ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 1997) starting with the latest pipeline data product (OLP V7.01)., 1997) starting with the latest pipeline data product (OLP V7.01).3 Deglitching. dark current subtraction. tail modeling. photometric checks as well as updown-corrections and defringing were applied.," Deglitching, dark current subtraction, tail modeling, photometric checks as well as updown-corrections and defringing were applied."4 The calibration used standard tables within the LA derived from observations of Uranus: the overall uncertainty is estimated as ~30% Cpriv.comm., The calibration used standard tables within the IA derived from observations of Uranus; the overall uncertainty is estimated as $\sim 30\%$ (priv.comm.5 SWS data centre)., SWS data centre).6 In reffiegrasdalen the ISOSWS spectrum is shown supplemented by the earlier broadband continuum observations from Grasdalen et al. (, In \\ref{figgrasdalen} the ISOSWS spectrum is shown supplemented by the earlier broadband continuum observations from Grasdalen et al. (71983). and by the recent NIR observations.,"1983), and by the recent NIR observations."8 The SWS spectrum shows prominent broad emission and/or absorption features due to dust and molecules. superimposed on a smooth continuum.," The SWS spectrum shows prominent broad emission and/or absorption features due to dust and molecules, superimposed on a smooth continuum."9 As confirmed by the detailed modeling (Sect., As confirmed by the detailed modeling (Sect.10 3.2) the continuum seen by SWS makes a transition from reddened photospheric-dominated emission in the NIR wavelengths to warm dust emission in the MIR., 3.2) the continuum seen by SWS makes a transition from reddened photospheric-dominated emission in the NIR wavelengths to warm dust emission in the MIR.11 The spectral peaks at 10.4 and jj are most readily identified as silicate emission features.," The spectral peaks at 10.4 and $\,\mu$ m are most readily identified as silicate emission features."12 Although the shorter wavelength feature is normally centred at shorter wavelengths in the 9- jm range. it appears here superimposed on broad-band molecular absorption from gaseous SiO. whose absorption minimum is seen around j/m. SiO bandheads are seen in the range 4.0 and jim (this structure 1s discussed for cool stars in detail by Aringer et al.," Although the shorter wavelength feature is normally centred at shorter wavelengths in the $\,$ $\,$ $\,\mu$ m range, it appears here superimposed on broad-band molecular absorption from gaseous SiO, whose absorption minimum is seen around $\,\mu$ m. SiO bandheads are seen in the range 4.0 and $\mu$ m (this structure is discussed for cool stars in detail by Aringer et al."13 1999)., 1999).14 The other very deep molecular absorption bands in the A 2.5 to jm region can be aseribed to H2O. In this regime the spectrum is very similar to synthetic spectra of K and M giants and supergiants (Decin et al.," The other very deep molecular absorption bands in the $\lambda$ 2.5 to $\,\mu$ m region can be ascribed to $_2$ O. In this regime the spectrum is very similar to synthetic spectra of K and M giants and supergiants (Decin et al."15 1997; Tsuji et al., 1997; Tsuji et al.16 1997): comparison shows that specifically H»O is prominent in IRAS 3004., 1997); comparison shows that specifically $_2$ O is prominent in IRAS $-$ 3004.17 Taken together. the solid-state and molecular features indicate that IRAS 3004 is an oxygen-rich high mass-loss star.," Taken together, the solid-state and molecular features indicate that IRAS $-$ 3004 is an oxygen-rich high mass-loss star."18 Although IIL| ts seen at A j/m. other fine structure lines are not prominent. the feature at A jim being an artifact of the calibration (priv.," Although II] is seen at $\lambda$ $\,\mu$ m, other fine structure lines are not prominent, the feature at $\lambda$ $\,\mu$ m being an artifact of the calibration (priv."19 comm., comm.20 LLutz and KKunze)., Lutz and Kunze).21Reduction Coude. version 2).,"Reduction Guide, version 2)."22 The two vields cousisteut results. particularly on the flare profile.," The two yields consistent results, particularly on the flare profile."23 Since the standard oue viclds sliehtIv better statistics in the X-ray spectrin. we will present it below.," Since the standard one yields slightly better statistics in the X-ray spectrum, we will present it below."24 After standard screcuing. the net exposure times are 37.1 ks aud 25.9 ksec for the CIS aud SIS detectors. respectively.," After standard screening, the net exposure times are 37.4 ks and 25.9 ksec for the GIS and SIS detectors, respectively."25 The source counts were extracted from a circular region of 3.5 and 5.0 arcium radius for SIS aud CIS. respectively.," The source counts were extracted from a circular region of 3.5 and 5.0 arcmin radius for SIS and GIS, respectively."26 The background counts were estimated frou the off-source reeion at the same off-axis angle with same area for cach of CUS detectors. aud from the source subtracted reeion of the same clip of CCD for each of the SIS detectors.," The background counts were estimated from the off-source region at the same off-axis angle with same area for each of GIS detectors, and from the source subtracted region of the same chip of CCD for each of the SIS detectors."27 The background accounts for about 5 perceut 6 total counts both for the SIS aud CUS., The background accounts for about 5 percent of total counts both for the SIS and GIS.28" The average uct source count rates. after correcting for the background. are L7O40.003. O.598+0.001. L.009E0.007 aud O.820+40.005 ets + for (152, GIS3. SISO aud 9151. respectively."," The average net source count rates, after correcting for the background, are $\pm$ 0.003, $\pm$ 0.004, $\pm$ 0.007 and $\pm$ 0.005 cts $^{-1}$ for GIS2, GIS3, SIS0 and SIS1, respectively."29 Light curves were extracted for the source and vackeround for cach detector., Light curves were extracted for the source and background for each detector.30 For both CIS detectors. i6 backerouncd count rate is nearlv constant during the observation. therefore. an average count rate ds used to estimate the background level.," For both GIS detectors, the background count rate is nearly constant during the observation, therefore, an average count rate is used to estimate the background level."31 For the SIS detectors. ιο extracted background rate secs correlated with the source due to the contamination of the ACN.," For the SIS detectors, the extracted background rate seems correlated with the source due to the contamination of the AGN."32 Therefore. it is only an upper limit to the true backeround. aud is used ouly for spectral analysis.," Therefore, it is only an upper limit to the true background, and is used only for spectral analysis."33 Since simaller extraction radii in the real sky are used for SIS detectors. the fraction of backeround light. thus. is estimated to be zinaller than in the CUS case.," Since smaller extraction radii in the real sky are used for SIS detectors, the fraction of background light, thus, is estimated to be smaller than in the GIS case."34 We will ignore the backerouud contribution to the SIS couutaate during the light curve analysis., We will ignore the background contribution to the SIS count-rate during the light curve analysis.35 The X-ray spectra were rebined to at least 25 couuts per each biu., The X-ray spectra were rebined to at least 25 counts per each bin.36 For the SIS spectrum. the response niatrices appropriate for the date of the observation (thus accounting for decline of the energv resolution as a function of time) were made using the scriptsisirinag.," For the SIS spectrum, the response matrices appropriate for the date of the observation (thus accounting for decline of the energy resolution as a function of time) were made using the script."37 For the GIS spectrum. the 1991 response matrices andgisde4rinf ) were adopted.," For the GIS spectrum, the 1994 response matrices and ) were adopted."38 Ancillary response files were made 0.for each detector usingesceaarf., Ancillary response files were made for each detector using.39 The ASCAÀ data preparation and the spectral aualvsis were performed using version 1.1 of the NSELECT package aud version 10.01 of NSPEC., The ASCA data preparation and the spectral analysis were performed using version 1.4 of the XSELECT package and version 10.01 of XSPEC.40 Since the efficiency of SIS detectors has decreased. due to the radiation damage aud the current calibration files does not account for this. SIS spectra ouly above 0.8 keV are used.," Since the efficiency of SIS detectors has decreased due to the radiation damage and the current calibration files does not account for this, SIS spectra only above 0.8 keV are used."41 The GIS spectra below 0.8 keV are not well calibrated aud will be uot used in the spectral fit., The GIS spectra below 0.8 keV are not well calibrated and will be not used in the spectral fit.42 The X- spectra in the full ASCAÀ band cannot be adequately described. by au absorbed power-law with a \?/d.of= 1058/921. which is accepted at a probability of only 110 ?.," The X-ray spectra in the full ASCA band cannot be adequately described by an absorbed power-law with a $\chi^2/d.o.f=1058/924$ , which is accepted at a probability of only 1 $^{-3}$."43 There ave systematic deviations at low cucreics., There are systematic deviations at low energies.44 Iu addition the fitted cola density 141.2 1029 73° is sienificautl: lower than the galactic value (1.5 1029 7)., In addition the fitted column density $\pm 1.2 $ $^{20}$ $^{-2}$ is significantly lower than the galactic value (4.5 $^{20}$ $^{-2}$ ).45 Iu order to see if this is due to soft N-rav excess. which was noticed in the Cdnea spectra (Remillard et al.," In order to see if this is due to soft X-ray excess, which was noticed in the Ginga spectrum (Remillard et al."46 1992). we initially fitted the spectra above 2.0 keV. Sinele power-law with the Galactic absorption provides a good fit to the joint CIS and SIS spectra 7 /d.o.f=631/636).," 1992), we initially fitted the spectrum above 2.0 keV. Single power-law with the Galactic absorption provides a good fit to the joint GIS and SIS spectra $\chi^2/d.o.f$ =631/636)."47 The best fitted photon index (P.—2.20!2 WoL is sheltly flatter iu the previous fit (D—2.25us)., The best fitted photon index $\Gamma=2.20_{-0.04}^{+0.02}$ ) is slightly flatter than the previous fit $\Gamma=2.25_{-0.03}^{+0.02}$ ).48 This spectral iudex natches well the oue obtained bv Leighlv et al. (, This spectral index matches well the one obtained by Leighly et al. (491999) or 1997 observation. suggesting no significant variation oei the spectral iudex between the two observations.,"1999) for 1997 observation, suggesting no significant variation in the spectral index between the two observations."50 Extrapolating this fif to low energies shows exceesses nm je soft N-rav band (Fie., Extrapolating this fit to low energies shows excesses in the soft X-ray band (Fig.51" 1). particularly below 1.2 keV. The excess is luger in the CIS spectra than iu the SIS aeones, and also larger in the SISO than iu the SISL. possibly xdicating the decreasing efficiency. of SIS already evident oei the cnereies just below 1.2 keV. If the soft excesses are modeled with black body emission. the best fit vields a kT=0.22+0.02 keV and a normalization 3.1!-410 ."," 1), particularly below 1.2 keV. The excess is larger in the GIS spectra than in the SIS ones, and also larger in the SIS0 than in the SIS1, possibly indicating the decreasing efficiency of SIS already evident in the energies just below 1.2 keV. If the soft excesses are modeled with black body emission, the best fit yields a $\pm$ 0.02 keV and a normalization $3.4_{-1.0}^{+1.3}\times$ $^{-5}$."52 The latter corresponds to a flux in (.8-2 keV flux of 21<10 22 eres tem 7., The latter corresponds to a flux in 0.8-2 keV flux of $\times$ $^{-12}$ ergs $^{-1}$ $^{-2}$.53 Though this fit is better than the sinele power-law fit bv A\y?=31. however. it is still statistically acceptable ouly at probability. ον/d.o.f.=1027/923).," Though this fit is better than the single power-law fit by $\Delta54\chi^2$ =31, however, it is still statistically acceptable only at probability $\chi^2/d.o.f.$ =1027/923)."55 After carefully exanuinius the residuals. we find that counts— in— the SIS detector is significantly lower than these of CIS at cucrey below 1.15 keV. This most likely is duc to the degeneration of the SIS sensitivity at low energies.," After carefully examining the residuals, we find that counts in the SIS detector is significantly lower than these of GIS at energy below 1.15 keV. This most likely is due to the degeneration of the SIS sensitivity at low energies."56" Iu fact. the ft is acceptable (926/8091. P,.=0.22) when the SIS data below 1.2 keV were ignored."," In fact, the fit is acceptable (926/894, $P_r$ =0.22) when the SIS data below 1.2 keV were ignored."57 This fit vields au kT=0.13|a keV and a normalization |m 10!., This fit yields an $_{-0.02}^{+0.03}$ keV and a normalization $_{-0.53}^{+1.10}$ $^{-4}$.58 The photon iudex for this fit is 005.2 similar to that derived for fittiug 2-10 keV spectrum.," The photon index for this fit is $_{-0.03}^{+0.02}$, similar to that derived for fitting 2-10 keV spectrum."59" Receuth, οDBrien et al. ("," Recently, O'Brien et al. ("602000) fouud that the soft excess extends up to 32 keV from their uch higher quality NATL spectrum and can be modeled as multiple temperature blackbody emission.,2000) found that the soft excess extends up to 3 keV from their much higher quality XMM spectrum and can be modeled as multiple temperature blackbody emission.61 The spectral slope of the power law conrponeut is 0.9. filly consistent with those fouud im other Sevtert 1 galaxies.," The spectral slope of the power law component is 0.9, fully consistent with those found in other Seyfert 1 galaxies."62 The steep hard X-ray component found iu the ASC'A προσ could be due to the contamination of the spectroscopically unresolved soft N-xav excess iu the ASCA 2-10 keV biu., The steep hard X-ray component found in the ASCA spectrum could be due to the contamination of the spectroscopically unresolved soft X-ray excess in the ASCA 2-10 keV band.63 No iron Kk line is detectable with the ASCA data., No iron K line is detectable with the ASCA data.64 Au upper nuit of equivalent width for a narrow Caussian line at 5.5 or 5.7 keV (6. band 6.7 keV. in the source rest frame} is LOcV. consistent with NMM result (O'Brien et al 2000).," An upper limit of equivalent width for a narrow Gaussian line at 5.5 or 5.7 keV (6.4 and 6.7 keV in the source rest frame) is 40 eV, consistent with XMM result (O'Brien et al 2000)."65 Fig., Fig.66" 2a shows the combined CIS aud SIS light curves for the count rates in 015-160 keV aud 0.6-10 keV bands. respectively,"," 2a shows the combined GIS and SIS light curves for the count rates in 0.8-10 keV and 0.6-10 keV bands, respectively."67 A large energetic flare started shortly after the observation., A large energetic flare started shortly after the observation.68 The count rate increased from 0.51 c 0.02 cts/s to L104 0.0L cts/s in about 2000 sec aud then decreased to 0.5048 0.02 cts/s in about 3500 sec., The count rate increased from 0.54 $\pm$ 0.02 cts/s to $\pm$ 0.04 cts/s in about 2000 sec and then decreased to $\pm$ 0.02 cts/s in about 3500 sec.69 Since there are observation gaps in between. the real variations nuelt be even faster.," Since there are observation gaps in between, the real variations might be even faster."70 We have examined possible contanunation sources., We have examined possible contamination sources.71 The background count rates are stable and at only a few percent level of the source count rates durimg the observation., The background count rates are stable and at only a few percent level of the source count rates during the observation.72 Concermine the dmupact of particle backeround. we have applied strict screcuing criteria to the CIS data (refer to The ASCA Data Reduction Caiide. version 2). the flare structure remained.," Concerning the impact of particle background, we have applied strict screening criteria to the GIS data (refer to The ASCA Data Reduction Guide, version 2), the flare structure remained."73 The source position measured in the ASCA CUS image is 05 59 11.1: -50 27 26.1 (equinox 2000). which has an offset of An=1:95 aud Aé=0.39' from the NED position of PISS 0558-501.," The source position measured in the ASCA GIS image is 05 59 41.1: -50 27 24.1 (equinox 2000), which has an offset of $\Delta\alpha=1.58'$ and $\Delta\delta=0.39'$ from the NED position of PKS 0558-504."74 ITowever. after correcting for a teniperature dependent deviation of the attitude solution (Cotthelf et," However, after correcting for a temperature dependent deviation of the attitude solution (Gotthelf et"75each of the faces except 2=0 Gvhich represents the photosphere].,each of the faces except $z=0$ (which represents the photosphere).76 To satisfy this it is assunued that the tangential compoucntfs of A are zero on cach of the faces. except 2=0.," To satisfy this it is assumed that the tangential components of ${\bf A}$ are zero on each of the faces, except $z=0$."77 In addition. the normal derivative of fi6 normal component of A is set to zero on each of these faces.," In addition, the normal derivative of the normal component of ${\bf A}$ is set to zero on each of these faces."78 If Equatio- (5)) is solved subjec to the above boundary conditions it is straight forward to show that the solution will have V.A=) evervwhere within the domain (Finnef... 199D.," If Equation \ref{eq:vectff}) ) is solved subject to the above boundary conditions it is straight forward to show that the solution will have $ \nabla . {\bf A} = 0$ everywhere within the domain (Finn, 1994)."79 Thus the initial condition 1s a potential fiek associated with the iuposed normal feld on the boundary with the choice of the Coulomb eaueo (Ν.Α= 0)., Thus the initial condition is a potential field associated with the imposed normal field on the boundary with the choice of the Coulomb gauge $\nabla . {\bf A} = 0$ ).80 The initial potential feld is cousructed from the first observed inagnetoerai at 19.12.05 UT on 1010 December 1996., The initial potential field is constructed from the first observed magnetogram at 19.12.05 UT on $^{th}$ December 1996.81 Tn Figure 5 zu illustration of the field lines of he potential ficld used as the initial couditiou can ρα seen., In Figure \ref{fig:fig9} an illustration of the field lines of the potential field used as the initial condition can be seen.82 From these field. linesit is clear that the decaying active region has a simple bipolar form., From these field lines it is clear that the decaying active region has a simple bipolar form.83 The field lines connecting between the positive flux (solid contours) aud neeaOs:ive fux (dash contours oru semi-circular loops., The field lines connecting between the positive flux (solid contours) and negative flux (dashed contours) form semi-circular loops.84 Iu Figure 6((a) the illustration shows the fick ines for the non-linear fox“o-free fell after davs of evolution., In Figure \ref{fig:fig10}( (a) the illustration shows the field lines for the non-linear force-free field after 4 days of evolution.85 This Sgure can be compared to Figure G(( j) where the correspouding field lines for a potential field. deποσα from the sale nori field component on the base are alotted.," This figure can be compared to Figure \ref{fig:fig10}( (b) where the corresponding field lines for a potential field, deduced from the same normal field component on the base are plotted."86 In each case the sarting point for the field lines is taken on the base within he positive flux region., In each case the starting point for the field lines is taken on the base within the positive flux region.87 On colmparing the two images it is clear that there are many differences iu the counectivivy ancl structure of the field., On comparing the two images it is clear that there are many differences in the connectivity and structure of the field.88 The main cifferaices occur low down along the PIL )etweecn the two nain polaritics., The main differences occur low down along the PIL between the two main polarities.89 Tere the fiek lines of the non-potential field have a uuch more sheared sructure as a result of energy and helicity beiug injected alce the field lines by he small scale convective molonis., Here the field lines of the non-potential field have a much more sheared structure as a result of energy and helicity being injected along the field lines by the small scale convective motions.90 Another major difference is that for the field LBies lying at f1ο southern end. the counectivitv of the feld is verv differen from that of the xotential field.," Another major difference is that for the field lines lying at the southern end, the connectivity of the field is very different from that of the potential field."91 This is becaise the counectivity within the non-linear force-free simulation is initially defined at the start o the sinulatiou aud js preserved throughout the «λαο. (except where numerical diffusion beconmies large)., This is because the connectivity within the non-linear force-free simulation is initially defined at the start of the simulation and is preserved throughout the simulation (except where numerical diffusion becomes large).92 The larecs feld lines within the simulation are oulv slightly cüffereut as the simall scale) convective motions have not been able to inject helicity along the full length of these field lines during the time period of the simulation., The largest field lines within the simulation are only slightly different as the small scale convective motions have not been able to inject helicity along the full length of these field lines during the time period of the simulation.93 Iun Figure τα). the evapi of total magnetic enerev stored within the coronal field cau be seen as a function of timc., In Figure \ref{fig:fig5}( (a) the graph of total magnetic energy stored within the coronal field can be seen as a function of time.94 The dotted line is for the nou-linear force-free field siuulation. while the solid line is for a poteutial ποια. deduced frou the same normal field coniponent ou the lower boundary as that of the nou-incar force-free field (see Section 3.2).," The dotted line is for the non-linear force-free field simulation, while the solid line is for a potential field deduced from the same normal field component on the lower boundary as that of the non-linear force-free field (see Section 3.2)."95 Both values are initially equal to, Both values are initially equal to96conrpared to the uuuerical solutions iu Figure d.,compared to the numerical solutions in Figure \ref{t_sunset_vs_epsilon}.97 For intermediate recirculation efücienceies. €z23. the sunset temperature has a peak.," For intermediate recirculation efficiencies, $\epsilon \approx 3$, the sunset temperature has a peak."98 This is due to advection of heat downstream Which becomes iore efficient as e increases. heating the sunset terminator.," This is due to advection of heat downstream, which becomes more efficient as $\epsilon$ increases, heating the sunset terminator."99 However. when e becomes too large. heat is distributed uniformly aloug a eiven longitude. causing the temperature to decrease agai. hence the peak at termediate e.," However, when $\epsilon$ becomes too large, heat is distributed uniformly along a given longitude, causing the temperature to decrease again, hence the peak at intermediate $\epsilon$."100 By combining the euergv transport model cescribed above with a geometrical model of the plauct’s wotions (both orbital aud rotational). we now produce model phase variations for an cutire planet.," By combining the energy transport model described above with a geometrical model of the planet's motions (both orbital and rotational), we now produce model phase variations for an entire planet."101 We model the planet as a erid of gas parcels: 10 longitude aud 20 latitude evid points., We model the planet as a grid of gas parcels: 40 longitude and 20 latitude grid points.102 We run the calculation for 3 orbital periods. with 1000 time steps per orbit.," We run the calculation for 3 orbital periods, with 1000 time steps per orbit."103 We adopt a perfectly edec-on orbital geometry in all cases. but otherwise use the appropriate orbital parameters (a. c. (ο). planetary radius ΟΠ). aud. stellar parameters (2... Ta. logy. [Fe/T).," We adopt a perfectly edge-on orbital geometry in all cases, but otherwise use the appropriate orbital parameters $a$, $e$, $\omega$ ), planetary radius $R_{p}$ ), and stellar parameters $R_{*}$, $T_{\rm eff}$, $\log g$, [Fe/H])."104 We can run the caleulatious for arbitrary waveleneths but only present here the leht curves for TRAC chamucl | (8 sau)., We can run the calculations for arbitrary wavelengths but only present here the light curves for IRAC channel 4 (8 $\mu$ m).105 Since ours is a one-laver model. the shape of the phase variations is essentialv unchauged if one adopts a different wavehbaud.," Since ours is a one-layer model, the shape of the phase variations is essentialy unchanged if one adopts a different waveband."106 The only free model parameters are lL. Taq. aud wage in practice we set cA=0 since the albedo does uot significantly affect the of the thermal phase varlatious and it appears that hot Jupiters have low albedos (Roweetal.2008:Cowan&Agol2010.andref-erencestherein).," The only free model parameters are $A$, $\tau_{\rm rad}$, and $\omega_{\rm rot}$; in practice we set $A=0$ since the albedo does not significantly affect the of the thermal phase variations and it appears that hot Jupiters have low albedos \citep[][and references therein]{Rowe_2008, Cowan_2010}."107 All stelhuü and planetary data are taken from exoplauct.cu. maintained by Jean Schneider: using uunubers from exoplanets.org did not perceptibly chauge our results.," All stellar and planetary data are taken from exoplanet.eu, maintained by Jean Schneider; using numbers from exoplanets.org did not perceptibly change our results."108 When the stellar data are not available. we have asstuned typical parameters for the appropriate spectral class. aud solar mictallicity.," When the stellar data are not available, we have assumed typical parameters for the appropriate spectral class, and solar metallicity."109 Iusofar as we are ouly concerned with the broadband mid-IR. brightuesses of the stars. our results should not depend sensitively on the input stellar parameters.," Insofar as we are only concerned with the broadband mid-IR brightnesses of the stars, our results should not depend sensitively on the input stellar parameters."110 Using the stars Tg. logg aud [Fe/TI]. we use the PHOENIX/NextGen stellar spectrum erids (auschildtctal.1999) to determine their brightness temperatures at the observed frequencies.," Using the stars' $T_{\rm eff}$, $\log g$ and [Fe/H], we use the PHOENIX/NextGen stellar spectrum grids \citep{Hauschildt_1999} to determine their brightness temperatures at the observed frequencies."111 For cach svaveband. we determine the ratio of the stellar flix to the blackbody flux at that eid stars Tig.," For each waveband, we determine the ratio of the stellar flux to the blackbody flux at that grid star's $T_{\rm eff}$."112 We then apply this factor to the Tig of the actual observed star., We then apply this factor to the $T_{\rm eff}$ of the actual observed star.113 There are many computational shortcuts that oue cau use with this analytic model., There are many computational shortcuts that one can use with this analytic model.114 The orbits are treated as edee-on and the planetary obliquity is assumed to be zero (this is strictly true for the core: for the atimosphere it simply means that the equatorial jet-stream flows in the East-West direction). so the D.E. need ouly he solved at one latitude on the cay-side (c.g.. the equator) aud those day-side heating curves are casily adjusted for other latitudes via Ty.," The orbits are treated as edge-on and the planetary obliquity is assumed to be zero (this is strictly true for the core; for the atmosphere it simply means that the equatorial jet-stream flows in the East-West direction), so the D.E. need only be solved at one latitude on the day-side (e.g., the equator) and those day-side heating curves are easily adjusted for other latitudes via $T_{0}$."115 The D.E. can then be solved analytically ou the planets wielt-side., The D.E. can then be solved analytically on the planet's night-side.116" The observed flux ratio depends on a combination of orbital factors (e. 6). planetary factors (A. Taq. wu) and viewiug ecometry (we and a. the usual phase angele: a=0 at eclipse; a=x at transit),"," The observed flux ratio depends on a combination of orbital factors $a$, $e$ ), planetary factors $A$, $\tau_{\rm rad}$, $\omega_{\rm rot}$ ), and viewing geometry $\omega$ and $\alpha$, the usual phase angle: $\alpha=0$ at eclipse, $\alpha=\pi$ at transit)."117 We show schematically in Figure 5 how we combine the orbital. anetaryv and viewing factors to obtain discdntegrated iecnmal light curves.," We show schematically in Figure 5 how we combine the orbital, planetary and viewing factors to obtain disc-integrated thermal light curves."118 The top pauel simply shows the dlanet’s distance from its host star: the second pancl VArows the planets orbital angular velocity: the third xuiel shows the equilibrium temperature at the sub-y.cllay point (solid line) and the highest temperature ou 1e model plauet (dotted line)., The top panel simply shows the planet's distance from its host star; the second panel shows the planet's orbital angular velocity; the third panel shows the equilibrium temperature at the sub-stellar point (solid line) and the highest temperature on the model planet (dotted line).119 The fourth panel slows ιο total absorbed flux (solid line) and the total emitted Hux (dotted line)., The fourth panel shows the total absorbed flux (solid line) and the total emitted flux (dotted line).120 The fifth panel shows the planets ---Thuninated fraction. f£=$(11cosa).," The fifth panel shows the planet's illuminated fraction, $f = \frac{1}{2}(1+\cos\alpha)$."121 The bottom panel shows the planet/star flux ratio at 8 juu as seeu from Earth., The bottom panel shows the planet/star flux ratio at 8 $\mu$ m as seen from Earth.122 We start the calculations with all of the parcels at T— Jy. but the planet reaches a periodic equilibrium iu a couple e-foldiug times (a few τας).," We start the calculations with all of the parcels at $T = T_{0}$ , but the planet reaches a periodic equilibrium in a couple e-folding times (a few $\tau_{\rm rad}$ )."123 If the planet had no heat capacity. the dotted nes would perfectly track the solid lines in the third and fourth paucls of Figure 5.," If the planet had no heat capacity, the dotted lines would perfectly track the solid lines in the third and fourth panels of Figure 5."124 The effect of a non-zero plauctary leat capacity, The effect of a non-zero planetary heat capacity125orbits.,orbits.126 On the shorter time scales of a typical observation the hardness ratios in the low state appear to be nearly constant., On the shorter time scales of a typical observation the hardness ratios in the low state appear to be nearly constant.127 There is a general slight tendency for the hardness ratios to get smaller with increasing count rate., There is a general slight tendency for the hardness ratios to get smaller with increasing count rate.128 In the high state orbit 34] there are strong indications of a hardening of the spectrum when the source brightens., In the high state orbit 341 there are strong indications of a hardening of the spectrum when the source brightens.129 NLS] galaxies are generally characterized by very steep spectra in the soft energy band (Boller et al., NLS1 galaxies are generally characterized by very steep spectra in the soft energy band (Boller et al.130 1996)., 1996).131 From observations of Gliozzi et al. (, From observations of Gliozzi et al. (1322000) find a steep power law with T~3 in the 0.1—2.4 keV energy range: in the 0.6-10 keV band Vaughan et al. (,2000) find a steep power law with $\Gamma \sim 3$ in the $-$ 2.4 keV energy range; in the $-$ 10 keV band Vaughan et al. (1331999) obtain Γ=2.26+0.03.,1999) obtain $\Gamma = 2.26 \pm0.03$.134 The XMM-Newton data (O'Brien et al., The $-$ Newton data (O'Brien et al.135 2001) clearly show a strong soft excess below ~2 keV over a harder power law at higher energies., 2001) clearly show a strong soft excess below $\sim $ 2 keV over a harder power law at higher energies.136 The PN data with their outstanding signal to noise ratio and their wide bandpass are ideally suited for a detailed spectral study of the source., The PN data with their outstanding signal to noise ratio and their wide bandpass are ideally suited for a detailed spectral study of the source.137 For the spectral analysis we used the latest available response matrices (version 6.3) issued in December 2002., For the spectral analysis we used the latest available response matrices (version 6.3) issued in December 2002.138 We extracted single and double events with quality flag = 0 from a rectangular region of 30x30 RAW pixels around the source position., We extracted single and double events with quality flag = 0 from a rectangular region of $\times$ 30 RAW pixels around the source position.139 The region includes ~ of the source photons but avoids the gap between the detector chips., The region includes $\sim$ of the source photons but avoids the gap between the detector chips.140" The background was taken on the same chip at distances as close to the source position as possible. avoiding contamination,"," The background was taken on the same chip at distances as close to the source position as possible, avoiding contamination."141 With a count rate of 2 20 counts s! in the high state the PN detector. operated in Full Window mode. showed strong indications of pile-up. clearly apparent from the XMMSAS task epatplot.," With a count rate of $\gta$ 20 counts $^{-1}$ in the high state the PN detector, operated in Full Window mode, showed strong indications of pile-up, clearly apparent from the XMMSAS task $epatplot$."142 We therefore discarded photons from the innermost (typically 2x3) RAW pixels at the core of the point spread function from the spectral analysis., We therefore discarded photons from the innermost (typically $2\times3$ ) RAW pixels at the core of the point spread function from the spectral analysis.143 In Fig., In Fig.144" 5 we show the power law fit in the 2-10 keV energy range to the data of orbit 153 (E22.13€0.03;Vg=0.90/303 d.o.f with a galactic Nj,=4.4x10-"" cm7 )."," \ref{figure:powl} we show the power law fit in the $-$ 10 keV energy range to the data of orbit 153 $\Gamma = 2.13\pm0.03;145\chi_{\rm red}^2 = 0.90 / 303$ d.o.f with a galactic $_H = 4.4\times 10^{20}$ $^{-2}$ )."146 The fitted model is extrapolated to lower energies and the ratio between data and model. given in the lower panel. clearly demonstrates the presence of a large soft X-ray excess over the hard power law.," The fitted model is extrapolated to lower energies and the ratio between data and model, given in the lower panel, clearly demonstrates the presence of a large soft X-ray excess over the hard power law."147 The spectrum of appears to be a carbon copy of that of the NLSI galaxy PG 084424349 (Brinkmann et al., The spectrum of appears to be a carbon copy of that of the NLS1 galaxy PG 0844+349 (Brinkmann et al.148 2003) even with respect to the δις blue bump' seen in both objects (O'Brien et al., 2003) even with respect to the `big blue bump' seen in both objects (O`Brien et al.149 2001) and it is very similar to that of 1H 0419-577 (Page et al., 2001) and it is very similar to that of 1H 0419-577 (Page et al.150 2002) and the other NLS] galaxy Mrk 896 (Page et al., 2002) and the other NLS1 galaxy Mrk 896 (Page et al.151 2003) studied with XMM-Newton., 2003) studied with XMM-Newton.152 The upper limits given for an iron line are rather low (O'Brien et al., The upper limits given for an iron line are rather low (O'Brien et al.153 2001) and the soft banc spectral excess is far too broad to be fitted by a single black body component., 2001) and the soft band spectral excess is far too broad to be fitted by a single black body component.154 A multiple blackbody (in the soft band) plus a power law at higher energies provides acceptable fits to the data. however. the physical nature of these different components remains obscure.," A multiple blackbody (in the soft band) plus a power law at higher energies provides acceptable fits to the data, however, the physical nature of these different components remains obscure."155 While a model with two Comptonization components gives an accurate description of the spectra. two power law models require absorption in excess of the galactic value and yield slightly worse fits.," While a model with two Comptonization components gives an accurate description of the spectra, two power law models require absorption in excess of the galactic value and yield slightly worse fits."156 For example. for the above mentioned orbit 153 (see as well Tab.," For example, for the above mentioned orbit 153 (see as well Tab."157 2) we obtain an Nj=7.79x107 em™. Doon=3.28£0.08. F4=1.62£0.10 with a -=1.163/578 d.of..," 2) we obtain an $_H = 7.79\times10^{20}$ $^{-2}$, $\Gamma_{\rm soft}=3.28\pm0.08$, $\Gamma_{\rm hard}=1.62\pm0.10$ with a $\chi_{\rm red}^2 = 1.163 / 578$ d.o.f.,"158 values. which are representative for the other orbits as well.," values, which are representative for the other orbits as well."159 The relatively long RGS observation of orbit 84 provides a sufficient number of photons for an accurate fit., The relatively long RGS observation of orbit 84 provides a sufficient number of photons for an accurate fit.160 We have reprocessed the RGS data using XMMSAS version 5.3.3 and the RGS response matrices were created with the SAS package resrmfgen., We have reprocessed the RGS data using XMMSAS version 5.3.3 and the RGS response matrices were created with the SAS package $rgsrmfgen$ .161 The spectral data were binned to contain at least 30 photons per energy channel., The spectral data were binned to contain at least 30 photons per energy channel.162 We fitted the RGS data with a single comp7T Comptonization model. available in Xspec (Titarchuk 1994). assuming galacticabsorption plus," We fitted the RGS data with a single $compTT$ Comptonization model, available in $Xspec$ (Titarchuk 1994), assuming galacticabsorption plus"1632.3-n Bok telescopes.,2.3-m Bok telescopes.164 We describe the results of these observations below., We describe the results of these observations below.165 The SPOL CCD hnagine/Spectropolarimetcr (Schunidtetal.1992a)— mounted ou the Steward Observatory 2.314 Dok telescope (INitt Peak. AZ) and the 1.51 Kuiper telescope BBieclow. AZ) was used to obtain spectropolarimetiy of SN 201110 over 10 welts.," The SPOL CCD Imaging/Spectropolarimeter \citep{schmidt92a} mounted on the Steward Observatory 2.3-m Bok telescope (Kitt Peak, AZ) and the 1.54 Kuiper telescope Bigelow, AZ) was used to obtain spectropolarimetry of SN 2011fe over 10 nights."166 We have grouped the 10 nights of observations into four Epochs in Table 1., We have grouped the 10 nights of observations into four Epochs in Table 1.167 Observatious covered aat a resolution of ~20 ((GO00 line 1 erating in first order. using a 571 «51 sslit and a Tova L3s blocking filter).," Observations covered at a resolution of $\sim$ 20 (600 line $^{-1}$ grating in first order, using a $\farcs$ $\times$ $\arcsec$ slit and a Hoya L38 blocking filter)."168 À rotatable senuachromatic halfwave plate was used to modulate incident polarization and a Wollaston priuu iu the collimated beam separated the orthogonally polarized spectra onto a thinned. autirefiection-coated 800 «1200 SITe CCD.," A rotatable semiachromatic half-wave plate was used to modulate incident polarization and a Wollaston prism in the collimated beam separated the orthogonally polarized spectra onto a thinned, anti-reflection-coated $\times$ 1200 SITe CCD."169 The cfficieney of the wave plate as a function of waveleneth is measured by inserting a fully-polarizing Nicol prin iuto the beam above the slit., The efficiency of the wave plate as a function of wavelength is measured by inserting a fully-polarizing Nicol prism into the beam above the slit.170 À series of four separate exposures that xuuple 16 orientations of the wave plate vields two independent. background-subtraeted measures of each of the normalized luecar Stokes parameters. q aud ," A series of four separate exposures that sample 16 orientations of the wave plate yields two independent, background-subtracted measures of each of the normalized linear Stokes parameters, $q\/$ and $u\/$."171Each night. several such sequences of observations of SN 2011fe were obtained aud combined. with the weighting of the individual measurements based on photon statistics.," Each night, several such sequences of observations of SN 2011fe were obtained and combined, with the weighting of the individual measurements based on photon statistics."172 The polavization results for September 15 aud 16 were iudistinguishable. so they were combined to vield the final result for the third observational epoch.," The polarization results for September 15 and 16 were indistinguishable, so they were combined to yield the final result for the third observational epoch."173" Similarly, the polarization spectra from the six observations obtained between September 26 and October 6 (Epoch 1) were averaged together. since we detected no inter-nieht variations in (Q or C over this time period."," Similarly, the polarization spectra from the six observations obtained between September 26 and October 6 (Epoch 4) were averaged together, since we detected no inter-night variations in $Q$ or $U$ over this time period."174 We confirmed that the instrumental polarization of SPOL mounted on the Dok and dEuiper telescopes is nmch less than through observations of the unpolarized standard stars 1211 and WD 212311 (Schinidtetal.1992b) during each epoch., We confirmed that the instrumental polarization of SPOL mounted on the Bok and Kuiper telescopes is much less than through observations of the unpolarized standard stars $^{\circ}$ 4211 and HD 212311 \citep{schmidt92b} during each epoch.175 The linear polarization position angle on the sky (0) was determined bv observing the interstellar polarization standards Illtuer 960 and VI (νο #112 (Sclunidtetal.19905210) during all epochs., The linear polarization position angle on the sky $\theta\/$ ) was determined by observing the interstellar polarization standards Hiltner 960 and VI Cyg 12 \citep{schmidt92b} during all epochs.176 Additional observations of the polarization standard stars 59°389 and 61°106 were nade during the third epoch (Table 1)., Additional observations of the polarization standard stars $^{\circ}$ 389 and $^{\circ}$ 106 were made during the third epoch (Table 1).177 The adopted correction from the instrmucutal to the standi equatorial fraane for 0 for all epochs was determunc: from the average position angle offset of Wiltner 960 anc VI Cre, The adopted correction from the instrumental to the standard equatorial frame for $\theta\/$ for all epochs was determined from the average position angle offset of Hiltner 960 and VI Cyg 12.178 Differences between the measured ane expected polarization position aueles were <073 for al of the standard stars., Differences between the measured and expected polarization position angles were $< 0\farcs3$ for all of the standard stars.179 During the first epoch. two field) stars within ~2! oof SN 201fc (2MASS J11031367|5115131 ane 2NTASS. J11025112]1Galactic5116288). were measured to check for siguificaut interstellar polarization (ISP) along the line-of-sight to the SN.," During the first epoch, two field stars within $\sim$ of SN 2011fe (2MASS J14031367+5415431 and 2MASS J14025413+5416288) were measured to check for significant Galactic interstellar polarization (ISP) along the line-of-sight to the SN."180" These stars vicldec a consistent estimate for Calactic ISP. with Pawo= at Ü=Ill—7 for 2\0ASS J11031367|5115131 aud Pag=O1640.0 at 0=109""t6"" for 2MASS J1102511315116288. assiuniug that Àj,,,;. the waveleugth where the interstellar polarization is at a maxi (Pig) is5550À.."," These stars yielded a consistent estimate for Galactic ISP, with $P_{max} = 0.11 \pm 0.03$ at $\theta = 114^{\circ} \pm 7^{\circ}$ for 2MASS J14031367+5415431 and $P_{max} = 0.16 \pm 0.03$ at $\theta = 109^{\circ} \pm1816^{\circ}$ for 2MASS J14025413+5416288, assuming that $\lambda_{max}$, the wavelength where the interstellar polarization is at a maximum $P_{max}$ ) is."182 The results for the field stars were averaged aud ων=0.134 at 0=112° was adopted as the Galactic ISP in the sighthue to SN 2011te., The results for the field stars were averaged and $P_{max} = 0.13$ at $\theta = 112^{\circ}$ was adopted as the Galactic ISP in the sightline to SN 2011fe.183 This low value for the Galactic ISP is consistent witli the high Calactic latitude of MIOL aud the very low estimated amount of extinction for the supernova., This low value for the Galactic ISP is consistent with the high Galactic latitude of M101 and the very low estimated amount of extinction for the supernova.184 The polarization spectra of SN 20111ο have been corrected for this level of Galactic ISP assiuniug that it is fit well by a Serkowski law (Willàugetal.1980:Serkowski.\lath-ewson.," The polarization spectra of SN 2011fe have been corrected for this level of Galactic ISP assuming that it is fit well by a Serkowski law \citep{wilking80,serkowski}."185&Ford 1975).. No estimate or correction for ISP within ΑΠΟ at the location of SN 2011fe has been mace (although see 833)., No estimate or correction for ISP within M101 at the location of SN 2011fe has been made (although see 3).186 Our reported values for the degree of polarization. 2. have been corrected for statistica bias Den(Wardle&I&rouberg1971).," Our reported values for the degree of linear polarization, $P\/$, have been corrected for statistical bias \citep{wardle74}."187. Our sequence of spectra are shown in the top pane ofFigure 1l.. displaviug the emergeuce of absorption features typical of SNe Ia. The contiuuu cussion is polarized with the red waveleueths wore highly poluizec than the blue waveleugths at carly epochs. reaching up to ~O.1%..," Our sequence of spectra are shown in the top panel ofFigure \ref{fig:spec-seq}, displaying the emergence of absorption features typical of SNe Ia. The continuum emission is polarized with the red wavelengths more highly polarized than the blue wavelengths at early epochs, reaching up to $\sim$."188 The polarization of the red coutiuuua THOOA)) exhibits a slight decrease with time. from about down to0.2%.. while contimmun polarization in the irange mereases from undetected up to," The polarization of the red continuum ) exhibits a slight decrease with time, from about down to, while continuum polarization in the range increases from undetected up to."189 The polarization of absorption lues is clearly present in blueshifted Si A6355À aabsorptiou. and it changes markedly with tine.," The polarization of absorption lines is clearly present in blueshifted Si $\lambda$ absorption, and it changes markedly with time."190 This lue polarization of SiΗ is shown in velocity space in Figure 2.., This line polarization of Si is shown in velocity space in Figure \ref{fig:si2-vel}.191 Before παπα at Epoch 1. Sii1 AG355A sshows polarization at the same position angle(PA) as the continuum. but is roughlv stronecr than the adjacent continuum in polarization degree.," Before maximum at Epoch 1, Si $\lambda$ shows polarization at the same position angle (PA) as the continuum, but is roughly stronger than the adjacent continuum in polarization degree."192 In the subsequent two epochs near maxiuun (Epochs 2 aud 3). however. Si A6355À aabsorptiou has ~0.2% polarization than the contiuuuu. and the absorption-line PA changes by about," In the subsequent two epochs near maximum (Epochs 2 and 3), however, Si $\lambda$ absorption has $\sim$ polarization than the continuum, and the absorption-line PA changes by about"193compatible with that observed by Fermi LAT.,compatible with that observed by Fermi LAT.194 The discussion about the SSC from the ES scenario in was also restricted to noting that the SSC peak frequency may be in the GeV range for reasonable parameter values., The discussion about the SSC from the ES scenario in was also restricted to noting that the SSC peak frequency may be in the GeV range for reasonable parameter values.195 Here we have shown that a reasonable set of parameters can be found that also implies a flux level at | GeV compatible with the one observed by Fermi LAT., Here we have shown that a reasonable set of parameters can be found that also implies a flux level at 1 GeV compatible with the one observed by Fermi LAT.196 Moreover. we have considered two additional scenarios (1.," Moreover, we have considered two additional scenarios (1."197 and 3.)., and 3.).198 We have shown that scenarios 2. (, We have shown that scenarios 2. (199SSC) and 4.,SSC) and 4.200 are viable explanations of the observed tail for a burst located at z~0.1., are viable explanations of the observed tail for a burst located at $z\sim 0.1$.201 To reproduce the high energy tail in a delayed IS scenario. the lately emitted shells should have a time variability of about | ms and a Lorentz factor of about F=300.," To reproduce the high energy tail in a delayed IS scenario, the lately emitted shells should have a time variability of about $1$ ms and a Lorentz factor of about $\Gamma=300$."202 In the ES shock scenario. the high energy tail can be explained by assuming a flat spectrum. Le. p=2.05. and that the short GRB is powered by a fireball with ar isotropic energy of about 10°! erg. expanding in an ISM with density ?=5 em7*.," In the ES shock scenario, the high energy tail can be explained by assuming a flat spectrum, i.e. $p=2.05$, and that the short GRB is powered by a fireball with an isotropic energy of about $10^{51}$ erg, expanding in an ISM with density $n=5$ $^{-3}$."203 These values of the parameters are order-of-magnitude estimates due to the uncertainties in the early-time afterglow flux. which was not observed for this burst.," These values of the parameters are order-of-magnitude estimates due to the uncertainties in the early-time afterglow flux, which was not observed for this burst."204 In particular. the fast cooling conditior (fio22.5 8). which is reasonable to expect at the early times we consider here. depends linearly on the chosen value of12 anc almost linearly on the early-time afterglow flux value.," In particular, the fast cooling condition $t_{cool}\gtrsim 2.5$ s), which is reasonable to expect at the early times we consider here, depends linearly on the chosen value of $n$ and almost linearly on the early-time afterglow flux value."205 Equating Eq. (20)), Equating Eq. \ref{prima}) )206 to Eq. (21)).," to Eq. \ref{primac}) ),"207" indeed one finds that £4,«RF. so that a value of7 1n the lower end of the range of values expectec for short GRBs would require a higher value of Fj,.y to ensure that /,,;z2.5 scooling).. These estimates. however. are the most robust that can be derived. from the publicly available data."," indeed one finds that $t_{cool}\propto n F_{1 \rm keV}^{2/3}$, so that a value of $n$ in the lower end of the range of values expected for short GRBs would require a higher value of $F_{1 \rm keV}$ to ensure that $t_{cool}\gtrsim 2.5$ s. These estimates, however, are the most robust that can be derived from the publicly available data."208 They are also sufficient to show that a solution does indeed exist for a reasonable set of parameters. which ts the aim of this work.," They are also sufficient to show that a solution does indeed exist for a reasonable set of parameters, which is the aim of this work."209 We emphasize that scenarios 2. 3. and 4. which are related to the emission from a lately emitted shell (2) or from the ES deceleration phase (3 and 4). all offer a natural explanation of the observed temporal delay between the high energy tail and the main burst.," We emphasize that scenarios 2, 3, and 4, which are related to the emission from a lately emitted shell (2) or from the ES deceleration phase (3 and 4), all offer a natural explanation of the observed temporal delay between the high energy tail and the main burst."210 Moreover. scenario 2 (emission from a lately emitted shell) may be consistent with the steeply declining emission from an extended X-ray tail that has been observed in association with some short GRBs before 100 s after the trigger time," Moreover, scenario 2 (emission from a lately emitted shell) may be consistent with the steeply declining emission from an extended X-ray tail that has been observed in association with some short GRBs before 100 s after the trigger time"211value.,value.212 It does not change the predicted differential luminosity distribution., It does not change the predicted differential luminosity distribution.213 The critical difference. however. between the soft X-ray cooling-flow problem and the classic cooling-flow problem is that the latter requires a clear explanation for why X-ray cooling does not appear to be carried to completion.," The critical difference, however, between the soft X-ray cooling-flow problem and the classic cooling-flow problem is that the latter requires a clear explanation for why X-ray cooling does not appear to be carried to completion."214 It is difficult to find a relevant heating. mixing. or cooling time scale that would be comparable to the X-ray cooling time.," It is difficult to find a relevant heating, mixing, or cooling time scale that would be comparable to the X-ray cooling time."215 If the time scale for a given process is too short it will overwhelm the cooling-flow (n2 x). and if the time-scale is too long. it is dynamically unimportant (à= 0).," If the time scale for a given process is too short it will overwhelm the cooling-flow $\alpha=\infty$ ), and if the time-scale is too long, it is dynamically unimportant $\alpha=0$ )."216 Below. we discuss the proposed physical processes and whether they can account. both energetically and dynamically. for the missing soft X-ray luminosity.," Below, we discuss the proposed physical processes and whether they can account, both energetically and dynamically, for the missing soft X-ray luminosity."217 There are three requirements for additional heating mechanisms to be compatible with the observations., There are three requirements for additional heating mechanisms to be compatible with the observations.218 First. the total time averaged heating power. <P>. has to roughly cancel the radiative losses so that the expression. is near unity.," First, the total time averaged heating power, $<$ $>$, has to roughly cancel the radiative losses so that the expression, is near unity."219 The denominator in the expression varies among the clusters in our sample by four orders of magnitude. so the proposed heating process must operate on a variety of scales.," The denominator in the expression varies among the clusters in our sample by four orders of magnitude, so the proposed heating process must operate on a variety of scales."220 Second. the heating has to be distributed spatially throughout the cooling-flow volume to cancel cooling everywhere.," Second, the heating has to be distributed spatially throughout the cooling-flow volume to cancel cooling everywhere."221 Third. the process has to be self-regulating. so that the time scale for heating remains comparable to the cooling time for all clusters.," Third, the process has to be self-regulating, so that the time scale for heating remains comparable to the cooling time for all clusters."222 Time-dependent AGN outflow heating models have been considered by à variety of authors (e.g. Rosner&Tucker 1989.. Tabor&Binney1993.. Churazoval. 2001.. Brüggen&Kaiser 2001.. Quilis 2001.. Davidetal. 2001.. Nulsen 2002)).," Time-dependent AGN outflow heating models have been considered by a variety of authors (e.g. \citealt{rosner}, , \citealt{tabor}, \citealt{churazov}, \citealt{brueggen}, \citealt{quilis}, \citealt{david}, \citealt{nulsen3}) )."223 Buoyant bubbles carrying relativistic plasma appear to be à common phenomena in clusters with central AGNs., Buoyant bubbles carrying relativistic plasma appear to be a common phenomena in clusters with central AGNs.224 The thermal energy seems to be enough to heat cooling-flows through cosmic ray interactions and mechanical heating. but it is unclear whether this energy gets properly channeled into the cooling volume (e.g. Loewenstein.Zweibel.Begelman 1991.. Fabianetal. 2001)).," The thermal energy seems to be enough to heat cooling-flows through cosmic ray interactions and mechanical heating, but it is unclear whether this energy gets properly channeled into the cooling volume (e.g. \citealt{loewenstein}, \citealt{fabian3}) )."225 Note that it is essential that the heat be distributed evenly throughout the region which is thermally unstable., Note that it is essential that the heat be distributed evenly throughout the region which is thermally unstable.226 In addition these models must be made self-regulating to counteract cooling at a rate proportional to the mass deposition rate. and with periods of heating roughly as long as periods of cooling.," In addition these models must be made self-regulating to counteract cooling at a rate proportional to the mass deposition rate, and with periods of heating roughly as long as periods of cooling."227 Clearly. it requires a significant degree of fine-tuning.," Clearly, it requires a significant degree of fine-tuning."228 There is considerable thermal energy in the outer regions of clusters that can destroy any existing cooling-flow through electron thermal conduction (e.g. Tucker&Rosner 1983.. Stewartetal. 1984.. Bertschinger&Meiksin 1986)).," There is considerable thermal energy in the outer regions of clusters that can destroy any existing cooling-flow through electron thermal conduction (e.g. \citealt{tucker}, \citealt{stewart}, \citealt{bertschinger}) )."229 The size of cooling-flows are only a few electron mean free paths in the absence of magnetic fields., The size of cooling-flows are only a few electron mean free paths in the absence of magnetic fields.230 The critical question is to what level is conduction suppressed by tangled magnetic fields. an issue which continues to be debated theoretically (Chandran&Cowley1998.. Narayan&Medvedev 2001)).," The critical question is to what level is conduction suppressed by tangled magnetic fields, an issue which continues to be debated theoretically \citealt{chandran}, \citealt{narayan}) )."231 Observationally. conduction is suppressed by factors near 100 in identified cold fronts (Ettorietal.2002.. Markeviteh 2000.. Vikhlinin.Markevitch&Murray 2001)). Voigtetal.(2002).. Zakamska&N," Observationally, conduction is suppressed by factors near 100 in identified cold fronts \citealt{ettori}, \citealt{markevitch}, \citealt{vikhlinin}) ). \cite{voigt}, \cite{zakamska},"232arayan (2001).. Fabian.Voigt.&Morris(2002) have demonstrated that the heat flow from the outer regions of clusters with a small suppression (> 107!) in the Spitzer conductivity would appear to cancel radiative losses 1n many clusters., \cite{fabian5} have demonstrated that the heat flow from the outer regions of clusters with a small suppression $>$ $10^{-1}$ ) in the Spitzer conductivity would appear to cancel radiative losses in many clusters.233 The spatial distribution of the heating and overall energetic requirements appear to be satisfied by conduction models. but there is no explanation for why the cluster would cool to their current temperature distribution.," The spatial distribution of the heating and overall energetic requirements appear to be satisfied by conduction models, but there is no explanation for why the cluster would cool to their current temperature distribution."234 Since conduction suppresses temperature gradients by definition. this mechanism alone does not solve the dynamical problem presented here.," Since conduction suppresses temperature gradients by definition, this mechanism alone does not solve the dynamical problem presented here."235 Markevitch(2001) hàs show- that clusters previously thought to be fully relaxed. exhibi=a temperature fronts consistent with plasma exhibiting large bulk motions im the gravitational potential., \cite{markevitch2} has shown that clusters previously thought to be fully relaxed exhibit temperature fronts consistent with plasma exhibiting large bulk motions in the gravitational potential.236 This provides another source of energy that has not been dissipated and therefore leads to an increase of the cooling time above previous estimates (Gomezetal.2002)). so that the time scales for radiative cooling and dynamical relaxation may be similar.," This provides another source of energy that has not been dissipated and therefore leads to an increase of the cooling time above previous estimates \citealt{gomez}) ), so that the time scales for radiative cooling and dynamical relaxation may be similar."237 There is no reason for this process to be self-regulating. however. and we would expect a much larger difference in the temperature distributions. depending on each cluster’s merger history.," There is no reason for this process to be self-regulating, however, and we would expect a much larger difference in the temperature distributions, depending on each cluster's merger history."238 This explanation also requires a conspiracy of factors to both cancel radiative cooling in global energetics. and ensure that the mergers occur with a frequency that allows some cooling.," This explanation also requires a conspiracy of factors to both cancel radiative cooling in global energetics, and ensure that the mergers occur with a frequency that allows some cooling."239 Future numerical simulations may test this further. and presumably observations of cooling-flows at a different epoch would not show the same effects.," Future numerical simulations may test this further, and presumably observations of cooling-flows at a different epoch would not show the same effects."240 The radiative isobaric cooling-flow model assumes that all of the thermal energy Is released in X-rays at high temperatures., The radiative isobaric cooling-flow model assumes that all of the thermal energy is released in X-rays at high temperatures.241 There may. however. be additional contributions from other cooling processes.," There may, however, be additional contributions from other cooling processes."242 There are three main requirements. for additional cooling channels to explain. the observations. which are similar to. but slightly different from the heating requirements.," There are three main requirements for additional cooling channels to explain the observations, which are similar to, but slightly different from the heating requirements."243 The first ts that the total power in the coolant be comparable to the missing soft X-ray luminosity., The first is that the total power in the coolant be comparable to the missing soft X-ray luminosity.244 Any coolant with power. Pooofun. reduces the total X-ray emission by a factor. The second requirement is that the ratio a needs to have a temperature dependence consistent with Equation (3) or that the cooling channel is self-regulating in the same sense as the discussed heating models.," Any coolant with power, $P_{coolant}$, reduces the total X-ray emission by a factor, The second requirement is that the ratio $\frac{P_{coolant}}{L_{x}}$ needs to have a temperature dependence consistent with Equation (3) or that the cooling channel is self-regulating in the same sense as the discussed heating models."245 The third requirement is that the energy should be released with a similar spatial distribution to the lowest temperature X-rays., The third requirement is that the energy should be released with a similar spatial distribution to the lowest temperature X-rays.246 Begelman&Fabian(1990) and Fabianetal.(2001) discussed the possibility that hot electrons are cooled conductively by interfaces with cold clouds., \cite{begelman} and \cite{fabian3} discussed the possibility that hot electrons are cooled conductively by interfaces with cold clouds.247 This leads to emission in the UV where the cooling function ts the highest. and is consistent energetically with the large observed Ha luminosities (Heckmanetal.1989.. Crawfordetal. 1999)) of 1077 to 1077 ergs/s in cooling-flows.," This leads to emission in the UV where the cooling function is the highest, and is consistent energetically with the large observed $\alpha$ luminosities \citealt{heckman}, \citealt{crawford}) ) of $10^{42}$ to $10^{44}$ ergs/s in cooling-flows."248 However. by itself. this model does not explain the observed temperature distribution in the soft X-ray band. since high temperature electrons are cooled by this process as well.," However, by itself, this model does not explain the observed temperature distribution in the soft X-ray band, since high temperature electrons are cooled by this process as well."249 In addition. in such a picture highly charged ions should also impact the cloud interfaces. resulting in charge exchange. which produces copious soft X- line emission.," In addition, in such a picture highly charged ions should also impact the cloud interfaces, resulting in charge exchange, which produces copious soft X-ray line emission."250 The spatial distribution of Ha is remarkably similar to the coolest X-rays (Ettorietal. 2002)) and the total luminosity ismarginally sufficient to account for the missing, The spatial distribution of $\alpha$ is remarkably similar to the coolest X-rays \citealt{ettori}) ) and the total luminosity ismarginally sufficient to account for the missing251lack of detectable thermal emission from the disk. the best-fit power-law index (C=1.7) is consistent with recent Chandra and XMM-Newton results and similar to the low hard state observed in galactic BHBs (MeClintock Remillard 2004) The power-law spectrum of the ULX in NGC 3379 suggests that the emission is dominated by Compton up-scattering of soft disk photons in a optically thin corona.,"lack of detectable thermal emission from the disk, the best-fit power-law index $\Gamma=1.7$ ) is consistent with recent Chandra and XMM-Newton results and similar to the low hard state observed in galactic BHBs (McClintock Remillard 2004) The power-law spectrum of the ULX in NGC 3379 suggests that the emission is dominated by Compton up-scattering of soft disk photons in a optically thin corona."252 The variability in the light curve could arise from a partial eclipse or absorption by cooler material in the outer parts of the accretion disk., The variability in the light curve could arise from a partial eclipse or absorption by cooler material in the outer parts of the accretion disk.253 The slow rise and fall times m the light curve (see Fig., The slow rise and fall times in the light curve (see Fig.254 8). along with the lack of any variation in hardness ratio. suggest that the intensity variation 1s due to a partial eclipse of the extended coronal emission with a period of 8-10 hours.," 8), along with the lack of any variation in hardness ratio, suggest that the intensity variation is due to a partial eclipse of the extended coronal emission with a period of 8-10 hours."255 While variability on the scales of months to years is well known for ULXs. there are only a few published cases of periodic. variability on the time scale of hours. all of which are in late-type galaxies (Sugiho et al.," While variability on the scales of months to years is well known for ULXs, there are only a few published cases of periodic variability on the time scale of hours, all of which are in late-type galaxies (Sugiho et al."256 2001. Cireinus; Bauer 2001: MS] Liu et al.," 2001, Circinus; Bauer 2001; M51 Liu et al."257 2002: NGC 628: Liu et al., 2002; NGC 628; Liu et al.258 2005)., 2005).259 The ULX in NGC 3379 is the only known ULX in an early-type galaxy with possible periodic behavior in its light curve on the time scale of hours., The ULX in NGC 3379 is the only known ULX in an early-type galaxy with possible periodic behavior in its light curve on the time scale of hours.260 Orbital periods of 8-10 hr are very common for LMXBs (Verbunt 1993)., Orbital periods of 8-10 hr are very common for LMXBs (Verbunt 1993).261 Assuming that the secondary star is filling its Roche lobe and transferring mass to the primary. we can estimate the mass of the secondary.," Assuming that the secondary star is filling its Roche lobe and transferring mass to the primary, we can estimate the mass of the secondary."262 Using the expression for the Roche lobe radius from Paezynski (1967) and Kepler's law gives P=89(R»/R.(M./M») hr (Verbunt 1993)., Using the expression for the Roche lobe radius from Paczynski (1967) and Kepler's law gives $P=8.9(R_2/R_{\odot})(\Mo / M_2)$ hr (Verbunt 1993).263 For main sequence stars (Ro/R.)=(ΜΜ.). indicating that if the period is 8-10 hr. then the secondary star is approximately a solar mass.," For main sequence stars $(R_2/R_{\odot}) = (M_2/ \Mo)$, indicating that if the period is 8-10 hr, then the secondary star is approximately a solar mass."264 The mass-radius relation for a He core burning star ora white dwarf predicts a much larger mass for the secondary which is unlikely in an early-type galaxy., The mass-radius relation for a He core burning star or a white dwarf predicts a much larger mass for the secondary which is unlikely in an early-type galaxy.265 The Chandra observation of the intermediate luminosity elliptical galaxy NGC 3379 shows that only a small fraction of the gas shed by evolving stars still resides within the hot ISM., The Chandra observation of the intermediate luminosity elliptical galaxy NGC 3379 shows that only a small fraction of the gas shed by evolving stars still resides within the hot ISM.266 A wavelet detection algorithm resolves of the emission within the central 5 kpe into point sources., A wavelet detection algorithm resolves of the emission within the central 5 kpc into point sources.267 The luminosity function of the point sources detected at greater than 46 significance is consistent with that found for other ellipticals observed by Chandra (Kim Fabbiano 2004)., The luminosity function of the point sources detected at greater than $4 \sigma$ significance is consistent with that found for other ellipticals observed by Chandra (Kim Fabbiano 2004).268 Unlike other ellipticals observed by Chandra. only of the point sources are associated with globular clusters. which is comparable to the fraction of LMXBs in our galaxy.," Unlike other ellipticals observed by Chandra, only of the point sources are associated with globular clusters, which is comparable to the fraction of LMXBs in our galaxy."269 The low specific frequency of globular clusters and the low fraction of X-ray point sources associated with globulars clusters in NGC3379 is actually more similar to Chandra observations of SO galaxies rather than ellipticals (e.g.. Blanton. Sarazin Irwin 2001).," The low specific frequency of globular clusters and the low fraction of X-ray point sources associated with globulars clusters in NGC3379 is actually more similar to Chandra observations of S0 galaxies rather than ellipticals (e.g., Blanton, Sarazin Irwin 2001)."270 Spectral analysis of the unresolved emission within. the central 15” (770 pe) indicates that of the emission probably arises from point sources with fluxes below the detection limit in the Chandra observation., Spectral analysis of the unresolved emission within the central $15^{\prime\prime}$ (770 pc) indicates that of the emission probably arises from point sources with fluxes below the detection limit in the Chandra observation.271 If the luminosity function of the detected point sources is valid at lower luminosities. then the diffuse power-law emission can be accounted for by approximately 40 sources with luminosities below 3.0«1077 ergs s7!.," If the luminosity function of the detected point sources is valid at lower luminosities, then the diffuse power-law emission can be accounted for by approximately 40 sources with luminosities below $3.0 \times 10^{37}$ ergs $^{-1}$."272 The remaining of the unresolved emission from the central 770 pe is well described by thermal emission with kT=0.6 keV. Assuming a uniform eas density in this region gives a gas mass of 5«10°M.. which can be supplied by stellar mass loss in 107 years.," The remaining of the unresolved emission from the central 770 pc is well described by thermal emission with $kT=0.6$ keV. Assuming a uniform gas density in this region gives a gas mass of $5 \times 10^5 \Mo$, which can be supplied by stellar mass loss in $10^7$ years."273 Such a small amount of gas indicates that the stellar mass loss ts either being expelled from the central regions in a wind or ts being accreted by the central black hole., Such a small amount of gas indicates that the stellar mass loss is either being expelled from the central regions in a wind or is being accreted by the central black hole.274 The X-ray luminosity of the central AGN is 8«10° eres s7!., The X-ray luminosity of the central AGN is $8 \times 10^{38}$ ergs $^{-1}$.275 If gas is being acereted by the central black hole at either the Bondi accretion rate or mass cooling rate. then the radiative efficiency of the black hole must be 107°. as in the ADAP or RIAF models models (Narayan Yi 1994 and Yuan Narayan 1995).," If gas is being accreted by the central black hole at either the Bondi accretion rate or mass cooling rate, then the radiative efficiency of the black hole must be $~\sim 10^{-6}$, as in the ADAF or RIAF models models (Narayan Yi 1994 and Yuan Narayan 1995)."276 If the gas is flowing out of the system in a wind. the energy outflow rate would be 5<10°? eres s7!. which is 4 orders of magnitude greater than the 1.4 GHz radio power of the AGN.," If the gas is flowing out of the system in a wind, the energy outflow rate would be $5 \times 10^{39}$ ergs $^{-1}$, which is 4 orders of magnitude greater than the 1.4 GHz radio power of the AGN."277 Such a large ratio between AGN mechanical and radio power is commonly found among cluster cooling flows with X-ray cavities and shocks (Birzan et al., Such a large ratio between AGN mechanical and radio power is commonly found among cluster cooling flows with X-ray cavities and shocks (Birzan et al.278 2004: Nulsen et al., 2004; Nulsen et al.279 200δα: Nulsen et al., 2005a; Nulsen et al.280 2005b: MeNamara et al., 2005b; McNamara et al.281 2005)., 2005).282"a"" The most luminous source in NGC3379 ts located 360 pc from the central AGN with a peak luminosity of 3.5\IO? eres s7!. corresponding to the Eddington luminosity of a 30M. object."," The most luminous source in NGC3379 is located 360 pc from the central AGN with a peak luminosity of $3.5 \times 10^{39}$ ergs $^{-1}$, corresponding to the Eddington luminosity of a $30 \Mo$ object."283 The spectrum of this source ts well fitted with an absorbed power-law model with P=1.7. which is similar to other ULXs observed by Chandra and XMM-Newton and the low-hard state of galactic black hole binaries.," The spectrum of this source is well fitted with an absorbed power-law model with $\Gamma=1.7$, which is similar to other ULXs observed by Chandra and XMM-Newton and the low-hard state of galactic black hole binaries."284 Examining the archival ROSAT HRI observation of NGC 3379 shows that the ULX was at a comparable luminosity 5 years prior to the Chandra observation., Examining the archival ROSAT HRI observation of NGC 3379 shows that the ULX was at a comparable luminosity 5 years prior to the Chandra observation.285 The long term stability of the ULX may pose a problem for the micro-quasar interpretation of ULXs in early-type galaxies., The long term stability of the ULX may pose a problem for the micro-quasar interpretation of ULXs in early-type galaxies.286 The light curve of the ULX in NGC 3379 varies smoothly by a factor of two during the Chandra observation., The light curve of the ULX in NGC 3379 varies smoothly by a factor of two during the Chandra observation.287 The slow rise and fall times in the light curve and the consistency of the power-law spectrum during the observation all suggest that the ULX is undergoing a partial eclipse of the extended corona surrounding an accretion disk with a period of 8-10 hr., The slow rise and fall times in the light curve and the consistency of the power-law spectrum during the observation all suggest that the ULX is undergoing a partial eclipse of the extended corona surrounding an accretion disk with a period of 8-10 hr.288 Assuming the secondary ts a main sequence star filling its Roche lobe gives a mass for the secondary of approximately IM.., Assuming the secondary is a main sequence star filling its Roche lobe gives a mass for the secondary of approximately $1 \Mo$.289 Variability has been observed in other ULXs. but the ULX in NGC 3379 is the only ULX in an elliptical galaxy with possible periodic behavior.," Variability has been observed in other ULXs, but the ULX in NGC 3379 is the only ULX in an elliptical galaxy with possible periodic behavior."290 Due to the high surface brightness density of sources in the central 1 kpe of NGC 3379. only a long Chandra observation can determine if the lightcurve of the ULX ts truly periodic.," Due to the high surface brightness density of sources in the central 1 kpc of NGC 3379, only a long Chandra observation can determine if the lightcurve of the ULX is truly periodic."291In simulatioi projects on galaxies 1t is customary to run a relatively large number of simulations to inter-compare and understand the effect of various. parameters.,In simulation projects on galaxies it is customary to run a relatively large number of simulations to inter-compare and understand the effect of various parameters.292 Thus. creating the initial conditions can be a considerable part of the work and it makes sense to streamline it.," Thus, creating the initial conditions can be a considerable part of the work and it makes sense to streamline it."293 In particular. the amount of CPU involved depends on the number of iteration steps made.," In particular, the amount of CPU involved depends on the number of iteration steps made."294 This number should be sufficiently large. so that the iteration procedure can converge. but not excessively large. so as not to needlessly waste time.," This number should be sufficiently large, so that the iteration procedure can converge, but not excessively large, so as not to needlessly waste time."295 It is thus necessary to be able to assess whether the iteration has converged or not., It is thus necessary to be able to assess whether the iteration has converged or not.296 The most straightforward way is of course to plot the evolution in time of various radial profiles (such as the density. the mean velocities and dispersions ete) and check by eye whether the variation between the two last iteration times Is sufficiently small.," The most straightforward way is of course to plot the evolution in time of various radial profiles (such as the density, the mean velocities and dispersions etc) and check by eye whether the variation between the two last iteration times is sufficiently small."297 This. however. can be very tedious. particularly if it is carried out a number of times for each initial conditions.," This, however, can be very tedious, particularly if it is carried out a number of times for each initial conditions."298 It is thus useful to prepare tools that can give information on whether a rough convergence has been achieved. before starting the visual examination.," It is thus useful to prepare tools that can give information on whether a rough convergence has been achieved, before starting the visual examination."299 In this appendix we will describe how this can be carried out in. practice., In this appendix we will describe how this can be carried out in practice.300 We aim to compare the system in the beginning and in the end of a short-term evolution during a single iterative step., We aim to compare the system in the beginning and in the end of a short-term evolution during a single iterative step.301 So we need tools to compare two N-body models (in this context. a gaseous disk consisting of SPH particles can also be considered as an N-body model).," So we need tools to compare two $N$ -body models (in this context, a gaseous disk consisting of SPH particles can also be considered as an $N$ -body model)."302 We note that the following algorithm ts fairly similar to a test of the statistical hypothesis that two N-body systems are just two random realizations of the same distribution function (hereafter DF)., We note that the following algorithm is fairly similar to a test of the statistical hypothesis that two $N$ -body systems are just two random realizations of the same distribution function (hereafter DF).303 Our algorithm is based on comparisons of profiles of different quantities., Our algorithm is based on comparisons of profiles of different quantities.304 We wish to compare profiles of some quantity Q along some axis A for both systems., We wish to compare profiles of some quantity $Q$ along some axis $A$ for both systems.305 We divide these systems into pieces along the axis A in a way that each piece contains approximately the same number of particles., We divide these systems into pieces along the axis $A$ in a way that each piece contains approximately the same number of particles.306 For this. we divide the first system into pieces. each containing the same number of particles and calculate the corresponding boundaries of these pieces in the first system.," For this, we divide the first system into pieces, each containing the same number of particles and calculate the corresponding boundaries of these pieces in the first system."307 We then divide the second system by means of these boundaries., We then divide the second system by means of these boundaries.308 In each piece we calculate a given quantity whose value we denonte by Q., In each piece we calculate a given quantity whose value we denonte by $Q$.309 Let σι]. qo»; be the calculated values in the i-th piece in the first and the second model. respectively.," Let $q_{1,i}$, $q_{2,i}$ be the calculated values in the $i$ -th piece in the first and the second model, respectively."310 If we consider the N-body system, If we consider the $N$ -body system311with our measurement of the dispersion.,with our measurement of the dispersion.312 Our uncertainty in the unlensed density is therefore dominated by clustering., Our uncertainty in the unlensed density is therefore dominated by clustering.313 We again turn to simulations to derive the error bars on our measurement., We again turn to simulations to derive the error bars on our measurement.314" As in §?? we simulate a population that is lensed. by a SIS with 67=13.7 aresec. but in this case we drew the true value of iy from a Gaussian distribution with mean 20.3 aremin? and dispersion 7,=yg. where as derived above."," As in $\S\ref{sec-sim}$ we simulate a population that is lensed by a SIS with $\theta_E=13.7$ arcsec, but in this case we draw the true value of $n_0$ from a Gaussian distribution with mean 20.3 $^2$ and dispersion $\sigma_n=\eta n_0$, where as derived above."315 Using the log-likelihood function in Equation LO and a fixed estimate20.8.. we show the resulting distribution of recovered. Ge for 200 realizations in Fig. 12..," Using the log-likelihood function in Equation \ref{eqn-lerr} and a fixed estimate, we show the resulting distribution of recovered $\theta_E$ for 200 realizations in Fig. \ref{fig-errsim}."316 We see. by comparison with Fig.," We see, by comparison with Fig."317 LO (the case where no was known precisely). that incorporating an error of produces a much broader distribution. with the result of greatly. increasing the error. bars on our. measurement.," \ref{fig-mldist} (the case where $n_0$ was known precisely), that incorporating an error of produces a much broader distribution, with the result of greatly increasing the error bars on our measurement."318 Applying Equation LO to the real data. we find θε=14n aresec ⋅ ⋰∎≼↛∪⊔↕⊓⇂⋖⊾⊔≼∙⋖⊾⊐∪↓⋅↙⇥∫∶↴∶↓⋅≟⊥⊽⊥↿∖≤⋗⋅↱≻⊲∕⋰∣≼∙∩⊔↕∐⇂⋖⋅⊔≼∙⋖⊾⊐⋡15.," Applying Equation \ref{eqn-lerr} to the real data, we find $\hat{\theta}_E=1.4^{+5.2}_{-1.4}$ arcsec confidence) or $\hat{\theta}_E=1.4^{+15.9}_{-1.4}$ confidence)."3199 ⋅ While the estimate of Gp itself is greatly reduced. the error bars make it compatible with the result of $77 within a 2e range.," While the estimate of $\theta_E$ itself is greatly reduced, the error bars make it compatible with the result of $\S\ref{sec-sim}$ within a $\sigma$ range."320 This section. illustrates the principal weakness of the depletion method as pointed out in SIE. namely the vital importance of accurately measuring ny.," This section illustrates the principal weakness of the depletion method as pointed out in SKE, namely the vital importance of accurately measuring $n_0$."321 With adN/yN0.1 which is not unreasonable eiven clustering on these scales. the depletion effect is made more dillicult to distinguish from variations in the background counts that are not due to lensing.," With a $\delta N/N \sim 0.1$ which is not unreasonable given clustering on these scales, the depletion effect is made more difficult to distinguish from variations in the background counts that are not due to lensing."322 However. this ellect could be countered by selecting similar clusters (e.g. by their A-rav temperatures). and stacking the depletion signal accordingly. thus calibrating the cluster. Zx-mass relation and obtaining an average cluster mass profile.," However, this effect could be countered by selecting similar clusters (e.g. by their X-ray temperatures) and stacking the depletion signal accordingly, thus calibrating the cluster $T_X$ -mass relation and obtaining an average cluster mass profile."323 Choosing a sample of 10 clusters would simultaneously increase the effective. background surface number density by a [factor of LO while reducing the yactional error in ny by a factor of /10.., Choosing a sample of 10 clusters would simultaneously increase the effective background surface number density by a factor of 10 while reducing the fractional error in $n_0$ by a factor of $\sqrt{10}$.324 Simulations show that for 10 clusters similar to Abell 2219. the confidence region on 8p=13.7 aresce would then shrink rom (as quoted. above) to onlyaresecz a casible project for upcoming LE survey telescopes.," Simulations show that for 10 clusters similar to Abell 2219, the confidence region on $\theta_E=13.7$ arcsec would then shrink from (as quoted above) to only; a feasible project for upcoming IR survey telescopes."325 Note that in practice scatter in the cluster properties would. increase his range somewhat., Note that in practice scatter in the cluster properties would increase this range somewhat.326 We present a study of the depletion. clleet around Abell 219. the first done in the infrared. using the newlv-available panoramic Ilt camera (CURSL).," We present a study of the depletion effect around Abell 2219, the first done in the infrared, using the newly-available panoramic IR camera (CIRSI)."327 We show (see Appendix A) that the sample can be ellectively exploited: bevond the completeness limit. as long as the lensect field anc the background. field. obey the same incompleteness functions and have minimal contamination bv [false objects.," We show (see Appendix A) that the sample can be effectively exploited beyond the completeness limit, as long as the lensed field and the background field obey the same incompleteness functions and have minimal contamination by false objects."328" ""This allows us to detect a clear dip in the radial number density profile of background: galaxies at small distances from the cluster centre.", This allows us to detect a clear dip in the radial number density profile of background galaxies at small distances from the cluster centre.329 The optical-infrarecl colours enable. us. to select a population of τοῦ background: galaxies with a Lat number-count slope in order to optimise the lensing signal and reduce foreground-background confusion., The optical-infrared colours enable us to select a population of red background galaxies with a flat number-count slope in order to optimise the lensing signal and reduce foreground-background confusion.330" For a population of red background. galaxies with an extremely Le slope (a= 0.185). we employ. maximum likelihood methods and a SIS model to derive an estimate ⋅ V. . ∪⊓↓↕∢⊾∟↓⊔⊳∖∢⋅↓⊔↓⋅⋯∐⊔⊳∖↙⇥⇇⊸∶↓⇀⊰⋅⋀⊥⊽⊐⋜↧↓⋅≼∼⊳∖⋖⊾≼⇍↿∖↻↻⊲∕⋰ye40 confidence limit when uncertainties is my are ignored). resulting velocity dispersion m,—S14.H2 Kms. +."," For a population of red background galaxies with an extremely flat slope $\alpha=0.185$ ), we employ maximum likelihood methods and a SIS model to derive an estimate of the Einstein radius $\theta_E=13.7^{+3.9}_{-4.2}$ arcsec confidence limit when uncertainties is $n_0$ are ignored), resulting velocity dispersion $\sigma_v=814^{+112}_{-139}$ km $^{-1}$."331" ""Phese values are consistent with the location of the redder of the two giant ares and the estimate a~930 km + of Smail (1995a).", These values are consistent with the location of the redder of the two giant arcs and the estimate $\sigma_v \sim 930$ km $^{-1}$ of Smail (1995a).332 We examine the uncertainty in the number counts. and derive a fractional error of on the normalisation. of he backeround number density (consistent with clustering on these scales).," We examine the uncertainty in the number counts, and derive a fractional error of on the normalisation of the background number density (consistent with clustering on these scales)."333 When this error is incorporated into the maximunr-likelihood analysis the error. bars become too arge to make a precise statement about the magnitude of the lensing (although our previous measurement is not ruled out)., When this error is incorporated into the maximum-likelihood analysis the error bars become too large to make a precise statement about the magnitude of the lensing (although our previous measurement is not ruled out).334 This demonstrates the crucial importance of the xickeround density 29 for an accurate depletion analysis as discussed in Schneider. Wine Erben (2000).," This demonstrates the crucial importance of the background density $n_0$ for an accurate depletion analysis as discussed in Schneider, King Erben (2000)."335 Finally. while we cannot at present use our current data o distinguish. between alternative models for the cluster," Finally, while we cannot at present use our current data to distinguish between alternative models for the cluster"336Hereafter we show the fit results for the literature sample and the relative x? maps for eerror computation to Fig. 3.4)).,Hereafter we show the fit results for the literature sample and the relative $\chi^2$ maps for error computation (analogous to Fig. \ref{fig_fit_errors}) ).337 The sources are sorted in redshift., The sources are sorted in redshift.338 In the (analogousright panels we show the spectral decomposition., In the right panels we show the spectral decomposition.339 The observed spectra are shown as a black continous line., The observed spectra are shown as a black continous line.340" The modeled components are: power-law continuum (blue dotted line), Balmer pseudo continuum (purple dashed line), nnormalized template (light blue dotted line), eemission line (red dotted line)."," The modeled components are: power-law continuum (blue dotted line), Balmer pseudo continuum (purple dashed line), normalized template (light blue dotted line), emission line (red dotted line)."341" The sum of the first set of components (power-law continuum + Balmer pseudo continuum + nnormalized is overplotted to the spectrum as green solid line, while the sum of all the components is overplotted as a redtemplate) solid line."," The sum of the first set of components (power-law continuum $+$ Balmer pseudo continuum $+$ normalized template) is overplotted to the spectrum as green solid line, while the sum of all the components is overplotted as a red solid line."342 Telluric absorption bands are indicated over the spectra with the symbol @: they are extracted from the ESO sky absorption spectrum measured on the Paranal site at a nominal airmass of 1., Telluric absorption bands are indicated over the spectra with the symbol $\Earth$: they are extracted from the ESO sky absorption spectrum measured on the Paranal site at a nominal airmass of 1.343" 'The nnormalization, obtained from the fit of the first set of components, depends on the power-law slope and its normalization (intercept)."," The normalization, obtained from the fit of the first set of components, depends on the power-law slope and its normalization (intercept)."344" In the left panel we show the x? domain analysis for error computation: a) two dimensional projections of the 3D x?-surfaces nnormalization vs Intercept, upper-left plot; nnormalization vs Slope, bottom-left plot; Intercept vs slope, bottom-right plot): contours represent iso-y? levels spaced by factor of 2 while the best fit case is marked with a dot; b) probability distribution for the template normalizationa (upper-right plot): the distribution has been obtained by marginalizing the 3-D probability distribution considering only the triplets for which x?—Xmin<1, the dashed vertical lines mark our estimate of the 1—c confidence level."," In the left panel we show the $\chi^2$ domain analysis for error computation: a) two dimensional projections of the 3D $\chi^2$ -surfaces normalization vs Intercept, upper-left plot; normalization vs Slope, bottom-left plot; Intercept vs slope, bottom-right plot): contours represent $\chi^2$ levels spaced by a factor of 2 while the best fit case is marked with a dot; b) probability distribution for the template normalization (upper-right plot): the distribution has been obtained by marginalizing the 3-D probability distribution considering only the triplets for which $\chi^2 -\chi_{min}^2< 1$, the dashed vertical lines mark our estimate of the $1-\sigma$ confidence level."345been summarized in Luetal.(2010).,been summarized in \citet*{Luetal10}.346.. We shall further demonstrate in this paper that au isotropic distribution of ITVS progenitors is incousistent with the spatial distribution of the detected IIVSs if they are originated from the GC., We shall further demonstrate in this paper that an isotropic distribution of HVS progenitors is inconsistent with the spatial distribution of the detected HVSs if they are originated from the GC.347 IIowever. the disk(s) origination of the detected IIVSs is cousistent with the distribution of the inclination aueles (relative to the disk(s)) of the detected IIVSs which further strenethen the conclusions mace iu Luetal.(2010).," However, the disk(s) origination of the detected HVSs is consistent with the distribution of the inclination angles (relative to the disk(s)) of the detected HVSs which further strengthen the conclusions made in \citet*{Luetal10}."348. The velocity distribution of IIVSs is related to. not oulv the production mechauisui but also the origi of heir progenitors., The velocity distribution of HVSs is related to not only the production mechanism but also the origin of their progenitors.349 Sesanaetal.(2007)— have studied he velocity distribution of IIVSs., \citet{Sesana07} have studied the velocity distribution of HVSs.350 They fouud that he velocity distribution of IIVSs produced bw the Τον wnechanisin for uubound injecting stellar binaries seclus to be consistent with the then detected IIVSs hough with limited statistics. while the IWS velocity distribution produced by the BBIT mechanisu appears o be too flat iu comparison with the observatious.," They found that the velocity distribution of HVSs produced by the TBK mechanism for unbound injecting stellar binaries seems to be consistent with the then detected HVSs though with limited statistics, while the HVS velocity distribution produced by the BBH mechanism appears to be too flat in comparison with the observations."351 Their results suggest that the IIVS velocity distribution nay be useful in distinguishiug the ejection mechanisuis., Their results suggest that the HVS velocity distribution may be useful in distinguishing the ejection mechanisms.352 Iu this paper. we shall further investigate the effects on the velocity distribution of IIVSs due to ciffereut origins of the ITVS progenitors. e.g.. those (binary) stars initially unbound to the MDBII but later injected iuto the uuediate vicinity of the MDII due to some uukuowu perturbations. and those (binary) stars imitiallvy bound to the MBIT but later evolved outo highly ecceutric orbits and migrated into the immediate vicinity of the MBIT.," In this paper, we shall further investigate the effects on the velocity distribution of HVSs due to different origins of the HVS progenitors, e.g., those (binary) stars initially unbound to the MBH but later injected into the immediate vicinity of the MBH due to some unknown perturbations, and those (binary) stars initially bound to the MBH but later evolved onto highly eccentric orbits and migrated into the immediate vicinity of the MBH."353 The paper is organized as follows., The paper is organized as follows.354 Iu Section ??.. we first stuarize the observational results on the spatial aud velocity distribution of the detected ITVSs.," In Section \ref{sec:obs}, we first summarize the observational results on the spatial and velocity distribution of the detected HVSs."355 Iu Section ??.. we explore the detailed dynamics of interactions between binary stars on bound orbits aud a central ΑΠΟΠ.," In Section \ref{sec:TBK}, we explore the detailed dynamics of interactions between binary stars on bound orbits and a central MBH."356" The consequences of these interactions are different from that between the unbotud binary stars on parabolic (or lyperbolic) orbits and the. MDII intensively investigated in the literature (οιο,,Hills1985:Bromleyetal.2006:Sesana 2007)."," The consequences of these interactions are different from that between the unbound binary stars on parabolic (or hyperbolic) orbits and the MBH intensively investigated in the literature \citep[e.g.,][]{Hills88,Bromley06,Sesana07}."357. The reason is that the stellar binary may experience multiple close encounters with the MBIT in the former case. while it oulv experiences a single close eucouuter m the latter case.," The reason is that the stellar binary may experience multiple close encounters with the MBH in the former case, while it only experiences a single close encounter in the latter case."358 Assundue realistic distributions of the properties of the initial stellar binaries. we then simulate both the spatial distribution aud the velocity distribution of IIVSs produced by the TBK mechanisin and compare the Ποσα) results with the observations iu Section [.," Assuming realistic distributions of the properties of the initial stellar binaries, we then simulate both the spatial distribution and the velocity distribution of HVSs produced by the TBK mechanism and compare the numerical results with the observations in Section \ref{sec:Result}."359? Iu Section ??.. we also explore the iuteractious between suele stars on bound orbits with a hvpothesized. DDII iu the GC.," In Section \ref{sec:BBH}, we also explore the interactions between single stars on bound orbits with a hypothesized BBH in the GC."360 These single stars are assumed to be injected iuto the iuiniediate viciuitv of the BBIT from cisk-like stellar structures (0... the CWS disk) surrounding the 3DIT. which is differcut from that adopted in Sesauaetal. (2007).," These single stars are assumed to be injected into the immediate vicinity of the BBH from disk-like stellar structures (e.g., the CWS disk) surrounding the BBH, which is different from that adopted in \citet{Sesana07}."361. With reasonable but simple assumptions on the parameters of the hypothetical DDBIT. the spatial aud velocity distributions of the ejected IIVSs are obtained.," With reasonable but simple assumptions on the parameters of the hypothetical BBH, the spatial and velocity distributions of the ejected HVSs are obtained."362 Comparison between the sinmlation results aud the observations are also discussed in Section ??.., Comparison between the simulation results and the observations are also discussed in Section \ref{sec:BBH}.363 The conchisions are elven in Section ??.., The conclusions are given in Section \ref{sec:Conclusion}.364 Survevs of IIVSs have detected 16 IIVSs uubound to the Galactic halo. 8 bound IIVSs. aud E IIVS ciucdidates (Brownetal.2005:IlirschEdelmannct2005:Brownetal.2007.2009a).," Surveys of HVSs have detected 16 HVSs unbound to the Galactic halo, 8 bound HVSs, and 4 HVS candidates \citep{Brown05,Hirsch05,Edelmann05,Brown07,Brown09a}."365. We stunuuazrize their spatial and velocity distributions iu this section., We summarize their spatial and velocity distributions in this section.366 The spatial distribution of the IIVSs detected so far is probably anisotropic (Abadietal.2009:Brownct2," The spatial distribution of the HVSs detected so far is probably anisotropic \citep{Abadi09,Brown09b}."367009b).. Luetal.(2010) use exeat circles to fit the spatial distribution of the detected IIVSs projected on the skv of an observer located at the GC. and they find that the distribution can be best fitted by two great. circles.," \citet{Luetal10} use great circles to fit the spatial distribution of the detected HVSs projected on the sky of an observer located at the GC, and they find that the distribution can be best fitted by two great circles."368 Their results sugeest that the spatial distribution of the detected IIVSs is cousistent with beiug located on the planes of two thin disks (Luctal.2010): (1) eleven of the unbound IIVSs (plus four bound oues aud two candidates: totally 17 objects) are spatially associated to a thin disk plaue with an orientation almost the same as that of CWS disk located witlin half a parsec frou the ceutral MDII (see Levin&Beloborodoy2003:Luetal.2009:Patunardetal.2006:Bartko2009.2010) }: (2) four of the uubouud IIVSs (plus three bound ones aud two candidates: totally 9 objects) are spatially associated to a thin disk plane with au orieutation simular to that of the northern aru of the miuispiral (or also the outer warped part of the CWS disk) im the CC.," Their results suggest that the spatial distribution of the detected HVSs is consistent with being located on the planes of two thin disks \citep*{Luetal10}: (1) eleven of the unbound HVSs (plus four bound ones and two candidates; totally 17 objects) are spatially associated to a thin disk plane with an orientation almost the same as that of CWS disk located within half a parsec from the central MBH (see \citealt{LB03,LuJ09,Paumard06,Bartko09a,Bartko09b}) ); (2) four of the unbound HVSs (plus three bound ones and two candidates; totally 9 objects) are spatially associated to a thin disk plane with an orientation similar to that of the northern arm of the minispiral (or also the outer warped part of the CWS disk) in the GC."369 The normals of the best-fit disk planes for these two ITVS populations aro 1 υ) (ο.ον Lk) aud (1767. 53°) πι Calactic coordinates. respectively (Luetal.2010).," The normals of the best-fit disk planes for these two HVS populations are $l$ $b$ $=$ $311\arcdeg$, $-14\arcdeg$ ) and $176\arcdeg$, $-53\arcdeg$ ) in Galactic coordinates, respectively \citep{Luetal10}."370". IIereafter. we refer to those detected IIVSsassociated with the above two best-fit planes as the first population aud the second population of IIVSs. respectively,"," Hereafter, we refer to those detected HVSsassociated with the above two best-fit planes as the first population and the second population of HVSs, respectively."371 We denote the inclination angle of each. IVS to its correspoudiug best-fit plane by O and describe the spatial distribution of the IIVSs by a normalized cumulative distribution fiction of their inclination angles P(O) (hereafter. OCDE). which represeuts the nuuber fraction of theIIVSs with inclination angles higher than Ο.," We denote the inclination angle of each HVS to its corresponding best-fit plane by $\Theta$ and describe the spatial distribution of the HVSs by a normalized cumulative distribution function of their inclination angles $P(\geq\Theta)$ (hereafter, $\Theta$ CDF), which represents the number fraction of theHVSs with inclination angles higher than $\Theta$."372 The observationua OCDFs for both populations of the IIVSs are shown iu Figure d and will be compared with the distributions obtained from numerical models in Sections Lane TY., The observational $\Theta$ CDFs for both populations of the HVSs are shown in Figure \ref{fig:f1} and will be compared with the distributions obtained from numerical models in Sections \ref{sec:Result} and \ref{sec:BBH}.373 For cach population. we shall compare the 3QO) of all the IIVSs Gucliding uubouud IIVSs. boum IIVSs. aud IIVS candidates) iustead of only uubouik ones. because (1) for the fist IIVS population. our lohuogorov Siürnov (I-8) test finds a likelihood. of 0.91 that the uubouud IIVSs aud all the IIVSs are drawu from the same OCDE: (2) for the second population. the ποτ of the uubouud IIVSs is only and the error cue to Poisson noise in the OCDE is substantial. therefore we do not show their OCDE in Figure 1. (aud eCDF in Figure 2. below. either).," For each population, we shall compare the $P(\geq\Theta)$ of all the HVSs (including unbound HVSs, bound HVSs, and HVS candidates) instead of only unbound ones, because (1) for the first HVS population, our $-$ Smirnov (K-S) test finds a likelihood of $0.94$ that the unbound HVSs and all the HVSs are drawn from the same $\Theta$ CDF; (2) for the second population, the number of the unbound HVSs is only 4 and the error due to Poisson noise in the $\Theta$ CDF is substantial, therefore we do not show their $\Theta$ CDF in Figure \ref{fig:f1} (and $v$ CDF in Figure \ref{fig:f2} below, either)."374 The gravitational potential of the Galaxy is not exactly spherical. aud its non-spherical component may deflect the radial trajectories of IIVSs after they were ejected from the GC fee.Yu&Aladau 2007)..," The gravitational potential of the Galaxy is not exactly spherical, and its non-spherical component may deflect the radial trajectories of HVSs after they were ejected from the GC \citep[e.g.,][]{YM07}. ."375 Caven the distance and the velocity span (30kpe<Ro«130kpc and 690lans|<v980kins ον sce Section ??4) of the detected IIVSs. however. the deviation due to," Given the distance and the velocity span $30\kpc<R<130\kpc$ and $690 \kms<v<980 \kms$ , see Section \ref{subsec:vd}) ) of the detected HVSs, however, the deviation due to"376System.,System.377 Followiug these discoveries. progress las beeu made in uncderstaucding planet formation. but the theory is still incomplete 2006).," Following these discoveries, progress has been made in understanding planet formation, but the theory is still incomplete ."378. The leading scenario for the formation of eiaut planets is the core accretion mechanuisiu., The leading scenario for the formation of giant planets is the core accretion mechanism.379 Icy planetesimals located beyond the suow line inb their host disk colide repeatedly to grow a core with a modest. gaseous atmosphere., Icy planetesimals located beyond the snow line in their host disk collide repeatedly to grow a core with a modest gaseous atmosphere.380 If this co'e succeeds in reachitσα crical 1dass of a few ens ol Earth masses. runaway accretion of a massive gaseous envelope Jloceecs alid leacls. ultimately. o the formation of a gaseous giaut platel 1996).," If this core succeeds in reaching a critical mass of a few tens of Earth masses, runaway accretion of a massive gaseous envelope proceeds and leads, ultimately, to the formation of a gaseous giant planet ."381. Some evidence supporting this scenario |an ©uerged in recent yeas. iut ie [oru ofa uetalliciCl reud for stars hosting planets )5).. he discovery of a high density hot Jupiter all tha of a ΠΡsinely rule‘o-leusing planet2006).," Some evidence supporting this scenario has emerged in recent years, in the form of a metallicity trend for stars hosting planets , the discovery of a high density hot Jupiter and that of a surprisingly low-mass micro-lensing planet."382. However. a loug-stauclit& clitficulty or the core accret1o scenario. which has not vet |)ee1 fully elucidated. is the fac tha the lnesc:ile recuired o build pe‘itical core nasses aud tlus large gaseous envelopes (109-10* vr ls COLiparable ) he lifetiJes €of proto-petary disks1999).," However, a long-standing difficulty for the core accretion scenario, which has not yet been fully elucidated, is the fact that the timescale required to build-up critical core masses and thus large gaseous envelopes $\sim 10^6$ $10^7$ yr) is comparable to the lifetimes of proto-planetary disks."383. Orbial inigration acds a layer of complication to theories of plajet. foriuatiOl., Orbital migration adds a layer of complication to theories of planet formation.384 Ax a result of gravitaticoal interactions with their gaseous disk1986). e orbits of ptlets in the terrestrial mass rauge are predicted to decay ou timescales (~10? vr) short. compa'ed to disk lifetimes19972.," As a result of gravitational interactions with their gaseous disk, the orbits of planets in the terrestrial mass range are predicted to decay on timescales $\sim38510^5$ yr) short compared to disk lifetimes."386b).. ligratio is slower for jxanets of much sinaller or iuuchi larger masses: in the first case because the Orque causiug[n]0 migration is quaclratic iu pallel Lass. aid in the second. case because the planet opens a gap aud then mierates ou the disks accretion timescale. which can be comparable to its ifetime.," Migration is slower for planets of much smaller or much larger masses: in the first case because the torque causing migration is quadratic in planet mass, and in the second case because the planet opens a gap and then migrates on the disk's accretion timescale, which can be comparable to its lifetime."387 While it is possible or »robable tal Inaly ter'estrial. planets form by agelomeratiouMD of stnaller bodies after tlie gas is goje. this is 1οἱ al option for the solicl cores of Jovian pallets since. iu the core accretion scenario. {1e cores Inst form belo' the gaseous envelopes eau ye accretec.," While it is possible or probable that many terrestrial planets form by agglomeration of smaller bodies after the gas is gone, this is not an option for the solid cores of Jovian planets since, in the core accretion scenario, the cores must form before the gaseous envelopes can be accreted."388 The prevalence of Jovian plauets with orbial periods o only. a few days deepeus the luystery a it suggests that these planets clic ulierate but stopped sli[9]t of mereing with their sta ‘Sal Orjtal adii where even the accretion tiijescale wold seem tolave been very short1996)., The prevalence of Jovian planets with orbital periods of only a few days deepens the mystery as it suggests that these planets did migrate but stopped short of merging with their stars at orbital radii where even the accretion timescale would seem to have been very short.389. Analytie caleulatious and most hycdro-dynamical sit—tlations of uigration usualM7 assulue a disk that is laminar apart [rom tle waves axl shocks excited by the panet itself, Analytic calculations and most hydro-dynamical simulations of migration usually assume a disk that is laminar apart from the waves and shocks excited by the planet itself.390 .But t leelective viscositv ol disks p'obably involves turbulence.(," But the effective viscosity of disks probably involves turbulence.,"3912001)..1).. al( lave found in 3D simulatious of magnueto-roalleoal turbuence that the i1stantaneous torque exe‘tect on a planet iu the terrestrial mwiass ral ge|s subject (to lοιασας many times its mean value. apparently caused by turbulent. density. fluctuations iu le planets vicinity.," and have found in 3D simulations of magneto-rotational turbulence that the instantaneous torque exerted on a planet in the terrestrial mass range is subject to fluctuations many times its mean value, apparently caused by turbulent density fluctuations in the planet's vicinity."392 In [act. uo obviOUS secular decay manifests itself in the orbits of planets with 1vass MyS1OAL. although because the simulationsH are limitedH to 4107> planetary orbits—coHupae >10? for Jupiter during the lifetime ol the proto-solar uebula—aud the predicted decay ii seninmnajor axls is SSCENLO% over this period.," In fact, no obvious secular decay manifests itself in the orbits of planets with mass $M_p\lesssim 10 M_\oplus$, although because the simulations are limited to $\sim 10^2$ planetary orbits—compare $\gtrsim 10^5$ for Jupiter during the lifetime of the proto-solar nebula—and the predicted decay in semimajor axis is $\lesssim 10\%$ over this period,"393value for low mass dwarf irregular galaxies. e.g. Lake et al.,"value for low mass dwarf irregular galaxies, e.g. Lake et al."394 1990. Begum et al.," 1990, Begum et al."395 2003). implies that the systematic rotation. if any. in the galaxy is smaller than the velocity dispersion.," 2003), implies that the systematic rotation, if any, in the galaxy is smaller than the velocity dispersion."396 Given the lack of any systematic rotation. it is difficult to accurately determine the total dynamical mass for the galaxy.," Given the lack of any systematic rotation, it is difficult to accurately determine the total dynamical mass for the galaxy."397 From the virial theorem. assuming HI distribution to be spherical with an isotropic velocity dispersion and negligible rotation. the indicative mass is (Hoffman et al.," From the virial theorem, assuming HI distribution to be spherical with an isotropic velocity dispersion and negligible rotation, the indicative mass is (Hoffman et al."398" 1996) Assuming c of 8 ""and taking the diameter of the galaxy ~ |. Skpe. gives a total mass of HIZSSOO3B to be —5.3.10M..."," 1996) Assuming $\sigma$ of 8 and taking the diameter of the galaxy $\sim $ 1.5 kpc, gives a total mass of HIZSS003B to be $\sim 5.3\times10^7 \rm{M_\odot}$."399" For the entire HIZSSOO03 system. if we assume the two galaxies to be in a bound circular orbit. then the indicative orbital mass is where r, is the projected separation and AV the radial velocity difference (Karachentsev. et al."," For the entire HIZSS003 system, if we assume the two galaxies to be in a bound circular orbit, then the indicative orbital mass is where $r_p$ is the projected separation and $\Delta V$ the radial velocity difference (Karachentsev et al."400 2002)., 2002).401" For a projected separation of ~0.7 kpe and a velocity difference of ~34.6 +. the indicative orbital mass is ~6.7.LO"" M... in good agreement with the total mass derived from the internal Kinematics."," For a projected separation of $\sim 0.7$ kpc and a velocity difference of $\sim 34.6$ , the indicative orbital mass is $\sim 6.7\times 10^8$ $_\odot$, in good agreement with the total mass derived from the internal kinematics."402 Silva et al. (, Silva et al. (4032005) highlight a puzzle regarding the metallicity of HIZSS003.,2005) highlight a puzzle regarding the metallicity of HIZSS003.404 The metallicity of HIZSSO03 system calculated from the younger HII region is smaller than that estimated from the color of the older red giant branch stars., The metallicity of HIZSS003 system calculated from the younger HII region is smaller than that estimated from the color of the older red giant branch stars.405 Given that the bulk of the stars are associated with the bigger galaxy but that the HIT region is in the smaller galaxy. the inconsistency in the derived metallicities is not surprising.," Given that the bulk of the stars are associated with the bigger galaxy but that the HII region is in the smaller galaxy, the inconsistency in the derived metallicities is not surprising."406 The low metallicity of the gas in the HIT region of the smaller galaxy HIZSSOO3B is also qualitatively consistent with what one would expect from the metallicity-luminosity relation., The low metallicity of the gas in the HII region of the smaller galaxy HIZSS003B is also qualitatively consistent with what one would expect from the metallicity-luminosity relation.407 Further. going by the stars identified as belonging to the HII region (Fig.," Further, going by the stars identified as belonging to the HII region (Fig."408 6 of Silva et al., 6 of Silva et al.409 2005) there is a trend for these stars to have a slightly smaller J-K color (consistent with a lower metallicity: Valenti et al., 2005) there is a trend for these stars to have a slightly smaller J-K color (consistent with a lower metallicity; Valenti et al.410 2004) than the median color of all stars identitied as belonging to HIZSSO03., 2004) than the median color of all stars identified as belonging to HIZSS003.411 The HIZSSO03 puzzle thus seems tat a qualitative level at least) resolved., The HIZSS003 puzzle thus seems (at a qualitative level at least) resolved.412 However. as is well known. an observed colour difference cannot be uniquely ascribed to a difference in the metallicity. but could also be due to a difference in the age of the stars Cage-metallicity” degeneracy) or from a temperature difference.," However, as is well known, an observed colour difference cannot be uniquely ascribed to a difference in the metallicity, but could also be due to a difference in the age of the stars (""age-metallicity"" degeneracy) or from a temperature difference."413 A more quantitative consistency check will have to await a detailed reanalysis of the near-IR data., A more quantitative consistency check will have to await a detailed reanalysis of the near-IR data.414 The observations presented in this paper were made with the Giant Metrewave Radio Telescope (GMRT)., The observations presented in this paper were made with the Giant Metrewave Radio Telescope (GMRT).415 The GMRT is operated by the National Center for Radio Astrophysics of the Tata Institute of Fundamental Research., The GMRT is operated by the National Center for Radio Astrophysics of the Tata Institute of Fundamental Research.416consequences in Section 4 before. drawing our conclusions in Section 5.,consequences in Section 4 before drawing our conclusions in Section 5.417 We perform our N-hocly simulations using the Nbody2 code (?))., We perform our $N$ -body simulations using the Nbody2 code \citealp{Aarseth2001}) ).418 Nbody2 is a fast and accurate direct-integration coce. optimised for the number of star particles used in this study CN= 1000).," Nbody2 is a fast and accurate direct-integration code, optimised for the number of star particles used in this study $N = 1000$ )."419 In our simulations there are two separate mass distributions which we wish to model: the stars ancl the background gas potential., In our simulations there are two separate mass distributions which we wish to model: the stars and the background gas potential.420 In all cases we model the stellar distribution as NW=1000 particles with equal masses of 0.5A/.. resulting in a total stellar mass of 500AL.., In all cases we model the stellar distribution as $N=1000$ particles with equal masses of $0.5 M_\odot$ resulting in a total stellar mass of $500 M_\odot$.421 Every particle has a gravitational softening length of 100 AU., Every particle has a gravitational softening length of 100 AU.422 We choose softened and equal-mass particles in order to avoid strong two-bodv interactions and mass segregation., We choose softened and equal-mass particles in order to avoid strong two-body interactions and mass segregation.423 ? and ? showed that both of these ellects can be extremely important in the violent collapse of cool. clumpy regions. however we wish to avoid complicating our simulations with these elfects as we are interested in the ellects of gas expulsion.," \cite{Allison2009b} and \cite{Allison2010} showed that both of these effects can be extremely important in the violent collapse of cool, clumpy regions, however we wish to avoid complicating our simulations with these effects as we are interested in the effects of gas expulsion."424" We distribute the stars within a radius of 1.5 pe with wo cdillerent clumpyv! morphologies: ‘fractal’. and ""elumpy xXummer'."," We distribute the stars within a radius of 1.5 pc with two different `clumpy' morphologies: `fractal', and `clumpy plummer'."425 Representative snapshots of the initial conditions ofa fractal and clumpy plummer distribution can be seen in he left and right-hand panels. respectively. of Fig. 2..," Representative snapshots of the initial conditions of a fractal and clumpy plummer distribution can be seen in the left and right-hand panels, respectively, of Fig. \ref{morphrep}."426 Fractal clusters are. produced: using the box fractal echnique described by 2: also used by ? and 2.., Fractal clusters are produced using the box fractal technique described by \cite{Goodwin2004}; also used by \cite{Allison2009a} and \cite{Allison2010}.427 In this paper we use a fractal dimension D=1.6 which corresponds o a highly clumpy initial distribution (see Fig. 2))., In this paper we use a fractal dimension $D = 1.6$ which corresponds to a highly clumpy initial distribution (see Fig. \ref{morphrep}) ).428 In clumpy plummers. cach sub-clump is modelled as an inciviclual Plummer sphere.," In clumpy plummers, each sub-clump is modelled as an individual Plummer sphere."429 The total stellar mass of 500 AL. is distributed into 16 sub-clumps of approximately equal mass., The total stellar mass of 500 $_\odot$ is distributed into 16 sub-clumps of approximately equal mass.430 Each sub-clump contains 31.0-31.5 AL. formed. from 62-63 particles., Each sub-clump contains 31.0-31.5 $_\odot$ formed from 62-63 particles.431 Ehe position of individual sub-clumips within the model star forming region follows the gas potential (see below)., The position of individual sub-clumps within the model star forming region follows the gas potential (see below).432 ‘The gas within the star-forming region is modelled as a static Plummer potential with a mass M. and ο ου., The gas within the star-forming region is modelled as a static Plummer potential with a mass $M_{\rm{g}}$ and scale-radius $r_{\rm{g}}$.433" The scale radius is set to ber,=1 pe. or ry=1.5 pe."," The scale radius is set to be $r_{\rm{g}} = 1$ pc, or $r_{\rm{g}} = 1.5$ pc."434" As the stars have a maximum radius of 1.5 pe this means that for r,=1.5 pe. the gas distribution seen by the stars is roughly uniform."," As the stars have a maximum radius of 1.5 pc this means that for $r_{\rm{g}} =4351.5$ pc, the gas distribution seen by the stars is roughly uniform."436 The relative masses of the eas potential within 1.5 pe and the stars set the SET (ο). that is the fraction of the initial cloud. mass converted into stars.," The relative masses of the gas potential within 1.5 pc and the stars set the SFE $\epsilon$ ), that is the fraction of the initial cloud mass converted into stars."437 “Phe mass of the gas potential is varied to obtain true SEEs of 20. 30 and 40 per cent (AL. —2000. 1167. 750 AL. ).," The mass of the gas potential is varied to obtain true SFEs of 20, 30 and 40 per cent $M_{\rm{g}}=$ 2000, 1167, 750 $M_\odot$ )."438 Note that a true SEE of 20 or 30 per cent will fail to produce a bound star cluster after. instantaneous gas expulsion if the gas and stars are initially virialised (see e.g. 7))., Note that a true SFE of 20 or 30 per cent will fail to produce a bound star cluster after instantaneous gas expulsion if the gas and stars are initially virialised (see e.g. \citealp{Baumgardt2007}) ).439 We emphasise that the gas potential does not. follow the initial stellar distribution. nor does it react to changes in the stellar distribution as it evolves (it is not live).," We emphasise that the gas potential does not follow the initial stellar distribution, nor does it react to changes in the stellar distribution as it evolves (it is not live)."440 These are obviously extreme simplifications. but as we will discuss later we feet that we capture the essence of the basic physics using such a simple model.," These are obviously extreme simplifications, but as we will discuss later we feel that we capture the essence of the basic physics using such a simple model."441 The virial ratio Q=77|O| is the ratio of the kinetic. 7. to potential energy. Q. of the system.," The virial ratio $Q = T/|\Omega|$ is the ratio of the kinetic, $T$, to potential energy, $\Omega$, of the system."442 We set the initial velocity dispersion of the stars relative to the total potential (gas stars) to set initial stellar virial ratios between zero (cold). 0.5 (virial equilibrium). and 0.9 (supervirial. but bound).," We set the initial velocity dispersion of the stars relative to the total potential (gas stars) to set initial stellar virial ratios between zero (cold), 0.5 (virial equilibrium), and 0.9 (supervirial, but bound)."443 For initial virial ratios ϐ)«0.5. the svstem will tend to collapse. and for Q>0.5 the system will tend to expand.," For initial virial ratios $Q<0.5$, the system will tend to collapse, and for $Q>0.5$ the system will tend to expand."444 Llowever. even for ϱ=0.5. although the svstem is in virial equilibrium. the elumpy initial conditions mean that it is in dynamical equilibrium.," However, even for $Q=0.5$, although the system is in virial equilibrium, the clumpy initial conditions mean that it is in dynamical equilibrium."445 Although voung star clusters form embedded within the the molecular gas from which they formed. few star clusters over ~5 Myr old remain associated with their gas (7)).," Although young star clusters form embedded within the the molecular gas from which they formed, few star clusters over $\sim 5$ Myr old remain associated with their gas \citealp{Proszkow2009}) )."446 This is likely as a result. of a number of mechanisms including radiative [feedback from massive stars. stellar winds from voung stars. and eventually the onset of the first supernova.," This is likely as a result of a number of mechanisms including radiative feedback from massive stars, stellar winds from young stars, and eventually the onset of the first supernova."447 The time at which gas removal begins to occur. and the duration of the gas removal process is uncertain. and dependent on the particular gas removal mechanism in operation.," The time at which gas removal begins to occur, and the duration of the gas removal process is uncertain, and dependent on the particular gas removal mechanism in operation."448 To simulate gas expulsion we instantancously remove the external gas potential after 3 Myr., To simulate gas expulsion we instantaneously remove the external gas potential after 3 Myr.449 This is approximately nmid-wav between the time at which gas removal from stellar winds and supernova feedback might be expected to occur for star clusters containing 1000 stars., This is approximately mid-way between the time at which gas removal from stellar winds and supernova feedback might be expected to occur for star clusters containing $\sim1000$ stars.450 Instantaneous gas removal is the most extreme form of gas removal as the stars have no chance to readjust to the change in the potential (e.g. 2: 7)), Instantaneous gas removal is the most extreme form of gas removal as the stars have no chance to readjust to the change in the potential (e.g. \citealp{Goodwin1997a}; \citealp{Baumgardt2007}) ).451 lt should be noted. that. both. the clumpy. plummoer and fractal clusters can vary considerably in. appearance depending on the random realisation used ancl the subsequent evolution is highlv stochastic (see 2))., It should be noted that both the clumpy plummer and fractal clusters can vary considerably in appearance depending on the random realisation used and the subsequent evolution is highly stochastic (see \citealp{Allison2010}) ).452 We therefore conduct a minimum of 5 ranclom realisations of cach parameter set., We therefore conduct a minimum of 5 random realisations of each parameter set.453 We set-up elumpy 500AZ. star clusters with AN.=1000 equal-mass particles within a static background. gas potential., We set-up clumpy $500 M_\odot$ star clusters with $N=1000$ equal-mass particles within a static background gas potential.454 The dynamical state of the stars varies [rom very cold. to almost unbound., The dynamical state of the stars varies from very cold to almost unbound.455 The stars dynamically evolve within the gas potential before its instantaneous removal after 3 Myr., The stars dynamically evolve within the gas potential before its instantaneous removal after 3 Myr.456 We measure the final properties of cach star cluster an additional 3 Myr after eas expulsion., We measure the final properties of each star cluster an additional 3 Myr after gas expulsion.457 A summary of the Κον parameters is provided in Table L.., A summary of the key parameters is provided in Table \ref{parstable}. .458narrower than observed. suggesting that line formation regions predicted by CMFGEN were confined to velocities/radii that were too small.,"narrower than observed, suggesting that line formation regions predicted by CMFGEN were confined to velocities/radii that were too small."459 Despite a continued success with reproducing the overall continuum energy distribution. CMFGEN failed to reproduce important line profiles. whenever hydrogen started recombining at and above the photosphere.," Despite a continued success with reproducing the overall continuum energy distribution, CMFGEN failed to reproduce important line profiles, whenever hydrogen started recombining at and above the photosphere."460 The Ha problem has not been clearly emphasized in the iterature. where one can see a great disparity in model atmosphere assumptions and agreement between theoretical predictions and observations. but no direct link to physical/numerical issues.," The $\alpha$ problem has not been clearly emphasized in the literature, where one can see a great disparity in model atmosphere assumptions and agreement between theoretical predictions and observations, but no direct link to physical/numerical issues."461 In he eighties and early nineties. the recognized importance of non-LTE effects confronted the strong limitations of computer echnology. so that only a few species were treated in non-LTE (.e.. usually hydrogen and helium). while the metals responsible or line blanketing were treated in LTE.," In the eighties and early nineties, the recognized importance of non-LTE effects confronted the strong limitations of computer technology, so that only a few species were treated in non-LTE (i.e., usually hydrogen and helium), while the metals responsible for line blanketing were treated in LTE."462 Eastman&Kirshner(1989). followed this approach to model the first ten days of SN 1987A. and did not encounter obvious difficulties with hydrogen ines. Schmutzetal.(1990).," \citet{Eastman_Kirshner_1989} followed this approach to model the first ten days of SN 1987A, and did not encounter obvious difficulties with hydrogen lines. \citet{Schmutz_etal_1990},"463.. using an approximate non-LTE echnique. had. on the contrary. great difficulty reproducing any of he Balmer lines. suggesting clumping as the culprit.," using an approximate non-LTE technique, had, on the contrary, great difficulty reproducing any of the Balmer lines, suggesting clumping as the culprit."464" H6flich(1988) reproduced the SN 1987A spectral evolution and the hydrogen ines. over many months. using a large ""turbulent"" velocity."," \citet{Hoeflich_1988} reproduced the SN 1987A spectral evolution and the hydrogen lines, over many months, using a large “turbulent” velocity."465 In he more sophisticated non-LTE CMFGEN (HillierDessart&Hillier2005a) models presented in Dessart&Hillier (20062)... we found that decreasing the turbulent velocity weakened ine-blanketing effects and increased. although only modestly. he strength of hydrogen lines.," In the more sophisticated non-LTE CMFGEN \citep{HM_98,DH_05a}466 models presented in \citet{DH_06a}, we found that decreasing the turbulent velocity weakened line-blanketing effects and increased, although only modestly, the strength of hydrogen lines."467 However. beyond 40 days after explosion. this tuning had no longer any important influence on he hydrogen lines.," However, beyond 40 days after explosion, this tuning had no longer any important influence on the hydrogen lines."468" The non-LTE model atmosphere codePHOENIX predicts strong Balmer lines at the hydrogen recombination epoch (Mitchelletal.2001:Baron 2003).. but this may stem from their adoption of non-thermal ionization/excitation due to ""Ni at the photosphere. sometimes just a few days after explosion and in mass shells moving at z: in SN 1987A (Mitchelletal.2001) or 9000 in SN 1993W (Baronetal.2003)."," The non-LTE model atmosphere codePHOENIX predicts strong Balmer lines at the hydrogen recombination epoch \citep{Mitchell_etal_2001,Baron_etal_2003}, but this may stem from their adoption of non-thermal ionization/excitation due to $^{56}$ Ni at the photosphere, sometimes just a few days after explosion and in mass shells moving at $\ge$ in SN 1987A \citep{Mitchell_etal_2001} or $\sim$ in SN 1993W \citep{Baron_etal_2003}."469" Hydrodynamical simulations of core-collapse SNe predict that ""Ni has velocities of at most ~4000kms.. the nickel fingers being strongly decelerated at the H/He interface (Fryxelletal.1991:Kifonidis2000. 2003)."," Hydrodynamical simulations of core-collapse SNe predict that $^{56}$ Ni has velocities of at most $\sim$, the nickel fingers being strongly decelerated at the H/He interface \citep{Fryxell_etal_1991,Kifonidis_etal_2000, Kifonidis_etal_2003}."470 The magnitude of this disagreement extends far beyond the uncertainties of explosion models and suggests a genuine incompatibility., The magnitude of this disagreement extends far beyond the uncertainties of explosion models and suggests a genuine incompatibility.471" Interestingly. lines remain strong for months in all Type II SNe. in objects as diverse as the ""peculiar"" SN. 1987A. the ""plateau"" SN. 1999em. and the ""low-luminosity"" SN. 1999br."," Interestingly, lines remain strong for months in all Type II SNe, in objects as diverse as the “peculiar” SN 1987A, the “plateau” SN 1999em, and the “low-luminosity” SN 1999br."472 CMFGEN models computed for these objects were unable to reproduce Balmer lines after  days in SN 1987A. ~40 days in SN 1999em. and ~20 days in SN 1999br. all coincident with hydrogen recombination in the ejecta.," CMFGEN models computed for these objects were unable to reproduce Balmer lines after $\sim$ 4 days in SN 1987A, $\sim$ 40 days in SN 1999em, and $\sim$ 20 days in SN 1999br, all coincident with hydrogen recombination in the ejecta."473 These three SNe have very different inferred ejecta properties and observed light curves., These three SNe have very different inferred ejecta properties and observed light curves.474 SN 1999br even synthesized an order of magnitude less Ni than average (Pastorelloetal.2004) for the Type II class., SN 1999br even synthesized an order of magnitude less $^{56}$ Ni than average \citep{Pastorello_etal_2004} for the Type II class.475 The only common property between these objects. which is connected to the Ha problem. is the recombination of the ejecta to a lower ionization state at the corresponding epoch.," The only common property between these objects, which is connected to the $\alpha$ problem, is the recombination of the ejecta to a lower ionization state at the corresponding epoch."476 Recently. Utrobin&Chugai(2005.UCOS) proposed that the effect of time-dependence. and the energy associated with changes in ionization/excitation. lead to a strong Ha line profile in SN 1987A during the recombination epoch.," Recently, \citet[UC05]{UC_05} proposed that the effect of time-dependence, and the energy associated with changes in ionization/excitation, lead to a strong $\alpha$ line profile in SN 1987A during the recombination epoch."477 They also found that barium lines were affected. and that. with their more consistent approach. ccould be fitted using the LMC metallicity value.," They also found that barium lines were affected, and that, with their more consistent approach, could be fitted using the LMC metallicity value."478 The steady-state models of Mazzalietal.(1992). supported instead an abundance enhancement of five., The steady-state models of \citet{Mazzali_etal_1992} supported instead an abundance enhancement of five.479 Time dependence has been invoked in the past by FranssonKozma(1993). to explain the late-time light curve of S 1987A. and the theoretical study of Pinto&Eastman(2000a.b) showed that time dependence had a critica impact on the radiative transfer in Type Ius. Pinto&(2000a.b).," Time dependence has been invoked in the past by \citet{Fransson_Kozma_1993} to explain the late-time light curve of SN 1987A, and the theoretical study of \citet{Pinto_Eastman_2000a,480Pinto_Eastman_2000b} showed that time dependence had a critical impact on the radiative transfer in Type Ias. \citet{Pinto_Eastman_2000a, Pinto_Eastman_2000b},"481. however. treat the material in LTE. 1.e.. do not solve the rate equations. focusing instead on the time-dependentdiffusion of photons through an optically thick Type Ia SN ejecta.," however, treat the material in LTE, i.e., do not solve the rate equations, focusing instead on the time-dependent of photons through an optically thick Type Ia SN ejecta."482 Similarly. Kasenetal.(2006) neglect explicit time dependence in the rate equations. computing the ionization and excitation state of the medium in LTE.," Similarly, \citet{Kasen_etal_2006} neglect explicit time dependence in the rate equations, computing the ionization and excitation state of the medium in LTE."483 Thus. although there is at present growing interest in accounting for time dependence in the radiation field. the often-used expedient of LTE. to maintain low CPU costs. has forced the neglect of both non-LTE and time-dependence in the level populations.," Thus, although there is at present growing interest in accounting for time dependence in the radiation field, the often-used expedient of LTE, to maintain low CPU costs, has forced the neglect of both non-LTE and time-dependence in the level populations."484 One exception to these time-dependent LTE approaches is the work of Hóflich(2003).. who treats time-dependence in the rate equations but. to our knowledge. has not discussed the associated effects on Type Π SN spectra.," One exception to these time-dependent LTE approaches is the work of \citet{Hoeflich_2003}, who treats time-dependence in the rate equations but, to our knowledge, has not discussed the associated effects on Type II SN spectra."485 In the present study. we investigate thoroughly the effects of time-dependence in the rate equations and their impact on inferred ejecta properties.," In the present study, we investigate thoroughly the effects of time-dependence in the rate equations and their impact on inferred ejecta properties."486 Note that time dependence in the radiation field is accounted for by adjusting the base luminosity so that the emergent synthetic flux matches the observed flux. using the bolometric-light evolution of SN 1999em as a guide (Dessart&Hillier2006a).," Note that time dependence in the radiation field is accounted for by adjusting the base luminosity so that the emergent synthetic flux matches the observed flux, using the bolometric-light evolution of SN 1999em as a guide \citep{DH_06a}."487. Here. we report the salient features of several non-LTE CMFGEN simulations. covering the early evolution for a range of Type II SN ejecta.," Here, we report the salient features of several non-LTE CMFGEN simulations, covering the early evolution for a range of Type II SN ejecta."488 We confirm the results of UCOS that time-dependence induces an over-ionization of the recombining ejecta and that it solves the Ha problem., We confirm the results of UC05 that time-dependence induces an over-ionization of the recombining ejecta and that it solves the $\alpha$ problem.489 However unlike UCOS. we self-consistently solve the radiation transfer equation — the coupling between the level populations and the radiation field is calculated and fully allowed for.," However unlike UC05, we self-consistently solve the radiation transfer equation — the coupling between the level populations and the radiation field is calculated and fully allowed for."490 Our more comprehensive study of the full spectrum further predicts that all lines. not just those of hydrogen. are significantly affected.," Our more comprehensive study of the full spectrum further predicts that all lines, not just those of hydrogen, are significantly affected."491 The ionization of the ejecta and its evolution are so strongly modified that we predict even mmany weeks after explosion., The ionization of the ejecta and its evolution are so strongly modified that we predict even many weeks after explosion.492 In the next section. we present out treatment of time-dependence in CMFGEN. which focuses here on the terms appearing in the statistical and radiative equilibrium equations (an appendix also provides further details).," In the next section, we present out treatment of time-dependence in CMFGEN, which focuses here on the terms appearing in the statistical and radiative equilibrium equations (an appendix also provides further details)."493 In. 822.5. we present the various model ealeulations performed to illustrate our discussion.," In 2.5, we present the various model calculations performed to illustrate our discussion."494 In $33. we present our results. discussing the effects of time dependence on the ejecta properties as well as the associated spectroscopic signatures.," In 3, we present our results, discussing the effects of time dependence on the ejecta properties as well as the associated spectroscopic signatures."495 We then present in $44 a comparison with a few representative observations. focusing on the well observed Type II Plateau SN 1999em and the low luminosity Type II SN 1999br.," We then present in 4 a comparison with a few representative observations, focusing on the well observed Type II Plateau SN 1999em and the low luminosity Type II SN 1999br."496 In $55. we discuss the implications of such time-dependent effects on our understanding and on our modeling of photospheric- Type II SN spectra. before giving our conclusions in $66.," In 5, we discuss the implications of such time-dependent effects on our understanding and on our modeling of photospheric-phase Type II SN spectra, before giving our conclusions in 6."497" Note that the salient features and key results presented here are also available in a concise. ""letter"". format in Dessart&Hillier (2006b).. to which we refer the hurried reader."," Note that the salient features and key results presented here are also available in a concise, “letter”, format in \citet{DH_06b}, , to which we refer the hurried reader."498An allernalive explanation for the additional measured reddening is (hat we have misinterpreted. as reddening a change in the (turnolE color over the extended distribution ol Ser.,An alternative explanation for the additional measured reddening is that we have misinterpreted as reddening a change in the turnoff color over the extended distribution of Sgr.499 Such a difference in turnolf color would require the extended Ser population be either older or more metal-rich than the Ser core population., Such a difference in turnoff color would require the extended Sgr population be either older or more metal-rich than the Sgr core population.500 The latter is unlikelv. given the known metallicity gradients.," The latter is unlikely, given the known metallicity gradients."501 However. (he lormer— an age difference — remains a possibility.," However, the former – an age difference – remains a possibility."502 Our analvsis explicitly includes an age differential in Ser by using only the older isochrones from Paper IV in our analvsis of the background leatures., Our analysis explicitly includes an age differential in Sgr by using only the older isochrones from Paper IV in our analysis of the background features.503 Paring down the Ser background population to only the oldest Slut population and Ser MPP from Paper IV. would move the backeround features closer by approximately 0.05 magnitudes in distance modulus., Paring down the Sgr background population to only the oldest SInt population and Sgr MPP from Paper IV would move the background features closer by approximately 0.05 magnitudes in distance modulus.504 Stripping the Ser stream population down to only Ser MPP would move the background [features closer by another 0.14 magnitudes., Stripping the Sgr stream population down to only Sgr MPP would move the background features closer by another 0.14 magnitudes.505 IIowever. neither of these changes would remove the readily apparent reddening difference between (he foreground. bulge cluster ancl background. Ser feature. because the older populations are also more metal poor ancl therefore have a bluer," However, neither of these changes would remove the readily apparent reddening difference between the foreground bulge cluster and background Sgr feature, because the older populations are also more metal poor and therefore have a bluer"506cluster spectrum most closely matches their template I& stars. consistent with the Starburst99 prediction that Ix II stars dominate the spectrin at the inferred cluster age (discussed in Section [.13).,"cluster spectrum most closely matches their template K stars, consistent with the Starburst99 prediction that K II stars dominate the spectrum at the inferred cluster age (discussed in Section \ref{age}) )."507 We adopt these results to measure the cluster mass with optical data., We adopt these results to measure the cluster mass with optical data.508 Iu the ACS FalWW image. we measure a half-ligbt radius of 119+2 as.," In the ACS F814W image, we measure a half-light radius of $119 \pm 2$ mas."509" Using this value aud the SCOL velocity dispersion. we fud an L-band virial mass of M,=7.0c1.3«Lo? M... for AL82-F. This is significantly lower than the opically-derived SCL mass estimate of L240.1ς109 AL. de to more accurate measure of the cluster’s halt-lishbit radius (sce Section [.1))."," Using this value and the SG01 velocity dispersion, we find an $I$ -band virial mass of $M_I = 7.0 \pm 1.2 \times 10^5$ $_{\odot}$ for M82-F. This is significantly lower than the optically-derived SG01 mass estimate of $1.2 \pm 0.1 \times 10^6$ $_{\odot}$ due to more accurate measure of the cluster's half-light radius (see Section \ref{acsdata}) )."510 Phoonietrv was derived bv iutegratiug over the fitted Ning uodels anc applviug the appropriate conversiou factors for each iustrineut aud filter., Photometry was derived by integrating over the fitted King models and applying the appropriate conversion factors for each instrument and filter.511 Details of the PSF fitting photometry and spectral cucrey distribution are presened in a companion paper €2).., Details of the PSF fitting photometry and spectral energy distribution are presented in a companion paper \citep{vacca04}.512" The observed cluster i-banud muuimosities as defined iu ον, not corrected for extinction. are {Εν=3840.6.10° L. aud Lrigy=Loto.107 L.."," The observed cluster in-band luminosities as defined in \citet{mccrady03}, not corrected for extinction, are $L_{F814} = 3.8 \pm 0.6 \times 10^5$ $_{\odot}$ and $L_{F160} = 4.0 \pm 0.7 \times 10^5$ $_{\odot}$."513" By comparing the derived light-to-mmass ΑΓ) ratio of AIS2-F to population svuthesis models, we may characterize the IME of the cluster."," By comparing the derived light-to-mass $L/M$ ) ratio of M82-F to population synthesis models, we may characterize the IMF of the cluster."514 Critical to this analysis are the cluster age aud line-of-sight extinction., Critical to this analysis are the cluster age and line-of-sight extinction.515 The spectruii of MBS2-F. imunecdiately places upper aud ower bounds ou he clusters age., The spectrum of M82-F immediately places upper and lower bounds on the cluster's age.516 There is no evidence of nebular euussion in the Z7- or A-baud. which ucdicates he absence of O stars and a iium cluster aee of 6 που.," There is no evidence of nebular emission in the $H$ - or $K$ -band, which indicates the absence of O stars and a minimum cluster age of 6--7 Myr."517 ? finds none of the features expected of AGB stars for the nuclear region of AIS82. setting an upper int of ~10? vears.," \citet{natascha98} finds none of the features expected of AGB stars for the nuclear region of M82, setting an upper limit of $\sim 10^8$ years."518 For more precise nuits ou the age. we turn to population svuthesis modelling.," For more precise limits on the age, we turn to population synthesis modelling."519 As noted in Sectki 3.. the F160W light of NIS2-F most closely matches cluplate spectral vpes in the ranee of INtTMOI. ? used Starburst99 population svuthesis models to determine the Hux-welehted average spectral type as a function of age for ορσνα] stellar populatious.," As noted in Section \ref{analysis}, the F160W light of M82-F most closely matches template spectral types in the range of K4I–M0I. \citet{gilbert02th} used Starburst99 population synthesis models to determine the flux-weighted average spectral type as a function of age for coeval stellar populations."520" Iu the Z7-baud. the cluster light is dominated by Ntλ0 stars for a brief period around 15 αν ancl during the ages of ~ LO60 Myr,"," In the $H$ -band, the cluster light is dominated by K4–M0 stars for a brief period around 15 Myr and during the ages of $\sim$ 40–60 Myr."521 SCGOL used Starburst99 models to fit the Πὸ and Πο Τ absorption profiles iu optical specra., SG01 used Starburst99 models to fit the $\delta$ and He I absorption profiles in optical spectra.522 Thev found that the best fits to the wines of the Balmer line aud depth of the helm liue suggest au age of 60+20 Myr., They found that the best fits to the wings of the Balmer line and depth of the helium line suggest an age of $60 \pm 20$ Myr.523 This is cousistent with the dominant spectral type of the /7-baud light. aud we thereore adopt an age range of LO60 Myr for M82-F. SGHW used BV photometry to determine line-of-sight extinction of Ay=2.8.," This is consistent with the dominant spectral type of the $H$ -band light, and we therefore adopt an age range of 40–60 Myr for M82-F. SG01 used $BVI$ photometry to determine line-of-sight extinction of $A_V = 2.8$."524 Applving the ? extinction law (Ry= 3.1) to the this value gives «πιο.=0.53 aud Arawo=1.65.," Applying the \citet{cardelli89} extinction law $R_V =5253.1$ ) to the this value gives $A_{F160W} = 0.53$ and $A_{F814W} =5261.63$."527 As an independent test. we calculate svuthetic colors for the nem-IR dominant evolved IKlMO stars based ou the ? stellar spectral library.," As an independent test, we calculate synthetic colors for the near-IR dominant evolved K4–M0 stars based on the \citet{pickles98} stellar spectral library."528 The svuthetic [FLGOW| |F222M| color for a I&II star is 0.35. versus 0.52 for MOI. From our plotometiy. we find [FIGOW [F222MI] = 0.364FEO.01 for AIS2-F. at the blue cud of the| expected color rauge.," The synthetic [F160W] $-$ [F222M] color for a K4I star is 0.35, versus 0.52 for M0I. From our photometry, we find [F160W] $-$ [F222M] = $0.36 \pm 0.04$ for M82-F, at the blue end of the expected color range."529 This iniplies that. /7-baud extinction to MBS2-F. is quite simall. essentially neglieible.," This implies that $H$ -band extinction to M82-F is quite small, essentially negligible."530 The optical (600-800 111) Light of the cluster is expected to be dominated by KII stars (SCOL)., The optical (600-800 nm) light of the cluster is expected to be dominated by KII stars (SG01).531 Syuthetic F555W| [F5LIW] colors for these stars in the Pickles library range from 1.19 to 1.15. versus the measured 1.7140.01 for AIS2-F. For a standard (πι=3.1) interstellar extinction curve. this color excess gives «ρα=031 to 0.66 mae.," Synthetic [F555W] $-$ [F814W] colors for these stars in the Pickles library range from 1.19 to 1.45, versus the measured $1.71 \pm 0.04$ for M82-F. For a standard $R_V = 3.1$ ) interstellar extinction curve, this color excess gives $A_{F814W} =5320.34$ to 0.66 mag."533 To caleulate the light-to-nass ratio. we need to deredden the cluster.," To calculate the light-to-mass ratio, we need to deredden the cluster."534 We adopt extinction of dgio=0.0!uu aud πω=0.50.2 based on the svuthetic photometry results.," We adopt extinction of $A_{F160W} = 0.0 ^{+0.1}_{-0.0}$ and $A_{F814W}535= 0.5 \pm 0.2$ based on the synthetic photometry results."536 For sake of comparison. Figure ?7 reflects both these estimates aud the extinctions implied by the SCUL estimate of ely.," For sake of comparison, Figure \ref{sb99plot} reflects both these estimates and the extinctions implied by the SG01 estimate of $A_V$."537 The Calactic dust map of ? indicates Galactic extinction along the line of sight to AIS2-F of Ay=0.Ls. Aran=028 and Ariouy=0.09.," The Galactic dust map of \citet{schlegel98} indicates Galactic extinction along the line of sight to M82-F of $A_V = 0.48$, $A_{F814W} = 0.28$ and $A_{F160W} = 0.09$."538 This provides a for the estimated extinction., This provides a cross-reference for the estimated extinction.539 We determine the huninmositv aud virial mass of the cluster independent of auv assumptions about the IME., We determine the luminosity and virial mass of the cluster independent of any assumptions about the IMF.540 This is iu contrast to photometric mass deteriinations. which are based on cluster colors and ages aud mist herexe assuue an TMF.," This is in contrast to photometric mass determinations, which are based on cluster colors and ages and must therefore assume an IMF."541 Our inethod enables us to constrain the cluster IME by comparing observed lisht-to-lass ratios mn various wavebands to population svutlesis nodels (2?)..," Our method enables us to constrain the cluster IMF by comparing observed light-to-mass ratios in various wavebands to population synthesis models \citep{sternberg98,mccrady03}."542 Dv:ipplving the adopted exiuction corrections for F. we find de-redcdened lisht-toaunass ratios of L/M=L6xU (L. AL.) at L6;120 aud L/A/=0.9+0.2 at Span. Figure 77. compares he measured £/AL ratio to »pulatiou svuthesis model xedietious for two fiducial IME forms.," By applying the adopted extinction corrections for M82-F, we find de-reddened light-to-mass ratios of $L/M = 0.6 \pm 0.1$ $_\odot$ $_\odot$ ) at $\mu$ m and $L/M = 0.9 \pm 0.2$ at $\mu$ m. Figure \ref{sb99plot} compares the measured $L/M$ ratio to population synthesis model predictions for two fiducial IMF forms."543 We use Starburst99 version L0. with au istantancous burst. solar mieallicity (2). and the Ilillier Pauldrach atinosphere moels.," We used Starburst99 version 4.0, with an instantaneous burst, solar metallicity \citep{mcleod93} and the Hillier Pauldrach atmosphere models."544 The derived. £/AL ratio of MBS2-F is too Heh for the standard ? IMFE over the full range of sCllar masses (0.100. ADL., The derived $L/M$ ratio of M82-F is too high for the standard \citet{kroupa01} IMF over the full range of stellar masses (0.1–100 $_{\odot}$ ).545 Rather it appears that the clusters IAIF is eCficient in low-1ass stars., Rather it appears that the cluster's IMF is deficient in low-mass stars.546 For example. the L/ÀA ratio is roughly cousisteut with a? IME truncated at a lower uass of about 2 AL...," For example, the $L/M$ ratio is roughly consistent with a \citet{salpeter55} IMF truncated at a lower mass of about 2 $_{\odot}$."547 If the cluster age were approximately 15 Myr. the derived LIAM vatios would ος consistent with the Iroupa IME: an independent determination ¢ft the clusters age could rule out this possibility.," If the cluster age were approximately 15 Myr, the derived $L/M$ ratios would be consistent with the Kroupa IMF; an independent determination of the cluster's age could rule out this possibility."548" Ii our analysis we assunue a pariculax form for the IMF ιο, Ixxoupa or Salpeter power avs) and inodifv the lower-nass cutoff to eeucrate the observed L/M ratio at the adopted age."," In our analysis we assume a particular form for the IMF (i.e., Kroupa or Salpeter power laws) and modify the lower-mass cutoff to generate the observed $L/M$ ratio at the adopted age."549 This method allows us to test the top-heavy IME hypothesis 1| fhe observed £/AL ratio is fit with au IMF extending «own to 0.1 M. as in cluster AICC-9 in ον there is no need to invoke an abnormal IME.," This method allows us to test the top-heavy IMF hypothesis — if the observed $L/M$ ratio is fit with an IMF extending down to 0.1 $_{\odot}$, as in cluster MGG-9 in \citet{mccrady03}, there is no need to invoke an abnormal IMF."550 Iun the present case. a torial (Ikroupa) IATF cannot explain the relatively large L/AM ratio of the cluster.," In the present case, a normal (Kroupa) IMF cannot explain the relatively large $L/M$ ratio of the cluster."551 An elevated lowerauass cutoff is not required. however.," An elevated lower-mass cutoff is not required, however."552 The observed L/M ratios could )o caused at the clusters age by flattening the slope of t16 IME. which would. change the relative proportions of stellar masses.," The observed $L/M$ ratios could be caused at the cluster's age by flattening the slope of the IMF, which would change the relative proportions of stellar masses."553" Although our cata cο not distinguish between changes to the lower mass cutoff or IME slope. it is evident that the IAIF is different than he Iroupa form. and different frou, other nearby SSCs in the M82 nuclear starburst."," Although our data do not distinguish between changes to the lower mass cutoff or IMF slope, it is evident that the IMF is different than the Kroupa form, and different from other nearby SSCs in the M82 nuclear starburst."554Q.2 dex. compared to those with low SSFR at fixed stellar mass.,"0.2 dex, compared to those with low SSFR at fixed stellar mass."555 The fact that their metallicities are estimated by a comparable but independent method (see Kewley&Dopita(2002). for details). further strengthens our result.," The fact that their metallicities are estimated by a comparable but independent method (see \citet{kd} for details), further strengthens our result."556 Around of all red star-forming galaxies are classified as star-forming or composite galaxies from their spectra., Around of all red star-forming galaxies are classified as star-forming or composite galaxies from their spectra.557 This is in agreement with the results of Graves.Faber.&Schiavon(2009) who also find ~30% of nearby red sequence galaxies from SDSS show presence of emission lines in their spectrum., This is in agreement with the results of \citet{gfs} who also find $\sim$ of nearby red sequence galaxies from SDSS show presence of emission lines in their spectrum.558 They analyse LINER like emission in these galaxies to show that they are systematically younger by 2.5-3 Gyrs than their quiescent counterparts without emission at fixed rotational velocity., They analyse LINER like emission in these galaxies to show that they are systematically younger by 2.5-3 Gyrs than their quiescent counterparts without emission at fixed rotational velocity.559 At >~0.1. Tremontietal.(2004) have shown that the metallicity is well correlated with the stellar mass of the galaxy.," At $z\!\sim\!0.1$, \citet{tremonti} have shown that the metallicity is well correlated with the stellar mass of the galaxy."560 These quantities correlate well for 8.S<log Μ΄ 10.5 M.. but the relation flattens thereafter.," These quantities correlate well for $\leq$ log $^{*}\leq$ 10.5 $_\odot$ , but the relation flattens thereafter."561 The fact that 60% of our red galaxies have log M* in the range 10.6- M. supports the hypothesis that a signiticant fraction of the red star-forming galaxies obtain their red colours from the residual older generations of stars., The fact that $\geq$ of our red galaxies have log $^*$ in the range 10.6-10.9 $_\odot$ supports the hypothesis that a significant fraction of the red star-forming galaxies obtain their red colours from the residual older generations of stars.562 We have also shown that ~S0% of all the red star-forming galaxies are likely to be attenuated by 70.2 mag in the SDSS :- (Fig. 4).," We have also shown that $\sim$ of all the red star-forming galaxies are likely to be attenuated by $>$ 0.2 mag in the SDSS $z$ -band (Fig. \ref{dust}) ),"563" and have bimodal Hs EW and D,, 4000 distributions (Figs. 5..6"," and have bimodal $_\delta$ EW and $_n$ 4000 distributions (Figs. \ref{hd},"564 and 7)) which are very different from that of the typical red sequence galaxies., \ref{d4000} and \ref{hd-d4}) ) which are very different from that of the typical red sequence galaxies.565" As discussed in refanalysis! and refanalysis2.. the red star-forming class of galaxies remain bimodal in the distributions of A.. Hs and D,,4000. even if the selection criterion based on SFR/M® is changed to a significantly different value (e.g. ~15-percentile. corresponding to log SFR/M” = -10 7)."," As discussed in \\ref{analysis1} and \\ref{analysis2}, the red star-forming class of galaxies remain bimodal in the distributions of $_z$, $_\delta$ and $_n$ 4000, even if the selection criterion based on $^*$ is changed to a significantly different value (e.g. $\sim$ 15-percentile, corresponding to log $^*$ = -10 $^{-1}$ )."566 This clearly indicates that the component of red star-forming galaxies that are similar in properties to the red sequence galaxies are not merely a result of scatter from the red sequence (quadrant lI: Fig. 2)). Butcher&Oe, This clearly indicates that the component of red star-forming galaxies that are similar in properties to the red sequence galaxies are not merely a result of scatter from the red sequence (quadrant 1; Fig. \ref{ssf-gr}) ).567mler(1984). found that clusters at moderate to high redshift contain an exeess of blue galaxies. compared to their low-redshift counterparts.," \citet{bo} found that clusters at moderate to high redshift contain an excess of blue galaxies, compared to their low-redshift counterparts."568" For the redshift regime of our sample ἐς~ 0.1. they found a uniform blue fraction f, of ~0.03 in all clusters within Κο. the radius containing of the cluster's red sequence population."," For the redshift regime of our sample $z\!\sim\!0.1$ ), they found a uniform blue fraction $_b$ of $\sim$ 0.03 in all clusters within $_{30}$, the radius containing of the cluster's red sequence population."569 This exercise has been repeated several times in recent years for many samples of clusters (Butcher&Oemlerorisetal. 2004).," This exercise has been repeated several times in recent years for many samples of clusters \citep{bo,m3,e2,d3}."570. Most studies of this kind detine blue’ galaxies in erms of a broadband colour that is bluer by 0.2 mag than that of he cluster's red sequence galaxies., Most studies of this kind define `blue' galaxies in terms of a broadband colour that is bluer by 0.2 mag than that of the cluster's red sequence galaxies.571 From the above discussion. it is clear that this cut leaves out a significant fraction of star-forming galaxies that have redder broadband colours. and classifies some j»ussively evolving galaxies as ‘star-forming’.," From the above discussion, it is clear that this cut leaves out a significant fraction of star-forming galaxies that have redder broadband colours, and classifies some passively evolving galaxies as `star-forming'."572" Margoniner&Carvalho(2000). found the blue fraction of galaxies to be f,20.03-70.09. similar to Butcher&Oemler (1984).. or 44 Abell clusters at 0.03::2::0.38 within a fixed cluster-centric distance of 0.7 Mpc. which translates into the mean Ro for most Abell clusters below 2=0.1."," \citet{m3} found the blue fraction of galaxies to be $_b$ $\pm$ 0.09, similar to \citet{bo}, , for 44 Abell clusters at $\leq$ $\leq$ 0.38 within a fixed cluster-centric distance of 0.7 Mpc, which translates into the mean $_{30}$ for most Abell clusters below $z\lesssim 0.1$."573 However. Margonineretal.(2001) measured the fraction to be (1.24-E0.07).—0.01 for clusters at >=0.25. again for galaxies within a fixed cluster-centric aperture of 0.7 Mpe.," However, \citet{m1} measured the fraction to be $(1.24\pm 0.07)z-0.01$ for clusters at $z\!\leq\!574 0.25$, again for galaxies within a fixed cluster-centric aperture of 0.7 Mpc."575 Elsewhere (Ellingsonetal.2001:DePropris 2004)3.. various multiples of cluster-centrie radius. sealed with rooo. have been used to show the effect of chosen aperture size on the blue fraction.," Elsewhere \citep{e2,d3}, various multiples of cluster-centric radius, scaled with $_{200}$, have been used to show the effect of chosen aperture size on the blue fraction."576" Ellingsonetal.(2001) suggest that the origin of the Butcher-Oemler effect lies in the fact that the relative fraction of ""blue"" galaxies on the outskirts of the clusters at higher redshifts is higher than in their local counterparts."," \citet{e2}577 suggest that the origin of the Butcher-Oemler effect lies in the fact that the relative fraction of `blue' galaxies on the outskirts of the clusters at higher redshifts is higher than in their local counterparts."578 If confirmed. this result ean have a eritical impact on the study ofevolution of galaxy properties.," If confirmed, this result can have a critical impact on the study of evolution of galaxy properties."579 It is worth mentioning here that even though most of these studies use optical spectra for most or all of their sample (except for Butcher&Oemler(1984))). the spectroscopic information is used only for assigning cluster membership.," It is worth mentioning here that even though most of these studies use optical spectra for most or all of their sample (except for \citet{bo}) ), the spectroscopic information is used only for assigning cluster membership."580 Recently. with the increasing availability of large multi-wavelength datasets. the possibility of the Buteher-Oemler effect being observed in other fundamental galaxy properties (e.g.shology.Gotoetal.2003b).. or in non-optical data (e.g.mid-IR.Saintonge.Tran&Holden 2008).. is being explored.," Recently, with the increasing availability of large multi-wavelength datasets, the possibility of the Butcher-Oemler effect being observed in other fundamental galaxy properties \citep[\eg~morphology,][]{goto03b}, or in non-optical data \citep[\eg~mid-IR, ][]{saintonge}, is being explored."581 The study of Wolf.Gray&Meisenheimer(2005) unraveled the oesence of young stars and dust in the red sequence galaxies in a cluster pair at z—0.17. while Bildfelletal.(2008). find that he colour profile of of the brightest cluster galaxies (BCOs) urn bluer by 0.5—1.0 mag towards their centres. compared to the average colours seen in the cluster's red sequence.," The study of \citet{wolf} unraveled the presence of young stars and dust in the red sequence galaxies in a cluster pair at $\sim$ 0.17, while \citet{bildfell} find that the colour profile of of the brightest cluster galaxies (BCGs) turn bluer by 0.5–1.0 mag towards their centres, compared to the average colours seen in the cluster's red sequence."582 All of this ws serious implications for Butcher-Oemler like effects based on global photometric properties., All of this has serious implications for Butcher-Oemler like effects based on global photometric properties.583 Our sample provides some additional insight to this discussion., Our sample provides some additional insight to this discussion.584 The presence of metals. and of colour gradients relatec to SFR in a galaxy. will affect the estimated fraction of “star-forming” galaxies in low redshift clusters.," The presence of metals, and of colour gradients related to SFR in a galaxy, will affect the estimated fraction of `star-forming' galaxies in low redshift clusters."585 The fact that nearby cluster galaxies are more metal-rich than those in high-redshif clusters. will artificially enhance the fraction of passive galaxies that are selected solely on the basis of their colour.," The fact that nearby cluster galaxies are more metal-rich than those in high-redshift clusters, will artificially enhance the fraction of passive galaxies that are selected solely on the basis of their colour."586 Such an effec is usually not accounted for while comparing the blue/star-forming galaxy fraction in clusters at different redshifts., Such an effect is usually not accounted for while comparing the blue/star-forming galaxy fraction in clusters at different redshifts.587 A quantitative analysis of this effect requires a consistent study of an unbiasec sample of mutually comparable galaxy clusters spanning a wide redshift range. for which both photometric and spectroscopic multi-wavelength data is available.," A quantitative analysis of this effect requires a consistent study of an unbiased sample of mutually comparable galaxy clusters spanning a wide redshift range, for which both photometric and spectroscopic multi-wavelength data is available."588 We leave this for a later consideration., We leave this for a later consideration.589 We divide a sample of 76.000 galaxies found in or near rich Abell clusters (z<0.12) in the SDSS spectroscopic catalogue. into four populations. defined by placing simple limits in (gο) colour (derived from photometry) and specitiestar formation rate (derived from the detailed modelling of optical spectra).," We divide a sample of $>$ 6,000 galaxies found in or near rich Abell clusters $\leq$ 0.12) in the SDSS spectroscopic catalogue, into four populations, defined by placing simple limits in $(g-r)^{0.1}$ colour (derived from photometry) and specificstar formation rate (derived from the detailed modelling of optical spectra)."590 While most blue galaxies have evidence of star formation. and red galaxies do not. this identifies two significant populations of blue passive galaxies and red star-forming galaxies.," While most blue galaxies have evidence of star formation, and red galaxies do not, this identifies two significant populations of blue passive galaxies and red star-forming galaxies."591 We trace the spectroscopic and photometric properties of galaxies in these four sub-samples in detail. using data available from SDSS DR4.," We trace the spectroscopic and photometric properties of galaxies in these four sub-samples in detail, using data available from SDSS DR4."592 The main results of our analysisean be summarised as follows:, The main results of our analysiscan be summarised as follows:593reflection is required. the inclination dependence of the iron line properties will be important for disentangling the enhancement mechanisms.,"reflection is required, the inclination dependence of the iron line properties will be important for disentangling the enhancement mechanisms."594 As shown in this work. if source motion is responsible or the enhancement. the EW of the line will decrease signicantly as one considers sources at highere inclination (note that the inclination of the disk can be measured robustly rom the iron line profile).," As shown in this work, if source motion is responsible for the enhancement, the EW of the line will decrease significantly as one considers sources at higher inclination (note that the inclination of the disk can be measured robustly from the iron line profile)."595 This cllect will be much stronger ian the inclination. dependence of the line just based on imb-darkening (George Fabian 1901)., This effect will be much stronger than the inclination dependence of the line just based on limb-darkening (George Fabian 1991).596 A careful analysis of existing. datasets might. allow suc. ra trend to be addressed., A careful analysis of existing datasets might allow such a trend to be addressed.597 CSR. gratefully acknowledges support from the National Science Foundation under grant ÀST9529175., CSR gratefully acknowledges support from the National Science Foundation under grant AST9529175.598 ACT thanks the Roval Society for support., ACF thanks the Royal Society for support.599 21 76% (Fuji .A. and the “COSC coincidence” problem(Steinhar," $24\%$ $76\% $ \citep{1}, $,\Lambda,$ and the ""cosmic coincidence"" problem\citep{2}."600dt Observational data indicates that O4=0.763 aud ο=0.237. so large value of O4 obviously predicts that the uuiverse is accelerating today. rather than decelerating as had long been believed.," Observational data indicates that $\Omega_{\Lambda}=0.763$ and $\Omega_{m}=0.237$, so large value of $\Omega_{\Lambda}$ obviously predicts that the universe is accelerating today, rather than decelerating as had long been believed."601 The observation evidence tells us that rate of expansion m the high-z region is slower than that in our neigliborhood., The observation evidence tells us that rate of expansion in the high-z region is slower than that in our neighborhood.602 Iu his condition. where as variation of the pa with respect to the time is equa to zero. this is provide a problem in cosinoloeyv. called fine tauniug. the quiutessence (cosmon-fBeld) solved this problem. bv using coupling between scalar feld and dar matter (FujiaucNish-loka1981:Weoiulvere 1989).," In this condition, where as variation of the $\rho _{\Lambda }$ with respect to the time is equal to zero, this is provide a problem in cosmology, called fine tanning, the quintessence (cosmon-field) solved this problem, by using coupling between scalar field and dark matter \citep{3b,3}."603. There are several cliffcrent theories. which rave been proposed by people. to interpret the accelerating universe. such as. holograjhic DE model (Li2001:Setare20072:IriaudFeli 2011).. ageerajhic DE models (Cai2007:WeiaudCai2008:Irunet aud scalar field models of DE. which incluiue quintessence field (NojiriandOdinSOV. 2003).. quiutui field (Elazaldeetal.2001:Fenge 2005).. oiautoui field (Caldwellctal.2003) aud many others.," There are several different theories, which have been proposed by people, to interpret the accelerating universe, such as, holographic DE model \citep{4,41a,4b,41d}, agegraphic DE models \citep{5,a,b,c} and scalar field models of DE, which including quintessence field \citep{61}, quintum field \citep{8a,8}, phantom field \citep{6} and many others."604 While the quantity of cosmological coustaut is ron zero. the DE component is more generally uoceled as quiutesscwee mnechauisin.," While the quantity of cosmological constant is non zero, the DE component is more generally modeled as quintessence mechanism."605 I is a scalar field rolling down a fia potential., It is a scalar field rolling down a flat potential.606 Iu quintessence 1uechauisui. he field ju Uuceative pressure aud therefore acts o accelerate expansion (Weimberg0051.," In quintessence mechanism, the field has negative pressure and therefore acts to accelerate expansion \citep{10}."607 Ikhouryv aud Wellan {2003) have introduced another ια nechamisin. which called chameleou iechanisi.," Khoury and Weltman (2003) have introduced another kind mechanism, which called chameleon mechanism."608 Iu lis mechamisin the scalar field acquire a mass whose naguitude depexls ou the local matter density (Braxetal.2 XL., In this mechanism the scalar field acquire a mass whose magnitude depends on the local matter density \citep{11}.609.. Also it is a παν to related an effective nass for scalar field o., Also it is a way to related an effective mass for scalar field $\phi$.610 Scalar field is expausion field. and cun © obtained from string theory (Orti/u.2001:001)... Also the chameleon niechauisui Is a wav to eive an effective mass to a Πο scalar field via field sef interaction and interaction between," Scalar field is expansion field, and can be obtained from string theory \citep{12,12a}.. Also the chameleon mechanism is a way to give an effective mass to a light scalar field via field self interaction and interaction between"611 (INomatsuetal.2009).. (Springeletal.2005).. (Bertone," \citep{art-Komatsuetal2009}, \citep{art-Springel2005Natur.435..629S}. \citep{rev-BertoneHS2005}."612etal.2005).. 10.770? 10.om? (Ahmedetal.2009)..," \citep{art-Bernabeietal2010AIPC.1223...50B,art-CDMSII2010science,art-Aalseth2010,art-Fitzpatrick2010}613 $10^{-32} {\rm cm^2}$ \citep{art-XENON10_SD2008,art-COUPP2008}) $10^{-40} {\rm cm}^2$ \citep{art-CDMSII_SI2009}."614 (Dergstrón)000) Sarkar2010) iuportaut complement to ¢lect detection searches for ight WIAMPs., \citep{art-Bergstrom2009NJPh} \citep{art-Frandsen2010PhRvL} important complement to direct detection searches for light WIMPs.615 These particles are trapped iu the Suus interior when they collide with nuclei aud lose (linear) nonientuin. and drift iuto the Suus core.," These particles are trapped in the Sun's interior when they collide with nuclei and lose (linear) momentum, and drift into the Sun's core."616 Collisions of captured particles with the local xuwvous trausfer and redistribute thermal οσον. aud lower the central eniperature bv a few perceut.," Collisions of captured particles with the local baryons transfer and redistribute thermal energy, and lower the central temperature by a few percent."617 In thermal equilibiuu. he kinetic energy of dark matter particles is balanced by he local exavitational potential (Sperec&Press1985 7," In thermal equilibrium, the kinetic energy of dark matter particles is balanced by the local gravitational potential \citep{art-SpergelPress1985}. ."618" An estimation of the radius of the dark matter core is even bv ry,~(91, where nPH and a, are. respectively. TOP)the massv ofimpfin, the proton aud the mass of the dark uatter particle. T, aud p, are the central temperature aud the central density of the Suus core. aud & aud G are. respectively. the Boltzimaun and Newton eravitational constants."," An estimation of the radius of the dark matter core is given by $r_x\sim \left(9 k T_c/4\pi G\rho_c m_p\right)\;\sqrt{m_p/m_x}$ where $m_p$ and $m_x$ are, respectively, the mass of the proton and the mass of the dark matter particle, $T_c$ and $\rho_c$ are the central temperature and the central density of the Sun's core, and $k$ and $G$ are, respectively, the Boltzmann and Newton gravitational constants."619 This expression approxinatelv gives the radius of the dark matter core in the Suu's interior., This expression approximately gives the radius of the dark matter core in the Sun's interior.620 It folkανν that the more massive a dark matter particle. the simaller is the radius of the dark matter core. aud the less ia»ortant is the impact of dark latter in the evolution oftje Sun.," It follows that the more massive a dark matter particle, the smaller is the radius of the dark matter core, and the less important is the impact of dark matter in the evolution of the Sun."621 The Suu shows acuplex pattern of surface oscillations whose restoring orcees are produced either by compressibility or buovancy., The Sun shows a complex pattern of surface oscillations whose restoring forces are produced either by compressibility or buoyancy.622 The pressure perturbations eive rise to acoustic sound waves in the high-frequency part of the spectrum. auk buovanev variations drive eravity waves in the low-frecuencv range of the spectra.," The pressure perturbations give rise to acoustic sound waves in the high-frequency part of the spectrum, and buoyancy variations drive gravity waves in the low-frequency range of the spectrum."623 The small amplitude surtac ‘perturbations observed. iu the Sun can be clescribec as a sun of cigenstates., The small amplitude surface perturbations observed in the Sun can be described as a sum of eigenstates.624 Each cigenstate has a sρα] counterpart that is defined by a spatial cigeifunetion that depends on the thermodvuamical strucure of the backeround state (the Suus internal structiro) aud a tine-depeudenut clecnfiuction that is characerized by the frequency μι," Each eigenstate has a spatial counterpart that is defined by a spatial eigenfunction that depends on the thermodynamical structure of the background state (the Sun's internal structure), and a time-dependent eigenfunction that is characterized by the frequency $\nu_{n,l}$."625 The numbers / and (0are positive integers. known as the degree aud radial order of t16 modoe(e.e..Cough 1993)..," The numbers $l$ and $n$are positive integers, known as the degree and radial order of the \citep[e.g.,][]{art-Gough1993}. ."626 During the last 50 wears. accurate measurements of," During the last 50 years, accurate measurements of"627sight has a value of ~ 607. declining to 10 bby JD +274. when y has a value of ~ 70°.,"sight has a value of $\sim$ $^{\circ}$, declining to 10 by JD +274, when $\chi$ has a value of $\sim$ $^{\circ}$."628" These widths correspond to speeds of 900 and 450 km s7!. respectively. and the data are represented fairly well by the relation where s, 1s the width cx translated into speed in km !."," These widths correspond to speeds of 900 and 450 km $^{-1}$, respectively, and the data are represented fairly well by the relation where $s_w$ is the width $\sigma$ translated into speed in km $^{-1}$ ."629 The speeds in the wings of the wind Πα line are even greater., The speeds in the wings of the wind $\alpha$ line are even greater.630 Thus typical wind speeds are very roughly an order of magnitude greater than the orbital speec of the compact object. anda parcel of wind covers a distance of roughly 1.5 105 km in a single day.," Thus typical wind speeds are very roughly an order of magnitude greater than the orbital speed of the compact object, anda parcel of wind covers a distance of roughly 1.5 $10^{8}$ km in a single day."631 This distance is several times larger than the semi-major axis of the binary system and because the fast wind is predominantly perpendicular to the accretion disk (see also Perez Blundell 2010) it tends to be out of the plane of the orbit., This distance is several times larger than the semi-major axis of the binary system and because the fast wind is predominantly perpendicular to the accretion disk (see also Perez Blundell 2010) it tends to be out of the plane of the orbit.632 It remains to make a quantitative estimate of the effect of any given region of the wind emitting over a period of perhaps several days., It remains to make a quantitative estimate of the effect of any given region of the wind emitting over a period of perhaps several days.633 | approximate the line of sight to the orbital plane (it actually makes an angle of ~12°) and suppose a circular orbit. so that the recessional velocity of a source co-moving with the compact object would be given by where w is given by 2z/P.," I approximate the line of sight to the orbital plane (it actually makes an angle of $\sim$ $^{\circ}$ ) and suppose a circular orbit, so that the recessional velocity of a source co-moving with the compact object would be given by where $\omega$ is given by $2\pi /P$."634" Thus when f is one quarter of the period. P after primary eclipse. the compact object is approaching with speed v, and is receding with speed v, a quarter of a period before primary eclipse."," Thus when $t$ is one quarter of the period $P$ after primary eclipse, the compact object is approaching with speed $v_x$ and is receding with speed $v_x$ a quarter of a period before primary eclipse."635" I now assume that a shell of wind lights up suddenly (say in He) at time ¢ but became detached a time s earlier. the centroid moving with speed v, tangential to the orbit."," I now assume that a shell of wind lights up suddenly (say in $\alpha$ ) at time $t$ but became detached a time $s$ earlier, the centroid moving with speed $v_x$ tangential to the orbit."636 For a delay s of 0.25P. the most redshifted centroid is observed when ;=P rather than 0.75P.," For a delay $s$ of $0.25P$ , the most redshifted centroid is observed when $t=P$ rather than $0.75P$."637 The phasing of the wind centroid relative to the photometric ephemeris only requires a delay of ~2 days., The phasing of the wind centroid relative to the photometric ephemeris only requires a delay of $\sim$ 2 days.638 The final step is to suppose that the H« emission dies away over a timescale of several days., The final step is to suppose that the $\alpha$ emission dies away over a timescale of several days.639" This will atfect the phase and also makes an average of the line-of-sight velocity of the Hw centroid. thereby reducing the amplitude of v, below v."," This will affect the phase and also makes an average of the line-of-sight velocity of the $\alpha$ centroid, thereby reducing the amplitude of $v_r$ below $v_x$."640 This may be calculated by specifying some emission function of s with a delay parameter r and a duration parameter 7: f(s:r.T).," This may be calculated by specifying some emission function of $s$ with a delay parameter $\tau$ and a duration parameter $T$; $f(s; \tau ,T)$."641 At time f. the centroid of the shell detached a time s earlier has recessional velocity given by The value perceived at time fis obtained by averaging over all s. using f(s:r.7) as the weight.," At time $t$, the centroid of the shell detached a time $s$ earlier has recessional velocity given by The value perceived at time $t$ is obtained by averaging over all $s$, using $f(s;\tau ,T)$ as the weight."642 The important point is that for durations of a few days the average over s. «v(t)>. represents very well the data in both amplitude and phase.," The important point is that for durations of a few days the average over $s$, $<v_r(t)>$ , represents very well the data in both amplitude and phase."643 For the purpose of illustration I have used two different functions for the emission factor f(s)., For the purpose of illustration I have used two different functions for the emission factor $f(s)$.644 In the first case I supposed a rectangular profile as a function of s. with a duration of T.," In the first case I supposed a rectangular profile as a function of $s$, with a duration of $T$."645 This switches on at s=tT—7/2 and switches off at s=7+77/2. it being supposed that 7 exceeds 7/2.," This switches on at $s= \tau - T/2$ and switches off at $s= \tau + T/2$, it being supposed that $\tau$ exceeds $T/2$."646 The weighted average is then This is not a realistic form. but it makes the point and the structure is easy to visualise.," The weighted average is then This is not a realistic form, but it makes the point and the structure is easy to visualise."647" For the particular case of the parameter r=7/2 (ignition immediately on launch) and duration time 7=P/2. the centroid of the wind 1s most redshifted at orbital phase 0. one quarter of a period late. and the amplitude is v,sincGe/2). which for v, 175 km s! is 111 km sl."," For the particular case of the parameter $\tau = T/2$ (ignition immediately on launch) and duration time $T=P/2$, the centroid of the wind is most redshifted at orbital phase 0, one quarter of a period late, and the amplitude is $v_x$ $(\pi /2)$, which for $v_x$ 175 km $^{-1}$ is 111 km $^{-1}$."648 These results are very close to the behaviour of the data., These results are very close to the behaviour of the data.649 The parameters 7 and r might exhibit some fluctuation with time - winds can be gusty., The parameters $T$ and $\tau$ might exhibit some fluctuation with time - winds can be gusty.650 A probably more realistic form is to suppose exponential decay of the emission factor after the initial light. up., A probably more realistic form is to suppose exponential decay of the emission factor after the initial light up.651 In this case the duration parameter 7 is the decay time of the exponential. and there is a delay 7 between launch and ignition.," In this case the duration parameter $T$ is the decay time of the exponential, and there is a delay $\tau$ between launch and ignition."652 The weighted average recession is now For the simple case of «T=1. the decay time Τ is about two days. the amplitude of the oscillation is v./v2 (124 km sl) and the recession velocity is greatest at orbital phase 0.875 for the case of instant ignition. 7.=0.," The weighted average recession is now For the simple case of $\omega T=1$, the decay time $T$ is about two days, the amplitude of the oscillation is $v_x/\sqrt 2$ (124 km $^{-1}$ ) and the recession velocity is greatest at orbital phase 0.875 for the case of instant ignition, $\tau =0$."653 Thus these simple models have demonstrated that both the amplitude and the phase of the centroid of the broad component of Ha. relative to the photometric ephemeris. are easily understood in terms of a wind that becomes detached fromthe orbiting source and decays away in Πα over a few days.," Thus these simple models have demonstrated that both the amplitude and the phase of the centroid of the broad component of $\alpha$, relative to the photometric ephemeris, are easily understood in terms of a wind that becomes detached fromthe orbiting source and decays away in $\alpha$ over a few days."654 The amplitude and phase of thewind centroid is reconciled with the way in which the line-of-sight wind speed varies with the nodding of the disk (Blundell. Bowler Schmidtobreick 2008).," The amplitude and phase of thewind centroid is reconciled with the way in which the line-of-sight wind speed varies with the nodding of the disk (Blundell, Bowler Schmidtobreick 2008)."6551n the magnitude-mean surface brightness diagram and the Fundamental Plane (PP.2)... dwarf ancl giant early-tvpe galaxies seem to form two distinct sequences joining at around Alp=IS mag (see?.andreferencesthercein)..,"In the magnitude-mean surface brightness diagram and the Fundamental Plane \citep[FP,][]{DD87}, dwarf and giant early-type galaxies seem to form two distinct sequences joining at around $M_B = -18$ mag \citep[see][and656references therein]{KFCB09}."657 Llowever. this bi-modal distribution can be explained as a projection of the two known monotonous relations of other structural properties of early-type galaxies. as. functions of a galaxy luminosity on-to this parameter space: (a) light) profile concentration index and (b) central surface brightness (?7?7?77)..," However, this bi-modal distribution can be explained as a projection of the two known monotonous relations of other structural properties of early-type galaxies as functions of a galaxy luminosity on-to this parameter space: (a) light profile concentration index and (b) central surface brightness \citep{GG03,HMI03,KDG03,Ferrarese+06}."658 Only objects classified as compact elliptical (cI2) or ultra-compact dwarf (UCD. ?2)) galaxies strongly depart from these relations.," Only objects classified as compact elliptical (cE) or ultra-compact dwarf (UCD, \citealp{MHI02,Drinkwater+03}) ) galaxies strongly depart from these relations."659 They represent the two classes of galaxies supposecdly forming by tidal threshing of more massive progenitors (??7).. i.e. they must have sharply decreased. their stellar masses during the evolution.," They represent the two classes of galaxies supposedly forming by tidal threshing of more massive progenitors \citep{BCDG01,BCDS03}, i.e. they must have sharply decreased their stellar masses during the evolution."660 Both cl and UCD classes are represented by only a [ον dozens of known members including several transitional cI/UC objects. discovered recently (27)...," Both cE and UCD classes are represented by only a few dozens of known members including several transitional cE/UCD objects discovered recently \citep{CM08,Price+09}."661 Since all these objectsD. are very dense ancl small. much. higher. stellar velocity clispersions are required to keep them in equilibrium. compared. to. dwarf elliptical (dL) or dwarf spheroidal (dSph) galaxies of similar luminosities. thus putting them above the locus of dis on the 0 vs Alp (2?) relation.," Since all these objects are very dense and small, much higher stellar velocity dispersions are required to keep them in equilibrium compared to dwarf elliptical (dE) or dwarf spheroidal (dSph) galaxies of similar luminosities, thus putting them above the locus of dEs on the $\sigma$ vs $M_B$ \citep{FJ76} relation."662 Stellar population properties of cls and UCDs are very different [rom typical cle/dsph usually being very old. (with rare. exceptions such as Messier 32) and notably more metal-rich., Stellar population properties of cEs and UCDs are very different from typical dE/dSph usually being very old (with rare exceptions such as Messier 32) and notably more metal-rich.663 Among known compact elliptical galaxies only AL 32 (Local group) NGC 4486B (Virgo cluster). NGC 5846À (NGC 5846 group). and. possibly. ACO 3526 J124853.0]411905.8 (Centaurus cluster) reside sullicientlv nearby. to allow. spatiallv-resolved: studies of their kinematies ancl stellar populations using ground-based telescopes.," Among known compact elliptical galaxies only M 32 (Local group), NGC 4486B (Virgo cluster), NGC 5846A (NGC 5846 group), and possibly ACO 3526 $J124853.91-411905.8$ (Centaurus cluster) reside sufficiently nearby to allow spatially-resolved studies of their kinematics and stellar populations using ground-based telescopes."664 They were considered. unique objects until the recent. discovery (??77T) of cEs located at a distance of the Coma cluster or further. which are. however. spatially unresolved for ground- optical observations.," They were considered unique objects until the recent discovery \citep{Mieske+05,Chilingarian+07,Price+09,Chilingarian+09} of cEs located at a distance of the Coma cluster or further, which are, however, spatially unresolved for ground-based optical observations."665 In this we report the detection. of the, In this we report the detection of the6661.Many [fundamental properties ofmatter al thequantum level can beannounced without ment,covariance requirements imposed on the discrete relations between the generators of the quark algebra.667ion, 2.668ing parücles andanti-particles. electriccharge ancl barvonicnumber conservation belongto (his category. Quantum mechanics itself can be formulated," At present, the most successful theoretical descriptions of fundamental interactions are based on the quark model, despite the fact that isolated quarks cannot be observed."669 without any mention ofspace. as wasshown byDorn. JordanandIHeisenberg [1].intheir version ofmatrix mechanics. orinJ., The only experimentally accessible states are either three-quark or three-anti-quark combinations (fermions) or the quark-anti-quark states (bosons).670von Neumann's [0]. formulation ofquantum theory interms ofthe C algebras. The non-conmiutati," Whenever one has to do with a tri-linear combination of fields (or operators), one must investigate the behavior of such states under permutations."671ve geometry [0].gives anotherexample ofinterpreting the space-time relationships inpure algebraicterms. Einstein'sdream wastobe abletoderive (heproperties ofmatter. and perhaps ilsvery existence. fromt," Let us introduce $N$ generators spanning a linear space over complex numbers, satisfying the following relations which are a cubic generalization of anti-commutation in the ususal (binary) case (see e.g. \cite{Kerner3}, \cite{VARKBLR}) ): with $j = e^{i \pi/3}$, the primitive cubic root of $1$."672he singularities of fields definedon, We have ${\bar{j}} = j^2$ and $1+j+j^2 = 0$.673the space-time. andifpossible. from ihe geometry and topology of the ο).Bul defend alternative point ofview supposing that(he existence ofma," We shall also introducea similar set of generators, ${\bar{\theta}}^{\dot{A}}$, $\dot{A}, \dot{B},... = 1,2,...,N$, satisfying similar condition with $j^2$ replacing $j$: Let us denote this algebra by ${\bf{\cal{A}}}$."674tter one withcanan tothat of Inthislisht. the ideatoderivethe iseeonmeltric primary properliesrespectof space-time.," We shall endow this algebra with a natural $Z_3$ grading, considering the generators $\theta^A$ as grade $1$ elements, and their conjugates ${\bar{\theta}}^{\dot{A}}$ being of grade $2$ ."675 theandspace-time. perhaps If the the space-time istobe derived [romthe interactions offandamental constituents ol matter.," The grades add up modulo $3$, so that the products $\theta^{A} \theta^{B}$ span a linear subspace of grade $2$, and the cubic products $ \theta^A \theta^B \theta^C$ are of grade $0$."676thenit seems reasonable to choosethe strongest ineractions available. which are (he interactions between quarks. The difficulty. resides inthe factthat we should deline these “quarks” (or (heir states) withoutanv mention of space-time. The minimal requirementsfor the definition of quarksat(heiniti," Similarly, all quadratic expressions in conjugate generators, ${\bar{\theta}}^{\dot{A}} {\bar{\theta}}^{\dot{B}}$ are of grade $2 + 2 = 4_{mod \, 3} = 1$, whereas their cubic products are again of grade $0$, like the cubic products od $\theta^A$ 's. Combined with the associativity, these cubic relations impose finite dimension on the algebra generated by the $Z_3$ graded generators."677alstage ofmodel buildingare the lollowing: 0.5cm2)The mathematical entities," As a matter of fact, cubic expressions are the highest order that does not vanish identically."678 representing quarks should form alinear space over complex numbers. so that we couldproduce their linear combinations coellicients. 0.5em 2) Thev shouldalso form an associative algebra. and AP) anti-quarks.and (he conjugation isomorphic algebras (iransformation (hat (wpemapsoneof corresponding these quarksontoanother.A A. algebras 0.5cm The Chree quark three anti-euark)and the quark-anti-quark combinations ," The proof isimmediate: 0.2cm 0.2cm 0.2cm and because $j^4 = j \neq 1$ , the only solution is Therefore the total dimension of the algebra defined via the cubic relations \ref{ternary1}) ) is equal to $N + N^2 + (N^3 - N)/3$: the $N$ generators of grade $1$, the $N^2$ independent products of two generators, and $(N^3-N)/3$ independent cubic expressions, because the cube of any generator must be zero, and the remaining $N^3-N$ ternary products are divided by $3$ , by virtue of the constitutive relations \ref{ternary1}) )."679shouldbe ze) distinguishedinà certain(orwav. for algebra spannedbythe generators. With thisin m, The conjugate generators${\bar{\theta}}^{\dot{B}}$ span an algebra ${\bf{\bar{\cal{A}}}}$ isomorphic with ${\bf{\cal{A}}}$ .680indwe ean start to explorethe algebraic propertiesofquarks, Both algebras splitquite naturally into sums of linear subspaces with definite grades:681Additionally we have to follow the dynamical evolution of halos and embedded: MDBlIs all the way to z=0 in order o determine the occupation fraction of. MDBlIIs ancl their ooperties.,Additionally we have to follow the dynamical evolution of halos and embedded MBHs all the way to $z=0$ in order to determine the occupation fraction of MBHs and their properties.682 We focus here on the ellect that MBLL ejections. namely due to gravitational waves recoils. have on the operties of the MBII population at z=0.," We focus here on the effect that MBH ejections, namely due to gravitational waves recoils, have on the properties of the MBH population at $z=0$."683 The magnitude of the recoil depends on the mass ratio of the merging MDlIIS. he spins of the MBlIs. the orbital parameters of the binary," The magnitude of the recoil depends on the mass ratio of the merging MBHs, the spins of the MBHs, the orbital parameters of the binary."684 First. to evaluate mass ratios. we have to model he mass-erowth5 of MBlIs.," First, to evaluate mass ratios, we have to model the mass-growth of MBHs."685 We base our modeling5 on jausible assumptions. supported by both simulations of AGN triggering and feedback. (Springelctal.2005).. and analvsis of the relationship between MDBII masses (Mg) and the properties of their hosts (Mebure&Dunlop2004:Writhe&Loeb 2005).," We base our modeling on plausible assumptions, supported by both simulations of AGN triggering and feedback \citep{Springel2005b}, and analysis of the relationship between MBH masses $M_{BH}$ ) and the properties of their hosts \citep{Mclure2004,Wyithe2005}."686. Wyithe&Loeb(2005). show that if the relationship between the mass ofà MBLIL and the velocity dispersion. of the host. found. for local galaxies. (Tremaine does not evolve with redshift. then the correlation between the masses of AIBLIs and their hosts evolves with redshift in a wav compatible with observational results by Mebure&Dunlop (2004).," \cite{Wyithe2005} show that if the relationship between the mass of a MBH and the velocity dispersion of the host found for local galaxies \citep{Tremaine2002,Ferrarese2000,Gebhardt2000} does not evolve with redshift, then the correlation between the masses of MBHs and their hosts evolves with redshift in a way compatible with observational results by \cite{Mclure2004}."687. Xdditionallv. Springeletal.(2005). suggest that the ditto Adleyσι relation is established during galaxy mergers that also fuel AIBIL aceretion and form bulges.," Additionally, \cite{Springel2005b} suggest that the ditto $M_{BH}-\sigma_*$ relation is established during galaxy mergers that also fuel MBH accretion and form bulges."688 We therefore assume that after every merger between two ealaxies with a mass ratio larger than 10. their \IBLIs attain the mass predicted by the Aleaσ. tor each of the merging galaxies.," We therefore assume that after every merger between two galaxies with a mass ratio larger than $1:10$, their MBHs attain the mass predicted by the $M_{BH}-\sigma_*$ for each of the merging galaxies."689 Lenec. although in our models the presence of a ML is not uniquely coupled with bulge formation. the mass of à black hole is set during the same event that forms the host bulge.," Hence, although in our models the presence of a MBH is not uniquely coupled with bulge formation, the mass of a black hole is set during the same event that forms the host bulge."690 Accordinglv. when a binary of MDlIs merge. their mass ratio scales with the Aldeaσι relation appropriate for the velocity cüspersions of the progenitor halos of the MILI.," Accordingly, when a binary of MBHs merge, their mass ratio scales with the $M_{BH}-\sigma_*$ relation appropriate for the velocity dispersions of the progenitor halos of the MBHs."691 Note that ifthe few—e. relation scales with redshift as suggested by. c.g. Wooetal.(2006):Treu(2004). the mass ratio of merging binaries would be unchanged. so the occupation fraction of black holes would not be allectect.," Note that if the $M_{BH}-\sigma_*$ relation scales with redshift as suggested by, e.g. \cite{Woo2006, Treu2004} the mass ratio of merging binaries would be unchanged, so the occupation fraction of black holes would not be affected."692 We further assume that AIBIIs merge within the merger timescale of their host halos. which is a likely assumption for MIB binaries formed after gas rich galaxy mergers (Escalaetal.2004:Dotti2006.2007 ).," We further assume that MBHs merge within the merger timescale of their host halos, which is a likely assumption for MBH binaries formed after gas rich galaxy mergers \citep{Escalaetal2004,Dottietal2006,Dotti2006c}."693. To determine the efficiency of MILI. cjeetions due to gravitational recoils. we need also information on the magnitude and. orientation of AIBIL spins at the time of the merger.," To determine the efficiency of MBH ejections due to gravitational recoils, we need also information on the magnitude and orientation of MBH spins at the time of the merger."694" We will express AIBLL spins as a function of the dimensionless parameter @—JifSine=cJ,(COALay. where J, is the angular momentum of the black hole."," We will express MBH spins as a function of the dimensionless parameter $\hat a \equiv J_h/J_{max}=c \, J_h/G \, M_{\rm MBH}^2$, where $J_h$ is the angular momentum of the black hole."695 Non-spinning MDlIs. or binaries where ALIBI spins are aligned with the orbital angular momentum are expected o recoil with velocities below 200 kms4+.," Non-spinning MBHs, or binaries where MBH spins are aligned with the orbital angular momentum are expected to recoil with velocities below 200 $\rm{km\,s^{-1}}$."696 The recoil velocity is largest for MBlIIS with large spins. when the spin vectors have opposite directions and are in the orbital plane (Campanellietal.2007a:Conzález2007:Canipan-οetal. 2007b).," The recoil velocity is largest for MBHs with large spins, when the spin vectors have opposite directions and are in the orbital plane \citep{Campanelli2007b,Gonzalez2007,Campanelli2007}."697. Assumine that Bills at the time of the merger always have antialignecl spins in the orbital plane (asinVolonteri2007) would. provide a strict upper limit to he elfect of the recoil., Assuming that BHs at the time of the merger always have antialigned spins in the orbital plane \citep[as in][]{Volonteri2007} would provide a strict upper limit to the effect of the recoil.698 However. the configuration vielding he highest recoil velocities is probably rather uncommon. as »xointed out by BogdanoviéoOetal.," However, the configuration yielding the highest recoil velocities is probably rather uncommon, as pointed out by \cite{Bogdanovic2007}."699(2007).. Bogdanoviéὃνοἱal.(2007) suggest that when the MBII merger happens in a gas rich environment. and is accompanied by accretion. the most ikely configuration has spins aligned (or anti-aligned) with he orbital angular momentum. thus avoiding the highest recoil velocity.," \cite{Bogdanovic2007} suggest that when the MBH merger happens in a gas rich environment, and is accompanied by accretion, the most likely configuration has spins aligned (or anti-aligned) with the orbital angular momentum, thus avoiding the highest recoil velocity."700 Conversely. in gas poor mergers there is no oeferential spin alignment. so all spin/orbital parameters configurations are equally probable.," Conversely, in gas poor mergers there is no preferential spin alignment, so all spin/orbital parameters configurations are equally probable."701 We will assume in the ollowing that orbital parameters and spin configuration are isotropically clistributed. likely providing a softmil o the strength of the recoil.," We will assume in the following that orbital parameters and spin configuration are isotropically distributed, likely providing a soft to the strength of the recoil."702 The distribution and. most. probable value. of ALBLI spins is observationallv [largely unconstrained., The distribution and most probable value of MBH spins is observationally largely unconstrained.703 “Phere is evidence that MBlISs in some local AGN ealaxies do spin (Streblyanskactal.2005:Conmastriet2006:Drenne- based on iron line profiles (Miller2007:Fabianetal.1989:Laor 1991).," There is evidence that MBHs in some local AGN galaxies do spin \citep{Streblyanska2005,Comastri2006,Brenneman2006}, based on iron line profiles \citep{Miller2007,Fabian1989,Laor1991}."704. High spins in bright quasars are also indicated by the high radiative elliciency of quasars. as. deduced: from observations. by applying Soltan's argument (Soltan1982:Wangetal.2006.andreferences.therein )..," High spins in bright quasars are also indicated by the high radiative efficiency of quasars, as deduced from observations, by applying Soltan's argument \citep [and references therein ]{Soltan1982,Wang2006}."705 However. neither observation firmly establishes that most MDlIIs have large spins. although there are theoretical. arguments to expect so. (Alocerskietal.1998:Volonteri2005) as spin-up is a natural consequence of prolonged. disc-mocdoe accretion for any hole that has (for instance) doubled. its mass by capturing material with constant angular momentun. axis (Barcleon1970:Phorne 1974).," However, neither observation firmly establishes that most MBHs have large spins, although there are theoretical arguments to expect so \citep{Moderski1998,Volonterietal2005} as spin-up is a natural consequence of prolonged disc-mode accretion for any hole that has (for instance) doubled its mass by capturing material with constant angular momentum axis \citep{Bardeen1970,Thorne1974}."706. lxingetal.(2005). argue instead that most MDIIs have very low or no spin. due to preferential accretion of counter-rotating material. or to short-lived accretion episodes (Ixingetal.2005).," \cite{King2005} argue instead that most MBHs have very low or no spin, due to preferential accretion of counter-rotating material, or to short-lived accretion episodes \citep{King2005}."707". Waiting for additionalobservations"". we Consider here two extreme cases. that likely allow us to bracket the typical configurations: cither that all AIBLIs have exactly null spin. or that all AIBLIs have @=0.9."," Waiting for additional, we consider here two extreme cases, that likely allow us to bracket the typical configurations: either that all MBHs have exactly null spin, or that all MBHs have $\hat a=0.9$."708 The latter value is slightly. lower than the canonical @=0.998 (Vhorne1974).. but it is consistent with magnetohyvcrodyvnamical simulations of dise acerction (Gammicetal.2004).," The latter value is slightly lower than the canonical $\hat a=0.998$ \citep{Thorne1974}, but it is consistent with magnetohydrodynamical simulations of disc accretion \citep{Gammieetal2004}."709.. We also run a control simulation where we set the recoil velocity to zero for all ALBLL mergers., We also run a control simulation where we set the recoil velocity to zero for all MBH mergers.710 For every galaxy merger we track jointly the dynamical evolution of the ALBIIs ancl of the host halo., For every galaxy merger we track jointly the dynamical evolution of the MBHs and of the host halo.711 In addition to the dynamics of AIBL binaries. as described above. we trace the mass evolution of their hosts. including the due to galaxy mergers and the due to mass stripping of the halo within the gravitational potential of the halo.," In addition to the dynamics of MBH binaries, as described above, we trace the mass evolution of their hosts, including the due to galaxy mergers and the due to mass stripping of the halo within the gravitational potential of the halo."712 Our treatment is very simple: we integrate the equation of motion of the satellite in the gravitational potential of the cluster (assuming a non singular isothermal sphere). including the cvnamiucal friction term.," Our treatment is very simple: we integrate the equation of motion of the satellite in the gravitational potential of the cluster (assuming a non singular isothermal sphere), including the dynamical friction term."713 At every step of the integration we compare the density of the satellite to the density of the cluster halo at the location of the satellite., At every step of the integration we compare the density of the satellite to the density of the cluster halo at the location of the satellite.714 ‘Tidal stripping occurs at the radius within which the mean density of the satellite exceeds the density of the galaxy interior to its orbital racius. (Lavlor&Babul 2001).., Tidal stripping occurs at the radius within which the mean density of the satellite exceeds the density of the galaxy interior to its orbital radius \citep{Taylor2001}. .715 We trace tidal stripping of all satellites from the time of the merger to.— 0., We trace tidal stripping of all satellites from the time of the merger to $z=0$ .71614479.9 line and selected stars with rather low rotational velocities aand. therefore. with the 44481.2 line well resolved from the 44479.9 line.,"4479.9 line and selected stars with rather low rotational velocities and, therefore, with the 4481.2 line well resolved from the 4479.9 line."717 We found for 52 stars the mean abundance logz(Mg)=7.67+ 0.21.," We found for 52 stars the mean abundance $\log \varepsilon({\rm Mg}) =7187.67\pm0.21$ ."719 The effect of uncertainties in the microturbulent »arameter oon log(Meg) is important. especially for coolest programme stars.," The effect of uncertainties in the microturbulent parameter on $\log \varepsilon({\rm Mg})$ is important, especially for coolest programme stars."720 For 16 such stars the vvalues were derived from lines. but not from aand llines as for other stars.," For 16 such stars the values were derived from lines, but not from and lines as for other stars."721 Being close to zero these D) values are less accurate than the ID) values., Being close to zero these ) values are less accurate than the ) values.722 When excluding these [6 stars. we obtained the mean abundance logz(Mg)=75S+0.15 for the remaining 36 stars.," When excluding these 16 stars, we obtained the mean abundance $\log723\varepsilon({\rm Mg}) = 7.59\pm0.15$ for the remaining 36 stars."724 This abundance is precisely confirmed from an analysis of the weak TISTT line for several hot B stars., This abundance is precisely confirmed from an analysis of the weak 7877 line for several hot B stars.725 This is our recommended Meg abundance for the B-type MS stars in the solar neighbourhood (with d< 800 pe)., This is our recommended Mg abundance for the B-type MS stars in the solar neighbourhood (with $d <$ 800 pc).726 Comparing the latter value with the solar magnesium abundance loge.(Mg)=7.55+0.02. one may conclude that he metallicity of the stars is very close to the solar one.," Comparing the latter value with the solar magnesium abundance $\log \varepsilon_{\sun}({\rm Mg}) =7277.55\pm0.02$, one may conclude that the metallicity of the stars is very close to the solar one."728" Our mean Tg abundance in B stars. as well as the position of the maximum in Fig.6. log(Mg).=7.64. is also very close to the proto-Sun magnesium abundance log2,,CMg)=7.62+0.02."," Our mean Mg abundance in B stars, as well as the position of the maximum in Fig.6, $\log729\varepsilon({\rm Mg}) = 7.64$, is also very close to the proto-Sun magnesium abundance $\log \varepsilon_{ps}({\rm Mg})=7.62\pm0.02$."730 We discussed he preceding determinations of the Mg abundance in B stars by Daflon et al. (, We discussed the preceding determinations of the Mg abundance in B stars by Daflon et al. (7312003).,2003).732 Their logz(Mg) values are somewhat lower han ours.," Their $\log \varepsilon({\rm733Mg})$ values are somewhat lower than ours."734 We showed that this difference in log:(Mg) is explained by differences inYj.," We showed that this difference in $\log \varepsilon({\rm735Mg})$ is explained by differences in."736". ""Thus. our results show that the Sun is not measurably enriched in metals as compared with the neighbouring voung stars."," Thus, our results show that the Sun is not measurably enriched in metals as compared with the neighbouring young stars."737 Two of us. LSL and SIR. are grateful to the staff of the Astronomy Department and McDonald Observatory of the University of Texas for hospitality during the visit in spring 2004.," Two of us, LSL and SIR, are grateful to the staff of the Astronomy Department and McDonald Observatory of the University of Texas for hospitality during the visit in spring 2004."738 DLL acknowledges the support of the Robert A. Welch Foundation of Houston. Texas.," DLL acknowledges the support of the Robert A. Welch Foundation of Houston, Texas."739hotspot components are described by homogeneous spheres with constant magnetic [field ancl constant properties of the relativistic electron populations.,hotspot components are described by homogeneous spheres with constant magnetic field and constant properties of the relativistic electron populations.740 The spectral energy clistributions of the emitting electrons are mocelled assuming the formalism described in Brunettietal.(2002)., The spectral energy distributions of the emitting electrons are modelled assuming the formalism described in \citet{gb02}.741". According to this model a population of seed. electrons (with  55) ds accelerated. at the shock ancl is injected in the downstream region with a spectrum dN(z/dt x ~Fo forse,«5πρι 5. being the maximum energy of the electrons accelerated at the shock."," According to this model a population of seed electrons (with $\gamma \leq742 \gamma_{*}$ ) is accelerated at the shock and is injected in the downstream region with a spectrum $\gamma$ )/dt $\propto$ $\gamma^{-p}$, for $\gamma_{*} < \gamma < \gamma_{c}$, $\gamma_{c}$ being the maximum energy of the electrons accelerated at the shock."743 Electrons accelerated at the shock are advected in the downstream region and age due to radiative losses., Electrons accelerated at the shock are advected in the downstream region and age due to radiative losses.744" Based on Brunettietal.(2002).. the volume integrated spectrum of the electron.population in the downstream region of size LZe (E and c being the age and the advection velocity of the downstream region) is given by either a steep power-law AN(s) xsI""P for 54«*5 5,.. where 5, is the maximum cnerev of"," Based on \citet{gb02}, the volume integrated spectrum of the electronpopulation in the downstream region of size $L \sim T v_{\rm adv}$ $T$ and $v_{\rm adv}$ being the age and the advection velocity of the downstream region) is given by either a steep power-law $N$ $\gamma$ ) $\propto \gamma^{-(p+1)}$ for $\gamma_{b} < \gamma < \gamma_{c}$ , where $\gamma_{b}$ is the maximum energy of"745“Hcluciall”,l”746Schuster Nissen (1989) οΗ] calibrations.. Ht is clear rom Lig.,Schuster Nissen (1989) [Fe/H] calibrations.. It is clear from Fig.747 4 that accurate metal abundances can be derived rom ΠΟH3 photometry. using the combined calibrations as clescribed above.," 4 that accurate metal abundances can be derived from $uvby-H\beta$ photometry, using the combined calibrations as described above."748 For the empirical Fe/l1l] calibrations of Schuster dssen (1989) the estimated standard deviations of a single ohotometric determination of. Fe/1l] were £0.14 at ο] =0.5 dex. and x0.21 at. Fe/H] z1.5 dex.," For the empirical [Fe/H] calibrations of Schuster Nissen (1989) the estimated standard deviations of a single photometric determination of [Fe/H] were $\pm 0.14$ at [Fe/H] $\approx -0.5$ dex, and $\pm 0.21$ at [Fe/H] $\approx -1.5$ dex."749 Comparisons »w Leltzing et al. (, Comparisons by Feltzing et al. (750(2001). of photometric— abunclances rom the Schuster Nissen (1989) calibration equations with abundances from two recent spectroscopic. studies Edvarelsson et al. (,2001) of photometric abundances from the Schuster Nissen (1989) calibration equations with abundances from two recent spectroscopic studies Edvardsson et al. (7511993) and Chen et al. (,1993) and Chen et al. (7522000) have shown hat these error estimates are overly conservative: they find a scatter of only £0.100.11 for their more metal-rich group. in very good agreement with the value of £0.12 found above rom a somewhat less homogeneous spectroscopic data set.,"2000) have shown that these error estimates are overly conservative; they find a scatter of only $\pm 0.10-0.11$ for their more metal-rich group, in very good agreement with the value of $\pm 0.12$ found above from a somewhat less homogeneous spectroscopic data set."753 In Fig., In Fig.754 5 the distribution of metallicity. ML]. for our sample stars is presented. ancl also shown is a fit to the listogram using three Gaussians.," 5 the distribution of metallicity, [M/H], for our sample stars is presented, and also shown is a fit to the histogram using three Gaussians."755 The sample is mix of all he stellar. populations that are represented. in the solar neighbourhood. the thin and thick disks. and the halo.," The sample is mix of all the stellar populations that are represented in the solar neighbourhood, the thin and thick disks, and the halo."756 As is expected. in the solar neighbourhood. the majority of the stars belong to the disk with the thin disk dominating. à significant but smaller contribution from the thickdisk. and only a few halo stars (2S: see Fig.," As is expected, in the solar neighbourhood, the majority of the stars belong to the disk with the thin disk dominating, a significant but smaller contribution from the thickdisk, and only a few halo stars $\approx 8$; see Fig."757 6 below)., 6 below).758 In Fig., In Fig.759 5 two main components can be seen. one with .0.95ΑΗ]0.5 dex (the disk contribution: thin plus thick) and the other with AZ/H]Z0.9 dex (mostly the halo stars).," 5 two main components can be seen, one with $-0.9 \la [M/H] \la +0.5$ dex (the disk contribution: thin plus thick) and the other with $[M/H] \la -0.9$ dex (mostly the halo stars)."760 A rough Gaussian fit has been made to this metallicity histogram using the mathematical package7., A rough Gaussian fit has been made to this metallicity histogram using the mathematical package.761.. One disk-like component has <AH]»-—0.04 dex. a dispersion of 0.37. and is nearly symmetric.," One disk-like component has $<[M/H]> \sim -0.04$ dex, a dispersion of $0.37$, and is nearly symmetric."762 Our sample. contains an obvious contribution from the thick disk with a Gaussian waving a mean abundance of <ΑΗ>~O45 dex ancl a dispersion of 0.41., Our sample contains an obvious contribution from the thick disk with a Gaussian having a mean abundance of $<[M/H]> \sim -0.45$ dex and a dispersion of $0.41$.763 There are eight halo stars with «ΑΗ]>L0.9 dex (see also Fig., There are eight halo stars with $<[M/H]> \la -0.9$ dex (see also Fig.764 6)., 6).765 Nevertheless. hin and thick-cdisk stars are not clearly distinguishable from. Fig.," Nevertheless, thin and thick-disk stars are not clearly distinguishable from Fig."766 5., 5.767 There exists no clean. straightforward: procedure or separating the stars of these different disk populations. which overlap considerably in the metallicity cistribution.," There exists no clean, straightforward procedure for separating the stars of these different disk populations, which overlap considerably in the metallicity distribution."768 ]xinematies are usually invoked to improve the thin/thick disk separation. and more recently a/ Fe] abundances (sec for example. Densbv. Feltzing Lundstrómnm: 22003).," Kinematics are usually invoked to improve the thin/thick disk separation, and more recently $\alpha/Fe$ ] abundances (see for example, Bensby, Feltzing Lundströmm 2003)."769 In Fig., In Fig.770 6 the Via. ML] ciagram for our sample stars is plotted.," 6 the $V_{\rm rot}$, [M/H] diagram for our sample stars is plotted."771 “Pwo components are clearly noted: the halo component. VuaS 100 km  and η]0.9 dex: the other disk-like. centered at Via~ 215 km s+ and ΔΕΗ] ~0.0 dex.," Two components are clearly noted: the halo component, $V_{\rm rot} \la $ 100 km $^{-1}$ and $[M/H] \la -0.9$ dex; the other disk-like, centered at $V_{\rm rot} \sim $ 215 km $^{-1}$ and [M/H] $\sim 0.0$ dex."772 The rotation velocity of the LSIt about the Galactic center is taken here to be 220 km s+ oso that Von=7| 220 kms + is the rest-frame rotation velocity of a given star (Ixerr LyndenBell 1986)., The rotation velocity of the LSR about the Galactic center is taken here to be 220 km $^{-1}$ so that $V_{\rm rot} = V' + $ 220 km $^{-1}$ is the rest-frame rotation velocity of a given star (Kerr LyndenBell 1986).773" More modern values for the circular speed of the Milky Way at the solar circle are somewhat larger. such as (3,=234E13 km s1 given by Pukugita Peebles (2004)."," More modern values for the circular speed of the Milky Way at the solar circle are somewhat larger, such as $\Omega_{\rm 0} = 234 \pm 13$ km $^{-1}$ given by Fukugita Peebles (2004)."774 Llere. V is the velocity with respect to the LSk.," Here, $V'$ is the velocity with respect to the LSR."775 It can be seen from Fig., It can be seen from Fig.776 6 that the majority of the stars have Via~ 200 kms+ ane AMI]0.5 dex., 6 that the majority of the stars have $V_{\rm rot} \sim $ 200 km $^{-1}$ and $[M/H] \geq -0.5$ dex.777 These stars are thin-disk stars., These stars are thin-disk stars.778" Even though there is scarcity of stars with MI]<—0.5 dex and Vi,« 150 kms. JF. Via increases approximately linearly with M/LE] between LO<MH]—0.5 dex."," Even though there is scarcity of stars with $[M/H] < -0.5$ dex and $V_{\rm rot}<$ 150 km $^{-1}$, $V_{\rm rot}$ increases approximately linearly with [M/H] between $-1.0<[M/H]<-0.5$ dex."779 For the ΑΗ]<LO dex. it appears that there is no correlation between ML] and Via. but there are too few stars for any firm conclusion.," For the $[M/H] < -1.0$ dex, it appears that there is no correlation between [M/H] and $V_{\rm rot}$, but there are too few stars for any firm conclusion."780 This Via. MM] diagram can be used to separate out the different stellar populations. as discussed in Nissen Schuster (1991) and in Schuster et al. (," This $V_{\rm rot}$ , [M/H] diagram can be used to separate out the different stellar populations, as discussed in Nissen Schuster (1991) and in Schuster et al. ("781(1993).,1993).782 In the former reference. a diagonal eut connecting (MI]. Va)=(0.8.0 ," In the former reference, a diagonal cut connecting ([M/H], $V_{\rm rot}) = (-0.3,0$ "783needed to proceed with the de-correlation process.,needed to proceed with the de-correlation process.784 This is very well possible in the case of dedicated iustruinents such as EKepler. as these have been specifically designed with such high precision aud stability measurements in πιά (Doruckietal.1996:Jenkinsetal. 2010).," This is very well possible in the case of dedicated instruments such as Kepler, as these have been specifically designed with such high precision and stability measurements in mind \citep{borucki96,jenkins10}."785. For iustraments that do not feature the calibration plau required to further de-correlate with instrumneut state paraneters. the solution is far less obvious.," For instruments that do not feature the calibration plan required to further de-correlate with instrument state parameters, the solution is far less obvious."786 We furthermore explored the de-correlation of eclipse signals observed. consecutively rather than in parallel., We furthermore explored the de-correlation of eclipse signals observed consecutively rather than in parallel.787" We demoustrated. using [Kepler data. that despite the formal violation of the ""justantanecous nixiug model. he proposed algoritlin is able to retrieve the desired signal componcut with good accuracy."," We demonstrated, using Kepler data, that despite the formal violation of the `instantaneous mixing model', the proposed algorithm is able to retrieve the desired signal component with good accuracy."788 Such an application is particularly Huportant for treating variability of the host-star which can significantly impair the quality of the final science result (eg.Czeslaetal.2009:Doisse 2011).," Such an application is particularly important for treating variability of the host-star which can significantly impair the quality of the final science result \citep[eg.][]{czesla09, boisse11, aigrain11,ballerini11}."789". It is furthermore interesting to note that pre and post-processing steps οιο, wavelets (Carter&Winn 2009).. Fourier based techuiques (Waldiiauuetal. 2011).. de-correlatiou using iustrunienut state parameters (Swainetal. 2008))). do not break the iustautancous mixing model aud cau be run in conjunction with ICA methods."," It is furthermore interesting to note that pre and post-processing steps (e.g. wavelets \citep{carter09}, Fourier based techniques \citep{waldmann11}, de-correlation using instrument state parameters \citep{swain08}) ), do not break the instantaneous mixing model and can be run in conjunction with ICA methods."790 This lakes inclependcut conrponent analysis a very powerful and versatile tool for uou-parainetric correlation of exoplauetary data sets;, This makes independent component analysis a very powerful and versatile tool for non-parametric de-correlation of exoplanetary data sets.791 Iun the light of searching aud characterising ever smaller and fainter cxoplanctary tarects. the development of novel de-trending routines becomesincreasingly critical.," In the light of searching and characterising ever smaller and fainter exoplanetary targets, the development of novel de-trending routines becomes increasingly critical."792 Based ou the coucepts of blind source deconvolution of imstantancously nüxed signals. we lave presented a first step towards 10n-paranmetriie corrections and data filters tha do not require additional information ou the systematic noise ofthe iustruiieut or stellar activity.," Based on the concepts of blind source deconvolution of instantaneously mixed signals, we have presented a first step towards non-parametric corrections and data filters that do not require additional information on the systematic noise of the instrument or stellar activity."793 Such algoritlius have two imiportaut applications: 1) For instruments that lack a calibration plan at the accuracy of 1 in flux variatio- which is required for spectroscopy of exoplauctary atmospheres. the spectroscopic signatures become inherently eutaueled aud dependent ou the method used to correct mstrumneut aud other svstenmiaties in the data.," Such algorithms have two important applications: 1) For instruments that lack a calibration plan at the accuracy of $^{-4}$ in flux variation, which is required for spectroscopy of exoplanetary atmospheres, the spectroscopic signatures become inherently entangled and dependent on the method used to correct instrument and other systematics in the data."794 The de-correlation of spectroscopic data was demoustrated using two HST/NICMOS data sets., The de-correlation of spectroscopic data was demonstrated using two HST/NICMOS data sets.795 2) Detections of faint cxoplanctary eclipses are often made cifieult by time-correlated activity of the host star., 2) Detections of faint exoplanetary eclipses are often made difficult by time-correlated activity of the host star.796 We demonstrated. using a siugle Kepler tiue serics. that much of the stellar variability can be removed in time series that span several exoplauctary eclipse events.," We demonstrated, using a single Kepler time series, that much of the stellar variability can be removed in time series that span several exoplanetary eclipse events."797 The algorithun proposed is a powerful tool for lighteurve de-treudius. which can be used by its OWL or iu conjunction with anv other type of data filtering or cleaning technique.," The algorithm proposed is a powerful tool for lightcurve de-trending, which can be used by its own or in conjunction with any other type of data filtering or cleaning technique."798 This becomes an invaluable advantage for data analysis when he instruments response function is uukuownu or oorlv. eliaracterised., This becomes an invaluable advantage for data analysis when the instrument's response function is unknown or poorly characterised.799" LDP.W. would like to thank Prof. E. Feigelson. he referee. Dr. C. Tiuctti. Dr. F. Abdalla aud Dr. ο, Fossey for comunenuts and suggestions that relped to ereatle inuprove this paper."," I.P.W. would like to thank Prof. E. Feigelson, the referee, Dr. G. Tinetti, Dr. F. Abdalla and Dr. S. Fossey for comments and suggestions that helped to greatly improve this paper."800 LP.W. is supported by au STFC Studeutship., I.P.W. is supported by an STFC Studentship.801To verify this qualitative picture would. however. require detailed numerical calculations.,"To verify this qualitative picture would, however, require detailed numerical calculations."802 This work has been financed by the KBN erants 2P03D-01016. and. 2P03D-02117.," This work has been financed by the KBN grants 2P03D-01016, and 2P03D-02117."803 Support from Multiprocessor Systems Group at Nicholas Copernicus University’s Computer Centre in providing facilities for the time/memory-consumine Monte. Carlo caleulations is appreciated., Support from Multiprocessor Systems Group at Nicholas Copernicus University's Computer Centre in providing facilities for the time/memory-consuming Monte Carlo calculations is appreciated.804 We are erateful to Gottfried. WKanbach and Alaurice Cos for valuable discussions on processing and analysis of high-energy. data for the Vela pulsar., We are grateful to Gottfried Kanbach and Maurice Gros for valuable discussions on processing and analysis of high-energy data for the Vela pulsar.805 We thank the anonvmous referee for bringing our attention to the paper by Sturner et al. (, We thank the anonymous referee for bringing our attention to the paper by Sturner et al. (8061995).,1995).807For an uuderdeuse universe. the density is described by and the ecueral solution of equation(6)) is with e» deteriiuiug peculiar motion as before: the particular solution is and is shown in Fie. € ,"For an underdense universe, the density is described by and the general solution of \ref{eq:freenewton}) ) is with $c_2$ determining peculiar motion as before; the particular solution is and is shown in Fig. \ref{fig:underdense}) )."808For the zero-energv/fiat wniverse with autieravitv. the deusitv is and the ecueral solution to equation (6)) is The integral does not appear to be expressable in closed form. which makes working with it somewhat iucouveuieut.," For the zero-energy/flat universe with antigravity, the density is and the general solution to equation \ref{eq:freenewton}) ) is The integral does not appear to be expressable in closed form, which makes working with it somewhat inconvenient."809 Dowever. some characteristics of if cau be derived which are sufficient for the present purpose.," However, some characteristics of it can be derived which are sufficient for the present purpose."810 For an uudoerdeuse universe. the distauce between the free particle aud the backgrouud particle with the same asviuptotie speed is more complicated than in the critical ease. but as y becomes large approaches a constant.," For an underdense universe, the distance between the free particle and the background particle with the same asymptotic speed is more complicated than in the critical case, but as $\eta$ becomes large approaches a constant."811 That is. the free particle stavs at least this far from its correspouding backeound particle. even at infinite times.," That is, the free particle stays at least this far from its corresponding backgound particle, even at infinite times."812 Iu the situation of a fat universe with the cosmological coustaut. the peculiar motion (62) function cau be approximated at carly times by," In the situation of a flat universe with the cosmological constant, the peculiar motion $c_2$ ) function can be approximated at early times by"813supplemented: by the heat conduction equation (Maciolek-Niedzwwiecki. Wrolik Zdziarski 1997: ROO).,"supplemented by the heat conduction equation }ek-Nied\'{z}wwiecki, Krolik Zdziarski 1997; R99)."814 The transition from the hot to cold. solution branch is very. sharp and its location can be obtained from the general condition of radiativeconductive equilibrium (R6ezaaisska 2000)., The transition from the hot to cold solution branch is very sharp and its location can be obtained from the general condition of radiative–conductive equilibrium (R\'{o}\\.{z}aa\'{n}sska 2000).815 Phe condition gives the temperature at the transition point where 7i is the surface temperature., The condition gives the temperature at the transition point where $\Ts$ is the surface temperature.816 For purely radiation heated disc atmosphere 72=ic. where Z1c is the temperature (Melee Begelman 1990: 16-Zaasska C'zerny20008).," For purely radiation heated disc atmosphere $\Ts = \TIC$, where $\TIC$ is the inverse-Compton temperature (McKee Begelman 1990; R\'{o}\\.{z}aa\'{n}sska Czerny2000a)."817 When the al? heating is also included. 7; is somewhat higher than Zic (16 2000).," When the $\alpha P$ heating is also included, $\Ts$ is somewhat higher than $\TIC$ (R\'{o}\\.{z}aa\'{n}sska 2000)."818 In a good. approximation. the transition occurs where the upper. stable branch of the = 7 curve changes to the middle. unstable branch (RCOG. R99. NIxI). The resulting structure is then basically two-lavereed: the upper. hot laver (LIL) and the lower. cold laver. although there is a thin transition laver in between the two (1199).," In a good approximation, the transition occurs where the upper, stable branch of the $\Xi$ $T$ curve changes to the middle, unstable branch (RC96, R99, NKK), The resulting structure is then basically two-layered: the upper, hot layer (HL) and the lower, cold layer, although there is a thin transition layer in between the two (R99)."819 For a sulliciently hard illuminating spectra hhieh ic) iron can be considered completely: ionized in the hot [aver. while it recombines to below in the cold [aver (NIxIEx: see also 22 in Zvveki Czerny 1904).," For a sufficiently hard illuminating spectra high $\TIC$ ) iron can be considered completely ionized in the hot layer, while it recombines to below in the cold layer (NKK; see also 2 in Żyycki Czerny 1994)."820 The model parameter crucial for spectral/timing predictions is the thickness of the hot laver. mua.," The model parameter crucial for spectral/timing predictions is the thickness of the hot layer, $\tauh$."821 The larger the thickness. the smaller. the fraction of primary radiation penetrating to the cold. laver anc giving rise {ο the usual reprocessecl component.," The larger the thickness, the smaller the fraction of primary radiation penetrating to the cold layer and giving rise to the usual reprocessed component."822 The reprocessed. componen is further C'omptonized as the photons escape through the hot laver., The reprocessed component is further Comptonized as the photons escape through the hot layer.823 The result (at least in the limited energy. ban corresponding to or data) is à reprocessec component with amplitude reduced compared to the usua eeometrical factor OΕπ (Iq. 8)).," The result (at least in the limited energy band corresponding to or data) is a reprocessed component with amplitude reduced compared to the usual geometrical factor $\Omega/4\pi$ (Eq. \ref{equ:refl}) ),"824 where © is the solid angle subtended by the reprocessor from the Xray source (Done Navakshin 2001)., where $\Omega$ is the solid angle subtended by the reprocessor from the X–ray source (Done Nayakshin 2001).825 The amplitude of the iron. spectra eatures is further reduced by the Comptonization., The amplitude of the iron spectral features is further reduced by the Comptonization.826 Two most important parameters determining the hickness of the hot laver are: the strength. of irradiation compared to internal disc emission. AN/fp. and the ratio of eravity at the base of the laver to Xray radiation pressure (RCOG. NIXIN).," Two most important parameters determining the thickness of the hot layer are: the strength of irradiation compared to internal disc emission, $\FX/\FD$, and the ratio of gravity at the base of the layer to X–ray radiation pressure (RC96, NKK)."827" Following NlxIx we parameterize the latter nu where where f,=píngc1.9 [or cosmic abundance.", Following NKK we parameterize the latter by where where $\mu_{\rm m} = \rho/\nH \approx 1.9$ for cosmic abundance.828 Obviously then. the structure of the hot laver has to be solved. simultaneously with the structure of the cold. disc. since ct depends on the dise thickness. df.," Obviously then, the structure of the hot layer has to be solved simultaneously with the structure of the cold disc, since $A$ depends on the disc thickness, $\Hd$."829 Nit used vertically averaged solutions of Shakura Sunvacy (1973: hereafter. SS) for the disc in their computations of μμ., NKK used vertically averaged solutions of Shakura Sunyaev (1973; hereafter SS) for the disc in their computations of $\tauh$.830 They assumed that total pressure. Poa.|Laat. should be continuous across the boundary between the two lavers. and obtained both 2... and Lea individually continuous across the boundary.," They assumed that total pressure, $\Pgas+\Prad$, should be continuous across the boundary between the two layers, and obtained both $\Pgas$ and $\Prad$ individually continuous across the boundary."831 In this paper we explicitly. solve equations of vertical structure of the cold. disc., In this paper we explicitly solve equations of vertical structure of the cold disc.832" We do this for the a£, SS disc. aa disc with energv generation. proportional to total pressure."," We do this for the $\alpha\Ptot$ SS disc, a disc with energy generation proportional to total pressure."833 We define. the input parameters of the computations in such a wav as to make the connection between accretion discs models ancl observable quantities obvious., We define the input parameters of the computations in such a way as to make the connection between accretion discs models and observable quantities obvious.834" First. we ceseribe calculations at a given. radius and then discuss radial dependence of 75,4."," First, we describe calculations at a given radius and then discuss radial dependence of $\tauh$."835 The structure of the LL at a given radius is computed. by combining the method of RCOG and ROO with computations of the vertical structure of X-ray illuminated. dises by Roaansska οἱ ((1999)., The structure of the HL at a given radius is computed by combining the method of RC96 and R99 with computations of the vertical structure of X-ray illuminated discs by R\'{o}\\.{z}aa\'{n}sska et (1999).836 For the LIL we follow. closely the method of C06 and ROO. with the important simplification of neglecting thermal conduction.," For the HL we follow closely the method of RC96 and R99, with the important simplification of neglecting thermal conduction."837 “Phe reason is) purely practical. as elforts to fully combine proper photo-ionization computations of the hot laver with vertical disc structure have only just begun (Dumont. Abrassart Collin 2000: ltó.zARSSEkA et alb.," The reason is purely practical, as efforts to fully combine proper photo-ionization computations of the hot layer with vertical disc structure have only just begun (Dumont, Abrassart Collin 2000; R\'{o}\\.{z}aa\'{n}sska et al.,"838 in preparation)., in preparation).839 This leaves us with an important. problem of selecting proper solution in the zone of instabilitv. where the svstem of equations has more than one solution for temperature.," This leaves us with an important problem of selecting proper solution in the zone of instability, where the system of equations has more than one solution for temperature."840 We adopt a simple prescription and select the highest value of Z as the solution., We adopt a simple prescription and select the highest value of $T$ as the solution.841 Comparing solutions with and without conduction in RCOG and 1099 one sees that our procedure may overestimate somewhat the total thickness of the hot and transition lavers tthe depth of the point where 7= Zip)., Comparing solutions with and without conduction in RC96 and R99 one sees that our procedure may overestimate somewhat the total thickness of the hot and transition layers the depth of the point where $T=\Teff$ ).842 However. the thickness of the hot laver. alone is not. alfected by our neglecting the thermal conduction.," However, the thickness of the hot layer alone is not affected by our neglecting the thermal conduction."843" The spectrum. of illuminating radiation is assumed to be a power law with a eutoll. fexbtte7/7, parameterized by the photon spectral index E and cutoll energy. Leo."," The spectrum of illuminating radiation is assumed to be a power law with a cutoff, $F_E \propto E^{-\Gamma+1} {\rm e}^{-E/E_{\rm c}}$, parameterized by the photon spectral index $\Gamma$ and cutoff energy, $E_{\rm c}$."844 Equations of vertical structure of the cold cise are the same as in LGALaadsska et (1999)., Equations of vertical structure of the cold disc are the same as in R\'{o}\\.{z}aa\'{n}sska et (1999).845 We assume that a certain fraction of eravitational energy. £. is dissipated within the dise (but the disc transports all the angular momentum. see WWitt. Czerny Zvvcki 1997).," We assume that a certain fraction of gravitational energy, $\xi$, is dissipated within the disc (but the disc transports all the angular momentum, see Witt, Czerny Żyycki 1997)."846 The remaining fraction. | £. is dissipated in an active corona and converted to hard X-ray radiation. of which a fraction 0.57) illuminates the disk. i.e. where is the gravitational energy. dissipation per unit area of the disc surface.," The remaining fraction, $1-\xi$ , is dissipated in an active corona and converted to hard X-ray radiation, of which a fraction $0.5 \eta$ illuminates the disk, i.e. where is the gravitational energy dissipation per unit area of the disc surface."847 Value of y=1 would thus correspond to a, Value of $\eta=1$ would thus correspond to a848Exomoons. the satellites of extrasolar planets have been often featured in fiction as habitable locations.,"Exomoons, the satellites of extrasolar planets, have been often featured in fiction as habitable locations."849 There is no deficit of known geiaut planets: Exoplanuct.ore (Wrightetal2010)0 lists approximately 10 eiaut exopluiets of total) within of the equilibriun temperature of Earth. as are 30 (3%)) of the planet candidates released in February 2011 (Doruclietal. 2011).," There is no deficit of known giant planets; Exoplanet.org \citep{ExoplanetOrg} lists approximately 40 giant exoplanets of total) within of the equilibrium temperature of Earth, as are 30 ) of the planet candidates released in February 2011 \citep{Borucki2011}."850. Though these observations are preliminary. they do show that habitable-zoue eiaut planets not only exist. but are conuuon.," Though these observations are preliminary, they do show that habitable-zone giant planets not only exist, but are common."851 Once a egiaut planet is known to be in a habitable zone. variations du its orbit. such as Trausit Tiuiuug Variation (TTV:Sartorctti and Transit Duration Variation (ΤΟΝKippiug 2009).. photometry (Szabóetal.2006).. or gravitational imuücroleusiug (Liebig&4Wanbseganss 2010).. allow the indirect detection of satellites.," Once a giant planet is known to be in a habitable zone, variations in its orbit, such as Transit Timing Variation \citep[TTV;][]{Sartoretti1999} and Transit Duration Variation \citep[TDV;][]{Kipping2009}, , photometry \citep{Szabo2006}, or gravitational microlensing \citep{Liebig2010}, allow the indirect detection of satellites."852 Thus. if potentially habitable cxomoons exist around trausitiug eiut planets. they may be detected at the same (or even ereater) rate as solitary habitable terrestrial planets;," Thus, if potentially habitable exomoons exist around transiting giant planets, they may be detected at the same (or even greater) rate as solitary habitable terrestrial planets."853 As vet. uo exomoons have been detected. but the wealth of ransit data from the Nepler mission should beein to fill his gap.," As yet, no exomoons have been detected, but the wealth of transit data from the Kepler mission should begin to fill this gap."854 Despite the existence of giant plaucts dn stellar wabitable zones. it ds far from certain how they arrived there.," Despite the existence of giant planets in stellar habitable zones, it is far from certain how they arrived there."855 Current giaut-plauet formation models asstune that they are created at distances bevoud 1ο stability. poiut of ice (e.g.LissauerL987:Boss 1997).. which miplies conditions not suitable to surface wabitability.," Current giant-planet formation models assume that they are created at distances beyond the stability point of ice \citep[e.g.][]{Lissauer1987,Boss1997}, which implies conditions not suitable to surface habitability."856 Disk uueration can bring giaut planets close to the star (Ward1997).. but ecnerally has a stopping point far too close to the star to be habitable (thus producing Πο Jupiters”).," Disk migration can bring giant planets close to the star \citep{Ward1997}, but generally has a stopping point far too close to the star to be habitable (thus producing ""Hot Jupiters"")."857 The host planets of potentially habitable exomoous therefore likely arrived at their final orbit through late-stage migration. driveu either by planctesimals (Ixirslietal.2009) or other eiaut ylancets (Weidensclilling&\arzazi1996).," The host planets of potentially habitable exomoons therefore likely arrived at their final orbit through late-stage migration, driven either by planetesimals \citep{Kirsh2009} or other giant planets \citep{Weidenschilling1996}."858. Tn the process of nügrating. the satellite svstenis of these giaut planet may have close encouuters with errestrial plauets or planetesimals. causing them to be disrupted or replaced.," In the process of migrating, the satellite systems of these giant planet may have close encounters with terrestrial planets or planetesimals, causing them to be disrupted or replaced."859 If either the Jovian or θαΕπστὰ systems were transported to L AU around a solar nass-star. both Callisto aud Titan would be at of their planets Till radii. thus implying that all the uajor satellites of the two planets would be on stable orbits.," If either the Jovian or Saturnian systems were transported to 1 AU around a solar mass-star, both Callisto and Titan would be at of their planet's Hill radii, thus implying that all the major satellites of the two planets would be on stable orbits."860 However. a close eucounuter could either excite heir orbits to ligh eccentricity (thus requiring tidal recizcularization). or could result iu the capture of a uuch larger terrestrial satellite.," However, a close encounter could either excite their orbits to high eccentricity (thus requiring tidal recircularization), or could result in the capture of a much larger terrestrial satellite."861 Neptune appears have to experienced this process during its mieration through the xoto-Ixuiper Belt. loosing any. original major satellites. while eaining Triton iun au inclined. retrograde orbit.," Neptune appears have to experienced this process during its migration through the proto-Kuiper Belt, loosing any original major satellites, while gaining Triton in an inclined, retrograde orbit."862 This was possibly due to a 1iomientuu-excehlauge reaction hat ejected the binazy companion of Triton (Agnor&Uaimiltou 2006).. though other scenarios are possible (at reduced: probabilitv).," This was possibly due to a momentum-exchange reaction that ejected the binary companion of Triton \citep{Agnor2006}, though other scenarios are possible (at reduced probability)."863 Αν capture process. though. will tend to produce very. loosely-bouud initial orbits. with ouly a small delta-v to escape velocity at periapsc.," Any capture process, though, will tend to produce very loosely-bound initial orbits, with only a small delta-v to escape velocity at periapse."864 Therefore. some method ust be used to determine the one-term evolution and stability (or lack thereof) for hese orbits.," Therefore, some method must be used to determine the long-term evolution and stability (or lack thereof) for these orbits."865 Tere we use a full οΤΕ (Isozai Cyele aud Tidal Friction) model to find the survival probability for a ranee of plysical conditions aud the detectability of he resulting svsten., Here we use a full KCTF (Kozai Cycle and Tidal Friction) model to find the survival probability for a range of physical conditions and the detectability of the resulting system.866 As shown bv Donuison(2010) and Sato&Asada (2010).. there are a range of stable orbits for Earthauass auets around eiaut plancts.," As shown by \citet{Donnison2010} and \citet{Sato2010}, there are a range of stable orbits for Earth-mass planets around giant planets."867 However. both of those uodels test ouly the stability of the orbit. rather than any evolution due to tidal effects.," However, both of those models test only the stability of the orbit, rather than any evolution due to tidal effects."868 On inclined exomoon orbits. the effects of stellar torques on the orbit can. hrough initiating I&ozai cvcles. dramatically accelerate he rate of tidal decay. orbit circularization. and spiu- svnchronization.," On inclined exomoon orbits, the effects of stellar torques on the orbit can, through initiating Kozai cycles, dramatically accelerate the rate of tidal decay, orbit circularization, and spin-orbit synchronization."869 As we will show. this process cau allow evenvery loose. inclined capture orbits to stabilize," As we will show, this process can allow evenvery loose, inclined capture orbits to stabilize"870this. in fact. is seen clearly in most cases in the colour index images. ancl also often in the broad-band images. especially theST NICMOS images.,"this, in fact, is seen clearly in most cases in the colour index images, and also often in the broad-band images, especially the NICMOS images."871 Such dust lanes are expected to be continuations of the dust lanes in the bar. ancl this is wha is seen in our images (see Shlosman 1999 for a theoretica review).," Such dust lanes are expected to be continuations of the dust lanes in the bar, and this is what is seen in our images (see Shlosman 1999 for a theoretical review)."872 ΝΑ. colour index images are not very sensitive to changes in stellar populations. and can outline clus structure clearly (see e.g. the ἐν map of MIOO in Ixnapen et al.," NIR colour index images are not very sensitive to changes in stellar populations, and can outline dust structure clearly (see e.g. the $I-K$ map of M100 in Knapen et al."873 1995a)., 1995a).874. We see clear ancl abundant observationa evidence for dust lanes on several scales. but most clearly in the (Nits.," We see clear and abundant observational evidence for dust lanes on several scales, but most clearly in the CNRs."875 Dust lanes in the bars are not well visible in general in our NIHU imaging due to the lower signal to noise ratios achieved in the bar regions., Dust lanes in the bars are not well visible in general in our NIR imaging due to the lower signal to noise ratios achieved in the bar regions.876 In. Paper IH. we present optical colour index maps which outline the dust lane structure in the bars and dises of our sample galaxies more clearly. and we study. the relationship between the shape of the dust lanes. the axial ratio. and the SE in the bar in more cletail.," In Paper II, we present optical colour index maps which outline the dust lane structure in the bars and discs of our sample galaxies more clearly, and we study the relationship between the shape of the dust lanes, the axial ratio, and the SF in the bar in more detail."877 Our colour maps have shown the presence of cireumnuclear rings in most of the galaxies in our sample., Our colour maps have shown the presence of circumnuclear rings in most of the galaxies in our sample.878 These rings are generally redder than other regions in the galaxy. by about 0.05. 0.1 magnitude in 4A and 44A., These rings are generally redder than other regions in the galaxy by about 0.05– 0.1 magnitude in $J-K$ and $H-K$.879 From the colour index maps or colour profiles alone it is not possible to make meaningful statements about quantities of extinguishing dust implied by the redcder colours., From the colour index maps or colour profiles alone it is not possible to make meaningful statements about quantities of extinguishing dust implied by the redder colours.880 In fact. there are indications from both optical and. NLR imaging and spectroscopy that the red. colours in CNRs in galaxies like the ones studied here may be inlluenced by voung stars. e.g. red supergiants (Ixnapen et al.," In fact, there are indications from both optical and NIR imaging and spectroscopy that the red colours in CNRs in galaxies like the ones studied here may be influenced by young stars, e.g. red supergiants (Knapen et al."881 1995a.b: Ixnapen. 1996: Elmeercen et al.," 1995a,b; Knapen 1996; Elmegreen et al."882 1997: Rweler Ixnapen 1999)., 1997; Ryder Knapen 1999).883 In Paper LI. we will compare the precise location of the JA and dfA features with those of SE regions as seen in comission. and try to place quantitative limits on the origins of the red light in the ςΝις.," In Paper III, we will compare the precise location of the $J-K$ and $H-K$ features with those of SF regions as seen in emission, and try to place quantitative limits on the origins of the red light in the CNRs."884 Two of the host galaxies of Sy nuclei (NGC 3516 and NGC 3982). which have colours consistent with those nmieasured by Peletier et al. (," Two of the host galaxies of Sy nuclei (NGC 3516 and NGC 3982), which have colours consistent with those measured by Peletier et al. ("8851999). also show a peculiar shape in the colour profiles. starting from a very red. value anc steeply decreasing until the radius of the ring. remaining constant afterwards.,"1999), also show a peculiar shape in the colour profiles, starting from a very red value and steeply decreasing until the radius of the ring, remaining constant afterwards."886 Peletier ct al. (, Peletier et al. (8871999) suggested. tha the red. LfLy (or J dv) colours in the cores of many ον galaxies could be due to a significant [fraction of therma radiation [rom hot dust heated by the Sy nucleus.,1999) suggested that the red $H-K$ (or $J-K$ ) colours in the cores of many Sy galaxies could be due to a significant fraction of thermal radiation from hot dust heated by the Sy nucleus.888 However. the two other ACN hosts in our sample (NGC 4303. aux NGC 6951) do not show significantly red nuclei.," However, the two other AGN hosts in our sample (NGC 4303 and NGC 6951) do not show significantly red nuclei."889dispersion iu the cluster aud a characteristic radius.,dispersion in the cluster and a characteristic radius.890 Figure TU shows a portion of the NIRSPEC echelle spectral of M8S2-F. compared to a series of template supereiaut spectra.," Figure \ref{spect} shows a portion of the NIRSPEC echelle spectrum of M82-F, compared to a series of template supergiant spectra."891" Features found in the spectra of supereiant stars are readilv ideuti&ed iu the cluster spectrum. although hey appear ""washed οπ due to the stellar velocity dispersion."," Features found in the spectra of supergiant stars are readily identified in the cluster spectrum, although they appear “washed out” due to the stellar velocity dispersion."892 Especially prominent are the rovibrational CO vandheads and umucrous Fe and ΟΠ lines., Especially prominent are the rovibrational CO bandheads and numerous Fe and OH lines.893 We have assembled an atlas of high-resolution NIRSPEC spectra of supergiant stars for use in cross-correlation analysis (?).. roni which we determine the dominant spectral type and inc-ofsight velocity dispersion.," We have assembled an atlas of high-resolution NIRSPEC spectra of supergiant stars for use in cross-correlation analysis \citep{mccrady03}, from which we determine the dominant spectral type and line-of-sight velocity dispersion."894" Dased upon the peak of he cross-correlation function. (Fieure ??)). the IT-baud spectruni of MS82-F ποτ closely matches spectral types in he range of NUMOL. The lne-ofsight velocity dispersion owed on cross-correlation with templates in this rauge iso,=13.5x02 kins |."," Based upon the peak of the cross-correlation function (Figure \ref{ccfplot}) ), the $H$ -band spectrum of M82-F most closely matches spectral types in the range of K4I–M0I. The line-of-sight velocity dispersion based on cross-correlation with templates in this range is $\sigma_r = 13.5 \pm 0.2$ km $^{-1}$."895" The value of e, decreases as a function of the simibuitv to the template spectra as measured bv the peak value of the cross-correlation function.", The value of $\sigma_r$ decreases as a function of the similarity to the template spectrum as measured by the peak value of the cross-correlation function.896 It is therefore possible that the stated value reflects some template uvisimatch bias due to our limited teiiplate spectra atlas. but this effect is snall (< 0.5 kau S1 |.," It is therefore possible that the stated value reflects some template mismatch bias due to our limited template spectra atlas, but this effect is small $<$ 0.5 km $^{-1}$ )."897 The simplest approach to determine the cluster mass is to measure the haltleht radius. assume that light traces mass. the cluster is spherical. and the velocity dispersion is isotropic. then apply the virial theorem.," The simplest approach to determine the cluster mass is to measure the half-light radius, assume that light traces mass, the cluster is spherical, and the velocity dispersion is isotropic, then apply the virial theorem."898 \[82-F preseuts a difficulty for this method: IST iuages (Figure ??)) clearly show that the cluster is elliptical in projection aud cannot. therefore. be spherical.," M82-F presents a difficulty for this method: HST images (Figure \ref{fitplot}) ) clearly show that the cluster is elliptical in projection and cannot, therefore, be spherical."899 To measure the radius. we fit the cluster using au elliptical version of the empirical ? model: where e and 6 are the characteristic leusths of tle minor and major axes. respectively. A4 is a scaling constant and Ao acts as a “tidal radius truncating the profile bevond a particular scale leneth.," To measure the radius, we fit the cluster using an elliptical version of the empirical \citet{king62} model: where $a$ and $b$ are the characteristic lengths of the minor and major axes, respectively, $k_1$ is a scaling constant and $k_2$ acts as a “tidal radius,” truncating the profile beyond a particular scale length."900 The fit therefore has four free parameters (Ay. Ko. à and b) to describe the liebt profile aud three more to describe the ceutroid location and position anele.," The fit therefore has four free parameters $k_1$, $k_2$, $a$ and $b$ ) to describe the light profile and three more to describe the centroid location and position angle."901 The ine mocel is convolved with a model PSF from Tiny Tiu (7)| and compared to the Πμαρσο, The King model is convolved with a model PSF from Tiny Tim \citep{krist95} and compared to the image.902", Fit paraincters are determined by iterative search over parameter space. using a Levenbure-\larquardt least-squares fit."," Fit parameters are determined by iterative search over parameter space, using a Levenburg-Marquardt least-squares fit."903 Fieure ?? shows the fit aud residuals for the ACS/IIRC FalIW image of M82-F. The halfleht radius iu projection along the major axis. ppys is the semudniajor axis of the ellipse that eucloses half the ux in the fitted ing model.," Figure \ref{fitplot} shows the fit and residuals for the ACS/HRC F814W image of M82-F. The half-light radius in projection along the major axis, $r_{hp}$, is the semimajor axis of the ellipse that encloses half the flux in the fitted King model."904" We determine 7j, munerically by stuum4ne the fiux iu a series of ellipses with the axial ratio defined by «à aud b.", We determine $r_{hp}$ numerically by summing the flux in a series of ellipses with the axial ratio defined by $a$ and $b$.905 Moute Carlo simulations of clusters indicate that a. b aud fy are siguifcantlv covariant: however. the fitted. projected lalflight radius along a given axis is accurate to about 2 percent.," Monte Carlo simulations of clusters indicate that $a$, $b$ and $k_2$ are significantly covariant; however, the fitted projected half-light radius along a given axis is accurate to about 2 percent."906" The halfinass radius may be determined by assume that light traces niass aud deprojectiug by dividing rj, by 0.766 (7).", The half-mass radius may be determined by assuming that light traces mass and deprojecting by dividing $r_{hp}$ by 0.766 \citep{spitzer87}.907. ? fit a spherical Nine model to MS2-F in the NICAIOS FLGOW nuage and found a projected halflelt radius of SO+1L mas., \citet{mccrady03} fit a spherical King model to M82-F in the NICMOS F160W image and found a projected half-light radius of $89 \pm 11$ mas.908" Our elliptical Ning function fit to the same iuage found rj,=113X2 along the major axis aud rp=62+] along the minor axis.", Our elliptical King function fit to the same image found $r_{hp}=113 \pm 2$ along the major axis and $r_{hp}=62 \pm 1$ along the minor axis.909" At the adopted distance of M82. the projected half-light radi along the major and minor axes are thus 1.97£0.16 pe and 1140.1 pc. respectively,"," At the adopted distance of M82, the projected half-light radii along the major and minor axes are thus $1.97 \pm9100.16$ pc and $1.1 \pm 0.1$ pc, respectively."911 To account for the ellipticity of the cluster. we assunie it is an oblate spheroid and compute the eravitational potential assuming that the cluster is homocoidal (7.Section2.3)..," To account for the ellipticity of the cluster, we assume it is an oblate spheroid and compute the gravitational potential assuming that the cluster is homoeoidal \citep[][Section 2.3]{binney87}. ."912 The mmuerical constaut iu the virial mass formmla may be separated iuto factors dependent upon the central concentration aud the ellipticitv., The numerical constant in the virial mass formula may be separated into factors dependent upon the central concentration and the ellipticity.913 The compact core plus extended euvelope structure of star clusters is simular to au η—5 polvtrope (7.p.13).., The compact core plus extended envelope structure of star clusters is similar to an $n=5$ polytrope \citep[][p. 13]{spitzer87}.914" For anv —5 polvtropic oblate ellipsoid with au isotropic velocity dispersion. the virial mass ds: where the eccentricity is 6=Vl(Z/R)\2. and R and Z are the equatorial and polar radii of the oblate spheroid. respectively,"," For an $n=5$ polytropic oblate ellipsoid with an isotropic velocity dispersion, the virial mass is: where the eccentricity is $e = \sqrt{1-(Z/R)^2}$, and $R$ and $Z$ are the equatorial and polar radii of the oblate spheroid, respectively."915 Figure ?? shows the fitted cluster lalf-light radii iu projection along the major and minor axes for the NICMOS aud ACS images., Figure \ref{halfradii} shows the fitted cluster half-light radii in projection along the major and minor axes for the NICMOS and ACS images.916 The observed axial ratio. afb. veprescuts a lower bound ou the ratio Z/Ri: an oblate cluster will appear rouuder than its intrinsic shape uuless viewed directly aloug the equatorial plauc.," The observed axial ratio, $a/b$ , represents a lower bound on the ratio $Z/R$; an oblate cluster will appear rounder than its intrinsic shape unless viewed directly along the equatorial plane."917 Averaging over all possible iucliuatious. we find that the observed. axial ratio of 0.55 corresponds to a imost-likelv intrinsic axial ratio of 0.35 with e=(0.77x0.07.," Averaging over all possible inclinations, we find that the observed axial ratio of $0.55$ corresponds to a most-likely intrinsic axial ratio of $0.35$ with $e=0.77 \pm 0.07$."918 We represent the uucertaintv on the viewing inclination as the difference )etween the augle-averaged value aud the lower bouud., We represent the uncertainty on the viewing inclination as the difference between the angle-averaged value and the lower bound.919 We believe the ellipticity of the cluster is intrinsic. rather hau the result of differcutial reddening.," We believe the ellipticity of the cluster is intrinsic, rather than the result of differential reddening."920 Extinction is very low at 2.2 gan. aud therefore the observed shape in the F222\0 nuages is verv likely intrinsic.," Extinction is very low at 2.2 $\mu$ m, and therefore the observed shape in the F222M images is very likely intrinsic."921 \oreover. he axial ratio is constant within the uncertainties across all wavebands frou 0.1 to 2.2 gan (Figure ??)).," Moreover, the axial ratio is constant within the uncertainties across all wavebands from 0.4 to 2.2 $\mu$ m (Figure \ref{halfradii}) )."922 If the ellipticitv were due to the distribution of dust arouud he cluster. the axial ratio should chiuge as a functiou of wavelength as the extinction ids expected to vary sienificantly between P aud K.," If the ellipticity were due to the distribution of dust around the cluster, the axial ratio should change as a function of wavelength as the extinction is expected to vary significantly between $B$ and $K$."923 The axial ratio does appear o increase sharply at the shortest IIST/ACS waveband (F250W)., The axial ratio does appear to increase sharply at the shortest HST/ACS waveband (F250W).924 We interpret this as a result of scatteriug of cluster Light by dust outside the cluster., We interpret this as a result of scattering of cluster light by dust outside the cluster.925 The ACS inages show strong spatial variations in extinction in the iunmediate vicinity of MBS2-F. Scattering and absorption in the ultraviolet compromise the quality of the fit to the liebt profile at very short waveleneths., The ACS images show strong spatial variations in extinction in the immediate vicinity of M82-F. Scattering and absorption in the ultraviolet compromise the quality of the fit to the light profile at very short wavelengths.926 Combining the NIRSPEC velocity dispersion with the NICALOS radius aud estimated eccentricity. we calculate an If-baud virial mass of Mj;=6.60.9«107 AL. for MS2-F.," Combining the NIRSPEC velocity dispersion with the NICMOS radius and estimated eccentricity, we calculate an $H$ -band virial mass of $M_H =9276.6 \pm 0.9 \times 10^5$ $_{\odot}$ for M82-F."928 The subscript ou the mass is used to emphasize that the virial mass is computed from a velocity dispersion aud size micasured in the ZZ baud., The subscript on the mass is used to emphasize that the virial mass is computed from a velocity dispersion and size measured in the $H$ band.929 In this manucr we minimize systematic errors by measuring both variables from the helt of the same stars and may seekvariations between different wavebancds., In this manner we minimize systematic errors by measuring both variables from the light of the same stars and may seekvariations between different wavebands.930 SCQUL found a velocitydispersion of 13.140.7 kin s+ for MS2-F based on cross-correlation analysis using cluster spectra in the 601759 mu rauge (overlapping the ACS FasliW bandpass}., SG01 found a velocitydispersion of $13.4 \pm 0.7$ km $^{-1}$ for M82-F based on cross-correlation analysis using cluster spectra in the 601–759 nm range (overlapping the ACS F814W bandpass).931 They concluded. that the, They concluded that the932reflection fractions measured in the high state of Cygnus |] (Gierlinski et al.,reflection fractions measured in the high state of Cygnus X-1 (Gierlinski et al.933 1999). wherein the disk may extend to the marginally stable circular orbit.," 1999), wherein the disk may extend to the marginally stable circular orbit."934 It is not likely that these results can be explained in terms of an anomalous Fe abundance., It is not likely that these results can be explained in terms of an anomalous Fe abundance.935" Allowing ./ and Aj, (1n pexriv) to vary. the abundance is poorly constrained: Ay,=1.002. and the emissivity drops only slightly to ./=5.0."," Allowing $\beta$ and $A_{Fe}$ (in pexriv) to vary, the abundance is poorly constrained: $A_{Fe} =9361.0^{+0.5}_{-0.7}$, and the emissivity drops only slightly to $\beta=5.0$."937 Fixing the emissivity at ./=3.0 and allowing the Fe abundance to vary yields a significantly worse fit (7=353.1 for 229 d.o.f.), Fixing the emissivity at $\beta=3.0$ and allowing the Fe abundance to vary yields a significantly worse fit $\chi^{2}=353.1$ for 229 d.o.f.)938 and Fe must be more than 30 times over-abundant., and Fe must be more than 30 times over-abundant.939 We note that the line strength and reflection fraction in our final fit are not strictly congruent. and that f=0.603 Is below the reflection fraction measured in MCG-6-30-15 (f£=1.5—2.0. Wilms et 22001) using a similar model.," We note that the line strength and reflection fraction in our final fit are not strictly congruent, and that $f=0.6^{+0.3}_{-0.1}$ is below the reflection fraction measured in MCG–6-30-15 $f=1.5-2.0$, Wilms et 2001) using a similar model."940 If we fix the f=1.5 in our final model. 7 increases only slightly (47=324.9 for 230 d.o.f.).," If we fix the $f=1.5$ in our final model, $\chi^{2}$ increases only slightly $\chi^{2}=324.9$ for 230 d.o.f.),"941 and the other fit parameters only change within their 10 confidence intervals., and the other fit parameters only change within their $\sigma$ confidence intervals.942 Thus. more congruent values of f are allowed by the data.," Thus, more congruent values of $f$ are allowed by the data."943 The high \- value associated with our final model could be due to unmodeled narrow spectral features. approximations in the model. and calibration issues.," The high $\chi^{2}$ value associated with our final model could be due to unmodeled narrow spectral features, approximations in the model, and calibration issues."944 We note a feature at approximately 7.0 keV. which may be a narrow edge due to neutral Fe or an Fe XXVI absorption line.," We note a feature at approximately 7.0 keV, which may be a narrow edge due to neutral Fe or an Fe XXVI absorption line."945 Alternatively. there may be an Fe / emission line near 7.4 keV due to tonized Fe species. which is superimposed upon the broader smeared edge fit by the reflection models.," Alternatively, there may be an Fe $\beta$ emission line near 7.4 keV due to ionized Fe species, which is superimposed upon the broader smeared edge fit by the reflection models."946 There is also weak evidence for a narrow absorption edge feature near 9.3 keV. consistent with Fe XXVI.," There is also weak evidence for a narrow absorption edge feature near 9.3 keV, consistent with Fe XXVI."947 Modeling these features and the addition of systematic errors below | keV are sufficient to make the fit acceptable., Modeling these features and the addition of systematic errors below 1 keV are sufficient to make the fit acceptable.948 We have observed à broad Fe Ko line profile in. the XMM-Newton//EPIC-pn spectrum of the Galactic black hole candidate XTE J1650—500 in the very high state., We have observed a broad Fe $\alpha$ line profile in the /EPIC-pn spectrum of the Galactic black hole candidate XTE $-$ 500 in the very high state.949 A comparison with the broad line profile observed with in Cygnus Χ- is shown in Figure 1., A comparison with the broad line profile observed with in Cygnus X-1 is shown in Figure 1.950 That such profiles are observed in very different systems. strongly suggests that broad Fe Ko lines in stellar-mass black holes stem from à common process.," That such profiles are observed in very different systems, strongly suggests that broad Fe $\alpha$ lines in stellar-mass black holes stem from a common process."951 Like the broad lines observed in some Seyfert AGNs. these lines are likely produced by irradiation of theinner disk.," Like the broad lines observed in some Seyfert AGNs, these lines are likely produced by irradiation of theinner disk."952 The Fe Ko line we have observed in XTE J1650—500 suggests a Kerr black hole with near-maximal angular momentum («c= 0.998)., The Fe $\alpha$ line we have observed in XTE $-$ 500 suggests a Kerr black hole with near-maximal angular momentum $a=0.998$ ).953 The aceretion disk emissivity profile measured with the Laor line model is inconsistent. with. the energy dissipation expected for standard. disks., The accretion disk emissivity profile measured with the Laor line model is inconsistent with the energy dissipation expected for standard disks.954 These results are very similar to those reported by Wilms et al. (, These results are very similar to those reported by Wilms et al. (9552001) using the same line and reflection models for the broad Fe Κα line observed in an XMM-Newton//EPIC-pn spectrum of the Seyfert galaxy MCG-6-30-15 (E=6.907.10 keV. W~300-400 eV. ΕΞ15-2. 3~4.3-5.0).,"2001) using the same line and reflection models for the broad Fe $\alpha$ line observed in an /EPIC-pn spectrum of the Seyfert galaxy MCG–6-30-15 $=6.97_{-0.10}$ keV, $\sim300$ –400 eV, $f=1.5-2$ , $\beta\sim4.3$ –5.0)."956 Those authors suggest that rotational energy extraction from the spinning black hole (Blandford Znajek 1977) or material in the plunging region (Agol Krolik 2000) may infuse the inner accretion disk with extra energy ντα Magnetic connections. creating the steep emissivity profile indicated by the Fe Ko line.," Those authors suggest that rotational energy extraction from the spinning black hole (Blandford Znajek 1977) or material in the plunging region (Agol Krolik 2000) may infuse the inner accretion disk with extra energy via magnetic connections, creating the steep emissivity profile indicated by the Fe $\alpha$ line."957 It is possible that rotational energy extraction may be at work in XTE J1650—500 as well., It is possible that rotational energy extraction may be at work in XTE $-$ 500 as well.958 If so. a fundamental general relativistic prediction may be confirmed across a factor of roughly 10° in black hole mass.," If so, a fundamental general relativistic prediction may be confirmed across a factor of roughly $10^{6}$ in black hole mass."959 This observation suggests a connection between the accretion geometry of stellar-mass black holes in the very high state. and that inferred in some Seyfert galaxies.," This observation suggests a connection between the accretion geometry of stellar-mass black holes in the very high state, and that inferred in some Seyfert galaxies."960 This is an important step towards understanding the nature of the very high state. and the variety of exotic phenomena observed in this state.," This is an important step towards understanding the nature of the very high state, and the variety of exotic phenomena observed in this state."961 The Blandford-Znajek process is also often invoked as à means of launching jets (Blandford 2001a. 2001b: see also Fender 2001).," The Blandford–Znajek process is also often invoked as a means of launching jets (Blandford 2001a, 2001b; see also Fender 2001)."962 That we have found an emissivity which might be explained by magnetic connections to the black hole or to matter in the plunging region in the very high state of XTE J1650—500 (detected at 7.5 mJy at 0.8 GHz with MOST in this state with a spectrum indicative of jets: S. Tingay. priv.," That we have found an emissivity which might be explained by magnetic connections to the black hole or to matter in the plunging region in the very high state of XTE $-$ 500 (detected at 7.5 mJy at 0.8 GHz with MOST in this state with a spectrum indicative of jets; S. Tingay, priv."963 comm.).," comm.),"964 suggests that the discrete radio ejections observed in some sources In this state (see Fender 2001) may be driven by rotational energy extraction., suggests that the discrete radio ejections observed in some sources in this state (see Fender 2001) may be driven by rotational energy extraction.965" Martocchia. Matt. Karas (2002) have shown that a ""lamp-post” reflection model may explain the steep disk emissivity implied in fits to the Fe Ko line in MCG-6-30-15."," Martocchia, Matt, Karas (2002) have shown that a ``lamp-post'' reflection model may explain the steep disk emissivity implied in fits to the Fe $\alpha$ line in MCG–6-30-15."966 This model assumes a source of power-law flux which illuminates the aceretion disk from a location directly above the black hole., This model assumes a source of power-law flux which illuminates the accretion disk from a location directly above the black hole.967 To explain ./~4. this model requires f£—4 — well above the values we measure.," To explain $\beta\sim4$, this model requires $f\sim4$ — well above the values we measure."968 Therefore. the lamp-post model may not adequately describe the accretion geometry of XTE J1650—500.," Therefore, the lamp-post model may not adequately describe the accretion geometry of XTE $-$ 500."969 We wish to thank project. scientist. Fred Jansen for executing our TOO request., We wish to thank project scientist Fred Jansen for executing our TOO request.970 RW was supported by NASA through Chandra fellowship grants PF9-10010. which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8—39073.," RW was supported by NASA through Chandra fellowship grants PF9-10010, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8–39073."971 This work is based on observations obtained with XMM-Newton... an ESA science mission with instruments and contributions directly funded by ESA Member States and the USA (NASA).," This work is based on observations obtained with , an ESA science mission with instruments and contributions directly funded by ESA Member States and the USA (NASA)."972"with 97% correctly classified SNe. and ~6556 having Py,>0.9.","with $97\%$ correctly classified SNe, and $\sim65\%$ having $P_{Ia}>0.9$."973 The posterior redshift scatter is marginallv reduced. compared to the constructed prior standard deviation of &=0.1. inclicating that (his precision in redshift is about the limit of what can be achieved with single epoch data in three bands.," The posterior redshift scatter is marginally reduced, compared to the constructed prior standard deviation of $\sigma=0.1$, indicating that this precision in redshift is about the limit of what can be achieved with single epoch data in three bands."974 For σι=920.3. i.e.. very broadly distributed and imprecise redshifts. and probably (he worst case scenario for photometric redshifts. we correctly classify ~76% of the SNe as type la. ancl improve (he scatter in the redshift determination froma =0.3 to an value oL ag~0.17. thus improving the redshift dispersion by almost a factor of 2.," For $\sigma_1=\sigma_2=0.3$, i.e., very broadly distributed and imprecise redshifts, and probably the worst case scenario for photometric redshifts, we correctly classify $\sim76\%$ of the SNe as type Ia, and improve the scatter in the redshift determination from $\sigma=0.3$ to an value of $\sigma\sim0.17$, thus improving the redshift dispersion by almost a factor of 2."975 On the other hand. it ean clearly be seen that the posterior redshift distribution is heavily biased towards lower z.," On the other hand, it can clearly be seen that the posterior redshift distribution is heavily biased towards lower $z$."976 This is a consequence of the [act Chat. the lower the redshilt. (he more freedom the minimization has in the other parameters.," This is a consequence of the fact that, the lower the redshift, the more freedom the minimization has in the other parameters."977 At lower z the SN template is inherently brighter and can be ‘aged and extinguished! in order to fit the observed magnitudes. while al higher 2 1 must be closer to peak ancl less extinguished.," At lower $z$ the SN template is inherently brighter and can be `aged' and extinguished in order to fit the observed magnitudes, while at higher $z$ it must be closer to peak and less extinguished."978 The most extreme scenario is (he absence of anv prior on (he redshift., The most extreme scenario is the absence of any prior on the redshift.979 This is probably relevant only to the few objects Chat have no measured host due to its faintness., This is probably relevant only to the few objects that have no measured host due to its faintness.980 In (his case. we drop to only ~605€ correct classifications. only slightly better than random assignment ol SN type.," In this case, we drop to only $\sim60\%$ correct classifications, only slightly better than random assignment of SN type."981 Not surprisingly. parameter space is wide enough to accommodate both tvpes. when no information on the host redshift exists. and the SN light/color curve is so scantily sampled.," Not surprisingly, parameter space is wide enough to accommodate both types, when no information on the host redshift exists, and the SN light/color curve is so scantily sampled."982 We can (hus conclude Chat single epoch photometry in three bands. combined with a reasonably well determined host galaxy vredshift. is sufficient to recognize SNe Ia. with only a lew alse negatives. and high confidence levels.," We can thus conclude that single epoch photometry in three bands, combined with a reasonably well determined host galaxy redshift, is sufficient to recognize SNe Ia, with only a few false negatives, and high confidence levels."983" In order to measure the performance of the SN-ABC in correctly classifving CC-SNe. we repeal the procedure described in §??.. applving (he same ""pseudo photometric recdshilts” to the much smaller sample of five type II-P. SNe. presented in Nugentetal.(2006)."," In order to measure the performance of the SN-ABC in correctly classifying CC-SNe, we repeat the procedure described in \ref{SNLS-Ia}, applying the same “pseudo photometric redshifts” to the much smaller sample of five type II-P SNe, presented in \citet{NUGENT_IIP06}."984.. We extract 25 ‘objects’ with same-day photometry [rom among (three of these SNe. which are al redshifts of 0.13 to 0.21.," We extract 25 `objects' with same-day photometry from among three of these SNe, which are at redshifts of 0.13 to 0.21."985 As shown in Figure 2.. when using the precise spectral redshifts. we achieve a perfect suecess rate with not a single object misclassified.," As shown in Figure \ref{SNLSIIP}, when using the precise spectral redshifts, we achieve a perfect success rate with not a single object misclassified."986 When using broader. more realistic. we reach success rates between 8556 [σι=65 0.03) and 75% (σι=oo 0.1).," When using broader, more realistic, z-pdfs, we reach success rates between $85\%$ $\sigma_1=\sigma_2=0.03$ ) and $75\%$ $\sigma_1=\sigma_2=0.1$ )."987 since (he redshifts of (hese SNe are signilicantlv lower (han those of the SNLS Ia sample. we exaniüne cases with comparatively smaller values of σι and σο (hat are more reasonable [or," Since the redshifts of these SNe are significantly lower than those of the SNLS Ia sample, we examine cases with comparatively smaller values of $\sigma_1$ and $\sigma_2$ that are more reasonable for"988For calculations. we asstune eg=5/3 and à=1/3 for Alfvénnic turbulence above the evro scale.,"For calculations, we assume $c_{3}=5/3$ and $a=1/3$ for Alfvénnic turbulence above the gyro scale."989 Using the paraincters for the ISM 3n Table 1. we calculate the erain velocity arisine from the chaotic acceleration by low frequency Alfvén waves in Figure 10 for the CNMD aud WIM.," Using the parameters for the ISM in Table 1, we calculate the grain velocity arising from the chaotic acceleration by low frequency Alfvénn waves in Figure \ref{f4} for the CNM and WIM."990 We show that the chaotic acceleration by low frequency Alfvén waves is subdominant to the fast aud Alfvénuic lyclrockyuamc drag., We show that the chaotic acceleration by low frequency Alfvénn waves is subdominant to the fast and Alfvénnic hydrodynamic drag.991" Obviously, it is inuch less important than evroresonance and TTD by fast modes."," Obviously, it is much less important than gyroresonance and TTD by fast modes."992 The possible reason is that the low frequency Alfvén waves cascade faster to small scale than the fast modes., The possible reason is that the low frequency Alfvénn waves cascade faster to small scale than the fast modes.993 The acceleration of dust erains by incompressible AMID turbulence was first studied by Lazarian Yau (2002)., The acceleration of dust grains by incompressible MHD turbulence was first studied by Lazarian Yan (2002).994 Yan Lazarian (2003) studied erain acceleration in compressible ΑΠΟ turbulence. and discovered a new acceleration mechanism based ou evroresouaut interactions of eras with waves.," Yan Lazarian (2003) studied grain acceleration in compressible MHD turbulence, and discovered a new acceleration mechanism based on gyroresonant interactions of grains with waves."995 This acceleration niechanisni increases erain velocities iu perpendicular direction to the mean magnetic field., This acceleration mechanism increases grain velocities in perpendicular direction to the mean magnetic field.996 YLDOL computed erain velocities arising from gvroresonance by fast MIID modes using quasi-lincar theory (QLT). aud compared the obtained results with different imechanisims. for various ΕΛΙΤ phases.," YLD04 computed grain velocities arising from gyroresonance by fast MHD modes using quasi-linear theory (QLT), and compared the obtained results with different mechanisms, for various ISM phases."997 They. found that the evroresouauce is the most efficicut mechamisin for eraiu acceleration in he ISM., They found that the gyroresonance is the most efficient mechanism for grain acceleration in the ISM.998 The effect of large scale compression on erain acceleration is shown by Yan (2009) to be less important han the evroresouauce in the ISM conditions. uuless the eraius nove with super-Alfvénuic velocities.," The effect of large scale compression on grain acceleration is shown by Yan (2009) to be less important than the gyroresonance in the ISM conditions, unless the grains move with super-Alfvénnic velocities."999 For very sinall grams (e.g polveyelie aromatic wdrocarbous and nanoparticles). Ivlev et al. (," For very small grains (e.g., polycyclic aromatic hydrocarbons and nanoparticles), Ivlev et al. ("10002010) sketched a new mechanisnmi of erain acceleration due o electrostatic interactions of erains with fluctuating charge aud provided rough estimates of erai velocities in the ISM.,2010) sketched a new mechanism of grain acceleration due to electrostatic interactions of grains with fluctuating charge and provided rough estimates of grain velocities in the ISM.1001 Woang Lazarian (2011) quantified this nechanisin using Moute Carlo simulations of charec ductuatious., Hoang Lazarian (2011) quantified this mechanism using Monte Carlo simulations of charge fluctuations.1002 They found that charge fluctuations cau accelerate erains to several times their thermal velocities., They found that charge fluctuations can accelerate grains to several times their thermal velocities.1003 We have revisited the treatment of evroresonauce acceleration for charged grains due to MOTD turbulence by accounting for the fluctuations of erain guidiug center from a regular trajectory along the mecan magnetic field (i.c. NLT huit)., We have revisited the treatment of gyroresonance acceleration for charged grains due to MHD turbulence by accounting for the fluctuations of grain guiding center from a regular trajectory along the mean magnetic field (i.e. NLT limit).1004 The fluctuations of the eniding center result in the broadening of resonance conditions a Delta function is replaced by a Gaussian fiction., The fluctuations of the guiding center result in the broadening of resonance conditions– a Delta function is replaced by a Gaussian function.1005 Such broadeuiug of resonance condition. allows some fraction of wave energy spent through the TTD acceleration., Such broadening of resonance condition allows some fraction of wave energy spent through the TTD acceleration.1006 As a result. erain velocities due to evroresonance acceleration are in general decreased by ~1554 in the NLT iuit.," As a result, grain velocities due to gyroresonance acceleration are in general decreased by $\sim 15\%$ in the NLT limit."1007 TTD acceleration is believed to be important when the parallel component of erain velocity along the iuaenuetie field exceeds the Alfvéuu speed V4., TTD acceleration is believed to be important when the parallel component of grain velocity along the magnetic field exceeds the Alfvénn speed $V_{\A}$.1008 Although evroresonance acceleration by fast modes can accelerate erains to ο>Vay. thei resulting velocity mostly perpendicular to the magnetic field. ie. µ=0. makes TTD uufavored because the resonance coudition ó(uke is not satisfied.," Although gyroresonance acceleration by fast modes can accelerate grains to $v\ge V_{\A}$, their resulting velocity mostly perpendicular to the magnetic field, i.e. $\mu=0$, makes TTD unfavored because the resonance condition $\delta (\omega-k_{\|}v_{\|})$ is not satisfied."1009 IDudeed. we found that TTD is efficient for jp2Va/e and negligible for µ«VWafe in the QLT limit.," Indeed, we found that TTD is efficient for $\mu>V_{\A}/v$ and negligible for $\mu<V_{\A}/v$ in the QLT limit."1010 This feature is cousistent with the result for acceleration of cosnüc ravs in Sclilickeiser Aller (199s)., This feature is consistent with the result for acceleration of cosmic rays in Schlickeiser Miller (1998).1011 The situation changes when the fluctuatious of the euidiue center are taken iuto account in the NLT., The situation changes when the fluctuations of the guiding center are taken into account in the NLT.1012 For this case. the resonance condition is broadened bevoud the à function. and cau be described by a Caussian fection.," For this case, the resonance condition is broadened beyond the $\delta$ function, and can be described by a Gaussian function."1013" As a result. TTD acceleration becomes iniportant for pocνο, inchiding 90° pitch angle."," As a result, TTD acceleration becomes important for $\mu <V_{\A}/v$, including $90^{\circ}$ pitch angle."1014 Tn addition to acceleration. TTD also induces the erain pitch angele scattering. which is dominant over the scattering bv evroresonance.," In addition to acceleration, TTD also induces the grain pitch angle scattering, which is dominant over the scattering by gyroresonance."1015 Since the efficiency. of the TTD scattering is uncertain. we considered in the paper two lmiting cases of inefiicicut and cfiicieut scattering in which the scattering is less aud more cficieut than the acceleration.," Since the efficiency of the TTD scattering is uncertain, we considered in the paper two limiting cases of inefficient and efficient scattering in which the scattering is less and more efficient than the acceleration."1016 The pitch angle is equal to 90° in the former. and isotropic in the latter.," The pitch angle is equal to $90^{\circ}$ in the former, and isotropic in the latter."1017 When the scattering is more effcicut than the acceleration. we showed that for the WNAL aud WIM. the TTD acceleration can increase substantially the erai velocity compared to results arising from gvroresonance.," When the scattering is more efficient than the acceleration, we showed that for the WNM and WIM, the TTD acceleration can increase substantially the grain velocity compared to results arising from gyroresonance."1018 Particularly. for evans huger than 5«10 αμ in the WIAL TTD acceleration is an order of maguitude ereater," Particularly, for grains larger than $5\times 10^{-6}$ cm in the WIM, TTD acceleration is an order of magnitude greater"1019"hundred parsees is suggestive of pseudobulges that have been identified photometrically in disk galaxies (Kormendy&Ken-&Drory2010:Weinzirletal.2009) and the ""central light excesses” identified in bulgeless disks (Bokeretal.2003).. including the late-type-disk M33 (Kent1987;Minnitietal. 1993).","hundred parsecs is suggestive of pseudobulges that have been identified photometrically in disk galaxies \citep{Kormendy:04,Fisher:08,Fisher:09,Fisher:10,Weinzirl:09} and the “central light excesses” identified in bulgeless disks \citep{Boker:03}, including the late-type-disk M33 \citep{Kent:87,Minniti:93}."1020. The effective radii of the pseudobulge components identified in the recent surveys by Fisher et aand Weinzirl et sseem to be compatible with our more optimistic models that ignore prompt dissolution. and are on average larger than the radii within which we detect surface density excess in the pessimistic models with 90% prompt dissolution.," The effective radii of the pseudobulge components identified in the recent surveys by Fisher et and Weinzirl et seem to be compatible with our more optimistic models that ignore prompt dissolution, and are on average larger than the radii within which we detect surface density excess in the pessimistic models with $90\%$ prompt dissolution."1021" We caution against direct. comparison because in the present work. m an attempt to emphasize sensitivity to the variation of the ICMF truncation mass scale M44,"" we have held the parameters of our dark halo and initial baryonic disk (or spheroid) fixed at values that seem to correspond to galaxies that are somewhat smaller than the typical pseudobulge hosts."," We caution against direct comparison because in the present work, in an attempt to emphasize sensitivity to the variation of the ICMF truncation mass scale $M_{\rm max}$, we have held the parameters of our dark halo and initial baryonic disk (or spheroid) fixed at values that seem to correspond to galaxies that are somewhat smaller than the typical pseudobulge hosts."1022 We can only conclude that a pseudobulge-like central stellar surface density increase is generic and that cluster migration is one potential contributor to pseudobulge assembly in disk galaxies. while other processes. such as angular momentum transport by stellar and gaseous bars. certainly also contribute. in line with the observation that pseudobulge hosts generally have nuclear bars. rings. or nuclear spirals (e.g..Kormendy&Kennicutt2004:Fisher&Drory 2008).," We can only conclude that a pseudobulge-like central stellar surface density increase is generic and that cluster migration is one potential contributor to pseudobulge assembly in disk galaxies, while other processes, such as angular momentum transport by stellar and gaseous bars, certainly also contribute, in line with the observation that pseudobulge hosts generally have nuclear bars, rings, or nuclear spirals \citep[e.g.,][]{Kormendy:04,Fisher:08}."1023 The most massive clusters that we have considered are still substantially less massive than the giant ~105—10?M. clumps that are observed to be present and are theoretically expected to be forming in globally gravitationally unstable. rapidly-star-forming massive disks at high redshift (e.g..therein )..," The most massive clusters that we have considered are still substantially less massive than the giant $\sim10^8-10^9\,M_\odot$ clumps that are observed to be present and are theoretically expected to be forming in globally gravitationally unstable, rapidly-star-forming massive disks at high redshift \citep[e.g.,][and1024 references1025 therein]{Noguchi:99,Bournaud:07,Elmegreen:08b,Dekel:09b,Tacconi:10}."1026 The super star clusters forming in these giant clumps should be more immune to dissolution in the tidal field of the galaxy and could reach the galactic central region intact., The super star clusters forming in these giant clumps should be more immune to dissolution in the tidal field of the galaxy and could reach the galactic central region intact.1027 We speculate that there could be a eritical characteristic ICMF mass scale above which clusters migrate intact and merge to produce a classical bulge (see.e.g..Immelietal.2004:Elmegreenetal.2008:Ceverino 2010).. and below which they suffer substantial mass loss en route to the galactic center and thus give rise to a pseudobulge.," We speculate that there could be a critical characteristic ICMF mass scale above which clusters migrate intact and merge to produce a classical bulge \citep[see,1028 e.g.,][]{Immeli:04,Elmegreen:08b,Ceverino:10}, and below which they suffer substantial mass loss en route to the galactic center and thus give rise to a pseudobulge."1029 The apparent agreement of NSC-mass-to-galactic-stellar- ratios in spheroidals (~2«107: Cótéetal.2006;Fer-rareseetal.2006b;Wehner&Harris 2006) and massive-black-hole-to-galactie stellar mass ratios in ellipticals and bulges (~[1—2]«102: e.g.. Kormendy&Richstone1995;2005:Hiring&Rix 2004) has prompted speculation that the same process may be responsible for the formation of NSCs and black holes.," The apparent agreement of NSC-mass-to-galactic-stellar-mass ratios in spheroidals $\sim2\times10^{-3}$; \citealt{Cote:06,Ferrarese:06b,Wehner:06}) ) and massive-black-hole-to-galactic stellar mass ratios in ellipticals and bulges $\sim[1-2]\times10^{-3}$; e.g., \citealt{Kormendy:95,Wandel:99,Kormendy:01,Merritt:01a,McLure:02,Marconi:03,Haring:04}) ) has prompted speculation that the same process may be responsible for the formation of NSCs and black holes."1030 While the formation and growth of a massive black hole undoubtedly requires a gas-dynamical. dissipative process. our results suggest that an NSC can be assembled nondissipatively. by the collisionless migration of star clusters. and thus. the observed agreement could be a coincidence.," While the formation and growth of a massive black hole undoubtedly requires a gas-dynamical, dissipative process, our results suggest that an NSC can be assembled nondissipatively, by the collisionless migration of star clusters, and thus, the observed agreement could be a coincidence."1031 Although the well-studied NSC host galaxy M33 does not contain a central massive black hole (Merrittetal.2001:Gebhardtetal.2001.andreferences therein).. another one. 44395. does (Filippenko&Ho2003).. and still others contain AGNs (Sethetal.2008).," Although the well-studied NSC host galaxy M33 does not contain a central massive black hole \citep[][and references1032 therein]{Merritt:01b,Gebhardt:01}, another one, 4395, does \citep{Filippenko:03}, and still others contain AGNs \citep{Seth:08}."1033. Since AGNs and the growth of a central black hole require gas inflow into the center of the galaxy. NSC growth from migrating disk clusters would not generally be accompanied. with black hole growth. because disk clusters contribute stellar mass without augmenting the black hole mass (although gas inflow may be enhanced by the migrating clusters. see. e.g.. Goodman&Rafikov2001:Chang2008)).," Since AGNs and the growth of a central black hole require gas inflow into the center of the galaxy, NSC growth from migrating disk clusters would not generally be accompanied with black hole growth, because disk clusters contribute stellar mass without augmenting the black hole mass (although gas inflow may be enhanced by the migrating clusters, see, e.g., \citealt{Goodman:01,Chang:08}) )."1034 This suggests that the central black hole mass in bulgeless disks should not be correlated with the mass of the NSC and that any pseudobulge that is present. unless the migrating clusters independently synthesize massive (or intermediate-mass) black holes which. in this case. they would deliver to the center to merge to form à more massive central black hole (Elmegreenetal.2008)..," This suggests that the central black hole mass in bulgeless disks should not be correlated with the mass of the NSC and that any pseudobulge that is present, unless the migrating clusters independently synthesize massive (or intermediate-mass) black holes which, in this case, they would deliver to the center to merge to form a more massive central black hole \citep{Elmegreen:08a}. ."1035clensity of more distant clusty galaxies is available.,density of more distant dusty galaxies is available.1036 There is an upper limit to the surface density of sources at mmm (Wilner Wright 1997): counts at p/m (Smail et 11997: Bareer ct 1998: LIolland et 11998: Hughes et 11998: Barecr et 119998: Blain et 1999b: Eales et 11999): upper imits (Small et 11997: Darger et 11998). and a new count (Blain et 22000) at pm: 175-jm.LSO counts rom Ixawara et ((1998) and Puget et ((1999): 95-5. counts from Wawara et ((1998): and 7- and 15-5 counts rom an extremely deep.50 image of Abcll22390 CATieri et 11999). which yields counts that are even. deeper han those determined in blank-Bield survevs by Oliver et ((1997). Aussel ct al. (," There is an upper limit to the surface density of sources at mm (Wilner Wright 1997); counts at $\mu$ m (Smail et 1997; Barger et 1998; Holland et 1998; Hughes et 1998; Barger et 1999a; Blain et 1999b; Eales et 1999); upper limits (Smail et 1997; Barger et 1998), and a new count (Blain et 2000) at $\mu$ m; $\mu$ m counts from Kawara et (1998) and Puget et (1999); $\mu$ m counts from Kawara et (1998); and 7- and $\mu$ m counts from an extremely deep image of 2390 (Altieri et 1999), which yields counts that are even deeper than those determined in blank-field surveys by Oliver et (1997), Aussel et al. ("10371999) and Flores et (1999).,1999) and Flores et (1999).1038" If the values of the activity parameter at recishift ZOLO. (m),1. listed in Tablell are usec to estimate the counts of galaxies at SSO and yam. then the results unclerpredict the observed counts by a luge factor."," If the values of the activity parameter at redshift zero, $(F\sigma)_0^{-1}$, listed in 1 are used to estimate the counts of galaxies at 850 and $\mu$ m, then the results underpredict the observed counts by a large factor."1039 The form of evolution of the merger ellicieney ος) is fixed. by the observed background radiation intensity. and so. keeping within the framework of our well-constrained. models. the value of the activity parameter (£m) at high. redshift must be allowed. to increase above its value at. recishift zero in order to account for the observations.," The form of evolution of the merger efficiency $x(z)$ is fixed by the observed background radiation intensity, and so, keeping within the framework of our well-constrained models, the value of the activity parameter $(F\sigma)^{-1}$ at high redshift must be allowed to increase above its value at redshift zero in order to account for the observations."1040 This has the ellect of increasing the luminosity of high-redshift mergers. thus increasing the 175- ancl μι counts.," This has the effect of increasing the luminosity of high-redshift mergers, thus increasing the 175- and $\mu$ m counts."1041 However. the background. radiation intensity and the Iow-redshift 60-74 counts remain unchanged.," However, the background radiation intensity and the low-redshift $\mu$ m counts remain unchanged."1042 The form of evolution of the activity parameter (£e)1 that is required to explain the data is illustrated in SS., The form of evolution of the activity parameter $(F\sigma)^{-1}$ that is required to explain the data is illustrated in 8.1043 In Fig.sSs(a) the ratio of the model predictions and the observed counts at wavelengths of 175 and m (Ixzwara et al., In 8(a) the ratio of the model predictions and the observed counts at wavelengths of 175 and $\mu$ m (Kawara et al.1044 1998: Blain et 11999b respectively) are compared as a function of the activity parameter in the four mocdels listed in H1., 1998; Blain et 1999b respectively) are compared as a function of the activity parameter in the four models listed in 1.1045 Phe same value of the activity parameter cannot account for the observed counts at both wavelengths simultaneously. and the value required to explain the low-redshift. 60-//mi counts is dillerent. from. either.," The same value of the activity parameter cannot account for the observed counts at both wavelengths simultaneously, and the value required to explain the low-redshift $\mu$ m counts is different from either."1046 The value of the activity. parameter required. to. [it the 60-.. 175- and S50-//imi counts increases monotonically.," The value of the activity parameter required to fit the 60-, 175- and $\mu$ m counts increases monotonically."1047 Because the median redshift of the galaxies contributing to the counts ab these redshifts is expected to increase monotonically. in SS(b) we present the ratio of the model predictions aud he observed. counts as a function of a parameter ps that describes a simple form of exponential redshift evolution of he activity. parameter. The exponential form provides a reasonable fit to the data. out. is only one example of a whole family of potential unctions.," Because the median redshift of the galaxies contributing to the counts at these redshifts is expected to increase monotonically, in 8(b) we present the ratio of the model predictions and the observed counts as a function of a parameter $p_\sigma$ that describes a simple form of exponential redshift evolution of the activity parameter, The exponential form provides a reasonable fit to the data, but is only one example of a whole family of potential functions."1048 Phe important feature is that the function chosen ο represent the activity parameter (£m)+ increases rapiclly with increasing recshift., The important feature is that the function chosen to represent the activity parameter $(F\sigma)^{-1}$ increases rapidly with increasing redshift.1049 The zero-redshift value of the activity parameter (ho)? is lixed by requiring that the low-reelshilt G0-j4 count prediction is in agreement with observations: see Ll., The zero-redshift value of the activity parameter $(F\sigma)^{-1}_0$ is fixed by requiring that the low-redshift $\mu$ m count prediction is in agreement with observations; see 1.1050 Phe values of the evolution. parameter pe that correspond. to the most reasonable fit for assumed. single, The values of the evolution parameter $p_\sigma$ that correspond to the most reasonable fit for assumed single1051the (2D) orbit (on sky) is not a circular edge-on orbit. but inclined and/or eccentric with LR 7329 D currently near the apastron. hence the small motion on sky.,"the (2D) orbit (on sky) is not a circular edge-on orbit, but inclined and/or eccentric with HR 7329 B currently near the apastron, hence the small motion on sky."1052 Phe orbital plane of Η 7329 could be in the line of sight («dcge-on like the debris disk aroundD LER. 7329 A). with Lh 7329 D currently near the largest angular separation from LII 7329 X. but with orbital motion mostly in the radial direction: such," The orbital plane of HR 7329 B could be in the line of sight (edge-on like the debris disk around HR 7329 A), with HR 7329 B currently near the largest angular separation from HR 7329 A, but with orbital motion mostly in the radial direction; such"1053"(1)) we can estimate AL.(final)=Ceetemex μη hence ecc:=Cétetina/te. Where € is a constant fucdec factor of order unitv that depends on the actual time evolution of the SFRs aud My, (Gud eg if it js time dependent).","\ref{eq:dotMstar}) ) we can estimate $M_*({\rm final})=\xi\epsilon_{\rm ff}/t_{\rm ff}\max(M_\H2)t_{\rm final}$ , hence $\epsilon_{\rm GMC}=\xi\epsilon_{\rm ff}t_{\rm final}/t_{\rm ff}$, where $\xi$ is a constant fudge factor of order unity that depends on the actual time evolution of the SFRs and $M_\H2$ (and $\epsilon_{\rm ff}$ if it is time dependent)."1054 We will estimate & for a simple tov model iu section 3.., We will estimate $\xi$ for a simple toy model in section \ref{sect:model}. .1055 Combining this result with equation (2)) aud (3)) we obtain: There are several wavs of creating large values of Hoare 0nd they correspond to the various terms iu this equation., Combining this result with equation \ref{eq:GMCeps}) ) and \ref{eq:GMCeta}) ) we obtain: There are several ways of creating large values of $\eta_{\rm GMC}$ and they correspond to the various terms in this equation.1056 First. eg could be time depeudenut.," First, $\epsilon_{\rm ff}$ could be time dependent."1057 For instance. it could sinoothly increase as the cloud collapse advances or. alternatively. vary stochastically about some average value.," For instance, it could smoothly increase as the cloud collapse advances or, alternatively, vary stochastically about some average value."1058" A second possibility is that some clouds may live for many free fall times. ne. fgi/fg Is large in a subset of (λος,"," A second possibility is that some clouds may live for many free fall times, i.e. $t_{\rm final}/t_{\rm ff}$ is large in a subset of GMCs."1059 The third factor in the third bracket in equation (1)) explain why jeje: can also be than €oaxrc., The third factor in the third bracket in equation \ref{eq:GMCeps2}) ) explain why $\eta_{\rm GMC}$ can also be than $\epsilon_{\rm GMC}$.1060" Finally. ον"" can be boosted if the observed IT, muss is siguificautly less than maxoWy,). i.c. if GAICS lose (à one way or another) a large fraction of their molecular hydrogen over their lite time."," Finally, $\eta_{\rm GMC}$ can be boosted if the observed $\H2$ mass is significantly less than $\max(M_\H2)$, i.e. if GMCs lose (in one way or another) a large fraction of their molecular hydrogen over their life time."1061 The latter seenario predicts that jesjo(7) should roughly scale κMy over the life time of CAICs., The latter scenario predicts that $\eta_{\rm GMC}(t)$ should roughly scale $\propto{}M_\H2^{-1}$ over the life time of GMCs.1062 Au observational sample of an of GMCs shows this trend (Muay90101., An observational sample of an of GMCs shows this trend \citep{2010arXiv1007.3270M}.1063 However. this trend cau also be produced by a selection effect based on stellar 1iass. e.g. selecting CAICs with M.2μμ excludes values of Hoare that are ΙΕΤΕ see equation (3)).," However, this trend can also be produced by a selection effect based on stellar mass, e.g. selecting GMCs with $M_* > M_{*,{\rm limit}}$ excludes values of $\eta_{\rm GMC}$ that are smaller than $M_{*,{\rm limit}}/M_\H2$, see equation \ref{eq:GMCeta}) )."1064 In fact. ἁπαπαν(2010). is selecting clouds based on ionizing hunuinositioes. which roughly corresponds to selecting clouds based the stellar mass formed within the last [1 Myr.," In fact, \cite{2010arXiv1007.3270M} is selecting clouds based on ionizing luminosities, which roughly corresponds to selecting clouds based the stellar mass formed within the last 4 Myr."1065" Such a selection effect explains why a different study of ~1011, GMCs find auch lower efficiencies Ladaetal.(2010)...", Such a selection effect explains why a different study of $\sim{}10^5 M_\odot$ GMCs find much lower efficiencies \cite{2010arXiv1009.2985L}.1066 The existence of the selection effect is an argunient against or in favor of an evolving €g. rather it shows that the CAICs with large values of Hoare: In the sample of Murray.(2010). are likely a heavily biased. subset.," The existence of the selection effect is an argument against or in favor of an evolving $\epsilon_{\rm ff}$, rather it shows that the GMCs with large values of $\eta_{\rm GMC}$ in the sample of \cite{2010arXiv1007.3270M} are likely a heavily biased subset."1067 In the case that eg is. in fact. a non evolving quantity aud the measured laree values of year are driven by changing molecular gas masses. we can dnake a rather generic prediction.," In the case that $\epsilon_{\rm ff}$ is, in fact, a non evolving quantity and the measured large values of $\eta_{\rm GMC}$ are driven by changing molecular gas masses, we can make a rather generic prediction."1068" The similarity of the sealing with GAIC (x My) of nac: on the oue haud. aud the lower boundary of the region excluded by the discussed selection. effect. on the other hand. iuplies that the observed GMCS with large values of Hoare: Should have rather similar IT» masses inax(AMg,)."," The similarity of the scaling with GMC $\propto{}M_\H2^{-1}$ ) of $\eta_{\rm GMC}$ , on the one hand, and the lower boundary of the region excluded by the discussed selection effect, on the other hand, implies that the observed GMCs with large values of $\eta_{\rm GMC}$ should have rather similar $\H2$ masses $\max(M_\H2)$."1069" The tov model that we discuss in section 3 predicts max(Mq,)~108LOTAL...", The toy model that we discuss in section \ref{sect:model} predicts $\max(M_\H2)\sim{}10^6-10^7 M_\odot$.1070 We note that this scenario explains rather naturally the absence of iiassive (Gm10° AL.) CMCS with high values of yore., We note that this scenario explains rather naturally the absence of massive $\gtrsim{}10^6$ $M_\odot$ ) GMCs with high values of $\eta_{\rm GMC}$.1071 A different issue can arise df one compares star formation rates and Πο masses in order to estimate ἐμτμ Via equation (1))., A different issue can arise if one compares star formation rates and $\H2$ masses in order to estimate $\epsilon_{\rm ff}/{t_{\rm ff}}$ via equation \ref{eq:dotMstar}) ).1072" For example. let us assiunoe that we measure SFRs aud Ty masses within small (Z100 pe) apertures around peaks of CO cinission (tracing the IL, mass) and peaks of Πα οσο (tracing star formation rates). see e.g. Schrubaetal.(2010)..."," For example, let us assume that we measure SFRs and $\H2$ masses within small $\lesssim{}100$ pc) apertures around peaks of CO emission (tracing the $\H2$ mass) and peaks of $H\alpha$ emission (tracing star formation rates), see e.g. \cite{2010arXiv1009.1651S}."1073 If we observe that CO peaks have lower SFRs at giveu IL lass colpared with peaks of Πα enüssion. does this iuplv a time-varving eg/fg?," If we observe that CO peaks have lower SFRs at given $\H2$ mass compared with peaks of $H\alpha$ emission, does this imply a time-varying $\epsilon_{\rm ff}/{t_{\rm ff}}$?"1074 The answer to that question depends ou the way the SFRs are measured., The answer to that question depends on the way the SFRs are measured.1075 SERs that are derived from ΓΓα cinission are effectively averaged over the past 5-10 Myr. which nueht well be a significant action of the lite time of the molecular cloud.," SFRs that are derived from $H\alpha$ emission are effectively averaged over the past 5-10 Myr, which might well be a significant fraction of the life time of the molecular cloud."1076 For SFRs hat are based on Πα μυ cinission this averaging iue span would be even longer., For SFRs that are based on $H\alpha$ $24\mu{}m$ emission this averaging time span would be even longer.1077 The star formation cficieucies per free-fall time that are estimated frou such a time averaged SER will be zinall initially (uo stars have (en formed over most of the time averaging interval simply because the GAIC has ouly formed receutlv)., The star formation efficiencies per free-fall time that are estimated from such a time averaged SFR will be small initially (no stars have been formed over most of the time averaging interval simply because the GMC has only formed recently).1078 The neasured SFRs will increase until the age of the GMC is siuilar to the averaging time span., The measured SFRs will increase until the age of the GMC is similar to the averaging time span.1079 In additiou. the Il amass of the cloud might evolve (possibly decrease) cading to an additional increase in the appareut value of eg/ty with time.," In addition, the $\H2$ mass of the cloud might evolve (possibly decrease) leading to an additional increase in the apparent value of $\epsilon_{\rm ff}/{t_{\rm ff}}$ with time."1080 If the followine three conditions are satisfied. a difference in the measured SER per imceasured IL» mass can provide strong evidence for a tinic-varviug star formation effücienev per free fall time.," If the following three conditions are satisfied, a difference in the measured SFR per measured $\H2$ mass can provide strong evidence for a time-varying star formation efficiency per free fall time."1081 First. the averaging times of the SFRs need to be small compared to ages of the observed clouds.," First, the averaging times of the SFRs need to be small compared to ages of the observed clouds."1082" Second. the observable IT, reservoirs need to be close to πας.) aud. finally. the free fall times of the clouds need to be known."," Second, the observable $\H2$ reservoirs need to be close to $\max(M_\H2)$, and, finally, the free fall times of the clouds need to be known."1083 A recent study that measures SET with reasonably short averaging times (2 Myr. Ladactal.2010)) estimates star formation efficiencies per free fall time of the order of 2! for most clouds in the sample. with the scatter mostly driven bv the mass of molecular eas of relatively low deusity (o<10! 7) that does not participate in the star formation.," A recent study that measures SFRs with reasonably short averaging times (2 Myr, \citealt{2010arXiv1009.2985L}) ) estimates star formation efficiencies per free fall time of the order of $2\%$ for most clouds in the sample, with the scatter mostly driven by the mass of molecular gas of relatively low density $n<10^4$ $^{-3}$ ) that does not participate in the star formation."1084 We will now discuss a tov model iu order to both excinplity the poiuts mace im section 2.. but also to provide a framework iu which we can make some quantitative predictions.," We will now discuss a toy model in order to both exemplify the points made in section \ref{sect:pitfalls}, but also to provide a framework in which we can make some quantitative predictions."1085 We should stress that the statements made in the previous section are completely eeneric aud do not depend on the specific assuuption that go iuto the model that we are goine to present., We should stress that the statements made in the previous section are completely generic and do not depend on the specific assumption that go into the model that we are going to present.1086 Our model is alinost iusultiuelv simples and. given that. our aiu is not to reproduce the full complexity in the evolution of GMCS or even. to be consistent with auv available observation.," Our model is almost insultingly simple, and, given that, our aim is not to reproduce the full complexity in the evolution of GMCs or even, to be consistent with any available observation."1087 On the other haud the model offers a pragluatic approach to the mass evolution of CAICs and iav be casily generalized to facilitate more complex scenarios., On the other hand the model offers a pragmatic approach to the mass evolution of GMCs and may be easily generalized to facilitate more complex scenarios.1088 The iusatzof the model is to supplement equation (1)) with an equivalent equation that describes the evolution of the II» mass: The extra term àM. is motivatedby. assuuing that stellar feedback is limitine the life time of molecular clouds. e.g. via photo-donization. thermal pressure or radiation pressure (Williams&Melee1997:Muay 2010)..," The ansatzof the model is to supplement equation \ref{eq:dotMstar}) ) with an equivalent equation that describes the evolution of the $\H2$ mass: The extra term $\alpha{}M_*$ is motivatedby assuming that stellar feedback is limiting the life time of molecular clouds, e.g. via photo-ionization, thermal pressure or radiation pressure \citep{1997ApJ...476..166W, 2010ApJ...709..191M, 2010arXiv1008.2383L}."1089 This feedback. should therefore couple to theformed stellar mass via some eficiency factor a that sets the time scale for the, This feedback should therefore couple to theformed stellar mass via some efficiency factor $\alpha$ that sets the time scale for the1090above test. to our. observations. namely burs and null sequences. returns values Z5; 60. verifving this conclusion of a non-random undermixing.,"above test to our observations, namely burst and null sequences, returns values $\simlt$ –60, verifying this conclusion of a non-random “undermixing”."1091 Reearding nul periodicity. we find only a suggestion in our observations of a very long periodicitv[αν too long in relation to their tota length for it to be significant.," Regarding null periodicity, we find only a suggestion in our observations of a very long periodicity—far too long in relation to their total length for it to be significant."1092" Thus the bursts and nulls of B1944|17 can be regarde as falling into two categories: a) short bursts or nulls of some 1-7 £P, that show a roughly random: distribution. and b) medium to lone bursts or nulls (720 7) tha can occasionally persist for several hundred: pulses and. are patently non-random."," Thus the bursts and nulls of B1944+17 can be regarded as falling into two categories: a) short bursts or nulls of some 1-7 $P_1$ that show a roughly random distribution, and b) medium to long bursts or nulls $>$ 20 $P_1$ ) that can occasionally persist for several hundred pulses and are patently non-random."1093 We will elaborate. further on. this distinction in 8&5., We will elaborate further on this distinction in 5.1094 We here investigate the properties. of the four modes identified by DCTII., We here investigate the properties of the four modes identified by DCHR.1095 Following their convention. we refer to the three drift modes as A-C. and the final burst mode as 7D.," Following their convention, we refer to the three drift modes as A-C, and the final burst mode as “D”."1096 The defining eharacteristies of modes A-D are the same at both P and L band. as are their frequencies of occurrence.," The defining characteristics of modes A-D are the same at both P and L band, as are their frequencies of occurrence."1097 The four modes can be readily distinguished. by eve due to their unique subpulse structures and intensities. as shown in Figure 4..," The four modes can be readily distinguished by eye due to their unique subpulse structures and intensities, as shown in Figure \ref{colourPS}."1098" The transitions between moces occur on a time scale of less than oneae... there are typically no observable ""transitions"" between modes."," The transitions between modes occur on a time scale of less than one, there are typically no observable “transitions” between modes."1099 We lind that within a sequence of 107 pulses there is a high probability of linding at least one occurrence of each mocle., We find that within a sequence of $10^3$ pulses there is a high probability of finding at least one occurrence of each mode.1100 I is interesting that this pulsar. which displavs an almost overwhelming variety of behaviors. is quite reliable in how often it. does SO.," It is interesting that this pulsar, which displays an almost overwhelming variety of behaviors, is quite reliable in how often it does so."1101 As seen in the colour polarization cisplav of Fig. 4..," As seen in the colour polarization display of Fig. \ref{colourPS},"1102 the stars mode changes are usually punctuated. by nulls. though there are some combinations of mode changes that characteristically occur adjacent to one another.," the star's mode changes are usually punctuated by nulls, though there are some combinations of mode changes that characteristically occur adjacent to one another."1103 As modes A and B exhibit subpulse drifting. they can best be characterized by their /% and. P; values. where £ is defined as the separation of subpulses within a period. anc Py is the separation between drift bands at a fixed. pulse phase.," As modes A and B exhibit subpulse drifting, they can best be characterized by their $P_2$ and $P_3$ values, where $P_2$ is defined as the separation of subpulses within a period, and $P_3$ is the separation between drift bands at a fixed pulse phase."1104 Aloce € characteristically displavs an organized vet stationary subpulse structure., Mode C characteristically displays an organized yet stationary subpulse structure.1105 Lastly. we classify those PSs which show no organized subpulse structure as modo D: it is worth noting that mode D is significantly weaker than the others.," Lastly, we classify those PSs which show no organized subpulse structure as mode D; it is worth noting that mode D is significantly weaker than the others."1106 Table 2 eives [5 and P. values for modes A. D. and €. The A mode is characterized. by prominent intervals of remarkably precise drifting subpulseswhich is paradoxical considering the stars otherwise unpredictable and discontinuous behavior.," Table \ref{modes} gives $P_2$ and $P_3$ values for modes A, B, and C. The A mode is characterized by prominent intervals of remarkably precise drifting subpulses—which is paradoxical considering the star's otherwise unpredictable and discontinuous behavior."1107 Mode. X ids. unique in its regularitv and is marked bv its negativelv-drifting bancs with a roughly 14-74 £5., Mode A is unique in its regularity and is marked by its negatively-drifting bands with a roughly $P_1$ $P_3$.1108 This 14-27) 2; feature can be seen in an Ir of a PS that includes all the moces. indicating its dominance (Weltevrede 2006. 2007).ILwo bright. central subpulses are usually seen in mode A. At L band. weak subpulses on the outer edges of the profile turn on and. olf with a period that is comparable to mode A's £5: see Figure 6..," This $P_1$ $P_3$ feature can be seen in an lrf of a PS that includes all the modes, indicating its dominance (Weltevrede 2006, 2007).Two bright, central subpulses are usually seen in mode A. At L band, weak subpulses on the outer edges of the profile turn on and off with a period that is comparable to mode A's $P_3$; see Figure \ref{modeA_modfold}."1109" Mode A always appears in bursts having durations of more than 15 periods: however. usually these bursts are even longer. typically some GO 100 2, and. remarkably. these A-mocde intervals are very rarely interrupted by nulls."," Mode A always appears in bursts having durations of more than 15 periods; however, usually these bursts are even longer, typically some 60 – 100 $P_1$ —and, remarkably, these A-mode intervals are very rarely interrupted by nulls."1110 The drifting subpulses of mode. D. are. visibly less ordered. than those of mode A: however they are clearly structured and negativelv-drifting., The drifting subpulses of mode B are visibly less ordered than those of mode A; however they are clearly structured and negatively-drifting.1111 P; is approximately half that of mode A at both L. and. P band: although clue, $P_3$ is approximately half that of mode A at both L and P band; although due1112resolution image is resolved out iu this image.,resolution image is resolved out in this image.1113 One max suspect that the diffuse EHI cussion (particularly that seen in between the three clumps iu the low resolution niap) is not real but is the result of beam smieaxiug., One may suspect that the diffuse HI emission (particularly that seen in between the three clumps in the low resolution map) is not real but is the result of beam smearing.1114 To check for this possibility. the individual channel maps iu the 25«25. data cube were inspected.," To check for this possibility, the individual channel maps in the $25^{''}\times25^{''}$ data cube were inspected."1115 In the channel maps. the peak of the diffuse euission in the ceutral region of the galaxv occurs at a differeut beloceutiic velocity than peak velocities of nearby EHI chuups. coutrary to what one would expect from beam smearing.," In the channel maps, the peak of the diffuse emission in the central region of the galaxy occurs at a different heliocentric velocity than peak velocities of nearby HI clumps, contrary to what one would expect from beam smearing."1116" As a further confirmation of this. the clean componcuts from the 25425 resolution data cube were couvolyed with a sinaller restoring beam of 10.«10. to eenerate a new data cube,"," As a further confirmation of this, the clean components from the $25^{''}\times25^{''}$ resolution data cube were convolved with a smaller restoring beam of $10^{''}\times10^{''}$, to generate a new data cube."1117 The diffuse euission is visible iu the channel maps in this cube. contrary to what would have been expected in case the diffuse cussion was cutirely due to beam simeariue (n which case the clean components would have been restricted to the three clumps).," The diffuse emission is visible in the channel maps in this cube, contrary to what would have been expected in case the diffuse emission was entirely due to beam smearing (in which case the clean components would have been restricted to the three clumps)."1118 As can be seen in Fig. 2..," 	As can be seen in Fig. \ref{fig:ov},"1119 each HT chump is associated with a chuup of optical emission., each HI clump is associated with a clump of optical emission.1120 However. for each chump. the peak optical enission is generally offset from the peak of the III cmiussion.," However, for each clump, the peak optical emission is generally offset from the peak of the HI emission."1121 The Πα iaage of ITodgeetal.(1989) shows that the optical clips also cuit copious amounts of IIo and are heuce regions of ou going star formation., The $\alpha$ image of \cite{hodge89} shows that the optical clumps also emit copious amounts of $\alpha$ and are hence regions of on going star formation.1122 Iu addition to the bright clumps. diffuse optical eiissiou is also seen in Fig. 2..," In addition to the bright clumps, diffuse optical emission is also seen in Fig. \ref{fig:ov}."1123 The optical emission has a πιο higher ellipticitv than the IIT emission aud the position angeles of the optical and ITE major axis can also be seen to be different., The optical emission has a much higher ellipticity than the HI emission and the position angles of the optical and HI major axis can also be seen to be different.1124" Quantitativelv. cllipse fittine to the outermost contours of the 107.&38"" aud «425 resolution III monent maps (lich are less distorted by the oxesence of the III chumps in the iuncr regious) gives a position anele of 7T7E5 degrees aud au inclination (assuimiug the oeintrinsic shape of the III disk to be circular) of 2843 degrees."," Quantitatively, ellipse fitting to the outermost contours of the $''\times38''$ and $^{''}\times25^{''}$ resolution HI moment maps (which are less distorted by the presence of the HI clumps in the inner regions) gives a position angle of $\pm$ 5 degrees and an inclination (assuming the intrinsic shape of the HI disk to be circular) of $\pm$ 3 degrees."1125 The values obtained from the two different resolution maps agree to within the error bars., The values obtained from the two different resolution maps agree to within the error bars.1126 Ou the other hand. these values are cousiderablv different from those obtained from eclipse fitting to the optical isophotes. which vields a position angle of 38.1 degrees aud an inclination of 57.7 degrees respectively (De Vaucouleurs Moss 1983).," On the other hand, these values are considerably different from those obtained from ellipse fitting to the optical isophotes, which yields a position angle of 38.4 degrees and an inclination of 57.7 degrees respectively (De Vaucouleurs Moss 1983)."1127 We return to lis issue in Sect. 3.3.., We return to this issue in Sect. \ref{ssec:discuss}.1128" The velocity field derived from the 25<25"" resolution data cube is shown iu Fie. l..", 	 The velocity field derived from the $25^{''}\times 25^{''}$ resolution data cube is shown in Fig. \ref{fig:mom1}. .1129 This velocity field is iu reasonable agreement (albeit of better quality) with that obtained by Carignanctal.(1990)., This velocity field is in reasonable agreement (albeit of better quality) with that obtained by \cite{carignan90}.1130. The velocity field shows closed coutours and is. to zeroth order. consisteut with a velocity field that would be produced by a rotating disk with au approximately north southkinematical major axis.," The velocity field shows closed contours and is, to zeroth order, consistent with a velocity field that would be produced by a rotating disk with an approximately north south kinematical major axis."1131 This would make the kinematical major axis roughly perpendicular to the major axis obtaiue from ellipse fitting o the IIT disk., This would make the kinematical major axis roughly perpendicular to the major axis obtained from ellipse fitting to the HI disk.1132 The kinematical major axis is also substantially uusalened with the major axis obtained by eclipse fitting to the optical isophotes., The kinematical major axis is also substantially misaligned with the major axis obtained by ellipse fitting to the optical isophotes.1133 Iu addition to this nisalieument. the kinematical ceuter of the velocity field is offse (to the north. as can be seen by comparing Fies.," In addition to this misalignment, the kinematical center of the velocity field is offset (to the north, as can be seen by comparing Figs."1134 and 2)) from the ceuter (as determined by ellipse fitting) of the III disk., \ref{fig:mom1} and \ref{fig:ov}) ) from the center (as determined by ellipse fitting) of the HI disk.1135 Apart from the iisalemmentsOo mentioned above. the velocity field of CTS also shows clear departures ποια what would be expected fron) an axisviunuetric rotating disk.," 	Apart from the misalignments mentioned above, the velocity field of GR8 also shows clear departures from what would be expected from an axisymmetric rotating disk."1136 The most important departure is that the isovelocity coutotrs in the outer regions of the ealaxy show large scale kinks., The most important departure is that the isovelocity contours in the outer regions of the galaxy show large scale kinks.1137 In addition. the velocity field shows several asvinunetries.," In addition, the velocity field shows several asymmetries."1138 The most prominent asvuunetry is between the northern aud southern half of the galaxy., The most prominent asymmetry is between the northern and southern half of the galaxy.1139 The closed dovelocitv contours in the sothern half are more clongated than those iu the northern halt., The closed isovelocity contours in the southern half are more elongated than those in the northern half.1140 Further. the kinks noted above are uch more prominent in the western part of the disk than iu the caster half.," Further, the kinks noted above are much more prominent in the western part of the disk than in the eastern half."1141 Since our velocity feld is better sampled compared to the velocity fields derived bv Loetal.(1993) ancl Carignanetal.(1990) these kinematical peculiarities are more clearly seen., Since our velocity field is better sampled compared to the velocity fields derived by \cite{lo93} and \cite{carignan90} these kinematical peculiarities are more clearly seen.1142 Iu particular. the offset between the morphological aud kinematical ceuter. which is appareut in our velocity field. is not seen im velocity fields derived earlier.," In particular, the offset between the morphological and kinematical center, which is apparent in our velocity field is not seen in velocity fields derived earlier."1143 Further. because of the lower seusitivitv. the kiuks in the isovelocity contours seen towards the edges of the ealaxy are nof seen that clearly iu the earlier velocity fields.," Further, because of the lower sensitivity, the kinks in the isovelocity contours seen towards the edges of the galaxy are not seen that clearly in the earlier velocity fields."1144 Following Carignanctal.(1990) we could try to fit GRea’s velocity fieldto that expected from a rotating disk., 	Following \cite{carignan90} we could try to fit GR8's velocity fieldto that expected from a rotating disk.1145A verv comprehensive work in this field was published by Rutledgeetal.(1997a).. based on 52 Galactic globular clusters covering a metallicity range of —2€ [Fe/Il] €—0.7.,"A very comprehensive work in this field was published by \citet{r97a}, based on 52 Galactic globular clusters covering a metallicity range of $-2\leq$ [Fe/H] $\leq-0.7$."1146 They compared the resulting calibration in (he Zinn&West(L984) and Carretta&Gratton metallicity scales., They compared the resulting calibration in the \citet{zw84} and \citet{cg97} metallicity scales.1147" While in the Carretta&Gratton(1997) scale a linear correlation between metallicity and equivalent width of the CaT lines at the level of the (IIB) j,5—0 (known as reduced equivalent width) was found for all clusters. this relationship was not linear when the Zinn&West(1984) scale was used."," While in the \citet{cg97} scale a linear correlation between metallicity and equivalent width of the CaT lines at the level of the horizontal-branch (HB) $_{HB}$ =0 (known as reduced equivalent width) was found for all clusters, this relationship was not linear when the \citet{zw84} scale was used."1148 In most studies. the run of CaT lines with metallicity has been investigated in globular clusters only. which have all similar ages.," In most studies, the run of CaT lines with metallicity has been investigated in globular clusters only, which have all similar ages."1149 If we wish to derive stellar metallicities in svstems in which star formation has taken place in the last few Gyr. such as clwart irregular galaxies or open clusters. it is necessary to address the role of age on the CaT strength.," If we wish to derive stellar metallicities in systems in which star formation has taken place in the last few Gyr, such as dwarf irregular galaxies or open clusters, it is necessary to address the role of age on the CaT strength."1150 Some authors have used (a few) voung open clusters to study the behaviour of the CaT with metallicity (e.g.Suntzelletal. 1992).. using the Zinn&West(1984) metallicity scale as reference.," Some authors have used (a few) young open clusters to study the behaviour of the CaT with metallicity \citep[e.g.][]{sunt92}, using the \citet{zw84} metallicity scale as reference."1151 Coleetal.(2004). very recently obtained a new relationship. using open and globular clusters covering —2< [Fe/II| <—0.2 and 2.5 € (age/Gvr) < 13 in the Carretta&Gratton(1997). scale.," \citet{c04} very recently obtained a new relationship, using open and globular clusters covering $-2\leq$ [Fe/H] $\leq-0.2$ and 2.5 $\leq$ (age/Gyr) $\leq$ 13 in the \citet{cg97} scale."1152 They. found a linear correlation among (he reduced equivalent width and metallicity., They found a linear correlation among the reduced equivalent width and metallicity.1153" This indicates a weak influence of age in the range of ages investigated (age > 2.5 (αντ),", This indicates a weak influence of age in the range of ages investigated (age $\geq$ 2.5 Gyr).1154 However. to apply (his relationship (o svstems wilh star formation over the last Gyr and/or wilh stars more metal-rich than the solar metallicity. it is necessary (ο investigate its behaviour further lor vounger ages and higher metallicities.," However, to apply this relationship to systems with star formation over the last Gyr and/or with stars more metal-rich than the solar metallicity, it is necessary to investigate its behaviour further for younger ages and higher metallicities."1155 The purpose of this paper is to obtain a new relationship between the equivalent width of the CaT lines aud metallicity. covering a range as wide as possible of age aud metallicity.," The purpose of this paper is to obtain a new relationship between the equivalent width of the CaT lines and metallicity, covering a range as wide as possible of age and metallicity."1156 Our sample covers —2.2< |Fe/1l] <+047 and 0.25 < Age/Gvr < 13., Our sample covers $-2.2\leq$ [Fe/H] $\leq$ +0.47 and 0.25 $\leq$ Age/Gyr $\leq$ 13.1157 The influence of age and (he variation of the CaT lines along the RGB are investigated., The influence of age and the variation of the CaT lines along the RGB are investigated.1158 In Section 2.. we present the cluster sample.," In Section \ref{sample}, we present the cluster sample."1159 In Section 3.. the observations and data reduction are described.," In Section \ref{obsdata}, the observations and data reduction are described."1160 The wav in which (he equivalent width of the the CaT lines has been computed is described in Section 4.. where the behaviour of the CaT with luminosity is also investigated.," The way in which the equivalent width of the the CaT lines has been computed is described in Section \ref{catriplet}, where the behaviour of the CaT with luminosity is also investigated."1161 In Section 5. we obtain the relationship between the equivalent width of the CaT lines aud metallicity. aud we discuss the influence of age and the [Ca/Fe] ratio in them.," In Section \ref{catmetallicityscale} we obtain the relationship between the equivalent width of the CaT lines and metallicity, and we discuss the influence of age and the [Ca/Fe] ratio in them."1162 Finally. the derived relationships are used in Section G (to obtain the metallicities of the open clusters Berkeley 39. Drumpler 5 and Collinder 110.," Finally, the derived relationships are used in Section \ref{derivedmetallicities}1163 to obtain the metallicities of the open clusters Berkeley 39, Trumpler 5 and Collinder 110."1164 To study (he behasiour of the CaT lines with metallicity. we have observed individual stars.with available V magnitudes. in 29 stellar clusters (15 open and 14 globular).," To study the behaviour of the CaT lines with metallicity, we have observed individual stars,with available V magnitudes, in 29 stellar clusters (15 open and 14 globular)."1165 OF the, Of the1166package.,package.1167 The I baud frames were obtained with exposure times iusufficieut for detailed photoimetrv. aud we used these frames for iutegral photometry ο].," The $I$ band frames were obtained with exposure times insufficient for detailed photometry, and we used these frames for integral photometry only."1168 The galaxy was observed iu he 21 cm Hine at the LOOm-class delecimetric radio telescope on 23. 25 aud 28 August 2001. for a total of lL hour per day.," The galaxy was observed in the 21 cm line at the 100m-class decimetric radio telescope on 23, 25 and 28 August 2004, for a total of 1 hour per day."1169 For further details ou the telescope. data acquisition and data reduction iiethods. iucludiug the ofi-line clinunation of radio frequency interference (RET). see Mounicr Ragaigue et al. (," For further details on the telescope, data acquisition and data reduction methods, including the off-line elimination of radio frequency interference (RFI), see Monnier Ragaigne et al. ("11702001).,2001).1171 The halfpower beam width of he telescope. of 42: fa d). is expected to cover the cutive dadistribution of the galaxy.," The half-power beam width of the telescope, of $\times$ $'$ $\alpha$$\times$$\delta$ ), is expected to cover the entire distribution of the galaxy."1172 Tn each daily observation a sufficiently wide velocity range around the galaxy profile was fouud to be free of REL m which the galaxys pprofile was detected in both polarizations.," In each daily observation a sufficiently wide velocity range around the galaxy profile was found to be free of RFI, in which the galaxy's profile was detected in both polarizations."1173 Residual RFI causes the jogative dip in the 15 500 - 15 800 rrange i he averaged data (Fig., Residual RFI causes the negative dip in the 15 500 - 15 800 range in the averaged data (Fig.1174 2)., 2).1175 The average of the three spectra (see Fig., The average of the three spectra (see Fig.1176 2). smioothed o a velocity resolution of 18L|. has an ris noise evel of 1.6 mJy," 2), smoothed to a velocity resolution of 18, has an rms noise level of 1.6 mJy."1177" The ealaxy profile has a peak fiux density of 10 uta a ceuter velocity ιο 219415 Ll. oa velocity width at of peak maxim Wy =206430 a velocity width at of peak uaxiuun Woy=25 L416 ον, and an integrated line &ux 1.80.21."," The galaxy profile has a peak flux density of 10 mJy, a center velocity 16 $\pm$ 15, a velocity width at of peak maximum $W_{50}$ $\pm$ 30, a velocity width at of peak maximum $W_{20}$ $\pm$ 46, and an integrated line flux $\pm$ 0.2."1178 Those η. line piuranueters are directly measured values: no corrections have been applied to them for. Ce. lustrimental resolution.," These global line parameters are directly measured values; no corrections have been applied to them for, e.g., instrumental resolution."1179 We estimated the uncertainties iuIp; aand the line widths following Schneider et al. (," We estimated the uncertainties in, and the line widths following Schneider et al. ("11801986. 1990).,"1986, 1990)."1181 A comparison with the stmuned CO(1-0) spectra of CGalletta et al. (, A comparison with the summed CO(1-0) spectra of Galletta et al. (11821997) shows that the widths of the profiles are comparable.,1997) shows that the widths of the profiles are comparable.1183 The 170 ddifference with the published central velocity of the CO profile could be to be due to the application of the relativistic Doppler shift formmla to the CO data velocity. without the autlors cine aware ofthis correction converting to the conveutional optical definition we use (V= e(A-Ay)/Ay) raises the CO center velocity. to 16 233211|... consistent with our vvalue and the published optical racia velocitics.," The 470 difference with the published central velocity of the CO profile could be to be due to the application of the relativistic Doppler shift formula to the CO data velocity, without the authors being aware of this correction – converting to the conventional optical definition we use $V=c$ $\lambda$ $\lambda_0$ $\lambda_0$ ) raises the CO center velocity to 16 $\pm$ 11, consistent with our value and the published optical radial velocities."1184 ESO 171-C26 is a lavee syste even the central galaxy Qvithout the rugs) is significantly larger aud much more DIuuinuous than the Milkv. Way (Table 2)., ESO 474-G26 is a large system – even the central galaxy (without the rings) is significantly larger and much more luminous than the Milky Way (Table 2).1185 The V-baud nuage ids cdisplaved in Fig., The $V$ -band image is displayed in Fig.1186 l and represented as au isophotal plot in Fig., 1 and represented as an isophotal plot in Fig.1187 3., 3.1188 The overall optical morphology of ESO 17-C26 is very intercsting and intriguing: a nearly spherical central body is, The overall optical morphology of ESO 474-G26 is very interesting and intriguing: a nearly spherical central body is1189If. following Faber et al. (,"If, following Faber et al. ("11901987). e» is constant elliptical galaxies would be structurally homologous systems aud the tilt would have to be explained as a systematic variation of masstolight (ML) ratio with huuinositv: M/Lx L. with συ ,"1987), $c_2$ is constant elliptical galaxies would be structurally homologous systems and the tilt would have to be explained as a systematic variation of mass–to–light (M/L) ratio with luminosity: $M/L\propto L^{\beta}$ , with $\beta$ $\pm$ 0.08."1191As discussed in the Introduction it is uulikelv hat this tilt cau be explained by stellar population effects. alone., As discussed in the Introduction it is unlikely that this tilt can be explained by stellar population effects alone.1192 One needs to combine two well shown observations: the svstematic variation of stellar populations with huninosity aud the change of observed structural properties along the carly-ype sequence from dwarf to giant ellipticals., One needs to combine two well known observations: the systematic variation of stellar populations with luminosity and the change of observed structural properties along the early-type sequence from dwarf to giant ellipticals.1193 Ideally both effects in combination would he able o account for the full tilt of the FP., Ideally both effects in combination would be able to account for the full tilt of the FP.1194 It has been shown (see e.g. Trujillo. Graham Caon 2001 and references therein) that elliptical ealaxies do not form a homologous structural aly aud that the huninositv.dependent departures youn the rb/! daw can be described by the ri Séórrsic model.," It has been shown (see e.g. Trujillo, Graham Caon 2001 and references therein) that elliptical galaxies do not form a homologous structural family and that the luminosity–dependent departures from the $^{1/4}$ law can be described by the $^{1/n}$ Sérrsic model."1195 The nonhomoloey is also reflected in the strong correlations between the shape xuwanmeter pj aud photometriciudepeudoeut galaxy xoperties as. for exaiuple. the central velocity dispersion (Graham. Trujillo Caon. 2001).," The nonhomology is also reflected in the strong correlations between the shape parameter $n$ and photometric–independent galaxy properties as, for example, the central velocity dispersion (Graham, Trujillo Caon, 2001)."1196 In Fig., In Fig.1197 5bb. we show the relation between he shape index » and the absolute Dbaud (iiodelindepeudent) magnitude for 200 elliptical ealaxies.," \ref{nohomo}b b, we show the relation between the shape index $n$ and the absolute B–band (model–independent) magnitude for 200 elliptical galaxies."1198 The galaxies used iu this plot correspond o ellipticals from the Virgo. Foruax aud Coma Clusters (Caon ot al.," The galaxies used in this plot correspond to ellipticals from the Virgo, Fornax and Coma Clusters (Caon et al."1199 1990: Caou. Capaccioli D'Onofrio 1991: Diugeeli Jerjeu 1998: Cutiórirez et al," 1990; Caon, Capaccioli D'Onofrio 1994; Binggeli Jerjen 1998; Gutiérrrez et al."1200 2001), 2004).

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