because it is potentially so extreme and unique, substantial effort has been put into unveiling s true nature, but as yet without conclusive results."150 The key observational data show that: (1) there is no evidence for variability on periods other than 5.1 aud 9.5 nuuutes in and VLOT Vul. respectively (Ramsayetal.2000.2002a):: (2) the optical dux maxiua lead the X-ray. maxima by about 90 degrees in both systems (Barrosetal.2007): and (3) the periods are decreasing in both svstcus (Strolumaver2002.2003.2001.2005:Takalaetal.2001:Ixraeletal.200 1).," The key observational data show that: (1) there is no evidence for variability on periods other than 5.4 and 9.5 minutes in and V407 Vul, respectively \citep{Ram00,Ram02a}; (2) the optical flux maxima lead the X-ray maxima by about 90 degrees in both systems \citep{Bar07}; and (3) the periods are decreasing in both systems \citep{Str02,Str03,Str04,Str05,Hak03,Hak04,Isr04}."151. Three competing models have been proposed for V£07 Vul andCuc., Three competing models have been proposed for V407 Vul and.152. One of them. the Intermediate Polar (IP) model predicts that these svstenis are not in fact ultracompact binaries but have rather mundane orbital periods of several hours.," One of them, the `Intermediate Polar (IP)' model, predicts that these systems are not in fact ultracompact binaries but have rather mundane orbital periods of several hours."153 The ultrashort periods then represent the spins of magnetic white dwarfs (Nortonetal. 2001)., The ultrashort periods then represent the spins of magnetic white dwarfs \citep{Nor04}.154. The N-ravs as well as the variable optical flux originate from the accretion flow crashing onto the magnetic poles of the magnetic white dwarf caving part of the accretors spin cycle., The X-rays as well as the variable optical flux originate from the accretion flow crashing onto the magnetic poles of the magnetic white dwarf during part of the accretor's spin cycle.155 The spiu-up of the X-ray and optical periods may be expected since the maguetic white dwarf is accreting matter of high specific augular momentum., The spin-up of the X-ray and optical periods may be expected since the magnetic white dwarf is accreting matter of high specific angular momentum.156 Lhe absence of variability ou the much longer orbital period could be explained if the orbital planes of both svstenis are viewed exactly face-on., The absence of variability on the much longer orbital period could be explained if the orbital planes of both systems are viewed exactly face-on.157 The observed phase offsets between the optical aud N-rax heht-curves are difficult to explain (Nortonetal.2001).. ancl the cussion lines are unusually weal for IPs: in V£07 Vul there appear to be uo enission lines at all (Ramsayetal.2002b:Steeghs 2006).," The observed phase offsets between the optical and X-ray light-curves are difficult to explain \citep{Nor04}, and the emission lines are unusually weak for IPs; in V407 Vul there appear to be no emission lines at all \citep{Ram02b,Ste06}."158 The second. ‘Unipolar Inductor (UI) τούς. is essentiallv a amore energetic version of the JupiterTo system (Wietal.2002:DallOssoct2006.2007).," The second, `Unipolar Inductor (UI)' model, is essentially a more energetic version of the Jupiter–Io system \citep{Wu02,Dal06,Dal07}."159. A inaguctic white dwarf is orbited by another. nou-magnetic one: the magnetic field induces an electrical poteutial across the non-magnetic white dwart which sets up currents along magnetic flux tubes connectiue the," A magnetic white dwarf is orbited by another, non-magnetic one; the magnetic field induces an electrical potential across the non-magnetic white dwarf which sets up currents along magnetic flux tubes connecting the"160aud by tlie central difference as in case of the uniform grid.,and by the central difference as in case of the uniform grid.161 Note that the gravity is evaluated oi the cell surface., Note that the gravity is evaluated on the cell surface.162 Equatious (11)) through (16)) need to be moclilied near the grid boundary., Equations \ref{dpoisson2}) ) through \ref{dpoisson4}) ) need to be modified near the grid boundary.163 We set the coucition that the gravity evaluated in the coarse grid is equal to the average gravity ou the smaller cel surfaces. e.g.. This eusures that our solution satisfies the Catss’s theorem.," We set the condition that the gravity evaluated in the coarse grid is equal to the average gravity on the smaller cell surfaces, e.g., This ensures that our solution satisfies the Gauss's theorem."164 When we stun up the uormal component of the gravity over the surface of a given volume. it equals to the mass contained in the volume multiplied by Li.," When we sum up the normal component of the gravity over the surface of a given volume, it equals to the mass contained in the volume multiplied by $ 4 \pi G $."165" In other words. the gravitational fiekl liue"" never euds at the grid level boundary."," In other words, the gravitational field line” never ends at the grid level boundary."166 This is also equivalent to set the Neumann coudition at the grid level boundary., This is also equivalent to set the Neumann condition at the grid level boundary.167 When the cell surface is on the eerid level boundary. we interpolate © in the coarse egrid to evaluate the gravity across the cell surface.," When the cell surface is on the grid level boundary, we interpolate $ \phi $ in the coarse grid to evaluate the gravity across the cell surface."168 As an example we show the interpolation formula to compute the gravity iu the :r-direction in the following., As an example we show the interpolation formula to compute the gravity in the $ x $ -direction in the following.169" When?=.V/2—1. we evaluate where 65a(t]4,5id denotes the gravitational⋅ poteutial⋅ at Grey.;2) = pUnaj=D6fives1)y,0.Bn "," When $ i \, = \, N/2 \, - \, 1$, we evaluate where $ \phi _{i+3/2,j,k} ^{*(\ell)} $ denotes the gravitational potential at $ (x, \, y, \, z) $ = $ \lbrack x _{i+3/2} ^{(\ell)} \, \equiv \,170x _{(i+1)/2} ^{(\ell-1)}, \, y _j ^{(\ell)}, \, z _k ^{(\ell)} 171\rbrack $."172[t is obtained by the interpolation ou the diagonal in tlie coarse cell surface., It is obtained by the interpolation on the diagonal in the coarse cell surface.173 When j aud A are odd numbers. it is evaluated to be," When $ j $ and $ k $ are odd numbers, it is evaluated to be"174The observation. of Stokes profiles iu spectral lines are ao valuable tool to inter information about the henuodvuanuical aud nagnetie properties of the solar asma.,The observation of Stokes profiles in spectral lines are a valuable tool to infer information about the thermodynamical and magnetic properties of the solar plasma.175 This information 1s cucoded in the amplitude aud he shape of the Stokes profiles., This information is encoded in the amplitude and the shape of the Stokes profiles.176 Therefore. it is importaut o avoid any effect that perturbs the shape because it can crucially mocify the iuforiation encoded iu the profile.," Therefore, it is important to avoid any effect that perturbs the shape because it can crucially modify the information encoded in the profile."177 Of special relevance is the asvuuuectry of the circular »olarization profile. which is kuown to )o related to the correlation vetween velocity and maeuetic field eracdicuts along the linc-of-siel: (LOS:Illiusetal.1975).," Of special relevance is the asymmetry of the circular polarization profile, which is known to be related to the correlation between velocity and magnetic field gradients along the line-of-sight \citep[LOS;][]{illing75}."178. This effect has been exploited o build atinospheric models with such eradieuts to explain asvuunetres around magnetic flux concentrations (Solanki&Pahllke1988:Cirossniiuii-&Monutavon 1993).," This effect has been exploited to build atmospheric models with such gradients to explain asymmetries around magnetic flux concentrations \citep{solanki88,grossman_doerth88,sanchez_almeida89,solanki93}."179". The situation is especially relevant iu the weakIvAuagnuetize zones of the quiet Sun away from active regions. where Stokes V. profiles present a virietv of shapes"" with strouglv asvuuuetric profiles (Siegwarthetal.2 H1)."," The situation is especially relevant in the weakly-magnetized zones of the quiet Sun away from active regions, where Stokes $V$ profiles present a variety of shapes with strongly asymmetric profiles \citep{sigwarth99,sanchez_almeida00,khomenko03,socas_pillet_lites04,marian08,viticchie_1_11,viticchie_2_11}."180. Earth-based observations are abwavs affected by the disturbing effect of the atmosphere., Earth-based observations are always affected by the disturbing effect of the atmosphere.181 As a conseque1ce. the diffraction limut of the telescope is practically never reached.," As a consequence, the diffraction limit of the telescope is practically never reached."182 It is often impossible to overcome the D Bit if the observations are not accompanied by an adaptive optics svstem and powerful post-processing mcthocds.," It is often impossible to overcome the 1"" limit if the observations are not accompanied by an adaptive optics system and powerful post-processing methods."183 For this reason. Khonmoeukoetal.(2005) and Shelvaeetal.(2007) analyze the effect of spatial simcaring on the Stokes asviunetries observed iu the pair of Fe lines at 630 nii ancl a 1565 nu.," For this reason, \cite{khomenko_shelyag05} and \cite{shelyag07} analyzed the effect of spatial smearing on the Stokes asymmetries observed in the pair of Fe lines at 630 nm and at 1565 nm."184 They concluded that asviuuetnes are heavilv disturbed by the lack of spatial resolution., They concluded that asymmetries are heavily disturbed by the lack of spatial resolution.185 They even discovered that it is possible to fiud regions in which the fiek polarity is different iu the two spectral regious (SanchezAlmeidaetal.2003:Rezaci 2007).. something fully attributed to the lack of spatial resolution.," They even discovered that it is possible to find regions in which the field polarity is different in the two spectral regions \citep{sanchez_almeida03,rezaei07}, something fully attributed to the lack of spatial resolution."186 The fundamental reason is that the shape of Stokes V. profiles in wealshy-imaenetized regions are verv coniplex a1 they change iu scales πιο smaller than the resolution clement of the largest Earth-based telescopes even in the ivpothetical abseuce of atinospliere., The fundamental reason is that the shape of Stokes $V$ profiles in weakly-magnetized regions are very complex and they change in scales much smaller than the resolution element of the largest Earth-based telescopes even in the hypothetical absence of atmosphere.187 Even if the telescope is put in a balloon at 10 au height Like Suurise (Solankietal.2010).. there Is sole renidniuse atmosphere (albeit small) which. ogether with he intrinsic aberrations of the telescope aud iustrunenuts. can modify the observations.," Even if the telescope is put in a balloon at 40 km height like Sunrise \citep{sunrise10}, there is some remaining atmosphere (albeit small) which, together with the intrinsic aberrations of the telescope and instruments, can modify the observations."188 For this reason. he IMaX iustrument ouboard Sunrise was designed to use he plase-diversity post-facto reconstruction algorithui (ασιαetal.1992VargasDoutuenez20093.," For this reason, the IMaX instrument onboard Sunrise was designed to use the phase-diversity post-facto reconstruction algorithm \citep{paxman92,santiago_vargas09}."189. Tn this PCV. we focus on the interesting problem of testing row the spatial aud spectral degradation produced by the Sunise/IMaX combination affects circular polarization asvuuuetrics aud if the post-recoustiuction aleorithuis can jclp us extract reliable information (comparable to the unperturbed svuthetic case) about them from degraded data.," In this paper, we focus on the interesting problem of testing how the spatial and spectral degradation produced by the Sunrise/IMaX combination affects circular polarization asymmetries and if the post-reconstruction algorithms can help us extract reliable information (comparable to the unperturbed synthetic case) about them from degraded data."190 To this cud. we use profiles svuthesized on 3D nodels of the solar photosphere.," To this end, we use profiles synthesized on 3D models of the solar photosphere."191 We degrade them to simulate the observational conditions of σαΊκοΤλ[αδ aud reconstruct the images using the phase-diversity algoritlin., We degrade them to simulate the observational conditions of Sunrise/IMaX and reconstruct the images using the phase-diversity algorithm.192 The snapshots that we have used correspond to individual time steps of a 3D maeneto-bydrodvuamical simulation of solar magneto-convectiou done with the MURAM code (Voeler2003:Voeleretal.2005:Cameron2011).," The snapshots that we have used correspond to individual time steps of a 3D magneto-hydrodynamical simulation of solar magneto-convection done with the MURAM code \citep{vogler_thesis03,vogler05,cameron_11}."193. Au initially vertical maguetic field of 200 CC streugth was introduced into already developed purely lvdrodvuaimical convection., An initially vertical magnetic field of 200 G strength was introduced into already developed purely hydrodynamical convection.194 The simulation box was split iuto 1 parts with the opposite polarities of the maguetic field in the adjaceut parts., The simulation box was split into 4 parts with the opposite polarities of the magnetic field in the adjacent parts.195 This magnetic field evolved self-consisteutlv. with convective motions., This magnetic field evolved self-consistently with convective motions.196 The redistribution of the magnetic field led to almost expoucutial decrease with time of its average unsigned value over the simulation domain., The redistribution of the magnetic field led to almost exponential decrease with time of its average unsigned value over the simulation domain.197 The snapshots used in the present work were taken 17. 36 and 112 minutes after the magnetic field was introduced.," The snapshots used in the present work were taken 17, 36 and 112 minutes after the magnetic field was introduced."198 At these time moments. the average unsigned magnetic," At these time moments, the average unsigned magnetic"199the total angular momentum of the star).,the total angular momentum of the star).200 Again solving for the conserved angular momentum. we find giving at the surface of the star. where we presume the particle is initially rotating with the spin of the star. and write the moment of inertia 727/0.," Again solving for the conserved angular momentum, we find giving at the surface of the star, where we presume the particle is initially rotating with the spin of the star, and write the moment of inertia $I=J/\Omega$."201 For the rapidly-rotating case. we consider the general metric for an axisymmetric stationary star. where the metric potentials p.5.o and w depend only on the coordinates + and 0.," For the rapidly-rotating case, we consider the general metric for an axisymmetric stationary star, where the metric potentials $\rho, \gamma, \alpha$ and $\omega$ depend only on the coordinates $\bar{r}$ and $\theta$."202 The coordinate r isrelated to the Schwarzschild coordinate r by r=rexp(i(5—p). so. that 2zrsinÜ is the circumference of a circle with constant 7 and 0.," The coordinate $\bar{r}$ isrelated to the Schwarzschild coordinate $r$ by $r =203\bar{r} \exp(\frac12(\gamma-\rho))$, so that $2 \pi r \sin \theta$ is the circumference of a circle with constant $\bar{r}$ and $\theta$."204 For further details about the interpretation of these coordinates and potentials. see Friedman. Ipser Parker (1986) and Morsink Stella (1999).," For further details about the interpretation of these coordinates and potentials, see Friedman, Ipser Parker (1986) and Morsink Stella (1999)."205 Given an equation of state. a mass and a rotation rate. the metric (15)) can be solved numerically.," Given an equation of state, a mass and a rotation rate, the metric \ref{rapid}) ) can be solved numerically."206 We use a code written by N.Stergioulas.. which assumes rigid rotation and is based on methods developed by Komatsu. Eriguchi Hachisu (1989) and Cook. Shapiro Teukolsky (1994).," We use a code written by N., which assumes rigid rotation and is based on methods developed by Komatsu, Eriguchi Hachisu (1989) and Cook, Shapiro Teukolsky (1994)."207 We present the properties of some rapidly-rotating models in Table 1., We present the properties of some rapidly-rotating models in Table 1.208 We consider two different equations of state (EOS). EOS L which is stiff and EOS APR which is softer.," We consider two different equations of state (EOS), EOS L which is stiff and EOS APR which is softer."209 EOS L (Pandharipande Smith 1975) is one of the stiffest EOS in the Arnett Bowers (1977) catalogue., EOS L (Pandharipande Smith 1975) is one of the stiffest EOS in the Arnett Bowers (1977) catalogue.210 EOS APR is the model Al8+év+UIX* computed by Akmal. Pandharipande Ravenhall (1998) which uses modern nucleon scattering data and first order special relativistic corrections.," EOS APR is the model $\delta v$ +UIX* computed by Akmal, Pandharipande Ravenhall (1998) which uses modern nucleon scattering data and first order special relativistic corrections."211 For each EOS. we consider two different masses. M=1.4M. and 2.0M... and two spin frequencies. 7=300Hz and 600Hz.," For each EOS, we consider two different masses, $M=1.4\ M_\odot$ and $2.0\ {\rm212M_\odot}$, and two spin frequencies, $\nu=300\ {\rm Hz}$ and $600\213{\rm Hz}$."214 The last column in Table | gives the break-up spin frequency in each case., The last column in Table 1 gives the break-up spin frequency in each case.215 We work in the equatorial plane. and do not consider the variations of the metric potentials with latitude.," We work in the equatorial plane, and do not consider the variations of the metric potentials with latitude."216 The specific angular momentum is (see also Morsink Stella 1999) where the three-velocity of à corotating particle as measured by a zero angular momentum observer is given by Again holding L constant as we vary the Schwarzschild coordinate radius r. we find where R is the equatorial radius ofthe star. subscripts denote partial differentiation and all quantities are evaluated at the equator.," The specific angular momentum is (see also Morsink Stella 1999) where the three-velocity of a corotating particle as measured by a zero angular momentum observer is given by Again holding $L$ constant as we vary the Schwarzschild coordinate radius $r$, we find where $R$ is the equatorial radius ofthe star, subscripts denote partial differentiation and all quantities are evaluated at the equator."217 In the slow rotation limit. equations (16)) and (18) reduce to equations (13)) and (14)).," In the slow rotation limit, equations \ref{eq:fastL}) ) and \ref{eq:fast}) ) reduce to equations \ref{eq:slowL}) ) and \ref{eq:slow}) )."218 Heyl (2000) recently calculated InO/dInr. with a rather different result (compare our eq. [14]]," Heyl (2000) recently calculated $d\ln\Omega/d\ln r$, with a rather different result (compare our eq. \ref{eq:slow}] ]"219 with his eq. [, with his eq. [22010].,10]).221 However. Abramowiez et al. (," However, Abramowicz et al. ("2222001) point out a sign error inHeyl’s ealeulation. and. more importantly. that Heyl assumes that the quantity L/E is conserved. as. for example. a particle in orbit CAbramowiez Prasanna 1990).,"2001) point out a sign error inHeyl's calculation, and, more importantly, that Heyl assumes that the quantity $L/E$ is conserved, as, for example, a particle in orbit (Abramowicz Prasanna 1990)."223 However. the energy E of a fluid element in the atmosphere is not conserved during the burst.," However, the energy $E$ of a fluid element in the atmosphere is not conserved during the burst."224 The correct conserved quantity. which we have considered in this section. is the angular momentum per particle L.," The correct conserved quantity, which we have considered in this section, is the angular momentum per particle $L$."225 In the slow rotation approximation. our result (eq. [14]])," In the slow rotation approximation, our result (eq. \ref{eq:slow}] ])"226 agrees with equation (9) of Abramowiez et al. (, agrees with equation (9) of Abramowicz et al. (2272001).,2001).228 We write dInO/dInr as —2.3. where is unity in the Newtonian limit.," We write $d\ln\Omega/d\ln r$ as $-2\beta$, where is unity in the Newtonian limit."229 We give the value of in Table |.., We give the value of $\beta$ in Table \ref{tab:models}.230 Figure 2. shows } as a function of neutron star mass for EOS APR and EOS L. and for v=300 and 600Hz.," Figure \ref{fig:beta} shows $\beta$ as a function of neutron star mass for EOS APR and EOS L, and for $\nu=300$ and $600\231{\rm Hz}$."232 We see that including the general relativistic angular momentum conservation law changes dInO/dInr by5-10%., We see that including the general relativistic angular momentum conservation law changes $d\ln\Omega/d\ln r$ by.233. In this section. we present calculations of the expansion and spin-down of the atmosphere. including the effects of general relativity and rapid rotation.," In this section, we present calculations of the expansion and spin-down of the atmosphere, including the effects of general relativity and rapid rotation."234 In the spirit of CB. we ignore latitudinal variations. and work in the equatorial plane.," In the spirit of CB, we ignore latitudinal variations, and work in the equatorial plane."235 First. ins 4.1. we discuss the effects of general relativity on the equations describing the hydrostatic and thermal structure of the atmosphere. and calculate the reduction in gravity at the equator due to rapid rotation.," First, in 4.1, we discuss the effects of general relativity on the equations describing the hydrostatic and thermal structure of the atmosphere, and calculate the reduction in gravity at the equator due to rapid rotation."236 In $4.2. we show how to include the general relativistic angular momentum conservation law that we obtained in 83.," In 4.2, we show how to include the general relativistic angular momentum conservation law that we obtained in 3."237 In $4.3. we rescale our fiducial results of $2 for the spin-down of a rigidly-rotating atmosphere to different masses. equations of state. and spin frequencies.," In 4.3, we rescale our fiducial results of 2 for the spin-down of a rigidly-rotating atmosphere to different masses, equations of state, and spin frequencies."238" In 84.4, we relax the assumption of rigid-rotation. and present the rotational profiles of the atmosphere for several different cases."," In 4.4, we relax the assumption of rigid-rotation, and present the rotational profiles of the atmosphere for several different cases."239 We now write down the differential equations describing the hydrostatic and thermal structure of the atmosphere including general relativity. and compare them to the Newtonian equations.," We now write down the differential equations describing the hydrostatic and thermal structure of the atmosphere including general relativity, and compare them to the Newtonian equations."240" We start by considering a non-rotating star. and then discuss the additional effects of rotation,"," We start by considering a non-rotating star, and then discuss the additional effects of rotation."241" For a spherical star. Thorne (1977) (see also Thorne 1967) gives the equation for mass conservation as where M, is the rest mass (number of baryons multiplied by baryon rest mass) within coordinate radius r. p is the rest mass density. and V ts the ""volume redshift factor."," For a spherical star, Thorne (1977) (see also Thorne 1967) gives the equation for mass conservation as where $M_r$ is the rest mass (number of baryons multiplied by baryon rest mass) within coordinate radius $r$, $\rho$ is the rest mass density, and ${\mathcal V}$ is the “volume redshift factor”."242 For slow rotation. Vir2(12MG3/r7. where Mtr) is the gravitational mass interior to 7.," For slow rotation, ${\mathcal V}(r)=(1-2M(r)/r)^{-1/2}$, where $M(r)$ is the gravitational mass interior to $r$ ."243 We adopt a plane parallel approximation in. the thin envelope. and write rZRF z/V. where =<R is the proper length.," We adopt a plane parallel approximation in the thin envelope, and write $r=R+z/{\mathcal V}$ , where $z\ll R$ is the proper length."244 Here. Y is the redshift factor at the surface of the star V= V(R).," Here, ${\mathcal V}$ is the redshift factor at the surface of the star ${\mathcal V}={\mathcal245V}(R)$ ."246" We define the rest mass column depth dy2 —M,/AzR.", We define the rest mass column depth $dy=-dM_r/4\pi R^2$ .247Because gravitational wave observatories like the (LISA) are expected to give approximate source localization clavs or even weeks in advance of merger (7).. one could hope for svnergistic observing campaiens (hat might catch the entire EM signal.,"Because gravitational wave observatories like the (LISA) are expected to give approximate source localization days or even weeks in advance of merger \citep{LH09}, one could hope for synergistic observing campaigns that might catch the entire EM signal."248 Alternatively. it may be feasible to use EM surveys with large solid-angle coverage to search for source Haring having the characteristics predicted here in order to identifv candidate black hole merger svstems before any gravitational wave detectors are ready.," Alternatively, it may be feasible to use EM surveys with large solid-angle coverage to search for source flaring having the characteristics predicted here in order to identify candidate black hole merger systems before any gravitational wave detectors are ready."249 The spectrum of this light is. at present. much more difficult than its huninositv (o predict with anv degree of confidence.," The spectrum of this light is, at present, much more difficult than its luminosity to predict with any degree of confidence."250 It may peak in the ultraviolet. but if it does. it is likely to be rather bluer than the familiar UV-peaking spectra of AGN (if the spectrum does peak in the UV. extinction in the host galaxy may obscure some nunber events).," It may peak in the ultraviolet, but if it does, it is likely to be rather bluer than the familiar UV-peaking spectra of AGN (if the spectrum does peak in the UV, extinction in the host galaxy may obscure some number events)."251 While the inner region still shines. its huminositv will likely be greater than that [rom greater radii. making the spectrum (to the degree it is (hermalizecd) closer to that of a single-temperature svslem.," While the inner region still shines, its luminosity will likely be greater than that from greater radii, making the spectrum (to the degree it is thermalized) closer to that of a single-temperature system."252 If it is only incompletely thermalized. a still harder spectrum night be expected.," If it is only incompletely thermalized, a still harder spectrum might be expected."253" At later times. when the outer disk dominates. the temperature corresponding (o a given radius is xnl?(rfr,)!ZI, (?).."," At later times, when the outer disk dominates, the temperature corresponding to a given radius is $\propto \eta^{1/8} (r/r_g)^{-1/2} M_7^{1/4}$ \citep{MP05}."254CY 2201-32 was observed bv the Chandra N-Bav Observatory with the ACIS-I instrament for 50.16 ks in 2000 July as part of the observation of the WCC90 field (PI Both).,CY 2201-32 was observed by the $Chandra$ X-Ray Observatory with the ACIS-I instrument for 50.16 ks in 2000 July as part of the observation of the HCG90 field (PI Bothum).255 We retrieved this inage from the archive and analyzed it using standard techuiques with the CIAO package (Castanderetal.2003a.. Του).," We retrieved this image from the archive and analyzed it using standard techniques with the CIAO package \citealt{Castander03a}, T05)."256 CY 2201-32 was detected in the soft baud (0.5-2.0 keV) with 11.6 + 3.9 counts aud undetected in the hard baud (2.0-8.0 keV)., CY 2201-32 was detected in the soft band (0.5-2.0 keV) with 11.6 $\pm$ 3.9 counts and undetected in the hard band (2.0-8.0 keV).257 We computed anX-ray flux of 10 Pere 2s Land N-vay luninosity of 10H cre Lan the soft band (T05)., We computed anX-ray flux of $f_x = 1.06 \times 10^{-15}$ erg $^{-2}$ $^{-1}$ and X-ray luminosity of $L_x = 1.49 \times 10^{44}$ erg $^{-1}$ in the soft band (T05).258 As part of the CYDER survey we imaged the CYDER D1 field CTO5) with the Cerro Tololo Iuter-Aunericau Observatory (CTIO) lin telescope using the Mosaic II camera in 2001 August., As part of the CYDER survey we imaged the CYDER D1 field (T05) with the Cerro Tololo Inter-American Observatory (CTIO) 4m telescope using the Mosaic II camera in 2001 August.259 We took images for a total of 6600 and 1800s in the V. and 7 bands. reaching limiting magnitudes of V—26.7 and JI=25.1 and effective secings of 1.07 and 0.97. respectively.," We took images for a total of 6600 and 1800s in the $V$ and $I$ bands, reaching limiting magnitudes of $V=26.7$ and $I=25.1$ and effective seeings of 1.0” and 0.9”, respectively."260 CY 2201-3201 appears iu these CTIO images as au edee-on spiral with a very bright uucleus/bulee with a total nieasured maguitude of Vynya=21.26 aud Liga=19.9L.? Ou 2003 October 31. we took spectra of the Nav optical counterparts in the CYDER DI field with the UTI VET FORS2 instrument.," CY 2201-3201 appears in these CTIO images as an edge-on spiral with a very bright nucleus/bulge with a total measured magnitude of $V_{Vega}=21.26$ and $I_{Vega}=19.94$ On 2003 October 31, we took spectra of the X-ray optical counterparts in the CYDER D1 field with the UT4 VLT FORS2 instrument."261 We used the 300V exisii which gives a resolution of R~520 (10.5 A) for our Ἱ shits., We used the 300V grism which gives a resolution of $R\sim 520$ (10.5 ) for our 1” slits.262 CY2201-3201 was observed in one of our masks., CY2201-3201 was observed in one of our masks.263 Given the multi-object purpose of the masks. all slits were oricuted uortl-south.," Given the multi-object purpose of the masks, all slits were oriented north-south."264" We took five exposures of 1800 x in secius condition of 0.50-0.75"" and bright/erey sky conditions.", We took five exposures of 1800 s in seeing condition of 0.50”-0.75” and bright/grey sky conditions.265 We reduced the spectra using standard routines., We reduced the spectra using standard routines.266 Surprisinely. for this source we found two spectra of à QSO at a redshift of 223.90 iu our best seciue spectra (sce Fig. 1)).," Surprisingly, for this source we found two spectra of a QSO at a redshift of z=3.90 in our best seeing spectra (see Fig. \ref{fig1}) )."267 The two QSO spectra were bleuded iu our worse secing exposures., The two QSO spectra were blended in our worse seeing exposures.268 Our 30 s mask. acquisition nage taken with a ποστς of 0.157 confirmed the existence of two point sources close to the ceuter of the edge-ou spiral galaxy. aud therefore confined the lensing nature of the svsteun.," Our 30 s mask acquisition image taken with a seeing of 0.45” confirmed the existence of two point sources close to the center of the edge-on spiral galaxy, and therefore confirmed the lensing nature of the system."269 We observed the CY 2201-3201 svstemi with the Magellan Clay telescope using the MagIC instrament ou 20014 September 8., We observed the CY 2201-3201 system with the Magellan Clay telescope using the MagIC instrument on 2004 September 8.270 MagIC has a pixel scale of 0.06917 pixel|., MagIC has a pixel scale of 0.0691” $^{-1}$.271 We took a socries of 300 s exposures in three filters (SDSS yg. r aud /) for a total of 1800. 2100. and 15800 s in the g. r aud / filters respectively.," We took a series of 300 s exposures in three filters (SDSS $g$, $r$ and $i$ ) for a total of 1800, 2400, and 1800 s in the $g$ , $r$ and $i$ filters respectively."272"Of course, the capability to measure II and y for X-rays may be many years away, but that technology is being developed.","Of course, the capability to measure $\Pi$ and $\chi$ for X-rays may be many years away, but that technology is being developed."273" For example, several X-ray polarimetry missions have already been studied and proposed to open up this very promising field of research over the next few years."," For example, several X-ray polarimetry missions have already been studied and proposed to open up this very promising field of research over the next few years."274 The most advanced project today—the Gravity and Extreme Magnetism (GEM) mission (Swank et al., The most advanced project today—the Gravity and Extreme Magnetism (GEM) mission (Swank et al.275" 2010), is planned for launch in 2014, with the primary goal of studying the polarimetric properties of the soft X-ray emission from bright black holes and neutron stars."," 2010), is planned for launch in 2014, with the primary goal of studying the polarimetric properties of the soft X-ray emission from bright black holes and neutron stars."276" Unfortunately, the GEM instruments will not be sensitive enough to study a relatively weak source, such as Sgr A*."," Unfortunately, the GEM instruments will not be sensitive enough to study a relatively weak source, such as Sgr A*."277" Indeed, for fluxes less than 1 milliCrab (the intensity reached by Sgr A* at the peak of the brightest flares), GEM would need a net observing time of more than 100 ks to detect a polarization fraction of or lower."," Indeed, for fluxes less than 1 milliCrab (the intensity reached by Sgr A* at the peak of the brightest flares), GEM would need a net observing time of more than 100 ks to detect a polarization fraction of or lower."278" But Sgr A*'s flares never last longer than 3 hr, so it would not be feasible to obtain such a deep exposure."," But Sgr A*'s flares never last longer than 3 hr, so it would not be feasible to obtain such a deep exposure."279" Moreover GEM, and even other future polarimetry projects, such as POLARIX (Costa et al."," Moreover GEM, and even other future polarimetry projects, such as POLARIX (Costa et al."280" 2010), could not provide angular resolutions better than ~1’, making it very difficult to identify the origin of a polarized signal from a crowded region, such as we have at the galactic center."," 2010), could not provide angular resolutions better than $\sim 1^\prime$, making it very difficult to identify the origin of a polarized signal from a crowded region, such as we have at the galactic center."281" Nonetheless, this field is only in its infancy."," Nonetheless, this field is only in its infancy."282" More promising missions, with better sensitivity and spatial resolution, will no doubt follow in the years to come."," More promising missions, with better sensitivity and spatial resolution, will no doubt follow in the years to come."283 And our results demonstrate the power of future simultaneous polarimetric observations in both the NIR and X-ray portions of the spectrum., And our results demonstrate the power of future simultaneous polarimetric observations in both the NIR and X-ray portions of the spectrum.284 This research was supported by NASA grant NNX08AX34G at the University of Arizona., This research was supported by NASA grant NNX08AX34G at the University of Arizona.285 Partial support was also provided by ONR grant N00014-09-C-0032., Partial support was also provided by ONR grant N00014-09-C-0032.286" In addition, FM is grateful to Amherst College for its support through a John Woodruff Simpson Lectureship."," In addition, FM is grateful to Amherst College for its support through a John Woodruff Simpson Lectureship."287" We also acknowledge the International Space Science Institute (ISSI) in Bern, where a large portion of this work was carried out."," We also acknowledge the International Space Science Institute (ISSI) in Bern, where a large portion of this work was carried out."288nunethod applied iu fjs wav gives us daa points with ligh spatial and velocity resolution over a Major fraction of the galaxy disk. aud our results demonstrate that. with caution. the uuuethod can be applied to deliver reliable pattern speeds in disk galaxies.,"method applied in this way gives us data points with high spatial and velocity resolution over a major fraction of the galaxy disk, and our results demonstrate that, with caution, the method can be applied to deliver reliable pattern speeds in disk galaxies."289 Although very simple. the radial tests that we have described in section Li) have proven useful to ect a first order estimation of a possible secondary pattern speed.," Although very simple, the radial tests that we have described in section \ref{sec:radius} have proven useful to get a first order estimation of a possible secondary pattern speed."290 Fie., Fig.291 7 shows that the pattern speeds decline steadilv as larger sections of the field are covered. aud exactly how much of the disk needs to be covered to get reliable values depends verv strongly on the size of the bars aud/or spiral aris.," \ref{fig:radialOpvalues} shows that the pattern speeds decline steadily as larger sections of the field are covered, and exactly how much of the disk needs to be covered to get reliable values depends very strongly on the size of the bars and/or spiral arms."292 Assundug that the epievclic approximation can be used. the pattern speeds can be used to identify resonances. such as the ILB. in our sample galaxies.," Assuming that the epicyclic approximation can be used, the pattern speeds can be used to identify resonances, such as the ILR, in our sample galaxies."293 The presence of au ILR does not alone imply a decoupling of the region inside it. however. au ILR is necessary for a decoupling of nested bars (e...7).," The presence of an ILR does not alone imply a decoupling of the region inside it, however, an ILR is necessary for a decoupling of nested bars \citep[e.g.,][]{EnglmaierShlosman2004}."294 We do trust the presence of secondary pattern speeds based on a combination of the radial behaviour of the (VoGosin(/). the presencethe ILR. aud the preseuce of morphologicallyf distinct featuresof such as an inner bar.," We do trust the presence of secondary pattern speeds based on a combination of the radial behaviour of the $\langle V\rangle / \langle x\rangle/\sin(i)$, the presence of the ILR, and the presence of morphologically distinct features such as an inner bar."295 Iu galaxies without au ILR. we do not claim the preseuce of a secondary pattern speed. thus. once certain of the mere presence of a secondary patteri speed. its presence can be confirmed using the full slit coverage but only for slits falling iu the region corresponding to the exteut of the immer bar.," In galaxies without an ILR, we do not claim the presence of a secondary pattern speed, thus, once certain of the mere presence of a secondary pattern speed, its presence can be confirmed using the full slit coverage but only for slits falling in the region corresponding to the extent of the inner bar."296 The uuuceric value of the secoudary pattern speed. ou the other side. is far more uncertain.," The numeric value of the secondary pattern speed, on the other side, is far more uncertain."297 We confirm our previous results from ? and since the nucertaimtics in deriving the secondary patter speeds are as large as50%... we do not include the values here. jowever. we note that the detected secondary patterus are of the order of two to three tines higher than the uain pattern speeds.," We confirm our previous results from \citet{Fathietal2007TW} and since the uncertainties in deriving the secondary pattern speeds are as large as, we do not include the values here, however, we note that the detected secondary patterns are of the order of two to three times higher than the main pattern speeds."298 Similar demonstrations have been srescnted in previous studies by 2?7?.. and ?..," Similar demonstrations have been presented in previous studies by \citet{Corsinietal2003, Hernandezetal2005TW, Emsellemetal2006}, and \citet{Fathietal2007TW}."299 Overall the results from applving the umoethod onu the naps of LO late-tvpe spiral galaxies can be listed as ollows: Tn six galaxies 23312. NGC22103. 11201. 11519. 66916. 77179. and ‘TT we have directlv derived the oof the main bar. aud in four galaxies LLS19. 55371. 55921. and 55961) we have been able to derive the oof the spiral anus.," Overall the results from applying the method on the maps of 10 late-type spiral galaxies can be listed as follows: In six galaxies 342, 2403, 4294, 4519, 6946, 7479, and 7741), we have directly derived the of the main bar, and in four galaxies 4519, 5371, 5921, and 5964) we have been able to derive the of the spiral arms."300Ὃν Dynamically. bars iud spiral arius can interact directly when they are corotating (6.8.NGC1365:7)... or by uneans of non-luear mode coupling in which case the r(€R) of the bar and the ILR of he spiral arms overlap (e.g...—77).," Dynamically, bars and spiral arms can interact directly when they are corotating \citep[e.g., NGC\,1365; ][]{Lindblad1999}, or by means of non-linear mode coupling in which case the $r(CR)$ of the bar and the ILR of the spiral arms overlap \citep[e.g., ][]{Taggeretal1987, MassetTagger1997}."301 In two galaxies 55921. and 55961) we have found that the MCR) of the spiral structure roughly coincides with he r(CR) of the bir. which suggests a rich variety of resonant interaction that have been predicted by theory. aud our derived να conplement the values for 10 Iate-ype barred spiral galaxies iu excellent agrecmieut with Os from αποΊσα] simulations using a live dark matter ralo or modified eravity.," In two galaxies 5921 and 5964) we have found that the $r(CR)$ of the spiral structure roughly coincides with the $r(CR)$ of the bar, which suggests a rich variety of resonant interaction that have been predicted by theory, and our derived s complement the values for 10 late-type barred spiral galaxies in excellent agreement with s from numerical simulations using a live dark matter halo or modified gravity."302 We use epicvclic approximation. as commonly used in models. to identify the location of the resonances iu our sample galaxies.," We use epicyclic approximation, as commonly used in models, to identify the location of the resonances in our sample galaxies."303 Three of our ten late-type spirals 11519. 66916. 77711) show evidence for au ILB. two of which suggest the presence of a secondary pattern speed.," Three of our ten late-type spirals 4519, 6946, 7741) show evidence for an ILR, two of which suggest the presence of a secondary pattern speed."304 Iu all three galaxies. the rotation curve shows a clear presence of a amore rapidly rotating coniponeut within the ILR. sugeesting that they harbour substantial amounts of the interstellar medium iu the ceutral regions.," In all three galaxies, the rotation curve shows a clear presence of a more rapidly rotating component within the ILR, suggesting that they harbour substantial amounts of the interstellar medium in the central regions."305 In all three cases. the vvolocitv dispersion is higher imside the ILR with a steep rise toward the nucleus.," In all three cases, the velocity dispersion is higher inside the ILR with a steep rise toward the nucleus."306 The combination of these two observational features supports the idea that the thickening of the gaseous component iu the central region could build a bulec-like component in late-tvpe spirals (sce also Paper I)., The combination of these two observational features supports the idea that the thickening of the gaseous component in the central region could build a bulge-like component in late-type spirals (see also Paper I).307 We note however that in strong bars such as in 7711. epicvelic approximation could break down. aud consequently. the location of resonances would not be valid.," We note however that in strong bars such as in 7741, epicyclic approximation could break down, and consequently, the location of resonances would not be valid."308 The preseut paper is the second iu a series in which we will pursue detailed dyuaiical analysis of late-type spiral ealaxies., The present paper is the second in a series in which we will pursue detailed dynamical analysis of late-type spiral galaxies.309 Our current results will be complemented with a full harmonic analysis of the velocity fields followed bv detailed nmuuerical smnulations. aud mere detailed estimates of the svsteinatic effects due to noun-coutiuuitv in the ccluitting eas by applviug the nuuethod to lieh resolution simulations.," Our current results will be complemented with a full harmonic analysis of the velocity fields followed by detailed numerical simulations, and more detailed estimates of the systematic effects due to non-continuity in the emitting gas by applying the method to high resolution simulations."310 Furthermore. a conbination of these information with a robust estimation of the bar aud spiral streusths could help us to better understaud the evolution of structure in spiral ealaxies.," Furthermore, a combination of these information with a robust estimation of the bar and spiral strengths could help us to better understand the evolution of structure in spiral galaxies."311 We thank the anonviuous referee for insightful cohbunents which helped us clarify some miportaut pots, We thank the anonymous referee for insightful comments which helped us clarify some important points312For the past quarter of a century the luminosity cistribution of galaxies has been represented by a Sehechter function (Schechter 1976).,For the past quarter of a century the luminosity distribution of galaxies has been represented by a Schechter function (Schechter 1976).313 This contains three defining parameters (see Eqn. 1)), This contains three defining parameters (see Eqn. \ref{eq:sch}) )314 vd from these parameters one can derive useful quantities such as the mean local luminosity density., and from these parameters one can derive useful quantities such as the mean local luminosity density.315 Over the past decade many measurements of the Schechter 1Ελ...[ Ilave |POCH nidole fee.[ους LEDstathiou. Ellis Peterson. LOSS: Loveday ct al.," Over the past decade many measurements of the Schechter parameters have been made (e.g. Efstathiou, Ellis Peterson, 1988; Loveday et al."316 1992: Aarzke et al., 1992; Marzke et al.317 1994. 1908: Zucca et al.," 1994, 1998; Zucca et al.,"318 1997)., 1997).319 Llowever when compared. the results from these recent surveys show a wide range in the derived Schechter parameters. Cross et a. (," However when compared, the results from these recent surveys show a wide range in the derived Schechter parameters, Cross et al. ("3202001) and hence a wide range in the inferred luminosity censity.,2001) and hence a wide range in the inferred luminosity density.321 The two most likely culprits for his variation are:, The two most likely culprits for this variation are:322Gtruciu Otruciu 0.5in 020111 020111 clures clures clures clures στlo clussilü ον CLUSSS ciusshbxlO 1102 ciutir ciurG cutis clures ,"6truein 9truein -0.5in 0.25in 0.25in cmr8 cmr8 cmr8 cmr8 cmr10 cmssi10 cmss10 cmss8 cmssbx10 2 cmti7 cmr6 cmti8 cmr8 \def\ref{\par\noindent\hangindent 15pt}323 "324"a [frame is to be expected in a theory of gravity in which e,4e for the following reason: in a theory wilh either interacting dynamical fields or with non-cvnamical ""prior-geometrical fields. (he speed of gravity is presumably a function of some cosmological values of the fields in the theory.","a frame is to be expected in a theory of gravity in which $c_g \ne c$ for the following reason: in a theory with either interacting dynamical fields or with non-dynamical “prior-geometrical” fields, the speed of gravity is presumably a function of some cosmological values of the fields in the theory."325" But because e,zc. its value depends on the velocity of the frame in which il is measured."," But because $c_g326\ne c$, its value depends on the velocity of the frame in which it is measured."327" There must therefore exist some frame in which ¢, takes its value directly from the cosmologically induced. values of the underlving fields Che only logical [rame is ihe mean rest [rame of the universe. and hence the rest frame of the CBR."," There must therefore exist some frame in which $c_g$ takes its value directly from the cosmologically induced values of the underlying fields – the only logical frame is the mean rest frame of the universe, and hence the rest frame of the CBR."328" Then. if a,40. there will be measurable effects in anv svstem that moves relative to Chis preferred. frame."," Then, if $\alpha_1 \ne 0$, there will be measurable effects in any system that moves relative to this preferred frame."329 With these strong bounds. ο<5xLO”.," With these strong bounds, $|\zeta| < 5 \times 10^{-5}$."330 Nevertheless a weaker bound on ay can be inferred [rom experiments without appealing to preferrecd-lrame effects., Nevertheless a weaker bound on $\alpha_1$ can be inferred from experiments without appealing to preferred-frame effects.331 We assume only (that the theory is a Lagrangian-based. theory of gravity. so (hat il possesses suitable conservation laws for total momentum and energy.," We assume only that the theory is a Lagrangian-based theory of gravity, so that it possesses suitable conservation laws for total momentum and energy."332" Then. Lunar laser ranging tests of the Nordvedt effect bound the combination |43—5a,=2o3/3|«10 0."," Then, Lunar laser ranging tests of the Nordvedt effect bound the combination $|4\beta-\gamma-3-10\xi/3-\alpha_1-2\alpha_2/3| < 10^{-3}$ ."333 The perihelion advance of Mercury. combined with the existing bounds on 5 yield |3—I|<3x10: Earth tide measurements force the bound le}<10.7., The perihelion advance of Mercury combined with the existing bounds on $\gamma$ yield $|\beta -1| < 3 \times 10^{-3}$; Earth tide measurements force the bound $|\xi| < 10^{-3}$.334 One is then left with the relatively generous bound jay—203/3|<1.6x107., One is then left with the relatively generous bound $|\alpha_1-2\alpha_2/3| < 1.6 \times 10^{-2}$.335 All bounds on à» come from considerations of prelerrecd-lrame effects., All bounds on $\alpha_2$ come from considerations of preferred-frame effects.336" Thus without appealing to prelerred-Diame tests. one would have to have an extraordinary. cancellation between a, and as to conform toNordivedt effect measurements. while still making ¢ large enough to make a measurable difference in Eq. (34))."," Thus without appealing to preferred-frame tests, one would have to have an extraordinary cancellation between $\alpha_1$ and $\alpha_2$ to conform toNordtvedt effect measurements, while still making $\zeta$ large enough to make a measurable difference in Eq. \ref{final}) )."337 We are grateful to Steve Carlip. Sergei Ixopeikin. Gerhard Schaffer. Kenneth Nordtvedt. and LHideki Asaca for useful discussions.," We are grateful to Steve Carlip, Sergei Kopeikin, Gerhard Schäffer, Kenneth Nordtvedt, and Hideki Asada for useful discussions."338 This work is supported in part by the National Science Foundation. under grant. no.," This work is supported in part by the National Science Foundation, under grant no."339 PIIY00-96522., PHY00-96522.340" Throughout these calculations. quantiles such as x,(s,) and v4(s,) appear. where sq is relardecdl (ime evaluated. using Eq. (15))."," Throughout these calculations, quantities such as ${\bf x}_a(s_a)$ and ${\bf341v}_a(s_a)$ appear, where $s_a$ is retarded time evaluated using Eq. \ref{retarded}) )."342" In the near zone. we use the expansion Xu(sy)=x,(0)4v,(0)s,4-...."," In the near zone, we use the expansion ${\bf343x}_a(s_a) = {\bf x}_a(0) + {\bf v}_a(0) s_a + \dots$."344 One is tempted to state that the (0) Chat appears means something other than coordinate lime equals zero., One is tempted to state that the $(0)$ that appears means something other than coordinate time equals zero.345 Bul this would not be correct., But this would not be correct.346 The trajectory of the body κια) is a function only of the parameter s. which is chosen to be directly. proportional to coordinate time.," The trajectory of the body ${\bf x}_a(u)$ is a function only of the parameter $u$, which is chosen to be directly proportional to coordinate time."347" By contrast. s, is not an independent. variable. instead it is a (wo-point dependent variable. determined bv both the field point (/.x) and the bodys trajectory."," By contrast, $s_a$ is not an independent variable, instead it is a two-point dependent variable, determined by both the field point $(t,{\bf x})$ and the body's trajectory."348" Equation (15)) serves to determine (albeit implicitly or iteratively) that value of the parameter 4=s, al which to evaluate x;(u).", Equation \ref{retarded}) ) serves to determine (albeit implicitly or iteratively) that value of the parameter $u=s_a$ at which to evaluate ${\bf x}_a(u)$ .349 The equation quoted above, The equation quoted above350numbers and distributions for these models.,numbers and distributions for these models.351" Restricting the discussion to the relevant sampling criteria (i.e., M,«—17) the M.DD06 and BB07, and D.BB06 and D_FF08 models have a galaxy number density given in Table 1.."," Restricting the discussion to the relevant sampling criteria (i.e., $_r$$<$$-$ 17) the D06 and B07, and B06 and F08 models have a galaxy number density given in Table \ref{table_times}."352" T'he number density of galaxies in the field for each model is quite similar, as well as in LGs."," The number density of galaxies in the field for each model is quite similar, as well as in LGs."353" However, the Durham models have significantly denser galaxy populations within CGs and vCGs."," However, the Durham models have significantly denser galaxy populations within CGs and vCGs."354 The physics which the different models employ to account for group environments appear to have significantly altered the nature of compact groups., The physics which the different models employ to account for group environments appear to have significantly altered the nature of compact groups.355" 'The relative proportions galaxies that are classified as being members of groups, along with the average group richness, are listed in Table 5.1.."," The relative proportions galaxies that are classified as being members of groups, along with the average group richness, are listed in Table \ref{numbers}."356 In this instance we define group richness as simply being the number of galaxies in a group., In this instance we define group richness as simply being the number of galaxies in a group.357" The percentage of galaxies associated with LGs (and the numbers of galaxies per loose group) is comparable between three of the four SAM variants, with the M_DD06 model showing approximately 6 percent fewer groups than the D.BB06 model."," The percentage of galaxies associated with LGs (and the numbers of galaxies per loose group) is comparable between three of the four SAM variants, with the D06 model showing approximately 6 percent fewer groups than the B06 model."358" The models diverge increasingly with decreasing linking length, with the Munich models, M_DD06 and M.BBOT7, having 5 to 6 times fewer vCGs than in the Durham models."," The models diverge increasingly with decreasing linking length, with the Munich models, D06 and B07, having 5 to 6 times fewer vCGs than in the Durham models."359" The M.DD06 model produces noticeably fewer rich groups at all linking lengths compared with the other Munich model, M.BBO07."," The D06 model produces noticeably fewer rich groups at all linking lengths compared with the other Munich model, B07."360 This indicates that the implementation of supernovae has a significant effect on the richness of group catalogues., This indicates that the implementation of supernovae has a significant effect on the richness of group catalogues.361" The Durham models, D.BB06 and D_FF08, have slightly richer loose groups than the Munich models."," The Durham models, B06 and F08, have slightly richer loose groups than the Munich models."362" This is associated with the smaller populations of medium brightness red galaxies in the Munich models, which may be the result of the differences in the creation of halo catalogues, the tracing of subhalo mergers, or due to radio mode AGN feedback."," This is associated with the smaller populations of medium brightness red galaxies in the Munich models, which may be the result of the differences in the creation of halo catalogues, the tracing of subhalo mergers, or due to radio mode AGN feedback."363" ??| compared compact groups in mock redshift catalogues to SDSS DR6 observations, and concluded that the M.DD06 SAM overproduces CGs by ~50%.."," \citet{McConnachie2008, McConnachie2009} compared compact groups in mock redshift catalogues to SDSS DR6 observations, and concluded that the D06 SAM overproduces CGs by $\sim$."364" By extension, Table 5.1 indicates that the D-BB06 and D_FF08 models result in an even more dramatic “overproduction” of CGs (by an order-of-magnitude)."," By extension, Table \ref{numbers} indicates that the B06 and F08 models result in an even more dramatic “overproduction” of CGs (by an order-of-magnitude)."365" Thus, in this regime, none of the models are good fits to the empirical data, and the Durham models are particularly poor."," Thus, in this regime, none of the models are good fits to the empirical data, and the Durham models are particularly poor."366 Figure 3 shows the galaxy distribution of galaxies with radius for the LGs of M.DD06 and D.BB06 models., Figure \ref{Fig:galpos} shows the galaxy distribution of galaxies with radius for the LGs of D06 and B06 models.367 The left panel shows the number of satellites versus radius in Mpc., The left panel shows the number of satellites versus radius in Mpc.368 The right panel of Fig., The right panel of Fig.369 3 shows the same plot with the radius scaled by the virial radius., \ref{Fig:galpos} shows the same plot with the radius scaled by the virial radius.370" Both panels show that there are more satellites in the inner regions of the D.BB06 LGs, relative to the outer regions, compared with the M.DD06 model."," Both panels show that there are more satellites in the inner regions of the B06 LGs, relative to the outer regions, compared with the D06 model."371" The red line in the right panel shows the 60 most massive SDSS4_YY08 observed Loose Groups, making them similar in mass range to the population used in making the simulation plots."," The red line in the right panel shows the 60 most massive Y08 observed Loose Groups, making them similar in mass range to the population used in making the simulation plots."372" T'his indicates that both models have a radial distribution of satellites which is more centrally concentrated than the observations, with the problem being particularly acute in the D.BB06 model."," This indicates that both models have a radial distribution of satellites which is more centrally concentrated than the observations, with the problem being particularly acute in the B06 model."373" This more concentrated distribution of satellites is also reflected in the distribution of nearest neighbour pair separation distances for LG members, seen in Fig. 4.."," This more concentrated distribution of satellites is also reflected in the distribution of nearest neighbour pair separation distances for LG members, seen in Fig. \ref{nearest}."374 It can be seen that the D-BB06 model the nearest neighbour separation is smaller than for the M.DD06 and Μ.ΒΒΟΤ., It can be seen that the B06 model the nearest neighbour separation is smaller than for the D06 and B07.375 We note that the D_FF08 model groups have very similar, We note that the F08 model groups have very similar376band is relatively uncertain.,band is relatively uncertain.377" Also, the trend of 114(c) Z02 may be overcome by the increase of KT, for harder spectra, see 114(a—b) in Z02, and see 113 in Z02 for example spectra from pointed observations showing this trend."," Also, the trend of 14(c) Z02 may be overcome by the increase of $kT_{\rm e}$ for harder spectra, see 14(a–b) in Z02, and see 13 in Z02 for example spectra from pointed observations showing this trend."378" For the intermediate state, up to Γ~ 2.32.5, the bolometric flux increases with the increasing I, see reff:gamma((a)."," For the intermediate state, up to $\Gamma\simeq 2.3$ –2.5, the bolometric flux increases with the increasing $\Gamma$, see \\ref{f:gamma}( (a)."379" The broad-band variability shows also a pivot at ~20 keV, above which the intermediate-state X-ray fluxes in reff:X,adio((a— —e)changef rombeingcorrelatedwithFyg to an anti-correlation."," The broad-band variability shows also a pivot at $\sim$ 20 keV, above which the intermediate-state X-ray fluxes in \\ref{f:X_radio}( (a–e) change from being correlated with $F_{\rm bol}$ to an anti-correlation."380" This has been modelled by Z02 and Gierliriski,Zdziarski&Done(2011) as due to a changing ratio of the flux irradiating a Comptonizing plasma to that dissipated in that plasma (see 114a-b in Z02, 10c in Gierliriskietal. 2011))."," This has been modelled by Z02 and \citet*{gzd11} as due to a changing ratio of the flux irradiating a Comptonizing plasma to that dissipated in that plasma (see 14a–b in Z02, 10c in \citealt{gzd11}) )."381" This may be caused by a varying the inner radius of an accretion disc surrounding the hot plasma (Done,Gierlitiski&Kubota2007).", This may be caused by a varying the inner radius of an accretion disc surrounding the hot plasma \citep*{dgk07}.382". The soft-state X-ray bolometric flux is dominated by photons below E -—3 keV. Below this energy the soft-state spectra are dominated by the disc component and above it, by a high-energy tail."," The soft-state X-ray bolometric flux is dominated by photons below $E\sim$ 3 keV. Below this energy the soft-state spectra are dominated by the disc component and above it, by a high-energy tail."383" The soft state variability has been modelled by Gilfanov&Revnivtsev (2001),, and later by Z02 and Gierliáskiet as a variable non-thermal corona above stable disc, see, e.g., 116 in Z02 and 110c in Gierliriskiaetal.(2011)."," The soft state variability has been modelled by \citet*{cgr01}, and later by Z02 and \citet{gzd11} as a variable non-thermal corona above a stable disc, see, e.g., 16 in Z02 and 10c in \citet{gzd11}."384". However, the disc blackbody emission is stable only on short time scales, whereas it does change significantly on long time scales, see, e.g., reff: X,adio((a)."," However, the disc blackbody emission is stable only on short time scales, whereas it does change significantly on long time scales, see, e.g., \\ref{f:X_radio}( (a)."385"T here sultingvariability patterniso ftheoverallspectrumchangingitsnormalizationbutwithmuchmorescatteri f Fx Fea at high energies, dominated by the emission of the varying corona, than in the blackbody component. reff:gamma(("," The resulting variability pattern is of the overall spectrum changing its normalization but with much more scatter if $F_{\rm X}$ $F_{\rm bol}$ at high energies, dominated by the emission of the fast-varying corona, than in the blackbody component. \\ref{f:gamma}( ("386"a), 4 show that the daily-averaged Fy,; changes, over the three states, by a factor of «10.","a), \ref{f:lc_bol} show that the daily-averaged $F_{\rm bol}$ changes, over the three states, by a factor of $\simeq$ 10."387" As expected, the highest and lowest fluxes correspond to the soft and hard state, respectively, consistent with the view that state transitions in Cyg X-1 are driven by changes of the accretion rate."," As expected, the highest and lowest fluxes correspond to the soft and hard state, respectively, consistent with the view that state transitions in Cyg X-1 are driven by changes of the accretion rate."388 The soft-state Fy.) is generally about a factor of ~3 higher that in the hard state., The soft-state $F_{\rm bol}$ is generally about a factor of $\simeq$ 3 higher that in the hard state.389" We note, however, that Fg; in the intermediate and soft states can become less than that in the hard state, see reff:gamma((a), 4,, 5((a-e)."," We note, however, that $F_{\rm bol}$ in the intermediate and soft states can become less than that in the hard state, see \\ref{f:gamma}( (a), \ref{f:lc_bol}, \ref{f:X_radio}( (a–e)."390 This appears to be the first such finding in Cyg X-1., This appears to be the first such finding in Cyg X-1.391" It may be indicative of hysteresis, usually present in transient sources (e.g., Dunnetal. 2008))."," It may be indicative of hysteresis, usually present in transient sources (e.g., \citealt{dunn08}) )."392" Its presence there is seen as a characteristic q track in the flux/hardness diagram, see, e.g.,"," Its presence there is seen as a characteristic q track in the flux/hardness diagram, see, e.g.,"393"The Lie derivative of E"" along an is or. with (2-2)). The four-dimensional divergence V,E"" cau be expressed iu terms of the three-dimensional divergeuce D;E' where we have used i,E""=0 aud Tere a, is the four-acceleration of a normal observer.","The Lie derivative of $E^a$ along $\alpha n^a$ is or, with \ref{t}) ), The four-dimensional divergence $\nabla_a E^a$ can be expressed in terms of the three-dimensional divergence $D_i E^i$ where we have used $n_a E^a = 0$ and Here $a_a$ is the four-acceleration of a normal observer."394" Since the extrinsic curvature A454 can be written the divergence of 1 satisfies Tusciting these expressions iuto (6-6)). we now find the intermediate result where we have also used E""D,luno=EVV,lina."," Since the extrinsic curvature $K_{ab}$ can be written the divergence of $n^a$ satisfies Inserting these expressions into \ref{divF}) ), we now find the intermediate result where we have also used $ E^a D_a \ln \alpha = E^a \nabla_a \ln395\alpha$."396" The term involvineC» D, in (6-13)) can be rewritten as where we have used equations (3- yy. (6-L0)) ancl (6-11))."," The term involving $B_a$ in \ref{divF2}) ) can be rewritten as where we have used equations \ref{epsilon}) ), \ref{a}) ) and \ref{K}) )."397 luserting this expression into (0-1: )) now vields Not surpriiuglv. this is the four-dinieusioual version of equation (3-8). which can be found by taking the spatial projection of (6-15).," Inserting this expression into \ref{divF2}) ) now yields Not surprisingly, this is the four-dimensional version of equation \ref{Edot}) ), which can be found by taking the spatial projection of \ref{J}) )."398 The next step is to contract (6-15)) with the Faraday tensor (3-1))., The next step is to contract \ref{J}) ) with the Faraday tensor \ref{faraday1}) ).399 Using {ο= 0. nue= Oand 0 several terms cancel. aud one finds This expression can now be inserted iuto the Euler equation (6-5)).," Using $n_a E^a=0$ , $n_a \epsilon^{abc} = 0$ and $n_a \Lie_{\alpha {\bf n}} E^a = 0$ several terms cancel, and one finds This expression can now be inserted into the Euler equation \ref{SWdot2}) )."400 For spatial components p;=0. so that the secoud line in (6-16)) vanuishes.," For spatial components $n_i = 0$, so that the second line in \ref{J2}) ) vanishes."401 The source tenu as?2FU!p can then be rewritten. Tf desired. the covariant derivatives in the last two terms can be converted into partial derivatives. which finally vields the Euler equation where we have expanded the Lie derivative of E.," The source term $\alpha \gamma^{1/2}402F_{ia} {\mathcal J}^a$ can then be rewritten If desired, the covariant derivatives in the last two terms can be converted into partial derivatives, which finally yields the Euler equation where we have expanded the Lie derivative of $E^i$."403" Note that in this equation the electric field terms cuter with the opposite sign frou those in the corresponding equation (3.2) of Sloan σπα (1985. hereafter SS). who further asstne 3=O=ty,"," Note that in this equation the electric field terms enter with the opposite sign from those in the corresponding equation (3.2) of Sloan Smarr (1985, hereafter SS), who further assume $\beta = 0 = K$."404 For nuucerical implementations. the most challeugiug term in Euler's equation is probably the time-cerivative of the electric field.," For numerical implementations, the most challenging term in Euler's equation is probably the time-derivative of the electric field."405 For ideal MIID. this term cau be rewritten by first expressing £ in terms of the magnetic fields Οἱ using the ideal MIID. relation (1-8)). aud thon using CL11)) to climinate the time-derivative of B (see Zhang 1989).," For ideal MHD, this term can be rewritten by first expressing $E^i$ in terms of the magnetic fields $B^i$ using the ideal MHD relation \ref{MHD}) ), and then using \ref{MHD_faraday}) ) to eliminate the time-derivative of $B^i$ (see Zhang 1989)."406 This term is likely to be μπα iu most applications: for example. it is Ole?/e7) times smaller than the last two terms on the right hand side of (6- Ls)).," This term is likely to be small in most applications; for example, it is $\mathcal{O}(v^2/c^2)$ times smaller than the last two terms on the right hand side of \ref{SWdot3}) )."407 Tn such cases. extrapolating aud iterating. or sole other simple treatineut. may be adequate to account for its contribution.," In such cases, extrapolating and iterating, or some other simple treatment, may be adequate to account for its contribution."408 It is instructive to take the Newtonian liuüt of equation (6-18)) aud recover a familiar expression., It is instructive to take the Newtonian limit of equation \ref{SWdot3}) ) and recover a familiar expression.409 With gog(11 20). where o is the Newtonian potential. we find Iu cartesian coordinates (53/72=1). the Newtonian limit of equation (6-18)) then becomes Or equivaleutl- where we have defiued the maguctic pressure and where V is the spatial eradieut operator.," With $g_{00}410\rightarrow -(1 + 2 \phi)$ , where $\phi$ is the Newtonian potential, we find In cartesian coordinates $\gamma^{1/2} = 1$ ), the Newtonian limit of equation \ref{SWdot3}) ) then becomes or equivalently where we have defined the magnetic pressure and where ${\bf \nabla}$ is the spatial gradient operator."411" Note that for a neutral plasina p,=0 the electric field E"" disappears cutirely from the above Newtoniau equation.", Note that for a neutral plasma $\rho_e = 0$ the electric field $E^a$ disappears entirely from the above Newtonian equation.412 We now catalogue the source terms p (2-10)). 5; (2-11). (2-12)) aud 5 (2-13)) that appear in the IEuuiltouian constraint5;; (2-6)). the momentum constraint (2-7)) aud the evolution equation (2-8)).," We now catalogue the source terms $\rho$ \ref{rho}) ), $S_i$ \ref{Si}) ), $S_{ij}$ \ref{Sij}) ) and $S$ \ref{trS}) ) that appear in the Hamiltonian constraint \ref{ham}) ), the momentum constraint\ref{mom}) ) and the evolution equation \ref{kdot}) )."413 Iuserting the fluidstress-cucrey tensor (5-1)) iuto equations (2-10)) - (2-13)) vields the fluid coutributious to the source ternis: Next we assciuble the= Pclectromagueticpali 1).contributions to the source terms., Inserting the fluidstress-energy tensor \ref{T_fluid}) ) into equations \ref{rho}) ) - \ref{trS}) ) yields the fluid contributions to the source terms: Next we assemble the electromagnetic contributions to the source terms.414 To do so. we first need to coustruct the," To do so, we first need to construct the"415to small but observable light curve variations on (he orbital period.,to small but observable light curve variations on the orbital period.416 More quantitatively. the expected peak-to-peak ellipsoidal variation is 2224Ma/.M4(Isini/«)x5 (?)..," More quantitatively, the expected peak-to-peak ellipsoidal variation is $\approx 2 M_2/M_1 (R_1 \sin i/a)^3$ \citep{vankerkwijk2010}. ."417 Figure 5.5 shows three example light curves from our simulations that illustrate the above effects., Figure \ref{fig:ellipvar} shows three example light curves from our simulations that illustrate the above effects.418 In each panel. we list (he semi-major axis Gn solar radius units). the relative size ofthe primary star (F21/a). and the level of expected peak-to-peak variations.," In each panel, we list the semi-major axis (in solar radius units), the relative size ofthe primary star $R1/a$ ), and the level of expected peak-to-peak variations."419" For example. (hie middle panel illustrates the case of an ED with «=325.4 BR. (2,4,=334 d) and Ry=55.3 Rh..."," For example, the middle panel illustrates the case of an EB with $a=325.4$ $_\odot$ $P_{\rm orb}=334$ d) and $R_1=55.3$ $_\odot$."420" The expected level of ellipsoidal variation is οον, and this is indeed what we observe in the light curve."," The expected level of ellipsoidal variation is $\approx$, and this is indeed what we observe in the light curve."421 For theminimum photometric signal-to-noise adopted in our simulations. variability aanplitudes of ~1% or larger should vield easily recovered periods by LSST.," For theminimum photometric signal-to-noise adopted in our simulations, variability amplitudes of $\sim$ or larger should yield easily recovered periods by LSST."422 We note that the relative proportion of giants in our test lighteurves (20'%)) is slightly higher than the proportion in the Galaxy -15%.. see Girardi οἱ al.," We note that the relative proportion of giants in our test lightcurves ) is slightly higher than the proportion in the Galaxy -, see Girardi et al."423 2011. in prep).," 2011, in prep)."424 That difference means (that the actual recoverability of Iong-period binaries of all types would be somewhat lower than the bottom panel in Figure 4.., That difference means that the actual recoverability of long-period binaries of all types would be somewhat lower than the bottom panel in Figure \ref{fig:aov1}.425 Neural networks will perform exceptionally. well for light curves whose parameters are within the boundaries of the (raining set (especially in terms of non-linear interpolation). but the performance will deteriorate exponentially when extrapolation is required. (?)..," Neural networks will perform exceptionally well for light curves whose parameters are within the boundaries of the training set (especially in terms of non-linear interpolation), but the performance will deteriorate exponentially when extrapolation is required \citep{freeman1991}."426 To assure optimal operation. we (rained (he network on as wide a range of plivsically plausible light curves as possible (viz.," To assure optimal operation, we trained the network on as wide a range of physically plausible light curves as possible (viz."427 Fig. 1))., Fig. \ref{fig:dists}) ).428 The EBs with successfully recovered periods were passed to the artificial engine (Eclipsing Binaries via Artificial Intelligence: ?)) to derive physical parameters of the svstems: 75/7). pp+po. eso. ecoso. and sin’.," The EBs with successfully recovered periods were passed to the artificial intelligence-based engine (Eclipsing Binaries via Artificial Intelligence; \citealt{prsa2008}) ) to derive physical parameters of the systems: $T_2/T_1$, $\rho_1+\rho_2$, $e \sin \omega$, $e \cos \omega$ , and $\sin i$."429 We first use (?) ιο findan analvtical approximationfor each light curve., We first use \citep{prsa2008} to findan analytical approximationfor each light curve.430 This is necessary. because, This is necessary because431 During the fit we neglect the hard state data indicated with open circles which where simulated. based on the GIO. 1655-40 observations with the dise flux lower than ες5510U erg st 7., During the fit we neglect the hard state data indicated with open circles which where simulated based on the GRO J1655-40 observations with the disc flux lower than $F_{d} = 5\times10^{-11}$ erg $^{-1}$ $^{-2}$.432 Among the 94 considered GIO 1655-40. hard state observations there were 11 datasets. that were well described. bv. the Comptonized continuum with a llux /) dominating significantly over the disc Dux. Zi in the total spectrum., Among the 94 considered GRO J1655-40 hard state observations there were 11 datasets that were well described by the Comptonized continuum with a flux $F_c$ dominating significantly over the disc flux $F_d$ in the total spectrum.433 A case of an AGN with similar geometry (ie. extremely low disc Εν). would be difficult to detect in optical/U due to the emission of a host galaxy that would dominateV. in this band., A case of an AGN with similar geometry (i.e. extremely low disc flux) would be difficult to detect in optical/UV due to the emission of a host galaxy that would dominate in this band.434 However. such an AGN would. still be detected in the N-rav. band with an N-rav SED resembling a power law.," However, such an AGN would still be detected in the X-ray band with an X-ray SED resembling a power law."435 Our fits result in for AGN SED sets simulated based on all four CIN mass distributions from Fig. 3..," Our fits result in for AGN SED sets simulated based on all four AGN mass distributions from Fig. \ref{fig:masses},"436 respectively., respectively.437 “Phe range of slopes we find in this correlation is consistent with that seen in real data., The range of slopes we find in this correlation is consistent with that seen in real data.438 For example. Cirupe ct al. (," For example, Grupe et al. ("4392010) found a slope of 124-E0.014 based on the study of 92 bright soft X-ray selected AGN observed: with Swift. (a. combination of narrow line and. broad. line Seyfert Is). while Lusso et al. (,"2010) found a slope of $\pm$ 0.014 based on the study of 92 bright soft X-ray selected AGN observed with Swift (a combination of narrow line and broad line Seyfert 1s), while Lusso et al. ("4402010) reported. a slope of 0.1542:0.010 in the NMM-COSMOS sample of 545 X-ray. selected type 1 AGN.,2010) reported a slope of $\pm$ 0.010 in the XMM-COSMOS sample of 545 X-ray selected type 1 AGN.441 Their correlations are indicated in Fig., Their correlations are indicated in Fig.442 4 with dotted and dashed lines. respectively.," \ref{fig:sim} with dotted and dashed lines, respectively."443 The best fits to the SEDs simulated using narrow (COSMOS) and broad (LINERS) mass distributions are indicated with solid lines in Figs., The best fits to the SEDs simulated using narrow (COSMOS) and broad (LINERs) mass distributions are indicated with solid lines in Figs.444 daad. The fitted slopes depend on the assumed numberof the soft state spectra in the AGN sample., \ref{fig:sim}a a–d. The fitted slopes depend on the assumed numberof the soft state spectra in the AGN sample.445 Figures 4aa and tec show how the correlation changes if we assume that NsLo% or of the AGN. respectively. are in a soft state. for the case of a narrow mass distribution from Lig.," Figures \ref{fig:sim}a a and \ref{fig:sim}c c show how the correlation changes if we assume that $N_S = 10$ or of the AGN, respectively, are in a soft state, for the case of a narrow mass distribution from Fig."446" Baa. For the four considered ACN mass distributions we obtained a!""=0.078 0.85 for Ns=10% and a""=0.107 0.121 for Ne=90%.", \ref{fig:masses}a a. For the four considered AGN mass distributions we obtained $a^{10} = 0.078$ –0.85 for $N_S = 10$ and $a^{90} = 0.107$ –0.121 for $N_S = 90$.447" Acelitionally. we check if the simulated CNs 6, is related. to the bolometric luminosity in Ecdelineton units."," Additionally, we check if the simulated AGN's $\alpha_{\rm ox}$ is related to the bolometric luminosity in Eddington units."448 In Fig., In Fig.449 4ee we plot aw. vs. LíLg for a narrow mass distribution (Eig., \ref{fig:sim}e e we plot $\alpha_{ox}$ vs. $L/L_{E}$ for a narrow mass distribution (Fig.450 3aa). assuming Ws=TO%..," \ref{fig:masses}a a), assuming $N_S = 70$."451 Laterestinely. the simulated N-rav. louclness correlates positively with the Ecdington ratio down to approximately Agi=0.01 LíLpg and below this value the correlation changes its sign.," Interestingly, the simulated X-ray loudness correlates positively with the Eddington ratio down to approximately $\lambda_{\rm crit} \approx 0.01$ $L/L_{\rm E}$ and below this value the correlation changes its sign."452 In Fie., In Fig.453 tee we superimpose our simulations ane the correlations found in real data by Lusso et al. (, \ref{fig:sim}c c we superimpose our simulations and the correlations found in real data by Lusso et al. (4542010) and Grupe et al. (,2010) and Grupe et al. (4552010) (dotted and dashed lines. respectively).,"2010) (dotted and dashed lines, respectively)."456 The correlation reported by Lusso ct al., The correlation reported by Lusso et al.457 matches the slope produced. by our. simulated SEDs down to the critical Eddington ratio. Aog.," matches the slope produced by our simulated SEDs down to the critical Eddington ratio, $\lambda_{\rm crit}$."458 These results do not depend. either on the properties of the adopted: mass distribution or on Ns., These results do not depend either on the properties of the adopted mass distribution or on $N_S$.459 We compare our simulated data with the known AGN samples. which have measurements. of both the monochromatic luminosity at and o4. ancl preferably also the black hole estimates.," We compare our simulated data with the known AGN samples, which have measurements of both the monochromatic luminosity at and $\alpha_{\rm ox}$, and preferably also the black hole estimates."460 We assume in this section that Ns=TO%.. but we stress that the results do not depend on this parameter.," We assume in this section that $N_S = 70$, but we stress that the results do not depend on this parameter."461 Neither Alerloni et al. (, Neither Merloni et al. (4622010) nor Shen et al. (,2010) nor Shen et al. (4632008) have A-ray observations for their complete samples.,2008) have X-ray observations for their complete samples.464 For that reason. first we consider the broad line AGN (a SDSS subsample) from Welly et al. (," For that reason, first we consider the broad line AGN (a SDSS subsample) from Kelly et al. ("4652007).,2007).466 We compare them with the simulated data resulting from hard (black/blue) and soft (orav/orange) state spectra of GRO J1655-40 scaled to the case of AGN. using the Shen et al. (," We compare them with the simulated data resulting from hard (black/blue) and soft (gray/orange) state spectra of GRO J1655-40 scaled to the case of AGN, using the Shen et al. ("4672008) mass distribution.,2008) mass distribution.468 We use the Shen et al., We use the Shen et al.469 distribution (not the Alerloni et al., distribution (not the Merloni et al.470 one) because it has the mean and ENIM close to those of the Kelly et al., one) because it has the mean and FWHM close to those of the Kelly et al.471 In Figs., In Figs.472 5aa b we superimpose the simulated: and observed. data., \ref{fig:data}a a–b we superimpose the simulated and observed data.473 Lt can be seen that the observations do not overlap with the simulated hard state AGN spectra. while hey do occupy the same region in the plot as the simulated soft state ACGN spectra.," It can be seen that the observations do not overlap with the simulated hard state AGN spectra, while they do occupy the same region in the plot as the simulated soft state AGN spectra."474 The interpretation of the spectral states of LINERs (Figs., The interpretation of the spectral states of LINERs (Figs.475 bec d) appears more complex since the data points erived from the real SEDs (Maoz 2007) overlap both with 10 hard and. soft. points (simulated: based on the LINIZIS mass distribution. Fie.," \ref{fig:data}c c–d) appears more complex since the data points derived from the real SEDs (Maoz 2007) overlap both with the hard and soft points (simulated based on the LINERs mass distribution, Fig."476 3cc)., \ref{fig:masses}c c).477 However. it can be seen in Fig.," However, it can be seen in Fig."478" hat in the case of the simulated soft state AGN. the SEDs jut result in [οσο889.5 41.3 (as reported by Maoz X07) require low black hole masses. MM.<10°. whereas in the case of simulated. hard state AGN. the SEDs require ack hole masses of M/M.~10. 107 to reach comparable og(iL,) at2500A.."," \ref{fig:massluv} that in the case of the simulated soft state AGN, the SEDs that result in $\log(\nu L_\nu)_o \approx 39.5$ –41.3 (as reported by Maoz 2007) require low black hole masses, $_{\odot} < 10^6$, whereas in the case of simulated hard state AGN, the SEDs require black hole masses of $_{\odot} \sim 10^6$ $^8$ to reach comparable $\log(\nu L_{\nu})$ at."479 Since the LINERs in Maoz (2007) have rather high masses (as indicated with the grav rectangles in lig. 6)), Since the LINERs in Maoz (2007) have rather high masses (as indicated with the gray rectangles in Fig. \ref{fig:massluv}) )480 we conclude that most probably. these objects are in a hard spectral state., we conclude that most probably these objects are in a hard spectral state.481 In Figs., In Figs.482 5eeÉ we perform similar comparison for a subsample of NLSI from Crupe et al. (, \ref{fig:data}e e–f we perform similar comparison for a subsample of NLS1 from Grupe et al. (4832010).,2010).484 We use the values of eg provided by the authors in Table !>. column 6. to caleulate the monochromatic luminosity at {from tabulated values of the UV slope. avy. and luminosity at ((columns 5 and 19. respectively).," We use the values of $\alpha_{\rm ox}$ provided by the authors in Table 5, column 6, to calculate the monochromatic luminosity at from tabulated values of the UV slope, $\alpha_{\rm UV}$, and luminosity at (columns 5 and 13, respectively)."485 We compare. the observations with the simulations for the mass distribution of the same sample (rig., We compare the observations with the simulations for the mass distribution of the same sample (Fig.486 3dd)., \ref{fig:masses}d d).487 Similarly as in the case of broad line AGN of Welly et al.," Similarly as in the case of broad line AGN of Kelly et al.,"488 the NLSIs in the sample of Grupe et al., the NLS1s in the sample of Grupe et al.489 do not overlap with the hard state simulated SEDs. while they do overlap with the simulated AGN in the soft state.," do not overlap with the hard state simulated SEDs, while they do overlap with the simulated AGN in the soft state."490 We studied. the scenario in which the main cillerence between the GBI and AGN nuclear emission follows [roni the dillerence. between the masses of the accreting black holes., We studied the scenario in which the main difference between the GBH and AGN nuclear emission follows from the difference between the masses of the accreting black holes.491 We assumed that the geometry. of the accretion low characterized by the ratio of the heating ancl cooling compactnesses. (ji /f.. stavs the same for both AGN and GBs in à given spectral state.," We assumed that the geometry of the accretion flow characterized by the ratio of the heating and cooling compactnesses, $\ell_h/\ell_s$ , stays the same for both AGN and GBHs in a given spectral state."492 With these assumptions.," With these assumptions,"493 For c€E. we compute: Taking the iufimuuir of both sides we arrive to the result.," For $c\in \R$, we compute: Taking the infimum of both sides we arrive to the result."494" α The next lemina gives an estimate of inf/[à—e| on sinall parabolic cubes in Define the term ry>0 as the greatest positive real number such that there exists Q4,CQj. ie.. We show the following: Call Q1. aud 05. the right aud the left neighbor sets of Qy defined respectively by: First let us meution that if the cube Q, lies in €, then inequality. (3.11)) is evident (see the equivalent delinition (3.9)) of the parabolic BALO, norm)."," $\hfill{\blacksquare}$ The next lemma gives an estimate of $\displaystyle495\inf_{c\in\R}\inm_{Q_{r}}|\tilde{u}-c|$ on small parabolic cubes in Define the term $r_{0}>0$ as the greatest positive real number such that there exists $Q_{r_{0}}\subseteq \Omega_{T}$, i.e., We show the following: Call $\Omega^{d}_{T}$ and $\Omega^{g}_{T}$ the right and the left neighbor sets of $\Omega_T$ defined respectively by: First let us mention that if the cube $Q_{r}$ lies in $\Omega_{T}$ then inequality \ref{moa3}) ) is evident (see the equivalent definition \ref{eq_bmo_nor}) ) of the parabolic $BMO_{p}$ norm)."496" Two remaining cases are tobe considered: either Q, intersects the set [e=0]U1]. or Q, lies in Q5.U Q5..."," Two remaining cases are tobe considered: either $Q_{r}$ intersects the set $\{x=0\}\cup\{x=1\}$, or $Q_{r}$ lies in $\Omega^{d}_{T}\cup497\Omega^{g}_{T}$ ."498" Our assumption (3.13)) on the radius of the parabolic cube makes it iiipossible that the cube Q, meets Q1. aud 05. at the same time.", Our assumption \ref{moa2}) ) on the radius of the parabolic cube makes it impossible that the cube $Q_{r}$ meets $\Omega^{d}_{T}$ and $\Omega^{g}_{T}$ at the same time.499" Therefore. aud iu order to make the proof simpler. we only. consider the following cases: eitler Q, intersects the set {or=Ob. or Q, lies in Q7."," Therefore, and in order to make the proof simpler, we only consider the following cases: either $Q_{r}$ intersects the set $\{x=0\}$, or $Q_{r}$ lies in $\Omega^{g}_{T}$."500" The proof is then divided iuto three main (Q, intersects the line {7=01). (First Again the assumption (3.13)) imposed on the radius r makes it possible to embed Q, iu a larger parabolic cube Qa,COp of radius 2r. whichis symmetric with respect to the line [Lr=0] (see Figure 1))."," The proof is then divided into three main $Q_{r}$ intersects the line $\{x=0\}$ (First Again the assumption \ref{moa2}) ) imposed on the radius $r$ makes it possible to embed $Q_{r}$ in a larger parabolic cube $Q_{2r}\subseteq \widehat{\Omega}_{T}$ of radius $2r$, whichis symmetric with respect to the line $\{x=0\}$ (see Figure \ref{cubes}) )."501" Then the center of the eube Qe,2» should be also on the same liue. but we do not require1that the two cubes Q, and Qe, have centers with the same ordinate /."," Then the center of the cube $Q_{2r}$ should be also on the same line, but we do not requirethat the two cubes $Q_{r}$ and $Q_{2r}$ have centers with the same ordinate $t$ ."502 Now. πας Leuuna 3.L. we deduce that:," Now, using Lemma \ref{Hgibi1}, , we deduce that:"503(~t ES) was observed in soft eanuna-ravs (25-300 keV).,$\sim t^{-1.8}$ ) was observed in soft gamma-rays (25-300 keV).504 Two separate enüssion components are favored iu this burst because the spectral characteristics of the tail were markedly different from those of the variable main CRB cluission., Two separate emission components are favored in this burst because the spectral characteristics of the tail were markedly different from those of the variable main GRB emission.505 The spectrum in the tail is consistent with that of a slow-cooling svuchrotron spectrum. similar to the behavior of low-energy afterglows (c.¢.. Bloomctal.1998.. Vreeswijketal. 1999)).," The spectrum in the tail is consistent with that of a slow-cooling synchrotron spectrum, similar to the behavior of low-energy afterglows (e.g., \cite{bloom98}, \cite{vreeswijk99}) )."506" The οσαανν produced by internal shocks aud the soft eamna-ravs of the ""afterelow may therefore overlap. he latter having a signature of power-law decay iu he svuchrotron afterglow model."," The gamma-rays produced by internal shocks and the soft gamma-rays of the “afterglow” may therefore overlap, the latter having a signature of power-law decay in the synchrotron afterglow model."507 If this is the case. at cast some CRBs in the BATSE database should show sjeuatures of the early external shock cussion.," If this is the case, at least some GRBs in the BATSE database should show signatures of the early external shock emission."508 These events would contain a soft eamuna-ray (or hard ταν) ail component that decays as a power-law in their time ustories. possibly superposed upon the variable gamuna-rav cuuission.," These events would contain a soft gamma-ray (or hard X-ray) tail component that decays as a power-law in their time histories, possibly superposed upon the variable gamma-ray emission."509 It has been shown that the peak frequency of the initial svuchrotron emission. which depends ou the xranieters of the system (see 52). can peak iu lard X- or gamma-rays (MészárosaudRees 1992)).," It has been shown that the peak frequency of the initial synchrotron emission, which depends on the parameters of the system (see $\S 2$ ), can peak in hard X-rays or gamma-rays \cite{meszaros92}) )."510" Further. it iuav be possible to see a sinoothlv decaving CRB that is the result of au external shock. 1.0. the CRB itself is a ""hiel-energv afterelow."," Further, it may be possible to see a smoothly decaying GRB that is the result of an external shock, i.e., the GRB itself is a “high-energy” afterglow."511 For such CRBs. the subsequeut afterelow emission iu N-ravs and optical would then simply be the evolution ofthe burst spectrum.," For such GRBs, the subsequent afterglow emission in X-rays and optical would then simply be the evolution of the burst spectrum."512 A situation like this night arise when the progenitor generates only a single chorey release (.6.. no internal shocks).," A situation like this might arise when the progenitor generates only a single energy release (i.e., no internal shocks)."513 It is well known that the temporal structures of GRBs are very diverse aud often contain complex. rapid variability.," It is well known that the temporal structures of GRBs are very diverse and often contain complex, rapid variability."514 Towever. some bursts exhibit smooth decay features that persist on timescales as long as. or even lonecr than. the variable emission of the burst.," However, some bursts exhibit smooth decay features that persist on timescales as long as, or even longer than, the variable emission of the burst."515 Our investigation focuses on the combined temporal aud spectral behavior of a suuple of LO BATSE CRBs that exhibit smooth decays during the later pliase of their tine histories., Our investigation focuses on the combined temporal and spectral behavior of a sample of 40 BATSE GRBs that exhibit smooth decays during the later phase of their time histories.516" Mauv of these eveuts fall into a category of bursts traditionally referred to as ""EREDs (Fast Rise. Expoucutial-like Decay). bursts with rapid rise times aud a smooth extended decay (INouveliotouetal. 19923)."," Many of these events fall into a category of bursts traditionally referred to as “FREDs” (Fast Rise, Exponential-like Decay), bursts with rapid rise times and a smooth extended decay \cite{kouveliotou92}) )."517 Iu 52 we present temporal and spectral properties of the afterglow svuchrotrou spectruu., In $\S 2$ we present temporal and spectral properties of the afterglow synchrotron spectrum.518 Iu 53 we examine the teiiporal behavior and spectral characterisitics of the decay chussion for the eveuts in our sample aud compare their spectra with the model svuchrotron spectrum., In $\S 3$ we examine the temporal behavior and spectral characterisitics of the decay emission for the events in our sample and compare their spectra with the model synchrotron spectrum.519 A color-color diagrams (CCD) technique is also applied to systematically explore the spectral evolution of each event., A color-color diagram (CCD) technique is also applied to systematically explore the spectral evolution of each event.520 Iu 5I sve preseut a set of higl-energy afterelow candidates. followed by a discussion of our results iu the framework of current fireball models.," In $\S 4$ we present a set of high-energy afterglow candidates, followed by a discussion of our results in the framework of current fireball models."521 Tuterual shocks are capable of liberatiug some fraction of the total fireball cuerey Ey=TyAdye?. leaving a significant fraction to be injected into the external ποπ via the external shock (INobavashietal. 1997)).," Internal shocks are capable of liberating some fraction of the total fireball energy $E_{0} = \Gamma_{0} M_{0} c^{2}$, leaving a significant fraction to be injected into the external medium via the external shock \cite{kobayashi97}) )."522 IIowever. recent siuulatiouns sugeest that iuterual shock cfiicicucies can approach ~10054 (Deloborodov 2000)).," However, recent simulations suggest that internal shock efficiencies can approach $\sim 100\%$ \cite{beloborodov00}) )."523" Nonetheless. as the blast wave sweeps up the external οςπια, it produces a relativistic forward shock aud a iuldly relativistic reverse shock in the opposite direction of the initial flow."," Nonetheless, as the blast wave sweeps up the external medium, it produces a relativistic forward shock and a mildly relativistic reverse shock in the opposite direction of the initial flow."524" The reverse shock decelerates the ejecta while the forward shock continuously accelerates the electrous ito a distiibution of energies described by a power law dipfds,x>,P. where +, is the electron Lorentz factor."," The reverse shock decelerates the ejecta while the forward shock continuously accelerates the electrons into a distribution of energies described by a power law $dn_{e}/d\gamma_{e} \propto \gamma_{e}^{-p}$, where $\gamma_{e}$ is the electron Lorentz factor."525" The distribution has a low-cuerey cutoff given by 5,4,€σοι ", The distribution has a low-energy cutoff given by $\gamma_{m} \le \gamma_{e}$.526Behind the shock. the accelerated electrons aud magnetic field acquire some fraction. e; aud ερ of the mterual cucreyv.," Behind the shock, the accelerated electrons and magnetic field acquire some fraction, $\epsilon_{e}$ and $\epsilon_{B}$ of the internal energy."527 The resulting svuchrotron spectrum of the relativistic electrons cousists of four power-law regions (Sarict1998)) defined by three critical frequencies r4. ve. and Pa. Where vy is the selfabsorption frequency. ο=mr.) is the cooling frequency. and My=vir) Is the characteristic svuchrotrou frequency (sce Figure 1 in Sarictal.1998)).," The resulting synchrotron spectrum of the relativistic electrons consists of four power-law regions \cite{sari98}) ) defined by three critical frequencies $\nu_{\rm a}$, $\nu_{\rm c}$, and $\nu_{\rm m}$, where $\nu_{\rm a}$ is the self-absorption frequency, $\nu_{\rm c} = \nu(\gamma_{\rm c})$ is the cooling frequency, and $\nu_{\rm m} = \nu(\gamma_{\rm m})$ is the characteristic synchrotron frequency (see Figure 1 in \cite{sari98}) )."528 Tere. we are only concerned with the hieh-energw spectrum. therefore we do not consider seltabsorption.," Here, we are only concerned with the high-energy spectrum, therefore we do not consider self-absorption."529" Electrous with 5,2+. cool down to ,. the Lorentz factor of an electron that cools on the hydrodynamic timescale of the shock (Piran19993)."," Electrons with $\gamma_{e} \ge \gamma_{\rm c}$ cool down to $\gamma_{\rm c}$, the Lorentz factor of an electron that cools on the hydrodynamic timescale of the shock \cite{piran99}) )."530" The electrous cool rapidly when sy,2σοι known asfast-cooling (LC. 14429vw). and cool more slowly when 544,€5&4. known asslow-cooling."," The electrons cool rapidly when $\gamma_{\rm m} \ge \gamma_{\rm c}$, known as (i.e., $\nu_{\rm m} > \nu_{\rm c}$ ), and cool more slowly when $\gamma_{\rm m} \le \gamma_{\rm c}$, known as."531 Tn the fast-cooling regime. the evolution of the shock may range from fully radiative (e.~1) to fully adiabatic (e.«1).," In the fast-cooling regime, the evolution of the shock may range from fully radiative $\epsilon_{e} \sim 1$ ) to fully adiabatic $\epsilon_{e} \ll 1$ )."532" In the slow-cooliug mode. the evolution can only be adiabatic. siuce +4,«σοι "," In the slow-cooling mode, the evolution can only be adiabatic, since $\gamma_{\rm m} < \gamma_{\rm c}$."533"The characteristic svuchrotrou frequency of an clectron with niunuuni Loreutz factor +, is (SariandPiran1999)) corresponding to a break iu the observed spectrum with cnerey where Pis the bulk Loreutz factor aud 04 is the coustaut deusitv of the ambient imediunu.", The characteristic synchrotron frequency of an electron with minimum Lorentz factor $\gamma_{\rm m}$ is \cite{sari99a}) ) corresponding to a break in the observed spectrum with energy where $\Gamma$ is the bulk Lorentz factor and $n_{1}$ is the constant density of the ambient medium.534 Although the frequency in equation 1 depeuds strougly ou the parameters of the system. the forward shock may very well peak initially iu hard X-ravs or m eannnia rays (Sari and Pian 1999).," Although the frequency in equation 1 depends strongly on the parameters of the system, the forward shock may very well peak initially in hard X-rays or in gamma rays (Sari and Piran 1999)."535 The sxuchrotron spectrum evolves with time according to the livdvodvuamic evolution of the shock and the eeconmetrv of the fireball (e.e.. spherical or collimated).," The synchrotron spectrum evolves with time according to the hydrodynamic evolution of the shock and the geometry of the fireball (e.g., spherical or collimated)."536" Specifically. the time dependence of 1 aud 14, will strongly depend on the time evolution of the Loreutz factor >(+)."," Specifically, the time dependence of $\nu_{\rm c}$ and $\nu_{\rm m}$ will strongly depend on the time evolution of the Lorentz factor $\gamma (t)$."537" Assundug a spherical blast wave and a homogeneous iiediuu. for radiative fast-cooling. p,x¢1)"" and pixt 2)"" while for adiabatic evolution (fast or slow-cooling} PaxE? aud myxt M2, "," Assuming a spherical blast wave and a homogeneous medium, for radiative fast-cooling, $\nu_{\rm m} \propto t^{-12/7}$ and $\nu_{\rm c} \propto t^{-2/7}$ , while for adiabatic evolution (fast or slow-cooling) $\nu_{\rm m} \propto t^{-3/2}$ and $\nu_{\rm c} \propto t^{-1/2}$ ."538"The shape of the svuchrotrou spectrum retains constant with time as ος and 14, evolve o lower values.", The shape of the synchrotron spectrum remains constant with time as $\nu_{\rm c}$ and $\nu_{\rm m}$ evolve to lower values.539" In the fast-cooling niodo. 74, decays faster han το. causing a transition m the spectrum from fast to slow-cooling."," In the fast-cooling mode, $\nu_{\rm m}$ decays faster than $\nu_{\rm c}$ , causing a transition in the spectrum from fast to slow-cooling."540 Since the breakfrequencies scale with time as a power- the spectral cherey ftux of the svuchrotron spectrum. Fy (ere 1 ? D) will also scale as a power- in time so that Bud.)~vt’.where the spectral and temporalpower-law indices. a and 9. depend on the eniporal ordering of m. relative to my. Le. fast or ," Since the breakfrequencies scale with time as a power-law, the spectral energy flux of the synchrotron spectrum, $F_{\nu}$ (erg $^{-1}$ $^{-2}$ $^{-1}$ ), will also scale as a power-law in time so that $F_{\nu}(\nu,t) \propto \nu^{\alpha}t^{\beta}$,where the spectral and temporalpower-law indices, $\alpha$ and $\beta$ , depend on the temporal ordering of $\nu_{\rm c}$ relative to $\nu_{\rm m}$ , i.e., fast or slow-cooling."541For radiative fast-cooling.," For radiative fast-cooling,"542A similar studyv has been couducted bv 7? nu he Anteinae (NCC 1038/1039).,A similar study has been conducted by \citet{mengel02} in the Antennae (NGC 4038/4039).543 They determined vial LASSCS axd Lieht-to-miass ratios for a sauple of five bright SSCs. aud compared the results to νιwious IATF forms using pomulation svuthesis models.," They determined virial masses and light-to-mass ratios for a sample of five bright SSCs, and compared the results to various IMF forms using population synthesis models."544 The clusters studied w Nene ‘Let al., The clusters studied by Mengel et al.545 appear to exhibit a raice of IMEs. with SOLO evicence of dependence ou location within the merger environmueut.," appear to exhibit a range of IMFs, with some evidence of dependence on location within the merger environment."546 Tn contrast. ο measure virial masses: for five clusters in nearby galaxies aud fonud light-to-auass ratios cosistent with a Kroupa or Sapeter IAIF.," In contrast, \citet{larsen04} measured virial masses for five clusters in nearby galaxies and found light-to-mass ratios consistent with a Kroupa or Salpeter IMF."547 They ound uo evidence for a deficiency of low-mass stars in hese clusters., They found no evidence for a deficiency of low-mass stars in these clusters.548 The ACS observatious. designed sp.cifically το study ie properties of ALS82-F. represcut a significant advance i quality over all earlier optical images.," The ACS observations, designed specifically to study the properties of M82-F, represent a significant advance in quality over all earlier optical images."549 ? nuaged je cluster with the xe-repair mission Plauetary Camera i 1992., \citet{o'connell95} imaged the cluster with the pre-repair mission Planetary Camera in 1992.550" The cluster fell at the edge of or between chips on the detector in their V- aud L-band equivaleut inages. and they deemed their W-banud deconvolution ""uot lughly reliable."," The cluster fell at the edge of or between chips on the detector in their $V$ - and $I$ -band equivalent images, and they deemed their $V$ -band deconvolution “not highly reliable.”"551 SCOL used archival WFPC2 tages in the EF139W. E555W aud PaliW filters (2)..," SG01 used archival WFPC2 images in the F439W, F555W and F814W filters \citep{degrijs01}."552 These images were designed for a separate study. of M82. and were not ideal for M82-F. The cluster fell on the WEL CCD. aud were significantly uudersampled due to the 100πας pixels.," These images were designed for a separate study of M82, and were not ideal for M82-F. The cluster fell on the WF4 CCD, and were significantly undersampled due to the 100-mas pixels."553 The two lonecr-waveleneth iuages were both saturated iu the cluster core., The two longer-wavelength images were both saturated in the cluster core.554 The ACS/IIRC images used exposure times specifically desigued for study of M82-F. aud with 25 mas pixels. are critically sampled above 177 mu.," The ACS/HRC images used exposure times specifically designed for study of M82-F, and with 25 mas pixels, are critically sampled above 477 nm."555 SCUOL did not decouvolve the PSF from the WFPC2 F139W Huaee. iustead estimating the broadening heuristically.," SG01 did not deconvolve the PSF from the WFPC2 F439W image, instead estimating the broadening heuristically."556 Dv contrast. we treated the PSF more rigorously using a iodel PSF as described in Section 2..," By contrast, we treated the PSF more rigorously using a model PSF as described in Section \ref{obs}."557" Both the ? and SCGOL studies found a projected halfleht radius of 160+20 mas for M82-F. using damages at 555 mu and 139 inui. respectively,"," Both the \citet{o'connell95} and SG01 studies found a projected half-light radius of $160 \pm 20$ mas for M82-F, using images at 555 nm and 439 nm, respectively."558" Our fits to the major axis of the cluster in ACS/IIRC images vield significantly smaller projected ιαΠο radii of 120+2 mas aud 12342 mas at 555 mm and 135 mu. respectively,"," Our fits to the major axis of the cluster in ACS/HRC images yield significantly smaller projected half-light radii of $120 \pm 2$ mas and $123 \pm 2$ mas at 555 nm and 435 nm, respectively."559 These values are more precise and more accurate than the radii determined from the ower-resolution optical data in earlier works., These values are more precise and more accurate than the radii determined from the lower-resolution optical data in earlier works.560 The axial ratio of MS2-FE is ~0.55 in all but the shortest wavelength nuage (Figure ??))., The axial ratio of M82-F is $\sim 0.55$ in all but the shortest wavelength image (Figure \ref{halfradii}) ).561 Fits to the nuages show a distinct trend of decreasing cluster size with iucreasing wavelength., Fits to the images show a distinct trend of decreasing cluster size with increasing wavelength.562 Light at shorter wavelengths is iacreasinely dominated bw hotter stars still ou the main sequence., Light at shorter wavelengths is increasingly dominated by hotter stars still on the main sequence.563 Iu a coeval population. these stars will be intermediate uass stars.," In a coeval population, these stars will be intermediate mass stars."564 Louger waveleugth light is dominated by cooler volved stars. stars originally wore massive than those at ιο clusters main sequence turnoff point.," Longer wavelength light is dominated by cooler evolved stars, stars originally more massive than those at the cluster's main sequence turnoff point."565 The negative correlation between cluster size aud observed wavelength suggests that the massive red evolved stars that dominate re near-IR light are more centrally concentrated than the oeitermediate-niass lnain sequence stars which dominate ιο optical light (?).., The negative correlation between cluster size and observed wavelength suggests that the massive red evolved stars that dominate the near-IR light are more centrally concentrated than the intermediate-mass main sequence stars which dominate the optical light \citep{sternberg98}.566 A key assumption of our method is that lieht traces nass within the cluster., A key assumption of our method is that light traces mass within the cluster.567 Mass segregation renders the oeiterpretatiou of the Lelt-to-mass ratio problematic., Mass segregation renders the interpretation of the light-to-mass ratio problematic.568 The rear-IR mieasurenmaeuts presented here trace the light of superent stars the inost massive stars currently xeseut in the cluster., The near-IR measurements presented here trace the light of supergiant stars — the most massive stars currently present in the cluster.569 If there is mass segregation. the rear-IR virial micasurcment probes only the core of the cluster. io. mass contained within the volume populated w these hiehest-mass stars.," If there is mass segregation, the near-IR virial measurement probes only the core of the cluster, i.e., mass contained within the volume populated by these highest-mass stars."570 As such. the derived mass would be a lower limit aud the IMFE of the cutive cluster uav follow the Kroupa form.," As such, the derived mass would be a lower limit and the IMF of the entire cluster may follow the Kroupa form."571 In this case. the IME ucasured in the core would appear “top-heavy because of mnass segregation.," In this case, the IMF measured in the core would appear “top-heavy” because of mass segregation."572 A nearby example of this effect is the voung. massive cluster R136 in the 30 Doradus uebula iu he Large Magellanic Cloud (LMC).," A nearby example of this effect is the young, massive cluster R136 in the 30 Doradus nebula in the Large Magellanic Cloud (LMC)."573 7. found that the uass function in B136 steepeus with increasing distauce ron the cluster center. iudicating strong mass segrecation.," \citet{brandl96} found that the mass function in R136 steepens with increasing distance from the cluster center, indicating strong mass segregation."574 At the adopted cluster age. stars more massive than SAL. have exploded as supernovac. and stars in the 658 AL. range have evolved off the main sequence (23...," At the adopted cluster age, stars more massive than $\sim 8$ $_\odot$ have exploded as supernovae, and stars in the 6–8 $_\odot$ range have evolved off the main sequence \citep{schaller92}."575 If we asstune that the core cousists solely of stars that are (and ronunants of progenitors which were) larecr than 2 M. as indicated by the LYM ratio. integration of the Ixrotpa IMP nuiples that t106 lucasured core mass represents oilv one-third of the current cluster mass.," If we assume that the core consists solely of stars that are (and remnants of progenitors which were) larger than 2 $_\odot$ as indicated by the $L/M$ ratio, integration of the Kroupa IMF implies that the measured core mass represents only one-third of the current cluster mass."576 The remaining stars (with masses smaller than 2 ML) would be distributed outside the core., The remaining stars (with masses smaller than 2 $_\odot$ ) would be distributed outside the core.577 This distribution of stars would thus require a total cluster mass of ~2<109 ML. to be consistent with a Ixroupa IME for the population of the entire cluster., This distribution of stars would thus require a total cluster mass of $\sim 2 \times 10^6$ $_{\odot}$ to be consistent with a Kroupa IMF for the population of the entire cluster.578 Alass segregation ids ecuerally associated with the eradual equipartition of cuerey via stellar encounters im old globular clusters (7)., Mass segregation is generally associated with the gradual equipartition of energy via stellar encounters in old globular clusters \citep{spitzer87}.579. Tiegh mass stars sink to the center of a cluster through dynamic interactions over the course of the relaxation time. typically of order 105 vears or a Globular cluster.," High mass stars sink to the center of a cluster through dynamic interactions over the course of the relaxation time, typically of order $10^8$ years for a globular cluster."580 We do not expect M82-F to exhibit nass segregation over its full extent at its adopted age., We do not expect M82-F to exhibit mass segregation over its full extent at its adopted age.581" If we assunie an average stellar mass of O87 ML. for a full Ioupa IME. the halfanass relaxation time (2). for \[S2-F is ty,=LsLOS vears roughlv au order of magnitude ouecr than the clusters current age."," If we assume an average stellar mass of 0.87 $_{\odot}$ for a full Kroupa IMF, the half-mass relaxation time \citep{meylan87}582 for M82-F is $t_{rh} = 4 \times 10^8$ years — roughly an order of magnitude longer than the cluster's current age."583 Recent studies; however. have found evideuce of mass seeregation iu sigmificautly vouuger clusters.," Recent studies, however, have found evidence of mass segregation in significantly younger clusters."584 7. fouud that he highest mass stars in the 0.5 Myi-old. Orion Nebula Cluster are preferentially located in the cluster ceuter. aud hat stars down to 0.3 AL. are less centrally concentrated han more massive stars within the inner 1.0 pe.," \citet{lynne98} found that the highest mass stars in the 0.8 Myr-old Orion Nebula Cluster are preferentially located in the cluster center, and that stars down to 0.3 $M_{\odot}$ are less centrally concentrated than more massive stars within the inner 1.0 pc."585 The nassive cluster R136 is mass segregated at an age of oulv 3 Myr (7)., The massive cluster R136 is mass segregated at an age of only 3 Myr \citep{brandl96}.586 Less massive LMC. clusters NCC 1805 (7).. NGC Tals. NGC 2001 and NCC 2100 (7). as well as NGC 330 (2). in the Sinall Magellanic Cloud all display παν segregation at ages of LO50 Myr.," Less massive LMC clusters NGC 1805 \citep{degrijs02b}, NGC 1818, NGC 2004 and NCG 2100 \citep{gouliermis04} as well as NGC 330 \citep{sirianni02} in the Small Magellanic Cloud all display mass segregation at ages of 10–50 Myr."587 Nuinerical simulations demonstrate that segregation of a clusters most massive stars occurs much more rapidly hau the halfiuass relaxation time (?).., Numerical simulations demonstrate that segregation of a cluster's most massive stars occurs much more rapidly than the half-mass relaxation time \citep{gerhard00}.588 Iudeed. if high πάσα stars are somehow concentrated at the ceuter of the cluster at the time of formation. the relaxation timescale here will be shorter.," Indeed, if high mass stars are somehow concentrated at the center of the cluster at the time of formation, the relaxation timescale there will be shorter."589 Dynamical mass segregation will lus proceed more rapidly at the core. on the order of a few crossing times (7)..," Dynamical mass segregation will thus proceed more rapidly at the core, on the order of a few crossing times \citep{degrijs02b}. ."590 Based ou the measured velocity dispersion aud halflight radius. the crossing time for \[s2- Fist.=1.1.10° vears.," Based on the measured velocity dispersion and half-light radius, the crossing time for M82-F is $t_c = 1.4 \times 10^5$ years."591 This is sienificautly: less than the age of the cluster. which iuplics that the core has had time to uudergo mass segregation.," This is significantly less than the age of the cluster, which implies that the core has had time to undergo mass segregation."592 ? showed that the cores of SSCs may uncereo significant dynamical evolution iu as little as 25 Myr., \citet{degrijs02a} showed that the cores of SSCs may undergo significant dynamical evolution in as little as 25 Myr.593 The voune age of \L82-F relativeto its, The young age of M82-F relativeto its594For LAINBs the timescale of tidal svuehronization is much shorter than the characteristic evolutionary Ginescale of the binary. so we can assume that the spin of the secondary star and the binary orbital revolution are always synchronized.,"For LMXBs the timescale of tidal synchronization is much shorter than the characteristic evolutionary timescale of the binary, so we can assume that the spin of the secondary star and the binary orbital revolution are always synchronized."595 Assuming rigid body rotation of (he secondary star and neglecting (he spin angular momentum of the neutron star. the total angular momentum of the binary svstem can be expressed as where {ο is the moment of inertia of the secondary star. & is the angular velocity of the binary.," Assuming rigid body rotation of the secondary star and neglecting the spin angular momentum of the neutron star, the total angular momentum of the binary system can be expressed as where $I_2$ is the moment of inertia of the secondary star, $\omega$ is the angular velocity of the binary."596 We consider three kinds of mechanisms of angular momentum loss., We consider three kinds of mechanisms of angular momentum loss.597 The first is the angular momentum loss due (ο gravitational radiation (Landau&Lifshitz1975) where c is the light speed.," The first is the angular momentum loss due to gravitational radiation \citep{landau}598 where c is the light speed."599 This mechanism is important only in very short period binary svslens., This mechanism is important only in very short period binary systems.600 The second angular momentum loss mechanism is for non-conservative mass transler., The second angular momentum loss mechanism is for non-conservative mass transfer.601 We assume that a fraction a of the translerred mass is accreted by the NS. and the remaining nass is ejected out of the binary as isotropic winds from the NS. carrying away the specific angular momentum of the Ns. In our numerical caleulations we have set a=0.," We assume that a fraction $\alpha$ of the transferred mass is accreted by the NS, and the remaining mass is ejected out of the binary as isotropic winds from the NS, carrying away the specific angular momentum of the NS, In our numerical calculations we have set $\alpha=0$."602 Alternatively. if the NS is spun up to be a millisecond pulsar. its radiation pressure may be strong enough to halt the transferred malter at (he L4 point aud quench the accretion.," Alternatively, if the NS is spun up to be a millisecond pulsar, its radiation pressure may be strong enough to halt the transferred matter at the $L_1$ point and quench the accretion."603" This ""radio ejection may cause almost all ihe matter from the secondary to be lost from the binary (Durderietal.2001.2002)."," This “radio ejection” may cause almost all the matter from the secondary to be lost from the binary \citep{burderi01,burderi02}."604. The corresponding rate of angular moment loss is where αι is the distance from the £4 point to the center of mass of the binary system., The corresponding rate of angular momentum loss is where $a_{L1}$ is the distance from the $L_1$ point to the center of mass of the binary system.605pass through one of these clumps. and ACN having compact chougl coupoucuts are then observed to sciutillate.,"pass through one of these clumps, and AGN having compact enough components are then observed to scintillate."606 ILowever. the clumps are sinall enough that they produce effectively no additional broadening.," However, the clumps are small enough that they produce effectively no additional broadening."607 This scenario is also broadly consistent with the notion of “clumps” of material producing extreme scattering events (FiedlerTawetsetal.TON?1987). and; parabolicvyee aresyyw in.1 pulsarev dynamicIm louspectrawet (HillHetTPal.*Π2005)., This scenario is also broadly consistent with the notion of “clumps” of material producing extreme scattering events \citep{fdjh87} and parabolic arcs in pulsar dynamic spectra \citep{hsabeh05}.608 We can also use the difference between the scintillating aud nou-scintillating sources to set quantitative limits ou the amount of racdio-wave scattering contributed by theICAL., We can also use the difference between the scintillating and non-scintillating sources to set quantitative limits on the amount of radio-wave scattering contributed by the.609 We adopt 0.5 amas at 1 ο (z36 from Table 2)) as the upper liit on the difference in the amount of scattering between the two populations., We adopt 0.5 mas at 1 GHz $\approx 3\sigma$ from Table \ref{tab:stats}) ) as the upper limit on the difference in the amount of scattering between the two populations.610 The implied scattering measure is SAL<10 spe an20/5 (Cordes&Lazio2006).," The implied scattering measure is $\mathrm{SM} \lesssim61110^{-4}$ kpc ${}^{-20/3}$ \citep{cl02}."612. Iu turn. the scattering micasure is given by where D is. the distance.. Fis. a fluctuation. . ↻⋜∐⋅⋜∐⊔↸∖↑↸∖↥⋅↸∖∐↸⊳⋜⋯↴∖↴↿∏⋜↧⊓∐∶↴∙⊾⋜↕↴∖↴↻↸∖↸⊳↑↴∖↴∪↕↑∐↸∖↕⊔↕↸⊳↥⋅≺∏≻∐⋅↖⇁↴∖↴∐∷∖↴ . ⋅ of. the plasmas. ορ is. the electron density.. aud Cap=LS om2 cn? is a constant.," In turn, the scattering measure is given by where $D$ is the distance, $F$ is a fluctuation parameter encapsulating aspects of the microphysics of the plasma, $n_e$ is the electron density, and $C_{\mathrm{SM}} = 1.8$ ${}^{-20/3}$ ${}^6$ is a constant."613 Fora characteristic redshift of approximately unity (Figure L)). the equivalent (angular-size) distauce is Dz1.5 Cpe. implying Fo2<10195 (n..," For a characteristic redshift of approximately unity (Figure \ref{fig:z}) ), the equivalent (angular-size) distance is $D614\approx 1.5$ Gpc, implying $\overline{Fn_e^2} \lesssim 10^{-10.5}$ ${}^{-6}$."615" For a barvoulc. matter cusity: O,h2=0.127-- (Sperecletal.200€bh. the imterealactic electron density can be no larger than 9.«2.2LO D asstunine that heli is fully ionized (Sokasian.Abel.&Ileruquist2002)."," For a baryonic matter density $\Omega_bh^2 = 0.127$ \citep{sbd+06}, the intergalactic electron density can be no larger than $\overline{n_e} < 2.2 \times 10^{-7}$ ${}^{-3}$, assuming that helium is fully ionized \citep{sah02}."616. Thus. we require FS105. so ax not to violate the inferred lits on scattering.," Thus, we require $F \lesssim61710^3$, so as not to violate the inferred limits on scattering."618 For reference. m the diffuse GalacticISAL. Fo0.2. aud in the Galactic spiral arms. Fo~10.," For reference, in the diffuse Galactic, $F \approx 0.2$, and in the Galactic spiral arms, $F \sim 10$."619" In turn. the F parameter is where ¢ is the normalized second moment of the fluctuations. e is the fractional variance im 25, within the plasma. 5 is the filling factor. aud fy is the largest scale ou which the density fluctuatious occur (or outer scale. if the plasma is turbulent). iu parsec units."," In turn, the $F$ parameter is where $\zeta$ is the normalized second moment of the fluctuations, $\epsilon$ is the fractional variance in $n_e$ within the plasma, $\eta$ is the filling factor, and $\ell_0$ is the largest scale on which the density fluctuations occur (or outer scale, if the plasma is turbulent), in parsec units."620 Assuning that ο—€~1. we conclude that yi?PEE=1037.," Assuming that $\zeta \sim \epsilon \sim6211$, we conclude that $\eta\ell_0^{2/3} \gtrsim 10^{-3}$."622 The ICAL is thought to be permeated by shocks (Davéetal.2001).. which might be expected to . ↽ ⋅ ⋅ ≼⊔⋅↕↖⇁↸∖∣∕≻," The IGM is thought to be permeated by shocks \citep{dco+01}, which might be expected to drive $\eta \to 1$."623↓∙≼∶↕↖↽↸∖∐↑↕∐∖↕⋜∐⋅∶↴⋅⊾↸∖↥⋅↴∖↴↸⊳⋜↧↕↸∖↴∖↴⋜∏↽⋜⊔↕⋜∏⋝↕↸∖↕∐⋅ heIGAL. (y~1 Alpe would not be unreasonable.," Given the larger scales available in the, $\ell_0 \sim 1$ Mpc would not be unreasonable."624 We are forced to conclude that the current nuits on imtergalactic scatterius. while broadly consistent with the current picture of theICAL. do not vet place significant constraints on its xoperties.," We are forced to conclude that the current limits on intergalactic scattering, while broadly consistent with the current picture of the, do not yet place significant constraints on its properties."625 While we find no indications of intergalactic scattering.. future. obscrvatious. are warranted.," While we find no indications of intergalactic scattering, future observations are warranted."626 Tu articular.. ifgt a scintillating. ACN-. is found.. close o the line of sight to a pulsar. a comparison votween the two lines of sight would provide strong constraints on the amount of Galactic liuterealactic scattering.," In particular, if a scintillating AGN is found close to the line of sight to a pulsar, a comparison between the two lines of sight would provide strong constraints on the amount of Galactic intergalactic scattering."627" Also. hieher-seusitivitv observations (οσοι, with the very loug baseline Tigh Sensitivity Array or HSA) targetiug scintillating AGN with larger diameters may provide additional constraints"," Also, higher-sensitivity observations (e.g., with the very long baseline High Sensitivity Array or HSA) targeting scintillating AGN with larger diameters may provide additional constraints."628 Many of the AGN with the largest diameters are not detected at the lower frequencies. frequencies at which the VLBA alone has a relatively low sensitivity.," Many of the AGN with the largest diameters are not detected at the lower frequencies, frequencies at which the VLBA alone has a relatively low sensitivity."629" The TSA could be used to verity whether these AGN do indeed have such largeMD scattering diameters or assess to what extent ↕∐⊓⋅∐↓↴∖↴↕↸⊳↴∖↴⊓⋅⋯⊳↑∪⋅↸∖↸⊳∪∐↑⋜∐⊔∐↕⋜↧↑↸∖↴∖↴↑∐↸∖↴∖↴↸⊳⋜↧⇈↸∖↥⋅⋃∶↴∙⊾ . . ciainueter estimates,", The HSA could be used to verify whether these AGN do indeed have such large scattering diameters or assess to what extent intrinsic structure contaminates the scattering diameter estimates.630 We- sununarize. our findings∙∙ as follows., We summarize our findings as follows.631. Iu our sample of 58ACN... approximately of the suuple exhibit ∙∙∙iutradav variabilityHat (iuterstellar: scintillation) with the other not showing intraday variability.," In our sample of 58, approximately of the sample exhibit intraday variability (interstellar scintillation) with the other not showing intraday variability."632 Iuterstellar scattering is nicasurable for most of theseACUN.. and the typical broadening diameter is 2 mas.," Interstellar scattering is measurable for most of these, and the typical broadening diameter is 2 mas."633 Scintillating ACN are typically at lower Calactic latitudes than the noun-sciutillatiugACN.. consistent with the scenario that iutradav variability is a propagation effect from the Galactic interstellar medimm.," Scintillating AGN are typically at lower Galactic latitudes than the non-scintillating, consistent with the scenario that intraday variability is a propagation effect from the Galactic interstellar medium."634 The maguitude of the inferred interstellar broadening measured toward the scintillatingACN... when scaled to higher frequencies. is comparable to that determined from analyses of the light curves for the more well-kuown lutraday variable sources.," The magnitude of the inferred interstellar broadening measured toward the scintillating, when scaled to higher frequencies, is comparable to that determined from analyses of the light curves for the more well-known intraday variable sources."635 However. we fiud no difference in the amount of scattering measured toward the sciutillating versus non-sciutillatiugAGN.," However, we find no difference in the amount of scattering measured toward the scintillating versus non-scintillating."636.. À consistent picture is one in which the sciutillation results frou localized regions (ποπας}. distributed throughout the Calactic disk. but which individually make little coutzibution to tlre ∖⊀ broadening.," A consistent picture is one in which the scintillation results from localized regions (“clumps”) distributed throughout the Galactic disk, but which individually make little contribution to the angular broadening."637⋅⊀∖⋅⋉ Iu our TANsune.vo of the AGN augnbuhave measured redshifts.," In our sample, of the AGN have measured redshifts."638 At best. a inareinal trend is found for scintillating (non- AC ' ↴∖↴↸⊳↕∐↑↕∐⋪↧↑↕∐∩⊀≚≼⊲⋀∖⊽↑∪∐⋪↧↖↽↸∖↴∖↴↕⊔⋪↧∐↸∖↥⋅↕⋪∐⋅∩⊾↸∖↥⋅⋪⋯∩⊾∏↕⋪∐⋅' Corger) aug," At best, a marginal trend is found for scintillating (non-scintillating) AGN to have smaller (larger) angular"639e.,.640g.).. We present Monte Carlo caleulations of the fluorescent Ne Ka line in 822. and discuss its observabilitv in 833 and $44.," We present Monte Carlo calculations of the fluorescent Ne $\alpha$ line in 2, and discuss its observability in 3 and 4."641" The X-ray Ne ""characteristic"" (fluorescence) Ίνα line al 14.61 corresponds to (he 2p—15 decay of the excited state resulting from ejection of an inner-shell 1s electron in neutral or near-neutral Neon bv either electron impact or photoionisation.", The X-ray Ne “characteristic” (fluorescence) $\alpha$ line at 14.61 corresponds to the $2p-1s$ decay of the excited state resulting from ejection of an inner-shell $1s$ electron in neutral or near-neutral Neon by either electron impact or photoionisation.642 In the case of the solar photosphere illuminated fom above by coronal X-rays. [Iuorescent lines will be produced. almost entirely. by photoionisation1954).," In the case of the solar photosphere illuminated from above by coronal X-rays, fluorescent lines will be produced almost entirely by photoionisation."643. pointed out that. for a given source spectrum. F(A). the observed flux of Ίνα photons from the photosphere depends on essentially three parameters: (he photospheric abundance A of the fluorescing species relative to (hat of other elements of significance lor the photoabsorption opacity in the vicinity of the 1s ionisation edge: the height  of the emitting source: and the heliocentric angle 9 between the emitting source and the observer.," pointed out that, for a given source spectrum, $F(\lambda)$ , the observed flux of $\alpha$ photons from the photosphere depends on essentially three parameters: the photospheric abundance $A$ of the fluorescing species relative to that of other elements of significance for the photoabsorption opacity in the vicinity of the $1s$ ionisation edge; the height $h$ of the emitting source; and the heliocentric angle $\theta$ between the emitting source and the observer."644 Fluorescent lines are formed in the region of an atmosphere corresponding to optical depth unity for the primary [Kx-shell ionisine photons., Fluorescent lines are formed in the region of an atmosphere corresponding to optical depth unity for the primary K-shell ionising photons.645 showed that in the case of the fInorescent lines from abundant elements O-Fe formed in the solar abmosphere. (his occurs below the chromosphere.," showed that in the case of the fluorescent lines from abundant elements O-Fe formed in the solar atmosphere, this occurs below the chromosphere."646 For the case of Ne (he solar atmospheric Model C (VALC) of indicates that the K-shell 7=1 depth occurs al a gas temperature of about 5000 Ix. just above the temperature minimum and about 700 km above the point where the continuum optical depth at 5000À.. 75000. is unity.," For the case of Ne the solar atmospheric Model C (VALC) of indicates that the K-shell $\tau=1$ depth occurs at a gas temperature of about 5000 K just above the temperature minimum and about 700 km above the point where the continuum optical depth at 5000, $\tau_{5000}$ , is unity."647 To estimate the expected intensity of the emergent Ne Ixo line we used a mocilied version of the 3D Monte Carlo radiative transfer code MOCASSIN2005)., To estimate the expected intensity of the emergent Ne $\alpha$ line we used a modified version of the 3D Monte Carlo radiative transfer code MOCASSIN.648". This code has been tested in detail for Fe IX, photospheric [Inorescence problems by comparison with the computations of2007)mainDodyCitationEnd79.", This code has been tested in detail for Fe $_\alpha$ photospheric fluorescence problems by comparison with the computations of.649 Computation of Ne Ix fluorescence is similar to that for Fe Ix ancl we describe our method here only in brief: the reader is referred to the earlier work for further details., Computation of Ne K fluorescence is similar to that for Fe K and we describe our method here only in brief; the reader is referred to the earlier work for further details.650 The fluorescence calculation involves Following the fate of monochromatic energy packets that sample (he spectrum of the overlving corona and (hat are incident on the photosphere., The fluorescence calculation involves following the fate of monochromatic energy packets that sample the spectrum of the overlying corona and that are incident on the photosphere.651 We assume (he photosphere to be “cold”. whereby all elements. including Ne. are neutral.," We assume the photosphere to be “cold”, whereby all elements, including Ne, are neutral."652 LEnergv packets canundergo photoabsorption or Compton scattering. the probabilitiesof," Energy packets canundergo photoabsorption or Compton scattering, the probabilitiesof"653Section L2).,Section 4.2).654 While Fieure© 3. inclicates that there is a ogeneral treuc ol larger shape parameters (u) for fainter dwarf ellipticals. aud for brighter central surface brightesses for brighter galaxies. the rotating a uou-rotatiug cwarf elliptical galaxies cannot be cdistitetushed in any of these figures.," While Figure \ref{fig:sersic} indicates that there is a general trend of larger shape parameters (n) for fainter dwarf ellipticals, and for brighter central surface brightnesses for brighter galaxies, the rotating and non-rotating dwarf elliptical galaxies cannot be distinguished in any of these figures."655 In fact. the cinematic samples are well mixed in terms of shape. stface brightuess. aud size.," In fact, the kinematic samples are well mixed in terms of shape, surface brightness, and size."656 Ju su-—uary. there appear to be no strong morphological dillereuces between rotating aud nou-rotati& chvarl elliptical galaxies in the Virgo cluster.," In summary, there appear to be no strong morphological differences between rotating and non-rotating dwarf elliptical galaxies in the Virgo cluster."657 Underlyi& disky aud boxy isophotes are seen iu botl kinematic samples (seealsoCelaetal.2003)., Underlying disky and boxy isophotes are seen in both kinematic samples \citep[see also][]{GGvM03}.658". The st""uctural parameters are similar as well.", The structural parameters are similar as well.659 hi le ext section. we investigate whether there are stellar population ciffereuces between the rotati& and non-rotating dwarl elliptical galaxies.," In the next section, we investigate whether there are stellar population differences between the rotating and non-rotating dwarf elliptical galaxies."660 As illustrated in Figure 1l.. many of the dwarf elliptical galaxies in this sample have a slight color gradieut.," As illustrated in Figure \ref{fig:surf}, many of the dwarf elliptical galaxies in this sample have a slight color gradient."661 However. this treud does uot appear to be correlated with the presence of a nucleatec regiou: several of the nucleated dEs have no color gradients while several of the uou-uucleated dEs do have a color gradient.," However, this trend does not appear to be correlated with the presence of a nucleated region; several of the nucleated dEs have no color gradients while several of the non-nucleated dEs do have a color gradient."662 Color graieuts are commonly seen in dEs. usually iu tlie seuse that the outer regions are redder than the iler regious (Vaderetal.LOSS:Jerjen.2000:Barazzaetal. 2003).," Color gradients are commonly seen in dEs, usually in the sense that the outer regions are redder than the inner regions \citep{VVLS88,JBF00,BBJ03}."663. In this sample. VCC 965. 1713. 1827. aud 2019 have color gradients iu this expected direction.," In this sample, VCC 965, 1743, 1857, and 2019 have color gradients in this expected direction."664 However. ap»xoxinately one half of tlie eurreut sample have color gradieuts iu the opposite sense: the inuer regious are redder than the outer regions of VCC 178. 513. 917. 990. 1036. 1122. 2050.," However, approximately one half of the current sample have color gradients in the opposite sense; the inner regions are redder than the outer regions of VCC 178, 543, 917, 990, 1036, 1122, 2050."665 A color gradient implies clilleriig star formation histories. or clillering metal conter1. in the inuer and outer regious of the galaxy.," A color gradient implies differing star formation histories, or differing metal content, in the inner and outer regions of the galaxy."666 It ds likely that both of these effects are relevaru to the interpretation of observed colors aud stellar »opulations [9]. Virgo dEs., It is likely that both of these effects are relevant to the interpretation of observed colors and stellar populations of Virgo dEs.667 For exam.je. a gaAXV may develop a color gradient if the outer gas is preferentially stripped olf as i falls iuto the Vire> cluster.," For example, a galaxy may develop a color gradient if the outer gas is preferentially stripped off as it falls into the Virgo cluster."668 Iu this scenario. the inner region of the galaxy may couiiue to have active sta: fornation while tlie outer regions a'e recuced [9] an aging stellar populaton (redder coors).," In this scenario, the inner region of the galaxy may continue to have active star formation while the outer regions are reduced to an aging stellar population (redder colors)."669 Sucl a scena1o easily explaius the observed. color &'adie usi1 most chwarl elliptical galaxies (redder iu tl eoUskirts)., Such a scenario easily explains the observed color gradients in most dwarf elliptical galaxies (redder in the outskirts).670 Alteriativelv. a coor gracdieut i1 the opposite sense cat ye created i “the inuer regO1 ‘elallis a larger fraction of its enriched naterial: if there is a metalicity graclieu. the more Ineal-rich stars (iuner regious) wil be recdcler llan the metal-poor stars (outski‘ts).," Alternatively, a color gradient in the opposite sense can be created if the inner region retains a larger fraction of its enriched material; if there is a metallicity gradient, the more metal-rich stars (inner regions) will be redder than the metal-poor stars (outskirts)."671 The relati veliportance of both of these ellects will depe16 ou the galaxys cetaile star loruation history aud lie interlace olf the galaxy witl he intracltsler ineciuin., The relative importance of both of these effects will depend on the galaxy's detailed star formation history and the interface of the galaxy with the intracluster medium.672 As shown in Fieure [. the oesence of a color gradieut does 1ot correlate with the kinematic properties of the dEs.," As shown in Figure \ref{fig:rot}, the presence of a color gradient does not correlate with the kinematic properties of the dEs."673 Galaxies wit1 a blue core (VCC 965 and 2019) or red core (VCC 213. 917. 900. 1036. and. 2050) are equally likely to be rotation dominated as galaxies with no stroug color," Galaxies with a blue core (VCC 965 and 2019) or red core (VCC 543, 917, 990, 1036, and 2050) are equally likely to be rotation dominated as galaxies with no strong color"674observer was equivalent to a star of SOOOI. matching the front face temperature observed by IIST.,"observer was equivalent to a star of 8000K, matching the front face temperature observed by HST."675 This model should correspond to the last data point in Figure 3.., This model should correspond to the last data point in Figure \ref{fig:ampVd}.676 The flux aiplitude in Figure 3 declines by a factor of 10113. and so we increased the mradiation iu our model uutil the flux amplitude had increased by this factor.," The flux amplitude in Figure \ref{fig:ampVd} declines by a factor of $^{1.2}$, and so we increased the irradiation in our model until the flux amplitude had increased by this factor."677 Over this range of interest. we found that represented the data to better than 25 percent for all values of Pj.," Over this range of interest, we found that represented the data to better than 25 percent for all values of $F_{irr}$."678 We also used tried using the bolometric correction and colours of model atmospheres elven iu Bessell ct al (1998) instead of blackbodies to represent the flux., We also used tried using the bolometric correction and colours of model atmospheres given in Bessell et al (1998) instead of blackbodies to represent the flux.679 We found this chauged . by less than 0.06 in the low iradiation case. which is that uost affected by the difference between model atmospheres aud black bodies.," We found this changed $x$ by less than 0.06 in the low irradiation case, which is that most affected by the difference between model atmospheres and black bodies."680 With a value forc we can now use the observations to derive a value of à by equating (2)) ο (3))., With a value for $x$ we can now use the observations to derive a value of $\eta$ by equating \ref{eqt:observe}) ) to \ref{eqt:response}) ).681 This vields: This result is just (2.20) consistent with the value. Prialuik (1986)., This yields: This result is just $\sigma$ ) consistent with the value Prialnik (1986).682 fud from purely theoretical considerations of j=Lit., find from purely theoretical considerations of $\eta=1.14$.683 Especially given the uature of the approxinatious iade. this sees fo support the conclusion that the photometric variation in V1500 Cre. aud bv implication other old novae. is caused by radiation from the white dsvarf.," Especially given the nature of the approximations made, this seems to support the conclusion that the photometric variation in V1500 Cyg, and by implication other old novae, is caused by irradiation from the white dwarf."684 The above shows that for at least the first 20 vears rou outhburs the white dwarf coolne models match the available observations., The above shows that for at least the first 20 years from outburst the white dwarf cooling models match the available observations.685 Caven the Prialnik-tvpe cooling aw. with the observed value of j. aud the temperature of the radiated face at some kuown time after outburst (from Sclunidt ot al.," Given the Prialnik-type cooling law, with the observed value of $\eta$, and the temperature of the irradiated face at some known time after outburst (from Schmidt et al."686 1995) then we can calculate the vpical time taken for irradiation of the surface to become icelieible., 1995) then we can calculate the typical time taken for irradiation of the surface to become negligible.687 The irradiation will drop off so that the Incomine radiation is less than double the nunheated surface Iuuinositv of the secondary star about 280+110 vears after the outburst of V1500 Cre., The irradiation will drop off so that the incoming radiation is less than double the unheated surface luminosity of the secondary star about $280\pm140$ years after the outburst of V1500 Cyg.688 Tutercstinely.o we fiud that in WY See. now over 200 vears since uova outburst. the imradiatiou from the white divarf has decline to these levels (Somers et al 1996). although in that svstem the dise is a complicating factor.," Interestingly, we find that in WY Sge, now over 200 years since nova outburst, the irradiation from the white dwarf has declined to these levels (Somers et al 1996), although in that system the disc is a complicating factor."689 Thus both V1500 Cre. and WY See suggestoo that white chwarts really do cool as the theory. predicts.," Thus both V1500 Cyg, and WY Sge suggest that white dwarfs really do cool as the theory predicts."690 The Jacobus Ἱναρίονι Telescope is operated on the island of La Palma by the Isaac Newton Croup in the Spanish Observatorio del Roque de los Muchachos of the Tustituto de Astrofisica de Canarias., The Jacobus Kapteyn Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias.691 We thank Cregorv Beekman and Coel Weller who helped with the observations. aud Alon Retter for conunenting ou the manuscript.," We thank Gregory Beekman and Coel Hellier who helped with the observations, and Alon Retter for commenting on the manuscript."692 TN was in receipt of a PPARC advanced fellowship when the majority of this work was carried out., TN was in receipt of a PPARC advanced fellowship when the majority of this work was carried out.693Aquila XN.1(=V1333 Aquilac) is known to undergo regular X-rav and optical outhursts on a timescale of ~1 vear (Ixaluzienski et al.,Aquila X–1(=V1333 Aquilae) is known to undergo regular X-ray and optical outbursts on a timescale of $\sim$ 1 year (Kaluzienski et al.694 1977: Pricclhorsky Terrell 1984: Charles 1980). much more frequently than the other neutron star transient Cen XN4 (AleClintock Remillard 1990).," 1977; Priedhorsky Terrell 1984; Charles 1980), much more frequently than the other neutron star transient Cen X–4 (McClintock Remillard 1990)."695 λα X1 therefore. presents us with regular. opportunities to test the models proposed to explain the X-ray outbursts occurring in these low-mass X-ray. binary transient svstenis., Aql X–1 therefore presents us with regular opportunities to test the models proposed to explain the X-ray outbursts occurring in these low-mass X-ray binary transient systems.696 λα X1 also exhibits type 1. N-rayv. bursts (Ixovama 1981: C'zerny. Czerny Crindlav LOST). indicating that the compact object is a neutron star.," Aql X–1 also exhibits type 1 X-ray bursts (Koyama 1981; Czerny, Czerny Grindlay 1987), indicating that the compact object is a neutron star."697 Observations in quiescence have shown that the mass-donating companion is a V—19.2 Wl JV. star (Shahbaz. Casares Charles L997).," Observations in quiescence have shown that the mass-donating companion is a V=19.2 K1 $\sc IV$ star (Shahbaz, Casares Charles 1997)."698 The optical counterpart brightens by ~25 magnitudes during A-ray outbursts. interpreted as reprocessing of radiation in the aceretion cise (Lhorstensen. Charles Bowyer LOTS: Canizares. MeClintock Grindlay 1980: Charles 1950: van DParadijs 1980).," The optical counterpart brightens by $\sim$ 2–5 magnitudes during X-ray outbursts, interpreted as reprocessing of radiation in the accretion disc (Thorstensen, Charles Bowyer 1978; Canizares, McClintock Grindlay 1980; Charles 1980; van Paradijs 1980)."699 The RN'PE ALL Sky Monitor recorcec an X-ray outburst of Aql X1 between late January and carly March. 1997 (Levine Thomas 1997)., The RXTE All Sky Monitor recorded an X-ray outburst of Aql X–1 between late January and early March 1997 (Levine Thomas 1997).700 By 30 March. L997 Aql XN1 was reported to be optically in quiescence (Llovaisky Chevalicr 19907)., By 30 March 1997 Aql X–1 was reported to be optically in quiescence (Ilovaisky Chevalier 1997).701 Xql X.1 then had another outburst in August 1997 (Charles (1997) reported that it had. brightened. to V—IQT.SN on August 7 1907). reaching a maximum level at around V—17.5 (Chevalier Llovaisky 1997).," Aql X–1 then had another outburst in August 1997 (Charles (1997) reported that it had brightened to V=17.8 on August 7 1997), reaching a maximum level at around V=17.5 (Chevalier Ilovaisky 1997)."702 In this letter we report on X-/optical/infrared photometry of Aql XN.1 obtained during the August 1997 outburst., In this letter we report on X-ray/optical/infrared photometry of Aql X–1 obtained during the August 1997 outburst.703 A complete journal of the infrared ancl optical photometric observations is presented in Table 1., A complete journal of the infrared and optical photometric observations is presented in Table 1.704 We obtained. A-band images of Aql XN.1 over a total of 16 nights in 1997 July and August using the Ohio State Infrared Imager/Speetrometer (DePov 1993) on the Perkins l.S-m telescope of the Ohio State and. Ohio Weslevan Universities at. Lowell Observatory., We obtained $K$ -band images of Aql X–1 over a total of 16 nights in 1997 July and August using the Ohio State Infrared Imager/Spectrometer (DePoy 1993) on the Perkins 1.8-m telescope of the Ohio State and Ohio Wesleyan Universities at Lowell Observatory.705 The 210 images were taken with the f//7 camera which provides a 2/77 Ποια of view at a resolution of 07663 pixel tthe secing was typically 2700., The 210 images were taken with the $f/7$ camera which provides a 7 field of view at a resolution of 63 $^{-1}$; the seeing was typically 9.706 AO standard. observing sequence consisted of five consecutive images of GO seconds for Aql N.1: the position of the object on the array was moved. between. exposures. so that the eroup could. be mecdian-stacked to produce a," A standard observing sequence consisted of five consecutive images of 60 seconds for Aql X–1; the position of the object on the array was moved between exposures, so that the group could be median-stacked to produce a"707In this section. we discuss the third. peak with a more complex gap structure by taking into account the azimuthal structure of the fractional gap thickness f. the ratio of the thicknesses of the main acceleration region to the whole gap thickness. fyfhe. and the particle number density in the main acceleration region. |gi.,"In this section, we discuss the third peak with a more complex gap structure by taking into account the azimuthal structure of the fractional gap thickness $f$, the ratio of the thicknesses of the main acceleration region to the whole gap thickness, $h_1/h_2$, and the particle number density in the main acceleration region, $1-g_1$."708 Firstly. we consider the azimuthal structure of fractional gap thickness ancl compare the caleulated light curves with the observations.," Firstly, we consider the azimuthal structure of fractional gap thickness and compare the calculated light curves with the observations."709 ὃν the definition of the gap fraction of equation (11)). foxb. we may choose the form of the aziniuthal distributionof f as. ↗∕ ∖∖⊽↓↥∢⊾↓⋅⋖⋅↥⇂↥∢⋅↙⊽∶∪⋅↓∖∣⋮↗↾∣⊔⋯⊳∣⋮⊔⋯↾↕⊳∖↿↓↕∢⊾⊔↓⋜∟∖⊲↓⊔⋯⊔↓∖⇁⋜↧↓⋯⊾∪⇂⋅ the polar cap radius. and the factor 0.18 is chosen by fitting the phase averagedoaspectrum.," By the definition of the gap fraction of equation \ref{def_fm}) ), $f\propto\frac{1}{r_p}$, we may choose the form of the azimuthal distributionof $f$ as, where the $C=0.18r_{p}^{max}$, $r_{p}^{max}$ is the maximum value of the polar cap radius, and the factor 0.18 is chosen by fitting the phase averaged-spectrum."710 The pulse profiles using the fractional thickness f deseribed by equation (22)) are shown in Figure 4.. where σι=0.05 and fyfhe=0.927 are the same with those of ligure 3..," The pulse profiles using the fractional thickness $f$ described by equation \ref{def_f}) ) are shown in Figure \ref{edlc_f}, where $g_1=0.05$ and $h_1/h_2=0.927$ are the same with those of Figure \ref{edlc_nd}."711 By comparing Figure 3. and 4.. we can find the ellects of azimuthal distribution of f on the pulse profilect.," By comparing Figure \ref{edlc_nd} and \ref{edlc_f}, we can find the effects of azimuthal distribution of $f$ on the pulse profiled."712 For example. the azimuthal structure of the fractional gap thickness produces more bridge emissions as well as a feature at the phase ~0.3 of the pulse profile (in particular for higher energy. bands) in Figure 4..," For example, the azimuthal structure of the fractional gap thickness produces more bridge emissions as well as a feature at the phase $\sim 0.3$ of the pulse profile (in particular for higher energy bands) in Figure \ref{edlc_f}."713" Figure 5. shows the polar cap radius r, (solid-line) and the resultant fractional gap thickness f (dashed-line) as a function of the polar angle.", Figure \ref{rp_phi} shows the polar cap radius $r_p$ (solid-line) and the resultant fractional gap thickness $f$ (dashed-line) as a function of the polar angle.714 In the south pole. the emissions on the magnetic field. lines emerging from polar angle larger (or smaller) than 180. produces the first. (or second) peak.," In the south pole, the emissions on the magnetic field lines emerging from polar angle larger (or smaller) than $180^{\circ}$ produces the first (or second) peak."715 As shown in Figure 5.. the fractional thickness f becomes maximum around the polar angle of 2007. where πρὸ) becomes minimum.," As shown in Figure \ref{rp_phi}, the fractional thickness $f$ becomes maximum around the polar angle of $^{\circ}$, where $r_p(\phi_p)$ becomes minimum."716 Becauselarger fraction thickness f produces a stronger £y) as equation. (10) indicates. the emissions on the magnetic field lines emerging from ~ 200° is more stronger than those from ~160 and from ~2407.," Becauselarger fraction thickness $f$ produces a stronger $E_{||}$ as equation (10) indicates, the emissions on the magnetic field lines emerging from $\sim$ $^{\circ}$ is more stronger than those from $\sim 160^{\circ}$ and from $\sim 240^{\circ}$."717 Consequently. third-peak-like structure is formed in the light curves of Figure 4..," Consequently, third-peak-like structure is formed in the light curves of Figure \ref{edlc_f}. ."718 In the electrodynamic point of view. the thickness of the screening region of the gap. fe δε will be determined by the photo-photon pair-creation rate between the >-rays," In the electrodynamic point of view, the thickness of the screening region of the gap, $h_2-h_1$ , will be determined by the photo-photon pair-creation rate between the $\gamma$ -rays"719Complex. threc-dimensional structures abound. in astLonomy On all scales from “Hulls” dust. agercerates in molecular clouds (Osscnkopl 1993: Stepnik et al.,"Complex, three-dimensional structures abound in astronomy on all scales from “fluffy” dust aggregrates in molecular clouds (Ossenkopf 1993; Stepnik et al."720" 2003). to cosmological large-scale structure that has been described as “sponge-Liκα (Cott. Dicdinson Alelott/| 1986). Op a ""skeleton"" (Sousbie et al."," 2003), to cosmological large-scale structure that has been described as “sponge-like” (Gott, Dickinson Melott 1986), or a “skeleton” (Sousbie et al."721 2WS) of clusters. filaments and voids (Barrow- Bhavsar Soonoda 1985: White et al.," 2008) of clusters, filaments and voids (Barrow, Bhavsar Sonoda 1985; White et al."722 LOST)., 1987).723 While as»ects. of these structures can be expressed. in ternis of simple. geometricalvemotivated properties such as their triaxialiN Or quacrupoe moment. these quantities are not able to capture the higher order complexity of the true shape.," While aspects of these structures can be expressed in terms of simple, geometrically-motivated properties such as their triaxiality or quadrupole moment, these quantities are not able to capture the higher order complexity of the true shape."724 The ciadlenge. thereOre. is to provide an accurate description of an arbitrary hree-dimensional (32d) shape. possibly over many physical length scales. in the hope that this can lead to improved. 1icoretical or analvtical insight into the structure in questior1.," The challenge, therefore, is to provide an accurate description of an arbitrary three-dimensional (3-d) shape, possibly over many physical length scales, in the hope that this can lead to improved theoretical or analytical insight into the structure in question."725 The hunlan visual svsem is more than capable of identifving structures ancl sub-structures for an individual 3-d2 object. but such qualitative interpretations only have limited. use it is not practical to attempt a classification of shapes bv eve when there are many thousands of objects ↿∪↓⊔⊳∖↓≻⋯⇍↿⊳∐↥∢⋅↓≻↓⋅∢⋅⇂∢⋅↓⋅↓⋅∢⋅∠⇂⋜↧↓↿⋖⊾↓⋅⊔⋜∐↓∖⇁∢⊾↓⊳∖⋜⋯⋯∐∪⊔↓⋜⋯⊾∠⇂lop ⋅ ⋠⋠ approach including: The approach we present in this paper is the extension of the two-dimensional (2-d) shapelet method. (Refregier 2003) to three dimensions.," The human visual system is more than capable of identifying structures and sub-structures for an individual 3-d object, but such qualitative interpretations only have limited use – it is not practical to attempt a classification of shapes by eye when there are many thousands of objects to The preferred alternative is an automated approach including: The approach we present in this paper is the extension of the two-dimensional (2-d) shapelet method (Refregier 2003) to three dimensions."726 Shapelets are sets of orthonormal basis functions based on the Llermite polynomial solutions of the quantum harmonic oscillator (QUO)., Shapelets are sets of orthonormal basis functions based on the Hermite polynomial solutions of the quantum harmonic oscillator (QHO).727 Simple analytic forms can be derived for the physical properties of 3-d structures (c.g. centre of mass. root-mean-square raclitts and," Simple analytic forms can be derived for the physical properties of 3-d structures (e.g. centre of mass, root-mean-square radius and"728a fairly “canonical” fast-rise exponential-decav morphology ot with. a double-peaked maximum.,a fairly “canonical” fast-rise exponential-decay morphology but with a double-peaked maximum.729 Phe second. of hese two maxima is approximately coincident with the ransition between the very high anc high/solt spectral states. as found by IHevnivtsev. Trucdolvubov Borozdin (2000).," The second of these two maxima is approximately coincident with the transition between the very high and high/soft spectral states, as found by Revnivtsev, Trudolyubov Borozdin (2000)."730 As the soft X-rav source decays it makes the ransition between high/soft and. low/harcl states (again. using spectral information from Itevnivtsev. Prudolvyuboy Dorozdin 2000) reaching the lowhard state approximately coincidentally with the onset of the BATSE observations.," As the soft X-ray source decays it makes the transition between high/soft and low/hard states (again, using spectral information from Revnivtsev, Trudolyubov Borozdin 2000) reaching the low/hard state approximately coincidentally with the onset of the BATSE observations."731 The third panel in Fig., The third panel in Fig.732 1. plots the ASM hardness ratio (312 keV)9/(1.53 keV)., \ref{fig:lightcurves} plots the ASM hardness ratio (3–12 keV)/(1.5–3 keV).733 Ht shows that the source was hard at the onset of the outburst and later softened., It shows that the source was hard at the onset of the outburst and later softened.734 Lt is not clear from the ASM plots when the source returned to the ow/hard state the transition seemed to be dominated by iarder energies. as presented in Revnivisey. Prudolvuboy Dorozdin (2000).," It is not clear from the ASM plots when the source returned to the low/hard state – the transition seemed to be dominated by harder energies, as presented in Revnivtsev, Trudolyubov Borozdin (2000)."735 lt is interesting to see that there is little. correlation oetween the X-ray and radio lighteurves., It is interesting to see that there is little correlation between the X-ray and radio lightcurves.736 The radio event appeared to begin while the X-ray source was in the very veh state but most of the radio emission is observed during he high/soft state., The radio event appeared to begin while the X-ray source was in the very high state but most of the radio emission is observed during the high/soft state.737 We show in the next section that the radio emission was optically thin throughout this event. vpical of cjection events as opposed to the compact jet which is associated. with the low/hared state.," We show in the next section that the radio emission was optically thin throughout this event, typical of ejection events as opposed to the compact jet which is associated with the low/hard state."738 Therefore the racio detections during the high/soft state do not contraclict orevious results (e.g. GX 339-4 or Cvg X-1): instead they represent discrete ejecta which are still in the process of expanding and decaving., Therefore the radio detections during the high/soft state do not contradict previous results (e.g. GX 339-4 or Cyg X-1); instead they represent discrete ejecta which are still in the process of expanding and decaying.739 The radio lighteurve is plotted. on an expanded. time axis in the top panel of Fig. 2.., The radio lightcurve is plotted on an expanded time axis in the top panel of Fig. \ref{fig:radio}.740 While the time resolution is insullicient to be sure. it appears that there was just one dominant optically thin radio event during this period.," While the time resolution is insufficient to be sure, it appears that there was just one dominant optically thin radio event during this period."741" ""This is supported by the fourth. plot. showing the spectral index which remained optically thin at the higher frequencies at all epochs."," This is supported by the fourth plot, showing the spectral index which remained optically thin at the higher frequencies at all epochs."742 Interestingly the spectral index during the final epoch was not zero as we would expect for the compact jet usually associated: with the low/hare state., Interestingly the spectral index during the final epoch was not zero as we would expect for the compact jet usually associated with the low/hard state.743 This would suggest the additional presence of residual optically thin material and we discuss the implications of this later., This would suggest the additional presence of residual optically thin material and we discuss the implications of this later.744 The second. and third. panels of Fig., The second and third panels of Fig.745 2. show the LP (νως1 2) and [ractional LP (EP: 100«Q2| 02/2) iehteurves respectively (but omitting the July 2 epoch due ο corrupted Stokes Q and U images)., \ref{fig:radio} show the LP $\sqrt{Q^2+U^2}$ ) and fractional LP (FP; $100\times\sqrt{Q^2+U^2}/I$ ) lightcurves respectively (but omitting the July 2 epoch due to corrupted Stokes Q and U images).746 The LP llux density racks that of Stokes / and reaches a maximum of —70 mv., The LP flux density tracks that of Stokes $I$ and reaches a maximum of $\sim$ 70 mJy.747 The FP appears to be anti-correlated with the flux density. reaching its minimum. value coincidentally with the peak of he Stokes £ lighteurve.," The FP appears to be anti-correlated with the flux density, reaching its minimum value coincidentally with the peak of the Stokes $I$ lightcurve."748 As the X-ray source returns to the owfhared state at the enc of the outburst. the radio LP increases to its maximum value of 23%ol," As the X-ray source returns to the low/hard state at the end of the outburst, the radio FP increases to its maximum value of $\sim23\%$."749e The observed. polarisation position angles (27.1) were determined. from the Stokes Q and C. images. using PA=iawctan(U/(). and plotted. in the bottom panel of Fig. 2..," The observed polarisation position angles $PA$ ) were determined from the Stokes $Q$ and $U$ images, using $PA=\frac{1}{2}\arctan(U/Q)$, and plotted in the bottom panel of Fig. \ref{fig:radio}."750 1n order to determine the degree to which Faraday depolarisation alfects the data. we then. plotted PA against the square of the wavelength. according to PA=|(RAL) (lig. 3)):," In order to determine the degree to which Faraday depolarisation affects the data, we then plotted $PA$ against the square of the wavelength, according to $PA=PA_0+(RM)\lambda^2$ (Fig. \ref{fig:pa}) );"751 this gives values for the intrinsic position angle (2 10} and rotation measure (A23) at each epoch., this gives values for the intrinsic position angle $PA_0$ ) and rotation measure $RM$ ) at each epoch.752 This was performed twice - once for the four epochs with data at all four observing frequencies and a second time for all epochs using only the 4800 ancl S640 Alllz points., This was performed twice - once for the four epochs with data at all four observing frequencies and a second time for all epochs using only the 4800 and 8640 MHz points.753 We find that. with a mean of 10.7 rad/nm2 and a range of 7.2124 /m?. the degree ancl variability of Faraday. rotation is relatively small. compared. with e.g. GRO 40 (llannikainen et al.," We find that, with a mean of 10.7 $^2$ and a range of 7.2–12.4 $^2$, the degree and variability of Faraday rotation is relatively small, compared with e.g. GRO $-$ 40 (Hannikainen et al."754 2000)., 2000).755 We discuss the implications of this in Section 6., We discuss the implications of this in Section 6.756 The radio lighteurve obtained by APCA is one of the few or which the rise time of a major Πάνο can be obtained., The radio lightcurve obtained by ATCA is one of the few for which the rise time of a major flare can be obtained.757 Lt is herefore possible to determine the minimum power required o launch such an ejection. provided we assume that the radio source js in à state of approximate equipartition (see c.g. Longair 1994. Fender 2006).," It is therefore possible to determine the minimum power required to launch such an ejection, provided we assume that the radio source is in a state of approximate equipartition (see e.g. Longair 1994, Fender 2006)."758 We find a lower limit to he minimum energy by assuming that the minimum energy electrons are radiating at 1.4 CGllz. the lowest observing requeney.," We find a lower limit to the minimum energy by assuming that the minimum energy electrons are radiating at 1.4 GHz, the lowest observing frequency."759 Then the minimum energy. Wi associated with an event is: We assume that the relativistic proton energies are negligible compared. with those of the electrons. giving ηΞ1.," Then the minimum energy, $W_{\rm min}$ associated with an event is: We assume that the relativistic proton energies are negligible compared with those of the electrons, giving $\eta = 1$."760 The rise time of the event was 5 days: the better time-resolution of the Green Bank Interferometer (CiBL: see Section 6) lighteurve confirms that there was no intervening peak., The rise time of the event was 5 days; the better time-resolution of the Green Bank Interferometer (GBI; see Section 6) lightcurve confirms that there was no intervening peak.761 Assuming that the ejected component was spherical. we can determine a volume of V=(cl)?M0107em*.," Assuming that the ejected component was spherical, we can determine a volume of $V=\frac{4\pi}{3}(ct)^3 \sim 9\times 10^{48}\, \mbox{cm}^3$."762 The radio lighteurve peaked at Sy613 my at vy=1.4 Cllz., The radio lightcurve peaked at $S_0\sim 613$ mJy at $\nu_0=1.4$ GHz.763" Therefore the monochromatic luminositv. L,=ΕπS.TASLot(edπρο)”Wiz Ll."," Therefore the monochromatic luminosity, $L_{\nu}=4\pi d^2S_{\nu}\sim7.3\times10^{13}(d/kpc)^2\,\,\mbox{WHz}^{-1}$ ."764 Phus the minimum energy required to produce the radio ejection was ὃν dividing this by the rise-time (5 days). we obtain the minimum jet power: We note that our assumed. rise-time is based on the," Thus the minimum energy required to produce the radio ejection was By dividing this by the rise-time (5 days), we obtain the minimum jet power: We note that our assumed rise-time is based on the"765The origin of the stellar initial mass function (IMF) is one of the outstanding unsolved problems in astrophysies.,The origin of the stellar initial mass function (IMF) is one of the outstanding unsolved problems in astrophysics.766 As stars form in dense molecular cores (see e.g. Ward-Thompson et al., As stars form in dense molecular cores (see e.g. Ward-Thompson et al.767 1994; Kirk et al., 1994; Kirk et al.768 2005; Ward-Thompson et al., 2005; Ward-Thompson et al.769 2007). it might well be expected that the IMF ts related to the mass function of those cores (the CMF).," 2007), it might well be expected that the IMF is related to the mass function of those cores (the CMF)."770 This idea is supported by observatioru of prestellar cores. which show that their mass functions are often similar to the IMF of Galactic field stars (Motte et al.," This idea is supported by observations of prestellar cores, which show that their mass functions are often similar to the IMF of Galactic field stars (Motte et al."771 1998: Testi Sargent 1998: Johnstone et al., 1998; Testi Sargent 1998; Johnstone et al.772 2000; Johnstone et al., 2000; Johnstone et al.773 2001: Motte et al., 2001; Motte et al.774 2001: Johnstone Bally 2006: Alves et al., 2001; Johnstone Bally 2006; Alves et al.775 2007: Young et al., 2007; Young et al.776 2006: Nutter Ward-Thompson 2007: Simpson et al., 2006; Nutter Ward-Thompson 2007; Simpson et al.777 2007)., 2007).778 Further support is given by the observation that Taurus may have both an unusual CMF (Onishi et al., Further support is given by the observation that Taurus may have both an unusual CMF (Onishi et al.779 2002) and an unusual IMF (Luhman 2004: see also Goodwin et al., 2002) and an unusual IMF (Luhman 2004; see also Goodwin et al.780 20049). although Kroupa et al. (," 2004c), although Kroupa et al. ("7812003) show that the IMF in Taurus may be compatible with the field IMF.,2003) show that the IMF in Taurus may be compatible with the field IMF.782 However. the relationship between the CMF and the IMF cannot be simple. as many. if not the vast majority. of stars form in binaries or higher-order multiple systems (see Goodwin Kroupa 2005: Duchénne et al.," However, the relationship between the CMF and the IMF cannot be simple, as many, if not the vast majority, of stars form in binaries or higher-order multiple systems (see Goodwin Kroupa 2005; Duchênne et al."783 2007 and Goodwin et al., 2007 and Goodwin et al.784 2007 and references therein; see also Clark et al., 2007 and references therein; see also Clark et al.785 2007)., 2007).786 Observations suggest that the binary frequency amongst young stars ts higher than in the field (see Goodwin et al., Observations suggest that the binary frequency amongst young stars is higher than in the field (see Goodwin et al.787 2007 and references therein) implying that binaries are destroyed by dynamical interactions in clusters (see Kroupa 1995a.b).," 2007 and references therein) implying that binaries are destroyed by dynamical interactions in clusters (see Kroupa 1995a,b)."788 However. Lada (2006) has argued that most M-dwarfs form as single stars. since the M-dwarf binary fraction is relatively low and there is no need to invoke dynamical destruction of low-mass binaries to form these (single) stars.," However, Lada (2006) has argued that most M-dwarfs form as single stars, since the M-dwarf binary fraction is relatively low and there is no need to invoke dynamical destruction of low-mass binaries to form these (single) stars."789 The opposing view is argued by Goodwin Kroupa (2005) and Goodwin Whitworth (2007)., The opposing view is argued by Goodwin Kroupa (2005) and Goodwin Whitworth (2007).790 If stars (or at least relatively high-mass stars) usually form in small-N multiples then there cannot be a trivial one-to-one relationship between the IMF to the CME, If stars (or at least relatively high-mass stars) usually form in $N$ multiples then there cannot be a trivial one-to-one relationship between the IMF to the CMF.791 Firstly. the mass of a core is distributed between a number of stars.," Firstly, the mass of a core is distributed between a number of stars."792 Secondly. some stars are expected to be ejected at an early age from small-N multiples (e.g. Reipurth Clarke 2001: Goodwin et al.," Secondly, some stars are expected to be ejected at an early age from $N$ multiples (e.g. Reipurth Clarke 2001; Goodwin et al."793 2007 and references therein; see also Section 3)., 2007 and references therein; see also Section 3).794 Thirdly. many binary systems are expected to be destroyed in clusters (Kroupa 1995a.b: Kroupa et al.," Thirdly, many binary systems are expected to be destroyed in clusters (Kroupa 1995a,b; Kroupa et al."795 2003: Goodwin Whitworth 2007; also see Goodwin et al., 2003; Goodwin Whitworth 2007; also see Goodwin et al.796 2007 and references therein)., 2007 and references therein).797 Thus the CMF should relate most closely to the initial mass function which. in turn. 15 modified by dynamical effects to produce a mixture of single and multiple systen=8.," Thus the CMF should relate most closely to the initial mass function which, in turn, is modified by dynamical effects to produce a mixture of single and multiple systems."798 In this paper we examine the relationship between the IMF and the CMF. in particular we use the new results for the CMF in Orton from Nutter Ward-Thompson (2007).," In this paper we examine the relationship between the IMF and the CMF, in particular we use the new results for the CMF in Orion from Nutter Ward-Thompson (2007)."799 In Section 2 we review observations of the CMF. in Section 3 we present our general method. and in Section 4 we compare the IMFs we produce with the observations.," In Section 2 we review observations of the CMF, in Section 3 we present our general method, and in Section 4 we compare the IMFs we produce with the observations."800 The first observational link. between the IMF and the CMF was made by Motte et al. (, The first observational link between the IMF and the CMF was made by Motte et al. (8011998) in a millimetre study of the p-Ophiuchi molecular cloud.,1998) in a millimetre study of the $\rho$ -Ophiuchi molecular cloud.802 They found that the high-mass slope of the CMF matched that of the IMF., They found that the high-mass slope of the CMF matched that of the IMF.803 This result has been confirmed for Ophiuchus (Johnstone et al., This result has been confirmed for Ophiuchus (Johnstone et al.804 2000: Young et al., 2000; Young et al.805 2006; Simpson et al., 2006; Simpson et al.806 2007) and a number of other nearby clouds. including Orion (Motte et al.," 2007) and a number of other nearby clouds, including Orion (Motte et al."807 2001: Johnstone et al., 2001; Johnstone et al.808 2001: Johnstone Bally 2006: Nutter Ward-Thompson 2007). the Pipe Nebula (Alves et al.," 2001; Johnstone Bally 2006; Nutter Ward-Thompson 2007), the Pipe Nebula (Alves et al."809 2007). and Taurus (Onishi et al.," 2007), and Taurus (Onishi et al."810 2002: however see Goodwin et al., 2002; however see Goodwin et al.811 2004c). as well as for more distant massive star-forming regions such as NGC 7538 and MI7 (Reid Wilson 2006a.b).," 2004c), as well as for more distant massive star-forming regions such as NGC 7538 and M17 (Reid Wilson 2006a,b)."812 While the slope of the CMF seems to be consistent from region to region. the position of the peak of the CMF appears to shift from ~0.1M. in nearby low-mass regions such as p- Ophiuchus (e.g. Motte et al.," While the slope of the CMF seems to be consistent from region to region, the position of the peak of the CMF appears to shift from $\sim\! 0.1~M_\odot$ in nearby low-mass regions such as $\rho$ -Ophiuchus (e.g. Motte et al."813 1998). to a higher mass of ~1M. in more distant and massive star-forming regions such as Orion (e.g. Nutter Ward-Thompson 2007).," 1998), to a higher mass of $\sim\! 1~M_\odot$ in more distant and massive star-forming regions such as Orion (e.g. Nutter Ward-Thompson 2007)."814 Very massive star-forming regions such as ΜΙΤ show a flattening of the CMF at an even higher mass of ~8M. (Reid Wilson 2006a.b). though the data are incomplete before a turn-over is seen.," Very massive star-forming regions such as M17 show a flattening of the CMF at an even higher mass of $\sim\!8158~M_\odot$ (Reid Wilson 2006a,b), though the data are incomplete before a turn-over is seen."816 Whether this 15 an intrinsic effect where the mass of the peak in the CMF is related to the mass of the stars being formed. or an observational effect," Whether this is an intrinsic effect where the mass of the peak in the CMF is related to the mass of the stars being formed, or an observational effect"817is significantly greater than (the optical and radio fluxes. and as long as one is in the Last cooling regime. Compton scattering of a single component cannot explain the LAT spectrum.,"is significantly greater than the optical and radio fluxes, and as long as one is in the fast cooling regime, Compton scattering of a single component cannot explain the LAT spectrum."818 Furthermore. curving the 2007 November Mares of454.3. detected by UVOT. XRT and DAT.INTEGRAL. and AGILE. the X-ravs were weakly variable. compared with other wavebands. but did seem to show correlated variability. (Vercelloneetal.2009).. which indicates they originate [rom (he same emission region.," Furthermore, during the 2007 November flares of, detected by UVOT, XRT and BAT, and , the X-rays were weakly variable, compared with other wavebands, but did seem to show correlated variability \citep{vercellone09}, which indicates they originate from the same emission region."819 One final possibility is (hat a hadronic model mav be possible to explain the LAT 5-rav spectrum (e.g..Mücke&Protheroe2001).. however. such models may have difficullies in explaining the correlated variability seen in (his source. since protons would evolve on longer timescales than electrons.," One final possibility is that a hadronic model may be possible to explain the LAT $\g$ -ray spectrum \citep[e.g.,][]{muecke01}, however, such models may have difficulties in explaining the correlated variability seen in this source, since protons would evolve on longer timescales than electrons."820 Assuming (he dual-component. Compton-scaltering scenario presented in this paper is correct. what can it tell us about the location of the οταν emission region?," Assuming the dual-component Compton-scattering scenario presented in this paper is correct, what can it tell us about the location of the $\g$ -ray emission region?"821 It implies that this region is Ry<r«E!ry. so that. using the parameters from the modeling of 3C 454.3. the location of the jet falls over a large range from 0.1pe<r«100pc.," It implies that this region is $R_i < r \ll822\G^4r_g$, so that, using the parameters from the modeling of 3C 454.3, the location of the jet falls over a large range from $0.1\ \pc < r \ll823100\ \pc$."824 IIowever. the external enerey density [rom disk and BLR radiations is xr. a steep decline. so that the blob must be within 550.1 pe for a significant scattering component.," However, the external energy density from disk and BLR radiations is $\propto r^{-3}$, a steep decline, so that the blob must be within $\approx 0.1$ pc for a significant scattering component."825 Recent modeling ol 3C 454.3 (Bonnolietal.2010) also finds that the 5-rav emitting region is within the DLR., Recent modeling of 3C 454.3 \citep{bonnoli10} also finds that the $\gamma$ -ray emitting region is within the BLR.826 By contrast. Sikoraetal.(2003). suggested that the 5-ravs observed by EGRET and AGILE were caused by Compton-seattering of radiation [rom hot dust by a blob located ~10 pe from the central black hole. though detailed modeling is still needed to determine if this model can explain the sharp spectral break in theFerm: observations.," By contrast, \citet{sikora08} suggested that the $\g$ -rays observed by EGRET and AGILE were caused by Compton-scattering of radiation from hot dust by a blob located $\sim 10$ pc from the central black hole, though detailed modeling is still needed to determine if this model can explain the sharp spectral break in the observations."827 The blazar 3C 279 also shows a similar spectral break during the onset of an extended episode of optical polarization. while the jet emission region could still be within the BLR region 2010a)..," The blazar 3C 279 also shows a similar spectral break during the onset of an extended episode of optical polarization, while the jet emission region could still be within the BLR region \citep{abdo10_3c279}."828" Whether (his model can predict similar spectral breaks in other FSRQs and low-synchrotron- blazars. such as AO 02354164 or PINS 1502--106 (Abdoetal.2010b).. depends mainly on the properties of the DLR in these sources. in particular. whether 755,45+qi/Hulij."," Whether this model can predict similar spectral breaks in other FSRQs and low-synchrotron-peaked blazars, such as AO 0235+164 or PKS 1502+106 \citep{abdo10_sed}, depends mainly on the properties of the BLR in these sources, in particular, whether $\tau_{BLR} \approx829r_g/R_i$."830 In specilic blazars. especially at higher z. 2 5-absorption by scattered disk radiation could sUll be effective.," In specific blazars, especially at higher $z$, $\g\g$ -absorption by scattered disk radiation \citep{reimer07} could still be effective."831 Detailed modeling of simultaneous SED clata will test these scenarios. as it does for the case of454.," Detailed modeling of simultaneous SED data will test these scenarios, as it does for the case of."8323.. If our model is correct. it provides evidence for a wind model of the DLR. (Murray&Chiang1995:Murray.1996:Elvis2000).," If our model is correct, it provides evidence for a wind model of the BLR \citep{murray95,chiang96,elvis00}."833. We are grateful to the anonymous releree for helpful comments., We are grateful to the anonymous referee for helpful comments.834 J.D.F. was supported bv NASA Swift Guest Investigator Grant DPR-NNGOSEDALI and NASA GLAST Science, J.D.F. was supported by NASA Swift Guest Investigator Grant DPR-NNG05ED411 and NASA GLAST Science835QusRO where R is the particle radius).,"$v_{\rm rms}$$\sim$$R836\varOmega$ where $R$ is the particle radius)."837 Discounting the former option. the result of the latter can be artificially exaggerated by the numerical scheme because we identify the collision between two superparticle swarms with the collision between two members of the swarms located at the respective swarm centres.," Discounting the former option, the result of the latter can be artificially exaggerated by the numerical scheme because we identify the collision between two superparticle swarms with the collision between two members of the swarms located at the respective swarm centres."838 In reality collisions would occur between neighbouring particles separated by less than their physical diameter., In reality collisions would occur between neighbouring particles separated by less than their physical diameter.839 The naive numerical algorithm would make the system settle for an equilibrium where μην(ο)... where ὃν is the grid spacing and also the typical distance between superparticle centres.," The naive numerical algorithm would make the system settle for an equilibrium where $v_{\rm rms}$$\sim840$$(\delta x) \varOmega$, where $\delta x$ is the grid spacing and also the typical distance between superparticle centres."841" This rms speed greatly exceeds the desired vq,~AO.", This rms speed greatly exceeds the desired $v_{\rm rms}\sim R \varOmega$.842 In other words. the naive collision algorithm will input artificial heating.," In other words, the naive collision algorithm will input artificial heating."843 Collisions between particles of radius R<ὃν can be modelled by subtracting the Keplerian shear part from the relative speed both for determining the collision time-scale and for determining the outcome of the collision., Collisions between particles of radius $R \ll \delta x$ can be modelled by subtracting the Keplerian shear part from the relative speed both for determining the collision time-scale and for determining the outcome of the collision.844" Decomposing the azimuthal velocity field as Y2v,+TUA where Tu=-(3/2)0x is the Keplerian shear velocity and ὃν is the peculiar velocity. we can calculate both the collision time-scale and outcome in terms of ὃν (together with v; and v)."," Decomposing the azimuthal velocity field as $\dot{y}=\tilde{v}_y +845v_y^{(0)}$, where $v_y^{(0)}=-(3/2) \varOmega x$ is the Keplerian shear velocity and $\tilde{v}_y$ is the peculiar velocity, we can calculate both the collision time-scale and outcome in terms of $\tilde{v}_y$ (together with $v_x$ and $v_z$ )."846 Lyraetal.(2009) applied a similar trick to subtract off the entire (Keplerian plus peculiar) gas velocity from the particle velocity., \cite{Lyra+etal2009} applied a similar trick to subtract off the entire (Keplerian plus peculiar) gas velocity from the particle velocity.847 However. two particles moving at the same velocity as the local gas do not necessarily avoid collisions. even if the gas is incompressible. since the particle motion 1s not completely coupled to the gas.," However, two particles moving at the same velocity as the local gas do not necessarily avoid collisions, even if the gas is incompressible, since the particle motion is not completely coupled to the gas."848 Therefore we choose in this paper to subtract off only the Keplerian orbital speed from the particle velocity., Therefore we choose in this paper to subtract off only the Keplerian orbital speed from the particle velocity.849 The dynamical equations of the Pencil Code are already formulated relative to the Keplerian shear. so subtracting off the shear is natural to the governing system of equations.," The dynamical equations of the Pencil Code are already formulated relative to the Keplerian shear, so subtracting off the shear is natural to the governing system of equations."850 Collisions relative to the Keplerian shear conserve both the total momentum and the momentum relative to the Keplerian shear. but the energy in elastic collisions is only conserved relative to the Keplerian shear.," Collisions relative to the Keplerian shear conserve both the total momentum and the momentum relative to the Keplerian shear, but the energy in elastic collisions is only conserved relative to the Keplerian shear."851 To see this. consider the kinetic energy of two particles. Here mm is the mass of a superparticle. assumed to be the same for both colliders.," To see this, consider the kinetic energy of two particles, Here $m$ is the mass of a superparticle, assumed to be the same for both colliders."852 An elastic collision solved in terms of Oy. Thy. Ve. Y42) conserves both the sum of the squares of those velocity components. as well as the squares of 0 and (the latter is true since the position x is not changed by the VTcollision).," An elastic collision solved in terms of $v_{x1}$, $\tilde{v}_{y1}$, $v_{x2}$, $\tilde{v}_{y2}$ ) conserves both the sum of the squares of those velocity components, as well as the squares of $v_{y1}^{(0)}$ and $v_{y2}^{(0)}$ (the latter is true since the position $x$ is not changed by the collision)."853" The difference in energy before and after the collision is therefore This result holds also in 3-D. The energy difference is generally not zero. even though Af,=—Atf4» by momentum conservation, since the offset Tu is not the same for the two particles."," The difference in energy before and after the collision is therefore This result holds also in 3-D. The energy difference is generally not zero, even though $\Delta \tilde{v}_{y1}=-\Delta \tilde{v}_{y2}$ by momentum conservation, since the offset $v_y^{(0)}$ is not the same for the two particles."854 The non-conservation is nevertheless small: the azimuthal velocity change in the collision is uncorrelated with the Keplerian shear velocity. so CARuu=0.," The non-conservation is nevertheless small: the azimuthal velocity change in the collision is uncorrelated with the Keplerian shear velocity, so $\langle \Delta \tilde{v}_y v_y^{(0)} \rangle_{\rm box}\approx0$."855 The particle integrator's slight non-conservation of Keplerian orbits ts not a serious limitation in simulations where the dynamies ts driven by hydrodynamical instabilities and drag forces., The particle integrator's slight non-conservation of Keplerian orbits is not a serious limitation in simulations where the dynamics is driven by hydrodynamical instabilities and drag forces.856 The correct relative Keplerian shear based on the physical size of the particles can in principle be added artificially. to obtain the correct energy release from the shear. but this ts negligible for 1-10 em particles considered 1n this paper.," The correct relative Keplerian shear based on the physical size of the particles can in principle be added artificially, to obtain the correct energy release from the shear, but this is negligible for 1–10 cm particles considered in this paper."857 The total angular momentum of two colliding particles. is conserved in the collisions. both with and without Keplerian shear in the collision. as long as the force during the collision acts along the line connecting the two particles.," The total angular momentum of two colliding particles, is conserved in the collisions, both with and without Keplerian shear in the collision, as long as the force during the collision acts along the line connecting the two particles."858 This is the case both with and without Keplerian shear., This is the case both with and without Keplerian shear.859" For equal-mass particles we can write the change in the velocity as Av,2—Avs=c(r>—ri). giving The above arguments for energy and angular momentum conservation are generalisible to distinct particle masses as well."," For equal-mass particles we can write the change in the velocity as $\Delta \vc{v}_1 = -\Delta \vc{v}_2 = c (\vc{r}_2-\vc{r}_1)$, giving The above arguments for energy and angular momentum conservation are generalisible to distinct particle masses as well."860 However. while the Monte Carlo collision scheme in itself is fully consistent with distinct particle masses. correct energy equipartition among particle sizes can not be obtained with equal-mass superparticles (see discussion in A.1.)).," However, while the Monte Carlo collision scheme in itself is fully consistent with distinct particle masses, correct energy equipartition among particle sizes can not be obtained with equal-mass superparticles (see discussion in )."861 In the following we use the abbreviations KS for collisions that include Keplerian shear and NS for collisions where the Keplerian shear is subtracted off when determining the collision time-scale and outcome., In the following we use the abbreviations KS for collisions that include Keplerian shear and NS for collisions where the Keplerian shear is subtracted off when determining the collision time-scale and outcome.862 shows the evolution of the particle rms speed in a shearing box simulation., shows the evolution of the particle rms speed in a shearing box simulation.863 The top panel shows the decay of initially random particle motion by inelastic (e.= 0.3) collisions for KS collisions and for NS collisions., The top panel shows the decay of initially random particle motion by inelastic $\epsilon=0.3$ ) collisions for KS collisions and for NS collisions.864 KS collisions decay towards vins(0:3). the random motion released by the Keplerian shear in a single collision.," KS collisions decay towards $v_{\rm rms}\approx(\delta865x)\varOmega$, the random motion released by the Keplerian shear in a single collision."866 NS collisions on the other hand continue to decay towards zero., NS collisions on the other hand continue to decay towards zero.867 In the bottom panel of we start with zero random motion and observe how elastic (e=1.0) KS collisions heat up the system., In the bottom panel of we start with zero random motion and observe how elastic $\epsilon=1.0$ ) KS collisions heat up the system.868 Rerunning the simulation with elastic NS collisions from various starting times of the KS simulation shows clearly that the evolution of the system is very similar as long as the particle rms speed is larger than (0.1)Q., Rerunning the simulation with elastic NS collisions from various starting times of the KS simulation shows clearly that the evolution of the system is very similar as long as the particle rms speed is larger than $(\delta x) \varOmega$.869 In actual simulations with gas and hydrodynamical instabilities driving particle dynamics with characteristic motion much faster than v(03)Q. one can subtract off the Keplerian shear term when determining the time-scale and outcome of collisions and still model the correct system. without any spurious energy released by bloated particles.," In actual simulations with gas and hydrodynamical instabilities driving particle dynamics with characteristic motion much faster than $v\sim(\delta x)\varOmega$, one can subtract off the Keplerian shear term when determining the time-scale and outcome of collisions and still model the correct system, without any spurious energy released by bloated particles."870 Armed with à collision algorithm for superparticles. we are now ready to explore the effect of particle collisions on particle concentration by streaming instabilities and. planetesimal formation by self-gravity.," Armed with a collision algorithm for superparticles, we are now ready to explore the effect of particle collisions on particle concentration by streaming instabilities and planetesimal formation by self-gravity."871 The streaming instability feeds off the relative (streaming) motion of gas and particles in protoplanetary dises and has a characteristic length scale comparable to the sub-Keplerian length ar (Youdin&Good-man. 2005)., The streaming instability feeds off the relative (streaming) motion of gas and particles in protoplanetary discs and has a characteristic length scale comparable to the sub-Keplerian length $\eta r$ \citep{YoudinGoodman2005}.872. Here 77 is the radial pressure gradient parameter of Nakagawaetal.(1986) and + is the distance to the central star.," Here $\eta$ is the radial pressure gradient parameter of \cite{Nakagawa+etal1986}873 and $r$ is the distance to the central star."874 Johansenetal.(2009) and Bai&Stone(2010b) demonstrated that the streaming instability leads to strong particle clumping when the heavy element abundance of the disc is above a threshold value of Z=0.02 for particle sizes, \cite{Johansen+etal2009} and \cite{BaiStone2010b} demonstrated that the streaming instability leads to strong particle clumping when the heavy element abundance of the disc is above a threshold value of $Z\approx0.02$ for particle sizes875the derived value of ΔΤΕ.,the derived value of $\Delta T_{\rm e}$.876" We note that although this is a quantitatively meaningful approximation, its validation would require the modeling of the absorption by C» in dense helium, which is a complex task, restricted by the limited applicability of quantum methods beyond DFT to many particle systems."," We note that although this is a quantitatively meaningful approximation, its validation would require the modeling of the absorption by $\rm C_2$ in dense helium, which is a complex task, restricted by the limited applicability of quantum methods beyond DFT to many particle systems."877 In Fig., In Fig.878" 4 we show the optical spectrum of the cool DQp white dwarf LHS290 (Bergeronetal,1997) together with a set of synthetic spectra.", \ref{F4} we show the optical spectrum of the cool DQp white dwarf LHS290 \citep{Bergeron97} together with a set of synthetic spectra.879" The overall spectral energy distribution of that star is best reproduced by models with Teg=5800K (Fig. 5),"," The overall spectral energy distribution of that star is best reproduced by models with $T_{\rm eff}\rm=5800 \, K$ (Fig. \ref{F5}) ),"880 and we assume this temperature in our analysis and fix the gravity at logg=8(cgs).," and we assume this temperature in our analysis and fix the gravity at $\log g=8 \,\rm (cgs)$."881" The C/He and H/He abundances are fitted to best reproduce the peaks of the Av—0,—1 bands."," The C/He and H/He abundances are fitted to best reproduce the peaks of the $\Delta\nu=0,-1$ bands."882" Assuming pure He atmosphere the strength of the Swan bands is reproduced with C/He=1.25-1077, but with the computed correction for T, the spectrum is far tootorted!."," Assuming pure He atmosphere the strength of the Swan bands is reproduced with $\rm C/He=1.25\cdot 10^{-7}$, but with the computed correction for $T_{\rm e}$ the spectrum is far too."883". The observed spectrum can be fairly well reproduced by a model with photospheric density ~0.05g/cm?, or assuming that the Το dependence on the density is weaker, AT.~0.2ρμε."," The observed spectrum can be fairly well reproduced by a model with photospheric density $\rm \sim 0.05 \, g/cm^3$, or assuming that the $T_{\rm e}$ dependence on the density is weaker, $\Delta T_{\rm e}\rm \sim0.2\rho_{\rm He}$."884" The first case is realized by the addition of hydrogen to the atmosphere, which increases the opacity and lowers the photospheric density."," The first case is realized by the addition of hydrogen to the atmosphere, which increases the opacity and lowers the photospheric density."885 The required amount of hydrogen is H/He=6.75-102., The required amount of hydrogen is $\rm H/He=6.75 \cdot 10^{-3}$.886 In both cases the observed spectrum is fairly well reproduced., In both cases the observed spectrum is fairly well reproduced.887" The minima of the bands are blueshifted, as most of the absorption occurs close to the photosphere (Fig. 5))."," The minima of the bands are blueshifted, as most of the absorption occurs close to the photosphere (Fig. \ref{F5}) )."888" The long-wavelength parts of the bands resemble those of the standard Swan absorption, because part of the absorption occurs in the less dense upper atmospheric layers, where C> is unperturbed."," The long-wavelength parts of the bands resemble those of the standard Swan absorption, because part of the absorption occurs in the less dense upper atmospheric layers, where $\rm C_2$ is unperturbed."889" We notice that the abundances of molecular carbon and the resulting strength of its molecular bands could also be affected by high density, which could eventually impact the reported carbon abundances."," We notice that the abundances of molecular carbon and the resulting strength of its molecular bands could also be affected by high density, which could eventually impact the reported carbon abundances."890" The so-called DQp stars represent a puzzle in the understanding of evolution of cool, helium-dominated white dwarf atmospheres."," The so-called DQp stars represent a puzzle in the understanding of evolution of cool, helium-dominated white dwarf atmospheres."891" The DQ stars disappear at Τε~6000K, and few stars with apparently distorted Swan bands were detected at lower effective temperatures."," The DQ stars disappear at $T_{\rm eff}\rm \sim 6000 \, K$, and few stars with apparently distorted Swan bands were detected at lower effective temperatures."892" All explanation through the formation of different species, like (2Η. magnetic fields, or roto-vibrational excitations failed to explain the spectral features of these stars or definitely assign them as the distorted bands of Co."," All explanation through the formation of different species, like $\rm C_2H$, magnetic fields, or roto-vibrational excitations failed to explain the spectral features of these stars or definitely assign them as the distorted bands of $\rm C_2$."893 We show that the distortion of Swan bands originates in the pressure-induced increase in the electronic transition energy between states involved in the transition., We show that the distortion of Swan bands originates in the pressure-induced increase in the electronic transition energy between states involved in the transition.894" This results in a blueshift of the molecular bands minima, and explains why the red edges of the bands match the spectra of normal DQ stars (Swan bands)."," This results in a blueshift of the molecular bands minima, and explains why the red edges of the bands match the spectra of normal DQ stars (Swan bands)."895" Our results, when applied to the current atmosphere models, predict Swan bands shifts that are too large compared with the observed ones."," Our results, when applied to the current atmosphere models, predict Swan bands shifts that are too large compared with the observed ones."896" This indicates that the density at the photosphere of DQp stars does not excess 0.05g/cm, and the input physics in the models or the understanding of the atmospheres of these stars, especially the pollution by hydrogen, requires further improvements."," This indicates that the density at the photosphere of DQp stars does not excess $0.05 \rm \,g/cm^3$, and the input physics in the models or the understanding of the atmospheres of these stars, especially the pollution by hydrogen, requires further improvements."897"from CG09 (note that we show DR6 to be consistent with the mocks, but similar results are found for DR7, see GCH).","from CG09 (note that we show DR6 to be consistent with the mocks, but similar results are found for DR7, see GCH)."898 'To compare to simulations we have scaled the LRG data as: with A—1.2 and K——0.005., To compare to simulations we have scaled the LRG data as: with $A=1.2$ and $K=-0.005$.899" The value of A accounts for the differences between the simulation and LRG data in 8, growth and bias."," The value of $A$ accounts for the differences between the simulation and LRG data in $\beta$, growth and bias."900" The value of K represents a possible, but quite minor (0.2596), error (contamination or sampling fluctuation) in the overall mean density of the sample."," The value of $K$ represents a possible, but quite minor $0.25\%$ ), error (contamination or sampling fluctuation) in the overall mean density of the sample."901 This has little impact in the fit of models to data (covariance allows for a constant shift in the data) but improves the visual comparison in the figure (see Fig.17 in Sanchez et al 2009)., This has little impact in the fit of models to data (covariance allows for a constant shift in the data) but improves the visual comparison in the figure (see Fig.17 in Sanchez et al 2009).902 As indicated by Fig.1 the mocks represent quite well the variation seen in the observational data., As indicated by \ref{fig:correlation} the mocks represent quite well the variation seen in the observational data.903" We use two models to fit the correlation £(r): 1)model: it uses the mean of all the mocks in order to have a perfect BAO model (with bias,redshift space and linearities effects included)."," We use two models to fit the correlation $\xi(r)$: 1): it uses the mean of all the mocks in order to have a perfect BAO model (with bias,redshift space and non-linearities effects included)."904 2)model: a non-physical model that imitates well the broad band correlation but does not include à BAO peak., 2): a non-physical model that imitates well the broad band correlation but does not include a BAO peak.905 We use the no-wiggle power spectrum of Hu (2001) with same wCDM parameters as the simulation., We use the no-wiggle power spectrum of Hu (2001) with same $\omega$ CDM parameters as the simulation.906 Fig.l compares the BAO (solid line) with the no-BAO model (long-dashed line)., \ref{fig:correlation} compares the BAO (solid line) with the no-BAO model (long-dashed line).907 Our null test is: does the data prefer the BAO to the no-BAO model at 3-sigma confidence level (CL)?, Our null test is: does the data prefer the BAO to the no-BAO model at 3-sigma confidence level (CL)?908" To simplify the analysis and interpretation, the only free parameter that we fit is the global amplitude A of the correlation, which includes a possible bias (as we are using halos) and a constant redshift distortion boost (Kaiser 1987)."," To simplify the analysis and interpretation, the only free parameter that we fit is the global amplitude $A$ of the correlation, which includes a possible bias (as we are using halos) and a constant redshift distortion boost (Kaiser 1987)."909" We use the correlation function £;(r;) measured in the i-th mock at separation rj to perform a x? fit and find the best fit amplitude A; for either BAO or no-BAO models (which are labeled generically as £;): The indexes { and k run over the Ny=20 bin separations, ie v—19 degrees of freedom."," We use the correlation function $\xi_i(r_j)$ measured in the $i$ -th mock at separation $r_j$ to perform a $\chi^2$ fit and find the best fit amplitude $A_i$ for either BAO or no-BAO models (which are labeled generically as $\xi_m$ ): The indexes $j$ and $k$ run over the $N_b=20$ bin separations, ie $\nu=19$ degrees of freedom."910 Bins are linearly spaced with Ar—5 Mpc/h between 30 and 130 Mpc/h (we find similar results in the range 20-150 Mpc/h)., Bins are linearly spaced with $\Delta r=5$ Mpc/h between 30 and 130 Mpc/h (we find similar results in the range 20-150 Mpc/h).911" The covariance matrix Cj, is estimated from the mocks: where (rj)=στοΣι&(rj) is the mean value in bin j.", The covariance matrix $C_{jk}$ is estimated from the mocks: where $\bar{\xi}(r_j) \equiv {1\over{216}} \sum_i \xi_i(r_j)$ is the mean value in bin $j$.912" The resulting distribution of values of x? for the BAO model peaks around x?~v=19 and is quite broad (Ax?~Vv~ 6, as expected)."," The resulting distribution of values of $\chi^2_i$ for the BAO model peaks around $\chi^2_i \simeq \nu = 19$ and is quite broad $\Delta\chi^2913\simeq \sqrt{2\nu} \simeq 6$ , as expected)."914 The no-BAO model peaks at larger values (x?~ 24) and is slightly broader (Ax?~ 7.7).," The no-BAO model peaks at larger values $\chi^2_i915\simeq 24$ ) and is slightly broader $\Delta\chi^2 \simeq 7.7$ )."916" The real LRG data produces x?=20 for the BAO model and X?=25 for the no-BAO model, well within the values found for most of the mocks."," The real LRG data produces $\chi^2=20$ for the BAO model and $\chi^2=25$ for the no-BAO model, well within the values found for most of the mocks."917" Thus, given the large errorbars, the real data seems to match quite well our mocks, despite the differences in the modeled values of 8, bias and z mentioned above."," Thus, given the large errorbars, the real data seems to match quite well our mocks, despite the differences in the modeled values of $\beta$, bias and $z$ mentioned above."918 In Fig.2 we plot the histogram of the differences between the x? values in the fits to the BAO and no-BAO models for each mock., In \ref{fig:dchi2} we plot the histogram of the differences between the $\chi^2_i$ values in the fits to the BAO and no-BAO models for each mock.919 Negative values mean that the mock prefers the BAO model over no-BAO model., Negative values mean that the mock prefers the BAO model over no-BAO model.920" A difference at 30 CL between both models, ie Ax?« —9, only happens in"," A difference at $3\sigma$ CL between both models, ie $\Delta\chi^2 < -9$ only happens in"921but lacked the spatial resolution needed to properly separate and interpret these sources (Sakuraietal.2001)).,but lacked the spatial resolution needed to properly separate and interpret these sources \cite{skts01}) ).922 As the first part of an effort to understand the X-ray emission from Vela-like pulsars. here we present observations of pulsar wwith the (XMM-Newton)). the first observatory to provide sufficient angular. spectral. and temporal resolution to separately identify all the processes described above.," As the first part of an effort to understand the X-ray emission from Vela-like pulsars, here we present observations of pulsar with the ), the first observatory to provide sufficient angular, spectral and temporal resolution to separately identify all the processes described above."923 aalso has much higher sensitivity (effective area 4650 em? at 1.5 keV) than previous missions. making it well-suited for studying faint sources such as seen here.," also has much higher sensitivity (effective area 4650 $^2$ at 1.5 keV) than previous missions, making it well-suited for studying faint sources such as seen here."924 Observations of PSR wwere carried out with oon 2001 October 16 and 2001 October 18. in two observations each of length ~30 ks. as summarized in Table ]..," Observations of PSR were carried out with on 2001 October 16 and 2001 October 18, in two observations each of length $\sim$ 30 ks, as summarized in Table \ref{tab_obs}."925 The data described here correspond to the three X-ray imaging instruments on boardXMM-Newton., The data described here correspond to the three X-ray imaging instruments on board.926".. The EPIC ΜΟΡΙ and MOS2 detectors were operated in the standard “full frame"" mode. in which seven CCDs in each detector are used to produce an approximately circular. field-of-view of diameter 30. with a time resolution for each CCD frame of 2.6 s. The EPIC pn detector was operated in ""small window"" mode. in which only a central 4« square region is active. but for which the time resolution is 5.7 ms."," The EPIC MOS1 and MOS2 detectors were operated in the standard “full frame” mode, in which seven CCDs in each detector are used to produce an approximately circular field-of-view of diameter $30'$, with a time resolution for each CCD frame of 2.6 s. The EPIC pn detector was operated in “small window” mode, in which only a central $4'\times4'$ square region is active, but for which the time resolution is 5.7 ms."927 In this mode a significant fraction of each 5.7-ms frame is used to read out the CCD. resulting in a dead-time fraction of (Kusteretal. 1999)).," In this mode a significant fraction of each 5.7-ms frame is used to read out the CCD, resulting in a dead-time fraction of \cite{kbkb99}) )."928 To avoid optical contamination of the field. the medium and thin blocking filters were used for the MOS and pn detectors. respectively.," To avoid optical contamination of the field, the medium and thin blocking filters were used for the MOS and pn detectors, respectively."929 Initial processing of the data was carried out at the SScience Operations Centre (SOC)., Initial processing of the data was carried out at the Science Operations Centre (SOC).930 We analyzed the resulting event files using the SSoftware Analysis System (SAS). version 5.3.0.," We analyzed the resulting event files using the Software Analysis System (SAS), version 5.3.0."931 The data were first filtered to remove hot pixels and other bad data. and to only allow standard event grades (patterns O to 12 for MOS] and MOS2. patterns 0 to 4 for pn).," The data were first filtered to remove hot pixels and other bad data, and to only allow standard event grades (patterns 0 to 12 for MOS1 and MOS2, patterns 0 to 4 for pn)."932 Each of these data sets was examined for periods of high background by only considering events with energies in the range 10-15 keV. Times at which flares or high levels were seen in the X-ray count rate for this bandpass were excluded., Each of these data sets was examined for periods of high background by only considering events with energies in the range 10–15 keV. Times at which flares or high levels were seen in the X-ray count rate for this bandpass were excluded.933 This latter filtering excluded a significant fraction of each observation: the resulting useful exposure times are listed in Table I., This latter filtering excluded a significant fraction of each observation; the resulting useful exposure times are listed in Table \ref{tab_obs}.934 For each observation and detector listed in Table [.. the data set was corrected was for vignetting losses using the SAS task EVIGWEIGHT.," For each observation and detector listed in Table \ref{tab_obs}, the data set was corrected was for vignetting losses using the SAS task EVIGWEIGHT."935 Next. an energy filter was applied to include only events falling in the energy range 0.5-10 keV. other energies being dominated by background.," Next, an energy filter was applied to include only events falling in the energy range 0.5–10 keV, other energies being dominated by background."936 Finally. all the MOS and pn data were combined to form a single image for each type of detector.," Finally, all the MOS and pn data were combined to form a single image for each type of detector."937" For the MOS CCDs. the flat-fielded images have a plate seale of 171 pixel!: for the pn CCD. the flat-fielded image has a plate scale of 4/4 pixel""!"," For the MOS CCDs, the flat-fielded images have a plate scale of $1\farcs1$ $^{-1}$; for the pn CCD, the flat-fielded image has a plate scale of $4\farcs4$ $^{-1}$."938 The high background count-rate for rrequires careful analysis in. order to extract accurate source spectra., The high background count-rate for requires careful analysis in order to extract accurate source spectra.939 The background contribution to the data consists of two main components (see Lumbetal.2002): a diffuse X-ray background. assumed to have a smooth spatial distribution over the observed field. and a particle background. which shows spatial variations across the detector.," The background contribution to the data consists of two main components (see \cite{lwpd02}) ): a diffuse X-ray background, assumed to have a smooth spatial distribution over the observed field, and a particle background, which shows spatial variations across the detector."940 For à source not much larger than the point spread function (PSF). we determine the spectrum by extracting data from both a small region enclosing the source. and from a reference spectrum immediately adjacent.," For a source not much larger than the point spread function (PSF), we determine the spectrum by extracting data from both a small region enclosing the source, and from a reference spectrum immediately adjacent."941 The spectrum of interest is then obtained by subtracting the reference spectrum from the source spectrum. scaling appropriately to account for the differing areas of the extraction regions for the two fields.," The spectrum of interest is then obtained by subtracting the reference spectrum from the source spectrum, scaling appropriately to account for the differing areas of the extraction regions for the two fields."942 This approach assumes that because of the proximity of the two extraction regions. the differences in the background components are negligible between source and reference spectra.," This approach assumes that because of the proximity of the two extraction regions, the differences in the background components are negligible between source and reference spectra."943 Analysis of extended sources is complicated by the spatially varying nature of the background., Analysis of extended sources is complicated by the spatially varying nature of the background.944 Both the diffuse X-ray background and the source photons are vignetted by the mmiurrors. resulting m à background component that varies dramatically with detector position.," Both the diffuse X-ray background and the source photons are vignetted by the mirrors, resulting in a background component that varies dramatically with detector position."945 The particle background. however. is unaffected by the mirrors. resulting in a background component that is largely independent of detector position.," The particle background, however, is unaffected by the mirrors, resulting in a background component that is largely independent of detector position."946 Given these complications. we follow the prescription given in Appendix A of Arnaud ((2002)). in which reference spectra from adjacent regions are used to correct for the X-ray background. and spectra from blank-field observations supplied by the are used to account for the particle background.," Given these complications, we follow the prescription given in Appendix A of Arnaud \nocite{aml+02}) ), in which reference spectra from adjacent regions are used to correct for the X-ray background, and spectra from blank-field observations supplied by the are used to account for the particle background."947 Once these corrections had been applied. spectra were grouped so that there were at least 50 counts per spectral bin for compact sources. and 100 counts per bin for extended sources.," Once these corrections had been applied, spectra were re-grouped so that there were at least 50 counts per spectral bin for compact sources, and 100 counts per bin for extended sources."948 For analysis of EPIC MOS data. we used the responses supplied by the to provide information on the redistribution matrix and effective area of each CCD: all_2&.2sp. while for MOS2 we .5.zsp.," For analysis of EPIC MOS data, we used the responses supplied by the to provide information on the redistribution matrix and effective area of each CCD: specifically, for the MOS1 CCD we used the response file, while for MOS2 we used."949 For analysis of EPIC pn data. we generated our own response files using the SAS tasks RMFGEN and ARFGEN.," For analysis of EPIC pn data, we generated our own response files using the SAS tasks RMFGEN and ARFGEN."950 Subsequent spectral fitting and analysis were carried out using XSPEC version 11.1.0., Subsequent spectral fitting and analysis were carried out using XSPEC version 11.1.0.951" In the ""small window"" mode used here. the EPIC pn CCD has sufficient time resolution to search for X-ray pulsations from PSRB1823-13."," In the “small window” mode used here, the EPIC pn CCD has sufficient time resolution to search for X-ray pulsations from PSR."952. Due to improvements in the time-tagging of events since the time when pipeline processing was carried out on the data by the SOC. we completely reprocessed the pn data from the raw observation data files. using the SAS task EPCHAIN.," Due to improvements in the time-tagging of events since the time when pipeline processing was carried out on the data by the SOC, we completely reprocessed the pn data from the raw observation data files, using the SAS task EPCHAIN."953" After filtering the data as described in refsec,bsabove. wethencorrectedthearrivaltimeso feacheventtocorrespo."," After filtering the data as described in \\ref{sec_obs} above, we then corrected the arrival times of each event to correspond to a reference frame at the solar system barycenter."954 ," For a given extraction region and energy range, a pulsation analysis could then be carried out on the resulting arrival times."955The EPIC MOS image of PSR iis shown in Figures | and 2..," The EPIC MOS image of PSR is shown in Figures \ref{fig_mos_all}956 and \ref{fig_mos_zoom}."957 Because a significant contribution to the background emission is from high-energy particles. the vignetting correction which has been applied to the data gives," Because a significant contribution to the background emission is from high-energy particles, the vignetting correction which has been applied to the data gives"958"manner, as discussed by (2008).","manner, as discussed by ."959".. These issues are not insurmountable, but further work needs to be done to refine flexion measurement, and alternative approaches for measuring flexion can provide a valuable insight to the strengths and weaknesses of each method."," These issues are not insurmountable, but further work needs to be done to refine flexion measurement, and alternative approaches for measuring flexion can provide a valuable insight to the strengths and weaknesses of each method."960 In this paper we introduce a new method for weak lensing flexion measurement., In this paper we introduce a new method for weak lensing flexion measurement.961" Instead of measuring derived quantities (such as weighted surface brightness moments, as in both the shapelets and HOLICs methods), we instead fit the lensed galaxy objects with a parameterized, Analytic Image Model (AIM) which is invariant to the mass-sheet degeneracy."," Instead of measuring derived quantities (such as weighted surface brightness moments, as in both the shapelets and HOLICs methods), we instead fit the lensed galaxy objects with a parameterized, Analytic Image Model (AIM) which is invariant to the mass-sheet degeneracy."962" By comparing model images to the data image in “pixel-space” and optimizing a figure of merit over a reasonable range of model parameter values, we constrain the flexion fields."," By comparing model images to the data image in “pixel-space” and optimizing a figure of merit over a reasonable range of model parameter values, we constrain the flexion fields."963" This method has the advantage that surface brightness errors are well understood (and typically Gaussian), thus the optimization algorithm can provide reliable estimates of the errors on the best-fit parameters."," This method has the advantage that surface brightness errors are well understood (and typically Gaussian), thus the optimization algorithm can provide reliable estimates of the errors on the best-fit parameters."964" Uncertainties in the flexion measured by shapelet and moment methods are quantified on average, rather than for each individual object, and primarily estimate the uncertainty in the mass reconstruction instead of the uncertainty in the measured flexion."," Uncertainties in the flexion measured by shapelet and moment methods are quantified on average, rather than for each individual object, and primarily estimate the uncertainty in the mass reconstruction instead of the uncertainty in the measured flexion."965" Direct error estimates for each component of the 1-flexion and 3-flexion values from each individual lensed object is a very desirable property, as it allows us to accurately weight the flexion measurements from each object in mass reconstructions."," Direct error estimates for each component of the 1-flexion and 3-flexion values from each individual lensed object is a very desirable property, as it allows us to accurately weight the flexion measurements from each object in mass reconstructions."966 This paper is structured as follows: refsec:flexionintro reviews the basic flexion formalism used throughout the paper., This paper is structured as follows: \\ref{sec:flexionintro} reviews the basic flexion formalism used throughout the paper.967 refsec:aimintro describes the the principle of the AIM method and the specific implementation used here., \\ref{sec:aimintro} describes the the principle of the AIM method and the specific implementation used here.968" refsec:aimtest describes the procedure used to test the AIM method on simulated data images, validating the accuracy of the fitting procedure and the accuracy of the error estimates."," \\ref{sec:aimtest} describes the procedure used to test the AIM method on simulated data images, validating the accuracy of the fitting procedure and the accuracy of the error estimates."969ddeveloped by Metz(2008) is à new implementation of the particle-mesh code (Bienetal.1991:Fellhauer2000).,"developed by \cite{metz} is a new implementation of the particle-mesh code \citep{bien,fell00}."970. Differences in the implementation of the algorithin make the new code munuch more efficient than the former., Differences in the implementation of the algorithm make the new code much more efficient than the former.971 hhad been implemented in the FORTRAN languageOme with a particular focus on the minimization of usage of the random access memory (RAM). which is uo longer a big issue in current days.," had been implemented in the FORTRAN language with a particular focus on the minimization of usage of the random access memory (RAM), which is no longer a big issue in current days."972 iis now being implemented in the modern pprogramunineg lauguage using object o‘jented programuniug techulques., is now being implemented in the modern programming language using object oriented programming techniques.973 The algorithuu has been üunpleimenutec with a focus on the performance of the code. but at tle same time keeping memory consumption at a low level.," The algorithm has been implemented with a focus on the performance of the code, but at the same time keeping memory consumption at a low level."974 uunakes particular optimal use of modern witti-core processor techologies., makes particular optimal use of modern multi-core processor technologies.975 The code solves the Poissou equation oi a system of Cartesiai grids., The code solves the Poisson equation on a system of Cartesian grids.976 The local universe is covered by a fixed coarse grid which contains the orbit of the CC around the center of the Milky Way., The local universe is covered by a fixed coarse grid which contains the orbit of the CC around the center of the Milky Way.977 In order to get good resolution of tlie sta “clusters two grids wit1 high aud mecitua resolution are focused ou each star cluster ollowiug their trajectories., In order to get good resolution of the star clusters two grids with high and medium resolution are focused on each star cluster following their trajectories.978 The individual high resolution grids cover an eutire star cluster. whereas the moeclitun resolution grids of every star cluster embed the whole initial CC.," The individual high resolution grids cover an entire star cluster, whereas the medium resolution grids of every star cluster embed the whole initial CC."979 All grids contain 1287 erid ceIs., All grids contain $^{3}$ grid cells.980 The CC orbits in an analytical Galactic potential (see Sect. 2.2.1))., The CC orbits in an analytical Galactic potential (see Sect. \ref{potential_mw}) ).981 For each particle in the CC he acceleration from the galactic potential is added as an analytical formula to the grid-based acceleration computed by solving the Poisson equatiou., For each particle in the CC the acceleration from the galactic potential is added as an analytical formula to the grid-based acceleration computed by solving the Poisson equation.982 The coordiuate system is chosen such that tLe disk of the lies in the x-y-plaue with origin at the Cralactic center., The coordinate system is chosen such that the disk of the lies in the x-y-plane with origin at the Galactic center.983 Iu our computations the Milky Way is represented by an analytical potential. which consists ol a a bulee-. aud a halo compouent.," In our computations the Milky Way is represented by an analytical potential, which consists of a a bulge-, and a halo component."984 The clisk is inodeled by a Mivamoto-Nagai potential (Mivamoto&Nagai 1975). with A44=1.0x10! M. dq=6.9 kpc. auc by=0.26kpc.," The disk is modeled by a Miyamoto-Nagai potential \citep{miya1975}, , with $M_{\rm d}=1.0 \times 10^{11}$ $_{\odot}$, $a_{\rm d}=6.5$ kpc, and $b_{\rm d}=0.26$kpc."985 The bulge is represented bya Heruquist potential (Heruquist 1990)..," The bulge is represented bya Hernquist potential \citep{hern1990}, ,"986Our conclusion. was thus that the models found by ZEEMAN with strong variation in abundance with magnetic co-latitude are unphysical.,Our conclusion was thus that the models found by ZEEMAN with strong variation in abundance with magnetic co-latitude are unphysical.987 In faet there is no convincing evidence for strong abundance variations on a global scale., In fact there is no convincing evidence for strong abundance variations on a global scale.988 We have therefore adopted a much simpler approach to abundance modelling., We have therefore adopted a much simpler approach to abundance modelling.989 The abundance of each element studied is assumed to be uniform over the stellar surface., The abundance of each element studied is assumed to be uniform over the stellar surface.990 The best fits we obtain to groups of lines in various spectral windows of our chosen five spectra. sampling the rotation cycle of the star. of course do not yield the same mean abundance in all windows.," The best fits we obtain to groups of lines in various spectral windows of our chosen five spectra, sampling the rotation cycle of the star, of course do not yield the same mean abundance in all windows."991 We use the standard deviation of the abundances found in different windows as a simple measure of the uncertainty of the value of the best fit mean abundance., We use the standard deviation of the abundances found in different windows as a simple measure of the uncertainty of the value of the best fit mean abundance.992 It will be seen that the uniform abundance values determined for different spectral windows are roughly concordant. and that with this simple assumption we can fit all spectral lines modelled fairly well at all phases. giving us some confidence that the derived average abundances are meaningful.," It will be seen that the uniform abundance values determined for different spectral windows are roughly concordant, and that with this simple assumption we can fit all spectral lines modelled fairly well at all phases, giving us some confidence that the derived average abundances are meaningful."993 Because of the large wavelength coverage of the available spectra of HD 318107. our data are sufficient to obtain first approximations to the chemical abundance distribution for O. Μα. Si. Ca. Ti. Cr. Fe. Nd. and Pr. and useful upper limits for the abundance of He and Mn.," Because of the large wavelength coverage of the available spectra of HD 318107, our data are sufficient to obtain first approximations to the chemical abundance distribution for O, Mg, Si, Ca, Ti, Cr, Fe, Nd, and Pr, and useful upper limits for the abundance of He and Mn."994 The large wavelength coverage also means that multiple lines of many elements can be found that have a variety of strengths and splitting patterns., The large wavelength coverage also means that multiple lines of many elements can be found that have a variety of strengths and splitting patterns.995 The mean abundance values found for the elements studied are listed in Table 3.. together with the uncertainties estimated from the scatter of fits to (usually two) different. spectral windows.," The mean abundance values found for the elements studied are listed in Table \ref{avgabund}, together with the uncertainties estimated from the scatter of fits to (usually two) different spectral windows."996 For elements for which only a single line or region was available. we have estimated the uncertainty as +0.2 dex.," For elements for which only a single line or region was available, we have estimated the uncertainty as $\pm 0.2$ dex."997" For comparison, the solar abundances reported by ? are tabulated as well."," For comparison, the solar abundances reported by \citet{Aspletal09} are tabulated as well."998 The quality of the fits 1s lustrated with short spectral windows. showing the comparison of uniform abundance models with the five observed / spectra used for the fitting. in Figures 3. and 4..," The quality of the fits is illustrated with short spectral windows, showing the comparison of uniform abundance models with the five observed $I$ spectra used for the fitting, in Figures \ref{spec48} and \ref{spec50}."999 In each figure the model spectra have been computed with the global mean from Table 3 rather than the local best fits., In each figure the model spectra have been computed with the global mean from Table \ref{avgabund} rather than the local best fits.1000 The lines used and the consistency of the fits are discussed element by element below., The lines used and the consistency of the fits are discussed element by element below.1001Classical SgIENEND are characterized by sinall orbital radii Rua=(152.5). aud by flux variability of a factor =20.,"Classical sgHMXB are characterized by small orbital radii $R_{orb}=(1.5-2.5)~R_*$, and by flux variability of a factor $\lesssim20$."1002 Such variabilities were modelled in term of win Inhomogencitics arecly trigeered by the lydrodvuamic aud plioto-1ouisation effects of the accreting object on the conrpanion andimer stellar wind (?7)..," Such variabilities were modelled in term of wind inhomogeneities largely triggered by the hydrodynamic and photo-ionisation effects of the accreting object on the companion and inner stellar wind \citep{blondin91, blondin94}."1003 At simall orbita radi. the companion is close to fill its Roche lobe. which rigecrs tidal streuus.," At small orbital radii, the companion is close to fill its Roche lobe, which triggers tidal streams."1004 Iu addition the N-ray source ionizes he wind acceleraion zone. prevents wind acceleration aux oeenerates slower velocities. denser winds. larger accretion radius axd finalls> lavecr X-ray luminosities.," In addition the X-ray source ionizes the wind acceleration zone, prevents wind acceleration and generates slower velocities, denser winds, larger accretion radius and finally larger X-ray luminosities."1005 Whether or iot the stellar wind is intrinsically clumipy at low raclius. he effec of the ¢‘ommpact object on the wind is expected o be inuyortant.," Whether or not the stellar wind is intrinsically clumpy at low radius, the effect of the compact object on the wind is expected to be important."1006 The aad difference between SEXT aud classical SeIIMUND. could therefore be their orbital radius., The main difference between SFXT and classical sgHMXB could therefore be their orbital radius.1007 At very ow orbital racdius (κ1.5Rj} tidal accretion will taxe dace trough au accretion disk aud the system will soon evolve to a conuon envelope stage., At very low orbital radius $(<1.5~R_*)$ tidal accretion will take place through an accretion disk and the system will soon evolve to a common envelope stage.1008" At low orbital radius (~2R) the wind wi] be perturbed in amy case and efficien wind accretion will lead to copious aux persisteut N-ray cunission (1079δεorefs),", At low orbital radius $(\sim 2~R_*)$ the wind will be perturbed in any case and efficient wind accretion will lead to copious and persistent X-ray emission $(10^{36-37}~\rm{erg/s})$.1009 At buger orbital radius (~10R.) aud if the wiid is chuupy. the SEXT behavior is expected as deseribed above.," At larger orbital radius $(\sim 10~R_*)$ and if the wind is clumpy, the SFXT behavior is expected as described above."1010 If the wind cluups do not form for any reason. the average accretion rate will remain too low aud the «mrces will remain mostly uudetected by the current hard N-vay surveviue iustrunentalon.," If the wind clumps do not form for any reason, the average accretion rate will remain too low and the sources will remain mostly undetected by the current hard X-ray surveying instrumentation."1011 INTEGRAL tripled the uumber of super-giant IIMNXD systems known in the Calaxy and reveaed two new populations: the :vbsorbed aud tie fast trausient (SENT) systenis., INTEGRAL tripled the number of super-giant HMXB systems known in the Galaxy and revealed two new populations: the absorbed and the fast transient (SFXT) systems.1012 The typical hard. N-rav variability factor is =20 in classical aud absorbed systems aud 2110 in SEXT., The typical hard X-ray variability factor is $\lesssim 20$ in classical and absorbed systems and $\gtrsim 100$ in SFXT.1013" We have also identified some ""juteriiediate systems with sunaller variability factors that could be eiticr SENT or classical svstenis.", We have also identified some “intermediate” systems with smaller variability factors that could be either SFXT or classical systems.1014 The SEXT behavior is best explained by the interaction between the accreting compact object aud a chuupy stellar wixd (2?)..," The SFXT behavior is best explained by the interaction between the accreting compact object and a clumpy stellar wind \citep{IntZand2005,Leyder2007}."1015 Using the hard N-ray variability observed by INTEGRAL in a sample of SENT we have derived. tyveal wind chuup parameters., Using the hard X-ray variability observed by INTEGRAL in a sample of SFXT we have derived typical wind clump parameters.1016 The compact object orbital racis are probably relatively arec (10 BR.) and the clumps which generate most of the hard rav Cluission hayο a size of a few teuth of R.., The compact object orbital radius are probably relatively large $10~R_*$ ) and the clumps which generate most of the hard X-ray emission have a size of a few tenth of $R_*$ .1017" The clip mass is ο he order or 41077121222""e (for. a column density of |0772223=?eu.2 7) aud the correspoudiug: mass-loss rate is LO67AF,v.", The clump mass is of the order or $10^{22-23}~\rm{g}$ (for a column density of $10^{22-23}~\rm{cm}^{-2}$ ) and the corresponding mass-loss rate is $10^{-(5-6)}~\rm{M_{\odot}/y}$.1018 At the orbital radits. the cluup separation is of fhe order of R and thei volume filline factor is 0.02.," At the orbital radius, the clump separation is of the order of $R_*$ and their volume filling factor is $0.02$."1019 Depeudiug how the chuup «cusity Varics with radius. the average volume filliug factor could be as large as 0.1.," Depending how the clump density varies with radius, the average volume filling factor could be as large as 0.1."1020 These parauxtors are d good agreement with the macro clumping scenario proposed by ?.., These parameters are in good agreement with the macro clumping scenario proposed by \cite{OskinovaHamannFeldmeier2007}.1021" The observed ratio between the fare and quiesceut count rates indicate denusitv ratios between the clumps and the inter-clunirp miceuu which vary between 15 to 50 in ""Iuteriuediate svs↸∖⋯↴∖↴⋜⋯≼⊔∪− ↽⋅≽‘in SEXT.", The observed ratio between the flare and quiescent count rates indicate density ratios between the clumps and the inter-clump medium which vary between 15 to 50 in “Intermediate” systems and $10^{2-4}$ in SFXT.1022 Such ratios and the observed ¢i1uup deusities are m reasonable agreement with∐∖↻↥⋅↸∖≼∐↸⊳↑↕∪∐↴∖↴∪↕≯∐∐↸∖≼⊔⋅↕↖⇁↸∖∐↕∐↴∖↴↑⋜∏⋝∐↕↑↕↸∖↴∖↴ at large radii (?).., Such ratios and the observed clump densities are in reasonable agreement withthe predictions of line driven instabilities at large radii \citep{Runacres2005}.1023 (6) different prescriptions adopted here Lr m . . originalGi model presented in Calurawith et al., where Below we discuss the different prescriptions adopted here with respect to the original model presented in Calura et al.1024" respect to We note here that the modifications have been made through changes in the parameters (e.g. o, τοι). whereas the general scheme and the above equations hold for both the Calura et al."," We note here that the modifications have been made through changes in the parameters (e.g. $\delta_i^{II}$ , $\tau_{0,i}$ ), whereas the general scheme and the above equations hold for both the Calura et al."1025 and the present formulations., and the present formulations.1026rcing that the parent mioclel. Mo ancl White (1996). deals with the unweighted halo correlation function.,"being that the parent model, Mo and White (1996), deals with the unweighted halo correlation function."1027 Pherclore anv comparison with a weighted. halo correlation function. will not work., Therefore any comparison with a weighted halo correlation function will not work.1028 Llowever. as we argued in€3.. the mass weighted correlation function is a better candidate for the galaxy correlation function.," However, as we argued in, the mass weighted correlation function is a better candidate for the galaxy correlation function."1029 Unweighted halo correlation function predicts an anti-bias at late times., Unweighted halo correlation function predicts an anti-bias at late times.1030 This is never seen in the weighted correlation function and hence the large mismatch., This is never seen in the weighted correlation function and hence the large mismatch.1031 Some authors have constructed analytical models. to understand. the evolution of bias (Catelan et al., Some authors have constructed analytical models to understand the evolution of bias (Catelan et al.1032 1997. and the references cited. therein) field. where the concept. is generalised [rom statistical bias (only a function of epoch) toa bias that depends both on position and epoch., 1997 and the references cited therein) field where the concept is generalised from statistical bias (only a function of epoch) to a bias that depends both on position and epoch.1033 In these mocels the mapping from the initial halo distribution to the final one is done using perturbative or approximate methocwa, In these models the mapping from the initial halo distribution to the final one is done using perturbative or approximate methods.1034 ln we described. evolution of the correlation. function for mass contained in halos of mass greater than a given ceutoll, In we described evolution of the correlation function for mass contained in halos of mass greater than a given cutoff.1035 These results. when applied to galaxies. have many important implications.," These results, when applied to galaxies, have many important implications."1036 In.$5.1... we will discuss the calculation of the initial power spectrum from the observed galaxy correlation function in view of the results presented inEJ.," In, we will discuss the calculation of the initial power spectrum from the observed galaxy correlation function in view of the results presented in."1037 In we turn to the question of evolution. of galaxy/quasar clustering and its relation with the evolution of halo clustering., In we turn to the question of evolution of galaxy/quasar clustering and its relation with the evolution of halo clustering.1038 Lastly. we outline some implications of these results for evolution of the inter-ealactic medium ancl ealaxy formation moclels in€5.," Lastly, we outline some implications of these results for evolution of the inter-galactic medium and galaxy formation models in."10393.. In this section. we assume that the halo distribution and galaxy distribution are the same at the present epoch.," In this section, we assume that the halo distribution and galaxy distribution are the same at the present epoch."1040 This is à reasonable assumption for studying galaxy clustering at a given epoch. as long as the mass of halos is not too cillerent from the mass of tvpical galaxies studied in surveys.," This is a reasonable assumption for studying galaxy clustering at a given epoch, as long as the mass of halos is not too different from the mass of typical galaxies studied in surveys."1041 The shapes of mass and galaxy correlation functions are dillerent. even at late times (fig.2. [ο and fie).," The shapes of mass and galaxy correlation functions are different, even at late times (fig.2, fig.3 and fig.4)."1042 ‘These differences introduce errors in calculation of the initial »ower spectrum from observations of galaxy clustering using scaling relations (PeacockancDocels1996)., These differences introduce errors in calculation of the initial power spectrum from observations of galaxy clustering using scaling relations \cite{pd96}.1043". Lig.5 shows the non-linear index n,; as a function of he linear index ny, of the averaged correlation function.", Fig.5 shows the non-linear index $n_{nl}$ as a function of the linear index $n_{lin}$ of the averaged correlation function.1044 We define ni; as in eqn.(5)) except that 0 ds replaced by £., We define $n_{nl}$ as in \ref{index}) ) except that $\sigma^2$ is replaced by $\bar\xi$.1045 This relation between the indices is obtained by using the »ower law fit (BaglaandPadmanabhan1997). in the quasi-inear regime (1<£200) to the scaling relation between 1e linear and the non-linear correlation function (Llamilton 1991).," This relation between the indices is obtained by using the power law fit \cite{crit} in the quasi-linear regime $1 \le \bar\xi1046\le 200$ to the scaling relation between the linear and the non-linear correlation function \cite{hamil}."1047". This figure shows that this relation Uattens out or indices above ny,=1.", This figure shows that this relation flattens out for indices above $n_{nl}=-1$.1048 Two reasons contribute to this altening: Gravitational instability acts to decrease (but not. to erase) the dilferences. between dillerent. initial conditions., Two reasons contribute to this flattening: Gravitational instability acts to decrease (but not to erase) the differences between different initial conditions.1049 Vherefore. any uncertainties in. the non-linear mass correlation function translate into much larger uncertainties in the initial power spectrum.," Therefore, any uncertainties in the non-linear mass correlation function translate into much larger uncertainties in the initial power spectrum."1050 The cilferenee in the shape/slope and the amplitude of the galaxy correlation function and the mass correlation function is one such uncertainty., The difference in the shape/slope and the amplitude of the galaxy correlation function and the mass correlation function is one such uncertainty.1051" ln order to assess this amplification of uncertainty in a quantitative manner. we have mapped a narrow range of non-linear indices. n,;=L201 (5= LS+0.1). to the corresponding linear indices."," In order to assess this amplification of uncertainty in a quantitative manner, we have mapped a narrow range of non-linear indices, $n_{nl}=-1.2 \pm 0.1$ $\gamma = 1.8 \pm 0.1$ ), to the corresponding linear indices."1052" The permitted range of linear indices is much larger (nj,—1.52 0.2: 5:cL5x 0.2)."," The permitted range of linear indices is much larger $n_{lin} \simeq -1.51053\pm 0.2$ ; $\gamma \simeq 1.5 \pm 0.2$ )."1054Our results break clown along2 the lines of those DAZs with known close companions| (a<0.02 AU) and those with greater separations.,Our results break down along the lines of those DAZs with known close companions $<$ 0.02 AU) and those with greater separations.1055" At smaller separations. the calculated mass loss rates agree reasonably well with the upper limit to the wind around Proxima Centauri (fe,?7).."," At smaller separations, the calculated mass loss rates agree reasonably well with the upper limit to the wind around Proxima Centauri \citep{wargelin02,wood02}."1056 The mass loss rates I caleulate are about (wo orders of maenitude5 smaller than Proxima Centauris smaller upper limit. with the exception of WD 0419-487 which is comparable. though larger (han the other two M dwarls.," The mass loss rates I calculate are about two orders of magnitude smaller than Proxima Centauri's smaller upper limit, with the exception of WD 0419-487 which is comparable, though larger than the other two M dwarfs."1057 This larger rate could be explained bv moderate Roche lobe overflow. evaporation of the companion by the DAZ. or efficient. capture of the companions wind by a magnetic field.," This larger rate could be explained by moderate Roche lobe overflow, evaporation of the companion by the DAZ, or efficient capture of the companion's wind by a magnetic field."1058 ID WD 0419-487 was efficiently. capturing all of its companions wind. Mg would [all nicely in with those observed for the other (wo close binaries.," If WD 0419-487 was efficiently capturing all of its companion's wind, $\dot{M}_{RD}$ would fall nicely in with those observed for the other two close binaries."1059 On (he other hand. the mass loss rates determined for the widely separated companions are three to four orders of magnitude larger than (he Solar wind.," On the other hand, the mass loss rates determined for the widely separated companions are three to four orders of magnitude larger than the Solar wind."1060 This is despite a slightly igher uncertainty of the accretion rate onto the white dwarls., This is despite a slightly higher uncertainty of the accretion rate onto the white dwarfs.1061 Most of these uncertainties would conspire to create a higher accretion rate., Most of these uncertainties would conspire to create a higher accretion rate.1062 For WD 1210-4464. a lower accretion rate is possible if the detected equivalent width corresponds to a lower abundance (han asstumect.," For WD 1210+464, a lower accretion rate is possible if the detected equivalent width corresponds to a lower abundance than assumed."1063 However. even at the smallest lower limit of the ? survey ([Ca/I}~+12.8). the inferred nass loss rate of the companion would be equivalent to the Solar Wind ancl (wo orders of nagnitude higher than the close binaries.," However, even at the smallest lower limit of the \citet{zuckerman03}1064 survey $\sim$ 12.8), the inferred mass loss rate of the companion would be equivalent to the Solar Wind and two orders of magnitude higher than the close binaries."1065 It is possible that (hese svstemis are hierarchical triples with companions undetected by radial velocity observations but in orbits similar to the close binaries., It is possible that these systems are hierarchical triples with companions undetected by radial velocity observations but in orbits similar to the close binaries.1066 WD 12104464 and WD1049+103 have FRI4W photometry consistent. with sinele DAZs. neglecting their resolved companions.," WD 1210+464 and WD1049+103 have F814W photometry consistent with single DAZs, neglecting their resolved companions."1067 This strongly arenes that anv further unresolved companions would have to be quite dim ancl of low mass., This strongly argues that any further unresolved companions would have to be quite dim and of low mass.1068 Conversely. M. divas could have (he super solar rates predicted by (he earlier results. but in light of the estimated winds of Proxima Centauri and the three close M dwarls this seems unlikely.," Conversely, M dwarfs could have the super solar rates predicted by the earlier results, but in light of the estimated winds of Proxima Centauri and the three close M dwarfs this seems unlikely."1069 Furthermore. eiven the inferred total ages of the host white dwarls. (he companions would have either completely evaporated or lost a large Iraction of their total mass.," Furthermore, given the inferred total ages of the host white dwarfs, the companions would have either completely evaporated or lost a large fraction of their total mass."1070 The low mass loss rates for the three closest binaries has (wo possible interpretations., The low mass loss rates for the three closest binaries has two possible interpretations.1071 Either (he mechanism for accretion is suppressed relative to Boncli-Llovle accretion by several orders of magnitude if one expects M cdwarf winds to be similar to (he Sun. or M οναΕ winds are quenched even in situations where thev are rotating quickly and should have significant aclivitv due to strong magnetic fields.," Either the mechanism for accretion is suppressed relative to Bondi-Hoyle accretion by several orders of magnitude if one expects M dwarf winds to be similar to the Sun, or M dwarf winds are quenched even in situations where they are rotating quickly and should have significant activity due to strong magnetic fields."1072 Some evidence [or the quenching of winds for low Inass stars comes from ?.. who find that. very late spectral (vpe stars have lower indicators of activity due (o a corona or chromosphere.," Some evidence for the quenching of winds for low mass stars comes from \citet{mohanty03}, who find that very late spectral type stars have lower indicators of activity due to a corona or chromosphere."1073 This has been noted in studies of (he angular momentum evolution of CVs. where fully convective companions were believed to have lost less auigular momentumdue to an inellicient dvnamo process (?)..," This has been noted in studies of the angular momentum evolution of CVs, where fully convective companions were believed to have lost less angular momentumdue to an inefficient dynamo process \citep{durney93}. ."1074in Fig. 4.,in Fig. \ref{fig:l709}.1075" Source ""A"" lies slightly outside the FWHM of the AMI primary beam and has a primary beam corrected continuum flux of Sjg=245—13 mmiy."," Source “A” lies slightly outside the FWHM of the AMI primary beam and has a primary beam corrected continuum flux of $S_{16} =1076245\pm13$ mJy."1077 This is consistent with fluxes from the literature of So1ος=374—24 mmiJy (Texas). $y)42=270.27 mmiJy (Effelsberg 21emy. $+695=310—31 mmJy (Effelsberg Ilem) and Syy5=330.29 mmly (GB6) indicating a source with spectral index à=0.070.02. see Fig. 5..," This is consistent with fluxes from the literature of $S_{0.365} = 374\pm24$ mJy (Texas), $S_{1.42}=270\pm27$ mJy (Effelsberg 21cm), $S_{2.695}=310\pm31$ mJy (Effelsberg 11cm) and $S_{4.85}=330\pm29$ mJy (GB6) indicating a source with spectral index $\alpha = 0.07\pm0.02$, see Fig. \ref{fig:l709a}."1078 The NVSS flux density for this object is slightly —_lower. Syyss|.1—218.6.6 mmJy suggesting that the source is extended.," The NVSS flux density for this object is slightly lower, $S_{\rm{NVSS},1.4} =1079218\pm6.6$ mJy suggesting that the source is extended."1080" A second. and fainter. object in the field is just north-west of the pointing centre. Source ""B""."," A second, and fainter, object in the field is just north-west of the pointing centre, Source “B”."1081 This object has a flux density of Sjg=0.5 6.0.mmly in the AMI map and is most probably a combination of three unresolved point sources. which may be found in the NVSS catalogue. all falling within an AMI synthesized beam at this position.," This object has a flux density of $S_{16} = 6.0\pm0.5$ mJy in the AMI map and is most probably a combination of three unresolved point sources, which may be found in the NVSS catalogue, all falling within an AMI synthesized beam at this position."1082 These sources have a combined flux density of S$)4=11.0.0.5 mmly. indicating a decrease in flux at GGHz.," These sources have a combined flux density of $S_{1.4} = 11.0\pm0.5$ mJy, indicating a decrease in flux at GHz."1083" The slight extension to the south of this object. ""C"". is not coincident with any NVSS point sources and may be associated with L709."," The slight extension to the south of this object, “C”, is not coincident with any NVSS point sources and may be associated with L709."1084 The object is present at the So level in the combined channel map with a flux of Sig=1.610.51 mmlv.," The object is present at the $\sigma$ level in the combined channel map with a flux of $S_{16} =10851.61\pm0.31$ mJy."1086 In the consitituent channel maps the source is present with flux densities varving between | and 46., In the consitituent channel maps the source is present with flux densities varying between 1 and $\sigma$.1087 At this level of significance it is difficult to fit a reliable spectral index. however the flux density appears to be steeply falling with increasing frequency.," At this level of significance it is difficult to fit a reliable spectral index, however the flux density appears to be steeply falling with increasing frequency."1088" As the source appears point-like this would suggest that Source ""C"" is not associated with L709 but is instead a faint steep spectrum extragalactic point source.", As the source appears point-like this would suggest that Source “C” is not associated with L709 but is instead a faint steep spectrum extragalactic point source.1089 At GGHz we see a ridge of emission towards L860. see Fig. 6..," At GHz we see a ridge of emission towards L860, see Fig. \ref{fig:l860}."1090 We investigate its spectral properties using analysis Case (1)., We investigate its spectral properties using analysis Case (1).1091 Although it possesses no obvious counterpart in the unsampled CGPS dataset. a matched image shows the same structure at |.4GGHz.," Although it possesses no obvious counterpart in the unsampled CGPS dataset, a matched image shows the same structure at GHz."1092 To the north of the field two point-like radio sources may be found (A B». whilst the ridge of extended emission that runs north-south across the pointing centre may be divided into three distinct sub-regions of emission (C. D E».," To the north of the field two point-like radio sources may be found (A B), whilst the ridge of extended emission that runs north–south across the pointing centre may be divided into three distinct sub-regions of emission (C, D E)."1093 The morphology of these sub-regions is not well deseribed by a Gaussian model., The morphology of these sub-regions is not well described by a Gaussian model.1094 Although both C D might be considered to be associated with L860 the derived flux densities. see Table 2.. and their spectral indices indicate that there is no excess emission present at microwave frequencies for these sources.," Although both C D might be considered to be associated with L860 the derived flux densities, see Table \ref{tab:list}, and their spectral indices indicate that there is no excess emission present at microwave frequencies for these sources."1095 No radio emission can be seen directly towards L917 at GGHz. although a ridge of emission runs north-south slightly to the west of the pointing centre. see Fig. 7..," No radio emission can be seen directly towards L917 at GHz, although a ridge of emission runs north–south slightly to the west of the pointing centre, see Fig. \ref{fig:l917i12}."1096 We investigate the spectral properties of this ridge primarily using analysis Case (1)., We investigate the spectral properties of this ridge primarily using analysis Case (1).1097 This ridge has three separate peaks. which are evident in both the GGHz sampled data and the AMI data at GGHz.," This ridge has three separate peaks, which are evident in both the GHz sampled data and the AMI data at GHz."1098 We fit for the flux density of each peak separately using the flux extraction method described in Section ??.., We fit for the flux density of each peak separately using the flux extraction method described in Section \ref{sec:l675}.1099 These peaks (A. B C) all appear to have slightly more flux at GGHz than at GGHz. see Table 2..," These peaks (A, B C) all appear to have slightly more flux at GHz than at GHz, see Table \ref{tab:list}."1100 Using additional data at GGHz from the Effelsberg telescope sampled under Case (2) we can fill in more of the flux spectrum., Using additional data at GHz from the Effelsberg telescope sampled under Case (2) we can fill in more of the flux spectrum.1101 The peaks A and C show a spectrum consistent with a region of optically thin free-free emission. see Fig. 8..," The peaks A and C show a spectrum consistent with a region of optically thin free–free emission, see Fig. \ref{fig:l917spec}."1102" In ""B"". the closest peak to the pointing centre we see a large excess at GGHz relative to GGHz. although it is not clear if this excess is caused by anomalous emission."," In “B”, the closest peak to the pointing centre we see a large excess at GHz relative to GHz, although it is not clear if this excess is caused by anomalous emission."1103 At GGHz the emission has a largely, At GHz the emission has a largely1104the expected secular trend might be difficult to disceru amid the fluctuatious.,the expected secular trend might be difficult to discern amid the fluctuations.1105 The possibility that planetary torques are stochastic raises several Issues: The methods adopted in this paper allow us to explore the second and third issues above. but uot the first.," The possibility that planetary torques are stochastic raises several issues: The methods adopted in this paper allow us to explore the second and third issues above, but not the first."1106 In, In1107HII radio galaxies depends on the optical luminosity of the host galaxy (Ledlow&Owen 1996)).,II radio galaxies depends on the optical luminosity of the host galaxy \citealt{Ledlow1996}) ).1108 At absolute magnitudes of M=-2lL the break is at Ljj=107WHz '. whereas at M=—24 it is two orders of magnitude higher. at Lii1075W Hz!.," At absolute magnitudes of ${\rm M}=-21$, the break is at $L_{1.4}=10^{24}\,{\rm W\,Hz^{-1}}$ , whereas at ${\rm1109 M}=-24$ it is two orders of magnitude higher, at $L_{1.4}=10^{26}\,{\rm W\,Hz^{-1}}$ ."1110 The IFRS have magnitudes of more than 24.5 (the optical observations). hence their absolute magnitudes are greater than M=—21.5 at z=2 and greater than M=-23.9 at >=2.," The IFRS have magnitudes of more than ${\rm R}=24.5$ (the optical observations), hence their absolute magnitudes are greater than ${\rm M}=-21.5$ at $z=2$ and greater than ${\rm M}=-23.9$ at $z=2$."1111 At redshifts of 5. all IFRS would exceed a GGHz luminosity of 107?WHz'. so could safely be classified as III objects. independent of the optical luminosities of their host galaxies.," At redshifts of 5, all IFRS would exceed a GHz luminosity of $10^{26}\,{\rm W\,Hz^{-1}}$, so could safely be classified as II objects, independent of the optical luminosities of their host galaxies."1112 At redshifts of 2. however. only the brighter IFRS reach 107WHz and for those with smaller GGHz luminosities this classification1. can not be made.," At redshifts of 2, however, only the brighter IFRS reach $10^{26}\,{\rm W\,Hz^{-1}}$, and for those with smaller GHz luminosities this classification can not be made."1113 We measured the spectral indices by fitting a power-law to all available radio data for each source. weighting the data points by their errors. and ensuring that the data were convolved to the same beam size as far as this was possible (see Section 2.1.1)).," We measured the spectral indices by fitting a power-law to all available radio data for each source, weighting the data points by their errors, and ensuring that the data were convolved to the same beam size as far as this was possible (see Section \ref{sec:obs}) )."1114 In cases where only two data points were available the spectral index was calculated using these flux densities. and errors were calculated using error propagation.," In cases where only two data points were available the spectral index was calculated using these flux densities, and errors were calculated using error propagation."1115 These values are given t Table 1., These values are given in Table 1.1116 To compare the distribution to other sources we calculated the spectral index using the GGHz and GGHz data only., To compare the distribution to other sources we calculated the spectral index using the GHz and GHz data only.1117 A histogram of the distribution of spectral indices is shown Ἡ Figure 1.. along with the spectral indices between GGHz and GGHz of all sources in the ELAIS field (Zinn et al..," A histogram of the distribution of spectral indices is shown in Figure \ref{fig:spix}, along with the spectral indices between GHz and GHz of all sources in the ELAIS field (Zinn et al.,"1118 i prep) and of the AGN contained therein. which were classified based on morphology. spectroscopy. or radio excess over the radio-IR relation (see Norrisetal.2006 and Middelbergetal. 2008a)).," in prep) and of the AGN contained therein, which were classified based on morphology, spectroscopy, or radio excess over the radio-IR relation (see \citealt{Norris2006a} and \citealt{Middelberg2008a}) )."1119 The median spectral index of the general source populatio in the ELAIS field is —0.56. the median of AG spectral indices ts —0.82. and the median of the IFRS is —1.40.," The median spectral index of the general source population in the ELAIS field is $-0.86$, the median of AGN spectral indices is $-0.82$, and the median of the IFRS is $-1.40$."1120 The distribution of the IFRS is clearly biased towards low values. and the tal of indices larger than -0.7 Is missing completely.," The distribution of the IFRS is clearly biased towards low values, and the tail of indices larger than $-0.7$ is missing completely."1121 A two-tailed Kolmogorov-Smirnov test shows that the IFRS distribution differs significantly from the general population (p= 0.0028) and also from the general AG population (p= 0.0014)., A two-tailed Kolmogorov-Smirnov test shows that the IFRS distribution differs significantly from the general population $p=0.0028$ ) and also from the general AGN population $p=0.0014$ ).1122 Since there is plenty of evidence that IFRS are AGN-driven. the difference in spectral index between the AGN and IFRS populations must arise from IFRS having rather peculiar properties. which show up because they have been selected by IR faintness.," Since there is plenty of evidence that IFRS are AGN-driven, the difference in spectral index between the AGN and IFRS populations must arise from IFRS having rather peculiar properties, which show up because they have been selected by IR faintness."1123 IFRS could be AGN in a younger evolutionary stage. at higher redshifts. or in different environments.," IFRS could be AGN in a younger evolutionary stage, at higher redshifts, or in different environments."1124 We note that the general AGN population also contains numerous subclasses such as compact steep-spectrum sources (CSS) and gigahertz-peaked spectrum sources (GPS). which have peculiar spectral energy distributions. but are not considered separately in this analysis.," We note that the general AGN population also contains numerous subclasses such as compact steep-spectrum sources (CSS) and gigahertz-peaked spectrum sources (GPS), which have peculiar spectral energy distributions, but are not considered separately in this analysis."1125 The 4.8GGHz and 8.6GGHz observations have higher resolution than the GGHz and GGHz observations. and are less sensitive to extended emission.," The GHz and GHz observations have higher resolution than the GHz and GHz observations, and are less sensitive to extended emission."1126 The spectral index between GGHz and GGHz is therefore not physically meaningful. because the data at the higher frequency are sensitive to more compact structures than the GGHz and GGHz observations.," The spectral index between GHz and GHz is therefore not physically meaningful, because the data at the higher frequency are sensitive to more compact structures than the GHz and GHz observations."1127 However. within each pair of bands GGHz or GGH2z) the uv coverage has been matched and so the spectral indices are physically relevant to the size scale being studied.," However, within each pair of bands GHz or GHz) the uv coverage has been matched and so the spectral indices are physically relevant to the size scale being studied."1128 We compared the low-frequency GGHz) and high-frequency GGHz) spectral indices of IO targets. 7 of which have measured flux densities at GGHz. GGHz. 4.8GGHz. and GGHz. and 3 of which have upper limits at GGHz.," We compared the low-frequency GHz) and high-frequency GHz) spectral indices of 10 targets, 7 of which have measured flux densities at GHz, GHz, GHz, and GHz, and 3 of which have upper limits at GHz."1129 In these cases. we used 3 times the Image rms as an upper limit on the flux density to compute the spectral index (the comparatively small span in frequency enlarges the error bars in these cases).," In these cases, we used 3 times the image rms as an upper limit on the flux density to compute the spectral index (the comparatively small span in frequency enlarges the error bars in these cases)."1130 We show in Figure 2. these two spectral indices and indicate with a straight line where they would be equal.," We show in Figure \ref{fig:spix_hi_lo}1131 these two spectral indices and indicate with a straight line where they would be equal."1132 Clearly the spectra steepen towards higher frequencies., Clearly the spectra steepen towards higher frequencies.1133 We note that the median TM=-].0 of all IFRS is lower than the median TM=-].I4 of the 10 sources which also have a measurement or limit for ay.8.6, We note that the median $\alpha_{1.4}^{2.4}=-1.40$ of all IFRS is lower than the median $\alpha_{1.4}^{2.4}=-1.14$ of the 10 sources which also have a measurement or limit for $\alpha_{4.8}^{8.6}$.1134 This ts (1) because of the selection effect that the very steep-spectrum sources tend to have escaped detection at the higher frequencies: and (11) because of the use of upper limits at GGHz. meaning that the true spectral index in these three cases is lower than specified by us.," This is (i) because of the selection effect that the very steep-spectrum sources tend to have escaped detection at the higher frequencies; and (ii) because of the use of upper limits at GHz, meaning that the true spectral index in these three cases is lower than specified by us."1135 In some cases (CSS538. ES318. ES419. ES749. ES798. and ES973) the spectral index derived from. lower-frequency observations. predicts GGHz or GGHz flux densities which are incompatible with the measurements at. these frequencies.," In some cases (CS538, ES318, ES419, ES749, ES798, and ES973) the spectral index derived from lower-frequency observations predicts GHz or GHz flux densities which are incompatible with the measurements at these frequencies."1136 However. in some other cases such as CS703. ES427. or ES509 the detections at the highest frequencies align very well with the lower frequencies. and tightly follow power-laws.," However, in some other cases such as CS703, ES427, or ES509 the detections at the highest frequencies align very well with the lower frequencies, and tightly follow power-laws."1137 We consider this as evidence that the calibration is not systematically wrong since the same methods were used in all cases., We consider this as evidence that the calibration is not systematically wrong since the same methods were used in all cases.1138 Instead we consider two effects as potential causes of this discrepancy. (, Instead we consider two effects as potential causes of this discrepancy. (1139i) Sources are resolved out.,i) Sources are resolved out.1140 The 843MMHz. GGHz and GGHz data have excellent uv coverage at spacings below Skk2 (which corresponds to an angular seale of 4].25aaresec). and even have good coverage at spacings shorter than. KI? aaremin).," The MHz, GHz and GHz data have excellent uv coverage at spacings below $\lambda$ (which corresponds to an angular scale of arcsec), and even have good coverage at spacings shorter than $\lambda$ arcmin)."1141 On the other hand. in our matched-resolution images at GGHz and GGHz the shortest baseline used was 7kk.t aaresee- note that one goal of these observations was to image the targets with high resolution. hence long baselines were selected).," On the other hand, in our matched-resolution images at GHz and GHz the shortest baseline used was $\lambda$ arcsec- note that one goal of these observations was to image the targets with high resolution, hence long baselines were selected)."1142 This means that even tapered images cannot reveal large-scale structure, This means that even tapered images cannot reveal large-scale structure1143All known black holes belong to two families: stellar-mass black joles are seen in X-ray binaries. while super-massive ones are oesent in the centres of galaxy bulges sometimes revealing hemselves as Active Galactic Nuclei (AGN).,"All known black holes belong to two families: stellar–mass black holes are seen in X–ray binaries, while super–massive ones are present in the centres of galaxy bulges sometimes revealing themselves as Active Galactic Nuclei (AGN)."1144" While the former lave masses up to ~ZOAL. (e.g. Fryer Kalogera 2001). the latter ave masses in the range ~ 10""—10""AL. . the smaller-mass massive black hole to date being that in NGC 4395 with a mass of a ew times LO”AZ. (Peterson et al."," While the former have masses up to $\sim 20 M_\odot$ (e.g. Fryer Kalogera 2001), the latter have masses in the range $\sim 10^6$ $10^9~M_\odot$ , the smaller–mass super--massive black hole to date being that in NGC 4395 with a mass of a few times $10^{5}~M_\odot$ (Peterson et al."1145 2005)., 2005).1146 Although it has long been hought that intermediate-mass black holes IMBH) with masses ~ QU—107AL. may form in dense stellar clusters (e.g. Frank Rees 1976: Portegies Zwart et al., Although it has long been thought that intermediate–mass black holes (IMBH) with masses $\sim 10^2$ $10^4~M_\odot$ may form in dense stellar clusters (e.g. Frank Rees 1976; Portegies Zwart et al.1147 1999). there are no known IMBHs tilling the mass-gap between the two known families.," 1999), there are no known IMBHs filling the mass–gap between the two known families."1148" If present. active IMBHs may reveal themselves as accreting X-ray sources exceeding by a large factor the Eddington luminosity of black holes (LER,—2.6«107 eres 1 fora mass” stellar-mass black hole of 20A. 3."," If present, active IMBHs may reveal themselves as accreting X–ray sources exceeding by a large factor the Eddington luminosity of stellar--mass black holes $_{\rm{20~M_\odot}}^{\rm{Edd}} = 2.61149\times 10^{39}$ erg $^{-1}$ for a ``maximal--mass'' stellar–mass black hole of $20~M_\odot$ )."1150" Ultra-Luminous X-ray sources (ULX)are off-nuclear X-ray sources seen in other galaxies (than the Milky Way) with luminosities exceeding LE,llxp; Gee e.g. Colbert Mushotzky 1999: Mushotzky 2004).", Ultra–Luminous X–ray sources (ULX)are off–nuclear X–ray sources seen in other galaxies (than the Milky Way) with luminosities exceeding $_{\rm{20~M_\odot}}^{\rm{Edd}}$ (see e.g. Colbert Mushotzky 1999; Mushotzky 2004).1151 Since the Eddington argument implies a lower limit of 20AZ. on the mass of the central object. ULXs are often regarded as IMBH-eandidates (see e.g. Miller Colbert 2003: Fabbiano 2005).," Since the Eddington argument implies a lower limit of $20~M_\odot$ on the mass of the central object, ULXs are often regarded as IMBH–candidates (see e.g. Miller Colbert 2003; Fabbiano 2005)."1152 However. inferring a lower limit on the mass of an accreting compact object only from its bolometric luminosity can lead to misleading results.," However, inferring a lower limit on the mass of an accreting compact object only from its bolometric luminosity can lead to misleading results."1153 This is because. if potential anisotropies of emission (e.g. beaming. see Reynolds et al.," This is because, if potential anisotropies of emission (e.g. beaming, see Reynolds et al."1154 1997: King et al., 1997; King et al.1155 2001) or accretion (e.g. radiation—driven inhomogeneous accretion. see Begelman 2002) are not taken into account. the lower limit on the mass of the object may be severely overestimated.," 2001) or accretion (e.g. radiation–driven inhomogeneous accretion, see Begelman 2002) are not taken into account, the lower limit on the mass of the object may be severely over–estimated."1156 Both the beaming and inhomogeneous accretion scenarios can be invoked to explain luminosities up to a few times 107 erg + with accretion on standard stellar-mass black holes., Both the beaming and inhomogeneous accretion scenarios can be invoked to explain luminosities up to a few times $10^{40}$ erg $^{-1}$ with accretion on standard stellar–mass black holes.1157 However. geometric beaming (e.g. a funnel geometry) and inhomogeneous accretion can only provide an effective luminosity exceeding the Eddington limit by a factor ~23 (Madau 1988) and ~10. (Ruszkowski Begelman 2003) respectively.," However, geometric beaming (e.g. a funnel geometry) and inhomogeneous accretion can only provide an effective luminosity exceeding the Eddington limit by a factor $\sim$ 23 (Madau 1988) and $\sim$ 10, (Ruszkowski Begelman 2003) respectively."1158 Thus. for ULXs with luminosities exceeding 107. erg s+. relativistic beaming seem the only option to avoidthe presence of an IMBH.," Thus, for ULXs with luminosities exceeding $10^{41}$ erg $^{-1}$ , relativistic beaming seem the only option to avoidthe presence of an IMBH."1159best possible calibration and homogeneity of our photometric measurements.,best possible calibration and homogeneity of our photometric measurements.1160 We followed the ISOCAA handbook (Blomimaertetal.2001) and used the CLA software 2000). to subtract clarks. remove cosmic rays hits. remove the effect of flux transients. and finally [latfield. re-sample and co-add the individual exposures.," We followed the ISOCAM handbook \citep{isohandbook} and used the CIA software \citep{cia} to subtract darks, remove cosmic rays hits, remove the effect of flux transients, and finally flatfield, re-sample and co-add the individual exposures."1161 The twpical useful field of view of the images is about (1.5arecmin)? sampled with (3arcsec)? pixels.," The typical useful field of view of the images is about $(1.5 \rm{arcmin})^2$ sampled with $(31162\rm{arcsec})^2$ pixels."1163 Most of the detected 3C! sources were not or only barely spatially resolved by ISOCAM., Most of the detected 3C sources were not or only barely spatially resolved by ISOCAM.1164 In those cases. apertures wilh a radius of 10 arcsec were used. and aperture losses were modelled using svnthetic point spread functions (Okumura1905," In those cases, apertures with a radius of 10 arcsec were used, and aperture losses were modelled using synthetic point spread functions \citep{PSF}."1165"), For extended sources. we chose apertures which measure (he spatially integrated fIux of the source."," For extended sources, we chose apertures which measure the spatially integrated flux of the source."1166 For most ο sources. photometric information at optical. near-infrared. and/or infrared. and mm wavelengths is available.," For most 3C sources, photometric information at optical, near-infrared and/or far-infrared, and mm wavelengths is available."1167 We compiled SEDs between 0.5 and 1300. jm for all sources in our sample using data listed in the(NED). the ISOPHOT measurement given in Laasetal.(2003b) and other recent papers (see SEIID.," We compiled SEDs between 0.5 and 1300 $\mu$ m for all sources in our sample using data listed in the, the ISOPHOT measurement given in \citet{Haas} and other recent papers (see SFKH)."1168 In compiling the SEDs. we only used photometric data which includes. like our own ISOCAM photometry. the integrated Πας from the whole host galaxy.," In compiling the SEDs, we only used photometric data which includes, like our own ISOCAM photometry, the integrated flux from the whole host galaxy."1169 For each SED. we estimated (he contribution of svnchrotron radiation to the MIR fluxes by extrapolating the radio core [Iux.," For each SED, we estimated the contribution of synchrotron radiation to the MIR fluxes by extrapolating the radio core flux."1170 We found that the svnchrotron radiation is a negligible contribution to the ATHE. thax for all SEDs used in this paper., We found that the synchrotron radiation is a negligible contribution to the MIR flux for all SEDs used in this paper.1171 We retrieved ISOCAAM images for a total of ssources., We retrieved ISOCAM images for a total of sources.1172 The rms noise in (he reduced images ranges [rom 0.5 to 5 Πιν., The rms noise in the reduced images ranges from 0.5 to 5 mJy.1173 We detected a total ol egalaxies., We detected a total of galaxies.1174 The high detection rate indicates that hot dust is common in raclo-loud ACGNs. and that ος sources are bright enough in the MIB. so that they will be readily accessible to detailed studies by [uture instruments such as SIRTF.," The high detection rate indicates that hot dust is common in radio-loud AGNs, and that 3C sources are bright enough in the MIR so that they will be readily accessible to detailed studies by future instruments such as SIRTF."1175 A steep rise of the flux from optical wavelengths below μην to the MIR indicates the presence of a sienilicant amount of dust al Z722 300Ix. [or a large fraction of our sample., A steep rise of the flux from optical wavelengths below $\mu$ m to the MIR indicates the presence of a significant amount of dust at $T\approx300$ K for a large fraction of our sample.1176 In order to estimate the contribution of stars to the MIR. we fitted 4000Ix black body spectra to (he short wavelength part of the SEDs.," In order to estimate the contribution of stars to the MIR, we fitted 4000K black body spectra to the short wavelength part of the SEDs."1177 This temperature deliberately was taken to be on the low side of the range of possible average stellar temperatures so that the MIR. emission attributed to stars is an upper limit., This temperature deliberately was taken to be on the low side of the range of possible average stellar temperatures so that the MIR emission attributed to stars is an upper limit.1178 Taking this stellar contribution into account. we found clear evidence of dust in ssources. 1.0. redshift source with a clear detection of hot dust is," Taking this stellar contribution into account, we found clear evidence of dust in sources, i.e. redshift source with a clear detection of hot dust is"1179viewius anele. the moat flow. and the Evershed flow (Schaviuer et al.,"viewing angle, the moat flow, and the Evershed flow (Scharmer et al."1180 2008)., 2008).1181 The realisin required to achieve such coniparison with observations ds easily indssed dgN ignoring anv oo several pieces of physics that. though uot importa iu he opaque eax pressure doniüuated deeper lavers. )conie crucial at the observed surface.," The realism required to achieve such comparison with observations is easily missed by ignoring any of several pieces of physics that, though not important in the opaque gas pressure dominated deeper layers, become crucial at the observed surface."1182 To reproduce 1C structure of the nmüagnetic field at the surface of aspot. a proper treatiueit of the naenetic Bell iu ic tenuous. low-.) atIosphere above the surface is riticul.," To reproduce the structure of the magnetic field at the surface of a spot, a proper treatment of the magnetic field in the tenuous, $\beta$ atmosphere above the surface is critical."1183 The hieh Alfvénn speeds rere strouely restric je kind of naenetic conferrations tla are possible near 1C observed surface {«, The high Alfvénn speeds here strongly restrict the kind of magnetic configurations that are possible near the observed surface (cf.1184 Toiscussion iu Paper I)., discussion in Paper I).1185" Mos M the traditional ""agnetoconvection experimuents muss us »olut ""Mosethi:leaving «mit the maeneically dominated uospliere", Most of the traditional `magnetoconvection' experiments miss this point by leaving out the magnetically dominated atmosphere altogether.1186 Atclupts o interpret suuspo strucure by analogy with such modeIs. or interpretations ASCE on nienuetie turl»ileuce fornalisiis can not be IOCfed to add imc to uncdersπως of observed 1s]ot structure.," Attempts to interpret sunspot structure by analogy with such models, or interpretations based on magnetic turbulence formalisms can not be expected to add much to understanding of observed sunspot structure."1187 Tjo respouse of the :πιοος Πο]ε] is fast coipared with the chauges takΠιο place at its plotospieric »ounucdarv., The response of the atmospheric field is fast compared with the changes taking place at its photospheric boundary.1188 As a result it takes ace approximately along aories of nini chereyv states COTECSPOLlue to he ¢changing boundary conditious., As a result it takes place approximately along a series of minimum energy states corresponding to the changing boundary conditions.1189" The secular daterm of variatioIs in field ποιο[um ixd lucTimation. which observers have interpreted m terms of tin floating fiux ubes, is simply the expected response of the atinospjoric naeletic field to the opening of a sap )etwoeen the field lines below he surace, aded by strfacὉ cooling of 10rlzoutal convecive (Evershed) flows along he fibuneuts (see discussion iu Nordnd aud Sclarlucr 20t9)."," The peculiar pattern of variations in field strength and inclination, which observers have interpreted in terms of thin floating flux tubes, is simply the expected response of the atmospheric magnetic field to the opening of a gap between the field lines below the surface, aided by surface cooling of horizontal convective (Evershed) flows along the filaments (see discussion in Nordlund and Scharmer 2009)."1190 Flux tubes SUSPC1ided in such a naenetically donunated atiiosphere. while computationally counveuieut as a one-dinensional recWCion. are plysically wurealisic LOM-CCΠλ structires.," Flux tubes suspended in such a magnetically dominated atmosphere, while computationally convenient as a one-dimensional reduction, are physically unrealistic non-equilibrium structures."1191 ]t ids not surIse that nothing like tubes (twised or otherwise) turus up in f nuuvical simulations., It is not surprising that nothing like tubes (twisted or otherwise) turns up in the numerical simulations.1192 Att1ο sale time. the observatio leave ess and less room for these coustructions. as t spatal resolution achieve with nuproviue teclinology lucreasses (Scharimer 2009).," At the same time, the observations leave less and less room for these constructions, as the spatial resolution achieved with improving technology increases (Scharmer 2009)."1193 Ahch effort has been devoted to inversion of PAxectropolarinietric Observations into (1nagnetic) tuoseric structure models., Much effort has been devoted to inversion of spectropolarimetric observations into (magnetic) atmospheric structure models.1194 Such IVCLSIOUS are notoriously poorly coustrained., Such inversions are notoriously poorly constrained.1195" του are regularized iu xactiee bv miposiug an assumed structure on the field configuration. such as the popular enmibedded: fiux tulICS propose fust in the ""iuconbed model of Solan alu Alontavon (1993)."," They are regularized in practice by imposing an assumed structure on the field configuration, such as the popular embedded flux tubes proposed first in the `uncombed' model of Solanki and Montavon (1993)."1196 Such inversion produces auswers whether or no there is a sound plvsical bass for the ASSIned strucure. however (for exanuple. asstuuptious violating divB=0. DDBorrero et al.," Such inversion produces answers whether or not there is a sound physical basis for the assumed structure, however (for example, assumptions violating $\mr{ div}\,{\bf B}=0$, Borrero et al."1197 2006)., 2006).1198 Fits obtained in this wav thus οἼνο a musleading sense of confirmation of the input models., Fits obtained in this way thus give a misleading sense of confirmation of the input models.1199" 7,akharov e al. (", Zakharov et al. (12002008) propose to accomodate classical Daielson rolls within a gap model bv placing them. inside tthe gaps.,2008) propose to accomodate classical Danielson rolls within a gap model by placing them inside the gaps.

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