source,target 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}) )." " Therefore we adopt for times />£4. where /,=100vr."," Therefore we adopt n(t)=10^7 ( , for times $t > t_1$, where $t_1 = 100~{\rm yr}$." On the assumption of constant clump mass throughout the expansion. this gives ," On the assumption of constant clump mass throughout the expansion, this gives (." The 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 (." -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) = (." 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) = (." 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." 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 $\chi$ ," The 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}. 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}." 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" P=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}) )." 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)." 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}." . 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." 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." 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." 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)." 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." 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. 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)." The Compton reflectionspectrum was tlie sane as that wed for model {., The Compton reflectionspectrum was the same as that used for model 4. 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 $32.4^{+6.8}_{-6.2}$ ) $\times 10^{22}$ $^{-2}$ $\chi^{2} = 188.5$; $d.o.f = 296$; see Table \ref{tbl-3}) )." 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). " 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. " 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." 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." 1993. Done. Macejski Sumith 1996: IAS 01575-7537. Vigjiali οἱ al.," 1993, Done, Madejski Smith 1996; IRAS 04575-7537, Vignali et al." 1998: Mrk 3. Turner et al.," 1998; Mrk 3, Turner et al." 1997. Cappi et al.," 1997b, Cappi et al." 1999. Georgantopoulos et al.," 1999, Georgantopoulos et al." 1999: GC 1582. Turner et al.," 1999; NGC 7582, Turner et al." 2000)., 2000). 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)." 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 $\Gamma = 1.77^{+0.10}_{-0.05}$ , $N_{\rm H1} = (111^{+52}_{-32}) \times 10^{22}$ $^{-2}$ 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}) )." 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 $N_{\rm H} \sim 10^{24}$ $^{-2}$ would be $\sim 500$ eV \citep{lc93} with respect to the absorbed continuum, but" obtained 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. " 2009), PKS 1502+106 (Abdo et al."," 2009), PKS $+$ 106 (Abdo et al." " 2010a), PKS B1510—089 (Tavecchio et al."," 2010a), PKS $-$ 089 (Tavecchio et al." " 2010), 3C 454.3 (Foschini et al."," 2010), 3C 454.3 (Foschini et al." " 2010, Tavecchio et al."," 2010, Tavecchio et al." " 2010, Ackermann et al."," 2010, Ackermann et al." 2010) and 3C 273 (Abdo et al., 2010) and 3C 273 (Abdo et al. 2010b)., 2010b). 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. " The Large Area Telescope (LAT, Atwood et al."," The Large Area Telescope (LAT, Atwood et al." " 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." " 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)." " 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." " 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." " 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 $^{-2}$ $^{-1}$." " 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)." " 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." " 2010, Ackermann et al."," 2010, Ackermann et al." 2010)., 2010). " 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." " 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." " 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 $z=0.432$ )." We report here the results of this analysis., We report here the results of this analysis. " 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." 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. " 2010, Tavecchio et al."," 2010, Tavecchio et al." " 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." " 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." " 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)." " 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)." 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. ". 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. (" "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." " Moreover, while in Foschini et al. ("," Moreover, while in Foschini 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 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." " 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." " 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)." 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. " 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." The extracted light curves are displayed in Figs. (1--3))., The extracted light curves are displayed in Figs. \ref{fig:curva3c273}- \ref{fig:curva3c454}) ). " 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)." " 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)." 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. " 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." 2011)., 2011). " 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:" "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}. .ThefitoftheUV spectrumoftheprimarvisshowninF, The fit of the UV spectrum of the primary is shown in \\ref{fit_UV_1}. ThederivedparametersaregatheredinTable2 (bottom part), The derived parameters are gathered in Table \ref{tab_orb} (bottom part). Th lead, The quality of the fit is on average very good. sto, Only a few features are not reproduced. a, This is the case of the lines around 4550. better Fit. butinthatcasetheotherdiagnosticsarelesswellre," Increasing leads to a better fit, but in that case the other diagnostics are less well reproduced." produ ," This problem is frequently observed in our models, and the origin is not known at present." ," Hence, we decided not to rely on these lines in the present study." better 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." " This investigation was made with the NIGHTFALLprogramme"".", This investigation was made with the NIGHTFALL. 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. 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. 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}) )." Themassratioandtheorbitalperiodarethoseobtained fromtheo ) , The mass ratio and the orbital period are those obtained from the orbital solution (see \\ref{tab_orb}) ). Westressthatthezero phaseof thelightcurve fitcorrespond sto , We stress that the zero phase of the light curve fit corresponds to the zero phase of the orbital solution. The light curve (Fig. 7)), The light curve (Fig. \ref{fit_lc}) ) does not exhibit any eclipses but ellipsoidal variations are clearly visible., does not exhibit any eclipses but ellipsoidal variations are clearly visible. 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. ? 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." their 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. 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." 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}) ). , "and the scan direction, respectively.","and the scan direction, respectively." 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}. . 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. " 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." 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. " 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." " 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" The 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. Yet planets are not the sole close companions to solar-type stars., Yet planets are not the sole close companions to solar-type stars. 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." " 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}) ). 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." 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." 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}) ). 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." " 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." ? found another deficit of brown dwarf companions between 75-1200 AU., \citet{mccarthy04} found another deficit of brown dwarf companions between 75-1200 AU. ? 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." " 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 $''$. 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. 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." 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}." 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." 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." 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). 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." 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”)." 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. Inaddition. the eccentricities of most of the companions are so," Inaddition, the eccentricities of most of the companions are so" LISA.,LISA. 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." 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." 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." 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." Two 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}." . 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." It mav curently be expericucing stable mass transfer hrough Roche-lohe overflow., It may currently be experiencing stable mass transfer through Roche-lobe overflow. 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." 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}." . Three competing models have been proposed for V£07 Vul andCuc., Three competing models have been proposed for V407 Vul and. . 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." 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}. . 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. 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. 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. 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}." 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}." . 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" aud by tlie central difference as in case of the uniform grid.,and by the central difference as in case of the uniform grid. Note that the gravity is evaluated oi the cell surface., Note that the gravity is evaluated on the cell surface. 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. 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." 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 $." " 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." 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. 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." 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. " 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 \, x _{(i+1)/2} ^{(\ell-1)}, \, y _j ^{(\ell)}, \, z _k ^{(\ell)} \rbrack $." [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. When j aud A are odd numbers. it is evaluated to be," When $ j $ and $ k $ are odd numbers, it is evaluated to be" The 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. 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. 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." 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}." . 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}." ". 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}." . 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. 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." 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." 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." 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. 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." 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. 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." 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}." . 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." 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." 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. 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}." . 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. 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. This magnetic field evolved self-consisteutlv. with convective motions., This magnetic field evolved self-consistently with convective motions. 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. 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." At these time moments. the average unsigned magnetic," At these time moments, the average unsigned magnetic" the total angular momentum of the star).,the total angular momentum of the star). 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 $I=J/\Omega$." 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 $\theta$." 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 $r = \bar{r} \exp(\frac12(\gamma-\rho))$, so that $2 \pi r \sin \theta$ is the circumference of a circle with constant $\bar{r}$ and $\theta$." 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)." 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." 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)." We present the properties of some rapidly-rotating models in Table 1., We present the properties of some rapidly-rotating models in Table 1. 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." 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. 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." 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 $2.0\ {\rm M_\odot}$, and two spin frequencies, $\nu=300\ {\rm Hz}$ and $600\ {\rm Hz}$." 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. 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." 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." 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}) )." 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}] ]" with his eq. [, with his eq. [ 10].,10]). However. Abramowiez et al. (," However, Abramowicz et al. (" 2001) 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)." 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." 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 $L$." In the slow rotation approximation. our result (eq. [14]])," In the slow rotation approximation, our result (eq. \ref{eq:slow}] ])" agrees with equation (9) of Abramowiez et al. (, agrees with equation (9) of Abramowicz et al. ( 2001).,2001). 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." We give the value of in Table |.., We give the value of $\beta$ in Table \ref{tab:models}. 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 $600\ {\rm Hz}$." 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. . 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." 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." 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." 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." 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." " 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." 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." " 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." " 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”." 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 $r$ ." We adopt a plane parallel approximation in. the thin envelope. and write rZRF z/V. where =. 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)." 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. 3dd)., \ref{fig:masses}d d). 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.," the NLSIs in the sample of Grupe et al., the NLS1s in the sample of Grupe et al. 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." 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. 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." With these assumptions.," With these assumptions," 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." " 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 $\displaystyle \inf_{c\in\R}\inm_{Q_{r}}|\tilde{u}-c|$ 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)." " 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 $\Omega^{d}_{T}\cup \Omega^{g}_{T}$ ." " 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. " 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 $\Omega^{g}_{T}$." " 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}) )." " 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 $t$ ." Now. πας Leuuna 3.L. we deduce that:," Now, using Lemma \ref{Hgibi1}, , we deduce that:" (~t ES) was observed in soft eanuna-ravs (25-300 keV).,$\sim t^{-1.8}$ ) was observed in soft gamma-rays (25-300 keV). 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. 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}) )." " 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." 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." 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." 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}) )." " 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." 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." 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)." 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." 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." 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. " 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}) )." 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. 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. 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. 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." 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}) )." 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}) )." " 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." " 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." " The distribution has a low-cuerey cutoff given by 5,4,€σοι ", The distribution has a low-energy cutoff given by $\gamma_{m} \le \gamma_{e}$. Behind 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." 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}) )." 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." " 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}) )." " 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." 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 $\epsilon_{e} \ll 1$ )." " 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 $\gamma_{\rm m} < \gamma_{\rm c}$." "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. 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)." 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)." " 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 $\gamma (t)$." " 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 $\nu_{\rm c} \propto t^{-1/2}$ ." "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. " 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." 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." For radiative fast-cooling.," For radiative fast-cooling," A 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). 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." The clusters studied w Nene ‘Let al., The clusters studied by Mengel et al. 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." 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." 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. 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." ? 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. " 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.”" 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}." 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." The two lonecr-waveleneth iuages were both saturated iu the cluster core., The two longer-wavelength images were both saturated in the cluster core. 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." 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." 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}." " 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." " 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." 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. 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}) ). 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. 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. Iu a coeval population. these stars will be intermediate uass stars.," In a coeval population, these stars will be intermediate mass stars." 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." 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}. 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. Mass segregation renders the oeiterpretatiou of the Lelt-to-mass ratio problematic., Mass segregation renders the interpretation of the light-to-mass ratio problematic. 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. 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." 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." 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." 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)." 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." 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}." 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." 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. 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. 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}. . 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." 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. " 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} for M82-F is $t_{rh} = 4 \times 10^8$ years — roughly an order of magnitude longer than the cluster's current age." 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." 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." 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}. 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." 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}. 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." 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}. ." 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." 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." ? 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. The voune age of \L82-F relativeto its, The young age of M82-F relativeto its For 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." 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." We consider three kinds of mechanisms of angular momentum loss., We consider three kinds of mechanisms of angular momentum loss. 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} where c is the light speed." This mechanism is important only in very short period binary svslens., This mechanism is important only in very short period binary systems. The second angular momentum loss mechanism is for non-conservative mass transler., The second angular momentum loss mechanism is for non-conservative mass transfer. 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 $\alpha=0$." 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." " 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}." . 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. pass 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." 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." 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}. 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. 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. The implied scattering measure is SAL<10 spe an20/5 (Cordes&Lazio2006).," The implied scattering measure is $\mathrm{SM} \lesssim 10^{-4}$ kpc ${}^{-20/3}$ \citep{cl02}." . 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." 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 $D \approx 1.5$ Gpc, implying $\overline{Fn_e^2} \lesssim 10^{-10.5}$ ${}^{-6}$." " 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}." . Thus. we require FS105. so ax not to violate the inferred lits on scattering.," Thus, we require $F \lesssim 10^3$, so as not to violate the inferred limits on scattering." 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, $F \sim 10$." " 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." Assuning that ο—€~1. we conclude that yi?PEE=1037.," Assuming that $\zeta \sim \epsilon \sim 1$, we conclude that $\eta\ell_0^{2/3} \gtrsim 10^{-3}$." 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 $\eta \to 1$." ↓∙≼∶↕↖↽↸∖∐↑↕∐∖↕⋜∐⋅∶↴⋅⊾↸∖↥⋅↴∖↴↸⊳⋜↧↕↸∖↴∖↴⋜∏↽⋜⊔↕⋜∏⋝↕↸∖↕∐⋅ heIGAL. (y~1 Alpe would not be unreasonable.," Given the larger scales available in the, $\ell_0 \sim 1$ Mpc would not be unreasonable." 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." While we find no indications of intergalactic scattering.. future. obscrvatious. are warranted.," While we find no indications of intergalactic scattering, future observations are warranted." 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." " 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." 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." " 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. We- sununarize. our findings∙∙ as follows., We summarize our findings as follows. . 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." 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." 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." 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." 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." .. 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." ⋅⊀∖⋅⋉ Iu our TANsune.vo of the AGN augnbuhave measured redshifts.," In our sample, of the AGN have measured redshifts." 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" e.,. g.).. 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." " 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. 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." . 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." 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. 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." 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." 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. ". 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. 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. 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. 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." LEnergv packets canundergo photoabsorption or Compton scattering. the probabilitiesof," Energy packets canundergo photoabsorption or Compton scattering, the probabilitiesof" Section L2).,Section 4.2). 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." 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." 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." 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}. ". The st""uctural parameters are similar as well.", The structural parameters are similar as well. 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." 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." 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." 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}." . 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." 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." 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." 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. 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." 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)." 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). 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)." 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. 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." 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" observer 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." 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}. 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." 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 $F_{irr}$." 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. 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." 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}) ). 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). fud from purely theoretical considerations of j=Lit., find from purely theoretical considerations of $\eta=1.14$. 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." 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. 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." 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. 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. 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." 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." 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. 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." 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. Aquila 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. 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)." 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. 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." 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)." 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)." 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). 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). 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)." 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. 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. 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. 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. 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" 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. 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, $1-g_1$." 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." 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." 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}." 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." 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}." " 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. 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." 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." 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 $\sim 240^{\circ}$." 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}. ." 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" Complex. 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." " 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." 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." LOST)., 1987). 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." 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." 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." 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). 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" a 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. 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)." 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." The third panel in Fig., The third panel in Fig. 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). 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. 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)." 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. 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. 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." 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. 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}. 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." " ""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." 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. 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. The second. and third. panels of Fig., The second and third panels of Fig. 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). 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. 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." 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 $\sim23\%$." e 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}." 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}) );" 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. 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. 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." 2000)., 2000). We discuss the implications of this in Section 6., We discuss the implications of this in Section 6. 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. 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)." 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." 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 $\eta = 1$." 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. 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 $V=\frac{4\pi}{3}(ct)^3 \sim 9\times 10^{48}\, \mbox{cm}^3$." 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. " Therefore the monochromatic luminositv. L,=ΕπS.TASLot(edπρο)”Wiz Ll."," Therefore the monochromatic luminosity, $L_{\nu}=4\pi d^2S_{\nu}\sim7.3\times10^{13}(d/kpc)^2\,\,\mbox{WHz}^{-1}$ ." 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" The 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. 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. 1994; Kirk et al., 1994; Kirk et al. 2005; Ward-Thompson et al., 2005; Ward-Thompson et al. 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)." 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." 1998: Testi Sargent 1998: Johnstone et al., 1998; Testi Sargent 1998; Johnstone et al. 2000; Johnstone et al., 2000; Johnstone et al. 2001: Motte et al., 2001; Motte et al. 2001: Johnstone Bally 2006: Alves et al., 2001; Johnstone Bally 2006; Alves et al. 2007: Young et al., 2007; Young et al. 2006: Nutter Ward-Thompson 2007: Simpson et al., 2006; Nutter Ward-Thompson 2007; Simpson et al. 2007)., 2007). 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. 2002) and an unusual IMF (Luhman 2004: see also Goodwin et al., 2002) and an unusual IMF (Luhman 2004; see also Goodwin et al. 20049). although Kroupa et al. (," 2004c), although Kroupa et al. (" 2003) 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. 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." 2007 and Goodwin et al., 2007 and Goodwin et al. 2007 and references therein; see also Clark et al., 2007 and references therein; see also Clark et al. 2007)., 2007). 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. 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)." 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." 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). 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. 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." 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." 2007 and references therein; see also Section 3)., 2007 and references therein; see also Section 3). 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." 2003: Goodwin Whitworth 2007; also see Goodwin et al., 2003; Goodwin Whitworth 2007; also see Goodwin et al. 2007 and references therein)., 2007 and references therein). 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." 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)." 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." 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. ( 1998) in a millimetre study of the p-Ophiuchi molecular cloud.,1998) in a millimetre study of the $\rho$ -Ophiuchi molecular cloud. 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. This result has been confirmed for Ophiuchus (Johnstone et al., This result has been confirmed for Ophiuchus (Johnstone et al. 2000: Young et al., 2000; Young et al. 2006; Simpson et al., 2006; Simpson et al. 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." 2001: Johnstone et al., 2001; Johnstone et al. 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." 2007). and Taurus (Onishi et al.," 2007), and Taurus (Onishi et al." 2002: however see Goodwin et al., 2002; however see Goodwin et al. 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)." 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." 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)." 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 $\sim\! 8~M_\odot$ (Reid Wilson 2006a,b), though the data are incomplete before a turn-over is seen." 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" is 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." 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." 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." 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?" It implies that this region is Ry—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." 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 )." 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. 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. 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. KS collisions decay towards vins(0:3). the random motion released by the Keplerian shear in a single collision.," KS collisions decay towards $v_{\rm rms}\approx(\delta x)\varOmega$, the random motion released by the Keplerian shear in a single collision." NS collisions on the other hand continue to decay towards zero., NS collisions on the other hand continue to decay towards zero. 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. 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 $(\delta x) \varOmega$. 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." 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." 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}. . 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} and $r$ is the distance to the central star." 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 sizes the derived value of ΔΤΕ.,the derived value of $\Delta T_{\rm e}$. " 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." In Fig., In Fig. " 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. " 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}) )," 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 $\log g=8 \,\rm (cgs)$." " 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." " 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." ". 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, $\Delta T_{\rm e}\rm \sim0.2\rho_{\rm He}$." " 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." The required amount of hydrogen is H/He=6.75-102., The required amount of hydrogen is $\rm H/He=6.75 \cdot 10^{-3}$. In both cases the observed spectrum is fairly well reproduced., In both cases the observed spectrum is fairly well reproduced. " 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}) )." " 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." " 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." " 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." " 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." " 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 $\rm C_2$." 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. " 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)." " 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." " 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." "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)." '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 $K=-0.005$. " 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." " 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." 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). 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. " 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)." 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. 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. 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). 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)? " 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)." " 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." 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). " 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 $j$. " 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 $\Delta\chi^2 \simeq \sqrt{2\nu} \simeq 6$ , as expected)." 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 $\chi^2_i \simeq 24$ ) and is slightly broader $\Delta\chi^2 \simeq 7.7$ )." " 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." " 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." 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. 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. " 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" but 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}) ). 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." 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." 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}." 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. ".. 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." 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}) )." 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." 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). 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." 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)." 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. 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}. 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." 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." 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." " 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 $4\farcs4$ $^{-1}$." 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. 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." 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." 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." 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." 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. 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." 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." 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." 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." 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." 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." 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. " 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." . 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." " 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." ," For a given extraction region and energy range, a pulsation analysis could then be carried out on the resulting arrival times." The 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} and \ref{fig_mos_zoom}." 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" "manner, as discussed by (2008).","manner, as discussed by ." ".. 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." 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. " 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." " 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." " 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." " 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." " 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." 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. 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. " 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." ddeveloped 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}." . 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. 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." 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. 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." uunakes particular optimal use of modern witti-core processor techologies., makes particular optimal use of modern multi-core processor technologies. The code solves the Poissou equation oi a system of Cartesiai grids., The code solves the Poisson equation on a system of Cartesian grids. 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. 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. 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." All grids contain 1287 erid ceIs., All grids contain $^{3}$ grid cells. 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}) ). 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. 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. 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." 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." The bulge is represented bya Heruquist potential (Heruquist 1990)..," The bulge is represented bya Hernquist potential \citep{hern1990}, ," Our 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. 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. We have therefore adopted a much simpler approach to abundance modelling., We have therefore adopted a much simpler approach to abundance modelling. 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. 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." 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. 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." 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." 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. 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." 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." " For comparison, the solar abundances reported by ? are tabulated as well."," For comparison, the solar abundances reported by \citet{Aspletal09} are tabulated as well." 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}." 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. 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. Classical 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 $\lesssim20$." 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}." 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." 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." 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." 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. 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. " 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 $(10^{36-37}~\rm{erg/s})$. 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." 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." 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. 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. " 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. 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}." 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. 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 $R_*$ . " 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 $10^{-(5-6)}~\rm{M_{\odot}/y}$. 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 $0.02$." 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." 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}. " 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. 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}. (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. " 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." and the present formulations., and the present formulations. rcing 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." Pherclore anv comparison with a weighted. halo correlation function. will not work., Therefore any comparison with a weighted halo correlation function will not work. 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." Unweighted halo correlation function predicts an anti-bias at late times., Unweighted halo correlation function predicts an anti-bias at late times. 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. 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. 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. 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. 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. These results. when applied to galaxies. have many important implications.," These results, when applied to galaxies, have many important implications." 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." 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. 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." 3.. 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." 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." 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)." ‘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}. ". 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. 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 $\bar\xi$. 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 $1 \le \bar\xi \le 200$ to the scaling relation between the linear and the non-linear correlation function \cite{hamil}." ". This figure shows that this relation Uattens out or indices above ny,=1.", This figure shows that this relation flattens out for indices above $n_{nl}=-1$. 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. 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." 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. " 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." " 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 $n_{lin} \simeq -1.5 \pm 0.2$ ; $\gamma \simeq 1.5 \pm 0.2$ )." Our 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. " 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}." 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." 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." 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." 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." 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. Most of these uncertainties would conspire to create a higher accretion rate., Most of these uncertainties would conspire to create a higher accretion rate. 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." 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} 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." 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. 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." 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. 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." 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." 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. 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." 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." 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}. ." in Fig. 4.,in Fig. \ref{fig:l709}. " 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 $S_{16} = 245\pm13$ mJy." 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}." 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, $S_{\rm{NVSS},1.4} = 218\pm6.6$ mJy suggesting that the source is extended." " 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”." 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." 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." " 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." 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 $S_{16} = 1.61\pm0.31$ mJy." 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 $\sigma$. 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." " 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. 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}." We investigate its spectral properties using analysis Case (1)., We investigate its spectral properties using analysis Case (1). 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." 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)." 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. 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." 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}." 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). 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." 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}. 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}." 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. 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}." " 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." At GGHz the emission has a largely, At GHz the emission has a largely the expected secular trend might be difficult to disceru amid the fluctuatious.,the expected secular trend might be difficult to discern amid the fluctuations. 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." In, In HII 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}) ). 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 ${\rm M}=-24$ it is two orders of magnitude higher, at $L_{1.4}=10^{26}\,{\rm W\,Hz^{-1}}$ ." 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 $z=2$." 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." 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." 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}) )." 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." These values are given t Table 1., These values are given in Table 1. 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. 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.," 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}) )." 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 $-1.40$." 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." 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 $p=0.0014$ ). 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." 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." 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." 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." 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." 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." 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." 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)." 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} these two spectral indices and indicate with a straight line where they would be equal." Clearly the spectra steepen towards higher frequencies., Clearly the spectra steepen towards higher frequencies. 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 $\alpha_{4.8}^{8.6}$. 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." 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." 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." 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. Instead we consider two effects as potential causes of this discrepancy. (, Instead we consider two effects as potential causes of this discrepancy. ( i) Sources are resolved out.,i) Sources are resolved out. 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)." 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)." This means that even tapered images cannot reveal large-scale structure, This means that even tapered images cannot reveal large-scale structure All 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)." " 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." 2005)., 2005). 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. 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." " 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 $_{\rm{20~M_\odot}}^{\rm{Edd}} = 2.6 \times 10^{39}$ erg $^{-1}$ for a ``maximal--mass'' stellar–mass black hole of $20~M_\odot$ )." " 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). 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)." 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." 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." 1997: King et al., 1997; King et al. 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." 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. 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." 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." best possible calibration and homogeneity of our photometric measurements.,best possible calibration and homogeneity of our photometric measurements. 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." 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 $(3 \rm{arcsec})^2$ pixels." 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. 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}." "), 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." 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." 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)." 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." 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." 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. We retrieved ISOCAAM images for a total of ssources., We retrieved ISOCAM images for a total of sources. 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. We detected a total ol egalaxies., We detected a total of galaxies. 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." 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. 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." 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. 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" viewius anele. the moat flow. and the Evershed flow (Schaviuer et al.,"viewing angle, the moat flow, and the Evershed flow (Scharmer et al." 2008)., 2008). 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." 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." 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. Toiscussion iu Paper I)., discussion in Paper I). " 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. 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." 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. 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. " 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)." 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." ]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. 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)." 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. Such IVCLSIOUS are notoriously poorly coustrained., Such inversions are notoriously poorly constrained. " 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)." 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." 2006)., 2006). 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. " 7,akharov e al. (", Zakharov et al. ( 2008) 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. This provides a seuse of coutimuty with traclitiojii views of the pemnubra., This provides a sense of continuity with traditional views of the penumbra. It aso retains the flux tul(s proposed earlier. |mt moves thei from their plivsically awhkaward position iu the atinosphiere to a place below the observed surface.," It also retains the flux tubes proposed earlier, but moves them from their physically awkward position in the atmosphere to a place below the observed surface." The gaps pro»osed im Paper LII already. exaim the observatious well without such additions. howxvor. and the accditiou does not agree well with the magnetic expulsion process of convoective flows.," The gaps proposed in Paper I,II already explain the observations well without such additions, however, and the addition does not agree well with the magnetic expulsion process of convective flows." In addition (section 5.3.1)). a loneiitudcinal field. of any significaut streneth in the gaps would suppress aly corrugation of the filaments. especially on the very. short wavelengths actually seen in the stration.," In addition (section \ref{fluting}) ), a longitudinal field of any significant strength in the gaps would suppress any corrugation of the filaments, especially on the very short wavelengths actually seen in the striation." Nox the treatineut of the atmospheric magnetic field. the plivsics of radiation is of equal importance for reali in nunierical simulations.," Next to the treatment of the atmospheric magnetic field, the physics of radiation is of equal importance for realism in numerical simulations." Cooling bw radiation at the simface determines the thermal structure of the »emuubra aud drives the observed flows., Cooling by radiation at the surface determines the thermal structure of the penumbra and drives the observed flows. Ou the other wand. it also determines the detailed appearance of umnubral structure at the optical depth unity surface.," On the other hand, it also determines the detailed appearance of penumbral structure at the optical depth unity surface." Auv physically mecaninefil comparison with observations lius requires inclusiou of radiation plysics at a fairly well developed level., Any physically meaningful comparison with observations thus requires inclusion of radiation physics at a fairly well developed level. The fact that the required level of realiu in the reatmient of magnetic fields and radiation physics has row been reached. aud a significant degree of convergence with observations already. achieved. cau count as a major xeakthrough iu solu plivysics.," The fact that the required level of realism in the treatment of magnetic fields and radiation physics has now been reached, and a significant degree of convergence with observations already achieved, can count as a major breakthrough in solar physics." The formation of a gravitational wake is a cha‘acteristic feature o[ an astronomical object moving through a medium.,The formation of a gravitational wake is a characteristic feature of an astronomical object moving through a medium. We examine tle wake properties in detail auc provide the observable aspects in a quautitative way. by revisiting he previoIs seindanalvtie ancl 1umerical works(IxIxO7:: ]|xun 2010)) atd comparing the features with the inear trajectory counterparts discovered iu analytic aud nuuerical methods (Ostriker1999:Ixim&Wit2009).," We examine the wake properties in detail and provide the observable aspects in a quantitative way, by revisiting the previous semianalytic and numerical works; \citealp{kwt10}) ) and comparing the features with the linear trajectory counterparts discovered in analytic and numerical methods \citep{ost99,kim09}." . Thhe analytic formulae for the density wake iu tle previous work (reviewed in eq. [3]], he analytic formulae for the density wake in the previous work (reviewed in eq. \ref{equ:k07}] ] aud [1]]) do not give α cear iusight of 5diva- 4undfor arc-shapes., and \ref{equ:sol}] ]) do not give a clear insight of spiral- and/or arc-shapes. Hence it is adifficult to deduce the properties of the wake relevaut o the objec properties., Hence it is difficult to deduce the properties of the wake relevant to the object properties. A further calculation in this paper leads to purely aualytic soluion for the wake siape (eο [5]. shape..," A further calculation in this paper leads to purely analytic solution for the wake shape (eq. \ref{equ:mor}] ]),." Simple geometrical aIp'Oaches are adojoted to provide the pliysic‘al uuderstaucdiug of sucl shapes., Simple geometrical approaches are adopted to provide the physical understanding of such shapes. Density euliaelle1 rofiles are also investigated., Density enhancement profiles are also investigated. Since the emyivical€ formulae based oi the analytic analysis Oliline the naximum aud ininimuun: eusity euliaicellent very successfully. these cai be cli'ec n[9]»ted for interpretation of [uture simatiou ancl observationa data.," Since the empirical formulae based on the analytic analysis outline the maximum and minimum density enhancement very successfully, these can be directly adopted for interpretation of future simulation and observational data." Our deeper mnerstalic “the linear wake helps to uuderstaud, Our deeper understanding of the linear wake helps to understand. licularly. uoulinear aspects such as tle increase of backeroun density. the clisaopea‘ance of “arin boun«cary. and the appearance o‘a detached spiral shock E'e predictab elΟι a close |io1 of linear wake properties.," Particularly, nonlinear aspects such as the increase of background density, the disappearance of inner arm boundary, and the appearance of a detached spiral shock are predictable from a close inspection of linear wake properties." " ized by Boucli accretion racius rg circularly orbiting at a stance ry with an «xbital Ms iber M, ina static uniform gaseous ouur new fiicines for lilear wakes are as fol", an object characterized by Bondi accretion radius $r_B$ circularly orbiting at a distance $r_p$ with an orbital Mach number $\mach$ in a static uniform gaseous ur new findings for linear wakes are as follows: "The currently favoured model of cosmological structure formation asserts that the Universe is dominated by some form of non-baryonic Cold Dark Matter (hereafter CDM), and it makes a number of generic predictions about how the dark matter clusters on small scales.","The currently favoured model of cosmological structure formation asserts that the Universe is dominated by some form of non-baryonic Cold Dark Matter (hereafter CDM), and it makes a number of generic predictions about how the dark matter clusters on small scales." " Arguably the defining prediction of the CDM model is that the radial mass density profile of dark matter haloes is divergent at small radii, which leads to a central density “cusp”."," Arguably the defining prediction of the CDM model is that the radial mass density profile of dark matter haloes is divergent at small radii, which leads to a central density “cusp”." Characterising the form of this mass density profile has been one of the most active research problems in computational cosmology over the last decade., Characterising the form of this mass density profile has been one of the most active research problems in computational cosmology over the last decade. " The seminal study of Navarro, Frenk White (1996,1997; hereafter NFW) introduced the concept of a “universal” mass density profile for dark matter haloes that form in hierarchical clustering cosmologies."," The seminal study of Navarro, Frenk White (1996,1997; hereafter NFW) introduced the concept of a “universal” mass density profile for dark matter haloes that form in hierarchical clustering cosmologies." " This NFW profile is written as where rs is a scale radius and ρε is a characteristic density, which can be related to r4 once the virial mass of the halo is fixed; describes a one-parameter family of curves."," This NFW profile is written as where $r_s$ is a scale radius and $\rho_c$ is a characteristic density, which can be related to $r_s$ once the virial mass of the halo is fixed; equation \ref{eq:NFWspherical} describes a one-parameter family of curves." It is convenient to equation[I]rewrite equation[I] in the more general form where a is the central asymptotic logarithmic slope., It is convenient to rewrite equation \ref{eq:NFWspherical} in the more general form where $\alpha$ is the central asymptotic logarithmic slope. " The NFW profile is “universal” in the sense that it describes the ensemble averaged mass profile of dark matter haloes in dynamical equilibrium, independent of virial mass, cosmological parameters and initial power spectrum."," The NFW profile is “universal” in the sense that it describes the ensemble averaged mass profile of dark matter haloes in dynamical equilibrium, independent of virial mass, cosmological parameters and initial power spectrum." " During the last decade numerous studies have investigated whether or not the NFW profile does indeed provide an adequate description of the mass profile of dark matter haloes, and to understand the physical mechanisms that shape the functional form of the profile."," During the last decade numerous studies have investigated whether or not the NFW profile does indeed provide an adequate description of the mass profile of dark matter haloes, and to understand the physical mechanisms that shape the functional form of the profile." " NFW recognised that γε correlates with the virial mass of the halo, increasing with decreasing virial mass."," NFW recognised that $r_s$ correlates with the virial mass of the halo, increasing with decreasing virial mass." " They argued that this virial mass-scale radius relation is an imprint of the hierarchical assembly of haloes; low-mass haloes tend to collapse before high-mass haloes, when the mean density of the Universe is higher, and rs reflects the mean density of the Universe at the time of collapse."," They argued that this virial mass–scale radius relation is an imprint of the hierarchical assembly of haloes; low-mass haloes tend to collapse before high-mass haloes, when the mean density of the Universe is higher, and $r_s$ reflects the mean density of the Universe at the time of collapse." " The halo sample that formed the basis of ? contained of order 10* particles (and hence resolving the profile down to about of the virial radius, according to the convergence criteria of ?))."," The halo sample that formed the basis of \citet{1997ApJ...490..493N} contained of order $10^4$ particles (and hence resolving the profile down to about of the virial radius, according to the convergence criteria of \citet{2003MNRAS.338...14P}) )." Subsequent studies drew upon haloes containing about two orders of magnitude more particles within the virial radius and confirmed, Subsequent studies drew upon haloes containing about two orders of magnitude more particles within the virial radius and confirmed volume clensitv than the sselected sample: otherwise. (he uncertainties in (he experiment would increase quile substantially.,"volume density than the selected sample; otherwise, the uncertainties in the experiment would increase quite substantially." Ol course. if these conditions are not all fulfillel. a topological study of the laree scale ssource distribution will still reveal interesting information about galaxy formation and reionization.," Of course, if these conditions are not all fulfilled, a topological study of the large scale source distribution will still reveal interesting information about galaxy formation and reionization." hi particular. if the topological signature of isolated. bubbles is not observed ab anv redshift. it will indicate that the sources of ionizing radiation are of low luminosity and the bubbles they produce are consequently small.," In particular, if the topological signature of isolated bubbles is not observed at any redshift, it will indicate that the sources of ionizing radiation are of low luminosity and the bubbles they produce are consequently small." The genus number for the neutralionized interface can be predicted as a function of the ionized. volume fraction based on simple physical arguments that describe the way relonizalion progresses., The genus number for the neutral-ionized interface can be predicted as a function of the ionized volume fraction based on simple physical arguments that describe the way reionization progresses. " Formally. we define this interface"" as a fixed contour level in the οσα]. neutral [raction. ορ~0.5."," Formally, we define this “interface” as a fixed contour level in the local neutral fraction, $x_{thr} \sim 0.5$." So long as the boundaries of III regions are thin. as expected when reionization is driven primarily by stellar photons. the exact choice of 25. natters little.," So long as the boundaries of HII regions are thin, as expected when reionization is driven primarily by stellar photons, the exact choice of $x_{thr}$ matters little." After reionization begins but well before overlap. the IGAI consists of a collection of isolated. ionized bubbles embedded in a matrix of neutral gas.," After reionization begins but well before overlap, the IGM consists of a collection of isolated, ionized bubbles embedded in a matrix of neutral gas." Each bubble may correspond lo a single ionizing source. or to (he ensemble of all ionizing sources in a particular peak ol the density field (FZII: FO). or something in between.," Each bubble may correspond to a single ionizing source, or to the ensemble of all ionizing sources in a particular peak of the density field (FZH; FO), or something in between." In this regime. the genus number of the neutral-ionized interlace per unit volume is simply —1 (mes the number density of (surviving) ionized bubbles.," In this regime, the genus number of the neutral-ionized interface per unit volume is simply $-1$ times the number density of (surviving) ionized bubbles." Of course. anv practical measurement will depend on the ionizecl regions achieving some minimum detectable size. and the relevant number density should really be measured above this minimum size.," Of course, any practical measurement will depend on the ionized regions achieving some minimum detectable size, and the relevant number density should really be measured above this minimum size." The size will be closely related to the total ionizing photon production of the bubble. given by L;x/. the product of ionizing Iuminosity and source age or lifetime.," The size will be closely related to the total ionizing photon production of the bubble, given by $L_i \times t$, the product of ionizing luminosity and source age or lifetime." Iowever. it will also depend on the local gas density.," However, it will also depend on the local gas density." Once bubbles grow bevond the immediate neighborhood of the ionizing sources. the likely pattern of reionization depends on details of the model.," Once bubbles grow beyond the immediate neighborhood of the ionizing sources, the likely pattern of reionization depends on details of the model." Miralda-Escud'e et al (2000) used a semi-analvtic approach based on a statistical description of the IGM density distribution., et al (2000) used a semi-analytic approach based on a statistical description of the IGM density distribution. Thev argued (hat ionizing photon production is substantially balanced by recombinations., They argued that ionizing photon production is substantially balanced by recombinations. Because (he recombination rate per ion scales with the density of ionized gas. (μον conclude that the low-density regions will ionize first. and that a large fraction of ionizing photon production will be balanced by recombinations at the neutral-ionized interlace where the jonized gas is densest.," Because the recombination rate per ion scales with the density of ionized gas, they conclude that the low-density regions will ionize first, and that a large fraction of ionizing photon production will be balanced by recombinations at the neutral-ionized interface where the ionized gas is densest." As (ime goes bv and the ionizing photon production rate rises.," As time goes by and the ionizing photon production rate rises," a free parameter.,a free parameter. " Here ""Eδν is the critical surface density defined by the geometry. The profile of the dark matter halo is controversial."," Here $\Sigma_{cr}$ is the critical surface density defined by the geometry, The profile of the dark matter halo is controversial." Conventional theories where ACDAL is the preferred cosmology have been very successful. in. explaining the observed. large scale structure of the universe (eg Peebles 1984)., Conventional theories where $\Lambda$ CDM is the preferred cosmology have been very successful in explaining the observed large scale structure of the universe (eg Peebles 1984). SANTO. Frenk and Wute (1996: hevealter. NEW) used. N-bocky simulations to derive a density xrofile for such a cosmology.," Navarro, Frenk and White (1996; hereafter NFW) used N-body simulations to derive a density profile for such a cosmology." One feature of the NEW proile is à cuspy central region with a -l wlere powor , One feature of the NFW profile is a cuspy central region with $\alpha \sim$ -1 where $\rho \sim r^{\alpha}$ . "This steepens oa~ -ὃ lor mary. where ày, is the charicleristic scale eneth of the ido."," This steepens to $\alpha \sim$ -3 for $r{\gg}r_h$, where $r_h$ is the characteristic scale length of the halo." Recently. More acciurae simulations iwe pushed tjo cuspliness a ro~ UO to a79 -1.5 (eg Aloore et al.," Recently, more accurate simulations have pushed the cuspiness at $r \sim$ 0 to $\alpha \sim$ -1.5 (eg Moore et al." 1999a)., 1999a). Recent observational work bw cde Blok et al. (, Recent observational work by de Blok et al. ( 2001) on low surface brightness galaxies has shown the need for a core in the dark matter haloes. using optical rotation curves and fitting minimal discs.,"2001) on low surface brightness galaxies has shown the need for a core in the dark matter haloes, using optical rotation curves and fitting minimal discs." CDM has en. challenged. further by the missing satellite (Moore et al., CDM has been challenged further by the missing satellite (Moore et al. 1999b) anc angular momentum. problems (see recent discussion by Sommer-Larsen Doleov 200)., 1999b) and angular momentum problems (see recent discussion by Sommer-Larsen Dolgov 2001). The former considers the few satellite galaxies observed in orbit around our Galaxy compared: with that predicted. by the theory. and the latter refers to the predictions of CDM of too much angular momentum loss to support observed disc galaxies.," The former considers the few satellite galaxies observed in orbit around our Galaxy compared with that predicted by the theory, and the latter refers to the predictions of CDM of too much angular momentum loss to support observed disc galaxies." " Since there is no general agreement we have chosen to model the dark matter halo as a softened isothermal sphere (Ixormann. Schneider Bartelmann. 1994). where c, is the velocity dispersion. απο or. ds. the core or break radius."," Since there is no general agreement we have chosen to model the dark matter halo as a softened isothermal sphere (Kormann, Schneider Bartelmann, 1994), where $\sigma_v$ is the velocity dispersion and $r_c$ is the core or break radius." Phere are several reasons for this choice of profile., There are several reasons for this choice of profile. Firstly. it has one less parameter than an NEW[eore profile (no scale length. as distinct. from the core length).," Firstly, it has one less parameter than an NFW+core profile (no scale length as distinct from the core length)." Given the small number of degrees. of freeclom we have. an extra one is useful.," Given the small number of degrees of freedom we have, an extra one is useful." Secondly. the profile naturally asvmptotes to a flat rotation curve for krXgr. and finally. recent results find that. the two models are indistinguishable when he remaining mass components are taken into account (Weiner. Sellwood Williams. 2001. mocelled NGC 4123 with both profiles ancl found. their shape had a minor effect on the results).," Secondly, the profile naturally asymptotes to a flat rotation curve for $r \gg r_c$, and finally, recent results find that the two models are indistinguishable when the remaining mass components are taken into account (Weiner, Sellwood Williams, 2001, modelled NGC 4123 with both profiles and found their shape had a minor effect on the results)." In aclelition to this. the choice of a spherical halo is à simplification in that i precludes the need. to introduce another parameter.," In addition to this, the choice of a spherical halo is a simplification in that it precludes the need to introduce another parameter." This choice is partially justified by the cllipticities in the other components., This choice is partially justified by the ellipticities in the other components. They are adequate to. produce the recquirec ellipticity., They are adequate to produce the required ellipticity. Furthermore. recent results from. Ibata. οἱ al. (," Furthermore, recent results from Ibata et al. (" 2001) suggest dark matter haloes are spherical.,2001) suggest dark matter haloes are spherical. They. use evidence of the tidal stream from the Sagittarius chvarl galaxy to show that the halo potential cannot be Latter than g<0.7 and probably has q0.9. where q is the axis ralio.," They used evidence of the tidal stream from the Sagittarius dwarf galaxy to show that the halo potential cannot be flatter than $q<0.7$ and probably has $q>0.9$, where $q$ is the axis ratio." Llieh resolution imaging and detailed modelling of Lluchra’s Lens has provided us with many of the model parameters required for fitting a mass distribution., High resolution imaging and detailed modelling of Huchra's Lens has provided us with many of the model parameters required for fitting a mass distribution. Schmidt (1996) used I-band imaging to measure the disc ancl bulge scale engths. as well as to determine their ellipticities.," Schmidt (1996) used I-band imaging to measure the disc and bulge scale lengths, as well as to determine their ellipticities." These results were updated: values from. previous studies by Yee (1988) and Lluchra et al. (, These results were updated values from previous studies by Yee (1988) and Huchra et al. ( 1985).,1985). These data leave the cise and bulge mass-to-light ratios as the only fitting )aranmieters or these components., These data leave the disc and bulge mass-to-light ratios as the only fitting parameters for these components. The bar has a measured. ellipticity. »osition angle and major axis. and within mass-to-light ratio uncertainties is completely determined by Schmidt.," The bar has a measured ellipticity, position angle and major axis, and within mass-to-light ratio uncertainties is completely determined by Schmidt." Schmidt deconvolved the light distribution using wo οσοι bulee models. an exponential and a cle Vaucouleurs surface mass profile.," Schmidt deconvolved the light distribution using two different bulge models, an exponential and a de Vaucouleurs surface mass profile." Results from the literature show that one of these profiles commonly fits a bulge well., Results from the literature show that one of these profiles commonly fits a bulge well. Carollo et al. (, Carollo et al. ( 2001) show from observations that the bulge mass profile is mildly morphologically dependent.,2001) show from observations that the bulge mass profile is mildly morphologically dependent. For Sa-5b galaxies. such as 22305. both tvpes are observed and thus an exploration of both models is prudent.," For Sa-Sb galaxies, such as 2237+0305, both types are observed and thus an exploration of both models is prudent." One further constraint and. one check will be applied o the final rotation curve., One further constraint and one check will be applied to the final rotation curve. Neutral hydrogen observations w Barnes et al. (, Neutral hydrogen observations by Barnes et al. ( 1999) at the VLA provide two rotation »ounts in the outer regions of the galaxy.,1999) at the VLA provide two rotation points in the outer regions of the galaxy. In these regions. he visible matter has fallen below observational levels and he HE is acting as a tracer of the dark matter distribution.," In these regions, the visible matter has fallen below observational levels and the HI is acting as a tracer of the dark matter distribution." " Unfortunately, the data are not of high. enough. angular resolution to probe the rotation in the inner regions of he galaxy."," Unfortunately, the data are not of high enough angular resolution to probe the rotation in the inner regions of the galaxy." An additional piece of information is provided w gravitational lensing. where the position of the images in combination with the geometry of. the. source-LIens-observer svsteni gives the projected. mass enclosed. within he images (Rix. Schneider Baheall. 1992: Wambsganss Paezvuski. 1994).," An additional piece of information is provided by gravitational lensing, where the position of the images in combination with the geometry of the source-lens-observer system gives the projected mass enclosed within the images (Rix, Schneider Bahcall, 1992; Wambsganss Paczynski, 1994)." The consisteney of this value with the mass cistribution found will act as a check on the result., The consistency of this value with the mass distribution found will act as a check on the result. We define the image radius as the average of the radii of the four images from the centre of the galaxy., We define the image radius as the average of the radii of the four images from the centre of the galaxy. This corresponds to Fus = 0.9 aresee = 67Oh.) parsecs., This corresponds to $r_{im}$ = 0.9 arcsec $\equiv$ $_{70}^{-1}$ parsecs. " ""Phe halo is completely unconstrained observationally.", The halo is completely unconstrained observationally. We will Gt to both the scale length and the halo normalisation., We will fit to both the scale length and the halo normalisation. We therefore have seven parameters for which a fit is required. - four mass-to-light ratios. one COLO raclius and two co-ordinates of the source position.," We therefore have seven parameters for which a fit is required - four mass-to-light ratios, one core radius and two co-ordinates of the source position." We have as constraints. eight co-ordinates of image positions. two rotation points and one mass enclosed within the images.," We have as constraints, eight co-ordinates of image positions, two rotation points and one mass enclosed within the images." ‘These observational constraints are given in Table 1.., These observational constraints are given in Table \ref{values}. Phus. we have four degrees of freedom.," Thus, we have four degrees of freedom." The galaxy has been previously modelled. by many eroups., The galaxy has been previously modelled by many groups. Lluchra ct al. (, Huchra et al. ( 1985) undertook the initial work on he system. measuring cllipticities and scale lengths: and woviding a rucimentary lensing analysis.,"1985) undertook the initial work on the system, measuring ellipticities and scale lengths and providing a rudimentary lensing analysis." They assumed a circular lens model ancl showed that the inferred mass-o-light ratio is within current values for nearby galaxies., They assumed a circular lens model and showed that the inferred mass-to-light ratio is within current values for nearby galaxies. ]xent Falco (1988) approximated the galaxy as an oblate spheroid.citing the bulge and the bar as the two primary ensing components.," Kent Falco (1988) approximated the galaxy as an oblate spheroid,citing the bulge and the bar as the two primary lensing components." Their analysis attemptec to [it the, Their analysis attempted to fit the Fourth. even if a mechanism could be found to grow. choudrule-sized particulates (o ineler-sizecl bodies. one would have to worry about the rapid inward orbital diit associated with eas drag that would carry such bodies from 1. AU into the protosun on a time scale of only ~10? vr (Weidenschilling1977).,"Fourth, even if a mechanism could be found to grow chondrule-sized particulates to meter-sized bodies, one would have to worry about the rapid inward orbital drift associated with gas drag that would carry such bodies from 1 AU into the protosun on a time scale of only $\sim 10^2$ yr \citep{wei77}." . In contrast. mm- and kin-sizecl bodies have gas-clrag dift times in excess of LO? vr.," In contrast, mm- and km-sized bodies have gas-drag drift times in excess of $10^5$ yr." Only by the direct assemblage of chondrules and related objects into planetesimals. avoiding intermediate steps. can one prevent a rapid loss of solid material from the solar nebula by gas drag.," Only by the direct assemblage of chondrules and related objects into planetesimals, avoiding intermediate steps, can one prevent a rapid loss of solid material from the solar nebula by gas drag." such a direct-assemblage mechanism exists in the eravilational instability (GI) proposal put forth by Goldreich&Ward(1973)., Such a direct-assemblage mechanism exists in the gravitational instability (GI) proposal put forth by \citet{gw73}. .. A similar theory was advanced independently by sSalronov(1969)., A similar theory was advanced independently by \citet{saf69}. . In the Golcreich-Warcl theory. particulate settling vields a subcdisk of solids that is thin and non-dispersive enough (to make overdense regions undergo runaway local contraction.," In the Goldreich-Ward theory, particulate settling yields a subdisk of solids that is thin and non-dispersive enough to make overdense regions undergo runaway local contraction." This occurs when Toomre's criterion lor axisvmmeltric GI in a rotating disk (ihe nonaxisvmmetrie ease is similar) is satisfied: where Q is (he angular Ixeplerian rotation rate. ancl c and X are the velocity dispersion and surface densitv.," This occurs when Toomre's criterion for axisymmetric GI in a rotating disk (the nonaxisymmetric case is similar) is satisfied: where $\Omega$ is the angular Keplerian rotation rate, and $c$ and $\Sigma$ are the velocity dispersion and surface density." Throughout we use p and πο subscripts to reler. respectively. (o the particle and gas components of the disk.," Throughout we use “p” and “g” subscripts to refer, respectively, to the particle and gas components of the disk." The Goldreich-Ward instability should not be confused with the mechanism of Boss(2000).. who considers the formation of coreless gas eijant planets from GI of gas disks.," The Goldreich-Ward instability should not be confused with the mechanism of \citet{bo00}, who considers the formation of coreless gas giant planets from GI of gas disks." " 'Toomres criterion (1)) is equivalent (within factors of order unity) to the ""Roche"" limit which has been derived specifically for the case of stratified fluids(Goklreich1965;Sekiva 1983).."," Toomre's criterion \ref{eq:Q}) ) is equivalent (within factors of order unity) to the “Roche” limit which has been derived specifically for the case of stratified \citep{gl65,sek83}. ." " Sekiva finds GI to occur when the particulate plus gas space-densitvy. P=Poty. al a distance r from a star of mass M, exceeds a certain critical value in the midplane: At a distance r=1 AU [rom the Sun. pj=4xLO* g/em?. which implies a critical space density of rock (hat is roughly seven orders of magnitude less (han the internal density of compact rock."," Sekiya finds GI to occur when the particulate plus gas space-density, $\rho = \rho_{\rm g} + \rho_{\rm p}$, at a distance $r$ from a star of mass $M_\ast$ exceeds a certain critical value in the midplane: At a distance $r=1$ AU from the Sun, $\rho_{\rm R} = 4\times 10^{-7}$ $^3$, which implies a critical space density of rock that is roughly seven orders of magnitude less than the internal density of compact rock." " Thus. in the stages preceding actual planetesimal formation. we may (real the collection of solids as an additional ideal ""gas co-mixed with the real gas of the system."," Thus, in the stages preceding actual planetesimal formation, we may treat the collection of solids as an additional ideal “gas” co-mixed with the real gas of the system." Operating at a radius of r=1 AU. the sell-gravitating disturbance with the most unstable wavelength creates 5 km planetesimals in ~107 vr (Youdin&Shu2002).," Operating at a radius of $r=1$ AU, the self-gravitating disturbance with the most unstable wavelength creates $\sim 5$ km planetesimals in $\sim 10^3$ yr \citep{ys02}." . The process occurs on a (nme scale longer (han orbital periods ( 1 vr in thezone for terrestrial planet formation) because of the need to damp spin-up and random velocities during the, The process occurs on a time scale longer than orbital periods $\sim$ 1 yr in thezone for terrestrial planet formation) because of the need to damp spin-up and random velocities during the "Observe that for v€ very few models with negative S4 gri,< 0) are produced.","Observe that for $\nu\in[-20,20]$, very few models with negative $S_4$ $\ff\gnl<0$ ) are produced." " In fact, if the range of v is sufficiently large, no [—20,models20], with negative $4 are produced at (i.e.all."," In fact, if the range of $\nu$ is sufficiently large, no models with negative $S_4$ are produced at all." A simple explanation for this is as follows., A simple explanation for this is as follows. " If the highest non-zero cumulant of a non-Gaussian distribution is $4, then, for large v, the Edgeworth series expanded to n terms is of order S4v""."," If the highest non-zero cumulant of a non-Gaussian distribution is $S_4$, then, for large $\nu$, the Edgeworth series expanded to $n$ terms is of order $S_4 \nu^n$." " Hence, if $4«0, a sufficiently large v will render the expansion negative regardless of the"," Hence, if $S_4<0$, a sufficiently large $\nu$ will render the expansion negative regardless of the" We analyzed the statistical properties of this population to see if radio sources in the field of N31 field differed. frou those elsewhere. aud if so. how they differed.,"We analyzed the statistical properties of this population to see if radio sources in the field of M31 field differed from those elsewhere, and if so, how they differed." We analyzed both the radial. flux deusitv. aud spectral distribution of the GLG sources. and for comparison. data from the WENSS (2?) and NAINELSS radio survey (7). survers.," We analyzed both the radial, flux density, and spectral distribution of the GLG sources, and for comparison, data from the WENSS \citep{wenss} and XMM-LSS radio survey \citep{aaron} surveys." " The WENSS survey mapped the cutive sky north of à=307 at v=325 MITz with a limiting flux density density of Ls τι] and resolution of «82"". ayound M31 (?).. while the 325 MIIz field of the NAINELSS radio survey mapped a 5.6 deg? reeion of sky with a resolution of and a luniting flux density of LinJy ος properties similar to the observation preseuted here (?).. ↕↕⋟⋜↧↴∖↴"," The WENSS survey mapped the entire sky north of $\delta=30^{\circ}$ at $\nu=325$ MHz with a limiting flux density density of 18 mJy and resolution of $\times$ around M31 \citep{wenss}, while the 325 MHz field of the XMM-LSS radio survey mapped a $\sim$ 5.6 $\deg^2$ region of sky with a resolution of and a limiting flux density of 4 - properties similar to the observation presented here \citep{aaron}." ∏↴⋝↴∖↴↑⋜⋯↑↕⋜↕↕∐∏∐∐⋝↸∖↥⋅∪↕⋡↴∖↴⋯∐⋅↸⊳↸∖↴∖↴↕∐⊓⋅↕∐↴∖↴↕↸⊳↑∪⋀∖↕∶≩↕↖↖↽↸∖↥⋅↸∖ detected. we would expect to see an over-deusity of sources in the optical disk of M31.," If a substantial number of sources intrinsic to M31 were detected, we would expect to see an over-density of sources in the optical disk of M31." Iu addition. auy. substructure present in MOI is most likely svnunetric to some degree and might stand out iu the radial distribution of sources.," In addition, any substructure present in M31 is most likely symmetric to some degree and might stand out in the radial distribution of sources." " Unufortuuatelv. iuterpreting the raw radial distribution of sources is difficult because the eain of the telescope decreases toward the οςedee of the ΕΟΝ, as illustrated in Figure l1."," Unfortunately, interpreting the raw radial distribution of sources is difficult because the gain of the telescope decreases toward the edge of the FOV, as illustrated in Figure \ref{pbeam}." As a result. faint sources detectable iu the center of the FOV are undetectable at the edges. complicating models for the expectedobserved background radial distribution of sources.," As a result, faint sources detectable in the center of the FOV are undetectable at the edges, complicating models for the expected background radial distribution of sources." However. since the NMAML-LSS 325 MITz observation was also done using one poiutiug of the VLA A-array. its primary beam shape is very siuilar to that of this observation.," However, since the XMM-LSS 325 MHz observation was also done using one pointing of the VLA A-array, its primary beam shape is very similar to that of this observation." Therefore. the effect of the primary beans shape ou the radial distribution of sources should be the same for these two datasets.," Therefore, the effect of the primary beam's shape on the radial distribution of sources should be the same for these two datasets." As a result. the NMANL-LSS 325 ΑΠ data provides a good backeround radial distribution for this comparison.," As a result, the XMM-LSS 325 MHz data provides a good background radial distribution for this comparison." " The NAIALLSS radio survey also observed a ""λα feld. so the radial distribution of the sources is donuuated by lustrimental effects and uot bv structure intrinsic to the proeran source."," The XMM-LSS radio survey also observed a “blank” field, so the radial distribution of the sources is dominated by instrumental effects and not by structure intrinsic to the program source." We also conrpared the racial distribution of sources projected into the plane defined by the inclination of M31. which may contain more information about MO itself.," We also compared the radial distribution of sources projected into the plane defined by the inclination of M31, which may contain more information about M31 itself." This was done bv first converting the RA and DEC. of each source in the GLC and XMALLSS source Hist to aneular coordinates CX.Y ) relative to the ceuter of AISI (or. for the NMM.LSS sources. the pointing center of that observation) using the task WCSSPIT2NY. aud then translating these augular coordinates iuto the plane of N31 ou the sky CVars.-) yg.) using the following formulae: where 52° is the angele of the optical disk of M31 relative to N on the sky (?)..," This was done by first converting the RA and DEC of each source in the GLG and XMM-LSS source list to angular coordinates $X$ $Y$ ) relative to the center of M31 (or, for the XMM–LSS sources, the pointing center of that observation) using the task , and then translating these angular coordinates into the plane of M31 on the sky $X_{M31}$ $Y_{M31}$ ) using the following formulae: where $52^{\circ}$ is the angle of the optical disk of M31 relative to N on the sky \citep{braun}." Since the plane of M31 is inclined 777 to the plane of the sky. a circle of radius Rin AL31 would be an ellipse in the CVays7. Vays} coordinate xvstem.," Since the plane of M31 is inclined $77^{\circ}$ to the plane of the sky, a circle of radius R in M31 would be an ellipse in the $X_{M31}$ $Y_{M31}$ ) coordinate system." Using this fact. the distance of a source from the ceuter of the observation in the plane of M31. (Rays) was calculated using the following formula: As shown in Figure 6.. there are substautial differences )otwoeen the radial distribution ofthe NADIAI-LSS aud GLC survevs.," Using this fact, the distance of a source from the center of the observation in the plane of M31 $R_{M31}$ ) was calculated using the following formula: As shown in Figure \ref{disdist}, there are substantial differences between the radial distribution of the XMM-LSS and GLG surveys." The first difference is the ummber of sources in he ΑΕΕ (256) aud GLC survey (105)., The first difference is the number of sources in the XMM-LSS (256) and GLG survey (405). " Some of this difference is due to differences in the data analysis he NAQALLSS list does not include sources fouud iu smootled naps (""Ex GLC sources). only goes out to 1.31° from the »)utiues center Gu the GLC survey. the furthest source is L.75° from the pointing center). aud does not mclude sources wit 15325< bawdy (7). while the GLC survev las a So sensitivity of ~3 indy."," Some of this difference is due to differences in the data analysis – the XMM-LSS list does not include sources found in smoothed maps (“Ex” GLG sources), only goes out to $^{\circ}$ from the pointing center (in the GLG survey, the furthest source is $^{\circ}$ from the pointing center), and does not include sources with $S_{325}<4$ mJy \citep{aaron} while the GLG survey has a $\sigma$ sensitivity of $\sim$ 3 mJy." However. after applying he above limitations tothe GLG source list there are still sienificantly (2.90) more CLC sources (302) than NADL sources Some of this difference may be due," However, after applying the above limitations tothe GLG source list there are still significantly $2.9\sigma$ ) more GLG sources (302) than XMM-LSS sources Some of this difference may be due" suggests that tical dissipation is important in damping stellar obliquity In this paper. we show that tidal damping of spin-orbit misalignment can be much more ellicient than tidal damping of the orbit.,"suggests that tidal dissipation is important in damping stellar obliquity In this paper, we show that tidal damping of spin-orbit misalignment can be much more efficient than tidal damping of the orbit." In. another word. the ellective. tidal quality [actor for the former process can be much smaller than the latter.," In another word, the effective tidal quality factor for the former process can be much smaller than the latter." This provides a natural resolution to the conuncdrum ciscussed above., This provides a natural resolution to the conundrum discussed above. Alany previous works on tidal evolution in hot Jupiter systems (e.g. Rasio et al.," Many previous works on tidal evolution in hot Jupiter systems (e.g., Rasio et al." 1996: Sasselov 2003: Dobbs-Dixon et al., 1996; Sasselov 2003; Dobbs-Dixon et al. 2004: Barker Oeilvie 2009: Jackson et al., 2004; Barker Ogilvie 2009; Jackson et al. 2009: Levrard ct al., 2009; Levrard et al. 2009: llansen POLO: Matsumura et al., 2009; Hansen 2010; Matsumura et al. POLO) were based on the weak [σος theory of equilibrium tices., 2010) were based on the weak friction theory of equilibrium tides. " This. theory considers large-scale quaclrupole distortion of the star. and parameterizes tidal dissipation bv a dimensionless equality [actor Q, or more generally. by a constant tidal lag time ελ "," This theory considers large-scale quadrupole distortion of the star, and parameterizes tidal dissipation by a dimensionless quality factor $Q_\star$ or more generally, by a constant tidal lag time $\Delta t_L$." The theory was first formulated by Darwin (1880). and extensively applied: to solar-system. bodies (e.g... Goldreich Solter 1966) ancl stellar binaries (see Zahn 2008 for a review).," The theory was first formulated by Darwin (1880), and extensively applied to solar-system bodies (e.g., Goldreich Solter 1966) and stellar binaries (see Zahn 2008 for a review)." " These applications have proved very useful. since they provide empirical estimates or constraints on the values of Q, for various systems.", These applications have proved very useful since they provide empirical estimates or constraints on the values of $Q_\star$ for various systems. The most general (arbitrary orbital eccentricity ancl spin-orbit: inclination angle) and correct equations for tidal evolution based on this theory were derived by Alexander (1973). and were also elaborated w others (e.g. Hut. 1981: Eeeleton ct al.," The most general (arbitrary orbital eccentricity and spin-orbit inclination angle) and correct equations for tidal evolution based on this theory were derived by Alexander (1973), and were also elaborated by others (e.g., Hut 1981; Eggleton et al." 1998: Correia Laskar 2010)., 1998; Correia Laskar 2010). " Although it is well recognized that the equilibrium tide wory ds a parameterized. theory. with all the physics of idal dissipation hidden in a single parameter Q, or Ady he Love number of the body can be absorbed. into the lefinition of these parameters). it is not widely appreciated iu the effective tidal (Q, for different processes. (e.g. spin-orbit alignment and orbital decay) can be cdillerent."," Although it is well recognized that the equilibrium tide theory is a parameterized theory, with all the physics of tidal dissipation hidden in a single parameter $Q_\star$ or $\Delta t_L$ (the Love number of the body can be absorbed into the definition of these parameters), it is not widely appreciated that the effective tidal $Q_\star$ for different processes (e.g., spin-orbit alignment and orbital decay) can be different." 1n another word. the wicely-usec tidal evolution equations ράσο on. equilibrium. tide theory can be incorrect even at re parameterized level.," In another word, the widely-used tidal evolution equations based on equilibrium tide theory can be incorrect even at the parameterized level." Indeed. the conundrum: discussed in Sect.," Indeed, the conundrum discussed in Sect." 1.1 arises because Eq. (30)), 1.1 arises because Eq. \ref{eq:tTheta}) ) " assumes that the tidal Q, for stellar obliquity damping is similar to the €, for orbital decay.", assumes that the tidal $Q_\star$ for stellar obliquity damping is similar to the $Q_\star$ for orbital decay. In fact. this is incorrect. as we explain below.," In fact, this is incorrect, as we explain below." There are three channels of tidal dissipations in solar- stars: (i) I5quilibrium tides., There are three channels of tidal dissipations in solar-type stars: (i) Equilibrium tides. The large-scale quasi-static tidal rulge can be clamped by turbulent viscosity in the stars convective envelope (Zahn 1977.1989).," The large-scale quasi-static tidal bulge can be damped by turbulent viscosity in the star's convective envelope (Zahn 1977,1989)." ". The major uncertainty involves how the cllective viscosity derived from 1e mixing-length theory, of)/3 (where vc; and /, are re velocity ancl size of convective eddies. respectively). is reduced when the tidal forcing period iq. is shorter than jo convective turnover time 7;—l/;fe, (see Goodman Oh 1997)."," The major uncertainty involves how the effective viscosity derived from the mixing-length theory, $\sim v_t l_t/3$ (where $v_t$ and $l_t$ are the velocity and size of convective eddies, respectively), is reduced when the tidal forcing period $P_{\rm tide}$ is shorter than the convective turnover time $\tau_t=l_t/v_t$ (see Goodman Oh 1997)." Recent simulations (Penev et al., Recent simulations (Penev et al. 2009.2011) suggests ja the reduction factor is about Pif(2s7;) (Cor a limited range of 34). and the corresponding tidal Q. well exceeds 107 (Penev Sasselov 2011).," 2009,2011) suggests that the reduction factor is about $P_{\rm tide}/(2\pi\tau_t)$ (for a limited range of $P_{\rm tide}$ ), and the corresponding tidal $Q_\star$ well exceeds $10^8$ (Penev Sasselov 2011)." " An even larger Q, will result i£ the reduction factor (3/227)? is used (see Ogilvie Lin 2007) (", An even larger $Q_\star$ will result if the reduction factor $(P_{\rm tide}/2\pi\tau_t)^2$ is used (see Ogilvie Lin 2007). ( ii) Excitation and. damping of internal gravity waves (Goodman Dickson 1998: Ogilvie Lin 2007: Barker Oeilvie 2010.2011).,"ii) Excitation and damping of internal gravity waves (Goodman Dickson 1998; Ogilvie Lin 2007; Barker Ogilvie 2010,2011)." These waves (also called Hough. waves when mocdilied by rotation) are launched at. the bottom of the stars convective envelope. ancl propagate toward the stellar center., These waves (also called Hough waves when modified by rotation) are launched at the bottom of the star's convective envelope and propagate toward the stellar center. " 1 they attain sullicient amplitudes: at the center. wave breaking will occur: this will. produce significant tidal clissipation. corresponding to Q,afew10CP/1day)? assuming the orbital period 2? is much shorter than the spin period: see Barker Ogilvie (2010)]."," If they attain sufficient amplitudes at the center, wave breaking will occur; this will produce significant tidal dissipation, corresponding to $Q_\star \sim {\rm a~few}\times 10^5(P/1\,{\rm day})^{8/3}$ [assuming the orbital period $P$ is much shorter than the spin period; see Barker Ogilvie (2010)]." If the waves are rellectec coherently at the stellar center (og. by a small convective core) before nonlinear breaking Clorquem ct al.," If the waves are reflected coherently at the stellar center (e.g., by a small convective core) before nonlinear breaking (Terquem et al." " 1908). only weak dissipation will resul Q,=10°)."," 1998), only weak dissipation will result $Q_\star\go 10^8$ )." The latest caleulations by Barker Ogilvic (2010-2011) suggest that while the nonlinear wave breaking certainly occurs for binary stars. it is probably unimportan for exoplanetary systems. — this would explain the surviva of short-periock hot. Jupiters against orbital decay (see Weinberg et al.," The latest calculations by Barker Ogilvie (2010,2011) suggest that while the nonlinear wave breaking certainly occurs for binary stars, it is probably unimportant for exoplanetary systems – this would explain the survival of short-period hot Jupiters against orbital decay (see Weinberg et al." 2011). (, 2011). ( ii) Excitation and damping of inertial waves.,iii) Excitation and damping of inertial waves. οσο theoretical. works on dynamical tides in rotating planets (Ogilvie Lin 2004.2007: Ogilvie 2005.2009: Wu 2005a.b: Papaloizou Ivanov 2005: Goodman Lackner 2009) anc stars (Savonije Papaloizou 1997: Papaloizou Savoniji 1997: Savonije Witte 2002): Ogilvie Lin 2007) have emphasized. the importance of inertial waves driven by Coriolis force.," Recent theoretical works on dynamical tides in rotating planets (Ogilvie Lin 2004,2007; Ogilvie 2005,2009; Wu 2005a,b; Papaloizou Ivanov 2005; Goodman Lackner 2009) and stars (Savonije Papaloizou 1997; Papaloizou Savoniji 1997; Savonije Witte 2002); Ogilvie Lin 2007) have emphasized the importance of inertial waves driven by Coriolis force." When the tidal forcing frequeney (in. the rotating frame) c is less than twice the spin [requeney (Q.). short-wavelength inertial waves can be excited.," When the tidal forcing frequency (in the rotating frame) $\tomega$ is less than twice the spin frequency $\Omega_s$ ), short-wavelength inertial waves can be excited." In particular. when these waves are confined to a spherical shell (as in 16 convection zone outside the solid core of a giant planet x in the convective envelope of a solar-tvpe. star) tidal isturbances are concentrated in very narrow regions (called Cwave attractors”) where dissipation takes place (Ogilvie Lin 2004: Oegilvie 2009: Goodman Lackner 2009).," In particular, when these waves are confined to a spherical shell (as in the convection zone outside the solid core of a giant planet or in the convective envelope of a solar-type star), tidal disturbances are concentrated in very narrow regions (called “wave attractors”) where dissipation takes place (Ogilvie Lin 2004; Ogilvie 2009; Goodman Lackner 2009)." lt appears that this mechanism can explain the tidal Q (~ 10°) of giant planets and. when combined with internal gravity wave damping see (ii) above]. can also explain the issipation required for the circulavization of stellar binaries.," It appears that this mechanism can explain the tidal $Q$ $\sim 10^6$ ) of giant planets and, when combined with internal gravity wave damping [see (ii) above], can also explain the dissipation required for the circularization of stellar binaries." " Llowever. for solar-tvpe stars in hot Jupiter systems. the inertial wave dissipation mechanism is not expected. to operate. since the tidal frequeney a=2(QQO.) (assuming circular orbit and aligned stellar spin) is larger than 20, for typical parameters (e.g. 2.10 d and P— 1d)."," However, for solar-type stars in hot Jupiter systems, the inertial wave dissipation mechanism is not expected to operate, since the tidal frequency $\tomega=2(\Omega-\Omega_s)$ (assuming circular orbit and aligned stellar spin) is larger than $2\Omega_s$ for typical parameters (e.g., $P_s\sim 10$ d and $P\sim 1$ d)." The main point of our paper concerns inertial wave dissipation in the parent stars of hot Jupiter systems when the stellar spin S is misaligned with the orbital angular momentum L., The main point of our paper concerns inertial wave dissipation in the parent stars of hot Jupiter systems when the stellar spin ${\bf S}$ is misaligned with the orbital angular momentum ${\bf L}$. " For a circular binary. in the inertial coordinate system with the Z-axis alongL. the tidal potential has two components (to the quadrupole order). with [requencies ie,""=m'O (where m/= 0.2)."," For a circular binary, in the inertial coordinate system with the $Z$ -axis along${\bf L}$, the tidal potential has two components (to the quadrupole order), with frequencies $\omega_{m'}=m'\Omega$ (where $m'=0,2$ )." As seen in the rotating frame of the star. the tidal frequencies become quay with m=QO.cl.c2.," As seen in the rotating frame of the star, the tidal frequencies become _s, with $m=0,\pm 1,\pm 2$." For an aligned system. only the mo-om=2 component of the tidal potential is nonzeroand involved in tidal dissipation. (," For an aligned system, only the $m=m'=2$ component of the tidal potential is nonzeroand involved in tidal dissipation. (" Lhe m=η0 component is also nonzero. but it does not transfer energy and angular momentum since it is completely static.),"The $m=m'=0$ component is also nonzero, but it does not transfer energy and angular momentum since it is completely static.)" For misaligned svstems. however. all seven tidal components all combinations of (m.m) except m=— (k note that [or m'— 0. the m—l(2) component is physically," For misaligned systems, however, all seven tidal components [all combinations of $(m,m')$ except $m=m'=0$ ; note that for $m'=0$ , the $m=-1(-2)$ component is physically" subsonic turbulent torus.,subsonic turbulent torus. The inner flow shocks (he supersonically accreting gas before the latter feels its centrifugal barrier., The inner flow shocks the supersonically accreting gas before the latter feels its centrifugal barrier. We define a torus as an equatorial region with high-/ gas and subsonic radial velocity., We define a torus as an equatorial region with $l$ gas and subsonic radial velocity. The torus evolves., The torus evolves. Namely its density. gas pressure and size increase with (ime.," Namely its density, gas pressure and size increase with time." Subsequently (he inner sonic surface erows. too.," Subsequently the inner sonic surface grows, too." The two sonic surfaces eventually connect as the inner surface reaches the outer sonic surface., The two sonic surfaces eventually connect as the inner surface reaches the outer sonic surface. When (his happens. the accumulated matter withhigh / starts to flow out as in run J. The sonic surface topology changes and eventually the sonic surface has the figure eight shape.," When this happens, the accumulated matter withhigh $l$ starts to flow out as in run J. The sonic surface topology changes and eventually the sonic surface has the figure eight shape." We note (hat in run 1. the figure eight shape is achieved in a dillerent wav than in run J. The second row of panels rom (he top in Fig.," We note that in run I, the figure eight shape is achieved in a different way than in run J. The second row of panels from the top in Fig." 5. show that the matter flows out. but the shock propagation is delaved in comparison run J (the top row of panels).," \ref{fig:2} show that the matter flows out, but the shock propagation is delayed in comparison run J (the top row of panels)." " At the end of run L the flow is much more asvmnmetric than lor run J (e.g.. in run 1, there is a strong outflow toward the ‘north’ direction)."," At the end of run I, the flow is much more asymmetric than for run J (e.g., in run I, there is a strong outflow toward the `north' direction)." For 4=1.2 (run IL. the third row of panels in Fig. 5))," For $\gamma=1.2$ (run H, the third row of panels in Fig. \ref{fig:2}) )" the evolution of the sonic surface topology is similar (to that in run L The main difference is that the inner sonic surfaces evolves on longer (ime scale in run H (han run I. The second left panel of Fig., the evolution of the sonic surface topology is similar to that in run I. The main difference is that the inner sonic surfaces evolves on longer time scale in run H than run I. The second left panel of Fig. 5. captures a moment soon after the two sonic surlaces merged., \ref{fig:2} captures a moment soon after the two sonic surfaces merged. A delav in formation of the outflow is caused by the fact that for lower 5. the sound speed is lower and (he radius of the initial outer sonie surface is larger.," A delay in formation of the outflow is caused by the fact that for lower $\gamma$, the sound speed is lower and the radius of the initial outer sonic surface is larger." At the end of run IL. the flow is very asymmetric.," At the end of run H, the flow is very asymmetric." The simulation for 5=1.01 (run G. the bottom row of panel in Fig. 5))," The simulation for $\gamma = 1.01$ (run G, the bottom row of panel in Fig. \ref{fig:2}) )" shows Chat again {wo some surfaces form as in runs II and I. ILowever. the time scale lor two sonic surfaces lo merge is much longer in comparison to other 5 cases. because a large distant between the two surfaces ((he outer surfaces is al 2500. £25) and small sound speed.," shows that again two sonic surfaces form as in runs H and I. However, the time scale for two sonic surfaces to merge is much longer in comparison to other $\gamma$ cases, because a large distant between the two surfaces (the outer surfaces is at $\sim$ 500 $R_S$ ) and small sound speed." In run IH. we do not observe the formation of the outflow amd we see no shock propagating outward.," In run H, we do not observe the formation of the outflow and we see no shock propagating outward." The time scale of the inner sonic surface growth rate is very long. and we are not able to follow it. with 200 points in 8 direction. because of too long simulation time.," The time scale of the inner sonic surface growth rate is very long, and we are not able to follow it, with 200 points in $\theta$ direction, because of too long simulation time." Although not shown here. we performed a test simulation. with 2 times lower resolution in @ direction.," Although not shown here, we performed a test simulation, with 2 times lower resolution in $\theta$ direction." In this test run we observe (he sonic surface topologv change in 5=1.01 case too. but alter much longer time in comparison to other 5s (e.g.. Che topology in run G changes on a lime scale 150 (times longer than in run I!).," In this test run we observe the sonic surface topology change in $\gamma=1.01$ case too, but after much longer time in comparison to other $\gamma$ s (e.g., the topology in run G changes on a time scale 150 times longer than in run H!)." We see no outflow in the equatorial plane for this set of parameters. for very long simulation time. even after the figure eight sonic surface is formed.," We see no outflow in the equatorial plane for this set of parameters, for very long simulation time, even after the figure eight sonic surface is formed." " We also performed additional computations lor ?;—1.01 models with the hieher flow Lemperatures corresponding to A,=107 and 2x10.7. but keeping the same grid parameters as for RY=LO7 models."," We also performed additional computations for $\gamma$ =1.01 models with the higher flow temperatures corresponding to $R'_S=10^{-2}$ and $2\times 10^{-2}$, but keeping the same grid parameters as for $R'_S=10^{-3}$ models." As expected. in these additional runs. the flow evolves faster than in run Il. In particular. an outflow forms on a reasonable time scale.," As expected, in these additional runs, the flow evolves faster than in run H. In particular, an outflow forms on a reasonable time scale." Generally. we found that when we suppress (he eas pressure enough by decreasing 5 or decreasing ὃς. an outflow will take a verv long time to develop.," Generally, we found that when we suppress the gas pressure enough by decreasing $\gamma$ or decreasing $c_{\infty}$ , an outflow will take a very long time to develop." A delay in development of an outflow is a stronger, A delay in development of an outflow is a stronger (Crevesse and Anders 1991) aud using the default density of 1029 7.,(Grevesse and Anders 1991) and using the default density of $10^{10}$ $^{-3}$. The spatial distribution of the total focal-plane Cluission per unit volume at cach time is then obtained by iutegrating 1n cherey: Fig., The spatial distribution of the total focal-plane emission per unit volume at each time is then obtained by integrating in energy: Fig. 6 shows. for the reference simulation. cross-sections of the resulting distiibutious of plasma cussion in the ASCA/SIS baud at the same times and in tle same reeion as Fies.t and 5..," \ref{fig:imasca} shows, for the reference simulation, cross-sections of the resulting distributions of plasma emission in the ASCA/SIS band at the same times and in the same region as \ref{fig:imtemp} and \ref{fig:imdens}." The cross-sectious are taken on a plane across the Z axis., The cross-sections are taken on a plane across the Z axis. The emissiou at carly times is clearly concentrated iu the heating region aud mostly ina hin laver at the base of corona., The emission at early times is clearly concentrated in the heating region and mostly in a thin layer at the base of corona. Uutil t = 30 8 an aliiost spherical weak enission rout expands progressively aud is clearly associated tothe propagation of the thermal rout (sec Fie.1))., Until t = 30 s an almost spherical weak emission front expands progressively and is clearly associated tothe propagation of the thermal front (see \ref{fig:imtemp}) ). After t = 30 s another brighter rout rises from the base of he corona. with a less regular shape. aud is due to the density frout evaporating frou he chromosphere (see Fie.5)).," After t = 30 s another brighter front rises from the base of the corona, with a less regular shape, and is due to the density front evaporating from the chromosphere (see \ref{fig:imdens}) )." Soon after the heating is switched off (£ = 151). the bright knot at the base of the corona rapidly fades. due to the sudden temperature drop described in Sect. 3.2.2...," Soon after the heating is switched off (t = 154 s), the bright knot at the base of the corona rapidly fades, due to the sudden temperature drop described in Sect. \ref{sec:decay}." At t = 200 8 most of the ciission colucs from the evaporating front. which continues to expands but eraduallv fades away (t = 300 x).," At t = 200 s most of the emission comes from the evaporating front, which continues to expands but gradually fades away (t = 300 s)." Since the flare would not be resolved at stellar distances. we have then integrated the eLulsson distribution over the relevant region of the computational domain to obtain the light curve at the focal plane of ASCA/SIS aud the flux at Earth in the two selected spectral lines: where VHI..Zy4; is the domain volume.," Since the flare would not be resolved at stellar distances, we have then integrated the emission distribution over the relevant region of the computational domain to obtain the light curve at the focal plane of ASCA/SIS and the flux at Earth in the two selected spectral lines: where $V=\pi R_{max}^2 Z_{max}$ is the domain volume." Lu deriving the focal-plane light curve £(f)c we lave assumed. a standard distance of the faring source of 1 pe from the detector., In deriving the focal-plane light curve ${\cal E}(t)$ we have assumed a standard distance of the flaring source of 1 pc from the detector. Figure 7 shows the fare uct Πο curves at the ASCA/SIS focal plane. obtained by subtracting the count rate at the initial time of each simulation. taken as backgrouud non-flaring cluission. for all cases reported iu Table 1.. including the model of confined fare.," Figure \ref{fig:lc} shows the flare net light curves at the ASCA/SIS focal plane, obtained by subtracting the count rate at the initial time of each simulation, taken as background non-flaring emission, for all cases reported in Table \ref{tab:sim}, , including the model of confined flare." periods. not longer than a few years.,"periods, not longer than a few years." In fact. any attempt to obtain information by measuring astrometric shifts of the observed source star due to its wobble around the compact object or its radial velocity by means of Doppler-shifts of spectral lines. relates to the orbital period.," In fact, any attempt to obtain information by measuring astrometric shifts of the observed source star due to its wobble around the compact object or its radial velocity by means of Doppler-shifts of spectral lines, relates to the orbital period." " Withstanding the difficulties in obtaining such measurements for ""int stars. the fundamental properties already follow with the orbital period itself."," Withstanding the difficulties in obtaining such measurements for faint stars, the fundamental properties already follow with the orbital period itself." Kepler's third law would allow to find with Eqs. ¢17)), Kepler's third law would allow to find with Eqs. \ref{eq:tE}) ) " and 1919). and one would be able to obtain iteratively as Well as so that with the mass-radius relation for main-sequence stars Given that the signal amplitude of self-lensing due to a compact object in a binary system is less suppressed by the much smaller finite radius of a white dwarf as compared to a main-sequence star. and moreover the orbital period of detectable systems is smaller (given that the relevance of finite-source effects is quantitied by p,ox l/W/ay and thereby the frequency of signals is arger. ? concludedo that white dwarfs are the favourable targets or observing this effect. whereas the prospects for binaries involving main-sequence stars are rather bleak."," and \ref{eq:u0}) ), and one would be able to obtain iteratively as well as so that with the mass-radius relation for main-sequence stars Given that the signal amplitude of self-lensing due to a compact object in a binary system is less suppressed by the much smaller finite radius of a white dwarf as compared to a main-sequence star, and moreover the orbital period of detectable systems is smaller (given that the relevance of finite-source effects is quantified by $\rho_\star \propto 1/\sqrt{a}$ ), and thereby the frequency of signals is larger, \citet{Mae73} concluded that white dwarfs are the favourable targets for observing this effect, whereas the prospects for binaries involving main-sequence stars are rather bleak." However. the ortune changes substantially if one looks at the observability of suitable systems.," However, the fortune changes substantially if one looks at the observability of suitable systems." 9? considered the Sloan Digital Sky Survey (SDSS) as most favourable for observing whie dwarfs. and in fact. it has dramatically increased the number of known white dwarfs.," \cite{BT} considered the Sloan Digital Sky Survey (SDSS) as most favourable for observing white dwarfs, and in fact, it has dramatically increased the number of known white dwarfs." However. with the sample containing about 5.000 objects (2). it is ~107 times smaller as compared to the 2107 stars regularly monitored by current microlensing surveys (2)..," However, with the sample containing about 15,000 objects \citep{SDSS}, it is $\sim\,10^{4}$ times smaller as compared to the $2 \times 10^{8}$ stars regularly monitored by current microlensing surveys \citep{OGLE-III}." " For Na,~2LO” monitored stars and an event rate per observed star of4.10.'vr.+ (for 5 per cent photometric accuracy and [5 min sampling cadence). one finds a total event rate of D~74vr.|. where &<1 is a coverage factor accounting for the visibility of the Galactic bulge from the respective sites over the year. any losses due to weather or technical downtime. and imperfect cadence or data quality."," For $N_\rmn{obs} \sim 2 \times 10^{8}$ monitored stars and an event rate per observed star of $\gamma \sim 4 \times 10^{-7}~\mbox{yr}^{-1}$ (for 5 per cent photometric accuracy and 15 min sampling cadence), one finds a total event rate of $\Gamma \sim 74\,\kappa~\mbox{yr}^{-1}$, where $\kappa < 1$ is a coverage factor accounting for the visibility of the Galactic bulge from the respective sites over the year, any losses due to weather or technical downtime, and imperfect cadence or data quality." In contrast to earlier work. we therefore conclude that the detection of compact objects (in fact. predominantly black holes) in binary systems due to self-lensing of an observed main-sequence star companion is possible. provided that a high-cadence sampling substantially below 2 hrs is realised.," In contrast to earlier work, we therefore conclude that the detection of compact objects (in fact, predominantly black holes) in binary systems due to self-lensing of an observed main-sequence star companion is possible, provided that a high-cadence sampling substantially below 2 hrs is realised." The upcoming Korea Microlensing Telescope Network (KMTNet) has in fact been designed as a wide-field survey of the Galactic Bulge with 10-minute cadence (?2).., The upcoming Korea Microlensing Telescope Network (KMTNet) has in fact been designed as a wide-field survey of the Galactic Bulge with 10-minute cadence \citep{KMTNet}. Moreover. the MOA (Microlensing Observations in Astrophysics) survey already monitors some of its fields at that cadence (2)...," Moreover, the MOA (Microlensing Observations in Astrophysics) survey already monitors some of its fields at that cadence \citep{Sumi:planet}." Higher photometric accuracies of 0.3 per cent. achievable with space-based observations (22 or luckv-imaging cameras (2).. could result in 10 times as many observable signals due to self-lensing in binaries with a compact objects. whereas lower accuracies of 20 per cent would lead to about 10 times less objects being detected.," Higher photometric accuracies of 0.3 per cent, achievable with space-based observations \citep{Bennett:space1,Bennett:space2} or lucky-imaging cameras \citep{Uffe:planets}, could result in 10 times as many observable signals due to self-lensing in binaries with a compact objects, whereas lower accuracies of 20 per cent would lead to about 10 times less objects being detected." Given that the duration of the expected self-microlensing signals is of the order of a few hours. we issue a note of caution hat such is not mistaken for evidence of planetary-mass bodies that iss the line of sight to a background star.," Given that the duration of the expected self-microlensing signals is of the order of a few hours, we issue a note of caution that such is not mistaken for evidence of planetary-mass bodies that pass the line of sight to a background star." In fact. the MOA survey appears to show an excess of short-duration peaks as compared © expectations from stellar populations and the kinematics of the Tilky Way CK. Kamiya. private communication).," In fact, the MOA survey appears to show an excess of short-duration peaks as compared to expectations from stellar populations and the kinematics of the Milky Way (K. Kamiya, private communication)." In practice. one faces a rather hard job to distinguish between usually poorly-covered spikes of different origin.," In practice, one faces a rather hard job to distinguish between usually poorly-covered spikes of different origin." The self-lensing binary signals repeat in principle. but on an initially unknown ime-scale of months to years and are rather easy to miss.," The self-lensing binary signals repeat in principle, but on an initially unknown time-scale of months to years and are rather easy to miss." The discriminating power of the criterion of achromaticity of gravitational microlensing as opposed to stellar variability is also imited due to the lack of detail on the shape of the signal., The discriminating power of the criterion of achromaticity of gravitational microlensing as opposed to stellar variability is also limited due to the lack of detail on the shape of the signal. Only if a period of the binary system can be established. its physical characteristics can be determined.," Only if a period of the binary system can be established, its physical characteristics can be determined." interested in anv nighi-to-night variations over our 15 month span of observations.,interested in any night-to-night variations over our 15 month span of observations. Figure 2 presenis a comparison in the 2009/10 Zenith data., Figure \ref{fig:Octdiff} presents a comparison in the 2009/10 Zenith data. While (he 2010 February ancl 2009 March Zenith observations are almost indistinguishable. Che 2009 October and 2010 June data both differ by close to a half a magnitude per arcsec? in the red.," While the 2010 February and 2009 March Zenith observations are almost indistinguishable, the 2009 October and 2010 June data both differ by close to a half a magnitude per $^{2}$ in the red." " For the October data. this trend was also observed when looking al Tucson. Nogales. Phoenix and ""Nowhere"" and the broadband V. and. D magnitudes in Table 1. also show that the October magnitudes. are consistently hall à magnitude brighter."," For the October data, this trend was also observed when looking at Tucson, Nogales, Phoenix and “Nowhere"" and the broadband $V$ and $B$ magnitudes in Table \ref{tab:AllMags} also show that the October magnitudes are consistently half a magnitude brighter." ILowever. for the June data. dimming in the red was only observed in (he Zenith: measurements.," However, for the June data, dimming in the red was only observed in the Zenith measurements." We havent found anv acceptable explanations for this behavior., We haven't found any acceptable explanations for this behavior. Though. a similar skv brightness study at Mt. Graham found that conditions can cause a 0.5 magnitude increase in sky brightness. consistent with our October results (Pedani 2009).," Though, a similar sky brightness study at Mt. Graham found that non-photometric conditions can cause a 0.5 magnitude increase in sky brightness, consistent with our October results (Pedani 2009)." Thus. when an average spectrum or magnitude is shown (such as in Table 2)). we have combined only the February. March aid. June data except for al Zenith. where only the February ancl March data have been combined.," Thus, when an average spectrum or magnitude is shown (such as in Table \ref{tab:CompMags}) ), we have combined only the February, March and June data except for at Zenith, where only the February and March data have been combined." Arguably the most interesting decade to decade comparisons deal with the skv brightness al Tucson and Zenith., Arguably the most interesting decade to decade comparisons deal with the sky brightness at Tucson and Zenith. Figure 3. shows that in both cases (he largest change in brightness occurred between 1983 and 1999 and after 1999. the sky appears to have gottendarker.," Figure \ref{fig:20yrs} shows that in both cases the largest change in brightness occurred between 1988 and 1999 and after 1999, the sky appears to have gotten." A magnitude comparison between the 1999 and 2009/10 values in Table 2. shows that both the broadband. and narrowband magnitudes: additionally decreased., A magnitude comparison between the 1999 and 2009/10 values in Table \ref{tab:CompMags} shows that both the broadband and narrowband magnitudes additionally decreased. Much. of Chis change may be caused by the solar evele as well as neighboring Pima County's stringent lightening ordinances put into place in 2000. as cliseussecd in Section 4..," Much of this change may be caused by the solar cycle as well as neighboring Pima County's stringent lightening ordinances put into place in 2000, as discussed in Section \ref{D}." Comparisons between the average spectra al Zenith and the average spectra al Tucson. Phoenix. Nogales aud Nowhere for the 2009/10 data (as shown in Figure 4)) reveal just how much the population of surrounding cities affects (he sky elow.," Comparisons between the average spectra at Zenith and the average spectra at Tucson, Phoenix, Nogales and Nowhere for the 2009/10 data (as shown in Figure \ref{fig:ZenComp}) ) reveal just how much the population of surrounding cities affects the sky glow." The most prominent difference is observed when looking at Tucson. as expected. but interestingly there is relatively no difference between the spectra of Nogales and Nowhere.," The most prominent difference is observed when looking at Tucson, as expected, but interestingly there is relatively no difference between the spectra of Nogales and Nowhere." Additionally. according to Table 2.. the skv towards Phoenix is actually than the skv towards both Nowhere and Nogales.," Additionally, according to Table \ref{tab:CompMags}, the sky towards Phoenix is actually than the sky towards both Nowhere and Nogales." This suggests that most of the lisht pollution is being caused by Tucson. even when looking in a completely dilferent direction.," This suggests that most of the light pollution is being caused by Tucson, even when looking in a completely different direction." We also noticed a significant decrease in the sky brightness towards Tucson as the night proeressed., We also noticed a significant decrease in the sky brightness towards Tucson as the night progressed. Figure 5. shows the skv spectrum in 2010 February at both three hours after sunset and nine hours alter sunset., Figure \ref{fig:TucTime} shows the sky spectrum in 2010 February at both three hours after sunset and nine hours after sunset. A comparison of the skv spectrum taken in 2009 October ab two hours and eight hours after sunset shows a similar result., A comparison of the sky spectrum taken in 2009 October at two hours and eight hours after sunset shows a similar result. " Since all of the observations were taken when (he sun was greater than 18? below the horizon. we believe this change is due to households aud businesses switching off their lights rather than (he progression of twilight,"," Since all of the observations were taken when the sun was greater than $^{\circ}$ below the horizon, we believe this change is due to households and businesses switching off their lights rather than the progression of twilight." We did attempt to quantify the changes seen in the integrated flux of just the region, We did attempt to quantify the changes seen in the integrated flux of just the region qualitative picture.,qualitative picture. For example. the factors by which the star formation has to be reduced in the burst galaxies woul change from around 0.5 to 0.25. Le. we would still identify a strong wind developing in these systems. consistent with the evidence in [favour of winds having cleared the loca dSphs of their gas.," For example, the factors by which the star formation has to be reduced in the burst galaxies would change from around 0.8 to 0.25, i.e., we would still identify a strong wind developing in these systems, consistent with the evidence in favour of winds having cleared the local dSphs of their gas." Basically. in the context of the recen hyedrodynamical simulations mentioned. above. the masses of the ejected: winds of our figure S are probably uncertain and have to be multiplied by a factor of between 1.0 ane 0.3.," Basically, in the context of the recent hydrodynamical simulations mentioned above, the masses of the ejected winds of our figure 8 are probably uncertain and have to be multiplied by a factor of between 1.0 and 0.3." 'To conclude: 1) We have performed. a detailed. exploration of the parameter space available to the four local dSph galaxies studied here. in terms of the gas accretion regimes. and metallicities of the formed. stars and. ejectecl materials. by taking as external restrictions the star formation histories of these systems. as inferred. from. direct. statistical stuclics of their resolved. populations. together with the observed general properties of their dark haloes.," To conclude: 1) We have performed a detailed exploration of the parameter space available to the four local dSph galaxies studied here, in terms of the gas accretion regimes and metallicities of the formed stars and ejected materials, by taking as external restrictions the star formation histories of these systems, as inferred from direct statistical studies of their resolved populations, together with the observed general properties of their dark haloes." This shows that knowledge of the time structure ancl normalization of the star formation rate of external galaxies can be combined with physical and chemical modeling of these svstems to derive interesting information on their evolution and. clark matter haloes. the details of which furnish the boundary conditions within which the galaxies evolve.," This shows that knowledge of the time structure and normalization of the star formation rate of external galaxies can be combined with physical and chemical modeling of these systems to derive interesting information on their evolution and dark matter haloes, the details of which furnish the boundary conditions within which the galaxies evolve." 2) From the observed abundance ratios of Ursa Minor. in combination with the physies of gas Hows and our chemical models. we find strong suggestions that this galaxy. often thought of as the prototypical old. single burst and low metallicity dSph. might in fact have experienced a complex star formation history.," 2) From the observed abundance ratios of Ursa Minor, in combination with the physics of gas flows and our chemical models, we find strong suggestions that this galaxy, often thought of as the prototypical old, single burst and low metallicity dSph, might in fact have experienced a complex star formation history." This has remained hidden from cirect studies of its resolved stellar population by its large age. ie. evervthing happened more than 10 Cars ago. but it was not simple.," This has remained hidden from direct studies of its resolved stellar population by its large age, i.e. everything happened more than 10 Gyrs ago, but it was not simple." 3) We founcl evidence for a slight unclerestimate of Hus asthetotalextent of their dark halos or ofa significant metal rich ejecta. with reality probably falling somewhere in between.," 3) We found evidence for a slight underestimate of $R_{tidal}$ as the total extent of their dark halos or of a significant metal rich ejecta, with reality probably falling somewhere in between." 4) Comparison of the predicted abundance ratios with the available cata shows a broad consistenev of our chemical and physical modeling with the relevant observations., 4) Comparison of the predicted abundance ratios with the available data shows a broad consistency of our chemical and physical modeling with the relevant observations. 5) X simple physical criterion to estimate when a dSsph system might sustain extended star formation. as opposed to being subject to a single burst of activity is presented. which neatly separates into those two classes the ealaxies we studied.," 5) A simple physical criterion to estimate when a dSph system might sustain extended star formation, as opposed to being subject to a single burst of activity is presented, which neatly separates into those two classes the galaxies we studied." The authors wish to thank the referee. Andrea Ferrara. for a very careful reacing of the manuscript. and for helpful sugeestions which improved the clarity and quality. of the presentation.," The authors wish to thank the referee, Andrea Ferrara, for a very careful reading of the manuscript, and for helpful suggestions which improved the clarity and quality of the presentation." The work of L. Carigi was partially supported by DOGADA/UNAM through project IN-109696., The work of L. Carigi was partially supported by DGAPA/UNAM through project IN-109696. Carigi thanks the Institute of Astronomy. Cambridge. for a summer visitors grant.," Carigi thanks the Institute of Astronomy, Cambridge, for a summer visitors grant." When a low-mass star (0.5—2M. ) evolves olf the main sequence and up the red giant branch (RGB). its outer convective envelope extends inward. probing the CN-processed region ol the hvdrogen-burning core and propagating (he processed material up to the stellar surface.,"When a low-mass star $0.8-2M_\odot$ ) evolves off the main sequence and up the red giant branch (RGB), its outer convective envelope extends inward, probing the CN-processed region of the hydrogen-burning core and propagating the processed material up to the stellar surface." " Standard stellar evolution models predict (his ""dlredge-up"" to result in a decrease of the surface I2C/PC and PC/!N ratios on the stellar surface (Iben1967).", Standard stellar evolution models predict this “dredge-up” to result in a decrease of the surface $^{12}$ $^{13}$ C and $^{12}$ $^{14}$ N ratios on the stellar surface \citep{Iben:67}. . While an extensive body of observational evidence grew demonstrating that sueh abundance changes do indeed occur. the changes observed were often more extreme than evolutionary model predictions (see.e.g..reviewsbyIben&Renzini1984:Charbonnel2005;Chanameéetal.2005).," While an extensive body of observational evidence grew demonstrating that such abundance changes do indeed occur, the changes observed were often more extreme than evolutionary model predictions \citep[see, e.g., reviews by][]{Iben.Renzini:84,Charbonnel:05,Chaname.etal:05}." . The more salient clisagreements were for metal-poor field aud globular cluster giants. for which the PC /UC ratio approaches the CN-cvele equilibrium value of ~4 2001)..," The more salient disagreements were for metal-poor field and globular cluster giants, for which the $^{12}$ $^{13}$ C ratio approaches the CN-cycle equilibrium value of $\sim 4$ \citep[e.g.\ ][]{Suntzeff.Smith:91,Shetrone.etal:93, Shetrone:96,Carretta.etal:00,Gratton.etal:00,Keller.etal:01}." Since the realisation that both PC/PC and PC/'EN ratios decrease with increasing luminosity along the RGB (e.g.Gilroy&Brown1991:Ixraft.1994:Charbonneletal.1998:Grattonetal.2000:Ixeller 2001).. a variety of mechanisms (o produce extra mixing between core and envelope on the RGB have been proposed to explain the observations (see.e.g..Angelouetal.2011.forarecentsummary)..," Since the realisation that both $^{12}$ $^{13}$ C and $^{12}$ $^{14}$ N ratios decrease with increasing luminosity along the RGB \citep[e.g.\ ][]{Gilroy.Brown:91,Kraft:94,Charbonnel.etal:98,Gratton.etal:00,Keller.etal:01}, a variety of mechanisms to produce extra mixing between core and envelope on the RGB have been proposed to explain the observations \citep[see, e.g.,][for a recent summary]{Angelou.etal:11}." Of these. the thermohaline instability pointed out by Charbonnel&Zahn(2007b.seealsoEggletonetal.2006 who first noted the molecular weight inversion (hal causes appears most promising.," Of these, the thermohaline instability pointed out by \citet[][see also \citealt{Eggleton.etal:06} who first noted the molecular weight inversion that causes appears most promising." " The instability sets in bevond the RGB ""bumpthe point in the RGB huninosity function where the oulward progress of the II-burning shell encounters the compositionally uniform lavers resulting from the deepest extent of convection during the first dredge-up.", The instability sets in beyond the RGB “bump”—the point in the RGB luminosity function where the outward progress of the H-burning shell encounters the compositionally uniform layers resulting from the deepest extent of convection during the first dredge-up. " It results from the mean molecular weight of this region exceeding that of a laver just above the II-burning shell in which the mean molecular weight is reduced by the reaction ""He(He.2p)IHe 1971)."," It results from the mean molecular weight of this region exceeding that of a layer just above the H-burning shell in which the mean molecular weight is reduced by the reaction $^3$ $^3$ $^4$ He \citep{Abraham.Iben:70,Ulrich:71}." . several recent studies have discussed thermohaline mixing and ils apparent success in comparisons of model predictions with observed abundances on the RGB (e.g.Charbonnel&2010b:Angelouetal. 2011).," Several recent studies have discussed thermohaline mixing and its apparent success in comparisons of model predictions with observed abundances on the RGB \citep[e.g.][]{Charbonnel.Zahn:07,Recio-Blanco.De_Laverny:07, Stancliffe.etal:09,Charbonnel.Lagarde:10,Cantiello.Langer:10,Denissenkov:10,Smiljanic.etal:10,Tautvaisiene.etal:10b,Angelou.etal:11}." . Thermohaline mixing on the RGB changes both the surface IPC and PO/UN ratios aller (he end of the first dredge-up. in contrast to classical models that do not include extra mixing.," Thermohaline mixing on the RGB changes both the surface $^{12}$ $^{13}$ C and $^{12}$ $^{14}$ N ratios after the end of the first dredge-up, in contrast to classical models that do not include extra mixing." In principle. comparison of predicted and observed values of both ratios should provide a more stringent test of the theory than either ratio alone.," In principle, comparison of predicted and observed values of both ratios should provide a more stringent test of the theory than either ratio alone." The IC /PC vatio can usually be determined [rom CN molecular features for RGB stars with a precision of ~20% , The $^{12}$ $^{13}$ C ratio can usually be determined from CN molecular features for RGB stars with a precision of $\sim 20$ which were essentially the same in both cases. aud not upon star formation histories.,"which were essentially the same in both cases, and not upon star formation histories." Since a very clear distinction appears in the moclel parameters between the “burst” and the 7complex galaxies we treated. one can try to trace this clear dichotomyv. to intuitive physical dilferences between the two sets of objects.," Since a very clear distinction appears in the model parameters between the “burst” and the “complex” galaxies we treated, one can try to trace this clear dichotomy to intuitive physical differences between the two sets of objects." A zero order criterion that neatly. mirrors this division is eiven below., A zero order criterion that neatly mirrors this division is given below. lt is clear that the gravitational potential energy. of the gas component will scale with the total gravitational enerev of the system. which will scale with Ααfron:," It is clear that the gravitational potential energy of the gas component will scale with the total gravitational energy of the system, which will scale with $M_{total}/R_{total}$." On the other hand. the thermal energv of the eas will scale with the star formation rate of the svstem. considering the star formation episodes of these galaxies to have been of comparable duration. we can expect the criterion 7?—(MicraBiss)SEuuu do divide the sample between the single burst and the complex galaxies.," On the other hand, the thermal energy of the gas will scale with the star formation rate of the system, considering the star formation episodes of these galaxies to have been of comparable duration, we can expect the criterion $P=(M_{total}/R_{total})/SFR_{max}$ to divide the sample between the single burst and the complex galaxies." Indeed. taking Mo; equal to the dynamical masses given. by. Mateo (1998). in units of 10A7... yaa equal to the inferred. tidal radius. in units of κρο and. S220. given by the maximum of the LIGY results for cach galaxy. in units of 107A4./Cyr. we obtain 2 = 17.0. 16.0. 11.0 and 3.8. for Carina. Leo LI. Leo ILE and Ursa Minor. respectively.," Indeed, taking $M_{total}$ equal to the dynamical masses given by Mateo (1998), in units of $10^{6} M_{\odot}$, $R_{total}$ equal to the inferred tidal radius, in units of kpc, and $SFR_{max}$ given by the maximum of the HGV results for each galaxy, in units of $10^{5} M_{\odot}/Gyr$, we obtain $P$ = 17.0, 16.0, 11.0 and 3.8, for Carina, Leo I, Leo II and Ursa Minor, respectively." Thus. despite there being no clear distinction in total masses. luminosities or tidal radii. the parameter 2? clearly separates the two groups.," Thus, despite there being no clear distinction in total masses, luminosities or tidal radii, the parameter $P$ clearly separates the two groups." We can derive the empirical limit of P7(12.15) asa requirement for à να spheroidal galaxy to have extended. episodes of star formation., We can derive the empirical limit of $P>(12-15)$ as a requirement for a dwarf spheroidal galaxy to have extended episodes of star formation. " In this wav. knowledge of AM,Brora and of the integrated Luminosity of a dSph galaxy would sullice to give a first indication of the temporal structure of its SER. with SEBI, estimated from the total luminosity and the age of the universe."," In this way, knowledge of $M_{total}, R_{total}$ and of the integrated luminosity of a dSph galaxy would suffice to give a first indication of the temporal structure of its SFR, with $SFR_{max}$ estimated from the total luminosity and the age of the universe." The division of burst and complex galaxies in our sample through the P criterion. also suggests that the star forming regime of Carina. Leo | and galaxies of their same class. might have actually been regulated mostly by internal processes.," The division of burst and complex galaxies in our sample through the $P$ criterion, also suggests that the star forming regime of Carina, Leo I and galaxies of their same class, might have actually been regulated mostly by internal processes." Perhaps the secondary accretion episode is in fact the re-aceretion of the same gas that was ejected bv the first wind. plausibly held in an extended. reservoir.," Perhaps the secondary accretion episode is in fact the re-accretion of the same gas that was ejected by the first wind, plausibly held in an extended reservoir." At this point the boundary. conditions fixed by the Milky Way would. determine the details of subsequent. accretion events., At this point the boundary conditions fixed by the Milky Way would determine the details of subsequent accretion events. In the above scenario the metallicities of the second wind would be even higher than what the model predicts., In the above scenario the metallicities of the second wind would be even higher than what the model predicts. The inclusion. of the Ursa Minor. variant. model into this criterion would imply low values for ο{Ενω in this system. suggesting a very extended SEI history. all bevond LO Gyr.," The inclusion of the Ursa Minor variant model into this criterion would imply low values for $SFR_{max}$ in this system, suggesting a very extended SFR history, all beyond 10 Gyr." Finally. we present in figure S the total ejected masses in the winds of models «dm. for all the galaxies.," Finally, we present in figure 8 the total ejected masses in the winds of models .dm, for all the galaxies." Phe scconc winds in Carina and Leo LE are shown multiplied bv a factor of 2. to distinguish them from the first ones in the figure.," The second winds in Carina and Leo I are shown multiplied by a factor of 2, to distinguish them from the first ones in the figure." Ht can be seen that the second wind develops in material which has been enriched by the SNla events formed also during the firs burst. together with all SN types of the second. burst.," It can be seen that the second wind develops in material which has been enriched by the SNIa events formed also during the first burst, together with all SN types of the second burst." We give also the metallicities and elemental ratios of this ejecta. relevant to problems of metal enrichment in the halo. ane in treating the contribution of svstems similar to the loca dSph’s in the more general context of metal enrichment in clusters and in the high redshift universe. were such smal svstems in [act dominate the luminosity function of galaxies.," We give also the metallicities and elemental ratios of this ejecta, relevant to problems of metal enrichment in the halo, and in treating the contribution of systems similar to the local dSph's in the more general context of metal enrichment in clusters and in the high redshift universe, were such small systems in fact dominate the luminosity function of galaxies." This allows us to identify the ranges of abuncances anc abundance ratios likely to be relevant in the problems listec above., This allows us to identify the ranges of abundances and abundance ratios likely to be relevant in the problems listed above. A final caveat must be mentioned in connection with our wind criterion where the energy. produced by the SNae is compared to the total gravitational potential energv. of the halo of the svstems being. treated., A final caveat must be mentioned in connection with our wind criterion where the energy produced by the SNae is compared to the total gravitational potential energy of the halo of the systems being treated. In. Mori. Ferrara ancl Macau (2001) careful hydrodynamical simulations of SN explosions in small galaxies are performed. reaching the conclusion that. only about of the ejeetecl energy. is available to heat and. push the ESAT around.," In Mori, Ferrara and Madau (2001) careful hydrodynamical simulations of SN explosions in small galaxies are performed, reaching the conclusion that only about of the ejected energy is available to heat and push the ISM around." This. result derives mostly from considering radiative losses. and the clleets of the geometry of the problem. SN. exploding in the outskirts of the galaxy will loose a fraction. of their energv similar to the solid. angle over which the galaxy is not seen.," This result derives mostly from considering radiative losses, and the effects of the geometry of the problem, SN exploding in the outskirts of the galaxy will loose a fraction of their energy similar to the solid angle over which the galaxy is not seen." The precise ellicicney factors for SN. explosions necessarily depend on the details of how the SN explosions are cistributed. what dark matter profile is adopted and how stronely the SNae are grouped into associations.," The precise efficiency factors for SN explosions necessarily depend on the details of how the SN explosions are distributed, what dark matter profile is adopted and how strongly the SNae are grouped into associations." The results of Mori. Ferrara ancl Macau (2001) are however indicative of an ellicieney factor of between unity and a third applving to the cases we are treating here.," The results of Mori, Ferrara and Madau (2001) are however indicative of an efficiency factor of between unity and a third applying to the cases we are treating here." This introduces. some uncertainties into our results. but not enough to change the," This introduces some uncertainties into our results, but not enough to change the" predominately through episodic accretion events that act to lower their spin.,predominately through episodic accretion events that act to lower their spin. Using cosmological simulations which followed the buildup of large SAIBIs at 2=6. 7. showed that black hole mergers can coutribute to the spin-dowu of SMIBIIs as well. resulting in low radiative efficiencies and rapid growth.," Using cosmological simulations which followed the buildup of large SMBHs at $z=6$ , \citet{Sijackietal09} showed that black hole mergers can contribute to the spin-down of SMBHs as well, resulting in low radiative efficiencies and rapid growth." A decrease iu radiative efficiency must be reconciled with observations of am lucreasc in the fraction of radio-loud quasars with decreasing redshift (?7).. which would suggest SMDIIS with larger spins (and hence larger efficieucies) at low-:.," A decrease in radiative efficiency must be reconciled with observations of an increase in the fraction of radio-loud quasars with decreasing redshift \citep{Jiangetal07}, which would suggest SMBHs with larger spins (and hence larger efficiencies) at $z$." Therefore. nuderstauding the behavior of angular niomenutun iu the circunmnuclear region is au muportaut part of modeliue accretion. and subsequently ACN feedback.," Therefore, understanding the behavior of angular momentum in the circumnuclear region is an important part of modeling accretion, and subsequently AGN feedback." Suuulatious that follow the erowth of SMDIIs over cosnmiological times. or over the duration of a galaxy uereer. often cannot follow the cieununuuclear regions of galaxies with lieh enough resolution to describe he accretion flow in detail.," Simulations that follow the growth of SMBHs over cosmological times, or over the duration of a galaxy merger, often cannot follow the circumnuclear regions of galaxies with high enough resolution to describe the accretion flow in detail." Such simulations iuust uake approximations for the accretion rates using the xoperties of the galaxies on scales that are resolved., Such simulations must make approximations for the accretion rates using the properties of the galaxies on scales that are resolved. A conimuion technique is to assume that the unresolved disk is fed by Boudi-type accretion (227)... as in for exiuuple he sioothed particle Lydrodvuaimics simulations of ? who estimate the accretion rate based on the xoperties of the eas on a scale of ~ 100pc.," A common technique is to assume that the unresolved disk is fed by Bondi-type accretion \citep{HoyleLyttleton39, BondiHoyle44, Bondi52}, as in for example the smoothed particle hydrodynamics simulations of \citet{Springeletal05a} who estimate the accretion rate based on the properties of the gas on a scale of $\sim100 \dim{pc}$." The assuniptiou of Doudi accretion appears to be reasonable or following evolution over cosmiolosgical times. where he average accretion rate onto the black hole caunot © nore than the average accretion rate through iu radius. since the fuel supply is limited by huge scales.," The assumption of Bondi accretion appears to be reasonable for following evolution over cosmological times, where the average accretion rate onto the black hole cannot be more than the average accretion rate through any radius, since the fuel supply is limited by large scales." Previous cosinological simulations have been successful in reproducing observed population demographics aud trends. such as the black hole mass function aud galaxy colors aud morphologics (asiu.c.e..2??)..," Previous cosmological simulations have been successful in reproducing observed population demographics and trends, such as the black hole mass function and galaxy colors and morphologies \citep[as in, e.g.,][]{DiMatteo08, Croftetal09, McCarthyetal09}." However. for detailed studies of the erowth and evolution of individual SMBUs or of the coupling between ACN feedback and the black hole accretion rate. more accurate descriptions of the accretion rate aud its dependence on the scale features of the host galaxy are desirable.," However, for detailed studies of the growth and evolution of individual SMBHs or of the coupling between AGN feedback and the black hole accretion rate, more accurate descriptions of the accretion rate and its dependence on the small-scale features of the host galaxy are desirable." Suialbseale simulations have addressed seas cyaics iu subealactic-scale disks with high resolution (7277777).. finding the development of a turbulent. nulti-pliase interstellar imuedimm.," Small-scale simulations have addressed gas dynamics in subgalactic-scale disks with high resolution \citep{Fukuda00, Wada01, WadaNorman01,Escala07,WadaNorman07,KawakatuWada08}, finding the development of a turbulent, multi-phase interstellar medium." The approximation of Donudi accretion in such an environment is not necessarily invalid., The approximation of Bondi accretion in such an environment is not necessarily invalid. 7 have shown that modified forms of the Boudi prescription cau describe accretion iu turbulent environments., \citet{Krumholzetal05} have shown that modified forms of the Bondi prescription can describe accretion in turbulent environments. Α simulation must be equipped to model the properties of the turbulence in order to cluplov the amocified Bondi prescription., A simulation must be equipped to model the properties of the turbulence in order to employ the modified Bondi prescription. If the eas contains a significant amount of angular momenta. the ποαπο DBoucdi prescription gives inaccurate estimates of the accretion rate as well (??).. Ul," If the gas contains a significant amount of angular momentum, the unmodified Bondi prescription gives inaccurate estimates of the accretion rate as well \citep{ProgaBegelman03, Krumholzetal06}." owever. even modified Boudi prescriptions become inapplicable in the case of the sclferavitating. rotationally supported disks that are likely to form as large amounts of eas are driven imd in high-redshift ealaxies.," However, even modified Bondi prescriptions become inapplicable in the case of the self-gravitating, rotationally supported disks that are likely to form as large amounts of gas are driven inward in high-redshift galaxies." As the use of adaptive techniques increasingly improves the resolution of cosmological stmmlatious. accretion onto black holes can no longer be described by approximate prescriptions such as Bondi accretion.," As the use of adaptive techniques increasingly improves the resolution of cosmological simulations, accretion onto black holes can no longer be described by approximate prescriptions such as Bondi accretion." Iu the present paper. we use cosmological adaptive mesh refinement simulations with a large dynamic rauge to study the transport of gas and angular moinceutuii through the circumuuelear disk of au SAIBIT host galaxy over fune.," In the present paper, we use cosmological adaptive mesh refinement simulations with a large dynamic range to study the transport of gas and angular momentum through the circumnuclear disk of an SMBH host galaxy over time." The goal is to provide a description of accretion that can be compared to prescriptions typically applied in larger scale simulations., The goal is to provide a description of accretion that can be compared to prescriptions typically applied in larger scale simulations. It will be shown that in the limiting case of relative quiesceuce (c.e.. in between morecr events and without ACN feedback) acerction is a stochastic rather than a coutiuuous process.," It will be shown that in the limiting case of relative quiescence (e.g., in between merger events and without AGN feedback) accretion is a stochastic rather than a continuous process." The method behind the simulations used here is described in detail iu 7. hereafter Paper I. aud in ?..," The method behind the simulations used here is described in detail in \citet{Levineetal08}, hereafter Paper I, and in \citet{MyThesis}." In Section 2.. we briefiv sununarize the details of the simulations.," In Section \ref{sec:simtr}, we briefly summarize the details of the simulations." The results of the simulations are given m Sections 3—5.. iucludiug an analysis of the mass accretion rate and the angular momentum of the eas in the circummnuclear region of the ealaxy.," The results of the simulations are given in Sections \ref{sec:mass}- \ref{sec:mom}, including an analysis of the mass accretion rate and the angular momentum of the gas in the circumnuclear region of the galaxy." Finally. we sinnaarize aud discuss the results in Section 6..," Finally, we summarize and discuss the results in Section \ref{sec:disctr}." " The simulations presented here were run usus the Adaptive Refinement Tree CART) code (2??).. following the ""zoourin method described in detail iu Paper I. The code follows gas bydrodvuaiics on an adaptive mesh and iucludes dark matter aud stellar particles."," The simulations presented here were run using the Adaptive Refinement Tree (ART) code \citep{Kravtsovetal97, KravtsovPhD, Kravtsovetal02}, following the “zoom-in” method described in detail in Paper I. The code follows gas hydrodynamics on an adaptive mesh and includes dark matter and stellar particles." The gas cooling and heating rates are tabulated as functions of density. temperature. metallicity. aud redshift over the emperature range 107«Tc10K wing (2).. which accounts for the metallicity of the gas. the orluation of molecular lydrogen aud cosmic dust. aud UV heating due to cosmological ionizing background.," The gas cooling and heating rates are tabulated as functions of density, temperature, metallicity, and redshift over the temperature range $10^20.2 for its redshift was derived bv ? based on the absence of anv extended. structure of a host galaxy. in a direct image taken with the 3.5m Calar Alto telescope., A lower limit of $z>0.2$ for its redshift was derived by \citet{StickelKuhr93} based on the absence of any extended structure of a host galaxy in a direct image taken with the 3.5m Calar Alto telescope. The 5 Gllz VLBI image o£ ? shows a jet emerging from, The 5 GHz VLBI image of \citet{Taylor94} shows a jet emerging from light curves presented at 7 aud 131uu have selected data correspondiug toue spacings greater than,light curves presented at 7 and 13mm have selected data corresponding to spacings greater than In order to derive most conservative errors for the RV semi-amplitude AK and the system velocity y we fixed the most likely period and created new RV datasets with a bootstrapping algorithm.,In order to derive most conservative errors for the RV semi-amplitude $K$ and the system velocity $\gamma$ we fixed the most likely period and created new RV datasets with a bootstrapping algorithm. Ten thousand RV datasets were obtained by random sampling with replacement from the original dataset., Ten thousand RV datasets were obtained by random sampling with replacement from the original dataset. In each case an orbital solution was calculated in the way described above., In each case an orbital solution was calculated in the way described above. The standard deviation of these results was adopted as error estimate., The standard deviation of these results was adopted as error estimate. The RV curves are given in Figs., The RV curves are given in Figs. 2 and 3.., \ref{rv1} and \ref{rv2}. The residuals of the RV curves after subtracting the best orbital solution are of the same order in all cases (see Figs. 2.. 3)).," The residuals of the RV curves after subtracting the best orbital solution are of the same order in all cases (see Figs. \ref{rv1}, \ref{rv2}) )." The aceuracy is limited by the resolution of the spectra and their signal-to-noise., The accuracy is limited by the resolution of the spectra and their signal-to-noise. Combining data obtained with different instruments is also expected to contribute to the systematic error., Combining data obtained with different instruments is also expected to contribute to the systematic error. Nevertheless. we found that all orbital solutions given here are significant (see Table 4)).," Nevertheless, we found that all orbital solutions given here are significant (see Table \ref{tab:sig}) )." Edelmann et al. (2005)), Edelmann et al. \cite{edelmann05}) ) reported the discovery of small eccentricities (e.< 0.06) in the orbital solutions of five close hot subdwarf binaries., reported the discovery of small eccentricities $e<0.06$ ) in the orbital solutions of five close hot subdwarf binaries. All of these binaries are expected to have formed via common envelope ejection., All of these binaries are expected to have formed via common envelope ejection. Although the CE phase is very short. it should nevertheless be very efficient in circularising the binary orbits.," Although the CE phase is very short, it should nevertheless be very efficient in circularising the binary orbits." That is why the discovery of Edelmann et al. (2005)), That is why the discovery of Edelmann et al. \cite{edelmann05}) ) came as a surprise., came as a surprise. Napiwotzki et al. (, Napiwotzki et al. ( in prep.),in prep.) found more such systems with even shorter periods., found more such systems with even shorter periods. In order to investigate whether the orbital solutions of our programme binaries can be improved by allowing for eccentricity. we fitted eccentric orbits to our radial velocity data and performed statistical tests (F-test. see Pringle 1975.. and the Bayesian information criterion BIC) to check whether eccentric solutions are significant or not.," In order to investigate whether the orbital solutions of our programme binaries can be improved by allowing for eccentricity, we fitted eccentric orbits to our radial velocity data and performed statistical tests (F-test, see Pringle \cite{pringle75}, and the Bayesian information criterion BIC) to check whether eccentric solutions are significant or not." In all cases the circular solutions were preferred., In all cases the circular solutions were preferred. However. the derived upper limits for the orbital eccentricities range from 0.15 to 0.3. which means that low eccentricities as the ones reported by Edelmann et al. (2005))," However, the derived upper limits for the orbital eccentricities range from $0.15$ to $0.3$, which means that low eccentricities as the ones reported by Edelmann et al. \cite{edelmann05}) )" cannot be firmly excluded., cannot be firmly excluded. Atmospheric parameters have been determined by fitting model spectra to the hydrogen Balmer and helium lines in the way described in Geier et al. (2007))., Atmospheric parameters have been determined by fitting model spectra to the hydrogen Balmer and helium lines in the way described in Geier et al. \cite{geier07}) ). The single spectra have been corrected for their orbital motion and coadded., The single spectra have been corrected for their orbital motion and coadded. " Depending on the effective temperature of the stars. LTE models with solar metallicity (7a,« 30000K) or ten times solar metallicity (Tay>30000K) have been used."," Depending on the effective temperature of the stars, LTE models with solar metallicity $T_{\rm eff}<30\,000\,{\rm K}$ ) or ten times solar metallicity $T_{\rm eff}>30\,000\,{\rm K}$ ) have been used." The enhanced metallicity models account for the radiative levitation of heavy elements in the diffusion dominated atmospheres (for a detailed discussion see O'Toole Heber 2006))., The enhanced metallicity models account for the radiative levitation of heavy elements in the diffusion dominated atmospheres (for a detailed discussion see O'Toole Heber \cite{otoole06}) ). In order to investigate systematic effects. introduced by the individual instruments. especially the different resolutions and wavelength coverages. the parameters have beer derived separately from spectra taken with different instruments.," In order to investigate systematic effects introduced by the individual instruments, especially the different resolutions and wavelength coverages, the parameters have been derived separately from spectra taken with different instruments." As can be seen in Table Al no constant systematic shifts are present., As can be seen in Table \ref{tab:atm} no constant systematic shifts are present. The weighted means have been calculated and adopted as final solutions., The weighted means have been calculated and adopted as final solutions. Typical systematic errors introduced by different model grids are of the order of 40.05 in logg and 500K in Toy (e.g. Lisker et al. 2005:;," Typical systematic errors introduced by different model grids are of the order of $\pm0.05$ in $\log{g}$ and $500\,{\rm K}$ in $T_{\rm eff}$ (e.g. Lisker et al. \cite{lisker05};" Geier et al. 2007))., Geier et al. \cite{geier07}) ). " These uncertainties were added in quadrature to the statistical errors,", These uncertainties were added in quadrature to the statistical errors. Three of our programme stars have been classified as hot subdwarfs by Eisenstein et al. (2006)).," Three of our programme stars have been classified as hot subdwarfs by Eisenstein et al. \cite{eisenstein06}) )," but the authors pointed out that the atmospheric parameters of the sdO/Bs given in their catalogue are not accurate., but the authors pointed out that the atmospheric parameters of the sdO/Bs given in their catalogue are not accurate. All stars of our sample are situated on or near the Extreme Horizontal Branch (EHB) and are most likely core-helium burning stars (see Fig. 5)., All stars of our sample are situated on or near the Extreme Horizontal Branch (EHB) and are most likely core-helium burning stars (see Fig. \ref{tefflogg}) ). Since the orbital periods of these binaries are short. they can only have formed via common envelope ejection.," Since the orbital periods of these binaries are short, they can only have formed via common envelope ejection." Population synthesis models (Han et al. 2002.. 2003))," Population synthesis models (Han et al. \cite{han02}, \cite{han03}) )" predict a mass range of ων=0.37—0.48Μ. for sdBs in binaries formed in this way.," predict a mass range of $M_{\rm sdB}=0.37-0.48\,M_{\rm \odot}$ for sdBs in binaries formed in this way." The mass distribution shows a sharp peak at a mass of about 0.47M...," The mass distribution shows a sharp peak at a mass of about $0.47\,{\rm M_{\odot}}$." This theoretical mass distribution is consistent with analyses of close binary systems (e.g. Geter et al. 2007::, This theoretical mass distribution is consistent with analyses of close binary systems (e.g. Geier et al. \cite{geier07}; For et al. 2010)), For et al. \cite{for10}) ) as well as asteroseismic analyses of pulsating sdBs (see Charpinet et al., as well as asteroseismic analyses of pulsating sdBs (see Charpinet et al. 2008 and references therein)., \cite{charpinet08} and references therein). If the progenitor star was massive enough on the main sequence to ignite core helium-burning under non-degenerate conditions. the sdB mass may be as low as 0.3M...," If the progenitor star was massive enough on the main sequence to ignite core helium-burning under non-degenerate conditions, the sdB mass may be as low as $0.3\,{\rm M_{\odot}}$." A small fraction of the sdB population is predicted to be formed in that way (Han et al. 2002.. 2003)).," A small fraction of the sdB population is predicted to be formed in that way (Han et al. \cite{han02}, \cite{han03}) )." Especially for sdB binaries with massive companions this formation scenario may become important., Especially for sdB binaries with massive companions this formation scenario may become important. Since the programme stars are single-lined spectroscopic binaries. only their mass functions can be calculated.," Since the programme stars are single-lined spectroscopic binaries, only their mass functions can be calculated." " Although(Meomp the RV semi-amplitude K and the period P can be derived from the RV curve. the sdB mass Αμ. the companion mass Mi, and the inclination angle / remain free parameters."," Although the RV semi-amplitude $K$ and the period $P$ can be derived from the RV curve, the sdB mass $M_{\rm sdB}$, the companion mass $M_{\rm comp}$ and the inclination angle $i$ remain free parameters." Adopting Mug=0.437M. and i<90° we derive a lower limit for the companion mass (see refrvmasses )).," Adopting $M_{\rm sdB}=0.47\,{\rm M_{\odot}}$ and $i<90^{\rm \circ}$ we derive a lower limit for the companion mass (see \\ref{rvmasses}) )." For minimmum compaion masses lower than 0.45M.. the companion may be a late type main sequence star or a compact object like a WD.," For mum companion masses lower than $0.45\,M_{\rm \odot}$ the companion may be a late type main sequence star or a compact object like a WD." Main sequence stars in this mass range are outshined by the sdBs and not visible in optical spectra (Lisker et al. 2005))., Main sequence stars in this mass range are outshined by the sdBs and not visible in optical spectra (Lisker et al. \cite{lisker05}) ). " That is the reason why the companions"" nature still remains unknown for most of the 80 known sdB systems with low minimum compaion masses (see Fig. 7)).", That is the reason why the companions' nature still remains unknown for most of the $\simeq$ 80 known sdB systems with low minimum companion masses (see Fig. \ref{periodK}) ). If on the, If on the to acknowledee the hospitality of Stanford. University during a visit in March 2011 for work on the data set recorded bx the MDI instrument on the SOIIO spacecraft.,to acknowledge the hospitality of Stanford University during a visit in March 2011 for work on the data set recorded by the MDI instrument on the SOHO spacecraft. SOIIO is a project of international cooperation between ESA and NASA., SOHO is a project of international cooperation between ESA and NASA. The identification algorithm has been developed in a pragmatic way. wilh the selection criteria. aud. (hresholds represented by a set of [ree parameters.," The identification algorithm has been developed in a pragmatic way, with the selection criteria and thresholds represented by a set of free parameters." The values of these [ree parameters have been manually optimized and Chen fixed. by comparing the program identifications with visual inspections for a selection of magnetogranms representing all phases of solar activity. [rom the most active and crowded phase. to the most quiet phase.," The values of these free parameters have been manually optimized and then fixed, by comparing the program identifications with visual inspections for a selection of magnetograms representing all phases of solar activity, from the most active and crowded phase, to the most quiet phase." The parameters have been optimized such (hat (he same parameter set can be used for all (he magnetograms. for all phases of the solar activity cycle.," The parameters have been optimized such that the same parameter set can be used for all the magnetograms, for all phases of the solar activity cycle." Once (his manual program optimization has been done. the rest is automatic.," Once this manual program optimization has been done, the rest is automatic." The optimized IDL program is run in batch mode in a loop analysing each of the 73.838 MDI magnetograms one bv one.," The optimized IDL program is run in batch mode in a loop analysing each of the 73,838 MDI magnetograms one by one." For each analvsed magnetogram an IDL save file is written that contains all the extracted bipolar region parameters with (he relevant housekeeping data., For each analysed magnetogram an IDL save file is written that contains all the extracted bipolar region parameters with the relevant housekeeping data. The effective computing time needed to run this large IDL batch job at Stanford was about 2 weeks., The effective computing time needed to run this large IDL batch job at Stanford was about 2 weeks. (2008).. are a crucial element of the next generation analysis toolbox for galaxy cluster studies.,", are a crucial element of the next generation analysis toolbox for galaxy cluster studies." Placing well-motivated priors on the shapes of galaxy clusters is crucial to future work modelling the most massive structures in the universe. and understanding both their characteristics as individuals and a population.," Placing well-motivated priors on the shapes of galaxy clusters is crucial to future work modelling the most massive structures in the universe, and understanding both their characteristics as individuals and a population." While structure formation simulations provide a good starting point for such priors. using their predictions does of course bias all results towards agreement with those simulations.," While structure formation simulations provide a good starting point for such priors, using their predictions does of course bias all results towards agreement with those simulations." One good alternative is to use a distribution of 2d axis ratios observed in a sample of galaxy clusters. preferably from muss-sensitive methods (e.g. lensing mass reconstructions) and from this construct a 3d shape prior.," One good alternative is to use a distribution of 2d axis ratios observed in a sample of galaxy clusters, preferably from mass-sensitive methods (e.g. lensing mass reconstructions) and from this construct a 3d shape prior." For this. even the simplest elliptical lensing models would be adequate. as CK07 showed that even a Singular Isothermal Ellipsoid model consistently recovered projected axis ratios accurately. even if the true lensing profile was NFW tthis is not true for other model parameters).," For this, even the simplest elliptical lensing models would be adequate, as CK07 showed that even a Singular Isothermal Ellipsoid model consistently recovered projected axis ratios accurately, even if the true lensing profile was NFW (this is not true for other model parameters)." While the necessity and importance of these priors may be discomforting. using standard techniques and simpler models is simply disguising the problem. as such models contain highly-restrictive hidden priors.," While the necessity and importance of these priors may be discomforting, using standard techniques and simpler models is simply disguising the problem, as such models contain highly-restrictive hidden priors." Bayesian techniques such as the one oresented in this paper are simply tools that allow us to better understand the true constraints we can place on physical models. not solutions in themselves to physical problems.," Bayesian techniques such as the one presented in this paper are simply tools that allow us to better understand the true constraints we can place on physical models, not solutions in themselves to physical problems." The broad yosterior probability distributions for the triaxial NEW profiles fit to simulated lensing data in this paper indicate the weakness of our current constraints. and emphasise the need for focus on he careful combination of complementary data types to further constrain galaxy cluster structure models.," The broad posterior probability distributions for the triaxial NFW profiles fit to simulated lensing data in this paper indicate the weakness of our current constraints, and emphasise the need for focus on the careful combination of complementary data types to further constrain galaxy cluster structure models." " To this end. this Bayesian ICMC triaxial NFW fitting method provides. through the prior orobability functions. a statistically robust and straightforward way © combine constraints from data types with very different error ""roperties."," To this end, this Bayesian MCMC triaxial NFW fitting method provides, through the prior probability functions, a statistically robust and straightforward way to combine constraints from data types with very different error properties." This MCMC triaxial NFW fitting method. using fully tested look-up tables to significantly speed up the calculation of the triaxial NFW lensing quantities. can be implemented for a standard weak lensing data set on a single fast processor in about | day. making it fully feasible for use across even the largest existing lens surveys.," This MCMC triaxial NFW fitting method, using fully tested look-up tables to significantly speed up the calculation of the triaxial NFW lensing quantities, can be implemented for a standard weak lensing data set on a single fast processor in about 1 day, making it fully feasible for use across even the largest existing lens surveys." To begin this process. in a companion paper Corless. King.," To begin this process, in a companion paper Corless, King," We have recently shown that in a rotating. turbulence-free ancl isothermal gaseous nebula with a censitv function that maximizes locally. the combined effect of gas drag and pressure eradients at lvclrostatic equilibrium. causes solids to migrate toward the locations ol local density enhancements (IHaghighipour&Boss2003.herealterILDO3)..,"We have recently shown that in a rotating, turbulence-free and isothermal gaseous nebula with a density function that maximizes locally, the combined effect of gas drag and pressure gradients at hydrostatic equilibrium, causes solids to migrate toward the locations of local density enhancements \citep[][hereafter HB03]{Hag03}." The motions of solids in ILDO3 were restricted to the midplane of the nebula and (he variation of the gas density along the direction perpendicular to the midplane was neglected., The motions of solids in HB03 were restricted to the midplane of the nebula and the variation of the gas density along the direction perpendicular to the midplane was neglected. The results of our numerical simulations of (he ανπαΙός of micron-sized dust grains to 100 meter-sized objects indicated (hat the radial motions of such solids could be equite rapid when (heir sizes range from 1 em to 1 m., The results of our numerical simulations of the dynamics of micron-sized dust grains to 100 meter-sized objects indicated that the radial motions of such solids could be quite rapid when their sizes range from 1 cm to 1 m. "The first question arises because of the presence of the large temperature plateau noted earlier, which persists despite the fact that we evolve the system for many cooling times at these radii.","The first question arises because of the presence of the large temperature plateau noted earlier, which persists despite the fact that we evolve the system for many cooling times at these radii." " Clearly, the cooling must be balanced by some form of heating, and since the gas motions are subsonic, the only real candidate is compression heating."," Clearly, the cooling must be balanced by some form of heating, and since the gas motions are subsonic, the only real candidate is compression heating." We estimate the compressional heating timescale as: where y=5/3 and V.v=ice) , We estimate the compressional heating timescale as: where $\gamma = 5/3$ and $\nabla \cdot v = \frac{1}{r^2} \frac{\partial (r^2 v_r)}{\partial r}$. "For simplicity, we only include the radial term, focusing on the role that the cooling flow plays in establishing the temperature plateau (we note that non-radial terms could decrease the heating time in the center, although manual inspection of the velocity indicates that the effect is "," For simplicity, we only include the radial term, focusing on the role that the cooling flow plays in establishing the temperature plateau (we note that non-radial terms could decrease the heating time in the center, although manual inspection of the velocity indicates that the effect is minor)." We plot in Figure 7 the ratio of Over teool. At minor)., We plot in Figure \ref{fig_compress} the ratio of $t_{\rm compress}$ over $t_{\rm cool}$. "early times, over a large range of radius, tcompressfcompress©tcool-"," At early times, over a large range of radius, $t_{\rm compress} \approx t_{\rm cool}$." " The inflow velocities which drive this heating are slight, a few tens of over much of this range, as seen in Figure 3,, rising km/sat small radius as the global cooling catastrophe sets in."," The inflow velocities which drive this heating are slight, a few tens of km/s over much of this range, as seen in Figure \ref{fig_vr}, rising at small radius as the global cooling catastrophe sets in." " This brings us to the second question, the evolution of the gas within the transition radius."," This brings us to the second question, the evolution of the gas within the transition radius." " As the cluster evolves, the cooling rate becomes higher in the center, requiring a larger inflow velocity to provide sufficient compressional heating."," As the cluster evolves, the cooling rate becomes higher in the center, requiring a larger inflow velocity to provide sufficient compressional heating." " When this required velocity exceeds the sound speed, or if the gas becomes rotationally supported, compressional heating can on longer balance cooling and becomes larger than teoo. inside the transition radius."," When this required velocity exceeds the sound speed, or if the gas becomes rotationally supported, compressional heating can on longer balance cooling and $t_{\rm compress}$ becomes larger than $t_{\rm cool}$ inside the transition radius." " ἔοοπιριοςςIf the inflow velocity grew to the sound speed, as would occur for a purely radial evolution, the transition radius would be identified as a sonic point, and inside the gas would freely fall toward the black hole."," If the inflow velocity grew to the sound speed, as would occur for a purely radial evolution, the transition radius would be identified as a sonic point, and inside the gas would freely fall toward the black hole." " We found this to occur in our lower resolution simulations (discussed in more detail below); however, in our best resolved, standard simulation, we find that the cold gas inside the transition radius forms a rotationally supported disk."," We found this to occur in our lower resolution simulations (discussed in more detail below); however, in our best resolved, standard simulation, we find that the cold gas inside the transition radius forms a rotationally supported disk." " This is shown in Figure 8,, which shows an estimate of the rotational velocity of the gas (computed by dividing the magnitude of the total specific angular momentum of the gas in a shell by the radius of that shell), compared to the Keplerian velocity."," This is shown in Figure \ref{fig_rotation}, which shows an estimate of the rotational velocity of the gas (computed by dividing the magnitude of the total specific angular momentum of the gas in a shell by the radius of that shell), compared to the Keplerian velocity." " At late times, inside the transition radius, the gas becomes rotationally supported."," At late times, inside the transition radius, the gas becomes rotationally supported." " In Figure 9,, we show the projected density and density-weighted temperature in the central 330 pc for a slice of gas with a z-thickness of about 16.6 pc."," In Figure \ref{fig_project2}, we show the projected density and density-weighted temperature in the central 330 pc for a slice of gas with a z-thickness of about $16.6$ pc." " This z-projection clearly shows the disk (x- and y-projections — not shown here — clearly demonstrate that this is a thin disk), which has a radius of about 50 pc."," This z-projection clearly shows the disk (x- and y-projections – not shown here – clearly demonstrate that this is a thin disk), which has a radius of about 50 pc." " In fact, in this particular run, we find an inner disk and an outer polar ring, which shows some sign of forming denser fragments; typical densities in the disk are of order 10? cm~?, but note that the disk is not well-resolved and so the detailed disk structure shown here should be treated with caution."," In fact, in this particular run, we find an inner disk and an outer polar ring, which shows some sign of forming denser fragments; typical densities in the disk are of order $10^3$ $^{-3}$, but note that the disk is not well-resolved and so the detailed disk structure shown here should be treated with caution." " In this paper, we have presented results from the highest resolution simulation of the onset of cooling in à cool-core cluster."," In this paper, we have presented results from the highest resolution simulation of the onset of cooling in a cool-core cluster." " We have demonstrated that the flow is remarkably uniform, with thermal instabilities not growing outside of the central few hundred pc, where the temperature drops rapidly at a point we have termed the transition radius."," We have demonstrated that the flow is remarkably uniform, with thermal instabilities not growing outside of the central few hundred pc, where the temperature drops rapidly at a point we have termed the transition radius." " In addition, we have shown that the flow natufrally generates a nearly constant temperature state outside of this transition radius."," In addition, we have shown that the flow natufrally generates a nearly constant temperature state outside of this transition radius." " Inside, à rotationally supported accretion disk forms around the central SMBH."," Inside, a rotationally supported accretion disk forms around the central SMBH." " This time-dependent flow is not in steady state and is not, without additional heating, a solution to the cool core problem."," This time-dependent flow is not in steady state and is not, without additional heating, a solution to the cool core problem." " Nevertheless, we have made substantial progress in delineating exactly when and where cold, dense gas first condenses out of the flow."," Nevertheless, we have made substantial progress in delineating exactly when and where cold, dense gas first condenses out of the flow." " However, there are a number of unanswered questions, including a better understanding of why this solution occurs ??)), a detailed examination of the observational (sectionpredictions of the the final simulation state (section 4.2)), a first attempt to examine the impact of thermal conduction (section ??)) and Type Ia SN heating from stars in the BCG ??))."," However, there are a number of unanswered questions, including a better understanding of why this solution occurs (section \ref{sec:potential}) ), a detailed examination of the observational predictions of the the final simulation state (section \ref{sec:obs}) ), a first attempt to examine the impact of thermal conduction (section \ref{sec:thermal}) ) and Type Ia SN heating from stars in the BCG (section \ref{sec:Ia}) )." " In section ??,, we show that high numerical (sectionresolution is required to obtain these results, and with lower resolution, the transition radius first forms at much larger radius."," In section \ref{sec:resolution}, we show that high numerical resolution is required to obtain these results, and with lower resolution, the transition radius first forms at much larger radius." " Finally, we argue that the results are robust to changes in the initial conditions (section ??)), and then compare these results to previous work (section ??))."," Finally, we argue that the results are robust to changes in the initial conditions (section \ref{sec:nonCC}) ), and then compare these results to previous work (section \ref{sec:comparison}) )." " 'To better understand what determines thestructure of the gas and why there are three regimes seen in the gas density, temperature and pressure profiles in Figure 2,, we carry out an approximate analytic analysis assuming hydrostatic equilibrium, which is valid before the cooling catastrophe happens (or at radii larger than the transition radius) when the inflow velocity v, «ος."," To better understand what determines thestructure of the gas and why there are three regimes seen in the gas density, temperature and pressure profiles in Figure \ref{fig_rho}, we carry out an approximate analytic analysis assuming hydrostatic equilibrium, which is valid before the cooling catastrophe happens (or at radii larger than the transition radius) when the inflow velocity $v_r \ll c_s$ ." In Fig.,In Fig. Lo we show the equivalent. width plane for the N-shaped. radio sources in our spectroscopic sample. superposed with the line dividing the weak-lined and strong-lined classes (solid line) as well as the loci of constant viewing angles as obtained by 7/— from their. simulations (dotted. lines).," \ref{angles} we show the equivalent width plane for the X-shaped radio sources in our spectroscopic sample, superposed with the line dividing the weak-lined and strong-lined classes (solid line) as well as the loci of constant viewing angles as obtained by \citet{L04} from their simulations (dotted lines)." Our optical spectra cover the locations of both and for all but one source | 5002) and we list the measurements in Table 1. (columns (6) and (S)).," Our optical spectra cover the locations of both and for all but one source $+$ 5002) and we list the measurements in Table \ref{general} (columns (6) and (8))." Two important results become evident. from Fig. 1.., Two important results become evident from Fig. \ref{angles}. Firstly. most N-shaped radio sources are viewed at relatively large angles (Óz 357).," Firstly, most X-shaped radio sources are viewed at relatively large angles $\phi \ga 35^{\circ}$ )." This result is supported by their large break values., This result is supported by their large break values. We measure C':0.25 for all but six sources and C':0.4 for roughly half the sample (22/53 sources: see Table 1.. column (4)).," We measure $C\ge0.25$ for all but six sources and $C\ge0.4$ for roughly half the sample (22/53 sources; see Table \ref{general}, column (4))." The observed result. is intuitive given that projection ellects are expected to distort the A-shape of the dilfuse radio emission at small. viewing angles. thus making it dillicult to recognize.," The observed result is intuitive given that projection effects are expected to distort the X-shape of the diffuse radio emission at small viewing angles, thus making it difficult to recognize." Llowever. it also means that strongly relativistically beamed: X-shaped. racio galaxies (i.e... N-shapecl radio quasars) will be dillicult to select based. on radio maps.," However, it also means that strongly relativistically beamed X-shaped radio galaxies (i.e., X-shaped radio quasars) will be difficult to select based on radio maps." Secondly. roughly half the sample.(23/53 sources). is classified as weak-linecl radio-Ioud AGN (CFable 1.. column (5)). with about hall of these objects (11/23. sources) having no or emission lines.," Secondly, roughly half the sample(23/53 sources) is classified as weak-lined radio-loud AGN (Table \ref{general}, column (5)), with about half of these objects (11/23 sources) having no or emission lines." Ες result. is rather suprising., This result is rather suprising. Since X-shaped raclio sources are generally known to have their active pair of lobes terminating in pronounced hot spots. as observed for FR LE radio galaxies. one would expect that. like these. they predominantly. have strong optical emission. lines.," Since X-shaped radio sources are generally known to have their active pair of lobes terminating in pronounced hot spots, as observed for FR II radio galaxies, one would expect that, like these, they predominantly have strong optical emission lines." Are then N-shapecl racio sources equally related to FR Is. which are known to have optical spectra with no or only weak emission lines. or do they simply contain an exceptionally large. number of the otherwise rather rare weak-lined LR. LHs (c.g...22)?7?," Are then X-shaped radio sources equally related to FR Is, which are known to have optical spectra with no or only weak emission lines, or do they simply contain an exceptionally large number of the otherwise rather rare weak-lined FR IIs \citep[e.g.,][]{Lai94, Tad98}?" In order to answer this question we have plotted in Fig., In order to answer this question we have plotted in Fig. 2 the total radio luminosity at 1.43 ClIz versus the absolute IH magnitude for the strong-lined (filled svmbols) and weals-lined. N-shaped: radio galaxies (open symbols). which we subclivicleck based. on the presence or lack of pronounced hotspots in their active lobes into sources. with FRO LH (squares) ancl ambiguous (triangles) radio morphology. respectively.," \ref{ledlow} the total radio luminosity at 1.4 GHz versus the absolute $R$ magnitude for the strong-lined (filled symbols) and weak-lined X-shaped radio galaxies (open symbols), which we subdivided based on the presence or lack of pronounced hotspots in their active lobes into sources with FR II (squares) and ambiguous (triangles) radio morphology, respectively." Luminosities were predominantly taken from ? and the radio morphology judged: visually from the ELIT maps and. where available. also from published. deeper racio maps (seereferencesin.2)..," Luminosities were predominantly taken from \citet{Cheung09} and the radio morphology judged visually from the FIRST maps and, where available, also from published, deeper radio maps \citep[see references in][]{Cheung07a}." We have included only sources viewed at relatively large angles. io. without broad emission lines and withbreak values C':0.25 (46 sources) since in their case relativistic beaming elfects are expected to be negligible.," We have included only sources viewed at relatively large angles, i.e., without broad emission lines and withbreak values $C\ge0.25$ (46 sources), since in their case relativistic beaming effects are expected to be negligible." Then. Fig.," Then, Fig." 2. represents the so-called Ledlow-Owen plot (2).. i.e. extended radio emission versus host galaxy luminosity. in which FR LE and FR 11 galaxies separate (below and above the solid line. respectively).," \ref{ledlow} represents the so-called Ledlow-Owen plot \citep{Led96}, i.e., extended radio emission versus host galaxy luminosity, in which FR I and FR II galaxies separate (below and above the solid line, respectively)." This separation. however. does not occur suddenly but rather via a transition region (?)..," This separation, however, does not occur suddenly but rather via a transition region \citep{Best09}. ." Fig., Fig. 2. shows that the large majority of weak-lined sources straccdle the FR L/Ldividing line. as N-shaped racio ealaxies generally do (???).. with only two | 5332 and J1434| 5906) ancl five objects 0033. | 5002. JOS13| 4347. | 1154. and | 2817) clearly in the FR Hand EIU LE regime. respectively.," \ref{ledlow} shows that the large majority of weak-lined sources straddle the FR I/IIdividing line, as X-shaped radio galaxies generally do \citep{Leahy92, Den02, Cheung09}, with only two $+$ 5332 and $+$ 5906) and five objects $-$ 0033, $+$ 5002, $+$ 4347, $+$ 1154, and $+$ 2817) clearly in the FR II and FR I regime, respectively." All but one of these sources have active lobes with an FR LH radio morphology. whereas | 4347 could be part of the recently identified Neshaped radio population without. pronounced: hotspots and similar to FR Is (7)..," All but one of these sources have active lobes with an FR II radio morphology, whereas $+$ 4347 could be part of the recently identified X-shaped radio population without pronounced hotspots and similar to FR Is \citep{Sar09}." ]t seems then that N-shaped. radio galaxies genuinely represent a transition population. and this in both radio »»wer and emission. line strengths.," It seems then that X-shaped radio galaxies genuinely represent a transition population, and this in both radio power and emission line strengths." This transition is illustrated in detail in Fig. 3.. ," This transition is illustrated in detail in Fig. \ref{nlrlext}, ," where we have plotted. the otal racio Iuminosity at 1.4 Gilg versus the luminosity of he narrow emission line region νεα. the latter calculated rom the luminosities of A3727 and A5007 ollowing ?..," where we have plotted the total radio luminosity at 1.4 GHz versus the luminosity of the narrow emission line region $L_{\rm NLR}$, the latter calculated from the luminosities of $\lambda 3727$ and $\lambda 5007$ following \citet{Raw91}." As Fig., As Fig. 3. shows. a clear transition point oween the two classes can be identified: at values. of Lxunc107 NV and Ly~10779 W (dashed. lines).," \ref{nlrlext} shows, a clear transition point between the two classes can be identified at values of $L_{\rm NLR} \sim 10^{35}$ W and $L_{\rm r} \sim 10^{25.6}$ W $^{-1}$ (dashed lines)." Interestingly. this point lies on the strong (22=98.65 ο) inear correlation present for the strong-lined X-shaped racio sources (solid line).," Interestingly, this point lies on the strong $P=98.6\%$ ) linear correlation present for the strong-lined X-shaped radio sources (solid line)." Seven sources in our spectroscopic sample have broad emunmiüssion lines and we discuss their. properties. below (Section 5.1))., Seven sources in our spectroscopic sample have broad emmission lines and we discuss their properties below (Section \ref{belr}) ). For these (with the exception of | 0657) and a further 22 sources we detect. besides A3127 and A5007 also other useful narrow emission lines. which we analyze in Section 5.2..," For these (with the exception of $+$ 0657) and a further 22 sources we detect besides $\lambda 3727$ and $\lambda 5007$ also other useful narrow emission lines, which we analyze in Section \ref{nelr}. ." We do not further discuss four sources | 2914. | 3435. 0012. and J1406 01548) that have only 113 λες. and 1Η).," We do not further discuss four sources $+$ 2914, $+$ 3435, $-$ 0012, and $-$ 0154) that have only $\beta$ $\lambda 4861$ , and ." The remaining 20sources in our sample have either no emissionlines or none besides. and LHI.., The remaining 20sources in our sample have either no emissionlines or none besides and . aand ffor our GROND e-. r-. 1- and z-band observations respectively.,"and for our GROND g-, r-, i- and z-band observations respectively." The times of mid-transit are given in Table 1.., The times of mid-transit are given in Table \ref{tab:fitpars}. " Firstly. outliers were removed from the K,-band light curve by excluding all points more than away from a median smoothed light curve."," Firstly, outliers were removed from the $_s$ -band light curve by excluding all points more than away from a median smoothed light curve." In this way 25 points were removed., In this way 25 points were removed. A clear residual trend 1 the out-of-transit baseline is visible in the light curve (Fig. 4)).," A clear residual trend in the out-of-transit baseline is visible in the light curve (Fig. \ref{fig:LC_NIR}) )," but we find no significant correlations with the positio1 on the detector or airmass. which we often see in other near-infrared njeasurements (e.g.2?)..," but we find no significant correlations with the position on the detector or airmass, which we often see in other near-infrared measurements \citep[e.g.][]{demooijandsnellen09,demooijetal11}." We therefore fitted the light cvrve with a second order polynomial simultaneously with the transit paraneters., We therefore fitted the light curve with a second order polynomial simultaneously with the transit parameters. As for the optical light curves. we only fitted for the time of mid-transit and. the. planet-to-star size ratio. keeping the impact parameter and semi-major axis fixed to the values tsed by ?..," As for the optical light curves, we only fitted for the time of mid-transit and the planet-to-star size ratio, keeping the impact parameter and semi-major axis fixed to the values used by \cite{beanetal10}." The fits were again performed using an MCMC analysis. as for the optical data. using 5," The fits were again performed using an MCMC analysis, as for the optical data, using 5" "cwarf galaxies. being among the most cdark-matter dominated structures in (he universe. help address the perceived. imbalance between the number of predicted low mass dark matter substructure and (hose observed today. the ""Missing Satellites Problem (IxIvpin1999:Mooreetal. 1999).","dwarf galaxies, being among the most dark-matter dominated structures in the universe, help address the perceived imbalance between the number of predicted low mass dark matter substructure and those observed today, the “Missing Satellites Problem” \citep{Klypin1999,Moore1999}." . As low mass substructures are the building blocks upon which ealaxies are formed under (he ACDM paradigm. the ability to probe dwarf galaxies provides invaluable knowledee into the history aud formation of the Local Group etal.2011).," As low mass substructures are the building blocks upon which galaxies are formed under the $\Lambda$ CDM paradigm, the ability to probe dwarf galaxies provides invaluable knowledge into the history and formation of the Local Group \citep{Tolstoy2009,Karlsson2011}." . Although the dark matter component can be tracked through the use of high resolution N-body simulations (Diemandetal.2007.2008:Springel2008;Wetzel2010).. a complete model of the evolution of these dwarls is still elusive.," Although the dark matter component can be tracked through the use of high resolution -body simulations \citep{Diemand2007,Diemand2008,Springel2008,Wetzel2010}, a complete model of the evolution of these dwarfs is still elusive." All of the known chwarls show signs of old stellar populations (Tolstoyetal.2009) with more of the star formation occurring in discrete bursty periods of star formationof order 25% of total star formation (Lee compared to more massive galaxies which experience roughly continuous star formation., All of the known dwarfs show signs of old stellar populations \citep{Tolstoy2009} with more of the star formation occurring in discrete bursty periods of star formation—of order $25\%$ of total star formation \citep{Lee2009}- —compared to more massive galaxies which experience roughly continuous star formation. This bursty behaviour. with bursts separated by gigavears. does not necessarily require interactions to trigger star formation (Broschοἱal.2004) with the blow-out ancl subsequent infall of neutral gas sullicient to create bursts in isolated dwarls Bland-ILawthorn 2003).," This bursty behaviour, with bursts separated by gigayears, does not necessarily require interactions to trigger star formation \citep{Brosch2004} with the blow-out and subsequent infall of neutral gas sufficient to create bursts in isolated dwarfs \citep{Valcke2008,Quillen2008}." . In a recent development. semi-analviic models of galaxy formation. combined with results from high-resolution dark matter simulations. have been used to model the physical properties of a Galactic dwarf galaxy. svstem (Lietal.2010).," In a recent development, semi-analytic models of galaxy formation, combined with results from high-resolution dark matter simulations, have been used to model the physical properties of a Galactic dwarf galaxy system \citep{Li2010}." . These models however cdo nol vet account for the underabundance of detected in these cbwarf galaxies over the last 40 vears (Einastoetal.1974:Gieevich&Putman2009.herealterGP09).," These models however do not yet account for the underabundance of detected in these dwarf galaxies over the last $40$ years \citep[hereafter GP09]{Einasto1974, Grcevich2009}." . The dependence ol the deleliciency on galactocentirie radius is evidence of significant üdal and/or ranmrpressure stripping of the dwarf galaxies which GDP09 attribute towards close-in. potentially highly eccentric orbits. allowing the (to be removed by a hot halo surrounding the Galaxy.," The dependence of the deficiency on galactocentric radius is evidence of significant tidal and/or ram-pressure stripping of the dwarf galaxies which GP09 attribute towards close-in, potentially highly eccentric orbits, allowing the to be removed by a hot halo surrounding the Galaxy." This removal lor close pericentres (X50 kpc) has been explained by a combination of tidal and ram pressure forces 2006)., This removal for close pericentres $\la50$ kpc) has been explained by a combination of tidal and ram pressure forces \citep{Mayer2006}. . Bul we now show that unassisted stvipping [als by an order of magnitude to explain ihe phenomenon of cdwarl galaxy. depletion. on scales of ~250 kpe as observed today. for anv reasonable orbit families re[sec: Mod)).," But we now show that stripping fails by an order of magnitude to explain the phenomenon of dwarf galaxy depletion, on scales of $\sim250$ kpc as observed today, for any reasonable orbit families \\ref{sec:Mod}) )." In re[sec:ltes.. we include the effects of early star. formation ancl find. Chat feedback-assisted stripping is essential to explain the observed effect.," In \\ref{sec:Res}, we include the effects of early star formation and find that feedback-assisted stripping is essential to explain the observed effect." Using modelsof dwarl infall. we then compare resulis [rom our model to the observed properties of the abundance in clwarls," Using modelsof dwarf infall, we then compare results from our model to the observed properties of the abundance in dwarfs" (Litvak1971)). (Enuucring&Wason1991: (Sarma. Tieftrmuksetal.19973). «τος Tieftruuketal.1997)) citealttec97)). ~0.7 Tp 1< fe) e sin Z Iv ysinunitsofthesaturationintensitgl; , \citealt{lit71}) \citealt{ew94}; \citealt*{str01}) \citealt{tgc97}) \citet{cgjw94} $<$ \citealt{tgc97}) \\citealt{tgc97}) $\sim$ $T_B$ \ref{fMP}$\times$ $I(v)$ $v$ $s$ $I$ $I(v)$ in 100 systems out to 100 Alpe (e.e..Harris&Racine1979:Ixissler-Patig1997:Ixundu&Whitmore 2002).,"in $\sim$ 100 systems out to $\sim$100 Mpc \citep[\eg][]{harris79, kisslerpatig, kundu2002}." . However. as galactocentric distances increase. the surface densities of clusters decrease. so in intracluster space. (he identification of globular clusters as point sources is exceedinelv. diffieult.," However, as galactocentric distances increase, the surface densities of clusters decrease, so in intracluster space, the identification of globular clusters as point sources is exceedingly difficult." As a result. there have been only a few. mostly indirect. studies of IGCs (Westetal.2003:JordanοἱMarin-Franchetal. 2003).. and their use as cosmological probes has largely been unexploited.," As a result, there have been only a few, mostly indirect, studies of IGCs \citep{west03, jordan03, franch03, bassino03}, and their use as cosmological probes has largely been unexploited." ]lere we describe the results of aT) search for intracluster elobular clusters (IGCs) in the nearby Virgo Cluster., Here we describe the results of a search for intracluster globular clusters (IGCs) in the nearby Virgo Cluster. At our adopted Virgo distance (16.2Alpe. 2006).. globular clusters have half-light radii of 20705. allowing them to be resolved on images taken with the Advanced Camera for Survevs (ACS).," At our adopted Virgo distance \citep[16.2~Mpc, see discussion in][]{VICS1}, globular clusters have half-light radii of $\gap~0 \farcs 05$, allowing them to be resolved on images taken with the Advanced Camera for Surveys )." Moreover. because of theACS’ excellent sensitivity. it is possible to use the instrument {ο detect individual stars within (he clusters aud estimate (heir metallicities via the color of the red giant branch.," Moreover, because of the excellent sensitivity, it is possible to use the instrument to detect individual stars within the clusters and estimate their metallicities via the color of the red giant branch." In Section 2. we describe our survey. and announce the discovery of four. well-resolved [GC candidates in Virgo.," In Section 2, we describe our survey, and announce the discovery of four, well-resolved IGC candidates in Virgo." In Section 3. we discuss the metallicities of these objects. and show that all ave metal poor. with photometric properties that differentiate them from (he elobular clusters of Virgos central cD galaxy. M87.," In Section 3, we discuss the metallicities of these objects, and show that all are metal poor, with photometric properties that differentiate them from the globular clusters of Virgo's central cD galaxy, M87." In Section 4. we compare the candidate IGCs to Galactic globular clusters and show that their half-leht and tidal radii are larger (han (heir Milkv. Way. counterparts.," In Section 4, we compare the candidate IGCs to Galactic globular clusters and show that their half-light and tidal radii are larger than their Milky Way counterparts." " We attribute these properties to the IGCs lack of Gdal processing. and use the radii to constrain the clusters"" origins."," We attribute these properties to the IGCs' lack of tidal processing, and use the radii to constrain the clusters' origins." We conclude bv estimating (he specific frequency of elobular clusters in Virgos intracluster space. and discussing the implications this number has for the origin of IGCs and future IGC survevs.," We conclude by estimating the specific frequency of globular clusters in Virgo's intracluster space, and discussing the implications this number has for the origin of IGCs and future IGC surveys." Between 30 May. 2005 and 7 June 2005 we used theSurvevs on the to obtain deep FOOGW ancl ES14W. images of a single Virgo intracluster field (0(2000) =12:28:10.80. 6(2000) —12:33:20.0. orientation 112.58 degrees). ο0.67 deg (200 kpe) from any large galaxv.," Between 30 May 2005 and 7 June 2005 we used the on the to obtain deep F606W and F814W images of a single Virgo intracluster field $\alpha(2000) = $ 12:28:10.80, $\delta(2000) = $ 12:33:20.0, orientation 112.58 degrees), $\sim 0.67$ deg $\sim 200$ kpc) from any large galaxy." The FslitW (-band) data consisted. of 22 exposures totaling 26880 s of integration time: the FGOGW (wide V-band) observations included 52 exposures totaling 63440 s. These data were co-addec using (he task within PyRAF (IXoekemoeretal.2002): this procedure removed all the cosmic ravs. corrected (he instruments geometric distortions. and improved (he sampling of our data to (03 +.," The F814W $I$ -band) data consisted of 22 exposures totaling 26880 s of integration time; the F606W (wide $V$ -band) observations included 52 exposures totaling 63440 s. These data were co-added using the task within PyRAF \citep{koekemoer}: this procedure removed all the cosmic rays, corrected the instrument's geometric distortions, and improved the sampling of our data to $0\farcs 03$ $^{-1}$." The details of these reductions. and an image of the field illustrating its position in the cluster is given by Williamsetal.(2006).," The details of these reductions, and an image of the field illustrating its position in the cluster is given by \citet{VICS1}." . Alter combining the data. we used SEextractor (Bertin&Arnouts1996). to identily all sources (extended and unresolved) brighter (han κιν= 24.5. near the peak of the," After combining the data, we used SEextractor \citep{bertin96} to identify all sources (extended and unresolved) brighter than $m_{\rm F814W} = 24.5$ , near the peak of the" 1995)). this leads to Αμιν51tday.,"), this leads to $R_{\rm BLR} \sim 5 \, \rm lt \, day$." Taking FWHM= from Table 2.. we obtain Mpy~2x10Mo.," Taking $\rm FWHM = 4600 \, km \, s^{-1}$ from Table \ref{lines}, we obtain $M_{\rm BH} \sim 2 \times 10^{7} M_{\sun}$ ." Following the prescription of Marconietal.(2008) to account for the possible role of radiation. pressure on the BLR. we derive a relatively small correction term to the black hole mass of ~0.6x107Mo.," Following the prescription of \citet{marconi08} to account for the possible role of radiation pressure on the BLR, we derive a relatively small correction term to the black hole mass of $\sim 0.6 \times 10^{7} M_{\sun}$." The virial estimate of Mg is then about 20-30 times lower than the values derived above., The virial estimate of $M_{\rm BH}$ is then about 20–30 times lower than the values derived above. At this stage the reason for the discrepancy is unclear., At this stage the reason for the discrepancy is unclear. Further clues on the properties of BL Lacertae come from the relationship of the observed BLR with the accretion disc., Further clues on the properties of BL Lacertae come from the relationship of the observed BLR with the accretion disc. The Optical Monitor XMM-Newton observations of BL Lacertae presented in Raiterietal.(2009) revealed a sharp up-=urn in the SED ultraviolet region. the characteristic signature of the Big Blue Bump associated with the emission of the accretion disc.," The Optical Monitor XMM-Newton observations of BL Lacertae presented in \citet{rai09} revealed a sharp up-turn in the SED ultraviolet region, the characteristic signature of the Big Blue Bump associated with the emission of the accretion disc." " From 66 and 7 in Raiterietal.(2009) one can estimate a dise luminosity at 2500 oof logL,(2500A)~29.4eres7!Hz!."," >From 6 and 7 in \citet{rai09} one can estimate a disc luminosity at 2500 of $\log L_\nu (2500 \AA) \sim 29.4 \rm \, erg \, s^{-1} \, Hz^{-1}$." This value is similar to that measured in type | AGN (both radio-loud and radio-quiet) like Fairall 9. PG 12294204. 3C 390.3. 3C 120. Mkn 509. PG 21304099. PG 0844-349. and Akn 120 (Vasudevan& 2009).," This value is similar to that measured in type 1 AGN (both radio-loud and radio-quiet) like Fairall 9, PG 1229+204, 3C 390.3, 3C 120, Mkn 509, PG 2130+099, PG 0844+349, and Akn 120 \citep{vas09}." . The luminosity of the broad Hf lines of these sources ranges from 0.2 to 0.6x10?ergs! (Kaspietal.2005).," The luminosity of the broad $\beta$ lines of these sources ranges from 0.2 to $0.6 \times 10^{43} \rm \, erg \, s^{-1}$ \citep{kas05}." . For BL Lacertae. considering its broad Ha line luminosity and the Ηα/ΗΡ flux ratio (see above). we obtain a factor of ~ 15-40 lower.," For BL Lacertae, considering its broad $\alpha$ line luminosity and the $\alpha$ $\beta$ flux ratio (see above), we obtain a factor of $\sim 15$ –40 lower." A comparison with broad-line radio galaxies in the 3CR sample (Buttighoneetal.2010) gives a similar result: the ratio between the broad Ha and the rest-frame UV flux ranges between 100 and 250Α.. while this ratio for BL Lacertae is -0.3A.," A comparison with broad-line radio galaxies in the 3CR sample \citep{but10} gives a similar result: the ratio between the broad $\alpha$ and the rest-frame UV flux ranges between 100 and 250, while this ratio for BL Lacertae is $\sim 0.3 \AA$." " This difference is preserved considering an AGN of very low BLR luminosity. ~100 smaller than BL Lacertae. the LINER galaxy NGC 4579 (Barthetal.1996.2001).. for which this value is ~275A,"," This difference is preserved considering an AGN of very low BLR luminosity, $\sim 100$ smaller than BL Lacertae, the LINER galaxy NGC 4579 \citep{bar96,bar01}, for which this value is $\sim 275 \AA$." Apparently. the BLR of BL Lacertae is strongly underluminous with respect to its disc emission when compared to other AGN.," Apparently, the BLR of BL Lacertae is strongly underluminous with respect to its disc emission when compared to other AGN." This suggests a possible interpretation for the different values of SMBH mass found above., This suggests a possible interpretation for the different values of SMBH mass found above. " In fact. Mpg scales with the BLR luminosity as MgyοLy?!"" "," In fact, $M_{\rm BH}$ scales with the BLR luminosity as $M_{\rm BH} \propto L_{\rm BLR}^{0.6-0.7}$." To account for an underestimate of the SMBH mass by a factor of 20-30. the BLR should be underluminous by a factor of 70-300. in broad agreement to what we derived considering the ratio between BLR and UV fluxes.," To account for an underestimate of the SMBH mass by a factor of 20–30, the BLR should be underluminous by a factor of 70–300, in broad agreement to what we derived considering the ratio between BLR and UV fluxes." We here explore how BL Lacertae would look like when seen with its jet pointing at a larger angle from our line of sight. Le. what extragalactic sources might represent the misoriented parent population.," We here explore how BL Lacertae would look like when seen with its jet pointing at a larger angle from our line of sight, i.e. what extragalactic sources might represent the misoriented parent population." We thus consider all quantities that are not affected by beaming and that might eventually depend on orientation only if there is selective obscuration. as ddue to a flattened circumnuclear dust structure. aa torus.," We thus consider all quantities that are not affected by beaming and that might eventually depend on orientation only if there is selective obscuration, as due to a flattened circumnuclear dust structure, a torus." " The host of BL Lacertae is a giant elliptical galaxy of absolute magnitude My.=-—25.33 (see Sect.3.2)). nearly two magnitudes brighter than the characteristic absolute magnitude M"" in this band (Schechter1976:Huangetal.2003)."," The host of BL Lacertae is a giant elliptical galaxy of absolute magnitude $M_K=-25.33$ (see \ref{mbh}) ), nearly two magnitudes brighter than the characteristic absolute magnitude $M^{*}$ in this band \citep{sch76,hua03}." . The emission from the accretion disc. to which we associate the emission in the near UV band at 2500 A.. amounts to 10777eres!Hz!.," The emission from the accretion disc, to which we associate the emission in the near UV band at 2500 , amounts to $10^{29.4} \rm \, erg \, s^{-1} \, Hz^{-1}$." " In order to estimate the contrast between the disc and the host we used the Raiterietal.(2009). black-body fit to the accretion disc emission. which gives an. R- flux of 0.95x107ergem""s!A! The host-galaxy observed magnitude R=15.55 (Scarpaetal.2000)... after correcting for Galactic extinction. translates into a flux of 3.07107?ereems!A."," In order to estimate the contrast between the disc and the host we used the \citet{rai09} black-body fit to the accretion disc emission, which gives an $R$ -band flux of $0.95 \times 10^{-15} \rm \, erg \, cm^{-2} \, s^{-1} \, \AA^{-1}$ The host-galaxy observed magnitude $R=15.55$ \citep{sca00}, after correcting for Galactic extinction, translates into a flux of $3.07 \times 10^{-15} \rm \, erg \, cm^{-2} \, s^{-1} \, \AA^{-1}$." This implies a ratio between host and nucleus of ~3. similar to that measured in Seyfert | and Broad Line radio galaxies (Bentzetal.20092).," This implies a ratio between host and nucleus of $\sim 3$, similar to that measured in Seyfert 1 and Broad Line radio galaxies \citep{bentz09b}." . The extended radio emission is also unaffected by orientation., The extended radio emission is also unaffected by orientation. By means of VLA maps at 20 em. Antonueci&Ulvestad(1985) estimated an extended radio flux of 40mJy.," By means of VLA maps at 20 cm, \citet{ant85} estimated an extended radio flux of $40 \, \rm mJy$." More recent VLA observations at 20 em for the MOJAVE project (Cooperetal.2007) resulted in an extended flux of ISmJy. essentially confirming the earlier results.," More recent VLA observations at 20 cm for the MOJAVE project \citep{coo07} resulted in an extended flux of $18 \, \rm mJy$, essentially confirming the earlier results." These high spatial resolution observations might. in principle. have missed diffuse low-surface brightness. steep-spectrum emission.," These high spatial resolution observations might, in principle, have missed diffuse low-surface brightness, steep-spectrum emission." We then consider the 74 MHz flux density measured for BL Lacertae in the VLA Low-frequency Sky Survey (VLSS. Cohenetal. 2007)). Foy21.46Jy.," We then consider the 74 MHz flux density measured for BL Lacertae in the VLA Low-frequency Sky Survey (VLSS, \citealt{coh07}) ), $F_{74} = 1.46 \, \rm Jy$." Even in the assumption that the radio core does not contribute significantly at this low frequency. this translates into an upper limit of ~180mJy at 1400 MHz (having adopted a radio spectral index of 0.7).," Even in the assumption that the radio core does not contribute significantly at this low frequency, this translates into an upper limit of $\sim 180 \, \rm mJy$ at 1400 MHz (having adopted a radio spectral index of 0.7)." This is an extremely conservative limit. considering that its radio core has a typical flux of ~ 2 Jy (see e.g. 2010)).," This is an extremely conservative limit, considering that its radio core has a typical flux of $\sim$ 2 Jy (see e.g. \citealt{kharb10}) )." Thus we are confident that a value of 40 mJy at 1400 MHz is well representative of the total extended emission in BL Lacertae., Thus we are confident that a value of 40 mJy at 1400 MHz is well representative of the total extended emission in BL Lacertae. This corresponds to a radio luminosity power of logPoy=30.57ergs!Hz!.," This corresponds to a radio luminosity power of $\log P_{\rm ext}= 30.57 \, \rm erg \, s^{-1} \, Hz^{-1}$." " From the point of view of the emission lines. we derived a broad He luminosity of ~4xIO""ergs! (see Sect.3.2))."," >From the point of view of the emission lines, we derived a broad $\alpha$ luminosity of $\sim 4 \times 10^{41} \, \rm erg \, s^{-1}$ (see \ref{mbh}) )." Considering the narrow emission lines. from Table 2. we estimate a [O IL] luminosity of ~4x10ere s7!.," Considering the narrow emission lines, from Table \ref{lines} we estimate a [O III] luminosity of $\sim 4 \times 10^{40} \, \rm erg \, s^{-1}$ ." The narrow emission line ratios can contribute to characterize the properties of an AGN. but unfortunately accurate measurements from our data are available only for [O ILI] and [NHP... As discussed in 33.. the narrow emission lines do not seem to have varied significantly in the last 20 years. so we can complement our data with those from the literature.," The narrow emission line ratios can contribute to characterize the properties of an AGN, but unfortunately accurate measurements from our data are available only for [O III] and [N. As discussed in 3.1, the narrow emission lines do not seem to have varied significantly in the last 20 years, so we can complement our data with those from the literature." However. the spectrum of Vermeulenetal. does not improve the situation. because the Hf line is detected. but a decomposition into narrow and broad component could not be performed.," However, the spectrum of \citet{ver95} does not improve the situation, because the $\beta$ line is detected, but a decomposition into narrow and broad component could not be performed." The observations by Corbettetal.(1996) cover only the red part of the spectrum C1> 6000À) where they saw a rather well-defined |O 116200 line., The observations by \citet{cor96} cover only the red part of the spectrum $\lambda \gtrsim 6000 \AA$ ) where they saw a rather well-defined [O $\lambda$ 6300 line. This enables us to locate BL Lacertae in à non-standard diagnostic plane defined bythe ratios [O I/[N ΗΙ and [ο HI[/[NII] refdiag)), This enables us to locate BL Lacertae in a non-standard diagnostic plane defined bythe ratios [O I]/[N II] and [O III]/[NII] \\ref{diag}) ). As a comparison. we show in this diagram the location of the 3CR sources (limited to a redshift of 0.3)," As a comparison, we show in this diagram the location of the 3CR sources (limited to a redshift of 0.3)" "values, computes the values of the lensing likelihood in equation (8.2)) and the prior in equation these are the two ingredients needed to obtain the posterior(6)); PDF in equation (6)).","values, computes the values of the lensing likelihood in equation \ref{eq:lenslike}) ) and the prior in equation \ref{eq:prior}) ); these are the two ingredients needed to obtain the posterior PDF in equation \ref{eq:bayes}) )." " As in the kinematics analysis, we use (77) to sample the posterior PDF."," As in the kinematics analysis, we use \citep{FerozHobson08, Feroz++09} to sample the posterior PDF." Figure 9 shows the resulting constraints on the same parameters as those in Figure 7.., Figure \ref{fig:PDF_Lens} shows the resulting constraints on the same parameters as those in Figure \ref{fig:PDF_Dyn}. " The degeneracy between the disk strength and the Einstein radius of the dark matter halo is visible, though not as strong as in the case of the kinematics-only analysis."," The degeneracy between the disk strength and the Einstein radius of the dark matter halo is visible, though not as strong as in the case of the kinematics-only analysis." The halo is highly flattened (a/c~ 0.3).," The halo is highly flattened $a/c\,\sim\,0.3$ )." The flattening is degenerate with the disk strength as shown in the top-left panel: a flattened halo is less massive and requires a more massive disk., The flattening is degenerate with the disk strength as shown in the top-left panel: a flattened halo is less massive and requires a more massive disk. The flattening is also degenerate with the halo Einstein radius: massive halos with high Ry7 need to be more flattened to reproduce the overall ellipticity of the projected mass as constrained by the lensing data., The flattening is also degenerate with the halo Einstein radius: massive halos with high $\RhE$ need to be more flattened to reproduce the overall ellipticity of the projected mass as constrained by the lensing data. " The scale radius of the dark-matter halo is not constrained, as expected since lensing only probes the distribution in the radial range spanned by the images, i.e., «0.5, or ~Akpc."," The scale radius of the dark-matter halo is not constrained, as expected since lensing only probes the distribution in the radial range spanned by the images, i.e., $\sim$$0\farcs5$, or $\sim$$4\kpc$." " Nonetheless, a small value of <1"" is rejected by the data at CI."," Nonetheless, a small value of $\lesssim 1''$ is rejected by the data at CI." The most probable lensing model (with highest posterior PDF) has a reduced y?=0.9., The most probable lensing model (with highest posterior PDF) has a reduced $\chi^2=0.9$. We show in Figure 10 the critical curves (solid) and caustics (dashed) of the most probable lensing model.," We show in Figure \ref{fig:critcaus} the critical curves (solid) and caustics (dashed) of the most probable lensing model." " The open symbols are the observed image positions, and the solid symbols are the modeled source positions."," The open symbols are the observed image positions, and the solid symbols are the modeled source positions." The figure illustrates the configuration of the 10-image system in relation to its 3-component source (the source positions are clustered into three groups)., The figure illustrates the configuration of the 10-image system in relation to its 3-component source (the source positions are clustered into three groups). The first group of sources is outside the astroid caustics and produces components la and 8., The first group of sources is outside the astroid caustics and produces components 1a and 8. " The second group is inside the astroid caustics and produces components 1, 3, 4 and 6."," The second group is inside the astroid caustics and produces components 1, 3, 4 and 6." " The third group is near a fold of the caustics and produces components 2, 5 and 7."," The third group is near a fold of the caustics and produces components 2, 5 and 7." " In this section, we present results on the mass distribution for the spiral galaxy based on the kinematics and lensing data sets."," In this section, we present results on the mass distribution for the spiral galaxy based on the kinematics and lensing data sets." " Since the two data sets are independent, the likelihood is = |n). P(d,.where d,the [η))kinematicsP(d, n)and P(d,lensing likelihoods(31) on the right-hand side are given by equations (7.3)) and (8.2)), respectively."," Since the two data sets are independent, the likelihood is ) = ), where the kinematics and lensing likelihoods on the right-hand side are given by equations \ref{eq:dynlike}) ) and \ref{eq:lenslike}) ), respectively." Figure 11 shows the result of sampling of the posterior., Figure \ref{fig:PDF_LensDyn} shows the result of sampling of the posterior. The reduced x? of the joint data set is 0.8., The reduced $\chi^2$ of the joint data set is $0.8$. The marginalized parameters with CI are listed in Table 5.., The marginalized parameters with CI are listed in Table \ref{tab:par_LensDyn}. " Although the kinematics constraints are significantly weaker than the lensing constraints, the panel (top-middle) in Figure 11 shows that the &q,9—Rn,gkinematics"," Although the kinematics constraints are significantly weaker than the lensing constraints, the $\kappa_{\rm d,0}$ $R_{\rm h,E}$ panel (top-middle) in Figure \ref{fig:PDF_LensDyn} shows that the kinematics" " B1706—44, the only other Vela-like pulsar for which oobservations are available (e.g. Mignani et 11999).","$-$ 44, the only other Vela-like pulsar for which observations are available (e.g. Mignani et 1999)." " 'This would confirm that Vela-like pulsars are intrinsically less efficient emitters in the optical than Crab-like pulsars, possibly even less efficient than middle-aged and old pulsars, like B0656+14, Geminga, B1055—52, B1929+10, and B0950--08."," This would confirm that Vela-like pulsars are intrinsically less efficient emitters in the optical than Crab-like pulsars, possibly even less efficient than middle-aged and old pulsars, like B0656+14, Geminga, $-$ 52, B1929+10, and B0950+08." The measurement of such a low emission efficiency in the optical band for Vela-like pulsars might then provide useful information to emission models of the neutron star magnetosphere., The measurement of such a low emission efficiency in the optical band for Vela-like pulsars might then provide useful information to emission models of the neutron star magnetosphere. We compared the flux upper limits of J1357-6429 and J1048—5832 with the extrapolations in the optical domain of the X and y-ray spectra., We compared the flux upper limits of $-$ 6429 and $-$ 5832 with the extrapolations in the optical domain of the X and $\gamma$ -ray spectra. " For J1357—6429, we assumed the X-ray spectral model of Esposito et ((2007), a power-law (PL) with photon index Ἐκ=14+40.5 plus a blackbody (BB) with temperature kT=0.167909 keV (Ng=0.4403x10?? cm-?), and the 4-ray spectral model of Lemoine-Goumard et (2011), a PL with photon index I,=1.54+0.41 and exponential cut-off at ~ 0.8 GeV. For J1048—5832, we assumed the X-ray spectral model of Marelli et ((2011), a PL with photon index Ty=2.420.5 (Ng=0.903x107? cm-?), and the y-ray spectral model of Abdo et ((2009), a PL with photon index I,=1.38+0.13 and exponential cut-off at ~ 2.3 GeV. Our optical flux upper limits are corrected for interstellar extinction based upon the Ny derived from the fit to the X-ray spectra."," For $-$ 6429, we assumed the X-ray spectral model of Esposito et (2007), a power-law (PL) with photon index $\Gamma_X=1.4\pm 0.5$ plus a blackbody (BB) with temperature $kT=0.16^{+0.09}_{-0.04}$ keV $N_H=0.4^{+0.3}_{-0.2} \times 10^{22}$ $^{-2}$ ), and the $\gamma$ -ray spectral model of Lemoine-Goumard et (2011), a PL with photon index $\Gamma_{\gamma} =1.54 \pm 0.41$ and exponential cut-off at $\sim$ 0.8 GeV. For $-$ 5832, we assumed the X-ray spectral model of Marelli et (2011), a PL with photon index $\Gamma_X= 2.4 \pm 0.5$ $N_H=0.9^{+0.4}_{-0.2} \times 10^{22}$ $^{-2}$ ), and the $\gamma$ -ray spectral model of Abdo et (2009), a PL with photon index $\Gamma_{\gamma}=1.38\pm 0.13$ and exponential cut-off at $\sim$ 2.3 GeV. Our optical flux upper limits are corrected for interstellar extinction based upon the $N_H$ derived from the fit to the X-ray spectra." The multi-wavelength spectral energy distributions (SEDs) of the two pulsars are shown in Fig., The multi-wavelength spectral energy distributions (SEDs) of the two pulsars are shown in Fig. " 5, where we accounted for both the lc uncertainty on the extrapolations of the X and 4-ray PL and the uncertainty on the extinction-corrected flux upper limits."," 5, where we accounted for both the $1 \sigma$ uncertainty on the extrapolations of the X and $\gamma$ -ray PL and the uncertainty on the extinction-corrected flux upper limits." " In the case of J1357—6429 (Fig.5, left) we see that the optical flux upper limits can be compatible with the extrapolation of the X-ray PL."," In the case of $-$ 6429 (Fig.5, left) we see that the optical flux upper limits can be compatible with the extrapolation of the X-ray PL." " Thus, it is possible that the expected optical PL spectrum indeed follows the extrapolation of the X-ray one, a case so far observed only for B1509—58 among all the optically-identified pulsars (see, e.g. Mignani et 22010a)."," Thus, it is possible that the expected optical PL spectrum indeed follows the extrapolation of the X-ray one, a case so far observed only for $-$ 58 among all the optically-identified pulsars (see, e.g. Mignani et 2010a)." " The optical flux upper limits are also compatible, with the possible exception of the R-band one, with the extrapolation of the 4-ray PL, which does not allow us to prove that there is a break in the optical/4-ray spectrum, as observed in other pulsars."," The optical flux upper limits are also compatible, with the possible exception of the R-band one, with the extrapolation of the $\gamma$ -ray PL, which does not allow us to prove that there is a break in the $\gamma$ -ray spectrum, as observed in other pulsars." " Indeed, a possible consistency between the y-ray and optical PL spectra has been found so far for a minority of cases only (Mignani et al,"," Indeed, a possible consistency between the $\gamma$ -ray and optical PL spectra has been found so far for a minority of cases only (Mignani et al.," " in preparation) like, e.g. the middle-aged pulsar B1055—52 (Mignani et 22010b)."," in preparation) like, e.g. the middle-aged pulsar $-$ 52 (Mignani et 2010b)." " To summarise, we can not rule out that a single model can describe the optical-to—y-ray magnetospheric emission of J1357—6429."," To summarise, we can not rule out that a single model can describe the $\gamma$ -ray magnetospheric emission of $-$ 6429." The multi-wavelength SED is different in the case of J1048—5832 (Fig., The multi-wavelength SED is different in the case of $-$ 5832 (Fig. " 5, right), for which the optical V-band upper limit is compatible with the extrapolation of the steep X-ray PL only for the largest values of the Nz but is well above the extrapolation of the flat y-ray one."," 5, right), for which the optical V-band upper limit is compatible with the extrapolation of the steep X-ray PL only for the largest values of the $N_H$ but is well above the extrapolation of the flat $\gamma$ -ray one." " This does not rule out that there is a break in the optical/X-ray PL spectrum, as observed in most pulsars (Mignani et 22010a), and that the optical spectrum follows the extrapolation of the y-ray PL."," This does not rule out that there is a break in the optical/X-ray PL spectrum, as observed in most pulsars (Mignani et 2010a), and that the optical spectrum follows the extrapolation of the $\gamma$ -ray PL." " Interestingly enough, at variance with the"," Interestingly enough, at variance with the" in the signal.,in the signal. " οανν, the primary effect of increasing σι is to broaden the pdf while not changing the error bars by much."," Similary, the primary effect of increasing $\sigma_\epsilon$ is to broaden the pdf while not changing the error bars by much." It is worth noting that previous theoretical work ou halo detection has focused on the peaks that can be individually detected with adequate signal to noise., It is worth noting that previous theoretical work on halo detection has focused on the peaks that can be individually detected with adequate signal to noise. These would correspond to the parts of the pdf with vy2toh. where sample variance is huge.," These would correspond to the parts of the pdf with $\nu\gsim 4-5$, where sample variance is large." Clearly the bulk of the information on the mass function aud iu distinguishiug models is at sinaller or negative peak heights and can be used only statistically by moceling the noise pdf., Clearly the bulk of the information on the mass function and in distinguishing models is at smaller or negative peak heights and can be used only statistically by modeling the noise pdf. The results presented in sections 2 and 3 show that the peak distribution frou lensing data has information ou the projected ass function of dark matter halos. and is sensitive to the cosimological model.," The results presented in sections 2 and 3 show that the peak distribution from lensing data has information on the projected mass function of dark matter halos, and is sensitive to the cosmological model." " The level of non-CGaussianity of the pdf is a powerful discrimant of models with ditfereut values of ο,", The level of non-Gaussianity of the pdf is a powerful discrimant of models with different values of $\Omega$. Figure 3. shows that the models can be distinguished frou the pdf over a wide rauge of peak heights at 2 to 36: by combining information at different peak heights aud smoothing scales we can obtain much ligher significance., Figure \ref{fighist} shows that the models can be distinguished from the pdf over a wide range of peak heights at 2 to $\sigma$; by combining information at different peak heights and smoothing scales we can obtain much higher significance. Further. the third and fourth moments of the peak distribution for different smoothing scales are scusitive to the cosinological ποσο]. as expected qualitatively from the shapes of the distribution.," Further, the third and fourth moments of the peak distribution for different smoothing scales are sensitive to the cosmological model, as expected qualitatively from the shapes of the distribution." We lave also compared the peak. distributions shown with a mociel with non-zero cosmiological coustaut O4=0.7., We have also compared the peak distributions shown with a model with non-zero cosmological constant $\Omega_\Lambda=0.7$. The peak distribution iu the Aauodoel lies in-between the Eiusteiu de-Sitter and open model with the same value of Quarter," The peak distribution in the $\Lambda$ -model lies in-between the Einstein de-Sitter and open model with the same value of $\Omega_{\rm matter}$." Bevoud the dependence ou the cosinological parameters. he peak pdf coutains information on the projected mass unction over all mass scales.," Beyond the dependence on the cosmological parameters, the peak pdf contains information on the projected mass function over all mass scales." It is important to test how accurately we can recover the pdf of peaks due to the chsing signal. aud hence the projected mass function. fron wide field leusiug surveys.," It is important to test how accurately we can recover the pdf of peaks due to the lensing signal, and hence the projected mass function, from wide field lensing surveys." A straightforward approach is to conrpare the measured pdf with the predictions of a set of uodels that include the level of noise observed iu the data., A straightforward approach is to compare the measured pdf with the predictions of a set of models that include the level of noise observed in the data. The best fit model can be fouud by minimizing the 47., The best fit model can be found by minimizing the $\chi^2$. We demonstrate in a forthcoming paper that the projected uass function and € can be simultaneously determined wousine the normalization aud shape of the distribution (Van Waerbeke Jain 1999)., We demonstrate in a forthcoming paper that the projected mass function and $\Omega$ can be simultaneously determined by using the normalization and shape of the distribution (Van Waerbeke Jain 1999). Since we use information roni all peak heights. not just the high-o peaks that cau be detected idivicdually. the mass function is constrained over nass scales ranging from ealactic to cluster sized halos.," Since we use information from all peak heights, not just the $\sigma$ peaks that can be detected individually, the mass function is constrained over mass scales ranging from galactic to cluster sized halos." A nore ambitious approach to recover the leusiug signal would be to de-couvolve the measured peak distribution using the analytical iiodel for the noise., A more ambitious approach to recover the lensing signal would be to de-convolve the measured peak distribution using the analytical model for the noise. The nearly perfect accuracy of the analytical noise model (see figure 1)). which we have checked for four cosmological models with different πλουήπιο scales and noise distribution. gives us confidence that the leusiug signal can be extracted from forthcoming data either using deconvolution. or bv comparing the forward convolution for a set of models.," The nearly perfect accuracy of the analytical noise model (see figure \ref{fignoise1}) ), which we have checked for four cosmological models with different smoothing scales and noise distribution, gives us confidence that the lensing signal can be extracted from forthcoming data — either using deconvolution, or by comparing the forward convolution for a set of models." Analytical predictions of peak statistics would be valuable iu. comparing theoretical predictions with observations., Analytical predictions of peak statistics would be valuable in comparing theoretical predictions with observations. Rebliuski et al (1999) have shown that predictions of peak uuuboer densities based ou the Schechter model aeree with the simulations for the a peaks., Reblinski et al (1999) have shown that predictions of peak number densities based on the Press-Schechter model agree with the simulations for the $\sigma$ peaks. Detailed analytical predictions of peak uuuber densities aud their aueular correlations by combining the Press-Schechter model aud its extensions with our noise nodel would be useful., Detailed analytical predictions of peak number densities and their angular correlations by combining the Press-Schechter model and its extensions with our noise model would be useful. Further work is also uceded to est the seusitivitv of the results to the shape of the dark uatter power spectrum., Further work is also needed to test the sensitivity of the results to the shape of the dark matter power spectrum. The dependence on the redshitt distribution of source galaxies needs to be computed as well since the level of won-Caussianity decreases for nore distant galaxies. inereasius the redshift of source ealaxies could mimic the effect of high-Q.," The dependence on the redshift distribution of source galaxies needs to be computed as well — since the level of non-Gaussianity decreases for more distant galaxies, increasing the redshift of source galaxies could mimic the effect of $\Omega$." To place the peaks approach in perspective. it is useful ο conipare it with the standard approach of measuring dark matter statistics using the ecutive field (without peal identification).," To place the peaks approach in perspective, it is useful to compare it with the standard approach of measuring dark matter statistics using the entire field (without peak identification)." The peak statistics rely on only a subset of the available information (the location aud height of peaks. and eveutually their profile). aud obtaining cosinological information from them requires additioual theoretical modeling compared to field statistics.," The peak statistics rely on only a subset of the available information (the location and height of peaks, and eventually their profile), and obtaining cosmological information from them requires additional theoretical modeling compared to field statistics." On the other hand. the use of peak statistics has both practical and theoretical advantages.," On the other hand, the use of peak statistics has both practical and theoretical advantages." Peak statistics are likely to be robust to certain kinds of svstematics sual. uukuownu errors in the ealaxy ellipticities that complicate tle use of field statistics.," Peak statistics are likely to be robust to certain kinds of systematics — small, unknown errors in the galaxy ellipticities that complicate the use of field statistics." For example. in practice. the shear measured from cllipticity data is multiplied by a factor larger than unity to account for the siueariug by the poit spread function.," For example, in practice, the shear measured from ellipticity data is multiplied by a factor larger than unity to account for the smearing by the point spread function." If this factor is estimated -imeorrectly. it could change the height but probably not the location of the peaks.," If this factor is estimated incorrectly, it could change the height but probably not the location of the peaks." It would then amount to a rescaling of the x- in the peak histograms. which docs not change the conrparisous amonest the cosmological models.," It would then amount to a rescaling of the x-axis in the peak histograms, which does not change the comparisons amongst the cosmological models." Ou the theoretical side. peak statistics can provide insights iuto the biasing of galaxies relative to the dark matter. by allowing us to consider the two distinct conrponeuts of biasing: first. the relation of galaxies to dark halos. aud second. of halos to the dark matter.," On the theoretical side, peak statistics can provide insights into the biasing of galaxies relative to the dark matter, by allowing us to consider the two distinct components of biasing: first, the relation of galaxies to dark halos, and second, of halos to the dark matter." By combining the measured clustering of galaxies with that of dark halos measured through peak statistics from lensing data. the first step in the biasing of galaxies can be directly probed.," By combining the measured clustering of galaxies with that of dark halos measured through peak statistics from lensing data, the first step in the biasing of galaxies can be directly probed." For the secoud step of relating halos to the dark matter. we will need to use successful measurements of feld lensine. or to iuterpret the data usine theoretical models for the relation of halos to the dark matter.," For the second step of relating halos to the dark matter, we will need to use successful measurements of field lensing, or to interpret the data using theoretical models for the relation of halos to the dark matter." We lave shown that the statistics of peaks provides a useful new approach to wide field) lensing., We have shown that the statistics of peaks provides a useful new approach to wide field lensing. It is complementary to the standard statistics such as ellipticity correlations over the field. aud ds directly linked το the projected distribution of dark matter halos.," It is complementary to the standard statistics such as ellipticity correlations over the field, and is directly linked to the projected distribution of dark matter halos." The characteristic nou-CGatssian shape of the peak distribution (its asviunietrie double peaked shape} makes it a powerful probe of the cosinological mocel as well as a useful test of the presence of svsteniaties errors., The characteristic non-Gaussian shape of the peak distribution (its asymmetric double peaked shape) makes it a powerful probe of the cosmological model as well as a useful test of the presence of systematics errors. We are grateful to Uros Soljk. Peter Schneiler. Ravi Sheth. Alex Szalav aud Simon White for helpful discussions.," We are grateful to Uros Seljak, Peter Schneider, Ravi Sheth, Alex Szalay and Simon White for helpful discussions." We thauk au anouvimous referee for coments., We thank an anonymous referee for comments. We use code to estimate the best fit weight factors corresponding to different frequency bands.,We use code to estimate the best fit weight factors corresponding to different frequency bands. " The code gives best choice of weights as W=(0.035,—0.378,—0.217,1.632,0.073) for K to W bands corresponding to ΚΑ)=1.17."," The code gives best choice of weights as ${\bf W} = (0.035, -0.378, -0.217, 1.632, -0.073)$ for K to W bands corresponding to $\mathcal K^c_{min}({\bf W}) = 1.17$." The complete procedure to estimate the weights takes only about a couple of minutes on an Intel 2.26 GHz processor., The complete procedure to estimate the weights takes only about a couple of minutes on an Intel 2.26 GHz processor. " As one might expect, V band gets the maximum positive weight since it is supposed to be the least foreground contaminated frequency band in the WMAP observation window."," As one might expect, V band gets the maximum positive weight since it is supposed to be the least foreground contaminated frequency band in the WMAP observation window." The kurtosis for cleaned map outside the G20 mask becomes 0.093., The kurtosis for cleaned map outside the G20 mask becomes $0.093$. We note that weights obtained from WMAP data have similar values to the mean weights obtained from Monte-Carlo simulations in Section 3.2.., We note that weights obtained from WMAP data have similar values to the mean weights obtained from Monte-Carlo simulations in Section \ref{validity}. " Using the weights described above we obtain the foreground cleaned CMB map (top panel of Fig. 3,,"," Using the weights described above we obtain the foreground cleaned CMB map (top panel of Fig. \ref{Gmap}," hereafter GMAP)., hereafter GMAP). " Although there are some visible signature of presence of residual foreground contamination in this map on the galactic plane (e.g. Cygnus region, Cassiopeia A, Carina nebula) all contaminations are confined only near the galactic plane."," Although there are some visible signature of presence of residual foreground contamination in this map on the galactic plane (e.g. Cygnus region, Cassiopeia A, Carina nebula) all contaminations are confined only near the galactic plane." We show the difference between GMAP and WMAP's 7 year ILC map outside the G20 mask in bottom panel of Fig. 3.., We show the difference between GMAP and WMAP's $7$ year ILC map outside the G20 mask in bottom panel of Fig. \ref{Gmap}. " In the unmasked difference map larger pixel amplitudes are confined near the galactic plane, making a narrow strip-like structure, with absolute pixel temperature exceeding 50jK."," In the unmasked difference map larger pixel amplitudes are confined near the galactic plane, making a narrow strip-like structure, with absolute pixel temperature exceeding $50 \mu K$." The bottom panel of Fig., The bottom panel of Fig. 3 shows that applying G20 mask significantly reduces pixel amplitude of the difference map.. We test for the distribution of pixel temperature of GMAP outside the G20 mask., \ref{Gmap} shows that applying G20 mask significantly reduces pixel amplitude of the difference map.. We test for the distribution of pixel temperature of GMAP outside the G20 mask. The average pixel temperature of this map outside the G20 mask is only 0.δδµΚ., The average pixel temperature of this map outside the G20 mask is only $0.85 \mu K$ . Hence we fit for a Gaussian probability function with mean 0 and variance s to the pixel temperature distribution of the masked GMAP., Hence we fit for a Gaussian probability function with mean $0$ and variance $s$ to the pixel temperature distribution of the masked GMAP. " From the fit we obtain, s=67.49—-0.12uK."," From the fit we obtain, $s = 67.49 \pm 0.12 \mu K$." We show the distribution outside G20 mask obtained from GMAP and the WMAP's ILC map in Fig. 4.., We show the distribution outside G20 mask obtained from GMAP and the WMAP's ILC map in Fig. \ref{res1}. We also show in this figure pixel temperature distributions of individual frequency bands., We also show in this figure pixel temperature distributions of individual frequency bands. The long tails for K and Ka bands are due to strong synchrotron contamination., The long tails for K and Ka bands are due to strong synchrotron contamination. We note that all the distributions corresponding to 5 frequency bands are asymmetric representing their non-Gaussian nature., We note that all the distributions corresponding to 5 frequency bands are asymmetric representing their non-Gaussian nature. Pixel temperature of simulated frequency maps have distributions similar to these histograms., Pixel temperature of simulated frequency maps have distributions similar to these histograms. To estimate power spectrum from GMAP we first apply G20 mask and estimate the partial sky CMB power spectrum., To estimate power spectrum from GMAP we first apply G20 mask and estimate the partial sky CMB power spectrum. We convert the partial sky power spectrum to the full sky estimate by inverting the mode-mode coupling matrix., We convert the partial sky power spectrum to the full sky estimate by inverting the mode-mode coupling matrix. Finally we remove both beam and pixel effect from this power spectrum., Finally we remove both beam and pixel effect from this power spectrum. We show the resulting power spectrum in Fig. 5.., We show the resulting power spectrum in Fig. \ref{cl}. As shown in this figure this power spectrum matches well with the ILC power spectrum estimated from the same sky region until /~ 100., As shown in this figure this power spectrum matches well with the ILC power spectrum estimated from the same sky region until $l \sim 100$ . Beyond this multipole range GMAP power spectrum has less power than the ILCpower spectrum., Beyond this multipole range GMAP power spectrum has less power than the ILCpower spectrum. From the GMAP we find C;=246.4uK? and C3=402.34K? consistent with ILC estimates (C;=248.8.K* and C3= 404.0μΚ2)., From the GMAP we find $C_2 = 246.4 \mu K^2$ and $C_3 = 402.3 \mu K^2$ consistent with ILC estimates $C_2 = 248.8 \mu K^2$ and $C_3 = 404.0 \mu K^2$ ). (here is a dramatically low degree of phase-coherence between the different racial segments.,there is a dramatically low degree of phase-coherence between the different radial segments. " If all the annuli were perfectly coherent. c4,=0σηη. PzS, and the light eurve would have aa~—1.5 power-law power spectrum wilh a lareer variance."," If all the annuli were perfectly coherent, $\Delta\psi_{n m} = 0 \, \forall n,m$ , $P \simeq S_b$ and the light curve would have a $\alpha \sim -1.5$ power-law power spectrum with a larger variance." On the other hand. if all the annuli were completely incoherent. the total flux power spectrum would still be a power-law wilh a~—1.5. but with a smaller variance.," On the other hand, if all the annuli were completely incoherent, the total flux power spectrum would still be a power-law with $\alpha \sim -1.5$, but with a smaller variance." The only wav (0 steepen (he slope of the spectrum is for the deeree of coherence to decline with increasing frequency., The only way to steepen the slope of the spectrum is for the degree of coherence to decline with increasing frequency. The level of coherence in (he variability of dF/dr is illusirated in Figure 14.. where we plot ον.) over the lower half of our frequenev range.," The level of coherence in the variability of $dF/dr$ is illustrated in Figure \ref{fig:dfdr-phase}, where we plot $\psi(\nu,r)$ over the lower half of our frequency range." At almost all radii. ον.ή). is incoherent in lrequency (negligible correlation lengths in p). but at fixed lrequency. there can be significant coherence in radius.," At almost all radii, $\psi(\nu,r)$ is incoherent in frequency (negligible correlation lengths in $\nu$ ), but at fixed frequency, there can be significant coherence in radius." " The pliases are sufficiently colerent between clilferent annuli that 5,2»5,. but their correlations lollow no simple pattern."," The phases are sufficiently coherent between different annuli that $S_b \gg S_a$, but their correlations follow no simple pattern." Different [reeuencies show different radial coherence patterns. making it impossible to state that radius + varies coherently with radius 7: rather. one ean only sav Chat certain modes al r are coherent with those at rl.," Different frequencies show different radial coherence patterns, making it impossible to state that radius $r$ varies coherently with radius $r^\prime$; rather, one can only say that certain modes at $r$ are coherent with those at $r^\prime$." The white dashed curve in Figure 14 shows the inflow rate vigggy as a function of radius. which we have defined to be the mass-weighted mean radial velocity of bound material divided by the local radial coordinate: A [huid element is considered bound if hu;>—1. and h is the fluid elements specilic enthalpy.," The white dashed curve in Figure \ref{fig:dfdr-phase} shows the inflow rate $\nu_\mathrm{inflow}$ as a function of radius, which we have defined to be the mass-weighted mean radial velocity of bound material divided by the local radial coordinate: A fluid element is considered bound if $h u_t > -1$, and $h$ is the fluid element's specific enthalpy." The time integral is performed over our standard epoch of /—[7000A7.15000.M|.," The time integral is performed over our standard epoch of $t=[7000M,15000M]$." For TALzr 20M. we find that rig(re)2[D8TuaQ)]I," For $7M \lesssim r \lesssim 20M$ , we find that $\nu_\mathrm{inflow}(r) \simeq [28 T_\mathrm{orb}(r)]^{-1}$." At smaller radii. the inflow accelerates until near (he ISCO and in the plunging region Viggo(r)~Qa.," At smaller radii, the inflow accelerates until near the ISCO and in the plunging region $\nu_\mathrm{inflow}(r) \sim \Omega_K$." Regions to the left of this curve are clearly more coherent than those to the right., Regions to the left of this curve are clearly more coherent than those to the right. That this should be so is nol loo surprising. given the ultimate dependence of energy release on mass inflow.," That this should be so is not too surprising, given the ultimate dependence of energy release on mass inflow." Indeed. T. proposed (hat the inner disks low [frequency variabili. can be entirely explained by variations spawned at larger radii (bv fluctuations in the stress (o pressure ratio) that are then advected inward with the accretion flow.," Indeed, \citet{1997MNRAS.292..679L} proposed that the inner disk's low frequency variability can be entirely explained by variations spawned at larger radii (by fluctuations in the stress to pressure ratio) that are then advected inward with the accretion flow." What is demonstrated in this phase picture is (hat (Iuctuations lower than the local inflow rate do indeed propagate coherently inward. whatever their initial source.," What is demonstrated in this phase picture is that fluctuations lower than the local inflow rate do indeed propagate coherently inward, whatever their initial source." ILowever. over much of the range of Irequencies studied here. {his criterion can be satislied only near the ISCO and in the plunging region itself.," However, over much of the range of frequencies studied here, this criterion can be satisfied only near the ISCO and in the plunging region itself." At these hieher frequencies (which. as we shall see in the next section. are often the object of most observational study). no such regular propagation pattern can be cliscerned.," At these higher frequencies (which, as we shall see in the next section, are often the object of most observational study), no such regular propagation pattern can be discerned." Returning to the question of why the power spectrum of the total fluxis steeper than that of the flix radiated by individual annuli. we now see that this can beexplained by the," Returning to the question of why the power spectrum of the total fluxis steeper than that of the flux radiated by individual annuli, we now see that this can beexplained by the" In order first to validate our set-up we examine our milicl-zero-hr simulation with ΠΟΙΑ and determine the growth rate using the kinetic energy of motions in the .r direction as described in refsec:analvsis..,In order first to validate our set-up we examine our mhd-zero-hr simulation with HYDRA and determine the growth rate using the kinetic energy of motions in the $x$ direction as described in \\ref{sec:analysis}. Figure 1. contains a plot of the log of the transverse kinetic energv as a function of time., Figure \ref{fig:ideal_validation_ek} contains a plot of the log of the transverse kinetic energy as a function of time. At carly times this growth is clearly exponential ancl can be fitted with a line of slope 2.63 implying a growth rate. normalised by the width of the shear laver ancl the initial relative velocity. for the dominant mode of the WIE instability. of O.A315.," At early times this growth is clearly exponential and can be fitted with a line of slope 2.63 implying a growth rate, normalised by the width of the shear layer and the initial relative velocity, for the dominant mode of the KH instability of 0.1315." We can compare this with the value of the erowth rate calculated. analytically by Miura.&Priteh-ett(1982). (their Figure 4) at this wavenumber of 0.13., We can compare this with the value of the growth rate calculated analytically by \citet{miura82} (their Figure 4) at this wavenumber of 0.13. While comparisons between linear studies of incompressible Hows. and numerical studies of compressible Lows are bound to dilfer to some extent. these results are seen to agree exceptionally. well.," While comparisons between linear studies of incompressible flows, and numerical studies of compressible flows are bound to differ to some extent, these results are seen to agree exceptionally well." We wish to examine not only the linear regime but also the non-linear regime., We wish to examine not only the linear regime but also the non-linear regime. We compare our results for the growth of magnetic energv with those of Malagolietal.(1996). (the upper panel of their Figure 5)., We compare our results for the growth of magnetic energy with those of \citet{mala96} (the upper panel of their Figure 5). Figure 2 contains a plot of the magnetic energy. calculated as ftiQ|LB;B7)dacdy. as a [function of time.," Figure \ref{fig:ideal_validation_b} contains a plot of the magnetic energy, calculated as $\int \! \int \frac{1}{2} \big( B_x^2 + B_y^2 + B_z^2 \big)\,dx\,dy $, as a function of time." The maximum magnetic energy reached in our simulations matches that of Malagolictal.(1996) to within10%., The maximum magnetic energy reached in our simulations matches that of \citet{mala96} to within. .. Our simulation reaches saturation at a later time but the exact time of saturation depends on the initial amplitude of the perturbation and so this is not a concern., Our simulation reaches saturation at a later time but the exact time of saturation depends on the initial amplitude of the perturbation and so this is not a concern. We are therefore confident of the behaviour of LLYDIA in simulating the WIL instability., We are therefore confident of the behaviour of HYDRA in simulating the KH instability. We now move on to investigating the influenee of multifluid AID cllects on the growth. saturation anc non-linear behaviour of this instability.," We now move on to investigating the influence of multifluid MHD effects on the growth, saturation and non-linear behaviour of this instability." We begin our study. of the multifluid WIL instability by choosing our Εις parameters to. ensure. our. ambipolar resistivity is dvwnamically significant while minimising the Hall resistivity., We begin our study of the multifluid KH instability by choosing our fluid parameters to ensure our ambipolar resistivity is dynamically significant while minimising the Hall resistivity. This allows us to isolate the inlluence of the ambipolar resistivity on the instability., This allows us to isolate the influence of the ambipolar resistivity on the instability. In order to increase the ambipolar resistivity we change the value of the collision cocllicient [or species 2 so that νου is decreased by 3 orders of magnitude from that given in table 1 for simulation ambi-mecd-hr and by 4 orders of magnitude for ambi-high-hr.," In order to increase the ambipolar resistivity we change the value of the collision coefficient for species 2 so that $K_{2,0}$ is decreased by 3 orders of magnitude from that given in table \ref{table:mf-params} for simulation ambi-med-hr and by 4 orders of magnitude for ambi-high-hr." ‘These alterations of Aso give values of ry of 3.510.5 and 3.5.10? respectively. and (ambipolar) magnetic« Ievnold's numbers. Rey. of 2.845107 and 2.84107 respectively.," These alterations of $K_{2,0}$ give values of $r_{\rm A}$ of $3.5\times10^{-3}$ and $3.5\times10^{-2}$ respectively, and (ambipolar) magnetic Reynold's numbers, $Re_{\rm m}$ , of $2.84\times10^2$ and $2.84 \times 10^1$ respectively." These simulations are examined in comparison to the full-Iow-hr simulation., These simulations are examined in comparison to the full-low-hr simulation. With a formal magnetic Itevnolds number 2845107. the diffusion in this set-up is predominantly numerical. and as such. it is effectively. an ideal MILD simulation.," With a formal magnetic Reynolds number $2.84\times10^5$, the diffusion in this set-up is predominantly numerical, and as such, it is effectively an ideal MHD simulation." In non-ideal MILD: we must ensure that the leneth scales over which the cilfusion of the magnetic Field (or the whistler waves in the case of Hall dominated Hows) must be resolved in order to properly. track the dynamics of the system., In non-ideal MHD we must ensure that the length scales over which the diffusion of the magnetic field (or the whistler waves in the case of Hall dominated flows) must be resolved in order to properly track the dynamics of the system. To this end we perform a resolution study. using simulations ambi-high-Ir. ambi-high-nir and ambi-high-hr (sce Table 2)).," To this end we perform a resolution study using simulations ambi-high-lr, ambi-high-mr and ambi-high-hr (see Table \ref{table:nomenclature}) )." " Figures 3 and 4. contain plots of the evolution of Ly, and. δα, lor cach of the simulations in our resolution stucdv.", Figures \ref{fig:ambi-res-ek} and \ref{fig:ambi-res-eb} contain plots of the evolution of $\Ek{x}$ and $E_{\rm b}$ for each of the simulations in our resolution study. It can be seen that the linear growth in ambi-hieh-lr is significantly lower than the two other simulations., It can be seen that the linear growth in ambi-high-lr is significantly lower than the two other simulations. However. the linear behaviour is almost identical for ambi-high-n ancl ambi-high-hr.," However, the linear behaviour is almost identical for ambi-high-mr and ambi-high-hr." Phe subsequent. non-linear behaviour is similar with only relatively small variations after /~11., The subsequent non-linear behaviour is similar with only relatively small variations after $t \sim 11$. The results of this study indicate that a resolution of 6400..200is sullicient to capture the initial growth. aud saturation of the instability., The results of this study indicate that a resolution of $6400\times200$is sufficient to capture the initial growth and saturation of the instability. Subsequently. the dynamies is captured at least qualitatively.," Subsequently, the dynamics is captured at least qualitatively." The winds from hot stars are thought to be generated by radiation pressure on optically thick UW resonance lines. aud the theory of line-cyviven flow is very successful in accounting many observed wind features (see Castor. Abbott Klein 1975. Abbott L980. Pauldrach 11986. IKuditzki 11989).,"The winds from hot stars are thought to be generated by radiation pressure on optically thick UV resonance lines, and the theory of line-driven flow is very successful in accounting many observed wind features (see Castor, Abbott Klein 1975, Abbott 1980, Pauldrach 1986, Kudritzki 1989)." Tn low cleusity winds. however. there exists the οκ]Εν that the radiation force aud the wind flow may decouple (Spriugiiauu Pauldrach 1992. Porter Drew 1995 [hereafter PD95]. Babel 1996).," In low density winds, however, there exists the possibility that the radiation force and the wind flow may decouple (Springmann Pauldrach 1992, Porter Drew 1995 [hereafter PD95], Babel 1996)." The decoupling process strips the metallic ions from the rest of the plasma. and as the radiative force on the flow is mediated by the ious. then the wind receives no further acceleration.," The decoupling process strips the metallic ions from the rest of the plasma, and as the radiative force on the flow is mediated by the ions, then the wind receives no further acceleration." The winds which are most ikelv to undergo this decoupling are D star winds (Babel 1996. PD95). aud metallic A star winds (Babel 1995).," The winds which are most likely to undergo this decoupling are B star winds (Babel 1996, PD95), and metallic A star winds (Babel 1995)." The frictional interaction between the metallic ious aud he rest of the wind may also seriously interfere with he radiative equilibrimu (Springmanun Pauldrach 1992. Cavley Οπου 1995).," The frictional interaction between the metallic ions and the rest of the wind may also seriously interfere with the radiative equilibrium (Springmann Pauldrach 1992, Gayley Owocki 1995)." " Decoupling radii for low density winds may be close to the photosphere for D stars (PD95) or indeed may be associated with the photosplere ou the case of some A star winds (Babel 1995). where there is no reeion outside the photosphere where a fully coupled wind CNists,"," Decoupling radii for low density winds may be close to the photosphere for B stars (PD95) or indeed may be associated with the photosphere on the case of some A star winds (Babel 1995), where there is no region outside the photosphere where a fully coupled wind exists." The lne-driven wind accelerates normally when fully coupled to the raciation feld. but once decoupled cannot receive anv further aceeration.," The line-driven wind accelerates normally when fully coupled to the radiation field, but once decoupled cannot receive any further acceleration." It is possible that the wind will decouple before it has reached escape velocity. in which case the decoupled flow will stall at some radius and fall back toward the star.," It is possible that the wind will decouple before it has reached escape velocity, in which case the decoupled flow will stall at some radius and fall back toward the star." It is his aspect of decoupled flows which is exaiuined in this paper., It is this aspect of decoupled flows which is examined in this paper. The rest of this paper is structured as follows: in we he physics of wind decoupling is examined. aud iu ivdrodyvuauical simulations of decoupled winds are preseuted.," The rest of this paper is structured as follows: in 2 the physics of wind decoupling is examined, and in 3 hydrodynamical simulations of decoupled winds are presented." The observational signatures of the shells are presented im LE and a diseussion aud conclusions are giveu πι 855., The observational signatures of the shells are presented in 4 and a discussion and conclusions are given in 5. There are two wavs in which the radiation aud matter fields iu a line-driven wind may decouple: jou stripping (PD95. Springmmamn Pauldrach 1992) aud shock decoupling (PD95. Ikrolik παντος 1985).," There are two ways in which the radiation and matter fields in a line-driven wind may decouple: ion stripping (PD95, Springmann Pauldrach 1992) and shock decoupling (PD95, Krolik Raymond 1985)." The plysics of jou stripping was first noted iu the coutext of electrical conductivity by Dreicer (1959. 1960) and has its roots iu the basic wmechanisim allowing optically thick metallic ion lines to mediate the force on a wind.," The physics of ion stripping was first noted in the context of electrical conductivity by Dreicer (1959, 1960) and has its roots in the basic mechanism allowing optically thick metallic ion lines to mediate the force on a wind." The metallic ious are accelerated via photon scattering off their UV lines., The metallic ions are accelerated via photon scattering off their UV lines. The ious then share this acceleration with the rest of the wind (livdroseen and lelini 1023) by a process simular to friction., The ions then share this acceleration with the rest of the wind (hydrogen and helium ions) by a process similar to friction. This frictional interaction depends on the relative drift velocity of the ions through the rest of the wind., This frictional interaction depends on the relative drift velocity of the ions through the rest of the wind. For low drift velocitics the force is proportional to the drift velocity. however it reaches a asim when the drift aud thermal kinetic cucreics are equal.," For low drift velocities the force is proportional to the drift velocity, however it reaches a maximum when the drift and thermal kinetic energies are equal." Bevoud this the frictional interaction decreases rapidly with increasing drift velocity., Beyond this the frictional interaction decreases rapidly with increasing drift velocity. Therefore if tlie ious? dift velocity does become large enough. then as there is little or no frictional iuteraction with the rest of the wincl. they may freely accelerate.," Therefore if the ions' drift velocity does become large enough, then as there is little or no frictional interaction with the rest of the wind, they may freely accelerate." This leaves the rest of the wind, This leaves the rest of the wind but these data generally are of resolution too low to isolate individual SSCs.,but these data generally are of resolution too low to isolate individual SSCs. Yet another method is to search for voung supernovae. (hus inferring a supernova rate that may give Clues about (the star-lormation rate within an SsC.," Yet another method is to search for young supernovae, thus inferring a supernova rate that may give clues about the star-formation rate within an SSC." However. the supernovae in (he clensest star-Iorming regions may be heavily obscured by dust. aud impossible to detect optically.," However, the supernovae in the densest star-forming regions may be heavily obscured by dust and impossible to detect optically." In this circumstance. voung radio supernovae may be detected more easily al centimeter wavelengths: milliarcsecoud resolution max be used to separate them from the more diffuse thermal and svachrotron radiation present in the SSCs (Neffetal.2004:Lonsdaleetal. 2006).," In this circumstance, young radio supernovae may be detected more easily at centimeter wavelengths; milliarcsecond resolution may be used to separate them from the more diffuse thermal and synchrotron radiation present in the SSCs \citep{nef04,rov05,lon06}." . We have made VLBI High Sensitivity Array (LISA) observations of three nearby chwarl galaxies. II Zw 40. He 2-10. and NGC 5253. containing either one or several SSCs Chat are separated by a few parsecs to (ens of parsecs.," We have made VLBI High Sensitivity Array (HSA) observations of three nearby dwarf galaxies, II Zw 40, He 2-10, and NGC 5253, containing either one or several SSCs that are separated by a few parsecs to tens of parsecs." Existing mid-inlrared aud radio interferometric images of these galaxies are sullicient to isolate the individual SSCs and estimate their total ionizing fluxes., Existing mid-infrared and radio interferometric images of these galaxies are sufficient to isolate the individual SSCs and estimate their total ionizing fluxes. All three target. galaxies displav significant Wolf-Rawvet. spectral features. indicating the presence of (at least) hundreds of massive stars that have evolved off the main sequence.," All three target galaxies display significant Wolf-Rayet spectral features, indicating the presence of (at least) hundreds of massive stars that have evolved off the main sequence." Our LISA imaging was carried out in an elfort to detect. voung radio supernovae within the SSCs in the dwarl galaxies. and hence to assess (he local supernova rates.," Our HSA imaging was carried out in an effort to detect young radio supernovae within the SSCs in the dwarf galaxies, and hence to assess the local supernova rates." This paper reports the results of our LSA supernova search. which reaches to detection thresholds near the power of Cas A in all three target. galaxies. and its implications for their stellar contents ancl supernova rales.," This paper reports the results of our HSA supernova search, which reaches to detection thresholds near the power of Cas A in all three target galaxies, and its implications for their stellar contents and supernova rates." We observed our (three target galaxies on 2005 FED 26/27 using the HSA (program ID DUO0S0)., We observed our three target galaxies on 2005 FEB 26/27 using the HSA (program ID BU030). The HSA observations made use of the LO antennas of the Verv Long Baseline Array (VLBA). 25 phasecl antennas of the Very Large Array (VLA). and the 100m Green Dank Telescope (GBT).," The HSA observations made use of the 10 antennas of the Very Long Baseline Array (VLBA), 25 phased antennas of the Very Large Array (VLA), and the 100m Green Bank Telescope (GBT)." The 305m Arecibo telescope also was used for I1 Zw 40. but Ie 2-10 and NGC 5253 are too [ar south to be accessible to Arecibo.," The 305m Arecibo telescope also was used for II Zw 40, but He 2-10 and NGC 5253 are too far south to be accessible to Arecibo." Each target was observed in dual-cireiular polarization at 4.991 GlIIz frequency. with total bandwidths of 32 MIIz at each polarization and 2-bit sampling.," Each target was observed in dual-circular polarization at 4.991 GHz frequency, with total bandwidths of 32 MHz at each polarization and 2-bit sampling." The total observing time for each target was between 2 and 4 hours. while the on-source integrations ranged from 1 to 2 hours.," The total observing time for each target was between 2 and 4 hours, while the on-source integrations ranged from 1 to 2 hours." Integration times were to less lor GBT. VLA. and. Arecibo. since these telescopes slew more slowly than ihe VLBA antennas.," Integration times were to less for GBT, VLA, and Arecibo, since these telescopes slew more slowly than the VLBA antennas." All three targets were known to be quite weak. so Chev were observed by means of phase-relerencing to an angularly nearby. calibrator source. separated [rom the lareel by 0.77 (o0 2.27.," All three targets were known to be quite weak, so they were observed by means of phase-referencing to an angularly nearby calibrator source, separated from the target by $0.7^\circ$ to $2.2^\circ$." Typical evele times in minutes were 1-2-1 (including slew times) for the calibrator-target-calibrator sequences: an additional 10-20 seconds was allowed on each calibrator or target for IL Zw 40. due to the slower slew speed of Arecibo.," Typical cycle times in minutes were 1-2-1 (including slew times) for the calibrator-target-calibrator sequences; an additional 10-20 seconds was allowed on each calibrator or target for II Zw 40, due to the slower slew speed of Arecibo." Details of the, Details of the The interplay between galaxies and the intergalactic medium,The interplay between galaxies and the intergalactic medium "The first term is noise due to stars near the edge of the DIRBE beam which will""tlieker* in and out of (he beam when observed with various centers aud position angles.",The first term is noise due to stars near the edge of the DIRBE beam which will“flicker” in and out of the beam when observed with various centers and position angles. The second term is the [lux error with an added allowance For variation in the fluxes between the DIRBE and 2ALASS observations as in Wright(2001).. with the modification that the allowance for variable stars was reduced from 0.1 to 0.001. reducing this allowance lrom ao = 0.34 tog = 0.02 magnitudes.," The second term is the flux error with an added allowance for variation in the fluxes between the DIRBE and 2MASS observations as in \citet{elw01}, with the modification that the allowance for variable stars was reduced from 0.1 to 0.001, reducing this allowance from $\sigma$ = 0.34 to $\sigma$ = 0.03 magnitudes." Statisticallv. the o's computed with the Wright(2001) value of 0.1 were too large to be justifiable.," Statistically, the $\sigma$ 's computed with the \citet{elw01} value of 0.1 were too large to be justifiable." Upon dividing the residuals Grom the linear fit to the DIRBE vs. 2NLASS intensities (described below) by the computed os. we noticed that the residual/o al all pixels was less (han one.," Upon dividing the residuals from the linear fit to the DIRBE vs. 2MASS intensities (described below) by the computed $\sigma$ 's, we noticed that the $\sigma$ at all pixels was less than one." The new value of 0.001 gives a statistically more reasonable distribution of residual/o values which is described at the end of (his Section., The new value of 0.001 gives a statistically more reasonable distribution of $\sigma$ values which is described at the end of this Section. The error estimates for all stars brighter than IX = 5.5 or J = 6.5 were set to & 1 mag to effectively remove pixels affected by confusion due (ο saturation from the final analysis., The error estimates for all stars brighter than K = 5.5 or J = 6.5 were set to $\pm$ 1 mag to effectively remove pixels affected by confusion due to saturation from the final analysis. Stars with reported null uncertainties were assigned an uncertainty of z 0.5 mag., Stars with reported null uncertainties were assigned an uncertainty of $\pm$ 0.5 mag. Since (he error in the DIRBE data is negligible (HIautseretal.1993).. all of the error comes from the caleulation of D; and is ascribed to DZ; lor the fits.," Since the error in the DIRBE data is negligible \citep{hau98}, all of the error comes from the calculation of $B_{i}$ and is ascribed to $DZ_{i}$ for the fits." " Figures 1.. 2. and 32. show plots of DZ; vs. D; for all pixels in each of (he 40 reeions in Kk. J. and L respectively where (he point sizes are inversely proportional to the above os. The fits in Kk. J and L have slopes of hy = 0.38. ry = 0.97 and ij, = 0.43 respectively with 40 independent intercepts in each band. derived using a weighted median procedure. i.e. finding the values of & ancl DZ(0) that minimize the sum: Derived intercepts for each [ield are given in Tables 1.. 2 and 3. [or Ix. J. and L respectively."," Figures \ref{kbdz}, \ref{jbdz} and \ref{lbdz} show plots of $DZ_i$ vs. $B_i$ for all pixels in each of the 40 regions in K, J, and L respectively where the point sizes are inversely proportional to the above $\sigma$ 's. The fits in K, J and L have slopes of $\kappa_K$ = 0.88, $\kappa_J$ = 0.97 and $\kappa_L$ = 0.43 respectively with 40 independent intercepts in each band, derived using a weighted median procedure, i.e. finding the values of $\kappa$ and DZ(0) that minimize the sum: Derived intercepts for each field are given in Tables \ref{ktable}, \ref{jtable} and \ref{ltable} for K, J, and L respectively." " The contributions [rom stars fainter than the 1Hth magnitude were evaluated statistically by fitting a power series of the form n,(n) = n4,10"""" to counts of 2\LASS stars in each ol the 40 regions. binned into 3 one-magnitude bins centered on m= 11.5. 12.5 and 13.5"," The contributions from stars fainter than the 14th magnitude were evaluated statistically by fitting a power series of the form $n_q$ (m) = $n_{\circ,q} 10^{\alpha m}$ to counts of 2MASS stars in each of the 40 regions, binned into 3 one-magnitude bins centered on m= 11.5, 12.5 and 13.5." " The fits resulted in 40 individual ja, and ay=0.288 and ay=0.276 where anv a<0.4 results in a converging flix contribution."," The fits resulted in 40 individual $n_{\circ,q}$ and $\alpha_K = 0.288$ and $\alpha_J = 0.276$ where any $\alpha < 0.4$ results in a converging flux contribution." " The intensity contribution from [aint stars in the q' region with solid angle Q, is then or. in the limit of infinitely fine bins."," The intensity contribution from faint stars in the $q^{th}$ region with solid angle $\Omega_q$ is then or, in the limit of infinitely fine bins," close agreement.,close agreement. " For the most part. objects classified as asteroids (comets) based on (heir orbits, have the physical properties expected of asteroids (comets) as far as can be observed."," For the most part, objects classified as asteroids (comets) based on their orbits, have the physical properties expected of asteroids (comets) as far as can be observed." Exceptions have given rise to a somewhat confusing and evolving svstem of nomenclature. used to describe small solar system bodies by a combination of their orbital properties and physical appearances.," Exceptions have given rise to a somewhat confusing and evolving system of nomenclature, used to describe small solar system bodies by a combination of their orbital properties and physical appearances." To clarify this we show. in Figure (1)). a two-parameter classification based on morphology. on the one hand. and the Tisserand parameter on the other.," To clarify this we show, in Figure \ref{classification}) ), a two-parameter classification based on morphology, on the one hand, and the Tisserand parameter on the other." Traditional comels lose mass and have 7;< 3., Traditional comets lose mass and have $T_J <$ 3. Those with 2 x7)< 3 are called Jupiter family comets and are thought (o originate in (he Ixuiper belt., Those with 2 $\le T_J <$ 3 are called Jupiter family comets and are thought to originate in the Kuiper belt. Comets with 7;< 2 are long-period or llallev family comets. with a source in the Oort cloud.," Comets with $T_J <$ 2 are long-period or Halley family comets, with a source in the Oort cloud." Inactive counterparts to the Jupiter family comets are called. variously. extinct. dead or dormant comets (Hartmann et al.," Inactive counterparts to the Jupiter family comets are called, variously, extinct, dead or dormant comets (Hartmann et al." 1937)., 1987). Thev are presumably former comets in which past heating bv the Sun has removed all near surface ice. although buried ice might remain ancl these objects could. in principle. reactivate.," They are presumably former comets in which past heating by the Sun has removed all near surface ice, although buried ice might remain and these objects could, in principle, reactivate." ]nnactive counterparts to the long-period and IHallev fanilv comets are called. Damocloics (Jewitt 2005)., Inactive counterparts to the long-period and Halley family comets are called Damocloids (Jewitt 2005). Again. these are likely objects in which near-surface ice has been lost.," Again, these are likely objects in which near-surface ice has been lost." In (his paper. we focus attention on the sub-set of the small-bodies which are dvnanmically asteroid-like (a«aj.T;> 3) but which lose mass. like comets.," In this paper, we focus attention on the sub-set of the small-bodies which are dynamically asteroid-like $a < a_J, T_J >$ 3) but which lose mass, like comets." These were called. “main-belt comets” bv IIsieh and Jewitt (2006) but here we use the term “active asteroids’. since some of the examples to be considered. while dvnamically asteroid-like ancl showing comet-like properties. are not in the main-belt.," These were called “main-belt comets” by Hsieh and Jewitt (2006) but here we use the term “active asteroids”, since some of the examples to be considered, while dynamically asteroid-like and showing comet-like properties, are not in the main-belt." Numerical integrations show that these are not recently captured comets from the Ixuiper belt (Fernandez et al., Numerical integrations show that these are not recently captured comets from the Kuiper belt (Fernandez et al. 2002. Levison et al.," 2002, Levison et al." 2006)., 2006). Scientific interest in these objects lies in the possibility (hat primordial water ice could have survived in asteroids despite early heating from embedded radioactive nuclei (Grimm ancl MeSween 1989) and heating bv (he sun., Scientific interest in these objects lies in the possibility that primordial water ice could have survived in asteroids despite early heating from embedded radioactive nuclei (Grimm and McSween 1989) and heating by the sun. Even greater interest is added by the possibility that the outer asteroid belt may have supplied part of the volatile inventory of the Earth (Morbidelli et al., Even greater interest is added by the possibility that the outer asteroid belt may have supplied part of the volatile inventory of the Earth (Morbidelli et al. 2000)., 2000). Additionally. active asteroids are a source of dust lor the Zocliacal cloud. while unseen counterpart bodies may supply dust to the debris disks of other stus (e.g. 5hannon and Wu 2011).," Additionally, active asteroids are a source of dust for the Zodiacal cloud, while unseen counterpart bodies may supply dust to the debris disks of other stars (e.g. Shannon and Wu 2011)." Alter briefly summarizing the current observational evidence concerning these active asteroids. we discuss (he surprisingly varied mechanisms through which a body is capable ol losing mass.," After briefly summarizing the current observational evidence concerning these active asteroids, we discuss the surprisingly varied mechanisms through which a body is capable of losing mass." A recent and complementary discussion focused on observational properties has been offered by Bertini (2011)., A recent and complementary discussion focused on observational properties has been offered by Bertini (2011). To-date. eleven active (or mass-shedding) asteroids have been reported.," To-date, eleven active (or mass-shedding) asteroids have been reported." The nine spatially resolved examples are shown [or comparison in Figure (2)). while their positions in the," The nine spatially resolved examples are shown for comparison in Figure \ref{image_compo}) ), while their positions in the" "Throughout the paper we have assumed that the velocity field of the galaxy is always observable out to four disc scale lengths, which in real observations is of course due to limited sensitivity not always possible.","Throughout the paper we have assumed that the velocity field of the galaxy is always observable out to four disc scale lengths, which in real observations is of course due to limited sensitivity not always possible." " Therefore, depending on the instrument, one might just observe the inner parts of the VF."," Therefore, depending on the instrument, one might just observe the inner parts of the VF." As a consequence distortions in the outskirts can be missed., As a consequence distortions in the outskirts can be missed. " Here we were interested in the principle effects of limited resolution on the appearance of the 2D velocity fields, without specifying a special instrument, i.e. for an idealized observation."," Here we were interested in the principle effects of limited resolution on the appearance of the 2D velocity fields, without specifying a special instrument, i.e. for an idealized observation." In a future work we want to study flux-limited velocity fields for special instruments for comparison with observed data., In a future work we want to study flux-limited velocity fields for special instruments for comparison with observed data. A second parameter that changes the appearance of the 2D velocity field is the inclination of the galaxy., A second parameter that changes the appearance of the 2D velocity field is the inclination of the galaxy. Throughout the paper we have adopted an inclination i=35°., Throughout the paper we have adopted an inclination $=$ $^{\circ}$. For an undisturbed galaxy typically a correction with the sine of the inclination is applied to the rotation curve., For an undisturbed galaxy typically a correction with the sine of the inclination is applied to the rotation curve. The appearance of a regular 2D field is not severely affected by inclination., The appearance of a regular 2D field is not severely affected by inclination. " In the case of an interacting galaxy, however, the appearance of the velocity field changes with inclination."," In the case of an interacting galaxy, however, the appearance of the velocity field changes with inclination." " A systematic investigation of the effects of inclination is, however, difficult, as they depend on the specific interaction geometry."," A systematic investigation of the effects of inclination is, however, difficult, as they depend on the specific interaction geometry." We sketch here the influence of inclination on the VF presented in Sect. ??.., We sketch here the influence of inclination on the VF presented in Sect. \ref{DR}. . " Instead of i=35°, we now choose i=80°, i.e. nearly edge-on."," Instead of $=$ $^{\circ}$, we now choose $=$ $^{\circ}$, i.e. nearly edge-on." The unequal mass edge-on merger of simulation 2 produces VF distortions mainly in the plane of the disc., The unequal mass edge-on merger of simulation 2 produces VF distortions mainly in the plane of the disc. " These distortions are therefore well visible at low inclinations, see Fig."," These distortions are therefore well visible at low inclinations, see Fig." 4 but get less prominent for higher inclinations., \ref{disturbed0105} but get less prominent for higher inclinations. In Fig., In Fig. 17 we show the same snapshot as in Fig., \ref{inclination} we show the same snapshot as in Fig. 4 but at an inclination of i=80° instead of i=35°., \ref{disturbed0105} but at an inclination of $=$ $^{\circ}$ instead of $=$ $^{\circ}$. " At z=0.5 the VF even appears regular, hence the interaction might not be recognized."," At $z=0.5$ the VF even appears regular, hence the interaction might not be recognized." Many recent studies have analysed the luminosity evolution of galaxies via the Tully-Fisher relation (e.g. Ziegler et al., Many recent studies have analysed the luminosity evolution of galaxies via the Tully-Fisher relation (e.g. Ziegler et al. " 2003, Bohhm et al."," 2003, Böhhm et al." " 2004, Bamford et al."," 2004, Bamford et al." " 2005, Nakamura et al."," 2005, Nakamura et al." " 2006, Flores et al."," 2006, Flores et al." 2006)., 2006). " Some of these studies also focussed on environmental effects, i.e. differences in the Tully-Fisher relation between field and cluster population."," Some of these studies also focussed on environmental effects, i.e. differences in the Tully-Fisher relation between field and cluster population." Ziegler et al. (, Ziegler et al. ( 2003) and Nakamura et al. (,2003) and Nakamura et al. ( "2006) find no significant differences between field and cluster galaxies, whereas Bamford et al. (","2006) find no significant differences between field and cluster galaxies, whereas Bamford et al. (" 2005) claim that galaxies in cluster are on average brighter than their field counterparts.,2005) claim that galaxies in cluster are on average brighter than their field counterparts. The Tully-Fisher relation (TFR) is also extensively used as test-bench for galaxy formation models., The Tully-Fisher relation (TFR) is also extensively used as test-bench for galaxy formation models. Portinari Sommer-Larsen (2007) investigated the redshift evolution of the Tully-Fisher relation in cosmological simulations., Portinari Sommer-Larsen (2007) investigated the redshift evolution of the Tully-Fisher relation in cosmological simulations. They find an offset between the observed and simulated Tully-Fisher relation at z=0., They find an offset between the observed and simulated Tully-Fisher relation at z=0. The evolution they find is intermediate between diverse observational results., The evolution they find is intermediate between diverse observational results. Parts of the discrepancies between the various observational results may be attributed to the waydistortions in the velocity fields of the galaxies are accounted for., Parts of the discrepancies between the various observational results may be attributed to the waydistortions in the velocity fields of the galaxies are accounted for. Tt is well-krown that normal active galactic ποια (AGNs) explain the cosnüc N-rav backeround (CNB) low several huudreds keV (for reviews see 1987:Fabian 1992: 2003. hereafter τοῦCall.Comastri. 2007).,"It is well-known that normal active galactic nuclei (AGNs) explain the cosmic X-ray background (CXB) below several hundreds keV (for reviews see 1987; 1992; 2003, hereafter U03;, 2007)." " It is also known hat rare ACNs of the blazar tvpe make a considerable contribution to the cosmic eauunarav backeround in the energv range from 100 MeV to 100 CoV. which has a jud power-law spectrum (almost fiat in the wf, plot). hough blazars may not explain all of the backeround Hix. leaving some room for possible coutributions frou. conipletelv different sources 2006. and references therein)."," It is also known that rare AGNs of the blazar type make a considerable contribution to the cosmic gamma-ray background in the energy range from 100 MeV to 100 GeV, which has a hard power-law spectrum (almost flat in the $\nu F_\nu$ plot), though blazars may not explain all of the background flux, leaving some room for possible contributions from completely different sources 2006, and references therein)." The origin of the ganuna-rav background at he eap between these two energv regions. he. νὰ10 MeV. has also been an intriguing iuvstery.," The origin of the gamma-ray background at the gap between these two energy regions, i.e., $\sim$ 1–10 MeV, has also been an intriguing mystery." " The ΑςUN spectra adopted iu population svuthesis models of the CXB cannot explain this componeut because of the asstuned exponential cut-off at a few hundred keV. The background spectrum in the 110 MeV. band. is much softer (photon iudex à ~2.8) than the CV. component. indicating a different origiu from that above 100 MeV (οιο, 1998)."," The AGN spectra adopted in population synthesis models of the CXB cannot explain this component because of the assumed exponential cut-off at a few hundred keV. The background spectrum in the 1–10 MeV band is much softer (photon index $\alpha \sim $ 2.8) than the GeV component, indicating a different origin from that above 100 MeV (e.g. 1998)." A few candidates have been proposed to explain the 110 MeV backerouud., A few candidates have been proposed to explain the 1–10 MeV background. One is the unclear decay ravs from type Ta supernovae (SNe Ia)(Clavton 1975: 1996: 1999)., One is the nuclear decay gamma-rays from type Ia supernovae (SNe Ia) 1975; 1996; 1999). ILowever. recent studies based on the latest neasureineuts of the cosmic SN Ia rates show that the background fiux expected frou: SNe Ta is about an order of magnitude lower than observed(Ahn.Komatsu. 2005:Strgewui 2005).," However, recent studies based on the latest measurements of the cosmic SN Ia rates show that the background flux expected from SNe Ia is about an order of magnitude lower than observed, 2005; 2005)." " There Is a class of blazars called ""MeV. blazars. whose spectra have peaks at ~ AIeV 1995: 2006). aud these MeV. blagars could potentially contribute to the MeWV backeround."," There is a class of blazars called “MeV blazars”, whose spectra have peaks at $\sim$ MeV 1995; 2006), and these MeV blazars could potentially contribute to the MeV background." However. quantitative estimate of the contribution is dificult because of the still 4.small sample available at present.," However, quantitative estimate of the contribution is difficult because of the still small sample available at present." " Aunililation of the dark matter particles has also Όσο discussed 2005a, 2005b: 2006:Lawson 2007). but there is no natural particle plivsics candidate for sucli a dark matter particle with a mass scale of ? MeV. The motivation of MeV dark matter has been iuspiredIs by the 511 keV line cussion from the Galactic center. but a few astrophysical explanations are possible for this line cluission 2006. anc references therein)."," Annihilation of the dark matter particles has also been discussed 2005a, 2005b; 2006; 2007), but there is no natural particle physics candidate for such a dark matter particle with a mass scale of $\sim$ MeV. The motivation of MeV dark matter has been inspired by the 511 keV line emission from the Galactic center, but a few astrophysical explanations are possible for this line emission 2006, and references therein)." An dmuportant feature of the AleV background spectrin is that its power-law spectrum issnoothly connected to the peak of the CNB spectrum., An important feature of the MeV background spectrum is that its power-law spectrum is connected to the peak of the CXB spectrum. Tf the origin of the MeV background is completely differeut roni that of the CAB. such a smooth counection would xo surprising.," If the origin of the MeV background is completely different from that of the CXB, such a smooth connection would be surprising." Rather. if seenis more plausible that he MeV background fux is composed of the same xopulatious that make the CNB. and simply the curreut AGN spectral models are not sufficient to describe the MeV spectra.," Rather, it seems more plausible that the MeV background flux is composed of the same populations that make the CXB, and simply the current AGN spectral models are not sufficient to describe the MeV spectra." The X-ray AGN spectra are well described. » the Comptonization of seed UV plotous by the vot coronal electrous 1991. 1995). aud he cut-off at —100 keV reflects the thermal οπου distribution of the hot electrons.," The X-ray AGN spectra are well described by the Comptonization of seed UV photons by the hot coronal electrons 1994, 1995), and the cut-off at $\sim$ 100 keV reflects the thermal energy distribution of the hot electrons." Althoueh the AGN spectra indeed show evideuce for such a cut-off 1995:ZdziuskiPoutanen. 2000). a small amount of additional uou-thermal electrons with a soft spectruni is sufficient to explain the MeV backeround.," Although the AGN spectra indeed show evidence for such a cut-off 1995;, 2000), a small amount of additional non-thermal electrons with a soft spectrum is sufficient to explain the MeV background." Due to the lanited sensitivity of current MeV eanunarav observations. the presence of such nou-thermal components is not strongly constrained even iu the spectra of nearby brightest AGNs.," Due to the limited sensitivity of current MeV gamma-ray observations, the presence of such non-thermal components is not strongly constrained even in the spectra of nearby brightest AGNs." Furthermore. it is believed that coronae aroundaccretion disks share some," Furthermore, it is believed that coronae aroundaccretion disks share some" "ollowiug factors: (1) The measured ellipticiies of clusters frequently depend on distance from the cluster center,",following factors: (1) The measured ellipticities of clusters frequently depend on distance from the cluster center. Some dispersion will therefore arise unless all rieasureimmeuts refer the same isoplote that which encloses half of the cluster Iuuiünosity iu projection. (, Some dispersion will therefore arise unless all measurements refer the same isophote that which encloses half of the cluster luminosity in projection. ( 2) Background subtraction may be a problem for the cast Iunuiuous clusters in the densest regions of the Magellanic Clouds. (,2) Background subtraction may be a problem for the least luminous clusters in the densest regions of the Magellanic Clouds. ( 3) Stochastic effects will affect all attempts to determine the shapes of the isoplotes of all clusters. particularly those that are faint or highly resolved.,"3) Stochastic effects will affect all attempts to determine the shapes of the isophotes of all clusters, particularly those that are faint or highly resolved." Since only a single series of observations exists for the fiatteniues of SAIC clusters (IKoutizas et al., Since only a single series of observations exists for the flattenings of SMC clusters (Kontizas et al. 1990) it is not possible vet to derive au incdependcut estimate for the errors iu the quoted ellipticities of SAIC clusters., 1990) it is not possible yet to derive an independent estimate for the errors in the quoted ellipticities of SMC clusters. Tu the LMC cluster age determinations. on a scale from I (very young) to VII (very old). were taken from Searle et al. (," In the LMC cluster age determinations, on a scale from I (very young) to VII (very old), were taken from Searle et al. (" 1980).,1980). These were supplemented by assignment to age class VIT for all of the globular clusters (van deu Berel 2000. p.101) in the LMC.," These were supplemented by assignment to age class VII for all of the globular clusters (van den Bergh 2000, p.104) in the LMC." Contrary to a previous result bv Fall Freuk (1981) the data. which are plotted in Figure 3. show uo evidence for auy correlation between the age class aud the flattening of clusters in the LAIC.," Contrary to a previous result by Fall Frenk (1984) the data, which are plotted in Figure 3, show no evidence for any correlation between the age class and the flattening of clusters in the LMC." Also giveu in Tables 2 aud 3 are values of the reddenine-fee paraincter ο) = (U-D) - 0.72 (B-V) introduced by Joliusou Moreau (1951)., Also given in Tables 2 and 3 are values of the reddening-free parameter Q = (U-B) - 0.72 (B-V) introduced by Johnson Morgan (1951). This paraicter has good scusitivity to cluster age for voune clusters. but may be affected by metallicity for the oldest clusters.," This parameter has good sensitivity to cluster age for young clusters, but may be affected by metallicity for the oldest clusters." In the tables uncertain values are followed by a colon., In the tables uncertain values are followed by a colon. The data in in Table 2 aud Table 3 are plotted in Figure L, The data in in Table 2 and Table 3 are plotted in Figure 4. This fleure shows no evidence for any correlation between LMC and SAIC cluster ellipticity aud the paramcter Q. which may be regarded as a proxy for age.," This figure shows no evidence for any correlation between LMC and SMC cluster ellipticity and the parameter Q, which may be regarded as a proxy for age." This is so because voung blue clusters have more uceative C values than do older ones., This is so because young blue clusters have more negative Q values than do older ones. Figure 5 shows a plot of the ellipticities of LAIC clusers asa function of their Iuniunositv., Figure 5 shows a plot of the ellipticities of LMC clusters as a function of their luminosity. Contrary to a xevious result by van deu BerghS (1983a) the data that are now available show no evidence for a correlation )otwoeen cluster Inuimosityv anc cluster flatteniug., Contrary to a previous result by van den Bergh (1983a) the data that are now available show no evidence for a correlation between cluster luminosity and cluster flattening. This result is true for both elobular clusters (shown in the feure as triangles) and for votneer clusters. which are potted as clots.," This result is true for both globular clusters (shown in the figure as triangles) and for younger clusters, which are plotted as dots." " The data in Table 1 clearvy show that the Galactic οobular clusters with A,« 1.0 mae are. on average. uuch less flattened than are trose of all of the clusters 11i the LMC."," The data in Table 1 clearly show that the Galactic globular clusters with $A_{v} <$ 1.0 mag are, on average, much less flattened than are those of all of the clusters in the LMC." A I-S test shows that the probability hat the Galactic and LMC custer flattening distributions were drawn from the same parent distribution is -7.0 were drawn frou the same flatenine distribution as the LMC clusters.", A K-S test shows that there is only a probability that the 12 Galactic clusters with $M_{v} >$ -7.0 were drawn from the same flattening distribution as the LMC clusters. " A comparison between all Galactic elobulu clusters with A,< 1. nae and the 10 objects im Table 2 which are classified as being either elobular clusters (van den Bergh 2000. or that belong to Searle et al. ("," A comparison between all Galactic globular clusters with $A_{v} <$ 1.0 mag and the 10 objects in Table 2 which are classified as being either globular clusters (van den Bergh 2000, or that belong to Searle et al. (" 1980) age class VIT. vields a probability of ouly that the LAIC and Galactic globulars were drawn from the same pareut population of fattening values.,"1980) age class VII, yields a probability of only that the LMC and Galactic globulars were drawn from the same parent population of flattening values." It is concluded that pxth elobular clusters and vounecr clusters in the LAIC are significautly more flattened than are Calactic elobular clusters., It is concluded that both globular clusters and younger clusters in the LMC are significantly more flattened than are Galactic globular clusters. Unfortunatelv little or no information is available ou the flatteniug distribution of Galactic ο201 clusters., Unfortunately little or no information is available on the flattening distribution of Galactic open clusters. However. casual inspection of the priuts of the Palomar Sky Survey sueecsts that Galactic open cluster are mostly almost circular in outline.," However, casual inspection of the prints of the Palomar Sky Survey suggests that Galactic open cluster are mostly almost circular in outline." This suggests that Galactic open clusters resemble Calactic elonmlars aud therefore differ svstematically from their counterparts in the Clouds of Magellan., This suggests that Galactic open clusters resemble Galactic globulars and therefore differ systematically from their counterparts in the Clouds of Magellan. The reason for lis systematic differenee between Calactic star clusters aud those in the Magellanic Clouds remains a 1uystery., The reason for this systematic difference between Galactic star clusters and those in the Magellanic Clouds remains a mystery. From the data in Table Lit is seen that the clusters iu the S11all \lagellanic Cloud are typically 10uch more flattened than those of the elobular clusters sumroundius the Galaxy., From the data in Table 1 it is seen that the clusters in the Small Magellanic Cloud are typically much more flattened than those of the globular clusters surrounding the Galaxy. A Ίο test shows only <0.01% probability that the flattening distributions of Galactic aud Simall Cloud clusters were dran from the same parent population., A K-S test shows only $<$ probability that the flattening distributions of Galactic and Small Cloud clusters were drawn from the same parent population. Ixoutezas et al. (, Kontezas et al. ( 1990) found the star clusters in the SAIC to be even flatter than those in the LMC.,1990) found the star clusters in the SMC to be even flatter than those in the LMC. This couclusiou is cousistent with the data in Table 2 (LAIC) and Table 3 (SAIC)., This conclusion is consistent with the data in Table 2 (LMC) and Table 3 (SMC). However.," However," Next.- draw ayΜΗ» H vando variates- p] with. zero mcan and unitB variance.B and formJ the sum p?D ,"Next, draw $2\ell-1$ Gaussian random variates $\rho_{\ell}^j$ with zero mean and unit variance, and form the sum $\rho_{\ell}^2 = \sum_{j=1}^{2\ell-1} |\rho_{\ell}^j|^2$." Then the desired power spectrum sample is giveu by Sampling biuued C's is verv similar., Then the desired power spectrum sample is given by Sampling binned $C_{\ell}$ 's is very similar. " First. we define the binning scheme to be uniform in C(6|1). uid choose some biu Hits (4,5, and £444."," First, we define the binning scheme to be uniform in $C_{\ell}\,\ell(\ell+1)$, and choose some bin limits $\ell_{\textrm{min}}$ and $\ell_{\textrm{max}}$." We then form the quantity The umber of independent harmonic modes in this sum ds 59—(nas|1)—Gui. aud therefore we draw 9 Cassia random variates pj with zero mean aud unit variance.," We then form the quantity The number of independent harmonic modes in this sum is $n \equiv (\ell_{\textrm{max}}+1)^2 - \ell_{\textrm{min}}^2$ , and therefore we draw $n$ Gaussian random variates $\rho^j$ with zero mean and unit variance." Next. we formu: the su The common bin sample value is then and the actual power spectruui sample coefficients are A second technique to speed up convergence is sub-space sampling.," Next, we form the sum The common bin sample value is then and the actual power spectrum sample coefficients are A second technique to speed up convergence is sub-space sampling." As described above. Cibbs sampling simply caus suupling oue parameter at a time while conditioning ou all others.," As described above, Gibbs sampling simply means sampling one parameter at a time while conditioning on all others." If beneficial. we may therefore choose to siuuple only a few Cys and o; s at a time while conditioning on all others.," If beneficial, we may therefore choose to sample only a few $C_{\ell}$ 's and $\sigma_{\ell}$ 's at a time while conditioning on all others." Specifically. we may extend the basic samplue scheme eiven iu Equation B2 as follows.," Specifically, we may extend the basic sampling scheme given in Equation \ref{eq:gibbs} as follows." " Suupling from P(GC,|s) for à sub-set follows exactly the same algoritlin as before.", Sampling from $P(C_{\ell}|\mathbf{s})$ for a sub-set follows exactly the same algorithm as before. " For P(spay|Cr-Shien.d) two trivial nocdificatious nist be made: The complementary sky signal that is conditioned upon must be subtracted frou the data prior to sampling. and the corresponding C, cocficicuts must be set to zero."," For $P(\mathbf{s}_{\textrm{low}}|C_{\ell}, \mathbf{s}_{\textrm{high}}, \mathbf{d})$ two trivial modifications must be made: The complementary sky signal that is conditioned upon must be subtracted from the data prior to sampling, and the corresponding $C_{\ell}$ coefficients must be set to zero." The advantage of this partitioning lies in the relationship between pre-conditioniug performance aud correlation cheth: The Markov chain correlation leneth is very short in the ligh signal-to-noise regime but very long in the low signal-to-noise regime., The advantage of this partitioning lies in the relationship between pre-conditioning performance and correlation length: The Markov chain correlation length is very short in the high signal-to-noise regime but very long in the low signal-to-noise regime. Thus. iu principle we would like to make a lareer nuuber of steps at hieh Cs than at low Cs; in order to obtain similar mixing properties evervwhere.," Thus, in principle we would like to make a larger number of steps at high $\ell$ 's than at low $\ell$ 's, in order to obtain similar mixing properties everywhere." On the other haud. most of the computational expense or (ος sampling is spent on sampling from P(s|C;.d) for which a linear svsteii must be solved using Conjugate CGradicuts.," On the other hand, most of the computational expense for Gibbs sampling is spent on sampling from $P(\mathbf{s}|C_{\ell}, \mathbf{d})$ for which a linear system must be solved using Conjugate Gradients." This linear svstem is dense in the high signal-to-noise regime. but nearly diagonal in the low sigual-to-noise reece.," This linear system is dense in the high signal-to-noise regime, but nearly diagonal in the low signal-to-noise regime." Therefore. by conditioning on the computationally expeusive high sienalto-noise components. we can sample he ligh-f components more ageressively with a low computational cost per sample.," Therefore, by conditioning on the computationally expensive high signal-to-noise components, we can sample the $\ell$ components more aggressively with a low computational cost per sample." For the analysispreseuted here. this is iuploimieuted through the following sampling scheme: Eriksenetal.(2001)..," For the analysispresented here, this is implemented through the following sampling scheme: \citet{eriksen:2004}." and the PDS one (a collimator). with exposure times of 27.3 (LECS). 90.3 (ALECS) and 46.0 (PDS) ks.,"and the PDS one (a collimator), with exposure times of 27.3 (LECS), 90.3 (MECS) and 46.0 (PDS) ks." A fit over the (110 keV) band with a simple powerlaw statistically agrees with the previous SC results (Fabian et al., A fit over the (1–10 keV) band with a simple power–law statistically agrees with the previous ASCA results (Fabian et al. 1997). both in spectral slope and. in. absolute flux.," 1997), both in spectral slope and in absolute flux." No evidence has been found of spectral features associated with Fe emission around ~1 keV. However. BeppoS AX data oovide us with interestinge information at both the lower and higher energies.," No evidence has been found of spectral features associated with Fe emission around $\sim 1$ keV. However, $Beppo$ SAX data provide us with interesting information at both the lower and higher energies." The extrapolation of such a powerlav below 1 keV. (and down to 0.4 keV) is well above the data. thus indicating either. absorption in exeess of the Galactic one. (column density Ny=140ET cm2E ) or an intrinsic.M llattening. of 10 spectrum (see Fig.," The extrapolation of such a power–law below 1 keV (and down to 0.4 keV) is well above the data, thus indicating either absorption in excess of the Galactic one (column density $N_{\rm H}=1.4\times 10^{20}$ $^{-2}$ ) or an intrinsic flattening of the spectrum (see Fig." 1)., 1). In Table 2 we report the results of 16 best fits with such additional components: if intrinsic to the source the corresponding column density is 1.851077 7., In Table 2 we report the results of the best fits with such additional components: if intrinsic to the source the corresponding column density is $\sim 7.8\times 10^{22}$ $^{-2}$. Errors are at the 90 per cent confidence level for one parameter., Errors are at the 90 per cent confidence level for one parameter. The quality of the data does not allow to gaatistically distinguish among these two possibilities., The quality of the data does not allow to statistically distinguish among these two possibilities. The Es»ectral slope and. intensity are mareinally consistent (at 208) with those inferred from the ASC'A and ROSAT data (Fabian et al 1997. Boller ct al 2000).," The spectral slope and intensity are marginally consistent (at $\sigma$ ) with those inferred from the ASCA and ROSAT data (Fabian et al 1997, Boller et al 2000)." Llowever. below 0.4 keV. there appears to be an excess above the model (see Fig.," However, below 0.4 keV, there appears to be an excess above the model (see Fig." 1)., 1). As this might be due to residuals in the background: subtraction. we performed. a more careful analvsis and in particular re-cxtractecl the spectrum. by considering the local background.," As this might be due to residuals in the background subtraction, we performed a more careful analysis and in particular re-extracted the spectrum by considering the local background." Phe low energy excess is still present at the 260 level and we therefore consider it. with reasonable probability. to be a real feature.," The low energy excess is still present at the $\sigma$ level and we therefore consider it, with reasonable probability, to be a real feature." ‘This emission has not been detected in the ROSAT data. taken ~ 2 months before. suggesting that this component müght be variable on intrinsic timescales 10 days.," This emission has not been detected in the ROSAT data, taken $\sim$ 2 months before, suggesting that this component might be variable on intrinsic timescales $\sim 10$ days." Note that (marginal) indications of variability were also present during the ROSAT observation itself (Boller et al 2000)., Note that (marginal) indications of variability were also present during the ROSAT observation itself (Boller et al 2000). A strong signal has been also detected in the PDS band., A strong signal has been also detected in the PDS band. llowever the [ux is well above the extrapolation of the LECS|MEXS powerlaw (see Fig., However the flux is well above the extrapolation of the LECS+MECS power–law (see Fig. 2)., 2). We thus checked. for possible contamination in the PDS field of view. and indeed found the presence of the BL Lac object. 112551426|428 which. fortuitously. has been observed by SAX four days after GB 1428|4217 (see Table 1).," We thus checked for possible contamination in the PDS field of view, and indeed found the presence of the BL Lac object 1ES1426+428 which, fortuitously, has been observed by SAX four days after GB 1428+4217 (see Table 1)." In collaboration with the 1E81426|428 proproposingS team. we thus tried to cisentangleο the contributions of the two sources in the PDS.," In collaboration with the 1ES1426+428 proposing team, we thus tried to disentangle the contributions of the two sources in the PDS." Also the spectrum of 15251426|428 is well described bv a power-law below 10 keV. (Costamante et al 2000). with a photon index steeper than that of CID1428|4217. E1.93.," Also the spectrum of 1ES1426+428 is well described by a power-law below 10 keV (Costamante et al 2000), with a photon index steeper than that of GB1428+4217, $\Gamma\sim 1.93$." Phe two observed PDS spectra are however very similar and significantly Latter than 1.9 (the data from the 11551426|428 dataset are even slightly harder)., The two observed PDS spectra are however very similar and significantly flatter than 1.9 (the data from the 1ES1426+428 dataset are even slightly harder). Pherefore this implies that. either the dominant. contribution in the PDS comes from CDI428|4217 (assuming its spectrum can be extrapolated from the LECS|MECS powerlaw) or that at higher X.rav energies a Latter component dominates in LES1126|428., Therefore this implies that either the dominant contribution in the PDS comes from GB1428+4217 (assuming its spectrum can be extrapolated from the LECS+MECS power–law) or that at higher X–ray energies a flatter component dominates in 1ES1426+428. In the former case. a joint spectral fit to the datasets or GDB1IJ28|4217 and 181426|428 with simple power-aw models requires CGB1428|4217 to vary. a factor of ~7 xetween the two observations. Le. over a timescale as short as 2 d. while the high redshift quasar did not. show such strong and fast lux variations in the previous observations (note that they correspond to an intrinsic timescale of ~ 8.4 i).," In the former case, a joint spectral fit to the datasets for GB1428+4217 and 1ES1426+428 with simple power-law models requires GB1428+4217 to vary a factor of $\sim 7$ between the two observations, i.e. over a timescale as short as 2 d, while the high redshift quasar did not show such strong and fast flux variations in the previous observations (note that they correspond to an intrinsic timescale of $\sim$ 8.4 hr)." In the second case. the hard. PDS spectrum. of the 11251426|428. dataset is presumed. to intrinsically flatten. similarly to that. observed. in other BL Lac objects (e.g. PINS2155304. Chiappetti et al 1999). where the (Lat) inverse Compton component starts dominating over the," In the second case, the hard PDS spectrum of the 1ES1426+428 dataset is presumed to intrinsically flatten, similarly to that observed in other BL Lac objects (e.g. PKS2155–304, Chiappetti et al 1999), where the (flat) inverse Compton component starts dominating over the" close.,close. In this case in fact the cells are opened. looking at their content.," In this case in fact the cells are opened, looking at their content." A widely used version of the opening criterion is which is derived from Barnes (1994)., A widely used version of the opening criterion is which is derived from Barnes (1994). In this equation / is the cell size. d is the distance of a particle from the cell center of mass. à is the distance from the cell center of mass and the cell geometric center and. finally. @ is the opening angle.," In this equation $l$ is the cell size, $d$ is the distance of a particle from the cell center of mass, $\delta$ is the distance from the cell center of mass and the cell geometric center and, finally, $\theta$ is the opening angle." This eriterion. which replaces the classical one. guarantees to avoid pathological situations when the center of mass is close to the cell border (Dubinski 1997).," This criterion, which replaces the classical one, guarantees to avoid pathological situations when the center of mass is close to the cell border (Dubinski 1997)." To obtain the force on a particle it is necessary to loop through the accumulated. interaction list. and. this loop represents the real amount of computation.," To obtain the force on a particle it is necessary to loop through the accumulated interaction list, and this loop represents the real amount of computation." It is evident that the interactions number is much smaller than in the classical PP method., It is evident that the interactions number is much smaller than in the classical PP method. Dubinski (1997) calculates that on average there are about 1000. interactions per particle in a simulation with one million particles., Dubinski (1997) calculates that on average there are about 1000 interactions per particle in a simulation with one million particles. The value of 8 is somewhat arbitrary. only at decreasing 0 values the number of openings increases and the forces are more accurate.," The value of $\theta$ is somewhat arbitrary, only at decreasing $\theta$ values the number of openings increases and the forces are more accurate." Hernequist (LOST) showed that using 6=1 implies errors on the particles accelerations amounting to La., Hernquist (1987) showed that using $\theta = 1$ implies errors on the particles accelerations amounting to $1\%$. Gravitational interactions are then softened to avoid numerical divergences when two particles get very close., Gravitational interactions are then softened to avoid numerical divergences when two particles get very close. This is done introducing a softening parameter ο which corresponds to attribute à dimension to the particles., This is done introducing a softening parameter $\epsilon$ which corresponds to attribute a dimension to the particles. We decide to use a Plummer softening. equal for all the particles. computed. looking at the inter-particles separation in the central regions of the system under investigation (Romeo. 1991).," We decide to use a Plummer softening, equal for all the particles, computed looking at the inter-particles separation in the central regions of the system under investigation (Romeo, 1997)." In the TreeSPLI code developed by Carraro et al (1998a) the Barnes Hut (1986) treecode has been included in the Code as à subroutine., In the TreeSPH code developed by Carraro et al (1998a) the Barnes Hut (1986) treecode has been included in the code as a subroutine. SPL is a method to solve the hvdro-dynamical conservation laws in Lagrangian form. which has been shown bw Alonaghan (1992) to be an example of an interpolating technique.," SPH is a method to solve the hydro-dynamical conservation laws in Lagrangian form, which has been shown by Monaghan (1992) to be an example of an interpolating technique." “Phe fluicl under study is sampled using particles. and the hyelro-dynamical quantities are estimated at particle positions.," The fluid under study is sampled using particles, and the hydro-dynamical quantities are estimated at particle positions." This is done smoothing cach particle physical properties with a kernel ( Gaussian. exponential or spline) over some smoothing lengths. and deriving gas properties adding up the contribution from a number of neighbors.," This is done smoothing each particle physical properties with a kernel ( Gaussian, exponential or spline) over some smoothing lengths, and deriving gas properties adding up the contribution from a number of neighbors." Benz (1990) in a famous review showed how to derive the SPLHE form of the hyero-dynamical equations., Benz (1990) in a famous review showed how to derive the SPH form of the hydro-dynamical equations. They read: In these equations fy is the particle smoothing length. which is estimated. according to the particle density (Benz 1990). and m. e. P. s and p are the mass. velocity. pressure. specifie internal energy ancl density associated with each particle.," They read: In these equations $h$ is the particle smoothing length, which is estimated according to the particle density (Benz 1990), and $m$, $v$, $P$, $u$ and $\rho$ are the mass, velocity, pressure, specific internal energy and density associated with each particle." Phe kernel W. has been taken from. Monaghan Lattanzio (1985). and. it is a spline kernel with compact support within 2 smoothing lengths: The kernel is then svmmetrically averaged according to lIernquist Ixatz (1989): This guarantees momentum. conservations.," The kernel W has been taken from Monaghan Lattanzio (1985), and it is a spline kernel with compact support within 2 smoothing lengths: The kernel is then symmetrically averaged according to Hernquist Katz (1989): This guarantees momentum conservations." Neighbors are searched. for walking down the tree. ancl looking at those gas particles which actually are within 2 smoothing The tensor Lj; is the viscosity. tensor. introduced. to treat thermal shocks: where Llere e;;=0.560;|ος) is the soundspeed. h;;=0.50); hj). and a and 3 are the viscosity. parameters. usually set 0 0.5 and 1.0. respectively.," Neighbors are searched for walking down the tree, and looking at those gas particles which actually are within 2 smoothing The tensor $\Pi_{ij}$ is the viscosity tensor, introduced to treat thermal shocks: where Here $c_{ij}=0.5(c_i+c_j)$ is the soundspeed, $h_{ij}=0.5(h_i+h_j)$ , and $\alpha$ and $\beta$ are the viscosity parameters, usually set to 0.5 and 1.0, respectively." The factor € is fixed to 0.01 and is meant to avoid divergencies., The factor $\epsilon$ is fixed to 0.01 and is meant to avoid divergencies. As amply discussed by Navarro Steinmetz (1997) this ormulation has the disadvantage of not vanishing in the case of shear dominated Hows. when VF =Oand ) ," As amply discussed by Navarro Steinmetz (1997) this formulation has the disadvantage of not vanishing in the case of shear dominated flows, when $\vec \nabla \cdot \vec v = 0$ and $\vec \nabla \times \vec v \neq 0$ ." In such a case. a spurious shear viscosity can develop. mainly in simulations involving a small number of particles.," In such a case, a spurious shear viscosity can develop, mainly in simulations involving a small number of particles." ‘To reduce the shear component we adopt the Balsara (1995) ormulation of the viscosity tensor where f; is a suitable function defined as and apczLO bIs à parameter meant to prevent numerical divergencies., To reduce the shear component we adopt the Balsara (1995) formulation of the viscosity tensor where $f_i$ is a suitable function defined as and $\eta \approx 10^{-4}$ is a parameter meant to prevent numerical divergencies. Time steps are. caleulated: according to the Courant condition with C zc 0.3., Time steps are calculated according to the Courant condition with $\cal C$ $\approx 0.3$ . In presence of gravity. a more stringent condition on," In presence of gravity, a more stringent condition on" been fixed accordingly.,been fixed accordingly. " Others. such as flow opening anele aud fiducial Loreutz factor. were picTed on the basis of typical values discussed in the literafure over niulv decades, to see if choice of such plausible values acuuits model lieht curves with the same characteristics as those observed."," Others, such as flow opening angle and fiducial Lorentz factor, were picked on the basis of typical values discussed in the literature over many decades, to see if choice of such `plausible' values admits model light curves with the same characteristics as those observed." Cutoff Lorentz factor. shock width aud optical depth (see roftransfer)). are adjusted im an atte]ot to reproduce heht curves looking most like the exampleUMBAO data.," Cutoff Lorentz factor, shock width and optical depth (see \\ref{transfer}) ), are adjusted in an attempt to reproduce light curves looking most like the example UMRAO data." The order fraction! aud orieutatious are subject to study in later sections., The `order fraction' and orientations are subject to study in later sections. " Figue 5 shows the evolution of fiux clensity. percentage polarization aud EVPA for this inodoel. without the inclusion of retarded tinae citects,"," Figure \ref{fig5} shows the evolution of flux density, percentage polarization and EVPA for this model, without the inclusion of retarded time effects." As described in oveftranster the calculations are done using dineusiouless quantities: to euide the eve’. time aud flux density have been arbitrarily scaled to values represetative of those seen in the UMRAO data.," As described in \\ref{transfer} the calculations are done using dimensionless quantities; to `guide the eye', time and flux density have been arbitrarily scaled to values representative of those seen in the UMRAO data." The typical claractoristics of UMRAO bursts described in the fractional fiux «Cusity Increase AS/<ο spectral evolution through a partially optically thick phase. percentage poavization with opacity/Faraday effects evident at the kwest frequency. and swing in EVPA by tens of deeoLCOS are adl reproduced.," The typical characteristics of UMRAO bursts described in \\ref{variability} – the fractional flux density increase $\Delta S/$, spectral evolution through a partially optically thick phase, percentage polarization with opacity/Faraday effects evident at the lowest frequency, and swing in EVPA by tens of degrees – are all reproduced." Note that im earlier modeliis it was found that to fit the spectral characteristics «ft the polarized flux density. a fairly low cutoff therma Loreutz factor (~ 20) was needed for some sources.," Note that in earlier modeling it was found that to fit the spectral characteristics of the polarized flux density, a fairly low cutoff thermal Lorentz factor $\sim 20$ ) was needed for some sources." Here the general characteristics of UMRAO outbursts are wellereproduced with a value that means opacity effects donate. with Faraday effects Όσιο onlv marginal: tlus nuplies that in general few low energy electrons are present m hese SOTIECCS," Here the general characteristics of UMRAO outbursts are well-reproduced with a value that means opacity effects dominate, with Faraday effects being only marginal: this implies that in general few low energy electrons are present in these sources." ", While use of retarded time in the inodeling would be necessary for detailed fits to data. the general characteristics of the total aud polarized fux density heht curves aud spectral behavior. even without usimg retarded time. reproduce the behavior exhibited by the data refvariability))."," While use of retarded time in the modeling would be necessary for detailed fits to data, the general characteristics of the total and polarized flux density light curves and spectral behavior, even without using retarded time, reproduce the behavior exhibited by the data \\ref{variability}) )." Table 1((0B) preseuts the model values corresponding to those derived. from the UMRAO database. ancdiscussed in refvariahilityv.," Table \ref{table1}( (B) presents the model values corresponding to those derived from the UMRAO database, anddiscussed in \\ref{variability}." . A comparison of these is made in refcouclusious.., A comparison of these is made in \\ref{conclusions}. . Figure 6 shows models Bl. D2. etc. ," Figure \ref{fig6} shows models B1, B2, etc. –" the same model as in Fie., the same model as in Fig. 5. (see Table 2)). but for a range of observer orieutation with respect to tl1ο shock plane.," \ref{fig5} (see Table \ref{table2}) ), but for a range of observer orientation with respect to the shock plane." Recall that ο= 07. so that the sheος normal lies in the .-: plane of the Cartesian coordinate svsteni.," Recall that $\psi=0\arcdeg$ , so that the shock normal lies in the $x$ $z$ plane of the Cartesian coordinate system." " The observer orieutatious explored here (07. 157. 907. 135. σου, 2257. 2707. and 315°) corres]youd to starting with a view parallel to the w-axis. ukL then rotating around the jet so that by panel (E) the observer is ""behiud the shock."," The observer orientations explored here $0\arcdeg$, $45\arcdeg$, $90\arcdeg$, $135\arcdeg$, $180\arcdeg$, $225\arcdeg$, $270\arcdeg$, and $315\arcdeg$ ) correspond to starting with a view parallel to the $x$ -axis, and then rotating around the jet so that by panel (E) the observer is `behind' the shock." As one would expect. the total flix density light curves are mininallv changed Xx a chanec in azinuthal orientation.," As one would expect, the total flux density light curves are minimally changed by a change in azimuthal orientation." " For au observer orientation within teus of degrees of Onn.07. orientation and aberration couspire to provide a more nearly ""face-on view of the shocked fiow. aud the perceutage volarization is nall."," For an observer orientation within tens of degrees of $\phi_{obs}=0\arcdeg$, orientation and aberration conspire to provide a more nearly `face-on' view of the shocked flow, and the percentage polarization is small." " Indeed. at 0,5;=O° the polarized flux deusity roni the shock region cancels the small orthogonally volarized flux density associated with the axial feld. as evidenced by the varied behavior iun EVPA in panel (A)."," Indeed, at $\phi_{obs}=0\arcdeg$ the polarized flux density from the shock region cancels the small orthogonally polarized flux density associated with the axial field, as evidenced by the varied behavior in EVPA in panel (A)." However. the percentage polarization is approaching x orieutations of 15 aud 335°. and exceeds at peak over a large range of angles.," However, the percentage polarization is approaching by orientations of $45$ and $335\arcdeg$, and exceeds at peak over a large range of angles." The important conclusion is hat azinuthal oricutation docs not play a major role in the total and polarized flux density outburst lieht curves: special conditions do not need to be invoked for »oluizations of this order to be seen. aud (subject to flow speed and polar oricutation) most oblique structures will eive rise to significant levels of polarized tux density.," The important conclusion is that azimuthal orientation does not play a major role in the total and polarized flux density outburst light curves; special conditions do not need to be invoked for polarizations of this order to be seen, and (subject to flow speed and polar orientation) most oblique structures will give rise to significant levels of polarized flux density." As he azimuthal augle does not play a siguificaut role. a value of 90° is adopted in what follows.," As the azimuthal angle does not play a significant role, a value of $90\arcdeg$ is adopted in what follows." Iu this section the ruu of percentage polarization witli jet iuclination for the transverse case is established. as a ueasure by which to judge the behavior iu the oblique case: it is then shown that adopting au oblique shock does uot radically change the behavior of percentage ohudzation in fact leacing to slehtly higher values at some angles.," In this section the run of percentage polarization with jet inclination for the transverse case is established, as a measure by which to judge the behavior in the oblique case; it is then shown that adopting an oblique shock does not radically change the behavior of percentage polarization – in fact leading to slightly higher values at some angles." " This provides further evidence that the ""hock in jet! model survives the introduction of oblique structures necessary to explain the temporal EVPA )ehawior seeu in the UAIRAO data. anc the evolution of features found in time sequences of VLBI maps."," This provides further evidence that the `shock in jet' model survives the introduction of oblique structures necessary to explain the temporal EVPA behavior seen in the UMRAO data, and the evolution of features found in time sequences of VLBI maps." Figure 7 shows models Cl. C2. etc...," Figure \ref{fig7} shows models C1, C2, etc., –" £he same model as in Fie., the same model as in Fig. 5 (see Table 2)). but contrasting transverse and oblique shocks for a range of observer orieutatiou with respect to the flow axis.," \ref{fig5} (see Table \ref{table2}) ), but contrasting transverse and oblique shocks for a range of observer orientation with respect to the flow axis." As orientation is chanecd. the free parameter 7 is adjustedto ensure a similar spectral behavior of the total flux density.," As orientation is changed, the free parameter $\tau$ is adjustedto ensure a similar spectral behavior of the total flux density." Tn panels CÀ-C) the shock is transverse. so the azimuthal location of the observer plavs no role in determining appearance. and the observer is viewing at angles 207. 107.and 607 respectively to the jet axis.," In panels (A-C) the shock is transverse, so the azimuthal location of the observer plays no role in determining appearance, and the observer is viewing at angles $20\arcdeg$, $40\arcdeg$,and $60\arcdeg$ respectively to the jet axis." Note that with increasing anele the decline in percentage polarization is rather slow., Note that with increasing angle the decline in percentage polarization is rather slow. Frou Hughes.Aller&(1985).. a flow with conrpression &=0.7. seen edge-on. aud iu the abseuce of opacity and Faraday effects; would be expected to exhibit polarized emission 25'4.. dropping ta ~8% at an anele of 507.," From \citet{hug85}, a flow with compression $\kappa=0.7$, seen edge-on, and in the absence of opacity and Faraday effects, would be expected to exhibit polarized emission $\sim25$, dropping to $\sim8$ at an angle of $50\arcdeg$." Caven the modest Loreutz factor of the shocked flow in the observer frame. ~3. radiation from this augle the critical cone of the flow (namely. at 1ο to the flow axis in the flow frame) would be seen by the observer viewing at 50° to the flow axis. an orientation spanned bv panels (B) aud (€) in the figure.," Given the modest Lorentz factor of the shocked flow in the observer frame, $\sim3$, radiation from this angle the critical cone of the flow (namely, at $140\arcdeg$ to the flow axis in the flow frame) would be seen by the observer viewing at $50\arcdeg$ to the flow axis, an orientation spanned by panels (B) and (C) in the figure." In the simple trausverse case. for this level of compression. quite high levels of polarization will be seen well bevoud those values of viewing augle usually adopted im blazar modeling.," In the simple transverse case, for this level of compression, quite high levels of polarization will be seen well beyond those values of viewing angle usually adopted in blazar modeling." Table 1((0€) presents the model values for Bun C1. corresponding to those derived from the UMRAO database. aud discussed in refvariability..," Table \ref{table1}( (C) presents the model values for Run C1, corresponding to those derived from the UMRAO database, and discussed in \\ref{variability}." The oulv huge difference compared witli the values preseuted in Table 1((D) is iu the jump in EVPA as expected. as well as iu the spread inEVPA at outburst end.," The only large difference compared with the values presented in Table \ref{table1}( (B) is in the jump in EVPA as expected, as well as in the spread inEVPA at outburst end." Iu panels (D-E) the original oblique shock is viewed at angles 307. 507. aud 707 to the jet axis. for an azimuthal oricutation of 907. (," In panels (D-F) the original oblique shock is viewed at angles $30\arcdeg$ , $50\arcdeg$ and $70\arcdeg$ to the jet axis, for an azimuthal orientation of $90\arcdeg$ . (" For auazimuthal orientation of 0 the situation will be approximately — subject to flow deflection aud differeut aberration as for the transverse,For anazimuthal orientation of $0\arcdeg$ the situation will be approximately – subject to flow deflection and different aberration – as for the transverse studied scaling relations for dwarf galaxies in two extreme cases. ie. the dark matter dominated case in which dark halo dominates the gravitational potential (Dekel&Silk1986). and the baryon dominated case of self-gravitating galaxies without darkmatter (Yoshii&Arimoto1987).,"studied scaling relations for dwarf galaxies in two extreme cases, i.e., the dark matter dominated case in which dark halo dominates the gravitational potential \citep{ds86}, and the baryon dominated case of self-gravitating galaxies without darkmatter \citep{ya87}." . Steinmetz&Navarro(1999). derived. for the first time by numerical simulations. the ΤΕΕ for luminous spiral galaxies in the CDM model. using a method of /V-body and smoothec jxurticle hydrodynamics (SPH) combined with star formation anc SN feedback explicitly.," \citet{sn99} derived, for the first time by numerical simulations, the TFR for luminous spiral galaxies in the CDM model, using a method of $N$ -body and smoothed particle hydrodynamics (SPH) combined with star formation and SN feedback explicitly." They also showed that the star formation rate is regulated for AZ/L to be almost constant., They also showed that the star formation rate is regulated for $M/L$ to be almost constant. However. the ;xoint of the ΤΕΕ turned out to differ from that observed. so tha he simulated spiral galaxies were too faint to be consistent with observations at the same circular velocity.," However, the zero-point of the TFR turned out to differ from that observed, so that the simulated spiral galaxies were too faint to be consistent with observations at the same circular velocity." It was therefore pointed out that processes of star formation and SN feedback in current jV pody/SPH simulations have to be improved (seealsoGovernatoe2007:Portinari&Sommer-Larsen 2007).," It was therefore pointed out that processes of star formation and SN feedback in current $N$ -body/SPH simulations have to be improved \citep[see also][]{g07, psl07}." Semi-analytic (SA) models of galaxy formation have been invented as a complementary approach to numerical simulations. in which complex processes such as star formation and SN feedback are simply modeled on galaxy scales.," Semi-analytic (SA) models of galaxy formation have been invented as a complementary approach to numerical simulations, in which complex processes such as star formation and SN feedback are simply modeled on galaxy scales." SA models have indeed succeeded in reproducing many observational results. for example. the luminosity function of galaxies as well as the TFR. by suppressing the formation of dwarf galaxies owing to SN feedback (Somerville&Primack1999:Coleetal.2000:Nagashima2005:Crotonetal. 2006).," SA models have indeed succeeded in reproducing many observational results, for example, the luminosity function of galaxies as well as the TFR, by suppressing the formation of dwarf galaxies owing to SN feedback \citep{sp99, c00, ny04, dlkw04, kjmb05, croton06}." . Recent progress in observational techniques has enabled to see much more properties of distant galaxies and faint dwarf galaxies beyond the limit of magnitude attained so far., Recent progress in observational techniques has enabled to see much more properties of distant galaxies and faint dwarf galaxies beyond the limit of magnitude attained so far. In contrast to the success of SA models in accounting for luminous galaxies. they came to face a serious discrepancy between predicted and observed dynamical properties of dwarf galaxies. while reproducing their photometric properties quite well (e.g.Coleetal.2000:Bosch 2002).," In contrast to the success of SA models in accounting for luminous galaxies, they came to face a serious discrepancy between predicted and observed dynamical properties of dwarf galaxies, while reproducing their photometric properties quite well \citep[e.g.][]{c00, vdb02}." . Here we would like to stress that the dynamical response to gas removal induced by SN explosions. which has been overlooked in most SÀ models. is unavoidable in dwarf. less massive galaxies.," Here we would like to stress that the dynamical response to gas removal induced by SN explosions, which has been overlooked in most SA models, is unavoidable in dwarf, less massive galaxies." Nagashima&Yoshii(2003). formulated. how the structure of spherical galaxies. responds. to. SN-induced gas removal in a gravitational potential of dark halo. and Nagashima&Yoshii(2004). incorporated this effect into a SA model to show tha many properties of elliptical galaxies. including the Faber-Jackson relation (Faber&Jackson1976).. can be reproduced to fain magnitudes of dwarf ellipticals.," \citet{ny03} formulated how the structure of spherical galaxies responds to SN-induced gas removal in a gravitational potential of dark halo, and \citet{ny04} incorporated this effect into a SA model to show that many properties of elliptical galaxies, including the Faber-Jackson relation \citep{fj76}, can be reproduced to faint magnitudes of dwarf ellipticals." A more sophisticated SA mode associated with high-resolution A’-body cosmological simulations also provides a good agreement between predicted and observed properties of galaxies (Nagashimaetal.2005)., A more sophisticated SA model associated with high-resolution $N$ -body cosmological simulations also provides a good agreement between predicted and observed properties of galaxies \citep{nyeyg05}. .. Accordingly. as a natural extension of Nagashima Yoshii's trial. it is worth investigating whether such a dynamical effect could also reproduce the observed TFR down to faint magnitudes in spiral galaxies.," Accordingly, as a natural extension of Nagashima Yoshii's trial, it is worth investigating whether such a dynamical effect could also reproduce the observed TFR down to faint magnitudes in spiral galaxies." In this paper. using the Kuzmin dise (Kuzmin1952.1956) as a galaxy dise embedded in a spherical dark halo. we present in Section 2 the general formulation for the dynamical response in size and rotation velocity of discs.," In this paper, using the Kuzmin disc \citep{k52, k56} as a galaxy disc embedded in a spherical dark halo, we present in Section 2 the general formulation for the dynamical response in size and rotation velocity of discs." In Section 3 we examine such effect for several choices of density distribution of dark halo., In Section 3 we examine such effect for several choices of density distribution of dark halo. In Section + we derive the resulting TFRs and dise size versus magnitude relations., In Section 4 we derive the resulting TFRs and disc size versus magnitude relations. In Section 5 we summarize the results of this paper., In Section 5 we summarize the results of this paper. Detailed derivations of analytic expressions are given in Appendix., Detailed derivations of analytic expressions are given in Appendix. In this section. we formulate the dynamical response accompanied by SN feedback to a spiral galaxy consisting of baryons and dark matter.," In this section, we formulate the dynamical response accompanied by SN feedback to a spiral galaxy consisting of baryons and dark matter." " We consider a thin baryonic disc or the Kuzmin disk embedded in an non-rotating spherical dark halo whose density profile is either NFW. homogeneous or r+,"," We consider a thin baryonic disc or the Kuzmin disk embedded in an non-rotating spherical dark halo whose density profile is either NFW, homogeneous or $r^{-1}$." We assume that the thin dise is axisymmetrical and rotation-dominated with negligible velocity dispersions., We assume that the thin disc is axisymmetrical and rotation-dominated with negligible velocity dispersions. Note that the density profile of the Kuzmin dise is more or less similar to the exponential dise except for the central region., Note that the density profile of the Kuzmin disc is more or less similar to the exponential disc except for the central region. The gas of low angular momentum in an extended halo collapses towards the galaxy centre on a dynamical timescale and dissipates the energy to cause a burst of star formation in the central region., The gas of low angular momentum in an extended halo collapses towards the galaxy centre on a dynamical timescale and dissipates the energy to cause a burst of star formation in the central region. On the other hand. the gas of higher angular momentum gradually falls onto a dise plane on a longer timescale and settle on a circular annulus of the dise at the radius according to the value of angular momentum of the gas.," On the other hand, the gas of higher angular momentum gradually falls onto a disc plane on a longer timescale and settle on a circular annulus of the disc at the radius according to the value of angular momentum of the gas." This fallen gas is converted into stars to form a stellar disc., This fallen gas is converted into stars to form a stellar disc. If the kinetic energy. which is released by SNe following the star formation. exceeds the binding energy of the disc. the remaining gas is removed out of the disc.," If the kinetic energy, which is released by SNe following the star formation, exceeds the binding energy of the disc, the remaining gas is removed out of the disc." This dise dynamically recovers a final equilibrium., This disc dynamically recovers a final equilibrium. In general. the final state could be either a puffed-up dise where velocity dispersions dominate over he rotation. or a thin dise where the rotation remains to dominate with negligible velocity dispersions (Biermann&Shapiro1979).," In general, the final state could be either a puffed-up disc where velocity dispersions dominate over the rotation, or a thin disc where the rotation remains to dominate with negligible velocity dispersions \citep{bs79}." . In this paper. it is enough to consider only the latter. because we are orimarily interested in scaling relations in spiral galaxies.," In this paper, it is enough to consider only the latter, because we are primarily interested in scaling relations in spiral galaxies." First. we consider that the gas removal occurs after all he material falls in to form the disc.," First, we consider that the gas removal occurs after all the material falls in to form the disc." In this case. the disc achieves a centrifugal equilibrium with the mass M; and he angular momentum -./; as an initial state.," In this case, the disc achieves a centrifugal equilibrium with the mass $M_i$ and the angular momentum $J_i$ as an initial state." Since the gus removal accompanies the simultaneous losses of mass and angular momentum. the dise should newly recover a centrifugal equilibrium with the mass y and the angular momentum -y as a final state. depending not only on the amount of such losses AAZ(CAL;Ay) and 2./(J;—Jp). but also on whether the time scale of such— losses is longer or shorter than the dynamical seale (Biermann 1979).," Since the gas removal accompanies the simultaneous losses of mass and angular momentum, the disc should newly recover a centrifugal equilibrium with the mass $M_f$ and the angular momentum $J_f$ as a final state, depending not only on the amount of such losses $\Delta M (M_i-M_f)$ and $\Delta J (J_i-J_f)$, but also on whether the time scale of such losses is longer or shorter than the dynamical scale \citep{bs79}." . On the other hand. the gas removal may well occur while the material is still falling into the disc.," On the other hand, the gas removal may well occur while the material is still falling into the disc." In this case. only a part of the material falls in to form the disc and almost no gas removal occurs afterwards.," In this case, only a part of the material falls in to form the disc and almost no gas removal occurs afterwards." The dise would then be settled in centrifugal equilibrium with the mass Jy and the angular momentum οἱ throughout from the beginning., The disc would then be settled in centrifugal equilibrium with the mass $M_f$ and the angular momentum $J_f$ throughout from the beginning. This situation is formally equivalent to the case such that the gas removal occurs on much shorter timescale compared to the dynamical timescale., This situation is formally equivalent to the case such that the gas removal occurs on much shorter timescale compared to the dynamical timescale. Therefore. the related formula below in this section could also apply to the situation considered here.," Therefore, the related formula below in this section could also apply to the situation considered here." The kinetic energy 7 due to rotation. the gravitational self plus interaction potential energy V. and the total angular momentum ./ of the Kuzmin dise of baryons in a dark halo are given by and," The kinetic energy $T$ due to rotation, the gravitational self plus interaction potential energy $W$ , and the total angular momentum $J$ of the Kuzmin disc of baryons in a dark halo are given by and" Since the maguetic moment does not change after the wind spin-down epoch. ji at the end of the wind spiu-down epoch is just the maguetie moment in the present RLOF spiu-up epoch as estimated above.,"Since the magnetic moment does not change after the wind spin-down epoch, $\mu_2$ at the end of the wind spin-down epoch is just the magnetic moment in the present RLOF spin-up epoch as estimated above." " By assuming that O(f,j)=Qo»<OSAL.. (typical values being ~LOtotesHAE1j."," The mass transfer rate (equal to the outburst mass accretion rate averaged over the source duty cycle) would then average to $\Mdot\sim10^{13}-10^{14}\rm\,g\,s^{-1}$, a value too small for an evolved donor or even a main sequence star with $M>0.8\msun$ (typical values being $\sim10^{15}-10^{16}\rm\,g\,s^{-1}$ )." The mass function. of has been reported in Papittoctal.(2011) aud correspouds to a miniuun donor mass of 0.137.. for a neutron star of 1.1M... The location of in the elobular cluster Terzan 5 allows to place further constraints on the donor nass., The mass function of has been reported in \citet{pap11} and corresponds to a minimum donor mass of $M_{\odot}$ for a neutron star of $1.4\msun$ The location of in the globular cluster Terzan 5 allows to place further constraints on the donor mass. Terza 5 is composed by two populatious of stars: one with sub-solar mictallicity (CZ=0.01. Y=0.26) and one with supra-solar iietallicitv (Z=0.03. Y=0.29: see Ferraroetal.2009)).," Terzan 5 is composed by two populations of stars: one with sub-solar metallicity $Z=0.01$, $Y=0.26$ ) and one with supra-solar metallicity $Z=0.03$, $Y=0.29$; see \citealt{fer09}) )." One interpretation of these discrepant metallicities and Helium abundances is that the cluster is composed by two different populations of stars with ages of 1231 Cyr (inetal poor) aud 642 Cor (iietal rich)., One interpretation of these discrepant metallicities and Helium abundances is that the cluster is composed by two different populations of stars with ages of $12\pm1$ Gyr (metal poor) and $6\pm2$ Gyr (metal rich). Tf sve asstme that the donor star beloues to the first population. strong coustraiuts cau be placed ou the donor star.," If we assume that the donor star belongs to the first population, strong constraints can be placed on the donor star." Since the orbital period of is ~21 hr. and asstuineg a münmuuni NS mass of Af... the minima orbital separation of the system is Aw0.02 AU.," Since the orbital period of is $\approx 21$ hr, and assuming a minimum NS mass of $\msun$, the minimum orbital separation of the system is $A\approx0.02$ AU." " By using the Roche lobe approximation of Evelctouao(1983): with ¢=Majf/AMvs beime the ratio of the donor aud accretor mass. the mium possible Roche lobe radius hat corresponds to the ninimimunn orbital separation aud he mudi mass ratio (AL,=OLAM... AMys=12M.) is LIAR..."," By using the Roche lobe approximation of \citet{egg83}: with $q=M_{d}/M_{NS}$ being the ratio of the donor and accretor mass, the minimum possible Roche lobe radius that corresponds to the minimum orbital separation and the minimum mass ratio $M_d=0.4\msun$, $M_{NS}=1.2\msun$ ) is $R_{\odot}$." After 12 Cyr all stars with a iass Mz1M. jiwe evolved to the red giant phase aud nieht have already turned into white dwarfs whereas all stars with AMz094M. (0c. the tum off mass of the metal-poor yopulation of Terzau 5. Ferraroetal. 2009)) are still on he main sequence.," After 12 Gyr all stars with a mass $M\simgreat 1\msun$ have evolved to the red giant phase and might have already turned into white dwarfs whereas all stars with $M\simless0.9\msun$ (i.e., the turn off mass of the metal-poor population of Terzan 5, \citealt{fer09}) ) are still on the main sequence." Considering the other extreme case of At;=LOAL.. aud AMys=2.042... the maxima Roche obe radius will be Lar...," Considering the other extreme case of $M_d=1.0\msun$ and $M_{NS}=2.0\msun$, the maximum Roche lobe radius will be $R_{\odot}$." To fill the Roche lobe therefore auv possible donor star of has to be an evolved star that has oft the main sequence aud has increased its radius to fit itx Roche lobe., To fill the Roche lobe therefore any possible donor star of has to be an evolved star that has left the main sequence and has increased its radius to fit its Roche lobe. The donor star mass falls in the rauge ΊοςMzl. aud is likely to be a sub-giaut.," The donor star mass falls in the range $0.9\simless\,M\simless\,1\,\msun$ and is likely to be a sub-giant." ". This result stronglv constrains the orbital separation of the system to be iu the range 0.023-0.026 AU for a total mass of the binary between 2.1 (1.2AL. NS aud 0.9AZ. donor) and 32M. (0M, NS aud LtAL.. donor).", This result strongly constrains the orbital separation of the system to be in the range $0.023$ $0.026$ AU for a total mass of the binary between 2.1 $1.2\msun$ NS and $\msun$ donor) and $\msun$ $2\msun$ NS and $1\msun$ donor). The iucliuation 7 of the binary is then constrained by using the projected seni-najor axis of (see Table 1): Identical considerations apply if the donor star belongs to the metal rich population. with the difference that the turn off mass will be higher by a few tenths of solar mass and theinclination sinaller by a few deerees.," The inclination $i$ of the binary is then constrained by using the projected semi-major axis of (see Table \ref{tab1}) ): Identical considerations apply if the donor star belongs to the metal rich population, with the difference that the turn off mass will be higher by a few tenths of solar mass and theinclination smaller by a few degrees." All these considerations assume that irradiation of the donor star is unimportant iu determing its radius.,All these considerations assume that irradiation of the donor star is unimportant in determining its radius. increase the amplitude of the precession are compensated by its slow revolution and fast rotation (see eq (15))) .,increase the amplitude of the precession are compensated by its slow revolution and fast rotation (see eq \ref{eq9}) )). " 'The nutation in longitude is given by: where ®;,$,O;,O/ and v; are respectively the leading amplitudes and the frequencies of the sinusoidal terms and can be found in Table 3.."," The nutation in longitude is given by: where $\Phi_{i}, \Phi'_{i}, \Theta_{i}, \Theta'_{i}$ and $\nu_{i}$ are respectively the leading amplitudes and the frequencies of the sinusoidal terms and can be found in Table \ref{tab1}." " Similarly, the nutation in obliquity is given by: where LI;I5,I;IT; and y; are given in Table 4.."," Similarly, the nutation in obliquity is given by: where $\Gamma_{i}, \Gamma'_{i}, \Pi_{i}, \Pi'_{i}$ and $\mu_{i}$ are given in Table \ref{tab2}." The corresponding arguments as a combination of Phoebe mean longitude and mean anomaly are determined empirically and given when they have been clearly identified., The corresponding arguments as a combination of Phoebe mean longitude and mean anomaly are determined empirically and given when they have been clearly identified. The residuals after substraction of (27)) and (28)) to the results of the numerical integration are the flat curves in Figs.8 and 9.., The residuals after substraction of \ref{FFTlo}) ) and \ref{FFTob}) ) to the results of the numerical integration are the flat curves in \ref{fig4} and \ref{fig5}. " The nutation in obliquity is dominated by two frequencies associated with the arguments 2D, and 2L,+M with respective periods 275.13 d and 183.45 d. In addition to these two frequencies, the nutation in longitude also presents another leading component with argument 2L,—M."," The nutation in obliquity is dominated by two frequencies associated with the arguments $2L_{s}$ and $2L_{s}+M$ with respective periods 275.13 d and 183.45 d. In addition to these two frequencies, the nutation in longitude also presents another leading component with argument $2L_{s}-M$." " The components which are not identified in Tables 3 and 4 as those with period 497 d and 260 d, already pointed out in Tables 1 and 2 (see Sect.??))."," The components which are not identified in Tables \ref{tab1} and \ref{tab2} as those with period 497 d and 260 d, already pointed out in Tables \ref{tab1new} and \ref{tab2new} (see \ref{3}) )." They probably come from the non Keplerian motion of Phoebe., They probably come from the non Keplerian motion of Phoebe. " As in the case for the precession, the nutations in longitude and in obliquity of Phoebe, which show respectively peak to peak variations of 26"" or 8"" are of the same order as the nutation of the Earth"," As in the case for the precession, the nutations in longitude and in obliquity of Phoebe, which show respectively peak to peak variations of 26"" or 8"" are of the same order as the nutation of the Earth" hieh redshifts. since (he evolution depends differently on the combination of the cosmological parameters.,"high redshifts, since the evolution depends differently on the combination of the cosmological parameters." While other independent observations can also be usecl such as the cluster mass [function and its evolution. and the CAIB spectrum of fluctuations the /à;—d (2) evolution provides an independent consistency test that uses a single sell-consistent method of cluster correlations.," While other independent observations can also be used – such as the cluster mass function and its evolution, and the CMB spectrum of fluctuations – the $R_0 - d$ $z$ ) evolution provides an independent consistency test that uses a single self-consistent method of cluster correlations." We use large-scale high-resolution cosmological simulations to determine the evolution of the cluster correlation function with redshift [rom z=0 to z=3 over a wide range of cluster masses., We use large-scale high-resolution cosmological simulations to determine the evolution of the cluster correlation function with redshift from $z = 0$ to $z = 3$ over a wide range of cluster masses. " Two cosmological models are studied: the standard flat LCDM model (with QO,,TEE= 0.3). which best fits numerous observations. aud. for comparison. a tilted Q,,=1 model (TSCDAL)."," Two cosmological models are studied: the standard flat LCDM model (with $\Omega_m = 0.3$ ), which best fits numerous observations, and, for comparison, a tilted $\Omega_m = 1$ model (TSCDM)." The evolutionary predictions are presented in a format suitable for direct comparisons with observations., The evolutionary predictions are presented in a format suitable for direct comparisons with observations. We find that the cluster. correlation strength increases with redshift [or fixed mass clusters: Le.. clusters are more strongly clustered in space at high redshift.," We find that the cluster correlation strength increases with redshift for fixed mass clusters; i.e., clusters are more strongly clustered in space at high redshift." The evolutionary increase of the correlation scale with redshift (in comoving units) is laster [or more massive clusters and at higher redshift., The evolutionary increase of the correlation scale with redshift (in comoving units) is faster for more massive clusters and at higher redshift. The increased. clustering of clusters at high. redshift. in spite of the decreased clustering of the underlving mass distribution. is due to the strongly increasing bias of clusters al high redshift: clusters represent higher-densitv peaks of the mass distribution at higher redshift.," The increased clustering of clusters at high redshift, in spite of the decreased clustering of the underlying mass distribution, is due to the strongly increasing bias of clusters at high redshift: clusters represent higher-density peaks of the mass distribution at higher redshift." The inereased bias dominates over the decreasing mass correlations and causes the clustering of clusters (o increase., The increased bias dominates over the decreasing mass correlations and causes the clustering of clusters to increase. We combine the evolution of the cluster correlation Iunction. with its dependence on cluster mass by determining the evolution of the richness-dependent cluster correlation function., We combine the evolution of the cluster correlation function with its dependence on cluster mass by determining the evolution of the richness-dependent cluster correlation function. We do so using the format of the correlation scale versus mean separation relation. Ry—d.," We do so using the format of the correlation scale versus mean separation relation, $R_0 - d$." This relation is easy to compare will observations., This relation is easy to compare with observations. Samples with intrinsically larger mean separations correspond to lower intrinsic cluster abundances aud thus to higher cluster richness and mass (for complete samples)., Samples with intrinsically larger mean separations correspond to lower intrinsic cluster abundances and thus to higher cluster richness and mass (for complete samples). We find that. remarkably. (he richness-cepenclent cluster correlation function. Ay—d is independent of redshift for these models for 2< for LCDM (using a fixed correlation function slope aud cluster mass defined. within a fixed comoving radius) and 2<1 for TSCDM (Figure 4).," We find that, remarkably, the richness-dependent cluster correlation function $R_0 - d$ is independent of redshift for these models for $z \la 2$ for LCDM (using a fixed correlation function slope and cluster mass defined within a fixed comoving radius) and $z \la 1$ for TSCDM (Figure 4)." " The amplitude of the Ay—d relation beeins to decline only at z2 for LCDM and z21 for TSCDM,.", The amplitude of the $R_0 - d$ relation begins to decline only at $z \ga 2$ for LCDM and $z \ga 1$ for TSCDM. Using a free correlation slope lil. or virial cluster masses. vields similar results but with a small amount of evolution (Z159 to 2£ for LCDM).," Using a free correlation slope fit, or virial cluster masses, yields similar results but with a small amount of evolution $\la 15\%$ to $z \la 2$ for LCDM)." " The non-evolvinge A,d relation implies that the strengtheninge of the cluster correlation", The non-evolving $R_0 - d$ relation implies that the strengthening of the cluster correlation correctly account for the measurement errors aud iutriusic scatter m order to eiure that the data analvsis. auc thus the scientific couclusious based on it. are truswort.,"correctly account for the measurement errors and intrinsic scatter in order to ensure that the data analysis, and thus the scientific conclusions based on it, are trustworthy." Alauy nmiethods have been proposed for performing linear regressiou whei intrinsic scatter is present and both variables are measured with error., Many methods have been proposed for performing linear regression when intrinsic scatter is present and both variables are measured with error. " These mecude methods tha correct the observed moments of the data (e.¢..Fuller1987:Akvitas&Bershacdy1996:Freedimanetal.2001). minimize an ‘effective’ u statistic (e...Clittou-Brock1967:Barker&Diana197[:Pressetal.1992:Trenaine2002).. assume a probability distribution for the truce independent variable values (so-callec""structuralequationmodels.οιὃν,Schafer1987.2001:Rov&Banerjee 2006):: Bayesian approaches to thes! models have also been developed (e.g.Zelluer1971:Call1989:Dellaportas&Stepheus1995:Carroll«5al.|909:Scheineset1999)."," These include methods that correct the observed moments of the data \citep[e.g.,][]{fuller87,bces,freed04}, minimize an `effective' $\chi^2$ statistic \citep[e.g.,][]{clut67,bark74,numrec,trem02}, assume a probability distribution for the true independent variable values \citep[so-called `structural equation models', e.g.,][]{schafer87,schafer01,roy06}; Bayesian approaches to these models have also been developed \citep[e.g.,][]{zell71,gull89,dell95,carroll99,scheines99}." . Iu addition. methods have been proposed to account for mneasuremenut error in censored regression Weiss 1993).," In addition, methods have been proposed to account for measurement error in censored regression \citep[e.g.,][]{stap84,weiss93}." . The most commonly used meτους in astronomy are the BCES estimator (Akritas&Bershady1996) aud the “FITENY” estimator {Pressetal.1992)., The most commonly used methods in astronomy are the BCES estimator \citep{bces} and the `FITEXY' estimator \citep{numrec}. . Both methods have their advantages and disadvantages. some of which Lave been poiuted ou by Tremaineetal.(2002).," Both methods have their advantages and disadvantages, some of which have been pointed out by \citet{trem02}." . However. neither method is applicable when the data coutain nou-doeteclolis.," However, neither method is applicable when the data contain non-detections." Ii this work I describe a Dayvesiau method for randlin5 lucasurement errors 1 astrononaical data analvsis., In this work I describe a Bayesian method for handling measurement errors in astronomical data analysis. " Alv ayproach starts by computing the likethood function of t1C COuplee data. Ίνοι, the likehhood fuuctiou of boh the unobserved true values of the data Hand the measured values of the data."," My approach starts by computing the likelihood function of the complete data, i.e., the likelihood function of both the unobserved true values of the data and the measured values of the data." " The measured data likehhood is then fouud by inteerating f1e likethood function for the ¢‘oumplete data over the unobserved true values (ο,ον,Litle&Rubin2002:Cte1naetal200L)."," The measured data likelihood is then found by integrating the likelihood function for the complete data over the unobserved true values \citep[e.g.,][]{lit02,gelman04}." . Tlis approach is kjown as structural equation inodelug of measurenient error probolus. aud has been stidied. from both a frequeutist. approach Schafer2)H:Aitken&Που2002) are La Davesiau approach (c.e..MüllerLeblond1f7:Richardsoneta. 2002).," This approach is known as `structural equation modelling' of measurement error problems, and has been studied from both a frequentist approach \citep[e.g.,][]{fuller87,carroll95,schafer01,aitken02} and a Bayesian approach \citep[e.g.,][]{muller97,rich97,rich02}." ". In this work. I extend the statistical inode of Carrolletal.(1999) to alow Or neasurelent errors of differcut magnitudes G.c.. heteroscedastic errors). non-detections. iud selectiπι effecs. so long as the selection friction can be modelled matlematically,"," In this work, I extend the statistical model of \citet{carroll99} to allow for measurement errors of different magnitudes (i.e., `heteroscedastic' errors), non-detections, and selection effects, so long as the selection function can be modelled mathematically." Ow urethod models the distribution of inependent variables as a weighted suni of Gaussians., Our method models the distribution of independent variables as a weighted sum of Gaussians. " The mixture of Catsslans model allows flexibility whe Lestimating the distribution of the true values of the independent varlale. thus increasing its robusness against model mispecification (ο,ος,IIuaugetal.2006)."," The mixture of Gaussians model allows flexibility when estimating the distribution of the true values of the independent variable, thus increasing its robustness against model mispecification \citep[e.g.,][]{huang06}." . The basic idea is that one can use a suitablv laree cuough uuuber of Gaussians to accurately approximate the true clistril)ution of indepeudent variables. even though in general the individual Gaussians have no plysical mcaig.," The basic idea is that one can use a suitably large enough number of Gaussians to accurately approximate the true distribution of independent variables, even though in general the individual Gaussians have no physical meaning." oO Ti6 paper is organized as follows., The paper is organized as follows. Iu 2 we sununuarlze some notation. and in 3 T review the effects o Dqneasurenmient error on the estimates or the regression slope aid correlation coefficient.," In \ref{s-notation} we summarize some notation, and in \ref{s-measerr} I review the effects of measurement error on the estimates for the regression slope and correlation coefficient." In 1I clescrilIC the statistical model audderive the likchhood fuuctious. aud iu 5 I describe how to incorporate showledge of the selection effects aud account or nou-detectiouns.," In \ref{s-statmod} I describe the statistical model andderive the likelihood functions, and in \ref{s-dcissues} I describe how to incorporate knowledge of the selection effects and account for non-detections." In6.1. [describe the prior distribution or this model. aud in 6.2 I describe a Cübys Ες for sampling roni the posterior distributious.," In\ref{s-prior} I describe the prior distribution for this model, and in \ref{s-markov} I describe a Gibbs sampler for sampling from the posterior distributions." " Iu 1 Τιse shuulatiou to illustrate the effectis""ness of this structural nodel and compare with the OLS. (Y X) and FITENY estimators."," In \ref{s-sims} I use simulation to illustrate the effectiveness of this structural model and compare with the OLS, $Y|X$ ), and FITEXY estimators." Finally. πι 5 Lilustrate the ucthod using astronomical data by )orforlulie a regression of the N-rav photon iucex. Py. ou the Eddington ratio using a sample of 39 τς0.83 racdio-quiet quasars.," Finally, in \ref{s-data} I illustrate the method using astronomical data by performing a regression of the X-ray photon index, $\Gamma_X$, on the Eddington ratio using a sample of 39 $z < 0.83$ radio-quiet quasars." " Sections ἐν, ον, aud 6 are solmewhat technical. aud tje reader Who is uuuterested im the nathematical and computational details may skip to them."," Sections \ref{s-statmod}, , \ref{s-dcissues}, , and \ref{s-compmeth} are somewhat technical, and the reader who is uninterested in the mathematical and computational details may skip to them." The II 111 protostellar svstem has been mapped at a resolution of ~ in 1.33 mum continmrum. and in (J2—1) and (/=2—1).,"The HH 111 protostellar system has been mapped at a resolution of $\sim$ in 1.33 mm continuum, and in $J=2-1$ ) and $J=2-1$ )." The 1.33 mm continuum emission shows a resolved clusty disk associated with the VLA | source perpendicular to the jet axis. with a Gaussian deconvolved size of ~ 240 AU.," The 1.33 mm continuum emission shows a resolved dusty disk associated with the VLA 1 source perpendicular to the jet axis, with a Gaussian deconvolved size of $\sim$ 240 AU." The and emissions toward (he dusty disk show a Ixepleriai rotation. indicating (hat the dusty disk is rotationally supported.," The and emissions toward the dusty disk show a Keplerian rotation, indicating that the dusty disk is rotationally supported." The density ancl temperature distributions in the disk derived from a simple disk model are found to be similar to those found in bright T-Tauri disks., The density and temperature distributions in the disk derived from a simple disk model are found to be similar to those found in bright T-Tauri disks. Thus. the disk can be a voung protoplanetary disk Chat could evolve into a T-Tauri disk in the late stage of star formation.," Thus, the disk can be a young protoplanetary disk that could evolve into a T-Tauri disk in the late stage of star formation." In addition. a hint of a low-velocity molecular outflow is also seen in and coming. out [rom the disk.," In addition, a hint of a low-velocity molecular outflow is also seen in and coming out from the disk." . T thank the SMA stalf for their efforts in running and maintaining the array., I thank the SMA staff for their efforts in running and maintaining the array. I also thank ihe referee for the valuable comments., I also thank the referee for the valuable comments. "In general. lor a given Z,,,,,5. there will be some lower limit on Spo). below which there will be too lew photons to measure ZZ,,5,:,..","In general, for a given $E_{peak,obs}$, there will be some lower limit on $S_{bolo}$, below which there will be too few photons to measure $E_{peak,obs}$." " AS Ey, moves lo higher energies. (he limit on 5j4; will sharply increase."," As $E_{peak,obs}$ moves to higher energies, the limit on $S_{bolo}$ will sharply increase." The result will roughly be a diagonal line across the Shoto—Epeatobs diagram. trom lower left to upper right. with any burst below that line nol having a measured. μου and not appearing in any sample of bursts in Section 3.," The result will roughly be a diagonal line across the $S_{bolo} - E_{peak,obs}$ diagram, from lower left to upper right, with any burst below that line not having a measured $E_{peak,obs}$ and not appearing in any sample of bursts in Section 3." We have made calculations of this threshold curve for DATSE. WETE. andSwift.," We have made calculations of this threshold curve for BATSE, HETE, and." " To do this. in à Monte Carlo sense. we constructed many simulated bursts over each detectors spectral range for many values of ,,;,,,: where the normalization and error bars of the spectra were determined bv the burst fluence."," To do this, in a Monte Carlo sense, we constructed many simulated bursts over each detector's spectral range for many values of $E_{peak,obs}$ where the normalization and error bars of the spectra were determined by the burst fluence." " These spectra were also for each spectrum. we then fitted both a power law times an exponential model (with the caleulated E,4. value) and a simple power law model."," These spectra were also for each spectrum, we then fitted both a power law times an exponential model (with the calculated $E_{peak,obs}$ value) and a simple power law model." " If the chi-square values for the two fits differed bv more than 15.0 (so that the model with the peak was a sufficiently. eood improvement on power law model given (he extra degree of [reedom). (hen we took the 5,4; for the burst to be above the threshold."," If the chi-square values for the two fits differed by more than 15.0 (so that the model with the peak was a sufficiently good improvement on power law model given the extra degree of freedom), then we took the $S_{bolo}$ for the burst to be above the threshold." " By varving the Eyratens. we were able to determine the threshold for measurement as a curve in the 554;—E,,,,, diagram."," By varying the $E_{peak,obs}$, we were able to determine the threshold for measurement as a curve in the $S_{bolo} - E_{peak,obs}$ diagram." As these lines are merely [or illustration. we do use the DRM lor these simulations.," As these lines are merely for illustration, we do use the DRM for these simulations." For DATSE. HWETE. andSwift. our calculated thresholds are presented as curves in Figures 1.. 8.. and 9..," For BATSE, HETE, and, our calculated thresholds are presented as curves in Figures \ref{fig:NaPBATSE}, \ref{fig:NaPHETE}, and \ref{fig:NaPSwift}." Amongst bursts appearing in the skies. the Eyeasons distribution is not flat. but rather bursts appear wilh a roughly log-normal distribution of Πως.," Amongst bursts appearing in the skies, the $E_{peak,obs}$ distribution is not flat, but rather bursts appear with a roughly log-normal distribution of $E_{peak,obs}$." For bright bursts. the mean value is 335 keV. with the FWIIAI stretehing from roughly 150-100 keV (Mallozzi et al.," For bright bursts, the mean value is 335 keV, with the FWHM stretching from roughly 150-700 keV (Mallozzi et al." 1995)., 1995). This mean value shifts significantlv as the bursts get dimmer. being 175 keV just above the BATSE trigger threshold (Mallozzi et al.," This mean value shifts significantly as the bursts get dimmer, being 175 keV just above the BATSE trigger threshold (Mallozzi et al." 1995)., 1995). The so-called “X-ray Flashes’ are simply bursts in the low-enerev tail of the distribution (Ixippen et al., The so-called `X-ray Flashes' are simply bursts in the low-energy tail of the distribution (Kippen et al. 2004: Sakamoto et al., 2004; Sakamoto et al. 2005: Péllangeon 2008)., 2005; Péllangeon 2008). " The existence of this single peak in the £55, histogram is highly significant and not [rom any instrumental or selection effect (Brainerd et al."," The existence of this single peak in the $E_{peak,obs}$ histogram is highly significant and not from any instrumental or selection effect (Brainerd et al." 1999)., 1999). In all. most bursts are between 100-700 keV. and bursts «30 keV or 221000 keV are rare.," In all, most bursts are between 100-700 keV, and bursts $<$ 30 keV or $>$ 1000 keV are rare." " This will directly. translate to unpopulated regions of the Shore—E,,;,,, diagram."," This will directly translate to unpopulated regions of the $S_{bolo} - E_{peak,obs}$ diagram." A direct simulation ol this distribution is given in Figure 4.., A direct simulation of this distribution is given in Figure \ref{fig:NaPDistMC}. The [ρω distribution will cause definite but gradiated eutoffs in the 5544—Epio. diagram.," The $E_{peak,obs}$ distribution will cause definite but gradiated cutoffs in the $S_{bolo} - E_{peak,obs}$ diagram." These cutoffs will be nearly vertical., These cutoffs will be nearly vertical. " The drop in the average EZ, will make the cutoff on the right have a slope down to the lower lelt."," The drop in the average $E_{peak,obs}$ will make the cutoff on the right have a slope down to the lower left." profile of the photodisk at the wavelength ofinterest!.,profile of the photodisk at the wavelength of. . This function is normalized as follows soJo that the total continuum flux emitted by the photodisk along the line of sight is equal to unity., This function is normalized as follows so that the total continuum flux emitted by the photodisk along the line of sight is equal to unity. If e(N.b) 1s the curve of growth for the given transition and Doppler parameter b. the equivalent width (EW) produced by an infinitesimal cloud column with cross section dA=rdédr is dEW=e|N.5b]Φ(0) dA.," If $g(N,b)$ is the curve of growth for the given transition and Doppler parameter $b$, the equivalent width $EW$ ) produced by an infinitesimal cloud column with cross section $dA=r\;d\theta\;dr$ is $dEW = g[N,b] \; \Phi(r,\theta)\;dA$ ." If we neglect the small contribution by photons scattered by the cloud into the line of sight. the total equivalent width is then computed integrating the contribution of each single infinitesimal element over the photodisk (see Appendix A for the details): So far we have considered the possibility that the Doppler parameter b can change across the cloud.," If we neglect the small contribution by photons scattered by the cloud into the line of sight, the total equivalent width is then computed integrating the contribution of each single infinitesimal element over the photodisk (see Appendix A for the details): So far we have considered the possibility that the Doppler parameter $b$ can change across the cloud." However. in the lack of evidence for significant variations over the scales of interest (see for instance Welty Fitzpatrick 2001)). in the following we will assume that 5 is constant across the relevant portion of the cloud.," However, in the lack of evidence for significant variations over the scales of interest (see for instance Welty Fitzpatrick \cite{welty}) ), in the following we will assume that $b$ is constant across the relevant portion of the cloud." We will briefly discuss the effects of à dependent Doppler parameter in Sect. 3.., We will briefly discuss the effects of a space-dependent Doppler parameter in Sect. \ref{sec:results}. With the aid of the outlined procedure. one can follow the time evolution of EW for any input cloud column density map. provided the photodisk’s expansion law is known.," With the aid of the outlined procedure, one can follow the time evolution of $EW$ for any input cloud column density map, provided the photodisk's expansion law is known." " In the assumption of homologous expansion (see for instance Jeffery Branch 1990)) the radius of the photosphere ή). is obtained multiplying the photospheric velocity vp,(7) by the time 7 elapsed from the explosion."," In the assumption of homologous expansion (see for instance Jeffery Branch \cite{jeffery}) ), the radius of the photosphere $r_{\rm ph}(t)$ is obtained multiplying the photospheric velocity $v_{\rm ph}(t)$ by the time $t$ elapsed from the explosion." For μμ) we adopted a best fit to values computed via SYNOW modeling of the spectroscopically normal SN 1994D. a standard Type Ia event (Branch et al. 2005)).," For $v_{\rm ph}(t)$ we adopted a best fit to values computed via SYNOW modeling of the spectroscopically normal SN 1994D, a standard Type Ia event (Branch et al. \cite{branch05}) )." During the photospheric phase (¢«100 days). ορ) is well approximated by an exponential law. and the best fit relation takes the following form: where Moh is expressed in AU and fin days from the explosion.," During the photospheric phase $t<$ 100 days), $v_{\rm ph}(t)$ is well approximated by an exponential law, and the best fit relation takes the following form: where $r_{\rm ph}$ is expressed in AU and $t$ in days from the explosion." " This law shows that the change in the photodisk dimensions 1s significant during the first two months: from day —10 to day +50 (counted from maximum light) ry, increases by more than a factor of 5 (60 AU to 320 AU).", This law shows that the change in the photodisk dimensions is significant during the first two months: from day $-$ 10 to day +50 (counted from maximum light) $r_{\rm ph}$ increases by more than a factor of 5 (60 AU to 320 AU). As for the photodisk surface brightness profile. this was computed using a modified version of the spectrumsynthesis code (Branch et al. 2005)).," As for the photodisk surface brightness profile, this was computed using a modified version of the spectrumsynthesis code (Branch et al. \cite{branch05}) )." " The profile. obtained from best fits of SN 1994D spectra for the D rest-frame wavelength. rapidly drops at r=ry, during the early phases (see Fig. 2))."," The profile, obtained from best fits of SN 1994D spectra for the D rest-frame wavelength, rapidly drops at $r=r_{\rm ph}$ during the early phases (see Fig. \ref{fig:prof}) )." As time goes by. a significant fraction of the flux (up to ~16% on day +15) is emitted above the photosphere. and it is due to scattering by the broad D doublet intrinsic to the SN (see for instance Jeffery Branch 1990)).," As time goes by, a significant fraction of the flux (up to $\sim$ on day +15) is emitted above the photosphere, and it is due to scattering by the broad D doublet intrinsic to the SN (see for instance Jeffery Branch \cite{jeffery}))." " At all epochs. q-0 for r/ry, 22.6. which we used as the effective external boundary of the ejecta."," At all epochs, $\Phi$ =0 for $r/r_{\rm ph}\geq$ 2.6, which we used as the effective external boundary of the ejecta." To include the time dependence we tabulated DC) for a number of epochs 10. —4. +7. +15. +28 and +50 days from B maximum) and subsequently used a linear interpolation to derive the profile at any given epoch.," To include the time dependence we tabulated $\Phi(r)$ for a number of epochs $-$ 10, $-$ 4, +7, +15, +28 and +50 days from $B$ maximum) and subsequently used a linear interpolation to derive the profile at any given epoch." The time from B maximum light was converted into ¢ using the rise time of SN 1994D (18 days: Vacca Leibundgut 1996))., The time from $B$ maximum light was converted into $t$ using the rise time of SN 1994D (18 days; Vacca Leibundgut \cite{vacca}) ). " In view of the lack of very early spectra. we conservatively assumed that =0 for r>ry, at (0."," In view of the lack of very early spectra, we conservatively assumed that $\Phi$ =0 for $r>r_{\rm ph}$ at t=0." We explored two possible cases: an isolated. homogeneous. spherical cloud with radius rc and offset c with respect to the line of sight: a patchy sheet with an input spectrum for the column density fluctuations.," We explored two possible cases: an isolated, homogeneous, spherical cloud with radius $r_C$ and offset $x_C$ with respect to the line of sight; a patchy sheet with an input spectrum for the column density fluctuations." In the first ease. the column density profile is NG’)=Nl— G'/rcV. where r' is the projected distance from the cloud center ( rx rco). and No is the column density corresponding to à ray going through the center of the cloud.," In the first case, the column density profile is $N(r^\prime)=N_0 \sqrt{1-(r^\prime/r_C)^2}$ , where $r^\prime$ is the projected distance from the cloud center ( $r^\prime\leq r_C$ ), and $N_0$ is the column density corresponding to a ray going through the center of the cloud." The average column density is (N)=2/3 No., The average column density is $\langle N\rangle$ =2/3 $N_0$ . As the case of an isolated. small cloud is probably quite unrealistic. it may be rather regarded as a simplified model of an over-density on an otherwise homogeneous sheet.," As the case of an isolated, small cloud is probably quite unrealistic, it may be rather regarded as a simplified model of an over-density on an otherwise homogeneous sheet." For the patchy sheet we adopted a procedure similar to the one deseribed by Deshpande (2000)), For the patchy sheet we adopted a procedure similar to the one described by Deshpande \cite{deshpande00b}) ). Molecular clouds (Elmegreen Falgarone 1996)). the diffuse ionized component (Cordes et al. 1991)).," Molecular clouds (Elmegreen Falgarone \cite{elmegreen}) ), the diffuse ionized component (Cordes et al. \cite{cordes}) )," and (Stanimiroviéet al. 1999:: , and (Stanimirovićet al. \cite{stanimirovic}; ; Deshpande. Dwarakanth Goss 2000)) have a fractal structure.characterized by a power-law behavior.," Deshpande, Dwarakanth Goss \cite{deshpande00a}) ) have a fractal structure,characterized by a power-law behavior." Therefore. if A=do/l is the wave-number corresponding to a given spatial scale/ (where /y is the maximum spatial scale under," Therefore, if $k=l_0/l$ is the wave-number corresponding to a given spatial scale$l$ (where $l_0$ is the maximum spatial scale under" "velocity 2:444),=CUMss|Alea)fr. plus the radial velocity corresponding to pointmass inspiral.","velocity $2\pi\nu_{\rm orb}=\sqrt{G(M_{\rm SS}+M_{BH})/r^{3}}$, plus the radial velocity corresponding to point–mass inspiral." v Every SPL particle in the star is given the same azimuthal velocity. and thus the svstem corresponds to one in which the star is not spinning in an external (inertial) frame of reference.," Every SPH particle in the star is given the same azimuthal velocity, and thus the system corresponds to one in which the star is not spinning in an external (inertial) frame of reference." We have two reasons for choosing a non-spinning star at the beginning of the run., We have two reasons for choosing a non-spinning star at the beginning of the run. This initial condition is believed. to be realistic since the shear viscosity of quark matter is believed to be smaller than in neutron-star matter. and in neutron stars tidal svnehronization can be neelected Cxochanck 1992: Bildsten Cutler 1992).," This initial condition is believed to be realistic since the shear viscosity of quark matter is believed to be smaller than in neutron-star matter, and in neutron stars tidal synchronization can be neglected (Kochanek 1992; Bildsten Cutler 1992)." Further. past experience (papers E through IV) caches us that the ejection of matter from tidally locked: polvtropes is much smaller than from non-spinning polytropes (for which the coalescence oocess js much. more violent).," Further, past experience (papers I through IV) teaches us that the ejection of matter from tidally locked polytropes is much smaller than from non-spinning polytropes (for which the coalescence process is much more violent)." The present. simulations. of quark-star coalescence resemble to à certain extent our earlier simulations for still »»Ivtropes. hence we expect the same dependence to hold here.," The present simulations of quark-star coalescence resemble to a certain extent our earlier simulations for stiff polytropes, hence we expect the same dependence to hold here." A quark star is the right choice for the initial conditions. if we are o place secure upper bounds on the amount of matter ejected from the αν.," A non-spinning quark star is the right choice for the initial conditions, if we are to place secure upper bounds on the amount of matter ejected from the binary." As it turns out. at the start of the dynamical calculation. a tical 1ος appears on the star. in the direction facing the black hole.," As it turns out, at the start of the dynamical calculation, a tidal bulge appears on the star, in the direction facing the black hole." This is simply because the initial configuration (1.c.. spherical star plus nis companion) is not in equilibrium at f=0.," This is simply because the initial configuration (i.e., spherical star plus point-mass companion) is not in equilibrium at $t=0$." Thereafter the star spirals in due to gravitational radiation reaction (at the initial binary separations eiven in Table 1.. the decay timescale due to the emission of gravitational waves is comparable to the orbital period).," Thereafter the star spirals in due to gravitational radiation reaction (at the initial binary separations given in Table \ref{IC}, the decay timescale due to the emission of gravitational waves is comparable to the orbital period)." In trial runs we have placed the star also at. various Larger initial separations., In trial runs we have placed the star also at various larger initial separations. The outcome of the coalescence was found to be insensitive to the choice of η., The outcome of the coalescence was found to be insensitive to the choice of $r_i$. We are in à position to compare the results presented here for. quark- cos. P—(ppo)/3.," We are in a position to compare the results presented here for quark-matter e.o.s., $P=c^{2}(\rho-\rho_{0})/3$," with those obtained for the polytropic cos., with those obtained for the polytropic e.o.s. " P=Αρ or P—αἱDips (here p, denotes the barvon rest- densitv).", $P=K\rho_b^\Gamma$ or $P=(\Gamma-1)\rho_bu$ (here $\rho_b$ denotes the baryon rest-mass density). We had. previously carried. out coalescence simulations.," We had previously carried out coalescence simulations," 5ο X-ray emission of hot gas 1 Üioand arouud galaxies depeuds heavily ou the properties of metals (ie.. elements heavier than μαι).,"Soft X-ray emission of hot gas in and around galaxies depends heavily on the properties of metals (i.e., elements heavier than helium)." Due to the conceurated enrichment of Type Ia supernovae (Ia SNe). the primary irou srovider of the universe. hot eas in galactic stellar spheroids fealactic bulges and ellipical galaxies). iu particular. is expected tolave a super-solar tron abundance.," Due to the concentrated enrichment of Type Ia supernovae (Ia SNe), the primary iron provider of the universe, hot gas in galactic stellar spheroids (galactic bulges and elliptical galaxies), in particular, is expected to have a super-solar iron abundance." Away [rom such a stellar spheroid. the i'on-rich hot gas might be dilited by iu-falling low-abuudance eas.," Away from such a stellar spheroid, the iron-rich hot gas might be diluted by in-falling low-abundance gas." Thus a monotonicaly decreasing i‘on abuudauce profile as a fhuction of galactic radius is also expected (e.g.. Buote2000a:Borganietal. 2008)) anc Lis uxleed observed. ou scales of the intragroup aud intracluser media.," Thus a monotonically decreasing iron abundance profile as a function of galactic radius is also expected (e.g., \citealt{Buote00apj,Borgani08}) ) and is indeed observed on scales of the intragroup and intracluster media." On sinaller scales (within individual stellar spheroids aud their iumeciate vicinity). however. irou abundauces of the hot gas seem to be at odds with the predictions.," On smaller scales (within individual stellar spheroids and their immediate vicinity), however, X-ray-inferred iron abundances of the hot gas seem to be at odds with the predictions." The abuudauces, The abundances luit. they again reduce to familiar expressions.,"limit, they again reduce to familiar expressions." We also uote that in terms of partial derivatives. equation (3-21)) can be expanded to vield where 5 is the determinaut of the spatialiuetric 5;;.," We also note that in terms of partial derivatives, equation \ref{Edot2}) ) can be expanded to yield where $\gamma$ is the determinant of the spatial metric $\gamma_{ij}$." This form of the clectric field evolution equation will be useful for applications in Paper II., This form of the electric field evolution equation will be useful for applications in Paper II. " Oluu’s law can be written (sec. eg. Jackson. 1999) the charee density as seen by an observer co-moving with the Suid foum-velocitv « (n coutrast to pi. which was defined as the charge density as observed by a nonual observer p"")."," Ohm's law can be written (see, e.g., Jackson, 1999) where $\sigma$ is the electrical conductivity and $\tilde \rho_e = -{\mathcal J}^a u_a$ is the charge density as seen by an observer co-moving with the fluid four-velocity $u^a$ (in contrast to $\rho_e$, which was defined as the charge density as observed by a normal observer $n^a$ )." " A3 | 1decompositionof Olini's law cau be derived by coutracting (L-1)) with »"" and 5,.", A $3+1$ decomposition of Ohm's law can be derived by contracting \ref{ohm}) ) with $n^a$ and $\gamma_a^{~b}$. " The former vields ou, E. have defined Τ as the Loreutz factor between normal aud Πτα observers We pu Projecting 1-13) iuto X. or. equivaleutly. evaluating the spatial components ο=7 of (L1)). vields Tere we have defied aud have used (3-19)) to relate ej). to €;55. giving vise to the shift tei iu CLE-1)) (the shift term is missing im some previous treatiuents. sce Section 8))."," The former yields where we have defined $W$ as the Lorentz factor between normal and fluid observers Projecting \ref{ohm}) ) into $\Sigma$, or, equivalently, evaluating the spatial components $a = i$ of \ref{ohm}) ), yields Here we have defined and have used \ref{epsilon_convert}) ) to relate $\epsilon_{itk}$ to $\epsilon_{ijk}$ giving rise to the shift term in \ref{ohm_spatial}) ) (the shift term is missing in some previous treatments, see Section \ref{sec8}) )." Dividing Olun’s law CLI-1)) by o and allowing σΣαχ vields the perfect conductivity coucdition According to (1-2)) aud (1-1)). this result is equivalent to the coudition that the electric field) vanish in the fluid rest frame Or which is often called the ideal ANID relation.," Dividing Ohm's law \ref{ohm}) ) by $\sigma$ and allowing $\sigma \rightarrow \infty$ yields the perfect conductivity condition According to \ref{ohm_time}) ) and \ref{ohm_spatial}) ), this result is equivalent to the condition that the electric field vanish in the fluid rest frame or which is often called the ideal MHD relation." When evaluated in a MiukowskEki spacetime. the last equation reduces to the familiar expression £;03 or E=νυνΕ.," When evaluated in a Minkowski spacetime, the last equation reduces to the familiar expression $E_i = - \epsilon_{ijk} v^j B^k$ or ${\bf E = -v \times B}$." We can now evaluate Faradavs law (3-10)) uuder the asstuuption of perfect conductivity., We can now evaluate Faraday's law \ref{Bdot}) ) under the assumption of perfect conductivity. Takiug the trace of {2-9)) viclds The above expression ean be combined with the Lie derivative ΟΠ) to give where we have used (3-933., Taking the trace of \ref{gdot}) ) yields The above expression can be combined with the Lie derivative $\Lie_{\bf \beta} B^i$ to give where we have used \ref{divB}) ). Inserting Cl-10)) together with the ideal ΑΠΟ equation (1-8)) iuto Faraday law (3-103) reveals that all the shift terms cancel. leaving It is convemicut to introduce the magnetic vector density in terius of which equation (1I-11)) and 0À9)) reduce to the particularly simple forms aud Iu Section 8. we compare with previous treatments aud correct errors ia some previously published equations.," Inserting \ref{rhs}) ) together with the ideal MHD equation \ref{MHD}) ) into Faraday's law \ref{Bdot}) ) reveals that all the shift terms cancel, leaving It is convenient to introduce the magnetic vector density in terms of which equation \ref{MHD_faraday}) ) and \ref{divB}) ) reduce to the particularly simple forms and In Section \ref{sec8} we compare with previous treatments and correct errors in some previously published equations." " Foror a perfectperfec uid.fluid. the sstYOSS-OLOYSVev tΤΟΝΟΥ TH""aq cui ]be written Ilere py is the restanass density as observed bv au observer coanovius with the fluid a"". P is the pressure. and / is the specific cuthalpy where e is the specific internal energy. deusity."," For a perfect fluid, the stress-energy tensor $T^{ab}_{\rm fluid}$ can be written Here $\rho_0$ is the rest-mass density as observed by an observer co-moving with the fluid $u^a$, $P$ is the pressure, and $h$ is the specific enthalpy where $\epsilon$ is the specific internal energy density." Iu the absence of electromagnetic fields. the equations of motion for the fluid cau be derived from the local conservation of enerev-auonmientui. aud the conservation of barvous. The resulting equatious can be cast m various fornis. depending ou how the the primitive fluid variables are chosen (sec. e.8.. Fout 2000 for a recent review).," In the absence of electromagnetic fields, the equations of motion for the fluid can be derived from the local conservation of energy-momentum, and the conservation of baryons, The resulting equations can be cast in various forms, depending on how the the primitive fluid variables are chosen (see, e.g., Font 2000 for a recent review)." The most frequently adopted relativistic οταν was originally developed by Wilson (1972: see also Hawley. Suiuvr Wilson. 1981). who defined a rest-iass density viable an internal energv density variable and a moment variable Note that the spatial vector 5; defined above is the fiuiel contribution to the source term 5; appeariug in Eisteiu's field equations (cf.," The most frequently adopted relativistic formalism was originally developed by Wilson (1972; see also Hawley, Smarr Wilson, 1984), who defined a rest-mass density variable an internal energy density variable and a momentum variable Note that the spatial vector $S_i$ defined above is the fluid contribution to the source term $S_i$ appearing in Einstein's field equations (cf.," equation (2-11)))., equation \ref{Si}) )). Iu. terms of these variables.the equation of contiuuitv becomes Coutracting (5-3)) with o viclds the ο equation," In terms of these variables,the equation of continuity becomes Contracting \ref{divT}) ) with $u^b$ yields the energy equation" lay serve as an indication of the ouset of star formation in the highest-z QSOs (see Sec. 11).,may serve as an indication of the onset of star formation in the highest-z QSOs (see Sec. \ref{intro}) ). The proxy usually used to trace the Fe/Ale abundance ratio at high-z is the Wane ratio., The proxy usually used to trace the Fe/Mg abundance ratio at high-z is the line ratio. In the past. uuncerous NIR-spectroscopy studies have been carricc out to analyze the Wine ratio in high-z QSOs2007).," In the past, numerous NIR-spectroscopy studies have been carried out to analyze the line ratio in high-z QSOs." . The combined results revealed an increase iu the scatter of the measured πιο ratios as a δεuction of redshift2007)., The combined results revealed an increase in the scatter of the measured line ratios as a function of redshift. .. A proposed explanation for the increased scatter is that some voung jects have been observed such a short time after the initial starburst that the DER has not been fully enriched with Fe vet., A proposed explanation for the increased scatter is that some young objects have been observed such a short time after the initial starburst that the BLR has not been fully enriched with Fe yet. We compute the ffüux by inteerating the normalized template over the rest-frame wavelength range 2200A s_2 > s_3$ . The corresponding semi-axes are oriented along the directions of the corresponding unit eigenvectors eij. e;» and δις.," The corresponding semi-axes are oriented along the directions of the corresponding unit eigenvectors ${\hat {\bf e}}_{s1}$, ${\hat {\bf e}}_{s2}$ and ${\hat {\bf e}}_{s3}$." The length of the semi-axes a; are with cvelie permutation for the other axes GN. is the number of volume elements within the void)., The length of the semi-axes $a_i$ are with cyclic permutation for the other axes $N$ is the number of volume elements within the void). " The longest axis is directed along e;,. the shortest along e,5."," The longest axis is directed along ${\hat {\bf e}}_{s1}$, the shortest along ${\hat {\bf e}}_{s3}$." " We quantify the shape of the void ellipsoids in terms of the two axis ratios go;=aoa, and a»= ases.", We quantify the shape of the void ellipsoids in terms of the two axis ratios $\eta_{21} = a_2/a_1$ and $\eta_{32} = a_3/a_2$ . " Amonest the triaxial void. ellpsoids we make a distinction. between oblate ones. with toyZ7gas. and. prolate ones having ne,< nao."," Amongst the triaxial void ellpsoids we make a distinction between oblate ones, with $\eta_{21}>\eta_{32}$, and prolate ones having $\eta_{21}<\eta_{32}$ ." 1 voids were spherical we would have οι=gs—1 (though. in reality. perfect sphericity does not exist)," If voids were spherical we would have $\eta_{21}=\eta_{32}=1$ (though, in reality, perfect sphericity does not exist)." In the density field in the upper righthand frame of figure 1 we have indicated the projected direction. of the longest axis of the voids by means of a bar along the corresponding eigenvector. with the length of the bar proportional to the size of the void axis.," In the density field in the upper righthand frame of figure \ref{fig:slices} we have indicated the projected direction of the longest axis of the voids by means of a bar along the corresponding eigenvector, with the length of the bar proportional to the size of the void axis." It allows a superficial comparison with the related WVI void patches (indicated by the solid black lines marking their boundary, It allows a superficial comparison with the related WVF void patches (indicated by the solid black lines marking their boundary). The lower lefthand. panel ).of figure 1. shows the shape-ellipsoids of cach void. within the region of the simulation box shown in the top-right panel., The lower lefthand panel of figure \ref{fig:slices} shows the shape-ellipsoids of each void within the region of the simulation box shown in the top-right panel. The centers of the shape-ellipsoids are located at the center of cach void. with their size scaled according to match the void volume: they give a convenient visual impression of the void. shapes ancl sizes., The centers of the shape-ellipsoids are located at the center of each void with their size scaled according to match the void volume: they give a convenient visual impression of the void shapes and sizes. The reasonably accurate degree. to which the. ellipsoicds rellect the shape of the voids may be inferred. from a comparison with the WVEI void regions themselves., The reasonably accurate degree to which the ellipsoids reflect the shape of the voids may be inferred from a comparison with the WVF void regions themselves. Clearly. the voids are. quite nonspherical.," Clearly, the voids are quite nonspherical." X. more uantitative impression of the shape distribution may be =ound in the second. and third. panel of fig., A more quantitative impression of the shape distribution may be found in the second and third panel of fig. 2. which show wt the voids are far from spherical., \ref{fig:shape} which show that the voids are far from spherical. The intrinsic triaxial shape of voids is apparent. from 1e distribution in the second panel of fig. 2.., The intrinsic triaxial shape of voids is apparent from the distribution in the second panel of fig. \ref{fig:shape}. This shows a scatter plot of of the two axis ratios. jo versus ios for every Poid in the sample.," This shows a scatter plot of of the two axis ratios, $\eta_{12}$ versus $\eta_{23}$ for every void in the sample." To guide the eve we have superimposed 1e inferred isodensity contours defined by the point density in the scatter plot., To guide the eye we have superimposed the inferred isodensity contours defined by the point density in the scatter plot. We find a slight asvmmetry: there are more prolate voids than oblate ones., We find a slight asymmetry: there are more prolate voids than oblate ones. The third panel shows that the distribution. of the ellipticity «©=1agfay is skewed towards higher values of οz-0.5.," The third panel shows that the distribution of the ellipticity $\epsilon = 1-a_3/a_1$ is skewed towards higher values of $\epsilon > 0.5$." Ehe void. population is marked by pronounced triaxial shapes: the average ratio between the smallest. and largest axis c/e5 0.49.," The void population is marked by pronounced triaxial shapes: the average ratio between the smallest and largest axis $c/a \approx 0.49$ ." " ""This ratio agrees with well with the value of 0.45 found by Shancarinefaf(2006). (which is perhaps a little surprising given the totally different void definitions used in that paper)", This ratio agrees with well with the value of $0.45$ found by \cite{shandarin2006} (which is perhaps a little surprising given the totally different void definitions used in that paper). 1n summary. we find. voids to be slightly prolate. with average axis ratios in the order of e:ba20.50.71.," In summary, we find voids to be slightly prolate, with average axis ratios in the order of $c:b:a\approx 0.5:0.7:1$." Two important factors contribute to this flattening., Two important factors contribute to this flattening. " Even though. internally, voids tenc to become more spherical as they expand. (leke1984)... perfect. sphericity will hardly ever be reached."," Even though, internally, voids tend to become more spherical as they expand \citep{icke1984}, perfect sphericity will hardly ever be reached." Before. voids would. be able to become spherical they would encounter. surrounding structures such as overdense filaments or planar walls., Before voids would be able to become spherical they would encounter surrounding structures such as overdense filaments or planar walls. Even more important may be the fact that. for voids. external tidal influences are particularly important: voids will always be rather moderate underdensities since they can never be more underdense than ὁ=1.," Even more important may be the fact that, for voids, external tidal influences are particularly important: voids will always be rather moderate underdensities since they can never be more underdense than $\delta=-1$." The external tidal forces drive a significanr anisotropy in the development of the volds. and in the extreme cases may cause complete collapse of the void along one or more of its axes.," The external tidal forces drive a significanr anisotropy in the development of the voids, and in the extreme cases may cause complete collapse of the void along one or more of its axes." This is another aspect of the way in which tidal forces shape the Cosmic Web. as has been emphasized by Bondefa£(1996).," This is another aspect of the way in which tidal forces shape the Cosmic Web, as has been emphasized by \cite{bondweb1996}." Large scale inlluences play a major role not only in shaping individual voids but also on their mutual arrangement. and organization., Large scale influences play a major role not only in shaping individual voids but also on their mutual arrangment and organization. A particularly important manifestation of this is the mutual alignment. between voids., A particularly important manifestation of this is the mutual alignment between voids. In this section we establish the significance. of this ellect. anc in the next section we analyse the correlation between the tical force field and the void orientation.," In this section we establish the significance of this effect, and in the next section we analyse the correlation between the tidal force field and the void orientation." We take the void centers in our sample to define a spatialpoint process., We take the void centers in our sample to define a spatialpoint process. Fhree void alignment measures havebeen investigated., Three void alignment measures havebeen investigated. Each is a marked correlation function (Beisbart and. assesses the degree of alignment as a function of the distance rr between," Each is a marked correlation function \citep{beiker2000, stoystoy1994} and assesses the degree of alignment as a function of the distance $r$ between" add weight to the topology argument.,add weight to the topology argument. Finally. more detailed testing of changes around the dusty reeinue (—M6.5) where stars can also be voune brown dwarts night usefully be investigated.," Finally, more detailed testing of changes around the dusty regime $\sim$ M6.5) where stars can also be young brown dwarfs might usefully be investigated." "was parameterized by Lu οἱ ((1993) using the power-law plus exponential form: where the rollover energv. /Z, was [found to scale as E,xL5owith Jx3.9.","was parameterized by Lu et (1993) using the power-law plus exponential form: where the rollover energy $E_r$ was found to scale as $E_r\propto L^{\beta}$ , with $\beta \approx 3.9$." Avalanche models also produce exponential waiting-time distributions BBiesecker 1994: Wheatland et 11993). although time-dependent driving alters (his NNorman οἱ 22001).," Avalanche models also produce exponential waiting-time distributions Biesecker 1994; Wheatland et 1998), although time-dependent driving alters this Norman et 2001)." Another approach to modeling [lare event statisties involves describing the energy balance in a [laring active region in terms of energv input and loss RRosner Vaiana 1975: Litvinenko 1994: Craig 2001)., Another approach to modeling flare event statistics involves describing the energy balance in a flaring active region in terms of energy input and loss Rosner Vaiana 1978; Litvinenko 1994; Craig 2001). A general model of this kind was presented in Wheatland Glukhov (1998). and developed in Wheatland (2008; 2009).," A general model of this kind was presented in Wheatland Glukhov (1998), and developed in Wheatland (2008; 2009)." Active regions are assumed to have a [ree energv £=E(f) which evolves in time / due to deterministic energy input at a rate (EL). aad due to random downwards jumps [rom energy. E to E' (flares) at arate described bv a transition function a(£.E'.1).," Active regions are assumed to have a free energy $E=E(t)$ which evolves in time $t$ due to deterministic energy input at a rate $\beta (E,t)$, and due to random downwards jumps from energy $E$ to $E^{\prime}$ (flares) at a rate described by a transition function $\alpha (E,E^{\prime},t)$." The resulting stochastic jump transition model mav be formulated either as a master equation lor the energy distribution P(E./) (Wheatland 2008). or as a stochastic dillerential equation for E(/) (Wheatland 2009).," The resulting stochastic jump transition model may be formulated either as a master equation for the energy distribution $P(E,t)$ (Wheatland 2008), or as a stochastic differential equation for $E(t)$ (Wheatland 2009)." In the steady state Hor a constant driving rate ancl a constant total mean rate of flaring). the model can reproduce the observed power-law Irecquency. size distribution. below an upper rollover delined approximately by the mean energv E of the steady-state distribution P(E).," In the steady state for a constant driving rate and a constant total mean rate of flaring), the model can reproduce the observed power-law frequency size distribution, below an upper rollover defined approximately by the mean energy $\overline{E}$ of the steady-state distribution $P(E)$." Flares with energy 29E are not observed because the active region is unlikely to have sufficient energv (o produce them., Flares with energy $\gg \overline{E}$ are not observed because the active region is unlikely to have sufficient energy to produce them. The model waiting-time distribution is exponential provided E is sullicientlv large that large flares are unlikely to significantly deplete the [ree energy. of the svstem., The model waiting-time distribution is exponential provided $\overline{E}$ is sufficiently large that large flares are unlikely to significantly deplete the free energy of the system. In (hat case the total mean rate of flaring is approximately independent of energy. and hence does not vary in lime. as (he active region energy. varies.," In that case the total mean rate of flaring is approximately independent of energy, and hence does not vary in time, as the active region energy varies." This produces a Poisson waiüng-üme distribution., This produces a Poisson waiting-time distribution. The stochastic jump (transition model. although idealised. helps to clarify ideas of energv storage and release in flares. and (heir relationship to the flare frequency-enereyv and wailine-lime distributions.," The stochastic jump transition model, although idealised, helps to clarify ideas of energy storage and release in flares, and their relationship to the flare frequency-energy and waiting-time distributions." SGacdies of flares statistics often use Che soft X-ray event lists generated by the US Space Weather PredictionCenter!.. which are derived [rom whole-Sun | 8A flax measurements from the Geostationary Observational Environmental (GOES) satellites.," Studies of flares statistics often use the soft X-ray event lists generated by the US Space Weather Prediction, which are derived from whole-Sun $1$ $8\,\mbox{\AA}$ flux measurements from the Geostationary Observational Environmental (GOES) satellites." The peak flux of GOES events is routinely used to classify flares: very small [Lares are labelled A and D class (peak fluxes exceeding LOWm7 and 10.*Wm7 respectively): small and medium flares are labelled C ancl M class (peak fluxes above 10Wm7 and LO?Wain7? respectively): and large fares are labelled X. class(peak flux above 10+Wan7).," The peak flux of GOES events is routinely used to classify flares: very small flares are labelled A and B class (peak fluxes exceeding $10^{-8}\,{\rm W}\,{\rm m}^{-2}$ and $10^{-7}\,{\rm W}\,{\rm m}^{-2}$ respectively); small and medium flares are labelled C and M class (peak fluxes above $10^{-6}\,{\rm W}\,{\rm m}^{-2}$ and $10^{-5}\,{\rm W}\,{\rm m}^{-2}$ respectively); and large flares are labelled X class(peak flux above $10^{-4}\,{\rm W}\,{\rm m}^{-2}$)." " A numerical sullix is used to indicate a nmmlliplicative factor. so that C3.1 indicates a peak flux of 3.1x10""Wan 7."," A numerical suffix is used to indicate a multiplicative factor, so that $3.1$ indicates a peak flux of $3.1\times 10^{-6}\,{\rm W}\,{\rm m}^{-2}$ ." be large enough to be able to produce a massive star which can go supernova to seed the Solar System with the observed short lived radioactive isotopes.,be large enough to be able to produce a massive star which can go supernova to seed the Solar System with the observed short lived radioactive isotopes. " Indeed, at cluster sizes of 104-10? stars, multiple supernovae are likely, allowing each supernova to be further away and exposing the Solar System to less mass loss."," Indeed, at cluster sizes of $^4$ $^5$ stars, multiple supernovae are likely, allowing each supernova to be further away and exposing the Solar System to less mass loss." A close encounter within the birth cluster has also been proposed to explain the existence of Sedna., A close encounter within the birth cluster has also been proposed to explain the existence of Sedna. " We find that this is within reason, showing that it is possible to produce a small fraction of KBOs at ~500 AU with eccentricity between 0.5 and 1."," We find that this is within reason, showing that it is possible to produce a small fraction of KBOs at $\sim$ 500 AU with eccentricity between 0.5 and 1." " However, we find that it is highly unlikely that encounters in the birth cluster could be responsible for truncation of the Kuiper Belt."," However, we find that it is highly unlikely that encounters in the birth cluster could be responsible for truncation of the Kuiper Belt." " There is only a small region of parameter space that allows for the destruction of the outer Kuiper Belt while leaving the inner Kuiper Belt intact, and any cluster capable of disrupting the outer Kuiper Belt would also be very likely to excite Neptune to a higher eccentricity than we observe."," There is only a small region of parameter space that allows for the destruction of the outer Kuiper Belt while leaving the inner Kuiper Belt intact, and any cluster capable of disrupting the outer Kuiper Belt would also be very likely to excite Neptune to a higher eccentricity than we observe." " Finally, we caution that disruption of planetary orbits by the gravity of passing stars may not be the only limiting factor when it comes to cluster size."," Finally, we caution that disruption of planetary orbits by the gravity of passing stars may not be the only limiting factor when it comes to cluster size." " ? argues that in a cluster of more than -10 stars, the ultraviolet radiation produced by massive stars would photoevaporate the Sun's protoplanetary disk, preventing formation of the outer planets."," \citet{Adams-2010} argues that in a cluster of more than $\sim 10^4$ stars, the ultraviolet radiation produced by massive stars would photoevaporate the Sun's protoplanetary disk, preventing formation of the outer planets." " However, this conclusion is highly sensitive to the rate of mass loss due to photoevaporation, which is highly uncertain."," However, this conclusion is highly sensitive to the rate of mass loss due to photoevaporation, which is highly uncertain." " The 104 star limit is based on a loss rate taken from ?,, but ? show that this rate is uncertain at the order of magnitude level."," The $10^4$ star limit is based on a loss rate taken from \citet{AdamsEtAl-2004}, but \citet{ErcolanoEtAl-2009} show that this rate is uncertain at the order of magnitude level." " Moreover, it is not entirely clear that photoevaporation inhibits planet formation; instead, by raising the dust-to-gas ratio, it may trigger gravitational instability (?).."," Moreover, it is not entirely clear that photoevaporation inhibits planet formation; instead, by raising the dust-to-gas ratio, it may trigger gravitational instability \citep{Throop-2005}." " Due to these uncertainties, the question of whether photoevaporation might provide a limit on the cluster size remains an open one for future research."," Due to these uncertainties, the question of whether photoevaporation might provide a limit on the cluster size remains an open one for future research." We thank G. Laughlin for extensive discussions and comments on the manuscript., We thank G. Laughlin for extensive discussions and comments on the manuscript. " MRK is supported by the Alfred P. Sloan Foundation, the National Science Foundation through grants AST-0807739 and CAREER-0955300, and NASA through Astrophysics Theory and Fundamental Physics Grant NNX09AK31G and a Chandra Space Telescope Grant."," MRK is supported by the Alfred P. Sloan Foundation, the National Science Foundation through grants AST-0807739 and CAREER-0955300, and NASA through Astrophysics Theory and Fundamental Physics Grant NNX09AK31G and a Chandra Space Telescope Grant." "same N metallicity as the cool component, then the model cannot fit the narrow line because too much emission comes from larger spatial regions.","same N metallicity as the cool component, then the model cannot fit the narrow line because too much emission comes from larger spatial regions." Table 2 shows the best fitting values of each of the parameters and their uncertainties., Table \ref{tab:fitresults} shows the best fitting values of each of the parameters and their uncertainties. The improvement in Y? is around 1000 over the single temperature model., The improvement in $\chi^2$ is around 1000 over the single temperature model. " The best fitting temperatures, 0.77 and 1.85 keV, are very close to the range of values found in the inner arcmin by (?).."," The best fitting temperatures, 0.77 and 1.85 keV, are very close to the range of values found in the inner arcmin by \citep{Fabian05}." " The best fitting iron metallicities, however, are substantially lower than the 1.5—2Z; peak values from and CCD spectra (?).."," The best fitting iron metallicities, however, are substantially lower than the $1.5-2 \Zsun$ peak values from and CCD spectra \citep{SandersEnrich06}." In fact all of the metallicities (except Ca) of each of the elements we measure from the RGS spectra are significantly lower than the CCD results., In fact all of the metallicities (except Ca) of each of the elements we measure from the RGS spectra are significantly lower than the CCD results. " CCD measurements indicate that the metallicities drops dramatically in the innermost region (?),, which may correspond with this low metallicity."," CCD measurements indicate that the metallicities drops dramatically in the innermost region \citep{SandersCent02}, which may correspond with this low metallicity." We will discuss this further in Section 5.4.., We will discuss this further in Section \ref{sect:metals}. " The lines from cooler temperature gas are narrower than the lines from hotter gas, leading to a larger spatial scale for the hot component (1.1 vs 0.3 arcmin)."," The lines from cooler temperature gas are narrower than the lines from hotter gas, leading to a larger spatial scale for the hot component (1.1 vs 0.3 arcmin)." The emission measure of the cooler component is only around 5 per cent of the hot component., The emission measure of the cooler component is only around 5 per cent of the hot component. We can extend the two-temperature model with more temperature components., We can extend the two-temperature model with more temperature components. Multitemperature fits with several free temperatures typically become unstable when spectral fitting., Multitemperature fits with several free temperatures typically become unstable when spectral fitting. " To avoid this we constructed a model containing components with fixed temperatures, allowing the emission measure of each component to vary."," To avoid this we constructed a model containing components with fixed temperatures, allowing the emission measure of each component to vary." We used a multi-temperature model containing five components (5x VAPEC))., We used a multi-temperature model containing five components $5\times$ ). " We used a range of temperatures in the model to account for the ranges of temperatures in the cluster the spectrum is sensitive to, with components at 0.4, 0.8, 1.6, 2.4 and 3.2 keV. We also tried an 8 component model, but the quality of the fit was only slightly improved and it was difficult to constrain the parameters."," We used a range of temperatures in the model to account for the ranges of temperatures in the cluster the spectrum is sensitive to, with components at 0.4, 0.8, 1.6, 2.4 and 3.2 keV. We also tried an 8 component model, but the quality of the fit was only slightly improved and it was difficult to constrain the parameters." The vacuum energy is the sum of five contributions: if A=$77zj-lrjav.ὃ denotes the Laplacian. come [rom the vacuum fluetuatious of the vector bosou. Higgs. real Goldstone. complex. Goldstone. and ghost fields.,"The vacuum energy is the sum of five contributions: if $\bigtriangleup=\sum_{j=1}^2 \, \frac{\partial}{\partial x_j}\cdot \frac{\partial}{\partial x_j}$ denotes the Laplacian, come from the vacuum fluctuations of the vector boson, Higgs, real Goldstone, complex Goldstone, and ghost fields." Cost. [Inctuatious. however. cancel the contribution of temporal vector bosons ancl real Qolstone particles. and the vacuum energy in the planar semi-local AHM is due only to Higgs particles. couples Goldstone bosous. and transverse massive vector bosons: At the criticalm pointH between Type I aud Type II superconductivity.H επ>=41. the enerey can be arranged inH a Bogomoluy splitting: Therefore. the solutions of the first-order equations D4d£iDob=0Fy£4(07—1) are absolute uiinima of the energy. heuce stable. iu each topological sector with a classical mass proportional to the maguetic flux.," Ghost fluctuations, however, cancel the contribution of temporal vector bosons and real Golstone particles, and the vacuum energy in the planar semi-local AHM is due only to Higgs particles, complex Goldstone bosons, and transverse massive vector bosons: At the critical point between Type I and Type II superconductivity, $\kappa^2=1$, the energy can be arranged in a Bogomolny splitting: Therefore, the solutions of the first-order equations $D_1 \Phi \pm i D_2 \Phi=0=F_{12} \pm \frac{1}{2} (\Phi^\dagger\Phi-1)$ are absolute minima of the energy, hence stable, in each topological sector with a classical mass proportional to the magnetic flux." It has been shown in [2] that there is a [dimensional moduli space of such solitonic solutions interpolating between the Nielseu-Olesen -NO in the sequel vortices of the Abelian Hives moclel and the C Pl-Iunps of the planar non-linear sigma model., It has been shown in \cite{GORS} that there is a $4l$ -dimensional moduli space of such solitonic solutions interpolating between the Nielsen-Olesen -NO in the sequel- vortices of the Abelian Higgs model and the ${\mathbb CP}^1$ -lumps of the planar non-linear sigma model. Assumiug a purely vorticial vector field plus the spherically symunetric ansatz gm—ςdria1.baderid=2nl. the lirst-order equations reduce to be solved together with the boundary conditions," Assuming a purely vorticial vector field plus the spherically symmetric ansatz $g= - \oint_{r=\infty} dx_i A_i = -l\oint_{r=\infty}{ [x_2dx_1-x_1dx_2]\over r^2}=2 \pi l$, the first-order equations reduce to be solved together with the boundary conditions" As idt cools. a supermassive star evolves toward lugher density along the mass-sheddding sequence aud is therefore stabilized bv. rotation until it reaches poiut AW,"As it cools, a supermassive star evolves toward higher density along the ding sequence and is therefore stabilized by rotation until it reaches point $A$." At this point. the star becomes unstable to radial perturbations and will collapse.," At this point, the star becomes unstable to radial perturbations and will collapse." We suuunarize the nunierical parameters characterizing point A iu Table 2Ne where they are compared with the fincines of the analytical model calculation of Section 3.2..," We summarize the numerical parameters characterizing point $A$ in Table 2, where they are compared with the findings of the analytical model calculation of Section \ref{anal}." Figure | shows the density profile at the critical point 109M£.. the central temperature is always less than 6<10*I.,"17.2.9) in Shapiro Teukolsky (1983) For SMSs with masses $M \gtrsim 10^6 M_{\odot}$, the central temperature is always less than $6 \times 10^7 K$." According: to Fowler (1966). this is the nini temperature required for ecuerating the SAIS’s luninositv via the CNO cvele.," According to Fowler (1966), this is the minimum temperature required for generating the SMS's luminosity via the CNO cycle." This justifies our assumption that nuclear reactions can be neglected., This justifies our assumption that nuclear reactions can be neglected. Iu this Section we discuss the evolution of a rotating SMS up to the ouset of instability., In this Section we discuss the evolution of a rotating SMS up to the onset of instability. In particular. we derive analytic expressions for the evolution of the mass. radius and aneular momentum as a fiction of time.," In particular, we derive analytic expressions for the evolution of the mass, radius and angular momentum as a function of time." The evolution of the three quantiies Is not indepeucdent., The evolution of the three quantities is not independent. lustead. they are couded by two relations. namely the requirement that the sar evolves aong inass-shedding (so that T/|JV| remains approximately constant). and that the aneular momentum loss cau be computed from the mass that leaves that star from the equator with the critical angular velocity.," Instead, they are coupled by two relations, namely the requirement that the star evolves along mass-shedding (so that $T/|W|$ remains approximately constant), and that the angular momentum loss can be computed from the mass that leaves that star from the equator with the critical angular velocity." This meaus that we can express. for Instance. the angular momentum loss J aud the change of radius # in terms of the mass loss M.," This means that we can express, for instance, the angular momentum loss $\dot J$ and the change of radius $\dot R$ in terms of the mass loss $\dot M$." The ouly relation that is vet to be determined fixes A and hence the overall timescale for the evolution of the three quantities., The only relation that is yet to be determined fixes $\dot M$ and hence the overall timescale for the evolution of the three quantities. Tn a similar caleulation. Bisnovatvitvogan. Zeldovvich Novvikkov (1967) estimated Ar bv coustructing au approximate stellar wind model. which they joined onto the outer envelope of the star.," In a similar calculation, Bisnovatyi-Kogan, vich kov (1967) estimated $\dot M$ by constructing an approximate stellar wind model, which they joined onto the outer envelope of the star." Their model depends on several unkuown nondinuensional parameters dealing with the wind solution., Their model depends on several unknown nondimensional parameters dealing with the wind solution. Vere. we take a ιο more naive approach. determining the mass loss rate from the requirement that the star remain in equilibrium as it cools in a quasistationary manner.," Here, we take a much more naive approach, determining the mass loss rate from the requirement that the star remain in equilibrium as it cools in a quasistationary manner." According to eq. (1)).," According to eq. \ref{M_Newton_K}) )," the mass loss rate is related to the change of A (or the eutropv). and is thus governed bv the stars luuinosity (see eq. €15))," the mass loss rate is related to the change of $K$ (or the entropy), and is thus governed by the star's luminosity (see eq. \ref{mdot2}) )" below)., below). As we have seen in Section 3.2.. the post-Newtonian corrections and rotational coutributions to the energv functional (20)) are iuportaut for determining the stability of SAISs. but they have a verv sinall effect ou the equilibrium structure and can therefore be ucelected for the purposes of this Section.," As we have seen in Section \ref{anal}, the post-Newtonian corrections and rotational contributions to the energy functional \ref{energy}) ) are important for determining the stability of SMSs, but they have a very small effect on the equilibrium structure and can therefore be neglected for the purposes of this Section." Accordingly. the mass AM of the star is well approximated by the Newtonian expression (1)). which only depends ou the polvtropic constant A.," Accordingly, the mass $M$ of the star is well approximated by the Newtonian expression \ref{M_Newton_K}) ), which only depends on the polytropic constant $K$ ." The time derivative of tle mass is given by The change of the total eutropy S of the star is related the Iuuninositv by Using the first law of ποιοςναλος. the right haud," The time derivative of the mass is given by The change of the total entropy $S$ of the star is related the luminosity by Using the first law of thermodynamics, the right hand" consistent the data.,consistent the data. To properly fit a log normal mass function we need (o include data from masses al (he peak and above (>0.10AL. )., To properly fit a log normal mass function we need to include data from masses at the peak and above $>0.10~M_{\odot}$ ). All three mathematical representations of (he mass function match the data with similar accuracy., All three mathematical representations of the mass function match the data with similar accuracy. Figure 19 shows the best fit models from each of the theoretical forms matched against the empirical KCAB densities., Figure \ref{fig:fit} shows the best fit models from each of the theoretical forms matched against the empirical KCAB densities. " All three luminosity functions are nearly identical to AL,~lr: only there do they begin to diverge.", All three luminosity functions are nearly identical to $M_J \sim 17$; only there do they begin to diverge. The Gvo-segment power law model has slightly hieher densiües (han the log normal model. while the abrupt stop in (he cutoff model is the result of the low-mass cutoff.," The two-segment power law model has slightly higher densities than the log normal model, while the abrupt stop in the cutoff model is the result of the low-mass cutoff." These dillerences are all well below the current detection limit. implving that it is very difficult to tell the difference between these models.," These differences are all well below the current detection limit, implying that it is very difficult to tell the difference between these models." This is what our Bavesian output told us., This is what our Bayesian output told us. The posterior distributions on the model parameters are either nol well constrained or completely dependant on the prior distribution., The posterior distributions on the model parameters are either not well constrained or completely dependant on the prior distribution. T wo properties of the calibrating INCAD dataset contribute to the weak constraints on ihe model parameter values., T wo properties of the calibrating KCAB dataset contribute to the weak constraints on the model parameter values. First. (he measurements for late-M to mid-L cdwarls 2005).. though the most reliable densitv determinations. fall within trough D of the luminosity function (Figure 13)).," First, the measurements for late-M to mid-L dwarfs \citep{kc03,kc05}, though the most reliable density determinations, fall within trough B of the luminosity function (Figure \ref{fig:fit}) )." This region is highly insensitive to changes in the value of (he model parameters (Figure 3))., This region is highly insensitive to changes in the value of the model parameters (Figure \ref{fig:sfmf}) ). Second. while the number densities of late-L ancl T dwarfs depend strongly on the slope of (he underlying mass fuction (see 822.2). their measured space densities have substantial uncertainties.," Second, while the number densities of late-L and T dwarfs depend strongly on the slope of the underlying mass fuction (see 2.2), their measured space densities have substantial uncertainties." Consequently. a wide range of parameter values fit the data: aud. with the data currently in hand. it is only possible to place weak constraints on the form of the substellar mass function.," Consequently, a wide range of parameter values fit the data; and, with the data currently in hand, it is only possible to place weak constraints on the form of the substellar mass function." since the field substellar mass function is weakly constrained with existing data. further observational efforts must be undertaken.," Since the field substellar mass function is weakly constrained with existing data, further observational efforts must be undertaken." There are both current. and future projects that can improve the mass funetion constraints., There are both current and future projects that can improve the mass function constraints. Follow-up observations of either SDSS or 2\TASS sources account for nearly all of the eurently known T dwarls. and that work is continuing (e.g.. Durgasser (2004))).," Follow-up observations of either SDSS or 2MASS sources account for nearly all of the currently known T dwarfs, and that work is continuing (e.g., \citet{burg04}) )." With a substantial fraction of both surveys analvzecl and their lower apparant magnitude detection limits filly probed. neither survey will extend coverage io significantly lower luminosities.," With a substantial fraction of both surveys analyzed and their lower apparant magnitude detection limits fully probed, neither survey will extend coverage to significantly lower luminosities." However. they will continue to bolster the statistics of lale-L and T dwarfs.," However, they will continue to bolster the statistics of late-L and T dwarfs." The Spitzer Space Telescope is capable of carrving out survevs lor T dwarls and discovering objects even cooler., The Spitzer Space Telescope is capable of carrying out wide-angle surveys for T dwarfs and discovering objects even cooler. The predicted mid-inlrared, The predicted mid-infrared the shock transition.,the shock transition. " A similar phenomena has been observed with satellites in the collisionless shocks in the aurora and the Earth's magnetosphere, where parallel electric fields together with strong particle acceleration are observed at the shock transition (seee.g.??).."," A similar phenomena has been observed with satellites in the collisionless shocks in the aurora and the Earth's magnetosphere, where parallel electric fields together with strong particle acceleration are observed at the shock transition \citep[see e.~g.\ ][]{Ergun:2001,Ergun:2009}." " We also note that parallel electric fields play a key role in reconnection of magnetic fields (?),, such as the reconfiguration that happens here, going from the mostly transverse current driven axial magnetic field upstream of the shock to the turbulent flux ropes seen downstream of the shock."," We also note that parallel electric fields play a key role in reconnection of magnetic fields \citep{Hesse:1988}, such as the reconfiguration that happens here, going from the mostly transverse current driven axial magnetic field upstream of the shock to the turbulent flux ropes seen downstream of the shock." " In the downstream region the plasma is very nearly neutral, with little density variation, but with a high level of magnetic turbulence."," In the downstream region the plasma is very nearly neutral, with little density variation, but with a high level of magnetic turbulence." " Our current simulation box for the ion-electron shock is not wide enough to allow for the largest magnetic structures, but using a 3D pair plasma simulation with a larger transverse volume we have observed how closed flux ropes are formed and are advected downwards from the shock, similar to what was seen by ?.."," Our current simulation box for the ion-electron shock is not wide enough to allow for the largest magnetic structures, but using a 3D pair plasma simulation with a larger transverse volume we have observed how closed flux ropes are formed and are advected downwards from the shock, similar to what was seen by \citet{Spitkovsky:2005}." In 2D models of collisionless shocks it has been found that particles are slowly accelerated by scattering off the filaments (?2??7)..," In 2D models of collisionless shocks it has been found that particles are slowly accelerated by scattering off the filaments \citep{Hededal:2004,Spitkovsky:2008b,Martins:2009}." " A few ""lucky"" particles cross back and forth over the shock interfaces a number of times, and this Fermi-like acceleration process slowly builds up a power-law tail of high energy particles, due to the quasi constant probability that a single high-energy particle is reflected in the strong transverse electric field near the shock (?).."," A few “lucky” particles cross back and forth over the shock interfaces a number of times, and this Fermi-like acceleration process slowly builds up a power-law tail of high energy particles, due to the quasi constant probability that a single high-energy particle is reflected in the strong transverse electric field near the shock \citep{Martins:2009}." " Even though the acceleration mechanism is not identical to the normal Fermi the power-law index is in agreement with process,theoretical resultingpredictions, and is approximatelygood o =2.3 — 2.6, where f(p)xΥ* at high energies."," Even though the acceleration mechanism is not identical to the normal Fermi process, the resulting power-law index is in good agreement with theoretical predictions, and is approximately $\alpha=$ 2.3 – 2.6, where $f(p) \propto \gamma^{-\alpha}$ at high energies." " In our 3D simulation we find the same emergence of a high energy tail distribution, on top of a relativistic Maxwellian downstream of the shock."," In our 3D simulation we find the same emergence of a high energy tail distribution, on top of a relativistic Maxwellian downstream of the shock." " We model it as where A; are normalizations, T is the temperature, o is the powerlaw slope, and γι A; are the locations and widths of the cut-offs."," We model it as where $A_i$ are normalizations, $T$ is the temperature, $\alpha$ is the powerlaw slope, and $\gamma_i$ $\Delta_i$ are the locations and widths of the cut-offs." " We impose the low energy cut-off so the power-law makes a smooth match to the Maxwellian, while the upper cut-off is time-dependent and grows with time."," We impose the low energy cut-off so the power-law makes a smooth match to the Maxwellian, while the upper cut-off is time-dependent and grows with time." " We find that in the 3D simulation the slope is shallower with a2.3, matching the theoretical prediction of ?,, for a Τ=15 relativistic shock of aj,=2.1."," We find that in the 3D simulation the slope is shallower with $\alpha=2.1-2.3$ , matching the theoretical prediction of \citet{Keshet:2005}, for a $\Gamma=15$ relativistic shock of $\alpha_{theo}=2.1$." The density and momentum distribution are some of the lowest order criteria to check when modeling a collisionless shock., The density and momentum distribution are some of the lowest order criteria to check when modeling a collisionless shock. " To assess the impact of our relatively limited simulation domain we compared the different 2D runs, finding that the limited box size has only a minor impact on the jump conditions and on the evolution of the filaments."," To assess the impact of our relatively limited simulation domain we compared the different 2D runs, finding that the limited box size has only a minor impact on the jump conditions and on the evolution of the filaments." " Analyzing the 2D runs we find that a box with 250x7000 cells contains a shock with velocity vg,20.42c, and a downstream to upstream density ratio of nj4/n,=3.24, while a box with twice the length, independent of the transverse size, more faithfully the analytic jump conditions."," Analyzing the 2D runs we find that a box with 250x7000 cells contains a shock with velocity $\vsh=0.42c$, and a downstream to upstream density ratio of $n_d/n_u=3.24$, while a box with twice the length, independent of the transverse size, more faithfully reproduces the analytic jump conditions." " With vg,=0.47c and a density reproducesjump of 3.12 it is in percent precision agreement with the analytic expectation for a relativistic gas ng/n,=laa/Uyaa—1]-1/[DCyaa 1)], where για is the adiabatic index of the gas, which is 4/3 (3/2) for a 3D (2D) relativistic gas."," With $\vsh=0.47c$ and a density jump of 3.12 it is in percent precision agreement with the analytic expectation for a relativistic gas $n_d/n_u = \gad / [\gad - 1] + 1 / [\Gamma (\gad - 1)]$ , where $\gad$ is the adiabatic index of the gas, which is 4/3 (3/2) for a 3D (2D) relativistic gas." " This is also seen in the 3D case, where we find v4,=0.27 and nq/ny=4.62, where analytically one expects vs,=0.31 and na/n,=4.2 (see figure 4))."," This is also seen in the 3D case, where we find $\vsh=0.27$ and $n_d/n_u = 4.62$, where analytically one expects $\vsh=0.31$ and $n_d/n_u=4.2$ (see figure \ref{fig:dens}) )." " Because we launch the shock reflecting cold streaming particles on a wall it takes some time until a proper, thermalized downstream region is created."," Because we launch the shock reflecting cold streaming particles on a wall it takes some time until a proper, thermalized downstream region is created." " The electromagnetic fields at and near the shock interface have to build up to a sufficient levelto scatter the particles, and the shock interface has to be far enough away from the wall at the upper boundary, so that upstream particles are scattered by the fields and thermalize thoroughly before they possibly reach the wall."," The electromagnetic fields at and near the shock interface have to build up to a sufficient level to scatter the particles, and the shock interface has to be far enough away from the wall at the upper boundary, so that upstream particles are scattered by the fields and thermalize thoroughly before they possibly reach the wall." This convergence can be monitored by looking at the v.y momentum near the wall., This convergence can be monitored by looking at the $v_z\gamma$ momentum near the wall. A camel shaped PDF signals that proper pressure support in the downstream region has still not been established., A camel shaped PDF signals that proper pressure support in the downstream region has still not been established. We find (see figure 5)) that the, We find (see figure \ref{fig:phasespace}) ) that the which are useful tools in the understanding of the dvnamices and kinematics of galaxies.,which are useful tools in the understanding of the dynamics and kinematics of galaxies. Dust lanes and nuclear rings appear to be the dominant circummuclear features., Dust lanes and nuclear rings appear to be the dominant circumnuclear features. Dust lanes have been interpreted as the location of garocks in the gas How., Dust lanes have been interpreted as the location of shocks in the gas flow. " ""Thus. the morphology. of the dust istribution can reveal characteristics of the dynamics of jese galaxies. (Athanassoula 1902) ancl of the kinematics {the eas."," Thus, the morphology of the dust distribution can reveal characteristics of the dynamics of these galaxies (Athanassoula 1992) and of the kinematics of the gas." According to Athanassoulas models. the degree { curvature of the dust. lanes is a direct. indicator of rw strength. of the bar for bars which are πο very strong.," According to Athanassoula's models, the degree of curvature of the dust lanes is a direct indicator of the strength of the bar for bars which are not very strong." Nuclear rings. which are usually sites of active star ormation (SE). occur at the location of strong. density enhancements in the gas. where the bar-driven inflow of eas slows clown in the vieinity of inner Lindblad resonances (ILRs: Athanassoula 1992: Heller Shlosman 1994: Buta Combes 1996: Shlosman 1999).," Nuclear rings, which are usually sites of active star formation (SF), occur at the location of strong density enhancements in the gas, where the bar-driven inflow of gas slows down in the vicinity of inner Lindblad resonances (ILRs; Athanassoula 1992; Heller Shlosman 1994; Buta Combes 1996; Shlosman 1999)." SE may result from the eas coming eravitationally unstable (Elmegreen 1994. 1997). or from triggering in miniature spiral arms (Ixnapen ct al.," SF may result from the gas becoming gravitationally unstable (Elmegreen 1994, 1997), or from triggering in miniature spiral arms (Knapen et al." 1995b. 2000).," 1995b, 2000)." Whereas imaging in the blue. ultraviolet. or in spectral lines like Lla traces the massive SE (e.g. Sersic Pastoriza 1967: Pogge 1989a.b: Ixnapen et al.," Whereas imaging in the blue, ultraviolet, or in spectral lines like $\alpha$ traces the massive SF (e.g. Sersic Pastoriza 1967; Pogge 1989a,b; Knapen et al." 1995a: Alaoz et al., 1995a; Maoz et al. 1996: Colina ct al., 1996; Colina et al. LOOT). near-infrared (NIU) imaging olfers very important advantages.," 1997), near-infrared (NIR) imaging offers very important advantages." Firstly. the presence of substantial ancl mostly: unquantified amounts of extinguishing (absorbing and scattering) dust in the CNRs hampers the interpretation of imaging at. especially the UV. anc optical wavelengths.," Firstly, the presence of substantial and mostly unquantified amounts of extinguishing (absorbing and scattering) dust in the CNRs hampers the interpretation of imaging at especially the UV and optical wavelengths." NER. particularly -band. emission is much less susceptible to extinction. by dust. (à factor of LO when comparing A to V). whereas colour index images such as £0A (Ixnapen et al.," NIR, particularly $K$ -band, emission is much less susceptible to extinction by dust (a factor of 10 when comparing $K$ to $V$ ), whereas colour index images such as $I-K$ (Knapen et al." 1995a) or Jdf ave clear morphological dust. indicators due to 1e relatively modest. changes in those colours caused. by lilferent stellar populations., 1995a) or $J-H$ are clear morphological dust indicators due to the relatively modest changes in those colours caused by different stellar populations. Secondly. NLR observations are of particular importance to the study of the CNRs because rev allow a better determination of the mass distribution (excluding dark matter).," Secondly, NIR observations are of particular importance to the study of the CNRs because they allow a better determination of the mass distribution (excluding dark matter)." NIU imaging is more sensitive to ight primarily from cool giants and cwarfs which dominate 10 mass or are at least directly proportional to it., NIR imaging is more sensitive to light primarily from cool giants and dwarfs which dominate the mass or are at least directly proportional to it. Llowever. as shown in the literature and by us in this paper. there can be significant. or even dominant. contributions from voung stars to the NI emission even in the A-band. so for objects with strong SE any estimate of the mass distribution made from NUR maps must take the varying ML ratio into account. (Ixnapen et al.," However, as shown in the literature and by us in this paper, there can be significant, or even dominant, contributions from young stars to the NIR emission even in the $K$ -band, so for objects with strong SF any estimate of the mass distribution made from NIR maps must take the varying $M/L$ ratio into account (Knapen et al." 1995a.b: Elmeercen et al.," 1995a,b; Elmegreen et al." 1997: Wada. Sakamoto Alinezaki 1998: Racer Ixnapen 1999).," 1997; Wada, Sakamoto Minezaki 1998; Ryder Knapen 1999)." The atlas of images presented in this paper (Paper L) represents the first results of a programme which studies the circumnuclear structures that appear at small scales (a few hundred parsees to a kpc) and their connection with the elobal cise structure in a sample of 12 barred spiral galaxies., The atlas of images presented in this paper (Paper I) represents the first results of a programme which studies the circumnuclear structures that appear at small scales (a few hundred parsecs to a kpc) and their connection with the global disc structure in a sample of 12 barred spiral galaxies. We present J.44 ancl A-images at subaresec resolution for all 12 sample galaxies. anc (LEST) archive {/-bancl images for 10 of them.," We present $J, H$ and $K$ -images at subarcsec resolution for all 12 sample galaxies, and ) archive $H$ -band images for 10 of them." In Paper HE rez Ixnapen 2000a). we present an accompanying optical data set of broad-band and Ho images of the complete cdises of all our sample galaxies. while in Paper HE rez Ixnapen 2000b) the morphological information is interpreted in terms of the structure and evolution of CNIts of barred. galaxies.," In Paper II rez Knapen 2000a), we present an accompanying optical data set of broad-band and $\alpha$ images of the complete discs of all our sample galaxies, while in Paper III rez Knapen 2000b) the morphological information is interpreted in terms of the structure and evolution of CNRs of barred galaxies." In Section 2. we cleseribe the observations ancl data reduction techniques.," In Section 2, we describe the observations and data reduction techniques." The imaging data are presented as à series of multi-panel figures. whieh show broad-band images. colour index images hiehlishting cust anc SE features against the dominant stellar luminosity. and radial profiles of ellipticitv. position angle. surface brightness and colour.," The imaging data are presented as a series of multi-panel figures, which show broad-band images, colour index images highlighting dust and SF features against the dominant stellar luminosity, and radial profiles of ellipticity, position angle, surface brightness and colour." The results are summarized in Section 3 for individual galaxies. ancl brielly discussed in Section 4. while concluding remarks are elven in Section 5.," The results are summarized in Section 3 for individual galaxies, and briefly discussed in Section 4, while concluding remarks are given in Section 5." The main selection criterion. for our sample is the presence of a bar and evidence of some circumnuclear structure associated with it. such as rings. nuclear bars or regions of SE.," The main selection criterion for our sample is the presence of a bar and evidence of some circumnuclear structure associated with it, such as rings, nuclear bars or regions of SF." Furthermore. the sample galaxies should. be nearby. bright and observable from the northern hemisphere.," Furthermore, the sample galaxies should be nearby, bright and observable from the northern hemisphere." Some of the sample galaxies are taken from the lists xublished by Sersic Pastoriza (1967) and Pogge (19892a.hb).," Some of the sample galaxies are taken from the lists published by Sersic Pastoriza (1967) and Pogge (1989a,b)." The sample can be considered. more anecdotal than comple in any sense., The sample can be considered more anecdotal than complete in any sense. " However. it does significantly increase 1e sample size when compared to published NUR studies of ο.""INS in barred galaxies. which rarely include more than wee objects ancl usually. discuss only one (e.g. Ixnapen et al."," However, it does significantly increase the sample size when compared to published NIR studies of CNRs in barred galaxies, which rarely include more than three objects and usually discuss only one (e.g. Knapen et al." 1995a.bh: Elmegreen et al.," 1995a,b; Elmegreen et al." LOOT: Laine et al., 1997; Laine et al. 1999: Racer |Ixnapen 1999)., 1999; Ryder Knapen 1999). With our new imaging. we also improve 10 spatial resolution. ancl show dillerent colour index maps. JÁN (primarily outlining dust. extinction) and {4FN (acicditionallv indicating the possible emission. due to hot ust in the case of the more active sample galaxies).," With our new imaging, we also improve the spatial resolution, and show different colour index maps, $J-K$ (primarily outlining dust extinction) and $H-K$ (additionally indicating the possible emission due to hot dust in the case of the more active sample galaxies)." Regan Mulchaey. (1999) showM57 1.6/5 ancl optical-infrared (basically & 441} colour index images of a sample of Sevífert (Sv) Ingalaxies. includingin] a number of CNR In]galaxies.," Regan Mulchaey (1999) show $\mu$ m and optical-infrared (basically $R-H$ ) colour index images of a sample of Seyfert (Sy) galaxies, including a number of CNR galaxies." Pwo of 1e galaxies in their sample are also included in our sample GC 3516 and NGC 3982)., Two of the galaxies in their sample are also included in our sample (NGC 3516 and NGC 3982). The 2H colour. however. is =nuch more sensitive to changes in stellar populations than 16 Λι colours used. in our paper.," The $R-H$ colour, however, is much more sensitive to changes in stellar populations than the NIR colours used in our paper." For 10 of our sample ealaxies. we have retrieved. in addition to our own data. {1 - images from the archive (Fig.," For 10 of our sample galaxies, we have retrieved, in addition to our own data, $H$ -band images from the archive (Fig." 1). and we comment on the high-resolution NER morphology of those objects.," 1), and we comment on the high-resolution NIR morphology of those objects." In ‘Table Lowe give some information about the classification of he galaxies of our sample. the predominant. cireumnuclear eature. as determined from the data. and the type of nuclear activity. if known.," In Table 1 we give some information about the classification of the galaxies of our sample, the predominant circumnuclear feature, as determined from the data, and the type of nuclear activity, if known." clispersions. for none of the colours studied in this paper. and for neither of the sides of the galactie planes.,"dispersions, for none of the colours studied in this paper, and for neither of the sides of the galactic planes." This suggests that. for a given galaxy. residual dust effects are not solely responsible for the observed scatter among the magnitudes of the vertical colour profiles.," This suggests that, for a given galaxy, residual dust effects are not solely responsible for the observed scatter among the magnitudes of the vertical colour profiles." We also examined possible correlations. between the observed. vertical colour gradients and other fundamental galaxy parameters. like their radial ane vertical scale xwameters. rotational velocities. ancl absolute Cfband) magnitudes. but did not detect any clear trends among these ALALLICLers.," We also examined possible correlations between the observed vertical colour gradients and other fundamental galaxy parameters, like their radial and vertical scale parameters, rotational velocities, and absolute -band) magnitudes, but did not detect any clear trends among these parameters." Finally. we investigated: possible correlations between radial and vertical colour gradients.," Finally, we investigated possible correlations between radial and vertical colour gradients." We used the ratios of he Band fFband scale lengths of our sample. galaxies as indicators of their radial colour gradients (see de CGrijs 1998 and references therein)., We used the ratios of the and -band scale lengths of our sample galaxies as indicators of their radial colour gradients (see de Grijs 1998 and references therein). However. other than the observation hat galaxies without measurable racial gradient. generally do not exhibit anv vertical (27) colour gradient. either. we do not find any significant correlation between the radial and vertical colour &radients. in any of the three colours studied in this paper.," However, other than the observation that galaxies without measurable radial gradient generally do not exhibit any vertical $(B-I)$ colour gradient either, we do not find any significant correlation between the radial and vertical colour gradients, in any of the three colours studied in this paper." This result is consistent. with our suggestion that the vertical colour gradients we measure are likely intrinsic. while the racial colour gradients are mainly reflecting residual extinction elfects (cle Crijs et al.," This result is consistent with our suggestion that the vertical colour gradients we measure are likely intrinsic, while the radial colour gradients are mainly reflecting residual extinction effects (de Grijs et al." 1997. cle Grijs 1008).," 1997, de Grijs 1998)." Broacd-bancl colours are relatively easy to obtain ancl are therefore the most widely used: colour diagnostics to date., Broad-band colours are relatively easy to obtain and are therefore the most widely used colour diagnostics to date. Aloreover. they. immediately reveal the approximate nature of a galaxv. which is to [first order determined bv the dominant stellar population and dust content.," Moreover, they immediately reveal the approximate nature of a galaxy, which is to first order determined by the dominant stellar population and dust content." The interpretation of the vertical colour. gradients obtained in the previous section depends: predominantly on the fundamental question whether one would expect anv measurable vertical stellar population gradient over the range used in our analvsis. and if so. what its magnituce would be.," The interpretation of the vertical colour gradients obtained in the previous section depends predominantly on the fundamental question whether one would expect any measurable vertical stellar population gradient over the range used in our analysis, and if so, what its magnitude would be." In the following. we will base the answer to this question on the observational evidence in our own Galaxy. due to observational constraints (e.g.. spatial resolution).," In the following, we will base the answer to this question on the observational evidence in our own Galaxy, due to observational constraints (e.g., spatial resolution)." The dust-free colours of a composite stellar system (ic. a galaxy) area function of its age and star formation history.," The dust-free colours of a composite stellar system (i.e., a galaxy) are a function of its age and star formation history." Thus. in order to address this question. we first need. to obtain the dependence. of the system's mean age on the wight above the Galactic plane.," Thus, in order to address this question, we first need to obtain the dependence of the system's mean age on the height above the Galactic plane." Although this seems to be a rather funcamental question. surprisingly little work has »en done in this field.," Although this seems to be a rather fundamental question, surprisingly little work has been done in this field." Jonch-Sorensen (1995) observed. for his sample of EF and carly C-type stars. that all stars vounger than 4 Cyr were ound at z« 500pc. whereas the age increases with increasing height above the Galactic plane up to at least ο 2kpe. where the minimum age is 4-5 Gyr.," rensen (1995) observed, for his sample of F and early G-type stars, that all stars younger than 4 Gyr were found at $z < 500$ pc, whereas the age increases with increasing height above the Galactic plane up to at least $z \simeq 2$ kpc, where the minimum age is 4-5 Gyr." Hoe also shows hat the logarithmic age distribution for stars found at 1<«2.5 kpe can be represented by a Gaussian distribution with a mean age of S Civr. approximately constant with height.," He also shows that the logarithmic age distribution for stars found at $1 < |z| < 2.5$ kpc can be represented by a Gaussian distribution with a mean age of $\sim 8$ Gyr, approximately constant with height." Phe width of the Gaussian distribution is comparable to the approximate accuracy of his age estimates for the faintest stars., The width of the Gaussian distribution is comparable to the approximate accuracy of his age estimates for the faintest stars. Ixnude (1997) studied a statistically significant sample of voung (£«1.7 Gyr) sharply. defined. main sequence subgiant A stars in the direction of the North Galactic Pole. with a sample median age of 0.75 Car. and concluded that they show a very clear trend of mean age with2 height. increasing almost linearly to ~0.75 Civr at 22:190200 pe. alter which the mean age distribution levels olf and remains approximately constant up to the completeness limit at 450 pe.," Knude (1997) studied a statistically significant sample of young $t < 1.7$ Gyr) sharply defined main sequence / subgiant A stars in the direction of the North Galactic Pole, with a sample median age of 0.75 Gyr, and concluded that they show a very clear trend of mean age with height, increasing almost linearly to $\sim 0.75$ Gyr at $z \simeq 150-200$ pc, after which the mean age distribution levels off and remains approximately constant up to the completeness limit at 450 pc." Apart [rom these papers. no other reference has been mace to the Galactic mean age distribution as a function of height above the plane.," Apart from these papers, no other reference has been made to the Galactic mean age distribution as a function of height above the plane." Pherefore. we will cliscuss two alternative and interdependent methods to obtain this information: ln either case. the observational results are controversial and show large discrepancies. however.," Therefore, we will discuss two alternative and interdependent methods to obtain this information: In either case, the observational results are controversial and show large discrepancies, however." The well-known dependence of metal abundance on age of the stars ancl open clusters in our Galaxy is one of the most important constraints on chemical evolution theories. although. after almost two decades of research in this field. a consensus on the exact correlation has not vet been reached.," The well-known dependence of metal abundance on age of the stars and open clusters in our Galaxy is one of the most important constraints on chemical evolution theories, although, after almost two decades of research in this field, a consensus on the exact correlation has not yet been reached." In a landmark. paper. Twarog (1980) published. the first detailed: study. of the local (solar. neighbourhood) AMI. in which he concluded. that the metallicity increased o» à [actor of about 4 between 13 and 4 Gyr ago. and only slightly since. then.," In a landmark paper, Twarog (1980) published the first detailed study of the local (solar neighbourhood) AMR, in which he concluded that the metallicity increased by a factor of about 4 between 13 and 4 Gyr ago, and only slightly since then." Although Carlbere οἱ al. (, Although Carlberg et al. ( 1985) claimed to have detected a serious discrepancy with Twarog’s (1980) AMI for the vounger stars. based on new metallicity anc age calibrations. ancl dillerences. in heir sample selection. modern determinations of the solar neighbourhood AMI based on high-accuracy observations of homogeneous. samples. of representative Galactic disc racers. agree relatively well. within the large scatter about he relation (see Sect. 4.1.2)).,"1985) claimed to have detected a serious discrepancy with Twarog's (1980) AMR for the younger stars, based on new metallicity and age calibrations, and differences in their sample selection, modern determinations of the solar neighbourhood AMR, based on high-accuracy observations of homogeneous samples of representative Galactic disc tracers, agree relatively well, within the large scatter about the relation (see Sect. \ref{scatter.sect}) )," with Twarog's (1980) original determination (e.g. Nissen. Eedvarcsson Gustafsson 1985: Ixnude. Schnedler Nielsen Winther 1987: Lec. Ann Sung 1989: Moeusinger. Reimann Stecklum 1991: Ecvardsson et al.," with Twarog's (1980) original determination (e.g., Nissen, Edvardsson Gustafsson 1985; Knude, Schnedler Nielsen Winther 1987; Lee, Ann Sung 1989; Meusinger, Reimann Stecklum 1991; Edvardsson et al." 1993: Ng Aortelli 1998: see Meusinger ct al., 1993; Ng Bertelli 1998; see Meusinger et al. 1991 and Carraro. Ne Portinari 1998 for reviews). although. Eclvardsson et al," 1991 and Carraro, Ng Portinari 1998 for reviews), although Edvardsson et al." is,'s Telescopio Nazionale Galileo (TNG) and the 2.7m at Mc Donald Observatory) with the aim to identify any possible anomalous behaviour which could be related to the dust properties of the cloud.,Telescopio Nazionale Galileo (TNG) and the 2.7m at Mc Donald Observatory) with the aim to identify any possible anomalous behaviour which could be related to the dust properties of the cloud. " Here, we present results for the two major diffuse bands at 5780 and 5797A."," Here, we present results for the two major diffuse bands at 5780 and 5797." . These two diffuse bands discovered by Heger (1922) show strength ratios that vary with the shape of the extinction curve (Krelowski et al., These two diffuse bands discovered by Heger (1922) show strength ratios that vary with the shape of the extinction curve (Krelowski et al. 1987)., 1987). " High molecular abundances - as for CH in the line of sight of Cernis 52 - appear in interstellar clouds characterized by a broad UV extinction bump (2175 A)), steep far-UV extinction and low 5780/5797 diffuse band intensity ratio."," High molecular abundances - as for CH in the line of sight of Cernis 52 - appear in interstellar clouds characterized by a broad UV extinction bump (2175 ), steep far-UV extinction and low 5780/5797 diffuse band intensity ratio." " Such clouds are called “zeta” type clouds (Krelowski and Sneden, 1995) and present strong molecular features in their spectra."," Such clouds are called “zeta” type clouds (Krelowski and Sneden, 1995) and present strong molecular features in their spectra." Examples of these clouds are found towards stars like ¢ Per and HD 23180 in Perseus where the 5780/5797 ratios (equivalent widths of 5780 to 5797) range between 1 and 2 (Krelowski et al., Examples of these clouds are found towards stars like $\zeta$ Per and HD 23180 in Perseus where the 5780/5797 ratios (equivalent widths of 5780 to 5797) range between 1 and 2 (Krelowski et al. 1996)., 1996). " Such values are much lower than those found by these authors in the so-called “sigma” clouds which present strikingly different extinction curves (see for a discussion Krelowski, Sneden and Hiltgen, 1995)."," Such values are much lower than those found by these authors in the so-called “sigma” clouds which present strikingly different extinction curves (see for a discussion Krelowski, Sneden and Hiltgen, 1995)." In Fig., In Fig. " 7, we plot our Mc Donald spectra of Cernis 52 in the spectral range of these DIBs in comparison with HD 23180."," 7, we plot our Mc Donald spectra of Cernis 52 in the spectral range of these DIBs in comparison with HD 23180." It is remarkable the similar strength of the 5780 DIB in both stars while the 5797 DIB is clearly stronger in Cernis 52., It is remarkable the similar strength of the 5780 DIB in both stars while the 5797 DIB is clearly stronger in Cernis 52. This leads to a smaller 5780/5797 ratio than in HD 23180 and fully supports the classification of the intervening cloud towards Cernis 52 as of “zeta” type., This leads to a smaller 5780/5797 ratio than in HD 23180 and fully supports the classification of the intervening cloud towards Cernis 52 as of “zeta” type. To our knowledge the UV extinction curve in this line of sight is unknown but based in the behaviour of the 5780/5797 DIBs we may expect a steep far-UV extinction., To our knowledge the UV extinction curve in this line of sight is unknown but based in the behaviour of the 5780/5797 DIBs we may expect a steep far-UV extinction. " It is well established that some diffuse bands like the 5797 correlate positively with the overall slope of the extinction curve while others like the 5780 show negative correlation (Megier, Krelowski and Weselak 2005)."," It is well established that some diffuse bands like the 5797 correlate positively with the overall slope of the extinction curve while others like the 5780 show negative correlation (Megier, Krelowski and Weselak 2005)." A postive correlation with the overall slope probably indicates an anticorrelation with the UV irradiation and the carrier of the 5797 band may benefit from shielding., A postive correlation with the overall slope probably indicates an anticorrelation with the UV irradiation and the carrier of the 5797 band may benefit from shielding. " If this is the case shielding is more effective in the Cernis 52 cloud than in the ""zeta"" cloud towards the star HD 23180 (also in Perseus but in a region without significant anomalous microwave emission).", If this is the case shielding is more effective in the Cernis 52 cloud than in the “zeta” cloud towards the star HD 23180 (also in Perseus but in a region without significant anomalous microwave emission). " The band at 5780A,, known to be more resistant to strong UV fields than the 5797 DIB, shows similar strength in both clouds."," The band at 5780, known to be more resistant to strong UV fields than the 5797 DIB, shows similar strength in both clouds." The DIB at 5850 is known to follow closely the behaviour of the 5797 DIB and correlates with the the overall slope of extinction (Megier et al., The DIB at 5850 is known to follow closely the behaviour of the 5797 DIB and correlates with the the overall slope of extinction (Megier et al. 2005)., 2005). We find that the strength of this DIB in Cernis 52 is also a factor two higher than in HD 23180., We find that the strength of this DIB in Cernis 52 is also a factor two higher than in HD 23180. The extinction in the UV reduces the flux of the UV radiation that is believed to ionize or destroy the carriers of these bands., The extinction in the UV reduces the flux of the UV radiation that is believed to ionize or destroy the carriers of these bands. We have scrutinized our spectra to search for bands of other PAHs with reliable gas phase measurements (see Salama 2008) and confirm in our new data the naphthalene band at 6707 previously found by Iglesias-Groth et al. (, We have scrutinized our spectra to search for bands of other PAHs with reliable gas phase measurements (see Salama 2008) and confirm in our new data the naphthalene band at 6707 previously found by Iglesias-Groth et al. ( 2008).,2008). " At various wavelengths we find marginal evidence for other broad bands that may correspond to PAH cations, and for relatively narrow absorptions that could be associated to carbon chains and carbon rings but confirmation may require higher quality measurements."," At various wavelengths we find marginal evidence for other broad bands that may correspond to PAH cations, and for relatively narrow absorptions that could be associated to carbon chains and carbon rings but confirmation may require higher quality measurements." The upper limits we, The upper limits we "and, for an isotropic distribution, should be uniformly distributed on the unit sphere.","and, for an isotropic distribution, should be uniformly distributed on the unit sphere." " These two angles define a rotation matrix that determines e, and e, acalone&Jokipii 1999).", These two angles define a rotation matrix that determines $\bm{e}_x$ and $\bm{e}_y$ \citep[e.g.][]{giacalonejokipii99}. . The amplitude of each mode is where the variance o? is chosen such that the turbulent field is normalized to give the required turbulence level:⋅, The amplitude of each mode is where the variance $\sigma^2$ is chosen such that the turbulent field is normalized to give the required turbulence level:. ⋅ We use the following form for the power spectrum where [ιο is the correlation length of the field and a is the asymptotic spectral index of the turbulence spectrum., We use the following form for the power spectrum where $L_{\rm c}$ is the correlation length of the field and $\alpha$ is the asymptotic spectral index of the turbulence spectrum. " For the three-dimensional fields used in this paper the normalization factor is AV,=Ark?Akn, and the Ak, are chosen such that there is equal spacing in logarithmic k-space, over the finite interval kg,10! gem versus time for the ;j=0.001 and ;?=0.005 cases with different resolutions., we plot the mass with density $>10^{-4}$ g $^{-3}$ versus time for the $\beta=0.001$ and $\beta=0.005$ cases with different resolutions. " It can be seen that the mass of the stellar core at which the feedback dramatically curtails the accretion decreases from zz10—11 down to 6 M, with increased resolution.", It can be seen that the mass of the stellar core at which the feedback dramatically curtails the accretion decreases from $\approx 10-11$ down to 6 $_{\rm J}$ with increased resolution. For a few years. the stellar cores grow at a rate of ~10 7M. yr! (even with the highest resolutions).," For a few years, the stellar cores grow at a rate of $\sim 10^{-3}$ $_\odot$ $^{-1}$ (even with the highest resolutions)." " With low-resolution (1.:10° SPH particles). the accretion onto the stellar cores ceases entirely after the launching of the outflows due to the formation of the ""holes! in the inner few AU of the discs."," With low-resolution $\le 1\times 10^6$ SPH particles), the accretion onto the stellar cores ceases entirely after the launching of the outflows due to the formation of the `holes' in the inner few AU of the discs." " However. using 3.10"" SPH particles. it is found that the stellar cores do continue to"," However, using $3\times 10^6$ SPH particles, it is found that the stellar cores do continue to" with the electromagnetic Force produced by the toroidal magnetic field. is always negative.,"with the electromagnetic force produced by the toroidal magnetic field, is always negative." This suggests that the pressure is smaller for larger toroidal magnetic fields., This suggests that the pressure is smaller for larger toroidal magnetic fields. lig., Fig. 3 shows the contour plots of the magnetic Dux 21 (left). the poloidal part of the pressure Z4 (centre). and that of the eas density Dà (right). while Fig.," \ref{fig:sol1A} shows the contour plots of the magnetic flux $\tilde{A}$ (left), the poloidal part of the pressure $P_A$ (centre), and that of the gas density $D_A$ (right), while Fig." " 4. shows the contour plots of the toroidal magnetic field £3, (left). the toroidal part of the pressure £%> (centre). and that of the gas density Do (right) in the y/fa—0 plane for m=n—4 and a—0.8."," \ref{fig:sol1Q} shows the contour plots of the toroidal magnetic field $B_\phi$ (left), the toroidal part of the pressure $P_Q$ (centre), and that of the gas density $D_Q$ (right) in the $\eta/a-\theta$ plane for $m=n=4$ and $a=0.8$." " The magnetic field is explicitly expressed as where ον, eo. and e,, are unit vectors in r. 6. and ὁ directions in the polar coordinate. respectively."," The magnetic field is explicitly expressed as where $\bmath e_r$, $\bmath e_\theta$, and $\bmath e_\phi$ are unit vectors in $r$ , $\theta$, and $\phi$ directions in the polar coordinate, respectively." " Note that D, and D,, ave zero at r=ROE) but Ba is not zero and it depends on time when ez1.", Note that $B_r$ and $B_\phi$ are zero at $r=R(t)$ but $B_\theta$ is not zero and it depends on time when $a \ne 1$. We will discuss the physical meaning of this result later in 827., We will discuss the physical meaning of this result later in \ref{sss2}. In later stage. the magnetic field becomes stationary. and the magnetic field becomes radial.," In later stage, the magnetic field becomes stationary, and the magnetic field becomes radial." In the limit /r. the pressure and the σας density inside the magnetic loop are eiven by Since the toroidal magnetic field tends to be zero in this limit. the pressure and density do not depend on theamplitude of the toroidal magnetic fields.," In the limit $t \gg r$, the pressure and the gas density inside the magnetic loop are given by Since the toroidal magnetic field tends to be zero in this limit, the pressure and density do not depend on theamplitude of the toroidal magnetic fields." poorly understood. because of the stroug selection bias against finding them at optical wavelengths.,"poorly understood, because of the strong selection bias against finding them at optical wavelengths." Micd-intrared(MIR) AGN searches can overcome this obstacle by penetrating through dust extinction to ideutifv most of the AGN population. including Type 2 Sevferts and burned ACNs.," Mid-infrared(MIR) AGN searches can overcome this obstacle by penetrating through dust extinction to identify most of the AGN population, including Type 2 Seyferts and buried AGNs." The original TRAS active galaxy samples provide an unbiased sample of local active galaxies., The original IRAS active galaxy samples provide an unbiased sample of local active galaxies. Usine the ISQCAMparallelmodesurcey of 10 square degrees at 6.7pau((LAV2). succeeded in finding redder Type d ACNs as well as Type 2.," Using the $ISOCAM\ parallel\ mode\ survey$ of 10 square degrees at (LW2), succeeded in finding redder Type 1 AGNs as well as Type 2's." Several searches have also been performed using the uear- aud mic-infrared bands in the Spitzer Space Telescope 2006)., Several searches have also been performed using the near- and mid-infrared bands in the Spitzer Space Telescope . . ANART performed an all-sky survey at 9 and as well as at four far-infrared (FIR) bands (65. 90. 110. and 160722)).," $AKARI$ performed an all-sky survey at 9 and as well as at four far-infrared (FIR) bands (65, 90, 140, and )." It provided improvements of about one order of inagnuitude compared to that of TIRAS in both spatial resolution aud seusitivitv iu the midufrared bands., It provided improvements of about one order of magnitude compared to that of IRAS in both spatial resolution and sensitivity in the mid-infrared bands. The details of the survey are described in(2010)., The details of the survey are described in. . Tu this paper. we present the first results of our search for AGNs based ou this AWARL AUR Al-Sky Surves.," In this paper, we present the first results of our search for AGNs based on this $AKARI$ MIR All-Sky Survey." We discovered two galaxies LEDA 81271 and IRAS 01250|2832. which have a compact hot. 2500 I& dust component.," We discovered two galaxies LEDA 84274 and IRAS 01250+2832, which have a compact hot $\gtrsim$ 500 K dust component." The hot dust compoucut may be heated by the ceutral cneine of the ACN. even though their optical spectra do not slow any ACN characteristics.," The hot dust component may be heated by the central engine of the AGN, even though their optical spectra do not show any AGN characteristics." The observations. data reduction. and results are described in Section 2..," The observations, data reduction, and results are described in Section \ref{sec:obs}." Iu Section 3.. we describe the multiwavelength properties of the two egalaxics aud in Section L the hot dust commpoucuts we fouud iu the galaxies are discussed.," In Section \ref{sec:multi}, we describe the multiwavelength properties of the two galaxies and in Section \ref{sec:hot} the hot dust components we found in the galaxies are discussed." The discussion 1s presented in Section 5.. and a sunuaniary is given in Section 7..," The discussion is presented in Section \ref{sec:dis}, , and a summary is given in Section \ref{sec:sum}." Throughout the paper. we assume a flat cosmology with ο—0:3. A—0.7. and ZZ=10laus+Mpe," Throughout the paper, we assume a flat cosmology with $\Omega = 0.3$, $\Lambda=0.7$, and $H_0 = 70\ \mathrm{km}\ \mathrm{s}^{-1}\ \mathrm{Mpc}^{-1}$." The initial identification of the ANARS MIR. AII-Sky Survey sources involves association with the Two Micron All Sky Survey (241ÀSS) catalog2006)., The initial identification of the $AKARI$ MIR All-Sky Survey sources involves association with the Two Micron All Sky Survey (2MASS) catalog. . This search highlights unusually red AWARE MIR. sources with Ε(θμι)Ες)»2. at high Galactic latitudes. |b]>30° after excluding regious around the Large aud S1iall Magellanic Clouds.," This search highlights unusually red $AKARI$ MIR sources with $F(9\mu\mathrm{m})/F(Ks) > 2$, at high Galactic latitudes, $|b|>30^{\circ}$ after excluding regions around the Large and Small Magellanic Clouds." To examine the origin of the excess of Εμια)Εν)>2. we performed follow-up observations with the AWARS ucar-iutrared(NIR) spectrometer.," To examine the origin of the excess of $F(9\mu\mathrm{m})/F(Ks) > 2$, we performed follow-up observations with the $AKARI$ near-infrared(NIR) spectrometer." Using the AAARZ spectra of the 2.5-5 waveleneth range. AGNs cau be distinguished by them red coutiuuun cussion. while strong polycyclic aromatic hwvdrocarbonus (PAID) enmüssiou is detected in star-formingo ogalaxies.," Using the $AKARI$ spectra of the 2.5-5 wavelength range, AGNs can be distinguished by their red continuum emission, while strong polycyclic aromatic hydrocarbons (PAH) emission is detected in star-forming galaxies." To measure the redshüft aud search optically for ACNor star-formation signatures. optical spectra were also taken with the Share 3am telescope at the Lick Observatory.," To measure the redshift and search optically for AGNor star-formation signatures, optical spectra were also taken with the Share 3m telescope at the Lick Observatory." "spectra and dust emission spectra at each redshift by associating models corresponding to similar values of (to within some uncertainty interval 0f,=0.15) in the two libraries. which we scale to the same total dust luminosity.","spectra and dust emission spectra at each redshift by associating models corresponding to similar values of (to within some uncertainty interval $\delta f_\mu=0.15$ ) in the two libraries, which we scale to the same total dust luminosity." . For each combined spectrum. we compute the synthetic photometry in the FUVeandNUV. 5Ds ugriz. 244.VS STHK. and 1I[2-. 25-. 60- and bbands.," For each combined spectrum, we compute the synthetic photometry in the $FUV$ and $NUV$, SDSS $ugriz$, 2MASS $JHK_s$ and 12-, 25-, 60- and bands." In the redshift range of the sample described in Section 2.. prominent optical nebular emission lines can significantly affect the observed galaxy fluxes in the SDSS gri bands.," In the redshift range of the sample described in Section \ref{dust:sample}, prominent optical nebular emission lines can significantly affect the observed galaxy fluxes in the SDSS $gri$ bands." The model spectra we use to interpret these data do not include nebular emission lines., The model spectra we use to interpret these data do not include nebular emission lines. Therefore. to interpret the optical fluxes of observed galaxies with these models. we first need to correct the observed SDSS gi magnitudes for potential contamination by nebular emission lines (e.g. 2).," Therefore, to interpret the optical fluxes of observed galaxies with these models, we first need to correct the observed SDSS $gri$ magnitudes for potential contamination by nebular emission lines (e.g., \citealt{Kauffmann2003b}) )." We use the corrections inferred by Jarle Brinchmann (private communication) from fits ofthe stellar continuum emission of each SDSS optical spectrum with ? models (we assume for simplicity that the correction derived in this way within the aperture sampled by the SDSS tibre applies to the galaxy as a whole)., We use the corrections inferred by Jarle Brinchmann (private communication) from fits of the stellar continuum emission of each SDSS optical spectrum with \cite{Bruzual2003} models (we assume for simplicity that the correction derived in this way within the aperture sampled by the SDSS fibre applies to the galaxy as a whole). We also compute A-corrections to the ultraviolet. optical and near-infrared magnitudes of each galaxy in the sample.," We also compute -corrections to the ultraviolet, optical and near-infrared magnitudes of each galaxy in the sample." To minimise these. we A-correct the magnitudes from the galaxy redshift to the closest redshift of the model grid described in Section 3.2.1.. be. 2=0.00. 0.05. 0.10. 0.15 or 0.20 (we use the version v3 of the code of 2).," To minimise these, we -correct the magnitudes from the galaxy redshift to the closest redshift of the model grid described in Section \ref{library}, i.e., $z=0.00$, 0.05, 0.10, 0.15 or 0.20 (we use the version v3 of the code of \citealt{Blanton2003}) )." This procedure cannot be extended to the 1I[2-. 25-. 60- and fflux densities. to which we do not apply any K-correction.," This procedure cannot be extended to the 12-, 25-, 60- and flux densities, to which we do not apply any -correction." We do not expect this to have any noticeable influence on our results. given the large effective width of the ffilter response functions and the relatively large observational uncertainties in these bands.," We do not expect this to have any noticeable influence on our results, given the large effective width of the filter response functions and the relatively large observational uncertainties in these bands." To account for the uncertainties linked to the -correction and emission-line correction. we add the following errors to the quoted flux uncertainties: 2. per cent forGALEX.. 2MASS. and SDSS = bands. and 1.5 per cent for the SDSS gri bands.," To account for the uncertainties linked to the $k$ -correction and emission-line correction, we add the following errors to the quoted flux uncertainties: 2 per cent for, 2MASS, and SDSS $z$ bands, and 1.5 per cent for the SDSS $gri$ bands." For the less accurate SDSS #-band photometry. we take an overall observational uncertainty of 10 per cent.," For the less accurate SDSS $u$ -band photometry, we take an overall observational uncertainty of 10 per cent." We perform spectral fits by comparing the observed spectral energy distribution of a galaxy to every model in the library at the corresponding redshift., We perform spectral fits by comparing the observed spectral energy distribution of a galaxy to every model in the library at the corresponding redshift. Specitically. for each observed galaxy. we compute the X7 goodness of fit of each model.," Specifically, for each observed galaxy, we compute the $\chi^2$ goodness of fit of each model." A model is characterised by a set of randomly drawn physical parameters., A model is characterised by a set of randomly drawn physical parameters. We build the likelihood distribution of any given physical parameter for the observed galaxy by weighting the value of that parameter in each model by the probability exp(47/2).," We build the likelihood distribution of any given physical parameter for the observed galaxy by weighting the value of that parameter in each model by the probability $\exp (-\chi^2/2)$." We take our final estimate of the parameter to be the median of the likelihood distribution. and the associated confidence interval to be the S4th percentile range.," We take our final estimate of the parameter to be the median of the likelihood distribution, and the associated confidence interval to be the 16th--84th percentile range." We use this approach to derive the likelihood distributions of several physical parameters of the galaxies in our sample. based on fits of the andNUV. SDSS ugriz. 2MASS Jifdy. and 112-. 25-. 60- and ffluxes.," We use this approach to derive the likelihood distributions of several physical parameters of the galaxies in our sample, based on fits of the and, SDSS $ugriz$, 2MASS $JHK_s$ and 12-, 25-, 60- and fluxes." " We focus particularly on: the star formation rate averaged over the last 107. yr.cz the stellar mass. Mz: the specific star formation rate. os=vc/ÀM,: the dust mass.Aa the total luminosity of the dust.£,)°"".. and the fraction of this contributed by the diffuse ISM.fj."," We focus particularly on: the star formation rate averaged over the last $10^8$ yr,; the stellar mass, $M_\ast$; the specific star formation rate, $\ssfr=\sfr/M_\ast$; the dust mass,; the total luminosity of the dust, and the fraction of this contributed by the diffuse ISM,." .. We first check how well the model can reproduce the observed spectral energy distributions of the galaxies in our sample., We first check how well the model can reproduce the observed spectral energy distributions of the galaxies in our sample. The histograms in Fig., The histograms in Fig. " 3. show. for each photometric band. the distribution of the difference between the observed luminosity £2"" and the best-tit model luminosity Lj"". in units of observational error σ."," \ref{fig:dust3} show, for each photometric band, the distribution of the difference between the observed luminosity $L_\nu^\mathrm{\,obs}$ and the best-fit model luminosity $L_\nu^\mathrm{\,mod}$, in units of observational error $\sigma$." Overall. the model provides remarkably consistent fits to the observed.ultraviolet. optical and infrared luminosities of the galaxies.," Overall, the model provides remarkably consistent fits to the observedultraviolet, optical and infrared luminosities of the galaxies." Fig., Fig. 3. shows small systematic offsets in the g. 7 and z bands. corresponding to an overestimate of the g-band flux and underestimates of the r- and z-band fluxes of the order of 0.01 mag.," \ref{fig:dust3} shows small systematic offsets in the $g$, $r$ and $z$ bands, corresponding to an overestimate of the $g$ -band flux and underestimates of the $r$ - and $z$ -band fluxes of the order of $0.01$ mag." These offsets may originate from a deficiency in stellar population synthesis models. further worsened by the potential contamination of the g and + bands by minor emission lines. which we neglected in our corrections of Section 3.2.2.," These offsets may originate from a deficiency in stellar population synthesis models, further worsened by the potential contamination of the $g$ and $r$ bands by minor emission lines, which we neglected in our corrections of Section \ref{corrections}. ." We note that the magnitude of these offsets is of the order of the, We note that the magnitude of these offsets is of the order of the about the X-rav source in which radiative driving was suppressed.,about the X-ray source in which radiative driving was suppressed. " In. Χο, for Los 10°"" erg his region extended: to all of the X-ray illuminated: wind (ie. no in the shadow of the companion)."," In X-3, for L $>$ $\rm {10^{37}}$ erg $^{-1}$, this region extended to all of the X-ray illuminated wind (i.e. not in the shadow of the companion)." Column densities. were obtained by integrating the particle densities where £ was « 2000. Le. assuming that all material not Lully ionizec contributes to Ny.," Column densities were obtained by integrating the particle densities where $\xi$ was $<$ 2000, i.e. assuming that all material not fully ionized contributes to $\rm {N_H}$." In our case. the X-ray source is brieh even in the Low State with L ~2.10% erg 3 an it might. be thought that strong suppression of radiative acceleration takes place.," In our case, the X-ray source is bright even in the Low State with L $\sim \rm {2\times 10^{37}}$ erg $^{-1}$ and it might be thought that strong suppression of radiative acceleration takes place." However. the binary separation of 40.2 1i. is larger in the black hole binary than the 19 It. in X-3.," However, the binary separation of 40.2 $\rm {R_{\sun}}$ is larger in the black hole binary than the 19 $\rm {R_{\sun}}$ in X-3." Thus the Hux of the X-ray source is reciucec bv a factor of 4 compared. with N-3 so that. simple scaling implies total suppression of radiative driving in the X-ray illuminated wind only for L > 410 erg s+.," Thus the flux of the X-ray source is reduced by a factor of 4 compared with X-3 so that simple scaling implies total suppression of radiative driving in the X-ray illuminated wind only for L $>$ $\rm {4\times 10^{37}}$ erg $^{-1}$." ‘This depends primarily on £ ancl our simple calculations show that wind with totally suppressed driving force would result in £ >» 100 only relatively close to the black hole., This depends primarily on $\xi$ and our simple calculations show that wind with totally suppressed driving force would result in $\xi$ $>$ 100 only relatively close to the black hole. ας it is clear that detailed hydrodynamic simulations of X-1 are required to delineate regions where radiative driving is suppressed., Thus it is clear that detailed hydrodynamic simulations of X-1 are required to delineate regions where radiative driving is suppressed. Εις would also reveal the details of the high density photoionization wake where normal wind in the X-rav shadow impacts on stalled wind (Fransson Fabian 1980: Bloncdin 1994). and of the shadow wind which emerges from the X-ray. shadow and may contribute to absorption (Dlondin 1994).," This would also reveal the details of the high density photoionization wake where normal wind in the X-ray shadow impacts on stalled wind (Fransson Fabian 1980; Blondin 1994), and of the shadow wind which emerges from the X-ray shadow and may contribute to absorption (Blondin 1994)." We have shown that there is a strong dependence of the frequeney of dipping in wwith orbital phase. and that this correlates approximately with the variation of column censity of the neutral component of the stellar wind. with phase A'y().," We have shown that there is a strong dependence of the frequency of dipping in with orbital phase, and that this correlates approximately with the variation of column density of the neutral component of the stellar wind with phase $N_{\rm H}(\phi)$." This suggests that dipping is caused by blobs of largely neutral material. the formation of which may depend: simply. on the neutral density at any. point in the wind.," This suggests that dipping is caused by blobs of largely neutral material, the formation of which may depend simply on the neutral density at any point in the wind." Our previous spectral fitting has shown that column density is typically. between 2 and 20.107 1L atom in dip spectra (Daluccinzkka-Church οἱ al., Our previous spectral fitting has shown that column density is typically between 2 and $\rm {20\times 10^{22}}$ H atom $^{-2}$ in dip spectra (Bałuccinśkka-Church et al. 1997)., 1997). " For a blob diameter of 10"" em (Ixitzunoto 1984) this gives densities of ~ 1015 107 .", For a blob diameter of $\rm {10^9}$ cm (Kitamoto 1984) this gives densities of $\sim$ $\rm {10^{12}}$ – $\rm {10^{13}}$ $^{-3}$. Our estimates for the wind density have maximuni values of total wind density between a few LO? and 102 em? [or no suppression of radiative driving and total suppression. respectively.," Our estimates for the wind density have maximum values of total wind density between a few $\rm {10^9}$ and $\rm {10^{11}}$ $^{-3}$ for no suppression of radiative driving and total suppression, respectively." A more realistic tvpical value might be 101 7., A more realistic typical value might be $\rm {10^{10}}$ $^{-3}$. Thus the blob censity is greater than the ambient wind density by factors of LOO - 1000., Thus the blob density is greater than the ambient wind density by factors of 100 - 1000. Lo such a higher density region. £ will be reduced. so that a high value in he ambient wind of 1000 would be reduced to 1 - 10. such that the photoionizing effects of the X-ray source are markeclly reduced.," In such a higher density region, $\xi$ will be reduced, so that a high value in the ambient wind of 1000 would be reduced to 1 - 10, such that the photoionizing effects of the X-ray source are markedly reduced." One possibility for blob formation is hat neutral material in the wind can act as a nucleus for Nob growth. since in the X-ray shadow of a small blob. hotoionization will be reduced and recombination into the slob will be rapid.," One possibility for blob formation is that neutral material in the wind can act as a nucleus for blob growth, since in the X-ray shadow of a small blob, photoionization will be reduced and recombination into the blob will be rapid." Other possibilities for blob formation also exist., Other possibilities for blob formation also exist. For example. the interaction of normal wind with stalled wind can lead to a high density region trailing behind he compact object (Fransson Fabian 1980: Blondin 904).," For example, the interaction of normal wind with stalled wind can lead to a high density region trailing behind the compact object (Fransson Fabian 1980; Blondin 1994)." In this region. instabilities anc density enhancements may orm.," In this region, instabilities and density enhancements may form." However this would not be exected to produce dipping waving the basic symmetry about ó ~ 0.5. Le. the line of centres. that we see.," However this would not be exected to produce dipping having the basic symmetry about $\phi$ $\sim$ 0.5, i.e. the line of centres, that we see." Similarly this would not be expected o account for the peak in dipping we see at ó ~ 0.6 as he high density region extends over a Large range of angles with respect to the primary whereas a stream produced by toche-Iobe overflow or tidal enhancement does not., Similarly this would not be expected to account for the peak in dipping we see at $\phi$ $\sim$ 0.6 as the high density region extends over a large range of angles with respect to the primary whereas a stream produced by Roche-lobe overflow or tidal enhancement does not. ln N-1. for the first time we [ind definite evidence for a stream from X-ray data in the enhanced number of dips at oO ~ 0.6. and the source appears to ο similar to 1700-371. in which it was concluded: that a stream was the cause of enhanced. absorption at. phase 1.6 (LINIx89).," In X-1, for the first time we find definite evidence for a stream from X-ray data in the enhanced number of dips at $\phi$ $\sim$ 0.6, and the source appears to be similar to 1700-371 in which it was concluded that a stream was the cause of enhanced absorption at phase 0.6 (HWK89)." Petterson (1978) showed that 226868 is illing its Roche lobe and will therefore will produce a stream which may be expected to produce absorption ellects at. ὦ ~0.6 Even if the star was only close to filling its Roche lobe. Dlondin et al. (," Petterson (1978) showed that 226868 is filling its Roche lobe and will therefore will produce a stream which may be expected to produce absorption effects at $\phi$ $\sim$ 0.6 Even if the star was only close to filling its Roche lobe, Blondin et al. (" 1991) have shown that a stream will still develop by tical enhancement of the stellar wine caused by he compact object.,1991) have shown that a stream will still develop by tidal enhancement of the stellar wind caused by the compact object. In the neutron star systems mocelled. he formation of a stream depends on the binary separation.," In the neutron star systems modelled, the formation of a stream depends on the binary separation." Llowever. a clear result. of this work was that the stream is produced. at phase ó ~ 0.6.," However, a clear result of this work was that the stream is produced at phase $\phi$ $\sim$ 0.6." In either case. a stream is oduced at a phase similar to that we found. here.," In either case, a stream is produced at a phase similar to that we found here." Blob ormation in a stream would. of course. be easier than in he wind because the density is already increased over the wind density reducing £.," Blob formation in a stream would, of course, be easier than in the wind because the density is already increased over the wind density reducing $\xi $." ln summary. we have shown that the distribution of dipping with orbital phase correlates approximately with the variation of column density of the neutral component of the stellar wind of H1D12226868 with phase.," In summary, we have shown that the distribution of dipping with orbital phase correlates approximately with the variation of column density of the neutral component of the stellar wind of 226868 with phase." Phere is in aclelition. extra dipping at ó 0.6.," There is in addition, extra dipping at $\phi$ $\sim$ 0.6." Phese elfects resemble the asvmmetry of absorption in the wind of Supergiant X-ray Dinaries. suggesting that the formation of absorbing blobs depends on the neutral density. and thus rellects the Αμ(ώ) variation.," These effects resemble the asymmetry of absorption in the wind of Supergiant X-ray Binaries, suggesting that the formation of absorbing blobs depends on the neutral density, and thus reflects the $N_{\rm H}(\phi)$ variation." to calibrate the Tully-Fisher relation. having distances determined by IST. 17 of these have new 3.6 san AB magnitudes (Seibert et al.,"to calibrate the Tully-Fisher relation, having distances determined by HST, 17 of these have new 3.6 $\mu$ m AB magnitudes (Seibert et al." 2012)., 2012). In Figure 5 we show the D. V. I and 3.6 jp sample of 17 calibrating galaxies for which there are data for all four wavelengths.," In Figure 5 we show the B, V, I and 3.6 $\mu$ sample of 17 calibrating galaxies for which there are data for all four wavelengths." The D. V. and I-band magnitudes have been corrected for inclination-induced extinction effects and their line widths have been corrected to edge-on 2000): no extinction correction has been applied to the 3.6 jin data.," The B, V, and I-band magnitudes have been corrected for inclination-induced extinction effects and their line widths have been corrected to edge-on 2000); no extinction correction has been applied to the 3.6 $\mu$ m data." The 1-0 scatter in these relations is 0.43. 0.31. 0.32 and 0.31 mag for the D. V. IL and 3.6 jam data. respectively: the outer lines follow ihe mean regressions al zE2-sigima.," The $\sigma$ scatter in these relations is $\pm$ 0.43, 0.37, 0.32 and 0.31 mag for the B, V, I and 3.6 $\mu$ m data, respectively; the outer lines follow the mean regressions at $\pm$ 2-sigma." Each of these galaxies entered the calibration with its own independently determined Cepheicd-calibratecl distauce from (2001)., Each of these galaxies entered the calibration with its own independently determined Cepheid-calibrated distance from (2001). In Figure 6. we show example Tully-Fisher 3.6 san relations for 4 out of 24 clusters of galaxies for which we have 3.67 data.," In Figure 6, we show example Tully-Fisher 3.6 $\mu$ m relations for 4 out of 24 clusters of galaxies for which we have $\mu$ m data." These data will provide an independent estimate of the value olf II. (Seibert 2012)., These data will provide an independent estimate of the value of $_\circ$ (Seibert 2012). " A remaining svstematic elfect in the determination of H, is the sensitivity ofthe Cepheid PL relation to metallicity.", A remaining systematic effect in the determination of $H_{\circ}$ is the sensitivity of the Cepheid PL relation to metallicity. We are undertaking three independent tests of the sensitivity of the Cepheid Leavitt Law to metallicitv: anv one of which could. in principle. calibrate (he effect ifit is measurable in the mid-IB. and all three of which combined. will robustly constrain the ellect.," We are undertaking three independent tests of the sensitivity of the Cepheid Leavitt Law to metallicity; any one of which could, in principle, calibrate the effect if it is measurable in the mid-IR, and all three of which combined, will robustly constrain the effect." The significant advantage of the micl-IR is that the relative insensitivity (ο extinction allows a more precise test of metallicity alone., The significant advantage of the mid-IR is that the relative insensitivity to extinction allows a more precise test of metallicity alone. The first test involves the LAIC alone (Freeclman et al., The first test involves the LMC alone (Freedman et al. 2011). (, 2011). ( 2003) present evidence that (he LAIC Cepheids themselves have a spread of metallicity amounting to 0.5 dex in |Fe/II].,2008) present evidence that the LMC Cepheids themselves have a spread of metallicity amounting to 0.5 dex in [Fe/H]. The mid-IR PL relations are predicted to have a residual dispersion of less than zE0.08 mag after time-averaged magnitudes are obtained and geometrical effects due to the three-dimensional extent and orientation of the LAIC are removed., The mid-IR PL relations are predicted to have a residual dispersion of less than $\pm$ 0.08 mag after time-averaged magnitudes are obtained and geometrical effects due to the three-dimensional extent and orientation of the LMC are removed. Any. metallicity effect must be buried within that small dispersion. along with any other second and. effects. ie. variations of radius aud temperature across the instability strip at fixed period. the presence or absence of (physical) red companions. plane-thickness variations in ihe LMC (over and above global tilt corrections) and residual differential extinction effects.," Any metallicity effect must be buried within that small dispersion, along with any other second and third-order effects, i.e., variations of radius and temperature across the instability strip at fixed period, the presence or absence of (physical) red companions, plane-thickness variations in the LMC (over and above global tilt corrections) and residual differential extinction effects." In Figure 7. we show the deviations of individual JUIN. 3.6 and 4.5 jm LMC. Cepheid magnitudes from the period-Iuminosity relation as a function of spectroscopic [Fe/I1I] metal abundances from Romaniello et al. (," In Figure 7, we show the deviations of individual JHK, 3.6 and 4.5 $\mu$ m LMC Cepheid magnitudes from the period-luminosity relation as a function of spectroscopic [Fe/H] metal abundances from Romaniello et al. (" 2008). |,2008). [ Fe/II] values range from approximately -0.6 to -ü.1 dex.,Fe/H] values range from approximately -0.6 to -0.1 dex. This plot is an updated version of Figure 2 from Freedman Madore (2011). now based on time-averaged magnitudes.rather than the two," This plot is an updated version of Figure 2 from Freedman Madore (2011), now based on time-averaged magnitudes,rather than the two" is generally lower than that predicted by the Kennicutt(1998) relation was also seen earlier for the global averaged values (Figure 35).,is generally lower than that predicted by the \cite{ken98} relation was also seen earlier for the global averaged values (Figure \ref{fig:tot}) ). Quantitative results from the pixel by pixel correlation are isted in Tables 4.., Quantitative results from the pixel by pixel correlation are listed in Tables \ref{tab:res}. The columns are: (1) Galaxy name. (2) the derived HI mass taken from Begumetal.(2008)... (3) sensitivity imit of FUV data (i.e. the RMS noise in the background emission). (4+) the best fit power law index. (5) coefficient of the power law fit. (6) the range of bins along the gas surface density axis over which he straight line representing the power law part was fitted.," The columns are: (1) Galaxy name, (2) the derived HI mass taken from \citet{ay08}, (3) sensitivity limit of FUV data (i.e. the RMS noise in the background emission), (4) the best fit power law index, (5) coefficient of the power law fit, (6) the range of bins along the gas surface density axis over which the straight line representing the power law part was fitted." As can be seen from the table. the parameters of the power aw fit vary substantially from galaxy to galaxy.," As can be seen from the table, the parameters of the power law fit vary substantially from galaxy to galaxy." Nonetheless. for all galaxies the star formation appears to continue smoothly until one reaches the sensitivity limit of the observations. i.e. there does not seem to be any evidence for a “threshold density” below which he star formation is completely quenched.," Nonetheless, for all galaxies the star formation appears to continue smoothly until one reaches the sensitivity limit of the observations, i.e. there does not seem to be any evidence for a “threshold density” below which the star formation is completely quenched." Figure 6 illustrates this soint., Figure \ref{fig:sim} illustrates this point. Panel (ay shows simulated data in which iis related to the bby a power law with index 2 and coefficient 4., Panel (a) shows simulated data in which is related to the by a power law with index $2$ and coefficient $-4$. These values iive been chosen to be similar to the observed power law indices and coefficients., These values have been chosen to be similar to the observed power law indices and coefficients. In panel (b) noise is added. as seen in the real data. his leads to a flattening of the scatter plot for hat are below the sensitivity threshold.," In panel (b) noise is added, as seen in the real data, this leads to a flattening of the scatter plot for that are below the sensitivity threshold." The horizontal line shows he 1c noise level., The horizontal line shows the $1\sigma$ noise level. In addition. the power law coefficient is allowed o vary by from pixel to pixel.," In addition, the power law coefficient is allowed to vary by from pixel to pixel." As can be seen the scatter in he plot increases towards high column densities. unlike that seen in the real data.," As can be seen the scatter in the plot increases towards high column densities, unlike that seen in the real data." In panel (c6) noise is added to the data as before. but the power law index is held constant at the value of 2.," In panel (c) noise is added to the data as before, but the power law index is held constant at the value of 2." The coefficient of the power law is however allowed to vary by506c.., The coefficient of the power law is however allowed to vary by. This results in a better match to the real data than varying the index, This results in a better match to the real data than varying the index ,_Q ). "For8g24 this condition is automatically satisfied, 1.ο., resonant ICS photons pair produce almost immediately upon being upscattered."," For$\beta_Q \ga 4$ this condition is automatically satisfied, i.e., resonant ICS photons pair produce almost immediately upon being upscattered." " For Bg< 4, Eq. (68))"," For $\beta_Q<4$ , Eq. \ref{betaRESeq}) )" puts a constraint on the gap height ., puts a constraint on the gap height $h$. " As we shall see below, most of the scatterings in the gap aredone byelectrons/positrons with *~min(c,), where γε=€c/kT (with T the surface blackbody temperature) and is the Lorentz factor of a fully-accelerated electron or positron [Eq. (53))]."," As we shall see below, most of the scatterings in the gap aredone byelectrons/positrons with $\gamma\sim\min(\gamma_c,\gamma_m)$, where $\gamma_c=\epsilon_c/kT$ (with $T$ the surface blackbody temperature) and $\gamma_m$ is the Lorentz factor of a fully-accelerated electron or positron [Eq. \ref{gammaeq}) )]." " For y=ym, Eq. (68))"," For $\gamma=\gamma_m$, Eq. \ref{betaRESeq}) )" " yields h - 56.9P; cm, where ντο,Q/— 1)."," yields h = 56.9 , where _Q)= )." For 7=we have, For $\gamma=\gamma_c$we have localized at the center of the tubes.,localized at the center of the tubes. To see this. consider a given flux tube. and model it as eviindrically svinmetric and monotonically decreasing im r wilh characteristic radial extent a. Consider now the effect of comparatively large or small 77.," To see this, consider a given flux tube, and model it as cylindrically symmetric and monotonically decreasing in $r$ with characteristic radial extent $a$, Consider now the effect of comparatively large or small $\eta$." In the case of large 5. the central region of a flax tube is smoothed by the collisional damping. (hus having a strong suppressive effect on the amplitude of (he current. filament associated wilh such a flux tube.," In the case of large $\eta$, the central region of a flux tube is smoothed by the collisional damping, thus having a strong suppressive effect on the amplitude of the current filament associated with such a flux tube." Large-implitude current. structures are localized (o the interfaces between flux tubes., Large-amplitude current structures are localized to the interfaces between flux tubes. In the process of mergers between like-signed filaments (and repulsion between uulike-siened). large current sheets are generated al these interfaces. similar to the large-amplitude sheets generated in MIID turbulence during mergers (INinmey&MeWilliams1995).," In the process of mergers between like-signed filaments (and repulsion between unlike-signed), large current sheets are generated at these interfaces, similar to the large-amplitude sheets generated in MHD turbulence during mergers \citep{kinney95}." .. For small η. relatively little suppression of isolated current filaments should occur: if these filaments are spatially separated owning to the buller provided by their associated flux tube. they can be expected to survive a long time ancl only be disrupted upon the merger with another large-scale [ας tube.," For small $\eta$, relatively little suppression of isolated current filaments should occur; if these filaments are spatially separated owning to the buffer provided by their associated flux tube, they can be expected to survive a long time and only be disrupted upon the merger with another large-scale flux tube." " Large η, then. allows current sheets to form at the boundaries between Εαν tubes while suppressing the spatiallv-separated. current filaments at [lux tube centers."," Large $\eta$, then, allows current sheets to form at the boundaries between flux tubes while suppressing the spatially-separated current filaments at flux tube centers." Small jj allows interface sheets and spatially separated filaments to exist., Small $\eta$ allows interface sheets and spatially separated filaments to exist. These simple arguments suggest that the evolution of (he large-amplitude structures aud {heir interaction with turbulence is thus strongly inlluenced bv the damping parameters., These simple arguments suggest that the evolution of the large-amplitude structures and their interaction with turbulence is thus strongly influenced by the damping parameters. As such. the magnitudes of the damping parameters are expected to affect the resultant. pulsar scintillation scalings.," As such, the magnitudes of the damping parameters are expected to affect the resultant pulsar scintillation scalings." The present paper considers the effect of variations of these damping, The present paper considers the effect of variations of these damping begins and the evolution will proceed towards lower mass ratios without considerable angular momentum loss (ALL).,begins and the evolution will proceed towards lower mass ratios without considerable angular momentum loss (AML). When the mass-ratio is reversed and became smaller than about 0.1 the orbital AML rate increases., When the mass-ratio is reversed and became smaller than about 0.4 the orbital AML rate increases. Lt is also indicated that the classical Algols are separated into two subclasses with respect to their orbital periods. Le. Po5 and P«5 cays.," It is also indicated that the classical Algols are separated into two subclasses with respect to their orbital periods, i.e. $>$ 5 and $<$ 5 days." ltecently. Dervisoogllu ct al. (," Recently, Dervişooğllu et al. (" 2010) re-discussed. spin angular momentum evolution. of the long period Algols.,2010) re-discussed spin angular momentum evolution of the long period Algols. They have demonstrated that even a small amount of mass transfer. eainer immediately spin up to the eritical rotational velocity.," They have demonstrated that even a small amount of mass transfer, gainer immediately spin up to the critical rotational velocity." However. the observed rotational velocities of gainers are smaller than 40 per cent of the critical rate.," However, the observed rotational velocities of gainers are smaller than 40 per cent of the critical rate." They considered generation. of magnetic fields in the radiative atmospheres in a dilferentially rotating star ancl proposed the possibility of mass and angular momentum loss driven by strong stellar winds in the intermeciatce-miass stars. similar to the primaries of the Algols.," They considered generation of magnetic fields in the radiative atmospheres in a differentially rotating star and proposed the possibility of mass and angular momentum loss driven by strong stellar winds in the intermediate-mass stars, similar to the primaries of the Algols." The slow rotation of the primaries in the Algol systems is explained. by a balance between the spin-up by mass accretion and. spin-down hy stellar wind linked to a magnetic field., The slow rotation of the primaries in the Algol systems is explained by a balance between the spin-up by mass accretion and spin-down by stellar wind linked to a magnetic field. Moreover. it is indicated that larger mass loss from the system is produce in the smaller magnetic fields.," Moreover, it is indicated that larger mass loss from the system is produced in the smaller magnetic fields." For the first time. Parthasarathy et al. (," For the first time, Parthasarathy et al. (" 1983) calle attention. to the carbon deficiencies. ancl nitrogen over-abuncdances in the atmospheres of secondary components of U Cop and U Sec.,1983) called attention to the carbon deficiencies and nitrogen over-abundances in the atmospheres of secondary components of U Cep and U Sge. Later on. Cugier and. Llarclorp (1988) indicated. the carbon deficiencies in the LUE-spectra of the gainers in 3 Per CXlgol) and A Tau.," Later on, Cugier and Hardorp (1988) indicated the carbon deficiencies in the IUE-spectra of the gainers in $\beta$ Per (Algol) and $\lambda$ Tau." Cugier (1989) expanded. his study on the Algols using the IUIZ archiva data and found similar results for six stars as in the case of Aleol and A Tau., Cugier (1989) expanded his study on the Algols using the IUE archival data and found similar results for six stars as in the case of Algol and $\lambda$ Tau. Tomkin and his collaborators (Tomkin. Lambert ancl Lemke 1993). observed eight. Algols in the optical wavelengths and compared the € abundances in the primaries with those at the single standard. stars having nearly the same elfective temperatures and. luminosities.," Tomkin and his collaborators (Tomkin, Lambert and Lemke 1993) observed eight Algols in the optical wavelengths and compared the C abundances in the primaries with those at the single standard stars having nearly the same effective temperatures and luminosities." They arrived at a result that the mass-gaining primaries of the semi-detachecl binaries have smaller. € abundance with respect to the standard stars., They arrived at a result that the mass-gaining primaries of the semi-detached binaries have smaller C abundance with respect to the standard stars. On the other hand. Yoon and Loneveutt (1992) measured € abundance for 12 Algol secondarics using the strength of g-band of the CLE molecule., On the other hand Yoon and Honeycutt (1992) measured C abundance for 12 Algol secondaries using the strength of $g$ -band of the CH molecule. The values of log2(C’) for the sample are smaller about 1.75 dex than those field G and Ix giants.," The values of $\log\,\varepsilon(C)$ for the sample are smaller about 0.25-0.75 dex than those field G and K giants." The distribution of €. N. O elements in the hydrogen-»irning core of initially more massive component of an Algol vpe system has been changed. during the main-sequence evolution.," The distribution of C, N, O elements in the hydrogen-burning core of initially more massive component of an Algol type system has been changed during the main-sequence evolution." In the Case D evolution. of the close. binary systems the more massive star expands and fills its Roche obe as well as develops convection., In the Case B evolution of the close binary systems the more massive star expands and fills its Roche lobe as well as develops convection. Convective mixing in he atmosphere may change the distribution of the C and However. carbon determinations for the primary and also or the secondary stars of Algol-tv binaries appear to be insullicient to arrive at à relevant quantitativepe analvsis and ests for acerction and mixing.," Convective mixing in the atmosphere may change the distribution of the C and N. However, carbon determinations for the primary and also for the secondary stars of Algol-type binaries appear to be insufficient to arrive at a relevant quantitative analysis and tests for accretion and mixing." Determinations of the carbon abundance for à large sample of Algols may act as major constraints on the evolution mocels for these svstems (Sarna and de Greve 1996. 1997).," Determinations of the carbon abundance for a large sample of Algols may act as major constraints on the evolution models for these systems (Sarna and de Greve 1996, 1997)." In this study. the results of spectroscopic observations of some Algols are presented.," In this study, the results of spectroscopic observations of some Algols are presented." The equivalent width (EW) of € IL A 4267 line was measured for the 18 svstenis., The equivalent width (EW) of C II $\lambda$ 4267 line was measured for the 18 systems. The dilferences of. EWs between the Aleol primaries and the standard stars having similar ellective temperatures were determined. and compared. with the orbital period increaseancl mass-transfer rates., The differences of EWs between the Algol primaries and the standard stars having similar effective temperatures were determined and compared with the orbital period increaseand mass-transfer rates. We present the carbon deficiencies. lor the largest. sample of Algoltvpe mass-transferring svstems ancl find. for the first time. that an evidence of a possible relationship between the carbon deficiency and mass transfer rate. at least for some systems which show orbital period increase.," We present the carbon deficiencies for the largest sample of Algol-type mass-transferring systems and find, for the first time, that an evidence of a possible relationship between the carbon deficiency and mass transfer rate, at least for some systems which show orbital period increase." The chemical abundance determinations from equivalent width analysis for the mass-losing secondary stars in the semi-detached Algol-twpe binaries could. only be mace during the totality. when the more massive primary star is completely eclipsed.," The chemical abundance determinations from equivalent width analysis for the mass-losing secondary stars in the semi-detached Algol-type binaries could only be made during the totality, when the more massive primary star is completely eclipsed." Out of the primary eclipse. the light contribution of the donors does not exceed a few per cent.," Out of the primary eclipse, the light contribution of the donors does not exceed a few per cent." During the primary eclipse the brightness of these systems are too low to be taken a spectrum in the totality. requiring a aree telescope and an appropriate spectrograph.," During the primary eclipse the brightness of these systems are too low to be taken a spectrum in the totality, requiring a large telescope and an appropriate spectrograph." Therefore we profer to take spectrum of the gainers which are dominate in the spectra and have enough ellective temperatures that he lines of ionized carbon and nitrogen. can be. formed., Therefore we prefer to take spectrum of the gainers which are dominate in the spectra and have enough effective temperatures that the lines of ionized carbon and nitrogen can be formed. Llowever. the primaries of the Aleols rotate fast enough hat the blending allects the spectral lines.," However, the primaries of the Algols rotate fast enough that the blending affects the spectral lines." The gainers in he classical Algols rotate at least five or more than that svnchronous rotation., The gainers in the classical Algols rotate at least five or more than that synchronous rotation. Therefore a few lines of the carbon species can be measured., Therefore a few lines of the carbon species can be measured. Spectroscopic observations were carried out at two sites. namely. Asiago and Turkish. National observatories.," Spectroscopic observations were carried out at two sites, namely, Asiago and Turkish National observatories." The targets were selected to the capability of the instruments., The targets were selected to the capability of the instruments. At the Asiago Observatory (ASL) the selected systems were observed. with the REOSC Echelle spectrograph and. CCD mounted at Cassegrain focus of the 182 em telescope., At the Asiago Observatory (ASI) the selected systems were observed with the REOSC Echelle spectrograph and CCD mounted at Cassegrain focus of the 182 cm telescope. The spectra cover the wavelength interval between 3900 and 7300AL. divided into 27 orders.," The spectra cover the wavelength interval between 3900 and 7300, divided into 27 orders." Phe average signal-to-noise ratio (S/N) and resolving power A/AXA were about ~ 150 and 500000. respectively.," The average signal-to-noise ratio (S/N) and resolving power $\lambda$ $\Delta \lambda$ were about $\sim$ 150 and 000, respectively." The observations were made between 10 and 20 March 2009 on successive nine nights., The observations were made between 10 and 20 March 2009 on successive nine nights. During this time interval 45 spectra of 14 Algols ancl 3 spectra of the three stancarel stars were obtained., During this time interval 45 spectra of 14 Algols and 3 spectra of the three standard stars were obtained. In the spectroscopic observations at. the Turkish National Observatory (TUG) the Couce Echelle Spectrometer (CES) attached. to the 150 em telescope wasused?., In the spectroscopic observations at the Turkish National Observatory (TUG) the Coude Echelle Spectrometer (CES) attached to the 150 cm telescope was. . Phe wavelength coverage of each spectrum was 3700-LO000 in 85 orders. with a resolving power of AfAX~ 0000 at 4267 and an average signal-to-noise ratio was ~ 150.," The wavelength coverage of each spectrum was 3700-10000 in 85 orders, with a resolving power of $\lambda$ $\Delta \lambda \sim$ 000 at 4267 and an average signal-to-noise ratio was $\sim$ 150." The observations were obtained on 28 and 29 May. 2010.," The observations were obtained on 28 and 29 May, 2010." During two nights observations 7 spectra of five Algols and 4 spectra of the three standard stars were obtained., During two nights observations 7 spectra of five Algols and 4 spectra of the three standard stars were obtained. ‘The position of the grating was chosen so that the € ILÀ 4267 line was recorded simultaneously in the 9th and 10th orders with the H5 line., The position of the grating was chosen so that the C II $\lambda$ 4267 line was recorded simultaneously in the 9th and 10th orders with the $\gamma$ line. Phe EWs can be measured only [or the stars earlier than AO spectral types., The EWs can be measured only for the stars earlier than A0 spectral types. For the cooler stars it downs to LOmA which is below our measuring limit., For the cooler stars it downs to 10 which is below our measuring limit. The echelle spectra were extracted ancl wavelength calibrated by using a bFe-Xr lamp source with help of the ΗΛΙΟ package., The echelle spectra were extracted and wavelength calibrated by using a Fe-Ar lamp source with help of the IRAF package. ence. the companion candidate is unlikely. to be a background giant or a foreground dwarf.,"Hence, the companion candidate is unlikely to be a background giant or a foreground dwarf." As discussed iu the previous section. a background object is very unlikely anvwiw.," As discussed in the previous section, a background object is very unlikely anyway." " Even considering the whole euseuible observed. the probability to fiud oue such object within 1.5"" of oue our tàreets is <0.7%."," Even considering the whole ensemble observed, the probability to find one such object within $1.5 ^{\prime \prime}$ of one our targets is $\le 0.7~\%$." The probability for the object beimg a forderound dwarf will be considered below., The probability for the object being a foreground dwarf will be considered below. For a coniauion to Cha Hah. we can assume the sae fextinction as towards the primary (A; = 0.17 mae. C2000).," For a companion to Cha $\alpha$ 5, we can assume the same extinction as towards the primary $_{\rm I}$ = 0.47 mag, C2000)." The eror should be ~0.07 mae. as estimated from |the errors iu R and L With the Rieke Lebofsky (1985) extinction law. we can then estimate dereddenued colors (Table 5). to be compared with intrinsic colors of latje-M. aud L chwarts (see e.g. Iàirkpatrick et al.," The error should be $\sim 0.07$ mag, as estimated from the errors in R and I. With the Rieke Lebofsky (1985) extinction law, we can then estimate dereddened colors (Table 5), to be compared with intrinsic colors of late-M and L dwarfs (see e.g. Kirkpatrick et al." 1999 2000. henceforth [1999 aud W2000).," 1999 2000, henceforth K1999 and K2000)." Few V-baud uaenitudes of L-dwarts are available so far. so that we could not compare our object to typical L-dearfs in this regard.," Few V-band magnitudes of L-dwarfs are available so far, so that we could not compare our object to typical L-dwarfs in this regard." " The comparison of RIJITIS, colors in Table 5 shows hat a spectral type of carly- to iid-L is most likely for our object.", The comparison of $_{\rm s}$ colors in Table 5 shows that a spectral type of early- to mid-L is most likely for our object. The observed magnitude difference between he M6 primary auc its companion of 3.8 to. L7 mae aud also its nou-detection in Io are consistent with spectral ype L (11999. W2000).," The observed magnitude difference between the M6 primary and its companion of 3.8 to 4.7 mag and also its non-detection in $\alpha$ are consistent with spectral type L (K1999, K2000)." As seen in Table 5. neither all he observed nor all the dereddened colors are perfectly consistent with auv single spectral type sub-class; but this is not surprising. because all (or most) known L-dwarts are uuch older aud more massive. aud evolutionary effects i he atmosphere are expected.," As seen in Table 5, neither all the observed nor all the dereddened colors are perfectly consistent with any single spectral type sub-class, but this is not surprising, because all (or most) known L-dwarfs are much older and more massive, and evolutionary effects in the atmosphere are expected." The RIS. colors of our colupalion candidate are consistent with those of vouug earbv-L dwarfs in σ On (Bejar et al., The $_{\rm s}$ colors of our companion candidate are consistent with those of young early-L dwarfs in $\sigma$ Ori (Bejar et al. 1999)., 1999). sources could have largest iutersection wader such a justification.,sources could have largest intersection under such a justification. " Colors derived from our observation fall between the typical colors of N- aud T-type asteroids, with A-type classification to be more likely."," Colors derived from our observation fall between the typical colors of X- and T-type asteroids, with X-type classification to be more likely." Considering we have combined C- aud X-class together. our classification is consistent with Ticks&Somers (2010)8 C-type classification.," Considering we have combined C- and X-class together, our classification is consistent with \citet{hic10}' 's C-type classification." To compare the simuiluities aud differences between the results of some receutl-couducted photometric aud spectroscopic NEA surveys we include the results from several surveys as listed iu Table L.. including deLeóuetal. (2010).. SINEO (Lazzirinetal.2005).. SALASS (Bus&Binuzcl2002:Binzeletal. 2001).. Dandyctal. (2003).. and Aueeli&Lazzaro(2002)Bus-DeMoeo's.," To compare the similarities and differences between the results of some recently-conducted photometric and spectroscopic NEA surveys, we include the results from several surveys as listed in Table \ref{tbl-1}, , including \citet{del10}, , SINEO \citep{laz05}, SMASS \citep{bus02,bin04}, \citet{dan03}, and \citet{ang02}." .. The classification results are firstly consolidated iuto several taxonomic conmmlexes based ou the scheme sugeestedOO by Binzeletal(2001) to allow the fractional abundances detected by cach survey to be comparable (Table 7))., The classification results are firstly consolidated into several taxonomic complexes based on the scheme suggested by \citet{bin04} to allow the fractional abundances detected by each survey to be comparable (Table \ref{tbl-7}) ). In addition. the taxonomic complexcs are further consolidatediuto two general categories. and ~S-like”. in order to determine the ratio of C/N-like aud S-like observed by each survey.," In addition, the taxonomic complexes are further consolidated into two general categories, and “S-like”, in order to determine the ratio of C/X-like and S-like observed by each survey." " Considering the definition by Morbidellietal.(2002) pattern... we consider the asteroids of class A. O. Q. R. S. U. and V as ""S-likc while the asteroids of class € and D as ""C/X-like”."," Considering the definition by \citet{mor02} , we consider the asteroids of class A, O, Q, R, S, U, and V as “S-like” while the asteroids of class C and D as ``C/X-like''." The degeneracy of X-coniplex is a problem. sjuce it inchides members with diverse physical properties., The degeneracy of X-complex is a problem since it includes members with diverse physical properties. As we dont have the fine physical data for cach N-conmiplex 1ieniber. we consider the assunption of a dark-to-bright ratio (equivaleut with our C/XN-like:S-like ratio. as we lave argued and presunued above) of 0.15 mong X-coniplex NEAs as given by Binzeletal.(2001) base on the albedo-taxouoniv correlation of 22 N-coniplex NEAs.," As we don't have the fine physical data for each X-complex member, we consider the assumption of a dark-to-bright ratio (equivalent with our C/X-like:S-like ratio, as we have argued and presumed above) of 0.45 among X-complex NEAs as given by \citet{bin04} base on the albedo-taxonomy correlation of 22 X-complex NEAs." For the two photometric surveys (ours aud Dandy ct al, For the two photometric surveys (ours and Dandy et al. s). thines are more complicated since C- and X-coniplex cannot be distinguished. πο we consider the relative number ofC- iud X-complex members among NEAs to be ~0.5 as determined bv Diuzel et aL.,"'s), things are more complicated since C- and X-complex cannot be distinguished, so we consider the relative number ofC- and X-complex members among NEAs to be $\sim0.5$ as determined by Binzel et al.," resulting a C/X-like:S-like ratio of (0.5|0.15)/(1.—0.15)zm1.13 in the combined C- aud N-couples for the two photometric surveys., resulting a C/X-like:S-like ratio of $(0.5+0.45)/(1-0.45)\approx1.73$ in the combined C- and X-complex for the two photometric surveys. Finally. the objects with several possible classifications are excluded f avoid inductiug further uncertainty.," Finally, the objects with several possible classifications are excluded to avoid inducting further uncertainty." As illustrac oeiu Table 8.. the surveys agree ou a dominate position of silicate composed asteroids (Q-. R-. S- an V-tvpeoj.," As illustrated in Table \ref{tbl-8}, the surveys agree on a dominate position of silicate composed asteroids (Q-, R-, S- and V-type)." The fractions of each complex tend to (0 Close on a larger sample 5». sugecsting that the fraction differences among the SUEVEYS are primary caused by randoni errors in observational sampling.," The fractions of each complex tend to be close on a larger sample $n$, suggesting that the fraction differences among the surveys are primary caused by random errors in observational sampling." Au interesting feature to look at is that the C/AN-like:S-like ratio appeared to be magnitude dependent., An interesting feature to look at is that the C/X-like:S-like ratio appeared to be magnitude dependent. The surveys with ZZ«17 (de Leóun et al, The surveys with $\overline{H}<17$ (de Leónn et al. s. Michelsen et al,"'s, Michelsen et al." s. and Aneecli Lazzaro9) all have the ratio smaller than 0.1. while the others all have the ratio huger than 0.1. sugecstine a rond of more C/X-like asteroids at a largerLf (siualler size).,"'s, and Angeli Lazzaro's) all have the ratio smaller than 0.1, while the others all have the ratio larger than 0.1, suggesting a trend of more C/X-like asteroids at a larger$H$ (smaller size)." This phenomenon has Όσοι noted w Rabinowitz(1998).. Morbidellietal. (2002).. Doudyetal.(2003). and Binzeletal. (2001).. mt no decisive conclusion were carriedoutdue to ack of data among large ZI (small size) asteroids.," This phenomenon has been noted by \citet{rab98}, \citet{mor02}, , \citet{dan03} and \citet{bin04}, , but no decisive conclusion were carriedoutdue to lack of data among large $H$ (small size) asteroids." By contrast. Morbidelli et al.," By contrast, Morbidelli et al." suggestedOO that the, suggested that the , ddoes not dominate the results.,does not dominate the results. " Previous models have assumed temperatures of around 50 K or 80 K, but we have shown that the gas (or at least a significant component of it) likely traces a higher temperature (~159 region."," Previous models have assumed temperatures of around 50 K or 80 K, but we have shown that the gas (or at least a significant component of it) likely traces a higher temperature $\sim 159$ K) region." " This distinction matters because assuming a K)lower temperature necessarily, and perhaps incorrectly, increases the density that is required to find solutions."," This distinction matters because assuming a lower temperature necessarily, and perhaps incorrectly, increases the density that is required to find solutions." " Kripsetal.(2008) found 2 best fit models for NGC 1068, one low-temperature/high-density and one high(unconstrained)-temperature/low density."," \citet{Krips:2008} found 2 best fit models for NGC 1068, one low-temperature/high-density and one high(unconstrained)-temperature/low density." " By examining the relative likelihoods over a large parameter space, we have demonstrated that there is broader support for their second solution, which matches well with our measurements."," By examining the relative likelihoods over a large parameter space, we have demonstrated that there is broader support for their second solution, which matches well with our measurements." " At the least, it is clear that"," At the least, it is clear that" Discovery of a post -AGB hydrogen clelicient star in globular cluster M5 (Dixon et al 2001) is an exciting new development which could piu down an age (aud possible mass) to the progenitor.,Discovery of a post -AGB hydrogen deficient star in globular cluster M5 (Dixon et al 2004) is an exciting new development which could pin down an age (and possible mass) to the progenitor. Iu suminary. it now appears that at least some EHe stars show euliauced abuudauces of lel s-process elements. e.g.. Y. Zr as well as a ls/hs ratio similar to RCBs.," In summary, it now appears that at least some EHe stars show enhanced abundances of light $s$ -process elements, e.g., Y, Zr as well as a ls/hs ratio similar to RCBs." The variation of the Is/lJd. ratio with decreasing metallicity suggests that s-processiug in RCBs aud. EHes is not similar t« that experieuced by post -AGB (and. AGB) stars (i.e.. ST/1.5 model of Busso et al.," The variation of the ls/hs ratio with decreasing metallicity suggests that $s$ -processing in RCBs and EHes is not similar to that experienced by post -AGB (and AGB) stars (i.e., ST/1.5 model of Busso et al." 2001)., 2001). " The abundance ratios suggest a single exposure of 7, of 0.1 to 0.2 +.", The abundance ratios suggest a single exposure of $\tau_{o}$ of 0.1 to 0.2 $^{-1}$. Ft is likely that this episode of s-process element production might have occured when the stars were passing through AGB phase for a second time., It is likely that this episode of $s$ -process element production might have occured when the stars were passing through AGB phase for a second time. The similarity iu the abuudauce patterus of majority RCBs aud majority EHes including the s-process elements aud the presence of eulianced abuudances of Ne aud Me in EHes does suggest that EHe pliase mieht be later in evolution to that of RCBs., The similarity in the abundance patterns of majority RCBs and majority EHes including the $s$ -process elements and the presence of enhanced abundances of Ne and Mg in EHes does suggest that EHe phase might be later in evolution to that of RCBs. The minority RCBs seems to be a more colerent. group iu abtuudauce distribution than earlier estimates indicated., The minority RCBs seems to be a more coherent group in abundance distribution than earlier estimates indicated. Minority EHes aud RCBs show a very situilar abuudauce patteru. except lor Si. Sc. aud Ca. (elements tliat could be tied up in dust).," Minority EHes and RCBs show a very similar abundance pattern, except for Si, Sc, and Ca, (elements that could be tied up in dust)." RCBs have IR excesses aud dust productiou episoces., RCBs have IR excesses and dust production episodes. The discovery of low ο ΙΟ ratio (1 — 10) in the minority RCB. CCrA does provide long awaited evidence for the mixiug of surface protous to the intershell region aud subsequent production of neutrons by PC.n) ο similar to Sakurai's object.," The discovery of low $^{12}$ $^{13}$ C ratio (4 $-$ 10) in the minority RCB, CrA does provide long awaited evidence for the mixing of surface protons to the intershell region and subsequent production of neutrons by $^{13}$ $(\alpha,n)^{16}$ O, similar to Sakurai's object." The similarity of abundance patterus of CCrA and VaeolCCen to that displayed by Sakurai's object in 1996 Oct inight encourage the suggestionMOD tliat all minority RCBs are formed through final flash., The similarity of abundance patterns of CrA and Cen to that displayed by Sakurai's object in 1996 Oct might encourage the suggestion that all minority RCBs are formed through final flash. I would like to thank my collaborators David Lambert. Gajendra Pandey. Simon Jeffery. for letting me use some results before publication.," I would like to thank my collaborators David Lambert, Gajendra Pandey, Simon Jeffery for letting me use some results before publication." I would also like to thank Martin Asplund for supplying me atmospheric models aud line lists for PCMC bands., I would also like to thank Martin Asplund for supplying me atmospheric models and line lists for $^{12}$ $^{13}$ C bands. I would like to express my thanks to David Young. Eswar Reddy aud Cajeudra Paudey for preparing the figures and other help.," I would like to express my thanks to David Yong, Eswar Reddy and Gajendra Pandey for preparing the figures and other help." E would also like express ny appreciation to the organisers of the coulereuce for their generous hospitality in Austin., I would also like express my appreciation to the organisers of the conference for their generous hospitality in Austin. second FUY component is the optically thick region at the outer edge the optically thin boundary. laver.,second FUV component is the optically thick region at the outer edge the optically thin boundary layer. We discuss the implications of this suggestion for VW Livi in detail in section 4. and we conclude this letter in section 5.," We discuss the implications of this suggestion for VW Hyi in detail in section 4, and we conclude this letter in section 5." " In quiescence VW. Livi has an optical magnitude of about 13.85. and an optical Εαν of about P5,=8.5erg cm7s (van Ameronegen et al."," In quiescence VW Hyi has an optical magnitude of about 13.8, and an optical flux of about $F_{opt}=8.5 \times 10^{-11}$erg $^{-2}$ $^{-1}$ (van Amerongen et al." LOST. Pringle et al.," 1987, Pringle et al." LOST)., 1987). " Because of its low mass aceretion rate and temperature (<8. 000K). the accretion dise is expected to be the main source of of the optical [lux in quiescence. namely fiis]=[5428510,m “erg Bo s. lo"," Because of its low mass accretion rate and temperature $ < 8,000$ K), the accretion disc is expected to be the main source of of the optical flux in quiescence, namely $F_{disc}=F_{opt} = 8.5 \times 10^{-11}$ erg $^{-2}$ $^{-1}$." "pThe energy. dissipated and radiated locally in the disc. is exactly half of the accretion energy (Shakura Sunvaev 1973. Lynden-Dell Prinele 1974): where € is the gravitational constant. M, is the mass ofthe WD. A, is the radius of the WD and AZ is the mass accretion rate."," The energy, dissipated and radiated locally in the disc, is exactly half of the accretion energy (Shakura Sunyaev 1973, Lynden-Bell Pringle 1974): where $G$ is the gravitational constant, $M_{wd}$ is the mass of the WD, $R_{wd}$ is the radius of the WD and $\dot{M}$ is the mass accretion rate." The remaining available accretion energy. in the form of rotational kinetic energy. is expected to be dissipated in the so called.layer (BL) - the interface between the inner edge of the fast rotating Ixeplerian disce and the slowly rotating surface of the accreting WD.," The remaining available accretion energy, in the form of rotational kinetic energy, is expected to be dissipated in the so called (BL) - the interface between the inner edge of the fast rotating Keplerian disc and the slowly rotating surface of the accreting WD." This energy amounts (IxIuznniakLOST): where Via is the (equatorial) rotational velocity of the WD surface and Vi(ua) is the Ixeplerian speed. at one stellar racüus., This energy amounts (Kluźnniak1987): where $V_{wd}$ is the (equatorial) rotational velocity of the WD surface and $V_K(R_{wd})$ is the Keplerian speed at one stellar radius. Por VW Livi we have Visin/= 400km s and we set Vi(2asin?z 3.200km (Godon et al.," For VW Hyi we have $V_{wd} \sin{i} = 400$ km $^{-1}$ and we set $V_K(R_{wd}) \sin{i} \approx 3,200$ km $^{-1}$ (Godon et al." 2004). this leads to a ratio Lgr/£L=0.77.," 2004), this leads to a ratio $L_{BL}/L_{disc}=0.77$." For a non-rotating WD one has Ler=LaiL., For a non-rotating WD one has $L_{BL}=L_{disc}=\frac{1}{2}L_{acc}$. " Because of its small radial extent. the BL is expected to be very hot (with a temperature Zp,& 107Ix) and optically thin during quiescenec. as the density there is very low."," Because of its small radial extent, the BL is expected to be very hot (with a temperature $T_{BL}\approx 10^{8}$ K) and optically thin during quiescence, as the density there is very low." This tiny component is therefore expected to emit. basically the other half of the accretion energy in the X-ray. bane., This tiny component is therefore expected to emit basically the other half of the accretion energy in the X-ray band. A-ray observations of VW Livi in quiescence first carried out with EXNOSAT and ROSATLT (van der Woerd Leise 1987. Belloni et al.," X-ray observations of VW Hyi in quiescence first carried out with EXOSAT and ROSAT (van der Woerd Heise 1987, Belloni et al." " 1991 - using a single. temperature plasma) revealed an X-ray bolometric llux Fxpa,81.51.910 tere ?s ", 1991 - using a single temperature plasma) revealed an X-ray bolometric flux $F_{X-ray} \approx 1.5-1.9 \times 10^{-11}$ erg $^{-2}$ $^{-1}$. Subsequent N-rayv observations with ASCA anc NMM-Newton (using two- ancl multiple-temperature plasma models (Llasenkopl Eracleous 2002. Pandel et al.," Subsequent X-ray observations with ASCA and XMM-Newton (using two- and multiple-temperature plasma models (Hasenkopf Eracleous 2002, Pandel et al." 2003 - respectively) revealed. a total X-ray bolometric Hux smaller by a factor of about 2: Fxpay725SN.10Dope em7s 4, 2003 - respectively) revealed a total X-ray bolometric flux smaller by a factor of about 2: $F_{X-ray} \approx 5-8 \times 10^{-12}$ erg $^{-2}$ $^{-1}$. ~The X-ray observations all revealed a temperature AL~ a few keV. ancl possibly as high as Adox6ske¥. Panelel ct al. (," The X-ray observations all revealed a temperature $kT \sim$ a few keV, and possibly as high as $kT \approx 6-8$ keV. Pandel et al. (" 2003) fit the line profile assuming that the X-ray emitting region is a thin equatorial belt near the surlace of the WD with a rotational velocity resin?=540 km ,2003) fit the line profile assuming that the X-ray emitting region is a thin equatorial belt near the surface of the WD with a rotational velocity $v \sin{i} = 540$ km $^{-1}$. llowever. so far the N-ray observations for VW. Lyi have revealed a much smaller BL luminosity than expected: Ler©Ομως (Belloni et al.," However, so far the X-ray observations for VW Hyi have revealed a much smaller BL luminosity than expected: $L_{BL} \approx 0.1 L_{disc}$ (Belloni et al." 1991). while from &eometrical consideration. namely assuming that the star occults half of the DL. Pandel et al. (," 1991), while from geometrical consideration, namely assuming that the star occults half of the BL, Pandel et al. (" 2003) obtained Ley£L;=0.2.,2003) obtained $L_{BL}/L_{disc} = 0.2$. In general the WD in DNe has a tvpical temperature of about Z4215.—50. 000Ix. and it is expected to dominate the ultraviolet (UV) light in most DNe in quiescence: Loy=Lag.," In general the WD in DNe has a typical temperature of about $T_{wd} \approx 15-50,000$ K, and it is expected to dominate the ultraviolet (UV) light in most DNe in quiescence: $L_{UV}=L_{wd}$ ." " For VW Livi in quiescence. carly IUIS Observations (Mateo Szkody 1984) revealed that the UV light from the svstem was dominated by the WD with Zipp,2. 000Ix. Verbunt et al. ("," For VW Hyi in quiescence, early IUE Observations (Mateo Szkody 1984) revealed that the UV light from the system was dominated by the WD with $T_{eff} = 18,000 \pm 2,000$ K. Verbunt et al. (" LOST) ancl Prinele et al. (,1987) and Pringle et al. ( 1987) lam estimated that the tux observed at LUE wavelengths was about the same as the one observed at optical wavelengths. namely Fr=Foum85S10 tore 7s +.,"1987) later estimated that the flux observed at IUE wavelengths was about the same as the one observed at optical wavelengths, namely $F_{UV}=F_{opt}= 8.5 \times 10^{-11}$ erg $^{-2}$ $^{-1}$." Much higher S/N spectra were later obtained with by Sion et al. (, Much higher S/N spectra were later obtained with by Sion et al. ( 1995. 1996. 2001). who confirmed the basic shape of the spectrum.,"1995, 1996, 2001), who confirmed the basic shape of the spectrum." They found that the WD had a temperature of about 20.000Ix. (which varied by at least 2.000 Ex. depending on the time since outburst) with a rotation rate of about ~ 400 km s," They found that the WD had a temperature of about 20,000K (which varied by at least 2,000 K, depending on the time since outburst) with a rotation rate of about $\sim$ 400 km $^{-1}$." Llowever. there have been some indications of an additional component besides the white dwarf in the PUY spectrum of VW Lyi and other DNe in quiescence (e.g. the presence of emission lines and the bottoms of Lyman alpha profiles which do not go to zero as in pure white dwarl).," However, there have been some indications of an additional component besides the white dwarf in the FUV spectrum of VW Hyi and other DNe in quiescence (e.g. the presence of emission lines and the bottoms of Lyman alpha profiles which do not go to zero as in pure white dwarf)." While the dominant component is that ofa WD. the second component is a rather Hat continuum with an ellective temperature that is much higher than that of the WD.," While the dominant component is that of a WD, the second component is a rather flat continuum with an effective temperature that is much higher than that of the WD." Long et al. (, Long et al. ( 1993) first suggested a fast rotating hot accretion belt around the WD as a second component to fitZUT observations of U Gem.,1993) first suggested a fast rotating hot accretion belt around the WD as a second component to fit observations of U Gem. Long et al. (, Long et al. ( 1993) remarked that the physical basis [or an aceretion belt might be the spin-up of the surface lavers of the WD during outburst and the slow conversion of kinetic cnerey to heat as a result of viscous heating in the differentially rotating atmosphere (Ixippehahn Thomas 978. Ixutter Sparks 1987. 1989).,"1993) remarked that the physical basis for an accretion belt might be the spin-up of the surface layers of the WD during outburst and the slow conversion of kinetic energy to heat as a result of viscous heating in the differentially rotating atmosphere (Kippehahn Thomas 1978, Kutter Sparks 1987, 1989)." The presence of the accretion belt was confirmed later for VW Livi from its 425775715 spectra (Sion et al., The presence of the accretion belt was confirmed later for VW Hyi from its spectra (Sion et al. 1995. 906 2001) and from its JUL spectra. (Cannsicke Deuermann 1996).," 1995, 1996 2001) and from its spectra (Gännsicke Beuermann 1996)." Ht was found that the second component contributed about of the FUY flux (with the WD contributing the remaining SO%)) and remains pretty much he same 5 days apart (Sion ct al., It was found that the second component contributed about of the FUV flux (with the WD contributing the remaining ) and remains pretty much the same 5 days apart (Sion et al. 2001)., 2001). ephemerids agree. because original Hipparcos eplicieris was nof working.,"ephemerids agree, because original Hipparcos ephemeris was not working." The primary star as defined by Ilpparcos is our iore inassive star so we decikled to retain it as primary. even if both (αμα (2001) aud Clausen et al. (," The primary star as defined by Hipparcos is our more massive star so we decided to retain it as primary, even if both Griffin (2001) and Clausen et al. (" 2001) adopted the reverse conveution.,2001) adopted the reverse convention. The strategv to obtain the primary tempcrature was described above., The strategy to obtain the primary temperature was described above. " 2 data provide (BoV)y — 0.625. which. transformed to the Jolinsou «πίσσα, leads to V3; = 0.53."," $-$ 2 data provide $(B-V)_{\rm T}$ = 0.625, which, transformed to the Johnson system, leads to $(B-V)_{\rm J}$ = 0.53." An inspection of the spectra and of the radial velocity curve tells us the two stars are not 1uuch different., An inspection of the spectra and of the radial velocity curve tells us the two stars are not much different. Supposing both stars have equal temperatures. the color sugecsts (according to Fitzecrald 1970 and Popper 1980 conversion tables) that they are somewhat hotter (Fs) than the reported CO spectral type.," Supposing both stars have equal temperatures, the color suggests (according to Fitzgerald 1970 and Popper 1980 conversion tables) that they are somewhat hotter (F8) than the reported G0 spectral type." The secondary eclipse, The secondary eclipse brigghtest young T Tauri stars and is surrounded by a massive disk.,ghtest young T Tauri stars and is surrounded by a massive disk. In all cases. (he internal partition function of the molecules is calculated by an explicit sum over (he known internal enerev levels of Ils or Ds as appropriate.,"In all cases, the internal partition function of the molecules is calculated by an explicit sum over the known internal energy levels of $_2$ or $_2$ as appropriate." Similarly. proper isotope scaling was applied for the approximate vibrational aud rotational properties of the chains (RossandYang2001).," Similarly, proper isotope scaling was applied for the approximate vibrational and rotational properties of the chains \citep{rossyang01}." . These four EOS models were applied to deuterium to compare with shock compression experiments aud to hydrogen to compute interior models of planets., These four EOS models were applied to deuterium to compare with shock compression experiments and to hydrogen to compute interior models of planets. These EOS are not intended (o constitute practical EOS models for purposes other than (his sensitivity study., These EOS are not intended to constitute practical EOS models for purposes other than this sensitivity study. They are rather simple representations of subsets of data Chat include enough physics to allow a reasonable calculation of adiabats., They are rather simple representations of subsets of data that include enough physics to allow a reasonable calculation of adiabats. Even though it predates all (he shock compression experimentis (hat we consider here. ihe cdeuterium EOS 5263 Uxerley1972:SESAMElibrary1992). provides a [air representation of the Sandia Hugoniot and we adopt it here.," Even though it predates all the shock compression experiments that we consider here, the deuterium EOS 5263 \citep{kerley72, sesame} provides a fair representation of the Sandia Hugoniot and we adopt it here." For hydrogen. we adopt the SESAME EOS 5251 (SESAMElibrary1992).. which is the deuterium EOS scaled in density.," For hydrogen, we adopt the SESAME EOS 5251 \citep{sesame}, which is the deuterium EOS scaled in density." The SESAME 5251 table provides only P(p.T) and Ü(p.T).," The SESAME 5251 table provides only $P(\rho,T)$ and $U(\rho,T)$." We computed the entropy by integrating the internal οποιον downward along isochores [from a high-T isotherm obtained rom (he Saumon-Chabrer EOS (Saumon. Chabrier Van Horn 1995).," We computed the entropy by integrating the internal energy downward along isochores from a $T$ isotherm obtained from the Saumon-Chabrier EOS (Saumon, Chabrier Van Horn 1995)." The calculated entropy does not recover (he limit of the ideal H5 gas. however.," The calculated entropy does not recover the limit of the ideal $_2$ gas, however." This is a consequence of the ron-scalabilitv of (he molecular internal energy aud entropy., This is a consequence of the non-scalability of the molecular internal energy and entropy. We found that in the molecular region (2?<0.2 Mbar). the SESAME deuterium Iugoniot is somewhat stiffer (han indicated by the better measurements made after il was developed (Nellisetal.1983).," We found that in the molecular region $P<0.2\,$ Mbar), the SESAME deuterium Hugoniot is somewhat stiffer than indicated by the better measurements made after it was developed \citep{nellis83}." . This is partly to blame for our inability to compute satisfactory models ol Jupiter and Saturn with this EOS (see section 4)., This is partly to blame for our inability to compute satisfactory models of Jupiter and Saturn with this EOS (see section 4). We have therelore patched the SESAME EOS in the molecular regime with an EOS that reproduces the low-7? Hugoniot data such as any of the above linear mixing EOS., We have therefore patched the SESAME EOS in the molecular regime with an EOS that reproduces the $P$ Hugoniot data such as any of the above linear mixing EOS. The patch is introduced bv smoothly switching from one EOS to the other bx applving the additive volume rule in the switching region. as if we were nüxing (wo different substances.," The patch is introduced by smoothly switching from one EOS to the other by applying the additive volume rule in the switching region, as if we were mixing two different substances." This preserves thermodynamic consistency., This preserves thermodynamic consistency. The transition is located between kkbar and 0.4 Mbar.," The transition is located between kbar and $\,$ Mbar." We label this EOSSESAME-p., We label this EOS. The resulting IIugoniots are nearly identical to SESAME IHugoniots. except at pressures below ~5O kbar.," The resulting Hugoniots are nearly identical to SESAME Hugoniots, except at pressures below $\sim 50\,$ kbar." " Because the SESAME entropy does not recover the ideal Il, gas entropy al low density but the molecular EOS patch does. the SESAME-p adiabat is shifted to higher 7 and lower p a( pressures above kbar."," Because the SESAME entropy does not recover the ideal $_2$ gas entropy at low density but the molecular EOS patch does, the SESAME-p adiabat is shifted to higher $T$ and lower $\rho$ at pressures above $\,$ kbar." Finally. we computed models with the EOS (Sammonetal.|1995).," Finally, we computed models with the EOS \citep{scvh}." . Like the SESAME EOS. it predates all experiments except the (P.V) gas gun data which il reproduces by construction (like the four LM EOS above).," Like the SESAME EOS, it predates all experiments except the $(P,V)$ gas gun data which it reproduces by construction (like the four LM EOS above)." It agrees better with the Sandia (D.V) IHIugoniot for P?zi0.7 Mbar and then shifts toward the NOVA IIugoniot at higher," It agrees better with the Sandia $(P,V)$ Hugoniot for $P \wig< 0.7\,$ Mbar and then shifts toward the NOVA Hugoniot at higher" absolute magnitudes are allectecd because of cosmological dimming and the Ix-correction.,absolute magnitudes are affected because of cosmological dimming and the K-correction. Galaxies at the maximum redshift of z=0.5 will have an apparent surface brightness 3 mag aresec7 fainter than their intrinsic surface brightness (1.7 mag 72 due to cosmological dimming and 1.3 mag aresee72 due to the Ix-correction. where A( 2.52).," Galaxies at the maximum redshift of $z=0.5$ will have an apparent surface brightness 3 mag $^{-2}$ fainter than their intrinsic surface brightness (1.7 mag $^{-2}$ due to cosmological dimming and 1.3 mag $^{-2}$ due to the K-correction, where $K(z)=2.5z$ )." Even galaxies at 2=0.25 will be fainter by 1.6 mag 7, Even galaxies at $z=0.25$ will be fainter by 1.6 mag $^{-2}$. " Thus a galaxy with central surface brightness of 21.5 mag aresec7 (7,=22.6 mag 7) and z=0.25 will not be detected with a threshold of 23 mag 2", Thus a galaxy with central surface brightness of 21.5 mag $^{-2}$ $\mu_e=22.6$ mag $^{-2}$ ) and $z=0.25$ will not be detected with a threshold of $23$ mag $^{-2}$. Recovering total magnitudes beforehand will give gor estimators for. the luminosity function. provided tha significant numbers of galaxies are not missing.," Recovering total magnitudes beforehand will give good estimators for the luminosity function, provided that significant numbers of galaxies are not missing." This is a particular problem if νο maximum redshift is very. high., This is a particular problem if your maximum redshift is very high. llowever. if galaxies aremissing because of cosmologica ellects. rather than being too intrinsically dim even a =0. the number density. can be recovered. using a surface brightness dependent volume correction as discussec in Cross et al. (," However, if galaxies aremissing because of cosmological effects, rather than being too intrinsically dim even at $z=0$, the number density can be recovered using a surface brightness dependent volume correction as discussed in Cross et al. (" 2001).,2001). Overall the variations recovered in. A. 67 and a between simulated surveys with limits of 24.«qq26 (ie. comparable to existing surveys) are. 19.740.1$. Iu particular. maux of the galaxies showing laugh Bahuner decrement values in the present study would not be detected in a UV survey τος to imis:=18.5.," In particular, many of the galaxies showing high Balmer decrement values in the present study would not be detected in a UV survey limited to $m_{\rm UV}=18.5$." Sample selection thus sccm to be a major source of bias when trving to investigate the correlation between dust obscuration aud SERs., Sample selection thus seem to be a major source of bias when trying to investigate the correlation between dust obscuration and SFRs. Given the large scatter present iu Figure 3.. a SER-dependent reddening correction is obviously unsuitable for application iu galaxies where a direct estimate of obscuration exists;," Given the large scatter present in Figure \ref{fig:balmer}, a SFR-dependent reddening correction is obviously unsuitable for application in galaxies where a direct estimate of obscuration exists." Ihoxeever. a trend for higher average Bahuer decrement (and greater distribution width) with Increasing SFR seems to exist.," However, a trend for higher average Balmer decrement (and greater distribution width) with increasing SFR seems to exist." This cau still be useful as a preliminary dust obscuration estimate for large samples of galaxies where no other measure of obscuration is available., This can still be useful as a preliminary dust obscuration estimate for large samples of galaxies where no other measure of obscuration is available. Although in practice the form of the derived relation may be comparable to the ones iu IHopkiusetal.(2001). aud Sullivanetal.(2001).. here we recognize that there is no tight correlation between obscuration aud SER. but an average obscuration nav still be defined for uv given SER.," Although in practice the form of the derived relation may be comparable to the ones in \citet{Hopkins01} and \citet{Sullivan01}, here we recognize that there is no tight correlation between obscuration and SFR, but an average obscuration may still be defined for any given SFR." As can be seen in Figure 3. the resulting correction will be affected by large uncertainties for individual galaxies. especially at laxge SERs.," As can be seen in Figure \ref{fig:balmer} the resulting correction will be affected by large uncertainties for individual galaxies, especially at large SFRs." The sample was thus split iuto 7 bius of log(SER) (as estimated from the radio huuinositv). cach having between 5 and 16 objects.," The sample was thus split into 7 bins of $\log$ (SFR) (as estimated from the radio luminosity), each having between 5 and 16 objects." The median loe(SFR) and Balmer decrement in each bin were then found (shown as asterisks iu Figure 3))., The median $\log$ (SFR) and Balmer decrement in each bin were then found (shown as asterisks in Figure \ref{fig:balmer}) ). A linear fit. taking iuto account the errors in both quantities. results in with a correlation coefficient of (0.8.," A linear fit, taking into account the errors in both quantities, results in with a correlation coefficient of 0.8." Keeping in uid the meaning aud limitations of this correlation. as seen in Fieure 3. one can now test itsusefulness as a first correction for the effect seen in Figure 2..," Keeping in mind the meaning and limitations of this correlation, as seen in Figure \ref{fig:balmer}, one can now test itsusefulness as a first correction for the effect seen in Figure \ref{fig:sfr14sfrha}. ." " The departure of the observed. Baliner decrement from the Case B value of 2.86 (e.¢..Brockleluwst1971)... can be related to the color excess for nebular cussion lines. E(B V)44,,. aud extinction. (A). by Substituting (3)) iuto (1)) eives a relation for the color excess as a function of SFR: Together with au appropriate extinction curve (the standard Galactic extinction curve of Cardelli.Clayton&Mathis(1989) with Ay=3.1. found by Calzetti(2001) to describe well the reddening of the ionized eas in star-foriunug galaxies). this cau then be used to correct ζω. and cousequeutlv. ΕΠ. for dust obscuration: where Ly""obs can either be the observed Πα hInuunositv or the ""effective"" Ta Inninositv derived from an observed Orr] fux."," The departure of the observed Balmer decrement from the Case B value of 2.86 \citep[e.g.,][]{Brocklehurst71}, can be related to the color excess for nebular emission lines, $E(B-V)_{gas}$, and extinction, $k(\lambda)$ , by Substituting \ref{balmersfr}) ) into \ref{balmer}) ) gives a relation for the color excess as a function of SFR: Together with an appropriate extinction curve (the standard Galactic extinction curve of \citet{Cardelli89} with $R_{V}=3.1$, found by \citet{Calzetti01} to describe well the reddening of the ionized gas in star-forming galaxies), this can then be used to correct $L_{\rm H\alpha}$, and consequently, $_{\rm H\alpha}$, for dust obscuration: where $L_{\rm H\alpha}^{obs}$ can either be the observed $\alpha$ luminosity or the “effective” $\alpha$ luminosity derived from an observed ] flux." Equation (5)) gives the relation between extinction aud hezutrinsic SFR., Equation \ref{ebvsfr}) ) gives the relation between extinction and the SFR. Assunüug this to be the value given w the radio luminosity could be a good. approximation. mit would create an artificial depeucence between the corrected SSER and the one from L.1€CGIIz.," Assuming this to be the value given by the radio luminosity could be a good approximation, but would create an artificial dependence between the corrected SFR and the one from GHz." Instead. since the orm for the SFR-dependent obscuration is monotonically Increasing. an iteration over possible values for iutriusic SER aud the corresponding obscuration can be performec until the calculated obscured SER. converges with the 6served. value (Hopkiusetal.2001).," Instead, since the form for the SFR-dependent obscuration is monotonically increasing, an iteration over possible values for intrinsic SFR and the corresponding obscuration can be performed until the calculated obscured SFR converges with the observed value \citep{Hopkins01}." . We note that this procedure does not take iuto account auv absorption of ioniziung photons bv dust inside TIT regions. Charlotei.(2002)...," We note that this procedure does not take into account any absorption of ionizing photons by dust inside HII regions. \citet{Charlot02}, ," modeling the observed spectra iu non-Sevfer ealaxies. estimate that this mecha is respousible for the loss of ~20% of ionizins photous.," modeling the observed spectra in non-Seyfert galaxies, estimate that this mechanism is responsible for the loss of $\sim$ of ionizing photons." Cüven the larec uncertaiutv associated with this value. however. we do uo itelmpt any correction. noting that its maenitude would uot significantly affect our results.," Given the large uncertainty associated with this value, however, we do not attempt any correction, noting that its magnitude would not significantly affect our results." Figure 6 shows the resulting dust corrected relation for the SFR from line aud radio huninosities., Figure \ref{fig:sfr14sfrhacorr} shows the resulting dust corrected relation for the SFR from line and radio luminosities. It is clear that the SFR-depeucdent dust absorption. while beiug a verv coarse approximation. eau successfully account for the first order offset between the SFRs derived from oor [OU] aud radio huuinosities for galaxies spauniug a broad range of redshifts (out to zzz 0.8).," It is clear that the SFR-dependent dust absorption, while being a very coarse approximation, can successfully account for the first order offset between the SFRs derived from or ] and radio luminosities for galaxies spanning a broad range of redshifts (out to $z \approx 0.8$ )." This would not be possible if the relations between Balmer decrements and SER drawn from previous samples (Ilopkiusctal.2001:Sullivanetal.2000) had been used.," This would not be possible if the relations between Balmer decrements and SFR drawn from previous samples \citep{Hopkins01,Sullivan01} had been used." The scatter still present has an rms of 0.1 dex about the best fit line. uaintained from the scatter in Figure 2..," The scatter still present has an rms of 0.4 dex about the best fit line, maintained from the scatter in Figure \ref{fig:sfr14sfrha}." The lack of au Huprovement lies iu the coarse relationship between SER and obscuration seen in Figure 3 the linear fit to the uedian values cannot correct for the range of obscuratious seen at cach SER., The lack of an improvement lies in the coarse relationship between SFR and obscuration seen in Figure \ref{fig:balmer} – the linear fit to the median values cannot correct for the range of obscurations seen at each SFR. There will be. of course. additional uncorrelated uechauisuis involved in the aand radio cussion Which contribute to the scatter seen. mt their quantificationwill only be possibleafter a precise account of the obscuration for cach imdividual galaxy.," There will be, of course, additional uncorrelated mechanisms involved in the and radio emission which contribute to the scatter seen, but their quantificationwill only be possibleafter a precise account of the obscuration for each individual galaxy." A radio selected sample of star forming salaxies to20.8 has been compiled from the Survey., A radio selected sample of star forming galaxies to$z \approx 0.8$ has been compiled from the . The use of radio selection minimises bias in the sample due to dustobscuration effects., The use of radio selection minimises bias in the sample due to dustobscuration effects. The relationship between, The relationship between Figure 5. shows travel-time shifts resulting from a flux tube of radius 2 Mm and field strength of 1 kG (e=0.13).,Figure \ref{fig.travel_times} shows travel-time shifts resulting from a flux tube of radius 2 Mm and field strength of 1 kG $\epsilon=0.13$ ). Figure 5aa shows the exact. Born-. and ray-approximation travel limes as a Iunction of 1 at fixed y.," Figure \ref{fig.travel_times}a a shows the exact, Born-, and ray-approximation travel times as a function of $x$ at fixed $y$." Inside the fIux tube. both the Dorn- and rav-approximation travel times reproduce the exact travel times at a good level of aceuracey.," Inside the flux tube, both the Born- and ray-approximation travel times reproduce the exact travel times at a good level of accuracy." As i increases {ο the right of the tube. wavefront healing (e.g.Nolet&Dahlen2000) is seen in the exact and Dorn approximation (ravel limes.," As $x$ increases to the right of the tube, wavefront healing \citep[e.g.][]{Nolet2000} is seen in the exact and Born approximation travel times." Wavelront healing. however. is not seenin the ταν approximation travel Gimes.," Wavefront healing, however, is not seenin the ray approximation travel times." Figure 5bb shows the travel times as a function of y al fixed v=10 Mam., Figure \ref{fig.travel_times}b b shows the travel times as a function of $y$ at fixed $x=10$ Mm. The Dorn approximation reproduces the exact travel times to within20'%., The Born approximation reproduces the exact travel times to within. . The rav approximation does not capture finite wavelength effects and does not capture the basic behavior of the travel times: it can be inaccurate by many orders of magnitude lor κά«1., The ray approximation does not capture finite wavelength effects and does not capture the basic behavior of the travel times; it can be inaccurate by many orders of magnitude for $kR \ll 1$. We note that. in Figure 5.. the contribution of the density jump (first term in Eq. (37]])," We note that, in Figure \ref{fig.travel_times}, the contribution of the density jump (first term in Eq. \ref{source}] ])" to the (ravel-lime shifts is neeligible compared to the contribution from the Lorentz force., to the travel-time shifts is negligible compared to the contribution from the Lorentz force. We have computed. in the [ist Born approximation. (he scattering of acoustic waves from a magnetic evlinder embedded in a homogeneous background medium.," We have computed, in the first Born approximation, the scattering of acoustic waves from a magnetic cylinder embedded in a homogeneous background medium." We showed (hat in the limit of weak magnete fiekl. (he Dorn approximation to the scattered. wavelield is correct to first order in the parameter e=D?/προ.," We showed that in the limit of weak magnetic field, the Born approximation to the scattered wavefield is correct to first order in the parameter $\epsilon=B^2/4\pi\rho c^2$." For typical values of the solar magnetic [Iux. the Dorn approximation should be eood at depths larger than a few hundred kin below the photosphere.," For typical values of the solar magnetic flux, the Born approximation should be good at depths larger than a few hundred km below the photosphere." The condition e<<1 is satisfied [or a 1-kG magnetic fibril at a depth οἱ 250 km (ez 0.1) and for a LO? G magnetic flux tube at the base of the convection zone (cz10 *)., The condition $\epsilon<<1$ is satisfied for a 1-kG magnetic fibril at a depth of 250 km $\epsilon \approx 0.1$ ) and for a $10^5$ G magnetic flux tube at the base of the convection zone $\epsilon \approx 10^{-7}$ ). Since the errors introduced by the Rytov and Born approximations are very similar (e.g.Woodwiid1989)... we suspect that a travel-time shift computed in the Rytov approximation would also tend to the exact solution as € tends to zero.," Since the errors introduced by the Rytov and Born approximations are very similar \citep[e.g.][]{Woodward1989}, we suspect that a travel-time shift computed in the Rytov approximation would also tend to the exact solution as $\epsilon$ tends to zero." Near (he photosphere. e is not small.," Near the photosphere, $\epsilon$ is not small." It has been suggested by many authors that in this case the Born approximation will fail., It has been suggested by many authors \citep[e.g.][]{Lindsey2004} that in this case the Born approximation will fail. An exception is the claim by Rosenthal(1995) that the Dorn approximation will remain valid for kG maenetiec fibrils in the limit where the radius of the magnetic element is much smaller than the wavelength., An exception is the claim by \citet{Rosenthal1995} that the Born approximation will remain valid for kG magnetic fibrils in the limit where the radius of the magnetic element is much smaller than the wavelength. We wish to test this last statement in our simple problem., We wish to test this last statement in our simple problem. Assuming .=0 for the sake of simplicity and taking the limit AJ—0. we find that for all e we have Thisshows that the Born approximation is not valid in the limit of small tube radius.," Assuming $k_z=0$ for the sake of simplicity and taking the limit $kR \rightarrow 0$, we find that for all $\epsilon$ we have Thisshows that the Born approximation is not valid in the limit of small tube radius." " Figure G shows the ratio AP /A,,. for Q—m.X 5. as a function of R when e=1 and"," Figure \ref{fig.ratio_of_A} shows the ratio ${ A^{\rm Born}_m} / {A_m}$ , for $0\leq m \leq 5$ , as a function of $R$ when $\epsilon=1$ and" such a way that the slope of the best fit is consistent with that of Fig. 2..,"such a way that the slope of the best fit is consistent with that of Fig. \ref{mass_comp}," but the average ratio between the two mass estimates is considerably smaller than one., but the average ratio between the two mass estimates is considerably smaller than one. Moreover. we note that the effect of contamination caused by the lensed objects in the measurements of the fluxes of a lens galaxy is small.," Moreover, we note that the effect of contamination caused by the lensed objects in the measurements of the fluxes of a lens galaxy is small." This is usually more relevant in the bluer filters. which are known to be less sensitive to photometric mass estimates. anc the measurements of total magnitudes through de Vaucouleurs profile fitting should further reduce this source of uncertainty.," This is usually more relevant in the bluer filters, which are known to be less sensitive to photometric mass estimates, and the measurements of total magnitudes through de Vaucouleurs profile fitting should further reduce this source of uncertainty." Values of q slightly larger than one. like those observed anc shown in the inset of Fig. 2..," Values of $q$ slightly larger than one, like those observed and shown in the inset of Fig. \ref{mass_comp}," may be explained by possible underestimates of MURuin). Which ean be ascribed to two different phenomena occurring in the galaxies: dust extinetior and metallicity values lower than the solar one.," may be explained by possible underestimates of $M_{\mathrm{phot}}^{*}(\le R_{\mathrm{Ein}})$, which can be ascribed to two different phenomena occurring in the galaxies: dust extinction and metallicity values lower than the solar one." In detail. both effects tend to give lower IR fluxes. which then result in lower mass estimates.," In detail, both effects tend to give lower IR fluxes, which then result in lower mass estimates." Nevertheless. several tests have supported the validity of the dust-free and solar metallicity model assumptions (e.g.. see Rettura et al. 2006)).," Nevertheless, several tests have supported the validity of the dust-free and solar metallicity model assumptions (e.g., see Rettura et al. \cite{ret06}) )." Finally. despite a number of assumptions. we conclude that the good agreement between the two mass estimators. within their respective uncertainties. is a very reassuring result.," Finally, despite a number of assumptions, we conclude that the good agreement between the two mass estimators, within their respective uncertainties, is a very reassuring result." This makes the presence of strong biases in one of the two methods very unlikely. and allows us to use either of them independently to measure reliably stellar masses.," This makes the presence of strong biases in one of the two methods very unlikely, and allows us to use either of them independently to measure reliably stellar masses." Although this study is based on a low redshift sample. we expect photometric mass estimates to be also accurate to high redshift. as long as the same optical/near-IR rest frame bands are covered.," Although this study is based on a low redshift sample, we expect photometric mass estimates to be also accurate to high redshift, as long as the same optical/near-IR rest frame bands are covered." We thank G. Bertin for useful comments on this manuscript., We thank G. Bertin for useful comments on this manuscript. We acknowledge the use of data from the accurate SDSS database., We acknowledge the use of data from the accurate SDSS database. The SDSS Web Site is http://www.sdss.org/., The SDSS Web Site is http://www.sdss.org/. inner disk.,inner disk. Stellar radial migration could give an explanation of this link (e.g. Haywood 2008b:: Schénnrich Binney 2009a))., Stellar radial migration could give an explanation of this link (e.g. Haywood \cite{Haywood-08b}; Schönnrich Binney \cite{Schonrich-09a}) ). It has been proposed that metal-rich stars found in the solar vicinity may have been formed in the inner Galactic. disk regions (e.g. Grenon 1999:; Ecuvillon et al. 20071: , It has been proposed that metal-rich stars found in the solar vicinity may have been formed in the inner Galactic disk regions (e.g. Grenon \cite{Grenon-99}; Ecuvillon et al. \cite{Ecuvillon-07}; ; Famaey et al. 2007:;, Famaey et al. \cite{Famaey-07}; Santos et al. 2008::, Santos et al. \cite{Santos-08}; Schónnrich Binney 2009b))., Schönnrich Binney \cite{Schonrich-09b}) ). Nevertheless. the origin and nature of these stars remains unclear and needs to be clarified.," Nevertheless, the origin and nature of these stars remains unclear and needs to be clarified." Although the present observations suggest that hamr stars (high-alpha. metal rich) may have originated from the inner disk (e.g. inner thick-disk members). they do not allow us to exclude the possibility that they represent a whole new Galactic population.," Although the present observations suggest that $\alpha$ mr stars (high-alpha, metal rich) may have originated from the inner disk (e.g. inner thick-disk members), they do not allow us to exclude the possibility that they represent a whole new Galactic population." More observations are neededto resolve this uncertainty., More observations are neededto resolve this uncertainty. "very rapid changes in flux (by factors of 120-170 %, with a statistical significance >3o) were observed within a timescale At<47 seconds.","very rapid changes in flux (by factors of 120–170 $\%$, with a statistical significance $>3\sigma$ ) were observed within a timescale $\Delta t<47$ seconds." " Thus, a large fraction of the emitting plasma must be confined to a region