ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Finally. we return to the implications of asymmetry [ον the use of SNe Ia lor cosmology.," Finally, we return to the implications of asymmetry for the use of SNe Ia for cosmology."3 A 10 percent asymmetry of the photosphere would not cause systematic difficulties for using SN la as distance indicators at the current level of accuracy. of about 20 percent., A 10 percent asymmetry of the photosphere would not cause systematic difficulties for using SN Ia as distance indicators at the current level of accuracy of about 20 percent.4 This level of asymmetry would. however. cause a directional dependence of the luminosity of order O.1™ (Hóflieh.1991).. and a corresponding. but smaller. dispersion in the relation of SNe Ia. This dispersion depends on the viewing-angle dependence of the luminosity variation and. (hus. the nature of the asymmetry.," This level of asymmetry would, however, cause a directional dependence of the luminosity of order $^{\rm m}$ \citep{Hoeflich:1991}, and a corresponding, but smaller, dispersion in the brightness-decline relation of SNe Ia. This dispersion depends on the viewing-angle dependence of the luminosity variation and, thus, the nature of the asymmetry."5 The angle dependence of the luminosity of a single SN Ia will not. in general. vary as the line of sieht to the equator. (hat is. as cos.," The angle dependence of the luminosity of a single SN Ia will not, in general, vary as the line of sight to the equator, that is, as $\theta$."6 Thus. even ina large sample. (his elfect is not expected to average out.," Thus, even in a large sample, this effect is not expected to average out."7 Whether (he remaining bias is slightly. positive or slehtly negative depends on the specifies of the asvmmnmetrc Iumimnosity distribution., Whether the remaining bias is slightly positive or slightly negative depends on the specifics of the asymmetric luminosity distribution.8 Whether this bias can be eliminated to the [ew percent level needed to determine the cosmological equation of state bv applying the ccorrection or bv emploving the CMAGIC method (Wangetal.2003) remains to be seen., Whether this bias can be eliminated to the few percent level needed to determine the cosmological equation of state by applying the correction or by employing the CMAGIC method \citep{Wang:2003} remains to be seen.9 We note that if such effects are present. then SN Ia are even more homogeneous than they seem [rom current dispersions in peak brightness.," We note that if such effects are present, then SN Ia are even more homogeneous than they seem from current dispersions in peak brightness."10 Ii principle. if the angle-dependent luminosity could be determined and removed cequadratically [rom Che data. the dispersion could be reduced from current values.," In principle, if the angle-dependent luminosity could be determined and removed quadratically from the data, the dispersion could be reduced from current values."11 More observations are required to wnelerstanel (he polarization behavior of SN la ancl its effect on laree samples of supernovae., More observations are required to understand the polarization behavior of SN Ia and its effect on large samples of supernovae.12 Once il is known from polarization statistics the phases in which the polarization is small. more weight can be assigned to the “low-risk” phases of the light curve.," Once it is known from polarization statistics the phases in which the polarization is small, more weight can be assigned to the “low-risk"" phases of the light curve."13 Even if there remains a bias due to the angle-dependence of the emitted, Even if there remains a bias due to the angle-dependence of the emitted14The N-body simulations described in Sect.,The N-body simulations described in Sect.15 3.2.0. allow to evaluate the effect that tides have in the stellar kinematies of Pal 14 1n the framework of the classical Newtonian dynamics., \ref{newt_sec} allow to evaluate the effect that tides have in the stellar kinematics of Pal 14 in the framework of the classical Newtonian dynamics.16 Quantifying this effect is important since it can. potentially affect the cluster velocity dispersion measured through the 109 sample (Kupper et al., Quantifying this effect is important since it can potentially affect the cluster velocity dispersion measured through the J09 sample (Kupper et al.17 2010)., 2010).18 The output distributions of predicted velocity dispersions for the two orbits are compared to the isolated model in Fig., The output distributions of predicted velocity dispersions for the two orbits are compared to the isolated model in Fig.19 I2. and Fig., \ref{tides2} and Fig.20 13 for M/L=1.885 and M/L=0.747. respectively.," \ref{tides3} for M/L=1.885 and M/L=0.747, respectively."21 It is apparent that the effect of tidal heating ts negligible in all cases., It is apparent that the effect of tidal heating is negligible in all cases.22 A small difference is noticeable only in the M/L=0.747 case when eccentric orbits are considered: in this case the distribution. while having the same peak value. present a larger dispersion and a tail extending toward larger velocity dispersions.," A small difference is noticeable only in the M/L=0.747 case when eccentric orbits are considered: in this case the distribution, while having the same peak value, present a larger dispersion and a tail extending toward larger velocity dispersions."23 The reason of this result can be found by looking at the spatial distribution of the JO9 sample: 16 out 17 target stars reside in the inner 2 areminutes. a region where tides have only a minor heating efficiency (see Fig. 2)).," The reason of this result can be found by looking at the spatial distribution of the J09 sample: 16 out 17 target stars reside in the inner 2 arcminutes, a region where tides have only a minor heating efficiency (see Fig. \ref{tides1}) )."24 The effect is indeed slightly more evident when a small M/L and an eccentric orbit are considered. since the effect of heating penetrates deeper into the cluster affecting the velocity of the two outermost targets.," The effect is indeed slightly more evident when a small M/L and an eccentric orbit are considered, since the effect of heating penetrates deeper into the cluster affecting the velocity of the two outermost targets."25 We conclude that the upper limit in the binary fraction derived in Sect., We conclude that the upper limit in the binary fraction derived in Sect.26 5.2. is not altered by this effect. at least for the two considered orbits.," \ref{binres_sec} is not altered by this effect, at least for the two considered orbits."27 Using a Monte Carlo approach. we performed an accurate comparison of the velocity dispersion of the globular cluster Pal 14 measured from high-resolution radial velocities with the predictions of a set of dynamical models spanning a wide range in M/L ratio. degree of anisotropy. binary fraction and orbital eccentricity in both Newtonian and MOND gravity.," Using a Monte Carlo approach, we performed an accurate comparison of the velocity dispersion of the globular cluster Pal 14 measured from high-resolution radial velocities with the predictions of a set of dynamical models spanning a wide range in $M/L$ ratio, degree of anisotropy, binary fraction and orbital eccentricity in both Newtonian and MOND gravity."28" The obtained results indicate that Newtonian models with a binary fraction fj,<30% and à M/L ratio compatible with the predictions of stellar evolutionary models are in good agreement with the kinematics of this stellar system.", The obtained results indicate that Newtonian models with a binary fraction $f_{b}<30\%$ and a $M/L$ ratio compatible with the predictions of stellar evolutionary models are in good agreement with the kinematics of this stellar system.29 On the other hand MOND models with the same M/L ratio appear to systematically overpredict the velocity dispersion for any assumption of the cluster anisotropy., On the other hand MOND models with the same $M/L$ ratio appear to systematically overpredict the velocity dispersion for any assumption of the cluster anisotropy.30 The same conclusion has been reached previously by JO9 but questioned by Gentile et al. (, The same conclusion has been reached previously by J09 but questioned by Gentile et al. (312010).,2010).32 Note that all these previous approaches compared the velocity dispersion with the prediction of theoretical models neglecting the information on the radial distribution of targets., Note that all these previous approaches compared the velocity dispersion with the prediction of theoretical models neglecting the information on the radial distribution of targets.33 This has an important impact m increasing the significance of the comparison as most of targets are actually located in the central part of the cluster where the difference between Newtonian and MOND models is. maximized., This has an important impact in increasing the significance of the comparison as most of targets are actually located in the central part of the cluster where the difference between Newtonian and MOND models is maximized.34 Moreover. our simulations showed the importance of the inclusion of the external field in the determining the velocity dispersion profile of MOND models for this cluster.," Moreover, our simulations showed the importance of the inclusion of the external field in the determining the velocity dispersion profile of MOND models for this cluster."35 This warns against using isolated MOND models for clusters with masses and Galactocentric distances similar to Pal 14 (see also Baumgardt et al., This warns against using isolated MOND models for clusters with masses and Galactocentric distances similar to Pal 14 (see also Baumgardt et al.36 2005. Haghi et al.," 2005, Haghi et al."37 2009. 2011).," 2009, 2011)."38 Similar difficulties for MOND in explaining the internal kinematics of GCs have been already found in previous studies on NGC2419 (Baumgardt et al., Similar difficulties for MOND in explaining the internal kinematics of GCs have been already found in previous studies on NGC2419 (Baumgardt et al.39 2009; Sollima Nipoti 2010: Ibata et al., 2009; Sollima Nipoti 2010; Ibata et al.40 201la.b).," 2011a,b)."41 In this last case the effect of the external field. which is a factor 1.4 weaker in modulus and —23 times smaller with respect to the cluster internal acceleration than in Pal 14. has been estimated to be negligible (Ibata et al.," In this last case the effect of the external field, which is a factor 1.4 weaker in modulus and $\sim$ 23 times smaller with respect to the cluster internal acceleration than in Pal 14, has been estimated to be negligible (Ibata et al."42 2011a)., 2011a).43 The conclusions are different when significantly lower values of M/L are considered for Pal 14., The conclusions are different when significantly lower values of $M/L$ are considered for Pal 14.44 In this case the predictions of MOND models are close the observed velocity dispersion (in particular when a 5o rejection criterion is adopted and eccentric orbits are considered). while Newtonian models predict a lower velocity dispersion.," In this case the predictions of MOND models are close the observed velocity dispersion (in particular when a $\sigma$ rejection criterion is adopted and eccentric orbits are considered), while Newtonian models predict a lower velocity dispersion."45 So. a combination of small M/L ratio. small binary fraction. relatively large orbital eccentricity and the adoption of a permissive rejection criterion provides a way-out for MOND.," So, a combination of small $M/L$ ratio, small binary fraction, relatively large orbital eccentricity and the adoption of a permissive rejection criterion provides a way-out for MOND."46 As the M/L ratio is a crucial parameter in the presented analysis. it is interesting to discuss in more detail the possibility of constraining its value.," As the $M/L$ ratio is a crucial parameter in the presented analysis, it is interesting to discuss in more detail the possibility of constraining its value."47 From a theoretical point of view. the M/L ratio of an old. metal-poor stellar population composed mainly by subsolar-mass stars is expected to be systematically larger than unity (1.5«M/L2.5: Fioc Roeca-Volmerange 1997; Bruzual Charlot 2003) and can reach M/E>3 if dark remnants are taken into account (Kruijssen 2009).," From a theoretical point of view, the M/L ratio of an old, metal-poor stellar population composed mainly by subsolar-mass stars is expected to be systematically larger than unity $1.5<M/L<2.5$; Fioc Rocca-Volmerange 1997; Bruzual Charlot 2003) and can reach $M/L>3$ if dark remnants are taken into account (Kruijssen 2009)."48 On the other hand. observational analyses performed on GCs in the Milky Way and M31 have shown the occurrence of a sparse number of clusters with M/L values as small as M/L~0.6 (Strader et al.," On the other hand, observational analyses performed on GCs in the Milky Way and M31 have shown the occurrence of a sparse number of clusters with M/L values as small as $\sim$ 0.6 (Strader et al."49 2009. 2011).," 2009, 2011)."50 It is worth noting that the low M/L=0.747 ratio adopted here corresponds to the minimum mass caleulated by JO9 assuming a decreasing mass function for stellar masses smaller tha the limiting magnitude of deep photometric HST observations of Pal I4 and neglecting the effect of dark remnants., It is worth noting that the low M/L=0.747 ratio adopted here corresponds to the minimum mass calculated by J09 assuming a decreasing mass function for stellar masses smaller than the limiting magnitude of deep photometric HST observations of Pal 14 and neglecting the effect of dark remnants.51 So M/LΞ0.747 must be considered a strong lower limit., So $M/L=0.747$ must be considered a strong lower limit.52 O the other hand. while the value of M/Lz1.885 derived by MeLaughlin van der Marel (2005) assumes a standard Chabrier (2003) IMF. J09 measured a shallower mass functio slope in the limited mass range covered by their observations which could in turn suggest a lower M/L as appropriate.," On the other hand, while the value of M/L=1.885 derived by McLaughlin van der Marel (2005) assumes a standard Chabrier (2003) IMF, J09 measured a shallower mass function slope in the limited mass range covered by their observations which could in turn suggest a lower M/L as appropriate."53" I general. the dynamical M/L ratios measured in GCs appear generally smaller than those predicted by population synthesis models ((M/L),/(M/L),,,=0.82£0.07 with some cluster"," In general, the dynamical M/L ratios measured in GCs appear generally smaller than those predicted by population synthesis models $(M/L)_{dyn}/(M/L)_{syn}=0.82\pm0.07$ with some cluster"54Draine et al. (,Draine et al. (552007) estimated it to be 1/140 for the Milky Way. and find for other galaxies that this fraction varies »etween 1/100 ancl 1/400 with the median L/190 for SINGS sample of galaxies.,"2007) estimated it to be 1/140 for the Milky Way, and find for other galaxies that this fraction varies between 1/100 and 1/400 with the median 1/190 for SINGS sample of galaxies."56 Ehe fiducial value of 1/100 is usually aken as the dust/Lll mass ratio in the Milkv Way., The fiducial value of 1/100 is usually taken as the dust/HI mass ratio in the Milky Way.57 Me assume that the heavy. elements. present in the interstellar matter condense into dust. with the fraction given by eq. (2)).," We assume that the heavy elements present in the interstellar matter condense into dust with the fraction given by eq. \ref{eq:dustZ}) ),"58 and dust to HIE ratio is universal in LIL regions., and dust to HI ratio is universal in HI regions.59 The HE survey (Zwaan et al., The HI survey (Zwaan et al.60 2005: Zhang et al., 2005; Zhang et al.61 2008) and the HH» survey (Ixeres et al., 2008) and the $_2$ survey (Keres et al.62 2003) give the cosmic value or the sum of atomic and molecular hydrogen to be where HE:Ho=0.700.30., 2003) give the cosmic value for the sum of atomic and molecular hydrogen to be where ${\rm HI:H_2\approx 0.70:0.30}$.63 With the assumption that dust resides in the LL region and the hydrogen to dust ratio is universal we estimate the global dust abundance in galactic clises. This is compared with the dust abundance estimated from obscuration due to galaxies in a galaxy survey (Driver et al.," With the assumption that dust resides in the HI region and the hydrogen to dust ratio is universal we estimate the global dust abundance in galactic discs, This is compared with the dust abundance estimated from obscuration due to galaxies in a galaxy survey (Driver et al."64 2007). Oisax35LO”.," 2007), $\Omega_{\rm dust~galaxy}=3\times 10^{-6}$."65 Dust may coagulate to form planets and may. be depleted., Dust may coagulate to form planets and may be depleted.66 Ehe amount we estimated. however. is disturbed itle by the planets formation. while they are not entirely negligible.," The amount we estimated, however, is disturbed little by the planets formation, while they are not entirely negligible."67 Alarey (2005) estimated that of nearby EC stars have detected. Jupiter-like planets within 20 AU with he planet mass cistrilxition {Αη~m.1., Marcy (2005) estimated that of nearby FGK stars have detected Jupiter-like planets within 20 AU with the planet mass distribution $dN/dm\sim m^{-1}$.68 In the recent analvsis Johnson et al. (, In the recent analysis Johnson et al. (692010) indicate that the fraction depends on the mass «X the central star and drops to or M dwarfs. which cminate the stars in number.,"2010) indicate that the fraction depends on the mass of the central star and drops to for M dwarfs, which dominate the stars in number."70 Taking Figure 4 of Johnson e al., Taking Figure 4 of Johnson et al.71 we estimate that 0.052 planets ormed per | AL. of uel consumed., we estimate that 0.052 planets formed per 1 $M_\odot$ of fuel consumed.72 Here. we extend. the range of stars to span the full range of Al and X stars. wv slightly extending t10 observed range which lies between 2510 2M..," Here we extend the range of stars to span the full range of M and A stars, by slightly extending the observed range which lies between 0.25 to $M_\odot$."73 The observed. planets are of the Jupiter type. which is dominated bv hydrogen and helium gas.," The observed planets are of the Jupiter type, which is dominated by hydrogen and helium gas."74 What concerns us iere is clust used to form the core of planets., What concerns us here is dust used to form the core of planets.75 Lowe take the core accretion mocel for the giant planet formation. the core mass is about. LOAL; per planet (Mizuno 1980: Pollack ct al.," If we take the core accretion model for the giant planet formation, the core mass is about $10M_\oplus$ per planet (Mizuno 1980; Pollack et al."76" 1996: Rice Armitage 2003). in agreement with the rocky core mass in the solar system planets. which is S.10.12A7, or Jupiter. Saturn and Uranus (e.g. Lodders Feeley 1998: Cuillot 1999)."," 1996; Rice Armitage 2003), in agreement with the rocky core mass in the solar system planets, which is $8, 10, 12M_\oplus$ for Jupiter, Saturn and Uranus (e.g., Lodders Fegley 1998; Guillot 1999)."77" The mass density borne by planetary. cores hat arose from coagulation of dust is Quinn:c810"" onlv 1/500 10 dust. abundance in eq.(5))."," The mass density borne by planetary cores that arose from coagulation of dust is $\Omega_{\rm78 planet}\simeq 8\times 10^{-9}$, only 1/500 the dust abundance in \ref{eq:discdust}) )."79 The knowledge concerning planets is still immature and the estimates given rere may. be subject to revision in the future., The knowledge concerning planets is still immature and the estimates given here may be subject to revision in the future.80 Integrating he mass function of planets given above around the Jupiter mass. we obtain a rough estimate of the mass density of danets to be Oui&T10|," Integrating the mass function of planets given above around the Jupiter mass, we obtain a rough estimate of the mass density of planets to be $\Omega_{\rm planet}\approx 7\times 10^{-7}$."81 We now calculate. the abundance. of dust. that. is expected to be produced. from the stellar evolution., We now calculate the abundance of dust that is expected to be produced from the stellar evolution.82 With he Chabrier/Salpeter initial mass function. the gas shed ov stars is 0.60 times the mass locked into stars with the resulting remnants given in section 1.," With the Chabrier/Salpeter initial mass function, the gas shed by stars is 0.60 times the mass locked into stars with the resulting remnants given in section 1."83 The majority of stars ave solar metallicity., The majority of stars have solar metallicity.84 We may consider that this is true even at non-zero redshift. possibly except for some galaxies very early in structure formation. as indicated by observations (c.g.. Shapley et al.," We may consider that this is true even at non-zero redshift, possibly except for some galaxies very early in structure formation, as indicated by observations (e.g., Shapley et al."85 2004: de Mello et al., 2004; de Mello et al.86 2004) as well as demonstrated. by a numerical model for galaxy formation in the ACDAL universe (Nagamine ct al., 2004) as well as demonstrated by a numerical model for galaxy formation in the $\Lambda$ CDM universe (Nagamine et al.87 2001). anc the metallicity estimated from high redshift quasars.," 2001), and the metallicity estimated from high redshift quasars."88 The cosmic time is short at high. redshift. where these considerations are more relevant., The cosmic time is short at high redshift where these considerations are more relevant.89 The dominant. part of time relevant. to star formation is at low redshift z<12., The dominant part of time relevant to star formation is at low redshift $z<1-2$.90 Alotivatec by these observations. we may take the approximation that all stars have the normal metallicity the same as at low recishift.," Motivated by these observations, we may take the approximation that all stars have the normal metallicity the same as at low redshift."91 We assume that the eas shec by stellar evolution has solar metallicity on average whether gas taken into star formation is pristine or already somewhat enriched., We assume that the gas shed by stellar evolution has solar metallicity on average whether gas taken into star formation is pristine or already somewhat enriched.92 The amount of dust. produced by gas shed by stars is then which is about 2.5 times larger than the global amount of dust in galactic discs given in (5))., The amount of dust produced by gas shed by stars is then which is about 2.5 times larger than the global amount of dust in galactic discs given in \ref{eq:discdust}) ).93 The total heavy. clement abundance calculated: with this approximation correctly reprocuces the abundance observed at zzO0. which in turn is constrained by the total energy output. as explored. by extragalactic background light. as shown in E04.," The total heavy element abundance calculated with this approximation correctly reproduces the abundance observed at $z\approx0$, which in turn is constrained by the total energy output as explored by extragalactic background light, as shown in FP04."94 We also stress that a number of uncertainties in the calculation. such as those in the initial mass function. mean metallicity. and the dust/Z ratio. cancel when one compares eq. (5))," We also stress that a number of uncertainties in the calculation, such as those in the initial mass function, mean metallicity, and the dust/Z ratio, cancel when one compares eq. \ref{eq:discdust}) )"95 with eq. (6)).," with eq. \ref{eq:SFdust}) ),"96 so that the error in the relative values is not excessively larger., so that the error in the relative values is not excessively larger.97 The integral of star formation rate still has a significant uncertainty. but it is constrained by the observed amount of stars at z=0 and the fraction of stellar mass loss with the aid of the initial final mass relation. as well as the energy output argument we quoted in section 1.," The integral of star formation rate still has a significant uncertainty, but it is constrained by the observed amount of stars at $z=0$ and the fraction of stellar mass loss with the aid of the initial final mass relation, as well as the energy output argument we quoted in section 1."98 We may take seriously that the eap between the two values. expected amount of dust. produced and that observed in the LU region of galaxies is real.," We may take seriously that the gap between the two values, expected amount of dust produced and that observed in the HI region of galaxies is real."99 This mismatch between the amount of dust that is ought to be produced in stellar evolution and that is observed implies that either we miss dust somewhere in the universe or dust produced. is destroved ancl not all survives to now., This mismatch between the amount of dust that is ought to be produced in stellar evolution and that is observed implies that either we miss dust somewhere in the universe or dust produced is destroyed and not all survives to now.100 At the beginning. the latter may look natural since lifetime of dust is thought to be not very long (Draine Salpeter 1979: Draine 1905: Jones. Tielens Hollenbach 1996: Dwek 1998).," At the beginning, the latter may look natural since lifetime of dust is thought to be not very long (Draine Salpeter 1979; Draine 1995; Jones, Tielens Hollenbach 1996; Dwek 1998)."101 We point out. however. that the recent. detection of dust. reddening observed in the galaxy quasar correlation oomotes us to investigate the former case.," We point out, however, that the recent detection of dust reddening observed in the galaxy quasar correlation promotes us to investigate the former case."102 Using a Large quasar sample and vet an even larger galaxy sample of he Sloan Digital Sky Survey. taking advantage of its high »ecision. multi-colour. photometry. Ménnard. et al. (," Using a large quasar sample and yet an even larger galaxy sample of the Sloan Digital Sky Survey, taking advantage of its high precision multi-colour photometry, Ménnard et al. ("1032010. jereafter. AISER) have found that the quasar light receives reddening when it passes through the vicinity. of galaxies.,"2010, hereafter MSFR) have found that the quasar light receives reddening when it passes through the vicinity of galaxies."104 The colour dependence of attenuation is in agreement with he dust extinction curve known for the Milky Way. although he ratio of total to selective extinction Ay24.943.2 is not well determined.," The colour dependence of attenuation is in agreement with the dust extinction curve known for the Milky Way, although the ratio of total to selective extinction $R_V\approx 4.9\pm3.2$ is not well determined."105 This implies that a large amount ofdust is »esent around. galaxies ranging from 2Okpe to a lew Alpe. which are clearly bevond galactic discs.," This implies that a large amount of dust is present around galaxies ranging from 20kpc to a few Mpc, which are clearly beyond galactic discs."106 The projected: surface density distribution. of dust .ollows rmοςl withH r the projected. distance. fromη the centre of the galaxy. similar to the galaxy mass distribution.," The projected surface density distribution of dust follows $\sim r^{-0.8}-r^{-1}$ with $r$ the projected distance from the centre of the galaxy, similar to the galaxy mass distribution,"107subtracting an extracted. profile derived by interpolation of he continua adjacent to cach spectral line. in a manner analogous to sky subtraction in. conventional spectral reduction.,"subtracting an extracted profile derived by interpolation of the continua adjacent to each spectral line, in a manner analogous to sky subtraction in conventional spectral reduction."108 This was relatively successful for those lines which iive no photospheric or circumstellar counterpart:SU]. O II] and. OLLI. though Ο HI] was alfected by the rapid non-inearlv declining response of the CCD at short wavelengths.," This was relatively successful for those lines which have no photospheric or circumstellar counterpart:[SII], [O II] and [OIII], though [O II] was affected by the rapid non-linearly declining response of the CCD at short wavelengths."109 In the case of the Balmer lines the combined. spatial »ofile from the photosphere ancl circumstellar dise has the same EFWILM in the spatial direction as the continuum. but must be scaled to account for the circumstellar emission.," In the case of the Balmer lines the combined spatial profile from the photosphere and circumstellar disc has the same FWHM in the spatial direction as the continuum, but must be scaled to account for the circumstellar emission."110 The orientation of the slit for the ESO blue spectrum - OL. OH]. and data is NW - SE through the star and the brightest. part of the nebulositv. thus in the context of the bowshock scenario it is usclully aligned along the direction of the stancoll distance /.," The orientation of the slit for the ESO blue spectrum - [OIII], [OII], and data is NW - SE through the star and the brightest part of the nebulosity, thus in the context of the bowshock scenario it is usefully aligned along the direction of the standoff distance $l$."111 Phe OLI) line was expected as it is observed to be amongst the strongest lines in many nebulae. including other bowshock nebulae. LU regions and PNe.," The [OIII] line was expected as it is observed to be amongst the strongest lines in many nebulae, including other bowshock nebulae, HII regions and PNe."112 Narrow band imaging of the field has not. produced a detection at OLLI] A4959.5007 and in the spectral data it is detected only weakly [rom the nebular regions brightest in413.," Narrow band imaging of the field has not produced a detection at [OIII] $\lambda$ 4959,5007 and in the spectral data it is detected only weakly from the nebular regions brightest in."113.. Ht is however observed as a strong feature. from regions much closer to the star itself. to the extent that extraction of the stellar spectrum. shows strong features at the aforementioned. wavelengths. (Figure. 2)). whereas extraction of the neighbouring nebular spectrum. detects them only very weakly.," It is however observed as a strong feature from regions much closer to the star itself, to the extent that extraction of the stellar spectrum shows strong features at the aforementioned wavelengths (Figure \ref{fig:OIII}) ), whereas extraction of the neighbouring nebular spectrum detects them only very weakly."114 This can be understood. with reference to Figure LO which shows spatial profiles of the ΟΙ) and OLLI] emission lines along the spatial axis., This can be understood with reference to Figure 10 which shows spatial profiles of the [OII] and [OIII] emission lines along the spatial axis.115" Whilst the OLLI]. emission. peaks close to the stellar location ancl rapidly crops olf, is observed. to considerably larger distances."," Whilst the [OIII] emission peaks close to the stellar location and rapidly drops off, is observed to considerably larger distances."116 Phe OLLI] emission profile is much more symmetric around the Be star. with only minor enhancement in the direction of strongest Balmer emission.," The [OIII] emission profile is much more symmetric around the Be star, with only minor enhancement in the direction of strongest Balmer emission."117 Additionally OLLI] is scen from the NW side of the Be star where there is negligible Balmer emission., Additionally [OIII] is seen from the NW side of the Be star where there is negligible Balmer emission.118 Where and are brightest there is scarcely any OLLI] emission at all., Where and are brightest there is scarcely any [OIII] emission at all.119 The453. and OH] emission appear to be coincident. though few conclusions can be drawn from the weak detection.," The, and [OII] emission appear to be coincident, though few conclusions can be drawn from the weak detection."120 All are seen only to the SE side of the Bo star. in a manner totally consistent with the distribution seen from the image in Figure S..," All are seen only to the SE side of the Be star, in a manner totally consistent with the distribution seen from the image in Figure \ref{fig:xtej0111halpha}."121" Detection from pixels 15.5 10 02.5 implies an angular diameter of13.9"". or 4.3 pe."," Detection from pixels 75.5 to 92.5 implies an angular diameter of, or 4.3 pc."122 The SAAO red. spectrum - and. SII] - shows the distribution of nebular emission., The SAAO red spectrum - and [SII] - shows the distribution of nebular emission.123 The size of the nebulosity appears to be the same as that of and with detection out to slightly. larger radii because of the much stronger signal. ," The size of the nebulosity appears to be the same as that of and, with detection out to slightly larger radii because of the much stronger signal. ["124SII] appears to trace the exactly.,SII] appears to trace the exactly.125 Ifa spectral classification of B0.5-D1 (CLIR ancl Covino et al. 2001) is accepted. it becomes. possible to calculate the Strómmegren radius within which a uniform cloud. of LI is completely. photoionized. (note this does not apply to the hollow bowshock model) ancl would be expected. to emitfla.," If a spectral classification of B0.5-B1 (CHR and Covino et al, 2001) is accepted it becomes possible to calculate the Strömmgren radius within which a uniform cloud of H is completely photoionized (note this does not apply to the hollow bowshock model) and would be expected to emit."126 This radius is sensitive to spectral class around. 0. in that this classification sensitively cetermines the Lyman continuum flux Qo depending upon the details of the stellar model used.," This radius is sensitive to spectral class around B0, in that this classification sensitively determines the Lyman continuum flux $Q_0$ depending upon the details of the stellar model used."127 Vacca et al. (, Vacca et al. (1281996) tabulate Qu for O3-D0.5V stars. so though one must perform an extrapolation to vield a result. for Bl. the function is a smooth one ancl so the result. expected to be accurate.,"1996) tabulate $Q_0$ for O3-B0.5V stars, so though one must perform an extrapolation to yield a result for B1, the function is a smooth one and so the result expected to be accurate."129 Incorporating the Martins et al. (, Incorporating the Martins et al. (1302002) dwanward revision by of Vacca et al,2002) downward revision by of Vacca et al.131is Qu. one arrives at 4.8107 at BO.5V and δε.107 at DIV. Suitably mocdifving the derivation of equation 6.1.10 from Ixitehin (1987). we arrive at the formula Using the observed nebular radius of 3.05pe requires N=76em at BOS or only [IN25.1em. at BIV. at the lower end of observed. nebular densities. and in agreement with the results of Section 3.3.2. using forbidden line ratios.,"'s $Q_0$, one arrives at $4.8\times10^{47}$ at B0.5V and $2.4\times10^{47}$ at B1V. Suitably modifying the derivation of equation 6A.1.10 from Kitchin (1987), we arrive at the formula Using the observed nebular radius of 3.05pc requires $N_e=7.6cm^{-3}$ at B0.5 or only $N_e=5.1cm^{-3}$ at B1V, at the lower end of observed nebular densities, and in agreement with the results of Section \ref{section:nebdensity} using forbidden line ratios."132 The use of SMC metallicities. reducing line blanketting ellects. raises Qo and thus requires slightly higher densities. but this elfect is only of the order of a [ew," The use of SMC metallicities, reducing line blanketting effects, raises $Q_0$ and thus requires slightly higher densities, but this effect is only of the order of a few."133 This suggests the scenario that the nebulosity is simply an LIL region. perhaps part of a cloud adjacent to and ionized byJ0111.," This suggests the scenario that the nebulosity is simply an HII region, perhaps part of a cloud adjacent to and ionized by."1342-7317.. so. and considering the fact that the calculated densities are very much at the lower end of the range For LILLE regions. why is this structure detectable at all?," If so, and considering the fact that the calculated densities are very much at the lower end of the range for HII regions, why is this structure detectable at all?"135 Most. OB stars rid their neighbourhood of gas carly in their existence via powerful winds., Most OB stars rid their neighbourhood of gas early in their existence via powerful winds.136 Phe answer may lie in 1 fact that as a BeXRB. has a large μα»ce motion (vandenHeuveletal.2000) and has impinged upon a cloud which it has subsequently ionized.," The answer may lie in the fact that as a BeXRB, has a large space motion \cite{vandenheuvel2000} and has impinged upon a cloud which it has subsequently ionized."137 H' this cloud increases in density towards the south-east. (lower [e in the images). the slightlv smaller raclius in this direction can be explained with the Strómmeren sphere argument (Rs= fn(Ng)). or as an ionization front propogating into the cloud.," If this cloud increases in density towards the south-east (lower left in the images), the slightly smaller radius in this direction can be explained with the Strömmgren sphere argument $R_S=fn(N_H)$ ), or as an ionization front propogating into the cloud."138and thus the magnetic field strength begins to increase once again.,and thus the magnetic field strength begins to increase once again.139 The average magnetic Ποια strength D in a galactic disk is à function of the turbulent energy. density., The average magnetic field strength $B$ in a galactic disk is a function of the turbulent energy density.140 Thus. apart [rom the amount of turbulence present. another important parameter is the size of the disk.," Thus, apart from the amount of turbulence present, another important parameter is the size of the disk."141 In the following section we use observations of local galaxies to constrain clisk sizes. and consequently find the value of es~0.003.," In the following section we use observations of local galaxies to constrain disk sizes, and consequently find the value of $\epsilon_{\rm grav} \sim 0.003$."142 This is the value adopted for the rest of the paper., This is the value adopted for the rest of the paper.143 Figure 3. shows the evolution of the magnetic field for each of these haloes., Figure \ref{fig:BcomponentsVsZ} shows the evolution of the magnetic field for each of these haloes.144" The volume of the radio disk used to calculate magnetic field strengths was taken as edsduae where the clisk radius is Rak=0.14245, (Shabala&Alexan-and we adopt disk thickness of Zi.=0.6 kpc (Pint&Alexander.1993)."," The volume of the radio disk used to calculate magnetic field strengths was taken as $\pi R_{\rm disk}^2 T_{\rm disk}$, where the disk radius is $R_{\rm disk} = 0.1 R_{\rm vir}$ \cite{SA09} and we adopt disk thickness of $T_{\rm disk}=0.6$ kpc \cite{FA93}."145. In practice. disk radii derived from radio observations are subject to selection effects.," In practice, disk radii derived from radio observations are subject to selection effects."146 We return to this point in the following section., We return to this point in the following section.147 Wey features of the model are evident in Figure 3.., Key features of the model are evident in Figure \ref{fig:BcomponentsVsZ}.148 In low-mass haloes. interplay between the infall of cool eas and star formation result in substantial contributions to the turbulent energy budget right up to z=0 (Figure 19).," In low-mass haloes, interplay between the infall of cool gas and star formation result in substantial contributions to the turbulent energy budget right up to $z=0$ (Figure \ref{fig:effPot}) )."149 s a result. the bulk of the turbulent (ancl hence magnetic Field) energy density is in the random component.," As a result, the bulk of the turbulent (and hence magnetic field) energy density is in the random component."150 As halo mass increases. so does the strength of AGN feedback.," As halo mass increases, so does the strength of AGN feedback."151 Consequently. the most massive ealaxies (Figure 3dd) are red and dead. with the bulk of the cooling and star formation taking place at 2>1.," Consequently, the most massive galaxies (Figure \ref{fig:BcomponentsVsZ}d d) are red and dead, with the bulk of the cooling and star formation taking place at $z \geq 1$."152 Thus. by 2 0agreater fraction of the turbulent energy has had time to be transferred to the ordered field than in their lowermass counterparts.," Thus, by $z=0$ a greater fraction of the turbulent energy has had time to be transferred to the ordered field than in their lower-mass counterparts."153 So far we have assumed that racio emission is uniforni across the disk., So far we have assumed that radio emission is uniform across the disk.154 Contrary to the assumptions used to plot Figures 3. and 2.. in real disks the emissivity typically. decays exponentially away [rom the disk centre. 1970).," Contrary to the assumptions used to plot Figures \ref{fig:BcomponentsVsZ} and \ref{fig:BvsMhalo}, in real disks the emissivity typically decays exponentially away from the disk centre \cite{Freeman70}."155. As a result. essentially all the source Dux is observed within a few scale heights. while the observed racial extent of the disk will be ereatly alfected by selection effects such as the limiting beam-averaged surface brightness.," As a result, essentially all the source flux is observed within a few scale heights, while the observed radial extent of the disk will be greatly affected by selection effects such as the limiting beam-averaged surface brightness."156 In. general. it ds dillieult to quantify these effects. and we choose to parametrise the size of the radio disk via the quantity eq. such that 2isuis—Clink!Pilisk-," In general, it is difficult to quantify these effects, and we choose to parametrise the size of the radio disk via the quantity $\epsilon_{\rm disk}$, such that $R_{\rm disk,radio}=\epsilon_{\rm disk} R_{\rm disk}$."157 Figure 4 compares preclictecl disk sizes with observations of late-tvpe galaxies from the sample of Fitt— Alexander (1993)., Figure \ref{fig:diskSizes} compares predicted disk sizes with observations of late-type galaxies from the sample of Fitt Alexander (1993).158" ""ποσο authors considered radio properties of an opticallv-complete subsample of 165 late-twpe galaxies brighter than magnitude By=|12. drawn from the Hevised Shapley Ames Catalogue (RSA: Sandage Tanmann 1981)."," These authors considered radio properties of an optically-complete subsample of 165 late-type galaxies brighter than magnitude $B_T = +12$, drawn from the Revised Shapley Ames Catalogue (RSA; Sandage Tammann 1981)."159 These were complemented bv VLA observations at 1.49 Giz (Condon1987).. vielding an opticallv-complete sample of 146 ealaxics with resolved. radio disks.," These were complemented by VLA observations at 1.49 GHz \cite{Condon87}, yielding an optically-complete sample of 146 galaxies with resolved radio disks."160 Of the remaining 19 galaxies. one hac unresolved. radio stucture. eight. more hack no radio detections: and the remainder sullered. (rom confusion or were not properly imaged by the observations.," Of the remaining 19 galaxies, one had unresolved radio stucture, eight more had no radio detections; and the remainder suffered from confusion or were not properly imaged by the observations."161 Stellar masses in. Figure. + and. the subsequent discussion were derived from A-band magnitudes under the assumption that all stars are of solar type (Shabalactal.2008:Nikolicetal. 2004).," Stellar masses in Figure \ref{fig:diskSizes} and the subsequent discussion were derived from $K$ -band magnitudes under the assumption that all stars are of solar type \cite{SAAR08,NikolicEA04}."162. Comparison of predicted: and observed disk sizes shows that setting cic=0.25 gives good agreement with observations., Comparison of predicted and observed disk sizes shows that setting $\epsilon_{\rm disk}=0.25$ gives good agreement with observations.163 It is worth noting that since smaller disks are associated with higher turbulent. energy densities (for fixed total turbulent energy). greater magnetic field strengths are predicted for these.," It is worth noting that since smaller disks are associated with higher turbulent energy densities (for fixed total turbulent energy), greater magnetic field strengths are predicted for these."164 iut Alexander (1993) used. the observed angular sizes of the radio disk to derive cquipartition magnetic field streneths., Fitt Alexander (1993) used the observed angular sizes of the radio disk to derive equipartition magnetic field strengths.165 They modelled. the svnchrotron disk. in cach ealaxy as having the radius given by imaging the galaxy at 1.49 111: and took an equivalent cüsk width of 0.6 kpc., They modelled the synchrotron disk in each galaxy as having the radius given by imaging the galaxy at 1.49 GHz; and took an equivalent disk width of 0.6 kpc.166 This is the disk thickness we adopt for the rest of this paper., This is the disk thickness we adopt for the rest of this paper.167 With disk volume fixed. magnetic field strength is a function ofa single parameter Gury. parametrising the elficiency with which the potential energy of infalling cold gas is converted to turbulent energy.," With disk volume fixed, magnetic field strength is a function of a single parameter $\epsilon_{\rm grav}$, parametrising the efficiency with which the potential energy of infalling cold gas is converted to turbulent energy."168 Phe predicted and observed: magnetic Ποιά strengths arc shown as a function of stellar mass [or dilferent. values of c. in Figure 5.., The predicted and observed magnetic field strengths are shown as a function of stellar mass for different values of $\epsilon_{\rm grav}$ in Figure \ref{fig:BvsMstars}. .169 VLA sensitivity. sets a limit on the strength. of the weakest detectable magnetic field in the Fitt Alexander (1993) sample., VLA sensitivity sets a limit on the strength of the weakest detectable magnetic field in the Fitt Alexander (1993) sample.170 This is given. by (see Pitt Alexander, This is given by (see Fitt Alexander171was not good enough to confirm the ssecond photometric variability quantitatively by means of a Fourier analysis of this sparse data set.,was not good enough to confirm the second photometric variability quantitatively by means of a Fourier analysis of this sparse data set.172" To determine the mass of0317-853,, we used synthetic bolometric colours and absolute magnitudes for carbon-oxygen (CO) core white-dwarf cooling models with thick hydrogen layers (My/M,= 107)Mngjliodels;; when required, we used oxygen-neon (ONe) core white-dwarf cooling models with hydrogen layers of My/M.=10~°"," To determine the mass of, we used synthetic bolometric colours and absolute magnitudes for carbon-oxygen (CO) core white-dwarf cooling models with thick hydrogen layers $M_{\rm H}/M_\ast=10^{-4}$ ); when required, we used oxygen-neon (ONe) core white-dwarf cooling models with hydrogen layers of $M_{\rm H}/M_\ast=10^{-6}$."173" We determined the “observed” absolute visual magnitude Mes=V+5logm—512.51 mag from V=14.90 and x=0.033279"".", We determined the “observed” absolute visual magnitude $M_V^{\rm obs}=V+5\log \pi -5=12.51$ mag from $V=14.90$ and $\pi=0.033279^{\prime\prime}$.174" For a given effective temperature and surface gravity, the theoretical bolometric magnitude My, the bolometric correction B.C.2Myy;—My, and mass m for wwere calculated."," For a given effective temperature and surface gravity, the theoretical bolometric magnitude $M_{\rm bol}$, the bolometric correction $M_{\rm bol}-M_V$, and mass $m$ for were calculated."175 The theoretical absolute visual magnitude was defined by The contour plots for |M?*—M1*| are shown in reffig:fit for the two possible core compositions., The theoretical absolute visual magnitude was defined by The contour plots for $|M_V^{\rm obs}-M_V^{\rm theo}|$ are shown in \\ref{fig:fit} for the two possible core compositions.176" For both compositions, a satisfactory minimum could be reached only for parts of the range of effective temperatures between 0000 and KK because the tables were limited to an upper value of logg=9.5 for the case of the CO cores (logg=9.5 corresponds to a mass of ffor KK and a mass of ffor KK) and to an upper limit of ffor the ONe models."," For both compositions, a satisfactory minimum could be reached only for parts of the range of effective temperatures between 000 and K because the tables were limited to an upper value of $\log g=9.5$ for the case of the CO cores $\log g=9.5$ corresponds to a mass of for K and a mass of for K) and to an upper limit of for the ONe models."177" We calculated the minimum of |M?5—ΜΜΟΟΙ for a given mass of our range of effective temperatures; when a mass solution could not be reached inside the calculated grids, we extrapolated the theoretical magnitudes."," We calculated the minimum of $|M_V^{\rm obs}-M_V^{\rm theo}|$ for a given mass of our range of effective temperatures; when a mass solution could not be reached inside the calculated grids, we extrapolated the theoretical magnitudes."178" For an effective temperature of 30000 KK, we estimated masses of 1.32+0.02 (CO core) and 1.28+0.02 (ONe core)."," For an effective temperature of $30\,000$ K, we estimated masses of $1.32\pm0.02$ (CO core) and $1.28\pm0.02$ (ONe core)."179" Our CO-core calculations are consistent with the estimates of(?), who assumed a distance of 30ppc."," Our CO-core calculations are consistent with the estimates of, who assumed a distance of pc."180 The highest temperature for which we could obtain a solution in the [Mors—Mt*| diagram is about 48000 KK from which we inferred a mass ofMsolar.," The highest temperature for which we could obtain a solution in the $|M_V^{\rm obs}-M_V^{\rm theo}|$ diagram is about $48\,000$ K from which we inferred a mass of."181 Any additional extrapolation may introduce substantial uncertainty because we are then approaching the Chandrasekhar limit., Any additional extrapolation may introduce substantial uncertainty because we are then approaching the Chandrasekhar limit.182" In the grid of theoretical values for ONe cores, we performed significant extrapolation to obtain solutions above KK (see reffig:extrapolation))."," In the grid of theoretical values for ONe cores, we performed significant extrapolation to obtain solutions above K (see \\ref{fig:extrapolation}) )."183" For Teg= 30000KK, we obtained a mass of 1.28 aand inferred an error of +0.015 from the uncertainty in the observed visual magnitude and the parallax."," For $\Teff=30\,000$ K, we obtained a mass of $1.28$ and inferred an error of $\pm 0.015$ from the uncertainty in the observed visual magnitude and the parallax."184" For an effective temperature of 50000 KK, we derived 1.38 with a slightly higher error estimate of 0.020 ddue to the uncertainty of the extrapolation."," For an effective temperature of $50\,000$ K, we derived $1.38$ with a slightly higher error estimate of $0.020$ due to the uncertainty of the extrapolation."185 The results are, The results are186(see Begeman 1989:: see also the discussion by Dutton et al.,(see Begeman \cite{begeman89}; see also the discussion by Dutton et al.187 2005)., 2005).188 For simplicity. in the folowing we will consider the galaxy as bulgeless and we will ignore the contribution of the gaseous disk.," For simplicity, in the following we will consider the galaxy as bulgeless and we will ignore the contribution of the gaseous disk."189 We recall that the simple analysis provided in Sect. ??..," We recall that the simple analysis provided in Sect. \ref{degremoval},"190 applied to the inner parts of the rotation curve. suggests that the maximum-disk decomposition for NGC 3198 has 3NPRONGC398=10.," applied to the inner parts of the rotation curve, suggests that the maximum-disk decomposition for NGC 3198 has $\beta_{max}^{NGC 3198}\approx 10$."191 In this case the rotation curve is provided with its observational errors., In this case the rotation curve is provided with its observational errors.192 To evaluate quantitatively the goodness of a given disk-halo decomposition. we then adopt the classical likelihood function: where Var[V(R;)] denotes the square of the error associated with the /-th rotation curve data-point.," To evaluate quantitatively the goodness of a given disk-halo decomposition, we then adopt the classical likelihood function: where $\mathrm{Var}\left[V(R_i)\right]$ denotes the square of the error associated with the $i$ -th rotation curve data-point."193 In order to bring out the explicit dependence of the likelihood A on the assumed value of V4. we note at the previous equation can be written as: in which the function v(Q.or.B) is normalized to unity at large radit.," In order to bring out the explicit dependence of the likelihood $\Lambda $ on the assumed value of $V_{\infty}$, we note that the previous equation can be written as: in which the function $v_{mod}(R,\alpha,\beta)$ is normalized to unity at large radii."194" We note that the rotation curve data from four to eleven ου. lengths suggest However in order to avoid a possible bias that might be introduced by ""freezing"" this quantity. we treat the asymptotic velocity V4 às a free parameter. to be determined by the fitting procedure together with « and f."," We note that the rotation curve data from four to eleven exponential lengths suggest However, in order to avoid a possible bias that might be introduced by “freezing"" this quantity, we treat the asymptotic velocity $V_{\infty}$ as a free parameter, to be determined by the fitting procedure together with $\alpha$ and $\beta$."195 Figure 15. shows the results of the parametric disk-halo decomposition in the (4.9) plane. that is. after integrating out the dependence on V4 in the likelihood Eq. (32)):," Figure \ref{p3198} shows the results of the parametric disk-halo decomposition in the $(\alpha, \beta)$ plane, that is, after integrating out the dependence on $V_{\infty}$ in the likelihood Eq. \ref{lik}) ):"196 The contours identify regions of 68% and 95% confidence level: the best-fit model is marked by a full dot., The contours identify regions of $68\%$ and $95\%$ confidence level; the best-fit model is marked by a full dot.197 Interestingly. two maxima exist. located along the disk-halo degeneracy strip described in the previous subsection. but with significantly different. physical properties.," Interestingly, two maxima exist, located along the disk-halo degeneracy strip described in the previous subsection, but with significantly different physical properties."198 In fact. for varying values of the asymptotic velocity V4. the location of the fit model in the(α.β) plane ((at fixed Vo) changes.," In fact, for varying values of the asymptotic velocity $V_{\infty}$, the location of the best-fit model in the $(\alpha, \beta)$ plane (at fixed $V_{\infty}$ ) changes."199 As a result. the integrated likelihood Eq. (35))," As a result, the integrated likelihood Eq. \ref{likred}) )"200 actually increases the amount of degeneracy associated with the parametric disk-halo decomposition., actually increases the amount of degeneracy associated with the parametric disk-halo decomposition.201 This is particularly evident from Fig. 16..," This is particularly evident from Fig. \ref {p3198p},"202 which shows the projections along the two separate parameters « and £ of the the likelihood itself. exhibiting a clear bimodality.," which shows the projections along the two separate parameters $\alpha$ and $\beta$ of the the likelihood itself, exhibiting a clear bimodality."203 The disk-halo decomposition is unable to select between a solution very close to the maximum-disk and a decomposition with a much lighter disk., The disk-halo decomposition is unable to select between a solution very close to the maximum-disk and a decomposition with a much lighter disk.204 The corresponding decompositions are illustrated in Figs., The corresponding decompositions are illustrated in Figs.205 17 and 18.. which show the two best-fit parametric decompositions. with projections on the (a.8) plane contained respectively in the two separate areas of the confidence regions in Fig. 15..," \ref{max3198} and \ref {min3198}, which show the two best-fit parametric decompositions, with projections on the $(\alpha, \beta)$ plane contained respectively in the two separate areas of the confidence regions in Fig. \ref{p3198}."206 This curious result may be related to the specific structure of the rotation curve of NGC 3198 (but see also Appendix Β)., This curious result may be related to the specific structure of the rotation curve of NGC 3198 (but see also Appendix B).207 In any case. the general statement holds. that the parametric decomposition ts unable to lead to a unique determination of the weight of the stellar disk.," In any case, the general statement holds, that the parametric decomposition is unable to lead to a unique determination of the weight of the stellar disk."208 For completeness. we record the coordinates of the best-fit model in the (V4.o.8) space. together with the related reduced y- value: Here we have defined The situation is completely different if. the disk-halo decomposition is performed by means of the self-consistent," For completeness, we record the coordinates of the best-fit model in the $(V_{\infty}, \alpha, \beta)$ space, together with the related reduced $\chi^2$ value: Here we have defined The situation is completely different if the disk-halo decomposition is performed by means of the self-consistent"209In the light curves (see Fig. 6)).,"In the light curves (see Fig. \ref{L_inj_lc}) ),"210 the more rapid electron cooling with increasing electron injection power manifests itself in an overall increasing amplitude of variability at all energies., the more rapid electron cooling with increasing electron injection power manifests itself in an overall increasing amplitude of variability at all energies.211 In parücular. as SSC! cooling becomes more important. even the harder N-rayvs begin {ο exhibit significant variability on the dvnamical time scale. in contrast to the dominated cases.," In particular, as SSC cooling becomes more important, even the harder X-rays begin to exhibit significant variability on the dynamical time scale, in contrast to the synchrotron-cooling dominated cases."212 Furthermore. while for very low injection powers. the svnchrotron cooling time scale for optical svuchrotron emission is comparable to the injection lime scale. resulting in a time delay of ~ a lew hr between X-ray. and optical emission. the optical light curve peaks at the end of the injection episode for hieher injection powers. simultaneously with the X-ravs.," Furthermore, while for very low injection powers, the synchrotron cooling time scale for optical synchrotron emission is comparable to the injection time scale, resulting in a time delay of $\sim$ a few hr between X-ray and optical emission, the optical light curve peaks at the end of the injection episode for higher injection powers, simultaneously with the X-rays."213 However. when SSC cooling becomes dominant. the gradually. increasing enerev densitv in the soft photon field during the injection episode actually has the ellect that the N-ray light curves are peaking al the beginning of the injection episode. which would. again. lead to a lime delay of ~ a few hr between X-ray and optical Lares.," However, when SSC cooling becomes dominant, the gradually increasing energy density in the soft photon field during the injection episode actually has the effect that the X-ray light curves are peaking at the beginning of the injection episode, which would, again, lead to a time delay of $\sim $ a few hr between X-ray and optical flares."214 Fig., Fig.215 Y illustrates how the tracks in the IHIDs at dillerent X-ray. energies are clrastically changing for different injection powers., \ref{L_inj_hic} illustrates how the tracks in the HIDs at different X-ray energies are drastically changing for different injection powers.216 In particular al X-ray. energies just below or at the svachrotron eutoff (I1 keV). the [Iux maxima are occurring at significantlv different. values of the local spectral index α [or different values of the injection power.," In particular at X-ray energies just below or at the synchrotron cutoff $\sim 1$ keV), the flux maxima are occurring at significantly different values of the local spectral index $\alpha$ for different values of the injection power."217 Specifically. the local spectral indices at the time of the peak flux are significantly smaller (harcer) lor larger values of the injection power.," Specifically, the local spectral indices at the time of the peak flux are significantly smaller (harder) for larger values of the injection power."218 Obvious changes in the orientation of the spectral hysteresis (racks are not found in these simulations., Obvious changes in the orientation of the spectral hysteresis tracks are not found in these simulations.219 As mentioned earlier (see Eq. 3)).," As mentioned earlier (see Eq. \ref{tau_sy}) ),"220 in (he test cases investigated here. the svnehrotron cooling (ime scale of electrons emitting svnchrotron radiation at X-ray energies. is shorter than the dvnamieal time scale. which is of the same order as the injection (ime scale.," in the test cases investigated here, the synchrotron cooling time scale of electrons emitting synchrotron radiation at X-ray energies, is shorter than the dynamical time scale, which is of the same order as the injection time scale."221" Consequently. our results can be qualitatively compared to those of Li&INusunose(2000) Lor the ""short cooling time limit”. bearing in mind that the parameter values in our simulations have been chosen appropriate for imtermediate and LBLs. while Li&lusunose(2000) focused on the application to the HBL Mik 421."," Consequently, our results can be qualitatively compared to those of \cite{lk00} for the “short cooling time limit”, bearing in mind that the parameter values in our simulations have been chosen appropriate for intermediate and LBLs, while \cite{lk00} focused on the application to the HBL Mrk 421."222 In particular the light curves displayed in thei Figs., In particular the light curves displayed in their Figs.223 9. 11 exhibit the same general trends as we have found in our set of simulations., 9 – 11 exhibit the same general trends as we have found in our set of simulations.224 In order to investigate the influence of an increasing contribution of external photons to the πο photon field for Compton scattering. we performed a series of simulations with increasing values of 7jpig. from Oto 1.," In order to investigate the influence of an increasing contribution of external photons to the soft photon field for Compton scattering, we performed a series of simulations with increasing values of $\tau_{\rm T, BLR}$, from 0 to 1."225 We note that the contribution from direct accretion disk photons to the photon energy densitv in (he emitüneg region is negligible in our base model., We note that the contribution from direct accretion disk photons to the photon energy density in the emitting region is negligible in our base model.226 Thus. in (he following. the external photons are primarily accretion disk photons reprocessed in the DLR.," Thus, in the following, the external photons are primarily accretion disk photons reprocessed in the BLR."227 An additional component due to direct accretion disk. photons, An additional component due to direct accretion disk photons228High dynamie range VLBI and VLA maps are available for NGC 6251 at 6. 13. and 18 em. showing a bright core. a jet/counterjet brightness ratio of ~80 to 1 (Jones et al.,"High dynamic range VLBI and VLA maps are available for NGC 6251 at 6, 13, and 18 cm, showing a bright core, a jet/counterjet brightness ratio of $\sim 80$ to 1 (Jones et al."229 1986)., 1986).230 The fact that the source has a nuclear structure and a large scale radio morphology. implies relativistic beaming.," The fact that the source has a nuclear structure and a large scale radio morphology, implies relativistic beaming."231 Blazars detected by EGRET are compact radio sources. with radio spectral indices =—0.5.," Blazars detected by EGRET are compact radio sources, with radio spectral indices $\geq -0.5$."232 The kpe-scale jet of NGC 6251 has a slightly smaller spectral index (-0.64) (Saunders et al., The kpc-scale jet of NGC 6251 has a slightly smaller spectral index (-0.64) (Saunders et al.233 1981). but it could account for relativistic electrons and inverse Compton emission in this source (Jones. et al.," 1981), but it could account for relativistic electrons and inverse Compton emission in this source (Jones, et al."234 1986)., 1986).235 Figure 5 shows the spectral energy distribution of NGC 6251 assuming that it is the counterpart to 3EG J1621+8203., Figure 5 shows the spectral energy distribution of NGC 6251 assuming that it is the counterpart to 3EG J1621+8203.236 The radio through optical data for the plot are from Ho (1999) and the references therein., The radio through optical data for the plot are from Ho (1999) and the references therein.237 TheROSAT data is from Worrall Birkinshaw (1994) who find that of the total PSPC flux comes from an unresolved component of diameter «4., The data is from Worrall Birkinshaw (1994) who find that of the total PSPC flux comes from an unresolved component of diameter $\leq 4''$.238 TheASCA data is from Sambruna. Eracleous Mushotzky (1999) and agrees with the continuum model of Turner et al. (," The data is from Sambruna, Eracleous Mushotzky (1999) and agrees with the continuum model of Turner et al. ("2391997) who analyzed the data previously.,1997) who analyzed the data previously.240 We have also included VLBI and VLA data at 2.22. 6. and 18 em (Jones et al.," We have also included VLBI and VLA data at 2.22, 6, and 18 cm (Jones et al."241 1986)., 1986).242 Similar to Cen A. the high energy gamma-ray emission from 3EG J1621+8203 represents a lower luminosity (3.«107 eres/s) than that of other EGRET blazars (typically 10? to 10* ergs/s).," Similar to Cen A, the high energy gamma-ray emission from 3EG J1621+8203 represents a lower luminosity $3\times 10^{43}$ ergs/s) than that of other EGRET blazars (typically $10^{45}$ to $10^{48}$ ergs/s)."243 Sreekumar et al. (, Sreekumar et al. (2441999) note that Cen A has a gamma-ray photon spectral index of 2.4040.28. which is steeper than the average power-law spectrum from gamma-ray blazars (2.15+ 0.04). and the spectrum of the extragalactic gamma-ray background (2.10237: 0.03).,"1999) note that Cen A has a gamma-ray photon spectral index of $2.40\pm 0.28$, which is steeper than the average power-law spectrum from gamma-ray blazars $2.15\pm 0.04$ ), and the spectrum of the extragalactic gamma-ray background $2.10\pm 0.03$ )."245 The gamma-ray spectral index of 3EG J1621+8203 has a larger error (2.27+0.53). but it may be worth noting that it too is probably steeper than the average blazar spectrum.," The gamma-ray spectral index of 3EG J1621+8203 has a larger error $\pm$ 0.53), but it may be worth noting that it too is probably steeper than the average blazar spectrum."246 Unlike Cen A. however. NGC 6251 has not been detected by either COMPTEL or OSSE.," Unlike Cen A, however, NGC 6251 has not been detected by either COMPTEL or OSSE."247 There is no upper limit for this source in the first COMPTEL source catalog (Schónnfelder et al., There is no upper limit for this source in the first COMPTEL source catalog (Schönnfelder et al.248 2000)., 2000).249 The sensitivity of EGRET to off-axis emission from AGN. whose jets are pointed away from our line-of-sight. needs to be addressed.," The sensitivity of EGRET to off-axis emission from AGN, whose jets are pointed away from our line-of-sight, needs to be addressed."250" The total amount of scattered energy. ΕΙ. as a function of viewing angle for an active galaxy may be estimated using the relation (see Dermer. Schlickeiser. Mastichiadis 1992; Weferling Schlickeiser 1999), where the gamma-ray flux seen by the observer is due to the scattered inverse Compton emission of ambient low energy photons by highly relativistic particles in the jet."," The total amount of scattered energy, $F_1$, as a function of viewing angle for an active galaxy may be estimated using the relation (see Dermer, Schlickeiser, Mastichiadis 1992; Weferling Schlickeiser 1999), where the gamma-ray flux seen by the observer is due to the scattered inverse Compton emission of ambient low energy photons by highly relativistic particles in the jet."251 In this case. the particles are assumed to be electrons and positrons. distributed in energy as a power-law with a spectral index of s.," In this case, the particles are assumed to be electrons and positrons, distributed in energy as a power-law with a spectral index of $s$."252 αὖ 1s the cosine of the angle between the jet axis and the direction to the observer. and D is the Doppler factor of the blob. defined as D=TUy! where Je is the bulk velocity of the plasma.," $\mu_s^*$ is the cosine of the angle between the jet axis and the direction to the observer, and $D$ is the Doppler factor of the blob, defined as $D=\Gamma^{-1}(1-\beta\mu_s^*)^{-1}$, where $\beta c$ is the bulk velocity of the plasma."253 Figure 6 shows the decrease in scattered energy for off-axis emission. using the above relation. for different viewing angles. corresponding to two typical values of Lorentz factors (D) seen in blazars.," Figure 6 shows the decrease in scattered energy for off-axis emission, using the above relation, for different viewing angles, corresponding to two typical values of Lorentz factors $\Gamma$ ) seen in blazars."254 The figure shows that a decrease in observer angle from 70° (e.g. Cen A) to 45° (e.g. NGC 6251) corresponds to an increase in the scattered energy by about a factor of 10. all other things assumed equal.," The figure shows that a decrease in observer angle from $70^\circ$ (e.g. Cen A) to $45^\circ$ (e.g. NGC 6251) corresponds to an increase in the scattered energy by about a factor of 10, all other things assumed equal."255 Cen A (z=0.0018) is the only source to be detected by EGRET with à large inclination angle. presumably due to its proximity to Earth.," Cen A $z=0.0018$ ) is the only source to be detected by EGRET with a large inclination angle, presumably due to its proximity to Earth."256 NGC 6251 (z20.0234) ts much further away. but it is possible that the source is still detectable by EGRET due to its smaller jet angle.," NGC 6251 $z=0.0234$ ) is much further away, but it is possible that the source is still detectable by EGRET due to its smaller jet angle."257 The threshold sensitivity of EGRET (7100 MeV) for a single 2-week observation was 3«1077 photons em s! (Thompson et al., The threshold sensitivity of EGRET $> 100$ MeV) for a single 2-week observation was $\sim 3\times 10^{-7}$ photons $^{-2}$ $^{-1}$ (Thompson et al.258 1993)., 1993).259 Due to the intrinsically low luminosity of radio galaxies and the limitations of EGRET's sensitivity. it is not surprising that many radio galaxies have not been detected as gamma-ray sources above 100 MeV thus far.," Due to the intrinsically low luminosity of radio galaxies and the limitations of EGRET's sensitivity, it is not surprising that many radio galaxies have not been detected as gamma-ray sources above 100 MeV thus far."260 It is very likely that more distant radio-loud AGN with intermediate inclination angles will be detected in the future with higher sensitivity gamma-ray instruments., It is very likely that more distant radio-loud AGN with intermediate inclination angles will be detected in the future with higher sensitivity gamma-ray instruments.261 FR I galaxies have been hypothesized to be the likely parent populations of BL Lac objects. which are believed to be beamed FR I galaxies (Padovani Urry 1990: Ghisellint et al.," FR I galaxies have been hypothesized to be the likely parent populations of BL Lac objects, which are believed to be beamed FR I galaxies (Padovani Urry 1990; Ghisellini et al."262 1993)., 1993).263 Since the number density of radio-loud FR I sources is nearly 1000 times larger than FSRQs and BL Lac objects. the possibility that such sources could form a new source class for future instruments like VERITAS (e.g. Weekes et al.," Since the number density of radio-loud FR I sources is nearly 1000 times larger than FSRQs and BL Lac objects, the possibility that such sources could form a new source class for future instruments like VERITAS (e.g. Weekes et al."264 2000) or GLAST (e.g. Gehrels Michelson 1999) ts an exciting one., 2000) or GLAST (e.g. Gehrels Michelson 1999) is an exciting one.265 NGC 6251=3EG J1621+8203 and Cen A=3EG J1324-4314 could be examples of such sources., NGC 6251=3EG J1621+8203 and Cen A=3EG J1324-4314 could be examples of such sources.266" In fact. there exists the likelihood that such “misaligned blazars"" could contribute to the extragalactic gamma-ray background around | MeV (Stienle et al."," In fact, there exists the likelihood that such “misaligned blazars” could contribute to the extragalactic gamma-ray background around 1 MeV (Stienle et al."267 1998: Sreekumar et al., 1998; Sreekumar et al.268 1999; Watanabe Hartmann 2001)., 1999; Watanabe Hartmann 2001).269relatively old stellar population.,relatively old stellar population.270 The SNIa rate is ~0.1 per 10!?M per century in galaxy clusters (Sharonetal., The SNIa rate is $\sim0.1$ per $10^{10}\ \rm{M_{\odot}}$ per century in galaxy clusters \citep{Sharon07}.271" Assuming each SNIa releases 10°! ergs thermal energy 2007)..into heating up the ICM, the heating rate then is expressed as Mejia, (in Mo) x10°8 ergs yr! Ms! and the SNIa heating timescale can be estimated as where pgas and Pstellar are the local gas and the stellar densities."," Assuming each SNIa releases $10^{51}$ ergs thermal energy into heating up the ICM, the heating rate then is expressed as $_{stellar}$ (in $\rm{M_{\odot}}$ ) $\times 10^{38}$ ergs $^{-1}$ $_{\odot}^{-1}$ and the SNIa heating timescale can be estimated as where $\rho_{\rm gas}$ and $\rho_{\rm stellar}$ are the local gas and the stellar densities."272" This timescale is plotted in Figure 6,, which shows that although SNIa can be an important source of heating at rS1 kpc and might slightly delay the formation of the cooling flow, it would not prevent the cooling catastrophe because too) is always shorter than ἔανια at all radii."," This timescale is plotted in Figure \ref{fig_time}, which shows that although SNIa can be an important source of heating at $r\lesssim 1$ kpc and might slightly delay the formation of the cooling flow, it would not prevent the cooling catastrophe because $t_{\rm cool}$ is always shorter than $t_{\rm SNIa}$ at all radii."273" To test the influence of resolution on our results, we perform simulations with Nroot=64 and 128 (keeping a= —1.2) to compare with our standard Nyoot=256 run."," To test the influence of resolution on our results, we perform simulations with $N_{\rm root} = 64$ and $128$ (keeping $\alpha = -1.2$ ) to compare with our standard $N_{\rm root} = 256$ run."274 Figure 12 shows the density and temperature profiles of the cooling gas at a similar stage of the evolution (~2 Myr after the cooling catastrophe starts)., Figure \ref{fig_resolution} shows the density and temperature profiles of the cooling gas at a similar stage of the evolution $\sim 2$ Myr after the cooling catastrophe starts).275" The overall behavior of the solution is seen to be relatively independent of resolution; however, there is a systematic trend for the temperature plateau in the intermediate region (between 100 pc and 20 kpc) to be even flatter as the resolution increases, while the transition radius shrinks."," The overall behavior of the solution is seen to be relatively independent of resolution; however, there is a systematic trend for the temperature plateau in the intermediate region (between 100 pc and 20 kpc) to be even flatter as the resolution increases, while the transition radius shrinks."276" We do keep the maximum refinement level constant (lmax=15), so the highest resolution achieved increases by a factor of two in each case; however, even for the lowest resolution run, this corresponds to 7 pc, considerably smaller than the ~100 pc transition radius."," We do keep the maximum refinement level constant $(l_{\rm max} = 15$ ), so the highest resolution achieved increases by a factor of two in each case; however, even for the lowest resolution run, this corresponds to 7 pc, considerably smaller than the $\sim 100$ pc transition radius."277" Therefore, we argue that it is not the maximum resolution that is the key, but the resolution achieved in the early stages of the collapse."," Therefore, we argue that it is not the maximum resolution that is the key, but the resolution achieved in the early stages of the collapse."278" Since the point where the cooling catastrophe happens (the transition radius) is sensitive to the temperature and density profiles at earlier stages, we want to well resolve the early evolution of the cooling gas in the center of the cluster."," Since the point where the cooling catastrophe happens (the transition radius) is sensitive to the temperature and density profiles at earlier stages, we want to well resolve the early evolution of the cooling gas in the center of the cluster."279" Changing a in the baryon mass refinement criterion (see Section ??)) can affect the resolution, especially in the early stage inside the cluster core, and has a significant impact on the final results."," Changing $\alpha$ in the baryon mass refinement criterion (see Section \ref{sec:methodology_refinement}) ) can affect the resolution, especially in the early stage inside the cluster core, and has a significant impact on the final results."280" The bottom two panels of Figure 12 show a comparison of runs with the same number of root cells Nyoot=128, but different values for a."," The bottom two panels of Figure \ref{fig_resolution} show a comparison of runs with the same number of root cells $N_{\rm root} = 128$, but different values for $\alpha$."281" Again, the results are shown at a point roughly 2 Myr after the cooling catastrophe starts."," Again, the results are shown at a point roughly $2$ Myr after the cooling catastrophe starts."282" At fixed radius, the gas density is lower and the temperature is higher with more negative a, and the transition radius is smaller."," At fixed radius, the gas density is lower and the temperature is higher with more negative $\alpha$, and the transition radius is smaller."283" Noticeably, with a=—0.1, the initial cooling region has a size of ~1 kpc, more than an order of magnitude larger than that in the run with a=—1.2."," Noticeably, with $\alpha = -0.1$, the initial cooling region has a size of $\sim 1$ kpc, more than an order of magnitude larger than that in the run with $\alpha = -1.2$."284 This is despite the fact that each calculation has the same maximum resolution., This is despite the fact that each calculation has the same maximum resolution.285 We also notice that there is a degeneracy between o and Nroot: a higher Nroot has a similar effect as a more negative o., We also notice that there is a degeneracy between $\alpha$ and $N_{\rm root}$: a higher $N_{\rm root}$ has a similar effect as a more negative $\alpha$.286 This is because they both result in better mass resolution (see Equation 5)) in the center of the cluster as the cooling catastrophe develops., This is because they both result in better mass resolution (see Equation \ref{eq:m_cell}) ) in the center of the cluster as the cooling catastrophe develops.287" If we only increase the maximum refinement level [μιαν without changing N,-oo¢ or a, the result does not change despite a smaller cell size at the highest refinement level."," If we only increase the maximum refinement level $l_{max}$ without changing $N_{root}$ or $\alpha$, the result does not change despite a smaller cell size at the highest refinement level."288 Thus we argue that it is crucial to have sufficiently high resolution at the early stage of the gas evolution., Thus we argue that it is crucial to have sufficiently high resolution at the early stage of the gas evolution.289" Although we have not been able to achieve completeconvergence in these calculations, it is clear that higher resolution tends to produce flatter temperature profiles and smaller transition radii."," Although we have not been able to achieve completeconvergence in these calculations, it is clear that higher resolution tends to produce flatter temperature profiles and smaller transition radii."290" Another difference between simulations with different resolution is that in low resolution runs (e.g. with N55,=64 and a= —0.2), the pressure drops dramatically inside rS1 κρο when the central gas density and temperature show a sudden change, forming a pressure hole which then grows deeper and larger with time."," Another difference between simulations with different resolution is that in low resolution runs (e.g. with $N_{root} = 64$ and $\alpha = -0.2$ ), the pressure drops dramatically inside $r \lesssim 1$ kpc when the central gas density and temperature show a sudden change, forming a pressure hole which then grows deeper and larger with time."291 The pressure hole is deeper when the resolution is lower., The pressure hole is deeper when the resolution is lower.292" The gas inflow velocity is larger than that in the high resolution runs and becomes supersonic at r~1 kpc where the pressure gradient is the steepest, forming a sonic point and leading to a cooling catastrophe."," The gas inflow velocity is larger than that in the high resolution runs and becomes supersonic at $r \sim 1$ kpc where the pressure gradient is the steepest, forming a sonic point and leading to a cooling catastrophe."293 Cold gas does not become rotationally supported as in the high resolutions runs but fragments inside the pressure hole via local cooling instability., Cold gas does not become rotationally supported as in the high resolutions runs but fragments inside the pressure hole via local cooling instability.294" Finally, we examine the impact of different methods for solving the hydrodynamics equations."," Finally, we examine the impact of different methods for solving the hydrodynamics equations."295" As noted earlier, we use the Zeus method for our simulations because of its fast performance, and robust treatment of cold regions."," As noted earlier, we use the Zeus method for our simulations because of its fast performance, and robust treatment of cold regions."296" 'To test the accuracy of its results, we also carried out test runs using the piecewise parabolic method (PPM), which is third-order accurate with its high-order spacial interpolation."," To test the accuracy of its results, we also carried out test runs using the piecewise parabolic method (PPM), which is third-order accurate with its high-order spacial interpolation."297" We used N,-oo¢= 64, a=—1.2 and found results which were in good agreement with the Zeus"," We used $N_{root} = 64$ , $\alpha = -1.2$ and found results which were in good agreement with the Zeus"298We have (hus verified equations and provided we show compactness of A.,We have thus verified equations and provided we show compactness of $K$.299 Bul before doing that we wish to point out the remarkable fact that for one-dimensional point interactions the formulae obtained above are correct with A=0 [IKR].., But before doing that we wish to point out the remarkable fact that for one-dimensional point interactions the formulae obtained above are correct with $K=0$ \cite{KR1}.300 In fact. for the o-interaction of strength a€RU{x} | the parameter a describes the boundary condition of the wave [unction V'(0.)—W'(0=aW(0) which can be formally interpreted as arising from a potential V.=ad where ὁ is the Dirac ó-function at 0 the wave operator is given by," In fact, for the $\delta$ -interaction of strength $\alpha\in \R\cup\{\infty\}$ – the parameter $\alpha$ describes the boundary condition of the wave function $\Psi'(0_+)-\Psi'(0_-) = \alpha \Psi(0)$ which can be formally interpreted as arising from a potential $V=\alpha\delta$ where $\delta$ is the Dirac $\delta$ -function at $0$ – the wave operator is given by"301well of the system.,well of the system.302 For the sake of simplicity. we use υπ=GAMG<RyR (where Mtr<R) is the enclosed total mass within A) estimated at FÉ; as an indicator of the eravitational mass for svstems iu both S230 aud S230NF.," For the sake of simplicity, we use $V_{\rm cir}^2 = G M(r< R)/R$ (where $M(r< R)$ is the enclosed total mass within $R$ ) estimated at $R_{\rm bar}$ as an indicator of the gravitational mass for systems in both S230 and S230NF."303 We calculated the sTFR for our simulated ealaxics bv the fitting of a relation of the form logM.=aloeον100nisEN Viog , We calculated the sTFR for our simulated galaxies by the fitting of a relation of the form $\log M_{\rm *} = \alpha \log (V_{\rm cir}/100 \ {\rm km \ s}^{-1}) + Y_{100}$ .304In the case of the local STER in S230. we found a slope of 3.68c0.09 and Vivo=9.12£0.26 in general agreement with observations (AIcGanehetal.2000:Bell&deJong2001).," In the case of the local sTFR in S230, we found a slope of $3.68 \pm 0.09$ and $Y_{100}= 9.42 \pm 0.26$ in general agreement with observations \citep{mcg00, bdj01}."305. As can be seen from Fie., As can be seen from Fig.306 2. (upper loft panel). the residuals of the linear fit to the relation (small box) depart systematically from zero at around 100 aus +. so tha svstenis with lower circular velocities tend to have smaller stellar niasses than the predictions obtained from the fitting.," \ref{tf} (upper left panel), the residuals of the linear fit to the relation (small box) depart systematically from zero at around 100 km $^{-1}$, so that systems with lower circular velocities tend to have smaller stellar masses than the predictions obtained from the fitting."307 Tuterestingly. this trend is consistent with the observations reported by AMcGauehetal.(2000).. auc from theoretical expectations (Larson|1971:Dekel&Sil-1986).," Interestingly, this trend is consistent with the observations reported by \citet{mcg00}, and from theoretical expectations \citep{larson04,ds86}."308. Iu order to analyse at which extent SN feedback might be responsible for this beliaviour. we compared these fiudiugs with the ones obtained for S230NF as shown in the upper right panel of Fig. 2..," In order to analyse at which extent SN feedback might be responsible for this behaviour, we compared these findings with the ones obtained for S230NF as shown in the upper right panel of Fig. \ref{tf}."309 We cau appreciate that SN feedback seenis to be crucial to reproduce the observe features iu the STER since when this iiechanisii is turned off. the sinulatec STER exhibits a linear behaviour with a slope of  Jinaercement with theoretical predictions.," We can appreciate that SN feedback seems to be crucial to reproduce the observed features in the sTFR since when this mechanism is turned off, the simulated sTFR exhibits a linear behaviour with a slope of $ \sim 3$ in agreement with theoretical predictions."310 We can also see that the wind-free rui predicts larger stellar 1iasses for systenis at a elven circular velocity since it cannot regulate the transformation of eas mto stars which is too efücieut in hvarodyvuiuuieal simulations., We can also see that the wind-free run predicts larger stellar masses for systems at a given circular velocity since it cannot regulate the transformation of gas into stars which is too efficient in hydrodynamical simulations.311 We also studied the bTFR in 8230 and S230NF ," We also studied the bTFR in S230 and S230NF (Fig. \ref{tf},"312ower panels)., lower panels).313 The bTFR is obtained by adding all barvous within A4. regardless of its plivsical state.," The bTFR is obtained by adding all baryons within $R_{\rm bar}$, regardless of its physical state."314" We can see that both models (with aud without SN feedback) predict a linear trend for the ITER. at least. for the rauge of velocities covered by these simmliatious,"," We can see that both models (with and without SN feedback) predict a linear trend for the bTFR, at least, for the range of velocities covered by these simulations."315 At .=0. the sinulated bDTFR in $230 has a slope of 3.2340.08 and Vivo=9.5640.23.," At $z=0$, the simulated bTFR in S230 has a slope of $3.23 \pm 0.08$ and $Y_{100} = 9.56 \pm 0.23$."316 These values are in general good agreement with observational results reported for late aud carly type galaxies (DeRijckeetal.2007:Cawovichal. 2010).," These values are in general good agreement with observational results reported for late and early type galaxies \citep{rijcke07, guro10}."317. Towever. we warn that the comparison with observations is tricky siuce we sunu up the total amount of eas. while observers are lanited by the instrmucutal techniques which give ouly access to gas mass with certain physical properties.," However, we warn that the comparison with observations is tricky since we sum up the total amount of gas, while observers are limited by the instrumental techniques which give only access to gas mass with certain physical properties."318 Iu the case of S230NF. the bTFR has a larger value of Vyyy because these galaxies have been able to retain their barvous in the central regious since no SN-driven outflows could be triggered.," In the case of S230NF, the bTFR has a larger value of $Y_{100}$ because these galaxies have been able to retain their baryons in the central regions since no SN-driven outflows could be triggered."319 We also note that S230NF viclds similar fittines to the STER. aud bTFR. indicating that stars dominate the barvonic phase at this redshift.," We also note that S230NF yields similar fittings to the sTFR and bTFR, indicating that stars dominate the baryonic phase at this redshift."320 As we have already: mentioned. the previous analysis has been done bv using the value of Vor at Ray as a kinematical indicator.," As we have already mentioned, the previous analysis has been done by using the value of $V_{\rm circ}$ at $R_{\rm bar}$ as a kinematical indicator."321 Tn order o analyse the dependance of our results ou the particular choice of the radius at which we measure Ware. we also compared the relations obtained by using Vic evaluated at 00Πω and LR.," In order to analyse the dependance of our results on the particular choice of the radius at which we measure $V_{\rm circ}$, we also compared the relations obtained by using $V_{\rm circ}$ evaluated at $0.5 R_{\rm bar}$ and $1.5 R_{\rm bar}$."322 We also estimated the παν value of the rotation curve Vg as can be seen from Fie. 3.., We also estimated the maximum value of the rotation curve $V_{\rm max}$ as can be seen from Fig. \ref{velos}.323 The siulated sTFR and bTFR are not sieuificantly affected o» windations in the radius at which Vig; Is estimated., The simulated sTFR and bTFR are not significantly affected by variations in the radius at which $V_{\rm circ}$ is estimated.324 The largest changes with respect ο Our previuos results (Fig. 2)), The largest changes with respect to our previuos results (Fig. \ref{tf}) )325 are obtained when mine Var. at ΟΠ]. as he velocity estimator., are obtained when using $V_{\rm circ}$ at $0.5 R_{\rm bar}$ as the velocity estimator.326 Nevertheless. all changes remain whithin a 6.," Nevertheless, all changes remain whithin a ${\sigma}$."327" It is also worth noting that. in these «μαa.πο, ως at fü, constitutes a eood proxy for he velocity Vias. Which is commonly eiiploved i many observational works."," It is also worth noting that, in these simulations, $V_{\rm circ}$ at $R_{\rm bar}$ constitutes a good proxy for the velocity $V_{\rm max}$, which is commonly employed in many observational works."328 Tables 2.Ne and 3. smnunarize the xuaneters correspouding to the linear fits to the ligh-nass eud (AL.>ΟΝΕ5. 13ofthe TFRs shown iu Fig. 3.., Tables \ref{tab:fits_stfr} and \ref{tab:fits_btfr} summarize the parameters corresponding to the linear fits to the high-mass end $M_{*} > 10^9 {\rm M_{\odot}} h^{-1}$ ) of the TFRs shown in Fig. \ref{velos}.329 We can appreciate that. in alb cases. the values of ἃ and του agree within a e.," We can appreciate that, in all cases, the values of $\alpha$ and $Y_{100}$ agree within a ${\sigma}$."330 Reearding the characteristic velocity where the sTFR bends. our findings suggest that it does not depend on the particular kinematical estimators tested in this paper (Fig. 3..," Regarding the characteristic velocity where the sTFR bends, our findings suggest that it does not depend on the particular kinematical estimators tested in this paper (Fig. \ref{velos},"331 small boxes)., small boxes).332 Iu the light of these results. hereafter we will coutiuue mine Vu at Bas as the kineniatical iucdicator for our calculations.," In the light of these results, hereafter we will continue using $V_{\rm circ}$ at $R_{\rm bar}$ as the kinematical indicator for our calculations."333 By comparing the STER aud bTER in $230. it is clear that adding the eas mass in the calculations contributes to restore the linearity of the TER over a larger velocity," By comparing the sTFR and bTFR in S230, it is clear that adding the gas mass in the calculations contributes to restore the linearity of the TFR over a larger velocity"334with other DLAs == 10757. sce section 4). it is amongst the most metal-rich systems known with Z—iz..,"with other DLAs = $\times 10^{20}$, see section 4), it is amongst the most metal-rich systems known with $Z \sim \frac{1}{3}Z_{\odot}$."335 In fact. Prochaska and Wolfe (1997) were able to detect some elements rarely seen in DLAs in this svstem. such as Ti.," In fact, Prochaska and Wolfe (1997) were able to detect some elements rarely seen in DLAs in this system, such as Ti."336 Conversely. Q1223|17 is à very high column density absorber. ---- 1111 aand therefore has a relatively high. column density of Fe despite its low metallicity (Pettini ct al.," Conversely, Q1223+17 is a very high column density absorber, = $\times 10^{21}$ and therefore has a relatively high column density of Fe despite its low metallicity (Pettini et al."337 1994: Prochaska et al., 1994; Prochaska et al.338 2001)., 2001).339 We present high resolution echelle spectra for these two high redshift QSOs., We present high resolution echelle spectra for these two high redshift QSOs.340 The data were obtained with UVES on the ¥LT 199 and Q1223|17) and with ΤΗ10 on the Ixeck telescope (21223|17)., The data were obtained with UVES on the VLT $-$ 199 and Q1223+17) and with HIRES on the Keck telescope (Q1223+17).341 A summary of the observations is given in Table 1., A summary of the observations is given in Table 1.342" Spectra of 199 were obtained over 3 nights from Alay 28-30 2000 with UVES on the ΝΕ in conditions of &oocd κοσμο, twpically 0.5 0.7 areseconds. although for brief periods extremes of 0.4 ancl 1.3 aresecs were reached."," Spectra of $-$ 199 were obtained over 3 nights from May 28-30 2000 with UVES on the VLT in conditions of good seeing, typically 0.5 – 0.7 arcseconds, although for brief periods extremes of 0.4 and 1.3 arcsecs were reached."343 A slit width of 1.0 aresee was fixed throughout the observations. oriented. along the parallactic angle.," A slit width of 1.0 arcsec was fixed throughout the observations, oriented along the parallactic angle."344 The data presented here were obtained with the dichroic LA.=390|564 configuration and read out in ο 2 pixel-binned. high-gain mode.," The data presented here were obtained with the dichroic 1 $\lambda_{cen}345= 390+564$ configuration and read out in 2 $\times$ 2 pixel-binned, high-gain mode."346 The blue arm CCD is a single thinned ELEY chip whereas the rec arm consists of a mosaic of a second. ELV chip and an MET. chip. separated. by approximately 0.96 mm.," The blue arm CCD is a single thinned EEV chip whereas the red arm consists of a mosaic of a second EEV chip and an MIT chip, separated by approximately 0.96 mm."347" A single dichroie setting therefore has non-contiguous wavelength coverage and in the A,=390|564 setting there are gaps between £525 4625 and 95000 5680.", A single dichroic setting therefore has non-contiguous wavelength coverage and in the $\lambda_{cen} = 390+564$ setting there are gaps between 4525 – 4625 and 5600 – 5680.348A... The extraction. of the spectra was achieved. using a customized. version of the UVISS pipeline which is based on ECUELLE routines in the data reduction package ΛΗΛ., The extraction of the spectra was achieved using a customized version of the UVES pipeline which is based on ECHELLE routines in the data reduction package MIDAS.349 A detailed: description of this process can be found. in Ballester et al. (, A detailed description of this process can be found in Ballester et al. (3502000).,2000).351 The spectra were optimally extracted separately for the three CCDs and the variation in the continuum Lux level. due primarily to the blaze function of the echelle grating. was removed.," The spectra were optimally extracted separately for the three CCDs and the variation in the continuum flux level, due primarily to the blaze function of the echelle grating, was removed."352 Phe resolution of the spectra. as determined from Thr are lines. is 243000. or approximately 7 FEWILI," The resolution of the spectra, as determined from ThAr arc lines, is $R \sim 43\,000$, or approximately 7 FWHM."353AL 1-D spectra were obtained. by joining the orders and converting the wavelengths to a vacuum heliocentric scale., 1-D spectra were obtained by joining the orders and converting the wavelengths to a vacuum heliocentric scale.354 The individual spectra were then co-added: with a weighting proportional to their S/N. The final step was to normalise the spectrum by dividing through hy a spline function fitted through absorption-free regions of data., The individual spectra were then co-added with a weighting proportional to their S/N. The final step was to normalise the spectrum by dividing through by a spline function fitted through absorption-free regions of data.355 Since most of the metal lines which we study here. are. found τοατα of the cemiussion. the continuum can be accurately fitted since there are relatively few absorption features and the S/N is quite high.," Since most of the metal lines which we study here are found redward of the emission, the continuum can be accurately fitted since there are relatively few absorption features and the S/N is quite high."356 The spectrum presented here of the των=2.466 DLA towards Q1223|17 is a composite of LILRIES plus UVES data., The spectrum presented here of the $z_{abs} = 2.466$ DLA towards Q1223+17 is a composite of HIRES plus UVES data.357 Phe UVES data were obtained during the same run as the 199 spectra and reduced in an identical way., The UVES data were obtained during the same run as the $-$ 199 spectra and reduced in an identical way.358" The only difference for the data of Q1223|17 is that they were obtained with the dichroic 2 A44,—437|S60 setting."," The only difference for the data of Q1223+17 is that they were obtained with the dichroic 2 $\lambda_{cen}359= 437+860$ setting."360 This mode ollers a larger. redder overall wavelength coverage at the expense of slightly larger inter-arm gaps (between 5000 6750 aand S5SOO — 8750 A3).," This mode offers a larger, redder overall wavelength coverage at the expense of slightly larger inter-arm gaps (between 5000 – 6750 and 8500 – 8750 )."361 In addition to the UVES data. we have obtained ~ 5 hours of Keek HIIS data. which are described in more detail by the comprehensive abundance analysis of Prochaska ct al. (," In addition to the UVES data, we have obtained $\sim$ 5 hours of Keck HIRES data, which are described in more detail by the comprehensive abundance analysis of Prochaska et al. ("3622001).,2001).363 In brief. the €5 decker was implemented. providing E'WIIM =8S rresolution with the setup covering Az47501200.A.," In brief, the C5 decker was implemented providing FWHM $\approx 8$ resolution with the setup covering $\lambda \approx 4750 - 7200$."364. The data were reduced with the ALAKEE software package developed by TE. Barlow for the extraction of LILRIES spectra., The data were reduced with the MAKEE software package developed by T. Barlow for the extraction of HIRES spectra.365 The coadded spectrum has S/N 2:30 per 2 ppixcl., The coadded spectrum has S/N $\approx 30$ per 2 pixel.366 ‘To obtain the strictest upper limit on the Co LL column density for the campec ssystom towards 1223]17. we coadded the LLRES and UVES spectra in the region spanning the Co LL A2012 transition.," To obtain the strictest upper limit on the Co II column density for the damped system towards Q1223+17, we coadded the HIRES and UVES spectra in the region spanning the Co II $\lambda$ 2012 transition."367 Each spectrum was rebinned to a common wavelength. scale and then optimally coadcded: resulting in a final spectrum with z36 per 2 ppixel., Each spectrum was rebinned to a common wavelength scale and then optimally coadded resulting in a final spectrum with $~\approx 36$ per 2 pixel.368 The H1 I column density of the two QSOs was determined by fitting fully damped profiles to the normalised. spectra using the Starlink package Dipso., The H I column density of the two QSOs was determined by fitting fully damped profiles to the normalised spectra using the Starlink package Dipso.369 Phe UVES spectrum of 199 was found to have a best fit == 4840.310°! aand a redshift of τς=.9207. Figure 1.," The UVES spectrum of $-$ 199 was found to have a best fit = $\pm 0.3 \times 10^{20}$ and a redshift of $z_{abs} = 1.9207$, Figure 1."370 Note that this fit is very. well constrained by the shape of the central trough and damping wings an he iis in good agreement with previously determined estimates (e.g. Pettini et al., Note that this fit is very well constrained by the shape of the central trough and damping wings and the is in good agreement with previously determined estimates (e.g. Pettini et al.371 1994) for this DLA., 1994) for this DLA.372 Phe LELEUIZS spectrum of Q1223|17 exhibits a relatively large cobumn density of LIL which is found to have a best fit o£ == SE030107 aand a redshift of τρ= 2.4661. also in good. agreement with the Pettini et al. (," The HIRES spectrum of Q1223+17 exhibits a relatively large column density of H I which is found to have a best fit of = $\pm 0.3 \times 10^{21}$ and a redshift of $z_{abs} = 2.4661$ , also in good agreement with the Pettini et al. ("3731994) measurement.,1994) measurement.374 A detailed analysis of other metal abundances in the DLAs towards Q2206 199 and Q1223]17 can be found in Prochaska ancl Wolfe. (1997) and. Prochaska οἱ al. (, A detailed analysis of other metal abundances in the DLAs towards $-$ 199 and Q1223+17 can be found in Prochaska and Wolfe (1997) and Prochaska et al. (3752001): here we simply concentrate on the detection of,2001); here we simply concentrate on the detection of3763.9m Telescope in Coonabarabran. NSW. Australia. using the 2 degree field (2dF) multi-object spectrograph (Lewisetal.2002).,"3.9m Telescope in Coonabarabran, NSW, Australia, using the 2 degree field (2dF) multi-object spectrograph \citep{lewis02}."377. The spectra cover the entire optical range (35007500 A)) at a resolution of about 2000. with exposure times of at least one hour per target. although a fraction of the objects were exposed for considerably longer. if they happened to He in a region where the 2dF tiles used by the survey overlapped (to insure greater completeness) or the field was reobserved (because of lower than expected signal).," The spectra cover the entire optical range $3500 < \lambda < 7500$ ) at a resolution of about 2000, with exposure times of at least one hour per target, although a fraction of the objects were exposed for considerably longer, if they happened to lie in a region where the 2dF tiles used by the survey overlapped (to insure greater completeness) or the field was reobserved (because of lower than expected signal)."378 As with all color-selected surveys. 207 suffers from significant contamination from QSO-colored stellar objects. such as white dwarfs. disk A stars. blue stragglers and BHB stars. although this is minimized by observing at high galactic latitude.," As with all color-selected surveys, 2Qz suffers from significant contamination from QSO-colored stellar objects, such as white dwarfs, disk A stars, blue stragglers and BHB stars, although this is minimized by observing at high galactic latitude."379 The data were reduced and redshifted via a semi-automated technique and whenever a stellar redshift (7.=0) was obtained. the object was discarded from further analysis but placed in the database.," The data were reduced and redshifted via a semi-automated technique and whenever a stellar redshift $z=0$ ) was obtained, the object was discarded from further analysis but placed in the database."380 We proceeded to retrieve all stellar spectra from the database and classify them on the basis of the equivalent widths of the H- and Hs Balmer lines. to identify a sample of 666 BHB stars.," We proceeded to retrieve all stellar spectra from the database and classify them on the basis of the equivalent widths of the $_{\gamma}$ and $_{\delta}$ Balmer lines, to identify a sample of 666 BHB stars."381 Following Yannyetal.(2000):Xueet(2008);Brown(2010) we first measured radial velocities for all star by cross correlating with synthetic templates from the library of Munartetal.(2005): the templates had temperatures and gravities typical of A-stars and field horizontal branch stars (Beersetal.2001).," Following \cite{yanny00,382xue08,brown10} we first measured radial velocities for all star by cross correlating with synthetic templates from the library of \cite{munari05}: the templates had temperatures and gravities typical of A-stars and field horizontal branch stars \citep{beers01}."383. We then fit Gaussian curves to the H5 and Hó lines and measured the width of the Gaussian fit at of the normalized continuum level: this indicator Dy» has been shown to be a good discriminator between BHB stars. blue stragglers and other contaminants (Pier1983:Yannyetal.2000).," We then fit Gaussian curves to the $\gamma$ and $\delta$ lines and measured the width of the Gaussian fit at of the normalized continuum level: this indicator $D_{0.2}$ has been shown to be a good discriminator between BHB stars, blue stragglers and other contaminants \citep{pier83,yanny00}."384. We only used spectra that we deemed to be of sufficient quality to allow a secure classification., We only used spectra that we deemed to be of sufficient quality to allow a secure classification.385 In order to be included in our sample radial velocities had to be determined to within 50 km Land the H and Hà widths had to have errors of less than20%., In order to be included in our sample radial velocities had to be determined to within 50 km $^{-1}$ and the $\gamma$ and $\delta$ widths had to have errors of less than.386. In order to classify stars as BHB stars we require that the mean Dy.2. from both lines. lie between 17 and 31 ((as in Pier1983:Yannyetal. 2000.. leaving a total of 666 BHB stars in our sample.," In order to classify stars as BHB stars we require that the mean $D_{0.2}$, from both lines, lie between 17 and 31 (as in \citealt{pier83,yanny00}, , leaving a total of 666 BHB stars in our sample."387 Figure | shows the distribution of the stars in the &4 vs. gy+ plane. where we transformed our Supercosmos —af; and b;—rg colors to the Sloan system by using stars in common in the equatorial region shared by 2Qz and the SDSS.," Figure 1 shows the distribution of the stars in the $u-g$ vs. $g-z$ plane, where we transformed our Supercosmos $u-b_J$ and $b_J-r_F$ colors to the Sloan system by using stars in common in the equatorial region shared by 2Qz and the SDSS."388 This is at least qualitatively similar to the color distribution of stars in previous work (e.g.. compare Fig.," This is at least qualitatively similar to the color distribution of stars in previous work (e.g., compare Fig."389 | in Brownetal. 2010)) and suggests that our sample is comparable to those used in previous studies. in terms of selection criteria and degree of contamination from blue stragglers and other objects.," 1 in \citealt{brown10}) ) and suggests that our sample is comparable to those used in previous studies, in terms of selection criteria and degree of contamination from blue stragglers and other A-colored objects."390" As our targets span a relatively narrow range in. colors (as selected by the 2Qz survey) we assumed an absolute magnitude of Af,,=0.7+0.2 which ts typical for BHB stars (Laydenetal.1996).", As our targets span a relatively narrow range in colors (as selected by the 2Qz survey) we assumed an absolute magnitude of $M_{b_J}=0.7 \pm 0.2$ which is typical for BHB stars \citep{layden96}.391. We finally used these distances. the known sky positions and the measured radial velocities to place all our stars on a eylindrical coordinate system at rest with respect to the centre of the Galaxy. assuming Solar positions as in Dehnen&Binney(1998).," We finally used these distances, the known sky positions and the measured radial velocities to place all our stars on a cylindrical coordinate system at rest with respect to the centre of the Galaxy, assuming Solar positions as in \cite{dehnen98}."392. This yields a 4-dimensional (position. distance and radial velocity) map of the galactic halo in two widely separated (150°) lines of sight.," This yields a 4-dimensional (position, distance and radial velocity) map of the galactic halo in two widely separated $150^{\circ}$ ) lines of sight."393 In Figure 2 we plot the 4D map of the Galactic halo we produced. projected along the three most relevant dimensions.," In Figure 2 we plot the 4D map of the Galactic halo we produced, projected along the three most relevant dimensions."394 It is clear from this figure that the halo of the Milky Way extends to at least 100 kpe from the Galactic centre. and likely well beyond (the edge of the map is set by the magnitude limit of 2Qz data). in both directions we survey.," It is clear from this figure that the halo of the Milky Way extends to at least 100 kpc from the Galactic centre, and likely well beyond (the edge of the map is set by the magnitude limit of 2Qz data), in both directions we survey."395 This is considerably larger than previously believed and comparable to the large metal-poor halo observed in the Andromeda galaxy (Chapmanetal.2006:KaliraiKoch2006501: 1t would include several of the dwarf galaxy satellites (including the Magellanie clouds) within the Galaxy’s stellar halo.," This is considerably larger than previously believed and comparable to the large metal-poor halo observed in the Andromeda galaxy \citep{chapman06,kalirai06,koch08}; ; it would include several of the dwarf galaxy satellites (including the Magellanic clouds) within the Galaxy's stellar halo."396 As a matter of fact the Sextans dwarf is visible in Fig., As a matter of fact the Sextans dwarf is visible in Fig.397 2 at.c~20 kpe and y~[50 kpe., 2 at $x \sim -20$ kpc and $y \sim +50$ kpc.398 Such large poor halos may be ubiquitous (e.g.. in NGC 3379 - Harrisetal.2007)) and may be a common byproduct of early galaxy formation.," Such large metal-poor halos may be ubiquitous (e.g., in NGC 3379 – \citealt{harris07}) ) and may be a common byproduct of early galaxy formation."399 In previous work. the SDSS has identified BHB stars out to 60 kpe from the Galactic centre (Xueetal.2008).. while the Hypervelocity Stars Survey (Brownetal.2010) found a BHB star sample to a distance of 75 kpe.," In previous work, the SDSS has identified BHB stars out to 60 kpc from the Galactic centre \citep{xue08}, while the Hypervelocity Stars Survey \citep{400brown10} found a BHB star sample to a distance of 75 kpc."401 The Spaghetti survey (Morrisonetal.2000;Starkenburg2009) has observed halo red giants to a distance of 100 kpe. and star counts in the COSMOS field identify a halo component to a distance of 80 kpe (Robinetal.2007).," The Spaghetti survey \citep{morrison00,starkenburg09} has observed halo red giants to a distance of 100 kpc, and star counts in the COSMOS field identify a halo component to a distance of 80 kpc \citep{robin07}."402. Our study reaches deeper than nearly all these and covers a larger field of view than all except the SDSS (it is comparable to the Hypervelocity Stars Survey coverage)., Our study reaches deeper than nearly all these and covers a larger field of view than all except the SDSS (it is comparable to the Hypervelocity Stars Survey coverage).403 However. we sample the BHB stars more densely as all potential targets have been targeted by the 2Qz survey. although of course we are not able to classify all stars.," However, we sample the BHB stars more densely as all potential targets have been targeted by the 2Qz survey, although of course we are not able to classify all stars."404 Since we cover nearly diametrically opposite areas on the sky. we argue that the detection of the stellar halo in our data is not due to possible diffuse structures on the sky that accidentally lie in our line of sight (as for pencil-beam studies such as COSMOS or the Spaghetti survey) and the Milky Way halo truly extends to large radi.," Since we cover nearly diametrically opposite areas on the sky, we argue that the detection of the stellar halo in our data is not due to possible diffuse structures on the sky that accidentally lie in our line of sight (as for pencil-beam studies such as COSMOS or the Spaghetti survey) and the Milky Way halo truly extends to large radii."405 Figure 3 shows the radial density profile of the halo along both directions we survey., Figure 3 shows the radial density profile of the halo along both directions we survey.406" In both cases we obtain a good fit to a single power law of index Ro27*"" "," In both cases we obtain a good fit to a single power law of index $R^{-2.5407\pm 0.2}$."408"This is somewhat shallower than the ~7?? found by Morrison2,etal.(2000) and predicted by theory. but is in good agreement with previous measurements using BHB stars by Xueetal.(2008) and Brownetal.(2010)."," This is somewhat shallower than the $\sim R^{-3}$ found by \cite{morrison00}409 and predicted by theory, but is in good agreement with previous measurements using BHB stars by \cite{xue08} and \cite{brown10}."410. We are of course incomplete in that we cannot detect and identify all BHB stars in 207., We are of course incomplete in that we cannot detect and identify all BHB stars in 2Qz.411 Thisincompleteness is a complex function of our ability to reliably classify stars as a function of spectroscopic signal-, Thisincompleteness is a complex function of our ability to reliably classify stars as a function of spectroscopic signal-to-noise.412 Naively. we would preferentially miss the mostdistant objects. that would tend to make the radial profile steeper than it actually is. while contamination from blue," Naively, we would preferentially miss the mostdistant objects, that would tend to make the radial profile steeper than it actually is, while contamination from blue"413"that the electron density is relatively constant, the fflux is a measure of mass surface density.","that the electron density is relatively constant, the flux is a measure of mass surface density."414" Therefore, the product ΓἨωσ” is a measure of the kinetic energy content of the ionized gas along the line of sight."," Therefore, the product $F_{\rm H \alpha} \sigma^{2}$ is a measure of the kinetic energy content of the ionized gas along the line of sight."415 The total energy associated with line splitting is calculated by substituting line width with the deviation of the central of each component from the flux-weighted average peakvelocity and summing the product of each components 'deviation with the square of its flux., The total energy associated with line splitting is calculated by substituting line width with the deviation of the central peak of each component from the flux-weighted average velocity and summing the product of each components 'deviation with the square of its flux.416" In 7,, we plot the various components of this energy content, Figurenamely, the energy associated with the velocity dispersion of the principal and secondary components (panels (a) and (b)), the energy content associated with the line splitting (panel (c)), and the sum of these three components (panel (d))."," In Figure \ref{fig7}, we plot the various components of this energy content, namely, the energy associated with the velocity dispersion of the principal and secondary components (panels (a) and (b)), the energy content associated with the line splitting (panel (c)), and the sum of these three components (panel (d))."417" In the figure, the energy scale has been normalized to the largest value in the data cube, so as to facilitate comparison between the components."," In the figure, the energy scale has been normalized to the largest value in the data cube, so as to facilitate comparison between the components."418 The energy associated with the velocity dispersion in each of the components shows a marked tendency to be high within the two funnels of ionized gas extending almost perpendicular to the stellar disk., The energy associated with the velocity dispersion in each of the components shows a marked tendency to be high within the two funnels of ionized gas extending almost perpendicular to the stellar disk.419 This is much more evident in terms of the energy content alignmentassociated with the line splitting shown in panel (c) and clearly defines an axis for the outflow (P.A.— +3°+3°))., This alignment is much more evident in terms of the energy content associated with the line splitting shown in panel (c) and clearly defines an axis for the outflow $ = +3$ $\pm 3$ ).420" This alignment would be expected if the gas motions lie along the surface of an expanding funnel, since the greatest expansion velocities seen in projection would lie along the axis of the funnel in this geometry."," This alignment would be expected if the gas motions lie along the surface of an expanding funnel, since the greatest expansion velocities seen in projection would lie along the axis of the funnel in this geometry."421 Figure 7 clearly shows that we are observing an ionized superwind moving out of the galaxy., Figure \ref{fig7} clearly shows that we are observing an ionized superwind moving out of the galaxy.422 The space velocities associated with the outflow are certainly greater than the ~130km s! implied by either the blueshift in the Na D -line absorption or the ~125km s! implied by the line splitting observed in the funnel., The space velocities associated with the outflow are certainly greater than the $\sim 130$ km $^{-1}$ implied by either the blueshift in the Na D -line absorption or the $\sim 125$ km $^{-1}$ implied by the line splitting observed in the funnel.423 The iimage of Figure 1 limits the cone opening angle to not more than60°., The image of Figure \ref{fig1} limits the cone opening angle to not more than.424". Therefore, if the predominant gas flow is along the surface of the cone, the actual outflow velocity would be ~250km s-!."," Therefore, if the predominant gas flow is along the surface of the cone, the actual outflow velocity would be $\sim 250$ km $^{-1}$."425 The outflow at P.A.—+3°+3° is neither perfectly aligned along the photometric minor axis of the galaxy or with the rotation axis., The outflow at $ = +3$ $\pm 3$ is neither perfectly aligned along the photometric minor axis of the galaxy or with the rotation axis.426 The photometric line of nodes measured by MendesdeOliveiraetal.(1998) for the stellar disk is at Ρ.Α. =84°+5°., The photometric line of nodes measured by \citet{Mendes98} for the stellar disk is at P.A. $= 84$ $\pm 5$.427". From the HST image, we estimate P.A. =80° +3°.."," From the HST image, we estimate P.A. $= 80$ $ \pm 3$ ."428" Thus, the photometric minor axis is at P.A.—352? +4°."," Thus, the photometric minor axis is at $ = 352$ $ \pm 4$."429". From our rotation curve (see Figure 4)), we infer that the polar direction is at P.A.—342? +3°."," From our rotation curve (see Figure \ref{fig4}) ), we infer that the polar direction is at $ = 342$ $ \pm 3$."430. The mild between the photometric and kinematic line of nodesdisagreement had been previously noted by MendesdeOliveiraetal.(2003)., The mild disagreement between the photometric and kinematic line of nodes had been previously noted by \citet{Mendes03}.431. This perturbation could be due to the ongoing merger activity in HCG 16., This perturbation could be due to the ongoing merger activity in HCG 16.432 The observations described in the previous section suggest that the geometry of the superwind is close to that of a hollow biconical outflow., The observations described in the previous section suggest that the geometry of the superwind is close to that of a hollow biconical outflow.433 Models of superwinds by Cooperetal.(2009) show that the filaments are entrained and accelerated by aoptically faster andemitting hotter outflow from the nuclear starburst region., Models of superwinds by \citet{Cooper09} show that the optically emitting filaments are entrained and accelerated by a faster and hotter outflow from the nuclear starburst region.434" In this model, the pressure of the optically emitting material is determined by the ram and thermal pressure of the hot medium."," In this model, the pressure of the optically emitting material is determined by the ram and thermal pressure of the surrounding hot medium."435" The filaments are ionized either by surroundingthe escape of UV photons from the central starburst, or, if the outflowing medium is optically thick to the escape of Lyman continuum photons, then by cloud shocks which propagate into the dense filaments as they are accelerated in the outflow."," The filaments are ionized either by the escape of UV photons from the central starburst, or, if the outflowing medium is optically thick to the escape of Lyman continuum photons, then by cloud shocks which propagate into the dense filaments as they are accelerated in the outflow."436 A study of the radial variation of surface brightness within the cone can help us to distinguish between these possibilities., A study of the radial variation of surface brightness within the cone can help us to distinguish between these possibilities.437" Let us consider two cases, either (1) that the outflow has constant velocity or (2) that the outflow velocity increases proportional to the radial distance."," Let us consider two cases, either (1) that the outflow has constant velocity or (2) that the outflow velocity increases proportional to the radial distance."438" Recall first the equation derived in the section; Fyqgο“ne, where X is the ionized mass previoussurface density and n, is the electron density."," Recall first the equation derived in the previous section; $F_{\rm H \alpha} \propto \Sigma n_{\rm e} $, where $\Sigma$ is the ionized mass surface density and $n_{\rm e}$ is the electron density."439" Since the gas pressure is given by P=nkT and the temperature of the ionized plasma is of order 10*K, we can write the fflux as Fug«XP."," Since the gas pressure is given by $P=nkT$ and the temperature of the ionized plasma is of order $10^4$ K, we can write the flux as $F_{\rm H \alpha} \propto \Sigma P $."440" In a photoionized entrained outflow, the ionized mass is conserved so for constant velocity of expansion, 2)οςr-l,where r is the radial distance from the cone apex."," In a photoionized entrained outflow, the ionized mass is conserved so for constant velocity of expansion, $\Sigma \propto r^{-1}$,where $r$ is the radial distance from the cone apex."441 The ram pressure in the hot flow decreases as Pοςr-?., The ram pressure in the hot flow decreases as $P \propto r^{-2}$.442" Therefore, in a constant-velocity photoionized entrained outflowwe expect Fugacr-?."," Therefore, in a constant-velocity photoionized entrained outflowwe expect $F_{\rm H \alpha} \propto r^{-3}$."443" In case (2) (an accelerating outflow), Fuοςr,"," In case (2) (an accelerating outflow), $F_{\rm H \alpha} \propto r^{-4}$."444" In a single shocked cloud, the luminosity at iis proportional to the energy flux across the cloud shock; ScHaXAcnev3, where A, is the cross-sectional area of the cloud, Τις is the of the clouds (or filaments), and Uc is the cloud shock densityvelocity, given in terms of the external pressure, P, by P= n,v2."," In a single shocked cloud, the luminosity at is proportional to the energy flux across the cloud shock; $S_{\rm c, H \alpha} \propto A_{\rm c} n_{\rm c} v_{\rm c}^{3}$, where $A_{\rm c}$ is the cross-sectional area of the cloud, $n_{\rm c}$ is the density of the clouds (or filaments), and $v_{\rm c}$ is the cloud shock velocity, given in terms of the external pressure, $P$ by $P = n_{\rm c} v_{\rm c}^{2}$ ."445" Therefore, we can rewrite the luminosity produced by a single cloud/ filament as"," Therefore, we can rewrite the luminosity produced by a single cloud/ filament as"446"envelope of, say, ~20 mmas radius or larger, it would map into a decrease in the visibility amplitude that would roughly match the observations in that part of the spectrum.","envelope of, say, $\sim$ mas radius or larger, it would map into a decrease in the visibility amplitude that would roughly match the observations in that part of the spectrum."447" Unfortunately, we do not have enough data to be able to characterize well this possible extra component of CO absorption."," Unfortunately, we do not have enough data to be able to characterize well this possible extra component of CO absorption."448 We have observed the AGB star RS Cap with VLTI/AMBER in the K band with medium-resolution mode (506 channels between 2.13 and um)., We have observed the AGB star RS Cap with VLTI/AMBER in the K band with medium-resolution mode (506 channels between 2.13 and $\mu$ m).449" We have estimated a Rosseland diameter of 7.95+ 0.07mmas in the continuum, which translates into an effective temperature of 3160x160 KK. The apparent size of the star increases monotonically by ~12% between 2.29 and 2.47um. We have detected lower than expected visibility amplitudes in all the CO band heads observed."," We have estimated a Rosseland diameter of $7.95\pm0.07$ mas in the continuum, which translates into an effective temperature of $\pm$ K. The apparent size of the star increases monotonically by $\sim12$ between 2.29 and $\mu$ m. We have detected lower than expected visibility amplitudes in all the CO band heads observed."450 These lower amplitudes translate into larger apparent sizes of the star in the CO band heads., These lower amplitudes translate into larger apparent sizes of the star in the CO band heads.451" Using the pressure/density model profiles obtained with the code, we have been able to generate synthetic visibilities and compare them directly to our AMBER observations."," Using the pressure/density model profiles obtained with the code, we have been able to generate synthetic visibilities and compare them directly to our AMBER observations."452" The fit is rather good, although we are unable to reproduce the low visibility amplitudes in the CO band heads using a mass for RS Cap estimated from the theoretical models of stellar evolution."," The fit is rather good, although we are unable to reproduce the low visibility amplitudes in the CO band heads using a mass for RS Cap estimated from the theoretical models of stellar evolution."453" In this sense, our situation resembles that of Quirrenbach et al. (2001)),"," In this sense, our situation resembles that of Quirrenbach et al. \cite{Quirrenbach2001}) ),"454 who observed interferometrically a sample of cool-giant stars in the TiO absorption band at nnm., who observed interferometrically a sample of cool-giant stars in the TiO absorption band at nm.455" The discrepancy between models and observations in the CO band heads might be resolved either by using a much lower mass for RS Cap (below 1MMo, thus in contradiction with the stellar-evolution models) or by additional unmodeled effects in the base of the stellar wind (a transition zone with prominent absorption in the CO bands)."," The discrepancy between models and observations in the CO band heads might be resolved either by using a much lower mass for RS Cap (below $_{\odot}$, thus in contradiction with the stellar-evolution models) or by additional unmodeled effects in the base of the stellar wind (a transition zone with prominent absorption in the CO bands)."456" To fit the observations at wavelengths longer than um, we have found that an narrow spherical water-vapor envelope around the star, similar to the models used in Perrin et al. (2004)),"," To fit the observations at wavelengths longer than $\mu$ m, we have found that an narrow spherical water-vapor envelope around the star, similar to the models used in Perrin et al. \cite{Perrin2004}) ),"457 must be added., must be added.458" We have modeled this envelope with a temperature of KK, a size twice that of the star, a width of 0.1 times the stellar radius, and a column density of 10?! οσα."," We have modeled this envelope with a temperature of K, a size twice that of the star, a width of 0.1 times the stellar radius, and a column density of $10^{21}$ $^{-2}$."459" Finally, there is a hint of an extended CO envelope around the star, based on the low visibility amplitudes at the CO band heads in the shortest baseline."," Finally, there is a hint of an extended CO envelope around the star, based on the low visibility amplitudes at the CO band heads in the shortest baseline."460Now a very natural candidate for the WDAL particle is a massive sterile neutrino mixed with an ordinary. neutrino (Dodelson Widrow 1994: Colombi. Dodelson Wiclrow 1996: Shi Fuller 1999: Dolgov Hansen 2001: Abazajian. Fuller Patel 2001).,"Now a very natural candidate for the WDM particle is a massive sterile neutrino mixed with an ordinary neutrino (Dodelson Widrow 1994; Colombi, Dodelson Widrow 1996; Shi Fuller 1999; Dolgov Hansen 2001; Abazajian, Fuller Patel 2001)."461 Since the mixing angle is temperature dependent (Nóttzold Rallelt LOSS) (and for small vacuum mixing angle. sin?20— 10°). only a small amount of these heavy neutrinos. relative to ordinary active neutrinos. can be produced at high temperatures.," Since the mixing angle is temperature dependent (Nöttzold Raffelt 1988) (and for small vacuum mixing angle, $\sin^22\theta \sim 10^{-7}$ ), only a small amount of these heavy neutrinos, relative to ordinary active neutrinos, can be produced at high temperatures."462 The distribution function of sterile neutrinos is. to à fair approximation. characterized by the temperature of massless neutrinos. but smaller by a [actor .V.," The distribution function of sterile neutrinos is, to a fair approximation, characterized by the temperature of massless neutrinos, but smaller by a factor ${\cal X}$."463 For a specific choice of mie and Oy today the value of .V can be found from therefore the two models produce the sume contribution to pio; OF WDAL particles today if distribution function in these two models. ancl their [rec-streaming effect is not equivalent.," For a specific choice of $m_W$ and $\Omega_W$ today the value of ${\cal X}$ can be found from therefore the two models produce the same contribution to $\rho_{tot}$ of WDM particles today if However, WDM particles with $m_W$ have a distribution function in these two models, and their free-streaming effect is not equivalent."464 The effect on. large scale structure was first. discussed. in. detail by Colombi et al. (, The effect on large scale structure was first discussed in detail by Colombi et al. (4651996).,1996).466 Ne. will use conventional WDAL (cCWDALD when referring to the first case. and sterile neutrino WDAL (SWDAL) for the second one.," We will use conventional WDM (cWDM) when referring to the first case, and sterile neutrino WDM (sWDM) for the second one."467 The two neutering models. are easily included in. a 3oltzman code. in order to compute the present matter power spectrum 24).," The two neutrino models are easily included in a Boltzman code, in order to compute the present matter power spectrum $P(k)$."468 Using the code (Seljak Zaldarriaga 1996). we have found. analytical fits for the transfer functions. Z'(&). relating the power spectrum in the WDAL to the CIAL scenario where P ds the power spectrum for cWDAL and a similar expression with 2°(A) for the s\WDAL model.," Using the code (Seljak Zaldarriaga 1996), we have found analytical fits for the transfer functions, $T(k)$, relating the power spectrum in the WDM to the CDM scenario where $P^W$ is the power spectrum for cWDM, and a similar expression with $P^{\nu}(k)$ for the sWDM model."469 These transfer functions. which essentially reflect the [ree streaming cut-oll. have the form where & is the wavenumber in units Mpc1 ep. 119. and à depends on the cosmological parameters as Numerically we find for eWDAL cl=1.07. 6=0.11. c=1.20 and d—1.11 in good agreement with Bode et al. (," These transfer functions, which essentially reflect the free streaming cut-off, have the form where $k$ is the wavenumber in units $h \mbox{Mpc}^{-1}$ , $\nu=1.12$ , and $\alpha$ depends on the cosmological parameters as Numerically we find for cWDM, $A=1.07$, $b=0.11$, $c=1.20$ and $d=-1.11$ in good agreement with Bode et al. ("4702001).,2001).471" For the sWDAL one can derive similar numbers bv noting that the mass in the ολΕΝ case dillers bv Cli,/2.,).", For the sWDM one can derive similar numbers by noting that the mass in the cWDM case differs by $(T_{W_0}/T_{\nu_0} )$.472 This means that if we have a dependence OFhnil for the sWDAL case in eq. (6)).," This means that if we have a dependence $\Omega_W^b h^c m_W^d$ for the sWDM case in eq. \ref{alph}) ),"473 ancl a dependence Qnhnd for the cWDAI case. then one finds which is solved bv bo=b|dí4. d=3díA and c=οdf2. in good agreement with what we found numerically. by explicitly. changing the massive neutrino shase-space distribution function as done hy Lesgourgues Pastor (1999).," and a dependence $\Omega_W^{b' }h^{c'} m_W^{d'}$ for the cWDM case, then one finds which is solved by $b'=b+d/4$, $d'=3d/4$ and $c'=c+d/2$, in good agreement with what we found numerically, by explicitly changing the massive neutrino phase-space distribution function as done by Lesgourgues Pastor (1999)."474 To be very explicit. this means that for a given cut-olf scale of the power spectrum one can find he corresponding mass of the elementary. particle. and the mass will ciller in the two cases.," To be very explicit, this means that for a given cut-off scale of the power spectrum one can find the corresponding mass of the elementary particle, and the mass will differ in the two cases."475 e.g. if for ολDM one finds nap=0.75 keV. then this corresponds in the s\WDAL case o mw=(Qih940vητοκο)P7OTSkeVzm2.6 keV. when using —0.7 and Oy=0.4.," E.g. if for cWDM one finds $m_W=0.75$ keV, then this corresponds in the sWDM case to $m_W = (\Omega_W h^2 \, 94476\mbox{eV}/0.75 \mbox{keV})^{-1/3} \cdot 0.75 \mbox{keV} \approx 2.6$ keV, when using $h=0.7$ and $\Omega_W=0.4$."477 In other words. if one relieves that sterile neutrinos indeed constitute the clark matter. and they are produced as described in (Dodelson Wicrow 1994: Colombi. Dodelson Widrow 1996: Dolgov Llansen 2001: Abazajian. Fuller Patel 2001). then the bounds obtained by Barkana et al. (," In other words, if one believes that sterile neutrinos indeed constitute the dark matter, and they are produced as described in (Dodelson Widrow 1994; Colombi, Dodelson Widrow 1996; Dolgov Hansen 2001; Abazajian, Fuller Patel 2001), then the bounds obtained by Barkana et al. ("4782001) ancl Naravanan et al. (,2001) and Narayanan et al. (4792000). ri270.75keV. should really be multiplied by a factor 3.4. and thedower bound on sterile neutrinos as clark matter is thus about 2.6 keV. This lower bound may be subject to minor corrections.,"2000), $m_W > 0.75 \, \mbox{keV}$, should really be multiplied by a factor $3.4$, and the bound on sterile neutrinos as dark matter is thus about $2.6$ keV. This lower bound may be subject to minor corrections."480 First. the temperature of the sterile neutrinos is. really slightly lower than the active neutrino temperature. since he sterile neutrinos are being produced while the muons are still present in the Universe. 7σε130 MeV (Langacker 1989: Ixainulzinen 1990: Darbieri Dolgov 1990. 1901).," First, the temperature of the sterile neutrinos is really slightly lower than the active neutrino temperature, since the sterile neutrinos are being produced while the muons are still present in the Universe, $T\approx481130$ MeV (Langacker 1989; Kainulainen 1990; Barbieri Dolgov 1990, 1991)."482 Similarly. or the neutrino states being produced above the QCD phase ransition. one must also take into account the quark degrees of freedom CXbazajian et al.," Similarly, for the neutrino states being produced above the QCD phase transition, one must also take into account the quark degrees of freedom (Abazajian et al."483 20012)., 2001a).484 Another effect. arises rom the fact that the produced sterile neutrino spectrum is not exactly thermal. but slightly. warmer in the sense that he higher momentum part is more populated than the lower momentum part (Dolgov Hansen 2001: Abazajian ct al.," Another effect arises from the fact that the produced sterile neutrino spectrum is not exactly thermal, but slightly warmer in the sense that the higher momentum part is more populated than the lower momentum part (Dolgov Hansen 2001; Abazajian et al."485 2001b)., 2001b).486 Furthermore. the factor of 3-4 found above depencds on the specific values of Oi and P. and can therefore change slightly.," Furthermore, the factor of 3-4 found above depends on the specific values of $\Omega_W$ and $h$, and can therefore change slightly."487 Lt is also worth noting. that if the sterile neutrinos are produced resonantly (Shi Fuller 1999). through a pre-existing lepton asymmetry. then the upper limit on 5 keV niw weaken substantially (Abazajian et al.," It is also worth noting, that if the sterile neutrinos are produced resonantly (Shi Fuller 1999), through a pre-existing lepton asymmetry, then the upper limit on 5 keV may weaken substantially (Abazajian et al."488 2001h)., 2001b).489 Sterile neutrinos in the keV mass range have à decay time that is of cosmological interest., Sterile neutrinos in the keV mass range have a decay time that is of cosmological interest.490 Recently a very interesting paper appeared. (Abazajianct al.2001b). where the signature from decaving sterile neutrinos in galaxies and clusters of galaxies was studied in detail ον.," Recently a very interesting paper appeared (Abazajianet al.2001b), where the signature from decaying sterile neutrinos in galaxies and clusters of galaxies was studied in detail ."491 X bound, A bound492In the bottom panel of Fig. 4..,"In the bottom panel of Fig. \ref{fig:fvsm},"493 the vertical profiles of the mean (solid lines) and fluctuating (dashed lines) magnetic fields for four representative runs are shown., the vertical profiles of the mean (solid lines) and fluctuating (dashed lines) magnetic fields for four representative runs are shown.494 We find that the mean magnetic field is mainly located in the shear region. whereas the turbulent field. on the other hand. is more spread out inside the convection zone.," We find that the mean magnetic field is mainly located in the shear region, whereas the turbulent field, on the other hand, is more spread out inside the convection zone."495 It is noteworthy that for a thick tachocline the mean field is almost comparable with the fluctuating one. covering a fraction of the stable layer where the fluctuations are weak (see continuous blue line).," It is noteworthy that for a thick tachocline the mean field is almost comparable with the fluctuating one, covering a fraction of the stable layer where the fluctuations are weak (see continuous blue line)."496 Simulations with higher resolution (see blue lines with diamond symbols in Fig. 4)), Simulations with higher resolution (see blue lines with diamond symbols in Fig. \ref{fig:fvsm}) )497 exhibit fluctuating magnetic field with vertical distribution and amplitude almost identical to the lower resolution case., exhibit fluctuating magnetic field with vertical distribution and amplitude almost identical to the lower resolution case.498 The vertical profile of the mean field is roughly the same as in the lower resolution case but of smaller amplitude., The vertical profile of the mean field is roughly the same as in the lower resolution case but of smaller amplitude.499 The structure of the magnetic fields depends strongly οἱ the structure of convection., The structure of the magnetic fields depends strongly on the structure of convection.500 In Fig., In Fig.501" 5. we show snapshots of vertical velocity τι} and azimuthal magnetic field (2,,) for arbitrary times in the saturated state for Runs S04. DO4. anc TOA (from left to right. respectively)."," \ref{fig:byuz} we show snapshots of vertical velocity $U_z$ ) and azimuthal magnetic field $B_y$ ) for arbitrary times in the saturated state for Runs S04, D04, and T04 (from left to right, respectively)."502 From the bottom panels of this figure. it is possible to distinguish that at the base of the convection zone. the toroidal field organizes in elongatec structures of both polarities which span all across the azimuthal direction if the penetrative downflows are less intense.," From the bottom panels of this figure, it is possible to distinguish that at the base of the convection zone, the toroidal field organizes in elongated structures of both polarities which span all across the azimuthal direction if the penetrative downflows are less intense."503 These stripes coexist with more random magnetic fields 1n regions located where jet-like overshooting is able to reach the stable layer., These stripes coexist with more random magnetic fields in regions located where jet-like overshooting is able to reach the stable layer.504 The size of the magnetic structures is at least equal or larger than the scale of the convective eddies., The size of the magnetic structures is at least equal or larger than the scale of the convective eddies.505 This is more evident for the streamwise direction where the field occupies the full extent of the domain., This is more evident for the streamwise direction where the field occupies the full extent of the domain.506 The strong toroidal fields are mainly confined in the shear region., The strong toroidal fields are mainly confined in the shear region.507 This can be seen in the bottom panels of Fig., This can be seen in the bottom panels of Fig.508 5. and also in the bottom panel of Fig. ]..," \ref{fig:byuz} and also in the bottom panel of Fig. \ref{fig:strat},"509 where it is clear that the curve corresponding to Run TO4 (blue line) has a broader profile than the one corresponding to Run S04 (black line)., where it is clear that the curve corresponding to Run T04 (blue line) has a broader profile than the one corresponding to Run S04 (black line).510 The presence of the KH instability is evident in the y: plane where wave like structures are observed., The presence of the KH instability is evident in the $yz$ plane where wave like structures are observed.511 If the tachocline 1s thicker. the effects of the KH-instability are weaker.," If the tachocline is thicker, the effects of the KH-instability are weaker."512 Another advantage of thicker shear layers is that they do not affect the thermodynamical properties of the fluid as strongly as in Sets S and T. The disadvantage ts that they produce broad and more diffuse magnetic fields which do not totally agree with the picture of a flux tube., Another advantage of thicker shear layers is that they do not affect the thermodynamical properties of the fluid as strongly as in Sets S and T. The disadvantage is that they produce broad and more diffuse magnetic fields which do not totally agree with the picture of a flux tube.513 This is discussed in more detail in the next section., This is discussed in more detail in the next section.514 These results are in contradiction with those of ? who used a similar setup in the Boussinesq approximation., These results are in contradiction with those of \cite{Tobias+etal_08} who used a similar setup in the Boussinesq approximation.515 We believe that the lack of a large-scale dynamo in their simulations may be due either to the wider shear profile that they used or to the smaller amplitude of the shear parameter., We believe that the lack of a large-scale dynamo in their simulations may be due either to the wider shear profile that they used or to the smaller amplitude of the shear parameter.516 However. a visual inspection of their figure 11 suggests that a large-scale dynamo could indeed exist in the horizontal plane.," However, a visual inspection of their figure 11 suggests that a large-scale dynamo could indeed exist in the horizontal plane."517 According to linear theory (2). thin magnetic flux tubes become buoyantly unstable when the condition 34 —1/5 is fulfilled.," According to linear theory \citep{spruit+vanbal_82}, thin magnetic flux tubes become buoyantly unstable when the condition $\beta \delta > -1/\gamma$ is fulfilled."518" Here §=2,9p/D7 is the plasma beta. 6=VoVag is the superadiabaticity (see Eq. 10))."," Here $\beta=2\mu_0 p/B^2$ is the plasma beta, $\delta = \nabla - \nabla_{\rm ad}$ is the superadiabaticity (see Eq. \ref{equ:super}) ),"519 and 5 is the ratio of specific heats., and $\gamma$ is the ratio of specific heats.520 This condition is. satisfied in the convection zone Where 6>0., This condition is satisfied in the convection zone where $\delta > 0$.521 From this relation it follows that below the convection zone. where 6<0. thin magnetic flux tubes require much higher field strength to become unstable.," From this relation it follows that below the convection zone, where $\delta < 0$, thin magnetic flux tubes require much higher field strength to become unstable."522 For à magnetic layer. the necessary and sufficient condition for the development of two-dimensional interchange modes. in which we are interested here. is given by (?): We find that for the cases with thinnest shear layer. the instability region is above the center of the shear layer where the toroidal magnetic field reaches its maximum value (see Fig. 6)).," For a magnetic layer, the necessary and sufficient condition for the development of two-dimensional interchange modes, in which we are interested here, is given by \citep{Newcomb_61}: We find that for the cases with thinnest shear layer, the instability region is above the center of the shear layer where the toroidal magnetic field reaches its maximum value (see Fig. \ref{fig:bi}) )."523 This implies that a large fraction of the magnetic field there becomes buoyantly unstable very quickly., This implies that a large fraction of the magnetic field there becomes buoyantly unstable very quickly.524 For the cases with a thick shear layer (Set T). the magnetic field is unstable only within the convection zone.," For the cases with a thick shear layer (Set T), the magnetic field is unstable only within the convection zone."525 The magnetic field distribution of the Run TO4 in Fig., The magnetic field distribution of the Run T04 in Fig.526 4. (blue line). indicates that a large fraction of the magnetic field is buoyantly stable.," \ref{fig:fvsm} (blue line), indicates that a large fraction of the magnetic field is buoyantly stable."527 This configuration may explain why in these cases larger mea magnetic fields develop with smaller shear parameters than i1 sets ο and D are used., This configuration may explain why in these cases larger mean magnetic fields develop with smaller shear parameters than in sets S and D are used.528 Note. however. that this conclusion is based on averaged quantities.," Note, however, that this conclusion is based on averaged quantities."529 The evolution of local magnetic structures is rather complex and possibly also affected by the KH instability., The evolution of local magnetic structures is rather complex and possibly also affected by the KH instability.530 The radial velocity gradient in Run TOA is smaller. so it is expected to have a less efficient KH instability and this should allow a longer stay of the magnetic field in the stable layer.," The radial velocity gradient in Run T04 is smaller, so it is expected to have a less efficient KH instability and this should allow a longer stay of the magnetic field in the stable layer."531 This is hard to demonstrate since it 1s difficult to disentangle these effects in the simulations., This is hard to demonstrate since it is difficult to disentangle these effects in the simulations.532 Nevertheless. it seems that the longer the magnetic field stays at the stable region the greater the final mean magnetic field strength.," Nevertheless, it seems that the longer the magnetic field stays at the stable region the greater the final mean magnetic field strength."533 Hence. according to ?.. the number of scale heights the magnetic flux concentrations may rise. and its final structure depends only on how strong the field is in comparison to the turbulent convective motions.," Hence, according to \cite{Fan_01}, the number of scale heights the magnetic flux concentrations may rise, and its final structure depends only on how strong the field is in comparison to the turbulent convective motions."534 In the simulations it is observed thatwhen the magnetic field rises it expands as a consequence of decreasing density., In the simulations it is observed thatwhen the magnetic field rises it expands as a consequence of decreasing density.535 The morphology of the magnetic fields in the > plane (see bottom panels of Fig. 5)), The morphology of the magnetic fields in the $xz$ plane (see bottom panels of Fig. \ref{fig:byuz}) )536 is reminiscent of the mushroom-shape that has been obtained in several 2D (2222?) and 3D (?22??) simulations of flux tube emergence.," is reminiscent of the mushroom-shape that has been obtained in several 2D \citep{schussler_79,moreno+emonet_96,Longcope+etal_96,537 Fan+etal_98,Emonet+Moreno_98}538 and 3D \citep{Fan_01,fan+etal_03,Fan_08,jouve+brun_09} simulations of flux tube emergence."539 Such expansion may result in the splitting and braking of the tube., Such expansion may result in the splitting and braking of the tube.540 We do not impose any twist on the tubes since the dynamo generates the magnetic field self-consistently and the possibilities span from events that do not rise at all to events where buoyant magnetic fields rise up to the very surface., We do not impose any twist on the tubes since the dynamo generates the magnetic field self-consistently and the possibilities span from events that do not rise at all to events where buoyant magnetic fields rise up to the very surface.541 In the horizontal y~ plane we observe that the magnetic field lines remain horizontal in the stable layer where they form., In the horizontal $yz$ plane we observe that the magnetic field lines remain horizontal in the stable layer where they form.542 When the magnetic field rises. the field lines bend in the convection zone. with their rising part in the middle of upward flows and other parts withheld to the downward flows.," When the magnetic field rises, the field lines bend in the convection zone, with their rising part in the middle of upward flows and other parts withheld to the downward flows."543" In Tables | and 2 we list the maximum values of £5, in the simulations.", In Tables \ref{tab:1} and \ref{tab:2} we list the maximum values of $B_y$ in the simulations.544" In most of the cases we find inax(D,)= 5D. and only in the models with a thicker (Runs TO4 and AROI) or a deeper shear layer (Run DO4). πας) can be somewhat"," In most of the cases we find ${\rm max}(B_y)\approx 5\Beq$ , and only in the models with a thicker (Runs T04 and AR01) or a deeper shear layer (Run D04), ${\rm max}(B_y)$ can be somewhat"545be half of the >gravitational luminosity. l]laving an optically thick boundary. [aver with a thickness opi. it will heat to a temperature of where σ is the Stefan-Doltzmann constant.,"be half of the gravitational luminosity Having an optically thick boundary layer with a thickness $\delta_{\rm{BL}}$, it will heat to a temperature of where $\sigma$ is the Stefan-Boltzmann constant."546 The temperature of the boundary laver for the parameters used in equations (8)) and (9)) is compatible with the hot temperatures of M31. RY as seen in the observations of Shara et al. (, The temperature of the boundary layer for the parameters used in equations \ref{eq:L_BL}) ) and \ref{eq:T_BL}) ) is compatible with the hot temperatures of M31 RV as seen in the observations of Shara et al. (5472010b) at late times.,2010b) at late times.548 The accretion luminosity is evenly divided. between the boundary. laver. ancl the accretion disk itself., The accretion luminosity is evenly divided between the boundary layer and the accretion disk itself.549 Phe aceretion disk temperature is much ower than the temperature of the boundary laver., The accretion disk temperature is much lower than the temperature of the boundary layer.550 Hence. it is expected that the averaged observed temperature will x! lower than the temperature of the boundary. layer.," Hence, it is expected that the averaged observed temperature will be lower than the temperature of the boundary layer."551 Let us now check what would be the optical depth of he transient a few vears after its eruption., Let us now check what would be the optical depth of the transient a few years after its eruption.552 We will assume spherical symmetry., We will assume spherical symmetry.553 The thickness of the shell. Aria. ejected during the eruption is determined. from the timescale of he eruption Af. in which thematerial is ejected. and the velocity roy it had during the eruption We take the mass of the spherically expanding shell M. and its average expansion velocity eg.," The thickness of the shell, $\Delta r_{\rm{er}}$, ejected during the eruption is determined from the timescale of the eruption $\Delta t_{\rm{er}}$ in which thematerial is ejected, and the velocity $v_{\rm{er}}$ it had during the eruption We take the mass of the spherically expanding shell $M_{\rm{ej}}$, and its average expansion velocity $v_{\rm{ej}}$."554 After a time period Af it would reach a distance of where the calibration is [rom M31 RY and the latest LISTE observations of Shara et al. (, After a time period $\Delta t$ it would reach a distance of where the calibration is from M31 RV and the latest HST observations of Shara et al. (5552010b).,2010b).556 The average density in the shell is therefore and the column density of the shell is lor a shell temperature of 1000Ix with. Hydrogen abundance XN=0.7 and metallicity Z=0.02 the opacity (from the same data by Ferguson. described. above). is πωΞ0.03engο+. and the optical depth is For temperatures in the range ~600 ~3000IX the Oopacity dis hejl and therefore the result that the shell beinggol optically thin is not sensitive to temperature.," The average density in the shell is therefore and the column density of the shell is For a shell temperature of $1000 \K$ with Hydrogen abundance $\rm{X}=0.7$ and metallicity $\rm{Z}=0.02$ the opacity (from the same data by Ferguson described above) is $\kappa_{\rm{ej}}= 0.03 \cm^2 \g^{-1}$, and the optical depth is For temperatures in the range $\sim 600$ – $\sim 3000 \K$ the opacity is $\kappa_{\rm{ej}}<1$ and therefore the result that the shell being optically thin is not sensitive to temperature."5571 I£ cust is formed the opacity can reach much higher values., If dust is formed the opacity can reach much higher values.558 Several researchers have suggested that dust. opacities can reach values of ~10engο+ and even higher (e.g. Llelling et al., Several researchers have suggested that dust opacities can reach values of $\sim 10 \cm^2 \g^{-1}$ and even higher (e.g. Helling et al.559 2000: Llenning Stognienko 1996: Pollack Alekay 1985: Pollack et al., 2000; Henning Stognienko 1996; Pollack Mckay 1985; Pollack et al.560 1994: Semenov et al., 1994; Semenov et al.561 2003)., 2003).562 However. these ugh opacities were not obtained for densities as low as ~10P. as in our case.," However, these high opacities were not obtained for densities as low as $\sim 10^{-17}$, as in our case."563 According to the studies discussed above for such densities. the opacity is tay1 in the emperature range 100 —1000Ix. which is the relevant range for our study.," According to the studies discussed above for such densities, the opacity is $\kappa_{\rm{ej}}<1$ in the temperature range $\sim 100$ – $\sim 1000 \K$, which is the relevant range for our study."564 From equations (119). (12)). (13)) and (1433). the time period it would take for the clusty shell to come Optically thin is We see that even if dust &rains are formed. a lew vears after the eruption my<<1. and the shell becomes optically thin.," From equations \ref{eq:r_ej}) ), \ref{eq:rho_ej}) ), \ref{eq:delta_N_ej}) ) and \ref{eq:tau_ej}) ), the time period it would take for the dusty shell to become optically thin is We see that even if dust grains are formed, a few years after the eruption $\tau_{\rm{ej}} << 1$, and the shell becomes optically thin."565 This result holds even if the ejected mass is as high as ΑμΞ0.1M.," This result holds even if the ejected mass is as high as $M_{\rm{ej,max}}=0.1~\rm{M_{\odot}}$."566 We therefore propose the following scenario for the outburst of M31 RV., We therefore propose the following scenario for the outburst of M31 RV.567 This scenario with different parameters is relevant to other ILOTs with low mass progenitors as well., This scenario with different parameters is relevant to other ILOTs with low mass progenitors as well.568 An interaction between two old stars. a primary with a mass of ~1M. and a less massive companion. led to the ejection of material that created a shell around the primary.," An interaction between two old stars, a primary with a mass of $\sim 1~\rm{M_{\odot}}$ and a less massive companion, led to the ejection of material that created a shell around the primary."569 Alternatively. this interaction might have been a miss loss episode of the companion due to tidal interaction with the primary.," Alternatively, this interaction might have been a mass loss episode of the companion due to tidal interaction with the primary."570 Approximately. a mass of Al;~0.01\ was cjectecl ancl created an expanding shell around. the stars.," Approximately, a mass of $M_{\rm{ej}} \sim 0.01~\rm{M_{\odot}}$ was ejected and created an expanding shell around the stars."571 Phe energy to eject the shell comes from aceretion of material onto the star(s)., The energy to eject the shell comes from accretion of material onto the star(s).572 The kinetic energy of the ejecta Is The racliated enerev Levanστ101erg (Mould et al.," The kinetic energy of the ejecta is The radiated energy $E_{\rm{er,rad}} \simeq 10^{46} \erg$ (Mould et al."573 1990)., 1990).574 Therefore the total energv. of the eruption is fori=oPadua|Eua09LOYerg.," Therefore the total energy of the eruption is $E_{\rm{er,tot}} = E_{\rm{er,kin}} + E_{\rm{er,rad}} \simeq 10^{47} \erg$."575 We assume that the companion which donated. the accreted anc ejected material had a highly eccentric orbit e= 0.85. and that the accretion episode occurred. close to. periastron where the tidal force was maximal.," We assume that the companion which donated the accreted and ejected material had a highly eccentric orbit $e \gtrsim 0.85$ , and that the accretion episode occurred close to periastron where the tidal force was maximal."576 Therefore. the accreted material [ell onto the star at approximately the free-fall velocity.," Therefore, the accreted material fell onto the star at approximately the free-fall velocity."577of siguiicant advantages.,of significant advantages.578 For instance. in the derivation of the solution. it i unnecessary to make anv sinall-anele approximations and. when compared to the manipulations of Ll Mueller matrices. the equivalent quatermion and 242 Jones matrix represcutations ercatly simplify the required algebra.," For instance, in the derivation of the solution, it is unnecessary to make any small-angle approximations and, when compared to the manipulations of $\times$ 4 Mueller matrices, the equivalent quaternion and $\times$ 2 Jones matrix representations greatly simplify the required algebra."579 As well. equatious (7)) and (9)) are specific to no particular basis. permitting the application of the formalism to ai variety of feed desigus ly xoper choice of the basis matrices. σ.," As well, equations \ref{eqn:congruence_transformation}) ) and \ref{eqn:polar_decomposition}) ) are specific to no particular basis, permitting the application of the formalism to a variety of feed designs by proper choice of the basis matrices, $\boldsymbol{\sigma}$."580 Perhaps most inuportantlv. as shown by Tamaker aud discussed below. he polar decomposition enables the deteriiuation of the ))ost Colmponent of the svsteni response using only au observation of au uupolarized source.," Perhaps most importantly, as shown by Hamaker and discussed below, the polar decomposition enables the determination of the boost component of the system response using only an observation of an unpolarized source."581 This simplification as beneficial iupact on experiauents where only the total intensity or fractional degree of polarization are of concern., This simplification has beneficial impact on experiments where only the total intensity or fractional degree of polarization are of concern.582 Consider the reception of unpolarized radiation. which wx al input average power spectrum matrix. P; —I7/2. where Eis the identity matrixand Ty is the total iuteusity.," Consider the reception of unpolarized radiation, which has an input average power spectrum matrix, $\bar{\bf{P}}_L$ ${\bf I}\;T_0/2$ , where ${\bf I}$ is the identity matrixand $T_0$ is the total intensity."583 Deeimniueg with equations (7)) aud (9)). the output average »ower spectrum can be trivially shown to be Notice that the phase of J is lost in the detection of he average power spectrum.," Beginning with equations \ref{eqn:congruence_transformation}) ) and \ref{eqn:polar_decomposition}) ), the output average power spectrum can be trivially shown to be Notice that the phase of $J$ is lost in the detection of the average power spectrum."584 For this reasou. the current echuique is iuseusitive to absolute phase terius arising iu he frequency response of the system. and may be used o determine only the relative phase differences between its components.," For this reason, the current technique is insensitive to absolute phase terms arising in the frequency response of the system, and may be used to determine only the relative phase differences between its components."585 The scalar factors. |J|? and Ty. are easily determined in a separate flux calibration procedure that will not be considered preseutly," The scalar factors, $|J|^2$ and $T_0$, are easily determined in a separate flux calibration procedure that will not be considered presently."586 Therefore. nuuav be found by taking the positive Wermitian square root of the measured average power spectrum matrix of au unpolarized source (see Appendix. À)).," Therefore, may be found by taking the positive Hermitian square root of the measured average power spectrum matrix of an unpolarized source (see Appendix \ref{app:solve}) )."587 This simple result iierits closer inspection., This simple result merits closer inspection.588 The svsteii response nav be corrected by inverting equation (1)). hat is. by calculating E=JLE’.," The system response may be corrected by inverting equation \ref{eqn:convolution_nu}) ), that is, by calculating $\mbf{E}={\bf J}^{-1}\mbf{E^\prime}$."589 Notice that. under he polar decomposition chosen iu equation (9)). the ))ost transformation is the first to be inverted.," Notice that, under the polar decomposition chosen in equation \ref{eqn:polar_decomposition}) ), the boost transformation is the first to be inverted."590 That is. regardless of the unknown rotation. the boost solution nay be used to completely invert the distortion of total intensity. Sy.," That is, regardless of the unknown rotation, the boost solution may be used to completely invert the distortion of total intensity, $S_0$."591 This consequence of the polar decomposition was considerable impact iu the field of high-precision oulsar tinung. where the average total intensity profile is used to determine the pulse time of arrival.," This consequence of the polar decomposition has considerable impact in the field of high-precision pulsar timing, where the average total intensity profile is used to determine the pulse time of arrival."592 Polariuetric distortions to the total intensity can significautl alter he shape of this profile aud svstematically alter arrival nue estimates. especially as a function of parallactic anele. or with fluctuations of ionospheric total electron content.," Polarimetric distortions to the total intensity can significantly alter the shape of this profile and systematically alter arrival time estimates, especially as a function of parallactic angle, or with fluctuations of ionospheric total electron content."593 With the boost component thus determined. the resulting distortions to total intensity can. iu principle. be completely corrected.," With the boost component thus determined, the resulting distortions to total intensity can, in principle, be completely corrected."594 It remains to solve for the rotation component ofJ. which max be determined using observations of calibrators with known polarization.," It remains to solve for the rotation component of, which may be determined using observations of calibrators with known polarization."595" Caven the known boost.(7). input polarization state. P,,. aud measured output state. P/. equation. (7)) is solved for the rotation.Ra(o)."," Given the known boost, input polarization state, $\bar{\bf P}_n$, and measured output state, $\bar{\bf596P}^\prime_n$, equation \ref{eqn:congruence_transformation}) ) is solved for the rotation,."597". Cousidering the equivalent three-dinensional Euclidiau rotation.(20). of the polarization vector. S. it is casily seen that. given a single pair of input. Sy. and output. οι”. polarization vectors. the rotatious that solve οι=R47(20)9,. where δι=[Sy]. form zu infinite set of rotations with axis confined oulv to a plane."," Considering the equivalent three-dimensional Euclidian rotation, of the polarization vector, $\mbf{S}$, it is easily seen that, given a single pair of input, $\mbf{S_1}$, and output, $\mbf{S_1}^\prime$, polarization vectors, the rotations that solve $\mbf{S_1}^\prime=\rotEn\mbf{S_1}$, where $|\mbf{S_1}^\prime|=|\mbf{S_1}|$, form an infinite set of rotations with axis confined only to a plane."598 Therefore. au observation of a secoud. noun-collinear calibrator source is required in order to uniquely determine the system response rotation.," Therefore, an observation of a second, non-collinear calibrator source is required in order to uniquely determine the system response rotation."599 Ablauy receivers are equipped with a linearly polarized noise diode that may be used to iuject a calibrator signal into the feed horn., Many receivers are equipped with a linearly polarized noise diode that may be used to inject a calibrator signal into the feed horn.600 This noise diode may be switched using a wide-band. auiplitude-auodulated square-wave.," This noise diode may be switched using a wide-band, amplitude-modulated square-wave."601 The “oft” or “low” fraction of the wave cousists of ouly the system. plus sky temperature. which shall be assumed to be unpolarized.," The “off” or “low” fraction of the wave consists of only the system plus sky temperature, which shall be assumed to be unpolarized."602" The ""ou or ""high fraction of the wave contains additional linearly. polarized radiation. described in quaternion forni by where Cy is the flux and V is the position angle of the calibrator diode."," The “on” or “high” fraction of the wave contains additional linearly polarized radiation, described in quaternion form by where $C_0$ is the flux and $\Psi$ is the position angle of the calibrator diode."603 A siuele linear noise diode provides oulv one kuown input calibrator state., A single linear noise diode provides only one known input calibrator state.604 Unless another calibrator is available. the technique iust be modified to solve for a reduced representation of the svsteni response.," Unless another calibrator is available, the technique must be modified to solve for a reduced representation of the system response."605" For the calibration described in this paper. wwas be decomposed into two rotations: Reg(AW).. allowing nuperfect alieuiieut. of the noise diode: followed byRg(@,).. allowing a differeutial path length between the two linear poluizatious (see Appendix A))."," For the calibration described in this paper, was be decomposed into two rotations: , allowing imperfect alignment of the noise diode; followed by, allowing a differential path length between the two linear polarizations (see Appendix \ref{app:solve}) )."606 It is importaut to distinguish AW aud $9; from the actual parameters of the receiver. as the polar decomposition docs not model the order in which the transformations plivsically occur.," It is important to distinguish $\Delta\Psi$ and $\Phi_I$ from the actual parameters of the receiver, as the polar decomposition does not model the order in which the transformations physically occur."607 When observing the artificial calibrator. it is iurportant that the noise diode be switched ou a time-scale πιο shorter than the interval over which the digitization thresholds are reset. in order that Py may be differentiated from the baseline. Pj.," When observing the artificial calibrator, it is important that the noise diode be switched on a time-scale much shorter than the interval over which the digitization thresholds are reset, in order that $\bar{\bf{P}}_H$ may be differentiated from the baseline, $\bar{\bf{P}}_L$ ."608" Πωπονο, the calibrator period must also be long enough to provide distinct ou-pulse aud off-pulse time samples iu the svuthesized filterbank."," However, the calibrator period must also be long enough to provide distinct on-pulse and off-pulse time samples in the synthesized filterbank."609 Caven the sampling interval. f; of the basebaud recorder. the calibrator period. 7. should be at least Tee7nptyN. where N is the ummber of chauucls in the svuthetic filterhaul and 05 is the desired uuniboer of phase bins in the integrated calibrator profile.," Given the sampling interval, $t_s$, of the baseband recorder, the calibrator period, $T_C$, should be at least $T_C \ge n_b t_s N$, where $N$ is the number of channels in the synthetic filterbank and $n_b$ is the desired number of phase bins in the integrated calibrator profile."610 In order to achieve clear separation of on-pulse aud off-pulse states. vp61 was chosen.," In order to achieve clear separation of on-pulse and off-pulse states, $n_b=64$ was chosen."611 As well. it was found that a Ποας with Vo=2018 channels sufficieutlIv. resolved the features of the frequency response.," As well, it was found that a filterbank with $N=2048$ channels sufficiently resolved the features of the frequency response."612 For cach hom-long observation ofPSR0715.. the pulsed calibrator was recorded for 4.5 minutes. cusuring sufficient signal-to-noise in each channel of the svuthetic filterbank.," For each hour-long observation of, the pulsed calibrator was recorded for 4.5 minutes, ensuring sufficient signal-to-noise in each channel of the synthetic filterbank."613 Data were reduced offline usingpsrdisp. a software package developed to process pulsar baseband data. described in the following section.," Data were reduced offline using, a software package developed to process pulsar baseband data, described in the following section."614 After forming a svuthetic flterbank. the Stokes parameters in cach channel were detected aud folded at the pulsed calibrator od.," After forming a synthetic filterbank, the Stokes parameters in each channel were detected and folded at the pulsed calibrator period."615 Teh aud low state polarimetric passbauds were formed from the average ou- and off-pulse Stokes xuanueters of the calibrator profile in cach chanucl., High and low state polarimetric passbands were formed from the average on- and off-pulse Stokes parameters of the calibrator profile in each channel.616 These oissbands were mediau filtered to remove spurious raclio-requencev interference. and interpolated to the required requencev resolution. as dictated by theparameters of the coherent dedispersion Kernel.," These passbands were median filtered to remove spurious radio-frequency interference, and interpolated to the required frequency resolution, as dictated by theparameters of the coherent dedispersion kernel."617 From this hieh frequeucv- polarimetric represcutation of thecalibrator. he frequency response matrixwas computed as described in Appendix A..," From this high frequency-resolution polarimetric representation of thecalibrator, the frequency response matrixwas computed as described in Appendix \ref{app:solve}. ."618 Figure P. plots represeutative examples of the determined frequency response parameters at, Figure \ref{fig:pcal} plots representative examples of the determined frequency response parameters at619but within our limited. sample. this does not appear to be the case.,"but within our limited sample, this does not appear to be the case."620 However. one has to bear in mind that. the RATE ASAL points we use are daily averages and. the system is known to change it’s optical ancl X-ray states at much shorter timescales.," However, one has to bear in mind that the RXTE ASM points we use are daily averages and the system is known to change it's optical and X-ray states at much shorter timescales."621 Ελπίς. together with the small amplitude of detected. X-ray level changes in the EXOSAT cata (Alachin et al..," This, together with the small amplitude of detected X-ray level changes in the EXOSAT data (Machin et al.,"622 1990) certainly adds uncertainty to our optical vs. X-ray [lux analysis., 1990) certainly adds uncertainty to our optical vs. X-ray flux analysis.623 Finally. we would like to draw attention to the dangers that lie in the conventional period analvsis (i.c. chance estimation based on white noise only).," Finally, we would like to draw attention to the dangers that lie in the conventional period analysis (i.e. chance estimation based on white noise only)."624 The significance level analvsis of any moderately. significant. peaks in the power spectra should. always include the possible elfects. of red noise., The significance level analysis of any moderately significant peaks in the power spectra should always include the possible effects of red noise.625 This is particularly truc for any acereting sources where the flickering from the accretion How will almost alwavs introduce characteristic time scales in the data. that in turn show up as light curve data points that are not totally independent.," This is particularly true for any accreting sources where the flickering from the accretion flow will almost always introduce characteristic time scales in the data, that in turn show up as light curve data points that are not totally independent."626 The data presented. here have been taken using ALFOSC. which is owned by the Instituto de Xstrofisica de Andalucia (LVA) and operated. at the Nordic Optical Telescope under agreement. between LAA and the NBUAKC of the Astronomical Observatory of Copenhagen.," The data presented here have been taken using ALFOSC, which is owned by the Instituto de Astrofisica de Andalucia (IAA) and operated at the Nordic Optical Telescope under agreement between IAA and the NBIfAFG of the Astronomical Observatory of Copenhagen."627 Phe authors eratefully acknowledge support. from the Academy of Finland., The authors gratefully acknowledge support from the Academy of Finland.628 Finally. we would like to thank the anonymous referee for very constructive criticism that helped to improve the paper considerably.," Finally, we would like to thank the anonymous referee for very constructive criticism that helped to improve the paper considerably."629is not required.,is not required.630" Because our picture can be modelled mathematically, we are able to validate it against the simulations, showing that the envisioned process indeed creates cores within the G10 simulations."," Because our picture can be modelled mathematically, we are able to validate it against the simulations, showing that the envisioned process indeed creates cores within the G10 simulations."631 This paper is organized as follows., This paper is organized as follows.632" Section ?? introduces improved simulations based on those of G10, and discusses the characteristics of these simulations which predict cusp-flattening, thus motivating a study of orbits in rapidly changing potentials (Section ??))."," Section \ref{sec:first-sims}633 introduces improved simulations based on those of G10, and discusses the characteristics of these simulations which predict cusp-flattening, thus motivating a study of orbits in rapidly changing potentials (Section \ref{sec:virial-eqs}) )."634" The initial discussion is, for simplicity, limited to power-law potentials but Section ?? removes this restriction, presenting more general equations to explain the detailed simulation results."," The initial discussion is, for simplicity, limited to power-law potentials but Section \ref{sec:second-sims} removes this restriction, presenting more general equations to explain the detailed simulation results."635" We relate our work to the wider literature and conclude in Section ??,, In a companion paper (Governato et al, in prep) we will discuss the scaling of the dark matter cores with galaxy masses."," We relate our work to the wider literature and conclude in Section \ref{sec:conclusions}, In a companion paper (Governato et al, in prep) we will discuss the scaling of the dark matter cores with galaxy masses."636" The smoothed particle hydrodynamics (SPH) simulations, run using the code (?),, are closely related to and improve upon those described in more detail by G10."," The smoothed particle hydrodynamics (SPH) simulations, run using the code \citep{2004NewA....9..137W}, are closely related to and improve upon those described in more detail by G10."637 Our new runs output more regular timesteps and include the effects of metal-line cooling according to the prescription of ?.., Our new runs output more regular timesteps and include the effects of metal-line cooling according to the prescription of \cite{2010MNRAS.407.1581S}.638 The simulations in this paper focus on the region hosting the galaxy denoted ‘DG1’ in G10., The simulations in this paper focus on the region hosting the galaxy denoted `DG1' in G10.639 The ‘zoom’ technique (e.g.?) allows for a high mass resolution of Mp—3x10?Mo (for gas particles) and Mp=1.6x104Mo (dark matter) with a softening of 86pc in a full ACDM cosmological context.," The `zoom' technique \cite[e.g.][]{1993ApJ...412..455K} allows for a high mass resolution of $M_{\mathrm{p}} = 3 \times 10^3 \, \Msol$ (for gas particles) and $M_{\mathrm{p}} = 1.6 \times 10^4\,\Msol$ (dark matter) with a softening of $86\,\pc$ in a full $\Lambda$ CDM cosmological context."640" We conducted analysis on the two most massive systems within this region: DGl itself (My,=3.7x1010M; at z= 0) and a somewhat smaller galaxy (My,=1.3x109M at z— 0)."," We conducted analysis on the two most massive systems within this region: DG1 itself $M_{\mathrm{vir}}=3.7 \times 10^{10}\,\Msol$ at $z=0$ ) and a somewhat smaller galaxy $M_{\mathrm{vir}}=1.3 \times64110^{10}\,\Msol$ at $z=0$ )."642" Most results will be presented for the latter case, because the former undergoes a major merger at z—3."," Most results will be presented for the latter case, because the former undergoes a major merger at $z=3$."643" Although our model does predict the correct flattening for DG1, its volatile merger history would introduce undue complexities into our discussion."," Although our model does predict the correct flattening for DG1, its volatile merger history would introduce undue complexities into our discussion."644" In the first run, denoted HT (“high threshold""), stars are allowed to form only at hydrogen densities exceeding 100cm~?."," In the first run, denoted HT (“high threshold”), stars are allowed to form only at hydrogen densities exceeding $100\,\mathrm{cm}^{-3}$."645" The second run, LT (“low threshold""), is identical to the first except that it allows stars to form at densities exceeding 0.1οι2."," The second run, LT (“low threshold”), is identical to the first except that it allows stars to form at densities exceeding $0.1\,\mathrm{cm}^{-3}$."646" As expected following G10, LT remains cusped, unlike HT which develops a 1kpc dark matter core at z=0 in both of its two most massive halos."," As expected following G10, LT remains cusped, unlike HT which develops a $1\,\kpc$ dark matter core at $z=0$ in both of its two most massive halos."647" In all cases the code consistently follows the feedback effects of the stellar populations (?) so that, after a delay of ~10Myr, significant amounts of thermal energy are deposited into the surrounding gas."," In all cases the code consistently follows the feedback effects of the stellar populations \citep{2006astro.ph..2350S} so that, after a delay of $\sim 10 \,648\Myr$, significant amounts of thermal energy are deposited into the surrounding gas."649" By z—2, when HT has developed a stablecore, LT and HT runs have formed an almost identical mass of stars (7x 107M.) and therefore the same quantity of supernova energy has been released (7x1056ergs).? The failure of LT to lose its cusp thus reflects a difference in the coupling mechanism, not in the absolute energy deposition."," By $z=2$, when HT has developed a stablecore, LT and HT runs have formed an almost identical mass of stars $7 \times65010^{7} \Msol$ ) and therefore the same quantity of supernova energy has been released $7 \times 10^{56}\, \ergs$ The failure of LT to lose its cusp thus reflects a difference in the coupling mechanism, not in the absolute energy deposition."651" Figure 1. gives immediate insight into the difference between HT (cusp-flattening) and LT (cusp-preserving) simulations by showing their spherically-averaged halo density profiles shortly before the cusp begins to flatten in HT, at z— 4."," Figure \ref{fig:den} gives immediate insight into the difference between HT (cusp-flattening) and LT (cusp-preserving) simulations by showing their spherically-averaged halo density profiles shortly before the cusp begins to flatten in HT, at $z=4$ ."652" Solid, dashed and dotted lines indicate respectively dark matter, gas and stellar"," Solid, dashed and dotted lines indicate respectively dark matter, gas and stellar"653using pixels with a constant velocity width of 2.1 although a subset of the spectra at 2<2.8 were binned! using Constant 0.03 »pixels.,"using pixels with a constant velocity width of 2.1, although a subset of the spectra at $z \le 2.8$ were binned using constant 0.03 pixels."654 The resolution of the MILNE spectra is 13.6, The resolution of the MIKE spectra is 13.6.655 bor: these spectra. 5.0 sinned pixels were used.," For these spectra, 5.0 binned pixels were used."656 Por both instruments the resolution is sullicient to resolve typical forest lines. which have Doppler parameters bz10 or EWIIMz24+.," For both instruments the resolution is sufficient to resolve typical forest lines, which have Doppler parameters $b657\gtrsim 10$ , or ${\rm FWHM} \gtrsim 24$."658 When making comparisons with he simulations. we smooth and. resample the simulations o match the resolution and binning of each QSO spectrum individually.," When making comparisons with the simulations, we smooth and resample the simulations to match the resolution and binning of each QSO spectrum individually."659 Provided that adequate sampling is used. we ouncl the curvature statistic (Section ??)) does not depend on the choice of binning. although it does depend on the resolution.," Provided that adequate sampling is used, we found the curvature statistic (Section \ref{sec:method}) ) does not depend on the choice of binning, although it does depend on the resolution."660 As described below. the curvature is measured in sections spanning 10h* MAMpe seetions.," As described below, the curvature is measured in sections spanning $h^{-1}$ Mpc sections."661 Ouly sections with a mean rms uncertainty in the normalized Dux of 0.06 per 2. were included. in the final analysis., Only sections with a mean $rms$ uncertainty in the normalized flux of 0.06 per 2.1 were included in the final analysis.662 Initial. continua were fit using slowlv-varving spline profiles., Initial continua were fit using slowly-varying spline profiles.663 Real cata are cillicult to continuum fit accurately. however. and we discuss our strategv for avoiding errorsdue to continuum fitting in Section ??..," Real data are difficult to continuum fit accurately, however, and we discuss our strategy for avoiding errorsdue to continuum fitting in Section \ref{sec:continuum}."664 In order to obtain temperature constraints [rom the [forest. we have used. detailed. simulated. spectra [or calibrating and interpreting our observational measurcments.," In order to obtain temperature constraints from the forest, we have used detailed simulated spectra for calibrating and interpreting our observational measurements."665 We performed a large set of high resolution. fully byelrodvnamiucal simulations which span a wide variety of possible thermal histories.," We performed a large set of high resolution, fully hydrodynamical simulations which span a wide variety of possible thermal histories."666 The simulations were run using the parallel νου]. codeGADGLET-3. which is an upelated version of the publicly available code (?).. and are summarized in Table 3..," The simulations were run using the parallel Tree-SPH code, which is an updated version of the publicly available code \citep{springel2005}, and are summarized in Table \ref{tab:sims}."667 The Biducial simulation volume is a 105 !MMpec »wiodic box containing 2512 gas and dark matter xwticles.," The fiducial simulation volume is a $10\,h^{-1}$ Mpc periodic box containing $2 \times 512^{3}$ gas and dark matter particles."668 his resolution is chosen specifically to resolve the forest at high redshift (2).., This resolution is chosen specifically to resolve the forest at high redshift \citep{boltonbecker2009}.669 Phe simulations were all started ab 2=99. with initial conditions generated using the ransfer function. of 7..," The simulations were all started at $z=99$, with initial conditions generated using the transfer function of \citet{eisensteinhu1999}."670" The cosmological parameters are On,= 0.26. Oy=0.74. OVA=0.023. 5=0.72. m=U.80. n.=0.96. consistent with recent studies of the cosmic microwave background (?7).."," The cosmological parameters are $\Omega_{\rm m}=0.26$ , $\Omega_{\Lambda}=0.74$, $\Omega_{\rm671 b}h^{2}=0.023$, $h=0.72$, $\sigma_{8}=0.80$, $n_{\rm s}=0.96$, consistent with recent studies of the cosmic microwave background \citep{reichardt2009,jarosik2010}."672 Phe IGM is assumed tobe of primordial composition with a helium fraction by mass of Y=0.24 (?).., The IGM is assumed tobe of primordial composition with a helium fraction by mass of $Y=0.24$ \citep{olive2004}. .673 Thegravitational softening length wasset, Thegravitational softening length wasset674mass-function and the spin-parameter distribution.,mass-function and the spin-parameter distribution.675 It can be seen that the mass-function changes mainly at the low mass end., It can be seen that the mass-function changes mainly at the low mass end.676" The changes are related to the mass discreteness: The more particles a halo is composed of, the easier it is to pick it up with our refinement criterion based on the number of particles within a cell."," The changes are related to the mass discreteness: The more particles a halo is composed of, the easier it is to pick it up with our refinement criterion based on the number of particles within a cell."677" Hence it can be readily understood that by forcing a smaller criterion, more halos with a small amount of particles will be found."," Hence it can be readily understood that by forcing a smaller criterion, more halos with a small amount of particles will be found."678" 'This is important for the completeness of the deduced halo catalogs: only when choosing a very small refinement criterion (S; 3.0), we are complete at the end."," This is important for the completeness of the deduced halo catalogs: only when choosing a very small refinement criterion $\lesssim 3.0$ ), we are complete at the end."679 The spin parameter distribution is also affected., The spin parameter distribution is also affected.680 We can see in the top row of figure 6 that the peak of the distribution shifts slightly and is reduced inheight®., We can see in the top row of figure \ref{fig:serial_lambda_ref} that the peak of the distribution shifts slightly and is reduced in.681". However, when only including halos with more than 100 particles (shown in the bottom panels of figure 6)) in the calculation of the distribution, the shift is reduced and the distributions coincide; note that the most massive halo in the analyses of B1500 is resolved with only 237 particles."," However, when only including halos with more than $100$ particles (shown in the bottom panels of figure \ref{fig:serial_lambda_ref}) ) in the calculation of the distribution, the shift is reduced and the distributions coincide; note that the most massive halo in the analyses of B1500 is resolved with only 237 particles."682" As we will discuss later, the choice of the refinement criterion severely impacts on the runtime and the memory requirements (see figure 14)) and hence should be lowered only with care."," As we will discuss later, the choice of the refinement criterion severely impacts on the runtime and the memory requirements (see figure \ref{fig:scaling_refref}) ) and hence should be lowered only with care."683 We will now investigate the effect of the size of the boundary zone and the number of processes., We will now investigate the effect of the size of the boundary zone and the number of processes.684" As the reference model we use a serial run with a domain grid of DomGrid—128 cells per dimension, a refinement criterion of DomRef—1.0 on the domain grid and a refinement criterion of RefRef—5.0 on the refinements; note that the pparameter has no effect in the case of a serial run."," As the reference model we use a serial run with a domain grid of $\DomGrid = 128$ cells per dimension, a refinement criterion of $\DomRef = 1.0$ on the domain grid and a refinement criterion of $\RefRef = 5.0$ on the refinements; note that the parameter has no effect in the case of a serial run."685" We also change the number of processes involved in the analysis from 1 (the reference analysis for each box) in factors of 2 to 16, in which case the pparameter has a very significant meaning: Recall that the volume decomposition scheme not only assigns to each CPU the associated unique volume, but also a copy of the boundary layer with a thickness of 1 cell."," We also change the number of processes involved in the analysis from $1$ (the reference analysis for each box) in factors of $2$ to $16$, in which case the parameter has a very significant meaning: Recall that the volume decomposition scheme not only assigns to each CPU the associated unique volume, but also a copy of the boundary layer with a thickness of $1$ cell."686 We increase the size of the decomposition grid from a 2*—16 (LB— 4) cells per dimension grid by factors of two up, We increase the size of the decomposition grid from a $2^4=16$ $\LB = 4$ ) cells per dimension grid by factors of two up687Supernova 2002ic (Wood-Vaseyetal.2002) is a very interesting event that shows both silicon absorption (Hamuyetal.2002) and hydrogen emission (Hamuyetal.2003)..,Supernova 2002ic \citep{iauc8019b} is a very interesting event that shows both silicon absorption \citep{iauc8028} and hydrogen emission \citep{hamuy03b}.688" This SN is the first case for which there is unambiguous evidence of the existence of circumstellar matter around a SN Ia and is therefore of great importance to the understanding of the progenitor systems and explosion mechanisms of SNe Ia. By studying the spectral polarimetry and the light curve of the Ha line, Wangetal.(2004) found the spatial extent of the hydrogen-rich material to be as large as 1077 cm and distributed in a quite asymmetric configuration, most likely in the form of a flattened disk."," This SN is the first case for which there is unambiguous evidence of the existence of circumstellar matter around a SN Ia and is therefore of great importance to the understanding of the progenitor systems and explosion mechanisms of SNe Ia. By studying the spectral polarimetry and the light curve of the $\alpha$ line, \citet{wang04} found the spatial extent of the hydrogen-rich material to be as large as $^{17}$ cm and distributed in a quite asymmetric configuration, most likely in the form of a flattened disk."689 The implied total mass of the hydrogen-rich CSM is a few solar masses., The implied total mass of the hydrogen-rich CSM is a few solar masses.690 Similar conclusions were reached by Dengetal.(2004)., Similar conclusions were reached by \citet{deng04}.691". In this paper, we present new photometry of SN 2002ic and discuss the implications for the interaction of the ejecta and the CSM."," In this paper, we present new photometry of SN 2002ic and discuss the implications for the interaction of the ejecta and the CSM."692 Sec., Sec.693 2 presents our data processing procedure and calibration for our photometry of SN 2002ic., \ref{sec:processing} presents our data processing procedure and calibration for our photometry of SN 2002ic.694" In Sec. 3,,"," In Sec. \ref{sec:lightcurve},"695 we discuss the light curve of SN 2002ic and the immediate implications from our data., we discuss the light curve of SN 2002ic and the immediate implications from our data.696 A more in-depth investigation and qualitative modeling of the light curve of SN 2002ic as an interaction of a SN Ia with surrounding CSM is presented in Sec. 5.., A more in-depth investigation and qualitative modeling of the light curve of SN 2002ic as an interaction of a SN Ia with surrounding CSM is presented in Sec. \ref{sec:modeling}.697 Our discussion in Sec., Our discussion in Sec.698 6 presents our interpretations of the structure of the CSM surrounding SN 2002ic.," \ref{sec:discussion}699 presents our interpretations of the structure of the CSM surrounding SN 2002ic."700" Finally, in Sec."," Finally, in Sec."701 7 we present some intriguing possibilities for the progenitor system of SN 2002ic and speculate on other possible SN 2002ic-like events., \ref{sec:conclusions} we present some intriguing possibilities for the progenitor system of SN 2002ic and speculate on other possible SN 2002ic-like events.702" We discovered SN 2002ic on images from the NEAT team (Pravdoetal.1999) taken on the Samuel Oschin 1.2-m telescope on Mt. Palomar, California."," We discovered SN 2002ic on images from the NEAT team \citep{pravdo99}703 taken on the Samuel Oschin 1.2-m telescope on Mt. Palomar, California."704" In preparation for searching, the images were transmitted from the telescope to the High-Performance Storage System (HPSS) at the National Energy Research and Scientific Computer Center (NERSC) in Oakland, California via the HPWREN (Braun2003) and ESnet (U.S.DepartmentofEnergy2004) networks."," In preparation for searching, the images were transmitted from the telescope to the High-Performance Storage System (HPSS) at the National Energy Research and Scientific Computer Center (NERSC) in Oakland, California via the HPWREN \citep{hpwren} and ESnet \citep{esnet} networks."705 These data were then automatically processed and reduced on the NERSC Parallel Distributed System Facility (PDSF) using software written at Lawrence Berkeley National Laboratory by WMWV and the Supernova Cosmology Project., These data were then automatically processed and reduced on the NERSC Parallel Distributed System Facility (PDSF) using software written at Lawrence Berkeley National Laboratory by WMWV and the Supernova Cosmology Project.706" The first-level processing of the NEAT images involved decompression and conversion from the NEAT internal format used for transfer to the standard astronomical FITS format, subtraction of the dark current for these thermoelectrically cooled CCDs, and flat-fielding with sky flats constructed from a sample of the images from the same night."," The first-level processing of the NEAT images involved decompression and conversion from the NEAT internal format used for transfer to the standard astronomical FITS format, subtraction of the dark current for these thermoelectrically cooled CCDs, and flat-fielding with sky flats constructed from a sample of the images from the same night."707" These processed images were then loaded into an image database, and archival copies were stored on HPSS."," These processed images were then loaded into an image database, and archival copies were stored on HPSS."708 The images were further, The images were further709ΗΡΛΙ3 slope.,ISM2 slope.710 Thus the bolometer noise in the 210 HSM2 map could mask a larger gradient than the gradient seen in the low noise 3.5 jiuuap., Thus the bolometer noise in the 240 ISM2 map could mask a larger gradient than the gradient seen in the low noise 3.5 map.711 The slope in the 3.5) iumnap is of the CIRB. while the reporte 210 IISM2 slope is 26451% of the CIRB.," The slope in the 3.5 map is of the CIRB, while the reported 240 ISM2 slope is $26 \pm 51\;\%$ of the CIRB."712 Furthermore. the 2 point correlation fuuction of the 3.5 rresidual (Dwek&Arendt1909). as a fraction of the CIRB. is smaller than the uncertainty in the 2 point correlation function of the 210 LISM2 map.," Furthermore, the 2 point correlation function of the 3.5 residual \citep{DA99}, as a fraction of the CIRB, is smaller than the uncertainty in the 2 point correlation function of the 240 ISM2 map."713" While DA98 obtained a lower limit on J, using galaxy counts at 2.2fan... we have determiued the value of Z4 by carefully subtracting the galactic sigual in our dark spot."," While DA98 obtained a lower limit on $I_\circ$ using galaxy counts at 2.2, we have determined the value of $I_\circ$ by carefully subtracting the galactic signal in our dark spot."714 Thus the Hauserefal...(L998 determination of the far-infrared CIRB aud our determination of the CIRB are logically equivaleut., Thus the \citet{HAKDO98} determination of the far-infrared CIRB and our determination of the near-infrared CIRB are logically equivalent.715 But oue has more coufideuce tn the Hauserefal(LO9S) result because Areneοαἱ.(1998) were able to cetermine their Z; at 100 Hu 3 areas with consistent restlis. and. because the zocdiacal light. (aud its mocleling error) are a muuch smaller fractio iof the CIRB at 210 tthan at 3.54n.," But one has more confidence in the \citet{HAKDO98} result because \citet{AOWSH98} were able to determine their $I_\circ$ at 100 in 3 areas with consistent results, and because the zodiacal light (and its modeling error) are a much smaller fraction of the CIRB at 240 than at 3.5."716. Although the utcertainty for the 2MÁÀSS spo is large. we find that the value of the residual signal derived (roin tie “dark spot” agrees with tle 2ALASS spot.," Although the uncertainty for the 2MASS spot is large, we find that the value of the residual signal derived from the “dark spot” agrees with the 2MASS spot."717 Iu the future. we will be able to further verify the isotropic uature of this signal.," In the future, we will be able to further verify the isotropic nature of this signal."718 Sitce 2MÁSS saturates ou stars that are quite faint for DIRBE. 2MLASS «ata can ouly be used iu regions with no bright stars.," Since 2MASS saturates on stars that are quite faint for DIRBE, 2MASS data can only be used in regions with no bright stars."719 The current 2MÁÀSS data release does uot cove: auy of our DIRBE dark spos., The current 2MASS data release does not cover any of our DIRBE dark spots.720 However. future data releases will eventually cover the whole sky. allowing a good isotropy cliec son the CIRB at 2.2 jun. Our accepted proposal to survey the darkes spot in the Southern sky at the South Pole SPIRES/ABL facility in the 3.5 bbaud curing the 19909 austral winter was not executed «ue to equipinent. problems.," However, future data releases will eventually cover the whole sky, allowing a good isotropy check on the CIRB at 2.2 $\mu$ m. Our accepted proposal to survey the darkest spot in the Southern sky at the South Pole SPIREX/ABU facility in the 3.5 band during the 1999 austral winter was not executed due to equipment problems."721 Surveying other dark spots at 3.5 wwould be very valuable but also very dilficult with erounn-based telescopes., Surveying other dark spots at 3.5 would be very valuable but also very difficult with ground-based telescopes.722 Even though our evidence for the isotropy of the near iulrared backgrouud is not stroug. the uncertainty in our final result is still dominated by the unceLainties in modeliug the zodiacal light.," Even though our evidence for the isotropy of the near infrared background is not strong, the uncertainty in our final result is still dominated by the uncertainties in modeling the zodiacal light."723 Our CIRB values a both 2.2 and 3.5 aare of the zodiacal light at the ecliptic poles. while t1e 210 bbackground fouud by Hauserefαἱ.(1998). is 3.6 times larger than the zocdiacal light at the ecliptic poles.," Our CIRB values at both 2.2 and 3.5 are of the zodiacal light at the ecliptic poles, while the 240 background found by \citet{HAKDO98} is 3.6 times larger than the zodiacal light at the ecliptic poles."724 Thus the near IR background is much more seusitive to zodiacal light errors thau the far IR background., Thus the near IR background is much more sensitive to zodiacal light errors than the far IR background.725 We compare our values to the values obtained by Hauserefaf(1998).. and DAYS in Figure 7..," We compare our values to the values obtained by \citet{HAKDO98}, and DA98 in Figure \ref{fig:DA98GWC}."726 Hauserefal.(1998) made no Claim for the CIRB since they did not get isotropy over a, \citet{HAKDO98} made no claim for the CIRB since they did not get isotropy over a727methods for distance determination (22) can make a significant contribution to the problem.,"methods for distance determination \citep{sale09,frew06} can make a significant contribution to the problem."728 The location. of the newly discovered PN. IPHASX J052531.194281945.1. at only four degrees from the direction of the Galactic Anticentre. motivated us to study this object further.," The location of the newly discovered PN IPHASX J052531.19+281945.1, at only four degrees from the direction of the Galactic Anticentre, motivated us to study this object further."729 In. Sect., In Sect.730 ?? the photometric and spectroscopic observations are presented: in Sect., \ref{obs} the photometric and spectroscopic observations are presented; in Sect.731 ?? a physical and chemical analysis is carried out: in Sect., \ref{analysis} a physical and chemical analysis is carried out; in Sect.732 ?? its distance Is studied: in Sect., \ref{dist} its distance is studied; in Sect.733 2? a discussion is provided. and in Sect.," \ref{disc} a discussion is provided, and in Sect."734 ?? the main conclusions are presented., \ref{conc} the main conclusions are presented.735 The PN was discovered by visually inspecting the IPHAS Πα - r' mosaics of the Anticentre region., The PN was discovered by visually inspecting the IPHAS $\alpha$ $-$ $r^{\prime}$ mosaics of the Anticentre region.736 The semi-automated searching method described in? missed the object due to its relatively large size (~ 10)., The semi-automated searching method described in \citet{viironen09b} missed the object due to its relatively large size $\sim$ ).737 The IAU approved name for this IPHAS object is. after its coordinates. IPHASX JOS2531.19+281945.1 (X for extended) whereas the LAU common PN name would be PNG 178.1-04.0.," The IAU approved name for this IPHAS object is, after its coordinates, IPHASX J052531.19+281945.1 (X for extended) whereas the IAU common PN name would be PNG 178.1-04.0."738 To abbreviate. in the following we will use the acronym IACPN (IPHAS Anti-Centre Planetary Nebula).," To abbreviate, in the following we will use the acronym IACPN (IPHAS Anti-Centre Planetary Nebula)."739 The IPHAS observations of [ACPN were carried out on November 2003 using the 2.5m Isaac NewtonTelescope and its Wide Field Camera under seeing condition of 1.3’ FWHM in the Ha images., The IPHAS observations of IACPN were carried out on November 2003 using the 2.5m Isaac NewtonTelescope and its Wide Field Camera under seeing condition of $\arcsec$ FWHM in the $\alpha$ images.740 Fig., Fig.741 | presents the Ha. +’ and 7 images of the object.," \ref{fig:1} presents the $\alpha$ , $r^{\prime}$ and $i^{\prime}$ images of the object."742 The exposure times are 120 s for Ha and 10 s for +’ and / images., The exposure times are 120 s for $\alpha$ and 10 s for $r^{\prime}$ and $i^{\prime}$ images.743" More details about IPHAS observations and the ""Sata reduction are given in ?. and ?..", More details about IPHAS observations and the data reduction are given in \cite{drew05} and \cite{gonzalez-solares08}.744 IACPN shows a roughly spherical morphology., IACPN shows a roughly spherical morphology.745 It 1s hardly “sible in the IPHAS / filter (see Fig. 1)., It is hardly visible in the IPHAS $i^{\prime}$ filter (see Fig. \ref{fig:1}) ).746 No objects are listed 1 SIMBAD within almost from the position of IACPN., No objects are listed in SIMBAD within almost from the position of IACPN.747 The first spectroscopic observations of LACPN were carried out at the Observatorio de San Pedro Márrtir (Mexico). and were presented by ? in a conference paper.," The first spectroscopic observations of IACPN were carried out at the Observatorio de San Pedro Márrtir (Mexico), and were presented by \cite{mampaso05} in a conference paper."748 Four 20 min exposures in the red and five 20 min exposures in the blue were obtained through a narrow (1) slit using the 2.1-m telescope and the B&CCh spectrograph (2 pix”! dispersion. 3 resolution. from 3720 to 7470 A)).," Four 20 min exposures in the red and five 20 min exposures in the blue were obtained through a narrow $\arcsec$ ) slit using the 2.1-m telescope and the Ch spectrograph (2 $^{-1}$ dispersion, 3 resolution, from 3720 to 7470 )."749 In addition. two 10 min exposures in the blue were obtained with a very wide slit in order to include the whole nebula and measure its total Hf flux.," In addition, two 10 min exposures in the blue were obtained with a very wide slit in order to include the whole nebula and measure its total $\beta$ flux."750 Furthermore. the MEZCAL echelle spectrograph was used with the same telescope to obtain a high dispersion spectrum (0.1 pix” !) around the He line.," Furthermore, the MEZCAL echelle spectrograph was used with the same telescope to obtain a high dispersion spectrum (0.1 $^{-1}$ ) around the $\alpha$ line."751 The MEZCAL spectrum allowed to measure the expansion and radial velocities of the nebula: the - diameter shell has a radial velocity of vise=13.5 km s! and expands at 17 km s! in the i1]] 6583 line (?).., The MEZCAL spectrum allowed to measure the expansion and radial velocities of the nebula: the $\sim$ diameter shell has a radial velocity of $v_{LSR} = 13.5$ km $^{-1}$ and expands at 17 km $^{-1}$ in the ] 6583 line \citep{mampaso05}.752 From the B&CCh spectra the PN nature of the nebula was confirmed and its absolute Hf flux was measured. giving Ε(Ηβ)=3.34x107 ere em? s.," From the Ch spectra the PN nature of the nebula was confirmed and its absolute $\beta$ flux was measured, giving $\beta)= 3.34 \times75310^{-14}$ erg $^{-2}$ $^{-1}$."754 Preliminary chemical abundances were presented by ?.., Preliminary chemical abundances were presented by \cite{mampaso05}.755 The William Herschel Telescope (WHT) -- ISIS spectrograph observations of LACPN were carried out in service mode on April 6. 2007.," The William Herschel Telescope (WHT) + ISIS spectrograph observations of IACPN were carried out in service mode on April 6, 2007."756 The seeing was ~0.9” and the weather conditions were good. except for the presence of light cirrus during the second half of the night.," The seeing was $\sim 0.9\arcsec$ and the weather conditions were good, except for the presence of light cirrus during the second half of the night."757 Three exposures of 20 min of the target were obtained in both the blue (3570-5115EVE dispersion. 0.8 pix!. resolution 3.2 A)) and the red (5540-10500Α.. 1.8 pix! dispersion. 6.5 resolution) arms with the slit located at PA. = 79°. Le. at the parallactic angle corresponding to the moment of observation.," Three exposures of 20 min of the target were obtained in both the blue (3570-5115; dispersion 0.8 $^{-1}$, resolution 3.2 ) and the red (5540-10500, 1.8 $^{-1}$ dispersion, 6.5 resolution) arms with the slit located at P.A. = $^o$, i.e. at the parallactic angle corresponding to the moment of observation."758 The slit width was 1., The slit width was $\arcsec$ .759 In addition. bias. lamp flats. and are exposures were obtained.," In addition, bias, lamp flats, and arc exposures were obtained."760 Unfortunately. no suitable observations of spectrophotometric standards are available for that night. as all standard stars were observed with a different instrumental configuration than our target.," Unfortunately, no suitable observations of spectrophotometric standards are available for that night, as all standard stars were observed with a different instrumental configuration than our target."761 For this reason. a spectrum of the standard star BD+332642 (?).. obtained on April 2. 2007 with the same setup as for the nebula. was used to fluxcalibrate its spectrum.," For this reason, a spectrum of the standard star BD+332642 \citep{oke90}, obtained on April 2, 2007 with the same setup as for the nebula, was used to fluxcalibrate its spectrum."762 Nevertheless. the blue and red observations of this standard star were obtained at different times of the night. and therefore under different weather conditions.," Nevertheless, the blue and red observations of this standard star were obtained at different times of the night, and therefore under different weather conditions."763 This prevents a precise matching of the blue anc red sides of the WHT spectrum. and therefore. an accurate determination of Ay using the Ha/Hf flux ratio.," This prevents a precise matching of the blue and red sides of the WHT spectrum, and therefore, an accurate determination of $A_V$ using the $\alpha$ $\beta$ flux ratio."764 For this reason. additional spectra of the nebula and standard star were acquired as deseribed below.," For this reason, additional spectra of the nebula and standard star were acquired as described below."765 Finally. and given that there is calibration data available for BD+33 2642 only up to 9200 (9). the fluxes for lines at longer wavelengths will not be considered.," Finally, and given that there is calibration data available for BD+33 2642 only up to 9200 \citep{oke90}, the fluxes for lines at longer wavelengths will not be considered."766 The data reduetion and calibration were carried out using the standard IRAF routines for longslit spectroscopy., The data reduction and calibration were carried out using the standard IRAF routines for longslit spectroscopy.767 A good measurement of the reddening of the nebula. Ay. is important for its distance determination (see Sec. ??))," A good measurement of the reddening of the nebula, $A_V$, is important for its distance determination (see Sec. \ref{dist}) )"768 and additional spectra of LACPN were secured in service mode on September 6. 2010 using the ALFOSC instrument at the Nordic Optical Telescope.," and additional spectra of IACPN were secured in service mode on September 6, 2010 using the ALFOSC instrument at the Nordic Optical Telescope."769 These spectra were obtained so as to cover the wavelength range from ~3800 tto 6800À.. e. to include simultaneously the main. Balmer lines (Ho. Hy. Hp. and He).," These spectra were obtained so as to cover the wavelength range from $\sim$ 3800 to 6800, i.e. to include simultaneously the main Balmer lines $\delta$, $\gamma$, $\beta$, and $\alpha$ )."770" The night was photometric and the seeing was 0.7"".", The night was photometric and the seeing was $0.7\arcsec$.771 Two 20 min exposures were obtained., Two 20 min exposures were obtained.772 The spectral dispersion was 1.5 pix”! and resolution 6 A., The spectral dispersion was 1.5 $^{-1}$ and resolution 6 .773. The slit was positioned accordingto the parallactic angle at the moment of observation (P.A. = 102°) and the slit width used was 1., The slit was positioned accordingto the parallactic angle at the moment of observation (P.A. = $^o$ ) and the slit width used was $\arcsec$ .774 Bias. lamp flats. and are exposures were obtained. and the standard star GI91-B2B was observed.," Bias, lamp flats, and arc exposures were obtained, and the standard star G191-B2B was observed."775 The data reduction and calibration were carried out using the standard IRAF routinesfor longslit spectroscopy., The data reduction and calibration were carried out using the standard IRAF routinesfor longslit spectroscopy.776introducing a double ring of flux at the surface where the eruption takes place.,introducing a double ring of flux at the surface where the eruption takes place.777 Introducing an a-coellicient concentrated near the surface is certainly a very approximate wav of incorporating the main idea of the BL approach into the mathematical theory of the PSIXR approach., Introducing an $\alpha$ -coefficient concentrated near the surface is certainly a very approximate way of incorporating the main idea of the BL approach into the mathematical theory of the PSKR approach.778 Justifving this procedure rigorously is even more difficult than justifvine the a-coelficient in the PSNR approach., Justifying this procedure rigorously is even more difficult than justifying the $\alpha$ -coefficient in the PSKR approach.779 However. this procedure produces the desired. effect of generating the poloidal field where we want (o generate it.," However, this procedure produces the desired effect of generating the poloidal field where we want to generate it."780 If magnetic buovancy is included in some wav to bring the strong toroidal field from the bottom to the top and then the concentrated o-effect acts on it. the net result is similar to what happens in Durnev5 double ring method.," If magnetic buoyancy is included in some way to bring the strong toroidal field from the bottom to the top and then the concentrated $\alpha$ -effect acts on it, the net result is similar to what happens in Durney's double ring method."781 Since (his procedure is easier to implement than Durnevs double ring method. one important question is whether this procedure is al least as good as Durnev5 double ring method.," Since this procedure is easier to implement than Durney's double ring method, one important question is whether this procedure is at least as good as Durney's double ring method."782 In this paper. we take a simple dvnamo model ancl present ealeulations done with both the methods.," In this paper, we take a simple dynamo model and present calculations done with both the methods."783 We show (hat the results are qualitatively similar., We show that the results are qualitatively similar.784 It may be noted that it is not our aim to build realistic models of the solar cvele in this paper., It may be noted that it is not our aim to build realistic models of the solar cycle in this paper.785 For exaniple. we have presented a contrasting study of these methods by assuming a differential rotation which does not vary. with latitude as in Choudhuri. Sehüsssler. Dikpati (1995).," For example, we have presented a contrasting study of these methods by assuming a differential rotation which does not vary with latitude as in Choudhuri, Schüsssler, Dikpati (1995)."786 This simplification allows the specific features of the two methods to be seen clearly., This simplification allows the specific features of the two methods to be seen clearly.787 A realistic differential rotation makes (he results immensely more complicated. which we shall discuss in our next paper in which an attempt. will be made to model the solar evcle properly.," A realistic differential rotation makes the results immensely more complicated, which we shall discuss in our next paper in which an attempt will be made to model the solar cycle properly."788 Durnev (1995. 1995. 1997) allowed flux eruption to take place only at one latitude ab a lime.," Durney (1995, 1995, 1997) allowed flux eruption to take place only at one latitude at a time."789 In Durnev's model. it is difficult to allow simultaneous eruptions in a band of latitudes. which happens in (he real Sun.," In Durney's model, it is difficult to allow simultaneous eruptions in a band of latitudes, which happens in the real Sun."790 The model of Choudhuri. Schüsssler. Dikpati (1995) did not incorporate magnete buovancy auc allowed the toroidal field to be brought to the surface from the bottom by meridional circulation.," The model of Choudhuri, Schüsssler, Dikpati (1995) did not incorporate magnetic buoyancy and allowed the toroidal field to be brought to the surface from the bottom by meridional circulation."791 To make comparisons will Durnev's double ring method. we now include magnetic buovancy in that model by allowing the magnetic field to erupt whenever il has a value larger than a critical value.," To make comparisons with Durney's double ring method, we now include magnetic buoyancy in that model by allowing the magnetic field to erupt whenever it has a value larger than a critical value."792 It may be, It may be793" E~ ιν 10°? &>erate)10 οταν 5-ravs ""Co >-rav ", $E \sim$ $\times$ $^{52}$ $E \gsim 10^{52}$ $\gamma$ $\gamma$ $^{56}$ $\gamma$ 794"Iu the traditional flare model particles are accelerated in the corona then precipitate along the field lines of a imaenetic loop to the chromosphere where thev are stopped producing brenisstrahlung enmuüssion iu the xocess,",In the traditional flare model particles are accelerated in the corona then precipitate along the field lines of a magnetic loop to the chromosphere where they are stopped producing bremsstrahlung emission in the process.795 In the classical thick-target model (?7).. it is asstuned that collisional iteraction of fast clectrous with he ambicut plasma leads to euergev-loss. while other uechanisius such as pitch angle scattering or mirroring of the electrons in a convereiug magnetic field are welected.," In the classical thick-target model \citep{Br71}, it is assumed that collisional interaction of fast electrons with the ambient plasma leads to energy-loss, while other mechanisms such as pitch angle scattering or mirroring of the electrons in a converging magnetic field are neglected."796 It is therefore expected that electrons with uegher enereijes penetrate deeper into the chromosphere fore they are fully stopped., It is therefore expected that electrons with higher energies penetrate deeper into the chromosphere before they are fully stopped.797 The stopping depth depends on the initial electron cuerey aud the aimbieut density., The stopping depth depends on the initial electron energy and the ambient density.798" Expressed in terms of the columu depth V(s)= δα». where nts) is the ambicut density aloug the electron path. the stopping depth is given as JN, 2N.where Ey is the initial energy of the accelerated Ielectron aud K=2aetA (223."," Expressed in terms of the column depth $N(s)=\int n(s)\mathrm{d}s$ , where $n(s)$ is the ambient density along the electron path, the stopping depth is given as $N_{stop}= E_0^2/2K$ , where $E_0$ is the initial energy of the accelerated electron and $K=2\pi e^4 \Lambda$ \citep{Br72, Br02}."799 The Coulomb logaritlin A has typical values of ~20 in the Gonized) corona aud ~7 in the (neutral) chromosphere (??)..," The Coulomb logarithm $\Lambda$ has typical values of $\sim 20$ in the (ionized) corona and $\sim 7$ in the (neutral) chromosphere \citep{Br73,Em78}."800 For an electron flux distribution F(E.s5) with cucrey £ at distance s from the poiut. of injection. the observed N-rav. flux at Earth is: where n(s) is the density. ACs) the width of the maguetic flux tube at distance s. AR the Sun-Earth distance and σε.E) the augle-averaged. bremisstralluung cross- (7).," For an electron flux distribution $F(E,s)$ with energy $E$ at distance $s$ from the point of injection, the observed X-ray flux at Earth is: where $n(s)$ is the density, $A(s)$ the width of the magnetic flux tube at distance $s$ , $R$ the Sun-Earth distance and $\sigma(\epsilon,E)$ the angle-averaged bremsstrahlung cross-section \citep{Ha97}."801. The isotropic approxiuation of emission is supported by statistical observatious (777) aud more recent IIEXR. observations using albedo iu imagine (7?) and spectroscopy (7)..," The isotropic approximation of emission is supported by statistical observations \citep{Ka88,Ves87, Ka07} and more recent HXR observations using albedo in imaging \citep{Ba11} and spectroscopy \citep{Ko06a}."802 For increasing density aloug 5. Eq.," For increasing density along $s$, Eq."803" 1 has a iiaxinuia for a given photon euergv €. νο, the observed INR cmission will have a απκτα at a certain chromospheric depth. depending ou encre."," \ref{beq}804 has a maximum for a given photon energy $\epsilon$, i.e. the observed HXR emission will have a maximum at a certain chromospheric depth, depending on energy."805 Observational evidence for heieht dependent IINR sources was found early ou iu stereoscopic observations (2) and in a statistical wav using Yohkoh (?).., Observational evidence for height dependent HXR sources was found early on in stereoscopic observations \citep{Ka83} and in a statistical way using Yohkoh \citep{Mat92}.806 ? derived that ΗΝ sources for energies 2150 keV should be at heights less than 2500 kii above the photosphere., \citet{Ka83} derived that HXR sources for energies $>150$ keV should be at heights less than $2500$ km above the photosphere.807 ? used test particle sinulatious to find the expected position as a function of energy incliding collisional pitch anele scattering aud magnetic mirroring and compared the results with observations from Yolikol., \citet{Fl96} used test particle simulations to find the expected position as a function of energy including collisional pitch angle scattering and magnetic mirroring and compared the results with observations from Yohkoh.808 This study demonstrated the iuflucuce of a converging magnetic field ou the height of the X-rav source. showiug that the Yohkol observations of 53.93 keV sources at average heights ~6000 kn presented bv 2 are consistent with partial trapping of electrons in a 1iiagnetic loop.," This study demonstrated the influence of a converging magnetic field on the height of the X-ray source, showing that the Yohkoh observations of $53-93$ keV sources at average heights $\sim 6000$ km presented by \citet{Mat92} are consistent with partial trapping of electrons in a magnetic loop."809 However. the use of Πα flare locations as the refereuce for height estimates could be the reason for the large heights found bv ?.," However, the use of $\alpha$ flare locations as the reference for height estimates could be the reason for the large heights found by \citet{Mat92}."810 The high spatial resolution of RIIESSI (7? now mikes it possible to study individual events with higher accuracy (272?) ," The high spatial resolution of RHESSI \citep{Li02,Hur02} now makes it possible to study individual events with higher accuracy \citep{As02, Mr06, Liu06}."811More receutlv ?. ane’? analyzed a lial event using the newly developed visibility techiuique (?, More recently \citet{Ko08} and \citet{Koet10} analyzed a limb event using the newly developed visibility technique \citep{Sc07}.812 This allows for measurements of IIXR. source positions width sub-aresecond resolution., This allows for measurements of HXR source positions with sub-arcsecond resolution.813 ? and ? went oue step further and computed the electron distributions fouud from iuverson of the N-ray visibilities.," \citet{Pr09} and \citet{Pe10}814 went one step further and computed the electron distributions found from inversion of the X-ray visibilities."815" Iu all those studies"" a decrease of the radial position of the sources wit1 Increasing energv is found.", In all those studies a decrease of the radial position of the sources with increasing energy is found.816 ? showed how this cau be used to determine the chromospheric density structure., \citet{Br02} showed how this can be used to determine the chromospheric density structure.817 This was applied by ? to an eveut ou 2002 February 20x and to a limb event on 2001 January 6 by? who found their observationsto be consistent with iu exponcutial chromospheric density profile with scale height 2: 150 Ian.," This was applied by \citet{As02}818 to an event on 2002 February 20 and to a limb event on 2004 January 6 by \citet{Koet10}819 who found their observationsto be consistent with an exponential chromospheric density profile with scale height $\approx$ 150 km."820 The TEXR source heights have been found to decrease, The HXR source heights have been found to decrease821The currently accepted. paradigm of large-scale structure lormation in ihe Universe is the gravitational instabilitv.,The currently accepted paradigm of large-scale structure formation in the Universe is the gravitational instability.822 Within this framework. inhomogeneities in matter distribution induce gravitational accelerations. which result in galaxies having (hal add to the IIubble flow.," Within this framework, inhomogeneities in matter distribution induce gravitational accelerations, which result in galaxies having that add to the Hubble flow."823 These velocities in turn enhance the growth of the inhomogeneities. causing strong coupling between cosmic velocity [ield and large-scale matter distribution.," These velocities in turn enhance the growth of the inhomogeneities, causing strong coupling between cosmic velocity field and large-scale matter distribution."824 In perturbation theory of Friediman-Lemaittre models. in (he linear regime. peculiar velocities ancl accelerations are ligned and proportional to each other at every point jitealtPes0)).," In perturbation theory of tre models, in the linear regime, peculiar velocities and accelerations are aligned and proportional to each other at every point \\citealt{Pe80}) )."825 More importantly. the proportionality coefficient of this relation is a simple function of 1e cosmological parameter of non-relativistic matter density. μι. and practically does not depend on je cosmologieal constant. (nor other forms of dark energy).," More importantly, the proportionality coefficient of this relation is a simple function of the cosmological parameter of non-relativistic matter density, $\Omm$, and practically does not depend on the cosmological constant (nor other forms of dark energy)."826" Additionally. as the relation holds also for the motion of the whole (LG) through the Universe. measurements of its peculiar velocity. anc acceleration may be used as a tool to dynamically constrain (he €, parameter."," Additionally, as the relation holds also for the motion of the whole (LG) through the Universe, measurements of its peculiar velocity and acceleration may be used as a tool to dynamically constrain the $\Omm$ parameter."827 The peculiar velocity of the LG is known trom the observed dipole anisotropy of the cosmic microwave background (CMD. ?)). interpreted as a kinematic effect. ancl reduced to the barycenter of the LG (?)..," The peculiar velocity of the LG is known from the observed dipole anisotropy of the cosmic microwave background (CMB, \citealt{Hinsh}) ), interpreted as a kinematic effect, and reduced to the barycenter of the LG \citep{CvdB}."828" It equals to eei=622435km/s and points in the direction (/.b)=(272°£3""28c) in Galactic coordinates."," It equals to $v_\mathrm{CMB}=622\pm35\kms$ and points in the direction $(l,b)=(272\dgr\pm3\dgr\!,\,28\dgr\pm5\dgr)$ in Galactic coordinates."829 This kinematic interpretation is strongly supported by the observed alienment of the CMD dipole with the direction of the peculiar acceleration of the LG. although the latter is much more difficult to estimate.," This kinematic interpretation is strongly supported by the observed alignment of the CMB dipole with the direction of the peculiar acceleration of the LG, although the latter is much more difficult to estimate."830 It requires knowledge of mass distribution in our cosnic neighborhood. ancl its determination had not been possible until deep all-skv galaxy. catalogs became available.," It requires knowledge of mass distribution in our cosmic neighborhood, and its determination had not been possible until deep all-sky galaxy catalogs became available."831 For that reason. the first attempts to measure the acceleration of the LG were made not earlier than 30 vears ago (??)..," For that reason, the first attempts to measure the acceleration of the LG were made not earlier than 30 years ago \citep{YST, DH82}."832 Using an all-sky catalog. such measurement can be made under (he assumption that visible (luminous) matter is a good tracer of the underlving clensity [ield.," Using an all-sky catalog, such measurement can be made under the assumption that visible (luminous) matter is a good tracer of the underlying density field."833 The general procedure is to estimate the so-called of à galaxy survey and infer the acceleration of the LG., The general procedure is to estimate the so-called of a galaxy survey and infer the acceleration of the LG.834 llowever. such inference requires several conditions to be met.," However, such inference requires several conditions to be met."835 First. the survey should cover the whole skv: second. (he observational proxy of (he gravitational force (most often the flux of the galaxy in (he photometric band of the survey) should have known properties: and last but not least. the," First, the survey should cover the whole sky; second, the observational proxy of the gravitational force (most often the flux of the galaxy in the photometric band of the survey) should have known properties; and last but not least, the"836"that Then we can relate (5) to p,(s) where C is a normalization constant.",that Then we can relate $p_m(s)$ to $p_v(s)$ where C is a normalization constant.837" If p.(s) follows a normal distribution. where s, is (he average (in volume) value of s. ancl σ is the clispersion. then Since |s)ds=1. the normalization Equation 13. can thus be rewritten as: where s4,=s.7+07."," If $p_v(s)$ follows a normal distribution, where $s_v$ is the average (in volume) value of $s$, and $\sigma$ is the dispersion, then Since $\int_{-\infty}^{\infty} p_m(s)ds =1$, the normalization Equation \ref{eq_pm_0} can thus be rewritten as: where $s_m = s_v + \sigma^2$."838" LThisB isB also a normal distribution.. with. the same dispersion. σ as (hat of p, but shifted average value s,,."," This is also a normal distribution, with the same dispersion $\sigma$ as that of $p_v$ but shifted average value $s_m$."839 Using the volume PDF normalization fevp-(sjds= Lit can be seen as noted. for example. by Ostriker.Stone.&Gamunie (2001)..," Using the volume PDF normalization $\int \rho \cdot p_v(s)ds = \int e^s p_v(s)ds = 1$ , it can be seen as noted, for example, by \citet{osg01}. ."840 This holds only if the density PDF is log-normal. (, This holds only if the density PDF is log-normal. (841Note that in this case C= 1.),Note that in this case $C= 1$ .)842" This derivation gives several properties of the density PDFs p,, and p,.", This derivation gives several properties of the density PDFs $p_m$ and $p_v$ .843 If one of them is log-normal. so is the other: and if thev are log-normal. the width & of both profiles should be equal (Eqs. [12]]," If one of them is log-normal, so is the other; and if they are log-normal, the width $\sigma$ of both profiles should be equal (Eqs. \ref{eq_pv}] ]"844" and |15]]). and the peaks of thePDFs p,,(s) andp.(s) should lie svmnetrically around zero (Eq. |16]])."," and \ref{eq_pm}] ]), and the peaks of thePDFs $p_m(s)$ and$p_v(s)$ should lie symmetrically around zero (Eq. \ref{eq_sm_sv}] ])."845 The Circinus galaxy (A1409-65) Is a nearby (—4 Mpe) gas rich spiral lying close to the galactic plane in a region of relatively low 271.5 mag) interstellar extinction (Freeman et al. 1977))., The Circinus galaxy (A1409-65) is a nearby $\simeq$ 4 Mpc) gas rich spiral lying close to the galactic plane in a region of relatively low $\simeq$ 1.5 mag) interstellar extinction (Freeman et al. \cite{freeman}) ).846 Several observed characteristics indicate that this galaxy hosts the nearest Seyfert 2 nucleus known., Several observed characteristics indicate that this galaxy hosts the nearest Seyfert 2 nucleus known.847 These include optical images showing a spectacular [OIL] cone (Marconi et al., These include optical images showing a spectacular [OIII] cone (Marconi et al.848 1994 hereafter M94)): optical/IR spectra rich in prominent and narrow coronal lines (Oliva et al., 1994 hereafter \cite{M94}) ); optical/IR spectra rich in prominent and narrow coronal lines (Oliva et al.849 1994. hereafter O94.. Moorwood et al.," 1994, hereafter \cite{O94}, Moorwood et al."850 1996. hereafter M96)): X-ray spectra displaying a very prominent Fe-K fluorescent line (Matt et al. 1996))," 1996, hereafter \cite{M96}) ); X-ray spectra displaying a very prominent Fe-K fluorescent line (Matt et al. \cite{matt96}) )"851 and optical spectropolarimetric data which reveal relatively broad Ha emission in polarized light (Oliva et al. 1998))., and optical spectropolarimetric data which reveal relatively broad $\alpha$ emission in polarized light (Oliva et al. \cite{oliva98}) ).852 Complementary to these is observational evidence that this galaxy has recently experienced a powerful nuclear starburst which is now traced by the near IR emission of red supergiants (Oliva et al. 1995..," Complementary to these is observational evidence that this galaxy has recently experienced a powerful nuclear starburst which is now traced by the near IR emission of red supergiants (Oliva et al. \cite{oliva95},"853 Maiolino et al. 1998)), Maiolino et al. \cite{maiolino}) )854 and which may have propagated outwards igniting the bright ring of O stars and HII regions visible in the image (M94))., and which may have propagated outwards igniting the bright ring of O stars and HII regions visible in the image \cite{M94}) ).855 Such a starburst could have been triggered by gas moving toward the nuclear region and eventually falling onto the aceretion disk around the black hole powering the AGN., Such a starburst could have been triggered by gas moving toward the nuclear region and eventually falling onto the accretion disk around the black hole powering the AGN.856 A debated issue is whether nuclear starbursts are common features of AGNs and if they are more common in type 2 than in type | Seyferts. as suggested by e.g. IOjy/m observations (Maiolino et al. 1995))," A debated issue is whether nuclear starbursts are common features of AGNs and if they are more common in type 2 than in type 1 Seyferts, as suggested by e.g. $\mu$ m observations (Maiolino et al. \cite{maiolino95}) )"857 and studies of the stellar mass to light ratios (O94))., and studies of the stellar mass to light ratios \cite{O94}) ).858 Since starbursts are predicted and observed to deeply modify the chemical abundances of the host galaxy (e.g. Matteucci Padovani 1993)). such an effect should also be evident in this and other Seyferts.," Since starbursts are predicted and observed to deeply modify the chemical abundances of the host galaxy (e.g. Matteucci Padovani \cite{matteucci93}) ), such an effect should also be evident in this and other Seyferts."859 However. to the best of our knowledge. no reliable measurement of metallicity for the narrow line region clouds of Seyfert 2s exists in the literature.," However, to the best of our knowledge, no reliable measurement of metallicity for the narrow line region clouds of Seyfert 2's exists in the literature."860 In particular. although has been since long known that the large [NII|/Ha ratio typical of Seyferts cannot be easily explained using simple models with normal nitrogen abundances (e.g. Osterbrock 1989.. Komossa Schulz 1997)). the question of whether its absolute (N/H) or relative (e.g. N/O) abundance is truly different than solar is still open.," In particular, although has been since long known that the large $\alpha$ ratio typical of Seyferts cannot be easily explained using simple models with normal nitrogen abundances (e.g. Osterbrock \cite{osterbrock89}, Komossa Schulz \cite{komossa97}) ), the question of whether its absolute (N/H) or relative (e.g. N/O) abundance is truly different than solar is still open."861 Finding a reliable method to derive metallicities and. therefore. to trace and put constraints on past starburst activity 1s the main aim of this paper.," Finding a reliable method to derive metallicities and, therefore, to trace and put constraints on past starburst activity is the main aim of this paper."862 We chose the Circinus galaxy as a benchmark because its emission line spectrum is characterized by remarkably narrow (S150 km/s. O94)) emission lines which are. particularly easy to measure and which indicate relatively low dynamical activity.," We chose the Circinus galaxy as a benchmark because its emission line spectrum is characterized by remarkably narrow $\la$ 150 km/s, \cite{O94}) ) emission lines which are particularly easy to measure and which indicate relatively low dynamical activity."863 This last aspect may be used to put tight constrains on the possible contribution of shock excitation which may complicate the modelling of the observed spectrum and the determination of metallicities., This last aspect may be used to put tight constrains on the possible contribution of shock excitation which may complicate the modelling of the observed spectrum and the determination of metallicities.864The AMIRI growth in our model generates (he locally confined super-INeplerian region aud (his flow is quasi-stable due to the support of gas pressure eradient which is also formed bv the MRI.,The MRI growth in our model generates the locally confined super-Keplerian region and this flow is quasi-stable due to the support of gas pressure gradient which is also formed by the MRI.865 Because unperturbed gas flow is sub-IxXeplerian due to global pressure gradient. the particles sullering gas crag are concentrated in the Ixeplerian domain al the outer-edge of (he super-Ixeplerian area.," Because unperturbed gas flow is sub-Keplerian due to global pressure gradient, the particles suffering gas drag are concentrated in the Keplerian domain at the outer-edge of the super-Keplerian area."866 Since the flow is in a quasi-steady state. particles are supplied from outer regions bv eas drag migration aud the particle density increases significantly.," Since the flow is in a quasi-steady state, particles are supplied from outer regions by gas drag migration and the particle density increases significantly."867 The process of particle concentration and the increasing rate of dust density. depend on the particle size. the initial racial widths of uustable/stable regions. aud (he initial setting as follows:," The process of particle concentration and the increasing rate of dust density depend on the particle size, the initial radial widths of unstable/stable regions, and the initial non-uniformity setting as follows:"868The VLA D array observations of the CO(2-1) emission from 12020725 are shown in Figure 1. with a spatial resolution of about 2”.,"The VLA D array observations of the CO(2-1) emission from 1202–0725 are shown in Figure 1, with a spatial resolution of about $''$."869 Figure la shows the summed emission in IF’s | and 2 for the 40 GlIz observations., Figure 1a shows the summed emission in IF's 1 and 2 for the 40 GHz observations.870 Shown in grevscale on Figure la is the Ly a image ol 12020725 [rom Ln οἱ al. (, Shown in greyscale on Figure 1a is the Ly $\alpha$ image of 1202–0725 from Hu et al. (8711996).,1996).872 Again. we have aligned the position of the optical QSO with the peak in the radio continuum. CO. and thermal dust. emission for the southern source.," Again, we have aligned the position of the optical QSO with the peak in the radio continuum, CO, and thermal dust emission for the southern source."873 Figures Ib and le show IEs 1 and 2. respectively. for the 40 GlIz observations.," Figures 1b and 1c show IFs 1 and 2, respectively, for the 40 GHz observations."874 Figure 1d shows the continuum image at 43 (αν., Figure 1d shows the continuum image at 43 GHz.875 Table 2 lists the results for the (wo components in 12020725., Table 2 lists the results for the two components in 1202–0725.876 Column 3 lists the position of the measured CO components., Column 3 lists the position of the measured CO components.877 Column 4 lists the Timm continuum flux densities al these positions. column 5 lists the observed CO παν densities. and column 6 lists the velocitv integrated CO emission.," Column 4 lists the 7mm continuum flux densities at these positions, column 5 lists the observed CO flux densities, and column 6 lists the velocity integrated CO emission."878 Column 7 lists (he 1.4 GlIz continuum flux densities. while column 8 lists the CO luminosities (in IX km ! pc).," Column 7 lists the 1.4 GHz continuum flux densities, while column 8 lists the CO luminosities (in K km $^{-1}$ $^{2}$ )."879 The southern. CO component is clearly detected in IE1 of the 40 Gllz observations (Fig., The southern CO component is clearly detected in IF1 of the 40 GHz observations (Fig.880 Lh). but is not seen in IF2. nor in the 43 GlIz continuum image (Figs.," 1b), but is not seen in IF2, nor in the 43 GHz continuum image (Figs."881 le and 1d)., 1c and 1d).882 The northern component shows up in both IF channels for the 40 GlIz observations (Figs la.b.c). but is not seen in the 43 Gllz continuum image (Fig Id).," The northern component shows up in both IF channels for the 40 GHz observations (Figs 1a,b,c), but is not seen in the 43 GHz continuum image (Fig 1d)."883 From the 43 GlIz image we sel a 2o upper limit of 0.16 mJv for the 43 GlIz continuum emission from both the northern aud southern components in 1202.0725., From the 43 GHz image we set a $\sigma$ upper limit of 0.16 mJy for the 43 GHz continuum emission from both the northern and southern components in 1202–0725.884 The lack of continuum emission al 43 Gllz [rom the northern component in 1202.0725 is significant in regard to the recent. possible detection of 0.3£0.15 mJ of continuum enission al 2mm by CGuilloteau (2001)., The lack of continuum emission at 43 GHz from the northern component in 1202–0725 is significant in regard to the recent possible detection of $0.8\pm0.15$ mJy of continuum emission at 3mm by Guilloteau (2001).885 The implied spectrum from 2mm to mum must be rising with a powerlaw index >1.9., The implied spectrum from 3mm to 7mm must be rising with a powerlaw index $> 1.9$.886 It also implies that the observed emission in IEs 1 aud, It also implies that the observed emission in IFs 1 and887A partial transit was observed with LT/RISE on 2010 May 21.,A partial transit was observed with LT/RISE on 2010 May 21.888 The full transit was not obtainable as the star set below the observing limits of the LT prior to egress., The full transit was not obtainable as the star set below the observing limits of the LT prior to egress.889 RISE is a frame transler CCD located on the robouc 2.0-m Liverpool Telescope (LT) on La Palma with a broad band V + R filter (?2)..," RISE is a frame transfer CCD located on the robotic 2.0-m Liverpool Telescope (LT) on La Palma with a broad band V + R filter \citep{Steele08, Gibson08}."890" The telescope was delocused by — 1.0 mm to give FWHM = 17 pixels = 9.2 arcsec, and the CCD was used in x2 binning mode with an exposure me of 65 s and ellecuvely no dead üme."," The telescope was defocused by $-$ 1.0 mm to give FWHM = 17 pixels = 9.2 arcsec, and the CCD was used in $\times$ 2 binning mode with an exposure time of 65 s and effectively no dead time."891" This allowed 215 images to be taken over the 3.9 h period, including | h of observations belore transit."," This allowed 215 images to be taken over the 3.9 h period, including 1 h of observations before transit."892 The data were reduced using the ULTRACAM pipeline (2) and differential photometry was performed relative to five nearby bright stars using an 18 pixel radius aperture., The data were reduced using the ULTRACAM pipeline \citep{Dhillon07} and differential photometry was performed relative to five nearby bright stars using an 18 pixel radius aperture.893the ALDDOG and D.BDB06 moclels. as representatives of their models lineage.,"the D06 and B06 models, as representatives of their model's lineage."894 We only discuss the results based on their descendants. M.BBOT and D.EFO0S. when they show significantly different behaviour from \LDDOG and D_BLBOG.," We only discuss the results based on their descendants, B07 and F08, when they show significantly different behaviour from D06 and B06."895 1n order to construct ao statistically significant (and representativo) galaxy group catalogue. we have worked with a set of sub-samples of the Millennium. Simulation. amounting to ~3% of the available volume. — specilicallv. 64 boxes of side length 12547 Alpe drawn from the database.," In order to construct a statistically significant (and representative) galaxy group catalogue, we have worked with a set of sub-samples of the Millennium Simulation, amounting to $\sim$ of the available volume, – specifically, 64 boxes of side length $h^{-1}$ Mpc drawn from the database."896 Our results are robust to the arbitrary selection of the box. having been tested. on alternate boxes of equal size.," Our results are robust to the arbitrary selection of the box, having been tested on alternate boxes of equal size."897 A luminosity limit of Ας 17 in the SDSS r- was imposed., A luminosity limit of $M_r$ $-$ 17 in the SDSS $r$ -band was imposed.898 At lower luminosity the effect. of the limited. mass resolution of the N-bock background. effects the completeness of the sample., At lower luminosity the effect of the limited mass resolution of the N-body background effects the completeness of the sample.899 We identify galaxy groups as overdensties in the galaxy population using an Fol algorithm (?7).., We identify galaxy groups as overdensties in the galaxy population using an FoF algorithm \citep{Geller1983}.900 No maximum number of members is set but we require that at east four galaxies are linked in order to define a group., No maximum number of members is set but we require that at least four galaxies are linked in order to define a group.901 Although this removes groups such as the Local group. it foll wsthe ?. definition of compact groups.," Although this removes groups such as the Local group, it follows the \citet{Hickson1982} definition of compact groups."902" We first. construct a ""loose. group” (LG) catalogue using a linking length of 0.2 times the mean inter-particle separation.(or in this case. inter-galactic separation)."," We first construct a “loose group” (LG) catalogue using a linking length of 0.2 times the mean inter-particle separation,(or in this case, inter-galactic separation)."903 We made this choice by assuming that the galaxies follow the dark matter., We made this choice by assuming that the galaxies follow the dark matter.904 This corresponds to a co-moving linking length of ~500h7 kpe., This corresponds to a co-moving linking length of $\sim$ $h^{-1}$ kpc.905 To examine the elfects of density we also define two “compact group catalogues. Compact (CX). and Very Compact ενCG). Groups using co-moving linking lengths of 1505.! kpe and 50h+ kpe. respectively.," To examine the effects of density we also define two “compact group” catalogues, – Compact (CG), and Very Compact (vCG), Groups – using co-moving linking lengths of $h^{-1}$ kpc and $h^{-1}$ kpc, respectively."906 The CG linking length of 1500+ kpe is similar to that advised. by 7.. based upon their 3D linking length analysis from mock catalogues of Hickson compact groups based on ΑΙ00.," The CG linking length of $h^{-1}$ kpc is similar to that advised by \citet{McConnachie2008}, based upon their 3D linking length analysis from mock catalogues of Hickson compact groups based on D06."907 The vCG linking length. is comparable to the projected linking length used by ? and? to identify groups. a value arrived at by calibrating to the ? catalogue using projected ealaxy separations.," The vCG linking length is comparable to the projected linking length used by \citet{Barton1996} and \citet{Allam2000} to identify groups, a value arrived at by calibrating to the \citet{Hickson1992} catalogue using projected galaxy separations."908 We note that the CG ealaxies are. by necessity of the eroup finding algorithm. subsets of the LG catalogue. in that every galaxy assembled into a group at short linking length. must be part of a group with a Larger linking length.," We note that the CG galaxies are, by necessity of the group finding algorithm, subsets of the LG catalogue, in that every galaxy assembled into a group at short linking length, must be part of a group with a larger linking length."909 Our catalogues also contains clusters and cluster cores. a point to which we return shortly.," Our catalogues also contains clusters and cluster cores, a point to which we return shortly."910 The physical interpretation of the linking length variation and its impact upon resulting ealaxy distribution is non-trivial., The physical interpretation of the linking length variation and its impact upon resulting galaxy distribution is non-trivial.911 Phe Fob algorithm essentially probes deeper into the potential well at. shorter. linking lengths. selecting only galaxies closer to the eluster/group core.," The FoF algorithm essentially probes deeper into the potential well at shorter linking lengths, selecting only galaxies closer to the cluster/group core."912 These galaxies are generally old. and have sunk deeper into the eluster potential. or they are galaxies near their respective orbital peri-centre.," These galaxies are generally old, and have sunk deeper into the cluster potential, or they are galaxies near their respective orbital peri-centre."913 The algorithm does not onv extract the inner region of eroups., The algorithm does not only extract the inner region of groups.914 Galaxies in the outskirs of clusters that happen to be close to one another can also be linked together., Galaxies in the outskirts of clusters that happen to be close to one another can also be linked together.915 This may either be due to à temporary aignment of galaxies that are simply ‘passing through’ that region. or because the galaxies were in close proximity. before hev entered the cluster. and have not vet been disbursed by ical forces.," This may either be due to a temporary alignment of galaxies that are simply `passing through' that region, or because the galaxies were in close proximity before they entered the cluster, and have not yet been disbursed by tidal forces."916 These peripheral eroups are essentially cluster sustructure. and are a natural part of the analysis.," These peripheral groups are essentially cluster substructure, and are a natural part of the analysis."917 Peripheral groups represent a small fraction of LCs. but represent ~20% of CGs and vCCGs.," Peripheral groups represent a small fraction of LGs, but represent $\sim$ of CGs and vCGs."918 Also worth noting. the linking length adopted for LCs can include ealaxies in haloes bevond the limit of the dark matter halo which the majority of the group members occupy.," Also worth noting, the linking length adopted for LGs can include galaxies in haloes beyond the limit of the dark matter halo which the majority of the group members occupy."919 This means that our LG catalogue is not exactly. equivalent. to eroups that are defined by the halo occupation of galaxies., This means that our LG catalogue is not exactly equivalent to groups that are defined by the halo occupation of galaxies.920 We compare the mergingὃνe histories and timescales of haloes and galaxies within the models., We compare the merging histories and timescales of haloes and galaxies within the models.921 Any cillerences will be important in determining he origin of various group properties., Any differences will be important in determining the origin of various group properties.922 To compare the lifetime of satellites we look ab a) the lifetimes of satellites that have merged. aud jus contribute to the mass aad Luminosity of the Central ο.maxy. and b) the lifetime of satellites that have not vet xnerged. and are hence satellites at z=0. and contribute to —10 Group catalogues.," To compare the lifetime of satellites we look at a) the lifetimes of satellites that have merged, and thus contribute to the mass and Luminosity of the Central Galaxy, and b) the lifetime of satellites that have not yet merged, and are hence satellites at $z=0$, and contribute to the Group catalogues."923 Figure 1. shows the distribution of merging times. clined as the time between a satellite first entering a halo viel being totally merged with the central galaxy.," Figure \ref{Fig:mtime} shows the distribution of merging times, defined as the time between a satellite first entering a halo and being totally merged with the central galaxy."924 We select 1e same 19 millennium simulation clusters from cach mocel to make a fair comparison between the codes and do not put any limit on the luminosity of infalline satellites., We select the same 19 millennium simulation clusters from each model to make a fair comparison between the codes and do not put any limit on the luminosity of infalling satellites.925 The -——istribution of merging times shows little dillerence between 1e models., The distribution of merging times shows little difference between the models.926 Phe average ALDDOG satellite has lasted 5.8 wer. while D_BBOG satellites last 6.2 Gyr. with standard eviations of ~1.," The average D06 satellite has lasted 5.8 Gyr, while B06 satellites last 6.2 Gyr, with standard deviations of $\sim 1$."927 We note. however. that twice as many satellites have merged in the Munich. model (317) than in 10 Durham model (152).," We note, however, that twice as many satellites have merged in the Munich model (317) than in the Durham model (152)."928 This result seems a little contradictory. as simular merging timescales should result in similar numbers of mergers.," This result seems a little contradictory, as similar merging timescales should result in similar numbers of mergers."929 We look to the number of satellites which do not merge in order to reconcile this., We look to the number of satellites which do not merge in order to reconcile this.930 Figure 2. shows the time of infall for the satellites into the host halo. for satellites that merge (Panel A). satellites that do not merge but rather remain as satellites at z=0 (Panel DB). and all satellites (Panel €).," Figure \ref{Fig:mtime2} shows the time of infall for the satellites into the host halo, for satellites that merge (Panel A), satellites that do not merge but rather remain as satellites at z=0 (Panel B), and all satellites (Panel C)."931 Again. the fact that more satellites merge in ALDDOG compared with D.DDB06. can be seen in panel A. but it can be seen that the dillerence is dominated. by satellites which fall in to the host halo at early times.," Again, the fact that more satellites merge in D06 compared with B06, can be seen in panel A, but it can be seen that the difference is dominated by satellites which fall in to the host halo at early times."932 By contrast. the number of satellites which do not merge at all is significantly larger for 112060. compared with M-DDOG.," By contrast, the number of satellites which do not merge at all is significantly larger for B06, compared with D06."933 The dillerence is greatest for satellites wuch acerete early., The difference is greatest for satellites which accrete early.934" This significant population of satellites wlich do not merge by z=0 can be expected to alfect the preyperties of groups which we present in the remainder of this study. both because of the lower number of satellies ""feeding"" the central galaxy in D-BBOG. and also the larger numbers of satellites whieh survive to be inclued in the group catalogues."," This significant population of satellites which do not merge by z=0 can be expected to affect the properties of groups which we present in the remainder of this study, both because of the lower number of satellites “feeding"" the central galaxy in B06, and also the larger numbers of satellites which survive to be included in the group catalogues."935 Panel € shows the infall time of all satellites, Panel C shows the infall time of all satellites936Interestingly enough. the star density peak has a very low contrast with the field. the lowest in our sample.,"Interestingly enough, the star density peak has a very low contrast with the field, the lowest in our sample."937 This fact may indicate that the central peak can be caused by an inter-stellar absorption This cluster has a complex structure., This fact may indicate that the central peak can be caused by an inter-stellar absorption This cluster has a complex structure.938" At Jr,=18 and Jinn=14 SDMs show a double structure with the second component 8 aremin to the East.", At $J_{lim}=13$ and $J_{lim}=14$ SDMs show a double structure with the second component 8 arcmin to the East.939" At η,15 this second component disappears. but we see another one 13 aremin apart. in the Noth-East direction."," At $J_{lim}=15$ this second component disappears, but we see another one 13 arcmin apart, in the Noth-East direction."940" At /;;,,=16 this component becomes prominent.", At $J_{lim}=16$ this component becomes prominent.941 Theoptical SDM also shows a complex structure with several secondary maxima., The SDM also shows a complex structure with several secondary maxima.942 The RSDP gives an estimate of cluster radius of about 17 This cluster stands out neatly in SDM for ο=13 and Juac14., The RSDP gives an estimate of cluster radius of about 17 This cluster stands out neatly in SDM for $J_{lim}=13$ and $J_{lim}=14$.943 At Jpn15 cluster is still visible. but we see comparable density fluctuations around them.," At $J_{lim}=15$ cluster is still visible, but we see comparable density fluctuations around them."944 At rj;=16 the cluster disappears against the background density fluctuations., At $J_{lim}=16$ the cluster disappears against the background density fluctuations.945 The RSDP suggests a cluster radius of about 9 areminutes., The RSDP suggests a cluster radius of about 9 arcminutes.946 Optical SDM shows asymmetric complex structure with at least two secondary density maxima., Optical SDM shows asymmetric complex structure with at least two secondary density maxima.947 This cluster is well defined for all limiting magnitudes., This cluster is well defined for all limiting magnitudes.948" At Ji,=14 it exhibits a double structure.", At $J_{lim}=14$ it exhibits a double structure.949 Neighbour density fluctuations become stronger when including fainter stars., Neighbour density fluctuations become stronger when including fainter stars.950 RSDP gives a cluster radius estimate of about 8 This cluster was listed in the paper of van den Bergh and Hagen (1975)., RSDP gives a cluster radius estimate of about 8 This cluster was listed in the paper of van den Bergh and Hagen (1975).951" It does not possess a clear density peak either in ""optical"" or in ""infrared"" SDM."," It does not possess a clear density peak either in ""optical"" or in ""infrared"" SDM."952 van den Bergh and Hagen (1975) write that cluster is visible in blue plates and not visible in red plates., van den Bergh and Hagen (1975) write that cluster is visible in blue plates and not visible in red plates.953 Possibly it is a sparse group of young stars with an angular size of about a degree or even more., Possibly it is a sparse group of young stars with an angular size of about a degree or even more.954 However. SDM plotted for a field 2x2 degrees large. do not show any density peak either.," However, SDM plotted for a field 2x2 degrees large, do not show any density peak either."955 This cluster is clearly defined for all limiting magnitudes., This cluster is clearly defined for all limiting magnitudes.956 Density fluctuations grow with increasing limiting magnitude and concentrate in the North-West quadrant with respect to the cluster., Density fluctuations grow with increasing limiting magnitude and concentrate in the North-West quadrant with respect to the cluster.957 RSDP gives a cluster radius estimate of about 10 areminutes., RSDP gives a cluster radius estimate of about 10 arcminutes.958 This is a relatively rich cluster with an angular radius of about 16-18 areminutes., This is a relatively rich cluster with an angular radius of about 16-18 arcminutes.959 It has a symmetric core and a slightly asymmetric halo elongated in the North direction., It has a symmetric core and a slightly asymmetric halo elongated in the North direction.960" RSDP of this cluster shows a ""step"" near rz8 In this Section we make use of the results of the star count analysis to derive estimates of the fundamental parameter. namely reddening. distance. and age for the clusters under study."," RSDP of this cluster shows a ""step"" near r=8 In this Section we make use of the results of the star count analysis to derive estimates of the fundamental parameter, namely reddening, distance, and age for the clusters under study."961 We only considered the stars that fall inside the core radius. as detined in previous Sections. with the aim to alleviate as much as possible field star contamination and render the cluster more visible.," We only considered the stars that fall inside the core radius, as defined in previous Sections, with the aim to alleviate as much as possible field star contamination and render the cluster more visible."962" The method we employed is based first on the inspection of the color-color diagram (TCD). in the B-V vs U-B color combination, to derive an independent estimate of the cluster mean reddening."," The method we employed is based first on the inspection of the color-color diagram (TCD), in the B-V vs U-B color combination, to derive an independent estimate of the cluster mean reddening."963 In this diagram. the position of stars with spectral types earlier than AO. only depends on reddening (Carraro et al.," In this diagram, the position of stars with spectral types earlier than A0, only depends on reddening (Carraro et al."964 2008)., 2008).965 Then. the analysis moves to the inspection of the color magnitude diagrams (CMD). in various color combinations. to derive estimates of the cluster distance and age.," Then, the analysis moves to the inspection of the color magnitude diagrams (CMD), in various color combinations, to derive estimates of the cluster distance and age."966 For the sake of homogeneity with previous studies Seleznev et al., For the sake of homogeneity with previous studies Seleznev et al.967 2010) we adopt here /?. 28.5 Kpe as the distance of the Sun to the Galactic center. and Ay = 3.1 as the ratio of total to selective absorpion oe," 2010) we adopt here $R_{\odot}$ =8.5 kpc as the distance of the Sun to the Galactic center, and $R_{V}$ = 3.1 as the ratio of total to selective absorpion $\frac{A_V}{E(B-V)}$."968 We stress. finally. that we are going to adopt solar metallicity for these clusters. as a working hypothesis. when no information is available from spectroscopy.," We stress, finally, that we are going to adopt solar metallicity for these clusters, as a working hypothesis, when no information is available from spectroscopy."969 This is partly justified by the clusters location in the inner disk., This is partly justified by the clusters location in the inner disk.970 Should solar metallicity clearly be unsuitable. we will then explore different values.," Should solar metallicity clearly be unsuitable, we will then explore different values."971 With the probable exception of IC 2714. most clusters in this paper are being studied for the first time.," With the probable exception of IC 2714, most clusters in this paper are being studied for the first time."972 We are. therefore. facing the well-known problem of associating reliable errors to distance and age.," We are, therefore, facing the well-known problem of associating reliable errors to distance and age."973 Without precise estimates of reddening and metallicity. it is extremely difficult to perform a proper error assessment.," Without precise estimates of reddening and metallicity, it is extremely difficult to perform a proper error assessment."974 This would imply. in theory. a full error propagation which would in general produce a very large iper-volume in the parameters? space with many solutions which would not pass a simple by-eye We will. therefore. limit ourselves to provide titting errors for the cluster reddening and apparent distance moduli. being totally aware that they most probably are only rough lower limits awaiting improvements as soon as more precise metallicity measurements will be available.," This would imply, in theory, a full error propagation which would in general produce a very large iper-volume in the parameters' space with many solutions which would not pass a simple by-eye We will, therefore, limit ourselves to provide fitting errors for the cluster reddening and apparent distance moduli, being totally aware that they most probably are only rough lower limits awaiting improvements as soon as more precise metallicity measurements will be available."975 However. in deriving distance. a full propogation is done taking into account the whole range of values for reddening and distance modulus.," However, in deriving distance, a full propogation is done taking into account the whole range of values for reddening and distance modulus."976 Finally. as far as the ages is considered. only fitting errors are reported. adopting solar metallicity (see below).," Finally, as far as the ages is considered, only fitting errors are reported, adopting solar metallicity (see below)."977 In Figure 8 we show the TCDs for eight of the nine program clusters., In Figure 8 we show the TCDs for eight of the nine program clusters.978 Unfortunately. we could not provide U-band photometry for Czernik 38 and therefore we are going to estimate its reddening simultaneously with age and distance from the CMD analysis. using theoretical isochrones. in a less effective way (see below).," Unfortunately, we could not provide U-band photometry for Czernik 38 and therefore we are going to estimate its reddening simultaneously with age and distance from the CMD analysis, using theoretical isochrones, in a less effective way (see below)."979 In each of the panel in Fig., In each of the panel in Fig.980 8 we show the TCD for the program clusters following their numbering as in Table |., 8 we show the TCD for the program clusters following their numbering as in Table 1.981 As anticipated. only stars within the core radius are used.," As anticipated, only stars within the core radius are used."982 The solid line is a zero reddening. solar metallicity. empirical zero age main sequence (ZAMS) taken from Schmidt-Kalert982).," The solid line is a zero reddening, solar metallicity, empirical zero age main sequence (ZAMS) taken from Schmidt-Kaler(1982)."983 In each panel. the same," In each panel, the same"984of the optical eclipses caused by the disk warp.,of the optical eclipses caused by the disk warp.985 Their failure to detect X-ray eclipses was interpreted as evidence that the X-ray emitting plasma ts at high latitudes., Their failure to detect X-ray eclipses was interpreted as evidence that the X-ray emitting plasma is at high latitudes.986 ? and ? examined ground-based optical photometry of ~800 young stars in the Orion Nebula Cluster. overlapping. for ~| week. with the Orion Ultradeep Project (COUP) observation of the same region.," \citet{sta06} and \citet{sta07} examined ground-based optical photometry of $\sim 800$ young stars in the Orion Nebula Cluster, overlapping, for $\sim 1$ week, with the Orion Ultradeep Project (COUP) observation of the same region."987 They found “very little evidence to suggest a direct causal link between the sources of optical and X-ray variability in PMS stars”., They found “very little evidence to suggest a direct causal link between the sources of optical and X-ray variability in PMS stars”.988" We have obtained two ~30kksee observations of the star-forming region 22264 overlapping with a dedicated CoRoT ""short run"".", We have obtained two $\sim$ ksec observations of the star-forming region 2264 overlapping with a dedicated CoRoT “short run”.989 The two observations. separated by approximately two weeks. were allocated from the Director's Discretionary Time.," The two observations, separated by approximately two weeks, were allocated from the Director's Discretionary Time."990 We present evidence that the soft X-ray and optical emissions are correlated for CTTSs (but not for WTTSs) and discuss the implications in terms of location of the X-ray emitting material and origins of the variability., We present evidence that the soft X-ray and optical emissions are correlated for CTTSs (but not for WTTSs) and discuss the implications in terms of location of the X-ray emitting material and origins of the variability.991 We observed the star-forming region NGC 2264 for 23.5 days with the CoRoT satellite in. March. 2008., We observed the star-forming region NGC 2264 for 23.5 days with the CoRoT satellite in March 2008.992 The two CCDs normally used for exoplanet observations cover a ~2 sq.degree field with the cluster fitting in a single CCD., The two CCDs normally used for exoplanet observations cover a $\sim$ 2 sq.degree field with the cluster fitting in a single CCD.993 High-quality. broadband m). optical lightcurves were obtained with a cadence of 512 or 32 seconds for 8150 pre-selected targets in the field. with magnitudes down to /~16.," High-quality, broadband $\mu$ m), optical lightcurves were obtained with a cadence of 512 or 32 seconds for 8150 pre-selected targets in the field, with magnitudes down to $I\sim16$."994 First results for NGC 2264 members were published by ?.. while a complete description of the observation is m preparation (Favata et al.).," First results for NGC 2264 members were published by \citet{ale10}, while a complete description of the observation is in preparation (Favata et al.)."995" We here use CoRoT ""white light"" lighteurves. as produced by the standard pipeline. cleaned of datapoints of dubious quality (status flag z 0) and all rebinned to 512 seconds."," We here use CoRoT “white light” lightcurves, as produced by the standard pipeline, cleaned of datapoints of dubious quality (status flag $\ne$ 0) and all rebinned to 512 seconds."996 The time series for ~1/3 of the stars in. our final sample actually contain color information., The time series for $\sim1/3$ of the stars in our final sample actually contain color information.997 We. however. decided to use only the sum of the fluxes in the three available bands. given the poor definition of the CoRoT photometric system.," We, however, decided to use only the sum of the fluxes in the three available bands, given the poor definition of the CoRoT photometric system."998 During the CoRoT pointing. we obtained two ACIS-I observations of a ~17x17’ field in NGC 2264. the first on 12 March. lasting kksee (ObsId: 9768). and the second on 28 March. lasting kksee (ObsId: 9769).," During the CoRoT pointing, we obtained two ACIS-I observations of a $\sim$$17\arcmin\times17\arcmin$ field in NGC 2264, the first on 12 March, lasting ksec (ObsId: 9768), and the second on 28 March, lasting ksec (ObsId: 9769)."999" The aim points were the same within 2""(R.À. 6:41:12.5. Dec. 49:29:32) and the roll angles differed by only ~4 degrees. so that the two fields overlap almost completely."," The aim points were the same within (R.A. 6:41:12.5, Dec. +9:29:32) and the roll angles differed by only $\sim4$ degrees, so that the two fields overlap almost completely."1000 A full account of the analysis of the observations will be provided by Flaccomio et al. (, A full account of the analysis of the observations will be provided by Flaccomio et al. (1001in preparation).,in preparation).1002 —In brief. we performed source detection on each field with PWdetect (2?) and then used (2) to extract individual source spectra and lightcurves.," In brief, we performed source detection on each field with PWdetect \citep{dam97} and then used \citep{bro10} to extract individual source spectra and lightcurves."1003 We here make use mainly of the mean observed fluxes during the two observations. in units of counts s| El-. Le.. countrates divided by the effective area of the detector at each source position.," We here make use mainly of the mean observed fluxes during the two observations, in units of counts $^{-1}$ $^{-2}$, i.e., countrates divided by the effective area of the detector at each source position."1004 In the following we study the optical and X-ray flux variations between the times of the two pointings., In the following we study the optical and X-ray flux variations between the times of the two pointings.1005 The reference source sample was defined starting with the 8] sources in common between the CoRoT and the datasets and with unambiguous cross-identifications with optical and NIR catalogs (??.2MASS)..," The reference source sample was defined starting with the 81 sources in common between the CoRoT and the datasets and with unambiguous cross-identifications with optical and NIR catalogs \citep[][2MASS]{sun08,sun09}."1006 We then excluded five stars whose CoRoT lighturves are affected by sudden flux variations. most likely spurious and due to cosmic rays.," We then excluded five stars whose CoRoT lighturves are affected by sudden flux variations, most likely spurious and due to cosmic rays."1007 In the X-ray band we consider two different energy ranges: 0.5-].S5kkeV (soft) and 1.5-8.0kkeV (hard)., In the X-ray band we consider two different energy ranges: keV (soft) and keV (hard).1008 To limit the uncertainties on the flux differences between the two observations we restricted our sample to stars with 25 X-ray photons detected in the band of interest in of the two observations., To limit the uncertainties on the flux differences between the two observations we restricted our sample to stars with $\geq$ 5 X-ray photons detected in the band of interest in of the two observations.1009 This condition leads to samples of 69 and 62 objects for the soft and hard X-ray bands. respectively.," This condition leads to samples of 69 and 62 objects for the soft and hard X-ray bands, respectively."1010 Finally. we excluded 14 objects from both samples: three are not low-mass stars. but Herbig Ae/Be stars. based on their spectral types and/or V-I colors: the other 1 showed evidence of strong X-ray flares during the observations.," Finally, we excluded 14 objects from both samples: three are not low-mass stars, but Herbig Ae/Be stars, based on their spectral types and/or V-I colors; the other 11 showed evidence of strong X-ray flares during the observations."1011 Although of interest. flares were excluded for the present investigation since our aim here is to investigate flux variability due either to accretion or to variable absorption. i.e. mechanisms unrelated to flaring activity.," Although of interest, flares were excluded for the present investigation since our aim here is to investigate flux variability due either to accretion or to variable absorption, i.e. mechanisms unrelated to flaring activity."1012 Our main conclusions. however. are hardly atfected by the exclusion of these 11 stars.," Our main conclusions, however, are hardly affected by the exclusion of these 11 stars."1013" The final samples of stars with ""good"" simultaneous optical and X-ray fluxes count 55 and 48 objects considering the soft and hard X-ray bands. respectively."," The final samples of stars with “good” simultaneous optical and X-ray fluxes count 55 and 48 objects considering the soft and hard X-ray bands, respectively."1014 The smaller sample is. with the exception of one star. à subset of the larger one.," The smaller sample is, with the exception of one star, a subset of the larger one."1015" We finally classify the stars in our sample as CTTSs or WTTSs following ?:: CTTSs are defined às stars with an H, equivalent width >10 Á.orH, width at of the peak intensity greater than ss! (datafrom??)sample..."," We finally classify the stars in our sample as CTTSs or WTTSs following \citet{ale10}: CTTSs are defined as stars with an $_\alpha$ equivalent width $>$$10$ $\AA$, or $_\alpha$ width at of the peak intensity greater than $^{-1}$ \citep[data1016from][]{dah05,fur06}."1017 The other stars were classified as WTTSs., The other stars were classified as WTTSs.1018 Like CTTS. all WTTS in our sample are almost certainly members of NGC 2264. being detected in X-rays and satisfying. in the vast majority of cases. other membership criteria based on radial velocity. optical variability. and position in optical color-magnitude diagrams (?2)..," Like CTTS, all WTTS in our sample are almost certainly members of NGC 2264, being detected in X-rays and satisfying, in the vast majority of cases, other membership criteria based on radial velocity, optical variability, and position in optical color-magnitude diagrams \citep{fur06,lam04}."1019 reffig shows scatter plots between the optical and X-ray fractional variability of CTTSs and WTTSs. separately for the soft and hard X-ray bands.," \\ref{fig} shows scatter plots between the optical and X-ray fractional variability of CTTSs and WTTSs, separately for the soft and hard X-ray bands."1020 Sample sizes. the results of the Spearman's (p) and Kendalls’s (7) rank correlation tests. and the correlation coefficients r are reported in the two panels.," Sample sizes, the results of the Spearman's $\rho$ ) and Kendalls's $\tau$ ) rank correlation tests, and the correlation coefficients $r$ are reported in the two panels."1021 The optical and soft X-ray variability of CTTSs is significantly correlated (null probabilities 0.03-0.06%))., The optical and soft X-ray variability of CTTSs is significantly correlated (null probabilities ).1022 No such statistical evidence is visible for WTTs. where the X-ray and optical variations appear to be uncorrelated.," No such statistical evidence is visible for WTTs, where the X-ray and optical variations appear to be uncorrelated."1023 Also. the amplitude of the optical variability is significantly higher for CTTSs than for WTTSs.," Also, the amplitude of the optical variability is significantly higher for CTTSs than for WTTSs."1024 An inspection of the lightcurves shows that regular rotational modulation dominates in ~80% of the WTTSs. while ~90% of the CTTSs show irregular or AA Tau-like variability (cf. 2)..," An inspection of the lightcurves shows that regular rotational modulation dominates in $\sim$ of the WTTSs, while $\sim$ of the CTTSs show irregular or AA Tau-like variability \citep[cf.][]{ale10}. ."1025(1993). the corresponding age is about 30 Myr.,"(1993), the corresponding age is about 30 Myr."1026 We adopted then 2545 Myr as a good estimation for NGC 2401 age., We adopted then $25 \pm 5$ Myr as a good estimation for NGC 2401 age.1027 As a control of the optical findings. we built up the CMDs indicated in Fig.," As a control of the optical findings, we built up the CMDs indicated in Fig."1028 S using 2MLASS data (see Sect. 2.3))., \ref{fig:cmd2} using 2MASS data (see Sect. \ref{sec:data3}) ).1029 Lf we only consider the infrared. colors (Fig., If we only consider the infrared colors (Fig.1030 Saa). the data spread. of dim and. pmi stars is very significant though their mean valucs approximately follow the ALS position given by Ixoornneef (1983).," \ref{fig:cmd2}a a), the data spread of $lm$ and $pm$ stars is very significant though their mean values approximately follow the MS position given by Koornneef (1983)."1031 It is obvious that this spread. is due to the infrared magnitude errors in the 2ALASS catalogue at the level of Az142:15 as it is stronely reduced when combined with optical data to obtain the VA index (Fig., It is obvious that this spread is due to the infrared magnitude errors in the 2MASS catalogue at the level of $K \approx 14-15$ as it is strongly reduced when combined with optical data to obtain the $V-K$ index (Fig.1032 Sbb)., \ref{fig:cmd2}b b).1033 So. the distance modulus fit in the infrared diagrams turns out to be quite acceptable: in addition. infrared. diagrams independently. confirm that the reddening law is normal as suggested by the optical PCDs of Fig. 6..," So, the distance modulus fit in the infrared diagrams turns out to be quite acceptable; in addition, infrared diagrams independently confirm that the reddening law is normal as suggested by the optical TCDs of Fig. \ref{fig:ccd1}. ."1034 As a final note. the infrared CAID of the C (see Sect. 3.2))," As a final note, the infrared CMD of the $CF$ (see Sect. \ref{sec:member}) )"1035 which is shown in Fig., which is shown in Fig.1036 See confirms that the region around the ALS has almost no stars reinforcing the real nature of the cluster., \ref{fig:cmd2}c c confirms that the region around the MS has almost no stars reinforcing the real nature of the cluster.1037 A singular object in the field of NGC. 2401 is the bright star 3i14 located at 178 south-cast from the cluster center., A singular object in the field of NGC 2401 is the bright star $\#~14$ located at $1\farcm8$ south-east from the cluster center.1038" This star was early. identified by Stephenson Sanduleak (1971) as LSS 440 who informed it is an OD-tvpe star with the Balmer continuum in emission (in an exceptionally pronounced wav) and the ££, line in emission too according to an independent 44, plate.", This star was early identified by Stephenson Sanduleak (1971) as LSS 440 who informed it is an OB-type star with the Balmer continuum in emission (in an exceptionally pronounced way) and the $H_{\alpha}$ line in emission too according to an independent $H_{\alpha}$ plate.1039 Το classify this star a series of spectra were obtained covering the spectral range 3400 - (see Sect. 2.22)., To classify this star a series of spectra were obtained covering the spectral range 3400 - 6750 (see Sect. \ref{sec:data2}) ).1040 Phe LSS 440 spectrum is shownin Fig., The LSS 440 spectrum is shownin Fig.1041 9 together with a detail of the most relevant. features., \ref{fig:lss440} together with a detail of the most relevant features.1042 This, This1043ou the Galactic plane of the Galactic coordinates (6.5).,"on the Galactic plane of the Galactic coordinates $(\ell,b)$."1044 Old OC's are mainly found outside the Solar circle. aud he inner Calaxy coutaius ‘ow OCS so far detected.," Old OCs are mainly found outside the Solar circle, and the inner Galaxy contains few OCs so far detected."1045 The interesting poiut is whether iuuer Galaxy clusters camot ο observed. because of stroug absorption aud crowding. or have been systematically dissolved. by the differeut idal effects combined (Bouatto&Bica.20072.audreferences therein).," The interesting point is whether inner Galaxy clusters cannot be observed because of strong absorption and crowding, or have been systematically dissolved by the different tidal effects combined \citep[][ and references therein]{Bonatto07a}."1046 In this context. the more OC's are identified (with their astrophysical parameters derived) iu he central parts. the more constraints can be established o settle this issuc.," In this context, the more OCs are identified (with their astrophysical parameters derived) in the central parts, the more constraints can be established to settle this issue."1047 We investigate the nature of 50 overdensities projected nearly towards the anti-ceutre. iu the sector P607 2007. with |b|20° that were classified by Frocbrich.Scholz&Raftery(2007) as probable OCs and labelled with quality flags 2 and 3.," We investigate the nature of 50 overdensities projected nearly towards the anti-centre, in the sector $160^\circ\,\leq\,\ell\,\leq 200^\circ$ , with $|b|\,\leq\,20^\circ$ that were classified by \citet{Froebrich07} as probable OCs and labelled with quality flags 2 and 3."1048 The candidates are analysed by nmeaus of 2\TASS colourauaguitude diagrams. stellar radial deusity profiles. and colowr-colour diagrams for voung objects.," The candidates are analysed by means of 2MASS colour-magnitude diagrams, stellar radial density profiles, and colour-colour diagrams for young objects."1049 Ficld-star decoutaminatiou is applied to uncover the clusters intrinsic CMD morphology. aud CAL filters are used to diseutaugle probable cluster mienibers.," Field-star decontamination is applied to uncover the cluster's intrinsic CMD morphology, and CM filters are used to disentangle probable cluster members."1050 Out of the 50 overdeusities. 16 )) are coufirmed as OCs.," Out of the 50 overdensities, 16 ) are confirmed as OCs."1051 Nine (18%)) are new OCs (FSR 735. FSR so7. FSR S12. FSR 526. FSR 852. FSR 901. FSR 911. FSR 953. aud FSR 955) aud we derived astroplivsical parameters.," Nine ) are new OCs (FSR 735, FSR 807, FSR 812, FSR 826, FSR 852, FSR 904, FSR 941, FSR 953, and FSR 955) and we derived astrophysical parameters."1052 They are OC's or embedded clusters with age in the range 5 Myr to 1 Gyr. at distances from the Sun 1.28Xd.5.78 aud Galactoceutric distances 8.5=παςXm12.9.," They are OCs or embedded clusters with age in the range 5 Myr to 1 Gyr, at distances from the Sun $1.28\lesssim{d}_{\odot}\lesssim5.78$ and Galactocentric distances $8.5\lesssim{R}_{GC}\lesssim12.9$."1053 Other 7 (LL%)) overdeusities ave previously catalogued OCs or enibedded. clusters (KIKC1. FSR 795. Cz 22. FSR 828. FSR 556. Czernik 21. and NCC 2251).," Other 7 ) overdensities are previously catalogued OCs or embedded clusters (KKC1, FSR 795, Cz 22, FSR 828, FSR 856, Czernik 24, and NGC 2234)."1054 We also derived paraueters for Cz 22 and NGC2231., We also derived parameters for Cz 22 and NGC2234.1055 Five are classified as uncertain cases and require deeper plotometry to establish their nature., Five are classified as uncertain cases and require deeper photometry to establish their nature.1056 The remaining FSR overdeusities appear to be field fluctuations., The remaining FSR overdensities appear to be field fluctuations.1057 Most of the new OCs are located close to spiral arius and/or close to the Galactic plane aud. probably because of this. the core radius appears to be smaller than the others at comparable Calactocentzic distance and age.," Most of the new OCs are located close to spiral arms and/or close to the Galactic plane and, probably because of this, the core radius appears to be smaller than the others at comparable Galactocentric distance and age."1058 Also for this reason. most of them were undetected in the past.," Also for this reason, most of them were undetected in the past."1059 We thank an anouvimous referee for significant comlicuts ancl sueeestions., We thank an anonymous referee for significant comments and suggestions.1060OO This publication makes use of data products from the Two Micron All Sky Survey. which is a joiut project of the University of Massachusetts and the Iufrared. Processing aud Analvsis Centre/California lustitute of Techuoloey. funded by the National Aeronautics and Space Administration aud the National Science. Foundation.," This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Centre/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation."1061 This research has made use of the WEBDA database. operated at the Lustitute for Astrouoiv of the University of Vienna. as well as Digitised Sky Survey images from the Space Telescope Science Iustitute obtained using the extraction tool from CADC (Canada).," This research has made use of the WEBDA database, operated at the Institute for Astronomy of the University of Vienna, as well as Digitised Sky Survey images from the Space Telescope Science Institute obtained using the extraction tool from CADC (Canada)."1062 We acknowledee support frou CNPq and Capes (Brazil)., We acknowledge support from CNPq and Capes (Brazil).1063Few years ago. measurements of high energy cosmic-ray (CR) electrons above 10 GeV were performed mainly by balloon-borne experiments (Kobayashi et al.,"Few years ago, measurements of high energy cosmic-ray (CR) electrons above $10$ GeV were performed mainly by balloon-borne experiments (Kobayashi et al."1064 2004 and references therein)., 2004 and references therein).1065 Their measurements showed that the electron spectrum follow a power-law behaviour of the form ££.' with the index PFzz3.2 without any significant features up to energies around 2 TeV. However. recent measurements made by the ATIC balloon experiment had found a sharp peak at fo= 600GeV (Chang et al.," Their measurements showed that the electron spectrum follow a power-law behaviour of the form $E^{-\Gamma}$ with the index $\Gamma\approx 3.2$ without any significant features up to energies around $2$ TeV. However, recent measurements made by the ATIC balloon experiment had found a sharp peak at $E\approx 600$ GeV (Chang et al."1066 2008)., 2008).1067 But. this feature was not later detected by two other experiments. the spaced-borne Fermi-LAT and the ground-based HESS experiments (Abdo et al.," But, this feature was not later detected by two other experiments, the spaced-borne Fermi-LAT and the ground-based HESS experiments (Abdo et al."1068 2009. Aharonian et al.," 2009, Aharonian et al."1069 2008b. 2009) which measured the energy spectrum in the range of 20€i6V—5TeV.," 2008b, 2009) which measured the energy spectrum in the range of $20\mathrm{GeV}-5\mathrm{TeV}$."1070 Their combined spectrum can be closely represented by a broken power-law with spectral indices Py23 and D»zc4 for energies below and above | TeV respectively., Their combined spectrum can be closely represented by a broken power-law with spectral indices $\Gamma_1\approx 3$ and $\Gamma_2\approx 4$ for energies below and above $1$ TeV respectively.1071 In standard CR. propagation. studies assuming a homogeneous source distribution. one way to explain such a spectral behavior is to assume that the electron source Palyectrum follow a power-law behavior with an exponential cut-off of the form exp(f/f.) with £x TeV. Radio and X-ray observations do support such a form of electron spectrum inside supernova remnants (SNRs). but with cut-off energies as high as ο=SO TeV as suggested by the study of Reynolds & Keohane 1999 considering magnetic field strengths of 1075/6 inside the remnants.," In standard CR propagation studies assuming a homogeneous source distribution, one way to explain such a spectral behavior is to assume that the electron source spectrum follow a power-law behavior with an exponential cut-off of the form $(-E/E_c)$ with $E_c\approx 1$ TeV. Radio and X-ray observations do support such a form of electron spectrum inside supernova remnants (SNRs), but with cut-off energies as high as $E_c\approx 80$ TeV as suggested by the study of Reynolds $\&$ Keohane 1999 considering magnetic field strengths of $10\mu$ G inside the remnants."1072 However. for young SNRs where magnetic field amplification seems to occur. the field strengths can reach values even more than 10010 (VOIK et al.," However, for young SNRs where magnetic field amplification seems to occur, the field strengths can reach values even more than $100\mu$ G (Völlk et al."1073 2005) and the maximum energies for the electrons can be strongly limited by radiative losses to values less than ~10 TeV. The observed break can also be an effect of inhomogeneous distribution of CR sources contributing to the electrons at higher energies (Atoyan et al., 2005) and the maximum energies for the electrons can be strongly limited by radiative losses to values less than $\sim 10$ TeV. The observed break can also be an effect of inhomogeneous distribution of CR sources contributing to the electrons at higher energies (Atoyan et al.1074 1995. Kobayashi et al.," 1995, Kobayashi et al."1075 2004. Blasi 2009).," 2004, Blasi 2009)."1076 This is because high energy electrons cannot travel far distances in the Galaxy due to their faster radiative cooling., This is because high energy electrons cannot travel far distances in the Galaxy due to their faster radiative cooling.1077 Therefore. it is possible that most of the TeV electrons that we measure in the Solar System are produced by few young nearby sources.," Therefore, it is possible that most of the TeV electrons that we measure in the Solar System are produced by few young nearby sources."1078 Then. the general assumption of a continuous source distribution may break down and a more reasonable treatment would be to take into account a discrete source distribution.," Then, the general assumption of a continuous source distribution may break down and a more reasonable treatment would be to take into account a discrete source distribution."1079 A common method to do this is to use the idea of separation of distant and nearby sources. Le. assuming a continuous distribution for the distant sources and considering known SNRs or pulsars as the nearby discrete sources.," A common method to do this is to use the idea of separation of distant and nearby sources, i.e., assuming a continuous distribution for the distant sources and considering known SNRs or pulsars as the nearby discrete sources."1080 One of the main uncertainties involved in such studies can be the effect of missing sources due to detection biases., One of the main uncertainties involved in such studies can be the effect of missing sources due to detection biases.1081 Moreover. even for the known sources. the lack of precise informations about the source parameters like the distance. age and the spectral informations can lead to strong uncertainties in the high energy electron spectrum.," Moreover, even for the known sources, the lack of precise informations about the source parameters like the distance, age and the spectral informations can lead to strong uncertainties in the high energy electron spectrum."1082 Recently Delahaye et al., Recently Delahaye et al.1083 2010 presented a detailed study using this method where they included all the known SNRs and pulsars located within 2 kpe from the Earth and they found that the total high energy spectrum from the nearby sources strongly depends on several source parameters including the assumed cut-off energy., 2010 presented a detailed study using this method where they included all the known SNRs and pulsars located within $2$ kpc from the Earth and they found that the total high energy spectrum from the nearby sources strongly depends on several source parameters including the assumed cut-off energy.1084 They also showed that the cut-off energy should be somewhere around a few TeV in order to explain, They also showed that the cut-off energy should be somewhere around a few TeV in order to explain1085scenario for the production of D and ?He during a second stage of nucleosynthesis.,scenario for the production of D and $^3$ He during a second stage of nucleosynthesis.1086 Studies of inhomogeneous big-bang nucleosynthesis as well as primordial nucleosynthesis in the presence of both matter and antimatter domains have been conducted since the late 2222272).," Studies of inhomogeneous big-bang nucleosynthesis as well as primordial nucleosynthesis in the presence of both matter and antimatter domains have been conducted since the late 70's \citep{Combes75, Aly1978, Witten1984, Alcock1987, Applegate87, Kurki00b, Rehm01}."1087" It has been shown that matter-antimatter annihilations at the frontiers of the domains can lead to the production of D, *He, and T (later decaying as *He) mainly through two channels of production: nucleodisruption (p*He and He*He reactions) and photodisintegration of He nuclei."," It has been shown that matter-antimatter annihilations at the frontiers of the domains can lead to the production of D, $^3$ He, and T (later decaying as $^3$ He) mainly through two channels of production: nucleodisruption $\bar{p}^4\rm{He}$ and $^4\rm{He}\bar{^4\rm{He}} $ reactions) and photodisintegration of $^4$ He nuclei."1088 These studies provide us with the necessary material to compute the amount of deuterium produced by these various mechanisms., These studies provide us with the necessary material to compute the amount of deuterium produced by these various mechanisms.1089 Our purpose in what follows is to demonstrate the possibility of deuterium secondary production., Our purpose in what follows is to demonstrate the possibility of deuterium secondary production.1090" We therefore consider that the emulsion has a static behavior, in the sense that its comoving size is assumed to remain constant."," We therefore consider that the emulsion has a static behavior, in the sense that its comoving size is assumed to remain constant."1091 More precise studies investigating the dynamical behavior of the emulsion are beyond the scope of this first paper and will be treated in upcoming studies., More precise studies investigating the dynamical behavior of the emulsion are beyond the scope of this first paper and will be treated in upcoming studies.1092 Annihilations at the frontiers of a domain are driven by the diffusion of nuclei towards the frontiers., Annihilations at the frontiers of a domain are driven by the diffusion of nuclei towards the frontiers.1093 The photodisintegration of He nuclei by energetic photons resulting from electromagnetic cascades induced by the annihilation photons and nucleodisruption are two possible processes that could produce deuterium., The photodisintegration of $^4$ He nuclei by energetic photons resulting from electromagnetic cascades induced by the annihilation photons and nucleodisruption are two possible processes that could produce deuterium.1094 The main quantity to consider is the diffusion length., The main quantity to consider is the diffusion length.1095 It represents the average distance over which a (anti-)nucleus can diffuse toward the frontier of the domain on a Hubble time., It represents the average distance over which a (anti-)nucleus can diffuse toward the frontier of the domain on a Hubble time.1096" This length gives an absolute lower bound to the size of the domains, as any concentration of (anti)matter smaller than this diffusion length would be annihilated during a Hubble time."," This length gives an absolute lower bound to the size of the domains, as any concentration of (anti)matter smaller than this diffusion length would be annihilated during a Hubble time."1097" The diffusion length is given by ?vODCD)ta(T),, where D is the diffusion coefficient and ty(7) is the Hubble time at temperature T. Using the diffusion coefficients given in ? and ?, we computed the comoving diffusion length represented in Fig. 6.."," The diffusion length is given by \citet{Applegate87}1098, where $D$ is the diffusion coefficient and $t_H(T)$ is the Hubble time at temperature T. Using the diffusion coefficients given in \citet{Jedamzik01} and \citet{Sihvola01}, we computed the comoving diffusion length represented in Fig. \ref{diff_length}."1099 We can distinguish three regimes of diffusion., We can distinguish three regimes of diffusion.1100 The first regime for T>1MeV is regulated by neutron diffusion., The first regime for $T\geq 1\;\rm{MeV}$ is regulated by neutron diffusion.1101" Since neutrons are neutral particles, their electromagnetic interactions with other charged particles are very weak."," Since neutrons are neutral particles, their electromagnetic interactions with other charged particles are very weak."1102" As the temperature decreases, neutrons disintegrate and diffusion is then maintained by protons, which being charged have a much lower diffusion coefficient, which causes a dip in the diffusion length around 100 keV. As the density decreases because of the expansion, the diffusion length gradually increases until the temperature reaches T~50keV."," As the temperature decreases, neutrons disintegrate and diffusion is then maintained by protons, which being charged have a much lower diffusion coefficient, which causes a dip in the diffusion length around 100 keV. As the density decreases because of the expansion, the diffusion length gradually increases until the temperature reaches $T\sim 50\;\rm{keV}$."1103" At this temperature, the density is low enough for the mean distance between protons to be larger than the Debye length of electrons."," At this temperature, the density is low enough for the mean distance between protons to be larger than the Debye length of electrons."1104" Protons therefore do not behave as free particles but drag electrons along with them, ensuring charge neutrality."," Protons therefore do not behave as free particles but drag electrons along with them, ensuring charge neutrality."1105 These electrons are themselves subject to Thomson drag (?) and thus limit the, These electrons are themselves subject to Thomson drag \citep{PeeblesPPC} and thus limit the1106(thick liue) aud that of their +~2 main progenitors (thin line). as a function of the preseut-day. halo mass.,"(thick line) and that of their $z \sim 2$ main progenitors (thin line), as a function of the present-day halo mass."1107" The bottom panel preseuts the differcut contributions to the preseut-day central galaxy stellar παπα,", The bottom panel presents the different contributions to the present-day central galaxy stellar mass.1108" The different curves in this plot are the same as those in Figure 3.. but referring now to :~2. with curve ""A representing the stars already in place in the central galaxies at +—2."," The different curves in this plot are the same as those in Figure \ref{fig:Fig9MPADurham}, but referring now to $z\sim 2$, with curve “A” representing the stars already in place in the central galaxies at $z\sim 2$."1109 The treuds are qualitatively very simular to the ones seen for the 2~1 progenitors in the previous sections., The trends are qualitatively very similar to the ones seen for the $z\sim1$ progenitors in the previous sections.1110 As expected. there is significantly less stellar mass already in ace in the main progenitor at ;—2.," As expected, there is significantly less stellar mass already in place in the main progenitor at $z\sim 2$."1111 The coutribution roni the simaller ceutral galaxies is more significant thaw hat for the 2~1 case. while the coutribution of the satellites is roughly the same.," The contribution from the smaller central galaxies is more significant than that for the $z\sim 1$ case, while the contribution of the satellites is roughly the same."1112 As less stellar mass is in ace at 2~2. the contribution of star formation frou 2~ to the present-day is substantial. at all halo masses: it is about LO% for central galaxies iu the highest mass iilos probed and hieher for those m lower mass halos.," As less stellar mass is in place at $z\sim2$, the contribution of star formation from $z\sim2$ to the present-day is substantial, at all halo masses; it is about $10\%$ for central galaxies in the highest mass halos probed and higher for those in lower mass halos."1113 Note that the “dowusizine” pattern is also evident here., Note that the “downsizing” pattern is also evident here.1114" Zheng. Coil. Zehavi (2007: ZCZ07) perform: TOD modeling of the hunuinositv-depenudeut projected. two-point correlation function for DEEP2 aud SDSS ealaxics. at 2~Land 2~(0. respectively,"," Zheng, Coil, Zehavi (2007; ZCZ07) perform HOD modeling of the luminosity-dependent projected two-point correlation function for DEEP2 and SDSS galaxies, at $z\sim1$ and $z\sim0$, respectively."1115 They inter the relationship between central galaxy hunuiuositv aud halo lass at these two redshifts aud establish an evolutionary lnk bv using the typical growth of dark matter halos obtained from uuimerical simulations., They infer the relationship between central galaxy luminosity and halo mass at these two redshifts and establish an evolutionary link by using the typical growth of dark matter halos obtained from numerical simulations.1116 Stellar masses are derived from the galaxies luninosity and color., Stellar masses are derived from the galaxies luminosity and color.1117 As a proof of concept. they estimate the evolution of galaxy stellar mass as a function of host halo mass.," As a proof of concept, they estimate the evolution of galaxy stellar mass as a function of host halo mass."1118 An approximate method is used to estimate the different contributions of mersers and star formation to the erowth of central ealaxies stellar mass., An approximate method is used to estimate the different contributions of mergers and star formation to the growth of central galaxies stellar mass.1119 In this section. we use the SAM results to eauge the potential of such phenomenological methods to constrain galaxv formation aud evolution models.," In this section, we use the SAM results to gauge the potential of such phenomenological methods to constrain galaxy formation and evolution models."1120" We first compare the stellar mass growth in central galaxies inferred by ZCZOT frou, DEEP? aud SDSS ealaxy clustering with that predicted by the SAM models.", We first compare the stellar mass growth in central galaxies inferred by ZCZ07 from DEEP2 and SDSS galaxy clustering with that predicted by the SAM models.1121 We then examine the validity of the assmuptious used in the ZCZÜT approach., We then examine the validity of the assumptions used in the ZCZ07 approach.1122 We first exanune the star formation efficiency and its evolution from redshift ~~1 to 0 obtained using the MPA SAAD model (our Fig. 1)), We first examine the star formation efficiency and its evolution from redshift $z\sim1$ to $0$ obtained using the MPA SAM model (our Fig. \ref{fig:Fig10mill50b}) )1123 aud iu ZCZOT (their , and in ZCZ07 (their Fig.112410)., 10).1125 Both approaches produce similar general treuds with halo mass. exhibiting peaked distributions at the wo redshifts. and at simular halo masses.," Both approaches produce similar general trends with halo mass, exhibiting peaked distributions at the two redshifts, and at similar halo masses."1126 The ZCZüT results also exhibit the halo “downsizing” effect. with the SEE peals shifting to a higher mass at the lieher redshift.," The ZCZ07 results also exhibit the halo “downsizing” effect, with the SFE peak shifting to a higher mass at the higher redshift."1127 The MPA SAM and ZCZÜT also find comparable values or the maximum SEE at 2~ 0., The MPA SAM and ZCZ07 also find comparable values for the maximum SFE at $z \sim 0$ .1128 However. at 2~lI. he SAM shows an overall higher SFE than computed iu ZCZOT (peaking at IS% and 12%. respectively). which rauslates iuto a larger amount of stars by that redshift.," However, at $z \sim 1$, the SAM shows an overall higher SFE than computed in ZCZ07 (peaking at $18\%$ and $12\%$, respectively), which translates into a larger amount of stars by that redshift."1129 Figure 5 shows the SAM predictions (solid lines) for he stellar mass as a function of halo mass aud the results obtained by ZCZO0T (dashed lines). over the halo nass range they probe.," Figure \ref{fig:Fig8MillHODerr} shows the SAM predictions (solid lines) for the stellar mass as a function of halo mass and the results obtained by ZCZ07 (dashed lines), over the halo mass range they probe."1130 Although the SAMs and ZCZO7 uethods produce sinülu trends. there are important quantitative cdisagreciments between them.," Although the SAMs and ZCZ07 methods produce similar trends, there are important quantitative disagreements between them."1131 The main differeuce is that the SAMs predict many more stars already in place at i— in the progenitor central ealaxies compared to the ZCZÜT results., The main difference is that the SAMs predict many more stars already in place at $z\sim 1$ in the progenitor central galaxies compared to the ZCZ07 results.1132" The differences are especially pronounced at imedimun aud low halo masses,", The differences are especially pronounced at medium and low halo masses.1133" This may be related to the kuown fact that the SAMs produce too many AZ, galaxies at high redshift (e.g. Iitzbichler&White"," This may be related to the known fact that the SAMs produce too many $M_\star$ galaxies at high redshift (e.g., \citealt{Kitzbichler07}) )."1134 2007)). ΑΕΙ~0. on the other haud. the agreement is quite good for low mass halos. while for ligh-mass halos (Eger than ~102275. TAL.) the SAMs seem to underpredict the stellar mass in ceutral ealaxies.," At $z \sim 0$, on the other hand, the agreement is quite good for low mass halos, while for high-mass halos (larger than $\sim 10^{12}\Msunh$ ) the SAMs seem to underpredict the stellar mass in central galaxies."1135" The AGN ""radio imnode feedback lecomes Huportant ou these mass scales (Bowerctal.2006).", The AGN “radio mode” feedback becomes important on these mass scales \citep{Bower06}.1136. This suggests that the SAMS might be overestimating the streneth of the feedback., This suggests that the SAMs might be overestimating the strength of the feedback.1137 As for the fraction of stellar mass in place in the Dol progenitor central galaxies. theSAMs prediction is about twice that inferred by ZCZOT. as shown iu," As for the fraction of stellar mass in place in the $z\sim 1$ progenitor central galaxies, theSAMs prediction is about twice that inferred by ZCZ07, as shown in"1138Following Custafssou et al. (,Following Gustafsson et al. (11391997) we write: where 3 is the angular distance from the star iu arcsec. fois the oscillator streneth of the liue. μμ Is the πο. density of scattering atoms iu cin5d ds the distance tothe star in parsec. and : ds the distauce along the line of sight iu cu.,"1997) we write: where $\beta$ is the angular distance from the star in arcsec, $f$ is the oscillator strength of the line, $N_{scatt}$ is the number density of scattering atoms in $^{-3}$, $d$ is the distance tothe star in parsec, and $z$ is the distance along the line of sight in cm."1140" Asstuning a powerlaw of the fori: N44=Nasyo, with Nags the muuber deusity at k= 10Mem. the iutegral is readily caleulatec and vields: Nast1001”{zumy?2D. wath Y. a consti depending on the value of 0."," Assuming a powerlaw of the form: $N_{scatt} = N_{s15} ({10^{15}\over r})^{\theta}$, with $N_{s15}$ the number density at $r=10^{15}$ cm, the integral is readily calculated and yields: $N_{s15} (10^{15})^{\theta} Y ({206265\over \beta d})^{(\theta +1)}$, with $Y$ a constant depending on the value of $\theta$."1141 From our observations we derive. fatUOπρο , From our observations we derive ${I_{scatt}(\beta)\over I_*}={0.0117\pm 0.0011\over \beta^{2.36\pm 0.03}}$.1142Adopting a distance of 110 pe for Deteleeuse from its Tipparcos parallax of 7.6341.61mas. we find the uuuboer density of scatteriug atoms to be NOK1)) = 6.0 «10.31&(1022/53120 24 The column density of neutral IK atoiis along the lineof sight to the star was derived by Bernat (1977) from the T699 eciretustcellar absorption line: N(K1) ~1«102 D7.," Adopting a distance of 140 pc for Betelgeuse from its Hipparcos parallax of $7.63\pm1.64$mas, we find the number density of scattering atoms to be $N$ ) = 6.0 $\times 10^{-4} \times (10^{15}/r)^{1.36}$ $^{-3}$ The column density of neutral K atoms along the lineof sight to the star was derived by Bernat (1977) from the 7699 circumstellar absorption line: $N$ ) $\sim 4 \times 10^{12}$ $^{-2}$."1143 IuteeratiugB our relation- or the radial depeudeuce. Bernat’s column deusity is reached by iutegratiug from infinity to an inner radius Πε = 9«10e) 2μι.," Integrating our relation for the radial dependence, Bernat's column density is reached by integrating from infinity to an inner radius $R_{inner}$ = $9 \times 10^{13}cm$ $\simeq 2R_{star}$."1144 This is a plausible value for the immer radius., This is a plausible value for the inner radius.1145 To halve he column density requires Rinne.2Reta., To halve the column density requires $R_{inner} \simeq 13R_{star}$.1146" To double or Rinner<Rega, Which makes uo seuse."," To double for $R_{inner} < R_{star}$, which makes no sense."1147 Iu short. our derived. racial dependence for the density of potassium atoms is consistent with the column density derived from he absorption line.," In short, our derived radial dependence for the density of potassium atoms is consistent with the column density derived from the absorption line."1148 For this reason and because our observed slope for κο1 is equal to that predicted. by Rodgers Classgold. we use the ratio of our observed to their predicted number deusitv versus radial distance directly to correct their mass loss rate.," For this reason and because our observed slope for $I_{scatt}(r)/I_*$ is equal to that predicted by Rodgers Glassgold, we use the ratio of our observed to their predicted number density versus radial distance directly to correct their mass loss rate."1149" This corresponds to a reduction of their mass loss rate roni M — Ls108 M, vL to2.4«106 AL. +.", This corresponds to a reduction of their mass loss rate from $\dot{M}$ = $4 \times 10^{-6}$ $M_\odot$ $^{-1}$ to $2.4 \times 10^{-6}$ $M_\odot$ $^{-1}$.1150" The revision is depeudenut ou our value of Z,44/1I which rests on an average of the stellar photospheric flux average OVOY 17 aaround the potassium line.", The revision is dependent on our value of $I_{scatt}/I_*$ which rests on an average of the stellar photospheric flux averaged over 17 around the potassium line.1151 The stellar fux intercepted by the outflowing gas of the shell is that on the blue wine of the line., The stellar flux intercepted by the outflowing gas of the shell is that on the blue wing of the line.1152 As already pointed out. we do not have access to the true photospheric spectriuu. aud he line profile can only be guessed at.," As already pointed out, we do not have access to the true photospheric spectrum, and the line profile can only be guessed at."1153 A rather conservative estimate of a factor of 2 lower flux at line ceuter leads to a rate larger by a factor of two., A rather conservative estimate of a factor of 2 lower flux at line center leads to a mass-loss rate larger by a factor of two.1154 A distance of 200 pec was asstmed by Rodgers Classgeold. aud. Classgold Iluseius., A distance of 200 pc was assumed by Rodgers Glassgold and Glassgold Huggins.1155 To correct the mass loss rate to the Tipparcos distance of d = L10 pc. we use the scaling eiven by Maron Caux (1992). ie. the brightuess at a eiven aneular distance from the star is approximately proportional to AI?AI.," To correct the mass loss rate to the Hipparcos distance of $d$ = 140 pc, we use the scaling given by Mauron Caux (1992), i.e., the brightness at a given angular distance from the star is approximately proportional to $\dot{M}^2/d$."1156 Adoption of d = 110 pe instead of 200 pe implies a reduction of AL by 85 ov M=2109M. V, Adoption of $d$ = 140 pc instead of 200 pc implies a reduction of $\dot{M}$ by 85 or $\dot{M} = 2 \times 10^{-6} M_\odot$ $^{-1}$.1157 Classgold IIuseius warn that the accuracy of au Af derived. from cussion is low (va factor of some 3 - 57)., Glassgold Huggins warn that the accuracy of an $\dot{M}$ derived from emission is low (“a factor of some 3 - 5”).1158 Although the subsequent analysis of the temperature profile (Rodgers Classgold 1991) may have reduced the uucertiüntwv. a factor of two uucertaintv secuus likely to be optimistic.," Although the subsequent analysis of the temperature profile (Rodgers Glassgold 1991) may have reduced the uncertainty, a factor of two uncertainty seems likely to be optimistic."1159 The derived rate is dependent too on the assiunuption of a spherically sviunietrice shell. an asstuuption probed observationally in the next section.," The derived rate is dependent too on the assumption of a spherically symmetric shell, an assumption probed observationally in the next section."1160 This uncertainty could iu principle be reduced bx observiug other enüssonu lines., This uncertainty could in principle be reduced by observing other emission lines.1161 In Πο of the higher abundance of Na and using the atomic concentrations xedieted w Rodgers Cdassgold’s (1991). the Na D chussion is expected to be strouger than that in the 7699 and 7665 lues;," In light of the higher abundance of Na and using the atomic concentrations predicted by Rodgers Glassgold's (1991), the Na D emission is expected to be stronger than that in the 7699 and 7665 lines."1162 Maron Coulain (1995) find that the Na D CUSSION is considerably fainter than expected although other mass osing M stars do show Na D ciuission stronger than the cussion., Mauron Guilain (1995) find that the Na D emission is considerably fainter than expected although other mass losing M stars do show Na D emission stronger than the emission.1163 These authors suggest that interstellar absorption is “the simplest explanation. though iof completely convincing”.," These authors suggest that interstellar absorption is “the simplest explanation, though not completely convincing”."1164 Fortunately. interstellar absorption in the lines is observed to be considerably weaker thau in the DD lines.," Fortunately, interstellar absorption in the lines is observed to be considerably weaker than in the D lines."1165 Beteleeuse has 0011 subjected to linierotus investigations of its uass loss rate using a varietv of spectroscopic indicators., Betelgeuse has been subjected to numerous investigations of its mass loss rate using a variety of spectroscopic indicators.1166 The Ikr-based rate may be conipared with a couple of determinations using tracers of a major constituent of the shell., The -based rate may be compared with a couple of determinations using tracers of a major constituent of the shell.1167" Bowers EKuapp (1987) detected 21 c emission to derive AL~La&10© AL, tifd = 110 pe.", Bowers Knapp (1987) detected 21 cm emission to derive $\dot{M} \sim 1.1 \times 10^{-6}$ $M_\odot$ $^{-1}$ if $d$ = 140 pc.1168 Tigeins et al. (, Huggins et al. (11691991) detected the 609 μπι fine structure line aud iuferred a mass loss rate also of ο6 My ford = 110 pe.,1994) detected the 609 $\mu$ m fine structure line and inferred a mass loss rate also of $\dot{M} \sim 1 \times 10^{-6}$ $M_\odot$ $^{-1}$ for $d$ = 140 pc.1170 The close agrecinent between these results and ours is encouraeiug but must be largely fortuitous., The close agreement between these results and ours is encouraging but must be largely fortuitous.1171 More recently. Iarper et al. (," More recently, Harper et al. ("1172"2001) estimated AJδι3«4410.PAZ, + from absorption features in ultraviolet lines.","2001) estimated $\dot{M} = 3.1 \pm 1.31173\times 10^{-6} M_\odot$ $^{-1}$ from absorption features in ultraviolet lines."1174 Azgiuuthal averagingOoC» produces a nooth run of the chussion lines flux with radial distance but masks a fascinating structure of incomplete shells aud clumps., Azimuthal averaging produces a smooth run of the emission line's flux with radial distance but masks a fascinating structure of incomplete shells and clumps.1175 This structure is illustrated iu Fig. 2.. 3.. ," This structure is illustrated in Fig. \ref{fig2}, , \ref{fig3}, ,"1176aud tL aud additionally in Fie. 6.. ," and \ref{fig4}1177 and additionally in Fig. \ref{fig5a}, ,"1178aud 7.., and \ref{fig5b}. .1179 Several features of the structure are seen by inspection: the appearance of thin incomplete shells. iuteuse chirps of small spatial exteut and velocity dispersion. aud nes of sight - particularly far from the star aud inside the outermost detected shell," Several features of the structure are seen by inspection: the appearance of thin incomplete shells, intense clumps of small spatial extent and velocity dispersion, and lines of sight - particularly far from the star and inside the outermost detected shell"1180then rapidly increases (to 40 my at 1.4 CGllz) towards the first peakat~TF6.,then rapidly increases (to 40 mJy at 1.4 GHz) towards the first peak at $\sim \p{-6}$.1181 X decrease with a similar slope follows. between ~7.6 and2.," A decrease with a similar slope follows, between $\sim \p{-6}$ and."1182. The flux density plateaus (at ~2] ιν at 1.4 Gllz) at all frequencies between and13.. and then rises again to a peak at ~7|22.," The flux density plateaus (at $\sim118321$ mJy at 1.4 GHz) at all frequencies between and, and then rises again to a peak at $\sim \p{+22}$."1184 The rise to the second. peak is slower than the first. and the subsequent decay is rather shallow.," The rise to the second peak is slower than the first, and the subsequent decay is rather shallow."1185 shows a sudden drop in the flux density. subsequently however the unpulsed emission remains clearly present at the two lower frequencies during our final observation at113.," shows a sudden drop in the flux density, subsequently however the unpulsed emission remains clearly present at the two lower frequencies during our final observation at."1186. Fhis is similar to data taken in. 1994 which shows unpulsed emission present at O.S4 1112 until at least (2).., This is similar to data taken in 1994 which shows unpulsed emission present at 0.84 GHz until at least \cite{jmmc99}.1187 The data do show. however. that unpulsed. emission is not. present at ὃν Giz from onwards and has also vanished at 4.8 Cillz by119.," The data do show, however, that unpulsed emission is not present at 8.4 GHz from onwards and has also vanished at 4.8 GHz by."1188" The Bux density at a [frequency vis given by S,=Cv"" where a denotes the spectral index.", The flux density at a frequency $\nu$ is given by $S_\nu=C \nu^{\alpha}$ where $\alpha$ denotes the spectral index.1189 We measure the spectral index for the non-pulsed. emission. using [ux densities obtained at cach of our four observing frequencies., We measure the spectral index for the non-pulsed emission using flux densities obtained at each of our four observing frequencies.1190 We apply a simple linear fit to log 8 - log v space and assume symmetrical errors in log S., We apply a simple linear fit to log $S$ - log $\nu$ space and assume symmetrical errors in log $S$.1191 The spectral indices are shown in Figure 3. and are consistent with a value of ~0.7 throughout.," The spectral indices are shown in Figure \ref{fig:si2000}1192 and are consistent with a value of $\sim -0.7$ throughout."1193 Phere is no evidence for optical depths ellects. at least at frequencies above 1 Cz.," There is no evidence for optical depths effects, at least at frequencies above 1 GHz."1194 Phis is similar to the behaviour in LOOT (?), This is similar to the behaviour in 1997 \cite{jmmc99}.1195 We do not attempt to measure the spectral index. of the pulsed. emission., We do not attempt to measure the spectral index of the pulsed emission.1196 At SA Gllz. diffractive scintillation significantly allects the observed flux density.," At 8.4 GHz, diffractive scintillation significantly affects the observed flux density."1197 The scintillation bandwidth of ~70 AIllz ancl timescale of ~10 min (7) match well with our observing bandwidth of ~120 Mllz and time of 20 min., The scintillation bandwidth of $\sim$ 70 MHz and timescale of $\sim$ 10 min \cite{mjsn97} match well with our observing bandwidth of $\sim$ 120 MHz and time of 20 min.1198 Furthermore. there is clear evidence for optical depth elfects at low frequency post-periastron.," Furthermore, there is clear evidence for optical depth effects at low frequency post-periastron."1199 In particular. the flux density at 1:4 Giz appears to increase steadilv from to whereas this is not the case at the two higher frequencies.," In particular, the flux density at 1.4 GHz appears to increase steadily from to whereas this is not the case at the two higher frequencies."1200 The circular. polarisation was obtained Lor cach pulse component for cach observation. with errors of order 5% at the lower frequencies. and ~104 at the higher frequencies due to the higher svstem temperature ancl lower Εαν density at these frequencies.," The circular polarisation was obtained for each pulse component for each observation, with errors of order $\sim 5 \%$ at the lower frequencies, and $\sim 10 \%$ at the higher frequencies due to the higher system temperature and lower flux density at these frequencies."

Showing the first 1,200 of 10401 lines. Download the file for the rest.