ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 We set the nominal values of ο=3/2 and 7/2 for the thin and. thick shell cases. respectively.," We set the nominal values of $g=3/2$ and $7/2$ for the thin and thick shell cases, respectively."3 Thus. (he only [ree parameter of the reverse shock emission is Dp.," Thus, the only free parameter of the reverse shock emission is $\Gamma_0$."4 For the forward shockwe use the time evolution of the svnchrotron spectrum in the appropriate regime (i.e. spherical [SAL [or /—ἐς Sari.Piran&Naravan1998.. and an expanding jet [or />/;: Sari.Piran&Llalpern 1999)): here /;. the jet break time. is the epoch at which T—8; land 0; is the half opening angle ofthe jet.," For the forward shockwe use the time evolution of the synchrotron spectrum in the appropriate regime (i.e. spherical ISM for $t<t_j$: \citealt{spn98}, and an expanding jet for $t>t_j$: \citealt{sph99}) ); here $t_j$, the jet break time, is the epoch at which $\Gamma\sim\theta_j^{-1}$ ,and $\theta_j$ is the half opening angle ofthe jet."5 To account [or possible extinction within the host galaxy. tet. we use the parametric extinction curvesof Cardelli. and Fitzpatrick&Massa (1988).. alongwith the interpolation caleulated by Reiehart(2001 )..," To account for possible extinction within the host galaxy, $A_V^{\rm host}$ , we use the parametric extinction curvesof \citet{ccm89} and \citet{fm88}, , alongwith the interpolation calculated by \citet{rei01}. ."6Observed flat rotational curves of many galaxies have been sibjeet of long-term controversy.,Observed flat rotational curves of many galaxies have been subject of long-term controversy.7 The observational [act that the azimuthal velocity of gas aud stars in the galactic plane is constaut over a large range of the distauces [rom the ceutre of a galaxy Las yjelded two main explanations., The observational fact that the azimuthal velocity of gas and stars in the galactic plane is constant over a large range of the distances from the centre of a galaxy has yielded two main explanations.8 Iu an attempt tosave the assertion that the Newtoniau gravitatioual tleory holds over the cosmological distauces. oue such theory assumes the presence of non-baryonie 1jassive dark halo surrounding a spiral disk.," In an attempt to save the assertion that the Newtonian gravitational theory holds over the cosmological distances, one such theory assumes the presence of non-baryonic massive dark halo surrounding a spiral disk."9 In this scenario. gravitational acceleration GAL«(r)/r which balances the centrifugal acceleration. rode/V7(r)/r. is. assumed to vary as yfL/r.," In this scenario, gravitational acceleration $GM_<(r)/r^2$ which balances the centrifugal acceleration $V^2(r)/r$, is assumed to vary as $1/r$."10 This. means that tle inass enclosed withit a certain radius r2 Ade(r). scales as xr.," This means that the mass enclosed within a certain radius $r$ , $M_<(r)$, scales as $\propto r$."11 However. this is not what is observed at large radii of tLe Galaxy.," However, this is not what is observed at large radii of the Galaxy."12 The secoud possible explanation of the flat rotational curves is 1iat the Newtoulan grwvity does 100 apply on Cosinological scales and further imodificatious are due (Milgrom 1950)., The second possible explanation of the flat rotational curves is that the Newtonian gravity does not apply on cosmological scales and further modifications are due (Milgrom 1983).13 Histo‘ically the atter explanation was not favoured due to abseuce of the general reativistic extension ofthe theory., Historically the latter explanation was not favoured due to absence of the general relativistic extension of the theory.14" However. this drawback was alleviated by the formulation of the gejeralisation of Einstein"" general 'elativity based on a pseudo-Bieimauniau metric tensor aud a skew-symuinetric rauk tl ο. ielcl. called inetric-skew-teusor gravity (MSTC)."," However, this drawback was alleviated by the formulation of the generalisation of Einstein's general relativity based on a pseudo-Riemannian metric tensor and a skew-symmetric rank three tensor field, called metric-skew-tensor gravity (MSTG)."15 The latter leads to a moclilied acceleration law hat cau explain the flat rotation curves of galaxies aud cluster lensiug without postulating exotic dark matter (Mollat 2005)., The latter leads to a modified acceleration law that can explain the flat rotation curves of galaxies and cluster lensing without postulating exotic dark matter (Moffat 2005).16 Recently. Brownstein MolIat. (2006) have shown that MSTC cau," Recently, Brownstein Moffat (2006) have shown that MSTG can"17This is because theholes.,This is because the.18 We do not consider the possibility that stars are made in the nucleus of the galaxies (as would be required by AL) and then redistributed throughout the galaxy. in. stellar-kinematical mergers because (1) the dense stellar cores so produced: will not be disrupted. by mergers (or secular evolution). (2) we would. require about LOO mergers. per L elliptical and the observed. merger rate (c.g. Carlberg et al.," We do not consider the possibility that stars are made in the nucleus of the galaxies (as would be required by ) and then redistributed throughout the galaxy in stellar-kinematical mergers because (1) the dense stellar cores so produced will not be disrupted by mergers (or secular evolution), (2) we would require about 100 mergers per $^{*}$ elliptical and the observed merger rate (e.g. Carlberg et al."19 2000) is not that high. and (3) the number density concordance described above is then Lost. due to the Large number of mergers.," 2000) is not that high, and (3) the number density concordance described above is then lost due to the large number of mergers."20" Van der Marel 1999. finds the black hole mass (in solar units) log),Mia&183|logy,Lv."," Van der Marel 1999 finds the black hole mass (in solar units) $\log_{10} M_{\rm BH} \approx -1.83 +21\log_{10} L_V$."22 Pherefore for a Schechter (1976). L elliptical galaxy (Ady= 21.5) at redshift z=0. the central black hole has mass 5.1.LO°AL.., Therefore for a Schechter (1976) $L^{*}$ elliptical galaxy $M_V = -21.5$ ) at redshift $z=0$ the central black hole has mass $5.1 \times 10^{8} {\rm M}_{\odot}$.23" For the same elliptical galaxy. the stellar core mass. is Aly,=1.60M. assuming. that the core is. approximately. isothermal at small raclii Ge<r, where ο. is the core raclius) that the galaxy has a de Vaucouleurs +t profile at. [large radi. that the ratio of +, to the de Vaucouleurs. elfective racdus ris 0.033 (derived from the sample of Lauer 1985). and a value of (AL/Ly)=3.86 for elliptical galaxies (see the discussion in Section 2.1.3 of Fukugita et al."," For the same elliptical galaxy, the stellar core mass is $M_{*c} = 1.6 \times 10^{9} {\rm M}_{\odot}$, assuming that the core is approximately isothermal at small radii $r<r_c$ where $r_c$ is the core radius), that the galaxy has a de Vaucouleurs $r^{1/4}$ profile at large radii, that the ratio of $r_c$ to the de Vaucouleurs effective radius $r_e$ is 0.033 (derived from the sample of Lauer 1985), and a value of $\left(M/L_V \right) = 3.86$ for elliptical galaxies (see the discussion in Section 2.1.3 of Fukugita et al."24 LOOS this assumes the stellar initial mass function. (EME) of Gould. Baheall Flynn 1996. whieh turns over at about 0.5 AL.. similar to the LME of Ixroupa. Tout Gilmore (1993) that we adopt below).," 1998 – this assumes the stellar initial mass function (IMF) of Gould, Bahcall Flynn 1996, which turns over at about 0.5 $_{\odot}$, similar to the IMF of Kroupa, Tout Gilmore (1993) that we adopt below)."25" ""Therefore. for tvpical luminous elliptical galaxies Given the scatter in the correlations presented. by. van der Alarel and Lauer. and the fact that many cores deviate significantly from isothermalitv. the most extreme galaxies may deviate from this ratio by as much an order. of maenitucle."," Therefore, for typical luminous elliptical galaxies Given the scatter in the correlations presented by van der Marel and Lauer, and the fact that many cores deviate significantly from isothermality, the most extreme galaxies may deviate from this ratio by as much an order of magnitude."26 For accretion onto a black hole. where 5 is the ellicicney of accretion anc AZ is the mass accretion rate.," For accretion onto a black hole, where $\eta$ is the efficiency of accretion and $\dot{M}$ is the mass accretion rate."27 For dust-enshroudecd star. formation where almost all the πας is absorbed and reraciated: at far-infrarecl wavelengths. the star formation rate (in AL. 1) is (Rowan-Robinson et al.," For dust-enshrouded star formation where almost all the flux is absorbed and reradiated at far-infrared wavelengths, the star formation rate (in $_{\odot}$ $^{-1}$ ) is (Rowan-Robinson et al."28" 1997) where £, (in L.) is the total luminosity generated. by the voung stars.", 1997) where $L_{*}$ (in $_{\odot}$ ) is the total luminosity generated by the young stars.29 This relation adopts a value of ὁ=0.45 appropriate to the stellar EME of Ixroupa et al. (, This relation adopts a value of $\phi = 0.45$ appropriate to the stellar IMF of Kroupa et al. (301993). and à value ofc=1 (see Section 3 of Rowan-Robinson et al.,"1993), and a value of $\epsilon = 1$ (see Section 3 of Rowan-Robinson et al."31 1997 for a definition of those parameters and a discussion of the derivation of this equation and other approaches)., 1997 for a definition of those parameters and a discussion of the derivation of this equation and other approaches).32 The LAL chosen here has been shown to be consistent with most current observations of both star-forming regions and. the solar neighbourhood (Gilmore Llowell 1998)., The IMF chosen here has been shown to be consistent with most current observations of both star-forming regions and the solar neighbourhood (Gilmore Howell 1998).33 Combining the two previous equations vields Accretion is a lot more ellicient than star-formation at eenerating. luminosity⋠⋠ per unit. mass: a 12 L. galaxy has a star formation rate of about SO M. vr+ but a2 12 L. ⊏↥⊔⋜↧⊳∖⋜⊔⋅↓↥⋜↧⊳∖⋜⋯⋯⇍≼∼↓⋅⋖⊾↿↓∪⊔↓⋅⋜⋯⊾∪⇂⋜↧∣⋡⋯∐↓↳∖↓⋅∙∖⇁↓⋅⇂∪↓⋅↗∣∶∪⋅↓ . ⊥⋅ (e.g. Chokshi Turner 1992)., Combining the two previous equations yields Accretion is a lot more efficient than star-formation at generating luminosity per unit mass: a $^{12}$ $_{\odot}$ galaxy has a star formation rate of about 80 $_{\odot}$ $^{-1}$ but a 2 $\times$ $^{12}$ $_{\odot}$ quasar has an accretion rate of about 1 $_{\odot}$ $^{-1}$ for $\eta = 0.1$ (e.g. Chokshi Turner 1992).34 Pherclore averaged over time in the SCUBA sources: This ratio is very big. meaning that the total power eencrated in the SCUBA sources comes almost. entirely [rom accretion if is correct.," Therefore averaged over time in the SCUBA sources: This ratio is very big, meaning that the total power generated in the SCUBA sources comes almost entirely from accretion if is correct."35 Note that. throughout this caleulation. we have been working backwards. deriving the properties of the progenitor from the properties of the remnants under the assumption that we can match particular progenitors to particular remnants: this is quite a different caleulation from one in which we start out with a cloud of gas and attempt to track its progress.," Note that throughout this calculation, we have been working backwards, deriving the properties of the progenitor from the properties of the remnants under the assumption that we can match particular progenitors to particular remnants; this is quite a different calculation from one in which we start out with a cloud of gas and attempt to track its progress."36 The fact that the power sources are so heavily accretion-dominated means that most SCUBA sources must be dust-enshrouded active galactic nucle: CAGNs) if is correct., The fact that the power sources are so heavily accretion-dominated means that most SCUBA sources must be dust-enshrouded active galactic nuclei (AGNs) if is correct.37 This is not surprising. since the SCUBA sources contribute at least 10 per cent of the bolometric Luminosity density of the Universe. and this could not be generated from the stars in gl cores alone. which comprise less than 1. per cent. by mass of the stars in the Universe. and. these are the only stars that the SCUBA sources are allowed to make if is correct.," This is not surprising, since the SCUBA sources contribute at least 10 per cent of the bolometric luminosity density of the Universe, and this could not be generated from the stars in gE cores alone, which comprise less than 1 per cent by mass of the stars in the Universe, and these are the only stars that the SCUBA sources are allowed to make if is correct."38 There exist. other reasons [or suggesting a connection between the SCUBA sources and dust-enshrouded ACNs., There exist other reasons for suggesting a connection between the SCUBA sources and dust-enshrouded AGNs.39 Apt Phe local supermassive DII density (Magorrian et al., 4pt The local supermassive BH density (Magorrian et al.40 1998. van der Marel 1999) is high and its production generates a bolometric background of (Trentham Blain. 2000) if they racliate at one-tenth of the Eddington luminosity and if the luminosity density of obscureedl ACGNs follows that measured by Bovle Terlevich (1998) for optical quasars.," 1998, van der Marel 1999) is high and its production generates a bolometric background of (Trentham Blain, 2000) if they radiate at one-tenth of the Eddington luminosity and if the luminosity density of obscured AGNs follows that measured by Boyle Terlevich (1998) for optical quasars."41 This equation follows [rom a consideration of the energy. released by accretion processes per comoving volume element. given a final MDO density some part pacNabers Of which was generated. by dust-enshrouded accretion.," This equation follows from a consideration of the energy released by accretion processes per comoving volume element given a final MDO density some part $\rho_{\rm AGN,dusty}$ of which was generated by dust-enshrouded accretion."42 Ehe fiducial pcs«deis is the estimate of Salucci et al. (," The fiducial ${\rho_{\rm AGN,dusty}}$ is the estimate of Salucci et al. ("431999) for obscurecl quasars.,1999) for obscured quasars.44 The SCUBA sources in Fig., The SCUBA sources in Fig.45 L generate about 7 nWm“sr which is close to this value.," 1 generate about 7 ${\rm nW}{\rm m}^{-2}{\rm sr}^{-1}$ ,which is close to this value."46 4ρι Phere is growing evidence that the hard. (30 keV) X-ray background. originates from absorbed: quasars which reracdiate energy absorbed at optical. ultraviolet. and soft. X-ray at. far-infrared and submillimetre wavelengths.," 4pt There is growing evidence that the hard (30 keV) X-ray background originates from absorbed quasars which reradiate energy absorbed at optical, ultraviolet, and soft X-ray at far-infrared and submillimetre wavelengths."47Feibclman 2000).,Feibelman 2000).48 Very much like in the case of Ix. 1-47. hese PNe have consicerably high. electron. temperatures (average 1). from optical. ISO and IUIS spectra for the three of them are 17200 Ix. up to 18300. IN).," Very much like in the case of K 4-47, these PNe have considerably high electron temperatures (average $T_e$, from optical, ISO and IUE spectra for the three of them are 17200 K up to 18300 K)."49 Therefore. we have he somewhat contradictory result that while Ix 4-47. seems o be an extreme bipolar PN in terms of its morphology and He anc N abundances. its O. Ne and S abundances rather resemble PNe in the Galactic halo. as its relatively arge height on the Galactic plane might also suggest. (see Section 1). ancl contrary to bipolar PNe which are highly concentrated toward the Galactic plane (Corradi Schwarz 1995).," Therefore, we have the somewhat contradictory result that while K 4-47 seems to be an extreme bipolar PN in terms of its morphology and He and N abundances, its O, Ne and S abundances rather resemble PNe in the Galactic halo, as its relatively large height on the Galactic plane might also suggest (see Section 1), and contrary to bipolar PNe which are highly concentrated toward the Galactic plane (Corradi Schwarz 1995)."50 To further investigate these issues. in the next two Sections we will model the sspectrum using. first. a shock excitation code. and. then. à pure photoionization moclel.," To further investigate these issues, in the next two Sections we will model the spectrum using, first, a shock excitation code, and, then, a pure photoionization model."51 Shock models have successfully reproduced. the emission line ratios. line profiles ancl. recently. velocity maps in LLL objects (Beck et al.," Shock models have successfully reproduced the emission line ratios, line profiles and, recently, velocity maps in HH objects (Beck et al."52 2004)., 2004).53 To check the possible inlluence of shock excitation on the sspectrum we have explored. ai variety of steady γα] models. for which we use the photoionization-shock code ALAPPINGS Le (Dopita. Binette Tuohy 1984: Dinette. Dopita Tuohy 1985).," To check the possible influence of shock excitation on the spectrum we have explored a variety of steady plane-parallel models, for which we use the photoionization-shock code MAPPINGS Ic (Dopita, Binette Tuohy 1984; Binette, Dopita Tuohy 1985)."54 One important characteristic of shock mocels is that the oreclictecl spectra strongly. depends on the preshock tioon., One important characteristic of shock models is that the predicted spectra strongly depends on the preshock on.55 We have compiled a set of fully pre-ionized shock models (i.c. the incident gas has been ionized) and a set of ocal equlibrium preionization for the gas entering the shock (as ceseribed by Shull Melxee 1979. Llartigan et al.," We have compiled a set of fully pre-ionized shock models (i.e. the incident gas has been ionized) and a set of local equlibrium preionization for the gas entering the shock (as described by Shull McKee 1979, Hartigan et al."56 LOST)., 1987).57" telative abundances typical of ""Evpe E PNe were assumed. and two values for the pre-shock density were considered (100. 1000 )."," Relative abundances typical of Type I PNe were assumed, and two values for the pre-shock density were considered (100, 1000 $^{-3}$ )."58 The input shock velocities were varied rom 95 to HO Km sο. ic. the range producing large rratios (Llartigan A)et al.," The input shock velocities were varied from 95 to 140 km $^{-1}$, i.e. the range producing large ratios (Hartigan et al."59 1987). as observed.," 1987), as observed."60 Note. however. hat the measured expansion velocity of the iis smaller than ((Corracli et al.," Note, however, that the measured expansion velocity of the is smaller than (Corradi et al."61 2000). pointing to lower shock velocities.," 2000), pointing to lower shock velocities."62 None of the predicted spectra could reproduce the large observed ratios of intermediate to high excitation emission ines with respect a Η Balmer line (ic./1147..5007A//1L2... Ne 111] aand He 4686/X//10L3)).," None of the predicted spectra could reproduce the large observed ratios of intermediate to high excitation emission lines with respect a H Balmer line (i.e., [Ne ] and He )."63 Moreover. the shocked. spectra xedieted by our models imply aand larger than the observed.| values.," Moreover, the shocked spectra predicted by our models imply and larger than the observed values."64 A Iarge discrepancy was also found. with the observed cemission line ratio. which is more than 2 times/ larger than he model values.," A large discrepancy was also found with the observed emission line ratio, which is more than 2 times larger than the model values."65 And. finally. iis very high. = 300. because the intensity of iis largely uncderstimated by these mocdels.," And, finally, is very high, $\approx$ 300, because the intensity of is largely understimated by these models."66 We conclude that the plane-parallel shock models are not able to reproduce the spectrum of the core of Ix 4-47., We conclude that the plane-parallel shock models are not able to reproduce the spectrum of the core of K 4-47.67 We have used the phototonization code CLOUDY 95.06 (Forlancl et al., We have used the photoionization code CLOUDY 95.06 (Ferland et al.68 1998)., 1998).69 CLOUDY needs as input the information on the shape and intensity of the radiation from the ionizing source. the chemical composition and geometry of the nebula. as well as its censity and size.," CLOUDY needs as input the information on the shape and intensity of the radiation from the ionizing source, the chemical composition and geometry of the nebula, as well as its density and size."70 As mentioned in Section 1. the distance of Ix 4-47. and thus its size and the luminosity of the central star. are poorly known.," As mentioned in Section 1, the distance of K 4-47, and thus its size and the luminosity of the central star, are poorly known."71 We adopt the distance of 5.9 kpc computed by TFajitsu Tamura (1998). although extending he calculations to the full range of distances from 3 kpc to 7 kpe proposed. by Corradi et al. (," We adopt the distance of 5.9 kpc computed by Tajitsu Tamura (1998), although extending the calculations to the full range of distances from 3 kpc to 7 kpc proposed by Corradi et al. ("722000).,2000).73 A spherical geometry. ancl a filling factor of 1.0 have en assumed.," A spherical geometry, and a filling factor of 1.0 have been assumed."74 Using the Ho and images from Corradi ct al. (, Using the $\alpha$ and images from Corradi et al. (752000) a core diameter. of 1.0 aresee was estimated contour extension corrected or the finite resolution: Tvlenda et al.,2000) a core diameter of 1.9 arcsec was estimated contour extension corrected for the finite resolution; Tylenda et al.76 2003)., 2003).77 The density was initially kept to constant ancl equal to its empirical value (1900. em. see. Table. 1).," The density was initially kept to constant and equal to its empirical value (1900 $^{-3}$, see Table 1)."78 However. as noted in he Introduction. Aacquist Kwok (1990). discovered. a wight and very compact radio core at the centre of Ix. 4- implying a high density of 72000 cm. (assuming an optically thin nebula at 5 CGllz. the distance of 5.9 kpe and ollowing CGoucdis 1982).," However, as noted in the Introduction, Aaquist Kwok (1990) discovered a bright and very compact radio core at the centre of K 4-47, implying a high density of 72000 $^{-3}$ (assuming an optically thin nebula at 5 GHz, the distance of 5.9 kpc and following Goudis 1982)."79 For this reason. models with much ugher density values were also explored.," For this reason, models with much higher density values were also explored."80 Dust grains have been included. since they have an important effect. particularly on the temperature structure of PNe.," Dust grains have been included, since they have an important effect, particularly on the temperature structure of PNe."81 This effect depends on the tvpe of grain (graphite and/or silicate). the grain abundances. and. the grain-size distribution. being more relevant in the inner regions of the nebula (see Dopita Sutherland 2000).," This effect depends on the type of grain (graphite and/or silicate), the grain abundances, and the grain-size distribution, being more relevant in the inner regions of the nebula (see Dopita Sutherland 2000)."82 Both graphite anc silicate grains were considered., Both graphite and silicate grains were considered.83 As we do not know the grain size distribution and grain abundances for Ix 4-47 and more in general for PNe. we adotped ISM size distribution. with ISAL gas-phase depletions due to grains. following van Lloof et al. (," As we do not know the grain size distribution and grain abundances for K 4-47 and more in general for PNe, we adotped ISM size distribution, with ISM gas-phase depletions due to grains, following van Hoof et al. ("842004).,2004).85 We adopted a blackbocs spectrum for the central star. with celerived from theLL3.. aand ecemission line ratios. using a modified. Zanstra method as done for instance by Alikolajewska ct al. (," We adopted a blackbody spectrum for the central star, with derived from the, and emission line ratios, using a modified Zanstra method as done for instance by ajewska et al. ("861999).,1999).87" Dhis eives Z,.rr—11300000 Ix. (from 4686AX//1L3)). and 0000 Ix. (πο 4686A//5876)).", This gives 000 K (from ) and 000 K (from ).88 AA Lower limit to the central star luminosity comes from the LIGAS spectral energy distribution (Lajitsu Tamura 1998). which gives Lz 16 D? L. (where D is the distance in kpe) vielding 550 L. at 5.9 kpc.," A lower limit to the central star luminosity comes from the IRAS spectral energy distribution (Tajitsu Tamura 1998), which gives $\ge$ 16 $^2$ $L_{\odot}$ (where D is the distance in kpc) yielding 550 $L_{\odot}$ at 5.9 kpc."89" As with the elemental abundances. we first run models with the empirical. abundances given in ‘Table 2. and subsequently with ""average"" values for either normal (Ivpe-1D. or Type-L PNe. following Ixingsburgh Barlow (1994)."," As with the elemental abundances, we first run models with the empirical abundances given in Table 2, and subsequently with “average” values for either normal (Type-II), or Type-I PNe, following Kingsburgh Barlow (1994)."90 CLOUDY models with the empirical abundances cdo not match the observed. line. Duxes., CLOUDY models with the empirical abundances do not match the observed line fluxes.91. Both helium and (6548 omission lines are largely overestimated. while oxygen. sulphur and neon lines are uncerestimated. mainlv because the very low Of. Νο anc 41 input abundances are not compensated. by ai high electron temperature in the model as empiricallv determined.," Both helium and ) emission lines are largely overestimated, while oxygen, sulphur and neon lines are underestimated, mainly because the very low O/H, Ne/H and S/H input abundances are not compensated by a high electron temperature in the model as empirically determined."92 Tests with Pype-LE PNe abundances were also not. successful because the predicted intensities are very low. which is expected as the main difference between “Pype-Lb and Ἔνροη abundances is that the latter are depleted. in. nitrogen by ao factor of —4 (dingsburgh Barlow 1994).," Tests with Type-II PNe abundances were also not successful because the predicted intensities are very low, which is expected as the main difference between Type-I and Type-II abundances is that the latter are depleted in nitrogen by a factor of $\sim$ 4 (Kingsburgh Barlow 1994)."93 Assuming, Assuming94at 23 make this estimate far too optimistic. but all of the models that match the observations require rj to be no largere than 500 kpe (which is likely still too optimistic:1 sec JaguiOla}). and are thus compatible with constraints placed on the metal distribution by travel-time arguments.,"at $z\gg 3$ make this estimate far too optimistic, but all of the models that match the observations require $\renrich$ to be no larger than $500$ kpc (which is likely still too optimistic; see ), and are thus compatible with constraints placed on the metal distribution by travel-time arguments."95 Optical depth distributions are caleulated. by firing 10 randomly. chosen lines of sight through the simulation volume and caleulating absorption spectra for both Ε1 and CIN. following the procedure outlined in e.g. Appendix At of(10998)., Optical depth distributions are calculated by firing $10^3$ randomly chosen lines of sight through the simulation volume and calculating absorption spectra for both $\hi$ and $\civ$ following the procedure outlined in e.g. Appendix A4 of.96. The mean HI optical depth in our simulations al z=3 is map=0.388. which is consistent with observations2008).," The mean $\hi$ optical depth in our simulations at $z=3$ is $\tau_{\rm eff}=0.388$, which is consistent with observations."97. In order to match observations with ILLIS on the Weck telescope. we convolve our spectra with a Gaussian line-spreacd function with a full-width-at-half-maximun of 6.6 km/s. and resample our spectra onto 1 kms pixels.," In order to match observations with HIRES on the Keck telescope, we convolve our spectra with a Gaussian line-spread function with a full-width-at-half-maximum of 6.6 km/s, and resample our spectra onto 1 km/s pixels."98 We do not add. noise to our spectra. but we have verified. that the addition of Gaussian. noise with a signal-to-noise ratio of greater than 25 docs not significantly alect anv of our results.," We do not add noise to our spectra, but we have verified that the addition of Gaussian noise with a signal-to-noise ratio of greater than 25 does not significantly affect any of our results."99 We generate absorption spectra for two transitions: ILI (1215.67A)) and the €IN. doublet(1548.20A.. 1550.78A)).," We generate absorption spectra for two transitions: $\hi$ ) and the $\civ$ doublet, )."100 In order to compare to the observed TOITH. distribution. we then bin pixels in 7Hi and calculate the median. zciv. corresponding to the redshifts of the pixels in each ILI bin.," In order to compare to the observed $\tauciv-\tauhi$ distribution, we then bin pixels in $\tauhi$ and calculate the median $\tauciv$ corresponding to the redshifts of the pixels in each $\hi$ bin."101" For each run. in addition to measuring the row7Hi relation. we calculate the fraction of the total mass (f) and volume (fy) that has been enriched from πο m; and h; are the SPLL particle mass and smoothing kernel. respectively, anc the sums in the numerator of cach fraction extend only over particles with non-zero metallicity."," For each run, in addition to measuring the $\tauciv-\tauhi$ relation, we calculate the fraction of the total mass $\fmass$ ) and volume $\fvol$ ) that has been enriched from Here, $m_i$ and $h_i$ are the SPH particle mass and smoothing kernel, respectively, and the sums in the numerator of each fraction extend only over particles with non-zero metallicity."102 We have verified that using ορ; instead of A? gives nearly identical volume filling fractions. as expected.," We have verified that using $m_i/\rho_i$ instead of $h_i^3$ gives nearly identical volume filling fractions, as expected."103 For the solar we use the metal mass fraction Z.=0.0127., For the solar we use the metal mass fraction $\zsun=0.0127$.104 Fig., Fig.105 1. shows a thin (1 comoving Mpc// thick) slice of the density field at z=3 through the centre of the simulation., \ref{fig:density} shows a thin (1 comoving $h$ thick) slice of the density field at $z=3$ through the centre of the simulation.106 Each panel shows a dillerent. combination of rz and m., Each panel shows a different combination of $\renrich$ and $\menrich$.107 Gas with zero metallicity is shown in grev-scale. while metal-enriched. gas is coloured red.," Gas with zero metallicity is shown in grey-scale, while metal-enriched gas is coloured red."108" In. addition. the values for fy and fi, are indicated for cach model."," In addition, the values for $\fvol$ and $\fmass$ are indicated for each model."109 Panels showing metal distributions that are consistent with the observations (see below) are outlined in green., Panels showing metal distributions that are consistent with the observations (see below) are outlined in green.110 The fractions of the mass and volume that are enriched do not track each other in a simple wav., The fractions of the mass and volume that are enriched do not track each other in a simple way.111 The ratio fi/fy is always Z1 because metals are only placed around collapsed structures and thus preferentially in overdense regions.," The ratio $\fmass/\fvol$ is always $\ge1121$ because metals are only placed around collapsed structures and thus preferentially in overdense regions."113" For m,=üLOYAL. changingH r; from. kkpe to kkpe changes the ratio fii/fy [rom 22.7 to 1.3. as a larger value of rz; at fixed. mz; allows metals to disperse further out of the high-density. peaks."," For $\menrich=10^{10}\,\msun$, changing $\renrich$ from kpc to kpc changes the ratio $\fmass/\fvol$ from 22.7 to 1.3, as a larger value of $\renrich$ at fixed $\menrich$ allows metals to disperse further out of the high-density peaks."114" Similarly. changing η, at fixed r,=250 kpe. we find that the ratio fu/fv rises from. 2.8 for m,=10""M. to 7.5 for m4=104M. because more massive haloes are preferentially located in higher density environments."," Similarly, changing $\menrich$ at fixed $\renrich=250$ kpc, we find that the ratio $\fmass/\fvol$ rises from 2.8 for $\menrich=10^{9}\,\msun$ to 7.5 for $\menrich=10^{11}\,\msun$, because more massive haloes are preferentially located in higher density environments."115 Given that we understand how changing the pattern of metal enrichment. alters the relative mass and volume filling factors. we now ask how this impacts the rouTHa relation.," Given that we understand how changing the pattern of metal enrichment alters the relative mass and volume filling factors, we now ask how this impacts the $\tauciv-\tauhi$ relation."116 The curves in Fig., The curves in Fig.117 20 show the relation between rci and τη in the svnthetic absorption spectra., \ref{fig:od} show the relation between $\tauciv$ and $\tauhi$ in the synthetic absorption spectra.118 Each panel corresponds to a dillerent mz., Each panel corresponds to a different $\menrich$.119" The solid lines in panels6.. ancl (log,(0;/M.)=9.10.11. respectively) show the predicted rou7Hi relation from the simulation with various imposed metallicity distributions."," The solid lines in panels, and $\log_{10}(\menrich/\msun)={9,10,11}$, respectively) show the predicted $\tauciv-\tauhi$ relation from the simulation with various imposed metallicity distributions."120" The cot-dashed— lines— in. panels— ancl (log,(n,/M.)28.9. respectively) show the predicted roaτην relations for the small volume. high-resolution simulation.LO0L2N212."," The dot-dashed lines in panels and $\log_{10}(\menrich/\msun)={8,9}$, respectively) show the predicted $\tauciv-\tauhi$ relations for the small volume, high-resolution simulation,."121. In every panel we compare. our simulated: predictions to the observed. optical depth: pixel statistics of(2003)... for the redshift range 2479<2x4.033. as published in(2005). shown as the vellow points with Lo error bars.," In every panel we compare our simulated predictions to the observed optical depth pixel statistics of, for the redshift range $2.479 \le z \le 4.033$, as published in, shown as the yellow points with $1\sigma$ error bars."122 The data come from six quasar spectra. 3388. Q1425|604. 1158. ΟΡΟ|230. 2269. and Q1055|461. that were taken with either the Weck/LURIES or the VLTE/UVES.," The data come from six quasar spectra, 388, Q1425+604, 158, Q1422+230, 269, and Q1055+461, that were taken with either the Keck/HIRES or the VLT/UVES."123 A full description of the sample is given in(2003)., A full description of the sample is given in.124. In each panel Z was chosen such that LOW10 ry=500 kpe curve exactly matches the observations at 1 highest value of zHi and the metallicity required for this normalisation is given in cach panel., In each panel $\zenrich$ was chosen such that the $\renrich=500$ kpc curve exactly matches the observations at the highest value of $\tauhi$ and the metallicity required for this normalisation is given in each panel.125 In the present work we are not aiming to reproduce the garape of the τονTHi relation in detail and. indeed. would not necessarily expect our simple models to be capable of oing this.," In the present work we are not aiming to reproduce the shape of the $\tauciv-\tauhi$ relation in detail and, indeed, would not necessarily expect our simple models to be capable of doing this."126 Rather. we require that the models. predict a median τονTH relation that is consistent with. or larger. aan observed and that the rouyτηι relation is not steeper aan observed.," Rather, we require that the models predict a median $\tauciv-\tauhi$ relation that is consistent with, or larger, than observed and that the $\tauciv-\tauhi$ relation is not steeper than observed."127" We elfectively combine the two conditions bv scaling Z in cach run to match the normalisation of we observed: τοντΗι relation at log),TH1=2.5. the largest optical depth probed. by the observations. and then requiring the model to predict median τον at lowτη tha are consistent with or greater than observed."," We effectively combine the two conditions by scaling $\zenrich$ in each run to match the normalisation of the observed $\tauciv-\tauhi$ relation at $\log_{10}\tauhi=2.5$, the largest optical depth probed by the observations, and then requiring the model to predict median $\tauciv$ at low$\tauhi$ that are consistent with or greater than observed."128 We stress that overprediction of τον is not a problem a small τη because our simple models make the assumption that the metallicity inside each enriched bubble is constan with radius., We stress that overprediction of $\tauciv$ is not a problem at small $\tauhi$ because our simple models make the assumption that the metallicity inside each enriched bubble is constant with radius.129 Phe overestimate at low τον could therefore be solved by imposing a metallicity that decreases with radius., The overestimate at low $\tauciv$ could therefore be solved by imposing a metallicity that decreases with radius.130 On the other hand. we will assume that underprediction of roa at low rHi signals the failure of the model because a metallicity that increases with radius is likely unphysical.," On the other hand, we will assume that underprediction of $\tauciv$ at low $\tauhi$ signals the failure of the model because a metallicity that increases with radius is likely unphysical."131 Such an unphysical metallicity gradient would. also have been required. if we hack chosen to scale the metallicity to match the low 7H points. because the unsuccessful. constant metallicity models predict much steeper τονΤΗ relations than observed (see Fig. 2)).," Such an unphysical metallicity gradient would also have been required if we had chosen to scale the metallicity to match the low $\tauhi$ points, because the unsuccessful, constant metallicity models predict much steeper $\tauciv-\tauhi$ relations than observed (see Fig. \ref{fig:od}) )."132 In fact. such an approach would not be possible for most of the models that we rule out. because they typically prediet the median rou to be zero at low ΤΗ 1.," In fact, such an approach would not be possible for most of the models that we rule out, because they typically predict the median $\tauciv$ to be zero at low $\tauhi$ ."133 1n principle. we could produce significantly better fits to," In principle, we could produce significantly better fits to"134 , 135"space FE, ?σι,can be identified with⋅⋅ the⋅ parabolic Hardy⋅ space HP*(Eg? 1).∣↽⊓1 ⋅<p<x.having theThe following square function characterizatiou stated informally as: This identification between the above two spaces is the following: Another useful space throughout our analysis is the parabolic inhomogeneous Besov space.","The space $\dot{F}^{0,a}_{p,2}$ can be identified with the parabolic Hardy space $H^{p,a}(\R^{n+1})$, $1\leq p<\infty$, having the following square function characterization stated informally as: This identification between the above two spaces is the following: Another useful space throughout our analysis is the parabolic inhomogeneous Besov space."136 The main difference in defining this space is the choice of the parabolic dyadic partition of unity that is now altered., The main difference in defining this space is the choice of the parabolic dyadic partition of unity that is now altered.137" Indeed. we take (ej)joo satisfying: Again.it is clear that vieοeyle)=1. Paleybut now for all z€IE""land in exactly the same way as above. we cau rewrite the Littlewood: decomposition with We then arrive to the following definition: For a detailed study of anisotropic Lizorkin-Triebel auc Besov spaces. we refer the reader to Triebel [21]."," Indeed, we take $(\psi_{j})_{j\geq 0}$ satisfying: Again,it is clear that $\sum_{j\geq 0} \psi_{j}(z) = 1$ , but now for all $z\in \R^{n+1}$, and in exactly the same way as above, we can rewrite the Littlewood-Paley decomposition with We then arrive to the following definition: For a detailed study of anisotropic Lizorkin-Triebel and Besov spaces, we refer the reader to Triebel \cite{Tri1}."138. We present two embedding resultsfrom Johnsen and Sickel [11].. aud Stécekert [19]..," We present two embedding resultsfrom Johnsen and Sickel \cite{Joh_Sic07}, and Stöcckert \cite{Stockert82}. ."139mechanism for the production of elliptical galaxies then they must be able to produce the correct scaling relations as well as the evolution of these scaling relations over time.,mechanism for the production of elliptical galaxies then they must be able to produce the correct scaling relations as well as the evolution of these scaling relations over time.140" ""Theoretical.hydrodynamical studies have shown that simulations of gas-rich galaxy mergers are capable of reproducing the observed scaling relations of elliptical galaxies if the correct. progenitor properties are used (???7?).."," Theoretical studies have shown that simulations of gas-rich galaxy mergers are capable of reproducing the observed scaling relations of elliptical galaxies if the correct progenitor properties are used \citep{Dekel06, RobertsonFP,141 HopkinsFP,Bournaud:2011a}."142 This is a step toward verifving the production. of scaling laws through mergers., This is a step toward verifying the production of scaling laws through mergers.143 However. current computing power only allows the simulation of relatively small numbers of mergers. and the space of possible merger initial conditions and progenitor properties is quite large.," However, current computing power only allows the simulation of relatively small numbers of mergers, and the space of possible merger initial conditions and progenitor properties is quite large."144 Furthermore. these simulations are not placed. within a cosmological context. making it more cdillieult to explore in detail the origin and evolution of scaling relations.," Furthermore, these simulations are not placed within a cosmological context, making it more difficult to explore in detail the origin and evolution of scaling relations."145 Currently. the primary theoretical tool for. studving he evolution of statistical samples of galaxies over cosmological timescales is semi-analvtic modeling. (SAM) (7???7?TTTTTTT?3) ," Currently, the primary theoretical tool for studying the evolution of statistical samples of galaxies over cosmological timescales is semi-analytic modeling (SAM) \citep{kwg1993, Cole94, SP1999, Cole00,146 Galics03, Croton06, DeLucia06, Bower06, S08, Fontanot09, Benson10,147 BensonBower10, Cook10, Guo10}."148These models. combine dark matter ido merger trees with analytic recipes for populating the ialos with galaxies., These models combine dark matter halo merger trees with analytic recipes for populating the halos with galaxies.149 Llowever. semi-analvtic models (SAAIs) do not currently incorporate realistic formulas for predicting he properties of the remnants of galaxy mergers including he effects of dissipation.," However, semi-analytic models (SAMs) do not currently incorporate realistic formulas for predicting the properties of the remnants of galaxy mergers including the effects of dissipation."150 The agreement between. current SAMSs ancl observed. earlv-tvpe. sealing relations is) not impressive., The agreement between current SAMs and observed early-type scaling relations is not impressive.151 In. particular. the observed: size-mass relation of earlv-tvpes is steeper than that of their potential type progenitors (7).. and the scatter in the observed. size- relation for earlv-twpes is remarkably small (??)..," In particular, the observed size-mass relation of early-types is steeper than that of their potential late-type progenitors \citep{Shen03}, and the scatter in the observed size-mass relation for early-types is remarkably small \citep{Shen03,152 Nair10}."153 The disspationless merger models currently. implemented within SAAS have thus far been unable to reproduce these features (o...77)..," The disspationless merger models currently implemented within SAMs have thus far been unable to reproduce these features \citep[e.g.,][]{Shankar10a,Guo10}."154 7. recently. developed a physicallv-motivated: analytic model for predicting the stellar hall-mass radii and central. velocity dispersions of merger remnants (?).., \citet{remnants} recently developed a physically-motivated analytic model for predicting the stellar half-mass radii and central velocity dispersions of merger remnants \citep{remnants}.155 The parameters in this new merger model were calibrated using a suite of galaxy merecr simulations (see Section 2))., The parameters in this new merger model were calibrated using a suite of galaxy merger simulations (see Section \ref{sec:methods2}) ).156 Llere we implement a simplified. version of this model using post-processing of merger outputs from the SAMSs developed by 2.. based on he Millennium simulation (?).. and ?..," Here we implement a simplified version of this model using post-processing of merger outputs from the SAMs developed by \citet{Croton06}, based on the Millennium simulation \citep{Springel05}, and \citet{S08}."157 This results in a »opulation of tens of thousands of merger. remnants. over a lage range of redshifts (0«z 3) complete with oedieted values of size. stellar mass. and velocity cüspersion.," This results in a population of tens of thousands of merger remnants over a large range of redshifts $0<z<3$ ) complete with predicted values of size, stellar mass, and velocity dispersion."158 Comparison of the mocelecd population of ellipticals with he observed scaling relations provides an important. test of the merger hypothesis as well as physical insight. into he origin and evolution of these relations via merging., Comparison of the modeled population of ellipticals with the observed scaling relations provides an important test of the merger hypothesis as well as physical insight into the origin and evolution of these relations via merging.159 Future work will implement our merger model self-consistentlv. within the semi-analvtic machinery rather than by post-processing., Future work will implement our merger model self-consistently within the semi-analytic machinery rather than by post-processing.160 Section 2.1 describes our analytic merger mocel for calculating the properties of stellar spheroids from galaxy mergers including energy. losses from dissipation., Section 2.1 describes our analytic merger model for calculating the properties of stellar spheroids from galaxy mergers including energy losses from dissipation.161 Section 2.2 explains how we implement our merger model using outputs from the ? and ? SAAIs.," Section 2.2 explains how we implement our merger model using outputs from the \citet{Croton06} and \citet{S08}162 SAMs."163 Section 3 systematically explores the elfects of the merger model., Section 3 systematically explores the effects of the merger model.164 In order to turn the rather shallow size-mass relation of disk galaxies into the steeper size-mass relation of observed. earlv-tvpe. galaxies. we find that idt is essential to include both. dissipation and the decreasing eas content of more massive progenitor disk galaxies.," In order to turn the rather shallow size-mass relation of disk galaxies into the steeper size-mass relation of observed early-type galaxies, we find that it is essential to include both dissipation and the decreasing gas content of more massive progenitor disk galaxies."165 In Section 4 we summarize the observational results that we compare with our model outputs. focusing especially on Sloan Digital Sky Survey (SDSS) data. [or nearby galaxy size vs. mass ancl other scaling relations. and on cata from several surveys (7). for the evolution of these relations to higher redshifts.," In Section 4 we summarize the observational results that we compare with our model outputs, focusing especially on Sloan Digital Sky Survey (SDSS) data for nearby galaxy size vs. mass and other scaling relations, and on data from several surveys \citep{Trujillo06} for the evolution of these relations to higher redshifts."166 In section 5 we use the predicted properties of progenitor disk galaxies from the two semi-analvtie models to predict the size-mass and other relations for spheroids formed in major gas-rich mergers and compare them. with the observations out to redshift =3., In section 5 we use the predicted properties of progenitor disk galaxies from the two semi-analytic models to predict the size-mass and other relations for spheroids formed in major gas-rich mergers and compare them with the observations out to redshift $z=3$.167 Section 6 summarizes these results and. discusses their implications and. some follow-on studies that are in progress., Section 6 summarizes these results and discusses their implications and some follow-on studies that are in progress.168 Finally. an Appendix. describes an. improvement in the treatment of the central clark matter in the analytic merger model of 7. that we used in ? and in the present paper.," Finally, an Appendix describes an improvement in the treatment of the central dark matter in the analytic merger model of \citet{remnants} that we used in \citet{Covington08} and in the present paper."169 We use a combination of modeling approaches to construct a theoretical framework for predicting the evolution of carly-tvpe sealing relations over cosmological time., We use a combination of modeling approaches to construct a theoretical framework for predicting the evolution of early-type scaling relations over cosmological time.170 In. previous work. a large suite of hwdrodynamical galaxy merger simulations were developed (222).," In previous work, a large suite of hydrodynamical galaxy merger simulations were developed \citep{thesis,171 Cox05, Cox08}."172 These simulations were performed using the N-body/SPLI code GADGET (77). and include hyverodyvnamies. star formation. and stellar feecback.," These simulations were performed using the N-body/SPH code GADGET \citep{SpGad,SH03}, and include hydrodynamics, star formation, and stellar feedback."173 The simulation suite contains mergers with a wide variety of progenitor properties. mass ratios. and merger orbits.," The simulation suite contains mergers with a wide variety of progenitor properties, mass ratios, and merger orbits."174 Variations in progenitor properties include a range of stellar misses. gas fractions. dark matter halo concentrations. bulge fractions. barvonic fractions. and gas clisk sizes.," Variations in progenitor properties include a range of stellar masses, gas fractions, dark matter halo concentrations, bulge fractions, baryonic fractions, and gas disk sizes."175 1n subsequent work. Covington ct al. (," In subsequent work, Covington et al. ("1762008. hereafter COS) constructed à. physicallv-motivated: analytic galaxy merger model capable of predicting the half-mass. raclii. stellar masses. and velocity dispersions of galaxy merger remnants given the properties of the progenitor ealaxies and the initial orbits of the mergers.,"2008, hereafter C08) constructed a physically-motivated analytic galaxy merger model capable of predicting the half-mass radii, stellar masses, and velocity dispersions of galaxy merger remnants given the properties of the progenitor galaxies and the initial orbits of the mergers."177 This model was calibrated using the galaxy merger suite described. above., This model was calibrated using the galaxy merger suite described above.178 Unlike previous similar models (??).. this mocel includes the ellects of star formation and energy loss due to dissipation.," Unlike previous similar models \citep{Cole00, Galics03}, this model includes the effects of star formation and energy loss due to dissipation."179 llere we combine a simplified. version of this new galaxy merger model with merger rates and. progenitor properties predicted: by two semi-analvtic models (SXMSs) in order to explore the ereation and evolution of the scaling relations of earlv-tvpe galaxies., Here we combine a simplified version of this new galaxy merger model with merger rates and progenitor properties predicted by two semi-analytic models (SAMs) in order to explore the creation and evolution of the scaling relations of early-type galaxies.180"using them comes from our numerical method, which calculates configurations based on a given distortion (axis ratio).","using them comes from our numerical method, which calculates configurations based on a given distortion (axis ratio)."181" Since magnetic distortions are typically very small, this means that even the axis ratio for the least non-spherical star we can specify (constrained by the grid resolution) corresponds to a very strong magnetic field."," Since magnetic distortions are typically very small, this means that even the axis ratio for the least non-spherical star we can specify (constrained by the grid resolution) corresponds to a very strong magnetic field."182" This is not necessarily a problem for normal MHD, but superconductivity will be broken at these field strengths, which exceed the second critical field of Πω~10!9 G. We are able to produce these models because the destruction of superconductivity is not built into them; the equations may be solved for any field strength."," This is not necessarily a problem for normal MHD, but superconductivity will be broken at these field strengths, which exceed the second critical field of $H_{c2}\approx 10^{16}$ G. We are able to produce these models because the destruction of superconductivity is not built into them; the equations may be solved for any field strength."183" Having done so, however, we need to check that these models are consistent with our expectations for NSs with superconducting protons."," Having done so, however, we need to check that these models are consistent with our expectations for NSs with superconducting protons."184" If they are, we may extrapolate our results back to more realistic models, where B«Πω."," If they are, we may extrapolate our results back to more realistic models, where $\Bav<\bar{H}_{c2}$."185" We perform this sanity check next, in figure 13.."," We perform this sanity check next, in figure \ref{toroidal_ellips}."186" We plot the scaling of ellipticity with average field strength B for NS models with toroidal magnetic fields, for normal (left) and type-II superconducting protons (right)."," We plot the scaling of ellipticity with average field strength $\Bav$ for NS models with toroidal magnetic fields, for normal (left) and type-II superconducting protons (right)."187" Note that all ellipticities are negative, since these configurations are prolate."," Note that all ellipticities are negative, since these configurations are prolate."188" In the left-hand plot we find that the measured numerical values agree very well with the expected scaling eox B?, with small deviations when B>10!"" G. We now turn to the right-hand plot of figure 13.."," In the left-hand plot we find that the measured numerical values agree very well with the expected scaling $\epsilon\propto B^2$ , with small deviations when $\Bav\gtrsim18910^{17}$ G. We now turn to the right-hand plot of figure \ref{toroidal_ellips}."190" This time we plot the ellipticity against B, not B?."," This time we plot the ellipticity against $\Bav$, not $\Bav^2$."191" First we look at configurations with ¢?-superconductivity, for a central critical field value H«1(0)=1015 G (the points on the line marked (a)) and also for H.1(0)=2x1016 G (the points on line (c))."," First we look at configurations with $\zeta^2$ -superconductivity, for a central critical field value $H_{c1}(0)=10^{16}$ G (the points on the line marked (a)) and also for $H_{c1}(0)=2\times 10^{16}$ G (the points on line (c))."192" In both cases we see that the points lie virtually on straight lines, showing that εοςB."," In both cases we see that the points lie virtually on straight lines, showing that $\epsilon\propto\Bav$."193" In addition, line (c) has twice the gradient of line (a)."," In addition, line (c) has twice the gradient of line (a)."194" This confirms that despite the high field strengths we are obliged to use (see the discussion above), we find the correct scaling of the ellipticity: eoxH«1B."," This confirms that despite the high field strengths we are obliged to use (see the discussion above), we find the correct scaling of the ellipticity: $\epsilon\propto H_{c1}\Bav$."195 This gives us more confidence about our results and means we can safely extrapolate to more typical NS field strengths., This gives us more confidence about our results and means we can safely extrapolate to more typical NS field strengths.196 We also present ellipticities for ¢3-superconductivity (points along line (b))., We also present ellipticities for $\zeta^3$ -superconductivity (points along line (b)).197 The level of distortion inthis case is very similar to that in the C? case., The level of distortion inthis case is very similar to that in the $\zeta^2$ case.198nmeaniugs as the TLOWWSOLL Cross section. electrou iuass and the speed of light.,"meanings as the Thomson cross section, electron mass and the speed of light."199 Suce ouly [ree electrous pa‘ticipate in Thomson scattering of the CMB photous. le integra Is €uw olf at the epoch of reiouization fa.," Since only free electrons participate in Thomson scattering of the CMB photons, the integral is cut off at the epoch of reionization $l_{\rm re}$."200 Sole Iniportant statistics of the SZ elfect inunediately. come to 1iud., Some important statistics of the SZ effect immediately come to mind.201" The first oO‘ler quantity is y. the mean y pa""anieter average over the whole sky. which measwes the toal theral energy content ofthe univewe."," The first order quantity is $\bar{y}$, the mean $y$ parameter averaged over the whole sky, which measures the total thermal energy content of the universe."202 Tie angular variation in y can be parameterizec by the two poiit correlation function of le temperatwe ποion ©. or equivaleutly the auguar power sj)ectrun Cy.," The angular variation in $y$ can be parameterized by the two point correlation function of the temperature fluctuation $\Theta$, or equivalently the angular power spectrum $C_l$."203 For a Claussiall Fallcdoum field. these (wo pa‘ameters would describe the statisics completely.," For a Gaussian random field, these two parameters would describe the statistics completely."204 Since the 5Z effect is dominated by nolinear structures. non-Craussiaulty may be siguificaut.," Since the SZ effect is dominated by non-linear structures, non-Gaussianity may be significant."205 So we investigate higher order statistics su] as the ssewness aud kurtosis of the y parameter to quantify the , So we investigate higher order statistics such as the skewness and kurtosis of the $y$ parameter to quantify the non-Gaussianity.206The SZ elect contalus coutributious [rom all ‘edsüfts and it is challengiug to recover the sineared. redshif informaion., The SZ effect contains contributions from all redshifts and it is challenging to recover the smeared redshift information.207 We have shown that cross Correlating the SZ ellect with a galaxy photometric recift survey. we can iier the redshilt “ESOvec IGM pressure-galaxy cross correlatjon aud the IGM prSSILEO allo correlation (Zhang&Pe12001)..," We have shown that cross correlating the SZ effect with a galaxy photometric redshift survey, we can infer the redshift resolved IGM pressure-galaxy cross correlation and the IGM pressure auto correlation \citep{Zhang01a}."208 This method is robust. but does not capture all the iOratio iin the SZ observation.," This method is robust, but does not capture all the information in the SZ observation."209 Iu this j»aper. we utilize the one point clistributjon function (PDF of he y paraiueter and the distribution of peaks in y to extract more information.," In this paper, we utilize the one point distribution function (PDF) of the $y$ parameter and the distribution of peaks in $y$ to extract more information."210 Since smoothing is aways present for a real experinent with a finite beam. we calculate the statistics of the y paraineer sinoothed on a given angular scale 0.," Since smoothing is always present for a real experiment with a finite beam, we calculate the statistics of the $y$ parameter smoothed on a given angular scale $\theta$."211 It we are interestecLin virialized objects. for example clusers aud groups of galaxies. we would expec them to be peaks in the smoothect or filtered πιαps. ViCy>gp).," If we are interested in virialized objects, for example clusters and groups of galaxies, we would expect them to be peaks in the smoothed or filtered $y$ maps. $N(y>y_p)$,"212 the σιiuulative distribution fuiction (CDF) of peaks with sinoothecl y parameter jeeerMD than certain valle. pp. is the raw observable.," the cumulative distribution function (CDF) of peaks with smoothed $y$ parameter bigger than certain value $y_p$, is the raw observable."213 The yy €DF is the 5Z analog to a luminosity unction., The $y_p$ CDF is the SZ analog to a luminosity function.214 I£ we choose a op hat window so that tie observation coue is large ough to include an etire object such as a cluster and is suiall enough hat tydically uo more tlian e such object cau be [οιuid aloug each cone. hen when the cone 15 ceiterecl at the ¢‘enter of each ject. a peak y= ypaj»pears in the sinoothlied nap.," If we choose a top hat window so that the observation cone is large enough to include an entire object such as a cluster and is small enough that typically no more than one such object can be found along each cone, then when the cone is centered at the center of each object, a peak $y\equiv y_p$ appears in the smoothed map."215 This yp is directly related othe total gas Wass aud temperature of individual object., This $y_p$ is directly related to the total gas mass and temperature of individual object.216 Asstuning a halo to be isothermal. the to aliass Al ofa halo is related to the gas teuperature T by AL/Als=(F/T4)7.," Assuming a halo to be isothermal, the total mass $M$ of a halo is related to the gas temperature $T$ by $M/M_8=(T/T_8)^{3/2}$."217 Als=L8x101(054/0.3)/7.IM. is the Inass coutained in a sl!Npe sphere of the universe of mean density today. which is roughly the uiass scale of clusters.," $M_8=1.8\times 10^{14} (\Omega_0/0.3) h^{-1} {\rm M}_{\sun}$ is the mass contained in a $8 {\rm h}^{-1}{\rm Mpc}$ sphere of the universe of mean density today, which is roughly the mass scale of clusters."218" Zu(z) is the correspoucing temperature of a halo with mass My at reclshilt ο,", $T_8(z)$ is the corresponding temperature of a halo with mass $M_8$ at redshift $z$.219 We then obtain Here. AQ is the solid angle of the cone. fy is the gas fraction of halos aud d4 is the angular cliameter distance.," We then obtain Here, $\Delta \Omega$ is the solid angle of the cone, $f_g$ is the gas fraction of halos and $d_A$ is the angular diameter distance."220 For- clusters aud groups. the typicaln augular size. at 2=41 is. about 4/1.," For clusters and groups, the typical angular size at $z=1$ is about $1^{'}$."221 For- the present cluster number deusity v(T>2keV)~10OfMpc* (Pen1998b).. the average number oL clusters in a cone with augular radius 0~20./ projected to 2 is about one allowing for the evolution of cluster number deusity.," For the present cluster number density $n(T>2 {\rm keV})\sim 22210^{-5} h^{-3} {\rm Mpc}^3$ \citep{Pen98b}, the average number of clusters in a cone with angular radius $\theta \sim 20^{'}$ projected to $z\sim 2$ is about one allowing for the evolution of cluster number density."223 So. the size of the smootling scale for the peak analysis should be between these two scales.," So, the size of the smoothing scale for the peak analysis should be between these two scales."224 In this case. the IN(y2yy) is just the number of halos with gy2 yp.," In this case, the $N(y>y_p)$ is just the number of halos with $y>y_p$ ,"225(Naze et citeNRM)).,(Naze et \\cite{NRM}) ).226 Whilst there i$ no obvious X-ray emission from stars A and C. there might be some X-ray emission associated with stars B and D. However. the latter two objects lie in the wings of the X-ray source associated with 1183. and their status as X-ray emitters can therefore not be ascertained with confidence.," Whilst there is no obvious X-ray emission from stars A and C, there might be some X-ray emission associated with stars B and D. However, the latter two objects lie in the wings of the X-ray source associated with 183, and their status as X-ray emitters can therefore not be ascertained with confidence."227 The lack of X-ray detections for stars A and C is somewhat surprising given their spectral types inferred above., The lack of X-ray detections for stars A and C is somewhat surprising given their spectral types inferred above.228 One possibility could be a larger interstellar column density. thus larger absorption of the X-ray emission than for other stars in 22 of similar spectral type.," One possibility could be a larger interstellar column density, thus larger absorption of the X-ray emission than for other stars in 2 of similar spectral type."229 However. this explanation needs to be confirmed using additional high angular resolution optical and X-ray observations.," However, this explanation needs to be confirmed using additional high angular resolution optical and X-ray observations."230 The various eclipsing binaries that we have studied in this paper yield distance estimates in the range 6.5 to larger than Okkpe., The various eclipsing binaries that we have studied in this paper yield distance estimates in the range 6.5 to larger than kpc.231 Whilst the uncertainty in these results is. difficult to evaluate. they are in very good agreement with the spectrophotometric distance of (8.0+I4) kkpe inferred in Paper I and clearly consistent with a cluster distance well beyond the kkpe proposed by Ascenso et ((2007)).," Whilst the uncertainty in these results is difficult to evaluate, they are in very good agreement with the spectrophotometric distance of $(8.0 \pm 1.4)$ kpc inferred in Paper I and clearly consistent with a cluster distance well beyond the kpc proposed by Ascenso et \cite{Ascenso}) )."232 We thus conclude that all available observations of the early-type stellar population of 22 are most consistent with a distance near kkpe in agreement with the distance inferred for 220a., We thus conclude that all available observations of the early-type stellar population of 2 are most consistent with a distance near kpc in agreement with the distance inferred for 20a.233 This result casts serious doubts on a possible association between the y-ray pulsar JJ1023.0—5746 (Ackermann et citeAckermann)) and the 22 cluster., This result casts serious doubts on a possible association between the $\gamma$ -ray pulsar $-$ 5746 (Ackermann et \\cite{Ackermann}) ) and the 2 cluster.234 If the distance of the pulsar were confirmed at kkpe. it would then appear more likely that the latter belongs to a foreground stellar population unrelated to the massive stars of 22. but possibly related to the PMS stars discussed by Ascenso et ((2007)). With respect to the multiplicity of early-type stars in 22. we stress that among the eleven O-type stars and one WNha star monitored during our campaign. which were not previously known to be binary systems. only one star 1167) was found to probably be a short-period spectroscopic binary system.," If the distance of the pulsar were confirmed at kpc, it would then appear more likely that the latter belongs to a foreground stellar population unrelated to the massive stars of 2, but possibly related to the PMS stars discussed by Ascenso et \cite{Ascenso}) With respect to the multiplicity of early-type stars in 2, we stress that among the eleven O-type stars and one WNha star monitored during our campaign, which were not previously known to be binary systems, only one star 167) was found to probably be a short-period spectroscopic binary system."235 The other targets did not display RV variations well above the uncertainties estimated from the RV dispersion of the DIBs., The other targets did not display RV variations well above the uncertainties estimated from the RV dispersion of the DIBs.236 To assess the significance of our results. we performed Monte Carlo. simulations (Hammersley Handscomb 1964)) of the RVs of a synthetic population of massive binaries.," To assess the significance of our results, we performed Monte Carlo simulations (Hammersley Handscomb \cite{HH}) ) of the RVs of a synthetic population of massive binaries."237 The parent distribution of the binary parameters of the population of massive binaries is unfortunately unknown. but we can make a series of reasonable assumptions.," The parent distribution of the binary parameters of the population of massive binaries is unfortunately unknown, but we can make a series of reasonable assumptions."238 Here. we have followed an approach similar to the one of Sana. Gosset Evans (2009)).," Here, we have followed an approach similar to the one of Sana, Gosset Evans \cite{SGE}) )."239 Following the latter authors. we adopt a bi-uniform period distribution in logP(days) with of the systems in the range 0.3€logP<1.0 and the remainder in the range 1.0«logP.€3.5.," Following the latter authors, we adopt a bi-uniform period distribution in $\log{P(days)}$ with of the systems in the range $0.3 \leq \log{P} \leq 1.0$ and the remainder in the range $1.0 < \log{P} \leq 3.5$."240 The eccentricity was assumed to be uniformly distributed between 0.0 and 0.9. with all systems with orbital periods shorter than four days assumed to have circular orbits.," The eccentricity was assumed to be uniformly distributed between 0.0 and 0.9, with all systems with orbital periods shorter than four days assumed to have circular orbits."241 The longitudes of periastron and true anomaly of the first observation were taken to be uniformly distributed in the [0.2] interval and we adopted a uniform distribution of the mass ratio g=m-2/ni between 0.1 and 1.0.," The longitudes of periastron and true anomaly of the first observation were taken to be uniformly distributed in the $[0,2\,\pi]$ interval and we adopted a uniform distribution of the mass ratio $q = m_2/m_1$ between 0.1 and 1.0."242 The lower limit to the range of mass ratio was chosen because. in practice. it would be very difficult to observe the reflex motion of an O-star for such à low-mass companion.," The lower limit to the range of mass ratio was chosen because, in practice, it would be very difficult to observe the reflex motion of an O-star for such a low-mass companion."243 Finally. the orbital inclination was taken to be uniform in cos/ between —1.0 and 1.0.," Finally, the orbital inclination was taken to be uniform in $\cos{i}$ between $-1.0$ and $1.0$."244 For four values of the primary mass (20. 30. 40. and 50M... spanning roughly the range of spectral types for which some observational information on multiplicity is available) we simulated a population of 100000. binary systems.," For four values of the primary mass (20, 30, 40, and $M_{\odot}$, spanning roughly the range of spectral types for which some observational information on multiplicity is available) we simulated a population of 100000 binary systems."245 For each system. we evaluated the maximum RV difference A RRV = maxAV(¢;)—minRV(¢4;) that would be measured on this system adopting the same temporal sampling as used for our five GIRAFFE-IFUobservations?.," For each system, we evaluated the maximum RV difference $\Delta$ RV = $\max{RV(\phi_i)} - \min{RV(\phi_i)}$ that would be measured on this system adopting the same temporal sampling as used for our five GIRAFFE-IFU."246. The results are summarized in refMC. and illustrated in refhisto.., The results are summarized in \\ref{MC} and illustrated in \\ref{histo}.247" If we assumed that a velocity difference of ss! were required to claim the detection of a binarysystem"". we would find that fewer than of the systems containing an VV primary star wwith a mass higher than 30M,.). and having an orbital period of shorter than ddays. would escape detection."," If we assumed that a velocity difference of $^{-1}$ were required to claim the detection of a binary, we would find that fewer than of the systems containing an V primary star with a mass higher than $M_{\odot}$ ), and having an orbital period of shorter than days, would escape detection."248 Only the lowest inclination systems would indeed remain undetected., Only the lowest inclination systems would indeed remain undetected.249 For longer orbital periods. the fraction of systems that would be missed by our GIRAFFE-IFU campaign steeply increases: for systems with orbital periods between 50 and ddays. about half of the binaries would escape detection.," For longer orbital periods, the fraction of systems that would be missed by our GIRAFFE-IFU campaign steeply increases: for systems with orbital periods between 50 and days, about half of the binaries would escape detection."250 However. owing to the assumed preponderance of short orbital-period systems. the total fraction of systems with a period up to ddays that we would miss. would still remain quite low (4 - 5%%)).," However, owing to the assumed preponderance of short orbital-period systems, the total fraction of systems with a period up to days that we would miss, would still remain quite low (4 - )."251 The same approach was applied to the sampling of the three GIRAFFE-ARGUS observations (see refMC2))., The same approach was applied to the sampling of the three GIRAFFE-ARGUS observations (see \\ref{MC2}) ).252 As could be expected. this sampling ts less efficient for the detection of binary systems.," As could be expected, this sampling is less efficient for the detection of binary systems."253 Nonetheless. for primary masses in the range 20 - M.« (corresponding roughly to VV spectral types). our simulations indicate that à binary system with a period shorter than ddays has less than a probability of escaping detection because ARRV 20kkm ss!.," Nonetheless, for primary masses in the range 20 - $M_{\odot}$ (corresponding roughly to V spectral types), our simulations indicate that a binary system with a period shorter than days has less than a probability of escaping detection because $\Delta$ RV $< 20$ $^{-1}$."254 Therefore. we can safely conclude that the probability that either of the stars 118. 171. 182. 183. 199. or 203 or stars A. B or C is a short-period binary system must be very low.," Therefore, we can safely conclude that the probability that either of the stars 18, 171, 182, 183, 199, or 203 or stars A, B or C is a short-period binary system must be very low."255 If these stars are indeed binaries. they must have either a very low orbital inclination. a very long orbital period. or both.," If these stars are indeed binaries, they must have either a very low orbital inclination, a very long orbital period, or both."256 The situation is a bit less clear for 220b for which we do observe a maximum RV difference above our threshold., The situation is a bit less clear for 20b for which we do observe a maximum RV difference above our threshold.257 However. as stated above. this result must be considered with," However, as stated above, this result must be considered with"258where the ecometric comoving angular diameter distance terms have been absorbed into ον).,where the geometric comoving angular diameter distance terms have been absorbed into $g(\chi)$.259 It is therefore now clear. given our earlier discussion. how weal lensing as à cosmological probe is particularly useful in. studies of modified gravity.," It is therefore now clear, given our earlier discussion, how weak lensing as a cosmological probe is particularly useful in studies of modified gravity."260 For this statistic is sensitive to the erowth of structure via the presence of the linear growth ctor squared (q (a)) in the matter power spectrum I5., For this statistic is sensitive to the growth of structure via the presence of the linear growth factor squared $g^{2}(a)$ ) in the matter power spectrum $P_{\delta}$.261 lt is sensitive to the expansion history through the ternis in the square brackets and. through the Hubble. drag in he growth of structure and. also. as discussed at the end of the last section. it is sensitive to the relation between he power spectrum of the potentials and density.," It is sensitive to the expansion history through the terms in the square brackets and through the Hubble drag in the growth of structure and also, as discussed at the end of the last section, it is sensitive to the relation between the power spectrum of the potentials and density."262" In. the equation above the relation from £2,,. to Ps has already oen performed. assuming GR as given routinely in the iterature.", In the equation above the relation from $P_{\phi + \psi}$ to $P_{\delta}$ has already been performed assuming GR as given routinely in the literature.263 Again. it is worth reiterating that if there is a modification to the Poisson equation. and/or το the anisolropic stress one must augment this powerspectrum with the approapriate prefactor given. for example. as in Equation(17).," Again, it is worth reiterating that if there is a modification to the Poisson equation and/or to the anisotropic stress one must augment this powerspectrum with the approapriate prefactor given, for example, as in Equation."264. In addition to these sensitivities it is worth adding that because the dellection is given by the potentiaLg which are sourced by mass irrespective of being barvonic or dark. weak lensing does not suller from any unknown bias.," In addition to these sensitivities it is worth adding that because the deflection is given by the potentials, which are sourced by mass irrespective of being baryonic or dark, weak lensing does not suffer from any unknown bias."265 That is. it probes the entirety of the mass distribution.," That is, it probes the entirety of the mass distribution."266 While this probe. in principle. is excellent. for our chosen study it is worthwhile noting that the shear signal is a small 174 distortion on the already existing intrinsic ellipticity.," While this probe, in principle, is excellent for our chosen study it is worthwhile noting that the shear signal is a small $1\%$ distortion on the already existing intrinsic ellipticity."267 This provides a thorough. technical challenge that is being combated with a combination of large galaxy nuniber analyses and refined shear measurement techniques (?.. ?. and ?)).," This provides a thorough technical challenge that is being combated with a combination of large galaxy number analyses and refined shear measurement techniques \citet{Heymans05}, \citet{Massey06} and \citet{Bridle08}) )."268 Further still. the first. cleteetions of weak lensing are particularly recent. (7... 7... 2? and ?)) and so in this wav lensing is very much a highly promising. vet developing. cosmological probe.," Further still, the first detections of weak lensing are particularly recent \citet{Bacon00}, \citet{Kaiser00}, \citet{Wittman00} and \citet{vanWaerbeke00}) ) and so in this way lensing is very much a highly promising, yet developing, cosmological probe."269 Despite this there are already a number of papers in the literature that have addressed. the relationship between weak lensing and mocified gravity or dark energy. such as 2.. 2.. 2.. 2. 2. 7 and ?..," Despite this there are already a number of papers in the literature that have addressed the relationship between weak lensing and modified gravity or dark energy, such as \citet{UzanBernardeau01}, \citet{Schimd05}, \citet{DoreMartigMellier07}, \citet{Schimd07}, \citet{AmendolaKunzSapone07}, \citet{Jain07} and \citet{Tsujikawa08}."270 With these studies and potential modified: gravity attributes in lensing it is imperitive to realise that there does exist. à severe caveat., With these studies and potential modified gravity attributes in lensing it is imperitive to realise that there does exist a severe caveat.271 This is due to the fact that lensing probes into the non-linear regime., This is due to the fact that lensing probes into the non-linear regime.272 We are fortunate to be able to use a fitting Function (IZ.g. 2)) for the non- in standard gravity., We are fortunate to be able to use a fitting function (E.g. \citealt{Smith03}) ) for the non-linearities in standard gravity.273 Unfortunately this is poorly understood in any deviation [from the current. framework and subsequent implementation of the fit would. technically. be invalid.," Unfortunately this is poorly understood in any deviation from the current framework and subsequent implementation of the fit would, technically, be invalid."274 Vherefore until N-body simulations have been undertaken that could. generalise the fitting function. or accurately quantify deviations from it we must strive to work in the linear regime as much as possible., Therefore until N-body simulations have been undertaken that could generalise the fitting function or accurately quantify deviations from it we must strive to work in the linear regime as much as possible.275 Although some attempts have been made at quantifving the validity of the present fits (IZ.g. ? and 2)) we keep. for now. a strict and linear only analysis.," Although some attempts have been made at quantifying the validity of the present fits (E.g. \citet{LaszloBean07} and \citet{Oyaizu08}) ) we keep, for now, a strict and linear only analysis."276 Phere are. in addition. other benefits in avoiding the inclusion of small scales such as the presence of intrinsic ellipticity correlations. shear-shape correlations and the presence of non-Gaussianity in the error.," There are, in addition, other benefits in avoiding the inclusion of small scales such as the presence of intrinsic ellipticity correlations, shear-shape correlations and the presence of non-Gaussianity in the error."277 We therefore utilise the data provided by FOS based on the CELUELS-wide survey which. due to its range of large angular scales (up to 230 arcminutes) probing the more linear regime. is ideal for work on non-LODAL cosmology such as this.," We therefore utilise the data provided by F08 based on the CFHTLS-wide survey which, due to its range of large angular scales (up to 230 arcminutes) probing the more linear regime, is ideal for work on non-LCDM cosmology such as this."278 The Canada-Erance-Hawaii Telescope. Legacy Survey (CELUPLS). based on the MEGAPRIAIE/AIEGACAAL instrument. is an ongoing survey with a target of 450 nights extending over 5 vears.," The Canada-France-Hawaii Telescope Legacy Survey (CFHTLS), based on the MEGAPRIME/MEGACAM instrument, is an ongoing survey with a target of 450 nights extending over 5 years."279 The recent analysis by ? has gone bevond the initial releases and investigations by 7? and ? which themselves were successful in. deriving constraints on the οax degeneracy ancl demonstrating the evolution of the shear signal with redshift., The recent analysis by \citet{Benjamin07} has gone beyond the initial releases and investigations by \citet{Semboloni06} and \citet{Hoekstra06} which themselves were successful in deriving constraints on the $\Omega_{m}- \sigma_{8}$ degeneracy and demonstrating the evolution of the shear signal with redshift.280 This was achieved in 7/— through a better understanding. of the redshift distribution and having an increased area., This was achieved in \citet{Benjamin07} through a better understanding of the redshift distribution and having an increased area.281 This. while marking significant progress. is still not the most optimal lensing analvsis for this work.," This, while marking significant progress, is still not the most optimal lensing analysis for this work."282 This is because they are potentially sensitive to the growth of structures on non-linear scales which. as we emphasised above. is undesirable for a current study of bevond-LEinstcin cosmology and weak lensing.," This is because they are potentially sensitive to the growth of structures on non-linear scales which, as we emphasised above, is undesirable for a current study of beyond-Einstein cosmology and weak lensing."283 We therefore look to the 3rd vear CELILTLS-wide release CP0003) given by ? (E08)., We therefore look to the 3rd year CFHTLS-wide release (T0003) given by \citet{Fu08} (F08).284 Although having a smaller Ποιά of view than ? it utilises much larger angular scales (into the linear regime) also avoiding many of the potential systematics mentioned at the end of the last section., Although having a smaller field of view than \citet{Benjamin07} it utilises much larger angular scales (into the linear regime) also avoiding many of the potential systematics mentioned at the end of the last section.285 Lt is because of this that both works reveal approximately equivalent cosmological constraints ancl little constraining power is lost., It is because of this that both works reveal approximately equivalent cosmological constraints and little constraining power is lost.286 The current sky coverage of 57deg. approximately 3DAmi’ of the final CELIUELS. target area. is reduced. to 34.2cdee7 alter masking and the removal of various contaminants.," The current sky coverage of $57 \mathrm{deg^{2}}$, approximately $35\%$ of the final CFHTLS target area, is reduced to $34.2 \mathrm{deg^{2}}$ after masking and the removal of various contaminants."287" Eventually including five bands this / band study stretches to à magnitude of 7,5=24.5 and encapsulating nearly 1.7 million galaxies has an elfective galaxy number density of n—l]33gal/arcmün.", Eventually including five bands this $i'$ band study stretches to a magnitude of $i'_{AB} = 24.5$ and encapsulating nearly 1.7 million galaxies has an effective galaxy number density of $n = 13.3 \mathrm{gal/arcmin^{2}}$.288 The data (E08) comes in the form of several two point statistics which are relevant to this study., The data (F08) comes in the form of several two point statistics which are relevant to this study.289 We choose to utilise the LE correlation Function which is shown in Equation and displayed: along with the cosmological best fit in Figure 4.., We choose to utilise the E correlation function which is shown in Equation and displayed along with the cosmological best fit in Figure \ref{fig:paper_E_correlation}.290" As lor the aperture mass <AL,> and shear top hat variance «[52 two point statistics this is a weighted transform of the convergence power spectrum.", As for the aperture mass $< \! M^{2}_{\mathrm{ap}} \!>$ and shear top hat variance $<|\gamma|^{2}>$ two point statistics this is a weighted transform of the convergence power spectrum.291 In this case it is given by a zeroth order Bessel function of the first kind Jy., In this case it is given by a zeroth order Bessel function of the first kind $J_{0}$.292 lt dis in this way that the two point functions vary in their sensitivity to. various aspects of the power spectrum and in turn any svstematios., It is in this way that the two point functions vary in their sensitivity to various aspects of the power spectrum and in turn any systematics.293£e sullers [from a constant olfset resulting from a mixing of E and. D-mocdes.,$\xi_{E}$ suffers from a constant offset resulting from a mixing of E and B-modes.294 A finite survey size introduces a maximum angular scale which prevents a complete calculation of the shear correlation function over larger ranges., A finite survey size introduces a maximum angular scale which prevents a complete calculation of the shear correlation function over larger ranges.295 This is needed. for a separation of I5 and B (?).., This is needed for a separation of E and B \citep{Kilbinger06}.296 Yo alleviate this we alter the statistic £g to £g|6 including the constant ollset c as an extra. parameter., To alleviate this we alter the statistic $\xi_{E}$ to $\xi_{E} + c'$ including the constant offset $c'$ as an extra parameter.297 An expression is then obtained for the olfset which represents the best fit ollset (d?de’= 0) for cach parameter choice., An expression is then obtained for the offset which represents the best fit offset $\mathrm{d} \chi^{2}/\mathrm{d} c' = 0$ ) for each parameter choice.298 This constitutes an analytic mareinalisation over e (2).., This constitutes an analytic marginalisation over $c'$ \citep{Lewis02}.299 We subsequently find the expression to be, We subsequently find the expression to be300aud is thus not able to account for two-body relaxation effects in granular media.,and is thus not able to account for two-body relaxation effects in granular media.301 However. a certain degree of erauularitvis a inherent property of N-body svstemis.," However, a certain degree of granularity is a inherent property of $N$ -body systems."302 This may then lead to discrepancies. expecially iu the unstable interval of negative specific heat. where ράσο trausitious may be sensitive to s1all scale plivsics.," This may then lead to discrepancies, especially in the unstable interval of negative specific heat, where phase transitions may be sensitive to small scale physics."303 Whereas thermostatistics is too smooth to account for muicroscopic physics in eranular seltf-eravitatiug media such as the interstellar eas. two-body relaxation is often too strong in N-body system due to computational limitations.," Whereas thermostatistics is too smooth to account for microscopic physics in granular self-gravitating media such as the interstellar gas, two-body relaxation is often too strong in $N$ -body system due to computational limitations."304. Especially. in. high. force. resolution. simulationsN. the force resolution. is. lareer. than the mass Boghosian resolution., Especially in high force resolution simulations where the force resolution is larger than the mass resolution.305 We refer to this iu Sect., We refer to this in Sect.306 6.1 where we discuss. amoung other thines. the effect of the eramularity on lone-range correlations appearing iu the interval of negativo specific heat.," \ref{corr} where we discuss, among other things, the effect of the granularity on long-range correlations appearing in the interval of negative specific heat."307 A further discrepancy between nature. analytical models and N-body models may be due to the eutropy used in eravo-thermal statistics (Tara Sakagaii 900111.," A further discrepancy between nature, analytical models and $N$ -body models may be due to the entropy used in gravo-thermal statistics (Taruya Sakagami \cite{Taruya01}) )."308 Iudeed. the entropy used in analytical models to find equilibrimm states via the maxinuun eutropy principle is the extensive Boltzmaun-Cabbs eutropy. that is im fact not applicable for nou-exteusive sclf-eravitating svsteuis.," Indeed, the entropy used in analytical models to find equilibrium states via the maximum entropy principle is the extensive Boltzmann-Gibbs entropy, that is in fact not applicable for non-extensive self-gravitating systems."309 Generalized thermostatistics includiug nou-exteusivitv are currently developed (Tsallis L98s8:: Sumivosli 2001:: Latora et al. 2001:, Generalized thermostatistics including non-extensivity are currently developed (Tsallis \cite{Tsallis88}; ; Sumiyoshi \cite{Sumiyoshi01}; Latora et al. \cite{Latora01};310 Leubner 20013)., Leubner \cite{Leubner01}) ).311 These formalis sugeest that non-extcusivity changes not all but some of1 the ∖classical thermodynamical∖⋅ry):EM resultsou: (PsallisNNje ΤοΟΟ..1999: 1999)).2⊾d. 1€ which agrees“Wye with∢⊾⋅∖∖↴ ourEM findings.," These formalisms suggest that non-extensivity changes not all but some of the classical thermodynamical results (Tsallis \cite{Tsallis99}; Boghosian \cite{Boghosian99}) ), which agrees with our findings."312 1ναιwhere Because currently it is a priori uot known which thermostatistical properties change i non-cxteusive svstenis aud cousisteut theoretical tools are not available. analytical results mustbe considered with caution.," Because currently it is a priori not known which thermostatistical properties change in non-extensive systems and consistent theoretical tools are not available, analytical results mustbe considered with caution."313tidal forces are time-dependeut and can vary ercatly depending on the orbital phase.,tidal forces are time-dependent and can vary greatly depending on the orbital phase.314 Here. we show that despite the large tidal forces at periastrou. our boundary conditions are well suited for the imodeliug of such systems.," Here, we show that despite the large tidal forces at periastron, our boundary conditions are well suited for the modeling of such systems."315 The system we model consists of two maisequence stars with massesof 1.10 and 1.50 AD. with au eccentricity of e=0.15 aud evolved for over four orbits {Port—Ll code units)., The system we model consists of two main-sequence stars with massesof $1.40$ and $1.50$ $_{\odot}$ with an eccentricity of $e=0.15$ and evolved for over four orbits $P_{\textrm{orb}}\simeq 44$ code units).316 The total uuuber of particles nears ~500.000 aud the location of the boundary is at ~75% of the stars radius. which. as shown in Fieure S. is deep inside the star so that the effects of tidal force are negligible.," The total number of particles nears $\sim500,000$ and the location of the boundary is at $\sim75\%$ of the stars' radius, which, as shown in Figure \ref{fig:encmass}, is deep inside the star so that the effects of tidal force are negligible."317 Iudeed. Figure 8. shows the radius of the primary euclosiug differcut fractious of the total bound ass (m SPIT particles) as a fiction of time for our binary svsteu.," Indeed, Figure \ref{fig:encmass} shows the radius of the primary enclosing different fractions of the total bound mass (in SPH particles) as a function of time for our binary system."318 For example. the radii coutaimineg GU to 90% of the total bound mass are shown to not changeX significantly during the whole duration of this simulation.," For example, the radii containing $60\%$ to $90\%$ of the total bound mass are shown to not change significantly during the whole duration of this simulation."319 Iu fact. only the outer radius of the star. containing over 95% of the bound mass. oscillates ching each orbit.," In fact, only the outer radius of the star, containing over $95\%$ of the bound mass, oscillates during each orbit."320 Therefore. in this case. the choice of the locaion of the boundary (dotted line} is well justified aud Figure 8. shows jii the use of our method for ecceatric binaries is acequate.," Therefore, in this case, the choice of the location of the boundary (dotted line) is well justified and Figure \ref{fig:encmass}321 shows that the use of our method for eccentric binaries is adequate."322 Replacing the core of a star with a ceutral poi ifagnass aud a boundary remains avaid approxinatiou asx long as the boundary is deep enough inside the cuveope of the star., Replacing the core of a star with a central point mass and a boundary remains a valid approximation as long as the boundary is deep enough inside the envelope of the star.323 We now present the results from the simulation prescuted in 6 .3.., We now present the results from the simulation presented in $\S$ \ref{sect:eccentric}. .324 In particular. we are interested iu the lass trauster rates observed alone the eccentric orbit.," In particular, we are interested in the mass transfer rates observed along the eccentric orbit."325function on Nyy for nine of the strongest les. assunius a carbon abunudauce of |C/II|2-2.5 aud a relative abundance pattern similar to that observed in population IT stars.,"function on $N_{\rm HI}$ for nine of the strongest lines, assuming a carbon abundance of [C/H]=-2.5 and a relative abundance pattern similar to that observed in population II stars."326" A more exhaustive list of lines is presented in [11]. which also discusses the dependence of the LOX on :. O5. aud the normalization of the radiation field J,."," A more exhaustive list of lines is presented in \cite{hel97b}, which also discusses the dependence of the LOX on $z$, $\Omega _b$, and the normalization of the radiation field $J_{\nu}$."327 This dependence is weak. aud the following predictious are believed to hold rather ecuerally in cosmological models of the forest:," This dependence is weak, and the following predictions are believed to hold rather generally in cosmological models of the forest:"328et al,et al.329 as members of the Virgo cluster we assign thei a distance of 17 AIpe., as members of the Virgo cluster we assign them a distance of 17 Mpc.330 These three galaxies are reported in figure 2b., These three galaxies are reported in figure 2b.331 For the most luminous (F12212|0919) the upper Πατ of Foo/Fu.2 is compatible with the general treud. the two faint Virgo dwarfs clearly disagree.," For the most luminous (F12242+0919) the upper limit of $\rm F_{60}/F_{0.2}$ is compatible with the general trend, the two faint Virgo dwarfs clearly disagree."332 Due to their füutuess not much information is available for thoi. F12259|LIT is classified as dE and F12235|0911 dE or Du. A large FIR to UV ratio is not expected for elliptical ealaxies. therefore these objects are probably not dE. We will see in section 6 that even the most FIR bright aud extincted objects known in the Universe follow aud exteud he trend found in figure 2b so the behavior of these two objects is difficult to wuclerstae.," Due to their faintness not much information is available for them, F12259+1141 is classified as dE and F12235+0914 dE or Im. A large FIR to UV ratio is not expected for elliptical galaxies, therefore these objects are probably not dE. We will see in section 6 that even the most FIR bright and extincted objects known in the Universe follow and extend the trend found in figure 2b so the behavior of these two objects is difficult to understand."333 We can try to estimate an extinction for the objects isted iu able 2., We can try to estimate an extinction for the objects listed in table 2.334 Ouly two (F12011165]9. F13011|2907) aave been detecος at oth GO aud 100422. For these wo galaxies we have he FIR fux to estimate the UV extinction (a lower lait for F13011]2907) using the oruula {οπιοαι] fit) established in section 3.1.," Only two (F12041+6519, F13041+2907) have been detected at both 60 and $\mu$ m. For these two galaxies we have the FIR flux to estimate the UV extinction (a lower limit for F13041+2907) using the formula (polynomial fit) established in section 3.1."335 For the eaOs:axies rot detected at LOO µ i we estimate arbitrarily lis flux such as fooπου=0.3 which is imutermediate jetween the values for warni aixl cool dust (Lousdale Uelou 1987)). i£ this value is incompatible witi the upper indt. we adopt the upper lait.," For the galaxies not detected at 100 $\mu$ m we estimate arbitrarily this flux such as $\rm f_{60}/f_{100}=0.3$ which is intermediate between the values for warm and cool dust (Lonsdale Helou \cite{lonsdale}) ), if this value is incompatible with the upper limit, we adopt the upper limit."336 The extinctions are listed iu table 2., The extinctions are listed in table 2.337 Adopting the relation of Meurer et al., Adopting the relation of Meurer et al.338 leads to extinctions larger by 0.1L mae., leads to extinctions larger by 0.4 mag.339 Three galaxies have a UV extinction huger than 3.5 mae. they are the two objects without any optical identification aud the faintest ealaxy of the table 2 detected in D. The three other cases (two non detectious and the uncertzn one) are less extreme (apyον2.5 mae).," Three galaxies have a UV extinction larger than 3.5 mag, they are the two objects without any optical identification and the faintest galaxy of the table 2 detected in B. The three other cases (two non detections and the uncertain one) are less extreme $\rm a_{UV}>\sim 2.5 ~mag$ )."340 Note that the upper limits found for these galaxies are compatible with the values fouud for some galaxies of the IRAS/FOCAÀ sample (figures 2)., Note that the upper limits found for these galaxies are compatible with the values found for some galaxies of the IRAS/FOCA sample (figures 2).341 For example the two most extincted galaxies of our sample. namely M82 aud IC732. have a UV extinction larger than 5 mae and a Foo/Eo» ratio larger than 2 in log unit.," For example the two most extincted galaxies of our sample, namely M82 and IC732, have a UV extinction larger than 5 mag and a $\rm F_{60}/F_{0.2}$ ratio larger than 2 in log unit."342WII Jised+24: Galactic nebulositv.,WHI J1824+24: Galactic nebulosity.343 Measurements are given for a ringlike structure. connected to more wisps going olf the edge of the field.," Measurements are given for a ringlike structure, connected to more wisps going off the edge of the field."344 This is conceivably a PN., This is conceivably a PN.345 WII J132314-24: Mottled Galactic nebulosity with distant galaxies in the background., WHI J1831+24: Mottled Galactic nebulosity with distant galaxies in the background.346 COMAW 5-577172: Multiarmed spiral galaxy. behind a lot of Galactic stars.," CGMW 5-5772: Multiarmed spiral galaxy, behind a lot of Galactic stars."347 WII JiStd4+28: A wisp of Galactic nebulositv., WHI J1844+28: A wisp of Galactic nebulosity.348 There is more in the field as well as leading out of it: (Bis is the most coherent. compact part.," There is more in the field as well as leading out of it; this is the most coherent, compact part."349 WII J18562-52: Very faint. (wo wisps of nebulosity forming a part of a circle.," WHI J1856+52: Very faint, two wisps of nebulosity forming a part of a circle."350 Although it is not much (Gf anv) brighter than flat-fielding residuals. observations at (wo different observing runs eive (he same shape and surface brightness.," Although it is not much (if any) brighter than flat-fielding residuals, observations at two different observing runs give the same shape and surface brightness."351 WII J1359--45: A few wisps which might outline a larger area of galactic nebulosity., WHI J1859+45: A few wisps which might outline a larger area of galactic nebulosity.352 WII J19092-50: Galactic nebulosity., WHI J1909+50: Galactic nebulosity.353 WII J1913+41: The brightest bit of Galactic nebulosity whieh just about fills the field., WHI J1913+41: The brightest bit of Galactic nebulosity which just about fills the field.354 The main uncertainty in surface brightness comes from not knowing what is skv ancl what is fainter nebulosity., The main uncertainty in surface brightness comes from not knowing what is sky and what is fainter nebulosity.355 WII J1919--44: Very nice bipolar PN., WHI J1919+44: Very nice bipolar PN.356 WII J1932+08: Face-on spiral. with a central bar (accentuated by a guiding error in our follow-up image).," WHI J1932+08: Face-on spiral, with a central bar (accentuated by a guiding error in our follow-up image)."357 WII J19334-55: A roundish piece of nebulosity., WHI J1933+55: A roundish piece of nebulosity.358 WII J1945+22: Large. [aint nebulositv.," WHI J1945+22: Large, faint nebulosity."359 Due to the high star density. the surface brightness measurements are even more uncertain than usual.," Due to the high star density, the surface brightness measurements are even more uncertain than usual."360 WII J20044-64: Swirls of Galactie nebulositv., WHI J2004+64: Swirls of Galactic nebulosity.361 Little or no Ila., Little or no $\alpha$.362 WIL J20242-52: A voundish bit of Galactic nebulositv., WHI J2024+52: A roundish bit of Galactic nebulosity.363 Crowcded field., Crowded field.364 WII J20314-00: Oval bit of Galactic nebulositv., WHI J2031+00: Oval bit of Galactic nebulosity.365 ZOAG (G093.12--08.90: A [ace-on. extineted spiral galaxy.," ZOAG G093.12+08.90: A face-on, extincted spiral galaxy."366 There are wisps of Galactic nebulosity within a few are minutes., There are wisps of Galactic nebulosity within a few arc minutes.367 IXIXR99-59: A diffuse. oval object. catalogued by Narachentsevοἱal.(1999). as a probable nearby dwarf galaxyv.," KKR99-59: A diffuse, oval object, catalogued by \citet{KKR99} as a probable nearby dwarf galaxy."368 Is morphology here. together with the [act that it has apparently not been seen in HI by Iluchtmeieretal.(2000a) nor in lla. bv. (2003).. lead us to believe it to be Galactic reflection nebulositv.," Its morphology here, together with the fact that it has apparently not been seen in HI by \citet{HKK00} nor in $\alpha$ by \citet{MKB03}, lead us to believe it to be Galactic reflection nebulosity."369 WII J2125+44: Bright (and near a bright star)., WHI J2125+44: Bright (and near a bright star).370 Probably a barred spiral. but. possibly," Probably a barred spiral, but possibly"371The cosmic microwave background (CMB) was discovered by Penzias and Wilson (1965).,The cosmic microwave background (CMB) was discovered by Penzias and Wilson (1965).372 Unique information about the earliest phases of the evolution of the Universe can be derived from CMB temperature and polarization maps., Unique information about the earliest phases of the evolution of the Universe can be derived from CMB temperature and polarization maps.373 Since its discovery. tremendous effort has been made to improve the CMB maps.," Since its discovery, tremendous effort has been made to improve the CMB maps."374 Significant improvement has been made with the ongoing ASA (WMAP. Benet et al.," Significant improvement has been made with the ongoing NASA (WMAP, Bennet et al."375 2003a). and with the Planck mission. launched in Ίαν 2009. it is expected that the sensitivity and angular resolution of the CMB maps will be improved by more than an order of magnitude.," 2003a), and with the Planck mission, launched in May 2009, it is expected that the sensitivity and angular resolution of the CMB maps will be improved by more than an order of magnitude."376 Unfortunately. the cosmological CMB signal is always mixed with emission from the Milky Way (synchrotron. free-free. and thermal dust emission).," Unfortunately, the cosmological CMB signal is always mixed with emission from the Milky Way (synchrotron, free-free, and thermal dust emission)."377 To extract the background cosmological information. it is essential to remove the galactic foregrounds without introducing systematic errors.," To extract the background cosmological information, it is essential to remove the galactic foregrounds without introducing systematic errors."378 Several algorithms have been developed to solve this key issue in CMB research., Several algorithms have been developed to solve this key issue in CMB research.379 A comprehensive review is given by Delabrouille and Cardoso (2007)., A comprehensive review is given by Delabrouille and Cardoso (2007).380 Of course. it is most desirable that the method for removing the galactic foregrounds produces both a power spectrum and a CMB map with insignificant systematic errors.," Of course, it is most desirable that the method for removing the galactic foregrounds produces both a power spectrum and a CMB map with insignificant systematic errors."381 For the Planck mission. 1t is an important requirement. since one of the main scientific goals is to search for non-Gaussian features in the CMB maps.," For the Planck mission, it is an important requirement, since one of the main scientific goals is to search for non-Gaussian features in the CMB maps."382 A lot of signals of individual sky pixels are averaged in order to derive the power spectrum. therefore. the crucial issue is not so much to minimize the random errors per sky pixel. but to minimize the systematic errors in the CMB map as a whole.," A lot of signals of individual sky pixels are averaged in order to derive the power spectrum, therefore, the crucial issue is not so much to minimize the random errors per sky pixel, but to minimize the systematic errors in the CMB map as a whole."383 From the FIRAS instrument onboard the COBE satellite. it is known that the CMB spectrum follows a black body spectrum very closely (Mather et al.," From the FIRAS instrument onboard the COBE satellite, it is known that the CMB spectrum follows a black body spectrum very closely (Mather et al."384 1999)., 1999).385 Fortunately. all known non-cosmological signals have very different spectral behaviour from a black body.," Fortunately, all known non-cosmological signals have very different spectral behaviour from a black body."386 It is thus possible to disentangle the different components of the microwave signals., It is thus possible to disentangle the different components of the microwave signals.387 The obtained accuracy will. of course. depend on the observational errors and frequency coverage of the data available.," The obtained accuracy will, of course, depend on the observational errors and frequency coverage of the data available."388 The ESA Planck mission was successfully launched in May 2009. and all systems have been working according to expectations ever since.," The ESA Planck mission was successfully launched in May 2009, and all systems have been working according to expectations ever since."389 An important part of the preparation of the mission has been evaluation of the available galactic foreground removal algorithms. based on detailed simulations. called the (PSM).," An important part of the preparation of the mission has been evaluation of the available galactic foreground removal algorithms, based on detailed simulations, called the (PSM)."390 This work was done by Planck Working Group 2. coordinated by J. Delabrouille and G. de Zotti.," This work was done by Planck Working Group 2, coordinated by J. Delabrouille and G. de Zotti."391 Comparisons of the 8 investigated methods can be found in Leach et ((2008)., Comparisons of the 8 investigated methods can be found in Leach et (2008).392 Norgaard-ielsen. and Jorgensen (2008. hereafter NNJ) have shown that with observational errors as expected from the Planck satellite. reasonable assumptions about the spectral behaviour of the galactic foregrounds. it is possible to use simple neural networks to extract the CMB temperature signal with negligible systematic errors.," rgaard-Nielsen and rgensen (2008, hereafter NNJ) have shown that with observational errors as expected from the Planck satellite, reasonable assumptions about the spectral behaviour of the galactic foregrounds, it is possible to use simple neural networks to extract the CMB temperature signal with negligible systematic errors."393 In the analysis of the same PSM data às used by Leach et al.((2008). Norgaard-Nielsen and Hebert (2009. hereafter NNH) have shown that neural networks can also significantly improve the removal of systematic errors in the CMB temperature determination for imaging data.," In the analysis of the same PSM data as used by Leach et (2008), rgaard-Nielsen and Hebert (2009, hereafter NNH) have shown that neural networks can also significantly improve the removal of systematic errors in the CMB temperature determination for imaging data."394 An analysis of the WMAP 5yr data Is presented here to show the improvement produced by neural networks. also for real observed data.," An analysis of the WMAP 5yr data is presented here to show the improvement produced by neural networks, also for real observed data."395 It is basically the same method as in NNJ and NNH. so the neural network references can be found there.," It is basically the same method as in NNJ and NNH, so the neural network references can be found there."396 The frequency maps obtained during the first 5 years of the WMAP mission (K. Ka. Q. V. W. centred at 22GHz. 33GHz. 41GHz. 61GHz. 94GHz. respectively) were taken from the official WMAP website:Anap/eurrent/m_products.," The frequency maps obtained during the first 5 years of the WMAP mission (K, Ka, Q, V, W, centred at 23GHz, 33GHz, 41GHz, 61GHz, 94GHz, respectively) were taken from the official WMAP website:."397cfit.. The PSM maps were taken from the Planck Working Group 2 Challenge-2 ftp area:2/PSM-maps., The PSM maps were taken from the Planck Working Group 2 Challenge-2 ftp area:.398v0.. PSM exposures maps (expected hits per sky pixel) are also provided., PSM exposures maps (expected hits per sky pixel) are also provided.399 In order to derive noise maps for each frequency the algorithm given at the WMAP website hàs been used. assuming that the noise is Gaussianly distributed.," In order to derive noise maps for each frequency the algorithm given at the WMAP website has been used, assuming that the noise is Gaussianly distributed."400 For each of the WMAP frequencies and each of the components (CMB. synchrotron. free-free. thermal and spinning dust) PSM provides maps without observational errors and no corrections," For each of the WMAP frequencies and each of the components (CMB, synchrotron, free-free, thermal and spinning dust) PSM provides maps without observational errors and no corrections"401radii and temperatures. as well as My and (V—7) are nicely reproduced.,"radii and temperatures, as well as $M_V$ and $(V-I)$ are nicely reproduced."402 For 12 Gyr the predicted radii start to be larger than observed. while in the other planes we obtain a good fit.," For 12 Gyr the predicted radii start to be larger than observed, while in the other planes we obtain a good fit."403 Thus we consider 12 Gyr as an upper limit to the ASAS-04 age., Thus we consider 12 Gyr as an upper limit to the ASAS-04 age.404 Note also that the BHAC98 model for 8 Gyr and the solar Z predicts the largest radit of all sets. despite predicting the lowest temperatures and luminosities.," Note also that the BHAC98 model for 8 Gyr and the solar $Z$ predicts the largest radii of all sets, despite predicting the lowest temperatures and luminosities."405 The presented models suggest that the radius and temperature discrepancies may not be significant for older stars., The presented models suggest that the radius and temperature discrepancies may not be significant for older stars.406 This seems to be supported by the recent discovery of à 0.88 + 0.86 M. evolved eclipsing binary in the famous globular cluster (Thompsonetal.2010)., This seems to be supported by the recent discovery of a 0.88 + 0.86 $_\odot$ evolved eclipsing binary in the famous globular cluster \citep{tho09}.407. Several sets of theoretical models succeeded to fit the observed radii and bolometric luminosities of this binary components with a single isochrone., Several sets of theoretical models succeeded to fit the observed radii and bolometric luminosities of this binary components with a single isochrone.408 The estimated age was 11.3 Gyr and |Fe/H|2-0.70 was assumed., The estimated age was 11.3 Gyr and [Fe/H]=-0.70 was assumed.409 Considering the similar masses of the ASAS-04 components we may expect that the almost perfect fits of¢>10 Gyr isochrones are plausible., Considering the similar masses of the ASAS-04 components we may expect that the almost perfect fits of $t>10$ Gyr isochrones are plausible.410 From the discussion above. we can deduce the age of ASAS-04 to be 5-12 Gyr and the metal abundance between 0.008 and 0.02 with the ranges of 8—I1 Gyr and Z from 0.012 to ~0.018 be the most probable ones.," From the discussion above, we can deduce the age of ASAS-04 to be $5 - 12$ Gyr and the metal abundance between 0.008 and 0.02 with the ranges of $8 - 11$ Gyr and $Z$ from 0.012 to $\sim0.018$ be the most probable ones."411 This makes, This makes412lo give where Q(r) is the total energv input to the wind.,to give where $Q(r)$ is the total energy input to the wind.413 Since we are interested in the terminal velocity of the outflow. we choose a point above the heating shell where the energy has reached its steady state value where the energy is constant in Figure 3.. top panel) and integrate outwards using the energy ancl Mach number at this point to solve (11)) as an initial value problem.," Since we are interested in the terminal velocity of the outflow we choose a point above the heating shell where the energy has reached its steady state value where the energy is constant in Figure \ref{fig:nrmdoten}, top panel) and integrate outwards using the energy and Mach number at this point to solve \ref{eq:machno}) ) as an initial value problem."414 Note that in [act the terminal velocity is determined by the (constant) value of the Bernoulli energy above, Note that in fact the terminal velocity is determined by the (constant) value of the Bernoulli energy above415number of bins ranging from 2 to 10.,number of bins ranging from 2 to 10.416" Roughly. one gets an idea of the distribution of the planet abundances with 6=3. but one can realistically only start talking about a ""planetary mass function"" for 625."," Roughly, one gets an idea of the distribution of the planet abundances with $b \geq 3$, but one can realistically only start talking about a “planetary mass function” for $b \geq 5$."417" While a planetary mass-radius-separation function yi)(ip.rp.ανAd.Z.7) depending on the stellar mass. metallicity. and age involves 6 parameters. less detailed ++parameter functions are e.g. the planetary mass-separation in,,ny.e:AL.Z) or mass radius function snasUpryM,Z) depending on stellar mass and metallicity. or a planetary mass-radius-separation function depending on stellar mass only. and 2-parameter functions would e.g. be the planetary mass function «τηνCn:M,) depending on stellar mass only. or the planetary mass-separation function ια(1.(1) irrespective of the stellar properties."," While a planetary mass-radius-separation function $\varphi_{m_\rmn{p},r_\rmn{p},a}(m_\rmn{p},r_\rmn{p},a;M_\star,Z,\tau)$ depending on the stellar mass, metallicity, and age involves 6 parameters, less detailed 4-parameter functions are e.g. the planetary mass-separation $\varphi_{m_\rmn{p},a}(m_\rmn{p},a;M_\star,Z)$ or mass radius function $\varphi_{m_\rmn{p},r_\rmn{p}}(m_\rmn{p},r_\rmn{p};M_\star,Z)$ depending on stellar mass and metallicity, or a planetary mass-radius-separation function depending on stellar mass only, and 2-parameter functions would e.g. be the planetary mass function $\varphi_{m_\rmn{p}}(m_\rmn{p};M_\star)$ depending on stellar mass only, or the planetary mass-separation function $\varphi_{m_\rmn{p},a}(m_\rmn{p},a)$ irrespective of the stellar properties."418 We now have a total sample of about 450 planets orbiting stars other than the Sun. where it took about 10 years to detect the first 150. then about 3 years to detect the next 150. and then just about | year to detect the equal number of 150.," We now have a total sample of about 450 planets orbiting stars other than the Sun, where it took about 10 years to detect the first 150, then about 3 years to detect the next 150, and then just about 1 year to detect the equal number of 150."419 Table 1. shows how long campaigns with a constant detection rate of 150 planets per year would have to last in order ο obtain the respective functions with desired accuracies., Table \ref{tab:nplanets} shows how long campaigns with a constant detection rate of 150 planets per year would have to last in order to obtain the respective functions with desired accuracies.420 Right now. the collected data allow to measure. [-parameter 'unctions. find the basic structure structure ()ο 10) of 2-parameter ‘unctions. see basic trends (>= 3) in 4-parameter functions. and some hint on the dependency of the planet abundance on further »uameters.," Right now, the collected data allow to measure 1-parameter functions, find the basic structure structure $b \geq 10$ ) of 2-parameter functions, see basic trends $b \geq 3$ ) in 4-parameter functions, and some hint on the dependency of the planet abundance on further parameters."421" With 150 planets per year. or more realistically. a fair ""actor of this rate. rough ideas (> 2:5) of 4-parameter planetary mass functions (5 5) and an indication of trends (b. 3) ‘or 6-parameter planetary mass functions are obtainable within oreseeable time frames. but the numbers call for more aggressive searches."," With 150 planets per year, or more realistically, a fair factor of this rate, rough ideas $b \geq 5$ ) of 4-parameter planetary mass functions $b \geq 5$ ) and an indication of trends $b \geq 3$ ) for 6-parameter planetary mass functions are obtainable within foreseeable time frames, but the numbers call for more aggressive searches."422" While stars with and without planets have been distinguished by referring to the fraction f,CV...Z.7.O) of stars that host planets and defining the differential planetary mass-radius-orbit function «(Πριr0:M,Z.7.02) to relate to these only. a further statistic is the distribution of the number of planets amongst all planetary systems."," While stars with and without planets have been distinguished by referring to the fraction $f_\rmn{p}(M_\star,Z,\tau,\Omega)$ of stars that host planets and defining the differential planetary mass-radius-orbit function $\varphi(m_\rmn{p},r_\rmn{p},a,\varepsilon; M_\star, Z, \tau,\Omega)$ to relate to these only, a further statistic is the distribution of the number of planets amongst all planetary systems."423 With multiplicity indices c; that denote the fraction of planetary systems containing & planets. where the planetary mass-radius-orbit function can be decomposed as where In general. all ji(mmyryec:Ad.Z.7.0) may be different.," With multiplicity indices $\zeta_k$ that denote the fraction of planetary systems containing $k$ planets, where the planetary mass-radius-orbit function can be decomposed as where In general, all $\hat{\varphi}_k(m_\rmn{p},r_\rmn{p},a,\varepsilon; M_\star, Z, \tau,\Omega)$ may be different."424 Together with the multiplicity indices ος. one would be left with an infinite number of parameters.," Together with the multiplicity indices $\zeta_k$, one would be left with an infinite number of parameters."425" This however can be meaningfully avoided by adopting a functional dependence of ος and 4, on k that is described by a small finite number of parameters.", This however can be meaningfully avoided by adopting a functional dependence of $\zeta_k$ and $\hat{\varphi}_k$ on k that is described by a small finite number of parameters.426" In particular. one might want to distinguish stars with a single planets to multiple-planet systems. described by Qj (with l Gh gilmore:M.Z.T.QO). and In fact. ὁ have argued that there is evidence for 4, being different from yfunut-"," In particular, one might want to distinguish stars with a single planets to multiple-planet systems, described by $\zeta_1$ (with $\zeta_\rmn{mult} = 1-\zeta_1$ ), $\hat{\varphi}_1(m_\rmn{p},r_\rmn{p},a,\varepsilon; M_\star, Z, \tau,\Omega)$, and In fact, \citet{Wright} have argued that there is evidence for $\hat{\varphi}_1$ being different from $\hat{\varphi}_\rmn{mult}$."427 The assessment of planetary multiplicity however poses a huge challenge for properly interpreting the observational data. given that our knowledge of the absence of further planets in observed systems is quite limited.," The assessment of planetary multiplicity however poses a huge challenge for properly interpreting the observational data, given that our knowledge of the absence of further planets in observed systems is quite limited."428 If Hot Jupiters are considered lonely. whereas Neptune-mass planets are frequently found in multiple systems (22).. how much does this have to be attributed to the faet that observational techniques that report Hot Jupiters are insensitive to less massive planets. whereas if the sensitivity extends down to lower masses. other such planets are spotted rather easily?," If Hot Jupiters are considered lonely, whereas Neptune-mass planets are frequently found in multiple systems \citep{Mayor:abundance,HARPS:abundance2}, how much does this have to be attributed to the fact that observational techniques that report Hot Jupiters are insensitive to less massive planets, whereas if the sensitivity extends down to lower masses, other such planets are spotted rather easily?"429 It is intriguing to see that observations of transit timing variations led to the suggestion of the presence of a 15 Earth-mass planet in the WASP-3 system (2). that was already Known to host a Hot Jupiter (2).., It is intriguing to see that observations of transit timing variations led to the suggestion of the presence of a 15 Earth-mass planet in the WASP-3 system \citep{MacPlanet} that was already known to host a Hot Jupiter \citep{WASP3}.430 Planets reported by microlensing in particular cannot be claimed to be the only ones in the system. they were just the only ones that revealed their presence during a transient event.," Planets reported by microlensing in particular cannot be claimed to be the only ones in the system, they were just the only ones that revealed their presence during a transient event."431 ? explicitly found that the acquired data do not exclude the presence of gas-giant planets at any separation orbiting the lens star, \citet{390further} explicitly found that the acquired data do not exclude the presence of gas-giant planets at any separation orbiting the lens star432Generally speaking. with these data it 1s not possible to firmly separate carbon-rich from oxygen-rich stars among our AGB candidates.,"Generally speaking, with these data it is not possible to firmly separate carbon-rich from oxygen-rich stars among our AGB candidates."433 However. for such metal-poor galaxies we would expect to find carbon-rich stars at colors Jy—Koz1.5 (e.g.?.andreferencestherein). and a few stars with these colors are indeed present in all of our target galaxies.," However, for such metal-poor galaxies we would expect to find carbon-rich stars at colors $J_0-K_0\gtrsim1.5$ \citep[e.g.][and references therein]{kang06}, and a few stars with these colors are indeed present in all of our target galaxies."434 We check whether our stellar samples contain dust enshrouded AGB stars., We check whether our stellar samples contain dust enshrouded AGB stars.435 This kind of objects are extremely faint or undetected in the optical. very red at NIR wavelengths and thus not easily detectable in the J-band because of incompleteness effects in our observations.," This kind of objects are extremely faint or undetected in the optical, very red at NIR wavelengths and thus not easily detectable in the $J$ -band because of incompleteness effects in our observations."436 For example. ? consider a sample of ~40 stellar clusters with a range of ages and metallicities in the Small and Large Magellanic Clouds.," For example, \citet{vanloon05} consider a sample of $\sim40$ stellar clusters with a range of ages and metallicities in the Small and Large Magellanic Clouds."437 They find a total of about 30 dust enshrouded AGB stars in ~20 young and intermediate-age clusters., They find a total of about 30 dust enshrouded AGB stars in $\sim20$ young and intermediate-age clusters.438 These stars are found at /-K>2.5. and have metallicities higher than [Fe/H|—0.9 dex.," These stars are found at $J-K>2.5$, and have metallicities higher than $=-0.9$ dex."439 However. for clusters with ages and metallicities comparable to our target galaxies. no dust enshrouded AGB stars were detected.," However, for clusters with ages and metallicities comparable to our target galaxies, no dust enshrouded AGB stars were detected."440 We thus do not expect a significant number of dust enshrouded stars to be present in our target galaxies., We thus do not expect a significant number of dust enshrouded stars to be present in our target galaxies.441 We search for stars that have good K-band measurement but no J- counterpart. and find two such objects in CenA-dEI. none in $GC1319.1-4216 and one in ESO269-066.," We search for stars that have good $K$ -band measurement but no $J$ -band counterpart, and find two such objects in CenA-dE1, none in SGC1319.1-4216 and one in ESO269-066."442 Of the mentioned sources. in CenA-dE] one is found slightly outside the limiting radius. while the second is close to the center but has a good measurement only for one of the two K-bands: in ESO269-066 the dust enshrouded candidate also has à bac measurement in one of the two bands.," Of the mentioned sources, in CenA-dE1 one is found slightly outside the limiting radius, while the second is close to the center but has a good measurement only for one of the two $K$ -bands; in ESO269-066 the dust enshrouded candidate also has a bad measurement in one of the two bands."443 We thus mention that these are candidates but could just as well be unresolved background galaxies (see previous Sect.)., We thus mention that these are candidates but could just as well be unresolved background galaxies (see previous Sect.).444 We can also look for additional AGB candidates by considering variability. which is an intrinsic. characteristic of luminous AGB stars.," We can also look for additional AGB candidates by considering variability, which is an intrinsic characteristic of luminous AGB stars."445 For all of the target galaxies we have at least two observations 1n the K-band. so we use the difference between the stellar magnitudes at different epochs as a_ variability indicator.," For all of the target galaxies we have at least two observations in the $K$ -band, so we use the difference between the stellar magnitudes at different epochs as a variability indicator."446 For a long period variable star. the typical maximum magnitude difference is ~O.1 to ~1.5 mag in the K-band. and the period is on the order of ~10°? days (seeforex-ample?.andreferences therein)..," For a long period variable star, the typical maximum magnitude difference is $\sim0.1$ to $\sim1.5$ mag in the $K$ -band, and the period is on the order of $\sim10^{2-3}$ days \citep[see for example][and references therein]{rejkuba03}."447 We should thus expect to see variations of a few tens of a magnitude at most. given the observing timescales for our targets (see Tab. 2)).," We should thus expect to see variations of a few tens of a magnitude at most, given the observing timescales for our targets (see Tab. \ref{infonir}) )."448 For CenA-dEI. there are three observations in the K-band due to one repeated observation.," For CenA-dE1, there are three observations in the $K$ -band due to one repeated observation."449 There are 36 days between the first and the last one (see Tab. 2)).," There are 36 days between the first and the last one (see Tab. \ref{infonir}) ),"450 which are barely enough to put a lower limit on the number of possible long-period variables., which are barely enough to put a lower limit on the number of possible long-period variables.451 We check whether there are variations between the different K-band observations. but find none.," We check whether there are variations between the different $K$ -band observations, but find none."452 We then also check the whole combined list of sources. looking for stars that display a magnitude variation of more than 3 times the combined photometric errors of the individual measurements.," We then also check the whole combined list of sources, looking for stars that display a magnitude variation of more than 3 times the combined photometric errors of the individual measurements."453 We find two additional variable sources that lie just below the lower limits of the AGB selection boxes. and thus include them in our AGB candidates list.," We find two additional variable sources that lie just below the lower limits of the AGB selection boxes, and thus include them in our AGB candidates list."454 However. when checking them or the images we find that their profiles look like those of barely resolved background galaxies.," However, when checking them on the images we find that their profiles look like those of barely resolved background galaxies."455 In Fig., In Fig.456 10. (upper panel) we display the A-band magnitude difference between the seconc and the third epochs. since these are the ones with better seeing. for all the candidate AGB stars except one. because it has a bad measurement in the second K-band observation.," \ref{variab} (upper panel) we display the $K$ -band magnitude difference between the second and the third epochs, since these are the ones with better seeing, for all the candidate AGB stars except one, because it has a bad measurement in the second $K$ -band observation."457 Shown (1 green) are also the two likely background galaxies., Shown (in green) are also the two likely background galaxies.458 The K-band observations of SGCI319.1-4216 were take 57 days apart. and three of the AGB candidates. display variability (blue dots in the central panel of Fig. 10)).," The $K$ -band observations of SGC1319.1-4216 were taken 57 days apart, and three of the AGB candidates display variability (blue dots in the central panel of Fig. \ref{variab}) )."459 Whe considering the entire sample. two stars that lie just leftwards of the NIR selection box. and are found inside the optical selectio box. are indeed variables exhibiting a luminosity change by more than 307 (green symbols).," When considering the entire sample, two stars that lie just leftwards of the NIR selection box, and are found inside the optical selection box, are indeed variables exhibiting a luminosity change by more than $3\sigma$ (green symbols)."460 We add the two latter to the number of candidate AGB stars for SGCI319.1-4216 (anc report them in the electronic version of Tab. 3))., We add the two latter to the number of candidate AGB stars for SGC1319.1-4216 (and report them in the electronic version of Tab. \ref{agb_list}) ).461 Also in this, Also in this4621851 and NGC 1904.,1851 and NGC 1904.463" These clusters were selected for being located at r=16.7 and 18.8 kpc from the galactic center, respectively."," These clusters were selected for being located at r=16.7 and 18.8 kpc from the galactic center, respectively."464" Compared to the other globular clusters studied so far, NGC 1851 and NGC 1904 are approximately twice as distant from the Milky Way center."," Compared to the other globular clusters studied so far, NGC 1851 and NGC 1904 are approximately twice as distant from the Milky Way center."465" Thus are experiencing a tidal heating, proportional to , about one order of magnitude smaller, making its effects negligible."," Thus are experiencing a tidal heating, proportional to $r^{-3}$, about one order of magnitude smaller, making its effects negligible."466" The initial selection of targets was based on their color, as derived from the analysis of ESO Imaging Survey frames and ESO 2.2m Wide Field Imager data."," The initial selection of targets was based on their color, as derived from the analysis of ESO Imaging Survey frames and ESO 2.2m Wide Field Imager data."467" Targets have been selected requiring color difference from the cluster main sequence V-1I«0.05 and V—I<0.1, and apparent magnitude of 19>m18 and 19>m17, respectively for NGC 1851 and 1904."," Targets have been selected requiring color difference from the cluster main sequence $V-I<0.05$ and $V-I<0.1$, and apparent magnitude of $19>m>18$ and $19>m>17$, respectively for NGC 1851 and 1904."468 The cut in luminosity was made close to the base of the giant branch to probe the cluster stellar population in a well populated region to ensure good probability to find cluster members at large distances from the cluster., The cut in luminosity was made close to the base of the giant branch to probe the cluster stellar population in a well populated region to ensure good probability to find cluster members at large distances from the cluster.469" Indeed, according to Milky Way stellar population models Vanhollebeke,Groenewegen,andGirardi(2009) we expect a contamination of only 0.029 and 0.118 stars per arcmin squared in the selected color-luminosity range."," Indeed, according to Milky Way stellar population models \cite{Vanhollebeke09} we expect a contamination of only 0.029 and 0.118 stars per arcmin squared in the selected color-luminosity range."470 With this surface density we expect a contamination of about, With this surface density we expect a contamination of about471matter to [low from the voids towards the surrounding galaxy walls. implying coneentric shells of matter may collide.,"matter to flow from the voids towards the surrounding galaxy walls, implying concentric shells of matter may collide."472 We therefore consider a model of a void surrounced bv àn overdense region., We therefore consider a model of a void surrounded by an overdense region.473" Within voids. due to the lower amount of matter than in the homogeneous background. the curvature of the space is negative. thus the explicit forms of mass (M) and curvature (expressed by the function. ZZ) are where Ady is the mass in the corresponding volume of the homogeneous universe lie. Aly=(4706Ac)2Porat? and Pots is the background density at the last scattering instant]. Al,=sAbaο 77. MS=03 kpe. a=12 kpc."," Within voids, due to the lower amount of matter than in the homogeneous background, the curvature of the space is negative, thus the explicit forms of mass $M$ ) and curvature (expressed by the function $E$ ) are where $M_0$ is the mass in the corresponding volume of the homogeneous universe [i.e. $M_0 = (4 \pi G /3c^2) \rho_{b,ls} r^3$ and $\rho_{b,ls}$ is the background density at the last scattering instant], $M_1 = 8 M_2 a^{-3} {\rm e}^{-3/2}$ , $M_2 = -0.3$ kpc, $a = 12$ kpc."474" where E,=4Esbeto ES=Ll1ο, ὁ= kpe."," where $E_1 = 4 E_2 b^{-2} {\rm e}^{-1}$, $E_2 = -1.1 \times 10^{-5}$, $b = 10.9$ kpc."475 lt should. be noted. that other models οἱ voids are also possible even ones which do not evolve. from initial rarclactions but from condensation. ef. Mustapha&Lellaby (2001).," It should be noted that other models of voids are also possible – even ones which do not evolve from initial rarefactions but from condensation, cf. \citet{MH01}."476.. However. this particular void. model was chosen because it develops. as we will show. a shell crossing singularity.," However, this particular void model was chosen because it develops, as we will show, a shell crossing singularity."477 As can bee seen for ro24 the mass distribution as well as the curvature is the same as in the homogeneous FLAW mioclels., As can bee seen for $r>24$ the mass distribution as well as the curvature is the same as in the homogeneous FLRW models.478 These functions were used as an initial condition specified. at the last scattering instant., These functions were used as an initial condition specified at the last scattering instant.479 The initial density distribution for these moccels is very close to the form given in the first panel of Fig L.., The initial density distribution for these models is very close to the form given in the first panel of Fig \ref{fig1}.480 One can see here that the void region extends from Iz1.5Alper. and is surrounded by the galaxy wall which has à density up to twice the value of the void.," One can see here that the void region extends from $R\approx 1.5$, and is surrounded by the galaxy wall which has a density up to twice the value of the void."481 We start the evolution of both. the pressurc-frec LemaittreTolman and the Lemaittre models from the same profile of mass and curvature clistributions., We start the evolution of both the pressure-free Lemaîttre–Tolman and the Lemaîttre models from the same profile of mass and curvature distributions.482 The only discrepaney between these models is with the equation of state. which was chosen to be of a polvtropic form The polvtropic index is chosen to be η=3/2 which is the case of à mono-atomic gas.," The only discrepancy between these models is with the equation of state, which was chosen to be of a polytropic form The polytropic index is chosen to be $n =3/2$ which is the case of a mono-atomic gas."483 This equation of state is à good approximation to deseribe degenerate star cores. giant gaseous planets. or even for rocky planets;," This equation of state is a good approximation to describe degenerate star cores, giant gaseous planets, or even for rocky planets."484 Thus. although realistic conditions within high-density regions inside walls might lead to a more complicated dependence of pressure. this simple polvtropie equation of state can be treated as a σου first approximation to the problem considered in thisLeller.," Thus, although realistic conditions within high-density regions inside walls might lead to a more complicated dependence of pressure, this simple polytropic equation of state can be treated as a good first approximation to the problem considered in this."485 The constant. Ix for the LemaitreTolman model. which is pressure-free. is A=0 and for Lemaittre moccl is chosen to be A=1.98Ott m? s. (," The constant K for the Lemaîttre–Tolman model, which is pressure-free, is $K=0$ and for Lemaîttre model is chosen to be $K = 1.98 \times 10^{14}$ $^2$ $^2$. ("486Sec. 71) ,Sec. \ref{evolution}) )487and A—Los107 n So(Sec. ??))., and $K = 1.08 \times 10^{14}$ $^2$ $^2$ (Sec. \ref{acousticosc}) ).488 These are very high values., These are very high values.489 For comparison the ratio of standard pressure of ai (pare=101.325 kPa) to its density (pi;=1.202 m) αἱ O° C is approximately equal to 7.84101 mes?) , For comparison the ratio of standard pressure of air $p_{air} = 101.325$ kPa) to its density $\rho_{air} = 1.292$ $^3$ ) at $^{\circ}$ C is approximately equal to $7.84 \times 10^4$ $^2$ $^2$.490Sue values were chosen in order to better depict the influence of pressure gradients on the evolution of matter., Such values were chosen in order to better depict the influence of pressure gradients on the evolution of matter.491 Llowever. even if such very stiff. equations of state are. emploved. their impact on the evolution is visible only when density eradients become large.," However, even if such very stiff equations of state are employed, their impact on the evolution is visible only when density gradients become large."492 Phus. the incorporation of this gradient of pressure mostly. affects only regions where the shell crossing singularities would occur.," Thus, the incorporation of this gradient of pressure mostly affects only regions where the shell crossing singularities would occur."493 The algorithm which is used to calculate the evolution in the LemaittreTolman model is the same asthe one used, The algorithm which is used to calculate the evolution in the Lemaîttre–Tolman model is the same asthe one used494and z>8.0 compared to that of Pen99.,and $z > 8.0$ compared to that of Pen99.495 We note that the error in our method decreases steadily with redshift approaching «0.014 at z=1100., We note that the error in our method decreases steadily with redshift approaching $< 0.014$ at $z=1100$.496" In comparison, for high redshifts, Pen99 error always stays ~ and does not decrease appreciably."," In comparison, for high redshifts, Pen99 error always stays $\sim$ and does not decrease appreciably."497 A contour plot of AE based on the method of Pen99 with various z and Qa is shown in figure 2.., A contour plot of $\Delta E$ based on the method of Pen99 with various $z$ and $\Omega_\Lambda$ is shown in figure \ref{ContourPen}. .498 Relatively complicated distribution of variations in the AE can be seen for the parameter space characterized by z and Qa., Relatively complicated distribution of variations in the $\Delta E$ can be seen for the parameter space characterized by $z$ and $\Omega_\Lambda$.499" However, a contour plot of AE for our method, whichis shown in Figure 3,, 5.."," However, a contour plot of $\Delta E$ for our method, whichis shown in Figure \ref{ContourWick}, \ref{HistoPenWick}."500consider the combination of three dillerent. requirements on them: Note that over the Galaxy. as a whole. the requirement on 0 only allects the distribution in 0 and the requirement on J only alfects the distribution in J the two distributions can be thought of asindependent?.,"consider the combination of three different requirements on them: Note that over the Galaxy as a whole, the requirement on $\bolth$ only affects the distribution in $\bolth$ and the requirement on $\bolJ$ only affects the distribution in $\bolJ$ – the two distributions can be thought of as."501. It is only because of the finite survey. volume. and therefore the finite range of 0 for which stars with for a given J will be observed. that. the J condition significantly allects the observed 9 distribution (and vice versa)," It is only because of the finite survey volume, and therefore the finite range of $\bolth$ for which stars with for a given $\bolJ$ will be observed, that the $\bolJ$ condition significantly affects the observed $\bolth$ distribution (and vice versa)."502" In Figure 10. I plot the density of the GCS stars as a function of JL, and J).", In Figure \ref{fig:actions} I plot the density of the GCS stars as a function of $J_\phi$ and $J_r$.503 The density of stars in my phase- model is also plotted. for comparison.," The density of stars in my phase-mixed model is also plotted, for comparison."504" For a given J,, there is a minimum 4,νι lor stars to reach the Solar neighbourhood. which can be thought of as a mininiun epievelic amplitude for a given guiding centreraclius*."," For a given $J_\phi$ there is a minimum $J_r=J_{r,min}$ for stars to reach the Solar neighbourhood, which can be thought of as a minimum epicyclic amplitude for a given guiding centre."505. This is the cause of the near-parabolie lower boundary scen in ligure 10.., This is the cause of the near-parabolic lower boundary seen in Figure \ref{fig:actions}.506 Phe Pleiades and Sirius moving groups can be clearly. seen as small overdensities in this plot., The Pleiades and Sirius moving groups can be clearly seen as small overdensities in this plot.507" The Lyacles moving group is seen as a rather more spread out overdensity al à range of J,. around. J;,0.97.75,4. tending towards slightly lower J, with increasing ο."," The Hyades moving group is seen as a rather more spread out overdensity at a range of $J_r$ , around $J_\phi=0.97J_{\phi,0}$, tending towards slightly lower $J_\phi$ with increasing $J_r$ ."508" The dotted ancl dashed. lines in Figure LO are 2:1 OLI and ILR lines respectively. these are lines along which 20,(J)|OF)=20, and 20,(J)Q,(J)=20, respectively. for cillerent values of £3. the perturber pattern speed. chosen such that the resonance lines reach J;=0 at J,ο.1. or Lido."," The dotted and dashed lines in Figure \ref{fig:actions}509 are 2:1 OLR and ILR lines respectively, these are lines along which $2\Omega_\phi(\bolJ)+\Omega_r(\bolJ)=2\Omega_p$ and $2\Omega_\phi(\bolJ)-\Omega_r(\bolJ)=2\Omega_p$ respectively, for different values of $\Omega_p$, the perturber pattern speed, chosen such that the resonance lines reach $J_r=0$ at $J_\phi=0.9,\,1$, or $1.1J_{\phi,0}$."510" Changing the value of Ον moves the resonance lines in -/,,. but does not significantly alter their &eracient in this range of J."," Changing the value of $\Omega_p$ moves the resonance lines in $J_\phi$, but does not significantly alter their gradient in this range of $\bolJ$."511 The Livacdes overdensity seems o lie around a Lindblad. resonance line. but this could. be either an OLR or LR bine it was this [act which lead SLO to claim this was an Lindblad resonance. but that one needed o investigate the distribution in angle to determine which one.," The Hyades overdensity seems to lie around a Lindblad resonance line, but this could be either an OLR or ILR line – it was this fact which lead S10 to claim this was an Lindblad resonance, but that one needed to investigate the distribution in angle to determine which one."512 Other resonances the 3:1 or 4:1 OLR. or ILI lines would appear very similar on Figure 10.. though the 2:1 Η ine is the furthest from the vertical.," Other resonances – the 3:1 or 4:1 OLR or ILR lines – would appear very similar on Figure \ref{fig:actions}, though the 2:1 ILR line is the furthest from the vertical."513 It is also worth noting hat the slope of the various resonance lines is sensitive to he Galactic potential in a logarithmic potential (of the kind. used by SLO). the gradients of the 2:1 OLR and ILH ines in this part of J-space are nearly identical.," It is also worth noting that the slope of the various resonance lines is sensitive to the Galactic potential – in a logarithmic potential (of the kind used by S10), the gradients of the 2:1 OLR and ILR lines in this part of $\bolJ$ -space are nearly identical."514 Lt may »f possible to use the slope of resonance lines in action space to provide information about the Galactic potential by comparing them to observed dynamical substructure. but that is bevond the scope of this study.," It may be possible to use the slope of resonance lines in action space to provide information about the Galactic potential by comparing them to observed dynamical substructure, but that is beyond the scope of this study."515" ‘To explore the expected distribution of stars in the Solar neighbourhood associated with a resonance. E consider a rrelated to the phase-mixecl uusecl previously. adjusted to include a resonant component: where fy is the distribution. function. described. in Section 3.. €' is a constant chosen such that the resonant component contributes S percent of the stars observed. in the Solar neighbourhood. and Jos is a function of J, and is chosen such that LOAdae)dΠοdies)=const. lor J.=0. andl 0,,,; is a function of ϐ,, and is chosen such that IB,s|me,=const."," To explore the expected distribution of stars in the Solar neighbourhood associated with a resonance, I consider a related to the phase-mixed used previously, adjusted to include a resonant component: where $f_0$ is the distribution function described in Section \ref{sec:num}, , $C$ is a constant chosen such that the resonant component contributes $8$ percent of the stars observed in the Solar neighbourhood, and $J_{\phi,res}$ is a function of $J_r$ and is chosen such that $l\Omega_r(J_r,J_{\phi,res})+m\Omega_\phi(J_r,J_{\phi,res}) 516= const$, for $J_z=0$, and $\theta_{r,res}$ is a function of $\theta_\phi$ and is chosen such that $l\theta_{r,res}+m\theta_\phi = const$."517" The values Ay. and Ap... give the width of the resonance peak around the exact resonance lines in JJ, and 8,.. respectively."," The values $\Delta_{J,res}$ and $\Delta_{\theta,res}$ give the width of the resonance peak around the exact resonance lines in $J_\phi$ and $\theta_r$, respectively."518" One could. equally. describe the width in action or angle in terms of a spread in J, or 6,, respectively. but for convenience I have chosen to describe it in terms of the coordinates with the e&reater ranges of values in these data."," One could, equally, describe the width in action or angle in terms of a spread in $J_r$ or $\theta_\phi$ respectively, but for convenience I have chosen to describe it in terms of the coordinates with the greater ranges of values in these data."519 Phe width Avy. is ellectivelv a width in frequency about the pattern speed. of the perturber.," The width $\Delta_{J,res}$ is effectively a width in frequency about the pattern speed of the perturber."520 1n the toy models E show here E take Avy.=0.014. Noes=0.3.," In the toy models I show here I take $\Delta_{J,res}=0.01J_{\phi,0}$ , $\Delta_{\theta,res}=0.3$."521 ] consider two toy models. cach designed. to. produce models with an overdensitv in phase-space in a similar volume to that where the ναός moving group is found (but not tuned to produce abest fit). one corresponding to an OLR (/=I. m= 2) and one corresponding to an ILI (= —]l1.m —2).," I consider two toy models, each designed to produce models with an overdensity in phase-space in a similar volume to that where the Hyades moving group is found (but not tuned to produce abest fit), one corresponding to an OLR $l=1$, $m=2$ ) and one corresponding to an ILR $l=-1$, $m=2$ )."522" For the OLR model. E take 6...|26,= 1.9. and for the ILIt mocel 06,,,;|24,=13."," For the OLR model, I take $\theta_{r,res}+2\theta_\phi=-1.9$ , and for the ILR model $-\theta_{r,res}+2\theta_\phi=1.3$."523" In the OLI case L take JuC],=0)0.975.459. and in the ILB Case Ayal.m0)—03985.,,n."," In the OLR case I take $J_{\phi,res}(J_r=0)=0.975J_{\phi,0}$, and in the ILR case $J_{\phi,res}(J_r=0)=0.985J_{\phi,0}$."524" Figure LL shows contour plots of the density in the 8, 9,, plane of the OLR. and LLL models. and plots of 6,|n6,, (as in Figure 6)) restricted to 5»=#2 in the interests of brevity."," Figure \ref{fig:IOLR_mod_cont}525 shows contour plots of the density in the $\theta_r$, $\theta_\phi$ plane of the OLR and ILR models, and plots of $\theta_r+n\theta_\phi$ (as in Figure \ref{fig:meat}) ) restricted to $n=\pm2$ in the interests of brevity."526 Both the ILIt and OLI. models reproduce some of the features of the HIvades overdensity., Both the ILR and OLR models reproduce some of the features of the Hyades overdensity.527 In. both cases the overdensity in angle space is somewhat triangular in shape. like the EIvades overdensity. rather than following a single line as one would expect if only the condition on angle (eq. 1))," In both cases the overdensity in angle space is somewhat triangular in shape, like the Hyades overdensity, rather than following a single line as one would expect if only the condition on angle (eq. \ref{eq:res}) )"528 was relevant., was relevant.529 In both cases the overdensity in angle is strong for the two cases mn=x2. as well for other values of n (not shown).," In both cases the overdensity in angle is strong for the two cases $n=\pm2$, as well for other values of $n$ (not shown)."530" In an elfort to explain the structure of the overdensity in the 6,.4,, plane. the upper panels of Figure 11. also show the lines 4,=6)... for the two models. and lines corresponding to the condition on J."," In an effort to explain the structure of the overdensity in the $\theta_r$, $\theta_\phi$ plane, the upper panels of Figure \ref{fig:IOLR_mod_cont} also show the lines $\theta_r=\theta_{r,res}$ for the two models, and lines corresponding to the condition on $\bolJ$."531" The latter are found by taking the condition that 1,=ενω.) Cor d,mhayesENpas OL Id=done.F2N es) ancl determining the two possible values of@ that a star with these actions would have at the Sun's position in the relevantpart of phase. space. lower values of J, correspond to smaller (ic. closer tozero) values of 6,,."," The latter are found by taking the condition that $J_\phi=J_{\phi,res}(J_r)$ (or $J_\phi=J_{\phi,res}\pm\Delta_{J,res}$ or $J_\phi=J_{\phi,res}\pm2\Delta_{J,res}$ ) and determining the two possible values of$\bolth$ that a star with these actions would have at the Sun's position – in the relevantpart of phase space, lower values of $J_r$ correspond to smaller (i.e. closer tozero) values of $\theta_\phi$ ."532" ""his gives a sense of the two competing cllects which (in addition to the general selection ellects illustratedin Figure 5)) determine the shape of the overdensity in", This gives a sense of the two competing effects which (in addition to the general selection effects illustratedin Figure \ref{fig:mod_0_cont}) ) determine the shape of the overdensity in533Additional position errors may have occurred because source OS (ol M98) is only 50 aresee away (ie the ENIM of the oll- PSE).,Additional position errors may have occurred because source 98 (of M98) is only 50 arcsec away (ie the FWHM of the off-axis PSF).534 Alternatively. the counterpart may be a variable AGN. undetected in the WRI and with Re24.5 mag at the epoch of the optical imaging.," Alternatively, the counterpart may be a variable AGN, undetected in the HRI and with $>$ 24.5 mag at the epoch of the optical imaging."535 Alrough this source is outside the complete survey ares. it is potentially of interest.," Although this source is outside the complete survey area, it is potentially of interest."536 It is listed by MOS as a |ank field (ie no counterpart with 1123 mae)., It is listed by M98 as a blank field (ie no counterpart with $<$ 23 mag).537 A possible extremely distant. cluster of. galaxies lies 20 aresee south of the PSPC position., A possible extremely distant cluster of galaxies lies 20 arcsec south of the PSPC position.538 The likely brightest. cluster galaxy (BCG) has 10223 mag. giving an estimated redshift zz L where the redshift has been estimated from the BCC magnitude by extrapolating the relation of Vikhlinin (1998).," The likely brightest cluster galaxy (BCG) has $\ga$ 23 mag, giving an estimated redshift $\ga$ 1.3, where the redshift has been estimated from the BCG magnitude by extrapolating the relation of Vikhlinin (1998)."539 Llowever. the detection in the LIRL data of a X-ray source coincident with a R=23 mag galaxy 9 arcsec south of the PSPC position suggests that this galaxy is the counterpart. and not the intra-cluster medium of the possible clistant cluster.," However, the detection in the HRI data of a X-ray source coincident with a R=23 mag galaxy 9 arcsec south of the PSPC position suggests that this galaxy is the counterpart, and not the intra-cluster medium of the possible distant cluster."540 This source is also outside the complete survey area but we list it here because a compact group of three galaxies of Reels mag lie within the PSPC error box., This source is also outside the complete survey area but we list it here because a compact group of three galaxies of $\approx$ 18 mag lie within the PSPC error box.541 The redshifts are unknown. but based on the BCC: magnitude probably lie in jo range Z=0.25-0.3.," The redshifts are unknown, but based on the BCG magnitude probably lie in the range z=0.25-0.3."542 This source is potentially an extremely distant. cluster., This source is potentially an extremely distant cluster.543 lt is listed. by MOS as a blank field., It is listed by M98 as a blank field.544 A galaxy of R=23.1 mage surrounded by several fainter galaxies lies within the PSPC error circle., A galaxy of R=23.1 mag surrounded by several fainter galaxies lies within the PSPC error circle.545 Near infra-red Ix band imaging (Newsam 1997) shows that many of the galaxies of very red: the brightest has R-h=4.2+0.4 and. R-L=1.6 (to be compared with R-h=2.6 anc R-L=0.6 for zero redshift’ ellipticals)., Near infra-red K band imaging (Newsam 1997) shows that many of the galaxies of very red; the brightest has $\pm$ 0.4 and R-I=1.6 (to be compared with R-K=2.6 and R-I=0.6 for zero redshift ellipticals).546 If this galaxy is the BCG of a cluster. then the redshift estimated from its Ro band magnitude is 221.3. and from its Ix18.9 magnitude. involving a less uncertain extrapolation. “1.5 ," If this galaxy is the BCG of a cluster, then the redshift estimated from its R band magnitude is $\ga$ 1.3, and from its K=18.9 magnitude, involving a less uncertain extrapolation, $\approx$ "547strounding the black hole is that of a standard accretion disk. this does not come about.,"surrounding the black hole is that of a standard accretion disk, this does not come about."548 We now consider two cases of accretion flow. which are not standard thin accretion disks. in which να advection of poloidal Seld is more likely to occur.," We now consider two cases of accretion flow, which are not standard thin accretion disks, in which inward advection of poloidal field is more likely to occur."549 Iu au acvection-dominated accretion flow (ADAF). the basic idea is that energy released in the accretion process is not radiated locally but is. rather. retained by the fluid as internal energv aud advected iuto the hole (see. for exaniple. Naravan Yi 1995: aud the review by Sveusson 1998).," In an advection-dominated accretion flow (ADAF), the basic idea is that energy released in the accretion process is not radiated locally but is, rather, retained by the fluid as internal energy and advected into the hole (see, for example, Narayan Yi 1995; and the review by Svensson 1998)."550 As fay as the present discussion is concerned. tle major difference between this kind of accretion flow aud the standard disk is that the disk is geometrically thick in the seuse that JP~HR.," As far as the present discussion is concerned, the major difference between this kind of accretion flow and the standard disk is that the disk is geometrically thick in the sense that $H\sim551R$."552 The accretion is driven bv viscous processes with a~1. aud heuce with eg~ey.," The accretion is driven by viscous processes with $\alpha\sim1$, and hence with $v_R\sim v_\phi$."553 What this implies (see Section 3.2) is that the invard How velocity is comparable in maeuitucde to the outward diffusiou velocity for a poloidal field threading the disk., What this implies (see Section 3.2) is that the inward flow velocity is comparable in magnitude to the outward diffusion velocity for a poloidal field threading the disk.554 This meaus that there could iu principle be some non-ieelieible radial advection of poloidal flux., This means that there could in principle be some non-negligible radial advection of poloidal flux.555 While it Πο]! ο possible to set up a steady coufleuration in which inward advection of poloidal flux is balanced at cach radius x outward diffusion. there is no reason to expect that the field threading the hole (which is in any case generated x currents in the disk) can significantly exceed the field hreacding the iuuer disk.," While it might be possible to set up a steady configuration in which inward advection of poloidal flux is balanced at each radius by outward diffusion, there is no reason to expect that the field threading the hole (which is in any case generated by currents in the disk) can significantly exceed the field threading the inner disk."556 It is evident that if we wish to produce significant advection of poloidal flux to the πιο disk regions it is necessary to ensure that the radial inflow velocity iu the disk exceeds the radial diffusive outflow rate of poloidal field., It is evident that if we wish to produce significant advection of poloidal flux to the inner disk regions it is necessary to ensure that the radial inflow velocity in the disk exceeds the radial diffusive outflow rate of poloidal field.557 Since this cannot be done uxiug a standard disk iu which the inflow is duc to outward diffusion of angular momentum through the disk. it follows that we ποσα to look for other mechanisnis for outward transport of aueular 1uonientuni.," Since this cannot be done using a standard disk in which the inflow is due to outward diffusion of angular momentum through the disk, it follows that we need to look for other mechanisms for outward transport of angular momentum."558 It the disk is selteravitatius. ax is thought to occur in the carly stages of protostellar disks. aud inu the outer regions of disks around galactic nuclei. then: non-axisviunietrie instabilities can eive rise fo significant outward trausport of angular momentum (Paczvisski LOTS: Boss 198 E:Authouv Carlbere 1988: Lin Priugle 1987. 1990: Sellwood Liu 1989: Laughlin. IKorchaei- Adams 1997).," It the disk is self-gravitating, as is thought to occur in the early stages of protostellar disks, and in the outer regions of disks around galactic nuclei, then non-axisymmetric instabilities can give rise to significant outward transport of angular momentum (Paczyńsski 1978; Boss 1984; Anthony Carlberg 1988; Lin Pringle 1987, 1990; Sellwood Lin 1989; Laughlin, Korchagin, Adams 1997)."559 Since such a process is not driven by lvdromaguetic oeiustabilities it is conceivable that the magnetic Praudtl nuuber στ be quite different frou unity. and that significant nmsvurd transport of poloidal field might be able to take place.," Since such a process is not driven by hydromagnetic instabilities it is conceivable that the magnetic Prandtl number might be quite different from unity, and that significant inward transport of poloidal field might be able to take place."560 Although the inner regions of disks around black holes either in ACN or in QCalactie binaries are not usually considered to be seltberavitating. there müeght be au iuterestiug exception here if one considers the disk generated in the dynamical iguptiou of a neutron star by a black hole. which occurs oe1 sone models for x-ray bursts (Rasio 1996: Móssziros Rees 1997: Paczvüsski 1998).," Although the inner regions of disks around black holes either in AGN or in Galactic binaries are not usually considered to be self-gravitating, there might be an interesting exception here if one considers the disk generated in the dynamical disruption of a neutron star by a black hole, which occurs in some models for $\gamma$ -ray bursts (Rasio 1996; Mésszárros Rees 1997; Paczyńsski 1998)."561" It has been argued by a nmuuber of authors DDBludford Pavue 1982: ιο Norman 1986: Kounigl 1989: Pelleticr ιο 1992: Lovelace. Romanova, Contopolous 1993) that a imaguetically driven disk wind might be the main mechanisii by which excess angular momentum is removed from disk material. and so nüght be the main mechanisina that drives au accretion disk."," It has been argued by a number of authors Blandford Payne 1982; Pudritz Norman 1986; Könnigl 1989; Pelletier Pudritz 1992; Lovelace, Romanova, Contopolous 1993) that a magnetically driven disk wind might be the main mechanism by which excess angular momentum is removed from disk material, and so might be the main mechanism that drives an accretion disk."562 Were again the inflow velocity can in principle significantly exceed any outward diffusion rate for poloidal field. especially if the poloidal ficld is strong enough to suppress the Balbus-Wawley iustabilitv.," Here again the inflow velocity can in principle significantly exceed any outward diffusion rate for poloidal field, especially if the poloidal field is strong enough to suppress the Balbus-Hawley instability."563 If sich a 1nechanisu were able to give rise to a steady state. it would be necessary to appeal to some process (such as the interchange iustabilitv: Spruit Taain 1990: Lubow Spruit 1995: Sprit. Stelle. Papaloizou 1995) that counterbalauces the steady inward drageing of poloidal field and allows outward diffusion of field to occur.," If such a mechanism were able to give rise to a steady state, it would be necessary to appeal to some process (such as the interchange instability; Spruit Taam 1990; Lubow Spruit 1995; Spruit, Stehle, Papaloizou 1995) that counterbalances the steady inward dragging of poloidal field and allows outward diffusion of field to occur."564 Thus. as in Section L2.1. it is envisaged that a steady poloidal field configuration is set up. with mad advection and outward diffusion producing a balance aud a steady eradieut in the poloidal feld.," Thus, as in Section 4.2.1, it is envisaged that a steady poloidal field configuration is set up, with inward advection and outward diffusion producing a balance and a steady gradient in the poloidal field."565 However. for the reasons discussed above. there is no reason to expect such physical processes to eive rise to a poloidal feld threading the hole that is significantly cubanced over the poloidal field threading the imuer disk.," However, for the reasons discussed above, there is no reason to expect such physical processes to give rise to a poloidal field threading the hole that is significantly enhanced over the poloidal field threading the inner disk."566 Iu addition. the idea that such a steady balance cau be set up at all has been brought into question (Lovelace. Romanova. Newman 1991: Lubow. Papaloizou. Pringle 1991b: Agapitou Papaloizon 1995).," In addition, the idea that such a steady balance can be set up at all has been brought into question (Lovelace, Romanova, Newman 1994; Lubow, Papaloizou, Pringle 1994b; Agapitou Papaloizou 1998)."567 The main vont here is that the process of wind removal of angular nuoiientunmi occurs locally and directly at each radius in the disk., The main point here is that the process of wind removal of angular momentum occurs locally and directly at each radius in the disk.568 Au annulus in the disk which succeeds in getting rid of angular momentum to a wind docs rot require the presence of neighbouring annuli to do so., An annulus in the disk which succeeds in getting rid of angular momentum to a wind does not require the presence of neighbouring annuli to do so.569 Thus different anuuli which manage to dispose of heir angular ποιο in this wav are to some extent independeut dynamical entities., Thus different annuli which manage to dispose of their angular momentum in this way are to some extent independent dynamical entities.570" Furthermore. cfiicicut removal of angular momentum from a particular annulus cads to mwurd movement. outward beudiug of poloidal ficld lines. and consequently euhauced wind outflow. enhanced removal of augulu ποιοτα, and further iuflow (Lubow. Papaloizou. Pringle 1991b). ("," Furthermore, efficient removal of angular momentum from a particular annulus leads to inward movement, outward bending of poloidal field lines, and consequently enhanced wind outflow, enhanced removal of angular momentum, and further inflow (Lubow, Papaloizou, Pringle 1994b). ("571This instability may be tempered by the fact that stroug bending of field) lines impedes au outflow bv iakine the disk sub-Neplerian: Ogilvie Livio 1998.),This instability may be tempered by the fact that strong bending of field lines impedes an outflow by making the disk sub-Keplerian; Ogilvie Livio 1998.)572 ILowever. even if such unstable wind driven accretion occurs (aud at least in the disks i cataclysinic variables there is evidence that it does not. Livio 1997). there is no particular reason to suppose that at any stage the streugth of the poloidal field threading the hole is slenificantly ereater that the streneth of the poloidal field threading the imuer disk. except possibly for brief dvuamical interludes.," However, even if such unstable wind driven accretion occurs (and at least in the disks in cataclysmic variables there is evidence that it does not, Livio 1997), there is no particular reason to suppose that at any stage the strength of the poloidal field threading the hole is significantly greater that the strength of the poloidal field threading the inner disk, except possibly for brief dynamical interludes."573" Thus. here again. it seenmis difficult to set up a credible picture iu which electromagnetic extraction of spin enerev from the hole donünates iu a steady. or even a time-averaged κακο, over electromagnetic extraction of spin cucrey frou the disk material."," Thus, here again, it seems difficult to set up a credible picture in which electromagnetic extraction of spin energy from the hole dominates in a steady, or even a time-averaged sense, over electromagnetic extraction of spin energy from the disk material."574 Dlaudford Zuajek (1977) noted that if the poloidal magnetic field threading the black hole is comparable iu, Blandford Znajek (1977) noted that if the poloidal magnetic field threading the black hole is comparable in575to fit several indices simultaneously could. spuriously. be interpreted as an indication of nou-solar abundance ratios.,"to fit several indices simultaneously could, spuriously, be interpreted as an indication of non-solar abundance ratios."576 Also. uiisiatches between observational data aud model SSPs are often taken as evidence for the presence of components which are not fully accounted for iu the models. such as nissiue (or extreme) stellar evolutionary stages or a composite population.," Also, mismatches between observational data and model SSPs are often taken as evidence for the presence of components which are not fully accounted for in the models, such as missing (or extreme) stellar evolutionary stages or a composite population."577" demonstrated that. for SSPs. the Fe5106 iudex traces Fe only. whilst [MgFo]. traces total uctallicity, Z (as first noted by 73)."," demonstrated that, for SSPs, the Fe5406 index traces Fe only, whilst [MgFe] traces total metallicity, $Z$ (as first noted by )."578 These two iudices. iu. conibiuation therefore provide an estimate of the level of a-eulianceient. or simply whether a population has non-solu abundance ratios.," These two indices, in combination therefore provide an estimate of the level of $\alpha$ -enhancement, or simply whether a population has non-solar abundance ratios."579 Figure L shows the Fe5106|AleFe} plane with lines from the DaSTI 11 Gyr (coustaut age) scaled-solar aud a-cuhanced models. jomed at »oiuts of approximately equal |Fe/T] (uote that at constant Z. [Fo/II| is lower for a-euhauced nodels than the corresponding scaled-solar ones).," Figure \ref{fig4} shows the Fe5406–[MgFe] plane with lines from the BaSTI 14 Gyr (constant age) scaled-solar and $\alpha$ -enhanced models, joined at points of approximately equal [Fe/H] (note that at constant $Z$ , [Fe/H] is lower for $\alpha$ -enhanced models than the corresponding scaled-solar ones)."580" Overplotted ire the results from the whole-isochrouc tests for increased 7,4, (LOO). inereased ogg (0.25 dex) aud iucreased/decreased. [Fo/TI] (0.15 dex)."," Overplotted are the results from the whole-isochrone tests for increased $T_{eff}$ (100K), increased $g$ (0.25 dex) and increased/decreased [Fe/H] (0.15 dex)."581 Iu this diagraiu one expects that ασ deviation i abundance ratios will move poiuts iorizontallv. ie. any degree of a-enhancenmeut uoves points from the scaled-solar liue on the eft. towards the a-cnhanced line on the right (see Figure 9 of uote that lines of different age are completely degenerate iu this diagram).," In this diagram one expects that any deviation in abundance ratios will move points horizontally, i.e. any degree of $\alpha$ -enhancement moves points from the scaled-solar line on the left, towards the $\alpha$ -enhanced line on the right (see Figure 9 of – note that lines of different age are completely degenerate in this diagram)."582 Hore it can be seen that altering auy of +the atinosplieric paralucters simply moves the scaled-solar SSP points along the scaled-solar line. changing the inferred |Fe/HI| but not altering the inferred abundance ratios for other elements to nou-solar ratios.," Here it can be seen that altering any of the atmospheric parameters simply moves the scaled-solar SSP points along the scaled-solar line, changing the inferred [Fe/H] but not altering the inferred abundance ratios for other elements to non-solar ratios."583 This is an important point to notice siuce individual clement abunudances. inclhudius several a clemenuts. appear to alter substantially. as demonstrated by the measured offsets in the various line iudices listed in Tables 1. aud 2..," This is an important point to notice since individual element abundances, including several $\alpha$ elements, appear to alter substantially, as demonstrated by the measured offsets in the various line indices listed in Tables \ref{tab:4Gtests} and \ref{tab:14Gtests}."584 Iu couclusion. we urge caution against the over-interpretation of stellay population parameters Toni line iudex data. m terms of the tuferred scaled-solar or non-caled-solu abuudauce ratios and also the inferred. presence of a composite »opulation. especially when nmultipledudex or full- fitting methods are eiiploved.," In conclusion, we urge caution against the over-interpretation of stellar population parameters from line index data, in terms of the inferred scaled-solar or non-scaled-solar abundance ratios and also the inferred presence of a composite population, especially when multiple-index or full-SED fitting methods are employed."585 We find that. or SSPs. Fe5106 in combination with |MgFCO| oxovides the iost robust indication of non-solar abundance ratios.," We find that, for SSPs, Fe5406 in combination with [MgFe] provides the most robust indication of non-solar abundance ratios."586 We remind the reader that our results potentially impact on all SPS methods. whether fitting functions or full SEDs are eniploved.," We remind the reader that our results potentially impact on all SPS methods, whether fitting functions or full SEDs are employed."587 Measured offsets for 23 commonly used diagnostic line indices are provided. aud we encourage the user to deteriuine the overall iupact ou their observational data and preferred fitting method.," Measured offsets for 23 commonly used diagnostic line indices are provided, and we encourage the user to determine the overall impact on their observational data and preferred fitting method."588 We thaul the anonviuous referee for a constructive report aud some useful suggestions which helped to put our results in context., We thank the anonymous referee for a constructive report and some useful suggestions which helped to put our results in context.589 SALP. would like to express heartfelt thanks to Elaine Siith-Freeiian for many useful diseussious aud for providing the initial motivation to dothis work., S.M.P. would like to express heartfelt thanks to Elaine Smith-Freeman for many useful discussions and for providing the initial motivation to dothis work.590 S.ALP. acknowledges financial support from the Scicuce Techuoloey Facilities Council (STFC) through a Postdoctoral Researcl Fellowship., S.M.P. acknowledges financial support from the Science Technology Facilities Council (STFC) through a Postdoctoral Research Fellowship.591The current study was limited. not only by the small FOV of TIP-IL which nowadays has a slit twice as long as during our observing campaign in 2005. but also by the observational gap on July 4th.,"The current study was limited, not only by the small FOV of TIP-II, which nowadays has a slit twice as long as during our observing campaign in 2005, but also by the observational gap on July 4th."592 Magnetic field extrapolations could undoubtedly shed more light on clarifying the magnetic structure of this filament., Magnetic field extrapolations could undoubtedly shed more light on clarifying the magnetic structure of this filament.593 It is now crucial to carry out more multrwavelength measurements. as the one presented in here. with higher cadence and bigger FOVs to fit the pieces of the puzzle together. in order to fully understand the origin. evolution and magnetie topology of AR filaments.," It is now crucial to carry out more multiwavelength measurements, as the one presented in here, with higher cadence and bigger FOVs to fit the pieces of the puzzle together, in order to fully understand the origin, evolution and magnetic topology of AR filaments."594 In particular. continuous vector magnetograms of active regions together with simultaneous imaging of the corona should be able to prove/disprove the proposed scenario for the last stages of their evolution.," In particular, continuous vector magnetograms of active regions together with simultaneous imaging of the corona should be able to prove/disprove the proposed scenario for the last stages of their evolution."595 The instrument suite on board the NASA/SDO satellite is the best candidate for such an study., The instrument suite on board the NASA/SDO satellite is the best candidate for such an study.596 , 597times larger than that monitored by current high-: SN Ia searches down to the same limiting magnitude 00z20) (Perlmutter 1999).,times larger than that monitored by current $z$ SN Ia searches down to the same limiting magnitude $m_B \approx 20$ ) (Perlmutter 1999).598" The simple fireball model (rie. a spherically symmetric relativistic external shock wave expanding into a homogeneous medium) has been ""in and out of the hospital"" for months. but notices of its death appear to be premature."," The simple fireball model (i.e., a spherically symmetric relativistic external shock wave expanding into a homogeneous medium) has been “in and out of the hospital” for months, but notices of its death appear to be premature."599" This amazes me. given the wealth of complexities one can easily imagine in the fireball itself and in its environment (Mésszárros 1999),"," This amazes me, given the wealth of complexities one can easily imagine in the fireball itself and in its environment (Mésszárros 1999)."600 If the simple relativistic fireball model (or even more complex variants of it) suffice to explain burst afterglows (see Figure 5). much can be learned. including the energy of the fireball per unit solid angle. the ratio of the energy in the magnetic field to that in relativistic electrons. and the density of the external medium into which the fireball expands (Wijers Galama 1999; van Paradijs 1999: Lamb. Castander Reichart 1999).," If the simple relativistic fireball model (or even more complex variants of it) suffice to explain burst afterglows (see Figure 5), much can be learned, including the energy of the fireball per unit solid angle, the ratio of the energy in the magnetic field to that in relativistic electrons, and the density of the external medium into which the fireball expands (Wijers Galama 1999; van Paradijs 1999; Lamb, Castander Reichart 1999)."601" It should be possible. in principle. to use the effects on the afterglow spectrum of extinction due to dust in the host galaxy and of absorption by the Lyman-o forest to determine the redshift of the burst itself. but so far. this goal has eluded modelers (see. e.g. Lamb. Castander Reichart 1999),"," It should be possible, in principle, to use the effects on the afterglow spectrum of extinction due to dust in the host galaxy and of absorption by the $\alpha$ forest to determine the redshift of the burst itself, but so far, this goal has eluded modelers (see, e.g, Lamb, Castander Reichart 1999)."602" Currently. we are in the regime in terms of what we learn from each individual because. given the diversity of GRBs. GRB afterglows. and host galaxies. we have yet to sample the full ""phase space"" of afterglow or host galaxy properties."," Currently, we are in the regime in terms of what we learn from each individual because, given the diversity of GRBs, GRB afterglows, and host galaxies, we have yet to sample the full “phase space” of afterglow or host galaxy properties."603" Still less have we sampled the full ""phase space"" of combinations of burst. afterglow. and host properties."," Still less have we sampled the full “phase space” of combinations of burst, afterglow, and host properties."604 At the same time. we are in the stronglynon-linear regime. in terms of what we learn from each individual of a burst afterelow.," At the same time, we are in the strongly regime, in terms of what we learn from each individual of a burst afterglow."605 The value of each astronomer's observation 1s enhanced by the observations made by all other astronomers., The value of each astronomer's observation is enhanced by the observations made by all other astronomers.606 As we have heard from several speakers at this workshop. the amount of information that can be gleaned from a given afterelow depends greatly on the number of measurements that exist both simultaneously in time and in wavelength. from the radio through the millimeter. sub-millimeter. near-infrared. optical. and X-ray bands.," As we have heard from several speakers at this workshop, the amount of information that can be gleaned from a given afterglow depends greatly on the number of measurements that exist both simultaneously in time and in wavelength, from the radio through the millimeter, sub-millimeter, near-infrared, optical, and X-ray bands."607 Furthermore. since the range of redshifts for the bursts (and therefore also their atterglows) is large. we cannot know in advance which bands will be crucial.," Furthermore, since the range of redshifts for the bursts (and therefore also their afterglows) is large, we cannot know in advance which bands will be crucial."608 Thus simultaneous or near-simultaneous multi-wavelength observations of burst afterglows are essential. and therefore observations by as many observers as possible must be encouraged.," Thus simultaneous or near-simultaneous multi-wavelength observations of burst afterglows are essential, and therefore observations by as many observers as possible must be encouraged."609 Finally. greater co-operation and co-ordination among observers is important. and should be facilitated. as has been done by setting up the invaluable service represented by the Gamma-Ray Burst Coordinate Network (GCN) (Barthelmy et al.," Finally, greater co-operation and co-ordination among observers is important, and should be facilitated, as has been done by setting up the invaluable service represented by the Gamma-Ray Burst Coordinate Network (GCN) (Barthelmy et al."610 1999)., 1999).611 Star forming regions consist of a cluster of O/B stars that lie in and around a clumpy cloud of dust and gas., Star forming regions consist of a cluster of O/B stars that lie in and around a clumpy cloud of dust and gas.612 We expect Ae>>1 for O/B stars embedded in the cloud. and Ay;~0 for O/B stars that have drifted out of the cloud and/or lie near the surface of the cloud and have expelled the gas and dust in their vicinity.," We expect $A_V >> 1$ for O/B stars embedded in the cloud, and $A_V \approx 0$ for O/B stars that have drifted out of the cloud and/or lie near the surface of the cloud and have expelled the gas and dust in their vicinity."613 Thus the optical/UV spectrum of star forming regions is à sum of the spectra of many hot (blue) stars. some of which are embedded in the cloud. and therefore heavily extinguished. and some of which lie on the surface or around the cloud. and are therefore essentially un-extinguished.," Thus the optical/UV spectrum of star forming regions is a sum of the spectra of many hot (blue) stars, some of which are embedded in the cloud, and therefore heavily extinguished, and some of which lie on the surface or around the cloud, and are therefore essentially un-extinguished."614 This composite spectrum is rather blue. and yields a value AVEzl when a single extinction curve Is fitted to it.," This composite spectrum is rather blue, and yields a value $A_V^{\rm eff}615\approx 1$ when a single extinction curve is fitted to it."616 The situation is very different when we consider an individual line-of-sight. as is appropriate for the afterglow of a GRB.," The situation is very different when we consider an individual line-of-sight, as is appropriate for the afterglow of a GRB."617 If the GRB source lies outside and far away from any star-forming region. we expect Aversion<1: if the GRB source lies outside but near a star-forming region. we expect Αμπο1 about half the time and Ay!altcrelow>>L about half the time.," If the GRB source lies outside and far away from any star-forming region, we expect $A_V^{\rm afterglow} \lesssim 1$; if the GRB source lies outside but near a star-forming region, we expect $A_V^{\rm afterglow} \lesssim6181$ about half the time and $A_V^{\rm afterglow} >> 1$ about half the time."619" Finally. if the GRB source is embedded Π the star-forming; region.; we expect AVS""afterglow>>4]."," Finally, if the GRB source is embedded in the star-forming region, we expect $A_V^{\rm afterglow} >> 1$."620 Thus. if GRB sources actually lie in star-forming regions. one would expect .1.o> (values of Ay~1030 are not uncommon for dense. cool molecular clouds in the Galaxy).," Thus, if GRB sources actually lie in star-forming regions, one would expect $A_V^{\rm afterglow} >> 1$ (values of $A_V \sim 10-30$ are not uncommon for dense, cool molecular clouds in the Galaxy)."621 Is this consistent with what we see?, Is this consistent with what we see?622 No., No.623 However. this may not mean that GRB sources do not lie in star-forming regions.," However, this may not mean that GRB sources do not lie in star-forming regions."624 The reason is that the soft X rays and the UV radiation from the GRB and its afterglow are capable. during the burst and immediately afterward. of vaporizing all of the dust in their path (Lamb Reichart 1999b).," The reason is that the soft X rays and the UV radiation from the GRB and its afterglow are capable, during the burst and immediately afterward, of vaporizing all of the dust in their path (Lamb Reichart 1999b)."625 Thus the value of Appt that we measure may have nothing to do with the pre-existing value of the extinction through the star-forming region in which the burst source is embedded. but may instead reflect merely the extinction due to dust and gas in the disk of the host galaxy.," Thus the value of $A_V^{\rm afterglow}$ that we measure may have nothing to do with the pre-existing value of the extinction through the star-forming region in which the burst source is embedded, but may instead reflect merely the extinction due to dust and gas in the disk of the host galaxy."626 The GRB. and its soft X-ray and UV afterglow. are also capable of tonizing gas in any envelope material expelled by the progenitor of the burst source and in the interstellar medium of the host galaxy.," The GRB, and its soft X-ray and UV afterglow, are also capable of ionizing gas in any envelope material expelled by the progenitor of the burst source and in the interstellar medium of the host galaxy."627" This will produce Strómmgren spheres or very narrow cones (if the burst and its afterglow are beamed) in hydrogen. helium and various metals (Bisnovatyi-Kogan Timokhin 1998. Timokhin Bisnovatyi-Kogan 1999, Mésszárros 1999)."," This will produce Strömmgren spheres or very narrow cones (if the burst and its afterglow are beamed) in hydrogen, helium and various metals (Bisnovatyi-Kogan Timokhin 1998, Timokhin Bisnovatyi-Kogan 1999, Mésszárros 1999)."628 Recombination of the tonized hydrogen eventually produces intense [CII]. [CIV]. [OVI] and [CIII] emission lines in the UV. and intense Πα and H./ emission lines in the optical.," Recombination of the ionized hydrogen eventually produces intense [CII], [CIV], [OVI] and [CIII] emission lines in the UV, and intense $\alpha$ and $\beta$ emission lines in the optical."629 However. the line fluxes may still not be strong enough to be detectable at the large redshift distances of GRB host galaxies.," However, the line fluxes may still not be strong enough to be detectable at the large redshift distances of GRB host galaxies."630 Interaction of the GRB and its soft X-ray afterelow with any envelope material expelled by the progenitor of the burst source and with the surrounding interstellar medium can also produce intense fluorescent iron line emission (see. e.g. Mésszárros 1999). but it is again difficult to see how the line flux could be large enough to be detectable or to explain the hints of a fluorescent iron emission line in the X-ray afterglows of GRB 980703 (Piro et al.," Interaction of the GRB and its soft X-ray afterglow with any envelope material expelled by the progenitor of the burst source and with the surrounding interstellar medium can also produce intense fluorescent iron line emission (see, e.g., Mésszárros 1999), but it is again difficult to see how the line flux could be large enough to be detectable or to explain the hints of a fluorescent iron emission line in the X-ray afterglows of GRB 980703 (Piro et al."631 1999) and GRB 980828 (Yoshida et al., 1999) and GRB 980828 (Yoshida et al.632" 1999),", 1999).633"this latter effect is commonly parameterized through electron acceleration parameters e, and &, both assumed to be on the order of ~107! (e.g., Bóttcher&Dermer (2010))).","this latter effect is commonly parameterized through electron acceleration parameters $\epsilon_e$ and $\zeta_e$, both assumed to be on the order of $\sim 10^{-1}$ (e.g., \cite{bd10}) )."634" Those parameters are defined so that e, is the fraction of swept-up proton energy transferred to relativistic electrons, and Z, the fraction of swept-up electrons that are accelerated to relativistic energies."," Those parameters are defined so that $\epsilon_e$ is the fraction of swept-up proton energy transferred to relativistic electrons, and $\zeta_e$ the fraction of swept-up electrons that are accelerated to relativistic energies."635" Specifically, if the electron acceleration process results in an electron spectral index of q>2, the cutoff is given by A A A A where [shock is the Lorentz factor of the (internal) forward or reverse shock resulting from the collision of two shells of relativistic ejecta, measured in the co-moving frame of the shocked material (Bóttcher&Dermer (2010)))."," Specifically, if the electron acceleration process results in an electron spectral index of $q > 2$, the low-energy cutoff is given by         where $\Gamma_{\rm shock}$ is the Lorentz factor of the (internal) forward or reverse shock resulting from the collision of two shells of relativistic ejecta, measured in the co-moving frame of the shocked material \cite{bd10}) )."636" While Pghock is a strong function of the relative Lorentz factors of the colliding shells, e, and Z, are expected to depend on the efficiency of the generation of turbulent magnetic fields mediating the energy transfer between protons and electrons behind the shock fronts."," While $\Gamma_{\rm shock}$ is a strong function of the relative Lorentz factors of the colliding shells, $\epsilon_e$ and $\zeta_e$ are expected to depend on the efficiency of the generation of turbulent magnetic fields mediating the energy transfer between protons and electrons behind the shock fronts."637" In Bóttcheretal.(2007), constraints on jet parameters could be derived from the estimated synchrotron peak flux in the 15 January 2006 SED, and a hint for hard lags among the optical (BVR) bands."," In \cite{bbj07}, constraints on jet parameters could be derived from the estimated synchrotron peak flux in the 15 January 2006 SED, and a hint for hard lags among the optical (BVR) bands."638 The synchrotron peak flux was translated into a magnetic-field estimate according to Eq., The synchrotron peak flux was translated into a magnetic-field estimate according to Eq.639 4 in, 4 in640ÀcTT74A.. respectively.,"$\lambda \sim 7774\,$, respectively."641 All the targets were selected from the photometric catalog published by(2004).. choosing only relatively isolated objects.," All the targets were selected from the photometric catalog published by, choosing only relatively isolated objects."642 Two different pointings were perlormed in order to sample the inner aud the most external regions of the cluster., Two different pointings were performed in order to sample the inner and the most external regions of the cluster.643 Our ability to observe BSS in the inner wwas grea(lv restricted by Che crowding of bot stars and fibers., Our ability to observe BSS in the inner was greatly restricted by the crowding of both stars and fibers.644 In each pointing ~30 BSS were observed. while ~20 fibers were used (o acquire skv spectra.," In each pointing $\sim 30$ BSS were observed, while $\sim 20$ fibers were used to acquire sky spectra."645 Seventeen BSS were observed in both the pointings and were used to test the internal accuracy of the abundance measures., Seventeen BSS were observed in both the pointings and were used to test the internal accuracy of the abundance measures.646 The total exposure time of each pointing was split in sub-exposures of about one hour each., The total exposure time of each pointing was split in sub-exposures of about one hour each.647 In summary. for each of the two pointings we have obtained 3 spectra sampling the lines and 2 for theOr.," In summary, for each of the two pointings we have obtained 3 spectra sampling the lines and 2 for the."648 By combining the sub-exposures we finally obtained mean spectra with a S/.V250 (per resolution element) for most of the selected BSS., By combining the sub-exposures we finally obtained mean spectra with a $S/N \ga 50$ (per resolution element) for most of the selected BSS.649 Raw spectra were recuced in IRAF following the stanclared procedure., Raw spectra were reduced in IRAF following the standard procedure.650 The task APALL was used to deline and extract the apertures and (o calibrate the one-dimensional spectra in wavelength. by adopting the dispersion solution derived by Th-Ar lamps accquired after each spectra.," The task APALL was used to define and extract the apertures and to calibrate the one-dimensional spectra in wavelength, by adopting the dispersion solution derived by Th-Ar lamps acquired after each spectra."651 A full description of the data analvsis will be given in a forthcoming paper (Sabbi et al., A full description of the data analysis will be given in a forthcoming paper (Sabbi et al.652 2006. in preparation).," 2006, in preparation)."653 Ilere we focus on the discussion of C and O abundances., Here we focus on the discussion of C and O abundances.654 The analvsis of ihe chemical abundances was performed using the ROSA package1, The analysis of the chemical abundances was performed using the ROSA package.655"9558), The equivalent width (EW) of each measurable line was measured by Gaussian fitüng of the line profile. adopting a relationship between EW anc EWIIM. as described in(2001): an iterative clipping average over a traction of the highest spectral points around each line was applied to define a local continuum."," The equivalent width (EW) of each measurable line was measured by Gaussian fitting of the line profile, adopting a relationship between EW and FWHM, as described in; an iterative clipping average over a fraction of the highest spectral points around each line was applied to define a local continuum."656 Abundances were derived [rom the measured EW once appropriate atmospheric parameters have been adopted., Abundances were derived from the measured EW once appropriate atmospheric parameters have been adopted.657" In. particular: (1) stellar temperatures (7~6600—8000 IXIN) were estimated by (he empirical relation log--—0.38(D—V)4-3.99. οριαπο from Che IL, temperatures of TO stars and of a few BSS. observed at high resolution (/2~ 40.000) with UVES2006): (2) gravites (logg~4.3. 4.8) were estimated Irom the BSSlocation in the Color Magnitude Diagram (CMD. see Fig. 5))."," In particular: (1) stellar temperatures $T\simeq 6600-8000$ K) were estimated by the empirical relation $\log T=-0.38 { (B-V)} +3.99$, obtained from the $_\alpha$ temperatures of TO stars and of a few BSS, observed at high resolution $R\sim 40,000$ ) with UVES; (2) gravities $\log g\simeq 4.3$ –4.8) were estimated from the BSSlocation in the Color Magnitude Diagram (CMD, see Fig. \ref{f2}) ),"658" and (3) a value of was assumed for the microturbulence velocity,", and (3) a value of was assumed for the microturbulence velocity.659 Finally. |Fe/I1I]|——0.67 has been adopted from(2004).," Finally, $=-0.67$ has been adopted from."660.. The derived abundances of [O/Fe]| were corrected for departures from the local thermodynamic equilibrium (NLTE). following 0.345...," The derived abundances of [O/Fe] were corrected for departures from the local thermodynamic equilibrium (NLTE), following ."661forward shock emission should be dominated at this time.,forward shock emission should be dominated at this time.662" Thus. we expect that At 5000 s. from equation (12) and (13) and using the constrained value of E and 5 from the forward shock LOR5 ""-gez.∣−26g,4,Hz⊜⋯⋯⋯∏⋅∖∖⇁⊜∶↔⊺⊜⊓∕⋯∣∿↻∙⊃⊝∖ and i4 3.29.10Mey3 Hz. so the optical frequency mp (4.7«10' Hz) is expected to be in the regime rj;<opcMa and the flux density should decline with a temporal index of ~—2."," Thus, we expect that At 5000 s, from equation (12) and (13) and using the constrained value of $E$ and $n$ from the forward shock emission, we get $\nu_{{\rm mr}}\sim 6.39\times66310^8\eta_3^2\epsilon_{{\rm er},-1}^2\epsilon_{{\rm Br},-1}^{1/2}$ Hz and $\nu_{{\rm cr}}\sim 3.29\times 10^{17}\epsilon_{{\rm Br},-1}^{-3/2}$ Hz, so the optical frequency $\nu_{{\rm opt}}$ $4.7\times 10^{14}$ Hz) is expected to be in the regime $\nu_{{\rm mr}} < \nu_{{\rm opt}} < \nu_{{\rm cr}}$ and the flux density should decline with a temporal index of $\simeq -2$."664" If the radio frequency rui, (8.5«10? Hz) also lies in the same regime (Le. Ly<Maio My) at 4.67« 1009. the radio flux then relates with the optical flux as Combining. Eqs.(17) and (18). we obtain p«1.5."," If the radio frequency $\nu_{{\rm radio}}$ $8.5\times 10^9$ Hz) also lies in the same regime (i.e. $\nu_{{\rm mr}} < \nu_{{\rm radio}} < \nu_{{\rm cr}}$ ) at $4.67\times 10^5$ s, the radio flux then relates with the optical flux as Combining Eqs.(17) and (18), we obtain $p<1.5$."665 Such à small p is inconsistent with the observed decay slope of the late-time optical and X-ray emission., Such a small $p$ is inconsistent with the observed decay slope of the late-time optical and X-ray emission.666" As rayx£777, we note that at 4.67« IOs. r4,>Maio only if ja>|126!,€3 ."," As $\nu_{{\rm mr}}\propto \hat t^{-73/48}$, we note that at $4.67\times 10^5$ s, $\nu_{{\rm mr}}>\nu_{{\rm radio}}$ only if $\eta_3>112\epsilon_{{\rm er},-1}^{-1}\epsilon_{{\rm Br},-1}^{-1/4}$ ."667 Since such an initial Lorentz factor ts too large. this spectral regime ts unlikely (see c.f.," Since such an initial Lorentz factor is too large, this spectral regime is unlikely (see c.f."668 loka 2010)., Ioka 2010).669 Radio flux from the reverse shock may be also affected by the synchrotron self absorption (SSA) of the radiating electrons., Radio flux from the reverse shock may be also affected by the synchrotron self absorption (SSA) of the radiating electrons.670 The SSA frequency in the slow cooling case is (Wu et al., The SSA frequency in the slow cooling case is (Wu et al.671" 20051) where co&15 Leis nearly a constant and X==""E e.is shock.the column density of electrons heated by the reverse "," 2005a) where $c_0\simeq 15$ is nearly a constant and $\Sigma=\frac{E/\eta672m_pc^2}{4\pi R^2}$ is the column density of electrons heated by the reverse shock."673"We find ri,<MaioMar requires Fsunνεο.Ἱεμνι210+ at 4.67 1008 according to equations (3). (19) and (20)."," We find $\nu_{{\rm mr}}<\nu_{{\rm radio}}<\nu_{\rm ar}$ requires $674E_{54}n_{-3}\epsilon_{{\rm er},-1}\epsilon_{{\rm Br},-1}\ga 10^4$ at $4.67\times67510^5$ s according to equations (3), (19) and (20)."676 If we substitute Es;22.0 and 7.3=0.40. which are derived from the constraints by the forward shock emission. into this inequality. we obtain ερegiZ1.25«107. which is unlikely.," If we substitute $E_{54}=2.0$ and $n_{-3}=0.40$, which are derived from the constraints by the forward shock emission, into this inequality, we obtain $\epsilon_{{\rm er},-1}\epsilon_{{\rm Br},-1}\gtrsim 1.25\times10^4$, which is unlikely."677 Therefore we conclude that SSA effect can not solve the problem that the reverse shock scenario for the optical emission overpredicts the radio emission., Therefore we conclude that SSA effect can not solve the problem that the reverse shock scenario for the optical emission overpredicts the radio emission.678 It is usually assumed that the blast wave that produces the afterglow emission is nearly adiabatic Rees 1997; Sart et al., It is usually assumed that the blast wave that produces the afterglow emission is nearly adiabatic Rees 1997; Sari et al.679 1998). re. the total kinetic energy of the relativistic shock is a constant.," 1998), i.e. the total kinetic energy of the relativistic shock is a constant."680 However. the energy loss of the blast wave could be significant under some circumstance.," However, the energy loss of the blast wave could be significant under some circumstance."681 The radiation efficiency of the blast wave Is given by (Wu et al., The radiation efficiency of the blast wave is given by (Wu et al.682" 200Sa) As we can see from the above equation. the energy loss is especially important in the ""fast-cooling"" case (1.8. νο) with a large ες."," 2005a) As we can see from the above equation, the energy loss is especially important in the ""fast-cooling"" case (i.e. $\nu_{\rm m} >\nu_{\rm c} $ ) with a large $\epsilon_{\rm e} $."683 In this case. the decreasing blast wave energy at early times will result in a faster decay of the afterglow emission than the adiabatic case.," In this case, the decreasing blast wave energy at early times will result in a faster decay of the afterglow emission than the adiabatic case."684 At late time. as 7» decreases with time. the radiation efficiency drops and the decay slope changes to the adiabatic case.," At late time, as $\frac{\nu_{\rm m} }{\nu_{\rm c} }$ decreases with time, the radiation efficiency drops and the decay slope changes to the adiabatic case."685 We examine whether this scenario can explain the fast decay in the early optical and high-energy LAT emission., We examine whether this scenario can explain the fast decay in the early optical and high-energy LAT emission.686 According to Huang et al. (, According to Huang et al. (6871999) and Wu et al. (,1999) and Wu et al. (6882005a). the isotropic-equivalent energy E of the blast wave evolve with time as The quantities describing the synchrotron spectrum in such a semi-radiative shock are similar to equations (3)-(5). except that the constant E in these equations should be replaced by a time-dependent E as deseribed by Eq. (,"2005a), the isotropic-equivalent energy $E$ of the blast wave evolve with time as The quantities describing the synchrotron spectrum in such a semi-radiative shock are similar to equations (3)–(5), except that the constant $E$ in these equations should be replaced by a time-dependent $E$ as described by Eq. ("68922).,22).690" So the synchrotron emission flux decays as F,«T0710070 for Vp<< iy."," So the synchrotron emission flux decays as $F_{{\rm \nu}}\propto691T^{-3(p-1+\epsilon)/(4-\epsilon)}$ for $\nu_{{\rm mf}}<\nu <\nu_{{\rm cf}}$ ."692 To explain the decay slope à=1.6 of the early optical emission in GRB 090902B with this model. we need €Z0.6.," To explain the decay slope $\alpha\ga 1.6$ of the early optical emission in GRB 090902B with this model, we need $\epsilon \ga 0.6$."693 Thus we need To explain the late optical. X-ray and radio observations. we also need: #F!opt(10?s)- 0.01mdy. E!radio10's)20.03ml y. and FXGOO8)):2 0.2;y (radio observations starts at about 1005. we extrapolate it to 10?s).," Thus we need To explain the late optical, X-ray and radio observations, we also need: $\kappa F_{{\rm opt}}^{\rm f}(10^5{\rm s})\simeq 0.01$ mJy, $F_{{\rm radio}}^{\rm f}(10^5{\rm s})\simeq 0.03$ mJy, and $F_{{\rm X}}^{\rm f}(10^5{\rm694s})\simeq 0.2 \mu$ Jy (radio observations starts at about $1.3\times69510^5$ s, we extrapolate it to $10^5$ s)."696" At 10°s. the two characteristic frequencies in the synchrotron spectrum are Myrc2.0«OPELτιεςHz MEand epjq7mous11LOVEEspPaPasPRapsέρωςΗΖ for e,20.6 and 4p22.2."," At $10^5$ s, the two characteristic frequencies in the synchrotron spectrum are $\nu_{{\rm mf}}\simeq 2.0\times 10^{12} E_{54}^{1/2}\epsilon_{{\rm Bf},-5}^{1/2}697{\rm Hz}$ and $\nu_{{\rm cf}}\simeq 1.1\times69810^{17}E_{54}^{-11/18}n_{-3}^{-10/9}\epsilon_{{\rm Bf},-5}^{-11/18} {\rm699Hz}$ for $\epsilon_{\rm e} =0.6$ and $p=2.2$."700 As rag. «Ix. Hio He in three different frequency regimes. we have three independent constraints on the shock parameters.," As $\nu_{{\rm opt}}$, $\nu_{{\rm X}}$, $\nu_{{\rm radio}}$ lie in three different frequency regimes, we have three independent constraints on the shock parameters."701" Finally we obtain For these parameters. the deceleration time of the blast wave Is Tyo.& 120s. and we can obtain the blast wave kinetic energy at the deceleration time 744, according to Eq.(22)). Le. EsTa)&50."," Finally we obtain For these parameters, the deceleration time of the blast wave is $T_{\rm dec}\simeq 120$ s, and we can obtain the blast wave kinetic energy at the deceleration time $T_{\rm dec}$ according to \ref{ET}) ), i.e. $E_{54}(T_{\rm dec})\simeq 50$."702 This energy is extraordinary large., This energy is extraordinary large.703 With such a high isotropic energy. we the flux density in LAT band at the deceleration time to be expectFs(a)& Hy. which is one order of magnitude higher than the observed flux (—0.1/Jy).," With such a high isotropic energy, we expect the flux density in LAT band at the deceleration time to be $F_{\rm704LAT}^{\rm f}(T_{\rm dec})\simeq 1\mu$ Jy, which is one order of magnitude higher than the observed flux $\simeq 0.1\mu {\rm Jy}$ )."705 Therefore. we conclude that this model can not explain the broadband data of GRB 090902B. Jets from GRBs may have complex structure.," Therefore, we conclude that this model can not explain the broadband data of GRB 090902B. Jets from GRBs may have complex structure."706 For the sake of calculation ease. the structured jet can be simplified as a two-component jet.," For the sake of calculation ease, the structured jet can be simplified as a two-component jet."707" It assumes that the Jet consists of two components: a narrow component with a relatively small half- angle (4) and a large isotropic-equivalent energy in the center. and àwide component with a larger half- angle (£y) and a smaller isotropic-equivalent energy (hereafter. we use the superscripts/subscripts ""NT and W? represents the quantities of the narrow component and the"," It assumes that the jet consists of two components: a narrow component with a relatively small half-opening angle $\theta_N$ ) and a large isotropic-equivalent energy in the center, and awide component with a larger half-opening angle $\theta_W$ ) and a smaller isotropic-equivalent energy (hereafter, we use the superscripts/subscripts 'N' and 'W' represents the quantities of the narrow component and the"708forms a central black hole of mass Ady.,forms a central black hole of mass $M_{\rm bh}$.709" The black hole mass fraction kr=μιAdal, Is assumed to obey. a loe- probability distribution with logry=35 and σ=O44 (Ihbunanu Loeb L999b) These values roughly reflect the distribution of jack hole to bulge mass ratios found iu a sample of 36 local galaxies (Alagorrian et al.", The black hole mass fraction $r\equiv M_{\rm bh}/M_{\rm halo}$ is assumed to obey a log-Gaussian probability distribution with $\log r_0=-3.5$ and $\sigma=0.5$ (Haiman Loeb 1999b) These values roughly reflect the distribution of black hole to bulge mass ratios found in a sample of 36 local galaxies (Magorrian et al.710 1998) for a xuvonie nass fraction of ~(Οιου)z0.1., 1998) for a baryonic mass fraction of $\sim (\Omega_{\rm b}/\Omega_0)\approx 0.1$.711" We further xoxtulate that each black hole cuits a timedepeucdent xoimetrie huuiuositvin proportion to its mass, L4—Myafg=MigLgaaexptt fy). where Lada=15x1U7Ay/AL.eres5 ds the Eddinetou luminosity. f is he time clapsed since the formation of the black hole. aud ty= lU)vr is the characteristic quasar lifetime."," We further postulate that each black hole emits a time–dependent bolometric luminosityin proportion to its mass, $L_{\rm q}\equiv M_{\rm bh}f_{\rm q}=M_{\rm bh}L_{\rm712Edd} \exp(-t/t_0)$ , where $L_{\rm Edd}=1.5\times10^{38}~M_{\rm bh}/{\rm713M_\odot}~{\rm erg~s^{-1}}$ is the Eddington luminosity, $t$ is the time elapsed since the formation of the black hole, and $t_0=10^6$ yr is the characteristic quasar lifetime."714 Finally. we assuine that the shape of the emitted spectrum follows he mean spectrum of the quasar sample iu Elvis et al. (," Finally, we assume that the shape of the emitted spectrum follows the mean spectrum of the quasar sample in Elvis et al. ("7151991) up to a photon cherey of LO keV. We extrapolate he spectrum up to ~50 keV. assuniug a spectral slope of a —U (or a photon iudex of -1).,"1994) up to a photon energy of 10 keV. We extrapolate the spectrum up to $\sim 50$ keV, assuming a spectral slope of $\alpha$ =0 (or a photon index of -1)."716 This simple model was demonstrated to accurately reproduce the evolution of the optical luminosity function in the Bband (Pei 1995) at redshifts :22.2 (Wana Loeb 1998)., This simple model was demonstrated to accurately reproduce the evolution of the optical luminosity function in the B–band (Pei 1995) at redshifts $z\gsim 2.2$ (Haiman Loeb 1998).717 Because our model mceorporates several sinplifiug assuiptious. we regard it as the minimal tov model which successtully reproduces the existing data.," Because our model incorporates several simplifying assumptions, we regard it as the minimal toy model which successfully reproduces the existing data."718 If one of our input assunipfious was drastically violated and our model had failed to ft the observed LF. then a uodification of its basic ineredicuts would be needed.," If one of our input assumptions was drastically violated and our model had failed to fit the observed LF, then a modification of its basic ingredients would be needed."719" Iu lusLetter, we focus on the predictions of this nüninmual nodel in auticipation of the forthcoming lauuch ofCXO: an investigation of a broader range of plausible tov nocels will be mace clsewhere."," In this, we focus on the predictions of this minimal model in anticipation of the forthcoming launch of; an investigation of a broader range of plausible toy models will be made elsewhere."720" We adopt the concordance cosmology of Ostriker Steinhardt (1995). namely à AC DAL model with a tilted power spectrum (Qy.04.0,ioyn) (0.35. 0.65. 0.0L. 1.65. 08T. 0.96)."," We adopt the concordance cosmology of Ostriker Steinhardt (1995), namely a $\Lambda$ CDM model with a tilted power spectrum $\Omega_0,\Omega_\Lambda, \Omega_{\rm b},h,\sigma_{8h^{-1}},n$ )=(0.35, 0.65, 0.04, 0.65, 0.87, 0.96)."721" Figure 1 shows the adopted spectrum of quasars. assunine a black hole mass μι=LOAD... placed at two different redshifts. 7,=Il aud 7.=6."," Figure \ref{fig:spectrum} shows the adopted spectrum of quasars, assuming a black hole mass $M_{\rm bh}=10^8{\rm M_\odot}$, placed at two different redshifts, $z_{\rm s}=11$ and $z_{\rm s}=6$."722 Iu computing the intergalactic absorption. we included the opacity of both livdrogen and helium as well as the effect of electron scattering.," In computing the intergalactic absorption, we included the opacity of both hydrogen and helium as well as the effect of electron scattering."723" We assumed that reionization occurred at z,=10 aud that at higher redshifts the IGM was homogeneous and fully neutral."," We assumed that reionization occurred at $z_{\rm724r}=10$ and that at higher redshifts the IGM was homogeneous and fully neutral."725" At lower redshifts. Qoioκτν, we included the livdrvogen opacity of the Ίνα forest given by Madau (1995). and extrapolated his fitting formulae for the evolution of the mmuberdensity of absorbers bevoud 2=5 when necessary."," At lower redshifts, $0<z<z_{\rm r}$, we included the hydrogen opacity of the $\alpha$ forest given by Madau (1995), and extrapolated his fitting formulae for the evolution of the numberdensity of absorbers beyond $z=5$ when necessary."726" As Figure 1 shows. the muninuun black hole mass detectable by the 2.1019crestan3 flux limit ofCVO (see below) is Af,~LOSΔΙ. at +=10 and Ay,~2«10*Mat 2=5."," As Figure \ref{fig:spectrum} shows, the minimum black hole mass detectable by the $\sim 2\times 10^{-16}~{\rm erg~s^{-1}~cm^{-2}}$ flux limit of (see below) is $M_{\rm bh}\sim 10^8~{\rm M_\odot}$ at $z=10$ and $M_{\rm bh}\sim 2\times10^7~{\rm M_\odot}$ at $z=5$."727 Iu our model. the correspouding halo masses are Mya~3.10H ALL. and Afi~6x1019ALL. respectively.," In our model, the corresponding halo masses are $M_{\rm halo}\sim 3\times10^{11}~{\rm M_\odot}$ , and $M_{\rm halo}\sim 6\times 10^{10}~{\rm M_\odot}$, respectively."728 Although such massive halos are rare. their abundance is detectable in wide-field surveys.," Although such massive halos are rare, their abundance is detectable in wide-field surveys."729 Note that an accurate determination of the spectrmu below ~0.1 κο could have provided an estimate of the reionization redshift τν., Note that an accurate determination of the spectrum below $\sim0.1$ keV could have provided an estimate of the reionization redshift $z_{\rm r}$.730 Uitortunately. this spectral regime suffers from Galactic absorption (O'Flaherty and Jakobsen 1997) aud is outside the 0.1.GkeV detection band ofCYO.," Unfortunately, this spectral regime suffers from Galactic absorption (O'Flaherty and Jakobsen 1997) and is outside the 0.4–6keV detection band of."731" Tn our model. the X.rav hiuuinosity fiction at a redshitt > fin MpeP(erg/s) 1| is eiven by a stun over halos that formed just before that redshift. ONENESS""TENarse where Ly is the observed ταν luuinosity in the iustruient* detection baud (0.5 3 keV for ROSAT and 0.1.6 keV for CNO): fx is the fraction of the quasar’s bolometric Wuninosity emitted in this baud: 4?N74Mdt is the black halo formation rate. eiven by a convolution of the PressSchechter halo mass function with equation (1)): and Af=?¢(-) fis the time elapsed from a cosmic time f until a redshift +."," In our model, the X–ray luminosity function at a redshift $z$ [in ${\rm732Mpc^{-3}~(erg/s)^{-1}}$ ] is given by a sum over halos that formed just before that redshift, (L_X,z) where $L_X$ is the observed X–ray luminosity in the instrument's detection band $0.5$ $3$ keV for ROSAT and 0.4–6 keV for ); $f_{\rm X}$ is the fraction of the quasar's bolometric luminosity emitted in this band; $d^2N/dM_{\rm bh}dt$ is the black halo formation rate, given by a convolution of the Press–Schechter halo mass function with equation \ref{eq:scat}) ); and $\Delta t=t(z)-t$ is the time elapsed from a cosmic time $t$ until a redshift $z$."733 Although our model was constructed so as to fit the observed optical LE. Figure 2. demonstrates that it is also in good aerecment with the data on the Xrax LF.," Although our model was constructed so as to fit the observed optical LF, Figure \ref{fig:LF} demonstrates that it is also in good agreement with the data on the X–ray LF."734 This implies that the choice of quasar spectrum im our model is reasonable., This implies that the choice of quasar spectrum in our model is reasonable.735 The solid curve in this fleure shows the prediction of equation (3)) at 2= 3.5. near the highest redshift where N-vay data is available.," The solid curve in this figure shows the prediction of equation \ref{eq:LF}) ) at $z=3.5$ , near the highest redshift where X-ray data is available."736 The bottom curve corresponds to a cutoff in circular velocity for the host halos of ea50kns Lo which is introduced here in," The bottom curve corresponds to a cutoff in circular velocity for the host halos of $v_{\rm circ}\geq 50~{\rm km~s^{-1}}$ , which is introduced here in"737Recent work has demonstrated that several [x gian stars exhibit. low-amplitude. long-term radial velocity (RY) variations with periods of several hundreds: of days (MeClure ct al.,"	Recent work has demonstrated that several K giant stars exhibit low-amplitude, long-term radial velocity (RV) variations with periods of several hundreds of days \nocite{mcc85} \nocite{irw89} \nocite{wal92} \nocite{hat93} (McClure et al."738 1985: Irwin. et al., 1985; Irwin et al.739 1989: Walker e al., 1989; Walker et al.740 1992: Ilatzes Cochran 1993)., 1992; Hatzes Cochran 1993).741 The nature of these variations is presently unknown., The nature of these variations is presently unknown.742 Racial pulsations can be excluded: as a cause since the period of the fundamenta racial mode is expected to be about a week. C, Radial pulsations can be excluded as a cause since the period of the fundamental radial mode is expected to be about a week. (743Ehese stars also show short-term variability on timescales of a few davs which are due to radial or nonracial pulsations.),These stars also show short-term variability on timescales of a few days which are due to radial or nonradial pulsations.)744 This eaves nonradial pulsations (NIA). rotational modulation w surface features. or low-niass companions as possible explanations for the long-period RY variations.," This leaves nonradial pulsations (NRP), rotational modulation by surface features, or low-mass companions as possible explanations for the long-period RV variations."745 Ix giant stars iive large radii and low projected: rotational velocities so he period of rotation for these stars is expected. to. be several hundreds ofdays., K giant stars have large radii and low projected rotational velocities so the period of rotation for these stars is expected to be several hundreds of days.746 Rotational modulation thus seenis o be a front-running hypothesis for explaining the lone-erm variabilitv., Rotational modulation thus seems to be a front-running hypothesis for explaining the long-term variability.747 Lf the surface features are related to stellar activity (spots. plage. ete.)," If the surface features are related to stellar activity (spots, plage, etc.)"748 then we should expect to find variations in the equivalent widths of lines. particularly ones ormed in the chromospheric.," then we should expect to find variations in the equivalent widths of lines, particularly ones formed in the chromospheric."749 Indeed. Lambert (1987) found variations in the He E line in Arcturus with the same period (233 clavs) that was later found in the RV variations.," Indeed, Lambert (1987) \nocite{lam87}750 found variations in the He I line in Arcturus with the same period (233 days) that was later found in the RV variations."751 Larson et al. (, Larson et al. (7521993) found evidence for the 545 day RW period in the equivalent width: variations of Ca IL in 3 Geminorum.,1993) found evidence for the 545 day RV period in the equivalent width variations of Ca II in $\beta$ Geminorum.753 I thus seems that the long-period variability is consistent with rotational moculation. at least for Arcturus and 3 Geminorum.," It thus seems that the long-period variability is consistent with rotational modulation, at least for Arcturus and $\beta$ Geminorum."754 The confirmation of rotational modulation as the source of the RY variability has. vet to be established. for Aldebaran (= a Tauri). a IX giant. with an HV. period of 643 clavs and a 2-4. (peak-to-peak) amplitude of (llatzes Cochran 1993: hereafter 11092).," 	The confirmation of rotational modulation as the source of the RV variability has yet to be established for Aldebaran $=$ $\alpha$ Tauri), a K giant with an RV period of 643 days and a $K$ (peak-to-peak) amplitude of (Hatzes Cochran 1993; hereafter HC93)."755 The interesting aspect of this variability is that is seems to have been oesent ancl coherent. (same amplitude ancl phase) in RV measurcments spanning over 12 vears., The interesting aspect of this variability is that is seems to have been present and coherent (same amplitude and phase) in RV measurements spanning over 12 years.756 IH surface structure is responsible for the RW variability of this star then it mus ος very. long-lived. which at first seems unlikely. but since nothing is known about surface structure on Ix. giants this ivpothesis cannot be summarilv rejected.," If surface structure is responsible for the RV variability of this star then it must be very long-lived, which at first seems unlikely, but since nothing is known about surface structure on K giants this hypothesis cannot be summarily rejected."757 The lifetime anc cohereney of the long-period RV. variations in. Xldebaran would normally argue in favour of a low-mass companion., The lifetime and coherency of the long-period RV variations in Aldebaran would normally argue in favour of a low-mass companion.758 After all. one would expect changes in the amplitude anc phase of the variations if they were due to a surface structure," After all, one would expect changes in the amplitude and phase of the variations if they were due to a surface structure"759certain regions of our focal plane. leaving others relatively uncderpopulated.,"certain regions of our focal plane, leaving others relatively underpopulated."760 We have simulated. the performance of our optimizations in real-life situations by making use of ealaxy mock catalogs extracted from the Bolshoi simulation (?).., We have simulated the performance of our optimizations in real-life situations by making use of galaxy mock catalogs extracted from the Bolshoi simulation \citep{Klypin2010}.761 Important. for this work. the clustering properties of mock galaxies match those of real galaxies with gooc accuracy.," Important for this work, the clustering properties of mock galaxies match those of real galaxies with good accuracy."762 The reason for using mock catalogs instead of real catalogs is that they provide us with more Iexibility when it comes to selecting dillerent samples with dilleren number densities., The reason for using mock catalogs instead of real catalogs is that they provide us with more flexibility when it comes to selecting different samples with different number densities.763 We have performed a 2-D projection of a simulation box of 250 Mpe/h on a side situated at. redshift l onto our focal plane and used the circular. velocity of haloes as an empirical threshold. for selecting cilleren densities., We have performed a 2-D projection of a simulation box of 250 Mpc/h on a side situated at redshift 1 onto our focal plane and used the circular velocity of haloes as an empirical threshold for selecting different densities.764 In order to allow for à fair comparison with the results presented in the previous sections. we have selecte catalogs with target-to-positioner ratios of ~ 0.5. 1. 3 ane 5.," In order to allow for a fair comparison with the results presented in the previous sections, we have selected catalogs with target-to-positioner ratios of $\sim$ 0.5, 1, 3 and 5."765 Simulations were performed with 9 different realizations for each η. obtained by rotating the box In Fig. 6..," Simulations were performed with 9 different realizations for each $\eta$, obtained by rotating the box In Fig. \ref{fig:mocks},"766 we show a portion of the focal plane of an instrument. represented by an array of patrol discs. in a sequence of the first tiles.," we show a portion of the focal plane of an instrument, represented by an array of patrol discs, in a sequence of the first tiles."767 The over-plotted dots svmbolize he projected. positions of targets belonging to a mock galaxy catalog with yo3., The over-plotted dots symbolize the projected positions of targets belonging to a mock galaxy catalog with $\eta \sim 3$.768 The first panel in this figure illustrates the initial situation where the entire sample of argets is to be observed., The first panel in this figure illustrates the initial situation where the entire sample of targets is to be observed.769 Note that. as explained. above. argets on the focal plane of the spectrograph. rather than ing randomly distributed. accumulate in filaments.," Note that, as explained above, targets on the focal plane of the spectrograph, rather than being randomly distributed, accumulate in filaments."770 The rest of the panels show the distribution of targets assigned o each tile by using the optimized. algorithm described in Section 4.., The rest of the panels show the distribution of targets assigned to each tile by using the optimized algorithm described in Section \ref{sec:draining}.771 In. this example. ~75% of targets have been selected alter 3 The performance of our optimizations with mock galaxy catalogs is presented in the same format às in previous sections in Fable 3. and Fig. 7..," In this example, $\sim 75\%$ of targets have been selected after 3 The performance of our optimizations with mock galaxy catalogs is presented in the same format as in previous sections in Table \ref{tab:real} and Fig. \ref{fig:real}."772 X direct consequence of the presence of clustering in our catalogs is that the fraction of targets assigned to each tile decreases significantly. as à comparison between Table 20 anc Table 3.7 demonstrates.," A direct consequence of the presence of clustering in our catalogs is that the fraction of targets assigned to each tile decreases significantly, as a comparison between Table \ref{tab:random} and Table \ref{tab:real} demonstrates."773 ηνίαιν. the probability that a single positioner has to deal with several targets is now higher ancl. consequently. it becomes harder to move targets towards the first. tiles.," Trivially, the probability that a single positioner has to deal with several targets is now higher and, consequently, it becomes harder to move targets towards the first tiles."774 As an example. with 51 and two tiles we could observe almost 94% of all targets in a random catalog. even whithout allowing for rotation of the focal plane.," As an example, with $\eta \sim 1$ and two tiles we could observe almost $94 \%$ of all targets in a random catalog, even whithout allowing for rotation of the focal plane."775 In a real catalog we could only assign S54 of targets in. the same number of tiles., In a real catalog we could only assign $85 \%$ of targets in the same number of tiles.776 Similarly. in areal catalog with 5 we would need 5in tiles to barely reach a completeness. of SOUL. at least S4 below our expectations from. random catalogs.," Similarly, in areal catalog with $\eta \sim 5$ we would need 5 tiles to barely reach a completeness of $80 \%$ , at least $8\%$ below our expectations from random catalogs."777 Again. we refer the reader to Table 3. for the exact fractions of targets assigned with a random approach. with the draining algorithm alone and with the draining algorithm complemented. with rotation of the focal plane.," Again, we refer the reader to Table \ref{tab:real} for the exact fractions of targets assigned with a random approach, with the draining algorithm alone and with the draining algorithm complemented with rotation of the focal plane."778 In order to analyze the performance of our optimizations as compared to à random approach we point the reader to Fig. 7.., In order to analyze the performance of our optimizations as compared to a random approach we point the reader to Fig. \ref{fig:real}.779 This figure shows that the gain provided. by our optimizations as compare to à greedy approach when implemented in a real-life situation is consistent. with what we could infer from. random catalogs., This figure shows that the gain provided by our optimizations as compare to a greedy approach when implemented in a real-life situation is consistent with what we could infer from random catalogs.780 X closer inspection. however. reveals that the gain provided by the draining algorithm alone is slightly smaller now. falling below 2%. whereas the gain achieved by combining this algorithm with a ROT optimization remains in the range of 56%.," A closer inspection, however, reveals that the gain provided by the draining algorithm alone is slightly smaller now, falling below $2\%$, whereas the gain achieved by combining this algorithm with a ROT optimization remains in the range of $5-6\%$."781 I only slight rotations were allowed (ROT? optimization) we could still improve the eLllicieney of the process in 3.54.5%. Note that. as mentioned previously. the results shown in this work were obtained. ignoring Liber collisions. as the ellect of these depends on the geometry of the fiber positioning robot itself. and. therefore. cannot be extrapolated to any fiber-fed spectrograph of this kind.," If only slight rotations were allowed (ROT2 optimization) we could still improve the efficiency of the process in $3.5-4.5\%$ Note that, as mentioned previously, the results shown in this work were obtained ignoring fiber collisions, as the effect of these depends on the geometry of the fiber positioning robot itself, and, therefore, cannot be extrapolated to any fiber-fed spectrograph of this kind."782 The tvpical number of these events obviously increases in mock ealaxy catalogs (and hence in real catalogs) due to the fact that objects are more clustered (the fraction of collisions is almost negligible in random catalogs)., The typical number of these events obviously increases in mock galaxy catalogs (and hence in real catalogs) due to the fact that objects are more clustered (the fraction of collisions is almost negligible in random catalogs).783 Even in real catalogs the fraction of objects in conflict. remains small for SLOL: even for y=5., Even in real catalogs the fraction of objects in conflict remains small for SIDE: $\lesssim 1\%$ even for $\eta=5$.784 However. an important advantage of the draining algorithm is that collisions can be solved optimally. and. additional methods. are not. needed.," However, an important advantage of the draining algorithm is that collisions can be solved optimally, and additional methods are not needed."785 The results presented in Table 3.7 and Fig., The results presented in Table \ref{tab:real} and Fig.786 7 would. basically not change if collisions were taken into account., \ref{fig:real} would basically not change if collisions were taken into account.787 Only very slight variations are expected in the very last tiles. which are not relevant in real-life observations.," Only very slight variations are expected in the very last tiles, which are not relevant in real-life observations."788 The results. presented. in this section confirm. that. despite the physical restrictions of this state-of-the-art. fiber positioning robots. it is possible to optimize a survey strateew in a remarkable wav just by assigning targets to tiles and positioners conveniently.," The results presented in this section confirm that, despite the physical restrictions of this state-of-the-art fiber positioning robots, it is possible to optimize a survey strategy in a remarkable way just by assigning targets to tiles and positioners conveniently."789 In addition. these results represent a strong support for allowing the focal plane of future instruments to rotate.," In addition, these results represent a strong support for allowing the focal plane of future instruments to rotate."790 We have shown how even a slight rotation produces a remarkable optimization., We have shown how even a slight rotation produces a remarkable optimization.791 In the next section we discuss on the implications of our results., In the next section we discuss on the implications of our results.792 The results on the optimization of the fiber positioning process that we present in this work are valid for any focal plane consisting of an array of positioners as that described in Section 3.., The results on the optimization of the fiber positioning process that we present in this work are valid for any focal plane consisting of an array of positioners as that described in Section \ref{sec:robot}. .793 To first order. therefore. our results are not dependent on the size ofthe tile or the number," To first order, therefore, our results are not dependent on the size ofthe tile or the number"7940.5 truecia The outer regions of M31 have become an increasingly complicated field of study as it has become clear in recent vears that the role of accretion in halo formation is of considerable importance.,0.5 truecm The outer regions of M31 have become an increasingly complicated field of study as it has become clear in recent years that the role of accretion in halo formation is of considerable importance.795 present star-count maps showing what appear to be extensive tidal disturbances iu the halo of M1. including iu the vicinity of the massive elobular cluster Cl.," \citet{fer02} present star-count maps showing what appear to be extensive tidal disturbances in the halo of M31, including in the vicinity of the massive globular cluster G1."796 Reitzel&Cuhathakurta(2002.hereafterRCGU2) find evidence for a subtle stream-like feature. in an outer halo field located 19 Ispc from the ceuter in projection along the southeastern ninor-axis. using a combination of kinematics and metallicity measuremeuts of red ejut brauch (RGB) stars;," \citet[][hereafter RG02]{rei02} find evidence for a subtle stream-like feature, in an outer halo field located 19 kpc from the center in projection along the southeastern minor-axis, using a combination of kinematics and metallicity measurements of red giant branch (RGB) stars."797 Cuhbathakurta&Reitzel(2002) confirm that this feature continues along the nünor axis in two inner halo fields located near the globular clusters C312 and C302. located 11 and 7 kpe from the uucleus of M31 respectively near the southeastern minor axis.," \citet{guh02}798 confirm that this feature continues along the minor axis in two inner halo fields located near the globular clusters G312 and G302, located 11 and 7 kpc from the nucleus of M31 respectively near the southeastern minor axis."799 ΑΟ5 two closest satellites M32 aud NGC 205 are known to be undergoing tidal stripping (Choi.Culiathaurta.&Johustou2002):: vet there is no definite proposal for a companion that night have been responsible for the large-scale streams seen iu the halo., M31's two closest satellites M32 and NGC 205 are known to be undergoing tidal stripping \citep*{cho02}; yet there is no definite proposal for a companion that might have been responsible for the large-scale streams seen in the halo.800 The area around Cl is a particularly interesting field to study; as this object has been proposed to be the core of a tidallv-disrupted dwarf galaxy (Alevlanetal.2001).," The area around G1 is a particularly interesting field to study, as this object has been proposed to be the core of a tidally-disrupted dwarf galaxy \citep{mey01}."801. Tf this is the case. one uüght expect to find the tidal debris surrouudiug the main body of the object with velocities and metallicites simular to Cl itself.," If this is the case, one might expect to find the tidal debris surrounding the main body of the object with velocities and metallicites similar to G1 itself."802 In addition. the field around CU is expected to have roughly equal umubers of N31 halo aud disk stars so this eives us the opportunity to study the disk population of AD further out (0—31 kpe) than las been done to date.," In addition, the field around G1 is expected to have roughly equal numbers of M31 halo and disk stars \citep*{rei98,hod95} so this gives us the opportunity to study the disk population of M31 further out $r\sim34$ kpc) than has been done to date."803 Ferguson&Johuson(2001). study a field 30 kpe from the nucleus of M31 along the NE major axis aud estimate a mean metallicity of [Fe/II|=0.7: they find that the population is mostly old (>8 Ctr) but there is evidence for an intermediate-age population as well., \citet{fer01} study a field 30 kpc from the nucleus of M31 along the NE major axis and estimate a mean metallicity of $\rm[Fe/H]\simeq-0.7$; they find that the population is mostly old $>8$ Gyr) but there is evidence for an intermediate-age population as well.804 Iu a paper that accoupanics this work. Richetal.(2003) report evidence for an iutermediate-age population," In a paper that accompanies this work, \citet{ric03} report evidence for an intermediate-age population"805The discovery of these two brown dwarf events is remarkable because each event had a hieh magnification. aud therefore required a very small distance of closest approach.,"The discovery of these two brown dwarf events is remarkable because each event had a high magnification, and therefore required a very small distance of closest approach."806 Such evenis are (herelore rare., Such events are therefore rare.807 Each of the two events therefore represents a large number of additional brown-dwarf events of short duration., Each of the two events therefore represents a large number of additional brown-dwarf events of short duration.808 It would be difficult to use the detection of these two events (to lormulate a realistic estimate of the total number of short-duration brown-dwarl-lens events presently expected., It would be difficult to use the detection of these two events to formulate a realistic estimate of the total number of short-duration brown-dwarf-lens events presently expected.809 Nevertheless. these detections add plausibility to (he estimates we have mace above. based on rate calculations and the combined OGLE and MOA detection rates.," Nevertheless, these detections add plausibility to the estimates we have made above, based on rate calculations and the combined OGLE and MOA detection rates."810 Figure 1 demonstrates (hat brown-dwarf events with τε in the range of 8—16 days can take place ab distances greater than a hundred pe for velocities in excess of ~50. km /., Figure 1 demonstrates that brown-dwarf events with $\tau_E$ in the range of $8-16$ days can take place at distances greater than a hundred pc for velocities in excess of $\sim 50~$ km $^{-1}$.811 Note in addition. that the total volume. hence the number of possible lenses ancl the rate of lensing by anv given population of lenses. increases with distance from us. (," Note in addition, that the total volume, hence the number of possible lenses and the rate of lensing by any given population of lenses, increases with distance from us. ("812See. e.g.. DiStefano 2008a. 2003b for details.),"See, e.g., Stefano 2008a, 2008b for details.)"813 Therefore the largest number of brown-dwarl lenses generating 8— 16-day events should have velocities 50 kms. + and be located at distances larger (han LOO pc., Therefore the largest number of brown-dwarf lenses generating $8-16$ -day events should have velocities $> 50~$ km $^{-1}$ and be located at distances larger than $100$ pc.814 This is consistent with (he events observed to date., This is consistent with the events observed to date.815 Consider a planetary svstem in which one planet serves as a lens. producing a event wilh a measured value of Te. Suppose Chat the star orbited by the planet lens is detected.," Consider a planetary system in which one planet serves as a lens, producing a short-duration event with a measured value of $\tau_E.$ Suppose that the star orbited by the planet lens is detected."816 Suppose further. that a sequence of high-resolution measurements allows the geometric parallax. proper motion. aud Einstein angle of the star to be measured (see. e.g. Di Stefano 2009).," Suppose further, that a sequence of high-resolution measurements allows the geometric parallax, proper motion, and Einstein angle of the star to be measured (see, e.g., Di Stefano 2009)."817" The combination of Dj and 9,5, produces a high-precision value ol the gravitational mass. M,. of the star."," The combination of $D_L$ and $\theta_{E,\ast}$ produces a high-precision value of the gravitational mass, $M_\ast,$ of the star."818 In general. the stellar mass is estimated based on spectral ancl flix information.," In general, the stellar mass is estimated based on spectral and flux information."819 A direct measurement of the gravitational mass allows stellar models to be tested., A direct measurement of the gravitational mass allows stellar models to be tested.820 In some cases. it max be possible to conduct subsequent transit or raclial-velocity studies to measure the gravitational mass of the star in a second wax. i.e. bv studsyiug the orbit of the planet that served as a lens and/or the orbits of other planets.," In some cases, it may be possible to conduct subsequent transit or radial-velocity studies to measure the gravitational mass of the star in a second way, i.e., by studying the orbit of the planet that served as a lens and/or the orbits of other planets."821 Thus. for some stars orbited by planet lenses. we may be able to compare (he gravitational ass measured via lensing with the gravitational mass measured via orbital dvnamics.," Thus, for some stars orbited by planet lenses, we may be able to compare the gravitational mass measured via lensing with the gravitational mass measured via orbital dynamics."822 Up to this point in our discussion. the planet has plaved only a peripheral role: (1) it produced a photometric event that alerted us to the possibility of measuring astrometric lensing by (he star. aud (2) it alerted us to (he presence of at least one planet orbiting the star. (hereby motivating subsequent transit and/or radial-velocity studies.," Up to this point in our discussion, the planet has played only a peripheral role: (1) it produced a photometric event that alerted us to the possibility of measuring astrometric lensing by the star, and (2) it alerted us to the presence of at least one planet orbiting the star, thereby motivating subsequent transit and/or radial-velocity studies."823 The lensing event can of course leach us a good deal about the planet., The lensing event can of course teach us a good deal about the planet.824 First. if finite-source-size elfects are detected. (hen 05prance can be directly measured.," First, if finite-source-size effects are detected, then $\theta_{E,planet}$ can be directly measured."825 The distance to the planet is. to high precision. the same as the distance to the central star.," The distance to the planet is, to high precision, the same as the distance to the central star."826" The combination of 0,prone and Dj measures the mass of the planet."," The combination of $\theta_{E,planet}$ and $D_L$ measures the mass of the planet."827 With the gravitational masses of both the planet and star measured. the mass ratio q can be computed.," With the gravitational masses of both the planet and star measured, the mass ratio $q$ can be computed."828 If. in addition. the projected orbital separation. a. between the central star and planet lens is less than roughlv 3.5Hp. or if the event “repeats”. then q and a can both be estimated from a fit to the planet-lens light curve.," If, in addition, the projected orbital separation, $a,$ between the central star and planet lens is less than roughly $3.5\, R_{E,\ast},$ or if the event “repeats”, then $q$ and $a$ can both be estimated from a fit to the planet-lens light curve."829 The value of 4 so measured can be checked [or consistency with the measured values of the planets and stars gravitational lüasses., The value of $q$ so measured can be checked for consistency with the measured values of the planet's and star's gravitational masses.830predominantly methanol.,predominantly methanol.831 It is not easy. to untangle the blending and derive useful inlormation from the resulting line prolile., It is not easy to untangle the blending and derive useful information from the resulting line profile.832" Instead we opted to observe (wo positions south of IRc2 with declination offsets of aancd100"".. respectively."," Instead we opted to observe two positions south of IRc2 with declination offsets of and, respectively."833 The two positions correspond to local maxima in the IC] map of OMC-L by Schilke.Phillips.&Wang(1995)., The two positions correspond to local maxima in the HCl map of OMC-1 by \citet{spw1995}.834. The (0. 60) position also coincides with the CS elump LSI (Mundyetal.1986).. and the (ο. 1007)) position Orion S. Figure 4 show the HC] J=1—0 spectra for the remaining sources in (he sample.," The (0, ) position also coincides with the CS clump LS1 \citep{mundy1986}, and the (0, ) position Orion S. Figure \ref{fig:spectra4} show the HCl $J=1-0$ spectra for the remaining sources in the sample."835 The HC] hvperfine structure. resulting from the interaction between the electric [ield and chlorine nuclear spin. splits the J=1—0 transition into three components. with the outer (vo separated by —6.35 and 8.22 rrespectivelv from the strongest middle component for LICL.," The HCl hyperfine structure, resulting from the interaction between the electric field and chlorine nuclear spin, splits the $J=1-0$ transition into three components, with the outer two separated by $-6.35$ and 8.22 respectively from the strongest middle component for ."836 ForCL. the separations are —5.05 aand 6.45|... respectively.," For, the separations are $-5.05$ and 6.45, respectively."837 Statistical weights for the upper level of the hyperfine transitions dictate optically thin line strength ratio of 1:3:2., Statistical weights for the upper level of the hyperfine transitions dictate optically thin line strength ratio of 1:3:2.838 In the observed sample. the (hree-component hvperline pattern is clearly seen in many sources. but (he components often do not conform to the optically thin ratio. indicating deviations rom the optically (hin limit or differences in excitation between (he three components.," In the observed sample, the three-component hyperfine pattern is clearly seen in many sources, but the components often do not conform to the optically thin ratio, indicating deviations from the optically thin limit or differences in excitation between the three components."839 Under the assumption that the hvperfine components share the same excitation and kinematic characteristics. lits to the line profiles can independently provide the optical depth and excitation temperature (Xwan&Scoville1975).," Under the assumption that the hyperfine components share the same excitation and kinematic characteristics, fits to the line profiles can independently provide the optical depth and excitation temperature \citep{kwan1975}."840. Such a utility is readily available in CLASS. the spectral line data reduction package developed ancl maintained by IAM.," Such a utility is readily available in CLASS, the spectral line data reduction package developed and maintained by IRAM."841 The HFS fit in CLASS provides four parameters: AT+Traine Vpsg. we the line width. ad Traine," The HFS fit in CLASS provides four parameters: $\Delta T\cdot\tau_{main}$, $V_{LSR}$, $w$ the line width, and $\tau_{main}$."842 Tain Is the total opticaldepth from all hvperfine components of the line. and," $\tau_{main}$ is the total opticaldepth from all hyperfine components of the line, and"843for calibration‘ of the interferometer. pnphase. enhancing‘? the coherence time of the visibilities ‘and ‘allowing© the detection of fainter target,"for calibration of the interferometer phase, enhancing the coherence time of the visibilities and allowing the detection of fainter targets."844 The typical s.one sigma image sensitivity. cerived [rom these datasets is approximately 1: mJv/beam., The typical one sigma image sensitivity derived from these datasets is approximately 1 mJy/beam.845 The angular resolution varies with source declination but is tvpically approximately LOO mas., The angular resolution varies with source declination but is typically approximately 100 mas.846 ligure 2 shows a typical e-VLBI image of one. of the sources in Table 1.. all of which were unresolved on scales of mamas or less.," Figure \ref{fig:J031010-573041} shows a typical e-VLBI image of one of the sources in Table \ref{table:observed_targets}, all of which were unresolved on scales of mas or less."847 ‘Table 3 lists the maximum angular size of cach source as measured [from the images using the MIIRLAD task IMETE., Table \ref{table:position_and_size} lists the maximum angular size of each source as measured from the images using the MIRIAD task IMFIT.848 Xn c-VLBI position is also listed for each source along with the flux density measured [rom the e-VLBL (~ O.Laaresee GCGllzbeam) and ΑΟ ( l5aaresec beam) images., An e-VLBI position is also listed for each source along with the GHz flux density measured from the e-VLBI $\sim0.1$ arcsec beam) and AT20G $\sim15$ arcsec beam) images.849 Phe uncertainty in the the eVLBI positions is dominated by the phase referencing of the calibration source. and is typically muimas in RA and DEC.," The uncertainty in the the e-VLBI positions is dominated by the phase referencing of the calibration source, and is typically mas in RA and DEC."850 Note that the [ANT20€C. and eVLBI Iux-density measurements are not simultaneous and. were made up to three vears apart., Note that the AT20G and e-VLBI flux-density measurements are not simultaneous and were made up to three years apart.851 The mean Lux ratio (ονοι vrsuc) is 0.90 with a standard: deviation of 0.22., The mean flux ratio $_{\rm VLBI}$ $_{\rm AT20G}$ ) is 0.90 with a standard deviation of 0.22.852 Howe exclude the source 255450. which appears to be variable (see SS44.1.2 below). the mean [lux ratio rises to 0.94 and the standard deviation drops to 0.15.," If we exclude the source $-$ 255450, which appears to be variable (see 4.1.2 below), the mean flux ratio rises to 0.94 and the standard deviation drops to 0.18."853 These results suggest that (i) the nearby AT20G GPS sources are compact. with ~90% of their GGlIA emission arising on scales smaller than," These results suggest that (i) the nearby AT20G GPS sources are compact, with $\sim$ of their GHz emission arising on scales smaller than"854value of E/AM results in higher expausiou velocitics of the ejecta and hotter post-shock gas. and a lower equilibrium ionization parzuuoeter.,"value of $E/M$ results in higher expansion velocities of the ejecta and hotter post-shock gas, and a lower equilibrium ionization parameter."855 However. the τοι! also decelerates more rapidly. causing Z to increase at a faster rate than for the η=12 case.," However, the remnant also decelerates more rapidly, causing $\Xi$ to increase at a faster rate than for the $n = 12$ case."856 This ultimately lunders the formation of cool gas relative to the 12 case. and only a small amount is able to form (see Table 2)).," This ultimately hinders the formation of cool gas relative to the $n = 12$ case, and only a small amount is able to form (see Table \ref{tab:mass_cool_gas}) )."857 Receutly. it is has become clear that there exists a class of type II supernova explosions which are under cuerectic(6.8... Zampier 2003)).," Recently, it is has become clear that there exists a class of type II supernova explosions which are under energetic, Zampieri \cite{Z2003}) )."858 For two explosions examined in detail. Zampieri al.(2003)) found AZ=LIAL. and E060.9<10ere.," For two explosions examined in detail, Zampieri \cite{Z2003}) ) found $M \gtsimm 14 \Msol$ and $E \approx 0.6 - 0.9 \times 10^{51} \erg$."859 We do uot expect remmauts with. such paraicters to evolve significantly differeutlv to our canonical models with Af=LOAL.. aud E=10ere., We do not expect remnants with such parameters to evolve significantly differently to our canonical models with $M = 10 \Msol$ and $E = 10^{51} \erg$.860 We lave calculated svuthetic Lue profiles for ciission from the cooled eas, We have calculated synthetic line profiles for emission from the cooled gas.861 The 2D axisviinietrie eric is rotated onto a 3D cartesian erid and the cussion from volume clemeuts containing cool gas was integrated udder the assmuption that it is optically thin and the volume emission rate varies as v7., The 2D axisymmetric grid is rotated onto a 3D cartesian grid and the emission from volume elements containing cool gas was integrated under the assumption that it is optically thin and the volume emission rate varies as $n^{2}$.862 Since the gas is cool. thermal Doppler broadening is neslieible.," Since the gas is cool, thermal Doppler broadening is negligible."863 A previous investigation (Dottorff 2000)) failed to reach aux strong couclisious concerning whether was favoured by observations. so it is not iucluded im our model.," A previous investigation (Bottorff \cite{BFBK2000}) ) failed to reach any strong conclusions concerning whether was favoured by observations, so it is not included in our model."864 The cussion is blue- or redshifted according to the line of sight velocity of the eas., The emission is blue- or redshifted according to the line of sight velocity of the gas.865 Absorption was also asstuned to be neelieible., Absorption was also assumed to be negligible.866fixed to 1.32. as reported by Capectal.(2007). from the ddata. eives a very poor result (42/5 = 897/16).,"fixed to 1.32, as reported by \citet{grupe07} from the data, gives a very poor result $\chi^2/\nu$ = 897/46)."867 The fit cau be improved by leaving the decay slope as a free parameter refley its... model2)," The fit can be improved by leaving the decay slope as a free parameter \\ref{lc_fits}, model 2)."868 Thisresultsinasingledecaugslopeofos = ].I5x00.010. but the light curve still deviates sieuificautlv a later times from this slope. resulting iu an unacceptable y2/r = 100/15.," This results in a single decay slope of $\alpha_3$ = 0.01, but the light curve still deviates significantly at later times from this slope, resulting in an unacceptable $\chi^2/\nu$ = 400/45."869 A broken power law fit to the entire late-tine Πο curve (nodel 3) reveals a break at about 2 Ms after the burst: iu contrast to the result of Capeetal.(2007).. in which we could fit the late-tine ddata with just one decay slope. the addition of the 2007 data requires a break in the ddata.," A broken power law fit to the entire late-time light curve (model 3) reveals a break at about 2 Ms after the burst; in contrast to the result of \citet{grupe07}, in which we could fit the late-time data with just one decay slope, the addition of the 2007 data requires a break in the data."870 The late decay slope. αι = 1.85. isdriven by the last two oobservations. while the \? is also strongly affected by two very ligh data points at ~2 MIs and ~5 Als. Makine the assumption that these two high points are late-time N-rav flares unrelated to the afterelow of the external shock. we removed them frou futher fits (sce models Laud 5).," The late decay slope, $\alpha_4$ = 1.85, isdriven by the last two observations, while the $\chi^2$ is also strongly affected by two very high data points at $\sim2$ Ms and $\sim5$ Ms. Making the assumption that these two high points are late-time X-ray flares unrelated to the afterglow of the external shock, we removed them from further fits (see models 4 and 5)."871" We then fit the data between LOO ks and 30 MIs with a broken power law Guodel6). obtaining a break of Diveak.3=1.01 MIs aud slopes of tlie(2132!dadete002 anda,=L61. ν"," We then fit the data between 100 ks and 30 Ms with a broken power law (model 6), obtaining a break time of $T_{\rm break,3} = 1.01^{+0.35}_{-0.22}$ Ms and slopes of $\alpha_3 = 1.32^{+0.02}_{-0.05}$ and $\alpha_4 = 1.61^{+0.10}_{-0.06}$."872αThis fit is plotted as d Jine iin m rofxravjc.., This fit is plotted as the dashed line in \\ref{xray_lc}.873 The last two oobservatious deviate from this fit. sugecsting a break at about a vear after the burst.," The last two observations deviate from this fit, suggesting a break at about a year after the burst."874 Because these last two points lave very few counts (and consequently large nucertaimtics). a broken power law fit to the late-time heht curve cannot constrain either the break time or the late-time decay slope a5 uuless at least one parameter is fixed.," Because these last two points have very few counts (and consequently large uncertainties), a broken power law fit to the late-time light curve cannot constrain either the break time or the late-time decay slope $\alpha_5$ unless at least one parameter is fixed."875 We therefore approached the question of a final break in steps., We therefore approached the question of a final break in steps.876" A suele power law fit to the lieht curve for T>1.2 Ms refle pits. model7ygivesa, = 1.68400.08 aud ὧν = 12/15."," A single power law fit to the light curve for $T \geq 1.2$ Ms \\ref{lc_fits}, model 7) gives $\alpha_4$ = 0.08 and $\chi^2/\nu$ = 12/15."877 Although this is already an acceptable fit. we investigated the possibility of a late-time break which is expected from CRB theory (c.f.ce.Zhangetal.2006for 30060).," Although this is already an acceptable fit, we investigated the possibility of a late-time break which is expected from GRB theory \citep[c.f. e.g.][]{zhang06, meszaros06}. ."878" At first we fitted the light curve 1.2 Ms xTzx 35 Ms with a single power law Guodel SN) which results in a, = 1.61IM and uvy = 6/13.", At first we fitted the light curve for $1.2$ Ms $\leq T \leq$ 35 Ms with a single power law (model 8) which results in $\alpha_4$ = $1.61^{+0.07}_{-0.13}$ and $\chi^2/\nu$ = 6/13.879 We then fitted a broken power law model to the eutire heht curve with 7> 1.2 Ms with αι fixed at 1.61 (the best-fit result when the last two oobservations are excluded: model δ in refley/ts) jtodeterminewhetherthedatarcquirea ver ylatebredk Adthetigittdonce fHe," We then fitted a broken power law model to the entire light curve with $T880>$ 1.2 Ms with $\alpha_4$ fixed at 1.61 (the best-fit result when the last two observations are excluded; model 8 in \\ref{lc_fits}) ) to determine whether the data require a very late break in the light curve slope."881gits. c inodelüygieesTisa) = 43/22. Ms and ο”.=1.65ML with 4?/»=6/11.," This fit \\ref{lc_fits}, model 9) gives $T_{\rm break,4}$ = $^{+4.2}_{-5.1}$ Ms and $\alpha_5=4.65^{+2.05}_{-1.34}$, with $\chi^2/\nu=6/14$."882 displavs the contour plot between the final break time and the final slope., \\ref{contour} displays the contour plot between the final break time and the final slope.883 It shows that they are still not swelbconstrained., It shows that they are still not well-constrained.884 Although the best-fit breax time is [1 Ms (2007 November). a break as carly as 26 Ms. with a late-time decay slope of a5 = 2.5. is consistent with the data at the lo level.," Although the best-fit break time is 41 Ms (2007 November), a break as early as $\sim 26$ Ms, with a late-time decay slope of $\alpha_5$ = 2.5, is consistent with the data at the $1 \sigma$ level."885 Iu addition to the broken power law fits with a sharp break. the late-time light. curve was also fitted by the sincothed double-broken power law model defined bx Beucrimannetal.(1999).," In addition to the broken power law fits with a sharp break, the late-time light curve was also fitted by the smoothed double-broken power law model defined by \citet{beuermann99}."886. Tere we found decay. slopes a3=Ll.20400.07. ay=1.70400.05. and 0522. 1100.26 with break times at LO9ELTL.OL As and 20 Mx (fixed).," Here we found decay slopes $\alpha_3$ 0.07, $\alpha_4$ 0.05, and $\alpha_5$ 0.26 with break times at 1.01 Ms and 20 Ms (fixed)."887 The smooth paramcter is fixed to 3.0 and 2.0 for the breaks at about 1 Ms and 20 Ms. respectively.," The smooth parameter is fixed to 3.0 and 2.0 for the breaks at about 1 Ms and 20 Ms, respectively."888 This results in an acceptable fit with 42/» = 12/32., This results in an acceptable fit with $\chi^2/\nu$ = 42/32.889 Possible interpretations of these temporal breaks are discussed iu rofdiscuss.., Possible interpretations of these temporal breaks are discussed in \\ref{discuss}.890 Temporal breaks are often associated with spectral breaks (e.g.Sarictal.1998:MészárosotZhangetal.," Temporal breaks are often associated with spectral breaks \citep[e.g. ][]{sari98, meszaros98, zhang06}."8912006)..— τοςayrprdisplagstheSwift NNReountrateandh, \\ref{lc_cr_hr} displays the XRT count rate and hardness ratio light curves for the interval between 100 ks and 5 Ms after the burst.892ardnessratiolig, The hardness ratios are plotted segment by segment.893htearces forthe itercalbet ac 0.3. after the break the spectruu hardens to IIR. ~0.15 with even larder values at later times.," While the hardness ratios before the break at 1 Ms after the burst are of order HR $\sim 0.3$ , after the break the spectrum hardens to HR $\sim 0.45$ with even harder values at later times."894 The spectrum before the 1. Ms break cau be fitted with asingle : absorbed power law with: Vy-=(31nmU.2655)«102!102 cm7 and an cucrey spectral slope 4 = L1s00.11 qev = Bl/s2)," The spectrum before the 1 Ms break can be fitted with a single absorbed power law with $N_{\rm H} = (1.34^{+0.27}_{-0.25})\times89510^{21}$ $^{-2}$ and an energy spectral slope $\beta_{\rm x}$ = 0.11 $\chi^2/\nu$ = 81/82)."896 The spectrum after the 1 Ms break was also fitted by an absorbed single power law uodel., The spectrum after the 1 Ms break was also fitted by an absorbed single power law model.897 Leaving the absorption column density as a free xwanmeter. however. results in an merease of the column deusitv. which does not secur plausible.," Leaving the absorption column density as a free parameter, however, results in an increase of the column density, which does not seem plausible."898 Therefore we fixed the absorption column deusity to Ny=131«10?! cn7. the value. obtained before the break.," Therefore we fixed the absorption column density to $N_{\rm H} = 1.34\times 10^{21}$ $^{-2}$, the value obtained before the break."899 This fit results in a slightly flatter cucrey spectral slope 3. = 8S9-EOO0.11., This fit results in a slightly flatter energy spectral slope $\beta_{\rm x}$ = 0.11.900 These values were used in PIMMS to convert he AACTS-S count rates into the fluxes eiven in retsrav oyandplottedin re feraye., These values were used in PIMMS to convert the ACIS-S count rates into the fluxes given in \\ref{xray_log} and plotted in \\ref{xray_lc}.901 The ddata μι be analyzed in the Poison Πιτ. coluplicating proper analysis of possible spectral various at vorv late times.," The data must be analyzed in the Poisson limit, complicating proper analysis of possible spectral variations at very late times."902" Usine the Bayesian approach described by Parkctal.(2006).. we estimated the harduess ratios in the aud their uncertainties. both before aud after the break at 38 Ms. We obtain mean values of 0.39 for the 2007 Marchli-June data (before the final break: 38 counts total) and 0.80 for the very late data (after the final break: δ counts total). with confidence lanits of IIR—0.60 to O17 and TR= L00to 0.58 respectively,"," Using the Bayesian approach described by \citet{park06}, we estimated the hardness ratios in the and their uncertainties, both before and after the break at 38 Ms. We obtain mean values of $-0.39$ for the 2007 March-June data (before the final break; 38 counts total) and $-0.80$ for the very late data (after the final break; 8 counts total), with confidence limits of $= -0.60$ to $-0.17$ and $= -1.00$ to $-0.58$ , respectively."903 Although this is a suggestion of spectral softening across the final break. wecannot exclude (at the sos LTbes fyestiloblity that the μανάτος» ratio is constant.," Although this is a suggestion of spectral softening across the final break, wecannot exclude (at the confidence level) the possibility that the hardness ratio is constant."904 Note that due to the different energv bands and detector response matrices it is not possible to compare the aud: hharducss ratios directly., Note that due to the different energy bands and detector response matrices it is not possible to compare the and hardness ratios directly.905 Even though GRB 0607209 was one of the brightest bursts detected in X-rays. it is uot the brightest oue so," Even though GRB 060729 was one of the brightest bursts detected in X-rays, it is not the brightest one so"906"Using the K-S test, we find the likelihoods of 1x107+ and 0.016 that the OCDFs of the simulated HVSs are the same as those from observations for the first and second population of the detect HVSs, respectively.","Using the K-S test, we find the likelihoods of $1\times 10^{-4}$ and $0.016$ that the $\Theta$ CDFs of the simulated HVSs are the same as those from observations for the first and second population of the detect HVSs, respectively."907" Therefore, we conclude that the detected HVSs are highly unlikely to be produced from the tidal breakup of isotropically distributed progenitorial binary stars."," Therefore, we conclude that the detected HVSs are highly unlikely to be produced from the tidal breakup of isotropically distributed progenitorial binary stars."908" This further strengthens the conclusion obtained in Luetal. (2010),, i.e., the detected HVSs are probably originated from two thin disks with orientations similar to the CWS disk and the northern arm of the minispiral (or the warped outer part of the CWS disk) in the GC, respectively."," This further strengthens the conclusion obtained in \citet{Luetal10}, i.e., the detected HVSs are probably originated from two thin disks with orientations similar to the CWS disk and the northern arm of the minispiral (or the warped outer part of the CWS disk) in the GC, respectively."909 Figure 13 shows the vCDFs for both the simulated HVSs (obtained from different models) and the observations., Figure \ref{fig:f13} shows the $v$ CDFs for both the simulated HVSs (obtained from different models) and the observations.910" Our numerical simulations show that the vCDF is almost independent of the thickness of the disk(s) where the HVS progenitors are originated, but it does depend on how close the stellar binaries can approach the MBH and on the initial distribution of the semimajor axes of the stellar binaries."," Our numerical simulations show that the $v$ CDF is almost independent of the thickness of the disk(s) where the HVS progenitors are originated, but it does depend on how close the stellar binaries can approach the MBH and on the initial distribution of the semimajor axes of the stellar binaries."911 Different models produce quite different vCDFs., Different models produce quite different $v$ CDFs.912" In the “LP” models and the “UB” models, for example, more than of the resulted HVSs (with v92700kms!) have velocities larger than the maximum velocity of the detected HVSs (c1000km51), while the “RW” models can produce a steep vCDF which is quite similar to the observational ones."," In the “LP” models and the “UB” models, for example, more than of the resulted HVSs (with $v^{\infty}_{\rm ej}\ga700 \kms$ ) have velocities larger than the maximum velocity of the detected HVSs $\sim1000 \kms$ ), while the “RW” models can produce a steep $v$ CDF which is quite similar to the observational ones."913" The models with log-normal distributions of ap; produce less HVSs at the high-velocity end because of the fraction of stellar binaries with small ap; (i.e., <0.3AU) is substantially smaller compared with that in those models with the Oppik law."," The models with log-normal distributions of $a_{\rm b,i}$ produce less HVSs at the high-velocity end because of the fraction of stellar binaries with small $a_{\rm b,i}$ (i.e., $\la 0.3\AU$ ) is substantially smaller compared with that in those models with the Öppik law."914" For the first HVS population, our K-S tests find 2.7x1079 (7.9x107?) and 2.5x107 (1.3x1072) likelihoods that the vCDFs obtained from the “LP-1” (“UB-1”) model and the “LP-2” (“UB-2”) model are drawn from the same distribution as the observational ones, respectively, which suggests that the first HVS population is unlikely to be produced by either of the “LP” model and the “UB” model."," For the first HVS population, our K-S tests find $2.7\times 10^{-6}$ $7.9\times 10^{-3}$ ) and $2.5\times 10^{-4}$ $1.3\times91510^{-2}$ ) likelihoods that the $v$ CDFs obtained from the “LP-1” (“UB-1”) model and the “LP-2” (“UB-2”) model are drawn from the same distribution as the observational ones, respectively, which suggests that the first HVS population is unlikely to be produced by either of the “LP” model and the “UB” model."916" For the second HVS population, the K-S likelihood is 0.01 (0.05) and 0.06 (0.07) for the “LP-1” (“UB-1”) model and the “LP- (“UB-2”) model, respectively."," For the second HVS population, the K-S likelihood is $0.01$ $0.05$ ) and $0.06$ $0.07$ ) for the “LP-1” (“UB-1”) model and the ``LP-2'' (“UB-2”) model, respectively."917" These numbers suggest that the second population is not likely to be produced by the “LP” or “UB” models with an initial ap,; distribution of 1/ay,;; but it may not be inconsistent with the “LP” (or “UB”) models with a log-normal distribution of ay, (though with limited statistics)."," These numbers suggest that the second population is not likely to be produced by the “LP” or “UB” models with an initial $a_{\rm b,i}$ distribution of $1/a_{\rm b,i}$ but it may not be inconsistent with the “LP” (or “UB”) models with a log-normal distribution of $a_{\rm b,i}$ (though with limited statistics)."918" However, the vCDFs resulted from the “RW” models appear to be consistent with the observations as the K-S tests find the likelihoods of 0.52 and 0.43 (0.52) that the observational vCDFSs of the (0.13)first (second) HVS population are the same as that obtained from the “RW-1” model and the *RW-2"" model, respectively."," However, the $v$ CDFs resulted from the “RW” models appear to be consistent with the observations as the K-S tests find the likelihoods of 0.52 (0.13) and 0.43 (0.52) that the observational $v$ CDFs of the first (second) HVS population are the same as that obtained from the “RW-1” model and the ``RW-2'' model, respectively."919 Adopting a different form of the Galactic potential may affect the estimation of the vCDF for the detected HVSs in Section 2 and the selection effects discussed in Section 4.1., Adopting a different form of the Galactic potential may affect the estimation of the $v$ CDF for the detected HVSs in Section 2 and the selection effects discussed in Section 4.1.920" For example, if adopting a simple Galactic potential model as that described by Equation (8) in Kenyonetal.(2008), the ug? of the detected HVSs ranges from 850kms! to 1200kms! and the slope of the vCDF is slightly flatter than that estimated in Section 2."," For example, if adopting a simple Galactic potential model as that described by Equation (8) in \citet{Kenyon08}, the $v^{\infty}_{\rm ej}$ of the detected HVSs ranges from $850 \kms$ to $1200 \kms$ and the slope of the $v$ CDF is slightly flatter than that estimated in Section 2."921" The simulated vCDFs from the models of “LP-1”, *LP-2"", “UB-1”, and “UB-2” are not likely to be consistent with the vCDF of the detected HVSs, while both the “RW-1” model and the “RW-2” model can produce a vCDF similar to that estimated for the detected HVSs according to the new Galactic potential."," The simulated $v$ CDFs from the models of “LP-1”, “LP-2”, “UB-1”, and “UB-2” are not likely to be consistent with the $v$ CDF of the detected HVSs, while both the “RW-1” model and the “RW-2” model can produce a $v$ CDF similar to that estimated for the detected HVSs according to the new Galactic potential."922 Our main conclusion that the TBK mechanism can reproduce the detected vCDF made in this section is not affected by the choice of the Galactic potential (also see discussion in Sesanaetal.(2007) and Kenyon (2008)))., Our main conclusion that the TBK mechanism can reproduce the detected $v$ CDF made in this section is not affected by the choice of the Galactic potential (also see discussion in \citet{Sesana07} and \citet{Kenyon08}) ).923" 'To close this section, we note here that the fraction of stellar binaries resulting in ejection of HVSs with properties similar to the detected ones is around"," To close this section, we note here that the fraction of stellar binaries resulting in ejection of HVSs with properties similar to the detected ones is around"924a inagnetar progenitor. and hiehlights a discrepancy vetween the presence of RSCs in Wel aud the predictions of evolutionary models. which sugecst that tle most uunous RSCGs should evolve from siguificautlv lower isses.,"a magnetar progenitor, and highlights a discrepancy between the presence of RSGs in Wd1 and the predictions of evolutionary models, which suggest that the most luminous RSGs should evolve from significantly lower masses."925 A first study of the binary fraction aunongst owoer-Iqnuinositvy ate-O II-III stars dno Wdl will be oreseuted. di ao subsequent paper iu this seres. but uaznyv binary svstenis are already available for follow-up study.," A first study of the binary fraction amongst lower-luminosity late-O II-III stars in Wd1 will be presented in a subsequent paper in this series, but many binary systems are already available for follow-up study."926 These include short-period spectroscopic biuariesE32...W23003:: Paper D. eclipsing binaries within the WR. OD supereiant and main sequence populations (Bonanos2007).. and N-rav. aud racdio-selected collidius-wind binaries (Clarketal.2008:Dougherty2010).," These include short-period spectroscopic binaries,; Paper I), eclipsing binaries within the WR, OB supergiant and main sequence populations \citep{bonanos}, and X-ray and radio-selected colliding-wind binaries \citep{clark08, dougherty}."927. Consideration of these data will allow further dvuamiucal constraints to be placed ou the progenitor masses of the evolved stars within Wdl as well as the general mass i1uninositv relation for stars in the upper reaches of the IIR diagram ae the post-MS patlisvavs they follow., Consideration of these data will allow further dynamical constraints to be placed on the progenitor masses of the evolved stars within Wd1 as well as the general mass luminosity relation for stars in the upper reaches of the HR diagram and the post-MS pathways they follow.928" Moreover. hey will vield the first characterisation of the binary xoperties of a homogeneous population of massive stars. of critical importance for studies of both star aud cluster ornation and miuuerous hieh-energy phenomena such as ""üupernovae. enmlla-rav bursters and the formation of ugh mass X-ray binaries."," Moreover, they will yield the first characterisation of the binary properties of a homogeneous population of massive stars, of critical importance for studies of both star and cluster formation and numerous high-energy phenomena such as supernovae, Gamma-ray bursters and the formation of high mass X-ray binaries."929where Tarsens (Teen) Is the true optical depth of the strong (weak) component. 71. 7» are the observed (apparent) optical depths and ἐν. {ο are the observed residual intensitics (normalized. by the local continuum. lu) al the same velocity for the strong and weak component of the doublet. respectively.,"where $\tau_{\rm strong}$ $\tau_{\rm weak}$ ) is the true optical depth of the strong (weak) component, $\tau_1$, $\tau_2$ are the observed (apparent) optical depths and $I_1$, $I_2$ are the observed residual intensities (normalized by the local continuum, $I_0$ ) at the same velocity for the strong and weak component of the doublet, respectively."930 If the lines are optically thin. then from these exact expressions the relation can be obtained which relates the covering factor to the observed residual intensities (Llamann Ferlanc 1999).," If the lines are optically thin, then from these exact expressions the relation can be obtained which relates the covering factor to the observed residual intensities (Hamann Ferland 1999)."931 1n what follows we shall use the label # to indicate a covering factor value obtained by means ofintensities., In what follows we shall use the label $R$ to indicate a covering factor value obtained by means of.932 All lines lor which an adjustment of the zero levelhas been performed with acre listecl in ‘Table 1..., All lines for which an adjustment of the zero levelhas been performed with are listed in Table \ref{tab:adj}.933 The Zero level adjustment. determined withVPELIT.. as a fraction of the continuum is eiven in column 7 and its le error in column 8.," The zero level adjustment, determined with, as a fraction of the continuum is given in column 7 and its $1\sigma$ error in column 8."934 The covering actor determined. from.4... {μι for these lines is given in column 9 of the Table.," The covering factor determined from, $f_R$, for these lines is given in column 9 of the Table."935 In principle. since the zero evel adjustment is introduced to compensate for an excess continuum Hux. the value for this adjustment should be in agreement with 1fn.," In principle, since the zero level adjustment is introduced to compensate for an excess continuum flux, the value for this adjustment should be in agreement with $1-f_R$."936 Ehe last column in Table 1 shows he value of 1fe For all entries. fj. in column 9.," The last column in Table \ref{tab:adj} shows the value of $1-f_R$ for all entries, $f_R$, in column 9."937 In other words. the last column can be thought of as giving an aadjustment based. on the residual. intensities.," In other words, the last column can be thought of as giving an adjustment based on the residual intensities."938 In one hen compares corresponding entries in columns 7 (actual adjustment used) and 10 (expected adjustment from residual intensities). one may notice that these agree to within leo for line 17. to within zle for lines 1. 4 and 15. and to within 20 or more for the rest of the lines.," If one then compares corresponding entries in columns 7 (actual adjustment used) and 10 (expected adjustment from residual intensities), one may notice that these agree to within $1\sigma$ for line 17, to within $\approxgt 1\sigma$ for lines 1, 4 and 15, and to within $2\sigma$ or more for the rest of the lines."939 We call this an It-tvpe comparison (see below) anc we shall return to this point later., We call this an R-type comparison (see below) and we shall return to this point later.940 Further. from Equations 2. and 3.2 it is clear that the ratio of the observed optical depths. 7;/7». depends both on f and on the true optical depth for cach component. and thus. for given b. on the column density.," Further, from Equations \ref{equ:et1} and \ref{equ:et2} it is clear that the ratio of the observed optical depths, $\tau_1/\tau_2$, depends both on $f$ and on the true optical depth for each component, and thus, for given $b$, on the column density."941 This.fheorcticad result is illustrated in for a line with b=10 aand clilferent values of the column density and covering factor., This result is illustrated in for a line with $b=10$ and different values of the column density and covering factor.942 lt can be seen hat for low column densities and/or high covering factors. this ratio is close tο 2.," It can be seen that for low column densities and/or high covering factors, this ratio is close to 2."943 This corresponds to the case where an ADR. is not οservable., This corresponds to the case where an ADR is not observable.944 Llowever. for given f and b there is a threshold in column density. above which the ratio will deviate significantly from 2 and. depending on the SNR in the region of the line. it will not be possible to fit the line with a model Voigt profile (which assumes a ratio of 2) without obtaining large resicluals.," However, for given $f$ and $b$ there is a threshold in column density, above which the ratio will deviate significantly from 2 and, depending on the SNR in the region of the line, it will not be possible to fit the line with a model Voigt profile (which assumes a ratio of 2) without obtaining large residuals."945 This elect is seen in1: relative to 75. τι is less than what eexpects and. hence. the fit appears markedly below the 1548 Iline ancl above the 1550 Iline.," This effect is seen in: relative to $\tau_2$, $\tau_1$ is less than what expects and, hence, the fit appears markedly below the 1548 line and above the 1550 line."946 This discrepancy is due to excess flux. getting. through atthe velocity where a particular doublet: is observed., This discrepancy is due to excess flux getting through atthe velocity where a particular doublet is observed.947 Lf the truce optical depth and the covering factor are known. the observed. continuum normalized. intensity is given by Equations 2. or 9 3..," If the true optical depth and the covering factor are known, the observed, continuum normalized intensity is given by Equations \ref{equ:et1} or \ref{equ:et2}. ."948 Thus. although the continuum," Thus, although the continuum"9491984).. but. no previous X-ray spectral or timing analvsis studies have been carried out for it.,", but no previous X-ray spectral or timing analysis studies have been carried out for it."950 In. order to ensure that these objects are not. intermediate: polars (APs) and to look for orbital ancl spin modulation in the data. the power spectra were calculated by using a Lomb- periodogram which is used for period analvsis of unevenly spaced data.," In order to ensure that these objects are not intermediate polars (IPs) and to look for orbital and spin modulation in the data, the power spectra were calculated by using a Lomb-Scargle periodogram which is used for period analysis of unevenly spaced data."951 When searching over the [requeney range 0.00001.0.03 Lz. no significant periodicities were seen at the 99 per cent confidence level.," When searching over the frequency range 0.00001–0.03 Hz, no significant periodicities were seen at the 99 per cent confidence level."952 We carried out X-ray spectral analysis in order to study the underlsing spectra of the source sample. ancl. ultimately. to caleulate the I[uxes and luminosities of the sources.," We carried out X-ray spectral analysis in order to study the underlying spectra of the source sample, and, ultimately, to calculate the fluxes and luminosities of the sources."953 To employ. Gaussian statistics. the N-ray spectra were binned al 20 ct  with and then fitted in1996).," To employ Gaussian statistics, the X-ray spectra were binned at 20 ct $^{-1}$ with and then fitted in."954. In CVs. the power source of X-ray. emission is known to be accretion onto the white dwarl.," In CVs, the power source of X-ray emission is known to be accretion onto the white dwarf."955 Phe accreted material is shock-heated to high temperatures (ρω 10502003). and this material has to cool before settling onto the white cwarl surface.," The accreted material is shock-heated to high temperatures $\sim$ 10–50, and this material has to cool before settling onto the white dwarf surface."956" Thus. the cooling gas [low is assumed to consist of a range of temperatures which vary from the hot shock temperature 75,4 to the empoerature of the optically thin cooling material which eventually settles onto the surface. of the white cwarl1997)."," Thus, the cooling gas flow is assumed to consist of a range of temperatures which vary from the hot shock temperature $kT_{max}$ to the temperature of the optically thin cooling material which eventually settles onto the surface of the white dwarf."957. Thus. when fitting X-ray spectra of CVs. cooling How spectral models should. represent more ohvsically correct. picture of the cooling plasma. unlike single temperature. spectral models.," Thus, when fitting X-ray spectra of CVs, cooling flow spectral models should represent more physically correct picture of the cooling plasma, unlike single temperature spectral models."958 Cooling Low naiocdels rave successfully been applied. to CV spectra in. previous studies by c.g. and., Cooling flow models have successfully been applied to CV spectra in previous studies by e.g. and.959(2003).. In this view. the multi-temperature characteristic is our motivation for emphasizing the cooling Low mocel in the rest of this work.," In this view, the multi-temperature characteristic is our motivation for emphasizing the cooling flow model in the rest of this work."960" The cdillerential emission measure GEMAE for an isobaric cooling How can be described. by where nm, is the mass of a proton. ji the mean molecular weight (~ 0.6). οςια) total emissivitv per volume in units oberg tem 7. M accretion rate. p. particle density. and & the Boltzmann constant."," The differential emission measure dEM/dT for an isobaric cooling flow can be described by where $m_{p}$ is the mass of a proton, $\mu$ the mean molecular weight $\sim$ 0.6), $\epsilon$ (T,n) total emissivity per volume in units of erg $^{-1}$ $^{-3}$, $\dot{M}$ accretion rate, $n$ particle density, and $k$ the Boltzmann constant."961 The source of the N-rav. emission above the white dwarf illuminates the surface of the white dwarf and thus causes a reflection. which is seen as Fe hea iron Illuorescence line at 6.4 keV 1901).," The source of the X-ray emission above the white dwarf illuminates the surface of the white dwarf and thus causes a reflection, which is seen as Fe $\alpha$ iron fluorescence line at 6.4 keV ."962. According to George Fabian. an infinite slab reflector subtencding a total solid angle of$2 = 2: where the X-ray source is located right above the slab. produces an equivalent width of up to  150 eV for the 6.4 keV. Fe Ίνα fluorescence line.," According to George Fabian, an infinite slab reflector subtending a total solid angle of $\Omega$ = $\pi$ where the X-ray source is located right above the slab, produces an equivalent width of up to $\sim$ 150 eV for the 6.4 keV Fe $\alpha$ fluorescence line."963 Ehe equivalent width of the 6.4 keV. iron line depends on the total abundance of the reflector1997).. the inclination angle between the surface of the rellector and the observer's line of sight. and the photon index of the spectrum of the X-ray emission source2009).," The equivalent width of the 6.4 keV iron line depends on the total abundance of the reflector, the inclination angle between the surface of the reflector and the observer's line of sight, and the photon index of the spectrum of the X-ray emission source."964. Even though we believe that the cooling How -tvpe multi-temperature model is the correct. description of the ηνμον of the cooling gas How in CVs. previous works have often used single temperature plasma moclels.," Even though we believe that the cooling flow -type multi-temperature model is the correct description of the physics of the cooling gas flow in CVs, previous works have often used single temperature plasma models."965 Για». in order o compare the cllects of two cillerent spectral models on he spectral fit parameters. we fitted the spectra with 1) a single temperature optically thin thermal plasma moclel and 2) a cooling Low model (mkcflow)) whichJmews6. was originally. developed to cdeseribe the cooling flows in clusters of galaxies1988).. adding photoclectric absorption to both models.," Thus, in order to compare the effects of two different spectral models on the spectral fit parameters, we fitted the spectra with 1) a single temperature optically thin thermal plasma model and 2) a cooling flow model ) which was originally developed to describe the cooling flows in clusters of galaxies, adding photoelectric absorption to both models."966 In order to investigate the equivalent. width of the 6.4 keV iron emission line. à Gaussian line was added. at 6.4 keV with a line width fixed at σξ 10 eV. The spectral fits did not necessarily require the 6.4 keV line. e.g. for SS Aur the ον = 0.96/629 when a Gaussian line at 6.4 keV. was not included.," In order to investigate the equivalent width of the 6.4 keV iron emission line, a Gaussian line was added at 6.4 keV with a line width fixed at $\sigma$ = 10 eV. The spectral fits did not necessarily require the 6.4 keV line, e.g., for SS Aur the $\chi^{2}_{\nu}$ $\nu$ = 0.96/629 when a Gaussian line at 6.4 keV was not included."967 TheSusaku NIST and Χο. spectra were fitted simultaneously for each source as well as the GIS and SES spectra of Z Cam and. WZ See with the models mentioned above.," The XIS1 and XIS0,2,3 spectra were fitted simultaneously for each source as well as the GIS and SIS spectra of Z Cam and WZ Sge with the models mentioned above."968 Some cata sets required additional components to improve the fits., Some data sets required additional components to improve the fits.969 Three of the sources. IUE Cas. VS93 Seo and Z Cam. required. partial covering absorption model.pcfabs.. to reduce residuals in the [ow energv end (between ~ 0.62 keV).," Three of the sources, HT Cas, V893 Sco and Z Cam, required partial covering absorption model, to reduce residuals in the low energy end (between $\sim$ 0.6–2 keV)."970 To reduce. residuals around 0.80. keV. in the SS Cvg spectrum. we added. a Gaussian line at 0:51 keV. with a line width of 0.24 keV letting the line energv and. width. both to vary free.," To reduce residuals around 0.80 keV in the SS Cyg spectrum, we added a Gaussian line at 0.81 keV with a line width of 0.24 keV letting the line energy and width both to vary free."971 For U Gom. single absorbed: optically thin. thermal plasma model vielded a 7/79 = 2.23/403.," For U Gem, single absorbed optically thin thermal plasma model yielded a $\chi^{2}$ $\nu$ = 2.23/403."972 Since thefit was not statistically satisfactory. we added a second. optically thin," Since thefit was not statistically satisfactory, we added a second optically thin"973which we actually use for computationalefficiency?.,which we actually use for computational.974". Finally, to complete the full specification of our chemical model, we need to estimate the column density of the molecular gas, Ny,, for the self-shielding factor given by Equation (ATi)."," Finally, to complete the full specification of our chemical model, we need to estimate the column density of the molecular gas, $N_\H2$, for the self-shielding factor given by Equation \ref{eq:sh2}) )."975" Unfortunately, we cannot simply use the Sobolev approximation to derive Ny, similar to the column density of dust in Equation (A9)), because H» absorption is concentrated in separate absorption lines and is sensitive to the internal velocity dispersion inside molecular clouds."," Unfortunately, we cannot simply use the Sobolev approximation to derive $N_\H2$ similar to the column density of dust in Equation \ref{eq:sd}) ), because $\H2$ absorption is concentrated in separate absorption lines and is sensitive to the internal velocity dispersion inside molecular clouds."976" These velocities are unresolved in our simulations, but can greatly reduce the self-shielding of molecular gas."," These velocities are unresolved in our simulations, but can greatly reduce the self-shielding of molecular gas."977" Dust, on the other hand, absorbs UV radiation in continuum and is thus not affected by velocity distribution of the gas."," Dust, on the other hand, absorbs UV radiation in continuum and is thus not affected by velocity distribution of the gas."978" Therefore, we introduce the following simple ansatz for the effective column density Ny, for Equation (ATI), where L, is the velocity coherence length of the molecular hydrogen inside molecular clouds."," Therefore, we introduce the following simple ansatz for the effective column density $N_\H2$ for Equation \ref{eq:sh2}) ), where $L_c$ is the velocity coherence length of the molecular hydrogen inside molecular clouds."979" Since we cannot deduce this quantity from observations or other calculations, we treat it as another parameter of our model."," Since we cannot deduce this quantity from observations or other calculations, we treat it as another parameter of our model."980" With the expressions for the shielding factors above, the only two parameters of our model are C, and L,."," With the expressions for the shielding factors above, the only two parameters of our model are $C_\rho$ and $L_c$."981 These parameters can only be determined by comparing the simulation results to the observational data., These parameters can only be determined by comparing the simulation results to the observational data.982" As the primary data sets used to calibrate the model, we use the measurements of atomic and molecular gas surface densities in nearby spirals from and measurements of gas fractions along the lines of sight to individual stars for atomic and molecular gas in the Milky Way and Magellanic Clouds(???)."," As the primary data sets used to calibrate the model, we use the measurements of atomic and molecular gas surface densities in nearby spirals from and measurements of gas fractions along the lines of sight to individual stars for atomic and molecular gas in the Milky Way and Magellanic Clouds."983. We calibrate the two parameters of the model: the clumping factor and the molecular coherence length L.., We calibrate the two parameters of the model: the clumping factor $C_\rho$ and the molecular coherence length $L_c$.984" We find, however, that there is no unique best-fit set of parameters."," We find, however, that there is no unique best-fit set of parameters."985" Instead, any combinationC, of these two parameters that satisfy the constraint provides an acceptable fit to the observational constraints."," Instead, any combination of these two parameters that satisfy the constraint provides an acceptable fit to the observational constraints."986" As an example, we show on the left panel of Figure[AT]] fits to the measurements (averaged over all galaxies they observed) for three combinations of the parameters L, and C,."," As an example, we show on the left panel of Figure \ref{fig:asjust} fits to the measurements (averaged over all galaxies they observed) for three combinations of the parameters $L_c$ and $C_\rho$."987" In general, higher clumping factors result in the lower atomic contents at high surface densities, but the trend is too weak to be of any statistically significant constraining power."," In general, higher clumping factors result in the lower atomic contents at high surface densities, but the trend is too weak to be of any statistically significant constraining power."988" As a fiducial set of parameters we choose the combination L,=0.3pc and C,=30.", As a fiducial set of parameters we choose the combination $L_c=0.3\dim{pc}$ and $C_\rho=30$.989" This choice provides a marginally better overall fit to the observations, and is also consistent with estimates of the gas clumping factor deep inside molecular clouds(?)."," This choice provides a marginally better overall fit to the observations, and is also consistent with estimates of the gas clumping factor deep inside molecular clouds."990". The fiducial value of C, is somewhat larger than the estimates of the clumping factor from numerical simulations of turbulent molecular clouds, C,=eo, where σἹηρ31—1.5 is the dispersion of the lognormal density distribution inside the clouds."," The fiducial value of $C_\rho$ is somewhat larger than the estimates of the clumping factor from numerical simulations of turbulent molecular clouds, $C_\rho = e^{\sigma_{\ln\rho}^2}$, where $\sigma_{\ln\rho}\approx 1 - 1.5$ is the dispersion of the lognormal density distribution inside the clouds."991" However, the value of C,=10, which was used in and is more consistent with the numerical simulations of turbulent molecular clouds would provide an almost equally good to the existing observations, if it is used with L,~1pc."," However, the value of $C_\rho=10$, which was used in and is more consistent with the numerical simulations of turbulent molecular clouds would provide an almost equally good to the existing observations, if it is used with $L_c\approx1\dim{pc}$."992" Any sub-cell model would be of limited value, if it was only applicable to a narrow range of numerical resolutions."," Any sub-cell model would be of limited value, if it was only applicable to a narrow range of numerical resolutions."993" In order to test the range of spatial resolutions over which our model performs robustly, we have re-run a subset of our test simulations,"," In order to test the range of spatial resolutions over which our model performs robustly, we have re-run a subset of our test simulations,"994We uote that dynamical [friction still operates in circtumstauces where mass accretion is [rustratecd.,We note that dynamical friction still operates in circumstances where mass accretion is frustrated.995 For example. a wind-emitting star moving through a eas cloud experiences mass loss rather than ass gain.," For example, a wind-emitting star moving through a gas cloud experiences mass loss rather than mass gain."996 Cloud gas inpacting the wind upstream is arrested or refracted in a bowshock. as analytically calculated by Wilkin(1996).," Cloud gas impacting the wind upstream is arrested or refracted in a bowshock, as analytically calculated by \citet{w96}."997. Downstream. the wind forms a supersonic jet.," Downstream, the wind forms a supersonic jet."998" As long as the upstream staudolL radius of the shock lies within r, aud the dowustreanr jet is relatively uarrow. the [ar-fielcl perturbatious are close to what we have obtained. aud equation (66)) lor F still applies."," As long as the upstream standoff radius of the shock lies within $r_s$ and the downstream jet is relatively narrow, the far-field perturbations are close to what we have obtained, and equation \ref{eqn:bondifric}) ) for $F$ still applies."999 When the object is actually able to accept eas freely. dynamical friction arises in two pliysically distinct ways.," When the object is actually able to accept gas freely, dynamical friction arises in two physically distinct ways."1000 First. there is the gravitational tug from the wake.," First, there is the gravitational tug from the wake."1001 Secoucl. momenttun is transferre directly to the object by gas falling onto it.," Second, momentum is transferred directly to the object by gas falling onto it."1002 Our findiug that these two forces sum to AZV is at least roughly consistent with simulations.," Our finding that these two forces sum to ${\dot M}\,V$ is at least roughly consistent with simulations."1003 In a numerical study directed primarily at the mass accretion issue. Rullert(1996) explicitly determined both force coutributious ou accretors of various size inary gas.," In a numerical study directed primarily at the mass accretion issue, \citet{r96} explicitly determined both force contributions on accretors of various size in a gas."1004 For aud0.6.. the sitmulation ended before the flow reache steady-state (see his Fig.," For and, the simulation ended before the flow reached steady-state (see his Fig."1005 2)., 2).1006 After initial transients clied out. the gravitational drag was steady unti fe13PFpg. where the Bondi-Hoyle time /pj is races.," After initial transients died out, the gravitational drag was steady until $t\approx 13\ t_{\rm BH}$, where the Bondi-Hoyle time $t_{\rm BH}$ is $r_{\rm acc}/c_{\rm s}$."1007 Therealter. this force component declined for the rest of the integration.," Thereafter, this force component declined for the rest of the integration."1008 At the end of the simulation =32 μι). the sum of the eravitationa t," At the end of the simulation $t = 32\ t_{\rm BH}$ ), the sum of the gravitational drag and momentum accretion forces was $1.2\ {\dot M}\,V$."1009he two forces quickly leveled off. with a sum equal to 1.137V.," For and the same Mach number, the two forces quickly leveled off, with a sum equal to $1.4\ {\dot M}\,V$."1010 However. this simulation rau ouly until /=LO/py. so it is not clear whether the gravitational drag would Lave later declined. as iu the first case.," However, this simulation ran only until $t = 10\ t_{\rm BH}$, so it is not clear whether the gravitational drag would have later declined, as in the first case."1011 Following historical precedeut. we lave restricted our investigation to an isothermal gas.," Following historical precedent, we have restricted our investigation to an isothermal gas."1012 For an isentropic gas with 5>l. it seems likely that the friction force will still be given by AZV. as loug as the aceretor is moving subsonically.," For an isentropic gas with $\gamma > 1$, it seems likely that the friction force will still be given by $\dot{M}\, V$, as long as the accretor is moving subsonically."1013 Verifving this equality analytically would require a perturbation study analogous to the present one., Verifying this equality analytically would require a perturbation study analogous to the present one.1014 We leave such a project for future investigators., We leave such a project for future investigators.1015 Again the current body of numerical studies is in broad accord with our expectation., Again the current body of numerical studies is in broad accord with our expectation.1016 determined the total friction force on an accretor moving through a 5=5/3 gas., \citet{r94} determined the total friction force on an accretor moving through a $\gamma=5/3$ gas.1017 For and 3=0.6. the friction force was 1.1AV at |=70fq.," For and $\beta=0.6$, the friction force was $1.1\ \dot{M}\, V$ at $t=70\ t_{\rm BH}$."1018 For and the same Mach nuuber. the flow liad not achieved steady state by /=19fpy.," For and the same Mach number, the flow had not achieved steady state by $t=19\ t_{\rm BH}$."1019 The total force was 1.8MV. atthis time. but was falling rapidly.," The total force was $1.8\ \dot{M}\, V$ atthis time, but was falling rapidly."1020 A future project of interest would be to redo these M.imulations over a range of 5- aud 5-values. running the simlations long enough until a true steady state is reached.," A future project of interest would be to redo these simulations over a range of $\beta$ - and $\gamma$ -values, running the simulations long enough until a true steady state is reached."1021 For the more general isentropic case. AZ cau uo longer be approximated by equation (52)).," For the more general isentropic case, $\dot{M}$ can no longer be approximated by equation \ref{eqn:intermdot}) )."1022 Iustead the value of M at a given V. decreases with higher 5-values. as shown aualytically by [or V=0. aud as seen in the simulations of Bullert(199[.1995.1996) [or accretors moving relative to the background gas.," Instead the value of $\dot{M}$ at a given $V$ decreases with higher $\gamma$ -values, as shown analytically by \citet{b52} for $V=0$, and as seen in the simulations of \citet{r94,r95,r96} for accretors moving relative to the background gas."1023 Isentropie [lows are less compressible than isothermal ones. so the wake will be less cdeuse.," Isentropic flows are less compressible than isothermal ones, so the wake will be less dense."1024 As a result. the friction force will also be lower. presumably by tle same amount as the accretion rate AL.," As a result, the friction force will also be lower, presumably by the same amount as the accretion rate $\dot{M}$ ."1025 Iu the present investigation. we have been unable to tease apart analytically the two force," In the present investigation, we have been unable to tease apart analytically the two force"1026he mereecdl product is a MS star with the stellar material completely mixed aud (b) uo mass is lost rou the system during the mereer process.,the merged product is a MS star with the stellar material completely mixed and (b) no mass is lost from the system during the merger process.1027 The no mass-loss assumptiou is based on the results ol SPH stimulations of MS-MS mereers(e.g... Sillsetal.2001)) but such calculations vield ouly a united amount of mixiug.," The no mass-loss assumption is based on the results of SPH simulations of MS-MS mergers, \citealt{sil2001}) ) but such calculations yield only a limited amount of mixing."1028 The rejuvenated age of the mereecd MS star is determiued clepeuding ou the amount of unburut hydrogen fuel gained by the hydrogen-burniug core as a result of the uixiug., The rejuvenated age of the merged MS star is determined depending on the amount of unburnt hydrogen fuel gained by the hydrogen-burning core as a result of the mixing.1029 Iun. case of a mass trausler across a MS-MS binary. clistinetion is mace between the cases when the original accretor MS star las a radiative or a couvective core.," In case of a mass transfer across a MS-MS binary, distinction is made between the cases when the original accretor MS star has a radiative or a convective core."1030 For a convective core. the core grows with the eain of mass and mixes with the uuburut bydrogen fuel so that the accreting MS star appears vounger.," For a convective core, the core grows with the gain of mass and mixes with the unburnt hydrogen fuel so that the accreting MS star appears younger."1031 For the case of a radiative core. the [Traction of the hydrogen burut in the hydrogeun-buruing core remains nearly unallectecl by the gain of mass so that the ellective age ol the MS star decreases.," For the case of a radiative core, the fraction of the hydrogen burnt in the hydrogen-burning core remains nearly unaffected by the gain of mass so that the effective age of the MS star decreases."1032 The ellective age is cleterminecl so as to keep the elapsed fraction of its MS lifetime unchauged., The effective age is determined so as to keep the elapsed fraction of its MS lifetime unchanged.1033 The initial cluster mass of A4(0)zzLO?AL. in our models correspouds to :N(0)=170667 stars., The initial cluster mass of $M_{cl}(0) \approx 10^5\Ms$ in our models corresponds to $N(0) = 170667$ stars.1034 To our knowledge. direct N-body computations with such a large μιαος of stars. where the clusters are fully inass-segregated aud all the massive stars are in binaries. are beiug reported [or the first time.," To our knowledge, direct N-body computations with such a large number of stars, where the clusters are fully mass-segregated and all the massive stars are in binaries, are being reported for the first time."1035 We evolve f initial models with the above NV(Q). generated using different raucom uumber seeds. until zz3 Myr.," We evolve 4 initial models with the above $N(0)$, generated using different random number seeds, until $\approx 3$ Myr."1036 We take this age as au upper limit of the age of R136 (Crowther 2010)..," We take this age as an upper limit of the age of R136 \citep{crw2010,pz2010}."1037" We do all the computations on “NVIDIA [80 GTX"" GPU platforms.", We do all the computations on “NVIDIA 480 GTX” GPU platforms.1038 From the above computations. we trace the bodies that are ejected from the clusters curing their evolution (within z3 Myr).," From the above computations, we trace the bodies that are ejected from the clusters during their evolution (within $\approx 3$ Myr)."1039 We consider a single-star/binary/imultiplet to be a runaway member [rom its host cluster if it is found moving away from the cluster beyoud R>10 pe distance from the cluster's center of density., We consider a single-star/binary/multiplet to be a runaway member from its host cluster if it is found moving away from the cluster beyond $R>10$ pc distance from the cluster's center of density.1040 Although our primary focus is on the runaway VMS5s. we consider the whole mass spectrum of ejected stars as well.," Although our primary focus is on the runaway VMSs, we consider the whole mass spectrum of ejected stars as well."1041 Fig., Fig.1042 2 shows the projected suapshots of the ruuaways with inasses AL>38M... combined from the 1 computatious. at /—1 Myr and 3 Myr evolutionary times.," \ref{fig:ejsnap} shows the projected snapshots of the runaways with masses $M>3\Ms$, combined from the 4 computations, at $t=1$ Myr and 3 Myr evolutionary times."1043 It cau be seen that by /23 Myr there are a siguificant. uumber of fast runaway VMSs with total (3-dimeusional) velocities upto se300 kins  anc a lew fast VMSs are already present at /—1 Myr., It can be seen that by $t=3$ Myr there are a significant number of fast runaway VMSs with total (3-dimensional) velocities upto $\approx 300$ km $^{-1}$ and a few fast VMSs are already present at $t=1$ Myr.1044 All these runaways are on their MSs aud heuce are OB stars., All these runaways are on their MSs and hence are OB stars.1045 We note that the vast majority of the massive ejected members are sinele stars — only 2 of the massive ejecta [rom our computations are found in hard binaries., We note that the vast majority of the massive ejected members are single stars — only 2 of the massive ejecta from our computations are found in hard binaries.1046 We shall discuss the multiplicity properties of the ejected stellar population iu detail in a future paper., We shall discuss the multiplicity properties of the ejected stellar population in detail in a future paper.1047" It. is worthwhile to note that although our adapted canonical IME has a 19041, upper limit. our models vield single-star runaways with masses upto zz220M... within /«3 Myr. cousicerably"," It is worthwhile to note that although our adapted canonical IMF has a $150\Ms$ upper limit, our models yield single-star runaways with masses upto $\approx 250\Ms$ within $t<3$ Myr, considerably"1048"thin disc by 30—70 km s! (Gilmore, Wyse Norris 2002), with Viag=50 km s! usually taken as a canonical value (see also Vallenari et al.","thin disc by $30-70$ km $^{-1}$ (Gilmore, Wyse Norris 2002), with $V_{\rm1049 lag}=50$ km $^{-1}$ usually taken as a canonical value (see also Vallenari et al."1050 2006)., 2006).1051" On the other hand, in external galaxies the difference in rotation velocity of thin and thick discs appears to be diverse and strongly dependent on galaxy mass, with lower mass galaxies having larger differences between thin and thick velocities (Yoachim Dalcanton 2008)."," On the other hand, in external galaxies the difference in rotation velocity of thin and thick discs appears to be diverse and strongly dependent on galaxy mass, with lower mass galaxies having larger differences between thin and thick velocities (Yoachim Dalcanton 2008)."1052" In terms of velocity dispersions, our results are in relatively good agreement with the observations of the Milky Way."," In terms of velocity dispersions, our results are in relatively good agreement with the observations of the Milky Way."1053 Vallenari et al. (, Vallenari et al. (10542006) estimated the velocity dispersion ellipsoid of the thin and thick discs of our Galaxy.,2006) estimated the velocity dispersion ellipsoid of the thin and thick discs of our Galaxy.1055" Their results for the thick disc are: (σ-,σφ,σε)~(74+11,507,38X7T) km s! at the solar radius."," Their results for the thick disc are: $(\sigma_r, \sigma_\phi, \sigma_z) \sim (74\pm 11, 50\pm 7, 38\pm 7)$ km $^{-1}$ at the solar radius."1056" For the thin disc, they estimate the velocity ellipsoid dividing stars into four stellar age bins, finding (07,04,02)~(25—34,2032,1018)kms! (with errors < 15%)."," For the thin disc, they estimate the velocity ellipsoid dividing stars into four stellar age bins, finding $(\sigma_r, \sigma_\phi, \sigma_z) \sim (25-34, 20-32, 10-18)\,{\rm1057 km\, s}^{-1}$ (with errors $\lesssim 15\%$ )."1058" As described above, the eight simulated galaxies are diverse and show a wide range in velocity dispersions that agree relatively well with these results (although we note that simulated galaxies are not expected to resemble the Milky Way in detail)."," As described above, the eight simulated galaxies are diverse and show a wide range in velocity dispersions that agree relatively well with these results (although we note that simulated galaxies are not expected to resemble the Milky Way in detail)."1059" Finally, we note that the velocity structure of the simulated stellar components is complex, in general having important asymmetries."," Finally, we note that the velocity structure of the simulated stellar components is complex, in general having important asymmetries."1060 Fig., Fig.1061 9 shows 2D face-on maps of tangential velocity for theeight simulations (including both disc and spheroid stars) within the inner 30 kpc., \ref{vtita_maps_stars} shows 2D face-on maps of tangential velocity for theeight simulations (including both disc and spheroid stars) within the inner $30$ kpc.1062" From these plots we can read off the velocity structure of simulated galaxies, the sizes of bulges and discs, and we can also observe bar patterns, particularly in Aq-C-5, Aq-E-5 and Aq-G-5 (see also the next section)."," From these plots we can read off the velocity structure of simulated galaxies, the sizes of bulges and discs, and we can also observe bar patterns, particularly in Aq-C-5, Aq-E-5 and Aq-G-5 (see also the next section)."1063" Aq-A-5, Aq-C-5, Aq-D-5 and Aq-E-5 have the largest tangential velocities, as expected since these are the most massive galaxies and therefore have higher circular velocities."," Aq-A-5, Aq-C-5, Aq-D-5 and Aq-E-5 have the largest tangential velocities, as expected since these are the most massive galaxies and therefore have higher circular velocities."1064" In the case of the disc starts to dominate at a relatively large radius, showing a ring-like structure."," In the case of the disc starts to dominate at a relatively large radius, showing a ring-like structure."1065" As we discuss below, the absence of a disc in Aq-F-5 is evident from this figure, and also the small disc component of Aq-H-5."," As we discuss below, the absence of a disc in Aq-F-5 is evident from this figure, and also the small disc component of Aq-H-5."1066 We find that the dynamical structure of discs found for our simulations is also present in the lower resolution runs., We find that the dynamical structure of discs found for our simulations is also present in the lower resolution runs.1067" In all cases, the older stars define thicker discs compared to the younger populations."," In all cases, the older stars define thicker discs compared to the younger populations."1068" In particular, Aq-E-5 and Aq-E-6b show very good agreement, as shown in Fig. 10.."," In particular, Aq-E-5 and Aq-E-6b show very good agreement, as shown in Fig. \ref{disk_dynamics_resolution}."1069" In this case, differences in tangential velocities and velocity dispersions are always lower than 5%."," In this case, differences in tangential velocities and velocity dispersions are always lower than $5\%$."1070" For the youngest stars (left-hand panel), tangential velocities are lower for Aq-E-6b than for Aq-E-5."," For the youngest stars (left-hand panel), tangential velocities are lower for Aq-E-6b than for Aq-E-5."1071" Velocity dispersion are, regardless of stellar age, larger for the lower resolution run."," Velocity dispersion are, regardless of stellar age, larger for the lower resolution run."1072 We detect more significant differences for Aq-C-6 and AqE-6 with respect to Aq-C-5 and Aq-E-5 respectively., We detect more significant differences for Aq-C-6 and Aq-E-6 with respect to Aq-C-5 and Aq-E-5 respectively.1073" In these cases, the tangential velocities are typically 15% lower in the low resolution runs, while velocity dispersions are ~50% larger."," In these cases, the tangential velocities are typically $15\%$ lower in the low resolution runs, while velocity dispersions are $\sim 50\%$ larger."1074 These results show that low resolution runs can artificially boost the degree of disc heating., These results show that low resolution runs can artificially boost the degree of disc heating.1075" In this section, we discuss the structure of the inner and outer spheroids of our simulated galaxies."," In this section, we discuss the structure of the inner and outer spheroids of our simulated galaxies."1076 In Figs., In Figs.1077" and 12,, we show maps of surface mass density for inner spheroids (up to 0.5X ropt) and outer spheroids (up to"," \ref{maps_innerspheroid} and \ref{maps_outerspheroid}, , we show maps of surface mass density for inner spheroids (up to $0.5\times1078r_{\rm opt}$ ) and outer spheroids (up to"1079inter-order gaps.,inter-order gaps.1080 Figure 11 shows a possible detection of one line., Figure \ref{f_n_8216_synthesis} shows a possible detection of one line.1081 The N abundance is log e(N)<7.1 but this might properly be considered an upper limit., The N abundance is $\log\epsilon$ $\leq 7.1$ but this might properly be considered an upper limit.1082" 0.2 cm The gf-values for the permitted and forbidden lines are taken from Wiese, Fühhr Deter (1996)."," 0.2 cm The $gf$ -values for the permitted and forbidden lines are taken from Wiese, Fühhr Deter (1996)."1083" On the McDonald spectrum, the forbidden oxygen lines at 5577A,, 6300 aand 6363 aare detected."," On the McDonald spectrum, the forbidden oxygen lines at 5577, 6300 and 6363 are detected."1084 Weak permitted lines of RMT 10 near aare also analyzed., Weak permitted lines of RMT 10 near are also analyzed.1085 Figure 12 shows the best-fitting synthetic spectrum for the O16156 rregion., Figure \ref{f_o_synthesis} shows the best-fitting synthetic spectrum for the 6156 region.1086 Forbidden and permitted lines give a very similar abundance., Forbidden and permitted lines give a very similar abundance.1087" The strong triplet at 7774 aand the 8446 feature give an abundance about 1.5 dex higher abundance, a difference attributed to non-LTE effects."," The strong triplet at 7774 and the 8446 feature give an abundance about 1.5 dex higher abundance, a difference attributed to non-LTE effects."1088 0.2 cm The g f-values are taken from the database., 0.2 cm The $gf$ -values are taken from the database.1089 Five lines were suitable for abundance analysis from the McDonald spectrum (Table 3)., Five lines were suitable for abundance analysis from the McDonald spectrum (Table 3).1090 RMT and 6 give somewhat different results but we assign all lines the 4same weight., RMT 4 and 6 give somewhat different results but we assign all lines the same weight.1091deviation of the amisotropic amplitude posteriors should vary with multipoles ἐν as done by Grocuchoom&Evilk-sen (2009).,"deviation of the anisotropic amplitude posteriors should vary with multipoles $\ell$, as done by \cite{groeneboom:2008b}."1092 Before performing a full-scale analysis of sinulated polarized Planck data. we wish to validate our code.," Before performing a full-scale analysis of simulated polarized Planck data, we wish to validate our code."1093 We therefore simulate a low-resolution ως—32 map with E- mode data included., We therefore simulate a low-resolution $N_{\textrm{side}}=32$ map with E- mode data included.1094 Assuming an anisotropic amplitude of gy.=1.0. we perform both a brute-force and a ietropolis-hastings analysis of a full-xky map with uo beam nor noise.," Assuming an anisotropic amplitude of $g_*=1.0$, we perform both a brute-force and a metropolis-hastings analysis of a full-sky map with no beam nor noise."1095 The resulting posteriors for the TT-case and the TT|TEEE-case are shown in Figure. 1.., The resulting posteriors for the TT-case and the TT+TE+EE-case are shown in Figure \ref{fig:simulated_posteriors}.1096 It is worth to note that the posterior is more narrow when inchiding polarization data. as there is more data available.," It is worth to note that the posterior is more narrow when including polarization data, as there is more data available."1097 A typical posterior of the estimated direction n together with the input TT|EE ACW-sigual is secu in Fieure 5.., A typical posterior of the estimated direction $n$ together with the input TT+EE ACW-signal is seen in Figure \ref{fig:res_asymmetric}.1098 We now consider a Plauck simmlation., We now consider a Planck simulation.1099 We first simulate a temperature-only ACW-anisotropic map with, We first simulate a temperature-only ACW-anisotropic map with11002009).,.1101". In this paper the vectors v. n,. and ng are delined in the spacecraft coordinate svstem."," In this paper the vectors $\bf v$ , $\bf n_{_A}$ , and $\bf n_{_B}$ are defined in the spacecraft coordinate system."1102" The errors of line-oEsight (LOS) vector. An, and n. will produce à pseudo-dipole difference signal The dipoles for each observations have to be removed from the raw data before because their intensities are roughly 10 to 20 times greater than those of the CMD anisolropies."," The errors of line-of-sight (LOS) vector, $\Delta \bf{n}_{_A}$ and $\Delta \bf{n}_{_B}$, will produce a pseudo-dipole difference signal The dipoles for each observations have to be removed from the raw data before map-making because their intensities are roughly 10 to 20 times greater than those of the CMB anisotropies."1103 A small error of antenna direction will produce an error in. predicted dipole intensity and (hen cause a pseudo-dipole signal in the resulting CMD map more noticeably through the Doppler dipole subtraction ., A small error of antenna direction will produce an error in predicted dipole intensity and then cause a pseudo-dipole signal in the resulting CMB map more noticeably through the Doppler dipole subtraction .1104 For example. a LOS error of ~7. just about a hall-pixel in the WMAP resolution. can consequently catse the dipole signal to be deviated by dx. which can not be ignored compared to the very weak CAIB signal.," For example, a LOS error of $\sim7'$, just about a half-pixel in the WMAP resolution, can consequently cause the dipole signal to be deviated by $\mu$ K, which can not be ignored compared to the very weak CMB signal."1105 An asvnehronous betweenthe attitude and differential data can also produce the signal., An asynchronous betweenthe attitude and differential data can also produce the pseudo-dipole signal.1106" The WALAP mission uses two separate clocks for the attitude data and science data respectively,", The WMAP mission uses two separate clocks for the attitude data and science data respectively.1107 Therelore. if (here is a small constant timing error. (here will be a constant direction difference between the “observed pixel” and the true pixel.," Therefore, if there is a small constant timing error, there will be a constant direction difference between the ""observed pixel"" and the true pixel."1108 This has the same ellect as a constant LOS error in spacecraft coordinates (Liu.Niong&Li2010)., This has the same effect as a constant LOS error in spacecraft coordinates \citep{liu10}.1109. Another possible source of pseudo-dipole signal in released WALAP maps is the sidelobe signal contamination., Another possible source of pseudo-dipole signal in released WMAP maps is the sidelobe signal contamination.1110 Like all radio telescopes. the WAIAP antennas have both main beam response and sidelobe response.," Like all radio telescopes, the WMAP antennas have both main beam response and sidelobe response."1111 The WAIAP antenna sidelobe response was described by Barnesοἱal.(2003) and the corresponding data file is publiclyavailable?., The WMAP antenna sidelobe response was described by \citet{barnes03} and the corresponding data file is publicly.1112. The data files are fits Format fall skv maps in spacecraft coordinates in which the sidelobe responses are given in normalized gain C. where the normalization rule is that the summation of all gains [or one antenna (including the main beam) equals to AN. the nmunber of pixels in themap.," The data files are fits format full sky maps in spacecraft coordinates in which the sidelobe responses are given in normalized gain $G$, where the normalization rule is that the summation of all gains for one antenna (including the main beam) equals to $N$, the number of pixels in themap."1113Thus for. eachdifferential⋅⊳⋅ observation.⋅ the recorded difference⋅⊳ signal⋅ is⋅ 357⋏∖↓↽↿4(6;—GP)T;/pua- N.,"Thus for eachdifferential observation, the recorded difference signal is $\sum_{i=0}^{N-1} (G_i^A-G_i^B)T_i/N$ ."1114 Let, Let1115"Here we use as additional constraints Li observations that we performed for a large sample of field red giant stars (subgiant, RGB, and early-AGB stars) with metallicities around solar.","Here we use as additional constraints Li observations that we performed for a large sample of field red giant stars (subgiant, RGB, and early-AGB stars) with metallicities around solar."1116 All sample stars have Hipparcos parallaxes so that their mass and evolutionary status could be relatively well determined (Charbonnel et al., All sample stars have Hipparcos parallaxes so that their mass and evolutionary status could be relatively well determined (Charbonnel et al.1117 in preparation)., in preparation).1118" In Fig.14 they are distinguished with respect to their mass (less or more massive than 2 M, in the left and right panels respectively).", In \ref{fig:Lagardeetal_posterIAU268_figb} they are distinguished with respect to their mass (less or more massive than 2 $_{\odot}$ in the left and right panels respectively).1119" Let us consider first the stars with initial masses lower than 2 Mc, whose Li properties are compared with predictions for the 1.5 and 2 Me models (left panel of Fig.14))."," Let us consider first the stars with initial masses lower than 2 $_{\odot}$, whose Li properties are compared with predictions for the 1.5 and 2 $_{\odot}$ models (left panel of \ref{fig:Lagardeetal_posterIAU268_figb}) )."1120 The theoretical Li behaviour is relatively straightforward., The theoretical Li behaviour is relatively straightforward.1121" On the main sequence and on the early-RGB, rotation-induced mixing leads to stronger Li depletion than in the standard case (compare e.g. the red curve with the black one); in this mass range indeed standard models predict no Li depletion on the main sequence and a N(Li) of the order of 1.5 at the end of the first dredge-up, which is at odds with the data."," On the main sequence and on the early-RGB, rotation-induced mixing leads to stronger Li depletion than in the standard case (compare e.g. the red curve with the black one); in this mass range indeed standard models predict no Li depletion on the main sequence and a N(Li) of the order of 1.5 at the end of the first dredge-up, which is at odds with the data."1122" After the end of the first dredge-up (Teff ~ 4800 K), the theoretical Li abundance remains temporarily constant as the convective envelope withdraws in mass."," After the end of the first dredge-up (Teff $\sim$ 4800 K), the theoretical Li abundance remains temporarily constant as the convective envelope withdraws in mass."1123" When thermohaline mixing becomes efficient (Teff ~ 4200 K), the theoretical Li abundance drops again in drastic manner (while it would stay constant in the standard case)."," When thermohaline mixing becomes efficient (Teff $\sim$ 4200 K), the theoretical Li abundance drops again in drastic manner (while it would stay constant in the standard case)."1124" After the star has reached the RGB tip its effective temperature increases (up to ~ 4800 K) as it settles on the clump, before decreasing again when the star starts climbing the early-AGB."," After the star has reached the RGB tip its effective temperature increases (up to $\sim$ 4800 K) as it settles on the clump, before decreasing again when the star starts climbing the early-AGB."1125 The second dredge-up that occurs then leads to a final decrease of N(Li)., The second dredge-up that occurs then leads to a final decrease of N(Li).1126" On this graph we do not plot the Li increase that is predicted to occur during the TP-AGB phase at a Teff of ~ 3200 K due to thermohaline mixing, and which is discussed in 4.1.2."," On this graph we do not plot the Li increase that is predicted to occur during the TP-AGB phase at a Teff of $\sim$ 3200 K due to thermohaline mixing, and which is discussed in 4.1.2."1127" As can be seen in Fig.14,, the present predictions are in perfect agreement with the data all along the evolutionary sequence and explain very well the upper limits observed for the brightest sample giant stars."," As can be seen in \ref{fig:Lagardeetal_posterIAU268_figb}, the present predictions are in perfect agreement with the data all along the evolutionary sequence and explain very well the upper limits observed for the brightest sample giant stars."1128 The observed Li dispersion at a given effective temperature reflects dispersion in the initial rotation velocity and in the initial stellar mass???)., The observed Li dispersion at a given effective temperature reflects dispersion in the initial rotation velocity and in the initial stellar mass.1129". The case of the more massive stars, whose Li observational behaviour is compared to predictions for the 2.5 and 2.7 Me models (right panel of Fig.14)) is even more simple."," The case of the more massive stars, whose Li observational behaviour is compared to predictions for the 2.5 and 2.7 $_{\odot}$ models (right panel of \ref{fig:Lagardeetal_posterIAU268_figb}) ) is even more simple."1130" In these objects indeed no thermohaline mixing occurs on the too short RGB, and rotation-induced mixing alone explains very well the data."," In these objects indeed no thermohaline mixing occurs on the too short RGB, and rotation-induced mixing alone explains very well the data."1131" In all the models that we have computed along the TP-AGB, non negligible fresh lithium production is obtained, although"," In all the models that we have computed along the TP-AGB, non negligible fresh lithium production is obtained, although"1132"the observed bispectrum in Eq. (17)), CtCes,","the observed bispectrum in Eq. \ref{eq:Dfnlanalyt}) ), $B^\mathrm{loc}_{\ell_1\ell_2\ell_3} /1133C_{\ell_1}C_{\ell_2}C_{\ell_3}$,"1134" which rapidly increases with multipole Bi°%,0,/Ce,as the product of spectra decreases more quickly than the bispectrum.", which rapidly increases with multipole as the product of spectra decreases more quickly than the bispectrum.1135 This leads to a 1/C dependence in squeezed configurations and to a 1/C? dependence in equilateral configurations., This leads to a $1/C_\ell$ dependence in squeezed configurations and to a $1/C_\ell^2$ dependence in equilateral configurations.1136" When the observed bispectrum is associated to CMB signal alone, its decrease cancels the increase of the weights so that the sum in Eq. (17))"," When the observed bispectrum is associated to CMB signal alone, its decrease cancels the increase of the weights so that the sum in Eq. \ref{eq:Dfnlanalyt}) )"1137 converges., converges.1138" Conversely, the sum diverges when the observed bispectrum is associated with a non-CMB signal and does not decrease with 6 as fast as the CMB."," Conversely, the sum diverges when the observed bispectrum is associated with a non-CMB signal and does not decrease with $\ell$ as fast as the CMB."1139 The bias Aff is maximal at 30 GHz and rapidly decreases with frequency., The bias $\Delta f_\mathrm{NL}^\mathrm{RAD}$ is maximal at 30 GHz and rapidly decreases with frequency.1140 It slightly increases again at the two highest frequencies following the amplitude of the bispectrum in temperature units which is plotted in the upper panel of Fig. 4.., It slightly increases again at the two highest frequencies following the amplitude of the bispectrum in temperature units which is plotted in the upper panel of Fig. \ref{fig:amplRAD}.1141 The relative error of ΔΙΑ for Ímax=700 is of the order of independently of the frequency.," The relative error of $\Delta1142f_\mathrm{NL}^\mathrm{RAD}$ for $\ell_{\mathrm{max}}=700$ is of the order of independently of the frequency."1143 It amounts to for €max=2048., It amounts to for $\ell_{\mathrm{max}}=2048$.1144 These errors bars were computed with simulations using the catalog of sources present in Sehgal et al., These errors bars were computed with simulations using the catalog of sources present in Sehgal et al.1145"’s maps As shown in Table 1,, masking sources above the ERCSC flux limit proves very efficient to significantly decrease the radio contamination to /wr at all the frequencies.","'s maps As shown in Table \ref{fnlradtable}, masking sources above the ERCSC flux limit proves very efficient to significantly decrease the radio contamination to $f_\mathrm{NL}$ at all the frequencies."1146" At a Planck-like resolution, £44.=2048, the bias AfR#? is reduced below unity above 150 GHz."," At a Planck-like resolution, $\ell_\mathrm{max}= 2048$, the bias $\Delta1147f_\mathrm{NL}^\mathrm{RAD}$ is reduced below unity above 150 GHz."1148 It is of the order of Planck's expected error bars at 90 GHz., It is of the order of Planck's expected error bars at 90 GHz.1149 At 30 GHz the bias is still important., At 30 GHz the bias is still important.1150" The bias due to IR sources Aft, is always negative, see Table 2.."," The bias due to IR sources $\Delta f_\mathrm{NL}^\mathrm{IR}$ is always negative, see Table \ref{fnlirtable}."1151" As a matter of fact, we have shown that the IR bispectrum peaks in squeezed configurations just like the CMB bispectrum and these configurations thus dominate the sum in Eq. (17))."," As a matter of fact, we have shown that the IR bispectrum peaks in squeezed configurations just like the CMB bispectrum and these configurations thus dominate the sum in Eq. \ref{eq:Dfnlanalyt}) )."1152" Moreover, in the squeezed limit the CMB bispectrum is negative while the IR bispectrum is positive."," Moreover, in the squeezed limit the CMB bispectrum is negative while the IR bispectrum is positive."1153" For the same reason as for radio sources, the bias AfMi blows up at high multipoles."," For the same reason as for radio sources, the bias $\Delta1154f_\mathrm{NL}^\mathrm{IR}$ blows up at high multipoles."1155" This is particularly important at a Planck-like resolution, max=2048, where primordial NG tests will need to carefully handle the contamination by IR sources."," This is particularly important at a Planck-like resolution, $\ell_\mathrm{max}=2048$, where primordial NG tests will need to carefully handle the contamination by IR sources."1156 The IR sources emission plummets at radio frequencies so that Afl is completely negligible below 220 GHz.," The IR sources emission plummets at radio frequencies so that $\Delta1157f_\mathrm{NL}^\mathrm{IR}$ is completely negligible below 220 GHz."1158 It becomes of the order of Planck's error bars at 277 GHz and it reaches WMAP’s central values for fri at 350 GHz., It becomes of the order of Planck's error bars at 277 GHz and it reaches WMAP's central values for $f_\mathrm{NL}$ at 350 GHz.1159 The relative error of Aft ranges between 6 and from 148 to 350 GHz for €max=700., The relative error of $\Delta f_\mathrm{NL}^\mathrm{IR}$ ranges between 6 and from 148 to 350 GHz for $\ell_{\mathrm{max}}=700$.1160 It ranges between 3 and for €max=2048. (, It ranges between 3 and for $\ell_{\mathrm{max}}=2048$. (1161These error bars were computed analytically with the weak NG approximation — see Appendix ??)) At higher frequencies the IR contamination to the bispectrum is likely larger but the contamination from our Galaxy needs to be taken into account as well.,These error bars were computed analytically with the weak NG approximation – see Appendix \ref{appendix:wngvar}) ) At higher frequencies the IR contamination to the bispectrum is likely larger but the contamination from our Galaxy needs to be taken into account as well.1162Using observations of the and transitions ofII2CO.. we have successfully. coustrained the spatial deusities of a sample of ealactic star-forming reeious.,"Using observations of the and transitions of, we have successfully constrained the spatial densities of a sample of galactic star-forming regions."1163 Both trausitious were observed toward 15 sources with relative ease. requiring an average of 17 min of iuteeration time aud resulting in ouly 2 nonudoetectious in the J=1 transition.," Both transitions were observed toward 18 sources with relative ease, requiring an average of 17 min of integration time and resulting in only 3 nondetections in the $J=4$ transition."1164 Accurate of the spatial deusitv η) were mnade“---Dicamus for 13 objects and useful lanits were placed on the une a colmbination of Large Velocity Gradieut (LVG) aud Loca Thermodvuamic Equilibrimm (LTE) analyses., Accurate measurements of the spatial density )] were made for 13 objects and useful limits were placed on the remainder using a combination of Large Velocity Gradient (LVG) and Local Thermodynamic Equilibrium (LTE) analyses.1165 Molecular ivdrogeu densities iu the range of ane ortho-formaldehyde colin densities per unit Lue width )etween and are foun or most sources. m general agreement with previous neasurements.," Molecular hydrogen densities in the range of and ortho-formaldehyde column densities per unit line width between and are found for most sources, in general agreement with previous measurements."1166 Detailed analyses of the advantages and limitations o this «ο... technique have also been provided., Detailed analyses of the advantages and limitations to this densitometry technique have also been provided.1167 deusitometry proves to be best suited to objects with z 100 EK. above which the LVG models come relatively independent of kineticο teniperaturoe.," densitometry proves to be best suited to objects with $\gtrsim$ 100 K, above which the LVG models become relatively independent of kinetic temperature."1168 Compared with the similarly utilized aud ransitious. the 7—3 aud | A--doublets provide higher spatial resolution aud scusitivity to hot. deuse material. which makes them more efficieut probes of spatial density iu wnolecular cores.," Compared with the similarly utilized and transitions, the $J=3$ and 4 -doublets provide higher spatial resolution and sensitivity to hot, dense material, which makes them more efficient probes of spatial density in molecular cores."1169 However. beam widths comparable o the auticipated source sizes make source structure considerations iniportant.," However, beam widths comparable to the anticipated source sizes make source structure considerations important."1170 Since nappiig mneasurenments inve vet to be conducted for these trausifious. the correlation between the spatial extent traced bv the J—35 and | K-doublets aud that of other deuse gas racers Is uncertain. naking spatial assuniptious based on past nieasuremoeuts problematic.," Since mapping measurements have yet to be conducted for these transitions, the correlation between the spatial extent traced by the $J=3$ and 4 -doublets and that of other dense gas tracers is uncertain, making spatial assumptions based on past measurements problematic."1171 This work serves as asuccessful proof-of-concept for he J=3/J| K-doublet densitometry echuique. adding a useful new diagnostic to the study of deuse molecular cuvironiments.," This work serves as asuccessful proof-of-concept for the $J=3/J=4$ -doublet densitometry technique, adding a useful new diagnostic to the study of dense molecular environments."1172 The Green Bank Telescope (CBT) staff was characteristically helpful and coutributed significantly o the success of our observing program., 	 The Green Bank Telescope (GBT) staff was characteristically helpful and contributed significantly to the success of our observing program.1173 The authors also thank the referee for several conuuenuts that ereatlv chhanced this work., The authors also thank the referee for several comments that greatly enhanced this work.1174 P. L M. would like to hank Tarold Dutuer aud the NRAOQ REU students of 2009 for their continued support., P. I. M. would like to thank Harold Butner and the NRAO REU students of 2009 for their continued support.1175 Funding for his project was provided bv the NSF through the NRAO REU Program (award No., Funding for this project was provided by the NSF through the NRAO REU Program (award No.1176 0755390) aud vo NRÀO though an undereraduate internship. Fucilities::, 0755390) and by NRAO though an undergraduate internship. :1177 , 1178corona (e.g. see 9105. or refer to (he density profile in Figure 1 to be discussed in 833).,"corona (e.g. see SI05, or refer to the density profile in Figure 1 to be discussed in 3)."1179" Roughly speaking. for ο=3xI0! km/s. lupSUH, when n>10°em ."," Roughly speaking, for $v_b=3\times 10^4$ km/s, $l_{\rm mfp} \lesssim H_\rho$ when $n>10^9$ $^{-3}$."1180 Therefore. we anticipate the inwarcd-propagating electron beam {ο heat up ambient media from the lower corona to the upper chromosphere.," Therefore, we anticipate the inward-propagating electron beam to heat up ambient media from the lower corona to the upper chromosphere."1181" This allows us to assume that the incoming electron beam starts dissipating lrom μας=1.148. (lower corona) to ry,=1.0012. (upper chromosphere).", This allows us to assume that the incoming electron beam starts dissipating from $r_{\rm max} =1.1R_{\odot}$ (lower corona) to $r_{\rm min}=1.001R_{\odot}$ (upper chromosphere).1182 We model the energy flux of the beam to decrease inwardly according to where fis a parameter (hat describes (he spacial distribution of the heating., We model the energy flux of the beam to decrease inwardly according to where $k$ is a parameter that describes the spacial distribution of the heating.1183" =1 corresponds to constant volumetric heating: namely, the heating rate per unit mass is higher in (he upper region (i.e. corona) than in the lower region (i.e. chromosphere)."," $k=1$ corresponds to constant volumetric heating; namely, the heating rate per unit mass is higher in the upper region (i.e. corona) than in the lower region (i.e. chromosphere)."1184 II 7=0.1. the heating rate per unit mass is more unilormlwv distributed.," If $k= 0.1$, the heating rate per unit mass is more uniformly distributed."1185 In (his work. we adopt =0.1 to resemble (he situation of a constant beam-heatine rate per unit mass.," In this work, we adopt $k=0.1$ to resemble the situation of a constant beam-heating rate per unit mass."1186" We also assume (hat the momentum flux of the beam J, clissipates in (he same manner as that described bv eq. (5))", We also assume that the momentum flux of the beam $P_b$ dissipates in the same manner as that described by eq. \ref{eq:F_b_diss}) )1187 for the energy flux., for the energy flux.1188" This implies that although the beam velocity ορ does not decay in our dissipation model. the beam density p, declines. meaning that more and more beam electrons have been transformed into thermal electrons as the beam progresses downwids in (he dissipation region."," This implies that although the beam velocity $v_b$ does not decay in our dissipation model, the beam density $\rho_b$ declines, meaning that more and more beam electrons have been transformed into thermal electrons as the beam progresses downwards in the dissipation region."1189 The beam heating al the footpoint of one open [fiekl line occurs when the planet's nagnetosphere is crossing the field line., The beam heating at the footpoint of one open field line occurs when the planet's magnetosphere is crossing the field line.1190 ence. by means of eq. (1)).," Hence, by means of eq. \ref{eq:R_mp}) ),"1191 the beam heating proceeds on the timescale The stellar atmosphere model is based on the 1-D magnetohydrocdvuamic simulation with radiative cooling and thermal conduction in an open flux tube (5105)., the beam heating proceeds on the timescale The stellar atmosphere model is based on the 1-D magnetohydrodynamic simulation with radiative cooling and thermal conduction in an open flux tube (SI05).1192 In the original simulation. the heating is given bv the nonlinear dissipation of the Alfvénn waves excited by (he eranulations at the photosphere.," In the original simulation, the heating is given by the nonlinear dissipation of the Alfvénn waves excited by the granulations at the photosphere."1193" In (he case of D,=1 G. we set arms average amplitude «dome1.8 km/s al the photosphere. which is estimated from (he scaling with the surface convective flux (Suzuki 2007) [rom the Sun (S105)."," In the case of $B_*=1$ G, we set a rms average amplitude $<dv_{\perp}> \sim 1.8$ km/s at the photosphere, which is estimated from the scaling with the surface convective flux (Suzuki 2007) from the Sun (SI05)."1194" In the case of the stronger field D,=5 G. (the larger rms velocity fluctuation <de2273.6 km/s is used for the experiment. which"," In the case of the stronger field $B_*=5$ G, the larger rms velocity fluctuation $<dv_{\perp}>1195\sim 3.6$ km/s is used for the experiment, which"1196Ultra-high energv cosmic ravs (ULLIECIS) are energetic particles (2107 eV) that must originate in the most powerlul particle accelerators in. the Universe.,Ultra-high energy cosmic rays (UHECRs) are energetic particles $> 10^{19}$ eV) that must originate in the most powerful particle accelerators in the Universe.1197 These extreme events have fascinatecl scientists from. the time of their ciscovery in. 1962 (Linsley19039).., These extreme events have fascinated scientists from the time of their discovery in 1962 \citep{linsley}.1198. Since then. speculation about their origin has Llourishecl (Pierpaoli&Ferrar2005:Ghisellinietal.2008:Cuesta&Prada 2009).," Since then, speculation about their origin has flourished \citep{pierpaoli,ghise,cuesta}."1199. Theoretically. active galactic nucle: (AGN) have long been awored as the best candidates for particle acceleration to hese extreme energies (Ginzburg&Svrovatskii1964:Lillas 1984).," Theoretically, active galactic nuclei (AGN) have long been favored as the best candidates for particle acceleration to these extreme energies \citep{ginzburg,hillas}."1200. Unfortunately. no firm astrophysical association has »en established.," Unfortunately, no firm astrophysical association has been established."

Showing the first 1,200 of 10316 lines. Download the file for the rest.