ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Iu this Letter we investigate the host environimenut of CRB 020819 in detail., In this Letter we investigate the host environment of GRB 020819 in detail.3 Tn Section 2. we detail our observations of the host galaxy aud explosion site of GRB 020819.," In Section 2, we detail our observations of the host galaxy and explosion site of GRB 020819."4 We derive a απνο of ISAL properties based ou these spectra. aud compare these parameters. along with cussion liue diagnostic ratios. to other LCRD host galaxies. star-forming galaxy samples from the general population. aud stellar population svuthesis and photoionization models (Section 3).," We derive a number of ISM properties based on these spectra, and compare these parameters, along with emission line diagnostic ratios, to other LGRB host galaxies, star-forming galaxy samples from the general population, and stellar population synthesis and photoionization models (Section 3)."5 Finally. we consider the imuplicatious of this unusual LORB lost environment on our current understanding of LORD progenitor scenarios (Section 1).," Finally, we consider the implications of this unusual LGRB host environment on our current understanding of LGRB progenitor scenarios (Section 4)."6 We obtained two separate spectra of the GRB 020819 spiral host galaxy. uxiug the Low Resolution Duaenmg Spectrograph (LRIS: Oke et 11995) on the Keck I telescope at Manna Wea.," We obtained two separate spectra of the GRB 020819 spiral host galaxy, using the Low Resolution Imaging Spectrograph (LRIS; Oke et 1995) on the Keck I telescope at Mauna Kea."7 Ou 2 November 2008 we obtained a spectrum of the host galaxy’s nucleus. aud ou 19 Noveiuber 2009 we obtained au additional spectra of he star-forming region associated with the CRB 020819 radio afterglow (Jakobsson et 22005).," On 2 November 2008 we obtained a spectrum of the host galaxy's nucleus, and on 19 November 2009 we obtained an additional spectrum of the star-forming region associated with the GRB 020819 radio afterglow (Jakobsson et 2005)."8 We used the oue 1 slitinask (~5.3 kpe at the cistance of the host) or both observations along with the 2300/5000. ein. he σσ dichroic. aud the (00/8500 erating at a ceutral wavelength ofSLOOA.," We used the long 1"" slitmask $\sim$ 5.3 kpc at the distance of the host) for both observations along with the 300/5000 grism, the 680 dichroic, and the 400/8500 grating at a central wavelength of."9. In 2008 the slit was centered ou a nearby bright star and turned to the position auele hat would place both the star aud the nucleus of the CRB 020819 host ou the slit (PA = 315.587)., In 2008 the slit was centered on a nearby bright star and turned to the position angle that would place both the star and the nucleus of the GRB 020819 host on the slit (PA = $^{\circ}$ ).10 In 2009. he slit was positioned such that both the host galaxy imcleus aud the “blob” designated as the explosion site w Jakobsson et ((2005) were positioned ou the slit (PA - 9.57).," In 2009, the slit was positioned such that both the host galaxy nucleus and the “blob"" designated as the explosion site by Jakobsson et (2005) were positioned on the slit (PA = $^{\circ}$ )."11 Ax a result. the observations were not taken at the parallactic angle.," As a result, the observations were not taken at the parallactic angle."12 The data were reduced using We used. the IRAF tasks aud «distributed by the W. M. Keck Observatories to subtract oversean from the nuages., The data were reduced using We used the IRAF tasks and distributed by the W. M. Keck Observatories to subtract overscan from the images.13 The spectra were extracted sine the task in the package., The spectra were extracted using the task in the package.14 Wavelcneth and flatfield calibrations were performed based on our observations of internal lamp flat fields and Ie. Ne. Ar. Cd. and Zu comparison lamp spectra.," Wavelength and flatfield calibrations were performed based on our observations of internal lamp flat fields and Hg, Ne, Ar, Cd, and Zn comparison lamp spectra."15 Flux calibration was performed using our observations of the spectrophotometric standard GD 2Ls (Oke 1990) on both uielts., Flux calibration was performed using our observations of the spectrophotometric standard GD 248 (Oke 1990) on both nights.16 From our 2008 observatious. we detected |OII|A3727. Ils. J|OIIIJA5007. Πα. and [NTIAAGS18.658 features ii cluission for the host ealaxy uncleus.," From our 2008 observations, we detected $\lambda$ 3727, $\beta$, $\lambda$ 5007, $\alpha$, and $\lambda\lambda$ 6548,6584 features in emission for the host galaxy nucleus."17 1.Iu 2009. problems with the response of the blue side CCD unfortunately prevented detection of ILJ aud |OITI[A5007 enission features iu the explosion site spectra: however. A3727. Πα. and [NIT|AAG5 [8.6581 e1uission features were detected at a redshift of +=0.11. coufiruüug its association with the bright spiral host.," In 2009, problems with the response of the blue side CCD unfortunately prevented detection of $\beta$ and $\lambda$ 5007 emission features in the explosion site spectra; however, $\lambda$ 3727, $\alpha$, and $\lambda\lambda$ 6548,6584 emission features were detected at a redshift of $z = 0.41$, confirming its association with the bright spiral host."18 Eauission line fluxes were determined using the IRAF task in the package to ft Cassianus to the liue profiles., Emission line fluxes were determined using the IRAF task in the package to fit Gaussians to the line profiles.19 The detected emissiou lines for the uucleus aud explosion site spectra are shown in Figure 1., The detected emission lines for the nucleus and explosion site spectra are shown in Figure 1.20 We doetermiued E(BV) in the direction of CRB P0819 based ou Πα aud UL} fluxes measured in the imcleus spectrum., We determined $B-V$ ) in the direction of GRB 020819 based on $\alpha$ and $\beta$ fluxes measured in the nucleus spectrum.21 We adopt the Cardelli et (1989) reddening law with Ry=d. a Bahuer decrement of lHo/IL/ = 2.57 (followiug Osterbrock 1989 for case D recombination). aud the waveleneth-dependent coustaut s(IHa) = 2.535 (Cardelli ct 11989).," We adopt the Cardelli et (1989) reddening law with $R_V = 3.1$, a Balmer decrement of $\alpha$ $\beta$ = 2.87 (following Osterbrock 1989 for case B recombination), and the wavelength-dependent constant $\alpha$ ) = 2.535 (Cardelli et 1989)."22 We find a total inc-ofsieht E(BWV) = 0.71 mae for the nucleus. of he GRB 020819 host ealaxyv: when Galactic extinction E(BVW) = 0.07 in the direction of the host (Schlegel et 11998) is accounted for. this suggests a host ECLV) = 01.61. or a host Ay=1.98.," We find a total line-of-sight $B-V$ ) = 0.71 mag for the nucleus of the GRB 020819 host galaxy; when Galactic extinction $B-V$ ) = 0.07 in the direction of the host (Schlegel et 1998) is accounted for, this suggests a host $B-V$ ) = 0.64, or a host $A_V = 1.98$ ."23 Iu the absence of an IL detection in the “blob” spectrum. we cannot determine an E(BV) for the explosion site.," In the absence of an $\beta$ detection in the “blob"" spectrum, we cannot determine an $B-V$ ) for the explosion site."24 Towever. our ον: exceeds the required Lost extinction of Ay50.61.5 niae proposed by Jakobsson et ((2005) to account for the absence of an optical afterglow.," However, our $A_V$ exceeds the required host extinction of $A_V \approx 0.6 - 1.5$ mag proposed by Jakobsson et (2005) to account for the absence of an optical afterglow."25 We adopt E(BV) = 0.71 as an approximation for the amount of extinction prescut at the explosion site., We adopt $B-V$ ) = 0.71 as an approximation for the amount of extinction present at the explosion site.26 The inctallicity diagnostics presented in Ἱνωνίο Dopita (2002) and WKkewley Ellison (2008) use strong optical cussion line ratios to determine metallicities and ionization parameters based on equations derived from photoionization models., The metallicity diagnostics presented in Kewley Dopita (2002) and Kewley Ellison (2008) use strong optical emission line ratios to determine metallicities and ionization parameters based on equations derived from photoionization models.27 Using the Ἱνον]ον Dopita (2002) polynomial relation between A3727 aud metallicity. we find log(O/II) | 12 = [NIT|AG589.0Lf + [OTO.1 for the nucleus of the GBR 020819 host galaxy.," Using the Kewley Dopita (2002) polynomial relation between $\lambda$ $\lambda$ 3727 and metallicity, we find log(O/H) + 12 = 9.0 $\pm$ 0.1 for the nucleus of the GBR 020819 host galaxy."28 We also adopt the [|NII|AG58 L/TIo diagnostic relation presented iu Pettini Pagel (200D). a diagnostic independent of extinction effects. aud fud a metallicity of log(O/II) | 12 = a8 + 0.1.," We also adopt the $\lambda$ $\alpha$ diagnostic relation presented in Pettini Pagel (2004), a diagnostic independent of extinction effects, and find a metallicity of log(O/H) + 12 = 8.8 $\pm$ 0.1."29 As this calibration is owed on au empirical ft to electron-teniperature based uetallicities. it is known to be svstematically offset from calibrations derived from theoretical photoionization nodels by ~0.2-0.3 dex: this is iu agreement with the netallicity discrepancy seen here (e.g. Ἱνανί]ον Ellison 2008 and references therein).," As this calibration is based on an empirical fit to electron-temperature based metallicities, it is known to be systematically offset from calibrations derived from theoretical photoionization models by $\sim$ 0.2-0.3 dex; this is in agreement with the metallicity discrepancy seen here (e.g. Kewley Ellison 2008 and references therein)."30 Frou. our spectrum of the explosion site. we similarly find log(O/II) | 12 = 9.0 x 0.1 adopting the Newley Dopita (2002) |NII]/|OII| relation aud log(O/T1T) | 12 = δι + 0 adopting the ατα Paecl (2001) |[NII|AG5S L/TIo. diagnostic.," From our spectrum of the explosion site, we similarly find log(O/H) + 12 = 9.0 $\pm$ 0.1 adopting the Kewley Dopita (2002) [NII]/[OII] relation and log(O/H) + 12 = 8.7 $\pm$ 0.1 adopting the Pettini Pagel (2004) $\lambda$ $\alpha$ diagnostic."31 For these abundance deteriiuatious we adopt the ΕΡΕ V) = 0.71 associated with the nucleus of the host., For these abundance determinations we adopt the $B-V$ ) = 0.71 associated with the nucleus of the host.32 At lower E(B Y) he inetalliitv derived from the dEewlev Dopita (2002) [NIT|/|OTI] relation increases (iud vice versa). but he Pettini Pagel (2001). Πα metallicity stavs constant: as a result we use this metallicity diagnostic or comparison throughout the remainder of this Letter.," At lower $B-V$ ) the metallicity derived from the Kewley Dopita (2002) [NII]/[OII] relation increases (and vice versa), but the Pettini Pagel (2004) $\alpha$ metallicity stays constant; as a result we use this metallicity diagnostic for comparison throughout the remainder of this Letter."33 The metallicity measured at the explosion site is identical ο that measured at the nucleus. to within the errors.," The metallicity measured at the explosion site is identical to that measured at the nucleus, to within the errors."34" Adopting R maguitudes fom Jakobsson et((2005). aud Af,=21.57 frou Brown et ((2001). we find a uniünositv of ~2f for the host galaxy and ~0.05£% "," Adopting $R$ magnitudes from Jakobsson et(2005), and $M^*_R = -21.57$ from Brown et (2001), we find a luminosity of $\sim2L*$ for the host galaxy and $\sim0.05L*$ "35"migrating 12.5M, planet approaches and they enter the 4:3 resonance at {~1.1x10.",migrating $12.5\;\mearth$ planet approaches and they enter the 4:3 resonance at $t\sim 1.1\times 10^4$.36" From this time the evolution of these two planets is similar to that of pairs of planets with q=1 described in Section ??:: the planets reach a quasi equilibrium state such that they evolve on non migrating orbits with a,~1.2 and az~1.4, and with eccentricities remaining almost constant."," From this time the evolution of these two planets is similar to that of pairs of planets with $q\ge 1$ described in Section \ref{qge1}: the planets reach a quasi equilibrium state such that they evolve on non migrating orbits with $a_1\sim 1.2$ and $a_2\sim 1.4$, and with eccentricities remaining almost constant."37 This lasts until the 10 Mg planet enters the 4:3 resonance with the second body at t~1.5x10., This lasts until the 10 $\mearth$ planet enters the 4:3 resonance with the second body at $t\sim 1.5\times 10^4$.38" Again, the third planet tends to push the innermost planets inward, but the corotation torques exerted on the 15 Mg planet are able to counterbalance this effect and the migration of this three-planet system is stalled."," Again, the third planet tends to push the innermost planets inward, but the corotation torques exerted on the 15 $\mearth$ planet are able to counterbalance this effect and the migration of this three-planet system is stalled."39 A similar process occurs each time a migrating planet is resonantly captured by the bodies located inside its orbit., A similar process occurs each time a migrating planet is resonantly captured by the bodies located inside its orbit.40" Over time we find that some planets slip from one resonance to another, but the system remains globally stable during these episodes."," Over time we find that some planets slip from one resonance to another, but the system remains globally stable during these episodes."41" For example, the fifth planetwith mass ms=5Mg slips from the 4:3 resonance with the 7.5Μο planet to the 5:4 resonance at t~4.5x104 and finally enters the 6:5 resonance at t—5.2x104."," For example, the fifth planetwith mass $m_5=5\;\mearth$ slips from the 4:3 resonance with the $7.5\;\mearth$ planet to the 5:4 resonance at $t\sim 4.5\times 10^4$ and finally enters the 6:5 resonance at $t\sim 5.2\times10^4$."42 The final outcome of the simulation is a system forming a series of resonances between adjacent bodies with each of them evolving on a non migrating orbit., The final outcome of the simulation is a system forming a series of resonances between adjacent bodies with each of them evolving on a non migrating orbit.43" Fig.10 displays the resonant angles y;=(p+Ld,—pÀi—ωι and yo=(p*1)4,—pa;c» corresponding to the (p*1):p commensurabilities that form between each pair of adjacent bodies.", \ref{model1angles} displays the resonant angles $\psi_1=(p+1)\lambda_o-p\lambda_i-\omega_i$ and $\psi_2=(p+1)\lambda_o-p\lambda_i-\omega_o$ corresponding to the $(p+1):p$ commensurabilities that form between each pair of adjacent bodies.44" We see that all commensurabilities that form are first order resonances, in agreement with results obtained by Cresswell Nelson (2006)."," We see that all commensurabilities that form are first order resonances, in agreement with results obtained by Cresswell Nelson (2006)."45" This simulation suggests that in a circumbinary disc, corotation torques exerted at the edge of the inner cavity provide an efficient mechanism against type I migration for a swarm of planets, and that resonant capture prevents close encounters, scattering and collisions when the initial planetary mass distribution decreases as a function of orbital radius."," This simulation suggests that in a circumbinary disc, corotation torques exerted at the edge of the inner cavity provide an efficient mechanism against type I migration for a swarm of planets, and that resonant capture prevents close encounters, scattering and collisions when the initial planetary mass distribution decreases as a function of orbital radius."46" In this model, the initial configuration of the system is such that moving from the innermost planet to the outermost one, planets have masses of my= 15, 7.5, 12.5, 5 and 10 Μο respectively."," In this model, the initial configuration of the system is such that moving from the innermost planet to the outermost one, planets have masses of $m_p=$ 15, 7.5, 12.5, 5 and 10 $\mearth$ respectively."47 A snapshost of the disc surface density at the beginning of the simulation is presented in the left panel of Fig., A snapshost of the disc surface density at the beginning of the simulation is presented in the left panel of Fig.48 12 and the evolution of the semimajor axes and eccentricities of planets for this model is illustrated in Fig. 11.., \ref{model22d} and the evolution of the semimajor axes and eccentricities of planets for this model is illustrated in Fig. \ref{model2}. .49" Once again, the innermost 15 Mg planet rapidly drifts toward the edge of"," Once again, the innermost 15 $\mearth$ planet rapidly drifts toward the edge of"50influence of the external pollution to retrieve the original elemental abundances.,influence of the external pollution to retrieve the original elemental abundances.51 A certain insight into the external pollution introduced here can be obtained by comparing the abundance patterns of Galactic halo stars and DLAs., A certain insight into the external pollution introduced here can be obtained by comparing the abundance patterns of Galactic halo stars and DLAs.52" As shown in Figure 3, the Zn/Fe ratios of DLAs (Prochaska&Wolfe2002) are, on average, larger than those of Galactic halo stars."," As shown in Figure 3, the Zn/Fe ratios of DLAs \citep{Prochaska_02} are, on average, larger than those of Galactic halo stars."53" Among the halo stars, dwarfs have, on average, lower Zn/Fe ratios than those of subgiants."," Among the halo stars, dwarfs have, on average, lower Zn/Fe ratios than those of subgiants."54" Since the element Fe is thought to be heavily depleted from gas onto dust grains, the feature of Zn/Fe ratios presented in Figure 3 suggests that the dwarfs with lower Zn/Fe ratios accreted the Fe that had been depleted from gas whereas higher Zn/Fe ratios in DLAs are results of this Fe depletion."," Since the element Fe is thought to be heavily depleted from gas onto dust grains, the feature of Zn/Fe ratios presented in Figure 3 suggests that the dwarfs with lower Zn/Fe ratios accreted the Fe that had been depleted from gas whereas higher Zn/Fe ratios in DLAs are results of this Fe depletion."55" The accretion of the depleted Fe will also explain the feature of Figures 2 since the elements Mg, Zn, and Na are known to be inclined to remain in the gas phase rather than depleted onto dust grains as compared to Fe."," The accretion of the depleted Fe will also explain the feature of Figures 2 since the elements Mg, Zn, and Na are known to be inclined to remain in the gas phase rather than depleted onto dust grains as compared to Fe."56" When Galactic halo stars pass through the Galactic disk, they might accrete the ISM contaminated by ejecta of SNe Ia. This process might reduce a/Fe ratios on the surfaces of stars."," When Galactic halo stars pass through the Galactic disk, they might accrete the ISM contaminated by ejecta of SNe Ia. This process might reduce $\alpha$ /Fe ratios on the surfaces of stars."57" However, this must increase Mn/Fe ratios at the same time, leading to the abundance patterns inconsistent with observations."," However, this must increase Mn/Fe ratios at the same time, leading to the abundance patterns inconsistent with observations."58" Furthermore, the accretion of the ISM hardly affect α/Έε ratios on the surfaces of stars with [Fe/H]>—2 because the accretion rate is too small (Yoshii1981)."," Furthermore, the accretion of the ISM hardly affect $\alpha$ /Fe ratios on the surfaces of stars with $>-2$ because the accretion rate is too small \citep{Yoshii_81}."59". The observed elemental abundances of dSph stars (Shetroneetal.2001,2003) also show similar relations with those of DLAs for Cr/Fe, Mn/Fe, and Zn/Fe (Fig."," The observed elemental abundances of dSph stars \citep{Shetrone_01b,Shetrone_03} also show similar relations with those of DLAs for Cr/Fe, Mn/Fe, and Zn/Fe (Fig."60 4)., 4).61" DSph stars have smaller Cr/Fe, Mn/Fe, and Zn/Fe ratios than the average values of Galactic halo stars as well as those of DLAs."," DSph stars have smaller Cr/Fe, Mn/Fe, and Zn/Fe ratios than the average values of Galactic halo stars as well as those of DLAs."62 The elements Cr and Mn are also known to be lightly depleted from the gas phase., The elements Cr and Mn are also known to be lightly depleted from the gas phase.63 A sign of the depletion of Fe onto dust grains becomes prominent for -the 2in DL As(Prochaska&Wolfe 2002)., A sign of the depletion of Fe onto dust grains becomes prominent for $-2$ in DLAs \citep{Prochaska_02}.64".Ontheotherhand, theelemamtslübutlunemgutffaktyl sushed gienh tlanetnbynetmldtaltyrangeas"," On the other hand, the elemental abundances of dSph stars behave in the same metallicity range as if they accrete Fe that was once depleted onto dust grains."65" As discussed in the preceding section, the surfaces of some nearby low-a stars are affected by dust grains."," As discussed in the preceding section, the surfaces of some nearby $\alpha$ stars are affected by dust grains."66" On the contrary, all the low-a dSph stars showing features of dust grains are very luminous stars residing near the tip of the RGB in the H-R diagram."," On the contrary, all the $\alpha$ dSph stars showing features of dust grains are very luminous stars residing near the tip of the RGB in the H-R diagram."67" In the next section, we will propose a mechanism to explain the origin of these low-a stars in different evolutionary stages."," In the next section, we will propose a mechanism to explain the origin of these $\alpha$ stars in different evolutionary stages."68" The envelope of a star expands as it evolves along the red giant branch (RGB), and finally the size reaches up to afew AU."," The envelope of a star expands as it evolves along the red giant branch (RGB), and finally the size reaches up to a few AU."69" Therefore if a star harbors planets, some of them will be eventually engulfed by their host star during the late stage of the RGB."," Therefore if a star harbors planets, some of them will be eventually engulfed by their host star during the late stage of the RGB."70" For instance, in our solar system, the sun is expected to eventually engulf all the terrestrial planets, though the gas giant planets will be beyond the reach of the evolved sun."," For instance, in our solar system, the sun is expected to eventually engulf all the terrestrial planets, though the gas giant planets will be beyond the reach of the evolved sun."71 The ongoing hunting of extra-solar planets has revealed that there are some planetary systems in which massive planets orbit their host stars with the semi-major axes of the order of only 1 AU., The ongoing hunting of extra-solar planets has revealed that there are some planetary systems in which massive planets orbit their host stars with the semi-major axes of the order of only 1 AU.72" The average mass and semi-major axis of the planet orbits are found to be 3M, and 1.2 AU in a sample of 107 planets in 93 planetary systems (Schneider2003),, though these estimates probably suffer from the observational bias."," The average mass and semi-major axis of the planet orbits are found to be $3M_J$ and 1.2 AU in a sample of 107 planets in 93 planetary systems \citep{Schneider_03}, though these estimates probably suffer from the observational bias."73 This leads to an implication that some fractions of stars with planets will be likely to engulf giant planets till the stars evolve to the tips of the RGBs., This leads to an implication that some fractions of stars with planets will be likely to engulf giant planets till the stars evolve to the tips of the RGBs.74" Though the mass of the dense core in a gas giant planet such as Jupiter and Saturn in our planetary system is uncertain, a large amount of Fe is expected to be contained in their cores, compared with terrestrial planets like Earth (Guillot1999)."," Though the mass of the dense core in a gas giant planet such as Jupiter and Saturn in our planetary system is uncertain, a large amount of Fe is expected to be contained in their cores, compared with terrestrial planets like Earth \citep{Guillot_99}."75. It is expected that Jupiter contains roughly five times more Fe than Earth with 0.38Mg of Fe (seeTable1inMurrayetal.2001).," It is expected that Jupiter contains roughly five times more Fe than Earth with $0.38M_\oplus$ of Fe \citep[see Table 176in][]{Murray_01}."77". Thus a giant planet with the mass of 3M; is expected to contain ~5Ma, of Fe.", Thus a giant planet with the mass of $3M_J$ is expected to contain $\sim 5M_\oplus$ of Fe.78 This iron mass is in factcomparable to the mass of Fe in the convection zone of a red giant star with mass of 0.8Mg and the metallicity [Fe/H]~ —1.5., This iron mass is in factcomparable to the mass of Fe in the convection zone of a red giant star with the mass of $0.8M_\odot$ and the metallicity $\sim -1.5$ .79 As oft," As a result, the engulfment of such a giant planet by a"80S/N loss with Chandra. anc a ~45% S/N loss with NMM compared to the optimal band pass.,"S/N loss with Chandra, and a $\sim 45$ S/N loss with XMM compared to the optimal band pass."81 The optimal band in this case has a maximum range trom 0.4—0.7 keV [or Chandra and 0.4—0.3 for NAIM. both of which are very narrow.," The optimal band in this case has a maximum range from $0.4-0.7$ keV for Chandra and $0.4-0.8$ for XMM, both of which are very narrow."82 At higher redshifts the S/N loss for the 0.5-2 keV band increases significantly., At higher redshifts the S/N loss for the 0.5-2 keV band increases significantly.83 As the plasma temperature increases (he optimal nd rapidly widens., As the plasma temperature increases the optimal band rapidly widens.84 For a 1 keV plasma at z=0.1 the optimal bands are in the range of0.6—1.2 keV. and have a S/N only better (han 0.5-2 keV. although (his (wpically increases with redshift.," For a 1 keV plasma at $z=0.1$ the optimal bands are in the range of $0.6-1.2$ keV, and have a S/N only better than 0.5-2 keV, although this typically increases with redshift."85 The results [ου a 6 off-axis response function for the Chandra ACIS-I instrument. with a lower CCD row number and hence smaller CTI. are very similar to the high row number. on-axis caleulations.," The results for a 6' off-axis response function for the Chandra ACIS-I instrument, with a lower CCD row number and hence smaller CTI, are very similar to the high row number, on-axis calculations."86 Variations in band limits between the two are <5%.. and therefore negligible.," Variations in band limits between the two are $\leq 5$, and therefore negligible."87 In a survey. where (he space density is to be recovered. the effective volume in which a source of a eiven intrinsic luminosity can be detected. is calculated based on the maximal redshilt of detectabilitv.," In a survey, where the space density is to be recovered, the effective volume in which a source of a given intrinsic luminosity can be detected, is calculated based on the maximal redshift of detectability."88 A drop in S/N compared to that expected propagates into a ~10 error in volume. consequently the band corrections suggested here are critical.," A drop in S/N compared to that expected propagates into a $\sim 10$ error in volume, consequently the band corrections suggested here are critical."89 With luminosities of 10!0 ere Hl. low mass. cool (KT<2 keV) groups and clusters of ealaxies will form a significant fraction of the extended emission X-ray svstems detectable to ο~0.5 in medium-deep Chandra ancd AMAL exposures.," With luminosities of $10^{41-43}$ erg $^{-1}$, low mass, cool $kT<2$ keV) groups and clusters of galaxies will form a significant fraction of the extended emission X-ray systems detectable to $z\sim 0.5$ in medium-deep Chandra and XMM exposures."90 Probing this population of collapsed svslenms is vital for improving our understanding of both the overall cluster mass function and ihe regime where gravitational collapse and astroplivsical energies are comparable Davies.Ponman.&Cannon 2000)., Probing this population of collapsed systems is vital for improving our understanding of both the overall cluster mass function and the regime where gravitational collapse and astrophysical energies are comparable \citep{llo00}.91. ] have demonstrated here that the choice of band-pass is critical in bot maximizing the detection sensitivity for clusters. and in ils correct euantification in order {ο recover the true space density of poor cluster svstems.," I have demonstrated here that the choice of band-pass is critical in both maximizing the detection sensitivity for clusters, and in its correct quantification in order to recover the true space density of poor cluster systems."92 The optimal bands presented here can serve as a relerence point for Chandra aud NMM surveys., The optimal bands presented here can serve as a reference point for Chandra and XMM surveys.93 For the radiation damaged ACIS-I on Chandra. once the data is processed to correct for much of the CTI effect (e.g. Townsleyetal. (2000))) the impact of the reduced spectral resolution on the optimal band limits is minimal (similarly for the inherent CTI in the back illuminated chips). and <5% in implitude at all energies.," For the radiation damaged ACIS-I on Chandra, once the data is processed to correct for much of the CTI effect (e.g. \citet{tow00}) ) the impact of the reduced spectral resolution on the optimal band limits is minimal (similarly for the inherent CTI in the back illuminated chips), and $\leq 5$ in amplitude at all energies."94 It appears that it can therefore be safely ignored in this situation., It appears that it can therefore be safely ignored in this situation.95 lt has been assumed here that cluster emission is isothermal., It has been assumed here that cluster emission is isothermal.96 In reality (his is often not the case. and sienifieant temperature structure or gradients are present in massive clusters.," In reality this is often not the case, and significant temperature structure or gradients are present in massive clusters,"97"heating can be derived directly from the rate of compression work per particle. pd(n.!)/d. and is given by where we have taken dn/dlzzn/t, appropriate for a uniform contracting spherical cloud with contraction time-scale /,,,CH=iyj where i>>Lis for slow contraction. and ap—1 is for fast one (i.e.. [ree-[all ease).","heating can be derived directly from the rate of compression work per particle, $pd(n^{-1})/dt$, and is given by where we have taken $dn/dt \approx n/t_{cn}$ appropriate for a uniform contracting spherical cloud with contraction time-scale $t_{cn} = \eta t_{ff}$ where $\eta >>1$ is for slow contraction, and $\eta \sim 1$ is for fast one (i.e., free-fall case)."98 The dissipation of magnetic energv would be considered as another heating mechanism. if (his energv is not simply radiated away by atoms. molecules. and grains.," The dissipation of magnetic energy would be considered as another heating mechanism, if this energy is not simply radiated away by atoms, molecules, and grains."99 The major field dissipation mechanism in the dense clouds is almost certainly ambipolar diffusion. which was examined by Scalo (1971) lor density dependency of magnetic field in a Iragmenting molecular cloud.," The major field dissipation mechanism in the dense clouds is almost certainly ambipolar diffusion, which was examined by Scalo (1977) for density dependency of magnetic field in a fragmenting molecular cloud."100 Padoan. Zweibel and Nordlund (2000) presented. calculations of [rictional heating by ion-neutral ον in three-dimensional simulations of turbulent. magnetized molecular clouds.," Padoan, Zweibel and Nordlund (2000) presented calculations of frictional heating by ion-neutral drift in three-dimensional simulations of turbulent, magnetized molecular clouds."101 Thev show thal average value of ambipolar dift heating rate can be significantly larger than the average of cosmic-ray heating rate., They show that average value of ambipolar drift heating rate can be significantly larger than the average of cosmic-ray heating rate.102 In addition. Nejad-Asghar (2007) considered a molecular slab under (he assumption of quasi-magnetohlvdrostatie equilibrium. concluded (hat ambipolar cit heating is inversely proportional to density and its value in some regions ol the slab can be significantly larger than the average heating rates of cosmic ravs and the dissipating turbulent motions.," In addition, Nejad-Asghar (2007) considered a molecular slab under the assumption of quasi-magnetohydrostatic equilibrium, concluded that ambipolar drift heating is inversely proportional to density and its value in some regions of the slab can be significantly larger than the average heating rates of cosmic rays and the dissipating turbulent motions."103 To gain an insight on the heating rate of ion-neutral friction. we assume (hat the pressure and eravitational force on the charged. fluid component are insignificant compared to the Lorentz force because of low ionization fraction. thus. the dift velocily ey is inversely. proportional to the density ancl directly. proportional to the gradient of magnetic pressure (see equation [8]] below).," To gain an insight on the heating rate of ion-neutral friction, we assume that the pressure and gravitational force on the charged fluid component are insignificant compared to the Lorentz force because of low ionization fraction, thus, the drift velocity $v_d$ is inversely proportional to the density and directly proportional to the gradient of magnetic pressure (see equation \ref{drift}] ] below)."104 Here we choose. in a general form. ryxKpd where &=ACB?η ds the change of magnetic pressure in leneth-scale Ar. and the value of b may be approximated near 3/2 (Chis value is rom the assumption of ionization equilibrium with the ion density being power law of the neutral density. with power 1/2).," Here we choose, in a general form, $v_d \propto \kappa105\rho^{-b}$ where $\kappa \equiv \Delta (B^2/2\mu_0)/ \Delta x$ is the change of magnetic pressure in length-scale $\Delta x$, and the value of $b$ may be approximated near $3/2$ (this value is from the assumption of ionization equilibrium with the ion density being power law of the neutral density with power $1/2$ )."106 Nejad-Asghar (2007) adopted the value of b in the range between 0.5 and 2.0 to examine the isobaric TI in the regions of a sell-egravitating molecular slab., Nejad-Asghar (2007) adopted the value of $b$ in the range between $0.5$ and $2.0$ to examine the isobaric TI in the regions of a self-gravitating molecular slab.107" The heating due to ambipolar diffusion is where £f;=54pef/""?v, is the drag force per unit. volume exerted on the neutrals by ions. 454p3.5xLOMkebs! is the collision drag in molecular clouds. and we used the relation p;=ep; between ion and neutral densities in ionization ecquilibrium state"," The heating due to ambipolar diffusion is where $\textbf{f}_d = \gamma_{AD} \epsilon \rho^{3/2} \textbf{v}_d$ is the drag force per unit volume exerted on the neutrals by ions, $\gamma_{AD} \sim 3.5 \times 10^{10} \mathrm{m^3.kg^{-1}.s^{-1}}$ is the collision drag in molecular clouds, and we used the relation $\rho_i=\epsilon\rho_n^{1/2}$ between ion and neutral densities in ionization equilibrium state"108"The co-existence. of an active. galactic. nucleus (AGN) and young stars in the central region of Seyfert galaxies is a widely known phenomenon, (e.g.Storchi-Bergmannetal.2000,2001;González-2007;Dorsetal. 2008),, supporting the so-called AGN-Starburst connection (e.g.Norman&Scoville1988;Terlevichetal.1990;Heckmanetal.1997;2004;Riffel 2009c).","The co-existence of an active galactic nucleus (AGN) and young stars in the central region of Seyfert galaxies is a widely known phenomenon, \citep[e.g.][]{sb00,sb01,gd01,cid04,asari07,dors08}, supporting the so-called AGN-Starburst connection \citep[e.g.][]{norman88,terlevich90,heckman97,heckman04,rogemar09c}."109. The above studies have pointed out that the main difference between the stellar population (SP) of active and non-active galaxies is an excess of intermediate age stars in the former., The above studies have pointed out that the main difference between the stellar population (SP) of active and non-active galaxies is an excess of intermediate age stars in the former.110" In addition, near-infrared (NIR) SP studies have revealed that the continuum is also dominated by the contribution of intermediate-age stellar population components (SPCs,Riffeletal.2007,2009d,2010b;Martinsetal. 2010)."," In addition, near-infrared (NIR) SP studies have revealed that the continuum is also dominated by the contribution of intermediate-age stellar population components \citep[SPCs,][]{rogerio07,rogerio09,rogemar10b,martins10}."111". In the NIR, another component is commonly detected in the nuclear spectra of Seyfert galaxies: unresolved hot dust emission (Riffeletal.2009b,c,d;Rodríguez-Ardilaal.2006;Rodríguez-Ardila,Riffel&Pastoriza 2005)."," In the NIR, another component is commonly detected in the nuclear spectra of Seyfert galaxies: unresolved hot dust emission \citep{rogemar09b,rogemar09c,rogerio09,ardila06,ardila05}."112". Thus, the study of the contribution of the SPs and other components to the circumnuclear continuum of active galaxies is a fundamental key in the understanding8 of the nature of their central engine."," Thus, the study of the contribution of the SPs and other components to the circumnuclear continuum of active galaxies is a fundamental key in the understanding of the nature of their central engine."113"8 Very recently, the use of integral field spectroscopy with adaptive optics at the Gemini North Telescope has allowed us to derive the contribution of distinct SPCs to the NIR spectra of active galaxies."," Very recently, the use of integral field spectroscopy with adaptive optics at the Gemini North Telescope has allowed us to derive the contribution of distinct SPCs to the NIR spectra of active galaxies."114" In addition, we have mapped SPCs spatial distributions and performed the first two-dimensional (2D) SP synthesis in the NIR of the nuclear region of an active galaxy (Mrk1066,Riffeletal. 2010b)."," In addition, we have mapped SPCs spatial distributions and performed the first two-dimensional (2D) SP synthesis in the NIR of the nuclear region of an active galaxy \citep[Mrk\,1066, ][]{rogemar10b}."115". A spatial correlation between the intermediate age SPC and partial ring of low stellar velocity dispersions (c'.) was found, supportinga the interpretation that the low-o-, structures commonly observed in the inner few hundreds parsecs of Seyfert galaxies are due to colder regions with more recent star formation than the underlying bulge (Barbosaetal.2006;Riffel2008a,2009a;Riffel&Storchi-Bergmann 2010d)."," A spatial correlation between the intermediate age SPC and a partial ring of low stellar velocity dispersions $\sigma_*$ ) was found, supporting the interpretation that the $\sigma_*$ structures commonly observed in the inner few hundreds parsecs of Seyfert galaxies are due to colder regions with more recent star formation than the underlying bulge \citep{barbosa06,rogemar08,rogemar09a,rogemar10d}."116". Using a different method — modelling the eequivalent width, supernova rate and mass-to-light ratio — Daviesetal.(2007) have quantified the star formation history in the centre of 9 nearby Seyfert galaxies using their code."," Using a different method — modelling the equivalent width, supernova rate and mass-to-light ratio — \citet{davies07} have quantified the star formation history in the centre of 9 nearby Seyfert galaxies using their code."117" They found that the ages of the stars which contribute most to the NIR continuum lie in the range MMyr, pointing out that these ages should be considered only as ""characteristic"", as they have not"," They found that the ages of the stars which contribute most to the NIR continuum lie in the range Myr, pointing out that these ages should be considered only as “characteristic"", as they have not"118Indeed. (Milgrom2009) uses a frame with one coordinate axis directed GC: as we will see below. it is approximately the opposite of the xr axis ofICRE?.,"Indeed, \citep{Mil09} uses a frame with one coordinate axis directed GC; as we will see below, it is approximately the opposite of the $x$ axis of."119. Although such an effect would manifest itself in (he strong-field regime existing in the planetary regions of the solar svstem. the functional form of 4 depends on the form of the MONDian interpolating CX) in the transition region in which XeI. re. approximately ad ry.," Although such an effect would manifest itself in the strong-field regime existing in the planetary regions of the solar system, the functional form of $q$ depends on the form of the MONDian interpolating $\mu(X)$ in the transition region in which $X\sim 1$, i.e. approximately at $r_t$."120 Let us start to examine just the case of a dark object placed in the same direction of GC., Let us start to examine just the case of a dark object placed in the same direction of GC.121 The right ascension α and declination ὁ of GC. assumed coincident with Ser A*. are (Reid&Brunthaler2004) The relations among a and 6 aud the ecliptical longitude A and latitude are. from standard spherical (trigonometry (Rov2005).. where e=23.43 deg is the of the Earths equator to the ecliptic.," The right ascension $\alpha$ and declination $\delta$ of GC, assumed coincident with Sgr $^{\ast}$, are \citep{Rei04}122 The relations among $\alpha$ and $\delta$ and the ecliptical longitude $\lambda$ and latitude $\beta$ are, from standard spherical trigonometry \citep{Roy05}, where $\epsilon=23.43$ deg is the obliquity of the Earth's equator to the ecliptic."123" Thus. since. bv definition. 0<Ax360° and peal-—90°5x+90"". vield for GC which tell us (hat GC is approximately directed in the opposite direction of the ICRF xo axis."," Thus, since, by definition, $0^{\circ}\leq \lambda \leq 360^{\circ}$ and $-90^{\circ}\leq\beta\leq +90^{\circ}$, yield for GC which tell us that GC is approximately directed in the opposite direction of the ICRF $x$ axis."124" The GC longitude and latitude viekd for the tidal parameter AC of a hypothetical X/Nenmesis object or. equivalently, lor the MOND cquadrupole parameter —4 "," The GC longitude and latitude yield for the tidal parameter $\mathcal{K}$ of a hypothetical X/Nemesis object or, equivalently, for the MOND quadrupole parameter $-q$ "125We use pre-determined functions of depth. up to a normalization constant. lor the ellective viscosity coelficients that we need. namely: This is (he same sealing thal we used in presenting (he perturbative result 2.. with the only difference that only the velocity in the direction of the external shear is used as the velocity scale.,"We use pre-determined functions of depth, up to a normalization constant, for the effective viscosity coefficients that we need, namely: This is the same scaling that we used in presenting the perturbative result \citet{Penev_Barranco_Marcus_08a}, with the only difference that only the velocity in the direction of the external shear is used as the velocity scale."126 In equation 13. we average together both horizontal components of the velocity. because on average there should be no physical difference between the two.," In equation \ref{eq: nu_xy_form}127 we average together both horizontal components of the velocity, because on average there should be no physical difference between the two."128 In practice. the different velocity scaling makes little difference. since as we can see [rom fig. 4.. ," In practice, the different velocity scaling makes little difference, since as we can see from fig. \ref{fig: rms_v},"129awav trom the boundaries all components of the velocity behave alike. except for the Lact that e. tends to be larger.," away from the boundaries all components of the velocity behave alike, except for the fact that $v_z$ tends to be larger."130 So. using the full r.nis.," So, using the full r.m.s."131 velocity instead of only one component. just leads to smaller values of the normalization constants A144; and A155.“0," velocity instead of only one component, just leads to smaller values of the normalization constants $K^0_{1313}$ and $K_{1212}^0$."132 We would like to verily the applicability of the effective viscosity. [ramework to the problem of turbulent dissipation. bv showing that substituting the turbulent. flow with a simple viscosity is able (ο capture not only the total amount of energy dissipated. but also the momentum transport. or in other words the spatial dependence of this dissipation.," We would like to verify the applicability of the effective viscosity framework to the problem of turbulent dissipation, by showing that substituting the turbulent flow with a simple viscosity is able to capture not only the total amount of energy dissipated, but also the momentum transport, or in other words the spatial dependence of this dissipation."133 For the z dependent c forcing. we would like to show that the work per unit mass done bv the forcing on the flow at each depth:," For the $z$ dependent $x$ forcing, we would like to show that the work per unit mass done by the forcing on the flow at each depth:"134 In this appendix. we outline an alternative derivation of the wave equation in the temporal gauge.," In this appendix, we outline an alternative derivation of the wave equation in the temporal gauge."135 Electric and magnetic fields can be expressed. in. terms of a vector potential From (5)) we have Assuming that all the relevant. quantities are functions of x. theparallel (to &) component of CX2)) takes the form. with ΕπΜΑ and The equation. of motion (2)) can be written into a similar form to (17)): which can be integrated to vield where ely)—.dj(q=0) and s=& corresponds to electrons. (1). and. positrons (..).," Electric and magnetic fields can be expressed in terms of a vector potential From \ref{eq:curlB}) ) we have Assuming that all the relevant quantities are functions of $\chi$, theparallel (to $\bkappa$ ) component of \ref{eq:A}) ) takes the form with $A_\parallel=\bkappa\cdot\bA$ and The equation of motion \ref{eq:EqMotion}) ) can be written into a similar form to \ref{eq:EqMotion3}) ): which can be integrated to yield where $A_{0\parallel}\equiv A_\parallel(\chi=0)$ and $s=\pm$ corresponds to electrons $+$ ) and positrons $-$ )."136. Assuming cf=(οο)1η ely). for the electron. component 3= one obtains where f is an integration constant.," Assuming $\tilde{A}=(e/m_ec)(A_\parallel-A_{0\parallel})$ , for the electron component $\beta=\beta_-$, one obtains where $f$ is an integration constant."137" Clearly. a physical solution requires the IIIS to be non-negative: this condition can be satislied only if fii,SFXuuu. Where Jy; and Jee ae the minimum and the maximum velocities at which the RIS is zero."," Clearly, a physical solution requires the RHS to be non-negative; this condition can be satisfied only if $\beta_{min}\leq \beta\leq\beta_{max}$, where $\beta_{min}$ and $\beta_{max}$ are the minimum and the maximum velocities at which the RHS is zero."138 The electric field can be found from Llere we reproduce the known result for a LAEAW in an electron gas. by retaining the electron component only.," The electric field can be found from Here we reproduce the known result for a LAEW in an electron gas, by retaining the electron component only."139Specilicallv. we set syDy—0 and η—go=νι0.,"Specifically, we set $\beta_0\equiv\beta_{-0}=0$ and $\eta_+=\eta_0=\eta_{_{GJ}}=0$."140" The maximum velocity can be expressed in terms of £i: Eq (22)) ancl (23)) reproduce an analytical form similar to that given by Akhiezeretal.(LOT5):: Consider the relativistic limit +,,—1/(113,)?cm|: Using Z2+(1+7/2). one linds Since JJ is a periodic function of X. we can define a period T by Vhe RIIS can be written into the formin the 5,7»1 Πα:If we define a frequency w=22/1. (B5)) leads to (33)inequation"," The maximum velocity can be expressed in terms of $\tilde{E}_0$ : Eq \ref{eq:EqMotion4}) ) and \ref{eq:waveE4}) ) reproduce an analytical form similar to that given by \citet{aetal75}: Consider the relativistic limit $\gamma_m\equiv1/(1-\beta^2_m)^{1/2}\gg1$; Using $\beta\approx \pm(1-\gamma^{-2}/2)$ , one finds Since $\beta$ is a periodic function of $\chi$ , we can define a period $T$ by The RHS can be written into the formin the $\gamma_m\gg1$ limit:If we define a frequency $\omega=2\pi/T$ , \ref{eq:T}) ) leads to \ref{eq:freq})"141orbits.,orbits.142 On the right is a plot of the shape of the spiral in the disc., On the right is a plot of the shape of the spiral in the disc.143 The sign of the gravitational torque is equal to sign of wy and so is negative in the first and third quadrants the torque ancl positive in the second. and fourth., The sign of the gravitational torque is equal to sign of $- x y$ and so is negative in the first and third quadrants the torque and positive in the second and fourth.144 As seen in the left plot. the gravitational torque is negative in the outermost region of the disc where it is strongest.," As seen in the left plot, the gravitational torque is negative in the outermost region of the disc where it is strongest."145 Ehe spiral there lics in the first and third quadrants. as seen in Fig. 9..," The spiral there lies in the first and third quadrants, as seen in Fig. \ref{final},"146 in order the provide à net negative gravitational torque that removes angular momentum from the disc às gas accretes., in order the provide a net negative gravitational torque that removes angular momentum from the disc as gas accretes.147 The left plot in Fig., The left plot in Fig.148 10. also shows the cumulative clise mass distribution., \ref{phase} also shows the cumulative disc mass distribution.149 More than of the cise mass is located inside a radius ο.ΓΗ. where orbits crossings of free particles occur.," More than of the disc mass is located inside a radius of $0.41 r_{\rm H}$, where orbits crossings of free particles occur."150 The local gravitational torque is negative for ro0.35rg., The local gravitational torque is negative for $r > 0.35 r_{\rm H}$.151 On the other hand. the cumulative gravitational torque on the dise inside the orbit crossing radius is actually positive.," On the other hand, the cumulative gravitational torque on the disc inside the orbit crossing radius is actually positive."152 This does, This does153with Ty iu vears. aud for e|Aaz The correlations among eal Ti;o. I were used iu the analvsis of left-right sviuuetriie models (|.,"with $T_{1/2}$ in years, and for $\epsilon_{V-A}^{V+A}\neq 0$ The correlations among $|\epsilon_{V\mp A}^{V+A}|$, $T_{1/2}$, $K$ were used in the analysis of left-right symmetric models \cite{LR}."154" Iu the model SU(2),«SU(2)©(1) we have for the mass of the rielt-handed J bosou aud its mixing angle ¢ with the left-handed one.", In the model $SU(2)_L\times SU(2)_R\times U(1)$ we have for the mass of the right-handed $W$ boson and its mixing angle $\zeta$ with the left-handed one.155" The correlation iunoug nmi, (Q). A. and Ti;» is shown iu Fie."," The correlation among $m_{W_R}$ $\zeta$ ), $K$ , and $T_{1/2}$ is shown in Fig."156" 1left (righf) for conservative value €=10 for the mixing parameter εξ[C,; Vii].", 1 ) for conservative value $\epsilon=10^{-6}$ for the mixing parameter $\epsilon=|U_{ei}V_{ei}|$ .157" It is clear that the closer ix A to 1 for the fixed value of Tyo the stronger is the lower bound ou i, (the upper bound ou à).", It is clear that the closer is $K$ to 1 for the fixed value of $T_{1/2}$ the stronger is the lower bound on $m_{W_R}$ (the upper bound on $\zeta$ ).158" We have also shown that the scusitivity of the angular correlation to the Wy, lass Hicreases with decreasing values of the effective Majorana neutrino mass ο |11]..", We have also shown that the sensitivity of the angular correlation to the $W_R$ mass increases with decreasing values of the effective Majorana neutrino mass $|\langle m\rangle|$ \cite{ABZ_PRD}.159 We thank Alexander Barabash and Fedor Siimkovic for helpful discussions., We thank Alexander Barabash and Fedor Šiimkovic for helpful discussions.160 One of ux (DVZ) would like to thaux DESY for the hospitality in Wamburewhere a eoodpart of this work was done., One of us (DVZ) would like to thank DESY for the hospitality in Hamburgwhere a goodpart of this work was done.161AM1L,$M^{-1}$.162 But even alter allowing for this effect. there is still a residual difference in the cutoff frequencies.," But even after allowing for this effect, there is still a residual difference in the cutoff frequencies."163 Sunwaev Revnivisey suggested (hal NSs have an additional high frequency. component in their variability spectra coming from the boundary laver region. whereas the DII candidates lack this component.," Sunyaev Revnivtsev suggested that NSs have an additional high frequency component in their variability spectra coming from the boundary layer region, whereas the BH candidates lack this component."164 If. correct. this argument. implies that BIL candidates must have event horizons.," If correct, this argument implies that BH candidates must have event horizons."165 In related. work. Done Cierlinsky (2003) studied (he X-ray spectra of bright DII ARBs and NS ARBs.," In related work, Done Gierlinsky (2003) studied the X-ray spectra of bright BH XRBs and NS XRBs."166" Thev defined a “hard color” and a ""πο color” to characterize the observed spectra and plotted these quantilites lor DII and NS systems in a color-color diagram.", They defined a “hard color” and a “soft color” to characterize the observed spectra and plotted these quantitites for BH and NS systems in a color-color diagram.167 They showed that there are several similarities between BIIs ancl NSs. but also some clear differences.," They showed that there are several similarities between BHs and NSs, but also some clear differences."168 In particular. a certain kind of pattern in the color-color diagram is seen only from NS svstems.," In particular, a certain kind of pattern in the color-color diagram is seen only from NS systems."169 Done Gierlinsky interpreted (his unique spectral component as emission from a boundary laver., Done Gierlinsky interpreted this unique spectral component as emission from a boundary layer.170 If their identification is correct. (hen the lack of a similar component in BIL ARBs implies that a boundary laver is missing. ie.. (these objects must have event horizons.," If their identification is correct, then the lack of a similar component in BH XRBs implies that a boundary layer is missing, i.e., these objects must have event horizons."171 When gas accretes on the surface of a neutron star. it becomes denser and hotter as il sinks under the weight of continued accretion. until at a certain depth it ignites thermonuclear reactions.," When gas accretes on the surface of a neutron star, it becomes denser and hotter as it sinks under the weight of continued accretion, until at a certain depth it ignites thermonuclear reactions."172 The ignited reactions are usually unstable. causing the accreted laver of gas to burn explosively within a verv short time.," The ignited reactions are usually unstable, causing the accreted layer of gas to burn explosively within a very short time."173 After the fuel is consumed. the star reverts to its accretion phase until the next thermonuclear instability is triggered.," After the fuel is consumed, the star reverts to its accretion phase until the next thermonuclear instability is triggered."174 The star (hus undergoes a semi-reeular series of thermonuclear explosions (see Lewin. van Paradijs Tuwun 1993: Bildsten 1993: for reviews).," The star thus undergoes a semi-regular series of thermonuclear explosions (see Lewin, van Paradijs Taam 1993; Bildsten 1998; for reviews)."175 These thermonuclear bursts. called Type I bursts. were first discovered from X-ray. binaries by Grindlay et al. (," These thermonuclear bursts, called Type I bursts, were first discovered from X-ray binaries by Grindlay et al. ("1761976).,1976).177 In a typical Tvpe I X-ray. burst. (he luminosity of the neutron star increases {ο nearly the Edcdington limit in less (han a second. and the fIux then declines over a period of seconds to tens of seconds.," In a typical Type I X-ray burst, the luminosity of the neutron star increases to nearly the Eddington limit in less than a second, and the flux then declines over a period of seconds to tens of seconds."178 The time interval between bursts is usually several hours to perhaps a day or 6wo., The time interval between bursts is usually several hours to perhaps a day or two.179 The physics of Type I bursts has been widely studied. and the broad features of the phenomenon are understood.," The physics of Type I bursts has been widely studied, and the broad features of the phenomenon are understood."180 Theoretical models generally agree equite well with observations (Lewin et al., Theoretical models generally agree quite well with observations (Lewin et al.181 1993: Bildsten 1998: Naravan Lev! 2003)., 1993; Bildsten 1998; Narayan Heyl 2003).182 Remarkably. no Type I burst has ever been seen in any. DII XRD (e.g.. Tournear et al.," Remarkably, no Type I burst has ever been seen in any BH XRB (e.g., Tournear et al."183 2003)., 2003).184 Why should this be the case?, Why should this be the case?185 Caleulations indicate that ifa DII candidate with (sav), Calculations indicate that if a BH candidate with (say)186for the .N LH] lines. the two assumptions for the electron density alfect only the nitrogen abundance.,"for the [N II] lines, the two assumptions for the electron density affect only the nitrogen abundance."187 In any case. the He/1l and N/O ratios both exhibit a strong enhancement which. together with the overall abundance pattern. makes A 70 à genuine Tvpe-I object (Peimbert Torres-Peimbert 1983: Ixingsburgh Barlow 1994).," In any case, the He/H and N/O ratios both exhibit a strong enhancement which, together with the overall abundance pattern, makes A 70 a genuine Type-I object (Peimbert Torres-Peimbert 1983; Kingsburgh Barlow 1994)."188 As highlv evolved nebulae are expected to be low density objects. we attach a greater importance to the analysis made with ον=100 .," As highly evolved nebulae are expected to be low density objects, we attach a greater importance to the analysis made with $n_e = 100$ $^{-3}$."189 Ho omay well be that Ar IV] and. CLE LE] emission originates in denser clumps. but in either analysis the contribution of Ar? to the elemental abundance is only 10 percent.," It may well be that [Ar IV] and [Cl III] emission originates in denser clumps, but in either analysis the contribution of $^{3+}$ to the elemental abundance is only 10 percent."190 llence. the argon abundance is essentially determined by Απ HI].," Hence, the argon abundance is essentially determined by [Ar III]."191 Similarly. sulphur is derived. in almost equal terms from. S LH] and S HI]. for which the ow density deduced. from. the S. LH] line ratio is more representative.," Similarly, sulphur is derived in almost equal terms from [S II] and [S III], for which the low density deduced from the [S II] line ratio is more representative."192 To estimate he errors in our abundance analysis we »erformed Alonte Carlo simulations., To estimate the errors in our abundance analysis we performed Monte Carlo simulations.193 ‘This involved 100 iterations of adcng wavelength-independent noise to our spectra and reperorming our analysis cach time., This involved 100 iterations of adding wavelength-independent noise to our spectra and reperforming our analysis each time.194 The noise evel selected was ofLL3 as judged from measurement of our spectra., The noise level selected was of $\beta$ as judged from measurement of our spectra.195" From the standard deviation of values derived in our simulations we find an error of 200 Ix for 7;.( O HI) and TiGCN H]). 0.009 dex for the He abundance. 0.018 dex for O. 0.034 dex for N. 0.028 dex for Ar and 0.049 dex for S. οσο are however formal errors since uncertainties concerning the ionisation correction factor and ""averaging 7;.( O LHI]) give a lower limit to the actual error of at least 0.1 dex for the oxygen abundance."," From the standard deviation of values derived in our simulations we find an error of 200 K for $T_e$ ([O III]) and $T_e$ ([N II]), 0.009 dex for the He abundance, 0.018 dex for O, 0.034 dex for N, 0.028 dex for Ar and 0.049 dex for S. These are however formal errors since uncertainties concerning the ionisation correction factor and `averaging' $T_e$ ([O III]) give a lower limit to the actual error of at least 0.1 dex for the oxygen abundance."196 Since weak emission lines were used to determine the Ne and Cl abundances. and the Ar IV] and ο η) densities. these values may only be scen as indicative.," Since weak emission lines were used to determine the Ne and Cl abundances, and the [Ar IV] and [Cl III] densities, these values may only be seen as indicative."197 Since the spectra did. not cover the Ne LI] lines. we could only estimate the neon abundance from the Ne IV]/L1E3ratio obtained from our extraction of the inner nebula.," Since the spectra did not cover the [Ne III] lines, we could only estimate the neon abundance from the [Ne $\beta$ ratio obtained from our extraction of the inner nebula."198 Thus. the Ne/O abundance ratio would be at least —0.58. which is larger than in the Sun. out. close to the average found in PNe.," Thus, the Ne/O abundance ratio would be at least $-0.58$, which is larger than in the Sun, but close to the average found in PNe."199 A number of consistency checks were also applied to the total spectrum., A number of consistency checks were also applied to the total spectrum.200 The intensities of the three Balmer lines match within 8 percent and we checked. whether all lines of the same ion should give the same ionic abundance., The intensities of the three Balmer lines match within 8 percent and we checked whether all lines of the same ion should give the same ionic abundance.201 The lle L lines give the same ionic abundance within about 10 percent. if one exeludes A5015 wiwhich is underestimated by a factor of 1.4. and the very weak lines A4713 and A4388AL.," The He I lines give the same ionic abundance within about 10 percent, if one excludes $\lambda$ 5015 which is underestimated by a factor of 1.4, and the very weak lines $\lambda$ 4713 and $\lambda$ 4388."202 Among the three Le LL lines A4541 iis overestimated by a factor of 1.7., Among the three He II lines $\lambda$ 4541 is overestimated by a factor of 1.7.203 Phe three lines of IN Η] and O LI] have the same ionic abundances within 3 percent., The three lines of [N II] and [O III] have the same ionic abundances within 3 percent.204 ‘Table δ lists two distance estimates of 2.4 kpc (Stanghellini. Shaw Villaver 2008. hereafter SSVOS) and 5.0 kpe from the mean-trend of the Lla surface brightness-racius relation (SBR) of Frew Parker (2006).," Table \ref{tab:dist} lists two distance estimates of 2.4 kpc (Stanghellini, Shaw Villaver 2008, hereafter SSV08) and 5.0 kpc from the mean-trend of the $\alpha$ surface brightness-radius relation (SBR) of Frew Parker (2006)."205 The SBR calculation adopted. an integrated. Ho. flux of log f£(ffa)=11.585. the mean of Dluxes measured. by Ixaler (1983) ancl Hua et al. (," The SBR calculation adopted an integrated $\alpha$ flux of log $F(H\alpha)=-11.85$, the mean of fluxes measured by Kaler (1983) and Hua et al. ("2061998). angular dimensions from. Tvlenda et al. (,"1998), angular dimensions from Tylenda et al. ("2072003). and the reddening from Acker et al. (,"2003), and the reddening from Acker et al. ("2081992).,1992).209 Also given in Jab., Also given in Tab.210 δ are distance-dependent. Iuminosities of the central, \ref{tab:dist} are distance-dependent luminosities of the central211ranges. for a total of 16 hours per day. with the remainder of the time divided among various calibration and pointing tasks (see Paper D),"ranges, for a total of 16 hours per day, with the remainder of the time divided among various calibration and pointing tasks (see Paper I)."212 Phase and amplitude calibration were accomplished through observations of bright Galactic sources. permitting determination of the calibrator flux on all baselines to better than2%.," Phase and amplitude calibration were accomplished through observations of bright Galactic sources, permitting determination of the calibrator flux on all baselines to better than."213". Absolute pointing error determined by offsets between DASI detected point source positions and PMN southern catalog coordinates (( 1994) was less than 2’, with a drift «I’ over the period during which each row was observed."," Absolute pointing error determined by offsets between DASI detected point source positions and PMN southern catalog coordinates \markcite{wright94}( 1994) was less than $2\arcmin$, with a drift $\ll 1\arcmin$ over the period during which each row was observed."214 The number of days for which each of the four rows was observed is 14. 24. 28 and 31 for the A. B. C and D rows. respectively. for a total integration time of 28-62 hours per field.," The number of days for which each of the four rows was observed is 14, 24, 28 and 31 for the A, B, C and D rows, respectively, for a total integration time of 28–62 hours per field."215 Absolute calibration of the telescope was achieved through measurements of external thermal loads: the calibrations were then transferred to bright. astronomical sources., Absolute calibration of the telescope was achieved through measurements of external thermal loads; the calibrations were then transferred to bright astronomical sources.216" The flux scales resulting from two independent calibrations performed in February 2000 and February 2001 are found to agree to0.300, consistent with our estimate of overall statistical uncertainty in the measurement and transfer procedure."," The flux scales resulting from two independent calibrations performed in February 2000 and February 2001 are found to agree to, consistent with our estimate of overall statistical uncertainty in the measurement and transfer procedure."217 The systematic uncertainty in. determining load coupling and effective temperature is3%.. which is the dominant contribution to the uncertainty in our overall flux scale.," The systematic uncertainty in determining load coupling and effective temperature is, which is the dominant contribution to the uncertainty in our overall flux scale."218 This uncertainty. expressed as a percentage of Cj. is at lo and is constant across all power spectrum bands.," This uncertainty, expressed as a percentage of $C_l$, is at $\sigma$ and is constant across all power spectrum bands."219 Band-power measurements are also affected. though weakly. by errors in the estimated aperture efficiency. on which our uncertainty is 4% (see Paper D.," Band-power measurements are also affected, though weakly, by errors in the estimated aperture efficiency, on which our uncertainty is $4\%$ (see Paper I)."220 This contributes a band-power uncertainty which is constant at 4% except in the three lowest-/ bands. where a cancellation of errors causes it to decrease.," This contributes a band-power uncertainty which is constant at $4\%$ except in the three $l$ bands, where a cancellation of errors causes it to decrease."221 In using the current DASI results for parameter estimation (Paper III). we have found no significant difference between treating this small beam uncertainty separately with its low-/ variation included. and folding it together with the /-independent flux scale uncertainty.," In using the current DASI results for parameter estimation (Paper III), we have found no significant difference between treating this small beam uncertainty separately with its $l$ variation included, and folding it together with the $l$ -independent flux scale uncertainty."222 We therefore adopt a total combined calibration uncertainty of (10). expressed as a fractional uncertainty on the C; band powers in AT/T ).," We therefore adopt a total combined calibration uncertainty of $\sigma$ ), expressed as a fractional uncertainty on the $C_l$ band powers in $\Delta T/T$ )."223 Raw data from the correlators. along with monitoring data from various telescope systems. are accumulated in 8.4-s integrations.," Raw data from the correlators, along with monitoring data from various telescope systems, are accumulated in 8.4-s integrations."224 These short integrations are edited before being combined for analysis., These short integrations are edited before being combined for analysis.225 Baselines are rejected for which the phase offset or relative gain between the real and imaginary multipliers exceed nominal values., Baselines are rejected for which the phase offset or relative gain between the real and imaginary multipliers exceed nominal values.226 Data are also rejected when an LO has lost phase lock. when a receiver has warmed. or to trim field scans so that all eight fields are observed over precisely the same azimuth range.," Data are also rejected when an LO has lost phase lock, when a receiver has warmed, or to trim field scans so that all eight fields are observed over precisely the same azimuth range."227 We also edit data for which noise correlations between baselines indicate strong atmospheric fluctuations., We also edit data for which noise correlations between baselines indicate strong atmospheric fluctuations.228 The edited and calibrated data are combined into. I-hr bins. with uncertainty in the bins estimated from the sample variance of the 8.4-s integrations.," The edited and calibrated data are combined into 1-hr bins, with uncertainty in the bins estimated from the sample variance of the 8.4-s integrations."229 In order to implement ground contamination common mode rejection. it is necessary that a given visibility be measured for all 8 fields in à row: we cut all baselines that do not satisfy this criterion.," In order to implement ground contamination common mode rejection, it is necessary that a given visibility be measured for all 8 fields in a row; we cut all baselines that do not satisfy this criterion."230 We apply more stringent edits for (1.) radi <40. which we find are more susceptible to contamination.," We apply more stringent edits for $(u,v)$ radii $<23140$, which we find are more susceptible to contamination."232 For these visibilities. we retain only data for which both the sun and moon are below the horizon.," For these visibilities, we retain only data for which both the sun and moon are below the horizon."233 To minimize the risk of biasing the power spectrum results. we do not edit the data based on the level of the signal.," To minimize the risk of biasing the power spectrum results, we do not edit the data based on the level of the signal."234 We have varied the threshold values of the weather. calibrator. and lunar/solar edit criteria with no significant effect on the results.," We have varied the threshold values of the weather, calibrator, and lunar/solar edit criteria with no significant effect on the results."235 Collectively. these edits reject about of the data.," Collectively, these edits reject about of the data."236 See Paper I for a more comprehensive description of the data edits., See Paper I for a more comprehensive description of the data edits.237 All observations of a given set of fields are then combined. and it is these 1560 combined visibilities per field (78 complex baselines \ 10 correlator channels. before edits) which form the input to the angular power spectrum likelihood analysis.," All observations of a given set of fields are then combined, and it is these 1560 combined visibilities per field (78 complex baselines $\times$ 10 correlator channels, before edits) which form the input to the angular power spectrum likelihood analysis."238 The DASI instrument makes direct measurements. of the Fourier plane. and the angular power spectrum can be extracted from the data without creating an image.," The DASI instrument makes direct measurements of the Fourier plane, and the angular power spectrum can be extracted from the data without creating an image."239 The calibrated output of the interferometer is the visibility. which ts the convolution of the Fourier Transform of the sky brightness distribution. AT(w)/T. with the antenna aperture field autocorrelation function. A(u.A). and e(A) Is à —2% correction between the Rayleigh-Jeans and Planck functions.," The calibrated output of the interferometer is the visibility, which is the convolution of the Fourier Transform of the sky brightness distribution, $\widetilde{\Delta T}(\mathbf{u})/T$, with the antenna aperture field autocorrelation function, $\widetilde{A}(\mathbf{u},\lambda)$, and $g(\lambda)$ is a $\sim2$ correction between the Rayleigh-Jeans and Planck functions."240 The aperture field autocorrelation function A(u.A) ts radially symmetric. peaking at |u|=0. and tapering smoothly to zero at |u|=D/A. where D is the aperture diameter.," The aperture field autocorrelation function $\widetilde{A}(\mathbf{u},\lambda)$ is radially symmetric, peaking at $\abs{u} = 0$ , and tapering smoothly to zero at $\abs{u} = D/\lambda$, where $D$ is the aperture diameter."241" In the flat-sky limit. which ts appropriate for the ~374 FWHM DASI fields. ((White 1999a, Hobson. Lasenby. Jones 1995); we assume /=27|u| over the /-range to which DASI is sensitive."," In the flat-sky limit, which is appropriate for the $\sim 3\fdg4$ FWHM DASI fields, \markcite{white99a,hobson95}( (White 1999a; Hobson, Lasenby, Jones 1995); we assume $l = 2 \pi \abs{u}$ over the $l$ -range to which DASI is sensitive."242 For a single visibility. a simple quadratic estimator S of the quantity 27Jul”Su)zUxDC;/(Qo is given by (White 1999b) where N is the instrument noise variance for the measured visibility V(u) and equation (4)) gives the number specific to the DASI apertures and a power spectrum in units of κ”.," For a single visibility, a simple quadratic estimator $\hat \mathcal{S}$ of the quantity $2 \pi243\abs{u}^2 S(\abs{u}) \approx l(l+l)C_l/(2 \pi)$ is given by \markcite{white99b}( (White 1999b) where $N$ is the instrument noise variance for the measured visibility $V(\mathbf{u})$ and equation \ref{eqn:sqedasi}) ) gives the number specific to the DASI apertures and a power spectrum in units of $\mu244\mathrm{K}^2$."245 The variance of the visibility is thus directly related to C) centered at the baseline length |u|=//(277). with width Alu]~12 (FWHM) determined by the width of the aperture field autocorrelation function.," The variance of the visibility is thus directly related to $C_l$ centered at the baseline length $\left|\mathbf{u}\right| =246l/(2 \pi)$, with width $\Delta \abs{u} \simeq 12$ (FWHM) determined by the width of the aperture field autocorrelation function."247 While the simple quadratic estimator above is useful for understanding the relationship. between the visibility and the angular power spectrum. we have chosen a maximum likelihood method in the present analysis.," While the simple quadratic estimator above is useful for understanding the relationship between the visibility and the angular power spectrum, we have chosen a maximum likelihood method in the present analysis."248 We have adopted the iterated quadratic estimator approach of Bond.Jaffe. (1998) to find the maximum likelihood values of the angular power spectrum for a piecewise flat /(/+1)C;/(25) power spectrum in nine bands.," We have adopted the iterated quadratic estimator approach of \markcite{bond97}{, (1998) to find the maximum likelihood values of the angular power spectrum for a piecewise flat $l(l+1)C_l/(2\pi)$ power spectrum in nine bands."249 A data veetor A of length N=1560«32 (before data edits) is constructed by combining observations of each visibilityfor each of the 32 fields., A data vector $\Delta$ of length $N = 1560 \times 32$ (before data edits) is constructed by combining observations of each visibilityfor each of the 32 fields.250 The likelihood function for a set of parameters 5 Is where the covariance matrix, The likelihood function for a set of parameters $\mathbf{\kappa}$ is where the covariance matrix251starts to fail for 2zd. although most of the cywuamical nupact occurs below or around this distance.,"starts to fail for $z\gtrsim d$, although most of the dynamical impact occurs below or around this distance."252 It is worthy to iieution that for the purpose of this work. the assumed lvdrodvuanucal nature of the jet could be loose to sole extent. as long as the magnetic to kinetic pressure ratio in the jet is smaller. sax. than ~0.1.," It is worthy to mention that for the purpose of this work, the assumed hydrodynamical nature of the jet could be loose to some extent, as long as the magnetic to kinetic pressure ratio in the jet is smaller, say, than $\sim 0.1$."253 Otherwise. the lateral magnetic pressure cal effecively preveut chunp penetration into the jet.," Otherwise, the lateral magnetic pressure can effectively prevent clump penetration into the jet."254 Moreover. assunuue that chumps managed to cuter the jet. magnetic pressure could suppress the development of shocks. imduce maguctic dissipation and non-thermal activity. and change strougly the chuup disruption process. softeuiug or potentiating it (e.g.Jonesetal.1996:Shin2008).," Moreover, assuming that clumps managed to enter the jet, magnetic pressure could suppress the development of shocks, induce magnetic dissipation and non-thermal activity, and change strongly the clump disruption process, softening or potentiating it \citep[e.g.][]{jon96,shi08}."255. lu any case. the flow evolution uuder a dvuauicallv dominant magnetic field is ou of the scope of this work.," In any case, the flow evolution under a dynamically dominant magnetic field is out of the scope of this work."256 We have performed three παπα simulations using a finite-cditference code namedRutperet.. which solves the equations of relativistic lvdrodvuamics idu three dimensions. written idu conservation form. using hieh-resolutiou-shock-capturiug methods.," We have performed three numerical simulations using a finite-difference code named, which solves the equations of relativistic hydrodynamics in three dimensions, written in conservation form, using high-resolution-shock-capturing methods."257 was parallelized with a lybrid scheme with both parallel processes (MPT) aud parallel threads (OpendIP) inside cach process (seePeruchoetal.2010b)., was parallelized with a hybrid scheme with both parallel processes (MPI) and parallel threads (OpenMP) inside each process \citep[see][]{pe10}.258. The simulations were performed dm Mare Nosti. at the Darcelona Supercomputing Centre (BSC) with 200 processors. cach of them with a duration of 1080 hours. amounting a total of 6.18«107 computational hours.," The simulations were performed in Mare Nostrum, at the Barcelona Supercomputing Centre (BSC) with 200 processors, each of them with a duration of 1080 hours, amounting a total of $6.48\times10^5$ computational hours."259 The simulations are set-up with au overpressured jet surrounded by the stellar wind of the massive conanion., The simulations are set-up with an overpressured jet surrounded by the stellar wind of the massive companion.260 We are thus implicitly assuniues that the]vow shock generatedby the jet when crossing this πιοπα (PDBI&10) is far enough aud the cocoon dilute enough that the wile jas occupied. the space surromuding the jet itself., We are thus implicitly assuming that the bow shock generated by the jet when crossing this medium (PBK10) is far enough and the cocoon dilute enough that the wind has occupied the space surrounding the jet itself.261 units.The oiwsieal size of the erid is. in (απο) jet radius l605«100RS.200F5. the last 200F5 in the direclon of xopaesation of the jet (+ coordinate).," The physical size of the grid is, in (base) jet radius units, $160\, R_{\rm j} \, \times \, 160 \, R_{\rm j} \, \times \,200\,R_{\rm j}$, the last $200\,R_{\rm j}$ in the direction of propagation of the jet $z$ coordinate)."262" The erid size iu thew aud y coordinates is divided iu two regions. the uer SOR; around the jet axis having homogeneous resolution. alc he outer 10R, ini cach direction beiug formedby cells with increasing size."," The grid size in the $x$ and $y$ coordinates is divided in two regions, the inner $80\,R_{\rm j}$ around the jet axis having homogeneous resolution, and the outer $40\,R_{\rm j}$ in each direction being formed by cells with increasing size."263" The resolutiou iu the homogeneous eric is I TheBR, at. with a total of 320«S00 cells."," The resolution in the homogeneous grid is 4 $R_{\rm j}$ at, with a total of $320 \times 320 \times 800$ cells."264 extended exid is composed by SO cells on cach side. resulting im a box with 180.&8OO cells.," The extended grid is composed by 80 cells on each side, resulting in a box with $480\times480\times800$ cells."265 In the snuulatious.2; i2—2«1019am. so the plivsical size of the eric is (3.23«1s1072 0n.," In the simulations, $R_{\rm j}=2\times10^{10}\,\mathrm{cm}$, so the physical size of the grid is $(3.2\times3.2\times4)\,\times \,10^{12}$ cm."266 Iu previous works (PBos. PBIS10). the wind was sinulatec as homogeneous. but if was already. suggested that a necessary iniproveiieut to those simulations should be the inclusion of iuhomoeseneities.," In previous works (PB08, PBK10), the wind was simulated as homogeneous, but it was already suggested that a necessary improvement to those simulations should be the inclusion of inhomogeneities."267 We have done this by randomly adding Ciussian-shiaped clunips in the side of the exid from where the stellar wind is injected., We have done this by randomly adding Gaussian-shaped clumps in the side of the grid from where the stellar wind is injected.268" The initial nuniber of clumps in the half of the homogeucous erid facing the star. 1500. has been calculated to eusure that the mean wind mass-loss rate is &LoOAL, "," The initial number of clumps in the half of the homogeneous grid facing the star, 1500, has been calculated to ensure that the mean wind mass-loss rate is $\approx 10^{-6}\,M_\odot$ /yr."269The chuup reals density is 10 times huger than the mean deusitv (οςLOMefem?). ie. 9«10.tefeu.and the mimi density between clumps has becu fixed to 3.10166cui.," The clump peak density is 10 times larger than the mean density $9\times10^{-15}\mathrm{g/cm^3}$ ), i.e., $9\times10^{-14}\mathrm{g/cm^3}$,and the minimum density between clumps has been fixed to $3\times10^{-16}\mathrm{g/cm^3}$."270 The whole wind region is set iu pressure equilibrimm (Py=«107ere fem?) with the higher deusity regions. and a velocity ey—2«105cim/s radial from the star (PBos. PDIK10).," The whole wind region is set in pressure equilibrium $P_{\rm w}=1.5\times10^{-3}~\mathrm{erg/cm^3}$ ) with the higher density regions, and a velocity $v_{\rm w}=2\times10^8~\mathrm{cm/s}$ radial from the star (PB08, PBK10)."271 Figure 2 shows cuts of the initial couditions in pressure and deusitv aloug the axis of oue of the simulated jets. aud Fie.," Figure \ref{fig:maps1} shows cuts of the initial conditions in pressure and density along the axis of one of the simulated jets, and Fig."272" 3 shows trausversal cuts at D222.2410""cin."," \ref{fig:maps2} shows transversal cuts at $z\simeq2.2\times10^{12}\,\mathrm{cm}$."273 We lave simulated two jets with differcut powers. jet Awith £)=3<1Pore/s and jet D with Li-=QUorefs (to be compared with jet 2 in PBKLo).," We have simulated two jets with different powers, jet A with $L_{\rm j}=3\times10^{36}\,\mathrm{erg/s}$ and jet B with $L_{\rm j}=10^{37}\,\mathrm{erg/s}$ (to be compared with jet 2 in PBK10)."274 The jets are set-up witha given opening angle but not in pressure equilibrium with the ambicut. as this has homogeneous pressure whereas the jet pressure decreases with :.," The jets are set-up with a given opening angle but not in pressure equilibrium with the ambient, as this has homogeneous pressure whereas the jet pressure decreases with $z$ ."275 The injection point in the erid would be located at 2«1011cin from the compact object. this is. well within the binary system.," The injection point in the grid would be located at $2\times10^{11}~\mathrm{cm}$ from the compact object, this is, well within the binary system."276 The jets have both injection densities of 1.2«10.Pefeu? and Lt&10Heg/eni?.ο aud a velocity e=LO!cms.," The jets have both injection densities of $4.2\times10^{-15}\mathrm{g/cm^3}$ and $1.4\times10^{-14}\mathrm{g/cm^3}$, and a velocity $v_{\rm j}=10^{10}\,\mathrm{cm/s}$."277 Thermal cooling termes. following the approximation used in Myasnikovoetal.(1998).. have been added to the code to account for the cooliug iu the cbuups.," Thermal cooling terms, following the approximation used in \cite{mya98}, have been added to the code to account for the cooling in the clumps."278 Table 3.1 sunuuarizes the jet and wind parameters used in the simulations., Table \ref{tab} summarizes the jet and wind parameters used in the simulations.279 We note that to simulate continuous wind injection. the 1p-wiud section ofthe ambient meditm is replenished with chuups when a portion of its volune has heen eniptied of the original ones.," We note that to simulate continuous wind injection, the up-wind section of the ambient medium is replenished with clumps when a portion of its volume has been emptied of the original ones."280 This is done without aux effec on the cyvuamics of the svstem. as the chuups are added im a region far from the interaction between the jet and the first chimps.," This is done without any effect on the dynamics of the system, as the clumps are added in a region far from the interaction between the jet and the first clumps."281 A third simulation was performed to illustrate the evolution of3 chuups interacting with jet A me(jet A)., A third simulation was performed to illustrate the evolution of 3 clumps interacting with jet A (jet $^\prime$ ).282 The chumps were located at 2=3.6 aud 12κcni. with Increasing distance to the ;jet in the w-direction such that the different chimps start their interaction with the jet subsequently.," The clumps were located at $z=3,\,6$ and $12\times10^{11}\,\mathrm{cm}$, with increasing distance to the jet in the $x$ -direction such that the different clumps start their interaction with the jet subsequently."283 In Fieure {νι the initial distribution of the chumps isshown in the axial density cut of the jet parallel to the staz-jet plane.," In Figure \ref{fig:maps3}, the initial distribution of the clumps isshown in the axial density cut of the jet parallel to the star-jet plane."284 are related with the mass of theLy. which is likely related with the development history of the star.," are related with the mass of the, which is likely related with the development history of the star."285 The eroups with pulsation period P«0.35 dd. aud P>O55 de show both lower abuudances than the large third eroup of periods 0.35Pκ0.55dd. It has the largest abundance aud the largest dispersion στοη., The groups with pulsation period $P<0.35$ d and $P>0.55$ d show both lower abundances than the large third group of periods $0.35<P<0.55$ d. It has the largest abundance and the largest dispersion $\sigma_{\rm [Fe/H]}$.286 Tt is uot a uniforii subsample ofLvrs., It is not a uniform subsample of.287. That this eroup is so ciffereut is also visible iu , That this group is so different is also visible in \\ref{RRvel.tab}.288"The dispersion iu C. V. Ο. $. 7, aud eec is larger in this subsample than in the two other period eroups."," .The dispersion in $U$, $V$, $\Theta$, $\Phi$, $I_{\rm z}$ and $ecc$ is larger in this subsample than in the two other period groups."289 This fact can © noted as well in refFELae (lower ngh panel)., This fact can be noted as well in \\ref{FE4.fig} (lower right panel).290 The eroup with periods of -0.35 dd. contains the RRe stars with abundances of 2<[Fe/H]«—1., The group with periods of $<0.35$ d contains the RRc stars with abundances of $-2<{\rm[Fe/H]}<-1$.291 The metallicity of the secoud period eroup ranges from solar to |Fe/Il] of =—2., The metallicity of the second period group ranges from solar to [Fe/H] of $\simeq-2$.292 These are RRab stars., These are RRab stars.293 Note that the period increases in this eroup toward decreasing metallicity., Note that the period increases in this group toward decreasing metallicity.294 Most of the oof our sample are in this eroup., Most of the of our sample are in this group.295 It combines with a large dispersion in metallicity and various orbit parameters. as can be recognised in roefFEDPER .tab.. probably represcuting different ages.," It combines with a large dispersion in metallicity and various orbit parameters, as can be recognised in \\ref{FEPER.tab}, probably representing different ages."296 The third eroup having periods ~0.6dd are RBab stars as well but with lower abundances., The third group having periods $\simeq0.6$ d are RRab stars as well but with lower abundances.297 This group is the field cequivalent to thein Oosterhoff II clusters., This group is the field equivalent to thein Oosterhoff II clusters.298 This last eroup is a very sul subsample of wwith relative loug periods aud ictallicitics |Fo/II| 1.6., This last group is a very small subsample of with relative long periods and metallicities [Fe/H] $<-1.6$ .299 are cousidered in refFEPER.tab.., are considered in \\ref{FEPER.tab}. .300 with eec20.15 have lower abundances (|Fe/II]= 1.15) than those with eec<0.5 ([Fe/H]= 0.90). as we expected.," with $ecc>0.45$ have lower abundances $\overline {[\rm Fe/H]}=-1.48$ ) than those with $ecc<0.45$ $\overline{[\rm Fe/H]}=-0.90$ ), as we expected."301 Like in refRRvel.tah we did not iuclude 7 with retrograde orbits having ecce< 0.15., Like in \\ref{RRvel.tab} we did not include 7 with retrograde orbits having $ecc<0.45$ .302 We did so because these stars do not fit iuto the group of low eccentricity stars which are cauclidate disk stars., We did so because these stars do not fit into the group of low eccentricity stars which are candidate disk stars.303 This eroup of retrograde hhas a low metallicity of [Fe/II|=1.55., This group of retrograde has a low metallicity of $\overline{[\rm Fe/H]} =-1.85$.304 τοΕΕLae shows the data of Tables ref{RRveLtab and 2 in graphical form: metallicity [Fe/T]| versus orbital velocity Ο. eec. ite. and period.," \\ref{FE4.fig} shows the data of Tables \\ref{RRvel.tab} and \ref{FEPER.tab} in graphical form: metallicity [Fe/H] versus orbital velocity $\Theta$, $ecc$ , $nze$, and period."305 Dividing the in imetalppoor and metal-rich groups as Laveen (1995). we also find that velocities for wwith οΠ >Lreveal a distribution different than those with lower metallicitics.," Dividing the in metal-poor and metal-rich groups as Layden (1995), we also find that velocities for with [Fe/H] $>-1$reveal a distribution different than those with lower metallicities."306" Wiel uetallicity stars with more disk-like circular velocities Ο cluster both at low eec and το, But the separation is not a strict one.", High metallicity stars with more disk-like circular velocities $\Theta$ cluster both at low $ecc$ and $nze$ But the separation is not a strict one.307 Even some datapoiutswith very low abundauce [Fe/T]<1.5 show Qz200 ecce<<OL aud niu< 0.2.," Even some datapointswith very low abundance [Fe/H]$\leq-1.5$ show $\Theta\simeq200$ , $ecc<0.4$ and $nze<0.2$ ."308 Altimaun de Doer (2000) fouud the same fact using a uch smaller sample of Lars.., Altmann de Boer (2000) found the same fact using a much smaller sample of .309are only possible within a very narrow window (~ 1.2 aremin) about an inclination of 90°.,are only possible within a very narrow window $\sim$ 1.2 arcmin) about an inclination of $^{\circ}$.310 If this were indeed the case. the transit of the tertiary component in front of the eclipsing pair should have occurred during mid 2001.," If this were indeed the case, the transit of the tertiary component in front of the eclipsing pair should have occurred during mid 2001."311 Also interesting to note is the near coplanarity of the eclipsing system and its companion., Also interesting to note is the near coplanarity of the eclipsing system and its companion.312 Varricatt Ashok (1999) found an inclination for the eclipsing pair of ijj=7975. which ts equivalent to /jj=10075 because of the degeneracy.," Varricatt Ashok (1999) found an inclination for the eclipsing pair of $i_{\rm EB}=79\fdg5$, which is equivalent to $i_{\rm EB}=100\fdg5$ because of the degeneracy."313 Thus. the third body's orbit appears to be within only of the orbit of the eclipsing pair.," Thus, the third body's orbit appears to be within only $^{\circ}$ of the orbit of the eclipsing pair."314 One question remains yet unaddressed. and this is the nature of the tertiary companion of R CMa.," One question remains yet unaddressed, and this is the nature of the tertiary companion of R CMa."315 With a measured mass of 0.34 .. one is tempted to classify R CMa C tentatively as a main sequence M3-4 star (Delfosse et al.," With a measured mass of 0.34 $_{\odot}$, one is tempted to classify R CMa C tentatively as a main sequence M3-4 star (Delfosse et al."316 2000)., 2000).317 However. another attractive possible scenario is a white dwarf (WD) as tertiary component.," However, another attractive possible scenario is a white dwarf (WD) as tertiary component."318 There is no direct evidence for a WD companion to R CMa. but the mass of the third body ts compatible with the low-end of the WD mass distribution found by Silvestri et al. (," There is no direct evidence for a WD companion to R CMa, but the mass of the third body is compatible with the low-end of the WD mass distribution found by Silvestri et al. ("3192001).,2001).320 The presence of a hot WD (Gay>10000 K) is unlikely from IUE observations of R CMa in the UV region. where no hot source has been detected.," The presence of a hot WD $T_{\rm eff}>10\,000$ K) is unlikely from IUE observations of R CMa in the UV region, where no hot source has been detected."321 Nonetheless. R CMa is an old disk population star so that a young WD ts. in principle. not expected.," Nonetheless, R CMa is an old disk population star so that a young WD is, in principle, not expected."322 If a WD is present. its original stellar mass would have to be greater than the mass of the mitial primary (now secondary) of R CMa.," If a WD is present, its original stellar mass would have to be greater than the mass of the initial primary (now secondary) of R CMa."323 From binary evolution theory. the best estimate of the initial mass of the original primary is about 1.4 .. (Sarma. Vivekananda Rao. Abhyankar 1996).," From binary evolution theory, the best estimate of the initial mass of the original primary is about $1.4$ $_{\odot}$ (Sarma, Vivekananda Rao, Abhyankar 1996)."324 This indicates a pre-WD evolution time for the companion of around 2-3 Gyr., This indicates a pre-WD evolution time for the companion of around 2–3 Gyr.325 Cooling sequences for WDs (Serenelli et al., Cooling sequences for WDs (Serenelli et al.326 2001) yield an effective temperature of ~5400 K at an age of ~3 Gyr. which is a reasonable estimate given the kinematic characteristics of R CMa.," 2001) yield an effective temperature of $\sim$ 5400 K at an age of $\sim$ 3 Gyr, which is a reasonable estimate given the kinematic characteristics of R CMa."327 Should the tertiary component turn out to be a WD. such an old and low-mass object might be exceedingly interesting since it could belong to the controversial class of blue WDs that have been claimed to play an important role in explaining the dark matter content of the galactic halo (Hodgkin et al.," Should the tertiary component turn out to be a WD, such an old and low-mass object might be exceedingly interesting since it could belong to the controversial class of blue WDs that have been claimed to play an important role in explaining the dark matter content of the galactic halo (Hodgkin et al."328 2000)., 2000).329 As the predicted temperatures both in the WD and M-star scenarios are fairly similar. only the very different expected lummosities can help identify the nature of the companion to R CMa.," As the predicted temperatures both in the WD and M-star scenarios are fairly similar, only the very different expected luminosities can help identify the nature of the companion to R CMa."330 Thus. the measure of the magnitudes of the tertiary component through direct imaging would be a definitive proof.," Thus, the measure of the magnitudes of the tertiary component through direct imaging would be a definitive proof."331 If we consider the M-star scenario. the absolute magnitude of the tertiary component would be My~11 mag. which translates to myz14 mag when using the parallax obtained ins refanalys..," If we consider the M-star scenario, the absolute magnitude of the tertiary component would be $M_{\rm V}\approx11$ mag, which translates to $m_{\rm V}\approx14$ mag when using the parallax obtained in \\ref{analys}."332 This is about 8 mag fainter than R CMa itself., This is about 8 mag fainter than R CMa itself.333 To give an example in the IR. the situation ts significantly improved in the K-band. where the magnitude difference is reduced to AKz4 mag.," To give an example in the IR, the situation is significantly improved in the K-band, where the magnitude difference is reduced to $\Delta334K\approx4$ mag."335 The tertiary component would be even fainter in the WD scenario., The tertiary component would be even fainter in the WD scenario.336 Indeed. the absolute magnitude can be estimated as Myz14 mag. which implies an apparent magnitude of myz17 mag.," Indeed, the absolute magnitude can be estimated as $M_{\rm337V}\approx14$ mag, which implies an apparent magnitude of $m_{\rm338V}\approx17$ mag."339 The difference with R CMa is therefore AVz1I mag.," The difference with R CMa is therefore $\Delta340V\approx11$ mag."341 In the IR the situation does not improve significantly. with a large magnitude difference of AK=10 mag.," In the IR the situation does not improve significantly, with a large magnitude difference of $\Delta K\approx10$ mag."342 These magnitudes and dynamic brightness ranges are challenging. but yet attainable with state-of-the-art— coronographs or Speckle spectrographs., These magnitudes and dynamic brightness ranges are challenging but yet attainable with state-of-the-art coronographs or Speckle spectrographs.343 Further— complications arise from the current spatial location of the tertiary component near the conjunction of its orbit with the eclipsing pair., Further complications arise from the current spatial location of the tertiary component near the conjunction of its orbit with the eclipsing pair.344 Figure 3 depicts the predicted orbits of both the eclipsing pair and the tertiary component on the plane of the sky.," Figure \ref{figsky}345 depicts the predicted orbits of both the eclipsing pair and the tertiary component on the plane of the sky."346 As can be seen. the separation between the eclipsing system and R CMa C ts only 27 mas as of 2002. which makes direct imaging very difficult.," As can be seen, the separation between the eclipsing system and R CMa C is only 27 mas as of 2002, which makes direct imaging very difficult."347 On an optimistic note. the situation will slowly improve in the future until à maximum separation of 2:078 is reached around year 2037.," On an optimistic note, the situation will slowly improve in the future until a maximum separation of $\approx$$0\farcs8$ is reached around year 2037."348 Claims of third body detections through the analysis of (O- residuals have sometimes been challenged., Claims of third body detections through the analysis of (O--C) residuals have sometimes been challenged.349 Spurious period changes caused by magnetic activity cycles. variable angular momentum loss. magnetic coupling. or other effects have beer argued to explain modulations 1n. the (O-C) residuals found in à number of eclipsing binary stars.," Spurious period changes caused by magnetic activity cycles, variable angular momentum loss, magnetic coupling, or other effects have been argued to explain modulations in the (O–C) residuals found in a number of eclipsing binary stars."350 Interestingly. R CMa would be a prime candidate for such spurious period changes because of its interactive nature.," Interestingly, R CMa would be a prime candidate for such spurious period changes because of its interactive nature."351 However. with over one period cycle in the LTT curve currently covered and. more importantly. with direct evidence from Hipparcos astrometry. the case for a tertiary companion to R CMa ts now tron-clad.," However, with over one period cycle in the LTT curve currently covered and, more importantly, with direct evidence from Hipparcos astrometry, the case for a tertiary companion to R CMa is now iron-clad."352 What only remains to be clarified at this point is whether this third star is an M dwarf or a WD., What only remains to be clarified at this point is whether this third star is an M dwarf or a WD.353 Also. the nature of the lower amplitude ~45 vr variation needs to be further explored with continued observations.," Also, the nature of the lower amplitude $\sim$ 45 yr variation needs to be further explored with continued observations."354 This paper presents a combined analysis of short-term accurate astrometry and long-term timing residuals applied to the eclipsing binary R CMa., This paper presents a combined analysis of short-term accurate astrometry and long-term timing residuals applied to the eclipsing binary R CMa.355 The study yields the complete orbital and physical properties of the tertiary component., The study yields the complete orbital and physical properties of the tertiary component.356 A determination of the mass of the third body is possible because the masses of the eclipsing binary components themselves are well-known from light and radial velocity curve analyses., A determination of the mass of the third body is possible because the masses of the eclipsing binary components themselves are well-known from light and radial velocity curve analyses.357 The example discussed here illustrated the capabilities of a method that will reach its full potential with the upcoming high-accuracy astrometric missions., The example discussed here illustrated the capabilities of a method that will reach its full potential with the upcoming high-accuracy astrometric missions.358 The improvements in precision of the future astrometric measurements are due to an increase up to a thousand-fold relative to Hippareos and the quality of the photometry (and thus the eclipse timings) will also improve., The improvements in precision of the future astrometric measurements are due to an increase up to a thousand-fold relative to Hipparcos and the quality of the photometry (and thus the eclipse timings) will also improve.359 More quantitatively. timings with accuracies of —10 s are now possible for select eclipsing binaries with sharp eclipses.," More quantitatively, timings with accuracies of $\sim$ 10 s are now possible for select eclipsing binaries with sharp eclipses."360 The detection of large planets (~ 10 My) in long-period orbits (~ 10- yr) around eclipsing binaries will be therefore a relatively easy task., The detection of large planets $\sim$ 10 $_{\rm J}$ ) in long-period orbits $\sim$ 10--20 yr) around eclipsing binaries will be therefore a relatively easy task.361 The short-term astrometry will confirm the detections and yield the complete orbital solution (most significantly the inclination) and thus the actual mass of the orbiting body., The short-term astrometry will confirm the detections and yield the complete orbital solution (most significantly the inclination) and thus the actual mass of the orbiting body.362 One of the unexpected outcomes of the Hipparcos mission has been that a primarily astrometric satellite can also provide valuable new results from its photometric measurements alone (numerous new variables. HD 209458 planetary transits. etc).," One of the unexpected outcomes of the Hipparcos mission has been that a primarily astrometric satellite can also provide valuable new results from its photometric measurements alone (numerous new variables, HD 209458 planetary transits, etc)."363 The data analysis of the next generations of astrometric satellites will surely benefit from a simultaneous analysis of the astrometric and photometric data., The data analysis of the next generations of astrometric satellites will surely benefit from a simultaneous analysis of the astrometric and photometric data.364 Astrometric missions such as GAIA will likely detect one million new eclipsing binaries (a smaller number is expected for FAME)., Astrometric missions such as GAIA will likely detect one million new eclipsing binaries (a smaller number is expected for FAME).365 About one per cent of the eclipsing binaries observed by Hipparcos has a 0.0001 day precision in the reference epoch. which is enough to detect the LTT effect that would arise from a 10 Jupiter mass third body with a 11 year period.," About one per cent of the eclipsing binaries observed by Hipparcos has a 0.0001 day precision in the reference epoch, which is enough to detect the LTT effect that would arise from a 10 Jupiter mass third body with a 11 year period."366 If we assume the same ratio for GAIA. hundreds to thousands of third bodies would be detected.," If we assume the same ratio for GAIA, hundreds to thousands of third bodies would be detected."367 Although GAIA astrometry alone will be able to give the orbit for the closest stars. the orbit for more distant stars will depend on the availability of ground-based light curves to define the reference epoch.," Although GAIA astrometry alone will be able to give the orbit for the closest stars, the orbit for more distant stars will depend on the availability of ground-based light curves to define the reference epoch."368 This method of combining LTT analysis and astrometry complements very well with the ongomg spectroscopic searches., This method of combining LTT analysis and astrometry complements very well with the ongoing spectroscopic searches.369 The LTT analysis favors the detection of long-period, The LTT analysis favors the detection of long-period370 2000)... Bursteinetal.(1988).," \citep{oco99,bro00}. \citet{bur88}."371. Mg» quiescent (Martinetal.2005).. Richetal.(2005) ς<0.2. Μα». Donasetal.(2007) Mg» (de199]).," $_2$ $quiescent$ \citep{mart05}, \citet{ric05} $z<0.2$ $_2$ \citet{don07} $_2$ \citep{dev91}."372. Bureauetal.(2011) could be seen among the guiescent ETGs only when the contaminations of star-forming galaxies and low-quality data were much more stringently removed than was done in Richetal.(2005)., \citet{bur11} could be seen among the $quiescent$ ETGs only when the contaminations of star-forming galaxies and low-quality data were much more stringently removed than was done in \citet{ric05}.373. The UV color-color diagram is another powerful tool to investigate the properties of hot stellar. populations responsible for the UVX., The UV color–color diagram is another powerful tool to investigate the properties of hot stellar populations responsible for the UVX.374 Particularly. the capability of the GALEX to observe the far-UV (FUV: 1528À) and UV (NUV: 2271 bandpasses simultaneously (Morrisseyetal.2005) let us À)securely estimate the UV spectral shape without instrumental biases.," Particularly, the capability of the GALEX to observe the far-UV (FUV; ) and near-UV (NUV; ) bandpasses simultaneously \citep{mor05} let us securely estimate the UV spectral shape without instrumental biases."375 As demonstrated by Dormanetal. (1995).. the UV color-color diagram. FUVΝΟΥ (as a measure of UV spectral shape) vs. FUV—r (or FUV—-V: as a measure of UVX strength) can trace the UV spectral shape and amplitude.," As demonstrated by \citet{dor95}, the UV color–color diagram, $FUV-NUV$ (as a measure of UV spectral shape) $vs.$ $FUV-r$ (or $FUV-V$; as a measure of UVX strength) can trace the UV spectral shape and amplitude."376 It is also useful to segregate different stellar population systems., It is also useful to segregate different stellar population systems.377 Richetal.(2005) employed this tool but found no systematic variation among. their ETGs at z<0.2., \citet{ric05} employed this tool but found no systematic variation among their ETGs at $z<0.2$.378 Reeetal.(2007) presented. another example to show that the brightest cluster galaxies (BCGs) are homogenous populations following an old stellar sequence with considerable amounts of color spread., \citet{ree07} presented another example to show that the brightest cluster galaxies (BCGs) are homogenous populations following an old stellar sequence with considerable amounts of color spread.379 In this Letter. we expand significantly the sample size of previous studies from the latest data release of the GALEX and SDSS to construct the UV color-color relation of the ETGs in the nearby universe. and reexamine our current understanding of UVX.," In this $Letter$, we expand significantly the sample size of previous studies from the latest data release of the GALEX and SDSS to construct the UV color–color relation of the ETGs in the nearby universe, and reexamine our current understanding of UVX."380 The initial sample of ETGs ts selected from the SDSS DR7 spectroscopic and photometricdatabase ina rathersimplisticway. with the following two criteria: Thesearchvolumeis limited as above in order to secure an unbiased sample from the SDSS spectroscopic survey.," The initial sample of ETGs is selected from the SDSS DR7 spectroscopic and photometricdatabase ina rathersimplisticway, with the following two criteria: Thesearchvolumeis limited as above in order to secure an unbiased sample from the SDSS spectroscopic survey."381 At, At382which hints for typical parameters. the optical emission is weak to mgz15.,"which hints for typical parameters, the optical emission is weak to $m_{\rm383R}\approx 15$."384 Similarly. for μαδιLOMHz corresponding to the wavelength A=170 nm. the upper limit of UVO'T carricc by Swift (see in http://swift.esfe.nasa.gov). the predicte emission is high up to mz12th magnitude.," Similarly, for $\nu_{\rm obs}=1.8\times 10^{15}~{\rm Hz}$ corresponding to the wavelength $\lambda=170$ nm, the upper limit of UVOT carried by Swift (see in http://swift.gsfc.nasa.gov), the predicted emission is high up to $m\simeq 12{\rm th}$ magnitude."385 Peer Waxman (2003) have caleulated the promp GRB spectra (2 O.1keV) in great. detail within the firebal model framework. and some important effects such as the e* pairs production/annihilation ancl so on have been taken into account.," Pe'er Waxman (2003) have calculated the prompt GRB spectra $>0.1{\rm keV}$ ) in great detail within the fireball model framework, and some important effects such as the $e^\pm$ pairs production/annihilation and so on have been taken into account."386 In order to estimate the valicity of our calculation. we compare our results with the detaile numerical caleulation (Peer Waxman 2003). and find tha our results do not show much cdillerence [from theirs.," In order to estimate the validity of our calculation, we compare our results with the detailed numerical calculation (Pe'er Waxman 2003), and find that our results do not show much difference from theirs."387" For example. for their low compactness case shown in their figure dL=10 eres. emep=10 ""7 pm9, δἱ=0.0L sandy= 300."," For example, for their low compactness case shown in their figure 4: $L=10^{52}{\rm ergs}$ $\epsilon_{\rm e}=\epsilon_{\rm388B}=10^{-0.5}$ , $p=3$, $\delta t=0.01~{\rm s}$ and $\eta=300$ ."389" The flux £54aMb10""Jv (we have extended their ligure to Pigas£2 eV energy range. at which energy band ἐνον v7)."," The flux $F_{\nu_{\rm R,obs}}\sim 5\times 10^{-5}{\rm Jy}$ (we have extended their figure to $h\nu_{\rm R,obs}\approx 2$ eV energy range, at which energy band $F_{\nu}\propto \nu^{5/2}$ )."390 With these parameters. our simple analytic result (see Eq. (," With these parameters, our simple analytic result (see Eq. ("391"14)) gives £54,onld.10""Jv.","14)) gives $F_{\nu_{\rm R,obs}}\sim 1.4\times 10^{-5}{\rm Jy}$."392 Therefore. as an approximation. we think our analytic results can be used to estimate the UVOptical emission from GRBs.," Therefore, as an approximation, we think our analytic results can be used to estimate the UV/Optical emission from GRBs."393 3clow we discuss the possible SSC (synchrotron sel-Compton) radiation. briellv., Below we discuss the possible SSC (synchrotron self-Compton) radiation briefly.394. The typical energy of the SSCRC radiation.ar can be cstimated; by hiiSNCerrail2&IS keV. o," The typical energy of the SSC radiation can be estimated by $h\nu_{\rm m}^{\rm SSC}\simeq 2\gamma_{\rm pair,m}^2395h\nu_{\rm m}\approx 18~{\rm keV}$ ."396"orThe ratio. of the SSC)pu luminosity. (Losc) to the synchrotron luminosity (La) of e pairsτμ can be estimated; by. 6—=Lune$5EGALUn5n where C,./Ug are the electronmagnetic. energy. density. respectively."," The ratio of the SSC luminosity $L_{\rm SSC}$ ) to the synchrotron luminosity $L_{\rm syn}$ ) of $e^\pm$ pairs can be estimated by $x\equiv{L_{\rm SSC}\over L_{\rm397syn}}={U_{\rm e}/(1+x)\over U_{\rm B}^{\rm b}}$, where $U_{\rm398e}/U_{\rm B}^{\rm b}$ are the electron/magnetic energy density respectively."399 Hence à=(€11vl|AC.UL)2—í(llο/fel)/2o0.6 for egO4.," Hence $x=(-1+\sqrt{1+4U_{\rm e}/U_{\rm B}^{\rm400b}})/2=(-1+\sqrt{1+4 E_{\rm \gamma,\nu>\nu_{\rm401cut}}/\epsilon_{\rm B} E_{\rm \gamma}})/2\sim 0.6$ for $\epsilon_{\rm B}\simeq 0.1$."402 LavfhàEssedorMAWorfenyeUTFg o).," $L_{\rm syn}/L\approx E_{\rm403\gamma,\nu>\nu_{\rm cut}}/(1+x)E_{\rm \gamma}\approx (\nu_{\rm404cut}/\nu_{\rm b})^{\rm (2-p)/2}/(1+x)$ ."405 Pherefore besofh8orefaye-ἷqo)&0404.," Therefore $L_{\rm406SSC}/L\approx x (\nu_{\rm cut}/\nu_{\rm b})^{\rm407(2-p)/2}/(1+x)\approx 0.04$."408 So the SSC component can change the observed soft 5 ray spectrum in some degree. which may help to explain the observed. X-ray excess in some GRBs (Band et al.," So the SSC component can change the observed soft $\gamma-$ ray spectrum in some degree, which may help to explain the observed X-ray excess in some GRBs (Band et al."409 1993)., 1993).410" For the highly magnetizecl fireball. the characteristic synchrotron emission frequency. of the new born e. pairs can be estimated by At the present case. we assume the electromagnetic enerey dominated over other ones. thus D"" can be estimated ∣⋡∙∖⇁∐↓⊔≈↻⋅∆⊰↓∪⋟≺∣⋜⋯⊳∖⊳∖↙↓−∠⋅⋅−− ↓∖⊽∪∖∖⊽⋡↥⇂↥⋖⋅⋖⋅↓∢⋅≼∙⋃⋅∪⊔∖∖⋰∐↓↕⋜↧∟∪↓⋅∢⋅⊔↿∠⇂⋅⋯∼⋯↓⋅⋎∣⊽ "," For the highly magnetized fireball, the characteristic synchrotron emission frequency of the new born $e^\pm$ pairs can be estimated by At the present case, we assume the electromagnetic energy dominated over other ones, thus $B^{\rm m}$ can be estimated by $B^{\rm m}\approx6.3\times10^3~{\rm Gauss}~\epsilon^{1/2}L_{\rm41152}^{1/2}\eta_{2.5}^{-3}\delta t_{-1}^{-1}$, $\epsilon=E_{\rm412B}/E_{\rm \gamma}\sim 1$."413"cools down to 5, at a timescale The characteristic frequeney with respect to σος 1s ↾∐↕⋖⋅⊳∖∙∖⇁↓∐∼↓⊔⋅∪⇂↓⋅∪⊔⊳∖⋖⊾∐⋅−⋜↧∣⋡≱∖∪↓⋅↓≻↿⋠↓∪⊔∐⋅⋖⋅⊏↥⋯⊾⊔≼∼∙∖⇁↿∖∕∕∣∆↙⊽∕∕⋯⊐ can be estimated by (Wu et al."," Now, the electron with a Lorentz factor $\gamma_{\rm e}$ $\gg\gamma_{\rm e,c}$ ) cools down to $\gamma_{\rm e,c}$ at a timescale The characteristic frequency with respect to $\gamma_{\rm e,c}$ is The synchrotron self-absorption frequency $\nu_{\rm a}>\nu_{\rm414m}$ ) can be estimated by (Wu et al."415 2003) where it is assumecd that the electrons/positrons carried by the fireball is far less than the e pairs generated in the rav phase (Zhang Mésszárros 2002)., 2003) where it is assumed that the electrons/positrons carried by the fireball is far less than the $e^\pm$ pairs generated in the $\gamma-$ ray phase (Zhang Mésszárros 2002).416" Now the peak Dux can be estimated by where ος=—NBGMESOgdARD ON.(nol. DSmD""noe."," Now the peak flux can be estimated by where $F_{\rm \nu_{\rm max}}^{\rm m}=N_{\rm rad}^{\rm m}\eta417P_{\rm \nu_{\rm m}}^{\rm m}(1+z)/4\pi D_{\rm L}^2$, $N_{\rm418rad}^{\rm m}=2N_{\rm e^\pm}t_{\rm life}^{\rm m}/\delta t$ , $P_{\rm419\nu_{\rm m}}^{\rm m}=e^3B^{\rm m}/m_{\rm e}c^2$."420 The observed. I. band lux can be estimated by which hints for typical parameters. the optical emission is weak to mpz16.," The observed R band flux can be estimated by which hints for typical parameters, the optical emission is weak to $m_{\rm R}\approx 16$."421 Similarly. for van.=LNLOMIz. the predicted emission is up to mc13th magnitude.," Similarly, for $\nu_{\rm obs}=1.8\times 10^{15}~{\rm Hz}$, the predicted emission is up to $m\simeq 13{\rm th}$ magnitude."422" In the present case. the typical energy of the SSC radiation""m can be estimated.' by fySNCo3.2255aheycm45 keV."," In the present case, the typical energy of the SSC radiation can be estimated by $h\nu_{\rm m}^{\rm SSC}\simeq 2\gamma_{\rm423pair,m}^2 h\nu_{\rm m}\approx 35~{\rm keV}$ ."424 Now. ae=(1|“llAGCUUBD/2(11VALAEny(V2Beeryvutfl For ELPoa CE.," Now, $x=(-1+\sqrt{1+4U_{\rm e}/U_{\rm B}^{\rm m}})/2=(-1+\sqrt{1+4425E_{\rm \gamma,\nu>\nu_{\rm cut}}/\epsilon E_{\rm426\gamma}})/2\approx E_{\rm \gamma,\nu>\nu_{\rm cut}}/\epsilon427E_{\gamma}$ for $E_{\rm \gamma,\nu>\nu_{\rm cut}}\ll \epsilon428E_{\rm \gamma}$ ."429 hus Lusc/LzmMAprle(vonfenyi?T]egO0le3. which implies that the SSC component can not change the observed soft > ray. spectrum significantly. at least for the typical parameters taken here.," Thus $L_{\rm SSC}/L\approx 1/[(1+x)\epsilon430(\nu_{\rm cut}/\nu_{\rm b})^{\rm (p-2)}]\approx4310.01\epsilon^{-1}$, which implies that the SSC component can not change the observed soft $\gamma-$ ray spectrum significantly, at least for the typical parameters taken here."432 GRBs are characterized by emission in the few hundred keV ranges with a non-thermal spectrum. X-ray. emission is weaker only a few percent of the energy is emitted below 10 keV and prompt emission at lower energies has not been observed. so far.," GRBs are characterized by emission in the few hundred $\rm keV$ ranges with a non-thermal spectrum, X-ray emission is $-$ only a few percent of the energy is emitted below 10 keV and prompt emission at lower energies has not been observed so far."433 One exception is the optical [Las= accompanying with CRB 990123 CXkerlofet al., One exception is the optical flash accompanying with GRB 990123 (Akerlof et al.434 1999). which is believed to be powered by the reverse shock (Sari Piran 1999).," 1999), which is believed to be powered by the reverse shock (Sari Piran 1999)."435 If such emission is the low-energv tail of the 5 ray emission.the light curves in the dillerent energy. baneWu. should be highly correlated. which is not the case (Sari Piran 1999).," If such emission is the low-energy tail of the $\gamma-$ ray emission,the light curves in the different energy bands should be highly correlated, which is not the case (Sari Piran 1999)."436 Akerlof et al. (, Akerlof et al. (4372000) have performed a search for optical counterparts to six GRBs with location errors of l square degree or better. but no optical counterpart has,"2000) have performed a search for optical counterparts to six GRBs with location errors of 1 square degree or better, but no optical counterpart has"438 , 439 Photometric redshift surveys oller a route to clelincating the larec-scale structure of the Universe that is increasingly competitive with spectroscopic redshift surveys (Buclavari et 22003: Seo Eisenstcin Amendola. Querecllini Ciallones 2004: Dolnev. Jain Takada 2004: Blake Bridle 2005: Phleps et 22006: Zhan et 22006. Blake et 22007: Padimanabhan et 22007).," Photometric redshift surveys offer a route to delineating the large-scale structure of the Universe that is increasingly competitive with spectroscopic redshift surveys (Budavari et 2003; Seo Eisenstein 2003; Amendola, Quercellini Giallongo 2004; Dolney, Jain Takada 2004; Blake Bridle 2005; Phleps et 2006; Zhan et 2006, Blake et 2007; Padmanabhan et 2007)."440 The ease with which modern imaging surveys can nmap large areas of sky το faint magnitude limits compensates for the absence of precise (but time-consuming) spectroscopic redshilt measurements for individual galaxies., The ease with which modern imaging surveys can map large areas of sky to faint magnitude limits compensates for the absence of precise (but time-consuming) spectroscopic redshift measurements for individual galaxies.441 An absolute pre-requisite. however. is the availability of high-quality photometric galaxy. recishifts with known error distributions (established for example via spectroscopy of sub-samples). together with accurate survey photometric calibration over large. angles of sky.," An absolute pre-requisite, however, is the availability of high-quality photometric galaxy redshifts with known error distributions (established for example via spectroscopy of sub-samples), together with accurate survey photometric calibration over large angles of sky."442 Recent observational efforts have enabled both of these criteria to be satisfied., Recent observational efforts have enabled both of these criteria to be satisfied.443 The Sloan Digital Sky Survey (SDSS: York ct 22000) has now provided. an accurately-calibrated imaging dataset over roughly a filth of the sky. which can be used to extract samples of galaxies in a uniform. manner.," The Sloan Digital Sky Survey (SDSS; York et 2000) has now provided an accurately-calibrated imaging dataset over roughly a fifth of the sky, which can be used to extract samples of galaxies in a uniform manner."444 In particular. a photometric catalogue of Liuninous Reel Galaxies (LRGs) can be reaclily extracted: using a series of well-understood. colour and magnitude cuts (Eisenstein et 22001).," In particular, a photometric catalogue of Luminous Red Galaxies (LRGs) can be readily extracted using a series of well-understood colour and magnitude cuts (Eisenstein et 2001)."445 Owing to their high luminosity ancl typical residence in the most massive dark matter haloes. LCs," Owing to their high luminosity and typical residence in the most massive dark matter haloes, LRGs"446(Város&Dwel1999:Wolf.IIlennig.Steckhun1999:Biauchi.Davies.&Alton— 2000).,"\citep{var99, wol99, bia00b}."447. Including the nuon-equilibriun enmuüssiou and aromatic feature eniüssion is much harder and. as a result. requires a siguificaut amount of CPU time.," Including the non-equilibrium emission and aromatic feature emission is much harder and, as a result, requires a significant amount of CPU time."448 Due to the complexity of the nou-equilibrimn aud aromatic feature cussion. someÉc- models use a sihapli&ed (Silvactal.1998) and/or empirical approach to includiug them.," Due to the complexity of the non-equilibrium and aromatic feature emission, some models use a simplified \citep{sil98} and/or empirical approach to including them."449 The model described iu this oper aud a companion paper (Misseltetal...Ww2000a). can idle arbitrary dust distributions aud fully iucludes. all lee dust emission components sclf-cousistcutly., The model described in this paper and a companion paper \citep{mis00} can handle arbitrary dust distributions and fully includes all three dust emission components self-consistently.450 The DIRTY model (DustI Radiative Transfer. Yeah!)," The DIRTY model (DustI Radiative Transfer, Yeah!)"451 erew out of spherically sviuuetric models which were used ο study reflection nebulae (Wittetal.1982:Cordon1991:Calzettietal. 1995).," grew out of spherically symmetric models which were used to study reflection nebulae \citep{wit82,gor94,cal95}."452. Using Monte Carlo techniques. hese models computed the radiative transfer through spherical shells of dust illuniuated by poiut sources.," Using Monte Carlo techniques, these models computed the radiative transfer through spherical shells of dust illuminated by point sources."453 The nodel used by Cordonetal.(1991) allowed for multiple ilhuuinatiug stars arbitrarily distributed throughout a spherical nebula aud the images of such a system cou © constructed for arbitrary lines-of-sight., The model used by \citet{gor94} allowed for multiple illuminating stars arbitrarily distributed throughout a spherical nebula and the images of such a system could be constructed for arbitrary lines-of-sight.454 As such. the Cordonetal.(1991) model is the direct ancestor of tl DIRTY model.," As such, the \citet{gor94} model is the direct ancestor of the DIRTY model."455 It is iuportaut to note that the aleorithiu used by Gordonetal.(1991).. while eivine the correct otal scattered leht value. gave too fat a distribution of scattered Πο across the system.," It is important to note that the algorithm used by \citet{gor94}, while giving the correct total scattered light value, gave too flat a distribution of scattered light across the system."456 The correct algorithiu or efücient computation of the appearance of a svsteni or a particular lince-ofsight is described by. Yuset-Zaceh.Morris.&White (1981)., The correct algorithm for efficient computation of the appearance of a system for a particular line-of-sight is described by \citet{yus84}.457" The motivation for the DIRTY model erew out of he conference ""Dust Survival iu Iuterstellar/Iutergalactic Media” held at the Space Telescope Scicuce Iustitute iu 1991.", The motivation for the DIRTY model grew out of the conference “Dust Survival in Interstellar/Intergalactic Media” held at the Space Telescope Science Institute in 1994.458 One of the major concerns at this couferencee was hat all Moute Carlo radiative transter models at that time asstumed a smooth distribution of dust. vet the interstellar uediunu is known to be chuupyv over a large range of size scales (Colomb.Poppel.&IIeiles.1980:Scalo1990:Rosen&Dregnau 1995).," One of the major concerns at this conference was that all Monte Carlo radiative transfer models at that time assumed a smooth distribution of dust, yet the interstellar medium is known to be clumpy over a large range of size scales \citep{col80, sca90, ros95}."459 We coustructed the DIRTY uodel to answer this concern., We constructed the DIRTY model to answer this concern.460 The main change was to nove from splierical shells to rectangular cells as the basic nuit of the dust censity distribution., The main change was to move from spherical shells to rectangular cells as the basic unit of the dust density distribution.461 Usine the simple system of a spherical nebula with a ceutral illuminating star. Witt&Cordon(1996) explored the differences between the radiative trausfer in μου aud chuupy 3-dimensional dust distributions.," Using the simple system of a spherical nebula with a central illuminating star, \citet{wit96} explored the differences between the radiative transfer in smooth and clumpy 3-dimensional dust distributions."462 The implications of chuupy dust for galaxies were discussed by Witt&Cordon(2000) using the concept of spherical galactic enviroments., The implications of clumpy dust for galaxies were discussed by \citet{wit00} using the concept of spherical galactic environments.463 The DIRTY model has beeu applied to starburst ealaxics (Gordonetal.1997.2000).. spiral galaxies al. 1998).. the UN. Cen reflection nebula (Clavtonct 19993.. aud the nucleus of M33 (Gordonetal.1999).," The DIRTY model has been applied to starburst galaxies \citep{gor97,464gor00}, spiral galaxies \citep{kuc98}, the UW Cen reflection nebula \citep{cla99}, and the nucleus of M33 \citep{gor99}."465. The DIRTY model was constructed to compute the radiative transter of photons from arbitrary distributions of photon ciuitters through arbitrary distributions of dust., The DIRTY model was constructed to compute the radiative transfer of photons from arbitrary distributions of photon emitters through arbitrary distributions of dust.466 This model self-cousisteutlv models the scattering aud absorption of photous through dust aud the re-cuiissiou of photous from dust., This model self-consistently models the scattering and absorption of photons through dust and the re-emission of photons from dust.467 The algorithm for the radiative transfer. including polarization. is based onu the work of Witt(1977).. Yusef-Zadeh.Morris.&White.(C198 D).. and Code&Whitney(1995).," The algorithm for the radiative transfer, including polarization, is based on the work of \citet{wit77}, \citet{yus84}, and \citet{cod95}."468.. The details of this aleorithin are the subject of this paper., The details of this algorithm are the subject of this paper.469 The re-ciuission of cucrey absorbed by the dust is the subject of a companion paper (Misseltetal.2000a).., The re-emission of energy absorbed by the dust is the subject of a companion paper \citep{mis00}.470 The radiative transfer of the re-enütted plotous is handled by the same algorithm as the stellar photons., The radiative transfer of the re-emitted photons is handled by the same algorithm as the stellar photons.471 This requires an iterative procedure to account for dust absorption aud scattering of re-cinitted photons and their subsequent re-enüssiou., This requires an iterative procedure to account for dust absorption and scattering of re-emitted photons and their subsequent re-emission.472 The details of the algorithms for the dust ciission and iterative procedure are given by Misseltetal.(2000a)., The details of the algorithms for the dust emission and iterative procedure are given by \citet{mis00}.473. The soal of the DIRTY model i$ to compute the radiative. transfer of photous through arbitrary distributions of dust., The goal of the DIRTY model is to compute the radiative transfer of photons through arbitrary distributions of dust.474 The lack of svuuuctries motivated us to use Monte Carlo techniques which are based on the work of Witt(1077)... Yusef-Zadeh.Morris.&White(1981).. and Code&Whitney|(1995j).," The lack of symmetries motivated us to use Monte Carlo techniques which are based on the work of \citet{wit77}, \citet{yus84}, and \citet{cod95}."475. The forward scattering nature of dust erains (Gordonetal.1991.1997) aud the observed multi-phase characteristics of the distribution of dust stronely argue for radiative transfer uodels based ou Monte Carlo techniques.," The forward scattering nature of dust grains \citep{gor94, gor97} and the observed multi-phase characteristics of the distribution of dust strongly argue for radiative transfer models based on Monte Carlo techniques."476 Such techuiques rely on the probabilistic uuderstaudius of the iuteraction of a photon with a dust erain and sufficient computing oer to evaluate this interaction for many paths through he distribution of the dust., Such techniques rely on the probabilistic understanding of the interaction of a photon with a dust grain and sufficient computing power to evaluate this interaction for many paths through the distribution of the dust.477 This approach allows us to efficiently compute what a system of stars and dust will ook like for auv lue-ofsight., This approach allows us to efficiently compute what a system of stars and dust will look like for any line-of-sight.478" In addition to the aleorithiu described in rofsec,lgorithin 2.3. themodelrequirestheph ysicaldese viptiono, randomnumbergencrator,"," In addition to the algorithm described in \\ref{sec_algorithm}- \ref{sec_unc}, the model requires the physical description of the dust grain properties, the dust distribution, the distribution of photon emitters, and a pseudo-random number generator."479 The physical description of the dust grain propertics Is eiven by the waveleneth dependent behavior of the dust optical depth. albedo. aud scattering phase function.," The physical description of the dust grain properties is given by the wavelength dependent behavior of the dust optical depth, albedo, and scattering phase function."480 The optical depth determines the probability of a photon interaction with a dust erain. the albedo determines the probability of the dust erain scattering (or absorbiug) the photon. and the scattering phase fiction gives the probability of the photon being scattered at a specific anele as well as the change in the polarization state of the photon as a result of the scattering.," The optical depth determines the probability of a photon interaction with a dust grain, the albedo determines the probability of the dust grain scattering (or absorbing) the photon, and the scattering phase function gives the probability of the photon being scattered at a specific angle as well as the change in the polarization state of the photon as a result of the scattering."481 We have taken the plivsical description of the dust properties from work by Claytonal.(2000) and Ita.Martin.&Ποια(1991)., We have taken the physical description of the dust properties from work by \citet{cla00} and \citet{kim94}.482. Claytonetal(2000). used MEM techniques to model the size distribution of dust eraius for dust extinction curves in the ADlkv Wax. Large Maecllanic Cloud. aud Simall Magellauic Cloud.," \citet{cla00} used MEM techniques to model the size distribution of dust grains for dust extinction curves in the Milky Way, Large Magellanic Cloud, and Small Magellanic Cloud."483 This work provides albedos aud scattering phase functions appropriate for the range of known imterstellar dust extinction curves., This work provides albedos and scattering phase functions appropriate for the range of known interstellar dust extinction curves.484 The DIRTY πού allows for arbitrary distributions of ust limited only by the amount of memory available to store the distribution., The DIRTY model allows for arbitrary distributions of dust limited only by the amount of memory available to store the distribution.485 This is accomplished by represcuting the dust distribution with a 3-dimensional erid., This is accomplished by representing the dust distribution with a 3-dimensional grid.486 Each evid cell represcuts a region of uniforin dust density., Each grid cell represents a region of uniform dust density.487 Thus. any dust eeomioetry can be represeuted with the smallest scale of iuhoimiogeneitv being the size of a erid cell.," Thus, any dust geometry can be represented with the smallest scale of inhomogeneity being the size of a grid cell."488 The physical dimensious of each axis of the erid are specified by separate l-dineusional arrays., The physical dimensions of each axis of the grid are specified by separate 1-dimensional arrays.489 This allows the pliysical dimensious of one axis to vary making it possible to efficiently model both cubical gcometrics as well as thin panucake-like ecometrics., This allows the physical dimensions of one axis to vary making it possible to efficiently model both cubical geometries as well as thin pancake-like geometries.490 In απο. this econmetrv allows for the represcutation of imulti-pliase or chuupy dust distributions.," In addition, this geometry allows for the representation of multi-phase or clumpy dust distributions."491 Iu the siuplest form. this is a two-phase medium with high-density clumps aud a low density inter-clunip region.," In the simplest form, this is a two-phase medium with high-density clumps and a low density inter-clump region."492 This type of dust distribution, This type of dust distribution493a consequence the signal to noise ratio (SNR) for most observations was not hieh enough to provide strinecut ower limits for separation aud Aim.,a consequence the signal to noise ratio (SNR) for most observations was not high enough to provide stringent lower limits for separation and $\Delta m$.494 We report here the yOSITIVE restIts obtained for two stars. ΠΟ 35515 aud IID 2901922. for which we measured separation. Am iud oositiou auele. and we eive the upper liuts we could attain for soue other cauclicdates.," We report here the positive results obtained for two stars, HD 38545 and HD 290492, for which we measured separation, $\Delta m$ and position angle, and we give the upper limits we could attain for some other candidates."495 The filters chosen for the observation were tuned to natch bothi the characteristics of the objects axd the SECINE concliΊος experienced durius the two nights., The filters chosen for the observation were tuned to match both the characteristics of the objects and the seeing conditions experienced during the two nights.496" We decided to lise he intermediate baie filters b aud y of he Strónuugren xvsteui and a dnuurow baud IL, filter or the very bright star TTD 38515.", We decided to use the intermediate band filters $b$ and $y$ of the Strömmgren system and a narrow band $_{\alpha}$ filter for the very bright star HD 38545.497 The expostre tine of cach specsle frame was 20 WIS for all stars observed. includiug those used for he fiel of view calibratioL and runs of 3000 freWes were ertqucd. cach with a toal iuteeration time o 60 sccolls per run.," The exposure time of each speckle frame was 20 ms for all stars observed, including those used for the field of view calibration, and runs of 3000 frames were performed, each with a total integration time of 60 seconds per run."498 Depending onu seciis conditioi aud onu the brightLess of the target star. up to 10 runs per olject were ortluec.," Depending on seeing conditions and on the brightness of the target star, up to 10 runs per object were performed."499 For cac hooject. we selected a reference sine star iu order to accmire the Specke Transfer Ficlon (STF) neeed to decouvove the atmospheric disturbance TOlu the power spectruu of the oject.," For each object, we selected a reference single star in order to acquire the Speckle Transfer Function (STF) needed to deconvolve the atmospheric disturbance from the power spectrum of the object."500 Since the behaviour oftre sccing Is variable with a time scale that may be oftre order of müiuutes. aud also depeuds on the zenith distance. we selected a suitabe STF star of comparable magnitude within few degrees of each target. aud we switched between them iaw times. thus allowing the best possible homogenceitv iu terms of temporal seciug variations.," Since the behaviour of the seeing is variable with a time scale that may be of the order of minutes, and also depends on the zenith distance, we selected a suitable STF star of comparable magnitude within few degrees of each target, and we switched between them many times, thus allowing the best possible homogeneity in terms of temporal seeing variations."501 We also selected two dotble stars having wellkuown orbital parameters for determining the detectors scale anc orientation. namcly ADSTsl AB aud ADS6650 AB. for which the orbital parameters are taken from Cole et al. (," We also selected two double stars having well–known orbital parameters for determining the detector's scale and orientation, namely ADS784 AB and ADS6650 AB, for which the orbital parameters are taken from Cole et al. ("5021992) aud Sodderhjcliu (1999) respectively aud which were observed with all the three filters meutioned above.,1992) and Södderhjelm (1999) respectively and which were observed with all the three filters mentioned above.503 The specke facility. after the cud of cach run. provides the accumuuated power spectrum of the collected speckle frames.," The speckle facility, after the end of each run, provides the accumulated power spectrum of the collected speckle frames."504" Ti6 power spectru nos civied bv the STE obtained froni observations of a nearby sar. canceliug out in this wav the contribution o tho atiuosphoric tualπο... affecting f10 ¢servation,"," The power spectrum is divided by the STF obtained from observations of a nearby star, canceling out in this way the contribution of the atmospheric turbulence affecting the observation."505 TUs lage ποprocessiig ds also need bot1 for removing some featires caused by t1C possible re)etitive noise mduc‘od ou the ceral Sigua axd to eliminate a typical crosssraped distirbince occurri when the specsle Hage of the olject Is lot «ntielv contained in the camera feld of view., This image pre–processing is also needed both for removing some features caused by the possible repetitive noise induced on the camera signal and to eliminate a typical cross–shaped disturbance occurring when the speckle image of the object is not entirely contained in the camera field of view.506 The power spec is then iuverte via Fast Fourier Trausorm (FFT). the autocorrelation function (ACF) of the brielHOSS distribution of the astronomical target is obtained.," The power spectrum is then inverted via Fast Fourier Transform (FFT), and the autocorrelation function (ACF) of the brightness distribution of the astronomical target is obtained."507 T it case of binary stars. the ACE. shows the characteris behaviour of a central peak with two opposite a svunnanietrie secondary peaks (see Fig.l)).," In the case of binary stars, the ACF shows the characteristic behaviour of a central peak with two opposite and symmetric secondary peaks (see \ref{fig:hd38545}) )."508 The distance )ctween the central peal and oue of the secondary. oues is the separation between the two compoucuts while the »ositiou angle is given by the orientation of the secondary oeak with 1807 uucertaintv., The distance between the central peak and one of the secondary ones is the separation between the two components while the position angle is given by the orientation of the secondary peak with $180^{\circ}$ uncertainty.509 The center of he secoudary )eaks ds retrieved bv fting a paraboloid with a sub.pixel »ecision., The center of the secondary peaks is retrieved by fitting a paraboloid with a sub–pixel precision.510 The maenitude difference is estimated * coniparine he iuteusities of the secondary aud the €nutral peaks., The magnitude difference is estimated by comparing the intensities of the secondary and the central peaks.511 The CLOCYSV contaimec in the two secoinary peaks ds σοιted by intcerating the AC'F signal deinited bv the xuabolokal fiting. and the gne procediwe ds applied otre central peak with is proper paralxJloidal fittiug.," The energy contained in the two secondary peaks is computed by integrating the ACF signal delimited by the paraboloidal fitting, and the same procedure is applied to the central peak with its proper paraboloidal fitting."512 The central pixel of the ACF is affected bv a large a1nount of spirlous signal eiveu o» the correlation of he noise and t16 background., The central pixel of the ACF is affected by a large amount of spurious signal given by the correlation of the noise and the background.513 In the integration process. its value has |jen substituted with that estimated by he htted paraoloid at the same position.," In the integration process, its value has been substituted with that estimated by the fitted paraboloid at the same position."514 Finally. t1ο conrALISO1 between the euergies o the secondary peaks aud hat of he ceutral one gives the magnitude difference.," Finally, the comparison between the energies of the secondary peaks and that of the central one gives the magnitude difference."515 The relative errors are compued using the errors of t parabolokal fittine., The relative errors are computed using the errors of the paraboloidal fitting.516 The nmavourable weather couditious (poor seclis ax stroug wind) divine the observatiois seriously aftered the instrument perfornance., The unfavourable weather conditions (poor seeing and strong wind) during the observations seriously affected the instrument performance.517 Even if the speckle iuterCronieIV is not as sensible to the seclue as other lüeh aneular resolution techuiues (io. Adapive Optics). the ow SNR achieved. surely compromised both the possiültv to detect very close Mary osvstenas (separation -y! 1). and the accuracy of the maguitiue difference nieasurenaents.," Even if the speckle interferometry is not as sensible to the seeing as other high angular resolution techniques (i.e. Adaptive Optics), the low SNR achieved surely compromised both the possibilty to detect very close binary systems (separation $<0\farcs{1}$ ), and the accuracy of the magnitude difference measurements."518 [Llowever. the obtained data are quite ClICOlraging and demonstrate that also when sccing," However, the obtained data are quite encouraging and demonstrate that also when seeing"519joint probability densitwv (for instance. 2).L0.d)) then describes the probabilitv (hat a randomlv-chosen target star in à photometric survey is a main-sequence eclipsing binary with properties near the given ones.,"joint probability density (for instance, $P(m_0, \Pi, \delta, d)$ ) then describes the probability that a randomly-chosen target star in a photometric survey is a main-sequence eclipsing binary with properties near the given ones."520 To obtain an estimate of the number of detections to be expected in the target sample from this class of object. one integrates this density over the interesting ranges of observable parameters aud multiplies by the number of target stars in (he sample.," To obtain an estimate of the number of detections to be expected in the target sample from this class of object, one integrates this density over the interesting ranges of observable parameters and multiplies by the number of target stars in the sample."521 Marginal probability densities (integrated over all parameters but one) are also useful. ancl some of these will be displaved below.," Marginal probability densities (integrated over all parameters but one) are also useful, and some of these will be displayed below."522 Unfortunately. the joint probability density in terms of (he observable parameters is nol ordinarily available.," Unfortunately, the joint probability density in terms of the observable parameters is not ordinarily available."523 Instead. one has empirical estimates (e.g.. Duquennoy&Mavor(1991).. henceforth called DM) of probability densities lor “physical” parameters taken sinely. such as PUT). PGno). P(cos7). and P(q). where / is the orbital inclination to the line of sight. and qis (he binary mass ratio.," Instead, one has empirical estimates (e.g., \citet{duq91}, henceforth called DM) of probability densities for “physical” parameters taken singly, such as $P(\Pi)$, $P(m_0)$, $P(\cos i)$, and $P(q)$, where $i$ is the orbital inclination to the line of sight, and $q$ is the binary mass ratio."524 To make these useful. one must [irst assume independence among (he various physical parameters. so Chat the joint density max be written as a product of the individual densiües.," To make these useful, one must first assume independence among the various physical parameters, so that the joint density may be written as a product of the individual densities."525 One must then transform the density (ng.IH.q.cos7) into a densitv on the observable parameters P(ng.IL.0.4).," One must then transform the density $P(m_0, \Pi, q, \cos i)$ into a density on the observable parameters $P(m_0, \Pi, \delta, d)$."526 Details of this process for the various cases will be published elsewhere: for current purposes. all (hat matters is that the transformations contain no essential singularities.," Details of this process for the various cases will be published elsewhere; for current purposes, all that matters is that the transformations contain no essential singularities."527 More important are the empirical distributions. the relations among stellar properties. aud the assumptions invoked to derive the initial joint. distributions and (he (transformations.," More important are the empirical distributions, the relations among stellar properties, and the assumptions invoked to derive the initial joint distributions and the transformations."528 These are described below., These are described below.529 ] characterized main-sequence binaries ((vpe MSU) by the 4 physical parameters discussed above. viz.. I.q.cos[myid.," I characterized main-sequence binaries (type MSU) by the 4 physical parameters discussed above, viz., $\{ m_0, \Pi, q, \cos i \}$."530 1 estimated. Pn) using the local main-sequence luminosity [function /NCM4-) giving (he space densitv of stars as a function of their V absolute magnitude. ihe mass-huminositv relation A(mg). and color-color relations (e.g. Mg(My). where Mg is the absolute magnitude for R-bancl photometry).," I estimated $P(m_0)$ using the local main-sequence luminosity function $N(M_V)$ giving the space density of stars as a function of their V absolute magnitude, the mass-luminosity relation $M_V(m_0)$, and color-color relations (e.g. $M_R(M_V)$, where $M_R$ is the absolute magnitude for R-band photometry)."531 E obtained all of these relations from the tables in Cox(2000).. except that I adjusted the Iuminosity function to provide better agreement with the observed. histogram of J-Ix color. for a field Iving on (he ealactic plane in Cvgnus. overlapping the proposed [field for the Kepler mission.," I obtained all of these relations from the tables in \citet{cox00}, except that I adjusted the luminosity function to provide better agreement with the observed histogram of J-K color, for a field lying on the galactic plane in Cygnus, overlapping the proposed field for the Kepler mission."532 Because of interstellar ex(ünetion. caleulating P(imig) also requires knowledge of the photometric banclpass and limiting magnitude appropriate to the survey being modeled. and of D... defined as (he typical distance needed to accumulate | magnitude of interstellar extinction in the V. band.," Because of interstellar extinction, calculating $P(m_0)$ also requires knowledge of the photometric bandpass and limiting magnitude appropriate to the survey being modeled, and of $D_e$, defined as the typical distance needed to accumulate 1 magnitude of interstellar extinction in the V band."533" I used D,=1000 pc. and assumed that all observations are in (he galactic plane."," I used $D_e = 1000$ pc, and assumed that all observations are in the galactic plane."534 I took (II) and P(q) frou DM. ancl assumed the fraction of spatially unresolved main-sequence stus having 2 or more components to be 0.49. in accord with their estimate.," I took $P(\Pi)$ and $P(q)$ from DM, and assumed the fraction of spatially unresolved main-sequence stars having 2 or more components to be 0.49, in accord with their estimate."535 I assumed orbital axes {ο be randomly oriented in space. eiving (cos/)=I.," I assumed orbital axes to be randomly oriented in space, giving $P(\cos i) = 1$."536 Finally. I adopted several simplifications to facilitate the caleulations.," Finally, I adopted several simplifications to facilitate the calculations."537 The most important of (hese were: (1) Lignored the luminosity of the secondary component. relative to that of the primary. (," The most important of these were: (1) I ignored the luminosity of the secondary component, relative to that of the primary. ("5382) I simplified the mass-raclius relation on (he main sequence. (aking radius (in solar units) to be numerically equal to mass,"2) I simplified the mass-radius relation on the main sequence, taking radius (in solar units) to be numerically equal to mass"539r.=—1.57 for a fixed halo mass).,$_{c}=-1.57$ for a fixed halo mass).540 While the density is not expected (to increase during mereime. Iernequist et al. (," While the density is not expected to increase during merging, Hernquist et al. ("5411993) propose a scheme whereby (he densitw decreases while the dispersion remains constant.,1993) propose a scheme whereby the density decreases while the dispersion remains constant.542 Dalcanton Ilogan interpret this as a result of more violent merging so that different merging histories al earlier times could account [or the variations in central densitv seen now., Dalcanton Hogan interpret this as a result of more violent merging so that different merging histories at earlier times could account for the variations in central density seen now.543 More observations are required to determine if (he apparent dichotomy in central densitv is real ancl if so what its origin is., More observations are required to determine if the apparent dichotomy in central density is real and if so what its origin is.544 For example. if we assume that the dichotomy extends to galaxy. clusters. then a model with the same mass as À1689 but with one tenth the central density will have its gas entropy floor raised by ~2.8.," For example, if we assume that the dichotomy extends to galaxy clusters, then a model with the same mass as A1689 but with one tenth the central density will have its gas entropy floor raised by $\sim2.8$."545 Such a change in central gas entropy floor is one characterization cdifferentiating cooling flow clusters from non cooling flow clusters., Such a change in central gas entropy floor is one characterization differentiating cooling flow clusters from non cooling flow clusters.546 The error bars in each panel of Fig., The error bars in each panel of Fig.547" 3 were calculated bv assuming an empirical approximation to  (equation (4)) in terms of the central density (ie. 5~L.80p,5) and variables p, and i, were (hen treated as independent with estimated uncertainties of £0.25 and £0.10 respectively.", 3 were calculated by assuming an empirical approximation to $\gamma$ (equation (4)) in terms of the central density (i.e. $\gamma\sim1.80\rho^{-0.0753}_{o}$ ) and variables $\rho_{o}$ and $_{c}$ were then treated as independent with estimated uncertainties of $\pm0.25$ and $\pm0.10$ respectively.548 Rotation curves derived from the model ancl the NEW profile can be very similar (e.g. the two A class galaxies in 823.1) while according to the model the data appear incompatible with standard CDM cosmological simulations which do not predict 'observable-sized! cores., Rotation curves derived from the model and the NFW profile can be very similar (e.g. the two A class galaxies in 3.1) while according to the model the data appear incompatible with standard CDM cosmological simulations which do not predict `observable-sized' cores.549 The similarity is most pronounced among objects in the hieh central density group., The similarity is most pronounced among objects in the high central density group.550 One property of our cored models which may be relevant to the missing satellite’ problem is that these structures ave more vulnerable to tidal disruption than the NEW models. especially those halos with low central densities.," One property of our cored models which may be relevant to the `missing satellite' problem is that these structures are more vulnerable to tidal disruption than the NFW models, especially those halos with low central densities."551" From this work a relation has been determined between Q, and (he mass of dark matter halos over a range from ~10? to ~105 AL..", From this work a relation has been determined between $_{o}$ and the mass of dark matter halos over a range from $\sim10^{9}$ to $\sim10^{15}$ $_{\odot}$.552" An observational challenge is to find the lower mass limit to objects with dark matter halos thus providing an estimate of the primordial value of Q (Q,).", An observational challenge is to find the lower mass limit to objects with dark matter halos thus providing an estimate of the primordial value of Q $_{p}$ ).553" Knowledge of Q, allows the determination of the mass of the dark matter particle (assuming that the particles are thermal) since then Q is proportional to the fourth power of the particle mass (e.g. equating the value of Q, found above for Fornax with Q, provides a lower limit on this mass of 431 ev).", Knowledge of $_{p}$ allows the determination of the mass of the dark matter particle (assuming that the particles are thermal) since then Q is proportional to the fourth power of the particle mass (e.g. equating the value of $_{o}$ found above for Fornax with $_{p}$ provides a lower limit on this mass of 431 ev).554 An additional constraint comes [rom an analvsis of the power spectrum of the Lya forest., An additional constraint comes from an analysis of the power spectrum of the $\alpha$ forest.555 From (his one can determine (he [ree streaming length (A5.) of the dark matter particle., From this one can determine the free streaming length $\lambda_{fs}$ ) of the dark matter particle.556 This quantity in turn is simply related (in the case of thermal particles) to the particle mass., This quantity in turn is simply related (in the case of thermal particles) to the particle mass.557 A recent determination of a limit on Ars by Seljak et al. (, A recent determination of a limit on $\lambda_{fs}$ by Seljak et al. (558"2006) implies a thermal dark matter particle mass limit of >10 kev (Le. Q,>1 which according to our scaling relation above implies dark matter halos with masses as low as ~10° AL. ).",2006) implies a thermal dark matter particle mass limit of $>10$ kev (i.e. $_{p}>1$ which according to our scaling relation above implies dark matter halos with masses as low as $\sim10^3$ $_{\odot}$ ).559 An attractive alternative to the above ‘classical’ WDM scenario has been. proposed bv Strigari et al. (, An attractive alternative to the above `classical' WDM scenario has been proposed by Strigari et al. (5602007).,2007).561 IE the particles are non-thermally produced by the decay of a, If the particles are non-thermally produced by the decay of a562lobes (e.g. RSOL). and the kinetic jet power (CL93).,"lobes (e.g. RS91), and the kinetic jet power (CF93)."563 This is likely to be of the same nature of similar correlations between the radio luminosity and the emission of narrow lines on extended. scales (e.g. Baum LHeckman 1989a.b).," This is likely to be of the same nature of similar correlations between the radio luminosity and the emission of narrow lines on extended scales (e.g. Baum Heckman 1989a,b)."564" The large scatter we find in the correlation is probably due to the non-simultaneous racio and X-ray data which enter in our calculation. as Lig, depends rather strongly on Pi."," The large scatter we find in the correlation is probably due to the non-simultaneous radio and X-ray data which enter in our calculation, as $\lk$ depends rather strongly on $F_{\rm x}$."565" In any case. the similarity of £j, and Lia, seems to indicate that a common factor regulates both the luminosity dissipatedduring the accretion phase and the kinetic power of the jet."," In any case, the similarity of $\lk$ and $\li$ seems to indicate that a common factor regulates both the luminosity dissipated during the accretion phase and the kinetic power of the jet."566 This clearly does not univocally define the factor responsible. however we suggest that this can be a piece of evidence in favour of the Κον role of magnetic fields.," This clearly does not univocally define the factor responsible, however we suggest that this can be a piece of evidence in favour of the key role of magnetic fields."567 Lt is also interesting to point out that the estimate of the broad. line luminosity can have important. predictive power on the models for the generation of the XN and especially 5. rav radiation in dilferent classes of blazars (sec e.g. the review by Sikora 1994) which stress the importance of Comptonization of the cilfuse radiation feld through which the jet propagates., It is also interesting to point out that the estimate of the broad line luminosity can have important predictive power on the models for the generation of the X– and especially $\gamma$ –ray radiation in different classes of blazars (see e.g. the review by Sikora 1994) which stress the importance of Comptonization of the diffuse radiation field through which the jet propagates.568 It should be however noticed that here the estimates of thejet Doppler factor implicitly assume that the XNray emission is mostly. produced. by the SSC mechanism., It should be however noticed that here the estimates of the jet Doppler factor implicitly assume that the X–ray emission is mostly produced by the SSC mechanism.569 Polarization information in the X.ray band (e.g. Celotti Matt. 1994) will be therefore extremely important to constrain the emission mocels., Polarization information in the X–ray band (e.g. Celotti Matt 1994) will be therefore extremely important to constrain the emission models.570 We thank the referee. 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V., Moles M., 1989, MNRAS, 239, 75 Pringle J., 1993, in Astrophysical Jets, Burgarella D., Livio M., O'Dea C., eds. ("580Cambridge University Press). p. 1 tawlines S.C... Saunders ItDE... 1991. Nature. 349. 138 (15891) toevnolds €.S.. Fabian AC... Celotti A. Rees MJ... 1996 AINILCAS. in press üchstone D.O.. Schmidt M. 1980 ApJ. 235. 361,"Cambridge University Press), p. 1 Rawlings S.G., Saunders R.D.E., 1991, Nature, 349, 138 (RS91) Reynolds C.S., Fabian A.C., Celotti A., Rees M.J., 1996, MNRAS, in press Richstone D.O., Schmidt M. 1980, ApJ, 235, 361"581 The closest event of massive star formation Is occurring at present in the direction of the Galactic anticenter (/=209°.5 —19°). in the Orion constellation.," The closest event of massive star formation is occurring at present in the direction of the Galactic anticenter $l=209^\circ, b=-19^\circ$ ), in the Orion constellation."582 The Orion Nebula (ON. M42) represents the most spectacular signature of star formation activity m this region.," The Orion Nebula (ON, M42) represents the most spectacular signature of star formation activity in this region."583 The ON ts a blister HII region carved into the OMC-1I giant molecular cloud by the UV flux emitted by a handful of OB stars. the so-called Orion citepMue08. odell..," The ON is a blister HII region carved into the OMC-1 giant molecular cloud by the UV flux emitted by a handful of OB stars, the so-called Orion \\citep{Mue08, odell}."584 The Trapezium stars are the most massive members of a rich G1z2000 members. Muenchetal. (2002))) cluster of young (1-3 Myr old. DaRioetal. (2010))) Pre-Main-Sequence objects (Orton Nebula Cluster. ONC).," The Trapezium stars are the most massive members of a rich $n\simeq 2000$ members, \citet{Mue02}) ) cluster of young (1-3 Myr old, \cite{DaRio10}) ) Pre-Main-Sequence objects (Orion Nebula Cluster, ONC)."585 Given its youth. vicinity. and low foreground extinction. the observed luminosity function. of the ONC can be converted into a true initial mass function with relatively modest assumptions (Muenchetal.2002.andreferencestherein)..," Given its youth, vicinity, and low foreground extinction, the observed luminosity function of the ONC can be converted into a true initial mass function with relatively modest assumptions \citep[and references therein]{Mue02}."586 It is largely for this reason that the Orton Nebula and its associated cluster are regarded as a critical benchmark for our uderstanding of the star formation process., It is largely for this reason that the Orion Nebula and its associated cluster are regarded as a critical benchmark for our understanding of the star formation process.587 In order to build a reliable luminosity function. especially in the substellar regime (brown dwarfs and planetary mass objects) and to explore its spatial variations with the distance from the cluster center. it is necessary to remove the contribution of non-cluster sources.," In order to build a reliable luminosity function, especially in the substellar regime (brown dwarfs and planetary mass objects) and to explore its spatial variations with the distance from the cluster center, it is necessary to remove the contribution of non-cluster sources."588 In principle. this requires the acquisition of thousand of spectra of faint sources distributed over the bright nebular background.," In principle, this requires the acquisition of thousand of spectra of faint sources distributed over the bright nebular background."589 On the other hand. the number of contaminant sources. both galactic and extragalactic. can be estimated using the most recent models for stellar and galaxy counts at various wavelegths.," On the other hand, the number of contaminant sources, both galactic and extragalactic, can be estimated using the most recent models for stellar and galaxy counts at various wavelengths."590 The main complication in this case arises from the presence of the OMC-1I. which provides a backdrop to the ONC of high and non-uniform extinction.," The main complication in this case arises from the presence of the OMC-1, which provides a backdrop to the ONC of high and non-uniform extinction."591 Deriving an accurate extinction map would be beneficial not only to better discriminate the ONC membership. but also to understand the 3-D4 distribution. of the cluster. still partially embedded within the ONC. and the evolutionary history of the region.," Deriving an accurate extinction map would be beneficial not only to better discriminate the ONC membership, but also to understand the 3-D distribution of the cluster, still partially embedded within the ONC, and the evolutionary history of the region."592 In this paper we present a reconstruction of the OMC-I extinetion map based on the analysis of the recent near-IR (NIR) source catalog of Robbertoetal.(2010) (RIO hereafter)., In this paper we present a reconstruction of the OMC-1 extinction map based on the analysis of the recent near-IR (NIR) source catalog of \citet{paperI} (R10 hereafter).593 In Section we briefly review the previous studies relevant to the Orion Nebula region., In Section we briefly review the previous studies relevant to the Orion Nebula region.594 In Section we illustrate our statistical method to disentangle background stars from the cluster population., In Section we illustrate our statistical method to disentangle background stars from the cluster population.595 By combining an estimate of the interstellar extinction affecting each contaminant star with the source count density. we derive the OMC-1 extinction map.," By combining an estimate of the interstellar extinction affecting each contaminant star with the source count density, we derive the OMC-1 extinction map."596 In Sect., In Sect.597 we apply a similar statistical procedure to the candidate cluster members. deriving an extinction map for the dust in the foreground Orion Nebula.," we apply a similar statistical procedure to the candidate cluster members, deriving an extinction map for the dust in the foreground Orion Nebula."598 Finally. in Sect.," Finally, in Sect."599 we compare our maps to previous studies. and we briefly discuss their main features and similarities to stellar distributions.," we compare our maps to previous studies, and we briefly discuss their main features and similarities to stellar distributions."600 A number of previous studies provide results relevant to the issue of the galactic reddening in the direction of OMC-1., A number of previous studies provide results relevant to the issue of the galactic reddening in the direction of OMC-1.601 Schlegeletal.(1998) (SFD98 hereafter) combined the COBE//DIRBE observations (100 aand 240 μπι) and the /RAS//ISSA observations (100 jim) to obtain a full-sky 100 mmap with ~6' resolution., \citet{Sch98} (SFD98 hereafter) combined the /DIRBE observations (100 and 240 ) and the /ISSA observations (100 ) to obtain a full-sky 100 map with $\sim6\arcmin$ resolution.602 On the basis of the correlation between the Mg line strength and the (8—V) color of elliptical galaxies. they were able to calibrate their column-density map toa E(B—V) color excess map.," On the basis of the correlation between the Mg line strength and the $(B-V)$ color of elliptical galaxies, they were able to calibrate their column-density map to a $E(B-V)$ color excess map."603 Their all-sky reddening map. available through the NASA/IPAC Infrared Science Dust Extinction Service web page. represents the benchmark for the following studies of our region.," Their all-sky reddening map, available through the NASA/IPAC Infrared Science Dust Extinction Service web page, represents the benchmark for the following studies of our region."604 The accuracy of the SFD98 maps has been analyzed by Arce&Goodman(1999).. who compared the extinction map of the Taurus dark cloud with the extinction maps obtained using," The accuracy of the SFD98 maps has been analyzed by \cite{Arce99}, who compared the extinction map of the Taurus dark cloud with the extinction maps obtained using"605"for 5<Nyx12, with the corresponding error bars (in our case in the optical, near-infrared and mid-infrared, between B and [8.0]; we note that the [24.0] filter is not used here).","for $5\le N_f\le 12$, with the corresponding error bars (in our case in the optical, near-infrared and mid-infrared, between B and [8.0]; we note that the [24.0] filter is not used here)."606" As we have already mentioned, we consider only data points with a flux S/N above 3."," As we have already mentioned, we consider only data points with a flux S/N above 3."607" Applying the method of L10 ($3), we are able to determine the rest-frame color (B-V) of our selected galaxies."," Applying the method of L10 3), we are able to determine the rest-frame color (B-V) of our selected galaxies."608" In Fig. 3,,"," In Fig. \ref{Fig:colors},"609" we display the average colors as a function of the age of the Universe when the galaxy is observed In this figure, we have also added the galaxies at z<2.5 from L10."," we display the average colors as a function of the age of the Universe when the galaxy is observed In this figure, we have also added the galaxies at $z<2.5$ from L10."610" The average gradient in color of the combined sample (including all galaxies in Fig. 3,,"," The average gradient in color of the combined sample (including all galaxies in Fig. \ref{Fig:colors},"611 0.8<z 3.8) is 0.0877+0.0093 Gyr!.," $0.8<z<3.8$ ) is $0.0877\pm6120.0093$ $^{-1}$."613" For the galaxies at z>2.5 analyzed in this paper, the gradient is 0.20+0.13 Gyr!."," For the galaxies at $z>2.5$ analyzed in this paper, the gradient is $0.20\pm6140.13$ $^{-1}$."615" As noted by L10, the gap in the galaxy data points in the lower right corner of Fig."," As noted by L10, the gap in the galaxy data points in the lower right corner of Fig."616 3 is at least partially an artifact of the sample intrinsic color bias as a function of redshift., \ref{Fig:colors} is at least partially an artifact of the sample intrinsic color bias as a function of redshift.617" The step at z«2.5 may be produced by the change in the color criterion to select EROs (z€ 2.5) or Z-EROS (z> 2.5), bearing in mind that our criteria for selecting Z-EROs emulates the colors of EROs at z=1.5 at higher redshifts (see §2)), hence we expect to find"," The step at $z\approx 2.5$ may be produced by the change in the color criterion to select EROs $z\le 2.5$ ) or Z-EROS $z>2.5$ ), bearing in mind that our criteria for selecting Z-EROs emulates the colors of EROs at $z=1.5$ at higher redshifts (see \ref{.criteria}) ), hence we expect to find"618lobe. down to about the level.,"lobe, down to about the level."619 ? have made a detailed empirical study of the WSRT primary beam. which shows significant four-fold symmetric structure out in the sidelobes (caused by the feed legs).," \citet{Popping-Braun:WSRT-beam} have made a detailed empirical study of the WSRT primary beam, which shows significant four-fold symmetric structure out in the sidelobes (caused by the feed legs)."620 More significantly. they have shown a quasi-periodic “ripple” in the off-axis beam gain as a function of frequency. with a period of ~17 MHz.," More significantly, they have shown a quasi-periodic “ripple” in the off-axis beam gain as a function of frequency, with a period of $\sim17$ MHz."621 This is commonly seen in the observed spectra of off-axis sources., This is commonly seen in the observed spectra of off-axis sources.622 Similarly to the WSRT cos* model. the VLA primary beam has a reasonable analytic approximation using Jine functions. which is valid to about the level of the main lobe (?)..," Similarly to the WSRT $\cos^3$ model, the VLA primary beam has a reasonable analytic approximation using Jinc functions, which is valid to about the level of the main lobe \citep{Uson-Cotton:VLA-beam}."623 ? has made electromagnetic simulations that show the sidelobe structure., \citet{Brisken:VLA-beam} has made electromagnetic simulations that show the sidelobe structure.624 What significantly complicates the VLA case tssquint (the beam pattern of the R and L receptors being offset w.r.t., What significantly complicates the VLA case is (the beam pattern of the R and L receptors being offset w.r.t.625 the pointing centre due to the feeds being off-axis). and parallactic angle rotation.," the pointing centre due to the feeds being off-axis), and parallactic angle rotation."626 An alt-az mount telescope. without a dish derotator such as that designed into ASKAP (?).. has an intrinsically time-variable beamshape in the /; frame. as the nominal beam pattern rotates with parallactic angle.," An alt-az mount telescope, without a dish derotator such as that designed into ASKAP \citep{ASKAP}, , has an intrinsically time-variable beamshape in the $lm$ frame, as the nominal beam pattern rotates with parallactic angle."627 Like any DDE. this causes significant spatial artefacts around off-axis sources that cannot be addressed by classical selfeal.," Like any DDE, this causes significant spatial artefacts around off-axis sources that cannot be addressed by classical selfcal."628 This has been a serious dynamic range limitation at the VLA. but some recent developments promise to alleviate the problem.," This has been a serious dynamic range limitation at the VLA, but some recent developments promise to alleviate the problem."629 ? describe a CLEAN-like algorithm (implemented in the Obit package) that corrects these artefacts during deconvolution: the RIME-derived AW-projection method of ?. can correct them during imaging., \citet{Uson-Cotton:VLA-beam} describe a CLEAN-like algorithm (implemented in the Obit package) that corrects these artefacts during deconvolution; the RIME-derived AW-projection method of \citet{SB:imageplane} can correct them during imaging.630 Note that both methods rely on an beam nodel. and have. to date. been only been applied to VLA data. for which the Brisken simulations provide a very detailed beam nodel.," Note that both methods rely on an beam model, and have, to date, been only been applied to VLA data, for which the Brisken simulations provide a very detailed beam model."631 It remains to be seen whether the more approximate nodels available for other instruments will prove to be a limiting factor., It remains to be seen whether the more approximate models available for other instruments will prove to be a limiting factor.632 The WSRT's equatorial mounts (and ASKAP's derotator) keep the beamshape stationary in the /m frame. thus avoiding this problem entirely.," The WSRT's equatorial mounts (and ASKAP's derotator) keep the beamshape stationary in the $lm$ frame, thus avoiding this problem entirely."633 A particularly troublesome situation arises when a sufficiently bright source is located in a sidelobe or near a null. where sky rotation causes rapid variation in the beam gain. and the accuracy of existing beam models ts low.," A particularly troublesome situation arises when a sufficiently bright source is located in a sidelobe or near a null, where sky rotation causes rapid variation in the beam gain, and the accuracy of existing beam models is low."634 Such sources have to be calibrated and subtracted separately. either via some kind of peeling procedure. or by using the differential gain approach described in Sect. 2.4.3..," Such sources have to be calibrated and subtracted separately, either via some kind of peeling procedure, or by using the differential gain approach described in Sect. \ref{sec:dEs}."635 Even at the WSRT. where rotation is not an issue and the beam gain remains (at least in principle) constant in time. sources in a sidelobe need to be treated very carefully. due to the rapid spectral variation caused by the 17 MHz ripple.," Even at the WSRT, where rotation is not an issue and the beam gain remains (at least in principle) constant in time, sources in a sidelobe need to be treated very carefully, due to the rapid spectral variation caused by the 17 MHz ripple."636 Instrumental polarization comes about due to the beam patterns of the two receptors being non-identical., Instrumental polarization comes about due to the beam patterns of the two receptors being non-identical.637 In RIME terms. this corresponds to E-Jones being diagonal rather than simply scalar: which causes an unpolarized off-axis source to “acquire” some Q (or V. if using circular receptors): The WSRT case is rather simple: the beamshape of each dipole is shghtly elongated rather than circularly symmetric.," In RIME terms, this corresponds to $E$ -Jones being diagonal rather than simply scalar: which causes an unpolarized off-axis source to “acquire” some $Q$ (or $V$, if using circular receptors): The WSRT case is rather simple: the beamshape of each dipole is slightly elongated rather than circularly symmetric."638 Since these beamshapes are stationary w.r.t., Since these beamshapes are stationary w.r.t.639" the sky. the net result is an ""apparent sky” with a non-uniform polarization response: Similarly to power beam attenuation. this effect can be removed (to the extent that the primary beam is known) via a linear correction to the final images."," the sky, the net result is an “apparent sky” with a non-uniform polarization response: Similarly to power beam attenuation, this effect can be removed (to the extent that the primary beam is known) via a linear correction to the final images."640 For the VLA. non-identical receptor beams are caused by the aforementioned squint: the squint offset rotates with parallactic angle (and thus as a function of time).," For the VLA, non-identical receptor beams are caused by the aforementioned squint; the squint offset rotates with parallactic angle (and thus as a function of time)."641 This leads to a rather complicated picture of instrumental polarization. but is essentially the same problem (with the same solutions) as primary beam rotation.," This leads to a rather complicated picture of instrumental polarization, but is essentially the same problem (with the same solutions) as primary beam rotation."642 Note that in contrast to the the WSRT case. the simulations of ? show that the VLA E-Jones has non-trivial elements on the off-diagonal.," Note that in contrast to the the WSRT case, the simulations of \citet{Brisken:VLA-beam} show that the VLA $E$ -Jones has non-trivial elements on the off-diagonal."643 This ts an example ofleakage., This is an example of.644. Leakage has been commonly associated with slight errors in dipole orientation. electromagnetic cross-talk. ete..," Leakage has been commonly associated with slight errors in dipole orientation, electromagnetic cross-talk, etc.,"645 and treated as a direction-independent effect (??):: Brisken’s results demonstrate that it is actually a DDE.," and treated as a direction-independent effect \citep{ME1,JEN:note185}; Brisken's results demonstrate that it is actually a DDE."646 Finally. it should be mentioned that the polarization aberration described by 9?) can also be treated as direction-dependent instrumental polarization (seePaperI.?.Sect.5.4)..," Finally, it should be mentioned that the polarization aberration described by \citet{Carozzi:ME3D} can also be treated as direction-dependent instrumental polarization \citep[see Paper I,][Sect.~5.4]{RRIME1}."647 The RIME makes it explicit that effects as (variable) primary beam attenuation. instrumental polarization. and leakage. which are treated separately Gf at all) in 2GC. can in fact be represented by a single Jones term. and treated via a single mechanism.," The RIME makes it explicit that effects as (variable) primary beam attenuation, instrumental polarization, and leakage, which are treated separately (if at all) in 2GC, can in fact be represented by a single Jones term, and treated via a single mechanism."648 Perhaps the most stark example of this is provided by aperture array beams. such as those of LOFAR (?)..," Perhaps the most stark example of this is provided by aperture array beams, such as those of LOFAR \citep{Yatawatta:LOFAR-beam}."649 With the dipoles of an aperture array fixed on the ground. £(/.i) towards any specific sky direction exhibits complex time-dependent behaviour in all four matrix elements.," With the dipoles of an aperture array fixed on the ground, $\jones{E}{}(l,m)$ towards any specific sky direction exhibits complex time-dependent behaviour in all four matrix elements."650 This completely blends the boundary between primary beams. leakage and instrumental polarization.," This completely blends the boundary between primary beams, leakage and instrumental polarization."651 All telescopes mispoint to some extent., All telescopes mispoint to some extent.652 This is caused by gravitational load. thermal expansion. wind pressure. errors in the drive mechanics or even the control software. etc.," This is caused by gravitational load, thermal expansion, wind pressure, errors in the drive mechanics or even the control software, etc."653In RIME terms. this can be represented by a station-dependent offset in the beam pattern. causing a nominally identical beamshape £ to produce a different response per station:,"In RIME terms, this can be represented by a station-dependent offset in the beam pattern, causing a nominally identical beamshape $\jones{E}{}$ to produce a different response per station:"654The low number density of the SDSS Luminous Rec Galaxy (LRG) samplesuggests that LRG pairs occupying the same dark matter halo can be separated [rom pairs occupying distinct dark matter halos with high fidelity.,The low number density of the SDSS Luminous Red Galaxy (LRG) sample that LRG pairs occupying the same dark matter halo can be separated from pairs occupying distinct dark matter halos with high fidelity.655 In (his paper we explore that intuition. and show that one-halo pairs can be identified with ~75% completeness and <27% contamination bv simple cuts in the (transverse separation Ar_ and LOS separation Ar).," In this paper we explore that intuition, and show that one-halo pairs can be identified with $\sim 75\%$ completeness and $\lesssim 27\%$ contamination by simple cuts in the transverse separation $\Delta r_{\perp}$ and LOS separation $\Delta r_{\parallel}$."656 Furthermore. these pairs can be grouped together using a Friends-of-Friencds (FoF) algorithin to estimate the LRG group multiplicity function.," Furthermore, these pairs can be grouped together using a Friends-of-Friends (FoF) algorithm to estimate the LRG group multiplicity function."657 We apply this technique to a sample of LRGs Irom SDSS to constrain their TOD., We apply this technique to a sample of LRGs from SDSS to constrain their HOD.658 We find that both the high values of a—2 and high satellite fractions reported in previous papers are inconsistent with the 0.16<z«0.36 SDSS LRG group multiplicity function measured here., We find that both the high values of $\alpha \sim 2$ and high satellite fractions reported in previous papers are inconsistent with the $0.16 < z < 0.36$ SDSS LRG group multiplicity function measured here.659 In contrast to previous methods which rely on 2 and 3 point statistics to constrain the HOD (as in 2)). our method probes the ΠΟ more directly bv estimating (he group multiplicity function [rom (he higher order statistics in the LRG density [field in the one-halo dominant We present an overview of the CiC method in 2.1 and apply it (o an approximately volume limited subsample of SDSS LRGs in 2.2.. addressing the complications of fiber collisions. incompleteness. and complex angular masks.," In contrast to previous methods which rely on 2 and 3 point statistics to constrain the HOD (as in \citet{kulkarni/etal:2007}) ), our method probes the HOD more directly by estimating the group multiplicity function from the higher order statistics in the LRG density field in the one-halo dominant We present an overview of the CiC method in \ref{overview} and apply it to an approximately volume limited subsample of SDSS LRGs in \ref{data}, addressing the complications of fiber collisions, incompleteness, and complex angular masks."660 The C3C* technique developed here requires calibration on mock galaxy catalogs., The CiC technique developed here requires calibration on mock galaxy catalogs.661 We summarize our N-bocly simulation parameters in8 2.3.., We summarize our $N$ -body simulation parameters in \ref{sims}.662 24 presents the ILOD model we emplov throughout this analvsis and details how we populate our simulations with galaxies., \ref{hodmodel} presents the HOD model we employ throughout this analysis and details how we populate our simulations with galaxies.663 2.5 describes the CiC technique to measure the LRG eroup multiplicity function and its calibration with simulations., \ref{CiCtechnique} describes the CiC technique to measure the LRG group multiplicity function and its calibration with simulations.664 The LOD parameters are fil using a maximum likelihood analvsis explicated in 2.6.., The HOD parameters are fit using a maximum likelihood analysis explicated in \ref{maximumL}.665 In 3. we present the CiC multiplicity function of our SDSS LRG subsample and describe the relation between the C3C and (rue eroup multiplicity. functions., In \ref{results} we present the CiC multiplicity function of our SDSS LRG subsample and describe the relation between the CiC and true group multiplicity functions.666 We present the constraints on the ΠΟ) parameters and (their implications for the fraction of LRGs that are satellites. as well as the mass distribution of halos hosting LRG eroups with κ satellites.," We present the constraints on the HOD parameters and their implications for the fraction of LRGs that are satellites, as well as the mass distribution of halos hosting LRG groups with $n_{sat}$ satellites."667" Mock catalogs produced using the CAC maximun likelihood HOD and a spherical overdensity (90) halo catalog agree with the ? measurement of ie,(r,) Lor this sample when the large scale bias is adjusted with a single parameter for the central galaxy LOD.", Mock catalogs produced using the CiC maximum likelihood HOD and a spherical overdensity (SO) halo catalog agree with the \citet{masjedi/etal:2006} measurement of $w_p(r_p)$ for this sample when the large scale bias is adjusted with a single parameter for the central galaxy HOD.668 In 23.5. we compare these resulis wilh a mock LRG catalog based on a FoF halo catalog and with other WOD measurements in the literature., In \ref{fofkulksec} we compare these results with a mock LRG catalog based on a FoF halo catalog and with other HOD measurements in the literature.669 We show that while the FoF and SO catalogs can both match the observed CiC multiplicity function. the FoF catalog produces mock catalogs with a deficit of halos at 1 AMpc/h that is evident in the projected correlation function.," We show that while the FoF and SO catalogs can both match the observed CiC multiplicity function, the FoF catalog produces mock catalogs with a deficit of halos at 1 $h$ that is evident in the projected correlation function."670 In 4. we comment on the strengths and weaknesses of the CiC! method and summarize our conclusions in 5.., In \ref{assessCiC} we comment on the strengths and weaknesses of the CiC method and summarize our conclusions in \ref{conc}.671with L«2L there is a weak suggestion of à somewhat lugher masstolight ratio.,with $L < 2L\ast$ there is a weak suggestion of a somewhat higher mass–to–light ratio.672" Similarh. ((AL),, for the elliptical and SO hosts is fairly constant for hosts with Losthere2L and has a value of (271426)hAL.δι."," Similarly, $(M_{260}^{\rm dyn}/L)_{b_J}$ for the elliptical and S0 hosts is fairly constant for hosts with $L \gs 2L^\ast$ and has a value of $(271 \pm 26) h~M_\odot/L_\odot$."673 Again. isi a slight sugeestion that elliptical aud SO hosts with Lc2L have a somewhat higher masstolight ratio.," Again, there is a slight suggestion that elliptical and S0 hosts with $L < 2L^\ast$ have a somewhat higher mass–to–light ratio."674" Iu contrast. over the range of host luminosities explored here. (ALG)lΤὸ, for: the spiral: hosts slows a clear monotonic. decrease with luminosity. and is consistent with a law of. the . formΜΜ...d»"," In contrast, over the range of host luminosities explored here, $(M_{260}^{\rm dyn}/L)_{b_J}$ for the spiral hosts shows a clear monotonic decrease with luminosity, and is consistent with a power--law of the form $(M_{260}^{\rm dyn}/L)_{b_J} \propto L^{-1.0 \pm 0.2}$."675 The 2dF aud SDSSU2 host/satelüte samples are of comparable depths and have similar sizes. so it is not uureasonable to make comparisous between them.," The 2dF and SDSS02 host/satellite samples are of comparable depths and have similar sizes, so it is not unreasonable to make comparisons between them."676 The comparison is. however. somewhat limited by the fact that the 2dF ealasies are selected in by. while the SDSS02 ealaxies are selected in’. with host Imminosities obtained in ul. gr’. and 2’. (," The comparison is, however, somewhat limited by the fact that the 2dF galaxies are selected in $b_J$, while the SDSS02 galaxies are selected in $r'$ , with host luminosities obtained in $u'$, $g'$, $r'$, $i'$, and $z'$. ("677The traustormation from the SDSS photometry is given by by=yf|0.1550σοιor’): Norberg et 22002).,The transformation from the SDSS photometry is given by $b_J = g' + 0.155 + 0.152(g'-r')$; Norberg et 2002).678 Also. SDSSO2 did not perform separate cvnamical analyses for the hosts of carly aud latetype galaxies. so a direct comparison is not possible in this case.," Also, SDSS02 did not perform separate dynamical analyses for the hosts of early– and late–type galaxies, so a direct comparison is not possible in this case."679 Tn all 5 SDSS photometric bands. SDSS02 find AS L. so that iu à giveu band. a single masstolight ratiox characterizes the hosts.," In all 5 SDSS photometric bands, SDSS02 find $M_{260}^{\rm dyn} \propto L$ , so that in a given band, a single mass–to–light ratio characterizes the hosts."680 That masstolight ratio is a sharply decreasing function of the central wavelength of the bandpass (6... a factor of order 3 lugher in « than in :/).," That mass–to–light ratio is a sharply decreasing function of the central wavelength of the bandpass (e.g., a factor of order 3 higher in $u'$ than in $z'$ )."681 In q'. SDSS02 find M/E=(ATLAloyhJL. and ini’ L(1154319M.fL..," In $g'$, SDSS02 find $M_{260}^{\rm dyn}/L = (171 \pm 40) h~M_\odot/L_\odot$ and in $r'$ $M_{260}^{\rm dyn}/L = (145 \pm 34) h~M_\odot/L_\odot$."682" These compare well with Ethe masstolight ratio that we obtain. (193+LUAM.fL..for the host galaxies our full sample that have Iumiuosities of £22L""."," These compare well with the mass–to–light ratio that we obtain, $(193\pm 14) 683h~M_\odot/L_\odot$ , for the host galaxies our full sample that have luminosities of $L \gs 2L^\ast$."684" Since we cannot compare our A5,di/L for host galaxies of different imnorpholosies to the results of SDSS02. we instead compare them to the weak lensing results of SDSSOL."," Since we cannot compare our $M_{260}^{\rm dyn}/L$ for host galaxies of different morphologies to the results of SDSS02, we instead compare them to the weak lensing results of SDSS01."685 SDSSOL did not classify their galaxies according ο visual morphology but. iustead. used spectral features ο place subsets of their lens galaxies into broad “carly and “latetype” categories.," SDSS01 did not classify their galaxies according to visual morphology but, instead, used spectral features to place subsets of their lens galaxies into broad ``early--'' and “late–type” categories."686 The carlytypes represcut about of the total number of lous galaxies. and the atetypes represent another of the total umuber of eus galaxies.," The early–types represent about of the total number of lens galaxies, and the late–types represent another of the total number of lens galaxies."687 Table 3 of SDSSOL shows that in the bluer uds. Ags7Lis somewhat morphologydependent. with he masstolight ratio of the ellipticals exceeding that of he eutire leis sample by a factor of 1.50.2 in gy’ aud bv a actor of 1.340.2 ine’.," Table 3 of SDSS01 shows that in the bluer bands, $M_{\rm 260}^{\rm lens}/L$ is somewhat morphology–dependent, with the mass–to–light ratio of the ellipticals exceeding that of the entire lens sample by a factor of $1.5\pm 0.2$ in $g'$ and by a factor of $1.3\pm 0.2$ in $r'$."688" Again. this compares well with our results for the elliptical/S0 hosts in the 2dF sample. where we find that A/S,/L for the clliptical/S0 hosts exceeds vat of the full sample ]i a factor of 1.14.0.2 for hosts with £22k” (e.g. ,LL)."," Again, this compares well with our results for the elliptical/S0 hosts in the 2dF sample, where we find that $M_{260}^{\rm dyn}/L$ for the elliptical/S0 hosts exceeds that of the full sample by a factor of $1.4\pm 0.2$ for hosts with $L \gs 2L^\ast$ (e.g., 4)."689 Our result tha ALxL+ for the spiral hosts is iu ear couflict with the results of SDSSOL. who fouud tha Agee/L seas independent of Inuinosity in all but the very duest baud Gu.," Our result that $M_{260}^{\rm dyn}/L \propto L^{-1}$ for the spiral hosts is in clear conflict with the results of SDSS01, who found that $M_{260}^{\rm lens}/L$ was independent of luminosity in all but the very bluest band $u'$ )."690 However. our result steiis from the fac iat the line of sight velocity dispersion is iudepenudeut of tuinosity for the spiral hosts.," However, our result stems from the fact that the line of sight velocity dispersion is independent of luminosity for the spiral hosts."691 While this is iuconsisteut with the leusiug results of SDSSOL. if is consistent with 1¢ dynamical results of Zaritsky et ((1997) who fou wat the velocity difference. de. between 69 isolated spira ealaxics 22.1<Mp 15.8) aud 115 satellites was iudepeudoeut of the inchuationcorrected IT-I linewidth of 1e host and was. therefore. independent of the Iuuinosity of the host (through. e.g.. the TullyFisher relation).," While this is inconsistent with the lensing results of SDSS01, it is consistent with the dynamical results of Zaritsky et (1997) who found that the velocity difference, $dv$, between 69 isolated spiral galaxies $-22.4 < M_B < -18.8$ ) and 115 satellites was independent of the inclination–corrected H-I linewidth of the host and was, therefore, independent of the luminosity of the host (through, e.g., the Tully–Fisher relation)."692 Whether the coutlict between the leusiug aud ναίστι results for the halos of spiral galaxies is due to differences in sample selection or due to svsteimnatic effects in one or both of the mass estinators remains to be doeteriuined., Whether the conflict between the lensing and dynamical results for the halos of spiral galaxies is due to differences in sample selection or due to systematic effects in one or both of the mass estimators remains to be determined.693 However. the ultimate completion of both the SDSS aud the 2PAFORS will aid tremendously iu the resolution of this issuic. and we look forward to the wealth of data that both survevs will provide in the near future.," However, the ultimate completion of both the SDSS and the 2dFGRS will aid tremendously in the resolution of this issue, and we look forward to the wealth of data that both surveys will provide in the near future."694 We are pleasedto thank the 2dFCRS team for making the 100k public data release available in a timely aud very userfricndly manner., We are pleasedto thank the 2dFGRS team for making the 100k public data release available in a timely and very user–friendly manner.695 Support under NSF coutract AST- CTGD. ALIS) is also eratefully acknowledged.," Support under NSF contract AST-0098572 (TGB, MJS) is also gratefully acknowledged."6962007).. the unprecedentecdly well-sampled lisht curve of this burst revealed several peaks over (he first ~50 s that were correlated with the variability in MeV. ganmmna- (Racusinetal.2008:Stamatikos2009:Deskin2010).. before switching over to a behavior more tvpical of afterglows.,", the unprecedentedly well-sampled light curve of this burst revealed several peaks over the first $\sim 50$ s that were correlated with the variability in MeV gamma-rays \citep{rac08,sta09,bes10}, before switching over to a behavior more typical of afterglows."697 Furthermore. the early optical Hluxes lie lar above low-energv extrapolations of the concurrent. üme-resolved Band spectra. clearly pointing to a distinct spectral component associated with the prompt phase (lacusinetal..—2003).," Furthermore, the early optical fluxes lie far above low-energy extrapolations of the concurrent, time-resolved Band spectra, clearly pointing to a distinct spectral component associated with the prompt phase \citep{rac08}."698. Among different possibilities. an interpretation attributing the optical and MeV. emission respectively to the svuchrotvon aud sviuchrotron-sell-C'ómpton (SSC!) processes have often been invoked (e.g.Racusinetal.2003).," Among different possibilities, an interpretation attributing the optical and MeV emission respectively to the synchrotron and synchrotron-self-Compton (SSC) processes have often been invoked \citep[e.g.][]{rac08}."699. For comparison with our hadronic cascade model. we focus on the time interval between Ty+12 s and Tj+ 22s where Zi is the Swilt/DAT trigger time. duringwhich the Band component reaches a maximunm luminositv of 1.0x10°erg s!.," For comparison with our hadronic cascade model, we focus on the time interval between $T_0+12$ s and $T_0+22$ s where $T_0$ is the Swift/BAT trigger time, duringwhich the Band component reaches a maximum luminosity of $1.0 \times 10^{53}~\mbox{erg}$ $\mbox{s}^{-1}$."700 The Band parameters we adopt are a=—0.45. 9= —3.5. and Ej=148 keV. noting that 2 is only constrained by the data to be 3<—3.412.," The Band parameters we adopt are $\alpha=-0.45$, $\beta=-3.5$ , and $E_{\rm peak}=748$ keV, noting that $\beta$ is only constrained by the data to be $\beta<-3.412$."701" Figure 2 illustrates our results for the parameters 2=LOM em. P=1000. U,/U.=45. and η.=3."," Figure \ref{fig:0803} illustrates our results for the parameters $R=10^{16}$ cm, $\Gamma=1000$, $U_{\rm p}/U_\gamma=45$, and $U_{\rm B}/U_\gamma=3$."702 Svunchrotron emission from the pair cascade softens the spectrum below ~100 keV so that the low-energv slope of the Band component becomes concordant with the observed value of a=—0.816., Synchrotron emission from the pair cascade softens the spectrum below $\sim 100$ keV so that the low-energy slope of the Band component becomes concordant with the observed value of $\alpha=-0.816$.703 The cascade emission continues down into the optical band with sole curvature and accounts well for the observed optical intensity as long as svnchrotron self-absorption does not set in. which necessitates D>1000 and R>LO! em.," The cascade emission continues down into the optical band with some curvature and accounts well for the observed optical intensity as long as synchrotron self-absorption does not set in, which necessitates $\Gamma>1000$ and $R>10^{16}$ cm."704 Such large values lor D and 2 imply a relatively low comoving photon density. aud (hus low photopion production effiienev. which scales as x2'P7.," Such large values for $\Gamma$ and $R$ imply a relatively low comoving photon density and thus low photopion production efficiency, which scales as $\propto R^{-1} \Gamma^{-2}$."705 This in turn calls for a proton huninositv Ly107?ergs! strongly dominating that in the Band component.," This in turn calls for a proton luminosity $L_{\rm p} \sim 10^{55}~\mbox{erg} \mbox{s}^{-1}$, strongly dominating that in the Band component."706 Note that a substantially larger energv budget than in MeV gamma-rays alone is also unavoidable in the SSC model for GRB 080319D due to luminous. second-order IC: emission in the GeV band 2008).," Note that a substantially larger energy budget than in MeV gamma-rays alone is also unavoidable in the SSC model for GRB 080319B due to luminous, second-order IC emission in the GeV band \citep{rac08}."707 Ocewring before the launch ofFermi. the GeV properties of GRB Os0319B remains largely unknown.," Occurring before the launch of, the GeV properties of GRB 080319B remains largely unknown."708 Upper limits at the level of ~10>ergem?s! above 10 GeV were obtained by MILAGRO (Aune 2010).., Upper limits at the level of $\sim 10^{-5} \ \mbox{erg}~\mbox{cm}^{-2}~\mbox{s}^{-1}$ above $10$ GeV were obtained by MILAGRO \citep{mil10}. .709 This does not contracict the high-energv component expected in our model. consisting of svuchrotvon emission from secondary pairs wil Iuminosity ~O.LL. andphoton index ~—2. extending up to a cutoff ~LOO GeV. due to internal 55-absorption (Figure 2)).," This does not contradict the high-energy component expected in our model, consisting of synchrotron emission from secondary pairs with luminosity $\sim 0.1 L_\gamma$ andphoton index $\sim -2$, extending up to a cutoff $\sim 100$ GeV due to internal $\gamma \gamma$ -absorption (Figure \ref{fig:0803}) )."710 The spectral shape is conspicuously different from (he sharply peaked one expected [rom second-order LC emission in the SSC interpretation (Racusinel 2008). providing an important disünguishing [feature lorUIIECT-3nduced. emission components.," The spectral shape is conspicuously different from the sharply peaked one expected from second-order IC emission in the SSC interpretation \citep{rac08}, , providing an important distinguishing feature forUHECR-induced emission components."711 The overall similarity of our model spectrum flor GRD 030913D. with that of GRB 090902Dalso encourages us to search for optical signatures in future Ferm: GRBs., The overall similarity of our model spectrum for GRB 080913B with that of GRB 090902Balso encourages us to search for optical signatures in future GRBs.712are consistent both with being constant and with varving by a similar fraction as in the two sources quoted before.,are consistent both with being constant and with varying by a similar fraction as in the two sources quoted before.713 The frequeney of oscillations during tvpe E. X-ray bursts detected in some sources are Consistent with the frequency separation of the two QPOs or with its first overtone., The frequency of oscillations during type I X-ray bursts detected in some sources are consistent with the frequency separation of the two QPOs or with its first overtone.714 Only in the source 11636-536 the averaged. frequency separation. Av=251 11. and the half of the [requency in typeE bursts. Maw=581 Lez. diller bx approximately (Méndez&vanParaclijs.1998)..," Only in the source 1636-536 the averaged frequency separation, $\Delta\nu=251$ Hz, and the half of the frequency in type I bursts, $\nu_{\rm burst}=581$ Hz, differ by approximately \cite{Mendez98c}."715 In the power spectrum of bursts of the same source Miller (1908). found. a second signal at 290 Tz ~ονημμιι.," In the power spectrum of bursts of the same source Miller \shortcite{Miller98c} found a second signal at 290 Hz $\sim 1/2716\nu_{\rm burst}$."717 Phese observations strongly favour the beat frequency model where the frequency separation between the two QPOs originates from the stellar spin. whereas the higher QPO is produced. by accreting eas in a stable. nearly circular orbit. around the neutron star.," These observations strongly favour the beat frequency model where the frequency separation between the two QPOs originates from the stellar spin, whereas the higher QPO is produced by accreting gas in a stable, nearly circular orbit around the neutron star."718 Though. it has to be clarified how the slightly varving frequency separation ancl the small deviation. of the frequency. separation from the burst frequency can be incorporated into this mocel.," Though, it has to be clarified how the slightly varying frequency separation and the small deviation of the frequency separation from the burst frequency can be incorporated into this model."719 Beside the two kilohertz QPOs and the burst oscillations. also QPOs with frequencies of a few tens of llertz were detected. in. some sources.," Beside the two kilohertz QPOs and the burst oscillations, also QPOs with frequencies of a few tens of Hertz were detected in some sources."720 Their. [frequencies correlate with the high frequency kilohertz QPOs., Their frequencies correlate with the high frequency kilohertz QPOs.721 These low frequeney QPOs were interpreted. by Stella Vietri (1998) to originate from the Lense-Thirring precession of the accreting disc due to the frame dragging cllect of the rapidly spinning neutron star (Lense&Thirring.1918).., These low frequency QPOs were interpreted by Stella Vietri \shortcite{Stella97a} to originate from the Lense-Thirring precession of the accreting disc due to the frame dragging effect of the rapidly spinning neutron star \cite{Lense18a}.722 Both. the identification of the high frequency. kilohertz QPOs with the orbital frequeney. of a stable circular orbit and the low [frequency QPOs with the [rame clrageine frequeney of the same orbit allow to constrain the mass of the neutron star and. also the EOS of neutron star matter (Lambetal..1998:Stella&Vietri.1998).," Both, the identification of the high frequency kilohertz QPOs with the orbital frequency of a stable circular orbit and the low frequency QPOs with the frame dragging frequency of the same orbit allow to constrain the mass of the neutron star and also the EOS of neutron star matter \cite{Lamb97a,Stella97a}."723. I£ the evidence for the detection of QPOs of the innermost stable circular orbit in the sources 11608-52.. 11636-536. (Ixazret.et.al. 1997).. and 11820-30 (Zhangetal.1998b) can be confirmed by future observations. the constraints are rather severe. allowing only a few still EOSs.," If the evidence for the detection of QPOs of the innermost stable circular orbit in the sources 1608-52, 1636-536 \cite{Kaaret97a}, and 1820-30 \cite{Zhang98c} can be confirmed by future observations, the constraints are rather severe, allowing only a few stiff EOSs."724 The frequency separation of the two kilohertz QPOs show that the neutron star in LAINBs are rapidly. rotating with periods ranging from 2.5 ms to 4 ms., The frequency separation of the two kilohertz QPOs show that the neutron star in LMXBs are rapidly rotating with periods ranging from 2.5 ms to 4 ms.725 Lt can therefore be expected that the geometry of the neutron star ancl its exterior space time is non-spherical., It can therefore be expected that the geometry of the neutron star and its exterior space time is non-spherical.726 Since the innermost stable orbit is located at only a lew kilometres above the stars surface. the deviation from the Ixerr space time are large ancl should. not be neglected.," Since the innermost stable orbit is located at only a few kilometres above the star's surface, the deviation from the Kerr space time are large and should not be neglected."727 La order to compare theoretical neutron star models with QPO observations. a completely: ecneral relativistic calculation of the rotating neutron star structure and space time geometry is therefore DOCOCSSÜAV.," In order to compare theoretical neutron star models with QPO observations, a completely general relativistic calculation of the rotating neutron star structure and space time geometry is therefore necessary."728 In order to study the impact ancl the discrimination power of the QPO data in greater detail. we select a broad collection of modern EOSs. which were obtained utilising numerous assuniptions about the dynamies and composition of super dense matter.," In order to study the impact and the discrimination power of the QPO data in greater detail, we select a broad collection of modern EOSs, which were obtained utilising numerous assumptions about the dynamics and composition of super dense matter."729 To mention several. these are: the many-body technique used to. determine. the EOS: the model for the nucleon-nucleon interaction: description. of electrically charge neutral neutron star matter in terms of either only neutrons and protons in. generalisecl chemical equilibrium (7 equilibrium) with electrons. and muons. or nucleons. hvperons anc more massive barvon states in 3 equilibrium with leptons: hbyperon coupling strengths in matter: inclusion of meson (π. ΔΑ} condensation: treatment of the transition of confined. hadronic matter into quark matter: and assumptions about the true ground. state of stronely interacting matter (1.0... absolute stability ofstrange quark matter relative to barvon matter).," To mention several, these are: the many-body technique used to determine the EOS; the model for the nucleon-nucleon interaction; description of electrically charge neutral neutron star matter in terms of either only neutrons and protons in generalised chemical equilibrium $\beta$ equilibrium) with electrons and muons, or nucleons, hyperons and more massive baryon states in $\beta$ equilibrium with leptons; hyperon coupling strengths in matter; inclusion of meson $\pi$, $K$ ) condensation; treatment of the transition of confined hadronic matter into quark matter; and assumptions about the true ground state of strongly interacting matter (i.e., absolute stability of strange quark matter relative to baryon matter)."730 The paper is organised as follows., The paper is organised as follows.731 In Sect., In Sect.732 2. we summarise the equations which govern the space time structure ancl compare the approximate values of the orbital frequencies. the radius of the innermost stable orbit. and the Lense-Thirring precession Lrequencies with the respective values from the exact numerical solution of Einstein's equations.," \ref{sec:equations} we summarise the equations which govern the space time structure and compare the approximate values of the orbital frequencies, the radius of the innermost stable orbit, and the Lense-Thirring precession frequencies with the respective values from the exact numerical solution of Einstein's equations."733 The physics of the EOSs is discussed in Sect. 3.., The physics of the EOSs is discussed in Sect. \ref{sec:eos}.734 The high frequeney kilohertz QPOs and their interpretation in combination with their compatibility with the different 2058s are discussed in Sect. 4.., The high frequency kilohertz QPOs and their interpretation in combination with their compatibility with the different EOSs are discussed in Sect. \ref{sec:constr1}.735 Phe implications of the identification of the low frequency QPOs with Lense-Thirring precession are presented in Sect. 5.., The implications of the identification of the low frequency QPOs with Lense-Thirring precession are presented in Sect. \ref{sec:constr2}.736 We summarise our results. the constraints to the neutron star masses. and the conclusions concerning the neutron star EOS in Sect. 6..," We summarise our results, the constraints to the neutron star masses, and the conclusions concerning the neutron star EOS in Sect. \ref{sec:concl}."737 The stationary. axis-symmetric. and asymptotic Hat metric in quasi isotropic coordinates reads where the metric coefficients gyμμ.) are functions of r and 6 only.," The stationary, axis-symmetric, and asymptotic flat metric in quasi isotropic coordinates reads where the metric coefficients $g_{\mu\nu}=g_{\mu\nu}(r,\theta)$ are functions of $r$ and $\theta$ only."738 The metric cocllicients are determined by the Einstein equation (e=C= 1) and the energv-monmoentuni conservatjon where T=(e|puoul pgis the stress-enereyv tensor of an ideal Iud with the 4-velocity the energy density e. and the pressure p.," The metric coefficients are determined by the Einstein equation $c=G=1$ ) and the energy-momentum conservation where ${\bf T}= (e+p){\bf u}\otimes{\bf u}+p\,{\bf g}$ is the stress-energy tensor of an ideal fluid with the 4-velocity the energy density $e$, and the pressure $p$."739 The Lorentz [actor Fis given by αταI. hence Q=aefn’ is the angular velocity of the Duid. with respect to an observer at infinitw.," The Lorentz factor $\Gamma$ is given by ${\bf u}\cdot{\bf u}=-1$, hence $\Omega=u^\varphi / u^t$ is the angular velocity of the fluid with respect to an observer at infinity."740 Phe proper velocity C of the Buid. with respect to the local Eulerian Observer Oy (Smarr&York.1978). is given by the equation Note that if the Iuid were at rest with respect to the, The proper velocity $U$ of the fluid with respect to the local Eulerian Observer $\mathfrak{O}_0$ \cite{Smarr78a} is given by the equation Note that if the fluid were at rest with respect to the7411172 is supplied by mass loss from stars dn this region.,4472 is supplied by mass loss from stars in this region.742 In our standard cooling flow model we rave asstued that all stellar ejecta rapidly cuters 1e hot interstellar phase Gu <104 yrs)., In our standard cooling flow model we have assumed that all stellar ejecta rapidly enters the hot interstellar phase (in $\lta 10^4$ yrs).743 It has occasionally becu suggested. (c.g. Thomas 1986) iat stellar ejecta cools before euterimg the hot eas. effectively reducing ας.," It has occasionally been suggested (e.g. Thomas 1986) that stellar ejecta cools before entering the hot gas, effectively reducing $\alpha_*$."744 However. we find iat the central peak im (re) aud δις) persists even if the stellar mass loss rate a. is reduced at sanall rs," However, we find that the central peak in $n(r)$ and $\Sigma_x(R)$ persists even if the stellar mass loss rate $\alpha_*$ is reduced at small $r$."745 Moreover. dynamical aremmeuts and eas cluperature and ioetalliityv eracieuts observed at argorradi(rὃς36032 strouely indicate that cooler. enriched stellar ejecta is couductively melting iuto 16 hot phase.," Moreover, dynamical arguments and gas temperature and metallicity gradients observed at larger radii $r \lta 3r_e$ ) strongly indicate that cooler, enriched stellar ejecta is conductively melting into the hot phase."746 Studies of the evolution of hot gas in elliptical ealaxies at UC Santa Cruz are supported bv NASA eraut. NAC 5-3060 aud NSF eraut. AST-980299| for which we are very grateful., Studies of the evolution of hot gas in elliptical galaxies at UC Santa Cruz are supported by NASA grant NAG 5-3060 and NSF grant AST-9802994 for which we are very grateful.747 ED is supported in part by Crant MURST-Cofiu 98., FB is supported in part by Grant MURST-Cofin 98.748 lin, .1in749xuticles emitting in dillerent parts of the old cocoon (outer structure) of 1453|3308. as well as in the inner lobes of his DDRG. and compare these with the above dynamical ages.,"particles emitting in different parts of the old cocoon (outer structure) of J1453+3308, as well as in the inner lobes of this DDRG, and compare these with the above dynamical ages."750" Phe already available data indicate that the lobes of he outer double are separated by 336 aresee corresponding o 1297 kpc. while the inner double has a separation of 41 aresec corresponding to 159 kpe (1. --τ km * 1 Q,,,20.27. O,=0.73. Spergel et al."," The already available data indicate that the lobes of the outer double are separated by 336 arcsec corresponding to 1297 kpc, while the inner double has a separation of 41 arcsec corresponding to 159 kpc $_\circ$ =71 km $^{-1}$ $^{-1}$, $\Omega_m$ =0.27, $\Omega_\Lambda$ =0.73, Spergel et al."751 2003)., 2003).752 Ehe 1.4-CLIz racio uminosities of the outer and inner doubles are 1077 W | and 107! W Lz* respectively., The 1.4-GHz radio luminosities of the outer and inner doubles are $\times$ $^{25}$ W $^{-1}$ and $\times$ $^{24}$ W $^{-1}$ respectively.753 The Duminosity of the outer double is above the ETUL/EIRLIE break. while that of the inner double is below it although it has an cclge-xightened structure.," The luminosity of the outer double is above the FRI/FRII break, while that of the inner double is below it although it has an edge-brightened structure."754 To achieve the above objectives we made new radio maps of J1453]3308 at a number of frequencies over a wee range [rom 240 to 4860 Mllz., To achieve the above objectives we made new radio maps of J1453+3308 at a number of frequencies over a large range from 240 to 4860 MHz.755 These observations iàve been made with an angular resolution high enough to image the lobes with at least 6 resolution elements along heir axes., These observations have been made with an angular resolution high enough to image the lobes with at least 6 resolution elements along their axes.756 The new observations and data reduction are described in Section 2., The new observations and data reduction are described in Section 2.757 The observational results. such as he radio maps showing the source structure. spectra and »olarisation parameters are presented in Section 3.," The observational results, such as the radio maps showing the source structure, spectra and polarisation parameters are presented in Section 3."758 The standard. spectral-ageing analvsis for the outer and. inner structures is described and the results presented in Section 4. while the concluding remarks are given in Section 5.," The standard spectral-ageing analysis for the outer and inner structures is described and the results presented in Section 4, while the concluding remarks are given in Section 5."759 The analysis presented in this paper is based on radio observations recently conducted with the GMIE and VLA. as well as on VLA archival data.," The analysis presented in this paper is based on radio observations recently conducted with the GMRT and VLA, as well as on VLA archival data."760 The observing log for both the CMICE and. VLA observations is listed in Table 1 which is arranged. as follows., The observing log for both the GMRT and VLA observations is listed in Table 1 which is arranged as follows.761 Columns | and 2 show the name of the telescope. and the array. configuration for the VLA observations: columns 3 and + show the frequency and. bandwidth used in making the images: column 5: the primary beamwidth in aremin: column 6: dates of the observations.," Columns 1 and 2 show the name of the telescope, and the array configuration for the VLA observations; columns 3 and 4 show the frequency and bandwidth used in making the images; column 5: the primary beamwidth in arcmin; column 6: dates of the observations."762 The phase centre for all the observations was near the core of the radio galaxy., The phase centre for all the observations was near the core of the radio galaxy.763 The observations were mace in the standard manner. with each observation of the tarect-source interspersecl with observations of 3€286 which was used as a phase calibrator as well as Dux density and bandpass calibrator.," The observations were made in the standard manner, with each observation of the target-source interspersed with observations of 3C286 which was used as a phase calibrator as well as flux density and bandpass calibrator."764 At each frequeney the source was observed. in a full-svnthesis run of approximately 9 hours including calibration overheacwa, At each frequency the source was observed in a full-synthesis run of approximately 9 hours including calibration overheads.765 The rms noise in the resulting images range from about 1 tat 240 Mllz to about 0.06 + at 1287 Mllz., The rms noise in the resulting images range from about 1 $^{-1}$ at 240 MHz to about 0.06 $^{-1}$ at 1287 MHz.766 Details about the array can be found at. the GAIRT website at., Details about the array can be found at the GMRT website at.767http://www.gmrt.ncra.tifr.res.in. The data collected were calibrated. and. reduced. in. the standard way using the NIUXO software package., The data collected were calibrated and reduced in the standard way using the NRAO software package.768 The Hux densities at the cillerent. frequencies are based on the scale of Baars et al. (, The flux densities at the different frequencies are based on the scale of Baars et al. (7691977).,1977).770 The source was observed with the CoD array at a frequency of 4860 MlIz to image the outer lobes and. determine their spectra by. comparing with the low-frequeney GMIE images., The source was observed with the CnD array at a frequency of 4860 MHz to image the outer lobes and determine their spectra by comparing with the low-frequency GMRT images.771 Phe integration time was about 6«.20 min. which allowed. us to reach an rms noise value of about 0.05 1.," The integration time was about $6\times20$ min, which allowed us to reach an rms noise value of about 0.05 $^{-1}$."772 Phe interferometric phases were calibrated every 20 min with the phase calibrator J1416|347., The interferometric phases were calibrated every 20 min with the phase calibrator J1416+347.773 The source 3€C286 was used as the primary [ux density ancl polarisation calibrator., The source 3C286 was used as the primary flux density and polarisation calibrator.774 For the image produced. from this data set correction for the primary beam pattern has been done., For the image produced from this data set correction for the primary beam pattern has been done.775 As in the case of the GALRT data. the VLA data were edited and reduced using the package.," As in the case of the GMRT data, the VLA data were edited and reduced using the package."776 Phe polarisation data reduction was done and the maps of the Stokes parameters J. Q and Ü were obtained using the procedures applied in the analysis of polarisation properties in a larger set of eiant radio galaxies (Machalski et al.," The polarisation data reduction was done and the maps of the Stokes parameters $I$, $Q$ and $U$ were obtained using the procedures applied in the analysis of polarisation properties in a larger set of giant radio galaxies (Machalski et al."777 2GO)., 2006).778 lo. study. the inner couble-lobecd structure of J1453|3308. derive its spectrum and estimate the radiative age. as well as to compare the resulting age with that of the outer lobes of the giant-sized. structure. we supplemented our GMBRI observations with VLA archival data.," To study the inner double-lobed structure of J1453+3308, derive its spectrum and estimate the radiative age, as well as to compare the resulting age with that of the outer lobes of the giant-sized structure, we supplemented our GMRT observations with VLA archival data."779 These observations which were mace in the snap-shot mode in the L (1365 MlIz). € (4860 MlIZ) and X. (S460 MlIZ) bands. also enabled us to study the spectrum ancl variability of the racio core.," These observations which were made in the snap-shot mode in the L (1365 MHz), C (4860 MHz) and X (8460 MHz) bands, also enabled us to study the spectrum and variability of the radio core."780 All Dux densities are on the Baars et al. (, All flux densities are on the Baars et al. (781L977) scale.,1977) scale.782 The images of the entire source using the GMIE and the VLA are presented in Figs., The images of the entire source using the GMRT and the VLA are presented in Figs.783 1 and 2. while the observational parameters and. some of the observed. properties are presented in Table 2 which is arranged as follows.," 1 and 2, while the observational parameters and some of the observed properties are presented in Table 2 which is arranged as follows."784 Column 1: frequency. of observations in MllIz. with the letter G or V representing either GMIBEE or VLA observations: columns 4: the major and minor axes of therestoring beam in," Column 1: frequency of observations in MHz, with the letter G or V representing either GMRT or VLA observations; columns $-$ 4: the major and minor axes of therestoring beam in"785of a given ion using the centre-of-gravity method (Kochukhov&Ryabchikova 2001)..,of a given ion using the centre-of-gravity method \citep{2001A&A...374..615K}.786" Spectral lines were identified using information from the VALD data base (Kupkaetal.1999) and identification lists of variable lines compiled for other roAp stars (e.g.,Ryabchikovaetal.2007b)."," Spectral lines were identified using information from the VALD data base \citep{1999A&AS..138..119K} and identification lists of variable lines compiled for other roAp stars \citep[e.g.,][]{2007A&A...462.1103R}."787. Our frequency analysis consisted of the following steps., Our frequency analysis consisted of the following steps.788" After obtaining mean RV measurements for each ion, we calculated the corresponding amplitude spectra using discrete Fourier transform and estimated an initial value for the pulsation period from the highest amplitude peak."," After obtaining mean RV measurements for each ion, we calculated the corresponding amplitude spectra using discrete Fourier transform and estimated an initial value for the pulsation period from the highest amplitude peak."789 We also computed a periodogram as described by Horne&Baliunas(1986) in order to assess the False Alarm Probability (FAP) of the signal detection., We also computed a periodogram as described by \citet{1986ApJ...302..757H} in order to assess the False Alarm Probability (FAP) of the signal detection.790 Then we applied a non-linear least-squares fitting procedure to improve the period and estimate an amplitude and phase of the RV variations., Then we applied a non-linear least-squares fitting procedure to improve the period and estimate an amplitude and phase of the RV variations.791" This analysis clearly showed the presence of pulsation variability ; 10~°) in the core of Ha and in the lines ofII,,σάΠ,, and rr."," This analysis clearly showed the presence of pulsation variability $<$ $10^{-5}$ ) in the core of $\alpha$ and in the lines of, and ."792". The RV amplitude reaches 150 ffor Ha, but it is only 40-60 ffor the three rare-earth ions."," The RV amplitude reaches 150 for $\alpha$, but it is only 40–60 for the three rare-earth ions."793" These four elements show periods of 22.85+0.39 min (Eu), 23.50+0.26 min (Ce), 23.85+0.27 min (Gd), and 24.05+0.51 min (Ha), yielding a weighted mean pulsation period of 23.56+0.16 min or a mean frequency of v=0.707+0.005 mHz, which is the lowest frequency detected in a roAp star."," These four elements show periods of $22.85\pm0.39$ min (Eu), $23.50\pm0.26$ min (Ce), $23.85\pm0.27$ min (Gd), and $24.05\pm0.51$ min $\alpha$ ), yielding a weighted mean pulsation period of $23.56\pm0.16$ min or a mean frequency of $\nu=0.707\pm0.005$ mHz, which is the lowest frequency detected in a roAp star."794 This period was adopted in the subsequent linear least-squares analysis of the remaining elements., This period was adopted in the subsequent linear least-squares analysis of the remaining elements.795 Several otherions show a probable (10? <FFAP;10~%) variation in the period range of 23-24 min with amplitudes of !.., Several otherions show a probable $10^{-5}<$ $<10^{-3}$ ) variation in the period range of 23–24 min with amplitudes of 10--130 .796 A single line of sshows the highest amplitude among metal lines., A single line of shows the highest amplitude among metal lines.797" We also detected variability in the lines ofIL,Π,, and somewhat unexpectedly,Fer."," We also detected variability in the lines of, and somewhat unexpectedly,."798". Combining information from 62 lines of the neutral iron, we were able to detect the pulsation amplitude of 7.44-1.1!."," Combining information from 62 lines of the neutral iron, we were able to detect the pulsation amplitude of $7.4\pm1.1$."799". At the same time, the RV curve constructed from 21 lines of ionized iron does not show any variation."," At the same time, the RV curve constructed from 21 lines of ionized iron does not show any variation."800 Phase shifts of ~ 00.1 of the pulsation period inferred from the RV curves of different ions probably reflect the difference in their formation heights., Phase shifts of $\sim$ 0.1 of the pulsation period inferred from the RV curves of different ions probably reflect the difference in their formation heights.801 Many roAp stars show large-amplitude pulsations in the lines of singly and doubly ionized Nd and Pr (Ryabchikovaetal.2007a)., Many roAp stars show large-amplitude pulsations in the lines of singly and doubly ionized Nd and Pr \citep{2007A&A...473..907R}.802". aand llines are relatively weak and heavily blended in the spectrum of177765,, unlike in typical roAp stars where these lines are among the strongest metal spectral features (Ryabchikovaet 2004).."," and lines are relatively weak and heavily blended in the spectrum of, unlike in typical roAp stars where these lines are among the strongest metal spectral features \citep{2004A&A...423..705R}."803 Neither singly nor doubly ionized lines of Pr and Nd provide precise RVs for ddue to blending by iron peak elements., Neither singly nor doubly ionized lines of Pr and Nd provide precise RVs for due to blending by iron peak elements.804 Our results indicate the absence of pulsation variability in the blends containing contributions by these ions with upper limits of © 115-20ms~*.., Our results indicate the absence of pulsation variability in the blends containing contributions by these ions with upper limits of $\approx$ 15–20.805" We also did not detect variability in the lines ofY/IL,LaIt,,IL, and Π."," We also did not detect variability in the lines of, and ."806. A marginal signal at the right frequency may be present in the lines of neutral and ionized Ti., A marginal signal at the right frequency may be present in the lines of neutral and ionized Ti.807 Representative RV curves and amplitude spectra are shown in Fig. 2.., Representative RV curves and amplitude spectra are shown in Fig. \ref{rv-freq}.808 The outcome of the linear least-squares fit with a fixed pulsation period is reported in Table 1 for all measured elements., The outcome of the linear least-squares fit with a fixed pulsation period is reported in Table \ref{ap-table} for all measured elements.809 This Table also gives the FAP information., This Table also gives the FAP information.810 The short duration of our monitoring of aallowed to cover only 3 pulsation cycles., The short duration of our monitoring of allowed to cover only 3 pulsation cycles.811 These observational data are insufficient to perform a very precise frequency analysis and assess possible presence of other frequencies., These observational data are insufficient to perform a very precise frequency analysis and assess possible presence of other frequencies.812" However, we note a systematic deviation of the mean RV curves ofCell,,GdIl,, and Ho core from the mono-periodic least-squares solution (see upper row in Fig. 2))."," However, we note a systematic deviation of the mean RV curves of, and $\alpha$ core from the mono-periodic least-squares solution (see upper row in Fig. \ref{rv-freq}) )."813" All three elements show a somewhat higher amplitude in the second half of the time-series, which indicates the presence of additional pulsation frequencies."," All three elements show a somewhat higher amplitude in the second half of the time-series, which indicates the presence of additional pulsation frequencies."814" We derived preliminary abundance estimates for ffrom equivalent widths using a modified version of ccode (WIDTHMr)) written by V. Tsymbal, where magnetic intensification effects are taken into account via the magnetic pseudo-microturbulence."," We derived preliminary abundance estimates for from equivalent widths using a modified version of code ) written by V. Tsymbal, where magnetic intensification effects are taken into account via the magnetic pseudo-microturbulence."815" We checked that this procedure works well for Fe, yielding a reasonable agreement with detailed magnetic spectrum synthesis calculations."," We checked that this procedure works well for Fe, yielding a reasonable agreement with detailed magnetic spectrum synthesis calculations."816" For instance, fitting 18 aand 33 Ilines with wwe obtained log(Nre/Ntot)=—3.40+0.22 for aand log(Nre/Ntot)=—3.25+0.32 for 11.."," For instance, fitting 18 and 33 lines with we obtained $\log (N_{\rm Fe}/N_{\rm tot})=-3.40\pm0.22$ for and $\log (N_{\rm Fe}/N_{\rm tot})=-3.25\pm0.32$ for ."817 The corresponding abundances retrieved with, The corresponding abundances retrieved with818One innovative aspect in the SHS design was the use of an EMCCD as detector.,One innovative aspect in the SHS design was the use of an EMCCD as a detector.819" This pioneering camera has had a profound ainfluence on photon starved imaging applications, as photon counting in astronomy (e.g.Dussault&Hoess 2004).."," This pioneering camera has had a profound influence on photon starved imaging applications, as photon counting in astronomy \citep[e.g.][]{dus2004}."820 The back-illuminated device combines photon collection efficiencies of up to QE with single photon sensitivity through the virtual elimination of the readout noise., The back-illuminated device combines photon collection efficiencies of up to QE with single photon sensitivity through the virtual elimination of the readout noise.821" During the commissioning of the instrument, in the observing period of 2008, a set of stars with different brightness were observed to estimate the overall sensitivity of the instrument."," During the commissioning of the instrument, in the observing period of 2008, a set of stars with different brightness were observed to estimate the overall sensitivity of the instrument."822 The results are summarized in Table 2., The results are summarized in Table 2.823 The photometry was performed by using a circular aperture of 6 pixels using the DAOPHOT package of IRAF., The photometry was performed by using a circular aperture of 6 pixels using the DAOPHOT package of IRAF.824" The table shows the star name, V-band magnitude, total flux in counts and signal-to-noise ratio (SNR)."," The table shows the star name, V-band magnitude, total flux in counts and signal-to-noise ratio (SNR)."825 Each measured parameter in the table represents the average value over all the sub-apertures., Each measured parameter in the table represents the average value over all the sub-apertures.826 All the images were corrected for dark current and pixel-to-pixel variations., All the images were corrected for dark current and pixel-to-pixel variations.827" The table shows the detection limit of the instrument, which is defined as the maximun magnitude at which the control software is able to compute a centroid for every subaperture of the lenslet array and keep close-loop operation."," The table shows the detection limit of the instrument, which is defined as the maximun magnitude at which the control software is able to compute a centroid for every subaperture of the lenslet array and keep close-loop operation."828 Such limit is 11.8 mag for SAOLIM., Such limit is 11.8 mag for SAOLIM.829" This detection limit is similar to that one of more complex and expensive AO systems, like ALFA, mounted at the 3.5m telescope of the Calar Alto observatory), which was able to use stars as faints as V12 to close the loop (Hippleretal. 2000).."," This detection limit is similar to that one of more complex and expensive AO systems, like ALFA, mounted at the 3.5m telescope of the Calar Alto observatory), which was able to use stars as faints as $\sim12$ to close the loop \cite{hip2000}. ."830" An empirical relationship between the SNR per sub-aperture measured by the SHS and the star brightness can be established by an exponential fitting to both parameters, yielding: in that way, the expected SNR can be estimated for any magnitude."," An empirical relationship between the SNR per sub-aperture measured by the SHS and the star brightness can be established by an exponential fitting to both parameters, yielding: in that way, the expected SNR can be estimated for any magnitude."831 The accuracy of the centroid algorithm during the wavefront reconstruction is determined by the SNR per sub-aperture., The accuracy of the centroid algorithm during the wavefront reconstruction is determined by the SNR per sub-aperture.832" Therefore, some experiments have to be performed with the aim to predict the capability of the system to compensate a turbulence under different seeing conditions and different star magnitudes."," Therefore, some experiments have to be performed with the aim to predict the capability of the system to compensate a turbulence under different seeing conditions and different star magnitudes."833" To do so, a reference fiber is fed with a white source and it was placed exactly at the focal plane of the telescope, simulating a perfect reference star."," To do so, a reference fiber is fed with a white source and it was placed exactly at the focal plane of the telescope, simulating a perfect reference star."834" By adding white noise to the whole image in steps of 0.5 counts, the RMS (eq 6) and the SNR can be measured as a function of the noise on the different images recorded by the SHS."," By adding white noise to the whole image in steps of 0.5 counts, the RMS (eq 6) and the SNR can be measured as a function of the noise on the different images recorded by the SHS."835" Finally, a relation between them can be established."," Finally, a relation between them can be established."836" This procedure was repeated until the SNR dropped to a low value when the uncertainty of the centroid coordinates was (~10),high."," This procedure was repeated until the SNR dropped to a low value $\sim$ 10), when the uncertainty of the centroid coordinates was high."837" Moreover, different seeing conditions were simulated by convolving the reference fiber pattern image with a Gaussian function with different widths."," Moreover, different seeing conditions were simulated by convolving the reference fiber pattern image with a Gaussian function with different widths."838" In total, 4000 realizations of the RMS and the SNR vs the standard deviation of the input noise were performed for this simulation."," In total, 4000 realizations of the RMS and the SNR vs the standard deviation of the input noise were performed for this simulation."839" An empirical relation between the input standard deviation of the simulated noise, and the output RMS of the reconstructed image and the final SNR of the detected sub-images was derived for each input seeing by fitting the simulated data setswith a 5th"," An empirical relation between the input standard deviation of the simulated noise, and the output RMS of the reconstructed image and the final SNR of the detected sub-images was derived for each input seeing by fitting the simulated data setswith a 5th"840"with a zero crossing in the region 0.65ο,","with a zero crossing in the region $0.6\,\simleq\,e$."841 A rough estimate for the shear error Ar/>~ due to these shape errors (asstuuine a flat ο distribution) is, A rough estimate for the shear error $\Delta\gamma/\gamma$ due to these shape errors (assuming a flat $e$ distribution) is.842" Figure 10 plots the RMS error ratio of the actual to the estimated πω..."" decouvolution fits. and is analogous to Fieure 6.."," Figure \ref{fig:dcvlerrorestimate} plots the RMS error ratio of the actual to the estimated $\sqrt{\langle\Delta\eta_+^2/\tilde{\sigma}_{\eta_+}^2\rangle}$ for deconvolution fits, and is analogous to Figure \ref{fig:nativeerrorestimate}."843" For the deconvolution. the error estimate σ,,aa docs fairly well for vz50. while viση, jli when vy«50."," For the deconvolution, the error estimate $\tilde{\sigma}_{\eta_+}$ does fairly well for $\nu\geq50$, while $\sqrt{\langle\Delta\eta_+^2/\tilde{\sigma}_{\eta_+}^2\rangle}$ $\simeq1-\frac{2}{\nu}$ when $\nu<50$."844 The open-circle poiuts in the righitiiost column of panels in Figure 7 mark a tenucency for the decouvolution procedure to underestinate the ellipticity of large objects., The open-circle points in the rightmost column of panels in Figure \ref{fig:dcvlshapeerror100} mark a tendency for the deconvolution procedure to underestimate the ellipticity of large objects.845 This can be traced to the fact that the Αν function is rather poorly described by a Gauss-Laguerre expansion., This can be traced to the fact that the Airy function is rather poorly described by a Gauss-Laguerre expansion.846 Iu our default procedure. the size of the basis set of the EGL expansion of the PSF is made similar to the size of the PSF itself: in this case the Airy function is poorly modelled. at radi mASD.," In our default procedure, the size of the basis set of the EGL expansion of the PSF is made similar to the size of the PSF itself; in this case the Airy function is poorly modelled at radii $\gg \lambda/D$."847 For example the Airy function las divergeut. second radial moment. while anv ECL expansion at πιάτο order has a finite second radial moment. mdicatiug that the ECL expansion has failed to capture the laree-r behavior ofthe Airy function.," For example the Airy function has divergent second radial moment, while any EGL expansion at finite order has a finite second radial moment, indicating that the EGL expansion has failed to capture the $r$ behavior of the Airy function."848 It takes GL order Nou— p|q282aud 16 to describe the first and second Αν ring. respectively: our simmlations use GL order 12 to describe the PSF.," It takes GL order $N_{\rm GL}\equiv p+q=8$ and $16$ to describe the first and second Airy ring, respectively; our simulations use GL order 12 to describe the PSF."849 Au cquivalent statement is tha. iu the Fourier domain. au EGL expansion fails to properly describe the sguall-& behavior of the Airy function.," An equivalent statement is that, in the Fourier domain, an EGL expansion fails to properly describe the $k$ behavior of the Airy function."850 This is uot surprisingC» since the Airy function las a cusp at &=0 πάσα is equivalent to raving infinite second moment ii real space)., This is not surprising since the Airy function has a cusp at $k=0$ (which is equivalent to having infinite second moment in real space).851" The cusp in turn results from the sharp edge of the ilunünatiou function of an unapodized circular ΗΧΟΥ,", The cusp in turn results from the sharp edge of the illumination function of an unapodized circular mirror.852 The poor description of the Airy function at aree r or sinall & becomes important when trying o decouvolve images of well-resolved galaxies. vecatise the shape information for large galaxies is carried at large r and small & relative to he PSF.," The poor description of the Airy function at large $r$ or small $k$ becomes important when trying to deconvolve images of well-resolved galaxies, because the shape information for large galaxies is carried at large $r$ and small $k$ relative to the PSF."853 The finite EGL expausion of the Airy PSF nudcerestimates its circularizing effect on aree galaxies. heuce the deconvolved shapes are oo round for large galaxies.," The finite EGL expansion of the Airy PSF underestimates its circularizing effect on large galaxies, hence the deconvolved shapes are too round for large galaxies."854 Marginallv-resolved ealaxies dont have this diffieulty because thev carry their ellipticitv information iu the part of &- space where the ECL expansion is a good match to the Airy function., Marginally-resolved galaxies don't have this difficulty because they carry their ellipticity information in the part of $k$ -space where the EGL expansion is a good match to the Airy function.855 We see that this ~Airv fuluc is uot au intrinsic §=ditiiculty of the shaq)o-1ueasurenmient iethodologv. but rather stems from a poor model of the PSF.," We see that this “Airy failure” is not an intrinsic difficulty of the shape-measurement methodology, but rather stems from a poor model of the PSF."856 This leads us to consider several possible sollolis: Tn these tests we implement the last of these three options. by bhuriug the postage-stamp and PSF nuages with a Gaussian that is a 1/1 of the size of the galaxy. aud then apply ddeconvolution using the smeared lage pair.," This leads us to consider several possible solutions: In these tests we implement the last of these three options, by blurring the postage-stamp and PSF images with a Gaussian that is a $1/4$ of the size of the galaxy, and then apply deconvolution using the smeared image pair."857 The blurring decreases the size nuismateli between the PSF aud ealaxy CL bases. which improves the accuracy of the GL expansion at the size scale relevant to the laree ealaxy.," The blurring decreases the size mismatch between the PSF and galaxy GL bases, which improves the accuracy of the GL expansion at the size scale relevant to the large galaxy."858 The blaring very slieltly iucreascs the scatter of the shape nieasurenaent. but ereatlv reduces the bias. as seen iu the figure.," The blurring very slightly increases the scatter of the shape measurement, but greatly reduces the bias, as seen in the figure."859" To παπαΊο, the cusp at &=0 in the Απ PSF is not well ft bv our default PSF characterization. leading to biases in the shape measurements."," To summarize, the cusp at $k=0$ in the Airy PSF is not well fit by our default PSF characterization, leading to biases in the shape measurements."860 This can be remedied in ΠΙΟ of wavs without invalidating our general approach., This can be remedied in a number of ways without invalidating our general approach.861 The previous section discussed shape measurenent accuracies with a well defined iuput shape aud, The previous section discussed shape measurement accuracies with a well defined input shape and862"the other surveys, recovers the fewest.","the other surveys, recovers the fewest."863" However, there is no simple answer to the question of which survey is most sensitive."," However, there is no simple answer to the question of which survey is most sensitive."864" Our synthetic data sets represent surveys of different stellar tracers (i.e. MSTO or RR Lyrae stars) selected with different observing M-giant,strategies."," Our synthetic data sets represent surveys of different stellar tracers (i.e. M-giant, MSTO or RR Lyrae stars) selected with different observing strategies."865" As a result, these data sets explore the space around the Galaxy with a variety in the numbers of stars, depths and accuracies in distance estimates, as outlined in and summarized in1."," As a result, these data sets explore the space around the Galaxy with a variety in the numbers of stars, depths and accuracies in distance estimates, as outlined in and summarized in."866". In addition to these differences in spatial exploration, systematic differences in the stellar populations of objects of different luminosities and accretion times (e.g.asreflectedinthe?) means that the choice of tracers affects the relative number of stars contributing to each data set from different accretion events."," In addition to these differences in spatial exploration, systematic differences in the stellar populations of objects of different luminosities and accretion times \citep[e.g. as867reflected in the stellar-mass/metallicity relation for Local Group868dwarfs, see][]{1974MNRAS.169..229L}869 means that the choice of tracers affects the relative number of stars contributing to each data set from different accretion events."870" illustrates this effect by plotting the sampling probability of accretion events in the L-t,-< plane relative to data set SI—- the sampling probability being computed as the distribution of stars in a survey in the L-ta«. probabilityplane (the L and tac of a star appearingbeing that of its parent satellite).", illustrates this effect by plotting the sampling probability of accretion events in the $L$ $t_{\rm acc}$ plane relative to data set S1– the sampling probability being computed as the probability distribution of stars appearing in a survey in the $L$ $t_{\rm acc}$ plane (the $L$ and $t_{\rm acc}$ of a star being that of its parent satellite).871" The top panel, for data set S2, clearly shows the expected bias of M-giants towards tracing the highest metallicity and hence highest luminosity events."," The top panel, for data set S2, clearly shows the expected bias of M-giants towards tracing the highest metallicity and hence highest luminosity events."872" In addition, M-giants are intermediate age stars, which means that such surveys do not contain stars from ancient accretion events."," In addition, M-giants are intermediate age stars, which means that such surveys do not contain stars from ancient accretion events."873" The second two panels show the probability for our deep MSTO surveys S3 and S3',sampling which differ only in the color range from which stars are selected."," The second two panels show the sampling probability for our deep MSTO surveys S3 and S3', which differ only in the color range from which stars are selected."874 Both surveys contain stars from lower luminosity objects and earlier accretion times than the S2 surveys., Both surveys contain stars from lower luminosity objects and earlier accretion times than the S2 surveys.875" A comparison of the two shows that as the red edge of the color limit increases, the sampling probability increases for old and high luminosity events (upper right hand region in the plots) and decreasing the red edge of the color limit has the opposite effect, i.e., sampling probability increases for recent and low luminosity events (lower left hand region in the plots)."," A comparison of the two shows that as the red edge of the color limit increases, the sampling probability increases for old and high luminosity events (upper right hand region in the plots) and decreasing the red edge of the color limit has the opposite effect, i.e., sampling probability increases for recent and low luminosity events (lower left hand region in the plots)."876 This is because a) the blue edge of the MSTO stars in an isochrone (knee shaped feature in the color magnitude diagram) shifts wards with the increase in age and metallicity of the stars and b) the high luminosity events are also metal rich., This is because a) the blue edge of the MSTO stars in an isochrone (knee shaped feature in the color magnitude diagram) shifts red-wards with the increase in age and metallicity of the stars and b) the high luminosity events are also metal rich.877 Increasing the photometric errors has an effect similar to increasing the color range., Increasing the photometric errors has an effect similar to increasing the color range.878 This is the reason why the sampling probability for high luminosity events is slightly higher for S3 as compared to S1 although both surveys have the same color limits., This is the reason why the sampling probability for high luminosity events is slightly higher for S3 as compared to S1 although both surveys have the same color limits.879" The fourth panel, for the RR Lyrae survey (data set S4), shows the strongest bias towards old and low-luminosity events as RR Lyraes are old, low-metallicity stars."," The fourth panel, for the RR Lyrae survey (data set S4), shows the strongest bias towards old and low-luminosity events as RR Lyraes are old, low-metallicity stars."880" The bottom panel, for the MSTO samples with SDSS sky-coverage and magnitude limits (i.e. data set S5), indicates"," The bottom panel, for the MSTO samples with SDSS sky-coverage and magnitude limits (i.e. data set S5), indicates"8812007)).,).882 In the present. paper we employ these process to simulate the mass evolution of a population of artificial clusters., In the present paper we employ these process to simulate the mass evolution of a population of artificial clusters.883 Propertics of the local SER are then derived. by comparing the simulated: age distribution function. (ADE) with that built for clusters in the Solar neighbourhood., Properties of the local SFR are then derived by comparing the simulated age distribution function (ADF) with that built for clusters in the Solar neighbourhood.884 This paper is organised as follows., This paper is organised as follows.885 In Sect., In Sect.886 ὸ we build the ADF for the Solar neighbourhood., \ref{OCADF} we build the ADF for the Solar neighbourhood.887 In Sect., In Sect.888 3. we briellv discuss the cluster mass-oss process., \ref{TCADF} we briefly discuss the cluster mass-loss process.889 In Sect., In Sect.890 4 we simulate the observed. ADP anc use it to constrain the local SER., \ref{sfr} we simulate the observed ADF and use it to constrain the local SFR.891 Concluding remarks are given in Sect. 5.., Concluding remarks are given in Sect. \ref{Conclu}.892 The number of star clusters with accurate age and distance determinations has been steadily increasing over the Last vears., The number of star clusters with accurate age and distance determinations has been steadily increasing over the last years.893 This is particularly true for the very voung clusters. most of which so embedded in their parent eas and. dust cloud that their stellar content is essentially inacessible to optical photometry.," This is particularly true for the very young clusters, most of which so embedded in their parent gas and dust cloud that their stellar content is essentially inacessible to optical photometry."894 However. the availability. of uniform. wide-field. anc rather deep near-intrared surveys (c.g.2XMASSL.. some covering essentially all the sky (PALASS). has led to the discovery - and allowed a robust xwameter derivat - of many such embedded clusters (EC's - E. Metal.2ee 03:: Dicaetal. 2003: Kumar.Davis 200433: BeanecIxeto&Clerkin 2006)): Donatto.San-osJr.& 2006:: Ortolaniοἱal. 2008:: Bonatto&Bica OOb: Bonatto&Bica 2009c:: Bonatto&Biea 2010a)). ogether with some old and/or very reddened OC's (ας. Froebrich.Scholz&Raftery20€ DicMEM&DBica2007 Donatto&Biea 2008:: DonattoNa20( Oa: Eroebrichetal. 2010:: Bonatto&ίσα 2010b)).," However, the availability of uniform, wide-field, and rather deep near-infrared surveys (e.g., some covering essentially all the sky (2MASS), has led to the discovery - and allowed a robust parameter derivation - of many such embedded clusters (ECs - e.g. \citealt{DBSB03}; ; \citealt{BDSB03}; ; \citealt{Kumar04}) ); \citealt{KKC06}) ); \citealt{N6611}; \citealt{DBSB48}; \citealt{N2244}; ; \citealt{Pi5}; ; \citealt{vdB92}) ), together with some old and/or very reddened OCs (e.g. \citealt{Froeb07}; \citealt{OldOC2}; \citealt{OldOC1}; \citealt{LKStuff}; \citealt{Froeb10}; \citealt{Teu34}) )."895 ‘Together with the several hundred: objects already indexed in the widely-used star cluster databases and DAMLO2!.. the. recent discoveries (together. with parameter derivation for poorly-stuclieck and/or unstucdied objects) areproving invaluable in constructing a more detailed. picture of the cluster ADP. especially in the Solar neighbourhood and for very voung clusters (Sect. 4))," Together with the several hundred objects already indexed in the widely-used star cluster databases and, the recent discoveries (together with parameter derivation for poorly-studied and/or unstudied objects) areproving invaluable in constructing a more detailed picture of the cluster ADF, especially in the Solar neighbourhood and for very young clusters (Sect. \ref{sfr}) )."896 We started by searching WEBDA ancl DAMLU22 [or clusters with available age (/3)) and distance from the Sun (d.))., We started by searching WEBDA and DAML02 for clusters with available age ) and distance from the Sun ).897 However. given the amount of new data routinely published. it usually takes a considerable time for both databases to incorporate the recently discovered. clusters. or to update previous entries with newly derived paranicters.," However, given the amount of new data routinely published, it usually takes a considerable time for both databases to incorporate the recently discovered clusters, or to update previous entries with newly derived parameters."898 Then. we complemented. the sample by searching the recent literature for clusters that still are not. listed in either database.," Then, we complemented the sample by searching the recent literature for clusters that still are not listed in either database."899 Cluster designations ancl coordinates have been checked. among all sources (WEBDA. DAMLO2. ancl literature) to avoid. duplicitv.," Cluster designations and coordinates have been checked among all sources (WEBDA, DAML02, and literature) to avoid duplicity."900 When multiple values of age audor distance occurred. we adopted those based on colour-magnitude clagrams (CMDs). or the more recent.," When multiple values of age and/or distance occurred, we adopted those based on colour-magnitude diagrams (CMDs), or the more recent."901 The final sample contains 1718 clusters (EC's anc OC's) with age and. distance. of which 442 are closer than kkpe from theSun’.," The final sample contains 1718 clusters (ECs and OCs) with age and distance, of which 442 are closer than kpc from the."902.. By far. most of the parameters have been taken from WEDDA and DAMLO2. which do not provide measurement uncertainties.," By far, most of the parameters have been taken from WEBDA and DAML02, which do not provide measurement uncertainties."903 Thus. based on our experience in working with clusters of different ages and distances. we adopted the following uniform error attribution: for d.«lkkpc. for d«d.(kpc)5. for 5«d.(kpe)9. and for d.2Okkpe: for [4«20 MMywr. [or 20«/4CMwvr)<100. for LOO«/4(Myr)<2000. and for £42000 Myr.," Thus, based on our experience in working with clusters of different ages and distances, we adopted the following uniform error attribution: for $\ds<1$ kpc, for $\rm1<\ds(kpc)<5$, for $\rm5<\ds(kpc)<9$, and for $\ds>9$ kpc; for $\ta<20$ Myr, for $\rm20<\ta(Myr)<100$, for $\rm100<\ta(Myr)<2000$, and for $\ta>2000$ Myr."904 Age uncertainties are explicitly. incorporated. into the ADE. which is defined as the fractional number of clustersper Myr. ADE=dNdla.," Age uncertainties are explicitly incorporated into the ADF, which is defined as the fractional number of clusters Myr, $ADF\equiv dN/d\ta$."905 Formally. if measurements of a given parameter x are normally (16. Gaussian) distributed around the average x with a standard. deviation o. the probability of finding it at a specific value X is given by ↙↴−≖↿∖⊤∣↴↓∪∣⋡⋯↓∠⊓↓∐⊳∖⇀∖∐↓⊲∖∖⊽∢⋅↓⊔⋅⊳∖⇂∠⇂⋖⋅∐⊔⋖⋅AfA νι.," Formally, if measurements of a given parameter $\chi$ are normally (i.e. Gaussian) distributed around the average $\bar\chi$ with a standard deviation $\sigma$, the probability of finding it at a specific value $\chi$ is given by $P(\chi)=\frac{1}{\sqrt{2\pi}\sigma}\,e^{{-\frac{1}{2}}\left(\frac{\chi-\bar\chi}906{\sigma}\right)^2}$."907 . . . ⋅ ⋅ a set of ⋅∖bins spanning. the whole range ofB ages. and having. widths that increase with age (to account for the decreasing number of clusters at older ages).," To build this ADF we first define a set of bins spanning the whole range of ages, and having widths that increase with age (to account for the decreasing number of clusters at older ages)."908Then. for a cluster with age and uncertainty ἐνcσ. we compute the probability that the age corresponds to a given bin. which is simply the cillerenee of the error functions at the bin borders.," Then, for a cluster with age and uncertainty $\ta\pm\sigma$, we compute the probability that the age corresponds to a given bin, which is simply the difference of the error functions at the bin borders."909 By doing this for all clusters and age bins. we have the number-cdensity of clusters in each age bin.," By doing this for all clusters and age bins, we have the number-density of clusters in each age bin."910 By definition. the integral of the ADF over the whole range of ages is the number of clusters.," By definition, the integral of the ADF over the whole range of ages is the number of clusters."911 Subsequently. bin widths can be adjusted to minimise the errors. so that the resulting ADE has statistically meaningful values over all ages.," Subsequently, bin widths can be adjusted to minimise the errors, so that the resulting ADF has statistically meaningful values over all ages."912 Star clusters lose mass continually by a combination of orocesses associated with stellar evolution ancl dvnamical interactions (both internal and. external to the cluster)., Star clusters lose mass continually by a combination of processes associated with stellar evolution and dynamical interactions (both internal and external to the cluster).913 tobust analytical descriptions of the niass-loss. processes - or clusters characterised by a wide variety. of paranictors and orbiting in different environments - have become available in recent vears. with model. parameters. derived rom theoretical grounds (e.g. Spitzer.LOST: Lamers.Baumeardt&Cieles 2010)) and. N-bocky simulations (e.g. Daumgardt&Makino2003 eaaeCiclos&Baumearet 2008)).," Robust analytical descriptions of the mass-loss processes - for clusters characterised by a wide variety of parameters and orbiting in different environments - have become available in recent years, with model parameters derived from theoretical grounds (e.g. \citealt{Spitzer87}; \citealt{Lamers10}) ) and N-body simulations (e.g. \citealt{BM03}; \citealt{GB08}) )."914 Formally. the time-rate of of mass of a cluster that was formed with the mass M;=AJ(0) can be expressed as: where the mass-loss process p are: (1) stellar evolution. (2) tidal effects by a steady field. (3) shocks with spiral arms. (4) encounters with C MCs.(5) evaporation. and (6) ejection.," Formally, the time-rate of change of mass of a cluster that was formed with the mass $M_i = M(0)$ can be expressed as: where the mass-loss process $p$ are: (1) stellar evolution, (2) tidal effects by a steady field, (3) shocks with spiral arms, (4) encounters with GMCs, (5) evaporation, and (6) ejection."915 For processes (1) - (4) we adopt the semi-analytical approach of Lamers&Cieles(2006) and Lamers.Daumgardt&Cicles (2010).., For processes (1) - (4) we adopt the semi-analytical approach of \citet{LG06} and \citet{Lamers10}. .916 In what follows weassumethat masses are alwaysexpressed in Solar masses )) and time in Myr: also. we write the equations interms of the remaining-mass fraction," In what follows weassumethat masses are alwaysexpressed in Solar masses ) and time in Myr; also, we write the equations interms of the remaining-mass fraction"917"spectrum matches the simulations very well up to about £=100, but rises more rapidly from about @>150.","spectrum matches the simulations very well up to about $\ell \approx 100$, but rises more rapidly from about $\ell > 150$."918" When constrained to the Kp0 region, the observed spectrum follows the simulations all the way up to @= 200, after which a very small bias toward high values may be seen."," When constrained to the Kp0 region, the observed spectrum follows the simulations all the way up to $\ell919= 200$ , after which a very small bias toward high values may be seen."920" Thus, the simulations seem to approximate the real sky satisfactory on the Kp0 region, while they underestimate the level of residual foregrounds in the inner Galactic regions."," Thus, the simulations seem to approximate the real sky satisfactory on the Kp0 region, while they underestimate the level of residual foregrounds in the inner Galactic regions."921" The defining criterion of the ILC method is of course minimum variance, and the rms of the high-latitude region of the LILC is 684K, while the corresponding number for the WILC is 72uK."," The defining criterion of the ILC method is of course minimum variance, and the rms of the high-latitude region of the LILC is $68\,\mu \textrm{K}$, while the corresponding number for the WILC is $72\,\mu \textrm{K}$."922" In other words, our set of weights results in lower variance, and is therefore better as far as the minimum variance definition is concerned."," In other words, our set of weights results in lower variance, and is therefore better as far as the minimum variance definition is concerned."923" However, this does not necessarily mean that the level of residual foregrounds is smaller."," However, this does not necessarily mean that the level of residual foregrounds is smaller."924" In this, the contrary is true: by computing the residual fractions of each foreground in the high-latitude region as described in the previous section, we find that our map actually has slightly more foreground residuals than the WILC; the fractional residual foreground levels in the high-latitude ILC Kp2 region of the LILC map are [-0.069, -0.011, 0.736], while for the WILC map they are 0.017, 0.424]."," In this, the contrary is true: by computing the residual fractions of each foreground in the high-latitude region as described in the previous section, we find that our map actually has slightly more foreground residuals than the WILC; the fractional residual foreground levels in the high-latitude ILC Kp2 region of the LILC map are [-0.069, -0.011, 0.736], while for the WILC map they are [-0.027,-0.017, 0.424]."925" As noted in the previous section, the amount of residual dust is high in the ILC maps — the method is able to remove only half of the dust present in the W-band, where the dust is the dominant foreground."," As noted in the previous section, the amount of residual dust is high in the ILC maps – the method is able to remove only half of the dust present in the W-band, where the dust is the dominant foreground."926" This result is thus in excellent agreement with the findings presented by Naselskyetal.(2003),, which concludes that the cleaned maps contain residual foregrounds which mainly originate from the W-band."," This result is thus in excellent agreement with the findings presented by \citet{naselsky:2003}, which concludes that the cleaned maps contain residual foregrounds which mainly originate from the W-band."927" As pointed out earlier, one of the major weaknesses of the ILC method is its inability to handle spatial variations in the spectral indices of the foregrounds."," As pointed out earlier, one of the major weaknesses of the ILC method is its inability to handle spatial variations in the spectral indices of the foregrounds."928" To remedy this weakness Bennettetal.(2003b) divided the sky into 12 disjoint regions, and computed one set of weights for each region."," To remedy this weakness \citet{bennett:2003b}929 divided the sky into 12 disjoint regions, and computed one set of weights for each region."930" Out of those 12 regions, 11 lie within the Kp2 Galactic plane, while the rest of sky was treated as one single region."," Out of those 12 regions, 11 lie within the Kp2 Galactic plane, while the rest of sky was treated as one single region."931" In light of the asymmetries recently reported by Eriksenetal.(2004a),, we have partitioned the high-latitude sky yet further, and subsequently computed weights for the Galactic hemispheres and quadrants individually."," In light of the asymmetries recently reported by \citet{Eriksen:2004a}, we have partitioned the high-latitude sky yet further, and subsequently computed weights for the Galactic hemispheres and quadrants individually."932 The results from these computations are shown in Table 3.., The results from these computations are shown in Table \ref{tab:regions}.933 We first consider the quadrant numbers (quadrants are defined by the standard Galactic reference system.), We first consider the quadrant numbers (quadrants are defined by the standard Galactic reference system.)934" While the NW, NE and SW quadrant numbers are approximately internally consistent, the SE quadrant stands out in the Q and V bands."," While the NW, NE and SW quadrant numbers are approximately internally consistent, the SE quadrant stands out in the Q and V bands."935" Thus, these numbers both support and ask question of the findings of Eriksenetal."," Thus, these numbers both support and ask question of the findings of \citet{Eriksen:2004a}."936" Certainly, the earlier results are supported in the sense (2004a)..that there is an asymmetry in the data, possibly marginally aligned from north-west to south-east."," Certainly, the earlier results are supported in the sense that there is an asymmetry in the data, possibly marginally aligned from north-west to south-east."937" However, large differences in the weight coefficients would be interpreted most naturally in terms of variations of the noise and foreground properties, in apparent contradiction to the frequency independence demonstrated both by Eriksenetal.(2004a) and Eriksenetal."," However, large differences in the weight coefficients would be interpreted most naturally in terms of variations of the noise and foreground properties, in apparent contradiction to the frequency independence demonstrated both by \citet{Eriksen:2004a} and \citet{Eriksen:2004b}."938" Further investigation is certainly warranted, but it may (2004b)..yet be that foregrounds could play a role in explaining the observed asymmetries."," Further investigation is certainly warranted, but it may yet be that foregrounds could play a role in explaining the observed asymmetries."939" Unfortunately, it is difficult to assess the significance of the variations in Table 3 properly, but we can make a few rough estimates."," Unfortunately, it is difficult to assess the significance of the variations in Table \ref{tab:regions} properly, but we can make a few rough estimates."940" We have generated 1000 simulated realizations, and computed quadrant weights as described above for each of these."," We have generated 1000 simulated realizations, and computed quadrant weights as described above for each of these."941" Then, for each realization we find the maximum absolute difference between any two quadrants, for each frequency."," Then, for each realization we find the maximum absolute difference between any two quadrants, for each frequency."942 The results from this exercise are summarized in Table, The results from this exercise are summarized in Table943tails consistent with those derived by 005 from the MOS data.,tails consistent with those derived by C03 from the MOS data.944 However. the patchy structure of the tails hints that there may be a substautial contribution frou faint backeround objects (such as the poiut source X resolved withChandra: see 22).," However, the patchy structure of the tails hints that there may be a substantial contribution from faint background objects (such as the point source `X' resolved with; see 2)."945 To separate such a contribution auc prove that the tails are not an artifact. they should be observed with a better spatial resolution.," To separate such a contribution and prove that the tails are not an artifact, they should be observed with a better spatial resolution."946 The excellent resolution of pprovides a close-up view iu the vicinity of Ccmines (right panel of 11) The image shows no emission 20” aliead of the pulsar. predicted by C03.," The excellent resolution of provides a close-up view in the vicinity of Geminga (right panel of 1) The image shows no emission $20''$ ahead of the pulsar, predicted by C03."947" DIustead. we see some diffuse cluission at a distance of 5"". 77, whose shape resembles aui extended perpendicular to the proper motion direction."," Instead, we see some diffuse emission at a distance of $5''$ $7''$, whose shape resembles an extended perpendicular to the proper motion direction."948 The arc aud the outer tails cannot be fitted with the same Wilkim’s model., The arc and the outer tails cannot be fitted with the same Wilkin's model.949" The αποκο polvgon of a 116.5 arcsec? area contaius 32 counts. of which 10.1 counts are estimated to belong to the backeround. (0.087. counts arcsec7. as measured ina 49""«98"" source-free rectangle north of the pulsar. shown in 22)."," The arc-like polygon of a 116.5 $^2$ area contains 32 counts, of which 10.1 counts are estimated to belong to the background (0.087 counts $^{-2}$ , as measured in a $49''\times 98''$ source-free rectangle north of the pulsar, shown in 2)."950 This gives 21.945.7 backeround-subtracted counts., This gives $21.9\pm 5.7$ background-subtracted counts.951" The arcs spectrum (DP—1.240.1 at fixed Ny=1.1«1078 απ2, as obtained from a power-law fit usine the C-statistic) is substantially harder than the pulsas spectrum."," The arc's spectrum $\Gamma=1.2\pm 0.4$ at fixed $N_{\rm H}=1.1\times 10^{20}$ $^{-2}$, as obtained from a power-law fit using the C-statistic) is substantially harder than the pulsar's spectrum."952 A structure of such size aud spectrum cannot be ascribed to PSF tails of the pulsars nuage. which docs not show anv significant pileup (the pulsus count rate is ouly 0.07 countsframe).," A structure of such size and spectrum cannot be ascribed to PSF tails of the pulsar's image, which does not show any significant pileup (the pulsar's count rate is only 0.07 counts/frame)."953 The average image ποιους of 1.0«10.7? counts 1 2? corresponds to au intensity Za;~0.9«10.19 eres cin2s JF 7. about 30 times brighter than the fails seen with EPIC.," The average image brightness of $1.0\times 10^{-5}$ counts $^{-1}$ $^{-2}$ corresponds to an intensity $I_{\rm arc}\sim 0.9\times 10^{-16}$ ergs $^{-2}$ $^{-1}$ $^{-2}$ , about 30 times brighter than the tails seen with EPIC."954 The: N-rav- huninositv: of:this: structure is: Lape~5«42S1075 d5ay CLES 1," The X-ray luminosity ofthis structure is $L_{\rm arc}\sim 9555\times 10^{28}$ $d_{200}^2$ ergs $^{-1}$."956" The most striking feature in the ACTS image is a ~ 5""- fad secu up to 25"" (7.5<10/9459) cur) frou the pulsar in the direction opposite to the pulsars proper motion."," The most striking feature in the ACIS image is a $\sim 5''$ -wide , seen up to $25''$ $7.5\times 10^{16}d_{200}$ cm) from the pulsar in the direction opposite to the pulsar's proper motion."957" The tail is apparently detached from the pulsar by 5"" 6"": its brightness is maximal at 8”. auc it fades with increasing distance from the pulsu."," The tail is apparently detached from the pulsar by $5''$ $6''$ ; its brightness is maximal at $\sim 8''$, and it fades with increasing distance from the pulsar."958" The average image Drightuess iu the 6"".«12"" box (see 11. right panel). which contains 37.146.6 backgrouud-subtracted counts. is 2.5410 couutss baresee 7."," The average image brightness in the $6''\times 12''$ box (see 1, right panel), which contains $37.1\pm 6.6$ background-subtracted counts, is $2.7\times10^{-5}$ counts $^{-1}$ $^{-2}$."959 Although the small iuuiber of counts precludes cetailed spectral analysis. the tails spectrmm can be described by a power-law model with P=1040.2. somewhat harder than the spectra of the outer tails.," Although the small number of counts precludes detailed spectral analysis, the tail's spectrum can be described by a power-law model with $\Gamma = 1.0\pm 0.2$, somewhat harder than the spectrum of the outer tails."960" The iuteusitv of the tail Gu the 6%«12"" box). aa—3410.19 eres 2 +t 7. is about 2 orders of maguitude higher than that of the tails secu with EPIC."," The intensity of the tail (in the $6''\times 12''$ box), $I_{\rm axial}961=3\times 10^{-16}$ ergs $^{-2}$ $^{-1}$ $^{-2}$, is about 2 orders of magnitude higher than that of the tails seen with EPIC."962" Its ΠΛ...(L340.2).102? 2 lo(ineasured from 19.1+7.3) backeromud-subtracted counts in a 6%<20"" box detached by 6"" from the pulsar). is close to the total luminosity of the putative outer tails."," Its luminosity, $L_{\rm axial}963= (1.3\pm 0.2)\times 10^{29}$ $d_{200}^2$ ergs $^{-1}$ (measured from $49.1\pm 7.3$ background-subtracted counts in a $6''\times 20''$ box detached by $6''$ from the pulsar), is close to the total luminosity of the putative outer tails."964" An inspection of the EPIC PN image shows sole patchy cauhancements along the tail direction. at a level of <2«10""o Counts - aresee7. but they are incistinetishable from background fluctuatious."," An inspection of the EPIC PN image shows some patchy enhancements along the tail direction, at a level of $\lesssim 2\times 10^{-7}$ counts $^{-1}$ $^{-2}$, but they are indistinguishable from background fluctuations."965 Heavily sincothed ACTS images show an eulauceineut south of the pulsar which apparently connects the arc with the southern outer tail (au example is shown in 22)., Heavily smoothed ACIS images show an enhancement south of the pulsar which apparently connects the arc with the southern outer tail (an example is shown in 2).966 The resiou of euhauced emission within the 829 arcsec? polveou inchides 105 counts., The region of enhanced emission within the 829 $^2$ polygon includes 105 counts.967 Subtracting 71.9 counts of the scaled background. we obtain 33.1410.8 excess couuts. which corresponds to an intensity a factor of 6 higher han that in the EPIC tails.," Subtracting 71.9 counts of the scaled background, we obtain $33.1\pm 10.8$ excess counts, which corresponds to an intensity a factor of 6 higher than that in the EPIC tails."968 The slope of the excess spectrum. P—1.00.1. is apparently similar to that of he axial tail.," The slope of the excess spectrum, $\Gamma = 1.0\pm 0.4$, is apparently similar to that of the axial tail."969 Thus. although the 36 cuhaucement cau judlv be considered as a fiin detection. its position aud shape support the reality of both this structure and the southern outer tail.," Thus, although the $3\,\sigma$ enhancement can hardly be considered as a firm detection, its position and shape support the reality of both this structure and the southern outer tail."970 No cuhancement is ποσα at the site of he northern outer tail: however. the northern tail looks ess sienificant aud more patchy in the EPIC images. aud only a small part of if was imaged with ACIS.," No enhancement is seen at the site of the northern outer tail; however, the northern tail looks less significant and more patchy in the EPIC images, and only a small part of it was imaged with ACIS."971 If the tails iu the EPIC nuages are real. the Geminea PWN is truly unique: a bow-shock-like structure with ong outer tails a short axial tail behiud the pulsar ive never been seen before i N-ravs.," If the tails in the EPIC images are real, the Geminga PWN is truly unique: a bow-shock-like structure with long outer tails a short axial tail behind the pulsar have never been seen before in X-rays."972 Before discussing xossible interpretations of the observed structures. we note hat the proper motion of Geminea. 07117 1. iuplies a oulsar speed e=160d kan L|. where d=dogg/sini.," Before discussing possible interpretations of the observed structures, we note that the proper motion of Geminga, 17 $^{-1}$, implies a pulsar speed $v = 160\,\tilde{d}$ km $^{-1}$, where $\tilde{d} = d_{200}/\sin i$."973" For a reasonable distance. it exceeds a typical sound speed in he interstellar iuediun (ISAT). e=15(p/0.6)HTT3 auos Lowhere po and T=d0/T, K are the molecular weight and tenmiperature."," For a reasonable distance, it exceeds a typical sound speed in the interstellar medium (ISM), $c_s = 15\, (\mu/0.6)^{-1/2} T_4^{1/2}$ km $^{-1}$, where $\mu$ and $T = 10^4 T_4$ K are the molecular weight and temperature."974" Asstmine that the speed of a yossible ISM flow at the location of Ceminga is much ower than e. the ram pressure due to the pulsar motion in the ISM is peanL3.«1019,482 cres 5m7. where | ds the ISM deusity im atomic mass uuits per eni. This eives an estimate Ry=Lt.1go,24 cni for the stand-off distance of the TS head. which translates iuto the projected angular distance Ry=δη1242,"," Assuming that the speed of a possible ISM flow at the location of Geminga is much lower than $v$, the ram pressure due to the pulsar motion in the ISM is $p_{\rm ram} = 4.3\times 10^{-10} n\, \tilde{d}^{2}$ ergs $^{-3}$, where $n$ is the ISM density in atomic mass units per $^3$, This gives an estimate $R_{\rm h} = 1.4\times 10^{16} n^{-1/2} \tilde{d}^{-1}$ cm for the stand-off distance of the TS head, which translates into the projected angular distance ${\cal R}_{\rm h} = 4\farcs8\, n^{-1/2} \tilde{d}^{-2}$."975" Thus, one can expect that Cominga is accompanied by a bow-shock PWN. with a characteristic size comparable to the sizes of the structures observed withChandra."," Thus, one can expect that Geminga is accompanied by a bow-shock PWN, with a characteristic size comparable to the sizes of the structures observed with."976" We will discuss possible interpretations of the whole PWN. starting cach fron an assumption on the nature of the axial tail. the brightest feature of the PWN,"," We will discuss possible interpretations of the whole PWN, starting each from an assumption on the nature of the axial tail, the brightest feature of the PWN."977 The axial tail could be iuterpreted as svuchrotrou Cluission from the shocked PW collimated by the ram pressure., The axial tail could be interpreted as synchrotron emission from the shocked PW collimated by the ram pressure.978 According to the sinulatious by BOS. who assunied an isotropic PW. the TS has a bullet-like shape.," According to the simulations by B05, who assumed an isotropic PW, the TS has a bullet-like shape."979" For large Mach που», =efe; and snall values of the inagnetizatiou parameter σ of the pre-shock PW (see leuuecl Corouiti 1981). the bullets exliudrical radius 1l rpyw~Ay, aud the distance of its back surface from the pulsar is Ri),— 624."," For large Mach numbers, ${\mathcal M} = v/c_s$, and small values of the magnetization parameter $\sigma$ of the pre-shock PW (see Kennel Coroniti 1984), the bullet's cylindrical radius is $r_{\rm TS} \sim R_{\rm h}$, and the distance of its back surface from the pulsar is $R_{\rm b} \sim 6 R_{\rm h}$ ."980 The shocked PW outside the TS is confined inside the CD surface which has a cylindrical shape belind the TS. with a radius rep~LRy.," The shocked PW outside the TS is confined inside the CD surface which has a cylindrical shape behind the TS, with a radius $r_{\rm CD} \sim 4 R_{\rm h}$."981 The collimated PW flows with subrelativistic velocities: 0.3 c in the immer channel. &<rms. and up to 0.50.9 e in the outer chaunel τωroxrep (see H13 and §33.3 in BOD).," The collimated PW flows with subrelativistic velocities: 0.1--0.3 $c$ in the inner channel, $r\lesssim r_{\rm TS}$, and up to 0.8–0.9 $c$ in the outer channel, $r_{\rm TS} \lesssim r \lesssim r_{\rm CD}$ (see 1–3 and 3.3 in B05)."982" First. one can speculate that the axial tail is the CD- cylindrical tubebehind the TS. which implies a CD radius of ~37, Ry~(""7s7. andRy,~5"" 3u7."," First, one can speculate that the axial tail is the CD-confined cylindrical tubebehind the TS, which implies a CD radius of $\sim 3''$, ${\cal R}_{\rm h} \sim 9830\farcs7\sin i$, and${\cal R}_b \sim 5''\sin i$ ."984" Iu this interpretation. one should expectbrightest cussion from the shocked PW at <1” ahead of the pulsar. hidden within the pulsar ππαρο,"," In this interpretation, one should expectbrightest emission from the shocked PW at $\lesssim 1''$ ahead of the pulsar, hidden within the pulsar image."985" The actually observed emission ~5"" 7"" ahead of the pulsar(the arc) is uot explained by this model.", The actually observed emission $\sim 5''$ $7''$ ahead of the pulsar(the arc) is not explained by this model.986 Being well outside the CD. the two outer tails cannot be associated with ashocked PW.," Being well outside the CD, the two outer tails cannot be associated with ashocked PW."987 Ouc might speculate that they are produced bv the shocked ISM, One might speculate that they are produced by the shocked ISM988"line “star-forming” and objects falling between the two lines ""composite"" objects.","line “star-forming"" and objects falling between the two lines “composite"" objects."989 The region dominated: by ionization [rom processes other than star formation is furthermore clivicdecl into Sevferts and LINERs (low-ionisation nuclear emission-line regions: Lieckman 1980)., The region dominated by ionization from processes other than star formation is furthermore divided into Seyferts and LINERs (low-ionisation nuclear emission-line regions; Heckman 1980).990 To split this region into Sevíert and LINER. types we use the diagonal dividing line suggested by Schawinskietal.(2007)., To split this region into Seyfert and LINER types we use the diagonal dividing line suggested by \citet{S07}.991.. Objects in the Sevfert. region ave clearly identified as classical obscured CEvpe 2) Sevíferts ACGNs). while the LINER. region is more controversial and. possibly represents a heterogeneous. population (see Section 6 of Lo2008. for a recent review of possible sources oLionisation for LINERS).," Objects in the Seyfert region are clearly identified as classical obscured (Type 2) Seyferts AGNs), while the LINER region is more controversial and possibly represents a heterogeneous population (see Section 6 of \citealt{H08} for a recent review of possible sources of ionisation for LINERs)."992 Reeent results from the SAUIRON survey by Sarzictal.(2009) show that the extended LINER. cussion seen in most SDSS [fibre spectra (whose physical footprint. corresponds to 2-3. kpc in the sample studied here) is inconsistent with a central point source for the ionisation. ruling out nuclear activity as the dominant source for the emission.," Recent results from the SAURON survey by \citet{Sarzi09} show that the extended LINER emission seen in most SDSS fibre spectra (whose physical footprint corresponds to 2-3 kpc in the sample studied here) is inconsistent with a central point source for the ionisation, ruling out nuclear activity as the dominant source for the emission."993 Intriguinglv. this is even the case when the presence of nuclear activity (e.g. from radio data) is detected.," Intriguingly, this is even the case when the presence of nuclear activity (e.g. from radio data) is detected."994 The position of red. spirals on a DIT. diagram is --lustrated in Figure 15 where points are coded (both in size and colour) by the stellar mass of the galaxy., The position of red spirals on a BPT diagram is illustrated in Figure \ref{redBPT} where points are coded (both in size and colour) by the stellar mass of the galaxy.995 Many more of the τος spirals than the blue are. placed: above 10 Wewleyetal.(2001) dividing line. indicating that jev are not dominated by emission [rom star forming regions. but their eas must be ionised by other mechanisms (30ΕΕ of all face-on clisky red spirals in redshift interval of 0.05-0.085. compared to 4+1& οἳ blue spirals).," Many more of the red spirals than the blue are placed above the \citet{Ke01} dividing line, indicating that they are not dominated by emission from star forming regions, but their gas must be ionised by other mechanisms $30\pm4\%$ of all face-on disky red spirals in redshift interval of 0.05-0.085, compared to $4\pm1\%$ of blue spirals)."996 As the plot indicates. a significant fraction of these galaxies are LINER-type (82+ 12%).," As the plot indicates, a significant fraction of these galaxies are LINER-type $82\pm12\%$ )."997 The remaining red spirals have many more composite objects than are found in the normal spiral population (49d5% compared to 15414 of blue spirals) with onlv a relatively small fraction being classed as starforming by the Ixaulfmannetal.(2003b) criterion (21x3A of red spirals compared to SId24 of blue spirals)., The remaining red spirals have many more composite objects than are found in the normal spiral population $49\pm5\%$ compared to $15\pm1\%$ of blue spirals) with only a relatively small fraction being classed as starforming by the \citet{K03b} criterion $21\pm3\%$ of red spirals compared to $81\pm2\%$ of blue spirals).998 Part of these trends can be explained. by the larger stellar masses of the red spirals. since it is well known hat Sevferts anc LINERs are more common in higher mass ealaxies (e.g.Waullmannetal.2003b).," Part of these trends can be explained by the larger stellar masses of the red spirals, since it is well known that Seyferts and LINERs are more common in higher mass galaxies \citep[e.g.][]{K03b}."999. Therefore for a fair comparison we Construct a sample of blue spirals selected rom the full blue spiral population in such a way that they rave the same mass distribution as the red spirals (our miass matched” blue spiral sample).," Therefore for a fair comparison we construct a sample of blue spirals selected from the full blue spiral population in such a way that they have the same mass distribution as the red spirals (our “mass matched"" blue spiral sample)."1000" We show 181 of these galaxies the same number as in the red spiral sample for ease of comparison) on the DI""T diagram in Figure 13..", We show 181 of these galaxies the same number as in the red spiral sample for ease of comparison) on the BPT diagram in Figure \ref{blueBPTmatched}.1001 Compared Oo this mass matched. sample of blue. spirals. rec spirals are still significantly more likely to host optically identified Seyfert|LINER. emission lines.," Compared to this mass matched sample of blue spirals, red spirals are still significantly more likely to host optically identified Seyfert+LINER emission lines."1002 οσα. 302:44 of rec spirals are above the Ixewleyetal.(2001) division and 48x554 are in the composite region.," Recall, $30\pm4\%$ of red spirals are above the \citet{Ke01} division and $48\pm5\%$ are in the composite region."1003 In comparison we find only 7+1X mass matched blue spirals in the Sevfert|LINER. region and 23cxlX in the composite region., In comparison we find only $7\pm1\%$ mass matched blue spirals in the Seyfert+LINER region and $23\pm1\%$ in the composite region.1004 Hed. spirals are therefore ~4 times as likely to have Sevfert|LINER. emission lines. and twice as likely to be composite objects when compared to similar blue spirals.," Red spirals are therefore $\sim$ 4 times as likely to have Seyfert+LINER emission lines, and twice as likely to be composite objects when compared to similar blue spirals."1005 We plot. in Figure. 14. the observed. fractions of Sevlert|LINEN. and starforming galaxies as a function of mass for both the red ancl blue spirals., We plot in Figure \ref{bptfractions} the observed fractions of Seyfert+LINER and starforming galaxies as a function of mass for both the red and blue spirals.1006 For both sub-populations the Sevfert|LINER. fraction increases with stellar mass. while the starforming [fraction decreases. however as previously commented. at a given stellar mass red spirals are roughly twice as likely to be classifed: as Sevlert(LINER. ancl less likely (roughly half as likely) to be classified as a starforming.," For both sub-populations the Seyfert+LINER fraction increases with stellar mass, while the starforming fraction decreases, however as previously commented, at a given stellar mass red spirals are roughly twice as likely to be classifed as Seyfert/LINER, and less likely (roughly half as likely) to be classified as a starforming."1007 Phere is a suggestion that the increase of Sevfert|LINER. fraction with mass is also faster in the red spirals than it is in the blue spirals (at the expense of “composite” objects. since the starforming fractions are seen to decrease at approximately the sume rate).," There is a suggestion that the increase of Seyfert+LINER fraction with mass is also faster in the red spirals than it is in the blue spirals (at the expense of “composite"" objects, since the starforming fractions are seen to decrease at approximately the same rate)."1008 AGN fractions in all galaxies have generally been shown to be independent of environment. (Miller. et. al., AGN fractions in all galaxies have generally been shown to be independent of environment (Miller et al.1009 2003. Sorrentino. Itadovich Rifatto 2006).," 2003, Sorrentino, Radovich Rifatto 2006)."1010 Llowever. recent work on X-ray selected ACGNs does suggest. an environmental dependence such that N-ray selected AGN are more common in groups than clusters (Arnoldctal.2009.thisworkalsocompare) and Leeetal.(2009). also suggest AGN are Less common in higher densities.," However, recent work on X-ray selected AGNs does suggest an environmental dependence such that X-ray selected AGN are more common in groups than clusters \citep[][this work also comments on the complete disjoint of X-ray selected and BPT selected AGN samples making such studies hard to compare]{Ar09} and \citet{L09} also suggest AGN are less common in higher densities."1011 Here. we see no signature of a density dependence of the Sevfert|LINER: fraction of red spirals. although we note that the red spiral sample is quite small to divide in this way and covers only a limited range of densities.," Here, we see no signature of a density dependence of the Seyfert+LINER fraction of red spirals, although we note that the red spiral sample is quite small to divide in this way and covers only a limited range of densities."1012 Rec spirals with emission lines which are not classified as coming [rom star formation are more likely to be classified as LINERS than similar objects in the blue spirals population. with N2+12% of those in red spirals being LINERS versus 57+7% in the mass matched. blue spirals.," Red spirals with emission lines which are not classified as coming from star formation are more likely to be classified as LINERS than similar objects in the blue spirals population, with $82\pm12\%$ of those in red spirals being LINERS versus $57\pm7\%$ in the mass matched blue spirals."1013 This means the Sevfert fractions of red ancl blue spirals of the same mass are actually quite similar (62:254. of ree spirals versus 3ckX of blue spirals) - the main difference in the two populations appears to be in the LINER. fraction which sugeests a link between LINER. emission and the shutting down of star formation in spiral galaxies., This means the Seyfert fractions of red and blue spirals of the same mass are actually quite similar $6\pm2\%$ of red spirals versus $3\pm1\%$ of blue spirals) - the main difference in the two populations appears to be in the LINER fraction which suggests a link between LINER emission and the shutting down of star formation in spiral galaxies.1014 Overall 25+4% of the red spirals are classified as having LINERs. while only 441% of the (mass matched) blue spirals meet the LINER criteria.," Overall $25\pm4\%$ of the red spirals are classified as having LINERs, while only $4\pm1\%$ of the (mass matched) blue spirals meet the LINER criteria."1015 Interestingly in visually classified carly type ealaxies. Schawinskietal.(2007) also found that an increase in LINER. fraction was associated with “stellar quiescencee. while Smoleié(2009). studying radio loud AGN also found that the radio AGN in the red sequence were dominated by low ionization AGN which were classified as LINEIHs in the BPT diagram.," Interestingly in visually classified early type galaxies, \citet{S07} also found that an increase in LINER fraction was associated with “stellar quiescence"", while \citet{Sm09} studying radio loud AGN also found that the radio AGN in the red sequence were dominated by low ionization AGN which were classified as LINERs in the BPT diagram."1016 The Balmer line emission from even a small amount of star formation is expected to dominate any AGN emission., The Balmer line emission from even a small amount of star formation is expected to dominate any AGN emission.1017 Schawinskietal.(2010)— study. the masking. of AGN (Seyfert) emission in star forming galaxies and show that for AGN OLD Luniinosities below 107 erg s+ most galaxies with star formation present will not be classified as AGN. and that only above 107Lo erg will the sample of ACN identified by optical emission lines be reasonably complete in the blue cloud.," \citet{Sc09} study the masking of AGN (Seyfert) emission in star forming galaxies and show that for AGN [OIII] luminosities below $10^{39}$ erg $^{-1}$ most galaxies with star formation present will not be classified as AGN, and that only above $10^{40}$ erg $^{-1}$ will the sample of AGN identified by optical emission lines be reasonably complete in the blue cloud."1018 We show in Figure 15. histograms of the OLLI] luminosities (extinction. corrected using the method described in Leectal. 2009)) of both red. ancl blue spirals (from the sample matehec in mass with the red. spirals) classified as having either Sevfert or LINER. emission., We show in Figure \ref{LOIII} histograms of the [OIII] luminosities (extinction corrected using the method described in \citealt{L09}) ) of both red and blue spirals (from the sample matched in mass with the red spirals) classified as having either Seyfert or LINER emission.1019 This, This1020EIS and time series of coronal images for three hours in each location.,EIS and time series of coronal images for three hours in each location.1021 EIS on repeated sparse rasters at 6 min cadence., EIS on repeated sparse rasters at 6 min cadence.1022 Spectra of emission lines listed in Table 1. were recorded with the wide slit and at exposure time of 25 s. Emission lines were selected to cover a wide range of temperature within a limited telemetry volume.," Spectra of emission lines listed in Table \ref{table:linelist}1023 were recorded with the wide slit and at exposure time of 25 s. Emission lines were selected to cover a wide range of temperature within a limited telemetry volume."1024 The resultant pixel resolution is after summing along the slit to increase the signal to noise ratio., The resultant pixel resolution is $\times$ after summing along the slit to increase the signal to noise ratio.1025" Each raster scan consists of 12 exposures with step size. and an area of 44x320""."," Each raster scan consists of 12 exposures with step size, and an area of $\times$."1026. The duration of the sequence was one hour due to the eclipse periods during the Sun-synchronous orbit., The duration of the sequence was one hour due to the eclipse periods during the Sun-synchronous orbit.1027 EIS data are calibrated with the standard procedures provided in the Solar Software tree (SSW:?).., EIS data are calibrated with the standard procedures provided in the Solar Software tree \citep[SSW;][]{freeland1998}.1028 A single Gaussian fit was applied to spectra to deduce radiance. Doppler velocity. and line width.," A single Gaussian fit was applied to spectra to deduce radiance, Doppler velocity, and line width."1029 A single Gaussian results in a reasonable fit in quiet conditions., A single Gaussian results in a reasonable fit in quiet conditions.1030 Spectral profiles taken during the microflares occasionally. deviate from Gaussian profiles because of enhancements in the wings. which are presented in Sect.," Spectral profiles taken during the microflares occasionally deviate from Gaussian profiles because of enhancements in the wings, which are presented in Sect."1031 4.3., 4.3.1032 As for EIS. the Doppler shift 1s deduced after compensating for the instrumental effect caused by temperature variations (?) and using the rest wavelengths of emission lines identified by ?..," As for EIS, the Doppler shift is deduced after compensating for the instrumental effect caused by temperature variations \citep{kamio2010b} and using the rest wavelengths of emission lines identified by \citet{brown2008}. ."1033 The contribution of the (25.637 nm blending in the (25.632 nm is subtracted by using the other 226.106 nm emission (?).., The contribution of the $\lambda$ 25.637 nm blending in the $\lambda$ 25.632 nm is subtracted by using the other $\lambda$ 26.106 nm emission \citep{kamio2009}.1034 Although a coronal blending remains in the red wing of the spectrum. is the dominant emission at that wavelength.," Although a coronal blending remains in the red wing of the spectrum, is the dominant emission at that wavelength."1035 Time series of coronal images were obtained to study the evolution of the microflares., Time series of coronal images were obtained to study the evolution of the microflares.1036 XRT recorded soft X-ray images with Al_ppoly and Be.tthin filters., XRT recorded soft X-ray images with poly and thin filters.1037 The former is sensitive to low temperature coronal emission down to |xI0? K and shows coronal structures 1n quiet regions., The former is sensitive to low temperature coronal emission down to $1\times10^6$ K and shows coronal structures in quiet regions.1038 The latter detects the higher temperature corona and normally results in à weak signal in quiet regions., The latter detects the higher temperature corona and normally results in a weak signal in quiet regions.1039 It was intended to capture the hot component in coronal bright points., It was intended to capture the hot component in coronal bright points.1040" A pair of X-ray filter images were obtained every 60 s. The area of the XRT images were 384384"".. and the EIS area was covered."," A pair of X-ray filter images were obtained every 60 s. The area of the XRT images were $\times$, and the EIS area was covered."1041 Co-alignment between EIS and XRT was performed by comparing the 219.512 nm radiance map from EIS and XRT ppoly images., Co-alignment between EIS and XRT was performed by comparing the $\lambda$ 19.512 nm radiance map from EIS and XRT poly images.1042 We estimate a co-alignment error of4”. which corresponds to the scan step of the EIS data.," We estimate a co-alignment error of, which corresponds to the scan step of the EIS data."1043 Other emission lines are registered after compensating for the north — south offset of the EIS spectra (?).., Other emission lines are registered after compensating for the north – south offset of the EIS spectra \citep{kamio2010b}.1044 EUVI obtained images with filters of 217.1 nm ix/x). 419.5 nm xi). and 4430.4 nm (Hen).," EUVI obtained images with filters of $\lambda$ 17.1 nm ), $\lambda$ 19.5 nm ), and $\lambda$ 30.4 nm )."1045 EUVI images with the set of filters. were recorded at a cadence of 10 min., EUVI images with the set of filters were recorded at a cadence of 10 min.1046 À coordinate conversion 1s necessary to find the bright points observed with XRT in the SECCHI/EUVI images., A coordinate conversion is necessary to find the bright points observed with XRT in the SECCHI/EUVI images.1047 The separation angles between the Earth and STEREO-A and B spacecrafts were 46.7? and 47.07. respectively.," The separation angles between the Earth and -A and B spacecrafts were $46.7^{\circ}$ and $47.0^{\circ}$, respectively."1048 Since the spacecraft is in low-Earth orbit (2).. XRT images are regarded as Earth view.," Since the spacecraft is in low-Earth orbit \citep{kosugi2007}, XRT images are regarded as Earth view."1049 Assuming that a coronal bright point was located on the solar surface. Heliocentric Earth Ecliptic coordinates of the bright point are deduced from its apparent position in XRT images.," Assuming that a coronal bright point was located on the solar surface, Heliocentric Earth Ecliptic coordinates of the bright point are deduced from its apparent position in XRT images."1050 The coordinates are transformed into spacecraft views by using the SPICE software package provided in the SSW tree., The coordinates are transformed into spacecraft views by using the SPICE software package provided in the SSW tree.1051 The position of the coronal bright point on the EUVI images is determined by taking x and v coordinates in the spacecraft view., The position of the coronal bright point on the EUVI images is determined by taking $x$ and $y$ coordinates in the spacecraft view.1052 In our data set. 10 microflares are identified in X-ray images (7 in quiet region and 3 in coronal hole) and are listed in Table 2..," In our data set, 10 microflares are identified in X-ray images (7 in quiet region and 3 in coronal hole) and are listed in Table \ref{table:bp}."1053 In the following. two representative events are described: one in a quiet region and the other in coronal hole.," In the following, two representative events are described: one in a quiet region and the other in coronal hole."1054 They are labelled as QRI and CHI in Table 2.., They are labelled as QR1 and CH1 in Table \ref{table:bp}.1055 Similarities and differences between the quiet region and the polar coronal hole and the implications for the coronal structures are discussed in Sect., Similarities and differences between the quiet region and the polar coronal hole and the implications for the coronal structures are discussed in Sect.1056 5., 5.1057 The top panel of Fig., The top panel of Fig.1058 1. shows a time series of a bright point in a quiet region near the East limb (QRI in Table 2))., \ref{fig:image} shows a time series of a bright point in a quiet region near the East limb (QR1 in Table \ref{table:bp}) ).1059 Each column presents a 100’x section of SECCHI/EUVI images in 230.4 nm (Hen). A17.1 nm (Feix/x). and 219.5 nm xm). and XRT images with Al_ppoly and Be_tthin filters.," Each column presents a $\times$ section of SECCHI/EUVI images in $\lambda$ 30.4 nm ), $\lambda$ 17.1 nm ), and $\lambda$ 19.5 nm ), and XRT images with poly and thin filters."1060 As the Al_ppoly images show. the bright point was located just inside the limb.," As the poly images show, the bright point was located just inside the limb."1061 The top row shows pre-event images of the bright point at 14:01 UTC., The top row shows pre-event images of the bright point at 14:01 UTC.1062 Enhanced emission was detected at the center of all panels at 14:11 UTC. which suggests that the microflare took place in a wide temperature range.," Enhanced emission was detected at the center of all panels at 14:11 UTC, which suggests that the microflare took place in a wide temperature range."1063 A significant emission increase is detected with the XRT tthin filter. which ts rare in a quiet region.," A significant emission increase is detected with the XRT thin filter, which is rare in a quiet region."1064 This is indicative of a hot component produced by the microflare. since the Be.tthin filter 1s only sensitive to the high temperature corona.," This is indicative of a hot component produced by the microflare, since the thin filter is only sensitive to the high temperature corona."1065 Difference images in 407.1. nm (Feix/x). and 219.5 nm xi). and XRT ppoly are derivedby subtracting pre-event images at 14:01. UTC to emphasize the temporal variation.," Difference images in $\lambda$ 17.1 nm ), and $\lambda$ 19.5 nm ), and XRT poly are derivedby subtracting pre-event images at 14:01 UTC to emphasize the temporal variation."1066 Emissions of the microflare reached their peaks just before 13:11. UTC while a significant dimming was observed in the, Emissions of the microflare reached their peaks just before 14:11 UTC while a significant dimming was observed in the1067within a IIubble time (???77??) εί for a contrary view see ?)).,"within a Hubble time \citep{GR00,AN02,Kazantz04,Escala05,Cuadra09,Dotti09}1068 (but for a contrary view see \cite{Lodato09}) )."1069 The presence of sizable «quantities of interstellar gas in (he parsec-scale environment (hen raises (he question of how much eas might find itself even closer to the pair al their moment of merger., The presence of sizable quantities of interstellar gas in the parsec-scale environment then raises the question of how much gas might find itself even closer to the pair at their moment of merger.1070 This is a subject οἱ great uncertainty., This is a subject of great uncertainty.1071" It has been argued. for example. (hat there should be little gas closer to the merging pair than ~100. 10007, (ry=GAL/e. where AL is the total mass of the svstem) because eventually the timescale for shrinkage of the binary orbit by gravitational wave radiation becomes shorter than the timescale for mass inflow due to internally generated [hid stresses (?).."," It has been argued, for example, that there should be little gas closer to the merging pair than $\sim 100$ $1000r_g$ $r_g \equiv GM/c^2$, where $M$ is the total mass of the system) because eventually the timescale for shrinkage of the binary orbit by gravitational wave radiation becomes shorter than the timescale for mass inflow due to internally generated fluid stresses \citep{MP05}."1072" On the other hand. the mass of such a cireumbinary disk might be as large as LOOAL. or more (????): if even LAL. were close enough to the merging black holes to be given heat equal to 1% of its rest mass. the total ~I0"" eremight well be large enough to produce observable radiation."," On the other hand, the mass of such a circumbinary disk might be as large as $\sim 100 M_{\odot}$ or more \citep{MP05,AN02,Rossi09,Corrales09}; if even $1 M_{\odot}$ were close enough to the merging black holes to be given heat equal to $1\%$ of its rest mass, the total $\sim 10^{50}$ erg—might well be large enough to produce observable radiation."1073 It is therefore a worlliwhile exercise to estimate what sort of light might be generated if even a small fraction ol the surrounding gas were able to make its wav in close to the merging black holes., It is therefore a worthwhile exercise to estimate what sort of light might be generated if even a small fraction of the surrounding gas were able to make its way in close to the merging black holes.1074 Because the amount of mass near the merging black holes is so difficult to estimate al present. the plan of (his paper is to explore prompt electromagnetic radiation in à way that is scaled to whatever gas mass is there.," Because the amount of mass near the merging black holes is so difficult to estimate at present, the plan of this paper is to explore prompt electromagnetic radiation in a way that is scaled to whatever gas mass is there."1075 Thus. we will first estimate the heat per unit mass (hat might be deposited in this gas. then. in order to find (he Iuninositv. estimate the timescale on which the energy is radiated.," Thus, we will first estimate the heat per unit mass that might be deposited in this gas, then, in order to find the luminosity, estimate the timescale on which the energy is radiated."1076 Next. (he more model-dependent subject of the spectrum will be broached.," Next, the more model-dependent subject of the spectrum will be broached."1077 Lastly. having seen how the light emitted depends on gas mass. we will discuss the issues related to whether an “interesting” amount of mass may be present.," Lastly, having seen how the light emitted depends on gas mass, we will discuss the issues related to whether an “interesting"" amount of mass may be present."1078 In oxder to avoid additional complications. we will ignore anv huumninositw due to accretion through the cireumbinary disk.," In order to avoid additional complications, we will ignore any luminosity due to accretion through the circumbinary disk."1079 Let us begin. then. with the supposition that immediatelv before a merger of two supermassive black holes there is al least some gas orbiting over a range of distances not too fay from the svstems center of mass.," Let us begin, then, with the supposition that immediately before a merger of two supermassive black holes there is at least some gas orbiting over a range of distances not too far from the system's center of mass."1080" To discuss the elect of the merger on this relatively nearby gas. it is useful to distinguish (wo regions: the inner gas (r/r, 10) and gas farther away (10—r/r,« 10°)."," To discuss the effect of the merger on this relatively nearby gas, it is useful to distinguish two regions: the inner gas $r/r_g \lesssim 10$ ) and gas farther away $10 < r/r_g < 10^3$ )."1081 These regions are distinguished both by the magnitude of the heating (μον are likely to experience and by the time at which it occurs., These regions are distinguished both by the magnitude of the heating they are likely to experience and by the time at which it occurs.1082 Because the inner gas is in the “near-field” regime. its gravitational environment during (he merger is better described as a nonlinear (me-dependent distortion of spacetime. rather {han a passage of gravitational waves.," Because the inner gas is in the “near-field"" regime, its gravitational environment during the merger is better described as a nonlinear time-dependent distortion of spacetime, rather than a passage of gravitational waves."1083 The amplitude and extent of the distortions are. in some sense. proportional to the binary mass ratio. reaching a maximum when the two," The amplitude and extent of the distortions are, in some sense, proportional to the binary mass ratio, reaching a maximum when the two"1084lice and/or PPAIL emission.,ice and/or PAH emission.1085 This is one of the explanation for the low HAC detectability among the local ULIRGs (Imanishietal.2003)., This is one of the explanation for the low HAC detectability among the local ULIRGs \citep{imanishi08}.1086. We have already. shown that the best analogs to our sources are the sources with red sspectra rather than the more typical local ULIRGs., We have already shown that the best analogs to our sources are the sources with red spectra rather than the more typical local ULIRGs.1087 There are five sources in the AIKADU sample that meet our criteria (i.e. ο 22)., There are five sources in the \citet{imanishi08} AKARI sample that meet our criteria (i.e. $\alpha_{3-4}$ $>$ 2).1088Ofthese. 3showlheH AC feature. andadi[ f. lice feature.," Of these, 3 show the HAC feature, and a different set of 3 show the ice feature."1089 This is roughly in better agreement with the observed detection rates [or our sample (but with very poor statistics!)., This is roughly in better agreement with the observed detection rates for our sample (but with very poor statistics!).1090 relhac.ishowstheHAC /silicateratiovs.hesilicatefeaturestrenglh [oroursourcescompearediwilhlocalU, \\ref{hac_si} shows the HAC/silicate ratio vs. the silicate feature strength for our sources compared with local ULIRGs.1091 LL measurements for local ULIRGs from severalstudies (Imanishietal.20062:Risalitiοἱ2006:Sanietal.2008:Lnanishi2008) combined with the silicate feature depths from Armusοἱal.(2007) and Sirockyetal.(2008).," To construct this figure, we use the $\tau_{\rm{3.4}}$ measurements for local ULIRGs from severalstudies \citep{imanishi_ulirgs,risaliti06,sani08,imanishi08} combined with the silicate feature depths from \citet{armus07} and \citet{sirocky08}."1092. We find that. while the ILAC detectability ol our sample is higher than the local ULIRG population. the IAC/silicate ratio appears consistent with that observed among local ULIRGs where the Ας: [eate is detected.," We find that, while the HAC detectability of our sample is higher than the local ULIRG population, the HAC/silicate ratio appears consistent with that observed among local ULIRGs where the HAC feature is detected."1093 For comparison we also show the data for embedded protostars Irom the review paper of Gibbetal.(2004)., For comparison we also show the data for embedded protostars from the review paper of \citet{gibb04}.1094. Note that the ILAC-to-silieate ratio observed in the MW is remarkably constant across a wide range of silicate feature depth., Note that the HAC-to-silicate ratio observed in the MW is remarkably constant across a wide range of silicate feature depth.1095 This is consistent with the diffuse ISM value of 00.06 (Pendletonοἱal.1994)., This is consistent with the diffuse ISM value of 0.06 \citep{pendleton94}.1096. Moreover. a recent study of the spatial variation of the optical depth in the Circinus galaxy. (the nearest AGN to the MW) found that although (he absolute optical depth: changed dramatically. this ratio remained nearly constant (Collingetal.2009).," Moreover, a recent study of the spatial variation of the optical depth in the Circinus galaxy (the nearest AGN to the MW) found that although the absolute optical depth changed dramatically, this ratio remained nearly constant \citep{colling09}."1097". An enhanced ILAC-to-silicate ratio was lirst reported. by Imanishi(2000) who studied a sample of 4 local obseured. AGN nuclei including NGCLOGS (shown in relhac,/)).", An enhanced HAC-to-silicate ratio was first reported by \citet{imanishi00} who studied a sample of 4 local obscured AGN nuclei including NGC1068 (shown in \\ref{hac_si}) ).1098 Dheir favoredinterprelalionofthisenhancedratiocomes fromthefollowingecplanalion eachoflhelwooplicaldepthsamplesthecolumndensilybeliveenusandi hesources, Their favored interpretation of this enhanced ratio comes from the following explanation: each of the two optical depth samples the column density between us and the sources.1099 IE [lhedustisiwellinivedandi dust at, If the dust is well mixed and in a screen approximation is valid the ratio is expected to remain constant (reflecting the relative abundance of the silicate and carbon grains and their optical properties).1100 aand ον IWIN dust at iis present. since the hotter dust is spatially closer to the power source. the ILAC feature arises from a larger column density than the silicate feature and hence the enhanced ratio.," However if a steep temperature gradient between the $\sim$ K dust at and $\sim$ K dust at is present, since the hotter dust is spatially closer to the power source, the HAC feature arises from a larger column density than the silicate feature and hence the enhanced ratio."1101 This is what is commonly referred to as à buried nucleus’ (seeFig.2Imanishietal. 2007).., This is what is commonly referred to as a `buried nucleus' \citep[see Fig.2][]{imanishi_irs}. .1102 Notice that this model addresses only the obscuration geometry: it is neither a statement about the, Notice that this model addresses only the obscuration geometry: it is neither a statement about the1103"conical extended jet model is also used to explain the emission from radio to ultraviolet wavelengths (seeSect.2.2in?,formoredetails)..",conical extended jet model is also used to explain the emission from radio to ultraviolet wavelengths \citep[see Sect.~2.2 in][for more details]{2001A&A...367..809K}.1104 The absorption by the infrared extragalactic background light at VHE is taken into account and modeled using the estimations as described in ? and references therein., The absorption by the infrared extragalactic background light at VHE is taken into account and modeled using the estimations as described in \citet{2006ApJ...648..774S} and references therein.1105 Here we model only nearby active galactic nuclei (AGNs) and hence this effect can be neglected., Here we model only nearby active galactic nuclei (AGNs) and hence this effect can be neglected.1106" The blob-in-jet model is particularly well adapted to the description of blazars, for which the jet is very close to the line of sight."," The blob-in-jet model is particularly well adapted to the description of blazars, for which the jet is very close to the line of sight."1107" In the following, the assumed cosmology is Hyp=70 ss! MMpc! for an Einstein-de Sitter universe, with 4=0.7 and Q,,=0.3."," In the following, the assumed cosmology is $H_0 = 70\ $ $^{-1}$ $^{-1}$ for an Einstein-de Sitter universe, with $\Omega_\Lambda=0.7$ and $\Omega_m=0.3$."1108" We assume that the population of electrons, which is responsible for the non-thermal emission in leptonic models, has a number density that can be described by a broken power- where Ky=Kiy,"" and y=E/mc?, where m is the electron mass and E its energy."," We assume that the population of electrons, which is responsible for the non-thermal emission in leptonic models, has a number density that can be described by a broken power-law: where $K_2=K_1 \gamma_\mathrm{br}^{n_2-n_1}$ and $\gamma=E/m c^2$, where $m$ is the electron mass and $E$ its energy."1109" These electrons radiate up to the X-ray range through the synchrotron process, and then re-interact with their own emitted photons by inverse Compton (IC) scattering, which is the so-called synchrotron self-Compton process."," These electrons radiate up to the X-ray range through the synchrotron process, and then re-interact with their own emitted photons by inverse Compton (IC) scattering, which is the so-called synchrotron self-Compton process."1110 This synchrotron emission comes from a population of electrons different from those producing the radio-IR emission of the extended jet., This synchrotron emission comes from a population of electrons different from those producing the radio-IR emission of the extended jet.1111 The SSC model has 8 significant parameters., The SSC model has 8 significant parameters.1112" The macrophysics processes are described by the magnetic field B, the radius of the emitting blob r, and the Doppler factor 6p=[Γιί—B5cos ο], where f is the speed of the moving blob in c unit, I;=(1—Brytl? is the blob Lorentz factor and 6 is the viewing angle."," The macrophysics processes are described by the magnetic field $B$, the radius of the emitting blob $r_b$ and the Doppler factor $\delta_b=\left[ \Gamma_b (1 - \beta_b \cos{\theta}) \right]^{-1}$ , where $\beta_b$ is the speed of the moving blob in $c$ unit, $\Gamma_b=(1-\beta_b^2)^{-1/2}$ is the blob Lorentz factor and $\theta$ is the viewing angle."1113" The radiative processes are parametrized by the description of the population of emitting particles, with the parameters Κι, yy, γε, n; and nz from Eq."," The radiative processes are parametrized by the description of the population of emitting particles, with the parameters $K_1$, $\gamma_\mathrm{br}$ , $\gamma_c$, $n_1$ and $n_2$ from Eq."1114"(1).. The value Of Ymin iS not crucial for the interpretation of the spectral energy distribution (SED), nor is y,, although it can become very relevant in cases where the X-rays have a hard slope with a spectral differential index a<1 (in the common f,οςv* notation)."," The value of $\gamma_\mathrm{min}$ is not crucial for the interpretation of the spectral energy distribution (SED), nor is $\gamma_c$, although it can become very relevant in cases where the X-rays have a hard slope with a spectral differential index $\alpha < 1$ (in the common $f_\nu \propto \nu^{-\alpha}$ notation)."1115 All these parameters can be constrained when detailed spectral data are available for a wide frequency range., All these parameters can be constrained when detailed spectral data are available for a wide frequency range.1116" In the present case, the spectral coverage of the nucleus of 887 is sparse and we need to find other ways to constrain the parameters."," In the present case, the spectral coverage of the nucleus of 87 is sparse and we need to find other ways to constrain the parameters."1117" One important constraint comes from the variability: where Afops is the variability timescale in the observer frame, implying r;/ójS5x1015 ccm for 887."," One important constraint comes from the variability: where $\Delta t_\mathrm{obs}$ is the variability timescale in the observer frame, implying $r_b/\delta_b \la 5 \times 10^{15}$ cm for 87."1118" The region of emission is then assumed to be close to the SMBH, to fulfill the variability constraint within magnetohydrodynamic (MHD) jet models."," The region of emission is then assumed to be close to the SMBH, to fulfill the variability constraint within magnetohydrodynamic (MHD) jet models."1119" For instance, ? models the jet formation zone using general relativistic magnetohydrodynamic simulations, applicable to GRBs, AGNs as 887 and black hole X-ray binaries."," For instance, \citet{2006MNRAS.368.1561M} models the jet formation zone using general relativistic magnetohydrodynamic simulations, applicable to GRBs, AGNs as 87 and black hole X-ray binaries."1120" He describes the broadening zone of the jet in the vicinity of the central black hole, and finds the Alfvénn surface at “50 1ρ."," He describes the broadening zone of the jet in the vicinity of the central black hole, and finds the Alfvénn surface at $\sim$ $r_g$."1121 We assume that the emission zone is located slightly above this surface to allow shocks and Fermi acceleration processes to develop in the jet., We assume that the emission zone is located slightly above this surface to allow shocks and Fermi acceleration processes to develop in the jet.1122" The results of ? further constrain some of our parameters for a distance of ~100r, from the SMBH, such as the value of the Lorentz factor I;S10 of the plasma blobs, the magnetic field B, and the half-opening angle ¢(r) of the jet given by his Eq. ("," The results of \citet{2006MNRAS.368.1561M} further constrain some of our parameters for a distance of $\sim$ $r_g$ from the SMBH, such as the value of the Lorentz factor $\Gamma_b \la 10$ of the plasma blobs, the magnetic field $B$, and the half-opening angle $\varphi(r)$ of the jet given by his Eq. ("112324).,24).1124 The case of 887 is of particular interest since its jet is exceptionally well mapped in radio VLBI., The case of 87 is of particular interest since its jet is exceptionally well mapped in radio VLBI.1125" ? observed the core of M887 in VLBI in February 1995 and March 1999, and showed that the opening angle increases quickly with decreasing distance to the core region, at the ppc (70 r,) scale."," \citet{2002NewAR..46..239B} observed the core of 87 in VLBI in February 1995 and March 1999, and showed that the opening angle increases quickly with decreasing distance to the core region, at the pc $\sim$ $r_g$ ) scale."1126" Such a widening at the base of the jet was also observed in AA at the ppc (~190000r,) scale by ? using the VLBI Space Observatory Programme.", Such a widening at the base of the jet was also observed in A at the pc $\sim$ $r_g$ ) scale by \citet{2006PASJ...58..211H} using the VLBI Space Observatory Programme.1127 A broadening zone in the jet formation region is found as well in MHD simulations., A broadening zone in the jet formation region is found as well in MHD simulations.1128" Moreover, the recently detected short term TeV variability seems to exclude the extended and outer regions as the source for VHE emission in 887."," Moreover, the recently detected short term TeV variability seems to exclude the extended and outer regions as the source for VHE emission in 87."1129 This is also argued by ? who present a modified leptonic model applied to 887 which takes into account a deceleration of the inner flow along the base of the jet., This is also argued by \citet{2005ApJ...634L..33G} who present a modified leptonic model applied to 87 which takes into account a deceleration of the inner flow along the base of the jet.1130 So it appears quite natural to assume that the VHE y-rays are emitted in the core widened jet region., So it appears quite natural to assume that the VHE $\gamma$ -rays are emitted in the core widened jet region.1131" We can then imagine that there are blobs of plasma, harboring very high energy electrons and propagating in the widened jet formation zone, that are dragged along with the bulk jet outflow."," We can then imagine that there are blobs of plasma, harboring very high energy electrons and propagating in the widened jet formation zone, that are dragged along with the bulk jet outflow."1132" In the case of misaligned objects such as 887, this can easily result in one blob moving along the line of sight and thus having about the same Lorentz factor as for blazars, allowing to reproduce the TeV emission in the framework of classic SSC models."," In the case of misaligned objects such as 87, this can easily result in one blob moving along the line of sight and thus having about the same Lorentz factor as for blazars, allowing to reproduce the TeV emission in the framework of classic SSC models."1133 However a model with a single relativistic blob moving and emitting exactly towards the observer would be statistically unlikely., However a model with a single relativistic blob moving and emitting exactly towards the observer would be statistically unlikely.1134" A way to deal with this statistical issue is to assume that the emission zone is a spherical cap centered on the SMBH, limited by the sheath of the jet and filled with several similar homogeneous blobs."," A way to deal with this statistical issue is to assume that the emission zone is a spherical cap centered on the SMBH, limited by the sheath of the jet and filled with several similar homogeneous blobs."1135" Consequently, as mentioned in ?,, we can consider differential Doppler boosting in the jet formation zone, near the core region."," Consequently, as mentioned in \citet{2006Sci...314.1424A}, we can consider differential Doppler boosting in the jet formation zone, near the core region."1136" This cap is located at a given distance Reap from the SMBH, which is a new free parameter in our model."," This cap is located at a given distance $R_\mathrm{cap}$ from the SMBH, which is a new free parameter in our model."1137" However, Reap can be constrained by MHD simulations (e.g.?) if we assume that it is located slightly above the Alfvénn surface, which is at about r, from the SMBH."," However, $R_\mathrm{cap}$ can be constrained by MHD simulations \citep[e.g.][]{2006MNRAS.368.1561M} if we assume that it is located slightly above the Alfvénn surface, which is at about $r_g$ from the SMBH."1138" This surface is continuous, but does not need to be homogeneous."," This surface is continuous, but does not need to be homogeneous."1139" We model it with a pattern of several blobs, whose individual radii are typically smaller than in the case of the “blob-in-jet”scenario."," We model it with a pattern of several blobs, whose individual radii are typically smaller than in the case of the “blob-in-jet”scenario."1140" For the sake of simplicity, weassume in this zone the presence of 7 blobs, one central blob and 6 further blobs distributed on a hexagon, located at 100r, from the SMBH, with macroscopic parameters derived from ? as specified in"," For the sake of simplicity, weassume in this zone the presence of 7 blobs, one central blob and 6 further blobs distributed on a hexagon, located at $r_g$ from the SMBH, with macroscopic parameters derived from \citet{2006MNRAS.368.1561M} as specified in"1141and v€CG. the format being. groups. with bright. central eroups/peripheral eroups/dim central groups.,"and vCG, the format being, groups with bright central groups/peripheral groups/dim central groups."1142 There is a difference between the three main mocels for LGs., There is a difference between the three main models for LGs.1143 The Durham models have à smaller fraction of Bright Contral Groups relative to dim. centrals. compared. with the Munich models.," The Durham models have a smaller fraction of Bright Central Groups relative to dim centrals, compared with the Munich models."1144 Vhis discrepancy continues to smaller linking lengths., This discrepancy continues to smaller linking lengths.1145 This likely driven by the greater number of mergers in the Munich. models. feeding the growth. of the central galaxy.," This likely driven by the greater number of mergers in the Munich models, feeding the growth of the central galaxy."1146 Ehe more sophisticated supernova feedback of the ΔΙΟΥ model has decreased the fraction of BOCs., The more sophisticated supernova feedback of the B07 model has decreased the fraction of BGGs.1147 The Munich moclels also have more peripheral groups at all linking lengths In Fig., The Munich models also have more peripheral groups at all linking lengths In Fig.1148 7 the luminosity [functions of the first ranked galaxies (ie. the brightest. galaxy in cach group) of our eroups have been plotted., \ref{fig:LFtype} the luminosity functions of the first ranked galaxies (i.e. the brightest galaxy in each group) of our groups have been plotted.1149 Phese have then been decomposed by group type. with distribution of first ranked. galaxies in bright central groups. the first ranked ealaxics in periphera groups and the first ranked galaxies in dim central groups.," These have then been decomposed by group type, with distribution of first ranked galaxies in bright central groups, the first ranked galaxies in peripheral groups and the first ranked galaxies in dim central groups."1150 ]t can be seen that. in the Munich. οΔΙΣ. for the denser groups. there is a Lage cillerence between the shape of the LP of the brightest galaxies in central ancl periphera eroups.," It can be seen that, in the Munich SAMs, for the denser groups, there is a large difference between the shape of the LF of the brightest galaxies in central and peripheral groups."1151 The clillerence is most extreme for the ALDDOG model. where the low magnitude tail is due. almost entirely. to peripheral eroups.," The difference is most extreme for the D06 model, where the low magnitude tail is due, almost entirely, to peripheral groups."1152 On the contrary. in the 1212060 moce the distribution of groups is not particularly cillerent for the different group types.," On the contrary, in the B06 model the distribution of groups is not particularly different for the different group types."1153 In this section groups consist of galaxies which lie within the same darkA matter halo. whose extent is determined by using a density contour defined bvÁa dark matter particle separation of 0.2 times the mean inter-particleA.separation.," In this section groups consist of galaxies which lie within the same dark  matter halo, whose extent is determined by using a density contour defined by a dark matter particle separation of 0.2 times the mean inter-particle separation."1154 This is not to be confused. with the linking length: used toÀdefined groups which acts on galaxies rather than dark matter particles., This is not to be confused with the linking length used to defined groups which acts on galaxies rather than dark matter particles.1155AGroups determined in this manner diller from those determined by using FobEÀalgorithms., Groups determined in this manner differ from those determined by using FoF algorithms.1156 Even for LGs there is not a one-to-one correspondence between halo eroups and Fol groups., Even for LGs there is not a one-to-one correspondence between halo groups and FoF groups.1157 The limit on the minimum number of galaxies used to define a group remains at four., The limit on the minimum number of galaxies used to define a group remains at four.1158 We examine the conditional luminosity functions in three cdillerent. group. mass bins., We examine the conditional luminosity functions in three different group mass bins.1159 These conditional, These conditional1160spectra.,spectra.1161 Estimation of stellar atmospheric parameters follows the procedures described by C2003., Estimation of stellar atmospheric parameters follows the procedures described by C2003.1162 We make use of photometric methods to compute effective temperatures and. bolometric corrections. and we require. therefore. good estimates of the interstellar extinction.," We make use of photometric methods to compute effective temperatures and bolometric corrections, and we require, therefore, good estimates of the interstellar extinction."1163 We adopted the AA; and E(b— jy) values directly from ATT. except for IID 6833. for which ATT did not derive such parameters. and IDE 232073. whieh ATT did not study.," We adopted the $M_{\rm V}$ and $b-y$ ) values directly from ATT, except for HD 6833, for which ATT did not derive such parameters, and HDE 232078, which ATT did not study."1164 Both stars lie at low Galactic latitude (6 = —8.0 ancl —2.3. respectively). ancl are quite distant. so reddening is a special problem.," Both stars lie at low Galactic latitude $b$ = $-8.0$ and $-2.3$, respectively), and are quite distant, so reddening is a special problem."1165 Table 1 summarizes the photometry emploved in our work., Table 1 summarizes the photometry employed in our work.1166 The /2—7 photometry is on the Cousins svstem., The $R-I$ photometry is on the Cousins system.1167" Thanks to the 2MASS Point Source Catalog (Skrutskie et 22006)4.. we were able to find V—A photometry lor all of our new program stars. although we transformed the 2M1ASS A magnitudes to the ""CIT"" system following the prescription given in the Explanatory Supplement to the 2\IASS Second Incremental Data Release. followed bv a transformation to the “PCS” svstems as described by Alonso et ((1994)."," Thanks to the 2MASS Point Source Catalog (Skrutskie et , we were able to find $V-K$ photometry for all of our new program stars, although we transformed the 2MASS $K$ magnitudes to the “CIT"" system following the prescription given in the Explanatory Supplement to the 2MASS Second Incremental Data Release, followed by a transformation to the “TCS"" systems as described by Alonso et (1994)."1168" Temperature estimates were obtained using the color-Z;y relations derived by Alonso. Αντρας, Martinez Roger (1999. 2001). based on Infrared Flix Method determinations."," Temperature estimates were obtained using the $T_{\rm eff}$ relations derived by Alonso, Arribas, Martinez Roger (1999, 2001), based on Infrared Flux Method determinations."1169 The published relations employ the “ICS” svstem V.—dy colors. and Johnson 2—I colors. so we (ranslormed the (2— £)e values of Table 1 into the Johnson system. using the relations eiven bx Fernie (1953).," The published relations employ the “TCS"" system $V-K$ colors, and Johnson $R-I$ colors, so we transformed the $R-I$ $_{\rm C}$ values of Table 1 into the Johnson system, using the relations given by Fernie (1983)."1170 When more than one temperature estimate was available. as was most often the case. we emploved a simple mean.," When more than one temperature estimate was available, as was most often the case, we employed a simple mean."1171 The average rms scatter when three or more temperatures estimates are available is 45 Ix. We assumed stellar masses of.. appropriate lor stars at the main sequence tui-olr in globular clusters.," The average rms scatter when three or more temperatures estimates are available is 45 K. We assumed stellar masses of, appropriate for stars at the main sequence turn-off in globular clusters."1172" Caleulation of gravities then followed from the M- values. transformed to Ad, alter addition of the bolometrie correction (Alonso et 11999)."," Calculation of gravities then followed from the $M_{V}$ values, transformed to $M_{\rm bol}$ after addition of the bolometric correction (Alonso et 1999)."1173 Table 2 summarizesthe resul(ant atmospheric parameters for our progranm stars., Table 2 summarizesthe resultant atmospheric parameters for our program stars.1174The site of the r—process has been the most enduring mvsterv in nucleosyntliesis theory since the publication of the seminal papers in this Ποια 1957)..,"The site of the $r-$ process has been the most enduring mystery in nucleosynthesis theory since the publication of the seminal papers in this field \citep{Cam57,Bur57}."1175 OF particular promise (in their (mes and for some even today) have been the many efforts suggesting Tvpe IH supernovae as the site with the relevant conditions arising either in or near the exploding core (initially championed by D?FII). with recent attention focused on aspects of neutrino interactions (Woosley&Ilolfnan1992:Woosleyetal.1994). or in the outer lavers," Of particular promise (in their times and for some even today) have been the many efforts suggesting Type II supernovae as the site with the relevant conditions arising either in or near the exploding core (initially championed by $^2$ FH), with recent attention focused on aspects of neutrino interactions \citep{wh92,woo94}, or in the outer layers"1176n-Pintado et (1993).,n-Pintado et (1993).1177" The intermediate radial velocity of the H66q@ line, however, might suggest the existence of a moderate maser component."," The intermediate radial velocity of the $\alpha$ line, however, might suggest the existence of a moderate maser component."1178" The He66a recombination line is also detected in our observations, and shows that the ionized helium to ionized hydrogen abundance ratio in MWC 349A is v 2 0.12 c 0.02."," The $\alpha$ recombination line is also detected in our observations, and shows that the ionized helium to ionized hydrogen abundance ratio in MWC 349A is $y^+$ = 0.12 $\pm$ 0.02."1179" Because of their shared kinematics, it i5 likely that the ionized helium gas and the thermally excited ionized hydrogen gas are well mixed."," Because of their shared kinematics, it is likely that the ionized helium gas and the thermally excited ionized hydrogen gas are well mixed."1180" The electron temperature of that eas is 6.300 + 600 K. High-resolution EVLA observations of this and other recombination lines (particularly the H53a at 0.7 em) might help resolve some of the pending issues concerning the kinematics of the gas in MWC 349A. On a more general note, we would like to stress that the present observations demonstrate the enormous potential of the EVLA to observe wide spectral lines."," The electron temperature of that gas is 6,300 $\pm$ 600 K. High-resolution EVLA observations of this and other recombination lines (particularly the $\alpha$ at 0.7 cm) might help resolve some of the pending issues concerning the kinematics of the gas in MWC 349A. On a more general note, we would like to stress that the present observations demonstrate the enormous potential of the EVLA to observe wide spectral lines."1181" When previous VLA observations had to rely on and often very uncertain procedures to remove a spectral baseline, the present observations provide a very clean identification of the line and extremely reliable determinations of the line parameters."," When previous VLA observations had to rely on and often very uncertain procedures to remove a spectral baseline, the present observations provide a very clean identification of the line and extremely reliable determinations of the line parameters."1182" We thank Clemens Thum and an anonymous referee for thoughtful comments on our manuscript, and Vivek Dhawan. Lorant Sjouwerman. Rick Perley. George Moellenbrock, and Michael Rupen for their help and advices at various stage of the data calibration."," We thank Clemens Thum and an anonymous referee for thoughtful comments on our manuscript, and Vivek Dhawan, Lorant Sjouwerman, Rick Perley, George Moellenbrock, and Michael Rupen for their help and advices at various stage of the data calibration."1183 We acknowledge the support of DGAPA. UNAM. and of CONACyT (Méxxico).," We acknowledge the support of DGAPA, UNAM, and of CONACyT (Méxxico)."1184 LL is indebted to the Guggenheim Memorial Foundation for financial support., LL is indebted to the Guggenheim Memorial Foundation for financial support.1185rotation curve. we also made simulations without the clark halo component.,"rotation curve, we also made simulations without the dark halo component."1186 In general. the caleulatecl rotation curves were then falling in the outer parts of the clises. but. the determined. pattern speeds were quite similar because the fitting was done mostly using features in the inner parts.," In general, the calculated rotation curves were then falling in the outer parts of the discs, but the determined pattern speeds were quite similar because the fitting was done mostly using features in the inner parts."1187 For eight galaxies (six with slow bars. two with fast bars). we also studied the elect of increasing the halo contribution.," For eight galaxies (six with slow bars, two with fast bars), we also studied the effect of increasing the halo contribution."1188 This was tested by multiplving the even Fourier amplitudes m53S of the force by a factor 0.75 or 0.5., This was tested by multiplying the even Fourier amplitudes $m=2 - 8$ of the force by a factor 0.75 or 0.5.1189 Phe ellect to the fitted. pattern. speed: was quite small. in. all. cases within the error estimates of the standard model series.," The effect to the fitted pattern speed was quite small, in all cases within the error estimates of the standard model series."1190 In a couple of cases. the fit was marginallv better when the amplitudes were multiplied by 0.75. but in all cases the fi was worse with multiplication factor 0.5.," In a couple of cases, the fit was marginally better when the amplitudes were multiplied by 0.75, but in all cases the fit was worse with multiplication factor 0.5."1191" ""his is in. good. agreement with our tests with the mass mocdoels for ESO 566-24 (seeFigures4and12in.2).. where we found. tha three mass models (no halo. a halo closely corresponding to universal rotation curve and dominating halo) all gave essentially the same pattern speed. although the quality of the fit was clearly different."," This is in good agreement with our tests with the mass models for ESO 566-24 \citep[see Figures 4 and 12 in ][]{rautiainen2004}, where we found that three mass models (no halo, a halo closely corresponding to universal rotation curve and dominating halo) all gave essentially the same pattern speed, although the quality of the fit was clearly different."1192 Also. modifving the mass node so that the major axis rotation curve determined. [rom the simulated. velocity Gelcl matched the observed one as closely as possible. changed the corotation resonance distance only slightlv.," Also, modifying the mass model so that the major axis rotation curve determined from the simulated velocity field matched the observed one as closely as possible, changed the corotation resonance distance only slightly."1193 ‘There is no unambiguous way to determine the bar radius (foràdetailed.analvsisseee.g.2)..," There is no unambiguous way to determine the bar radius \citep[for a1194 detailed analysis see e.g. ][]{athanassoula2002a}."1195 Some approaches rely on Fourier analysis of the surface brightness: the bar. is identified with the region where the m=2 (or m= +) phase angle is almost. constant. or where the amplitude drops to a certain [fraction of its maximum value.," Some approaches rely on Fourier analysis of the surface brightness: the bar is identified with the region where the $m=2$ (or $m=4$ ) phase angle is almost constant, or where the amplitude drops to a certain fraction of its maximum value."1196 Another method is to fit ellipses to isophotes — bar radius is then determined as the radius where the cllipticity reaches a maximum or where there is a steep drop in it., Another method is to fit ellipses to isophotes – bar radius is then determined as the radius where the ellipticity reaches a maximum or where there is a steep drop in it.1197 Desides these. there are also several other methods.," Besides these, there are also several other methods."1198 In RSL2005 we estimated lengths of the bars. by using visual inspection of deprojected. L-bancl images and isophotes and i=2 Fourier phase angles., In RSL2005 we estimated lengths of the bars by using visual inspection of deprojected H-band images and isophotes and $m=2$ Fourier phase angles.1199 In this studywe have basically followed. the same approach as ?? (seealso7). with slight mocdifications.," In this study,we have basically followed the same approach as \citet{erwin2004,erwin2005} \citep[see also][]{michel2006}, with slight modifications."1200 We first remove the surface brightness of the fitted: bulges from the images and then deproject them., We first remove the surface brightness of the fitted bulges from the images and then deproject them.

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