ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Finally. Figure 5 also plots the line of sight velocity vectors of cach galaxy. after subtracting out a mean Vireo velocity of L061 kin/s (Bingech 1999). aud. the estimated r200 (1.55 Mpc) for Vireo. determined by MeLaughllin (1999).," Finally, Figure \ref{virgogeom} also plots the line of sight velocity vectors of each galaxy, after subtracting out a mean Virgo velocity of 1064 km/s (Binggeli 1999), and the estimated r200 (1.55 Mpc) for Virgo, determined by McLaughlin (1999)."3 Without transverse velocities for these galaxies. a full dynamical interpretation is nmupossible: nonetheless. we can οἶσα useful information from this plot.," Without transverse velocities for these galaxies, a full dynamical interpretation is impossible; nonetheless, we can glean useful information from this plot."4 As Virgo'« ceutral galaxy. it is no surprise that AIST has a low line of sight motion (64=213 km/s) with respect to the cluster as a whole.," As Virgo's central galaxy, it is no surprise that M87 has a low line of sight motion $v_{\rm rel} = 243$ km/s) with respect to the cluster as a whole."5 Sitting  1 Alpe behind the cluster core. ATSUs low velocity (Lt kim/s) suggests it is either near apocenter ona low angular momentum orbit — likely having passed near the cluster ceuter a few Cor ago or moving on a more tanecutial orbit which keeps it out of the cluster center.," Sitting $\sim$ 1 Mpc behind the cluster core, M84's low velocity $-4$ km/s) suggests it is either near apocenter on a low angular momentum orbit – likely having passed near the cluster center a few Gyr ago -- or moving on a more tangential orbit which keeps it out of the cluster center."6 As MIO is not projected onto the cluster core. its low velocity 67 km/s) places little constraint on its orbit.," As M49 is not projected onto the cluster core, its low velocity $-67$ km/s) places little constraint on its orbit."7 ILoxcever. the presence of am X-rav bowshock to the north of N9 argues that the ealaxy is falling into Vireo’s hot iutracluster medium from the south (win Sarazin 1996).," However, the presence of an X-ray bowshock to the north of M49 argues that the galaxy is falling into Virgo's hot intracluster medium from the south (Irwin Sarazin 1996)."8 Ouly M86 aud M89 have sieuificaut line of sight motion with respect to the cluster center 1308 kimn/s aud =721 κής. respectively).," Only M86 and M89 have significant line of sight motion with respect to the cluster center $-1308$ km/s and $-724$ km/s, respectively)."9 M86 is either moving at high speed through the core. or just about to enter it. depending on the adopted. distance. while M89 either passed through the core ~ 1-2 Car ago (if it lacks significant transverse velocity) or Is on a niore tanecutial orbit that keeps it further from the core.," M86 is either moving at high speed through the core, or just about to enter it, depending on the adopted distance, while M89 either passed through the core $\sim$ 1-2 Gyr ago (if it lacks significant transverse velocity) or is on a more tangential orbit that keeps it further from the core."10 We first examine the enviromental question by, We first examine the environmental question by11where we have taken the timescale {ς [rom Equation 23. to be my7.27.05M.fMgion Gyr for fiducial temperature parameters ancl for joy«1.,"where we have taken the timescale $t_{\infty}$ from Equation \ref{growtime} to be $7.2 n_{ism,5}^{-3/2}f_v^4M_{BH,0,10}$ Gyr for fiducial temperature parameters and for $n_{ism,5} < 1$."12 For ο2 Gvr. the ensemble of about 10° black holes will produce ~107 erg |. as much luminosity as a modest Sevlert galaxy or a single black hole of about 10211. aaccreting near the Edcdington limit.," For $t \sim 2$ Gyr, the ensemble of about $10^6$ black holes will produce $\sim 10^{43}$ erg $^{-1}$, as much luminosity as a modest Seyfert galaxy or a single black hole of about $10^5$ accreting near the Eddington limit."13 For comparison. supernovae provide an input of about Loy~10” erg | in a galaxy like the Milky Wavy for which the star formation rate is about 1 to κο astar formation rate of 10 tinight give Lo~3x107 eres +.," For comparison, supernovae provide an input of about $L_{SN} \sim 10^{49}$ erg $^{-1}$ in a galaxy like the Milky Way for which the star formation rate is about 1 $^{-1}$, so a star formation rate of 10 $^{-1}$ might give $L_{SN} \sim143\times10^{42}$ erg $^{-1}$."15 The black hole input at about 2Gy is comparable to. and might even sliehtly exceed (he input. power from supernovae.," The black hole input at about 2Gy is comparable to, and might even slightly exceed the input power from supernovae."16 Figure 4 gives the luminosity versus time for various values of the interstellar density and Figure 5 illustrates the sensitivity of the luminosity to the velocity parameter.fJ...," Figure 4 gives the luminosity versus time for various values of the interstellar density and Figure 5 illustrates the sensitivity of the luminosity to the velocity parameter,$f_v$."17 The total energy liberated by the number of black holes. Nay. accreting from 14+lau to fis We will again adopt (he approximation of a constant value of μμ to write Invoking we can wrlle. which becomes For lyμι<<1 ly. this reduces to," The total energy liberated by the number of black holes, $N_{BH}$, accreting from $t_o + t_{delay}$ to $t$ is We will again adopt the approximation of a constant value of $R_{BH}$ to write Invoking we can write, which becomes For $t_0 + t_{delay} << t << t_{\infty}$ this reduces to"18sliding window smoothing over 5 PI channels.,sliding window smoothing over 5 PI channels.19 The spectra so derived are still somewhat noisy. but not at a level which alters (he results presented here.," The spectra so derived are still somewhat noisy, but not at a level which alters the results presented here."20 A grid of models is generated across a range of temperatures aud redshifts using XSPEC. with a MEIXAL plasma. 1/3rd Solar abundances. <nf> is set to a high Galactic Intitude maximum of 1xI0?!em?. and (he results are robust to reasonable variations im these quantities.," A grid of models is generated across a range of temperatures and redshifts using XSPEC, with a MEKAL plasma, 1/3rd Solar abundances, $<nH>$ is set to a high Galactic latitude maximum of $1\times 10^{21}$ $^2$, and the results are robust to reasonable variations in these quantities."21 Az is set to 0.1 and 1 is actually set over à range from 0.1 to 12.9 keV in steps of 0.1 keV. although only temperatures of 0.2. 0.5. 1.0. 2.0. 4.0. and 6.0 keV are presented here.," $\Delta z$ is set to $0.1$ and $kT$ is actually set over a range from 0.1 to 12.9 keV in steps of $0.1$ keV, although only temperatures of 0.2, 0.5, 1.0, 2.0, 4.0, and 6.0 keV are presented here."22 The spectra are then lorward-lolded through the on-axis RAIF’s and ARFE's for the respective instruments., The spectra are then forward-folded through the on-axis RMF's and ARF's for the respective instruments.23 In the case of the Chandra. [ront-illuminated. CCD device CACIS-D. off-axis responses are also used in an effort to evaluate the effect. of radiation damage induced charge-transler inefficiencies (CTI) (see 82.2 &33).," In the case of the Chandra front-illuminated CCD device (ACIS-I), off-axis responses are also used in an effort to evaluate the effect of radiation damage induced charge-transfer inefficiencies (CTI) (see 2.2 3)."24 All Chandra responses used here assume Chat basic CTI corrections have beeen applied (o the data (e.g. (2000)))., All Chandra responses used here assume that basic CTI corrections have beeen applied to the data (e.g. \citet{tow00}) ).25 The corrections reduce (he position dependence (on the chips) of the gain and evade distributions (which distort the inferred photon energies). but an energy ancl position dependent degradation of spectral resolution remains.," The corrections reduce the position dependence (on the chips) of the gain and grade distributions (which distort the inferred photon energies), but an energy and position dependent degradation of spectral resolution remains."26 An unrestricted search is then made for the maximal signal-to-noise bv varving the lower GE) aid upper (£5) energy bands independently. as a function of z.," An unrestricted search is then made for the maximal signal-to-noise by varying the lower $E_1$ ) and upper $E_2$ ) energy bands independently, as a function of $z$."27 Figures 1.2.3. and 4 present (he optimal band search results for. respectively. the Chandra ACIS-I. ACIS-S. the XNMM-Newton MOS. and PN instruments.," Figures 1,2,3, and 4 present the optimal band search results for, respectively, the Chandra ACIS-I, ACIS-S, the XMM-Newton MOS, and PN instruments."28 some of the energv band limits show clear features as a function of redshift. however these all correspond. (o. small variations in actual signal-to-noise. as is reflected. by the smoothness of the 0.5-2 keV (o optimal ratio curves.," Some of the energy band limits show clear features as a function of redshift, however these all correspond to small variations in actual signal-to-noise, as is reflected by the smoothness of the 0.5-2 keV to optimal ratio curves."29 The features are due to the combination ol the shape of the instrumental response and features in the background and source spectra., The features are due to the combination of the shape of the instrumental response and features in the background and source spectra.30 For example. in Figure 2. the upper limit band pass curve for 1=6 keV (heaviest line) exhibits a sharp drop as the spectrum redshifts Irom z=0.6 to 0.7.," For example, in Figure 2, the upper limit band pass curve for $kT=6$ keV (heaviest line) exhibits a sharp drop as the spectrum redshifts from $z=0.6$ to 0.7."31 This is entirely due to the location of a flourescent Si Ix-o. line (at ~1.7 keV) in the background. from reflection in the Chandra mirror assembly.," This is entirely due to the location of a flourescent Si $\alpha$ line (at $\sim 1.7$ keV) in the background, from reflection in the Chandra mirror assembly."32 As the redshift of the source increases a critical point is reached where the optimal band edge crosses this backeround line. and (he optimum jumps to a lower enerey.," As the redshift of the source increases a critical point is reached where the optimal band edge crosses this background line, and the optimum jumps to a lower energy."33 The Κον results may be summarized as follows., The key results may be summarized as follows.34 For all instruments. plasmas with AT<2 keV have optimal bands which differ significantly [rom the 0.5-2 keV bandpass.," For all instruments, plasmas with $kT<2$ keV have optimal bands which differ significantly from the 0.5-2 keV bandpass."35" For the coolest plasma considered here (0.2 keV. 2.3x10"" IN) at z=0.1 the 0.5-2 keV band sulfers a"," For the coolest plasma considered here $0.2$ keV, $2.3\times 10^6$ K) at $z=0.1$ the 0.5-2 keV band suffers a"36" For the coolest plasma considered here (0.2 keV. 2.3x10"" IN) at z=0.1 the 0.5-2 keV band sulfers a."," For the coolest plasma considered here $0.2$ keV, $2.3\times 10^6$ K) at $z=0.1$ the 0.5-2 keV band suffers a"37blown away.,blown away.38 The normalization changes slightly. by losing a factor of f /z.if rj is redetined as the Bondi accretion radius (as in WEN) for gas at the galaxy virial temperature.," The normalization changes slightly, by losing a factor of $f/\pi,$ if $r_1$ is redefined as the Bondi accretion radius (as in WFN) for gas at the galaxy virial temperature."39 It compares well with the results of Ferrarese Merritt (2000) and Gebhardt et al (2000) for reasonable values of f... £j and fo: The above result demonstrates that a wind is not essential for expelling the gas surrounding a growing black hole.," It compares well with the results of Ferrarese Merritt (2000) and Gebhardt et al (2000) for reasonable values of $f,$ $f_1$ and $f_2$: The above result demonstrates that a wind is not essential for expelling the gas surrounding a growing black hole."40 In the present model it appears more as if the galaxy potential determines the black hole mass. rather than the other way round.," In the present model it appears more as if the galaxy potential determines the black hole mass, rather than the other way round."41 Note however that the gravitational binding energy of a galactic bulge. where the velocity dispersion of the bulge is 300e300kms.ft. is Lug22010PegMyadsec.," Note however that the gravitational binding energy of a galactic bulge, where the velocity dispersion of the bulge is $300 v_{300}\kmps,$ is $E_{\rm bulge}\approx 2\times 10^{-6}v_{300}^2 M_{\rm bulge} c^2$."42 The energy from the central black hole Lyon&510ο“.," The energy from the central black hole $E_{\rm AGN}\approx 5\times4310^{-4}M_{\rm bulge} c^2$."44 So only one per cent of that energy can have a major effect on the formation of that bulge and that effect may have occurred when both the black hole and galaxy were young., So only one per cent of that energy can have a major effect on the formation of that bulge and that effect may have occurred when both the black hole and galaxy were young.45 For the above model with the free parameters set to the values given in section 3 of ΕΝ. we present in Figs.," For the above model with the free parameters set to the values given in section 3 of WFN, we present in Figs."46 1-4 results on the yield of Compton-thick quasars in deep exposures with Chandra and XMM., 1–4 results on the yield of Compton-thick quasars in deep exposures with Chandra and XMM.47 Firstly. Fig.," Firstly, Fig."48 | shows as a function of redshift the total areal density of Compton-thick AGN in the model with intrinsic luminosities in excess of L0t+., 1 shows as a function of redshift the total areal density of Compton-thick AGN in the model with intrinsic luminosities in excess of $10^{44}$.49 As discussed by WEN. however. such sources are obscured by Ny~12 when the obscured phase begins (where Mvp=1.5107! 7. the column density above which a source becomes Compton-thick). and by Ny3p at its end.," As discussed by WFN, however, such sources are obscured by $N_{\rm H} \sim 15 N_{\rm{T}}$ when the obscured phase begins (where $N_{\rm T}=1.5 \times 10^{24}$ , the column density above which a source becomes Compton-thick), and by $N_{\rm H} \sim 3 N_{\rm{T}}$ at its end."50 Since there is no scattered flux included in the model spectra and the direct emission is almost completely suppressed for NycLOA tespecially below keV). the vast majority of the sources contributing to Fig.," Since there is no scattered flux included in the model spectra and the direct emission is almost completely suppressed for $N_{\rm H} > 10N_{\rm T}$ (especially below ), the vast majority of the sources contributing to Fig."51 | will not be visible to Chandra or XMM., 1 will not be visible to Chandra or XMM.52 This is borne out by Figs., This is borne out by Figs.53" 2. 3 and 4. described below. which were produced by convolving the object spectra in the observed frame with ""response functions? giving the effective area of the telescope and detector combination under consideration."," 2, 3 and 4, described below, which were produced by convolving the object spectra in the observed frame with `response functions' giving the effective area of the telescope and detector combination under consideration."54 In Fig., In Fig.55 2 we show the areal density as a function of redshift of both the Compton-thick and Compton-thin AGN (the latter also includes the unobscured quasars). which would produce more than 30 counts in the band in a exposure with XMM on the EPIC pn chip.," 2 we show the areal density as a function of redshift of both the Compton-thick and Compton-thin AGN (the latter also includes the unobscured quasars), which would produce more than 30 counts in the band in a exposure with XMM on the EPIC pn chip."56 This is repeated in Fig., This is repeated in Fig.57 3 for a 100 ks exposure., 3 for a 100 ks exposure.58 Fig., Fig.59 4 shows the analogous plot for the band with the Chandra ACIS $3 chip. with the count hreshold reduced to 10 counts owing to the smaller PSF (and hus lower internal background) compared to XMM.," 4 shows the analogous plot for the band with the Chandra ACIS S3 chip, with the count threshold reduced to 10 counts owing to the smaller PSF (and thus lower internal background) compared to XMM."60 The majority of the detected objects contributing to the yields are quite close o the count thresholds., The majority of the detected objects contributing to the yields are quite close to the count thresholds.61 For example. if the XMM threshold is increased to 40 counts. the yield of Compton-thick (Compton-hin plus unobscured) AGN falls over all redshift by a factor 2—3 (1.5—2).," For example, if the XMM threshold is increased to 40 counts, the yield of Compton-thick (Compton-thin plus unobscured) AGN falls over all redshift by a factor 2–3 (1.5–2)."62 Similarly. increasing the Chandra detection threshold to 15 counts. results in a fall by a factor of 2.5 in the yield of Compton- objects. whilst the number of Compton-thin and unobscured objects are relatively unchanged.," Similarly, increasing the Chandra detection threshold to 15 counts, results in a fall by a factor of 2.5 in the yield of Compton-thick objects, whilst the number of Compton-thin and unobscured objects are relatively unchanged."63 Most of the predicted Compton-thick sources should become detectable in exposures of IMs (Fig., Most of the predicted Compton-thick sources should become detectable in exposures of 1Ms (Fig.64 5). such as are now being done with Chandra (e.g. Alexander et al 2001: Rosati et al 2001).," 5), such as are now being done with Chandra (e.g. Alexander et al 2001; Rosati et al 2001)."65 In an S4.S.L aremin? region and | Ms exposure we predict [82 sources (Compton thick and thin) in the 2-8 keV band whereas Alexander et al (2001) find 102., In an $8.4\times 8.4$ $^2$ region and 1 Ms exposure we predict 182 sources (Compton thick and thin) in the 2–8 keV band whereas Alexander et al (2001) find 102.66 We do not consider that this discrepancy in numbers is serious. since most of the sources would be close to the detection threshold.," We do not consider that this discrepancy in numbers is serious, since most of the sources would be close to the detection threshold."67 That many of the sources are seen in both soft and hard energy bands (Alexander et al 2001) is also not a major problem since a few per cent of the primary soft radiation may be scattered into our line of sight., That many of the sources are seen in both soft and hard energy bands (Alexander et al 2001) is also not a major problem since a few per cent of the primary soft radiation may be scattered into our line of sight.68 The important issue of the redshift distribution of the sources is considered in the next Section., The important issue of the redshift distribution of the sources is considered in the next Section.69 where we also discuss the implications of these resultsfor the interpretation of deep Chandra and XMM surveys., where we also discuss the implications of these resultsfor the interpretation of deep Chandra and XMM surveys.70? introduced the concept of completeness to study the selection ellects introduced by observatory architectures on clirect searches for sub-stellar Companions.,\citet{brown2004a} introduced the concept of completeness to study the selection effects introduced by observatory architectures on direct searches for sub-stellar companions.71 Assuming distributions for semi-major axis aud eccentricity of planetary orbits. Brown calculated the probability that a companion would fall outside the telescope's central obscuration during au observation of a star.," Assuming distributions for semi-major axis and eccentricity of planetary orbits, Brown calculated the probability that a companion would fall outside the telescope's central obscuration during an observation of a star."72 2? subsequently expauded this concept to include the selection ellects due to the photometric restrictions ou observability introduced. by telescope optics. and ? demonstrated how completeness could be evaluated for indirect Companion detection methods such as astrometry.," \citet{brown2005} subsequently expanded this concept to include the selection effects due to the photometric restrictions on observability introduced by telescope optics, and \citet{brown2009} demonstrated how completeness could be evaluated for indirect companion detection methods such as astrometry."73 Completeness has also, Completeness has also74is expected to start ~3 4 Myr alter the birth of a star cluster (Leitherer et al.,is expected to start $\sim$ 3 – 4 Myr after the birth of a star cluster (Leitherer et al.75 1999). the ages we have determined for the SSC £6 Myr) are consistent wilh such a supposition.," 1999), the ages we have determined for the SSC $\lsim 6$ Myr) are consistent with such a supposition."76 Given their measured radial velocities and estimated ages. the clusters must have formed within a few kpe of their current locations. unless their tangential velocities are considerably larger (han their radial velocities.," Given their measured radial velocities and estimated ages, the clusters must have formed within a few kpc of their current locations, unless their tangential velocities are considerably larger than their radial velocities."77 This latter feature rules out the idea (hat the clusters ormed at much larger radii in (he outer halo of the merging svstem. then fell into the nuclear regions:clusters.," This latter feature rules out the idea that the clusters formed at much larger radii in the outer halo of the merging system, then fell into the nuclear regions;."78 The alternative explanation. (hat we have caught the σος in the ejection phase. and that (he line splitting is caused by the ejection of gas by SSC [formed in the quiescent. diffuse gas (??7) is dillicult to reconcile with the observations.," The alternative explanation, that we have caught the SSC in the ejection phase, and that the line splitting is caused by the ejection of gas by SSC formed in the quiescent, diffuse gas \citep{Goodwin97a,Goodwin97b,Bastian06} is difficult to reconcile with the observations."79 Bi particular. in such a case it is not clear why (he component apparently at rest relative to the ambient gas has relatively broad lines and a [NII]6548/1Lo. ratio consistent with shocks or AGN photoionization. whereas the component shifted relative to the rest. [rane (presumably. the ejected component in (his scenario) has narrow lines and an HII region-like Πα. ratio characteristic of stellar photoionization: one would expect (he reverse {ο be (he case.," In particular, in such a case it is not clear why the component apparently at rest relative to the ambient gas has relatively broad lines and a $\alpha$ ratio consistent with shocks or AGN photoionization, whereas the component shifted relative to the rest frame (presumably the ejected component in this scenario) has narrow lines and an HII region-like $\alpha$ ratio characteristic of stellar photoionization; one would expect the reverse to be the case."80" Finally we note (hat. despite the apparently ""Iree-floating status indicated by (heir enussion line kinematics. (he SSC'/IILI regions are linked with a more extensive interstellar medium (ISAT) in (he host galaxies."," Finally we note that, despite the apparently “free-floating” status indicated by their emission line kinematics, the SSC/HII regions are linked with a more extensive interstellar medium (ISM) in the host galaxies."81 First. there is clear morphological evidence from our hieh resolution ACS images that the vong star clusters are associated with dust lanes in the host galaxy (see Figure 1).," First, there is clear morphological evidence from our high resolution ACS images that the young star clusters are associated with dust lanes in the host galaxy (see Figure 1)."82 Second. at the location of C1/€2. the grevscale representation of the long-slit spectrum (see Figure 11) shows a clear enhancement in (he fIux of the broad and narrow components. suggesting a link between (he HII regions and the more diffuse gas.," Second, at the location of C1/C2, the greyscale representation of the long-slit spectrum (see Figure 11) shows a clear enhancement in the flux of the broad and narrow components, suggesting a link between the HII regions and the more diffuse gas."83 It is interesting to compare our results for PNS1345—12 with previous studies of YSP in ULIRGs., It is interesting to compare our results for PKS1345+12 with previous studies of YSP in ULIRGs.84" ? carried out an IST imaging study concentrating on bright star forming, knots for a sample of nine ""warm ULIBGs. including PINS13454+12. using hieh resolution D- and I-band images taken with the Wide Field Planetary Camera on the IST."," \cite{Surace98} carried out an HST imaging study concentrating on bright star forming knots for a sample of nine “warm” ULIRGs, including PKS1345+12, using high resolution B- and I-band images taken with the Wide Field Planetary Camera on the HST."85 The stellar svnthesis models of ? were used (ο estimate the ages ancl masses of the bright knots in, The stellar synthesis models of \cite{Bruzual93} were used to estimate the ages and masses of the bright knots in86position of the high energv 5 rav peak.,position of the high energy $\gamma$ –ray peak.87 However. from. the decontamination we performed. the spectrum appears consistently to extend. to the higher detected: intrinsic energies. Le. 280 keV in the blazar rest. frame.," However, from the decontamination we performed, the spectrum appears consistently to extend to the higher detected intrinsic energies, i.e. 280 keV in the blazar rest frame."88 At the lowest energies. «1 keV. the BeppoSAX observations robustly confirmed the presence of a fattening in the spectrum found in the ROSAT PSPC spectrum (Boller et al.," At the lowest energies, $< 1$ keV, the $Beppo$ SAX observations robustly confirmed the presence of a flattening in the spectrum found in the ROSAT PSPC spectrum (Boller et al."89 2000)., 2000).90 Secondly. below 0.4 keV emission a factor  20 in excess of the [attened spectrum has been found (see Fig.," Secondly, below 0.4 keV emission a factor $\sim$ 20 in excess of the flattened spectrum has been found (see Fig."91 1)., 1).92 The origin of the Πα{οπής has been discussed in some detail by several authors (CapX οἱ al 1997. Fiore et al 1998. Elvis et al 1998. Boller οἱ al 2000. Yuan ct al 2000. Fabian et al 2000. Reeves Turner 2000). but no «elinite conclusion could. be crawn.," The origin of the flattening has been discussed in some detail by several authors (Cappi et al 1997, Fiore et al 1998, Elvis et al 1998, Boller et al 2000, Yuan et al 2000, Fabian et al 2000, Reeves Turner 2000), but no definite conclusion could be drawn."93 Certainly. the detection of such feature by dilleren instruments (ROSAT. ASCA. DeppoS AN) argues. agains any svstematic mis-calibration ellect.," Certainly, the detection of such feature by different instruments (ROSAT, ASCA, $Beppo$ SAX) argues against any systematic mis-calibration effect."94 The first interesting point which has been mace is tha the [lattening scems to be associated only with radiolou objects. therefore suggesting its origin to be intrinsic.," The first interesting point which has been made is that the flattening seems to be associated only with radio–loud objects, therefore suggesting its origin to be intrinsic."95 The number of good quality X-ray spectra of radio.quiet quasars ab zoc1.5 ds unfortunately limitec., The number of good quality X-ray spectra of radio–quiet quasars at $z> 1.5$ is unfortunately limited.96" However. the recen results by Vignali et al (2000). combined with the findings w Reeves ""Turner (2000). imply that in only 2 out of 15 radioquiet quasars (in the range 2=LS2.5) a positive detection of Dlattening corresponding to Ny1077 em ws been established. despite the biased selection of XNrav oud sources."," However, the recent results by Vignali et al (2000), combined with the findings by Reeves Turner (2000), imply that in only 2 out of 15 radio–quiet quasars (in the range $z=1.8-2.5$ ) a positive detection of flattening corresponding to $N_H \sim 10^{22}$ $^{-2}$ has been established, despite the biased selection of X–ray loud sources."97 For comparison. 5 out of 6 radioloud objects in the same redshift range have equivalent Nyz1077E em2 (sce Fig.," For comparison, 5 out of 6 radio–loud objects in the same redshift range have equivalent $N_H \ge 10^{22}$ $^{-2}$ (see Fig."98 6)., 6).99 We therefore favour the possibility that the lattening is due το an intrinsic property of the source. »ossiblv associated with the radioloudness. phenomenon.," We therefore favour the possibility that the flattening is due to an intrinsic property of the source, possibly associated with the radio–loudness phenomenon."100 evertheless we note that radio-Ioud objects tend to be more Xrav luminous and so vield the best spectra at a given redshift ancl therefore in the following we also discuss the »xossible role of absorption of intergalactic origin., Nevertheless we note that radio-loud objects tend to be more X–ray luminous and so yield the best spectra at a given redshift and therefore in the following we also discuss the possible role of absorption of intergalactic origin.101 We consider it unlikely that large (galactic) scale gas is responsible for the Nray absorption. given the large masses of gas implied by such hypothesis as well as the lack of any clear connection with the radioloud phenomenon.," We consider it unlikely that large (galactic) scale gas is responsible for the X–ray absorption, given the large masses of gas implied by such hypothesis as well as the lack of any clear connection with the radio–loud phenomenon."102 Vherefore in the followingὃν we concentrate on the nuclear and/or Cosmological properties which could account for such eature., Therefore in the following we concentrate on the nuclear and/or cosmological properties which could account for such feature.103 A further Κον piece of information is the presence of a systematic trend. of the Hattening in the spectra of radiooucl quasars to increase with redshift. (Cappi et al 1997. Fiore et al.," A further key piece of information is the presence of a systematic trend of the flattening in the spectra of radio--loud quasars to increase with redshift (Cappi et al 1997, Fiore et al."104 1998. Reeves Turner 2000).," 1998, Reeves Turner 2000)."105 The inclusion. of the recent. results on UNJI028.6-0844. (Yuan et al 2000). PAINO525-3343 (Fabian et al 2000) and €DI428|4217 itself strengthens and extends his behavior up to zc4.7. as shown in Fig.," The inclusion of the recent results on RXJ1028.6-0844 (Yuan et al 2000), PMN0525-3343 (Fabian et al 2000) and GB1428+4217 itself strengthens and extends this behavior up to $z\ge 4.7$, as shown in Fig."106 6., 6.107 Although no correlation. between the flattening and other spectral woperty has been previously found. we stress the possible oesence of a significant trend of increasing Ny with increasing hard X.rav (intrinsic 210 keV band) luminosity. as can be argued [rom Fig.," Although no correlation between the flattening and other spectral property has been previously found, we stress the possible presence of a significant trend of increasing $N_{\rm H}$ with increasing hard X–ray (intrinsic 2–10 keV band) luminosity, as can be argued from Fig."108 7., 7.109 Unfortunately small statistics do not allow us to cisentangle the redshift and. luminosity. dependences., Unfortunately small statistics do not allow us to disentangle the redshift and luminosity dependences.110 1n Fig., In Fig.111 6 we also show the line-of-sight value of Ny due to the intergalactic medium (IGM). assumine solar abundances., 6 we also show the line-of-sight value of $N_{\rm H}$ due to the intergalactic medium (IGM) assuming solar abundances.112 I£ the IGM was enriched by redshifts of abou 4 to the same metallicity as clusters of galaxies then the correlation with redshift could be explained., If the IGM was enriched by redshifts of about 4 to the same metallicity as clusters of galaxies then the correlation with redshift could be explained.113 As cliscussec in the ROSAT PSPC work on GB 1428|4217 Boller et a 2000) this conclusion does not agree with observations of the metallicity of the Lyman à forest., As discussed in the ROSAT PSPC work on GB 1428+4217 (Boller et al 2000) this conclusion does not agree with observations of the metallicity of the Lyman $\alpha$ forest.114 Only if there was a strong correlation between enrichment and temperature of the IGM phase might some agreement occur. but even then the enrichment requirements would be huge.," Only if there was a strong correlation between enrichment and temperature of the IGM phase might some agreement occur, but even then the enrichment requirements would be huge."115 A more. plausible interpretation of the apparen correlation shown in Fig., A more plausible interpretation of the apparent correlation shown in Fig.116 6 would then be that it arises from, 6 would then be that it arises from117of the core mass.,of the core mass.118" Note that equations (la-b) of being written as proportionalities. they are valid when fig9«fuos. and not just when toro,fas."," Note that equations (1a-b) of being written as proportionalities, they are valid when $\tau_{GExp} \propto \tau_{cross}$, and not just when $\tau_{GExp} \simeq \tau_{cross}$."119 The energy-driven feedback model. however. shows that gas can be expelled on time-scales shorter or longer than a erossing-time (see Fig. 7).," The energy-driven feedback model, however, shows that gas can be expelled on time-scales shorter or longer than a crossing-time (see Fig. \ref{fig:fb0p03}) )."120" One may be puzzled by a gas expulsion time-scale Tog longer than a core erossing-time 7,4, since it implies a gas velocity slower than the core escape velocity VW.", One may be puzzled by a gas expulsion time-scale $\tau_{GExp}$ longer than a core crossing-time $\tau_{cross}$ since it implies a gas velocity slower than the core escape velocity $V_e$.121 Yet. this is not necessarily surprising.," Yet, this is not necessarily surprising."122 The escape velocity is defined for objects subjected solely to gravity. while the shell of gas. in addition to being subjected to its own self-gravity. keeps being powered and pushed outwards by continuing stellar winds. ionized region over-pressure. etc.," The escape velocity is defined for objects subjected solely to gravity, while the shell of gas, in addition to being subjected to its own self-gravity, keeps being powered and pushed outwards by continuing stellar winds, ionized region over-pressure, etc."123 In other words. a shell velocity slower than the core escape velocity may not necessarily preclude the gas from being unbound from its parent core.," In other words, a shell velocity slower than the core escape velocity may not necessarily preclude the gas from being unbound from its parent core."124 Within the paradigm that most stars form in gas-embedded clusters. cluster infant weight-loss and infant mortality appear as significant drivers of galaxy field star populations2008).," Within the paradigm that most stars form in gas-embedded clusters, cluster infant weight-loss and infant mortality appear as significant drivers of galaxy field star populations."125". Consequently. reconstructing the star formation history of galaxies from their cluster age distribution requires a firm grasp on the time-evolution of the integrated bound Taction μι. that is. the bound fraction 75,4 of stars integrated over the core mass function at a given age2009)."," Consequently, reconstructing the star formation history of galaxies from their cluster age distribution requires a firm grasp on the time-evolution of the integrated bound fraction $\overline{F_{bound}}$, that is, the bound fraction $F_{bound}$ of stars integrated over the core mass function at a given age."126. As we now illustrate. this also requires a fair knowledge of he core mass-radius relation.," As we now illustrate, this also requires a fair knowledge of the core mass-radius relation."127 Building on the compact models of Fig., Building on the compact models of Fig.128" 3 (e. Doge=Skpe and Dog= 4&pey. Table 2 illustrates how75,,,5,/! varies with he slope 9 of the core mass-radius relation. and with the upper imit 7n, and slope PB of a power-law core mass function dNxmPum,"," \ref{fig:fb} (i.e. $D_{gal}=8\,kpc$ and $D_{gal}=4\,kpc$ ), Table \ref{tbl:gal} illustrates how$\overline{F_{bound}}$ varies with the slope $\delta$ of the core mass-radius relation, and with the upper limit $m_{up}$ and slope $-\beta$ of a power-law core mass function $dN \propto m^{-\beta} dm$."129" We consider two upper limits to the core mass range to illustrate the sensitivity of 5,,,/ to this parameter.", We consider two upper limits to the core mass range to illustrate the sensitivity of $\overline{F_{bound}}$ to this parameter.130" In he left part of Table 2.. 14)=3x107AL, is the upper limit to he mass range of the data shown in Fig. |.."," In the left part of Table \ref{tbl:gal}, $m_{up}=3 \times 10^4\,M_{\sun}$ is the upper limit to the mass range of the data shown in Fig. \ref{fig:obs},"131 and from which we obtain the normalizations of our core mass-radius relations., and from which we obtain the normalizations of our core mass-radius relations.132" In the right part. we adopt 7,5=107M..."," In the right part, we adopt $m_{up}=10^7\,M_{\sun}$."133 While most reported young cluster mass functions have B.~2 (see references in Section 4.1). he mass function of molecular cores is shallower with B1.71998)..," While most reported young cluster mass functions have $\beta \simeq 2$ (see references in Section \ref{subsec:mf}) ), the mass function of molecular cores is shallower with $\beta \simeq 1.7$."134 Given that uncertainty. Table 2 considers both cases p," Given that uncertainty, Table \ref{tbl:gal} considers both cases ."135rep).. When D<2. ligher-mass cores contribute a greater fraction of the total gas mass than their low-mass counterparts.," When $\beta < 2$, higher-mass cores contribute a greater fraction of the total gas mass than their low-mass counterparts."136" For instance. B=1.7 leads Oo cores more massive than 109A... to contribute ~50 For Peore models. F5, 1s independent of the core mass ‘unction parameters B and nn, since clusters experience mass-independent infant weigth-loss."," For instance, $\beta =1.7$ leads to cores more massive than $10^6\,M_{\sun}$ to contribute $\simeq 50$ For $\rho_{core}$ models, $\overline{F_{bound}}$ is independent of the core mass function parameters $\beta$ and $m_{up}$ since clusters experience mass-independent infant weigth-loss."137" As quoted earlier. the compact roore and βίος models do not lead to significantly different FrewUMeore) relations. which arealso similar for both D,=8kpe and (Fig. 39."," As quoted earlier, the compact $r_{core}$ and $\rho_{core}$ models do not lead to significantly different $F_{bound}(m_{core})$ relations, which arealso similar for both $D_{gal}=8kpc$ and $D_{gal}=4kpc$ (Fig. \ref{fig:fb}) )."138" This is a direct consequence of having rjr,0.05 (no or weak tidal field impact) over the whole core mass range 102- 107 M... for the rare and Peore models when D,z:A&pe (Fig. 4).", This is a direct consequence of having $r_h/r_t \lesssim 0.05$ (no or weak tidal field impact) over the whole core mass range $10^2$ $10^7$ $M_{\sun}$ for the $r_{core}$ and $\rho_{core}$ models when $D_{gal} \geq 4kpc$ (Fig. \ref{fig:crr}) ).139 As u result. the integrated bound fraction is ο0.3 for rio and po; models at Dog= 4-8 kkpe. irrespective of 6 and mu.," As a result, the integrated bound fraction is $\overline{F_{bound}} \simeq 0.3$ for $r_{core}$ and $\rho_{core}$ models at $D_{gal}=4$ $8$ kpc, irrespective of $\delta$ and $m_{up}$."140" In contrast. to raise 7/7, from LOTSM... to 10M... reduces Fround tor Leore models since in that case higher-mass embedded clusters are more efficiently destroyed than. their low-mass counterparts."," In contrast, to raise $m_{up}$ from $10^{4.5}\,M_{\sun}$ to $10^7\,M_{\sun}$ reduces $\overline{F_{bound}}$ for $\Sigma _{core}$ models since in that case higher-mass embedded clusters are more efficiently destroyed than their low-mass counterparts."141" Besides. this sensitivity of the integrated bound fraction 75,4 to the core mass upper limit is strengthened for shallow power-law core mass functions (B=1.7) and/or in case of stronger tidal field (e.g. D,=J&pe instead of Dy;=δκρο)."," Besides, this sensitivity of the integrated bound fraction $\overline{F_{bound}}$ to the core mass upper limit is strengthened for shallow power-law core mass functions $\beta=1.7$ ) and/or in case of stronger tidal field (e.g. $D_{gal} = 4kpc$ instead of $D_{gal} = 8kpc$ )."142 Independently of the tidal field impact. we note that the cluster-forming core mass-radius relation is also relevant to the two topics discussed in the next sections.," Independently of the tidal field impact, we note that the cluster-forming core mass-radius relation is also relevant to the two topics discussed in the next sections."143 The mass-radius relation of cluster-forming cores also determines their mean density and crossing-time Type. thus how fast clusters experience infant weight-loss following gas-expulsion: the shorter the core crossing-time. the faster cluster evolution through violent relaxation.," The mass-radius relation of cluster-forming cores also determines their mean density and crossing-time $\tau_{cross}$, thus how fast clusters experience infant weight-loss following gas-expulsion: the shorter the core crossing-time, the faster cluster evolution through violent relaxation."144 If cluster-forming cores have a constant surface density. more massive clusters evolve more slowly than their low-mass counterparts owing to their lower volume density. hence longer crossing-time.," If cluster-forming cores have a constant surface density, more massive clusters evolve more slowly than their low-mass counterparts owing to their lower volume density, hence longer crossing-time."145 In contrast. if cluster-forming cores have a constant radius. more massive clusters have a higher density. thus shorter crossing-time and the duration of their violent relaxation (in units of Myr) is shorter (see fig.," In contrast, if cluster-forming cores have a constant radius, more massive clusters have a higher density, thus shorter crossing-time and the duration of their violent relaxation (in units of Myr) is shorter (see fig."146 | in for an application to the time-evolution of the cluster mass function)., 1 in for an application to the time-evolution of the cluster mass function).147 Constant volume density cores are all characterised by the same crossing-time and. thus. evolve at the same rate through violent relaxation regardless of their mass.," Constant volume density cores are all characterised by the same crossing-time and, thus, evolve at the same rate through violent relaxation regardless of their mass."148" If the mean number density of cluster-forming cores is nj,77IQemI. unsO.35Mvr and all cluster stars due to become unbound owing to gas expulsion have erossed the tidal radius boundary by a cluster age of at most LOOTposs or MMyr."," If the mean number density of cluster-forming cores is $n_{H_2}\simeq10^4\,cm^{-3}$, $\tau_{cross}\simeq 0.45Myr$ and all cluster stars due to become unbound owing to gas expulsion have crossed the tidal radius boundary by a cluster age of at most $100 \tau_{cross}$ or Myr."149" If the core mean number density is 10 times higher. 7j,IQem.ὃς then Toss7O15Mvr. implying that violent relaxation is over by an age of ~I5 MMyr."," If the core mean number density is 10 times higher, $n_{H_2}\simeq10^5\,cm^{-3}$, then $\tau_{cross}\simeq 0.15Myr$, implying that violent relaxation is over by an age of $\simeq 15$ Myr."150" The core mass-radius relation is also relevant to self-enrichment models of old globular clusters. in which the cluster-forming core is often referred to as a ""protoglobular cloud’."," The core mass-radius relation is also relevant to self-enrichment models of old globular clusters, in which the cluster-forming core is often referred to as a `protoglobular cloud'."151 Blue populations of globular clusters in elliptical galaxies show a blue-tilt. i.e. brighter clusters are redder than their fainter counterparts.," Blue populations of globular clusters in elliptical galaxies show a `blue-tilt', i.e. brighter clusters are redder than their fainter counterparts."152 This colour-magnitude relation is often interpreted as the imprint of the higher efficiency of more massive clusters to retain type II supernova ejecta and to achieve greater metallicity., This colour-magnitude relation is often interpreted as the imprint of the higher efficiency of more massive clusters to retain type II supernova ejecta and to achieve greater metallicity.153 It must be borne in mind. however. that such a conclusion sensitively depends on the slope of the core mass-radius relation.," It must be borne in mind, however, that such a conclusion sensitively depends on the slope of the core mass-radius relation."154 While infer a positive slope for their predicted mass-metallicity relation. predict that massive clusters are more metal-rich.," While infer a positive slope for their predicted mass-metallicity relation, predict that massive clusters are more metal-rich."155 This discrepancy arises because of different assumed core mass-radius relations., This discrepancy arises because of different assumed core mass-radius relations.156 build on either constant protoglobular eloud radii or constant protoglobular cloud volume densities., build on either constant protoglobular cloud radii or constant protoglobular cloud volume densities.157" On the other hand. the model of (20013... applied to the Galactic Old Halo globular cluster system and developed before the ""blue-tilt in ellipticals was discovered. builds on pressure-bounded isothermal spheres for which ateare99 Feare."," On the other hand, the model of , applied to the Galactic Old Halo globular cluster system and developed before the `blue-tilt' in ellipticals was discovered, builds on pressure-bounded isothermal spheres for which $m_{core}\propto r_{core}$ ."158 Their conclusion that less massive clusters are more metal-rich arises because type IT supernova ejecta mix with a lower amount of primordial gas., Their conclusion that less massive clusters are more metal-rich arises because type II supernova ejecta mix with a lower amount of primordial gas.159 Contrasting the models of and therefore illustrates that the slope of the globular cluster mass-metallicity, Contrasting the models of and therefore illustrates that the slope of the globular cluster mass-metallicity160interacting particles are non-degenerate (1.e.. dilute) and non-relativistic (1e.. their rest mass energy is large compared to KT).,"interacting particles are non-degenerate (i.e., dilute) and non-relativistic (i.e., their rest mass energy is large compared to $kT$ )."161 Hence. one can use a Maxwell-Boltzmann velocity distribution with Newtonian kinetic energy because where the exponential factor involving the rest mass energy drops out with a proper normalization of the distribution function.," Hence, one can use a Maxwell-Boltzmann velocity distribution with Newtonian kinetic energy because where the exponential factor involving the rest mass energy drops out with a proper normalization of the distribution function."162 Also note that when both particles 1 and 2 obey Maxwell-Boltzmann statistics. so does their relative velocity (Clayton1968).," Also note that when both particles $1$ and $2$ obey Maxwell-Boltzmann statistics, so does their relative velocity \citep{cla68}."163. Hence. the thermally averaged capture rate per particle pair is given by where µ denotes the reduced mass for the particles 1 and 2.," Hence, the thermally averaged capture rate per particle pair is given by where $\mu$ denotes the reduced mass for the particles $1$ and $2$."164 In the photodisintegration reaction rate. however. the relative velocity of the photon with respect to the target nucleus is always the speed of light c.," In the photodisintegration reaction rate, however, the relative velocity of the photon with respect to the target nucleus is always the speed of light $c$."165 This eliminates any dependence of the reaction rate on the velocity distribution of the target nucler (Thielemannetal.1998)., This eliminates any dependence of the reaction rate on the velocity distribution of the target nuclei \citep{thi98}.166. Therefore. the photonuclear reaction rate (0cj-3 becomes an integral of the reaction eross section over a Planck energy distribution for the photons: Using the fact that for a Planck distribution we can equivalently write Eq. (7))," Therefore, the photonuclear reaction rate $\langle\sigma c\rangle_{\gamma3}$ becomes an integral of the reaction cross section over a Planck energy distribution for the photons: Using the fact that for a Planck distribution we can equivalently write Eq. \ref{eq:Inverse Reaction Rate}) )"167 in more familiar form where ¢(3)=1.20206 isthe Riemann zeta function and E. denotes the photon energy., in more familiar form where $\zeta(3) = 1.20206$ isthe Riemann zeta function and $E_{\gamma}$ denotes the photon energy.168 The integration threshold is the Q- value of the capture reaction (seeFigure 1)) or zero in the case of negative Q., The integration threshold is the $Q$ -value of the capture reaction (seeFigure \ref{fig:Energy Figure}) ) or zero in the case of negative $Q$.169 It is difficult to determine the cross section 7-3 directly from experiment., It is difficult to determine the cross section $\sigma_{\gamma3}$ directly from experiment.170 However. the interaction between photons and matter is very weak (e/hc<1) so that the reaction can be treated with first order perturbation theory.," However, the interaction between photons and matter is very weak $(e^{2}/\hbar c\ll1)$ so that the reaction can be treated with first order perturbation theory."171 In this case. the transition probabilities become proportional to the matrix elements of the perturbing Hamiltonian and the hermiticity of the perturbing Hamiltonian gives rise to a simple relation between the capture and disintegration cross sections.," In this case, the transition probabilities become proportional to the matrix elements of the perturbing Hamiltonian and the hermiticity of the perturbing Hamiltonian gives rise to a simple relation between the capture and disintegration cross sections."172 This is known as the (Blatt&Weisskopf 199])., This is known as the \citep{bla91}.173. Fora reaction involving a ground-state to ground-state transition for two nuclei with energy £. leading to a gamma ray with energy E.=EQ this is given by where sg;=2j;1 are the spin degeneracy factors for the ground state of the nuclei and the Kronecker delta function accounts for the special case of indistinguishable interacting nuclei.," For a reaction involving a ground-state to ground-state transition for two nuclei with energy $E$, leading to a gamma ray with energy $E_{\gamma}=E+Q$ this is given by where $g_{i} = 2 j_i + 1 $ are the spin degeneracy factors for the ground state of the nuclei and the Kronecker delta function accounts for the special case of indistinguishable interacting nuclei."174 Using this detailed balance equation.the photodisintegration rate for a single-state transition can be related to the forward capture rate.," Using this detailed balance equation,the photodisintegration rate for a single-state transition can be related to the forward capture rate."175 Substituting Eq. (10)), Substituting Eq. \ref{eq:Detailed Balance}) )176 into Eq. (7)), into Eq. \ref{eq:Inverse Reaction Rate}) )177 and also changing the variable from E. to E=E.—Q in the integration. one can average over the velocity distribution of the ground-state interacting nuclei (σον as follows: At this point. one usually introduces the approximation: Here. we point out that by inserting this approximation and then correcting for it. Eq. (11))," and also changing the variable from $E_{\gamma}$ to $E=E_{\gamma}-Q$ in the integration, one can average over the velocity distribution of the ground-state interacting nuclei $\langle\sigma c\rangle_{\gamma3}$ as follows: At this point, one usually introduces the approximation: Here, we point out that by inserting this approximation and then correcting for it, Eq. \ref{eq:Inverse Reaction Rate 2}) )"178 can be rewritten in the following exact form: where R is a small and dimensionless number which ts formally given by The generalization. of Eq. (13)), can be rewritten in the following exact form: where $R$ is a small and dimensionless number which is formally given by The generalization of Eq. \ref{eq:Ratio of Reaction Rates 3}) )179 to the average over thermally populated states among the initial and final nuclei is straightforward (Clayton1968:Iliadis.2007).," to the average over thermally populated states among the initial and final nuclei is straightforward \citep{cla68, Iliadis07}."180. One must first replace the ground state (g.s.), One must first replace the ground state (g.s.)181 to g.s., to g.s.182 forward reaction cross section 74» with a weighted average over the thermal population of states µ in the target nucleus |. and also sum over all final states 1n product nucleus 3. (," forward reaction cross section $\sigma_{1 2}$ with a weighted average over the thermal population of states $\mu$ in the target nucleus 1, and also sum over all final states in product nucleus $3$ . ("183Note that we only consider light particle (p.5). G15). or (0.5). reactions for which we can ignore their excitation.),"Note that we only consider light particle $(p,\gamma)$, $(n,\gamma)$, or $(\alpha,\gamma)$, reactions for which we can ignore their excitation.)"184 Thus. the effective stellar thermal forward rate becomes which can also be written as where the stellar enhancement factor Αι is defined by Usually. tabulated thermonuclear reaction rates are given as the ground state rate and the stellar enhancement factor must be determined from a statistical model calculation as in Holmesetal. (1976)... Woosleyet.al. (1978).. Rauscher and Rauscher&Thielemann (2004). ," Thus, the effective stellar thermal forward rate becomes which can also be written as where the stellar enhancement factor $R_{t t}$ is defined by Usually, tabulated thermonuclear reaction rates are given as the ground state rate and the stellar enhancement factor must be determined from a statistical model calculation as in \cite{Holmes76}, , \cite{Woosley78}, , \cite{Rauscher00} and \cite{Rauscher04}. ."185The thermally averaged photonuclear rate for a distribution of excitedstates in initial and final heavy nuclei then becomes The generalization of the detailed balance condition of Eq. (13)), The thermally averaged photonuclear rate for a distribution of excitedstates in initial and final heavy nuclei then becomes The generalization of the detailed balance condition of Eq. \ref{eq:Ratio of Reaction Rates 3}) )186 Is, is187Absorption from ionized matter in. the. X-ray spectrum of AGN (the so-called warm absorber) was discovered many years ago (Halpern 1984).,Absorption from ionized matter in the X-ray spectrum of AGN (the so-called warm absorber) was discovered many years ago (Halpern 1984).188 Since then. many advances in its understanding have been made. and we know now that it is present in about half of Seyfert galaxies (e.g. Reynolds 1997) and that the matter is photoronized.," Since then, many advances in its understanding have been made, and we know now that it is present in about half of Seyfert galaxies (e.g. Reynolds 1997) and that the matter is photoionized."189 Warm absorbers are also known to vary. and indeed the first discovered absorber was variable (Halpern 1984).," Warm absorbers are also known to vary, and indeed the first discovered absorber was variable (Halpern 1984)."190 The location of the warm absorber (or. indeed. of the absorbers. as more than one tonizing zone is often found) is. however. largely uncertain.," The location of the warm absorber (or, indeed, of the absorbers, as more than one ionizing zone is often found) is, however, largely uncertain."191 There is some evidence for its origin as a wind from the dusty torus envisaged in unification models for Seyfert galaxies (Blustin et al., There is some evidence for its origin as a wind from the dusty torus envisaged in unification models for Seyfert galaxies (Blustin et al.192 2005). but cases in which an origin from the disk seems to be preferred do also exist (Krongold et al.," 2005), but cases in which an origin from the disk seems to be preferred do also exist (Krongold et al."193 2007)., 2007).194 Mrk 704 ts a local (220.029234) Seyfert 1.2 galaxy (Veron-Cetty Veron 2010). bright enough in X-rays to be detected by Swift/BAT (Ajello et al.," Mrk 704 is a local $z$ =0.029234) Seyfert 1.2 galaxy (Veron-Cetty Veron 2010), bright enough in X-rays to be detected by $Swift$ /BAT (Ajello et al."195 2008)., 2008).196 In this paper we report on extreme warm absorber variability. on yearly time scales. revealed by two XMM-Newton observations. and possible variability on monthly time scales from short Swift/XRT observations.," In this paper we report on extreme warm absorber variability, on yearly time scales, revealed by two $Newton$ observations, and possible variability on monthly time scales from short Swift/XRT observations."197 The paper is organized as follows: in Section 2 we report on the XMM-Newton observations and data reduction. while the relative data analysis are discussed in Section 3.," The paper is organized as follows: in Section 2 we report on the $Newton$ observations and data reduction, while the relative data analysis are discussed in Section 3."198 Section 4 presents the analysis of the Suvfr and ASCA observations. while the results are summarized and discussed in Section 5.," Section 4 presents the analysis of the $Swift$ and $ASCA$ observations, while the results are summarized and discussed in Section 5."199 XMM-Newton observed Mrk 704 twice. on 2005-10- (OBSID:: 0300240101) and on 2008-11-02(OBSID: 0502091601).," $Newton$ observed Mrk 704 twice, on 2005-10-21 : 0300240101) and on 2008-11-02: 0502091601)."200 In both cases. EPIC pn and MOS were in Small Window mode (apart from MOS? in the first observation. which was in Full Frame mode). which ensures that no significant pile-up is present. as verified with the tool. in the pn detectors (the only one used for the analysis).," In both cases, EPIC pn and MOS were in Small Window mode (apart from MOS2 in the first observation, which was in Full Frame mode), which ensures that no significant pile-up is present, as verified with the tool, in the pn detectors (the only one used for the analysis)."201 Mrk 704 is by far the brightest source in the field of view., Mrk 704 is by far the brightest source in the field of view.202 Data were reduced with 10.0.0. using calibration files generated on 2010-6-11.," Data were reduced with 10.0.0, using calibration files generated on 2010-6-11."203 Screening for intervals of flaring particle background was done consistently with the choice of extraction radi. in an iterative process based on the procedure to maximize the signal-to-noise ratio described by Piconcellt et al. (," Screening for intervals of flaring particle background was done consistently with the choice of extraction radii, in an iterative process based on the procedure to maximize the signal-to-noise ratio described by Piconcelli et al. ("2042005).,2005).205 After this process. the net exposure time was of about 15 and 68 ks for the 2005 and the 2008 observation. respectively. adopting extraction radit of 36 and 40 aresec. and patterns O to 4.," After this process, the net exposure time was of about 15 and 68 ks for the 2005 and the 2008 observation, respectively, adopting extraction radii of 36 and 40 arcsec, and patterns 0 to 4."206 The background spectra were extracted from source-free circular regions with a radius of 50 aresec., The background spectra were extracted from source-free circular regions with a radius of 50 arcsec.207 The same regions were used for the timing analysis., The same regions were used for the timing analysis.208 Spectra were binned in order to oversample the instrumental resolution by at least a factor of 3 and to have no less than 30 counts in each background-subtracted spectral channel., Spectra were binned in order to oversample the instrumental resolution by at least a factor of 3 and to have no less than 30 counts in each background-subtracted spectral channel.209 The latter requirement allows us to use the y statistics as a goodness-of-fit-test., The latter requirement allows us to use the $\chi^2$ statistics as a goodness-of-fit-test.210 RGS source and background spectra were extracted with standard procedures. adopting the data reduction pipelineRGSPROC.. and choosing the NED optical nucleus of Mrk 704 as the reference point for the attitude solution.," RGS source and background spectra were extracted with standard procedures, adopting the data reduction pipeline, and choosing the NED optical nucleus of Mrk 704 as the reference point for the attitude solution."211 We will use in this paper only data from the EPIC pn and the RGS camera. because after the latest release of the EPIC pn redistribution and the RGS contamination model (May 2010) their cross-calibration is as good as (A. Pollock. private communication).," We will use in this paper only data from the EPIC pn and the RGS camera, because after the latest release of the EPIC pn redistribution and the RGS contamination model (May 2010) their cross-calibration is as good as (A. Pollock, private communication)."212 In Fig., In Fig.213 1. the 2-10 keV (upper panel). 0.3-2 keV. (middle panel) and the (2-10 keV)/(0.3-2 keV) hardness ratio (HR) light curves are shown for the first (left) and the second (right)," \ref{lc_obs} the 2-10 keV (upper panel), 0.3-2 keV, (middle panel) and the (2-10 keV)/(0.3-2 keV) hardness ratio (HR) light curves are shown for the first (left) and the second (right)"214The author would like to thank Alariangcla Bernardi. Nacho ‘Trujillo and Michele Cappellari for useful communications and Ancrey= Ixravtsov. Robert οἱµια. Joshua Frieman. Nick Cinecdin and Steve Went for helpful discussions ane conversations.,"The author would like to thank Mariangela Bernardi, Nacho Trujillo and Michele Cappellari for useful communications and Andrey Kravtsov, Robert Feldmann, Joshua Frieman, Nick Gnedin and Steve Kent for helpful discussions and conversations."215 The author also eratefullv acknowledges the referee. comments that were helpful. in clarifying and improving the manuscript significantly., The author also gratefully acknowledges the referee comments that were helpful in clarifying and improving the manuscript significantly.216 10° , $10^{6}$ 2172008).,.218". The origin of this non-trivial result lies in two facts: First, at late times, the emission is dominated by photons emitted off-axis (from angles 0>>T'—!, see figure 1))."," The origin of this non-trivial result lies in two facts: First, at late times, the emission is dominated by photons emitted off-axis (from angles $\theta \gg \Gamma^{-1}$, see figure \ref{fig1}) )."219" Due to the strong dependence of the Doppler shift on the angle to the line of sight, these photons are seen at much lower energies than photons emitted on-axis."," Due to the strong dependence of the Doppler shift on the angle to the line of sight, these photons are seen at much lower energies than photons emitted on-axis."220" Second, at any given instance, an observer sees simultaneously photons that are emitted from a range of radii and angles eq. "," Second, at any given instance, an observer sees simultaneously photons that are emitted from a range of radii and angles (see eq. \ref{eq:t_N}) )."221"As each photon has a finite probability of (seebeing emitted5)). from a given radius, and is seen at a particular Doppler shift, the observed spectrum and flux can only be described in terms of probability density functions (see refsec:prob))."," As each photon has a finite probability of being emitted from a given radius, and is seen at a particular Doppler shift, the observed spectrum and flux can only be described in terms of probability density functions (see \\ref{sec:prob}) )."222 These functions provide a mathematical tool to describe the probability of photons to be emitted from radius r and into angle 0., These functions provide a mathematical tool to describe the probability of photons to be emitted from radius $r$ and into angle $\theta$.223" Using these functions, we calculated an analytical approximation to the observed spectrum (eq. 3.1)),"," Using these functions, we calculated an analytical approximation to the observed spectrum (eq. \ref{eq:f_nu}) ),"224 which is the main result of this work., which is the main result of this work.225 'The analytical approximation was tested with a Monte-Carlo simulation that tracks the evolution of thermal photons in relativistically expanding plasma refsec:numerics))., The analytical approximation was tested with a Monte-Carlo simulation that tracks the evolution of thermal photons in relativistically expanding plasma \\ref{sec:numerics}) ).226 The simplified analytical calculations(8 are found to be in very good agreement with the accurate numerical results figure , The simplified analytical calculations are found to be in very good agreement with the accurate numerical results (see figure \ref{fig2}) ).227"In spite of the success(see in reproducing2)). the low energy spectral slopes at late times, the theory is still not completed."," In spite of the success in reproducing the low energy spectral slopes at late times, the theory is still not completed."228" For parameters characterizing GRBs, the thermal peak naturally falls at the sub-MeV range (see (T$25.)refsec:numerical, esults)), all hencetheobservedpeakcannaturwWledhpl inadi"," For parameters characterizing GRBs, the thermal peak ( $T_{\max}^{ob}$ ) naturally falls at the sub-MeV range (see \\ref{sec:numerical_results}) ), hence the observed peak can naturally be explained as having a thermal origin."229"eerim clostgino.Hoe aspltéceabl edrawbac s. Since above ty the flux decays rapidly, F(t)«t? eq. 3.1)),"," However, a noticeable drawback of the theory as stated in this manuscript, is that the same parameters lead to very short characteristic time scale, $t_N \approx 10^{-5}$ s. Since above $t_N$ the flux decays rapidly, $F_{\nu}(t) \propto t^{-2}$ (see eq. \ref{eq:f_nu}) ),"230" one expects relatively weak thermal signal (seeat t>>ty, which can stilla be very short time."," one expects a relatively weak thermal signal at $t \gg t_N$, which can still be very short time."231" We note though, that the calculation of ty in equation 5 is based on the assumption of constant outflow velocity."," We note though, that the calculation of $t_N$ in equation \ref{eq:t_N} is based on the assumption of constant outflow velocity."232" This assumption is too simplified: in order to reach high Lorentz factor, the plasma needs to undergo an acceleration phase, and so the average Lorentz factor below the photosphere is less than the terminal Lorentz factor."," This assumption is too simplified: in order to reach high Lorentz factor, the plasma needs to undergo an acceleration phase, and so the average Lorentz factor below the photosphere is less than the terminal Lorentz factor."233" As a result, we expect that in practice the characteristic time scale relevant for thermal emission in GRBs is longer than the one considered in equation 5.."," As a result, we expect that in practice the characteristic time scale relevant for thermal emission in GRBs is longer than the one considered in equation \ref{eq:t_N}."234 The exact delay time depends on several uncertain conditions., The exact delay time depends on several uncertain conditions.235" One is the content of the fireball: for example, Poynting-flux dominated fireball is expected to have slower acceleration than matter dominated fireball 2002;Drenkhahn&SpruitGian-nios(Drenkhahn&Spruit2005,2006)."," One is the content of the fireball: for example, Poynting-flux dominated fireball is expected to have slower acceleration than matter dominated fireball \citep{Drenk02,DS02, GS05, GS06}."236". Another is the baryon load (Joka2010),, and in particular the baryon distribution along the jet (Morsonyetal.2007;Lazzati2009;Mizutaetal.2010): although in this manuscript we considered a steady outflow, clearly the outflow in GRBs is characterized by regions of higher and lower densities, and is thus not steady (edge effects due to the finite opening angle may also play a role at late times)."," Another is the baryon load \citep{Ioka10}, and in particular the baryon distribution along the jet \citep{MLB07, LMB09, MNA10}: although in this manuscript we considered a steady outflow, clearly the outflow in GRBs is characterized by regions of higher and lower densities, and is thus not steady (edge effects due to the finite opening angle may also play a role at late times)."237" An additional source of discrepancy between the theoretical predictions developed in this paper and the observed spectrum, lies in the fact that the theory here does not consider any additional, non-thermal radiative processes."," An additional source of discrepancy between the theoretical predictions developed in this paper and the observed spectrum, lies in the fact that the theory here does not consider any additional, non-thermal radiative processes."238" As shown here, photospheric emission is capable of reproducing the peak energy and the low energy spectral slope (o in the “Band” function) seen in GRBs (at late times)."," As shown here, photospheric emission is capable of reproducing the peak energy and the low energy spectral slope $\alpha$ in the “Band” function) seen in GRBs (at late times)."239" However, photospheric emission is not capable of of producing high energy photons (above T9.< MeV), as are seen in some GRBs by the LAT detector on board theFermi satellite."," However, photospheric emission is not capable of of producing high energy photons (above $T_{\max}^{ob} \lesssim \MeV$ ), as are seen in some GRBs by the LAT detector on board the satellite."240" The inclusion of high energy, non-thermal photons, necessitates additional radiative mechanisms, that must take place following dissipation processes that occur above the photosphere (e.g.,inGRBO080916Canalysisoutflow;seeZhang&Pe’er 2009)."," The inclusion of high energy, non-thermal photons, necessitates additional radiative mechanisms, that must take place following dissipation processes that occur above the photosphere \citep[e.g., in GRB080916C241analysis of the high energy emission imply Poynting dominated outflow;242see][]{ZP09}."243". Additional radiative mechanisms, such as synchrotron emission or Compton scattering, naturaly produce a broad band energy spectrum, and thus may contribute not only to the high energy spectrum but to the low energy part (below the thermal peak) as well."," Additional radiative mechanisms, such as synchrotron emission or Compton scattering, naturally produce a broad band energy spectrum, and thus may contribute not only to the high energy spectrum but to the low energy part (below the thermal peak) as well."244" The overall observed spectra below the thermal peak is thus generally expected to be hybrid- i.e., composed of both thermal and non-thermal parts."," The overall observed spectra below the thermal peak is thus generally expected to be hybrid- i.e., composed of both thermal and non-thermal parts."245" The exact contribution of the non-thermal part may vary from burst to burst, depending on the values of the free model parameters, such as the radius of the photosphere, the dissipation radius, the strength of the magnetic field, etc."," The exact contribution of the non-thermal part may vary from burst to burst, depending on the values of the free model parameters, such as the radius of the photosphere, the dissipation radius, the strength of the magnetic field, etc."246" In principle, the inclusion of thermal photons contributes to the high energy, non thermal part of the spectrum as well, as these photons serve as seed photons for Compton scattering by the non-thermal electrons and hot pairs (Rees&Mészáros2005;Pe'eret 2010)."," In principle, the inclusion of thermal photons contributes to the high energy, non thermal part of the spectrum as well, as these photons serve as seed photons for Compton scattering by the non-thermal electrons and hot pairs \citep{RM05, PMR05, PMR06, LazBeg10,247 Bel10}."248. The exact contribution of the thermal photons depend on the optical depth at the dissipation radius., The exact contribution of the thermal photons depend on the optical depth at the dissipation radius.249" alot the resulting adissibethawspectrum has a complex shape, that is very different than either a thermal spectrum or the optically thin synchrotron - synchrotron self Compton (SSC) model predictions (Pe'eretal.2005,2006).."," If the dissipation radius is close to the photosphere, the resulting spectrum has a complex shape, that is very different than either a thermal spectrum or the optically thin synchrotron - synchrotron self Compton (SSC) model predictions \citep{PMR05, PMR06}."250" On the other hand, if the dissipation occurs at large radii, the two components, thermal and non-thermal, can be decoupled, a fact that can lead to a clear identification of the thermal component, as is in the case of GRB090902B"," On the other hand, if the dissipation occurs at large radii, the two components, thermal and non-thermal, can be decoupled, a fact that can lead to a clear identification of the thermal component, as is in the case of GRB090902B"251"VI The above constraints can be shown to lead to four parameter sub-regimes where viable solutions exist in the Hall regime, and to three in the Ohm regime (I refer the reader to KSW10 for more details)."," The above constraints can be shown to lead to four parameter sub-regimes where viable solutions exist in the Hall regime, and to three in the Ohm regime (I refer the reader to KSW10 for more details)."252 The constraints for the Hall regime are summarised in Table 1.., The constraints for the Hall regime are summarised in Table \ref{table:constraints}.253 These are differentiated by the values of the combinations Beofio and 2Λο (=2To|Gio| in this limit) in comparison with unity.," These are differentiated by the values of the combinations $\beta_{\rm e 0} \beta_{\rm i 0}$ and $2\Lambda_{\rm 0}$ $=2542\Upsilon_{\rm 0} |\beta_{\rm i 0}|$ in this limit) in comparison with unity."255 Our numerical solutions (SKW11) confirm these predictions: We find that no physically-relevant solutions are found outside the boundaries specified by these constraints., Our numerical solutions (SKW11) confirm these predictions: We find that no physically-relevant solutions are found outside the boundaries specified by these constraints.256 We also explored the dependence of the solutions on the model parameters., We also explored the dependence of the solutions on the model parameters.257" We found that increasing the relative contribution of the Hall diffusivity results in a smaller magnetically-reduced density scale-height, and in a higher location above the disc midplane of both the base of the wind and the sonic surface."," We found that increasing the relative contribution of the Hall diffusivity results in a smaller magnetically-reduced density scale-height, and in a higher location above the disc midplane of both the base of the wind and the sonic surface."258" As a result, the density at the sonic point, and the associated mass outflow rate, are reduced."," As a result, the density at the sonic point, and the associated mass outflow rate, are reduced."259" Our calculations also show that, in all diffusivity regimes, viable solutions satisfy the requirement that the neutral — ion momentum exchange time be shorter than the disc orbital time (Y 1)."," Our calculations also show that, in all diffusivity regimes, viable solutions satisfy the requirement that the neutral – ion momentum exchange time be shorter than the disc orbital time $\Upsilon \gtrsim 1$ )."260" This is, therefore, a fundamental constraint on the wind solutions considered here."," This is, therefore, a fundamental constraint on the wind solutions considered here."261" Finally, we found that the magnetic field polarity modifies both the properties of the solutions and the parameter ranges where these exist when the Hall regime is dynamically important."," Finally, we found that the magnetic field polarity modifies both the properties of the solutions and the parameter ranges where these exist when the Hall regime is dynamically important."262" This reflects the dependence of the Hall diffusivity on the sign of B,.", This reflects the dependence of the Hall diffusivity on the sign of $B_z$.263" Specifically, our analysis shows that for two of the Hall sub-regimes (Cases { and iii in Table 1)), positive and"," Specifically, our analysis shows that for two of the Hall sub-regimes (Cases $i$ and $iii$ in Table \ref{table:constraints}) ), positive and"264The final step then is to correct the biasing parameter. b. for the luminosity of our sample.,"The final step then is to correct the biasing parameter, $b$, for the luminosity of our sample."265 Norberg (2001) found from the analysis of the galaxy correlation functions on scales <105. Mpe that. Assuming that this relation also holds in our quasi-linear regime of S20h.+ Mpe. then allows us to determine «3 at redshift 7=0 and luminosity L=L..7 Table 3. shows the results for .7 derived in the analysis presented here. both before and after converting to redshift +=0 and luminosity £= L..," Norberg (2001) found from the analysis of the galaxy correlation functions on scales $<10\;h^{-1}$ Mpc that, Assuming that this relation also holds in our quasi-linear regime of $8-20\;h^{-1}$ Mpc, then allows us to determine $\beta$ at redshift $z=0$ and luminosity $L=L_*$ Table \ref{tab:xires} shows the results for $\beta$ derived in the analysis presented here, both before and after converting to redshift $z=0$ and luminosity $L=L_*$."266 Also shown are other results derived from the 2dFGRS by previous authors., Also shown are other results derived from the 2dFGRS by previous authors.267 It can be seen that there is a remarkably good agreement between all the results presented., It can be seen that there is a remarkably good agreement between all the results presented.268 We note that these results have been derived by applyinglinear corrections to a selection ofquasi-linear regimes. which may introduce systematic errors into our results.," We note that these results have been derived by applying corrections to a selection of regimes, which may introduce systematic errors into our results."269 This is a particular concern for the results of Verde (2002). which correspond to the smallest separation ranges used.," This is a particular concern for the results of Verde (2002), which correspond to the smallest separation ranges used."270 We have derived a variety of different parameterisations for the 2dFGRS correlation function. €(o.7). for different spectral types.," We have derived a variety of different parameterisations for the 2dFGRS correlation function, $\xi(\sigma,\pi)$, for different spectral types."271 The two types we have used can roughly be interpreted as dividing our galaxy sample on the basis of their relative amount of current, The two types we have used can roughly be interpreted as dividing our galaxy sample on the basis of their relative amount of current272ng22.887505107? em. yielding ke2520075135 keV em.,"$n_R=2732.88^{+0.19}_{-0.19}\times 10^{-5}$ $^{-3}$ , yielding $k_R =2745200^{+2140}_{-2140}$ keV $^{2}$ ."275" Correspondingly. we find k,=363) keV em’."," Correspondingly, we find $k_c=36^{+20}_{-20}$ keV $^{2}$."276 Finally. from Eq. (," Finally, from Eq. ("2778) we derive the total mass M=1.222«10M...,"8) we derive the total mass $M= 1.2^{+0.7}_{-0.7}\times27810^{15}\,M_{\odot}$."279 Note that if one insisted on applying the SM also to temperature and brightness profiles from the centroid on the basis of Eqs. (, Note that if one insisted on applying the SM also to temperature and brightness profiles from the centroid on the basis of Eqs. (280"6) and (7). one would obtain r;=104*1 kpe and a related lower bound &,z12410 keV env.","6) and (7), one would obtain $r_f=104^{+4}_{-4}$ kpc and a related lower bound $k_c\approx 124^{+120}$ keV $^2$."281 The large variance in the above parameters entering the entropy floors signals complex substructures. that may be interpreted as a high density. low entropy clump (‘cold drop’) around the ray peak.," The large variance in the above parameters entering the entropy floors signals complex substructures, that may be interpreted as a high density, low entropy clump (`cold drop') around the X-ray peak."282 Our results agrees with the analysis by Buote et al. (, Our results agrees with the analysis by Buote et al. (2832005). who in terms of two differently centered ./-models (Cavaliere Fusco-Femiano 1976) find two core sizes similar to our extensions /y.,"2005), who in terms of two differently centered $\beta$ -models (Cavaliere Fusco-Femiano 1976) find two core sizes similar to our extensions $r_f$."284 In view of the lack of radio emission and X-ray cavities. this complexity may be understood in terms of à merger having just remolded an inner region of the ICP (see Henning et al.," In view of the lack of radio emission and X-ray cavities, this complexity may be understood in terms of a merger having just remolded an inner region of the ICP (see Henning et al."285 2009)., 2009).286 We stress that such ICP substructures constitute a common. but progressively more pronounced trait. of Α1656. A2256 and A644.," We stress that such ICP substructures constitute a common, but progressively more pronounced trait, of A1656, A2256 and A644."287 In this paper we have analyzed with the Supermodel (SM) the profiles of X-ray temperature and surface brightness of the IntraCluster Plasma (ICP) in à set of six clusters (adding to the three ones preliminarily reported in CLFFO9) with existing detailed data., In this paper we have analyzed with the Supermodel (SM) the profiles of X-ray temperature and surface brightness of the IntraCluster Plasma (ICP) in a set of six clusters (adding to the three ones preliminarily reported in CLFF09) with existing detailed data.288 We have shown how effective is our SM to represent and understand the main Cool Core /Non Cool Core in terms of two physical parameters marking the full ICP entropy profile: the central value κ... and the outer slope a (see Figs.," We have shown how effective is our SM to represent and understand the main Cool Core /Non Cool Core in terms of two physical parameters marking the full ICP entropy profile: the central value $k_c$, and the outer slope $a$ (see Figs."289 1-7)., 1-7).290 Moreover. the SM makes sense of more profiles (see Figs.," Moreover, the SM makes sense of more profiles (see Figs."291" 8-11) in terms of the additional. physical parameter +, marking the extension of the entropy floor."," 8-11) in terms of the additional, physical parameter $r_f$ marking the extension of the entropy floor."292 The working of the SM may be reducedto thebones as follows., The working of the SM may be reducedto thebones as follows.293 The spatial scale for the temperature peak in the, The spatial scale for the temperature peak in the294Let us consider the thermodynamical properties of texture matter as such and in comparison with those for radiation fIuid (equasi-counterpart of texture) aud bubble matter 2+p=0.,Let us consider the thermodynamical properties of texture matter as such and in comparison with those for radiation fluid (quasi-counterpart of texture) and bubble matter $\varepsilon + p = 0$.295 First oL all. we trv (o answer the question. what is (hermodvnamical information we can obtain from an equation of state.," First of all, we try to answer the question, what is thermodynamical information we can obtain from an equation of state."296 The first thermodsynamical law savs: dE-Tds5-pdV.(l) On the other hand. following the clelinition of the entropy as a function of volume and lemperature. one can write US = Ede Comparing (hese equations. we obtain ," The first thermodynamical law says: E = T S - p V. On the other hand, following the definition of the entropy as a function of volume and temperature, one can write S = T + V. Comparing these equations, we obtain = = ( p + )."297Then the equality of mixecl derivatives vields the expression | y+ War which gives opportunities to obtain internal energy. as a function of volume and temperature from an equation of state., Then the equality of mixed derivatives yields the expression p + = T which gives opportunities to obtain internal energy as a function of volume and temperature from an equation of state.298 Let us introduce (he densities of energy and entropy such that E-ST. S= s(T)V and consider barotropic matter will linear equation of state (LEOS) p=g," Let us introduce the densities of energy and entropy such that (T) V, S=s(T) V, and consider barotropic matter with linear equation of state (LEOS) p =."299e) Then (5)) reads ure = (y+lesus) and we obtain the energy density TO τα," Then \ref{eq5}) ) reads T = +1), and we obtain the energy density = _0"300Alibertetal.(1999) are plotted using filled circles. while others are plotted using open circles.,"\citet{al99} are plotted using filled circles, while others are plotted using open circles."301 Plus sigus indicate results caleulated for stars evolving through the hot and cool edges of the instability strip. with the rate of period chanec in general being larger on the hot edge of the instability strip. ie.. for more massive stars.," Plus signs indicate results calculated for stars evolving through the hot and cool edges of the instability strip, with the rate of period change in general being larger on the hot edge of the instability strip, i.e., for more massive stars."302 Large svinbols denote stars of solar metallicity. Z= 102. iutermediate-sized sviibols denote stars witli uetallicities of Z=0.01 and Z=0.008. aud «πα sviubols denote stars of very low metallicity. Z—0.001 and Z=0.001.," Large symbols denote stars of solar metallicity, $Z = 0.02$ , intermediate-sized symbols denote stars with metallicities of $Z = 0.01$ and $Z = 0.008$, and small symbols denote stars of very low metallicity, $Z = 0.001$ and $Z = 0.004$."303 Lines have been drawn o enclose those regions within which the results or different crossing modes appear to cluster., Lines have been drawn to enclose those regions within which the results for different crossing modes appear to cluster.304 Sequences Of points indicate models tor which the ime resolution was fiue enough to calculate rate of period change over the cntire crossing of the instability strip., Sequences of points indicate models for which the time resolution was fine enough to calculate rate of period change over the entire crossing of the instability strip.305 The distribution of data points in Fie., The distribution of data points in Fig.306 we suggests a of varictydifferent couclusious regarding the models., 2 suggests a variety of different conclusions regarding the models.307 First. the different models for the vapid first crossing of the instability. strip are in very good aerecment. and display τον little variation with metallicity.," First, the different models for the rapid first crossing of the instability strip are in very good agreement, and display very little variation with metallicity."308 The first crossing of the strip is a rapid transition for all stars. regardless of individual differences in rotation rate. cte.," The first crossing of the strip is a rapid transition for all stars, regardless of individual differences in rotation rate, etc.,"309 and that is evident frou the models., and that is evident from the models.310 Evidenutly he computational codes used for calculating the ghases of shell hydrogeu. buruing in stars. while orhaps differing in detail from one source to another. generate nearly identical results. the small variation in rate of period change at specific oulsatiou period arising from the finite width of he instability strip aud the fact that more massive stars cross the strip at a greater luninosity aud at a faster rate than less iiassive stars.," Evidently the computational codes used for calculating the phases of shell hydrogen burning in stars, while perhaps differing in detail from one source to another, generate nearly identical results, the small variation in rate of period change at specific pulsation period arising from the finite width of the instability strip and the fact that more massive stars cross the strip at a greater luminosity and at a faster rate than less massive stars."311 For stars iu he first crossing of the strip. high rate of period increase at specific pulsation period corresponds ο stars on the hot edge of the strip. low rate of oriod increase to stars on the cool edge of the strip.," For stars in the first crossing of the strip, high rate of period increase at specific pulsation period corresponds to stars on the hot edge of the strip, low rate of period increase to stars on the cool edge of the strip."312 Negative period changes arise duriug the second crossing of the instability strip. which occurs diving the blue loop phase of stella evolution following the ouset of core helium burning.," Negative period changes arise during the second crossing of the instability strip, which occurs during the blue loop phase of stellar evolution following the onset of core helium burning."313 The extent of the blue loop cau depend upon a variety of factors (sec.forexample.Decker1985:Nu&Li 2001)... such as inetallieity. the treatincut of core overshooting. aud the distribution of CNO clemeuts thronghont the star.," The extent of the blue loop can depend upon a variety of factors \citep[see, for example,][]{be85,xl04}, such as metallicity, the treatment of core overshooting, and the distribution of CNO elements throughout the star."314 All factors affect how far a star enters the instability strip durug core helium burning. aud presumably affects how rapidly it evolves within the strip.," All factors affect how far a star enters the instability strip during core helium burning, and presumably affects how rapidly it evolves within the strip."315 Given the potentially huge differences in initial conditions for such stars as naim-sequenuce objects. for example. large variations iu initial rotation rate. one nuelt expect real stars to display large variations in how far they penctrate the Cepheid instability strip as core elim burning objects.," Given the potentially large differences in initial conditions for such stars as main-sequence objects, for example, large variations in initial rotation rate, one might expect real stars to display large variations in how far they penetrate the Cepheid instability stripm as core helium burning objects."316 Somewhat unexpectedly. there are also very large variatious among the models stars as well.," Somewhat unexpectedly, there are also very large variations among the models stars as well."317 Evidently. metallicity plavs ouly a minor role iu governing the at which stars traverse the instability strip.," Evidently, metallicity plays only a minor role in governing the at which stars traverse the instability strip."318 There is as much depeudeuce on the specifics of the stellar evolutionary code used., There is as much dependence on the specifics of the stellar evolutionary code used.319 The models of Alibertetal.(1999)... for example. eenerate faster rates of period decrease than do other models. despite the use of common opacity tables.," The models of \citet{al99}, for example, generate faster rates of period decrease than do other models, despite the use of common opacity tables."320 Models from individual sources are at least internally consistent in their predictions for stars of different masses and for stars du all portions of the second strip crossing., Models from individual sources are at least internally consistent in their predictions for stars of different masses and for stars in all portions of the second strip crossing.321 The rates of period decrease during mdividual strip crossings are also very simular to the variations predicted on the basis of mass differences. 1.0. predicted. variations iu rate of period decrease at a specific pulsation period are eenerallv small. except for long period Cepheids.," The rates of period decrease during individual strip crossings are also very similar to the variations predicted on the basis of mass differences, i.e, predicted variations in rate of period decrease at a specific pulsation period are generally small, except for long period Cepheids."322 The third crossing of the instability strip occurs diving the late stages of core lelimm buruiug. and gives rise to period increases. for which the predicted rates are depicted in the top portion of Fie.," The third crossing of the instability strip occurs during the late stages of core helium burning, and gives rise to period increases, for which the predicted rates are depicted in the top portion of Fig."323 2 along with those for the first crossing., 2 along with those for the first crossing.324 Mos of the comments regarding the second crossing of the strip apply equally to the third crossing., Most of the comments regarding the second crossing of the strip apply equally to the third crossing.325 Again. metallicity senis to play a less important role iu the predicted rates of period increase than differences in the evolutionary code.," Again, metallicity seems to play a less important role in the predicted rates of period increase than differences in the evolutionary code."326 The models of Alibertetal.(01999)— predict faster rates of period chauge (period increases 1n this case) tha do other models. although with less consistency for stars of ciffercut mass.," The models of \citet{al99} predict faster rates of period change (period increases in this case) than do other models, although with less consistency for stars of different mass."327 The rates of period increase durug individual strip crossings are also simular to the variatious predicted on the basis of mass differences. aud predicted variations in the rate of period increase at a specific pulsation period are eoncrally πια].," The rates of period increase during individual strip crossings are also similar to the variations predicted on the basis of mass differences, and predicted variations in the rate of period increase at a specific pulsation period are generally small."328 A wellknown problem arises for low-1ass stars in the second aud third crossings of the instability strip. siuce the blue loop phases of," A well-known problem arises for low-mass stars in the second and third crossings of the instability strip, since the blue loop phases of"329"For soft quark matter Gy=0 we obtain quark matter only in the 2SC phase, which extends up to about 1/3 of the star radius.","For soft quark matter $G_V=0$ we obtain quark matter only in the 2SC phase, which extends up to about 1/3 of the star radius."330" Increasing Gy has the effect of shifting the 2SC phase to larger radii, whereas the CFL phase develops at the center."," Increasing $G_V$ has the effect of shifting the 2SC phase to larger radii, whereas the CFL phase develops at the center."331" For the strongest coupling studied, all phases are present in the maximum mass star, with the combined 2SC and CFL paired quark matter confined within a radius that is about the half of the star."," For the strongest coupling studied, all phases are present in the maximum mass star, with the combined 2SC and CFL paired quark matter confined within a radius that is about the half of the star."332" Note that a similar internal structure is obtained for crystalline color-superconducting stars, where quark matter is confined within a radius of ~7 km for maximum mass stars with a radius ~12 km (Knippel&Sedrakian2009).."," Note that a similar internal structure is obtained for crystalline color-superconducting stars, where quark matter is confined within a radius of $\sim 7$ km for maximum mass stars with a radius $\sim 12$ km \citep{2009PhRvD..79h3007K}."333" Massive neutron stars are likely to develop cores composed of deconfined quark matter, which should be in one of the color"," Massive neutron stars are likely to develop cores composed of deconfined quark matter, which should be in one of the color"334Blantonetal.(2003) in their study of SDSS galaxies.,\citet{bl03} in their study of SDSS galaxies.335 [If in fact. galaxies are well described bv Sérrsic profiles. (hen is a useful surrogate for (he Sérrsic index ».," If, in fact, galaxies are well described by Sérrsic profiles, then is a useful surrogate for the Sérrsic index $n$."336" Consider. for instance. a galaxv whose surface brightness is perfectly described by a Sérrsic prolileof index »=2 and effective radius AH,=X."," Consider, for instance, a galaxy whose surface brightness is perfectly described by a Sérrsic profileof index $n = 2$ and effective radius $R_e = X$."337 The best-fitling exponential model for this ealaxv (fitting in the radial region OLN<RxLON) has f=LION: the best-fitting de Vaucoulerrs model has A.=0.80.N., The best-fitting exponential model for this galaxy (fitting in the radial region $0.1 X \leq R \leq 10 X$ ) has $R_e = 1.10 X$; the best-fitting de Vaucouleurs model has $R_e = 0.80 X$ .338 Combining the models gives fracDeV=0.51 [or this n=2 Sénsie galaxv., Combining the models gives $\texttt{fracDeV} = 0.51$ for this $n = 2$ Sérrsic galaxy.339 A similar fil to an ip=3 Sérrsic galaxy vields fracDeV=0.83., A similar fit to an $n = 3$ Sérrsic galaxy yields $\texttt{fracDeV} = 0.83$.340 In eeneral. if galaxies have Sérrsic profiles with 1<nx4. thenfracDeV.. as computed by the SDSS DR3 pipeline. is a monotonically increasing function of the Sérrsic index ». and thus can be used as a surrogate for n.," In general, if galaxies have Sérrsic profiles with $1 \leq n \leq 4$, then, as computed by the SDSS DR3 pipeline, is a monotonically increasing function of the Sérrsic index $n$, and thus can be used as a surrogate for $n$."341 A plot of the mean axis ratio (q) as a function of the parameter is shown in Figure 1.., A plot of the mean axis ratio $\langle q \rangle$ as a function of the parameter is shown in Figure \ref{fig:fdev}.342 The mean adaptive moments axis ratio (qu). indicated by the filled circles. shows an increasing trend. with fracDeV.. from (qu)=0.59 for galaxies with purely exponential profiles (fracDeV= 0) to (qm)=0.74 lor galaxies with pure de Vaucouleurs profiles (fracDeV= 1).," The mean adaptive moments axis ratio $\langle q_{\rm am} \rangle$, indicated by the filled circles, shows an increasing trend with , from $\langle q_{\rm am} \rangle = 0.59$ for galaxies with purely exponential profiles $\texttt{fracDeV} = 0$ ) to $\langle q_{\rm am} \rangle = 0.74$ for galaxies with pure de Vaucouleurs profiles $\texttt{fracDeV} = 1$ )."343 However. the trend in (q) is not a linear one: for galaxies with fracDeV<0.5. the value of (q) is nearly constant at (ϱ2 0.6: it is only at fracDeV=0.5 that (q) shows an increasing trend withfracDeV.," However, the trend in $\langle q \rangle$ is not a linear one; for galaxies with $\texttt{fracDeV} \la 0.5$, the value of $\langle q \rangle$ is nearly constant at $\langle q \rangle \approx 0.6$ ; it is only at $\texttt{fracDeV} \ga 0.5$ that $\langle q \rangle$ shows an increasing trend with."344. The mean isophotal axis ratio (qo3). indicated by the open circles in Figure 1.. shows less of a trend with£racDeV.," The mean isophotal axis ratio $\langle q_{25} \rangle$, indicated by the open circles in Figure \ref{fig:fdev}, shows less of a trend with."345. Except in (tlie case of nearly pure cle Vaucouleurs profiles (£racDeV= 0.9). the axis ratio of a galaxy in its outer regions doesnt seen (o depend on its surface brightness prolile.," Except in the case of nearly pure de Vaucouleurs profiles $\texttt{fracDeV} \ga 0.9$ ), the axis ratio of a galaxy in its outer regions doesn't seem to depend on its surface brightness profile."346 For convenience m analvsis.we have divided our galaxy sample into four classes. based on the value offracDeV.," For convenience in analysis,we have divided our galaxy sample into four classes, based on the value of."347". Galaxies with fracDeV< 0.1. corresponding to a Sérrsic index η<1.2. are called ex’ galaxies: (here are A.=44.289 ""ex. galaxies in our sample."," Galaxies with $\texttt{fracDeV} \leq 0.1$ , corresponding to a Sérrsic index $n \la 1.2$, are called `ex' galaxies; there are $N_{\rm ex} =34844{,}289$ `ex' galaxies in our sample."349 Galaxies wilh 0.1<fracDeV0.5. corresponding to 1.2Xn<2.0. are labeled ‘ex/de’ galaxies (CN 36.645).," Galaxies with $0.1 <350\texttt{fracDeV} \leq 0.5$, corresponding to $1.2 \la n \la 2.0$, are labeled `ex/de' galaxies $N_{\rm ex/de} = 36{,}645$ )."351 Galaxies with 0.5<fracDeV0.9. corresponding to 2.0SnS3.3. are labeled ‘defex’ galaxies (Naor= 13.780).," Galaxies with $0.5 < \texttt{fracDeV} \leq 0.9$, corresponding to $2.0 \la n \la 3.3$, are labeled `de/ex' galaxies $N_{\rm de/ex} = 13{,}780$ )."352 Finally. galaxies wilh fracDeV>0.9. corresponding to nZ3.3. are called ‘ce’ galaxies.," Finally, galaxies with $\texttt{fracDeV}353> 0.9$, corresponding to $n \ga 3.3$, are called `de' galaxies."354" The small fraction of ‘de’ galaxies in our sample (V4,= 2237) is partly due to the fact that the centrally concentrated de Vaucouleurs galaxies are less likely Lo satislv our resolution criterion. and partly due to the fact that galaxies with high Sérrsic indices are intrinsically rare: Blantonοἱal.(2003) estimated that only ~5% of the SDSS ealaxies in their sample had Sérrsic index η>3."," The small fraction of `de' galaxies in our sample $N_{\rm de} =3552237$ ) is partly due to the fact that the centrally concentrated de Vaucouleurs galaxies are less likely to satisfy our resolution criterion, and partly due to the fact that galaxies with high Sérrsic indices are intrinsically rare; \citet{bl03}356 estimated that only $\sim 5\%$ of the SDSS galaxies in their sample had Sérrsic index $n > 3$."357 The ‘de’ galaxies are rounder in their central regions than in their outer regions: 0.083.," The `de' galaxies are rounder in their central regions than in their outer regions: $\langle q_{\rm am} - q_{25} \rangle =3580.083$ ."359 This is consistent with the ‘cle’galaxies being relatively bright elliptical galaxies. for which the isophotal axisratios tend to decrease wilh increasing semimajor axis length (Iden.Forbes.&Terlevieh 2001)..," This is consistent with the `de'galaxies being relatively bright elliptical galaxies, for which the isophotal axisratios tend to decrease with increasing semimajor axis length \citep{rf01}. ."360 By contrast. (he‘ex’ galaxies are actually slightly flatter in (heir central regionsthan in their outer regions: (quà—q25)= —0.017.," By contrast, the`ex' galaxies are actually slightly flatter in their central regionsthan in their outer regions: $\langle q_{\rm am} -361q_{25} \rangle = -0.017$ ."362of the star. and the transition to non-axisymmetrie equilibrium is a matter simply of stretching this flux tube into a more complex arrangement.,"of the star, and the transition to non-axisymmetric equilibrium is a matter simply of stretching this flux tube into a more complex arrangement."363 In the process of stretching the tube. the toroidal component (i.e. the component parallel to the axis of the tube. the neutral line) is amplified (since the tube becomes narrower). and the poloidal component becomes weaker. eventually bringing the two components to roughly equal strengths. because the energy minimum for a given helicity. i.e. for a given product of toroidal and poloidal tield strengths. will have the two components roughly equal to each other.," In the process of stretching the tube, the toroidal component (i.e. the component parallel to the axis of the tube, the neutral line) is amplified (since the tube becomes narrower), and the poloidal component becomes weaker, eventually bringing the two components to roughly equal strengths, because the energy minimum for a given helicity, i.e. for a given product of toroidal and poloidal field strengths, will have the two components roughly equal to each other."364" At higher£,/£ ratios therefore. more stretching is required to make the two components equal."," At higher$E_{\rm p}/E$ ratios therefore, more stretching is required to make the two components equal."365 This can be clearly seen in fig. 16.., This can be clearly seen in fig. \ref{fig:map-higher}.366" Now. in the case where £,/E=1 the field has zero magnetic helicity and no amount of flux-tube stretching can result in an equilibrium."," Now, in the case where $E_{\rm p}/E=1$ the field has zero magnetic helicity and no amount of flux-tube stretching can result in an equilibrium."367 However. there are diffusive processes at work which can either create helicity or split the one original flux tube into two or more tubes which can have helicity of different signs and which add up to zero. although it is likely that a lot of time will pass before any equilibrium is reached and the energy of the equilibrium will be very much lower than the original energy.," However, there are diffusive processes at work which can either create helicity or split the one original flux tube into two or more tubes which can have helicity of different signs and which add up to zero, although it is likely that a lot of time will pass before any equilibrium is reached and the energy of the equilibrium will be very much lower than the original energy."368 In this paper. I have looked at the lower and upper limits on the fractions of energ' in the poloidal and toroidal components of an axisymmetric magnetic field.," In this paper, I have looked at the lower and upper limits on the fractions of energy in the poloidal and toroidal components of an axisymmetric magnetic field."369" To tind these limits. I took the output from a simulation where a ""turbulent! initial magnetic field evolves into an axisymmetrie equilibrium. ehanged the relative strengths of the poloidal and toroidal components by hand. and used that as the initial conditions for new simulations."," To find these limits, I took the output from a simulation where a `turbulent' initial magnetic field evolves into an axisymmetric equilibrium, changed the relative strengths of the poloidal and toroidal components by hand, and used that as the initial conditions for new simulations."370 This was supplemented with more analytic methods including the necessary and sufficient stability conditions found by Tayler(1973) (it is incidentally found that four of his six conditions are always met at every point in the star)., This was supplemented with more analytic methods including the necessary and sufficient stability conditions found by \citet{Tayler:1973} (it is incidentally found that four of his six conditions are always met at every point in the star).371 The two methods are in broad agreement., The two methods are in broad agreement.372" The result of this investigation is that while the upper limit on he poloidal energy fraction £),/£7 is around SOM. the lower limit depends on factors such as the radius of the neutral line mand can be between 1% and roughly 5% for a star constructed from a xolytrope of index »=3 (which approximates to an upper-main-sequence star) and where the ratio of magnetic to thermal energies LU=L/400."," The result of this investigation is that while the upper limit on the poloidal energy fraction $E_{\rm p}/E$ is around $80\%$, the lower limit depends on factors such as the radius of the neutral line $r_{\rm n}$ and can be between $1\%$ and roughly $5\%$ for a star constructed from a polytrope of index $n=3$ (which approximates to an upper-main-sequence star) and where the ratio of magnetic to thermal energies $E/U=1/400$."373" This lower limit is expected to be proportional to he ratio {εἰς so that (£5,/Lai~LOLYt."," This lower limit is expected to be proportional to the ratio $E/U$, so that $(E_{\rm p}/E)_{\rm crit} \sim 10 E/U$."374" These limits will also depend on other factors not explicitly explored here. such as he equation of state and density profile of the star. but these should not affect the results in more than a modest quantitative manner: ywwever in a NS we might expect a lower limit of (£5,/E)~ /U."," These limits will also depend on other factors not explicitly explored here, such as the equation of state and density profile of the star, but these should not affect the results in more than a modest quantitative manner; however in a NS we might expect a lower limit of $(E_{\rm p}/E)_{\rm crit} \sim 10^3 E/U$ ."375 The upper limit found here broadly confirms what was expectedE from the analysis in Paper II and from the analyses of Wright(1973) and Markey&Tayler (19743... who found that the toroidal field must be at least about a quarter of the strength of the," The upper limit found here broadly confirms what was expected from the analysis in Paper II and from the analyses of \citet{Wright:1973} and \citet{MarandTay:1974}, , who found that the toroidal field must be at least about a quarter of the strength of the"376of the sien of the ICAL temperature eradieut.,of the sign of the ICM temperature gradient.377 In our approach. we self-cousisteutlv included the amplification of the iuagnetie feld due to the shearing motions. eas conrpresson enhanced by radiative cooling. aud the kinematic dynanio associated with the anisotropic nature of conduction.," In our approach, we self-consistently included the amplification of the magnetic field due to the shearing motions, gas compression enhanced by radiative cooling, and the kinematic dynamo associated with the anisotropic nature of conduction."378 Our key fiudiugs The software used in this work was in part developed bv the DOE-supported ASC/Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago., Our key findings The software used in this work was in part developed by the DOE-supported ASC/Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago.379 AIR thauks the staff NASA Ames Research ceuter for technical help with performing the rus at the supercomputer where most of the mus were performed., MR thanks the staff NASA Ames Research center for technical help with performing the runs at the supercomputer where most of the runs were performed.380 We are indebted το Cliris Daley for his assistance with the particle aud eravity modules iu theFLASH code., We are indebted to Chris Daley for his assistance with the particle and gravity modules in the code.381 We thauk Eliot Quatacrt. Alaxin Markeviteh. Chistoph Pfronuner. Paul Nulsen. Chnristino Jones. Larry David. Dil Forman. Milos Alilosavljevic. John Zullone. Mikhail Medvedev. Steve Balbus. and Fabian Ueitsch for Tn order to check the tuplementation of the cosinological terius in the MIID equations we evolved spatially coustant imnatter density aud magnetic field while ueelecting any velocity perturbations.," We thank Eliot Quataert, Maxim Markevitch, Christoph Pfrommer, Paul Nulsen, Christine Jones, Larry David, Bill Forman, Milos Milosavljevic, John ZuHone, Mikhail Medvedev, Steve Balbus, and Fabian Heitsch for In order to check the implementation of the cosmological terms in the MHD equations we evolved spatially constant matter density and magnetic field while neglecting any velocity perturbations."382 The result of this test is shown in Figure 9., The result of this test is shown in Figure 9.383 In the left paucl we show the scaling of the temperature (i arbitrary units) with the cosmological expansion factor e., In the left panel we show the scaling of the temperature (in arbitrary units) with the cosmological expansion factor $a$.384 Shown are ie code result for the physical temperature aud the nower law fit (solid ancl dashed Lunes are practically incdistineuishable)., Shown are the code result for the physical temperature and the power law fit (solid and dashed lines are practically indistinguishable).385 The slope of Ti)να7 agrees with je standard theoretical expectation., The slope of $T(a)\propto a^{-2}$ agrees with the standard theoretical expectation.386 The right paucl shows the plivsical maguetic field in arbitrary units as a wmiction of the scaling parameter a aid a powerlaw fit to us relation. both as a function of thie scaling paraiueter a.," The right panel shows the physical magnetic field in arbitrary units as a function of the scaling parameter $a$ and a powerlaw fit to this relation, both as a function of the scaling parameter $a$."387 Hore again the fit is perfect. the soid aud dashed lines overlap. aud the slope of. the fielda is. (B(o)X@P 7) eusures re conservation of the magnetic flux.," Here again the fit is perfect, the solid and dashed lines overlap, and the slope of the field is $B(a)\propto a^{-2}$ ) ensures the conservation of the magnetic flux."388 Iu order to test the implementation of the anisotropic thermal conduction module we compared uear theory ALTI ervowth rates with the code results, In order to test the implementation of the anisotropic thermal conduction module we compared linear theory MTI growth rates with the code results.389 This test is very simular to the one discussed ia Parrish Stone (2008)., This test is very similar to the one discussed in Parrish Stone (2008).390" That is we set up a two dimensional stratified lydrostatic atinosphere with very shallow density aud temperature profiles such that where TZ and p, are coustauts"," That is, we set up a two dimensional stratified hydrostatic atmosphere with very shallow density and temperature profiles such that where $T_{o}$ and $\rho_{o}$ are constants."391" The characteristic Ienethscale 4,4, was set to of the horizontal height", The characteristic lengthscale $y_{o}$ was set to of the horizontal height392‘Thus. when we calculate the work function for the original mocel integrating between logg<=2.24 and the surface. we obtain similar growth rate values as those of the pertllell moclel(Eig.Bg. 9)).,"Thus, when we calculate the work function for the original model integrating between $\log q \leq -2.24$ and the surface, we obtain similar growth rate values as those of the pertHeH model(Fig. \ref{fig:cmpgrou}) )."393 In the case of low racial order g-mocdes (Pig. 6...," In the case of low radial order -modes (Fig. \ref{fig:zoommiecin-deltap},"394 solid lines) some subtle mode trapping seems still to be present., solid lines) some subtle mode trapping seems still to be present.395 This may be due to remnant mode trapping elTeets caused by the C-O/Lle transition. in the same wav as cescribed below for low radial order p-moces.," This may be due to remnant mode trapping effects caused by the C-O/He transition, in the same way as described below for low radial order -modes."396 When we cancel out the sharp peak of the C-O/Lle chemical transition. keeping the Le/ll peak. we still obtain the original pattern of trapped mocles. with total kinetic energy. erowth rate ancl period dilferences similar to those of the original model (Fig. 2..," When we cancel out the sharp peak of the C-O/He chemical transition, keeping the He/H peak, we still obtain the original pattern of trapped modes, with total kinetic energy, growth rate and period differences similar to those of the original model (Fig. \ref{fig:allgkin},"397 Fig., Fig.398 3. crosses ancl dashed. lines)., \ref{fig:allgdeltap} crosses and dashed lines).399 Thus. this chemical transition plavs no role in high racial order g-mode trapping.," Thus, this chemical transition plays no role in high radial order -mode trapping."400 However. for lower order modes (Fig. 6..," However, for lower order modes (Fig. \ref{fig:zoommiecin-deltap},"401 left panel. crosses ancl dashed lines). it may have some inlluence. which is revealed in certain alterations to the total kinetic energy of each mode.," left panel, crosses and dashed lines), it may have some influence, which is revealed in certain alterations to the total kinetic energy of each mode."402 The logarithm of the total kinetic energy. and corresponcing erowth rates. for the pmode spectrum are shown in Fig. 10..," The logarithm of the total kinetic energy, and corresponding growth rates, for the -mode spectrum are shown in Fig. \ref{fig:allpkin}."403 The depicted racial orders correspond to frequencies ranging from about 6 to 25 mllz., The depicted radial orders correspond to frequencies ranging from about 6 to 25 mHz.404 There are certain modes which show values higher than the mean kinetic energv in the original and perturbed models., There are certain modes which show values higher than the mean kinetic energy in the original and perturbed models.405 We investigate if this could also be an elfect of mode trapping., We investigate if this could also be an effect of mode trapping.406 Following again the asymptotic theory of nonracdial oscillations Classoul 1050 Smoeversctal.1995: Smevers& 2007)) pemocles of the same degree £ and consecutive racial order A. will have constant frequeney separation. Av. given by: Thus. the mode trapping signature for p-mocdoes would show up in the deviations in the large frequency spacing for the original and the perturbecl Lefll model (Fig. 11)).," Following again the asymptotic theory of nonradial oscillations \citealp{tassoul80}; ; \citealp{smeyers95}; \citealp{smeyers07}) ) -modes of the same degree $\ell$ and consecutive radial order $k$, will have constant frequency separation, $\Delta \nu$, given by: Thus, the mode trapping signature for -modes would show up in the deviations in the large frequency spacing for the original and the perturbed He/H model (Fig. \ref{fig:allpdeltanuk}) )."407 We have plotted the radial and horizontal cisplacement eigenfunctions [for the original model p-modes with niaximum (p9). intermediate (ps) and minimum (p?) total kinetic energv (Fig. 12)).," We have plotted the radial and horizontal displacement eigenfunctions for the original model -modes with maximum 9), intermediate 8) and minimum 7) total kinetic energy (Fig. \ref{fig:p9p8p7y1y2}) )."408 We found that all modes. show higher amplitude in the envelope. as expected for p-modes.," We found that all modes show higher amplitude in the envelope, as expected for -modes."409 We found that the pO mode shows the highest. amplitude in the outer envelope for the 3 modes under comparison., We found that the 9 mode shows the highest amplitude in the outer envelope for the 3 modes under comparison.410 Llowever. ultimately what accounts for the higher total kinetic energy is the higher amplitude of the eigenfunctions in the innermost lavers of the star. where the moce is trapped due to the pinching elfect of the C-O/Lle interface on the cigenfunetions.," However, ultimately what accounts for the higher total kinetic energy is the higher amplitude of the eigenfunctions in the innermost layers of the star, where the mode is trapped due to the pinching effect of the C-O/He interface on the eigenfunctions."411 This can be seen in Fig., This can be seen in Fig.412 13. (elt) that shows the local contribution to the kinetic energy of the trapped. normal anc confined. modes. pO. ps. pr. respectively. normalised to the maximum ofp," \ref{fig:indecinet-trabajop9p8p7} (left) that shows the local contribution to the kinetic energy of the trapped, normal and confined modes, 9, 8, 7, respectively, normalised to the maximum of."4137 Although not shown for the sake of clarity. the maximum. kinetic energy value for the pO trapped mode reaches one order of maenitude higher.," Although not shown for the sake of clarity, the maximum kinetic energy value for the 9 trapped mode reaches one order of magnitude higher."414 The plot of the differential work for a trapped. normal and confined moce (Fig. 13..," The plot of the differential work for a trapped, normal and confined mode (Fig. \ref{fig:indecinet-trabajop9p8p7},"415 right) shows that significant energv interchange is only produced. at the Z-bump: and here. driving is higher for the trapped mode.," right) shows that significant energy interchange is only produced at the Z-bump; and there, driving is higher for the trapped mode."416 As it is the case for low-radial order g-modes. à maximum in kinetic energy does not translate into a minimum growth rate value or the mode.," As it is the case for low-radial order -modes, a maximum in kinetic energy does not translate into a minimum growth rate value for the mode."417 This is explained. by the maximum kinetic energy being due to a higher amplitude of the eigenfunctions in the region logq0.8. which for p-modes does not ive significant influence on driving.," This is explained by the maximum kinetic energy being due to a higher amplitude of the eigenfunctions in the region $\log q \gtrsim -0.8$, which for -modes does not have significant influence on driving."418 Neither do the higher amplitudes of the cigenfunetions of the trapped. mode at he driving region lead to a maximum growth rate value. as consecutive higher racial order modes have even higher amplitudes.," Neither do the higher amplitudes of the eigenfunctions of the trapped mode at the driving region lead to a maximum growth rate value, as consecutive higher radial order modes have even higher amplitudes."419 We conclude that the influence of the work function prevails over the influence of the Kinetic energy in he computation of the growth rate., We conclude that the influence of the work function prevails over the influence of the kinetic energy in the computation of the growth rate.420 Pressure modes with higher racial orders. not shown in Fig. 10..," Pressure modes with higher radial orders, not shown in Fig. \ref{fig:allpkin},"421 display kinetic energy monotonically increasing. an elfect. of the nodes accumulating in the surface limit imposed by the boundary conditions. as it is well described in Charpinetetal.(2000).," display kinetic energy monotonically increasing, an effect of the nodes accumulating in the surface limit imposed by the boundary conditions, as it is well described in \citet{charpinet00}."422.. Phe trapping effect. caused. by the C-O/LIe transition is no longer produced. as is expected [or high-radial order pure p-mocdes propagating only in the external lavers of the star.," The trapping effect caused by the C-O/He transition is no longer produced, as is expected for high-radial order pure -modes propagating only in the external layers of the star."423 When we cancel the Le/ll. or the sharp peak of the C- chemical transitions in the Brunt-Vaiisalla frequency. ancl also the corresponding bumps in the sound. speed at these locations. we still find a Kinetic energy. pattern. and an oscillating profile of the growth rate. both similar to those of the original model (Fig. 10..," When we cancel the He/H, or the sharp peak of the C-O/He chemical transitions in the Brunt-Väiisällä frequency, and also the corresponding bumps in the sound speed at these locations, we still find a kinetic energy pattern, and an oscillating profile of the growth rate, both similar to those of the original model (Fig. \ref{fig:allpkin},"424 solid and dashed lines. respectively).," solid and dashed lines, respectively)."425 Therefore. neither the Πο. nor the C-O/Le chemical transition. nor the sound speed at these locations. seem to have any significant influence on the kinetic energy or on the tendeney to driving ofthe pamocdoes.," Therefore, neither the He/H, nor the C-O/He chemical transition, nor the sound speed at these locations, seem to have any significant influence on the kinetic energy or on the tendency to driving of the -modes."426 This result was the expected. for the growth rate. for reasons given above. but not for the kinetic energy. as we presumed the modification of the C-O/lle transition would show in the kinetic energv. profile. due to changes in the amplitude of the eigenfunctions.," This result was the expected for the growth rate, for reasons given above, but not for the kinetic energy, as we presumed the modification of the C-O/He transition would show in the kinetic energy profile, due to changes in the amplitude of the eigenfunctions."427 However. eigenfunction profiles similar to those of Fig.," However, eigenfunction profiles similar to those of Fig."428 12. are retained for trapped. normal and confined modes of the perturbed. models.," \ref{fig:p9p8p7y1y2}429 are retained for trapped, normal and confined modes of the perturbed models."430 The reason may be due to that. in fact. the €C-O/Ile transition still exists(see Fig. 7.. ," The reason may be due to that, in fact, the C-O/He transition still exists(see Fig. \ref{fig:n2pert}, ,"431left) as we only cancelled out its steep peak. eiving a softer profile.," left) as we only cancelled out its steep peak, giving a softer profile."432 We conclude for the g-mode spectrum that:, We conclude for the -mode spectrum that:433suddenly steepening in the following intervaln.,suddenly steepening in the following interval.434" Unfortunately. errors are such that again we are unable to make any statements regarding changes to Zi, or Pigου."," Unfortunately, errors are such that again we are unable to make any statements regarding changes to $F_{\rm K\alpha}$ or $\Gamma_{10-20}$."435 However. we note that fic. is generally high for these time intervals associated with this hard flare event.," However, we note that $F_{\rm K\alpha}$ is generally high for these time intervals associated with this hard flare event."436 Table 6. details these results., Table \ref{tab4-rxteflare} details these results.437 As with the flare. Fig.," As with the flare, Fig."438" 12. for the flare hints at changes in P, on short time intervals (e.g. and m) It is clear from the spectral analysis thus far that conditions can alter suddenly and erratically.", \ref{fig13-xteflareplts} for the flare hints at changes in $F_{\rm K\alpha}$ on short time intervals (e.g. and ) It is clear from the spectral analysis thus far that conditions can alter suddenly and erratically.439 In order to assess whether a more simplified picture exists. we investigate spectral features of the deep minima in contrast with flare type events. using a model that consist of simple power law and redshifted Gaussian component.," In order to assess whether a more simplified picture exists, we investigate spectral features of the deep minima in contrast with flare type events, using a model that consist of simple power law and redshifted Gaussian component."440 Table 8 confirms the findings of Section 4.2.1 such that in general. I5io tends to be flatter during the minima in contrast to the flare states.," Table \ref{tab6-intgammachange} confirms the findings of Section 4.2.1 such that in general, $\Gamma_{3-10}$ tends to be flatter during the minima in contrast to the flare states."441 A close comparison of Εςτο versus Γιο5o for the differing states suggests that we are largely seeing intrinsic changes in the power law slope rather than reflection. although it is likely that we are seeing contributions from both effects.," A close comparison of $\Gamma_{3-10}$ versus $\Gamma_{10-20}$ for the differing states suggests that we are largely seeing intrinsic changes in the power law slope rather than reflection, although it is likely that we are seeing contributions from both effects."442 Additionally. ratio plots of data against model using a power law fit show that there is a noticeable change in the line flux. profile. as well as the reflection component. similar to that seen in Fig.," Additionally, ratio plots of data against model using a power law fit show that there is a noticeable change in the line flux, profile, as well as the reflection component, similar to that seen in Fig."443 7aa. We find evidence from flux-correlated studies that Εντο steepens significantly with flux CAL40~0.06 for a doubling of the flux from tof4: Fig., \ref{fig7-ratioplts}a a. We find evidence from flux-correlated studies that $\Gamma_{3-10}$ steepens significantly with flux $\rm \Delta \Gamma_{3-10} \sim 0.06$ for a doubling of the flux from to; Fig.444 13au) while surprisingly. the iron line strength appears to remain constant (at most differing by ~1.5«10 from flux-correlated studies).," \ref{fig14-fluxgammaew}a a) while surprisingly, the iron line strength appears to remain constant (at most differing by $\sim 1.5 \times 10^{-5}$ from flux-correlated studies)."445 Changes to Dj.ου GNio20~ 0.3) and Vg CAT~200 eV) are also evident and anticorrelate with flux (Fig.," Changes to $\Gamma_{10-20}$ $\rm \Delta \Gamma_{10-20} \sim4460.3$ ) and $W_{\rm K\alpha}$ $\Delta W_{\rm K\alpha} \sim 200$ eV) are also evident and anticorrelate with flux (Fig."447 |3bb for the latter)., \ref{fig14-fluxgammaew}b b for the latter).448" A close look at events corresponding to deep minima versus flares reinforces the finding that changes to the intrinsic power law slope are evident. with a comparably steeper LF,το value during the flares."," A close look at events corresponding to deep minima versus flares reinforces the finding that changes to the intrinsic power law slope are evident, with a comparably steeper $\Gamma_{3-10}$ value during the flares."449 Figs., Figs.450" 13. illustrate that the behaviour of the intrinsic photon index and Vy, during the flares is consistent with the correlated behaviour.", \ref{fig14-fluxgammaew} illustrate that the behaviour of the intrinsic photon index and $W_{\rm K\alpha}$ during the flares is consistent with the flux-correlated behaviour.451 We find that reflection increases with flux when fitting flux-separated data with a complex model that includes the reflected spectrum., We find that reflection increases with flux when fitting flux-separated data with a complex model that includes the reflected spectrum.452 Curiously. reflection. fraction /?. anticorrelates with," Curiously, reflection fraction $R$ anticorrelates with"453Cosmic ravs (CR) seem an important source of atmospheric ionisation in the solar svslem planets.,Cosmic rays (CR) seem an important source of atmospheric ionisation in the solar system planets.454 Observation of Earth clouds. however. suggest that the actual charge production is not overly efficient. but nevertheless important for coagulation processes.," Observation of Earth clouds, however, suggest that the actual charge production is not overly efficient but nevertheless important for coagulation processes."455 Nicoll Harrison (2010) determine 17...150e per particle in cloud edees on Earth which can be directly. related (ο ionisation by cosmic ravs.," Nicoll Harrison (2010) determine $17\,\ldots\,150$ e per particle in cloud edges on Earth which can be directly related to ionisation by cosmic rays."456 The charging of the cloud particles is. however. not a direct result of the impact of the high enerey CR particle on the cloud but rather of the ion current that develops from the CH. ionisation of the gas above the cloud.," The charging of the cloud particles is, however, not a direct result of the impact of the high energy CR particle on the cloud but rather of the ion current that develops from the CR ionisation of the gas above the cloud."457 These ions attach to the cloud particles., These ions attach to the cloud particles.458 The question is whether galactie cosmic rays could be a global source of ionisation [or extrasolar low-mass objects., The question is whether galactic cosmic rays could be a global source of ionisation for extrasolar low-mass objects.459 Dust clouds are an integral part of the atnosphleres of very. low mass objects like Brown Dwarls and planets., Dust clouds are an integral part of the atmospheres of very low mass objects like Brown Dwarfs and planets.460 Clouds determine the local chemistry by element consumption and they. influence the radiative and convective energy. (ransport bv (heir large opacity in the atmospheres., Clouds determine the local chemistry by element consumption and they influence the radiative and convective energy transport by their large opacity in the atmospheres.461 The aim of this paper is to demonstrate (hat dust grains in Brown Dwarl abmospheres can be charged. and to investigate whether the presence of dust in Brown Dwarl atimosphleres can contribute to ils overall ionization level. a necessary. condition for magnetic coupling of the atmosphere.," The aim of this paper is to demonstrate that dust grains in Brown Dwarf atmospheres can be charged, and to investigate whether the presence of dust in Brown Dwarf atmospheres can contribute to its overall ionization level, a necessary condition for magnetic coupling of the atmosphere."462 For (his purpose. we focused on collisional processes of the dust phase to cause additional ionization of the atmosphere. an aspect that has not vel been considered in earlier research.," For this purpose, we focused on collisional processes of the dust phase to cause additional ionization of the atmosphere, an aspect that has not yet been considered in earlier research."463 We. however. acknowledge that a large variety of micro-physical processes can be involved into the ionisation of a mineral cloud which have nol vel been taken into account in our model.," We, however, acknowledge that a large variety of micro-physical processes can be involved into the ionisation of a mineral cloud which have not yet been taken into account in our model."464 We find that collisional energies can be hieh enough to ionize the cust phase over the whole extension of atmospheric clouds of a late tvpe Brown Dwarl CIagy—1600. log(g)= 5) and over a large part in a giant. plauet's," We find that collisional energies can be high enough to ionize the dust phase over the whole extension of atmospheric clouds of a late type Brown Dwarf $_{\rm eff}$ =1600, $\log(g)=5$ ) and over a large part in a giant planet's"465"irradiance followed the actual TSI variations, observed with Virgo, to a correlation coefficient of 0.9625.","irradiance followed the actual TSI variations, observed with Virgo, to a correlation coefficient of 0.9625."466" This corresponds to a standard deviation of relative to the variation of TSI, if the error introduced by the proxy reconstruction is uncorrelated with the true light curve."," This corresponds to a standard deviation of relative to the variation of TSI, if the error introduced by the proxy reconstruction is uncorrelated with the true light curve."467" Although it is not possible to tell how this error is distributed across the solar disk, we condend that the true astrometric jitter can not belarger than our estimates by more than this amount, which is when added in quadrature."," Although it is not possible to tell how this error is distributed across the solar disk, we condend that the true astrometric jitter can not be than our estimates by more than this amount, which is when added in quadrature."468" The error is carried by many classes of different spatial scale, but only large scale perturbations count in the integration in first moment."," The error is carried by many classes of different spatial scale, but only large scale perturbations count in the integration in first moment."469" Most of this error is probably confined to small-scale structures, which should cancel in integration."," Most of this error is probably confined to small-scale structures, which should cancel in integration."470" Known imperfections, such as the ringing features centered on the centers of activity, caused by too many plage classes, do not result in an appreciable image shift."," Known imperfections, such as the ringing features centered on the centers of activity, caused by too many plage classes, do not result in an appreciable image shift."471" Besides, some of the TSI variation not accounted for by the reconstruction is due to magnetic features appearing in the outer rim of the solar disk of the radius), which is missing in our data."," Besides, some of the TSI variation not accounted for by the reconstruction is due to magnetic features appearing in the outer rim of the solar disk of the radius), which is missing in our data."472 Planets revolving around their host stars produce sinusoidal variations in the astrometric position., Planets revolving around their host stars produce sinusoidal variations in the astrometric position.473" The main harmonic of these variations has the orbital period of the planet, and an amplitude defined by the mass of the star, the mass of the planet, and the orbital semimajor axis."," The main harmonic of these variations has the orbital period of the planet, and an amplitude defined by the mass of the star, the mass of the planet, and the orbital semimajor axis."474 Planets in eccentric orbits also produce higher-order harmonics (overtones) of smaller amplitudes., Planets in eccentric orbits also produce higher-order harmonics (overtones) of smaller amplitudes.475" The spectroscopic method of exoplanet detection, based on precision measurements of stellar radial velocity, utilizes the Lomb-Scargle periodogram analysis (e.g.,Fischeretal. 2008),, which is aimed at detecting statistically significant sinusoidal variations in irregularly sampled data with a zero mean (Scargle1982).."," The spectroscopic method of exoplanet detection, based on precision measurements of stellar radial velocity, utilizes the Lomb-Scargle periodogram analysis \citep[e.g.,][]{fis}, which is aimed at detecting statistically significant sinusoidal variations in irregularly sampled data with a zero mean \citep{sca}."476" A similar ""joint"" power spectrum periodogram was suggested for 2D astrometric detection by (2008).."," A similar “joint"" power spectrum periodogram was suggested for 2D astrometric detection by \citet{cat}."477" In order to evaluate the impact of magnetic jitter on detection of low-mass planets, we employ in this paper a generalized amplitude spectrum analysis, which, unlike the periodogram, includes the constant term in the set of fitting functions."," In order to evaluate the impact of magnetic jitter on detection of low-mass planets, we employ in this paper a generalized amplitude spectrum analysis, which, unlike the Lomb-Scargle periodogram, includes the constant term in the set of fitting functions."478" A constant offset in position is a physical astrometric parameter, which can not be simply subtracted from the raw data."," A constant offset in position is a physical astrometric parameter, which can not be simply subtracted from the raw data."479 The linear problem, The linear problem480 I-structure nuplies that the rig in 2 cannot have been produced by euission.,$I$ -structure implies that the ring in $P$ cannot have been produced by emission.481 Iu the next section. we first discuss what processes can cause the observed distiibutious of P. o aud RAL in the ving.," In the next section, we first discuss what processes can cause the observed distributions of $P$, $\phi$ and $RM$ in the ring."482 Subsequeutly. we shall describe iu Sect.," Subsequently, we shall describe in Sect."483 6 some known structures and objects in the ISAL ancl discuss whether these are related to the ring structure.," \ref{s5:conn} some known structures and objects in the ISM, and discuss whether these are related to the ring structure."484 From comparison of the 7 aud P maps in Fig. 9..," From comparison of the $I$ and $P$ maps in Fig. \ref{f5:ring},"485 it is clear that the structuic dn P cannot. even iu part. be caused by structure iu I.," it is clear that the structure in $P$ cannot, even in part, be caused by structure in $I$."486 Structure in P can also be created by unissine large-scale structure iu Q iud/or U. but iu Sect.," Structure in $P$ can also be created by missing large-scale structure in $Q$ and/or $U$, but in Sect."487 2.1 we have shown that in these observations mussing large-scale structure cannot dominate.," \ref{ss5:off}488 we have shown that in these observations missing large-scale structure cannot dominate."489 Therefore. the ring in P is most lik‘ly due toa lack of depolarization.," Therefore, the ring in $P$ is most likely due to a lack of depolarization."490 Several depolarization mechamisias can contribute to create the ring in P., Several depolarization mechanisms can contribute to create the ring in $P$.491 We shall discuss briefly the different depolarization mechanisius thought to be of importance (for details see Taverkorn et 22003a.)).," We shall discuss briefly the different depolarization mechanisms thought to be of importance (for details see Haverkorn et 2003a,b)."492 Depth depolarization is defined as all depolarization processes occurring alo1g the line of sight and can be due to different plivsica processes., Depth depolarization is defined as all depolarization processes occurring along the line of sight and can be due to different physical processes.493 First. if tle magnetic feld in a svuchrotron ¢παΤο medium has small-scale structure. then the emitted Gutrinsic) polarization augle of the svuchrotron raclation will varv along the line of sight. causing wavolereth independent depolarization.," First, if the magnetic field in a synchrotron emitting medium has small-scale structure, then the emitted (intrinsic) polarization angle of the synchrotron radiation will vary along the line of sight, causing wavelength independent depolarization."494 Secondly. if the medimm also coutains thermal electrons. the polarization angle o the radiation will be modulates by Faraday rotation as well which causes additioua depolwization (internal Faraday dispersion).," Secondly, if the medium also contains thermal electrons, the polarization angle of the radiation will be modulated by Faraday rotation as well, which causes additional depolarization (internal Faraday dispersion)."495 So siuall-scale structure in (parallel) magnetic field and/or tlerma electron density within the svuchrotron euittiue medium causes simulbscale depolarization., So small-scale structure in (parallel) magnetic field and/or thermal electron density within the synchrotron emitting medium causes small-scale depolarization.496 These processes were described analytically by Sokoloff et ((1998) for severa different geometries of the nmiedinu. aud nuuercallv in Ilaverkornu et ((20035) usine observational constraints.," These processes were described analytically by Sokoloff et (1998) for several different geometries of the medium, and numerically in Haverkorn et (2003b) using observational constraints."497" We modeled the effect of depth depolarization iu the observations of the riug-structure sine simple distributions of electron density 0», and maeunetic field DB on a rectangularC» C»erid.", We modeled the effect of depth depolarization in the observations of the ring-structure using simple distributions of electron density $n_e$ and magnetic field $B$ on a rectangular grid.498 These distributions are not self-cousisteut. but the oulv goal of this simple model is to obtain a P aud o distribution that is simular to the observations. aapproximately linear m o and vine-like in P.," These distributions are not self-consistent, but the only goal of this simple model is to obtain a $P$ and $\phi$ distribution that is similar to the observations, approximately linear in $\phi$ and ring-like in $P$ ."499" Svuchrotron radiation of cuussivity ©XDi is enütted in the regions where D, is nou-zero. aud ds Faracday-rotated while propagatingo through the iieciun. depending ou the local By aud ος distributions."," Synchrotron radiation of emissivity $\varepsilon500\propto B_{\perp}^2$ is emitted in the regions where $B_{\perp}$ is non-zero, and is Faraday-rotated while propagating through the medium, depending on the local $B_{\pl}$ and $n_e$ distributions."501" Furthermore. a polarized background contribution D, is added. which is also Faracday-rvotated."," Furthermore, a polarized background contribution $P_b$ is added, which is also Faraday-rotated."502 Both magnetic field coluponcuts. parallel and perpendicular to the liue of sieht. and the electron deusity distribution were assed to decrease as a power Luv outwards.," Both magnetic field components, parallel and perpendicular to the line of sight, and the electron density distribution were assumed to decrease as a power law outwards."503 The specific values of the power law indices were chosen so that the observed o and RA distributions were approximately reproduced (Fig. 10)).," The specific values of the power law indices were chosen so that the observed $\phi$ and $RM$ distributions were approximately reproduced (Fig. \ref{f5:sim}) ),"504 tthe maenetic field decreases as 1D (oulv at ro»ry. Where ry is a free parameter 00) and the electron cleasity decreases :we 0.," the magnetic field decreases as $r^{-5}$ (only at $r > r_0$, where $r_0$ is a free parameter too) and the electron density decreases as $r^{-0.4}$."505 This figurec» shows the model oitput P aud o at 5 frequencies; and RAL.," This figure shows the model output $P$ and $\phi$ at 5 frequencies, and $RM$."506" We have chosen By=3.5µία. Dj,=2wn eo—05 ?. and P,=1 Ik. This reproduces the sipe and magnitude of o and RAL reasonablv well. but the P distribulon is very differeut frou the observed ouc."," We have chosen $B_{\pl} = -3.5~\mu$ G, $B_{\perp} = -2~\mu$ G, $n_e = 0.2$ $^{-3}$, and $P_b = 4$ K. This reproduces the shape and magnitude of $\phi$ and $RM$ reasonably well, but the $P$ distribution is very different from the observed one."507 First. the predicted P at the center is 1üuch larger thaLis observed.," First, the predicted $P$ at the center is much larger than is observed."508 However. this «liscrepancy could be explaime| by assmniueac lotic maguetic field component at the center of the circle: (vitliotuo worrving vet what this coud mean physically).," However, this discrepancy could be explained by assuming a chaotic magnetic field component at the center of the circle (without worrying yet what this could mean physically)."509 This would result o—1 depolarization :uid a lower observed Pint 1ο center of +t10 modeled circle., This would result in depolarization and a lower observed $P$ in the center of the modeled circle.510 Ilowever. a nore severe problem ds posed bv the waveleneth ependence of the model xedietions.," However, a more severe problem is posed by the wavelength dependence of the model predictions."511" Although our uxxlels lave verv cliffereut DB aud η, distributions and cther sprerical or cvlincdrica sSviunietry. they all show a disinct wavelenetl depeudeuce of the peak in P. asin Fie. 10.."," Although our models have very different $B$ and $n_e$ distributions and either spherical or cylindrical symmetry, they all show a distinct wavelength dependence of the peak in $P$, as in Fig. \ref{f5:sim}."512 But frou the observations. he position of the peak in 7? does not clange with waveleugth. see ie.o 9..," But from the observations, the position of the peak in $P$ does not change with wavelength, see Fig. \ref{f5:ring}. ."513 The wavelenetlo «epeudeuce of P aprears to be a generic property of all models involving de]volarization due to depth depolarizatio1., The wavelength dependence of $P$ appears to be a generic property of all models involving depolarization due to depth depolarization.514 Towever. the mechauisin that can create waveleneth independent depolarization. ttangled magnetic fields. vields structure iu Il. contrary to what is observed.," However, the mechanism that can create wavelength independent depolarization, tangled magnetic fields, yields structure in $I$, contrary to what is observed."515 Therefore we conclude that depth depolarization cannot be the main process that creates the ving in P. although we do expect depth depolarization to be present. iin depolarizing the backeround.," Therefore we conclude that depth depolarization cannot be the main process that creates the ring in $P$, although we do expect depth depolarization to be present, in depolarizing the background."516 Demu depolarization. fthe averaeino out of polarization vectors within oue svuthesized bean. is senificaut iu the field.," Beam depolarization, the averaging out of polarization vectors within one synthesized beam, is significant in the field."517 As there is structure in RAL on beam scales. it is likely fhat RAL varies on scales sunaller than the beau as well.," As there is structure in $RM$ on beam scales, it is likely that $RM$ varies on scales smaller than the beam as well."518" Furtheruxxe. at the »o»tious of the depolarization canals. the iuflueuce of juni depoluization is clearly visible. see Sect, SX. ("," Furthermore, at the positions of the depolarization canals, the influence of beam depolarization is clearly visible, see Sect. \ref{ss5:can}. ("519Partial) beam depolarization can destrov the linear o(M )-xelatiou. but does not necessarilv do so.,"Partial) beam depolarization can destroy the linear $\phi(\lambda^2)$ -relation, but does not necessarily do so."520 At low xlarized iuteusities. the iuffueuce of beam de]volarization can be consideralle. and observed RAL values at low volarized intensity should be 1sed with care. as they ca- deviate from the truce RAL value.," At low polarized intensities, the influence of beam depolarization can be considerable, and observed $RM$ values at low polarized intensity should be used with care, as they can deviate from the true $RM$ value."521 Deuu depolarization. due to chaotic structure d- huization angle on scales smaller than the beam. can arise dueto taneled maeuetic fields and/or sinall- variations in thermal electron ceusity.," Beam depolarization, due to chaotic structure in polarization angle on scales smaller than the beam, can arise dueto tangled magnetic fields and/or small-scale variations in thermal electron density."522 À possible explanation for the lack of P iu the central part of the ving couldbe a chaotic magnetic field in the ceuter. while the outer parts of the rime must exhibit very cohercut," A possible explanation for the lack of $P$ in the central part of the ring couldbe a chaotic magnetic field in the center, while the outer parts of the ring must exhibit very coherent"523time for anything other than the tendeney for gap formation and the elobal cise morpholgv to be inferred.,time for anything other than the tendency for gap formation and the global disc morpholgy to be inferred.524 Consequently run G4 will not be discussed further here., Consequently run G4 will not be discussed further here.525 Run G5 has been described in paper LL. ancl showed a tendeney toward. clear gap formation with the response olt1e disc due to the presence of the planet being strongly. non linear.," Run G5 has been described in paper III, and showed a tendency toward clear gap formation with the response of the disc due to the presence of the planet being strongly non linear."526 Consequently the perturbations induced in the disc bv the protoplanet are very much larger than those tha arise because of the turbulence., Consequently the perturbations induced in the disc by the protoplanet are very much larger than those that arise because of the turbulence.527 This results in the Illuctuations in the torque experienced. by the protoplanet belig sienificantly smaller (in relative terms) than observed in the previously described. runs Cl. 62. and. €i3. and a well defined running time average of the torque. being obtained.," This results in the fluctuations in the torque experienced by the protoplanet being significantly smaller (in relative terms) than observed in the previously described runs G1, G2, and G3, and a well defined running time average of the torque being obtained."528 Figure 21. shows the running time average o “the orque per unit mass obtained from run G5. with the u»per ine corresponding to the inner disc torque. the lowest line corresponding to the outer cise torque. and the middle line he running time average of the total torque.," Figure \ref{fig22} shows the running time average of the torque per unit mass obtained from run G5, with the upper line corresponding to the inner disc torque, the lowest line corresponding to the outer disc torque, and the middle line the running time average of the total torque."529 Lt is clear rom his figure that a large torque is exerted on the protoplanet ior to gap formation. but that as the gap proceecs lo open and material is pushed. away from the planet the orque diminishes.," It is clear from this figure that a large torque is exerted on the protoplanet prior to gap formation, but that as the gap proceeds to open and material is pushed away from the planet the torque diminishes."530 The running time averaged torques due o the inner and outer disc appear to be approaching well defined asymptotic values. which are unalfected by turbiwent luctuations. but the continued decrease in the running (ime averages indicates that gap formation is still ongoing at the end of the simulation.," The running time averaged torques due to the inner and outer disc appear to be approaching well defined asymptotic values, which are unaffected by turbulent fluctuations, but the continued decrease in the running time averages indicates that gap formation is still ongoing at the end of the simulation."531 We note that the use of a closed. inner boundarv dn his simulation. combined. with the close proximity of the λαοί to the inner boundary. cause the density of inner disc to be maintained at an artificially high love after gap formation.," We note that the use of a closed inner boundary in this simulation, combined with the close proximity of the planet to the inner boundary, cause the density of the inner disc to be maintained at an artificially high level after gap formation."532 This leads o the net torque on 1ο λαοί being negative out. close to zero., This leads to the net torque on the planet being negative but close to zero.533 Under more σοιlora circumstances in which 10 inner disc can accrete onto the central star. an inner cavity is expected to form such the he torque on the protoplanet is dominated. by the outer disc (e.g. Nelson et al.," Under more general circumstances in which the inner disc can accrete onto the central star, an inner cavity is expected to form such that the torque on the protoplanet is dominated by the outer disc (e.g. Nelson et al."534 2000)., 2000).535 It we adopt the dise mode described. in section 3.1 used to normatlisecl the results oresented in figure 2.. anc estimate the migration time using equation 2 and a torque per unit mass due to the outer clise in ligure 21 of 1-210 then we obtain Taig2+10! vr. for a planet at 5.2 AU.," If we adopt the disc model described in section \ref{calibration} used to normalised the results presented in figure \ref{fig2}, and estimate the migration time using equation \ref{tmig-sim} and a torque per unit mass due to the outer disc in figure \ref{fig22} of $T=-10^{-5}$, then we obtain $\tau_{mig} \simeq 4 \times 10^4$ yr, for a planet at 5.2 AU."536 The tvpe IH migration time appropriate to gap forming protoplancts is given by the viscous evolution time Tig=(-EMo) where p=all-Q is the kinematic viscosity., The type II migration time appropriate to gap forming protoplanets is given by the viscous evolution time $\tau_{mig}= (2r_p^2)/(3 \nu)$ where $\nu=\alpha H^2 \Omega$ is the kinematic viscosity.537 Fora disc model with à27.10 and {ἐν=0.01. the estimated. type Η migration tin10 ds Τοντ—45.101 vr. in: reasonable agreement with. the reult obtained from the simulation (9.," For a disc model with $\alpha \simeq 7 \times 10^{-3}$ and $H/r=0.07$, the estimated type II migration time is $\tau_{mig}=4.5 \times 10^4$ yr, in reasonable agreement with the result obtained from the simulation G5."538 We note that the above estimates for type LE migration times correspond to disc models with full 2x azimuthal domains. and that it is unclear which precise value he running mean of the outer clise torque will approach once gap formation is complete.," We note that the above estimates for type II migration times correspond to disc models with full $2 \pi$ azimuthal domains, and that it is unclear which precise value the running mean of the outer disc torque will approach once gap formation is complete."539 Nonetheless. the reasonable agreement obtained in the estimates suggests that gap forming protoplanets in turbulent disces undergo migration at the expected type LE rate;," Nonetheless, the reasonable agreement obtained in the estimates suggests that gap forming protoplanets in turbulent discs undergo migration at the expected type II rate."540 A similar result was obtain ciun paper HE for tvpe HE migration rates in turbulent disces with full 27 azimuthal domains., A similar result was obtained in paper II for type II migration rates in turbulent discs with full $2 \pi$ azimuthal domains.541 lt is clear that a well defined trend. arises. when considering the interaction between embedded protoplanets ancl turbulent cises., It is clear that a well defined trend arises when considering the interaction between embedded protoplanets and turbulent discs.542 Lower mass objects that are unable to perturh the turbulent background. flow significantly are subject to strong torque Uuctuations that are likely to dominate. their orbital evolution., Lower mass objects that are unable to perturb the turbulent background flow significantly are subject to strong torque fluctuations that are likely to dominate their orbital evolution.543 As the protoplanet mass increases so that the amplitude of the spiral wakes that it excites become larger than the turbulent density fluctuations. the relative magnitudes of the torque Iuctuations decrease. and the migration is likely to become similar to tvpe I migration (although with a significant noise component).," As the protoplanet mass increases so that the amplitude of the spiral wakes that it excites become larger than the turbulent density fluctuations, the relative magnitudes of the torque fluctuations decrease, and the migration is likely to become similar to type I migration (although with a significant noise component)."544 For larger protoplanet masses that allow eap formation. the ellect of the turbulent Ductuations is small. with the migration being essentially the same as the standard type LE picture.," For larger protoplanet masses that allow gap formation, the effect of the turbulent fluctuations is small, with the migration being essentially the same as the standard type II picture."545 These trends are also observed in the shearing box simulations that are described below., These trends are also observed in the shearing box simulations that are described below.546 Details of the shearing box simulations Bal - Bat are given in table 2.., Details of the shearing box simulations Ba1 - Ba4 are given in table \ref{table2}.547" These were cach continued. from a siniulation with fully developed: turbulence. BaO alter inserting a protoplanet with values of the dimensionless parameter CAML,PO)=ALR?(AL,HU) measuring the mass of the protoplanet equal to 0.1.0.3.1 and. 2 respectively."," These were each continued from a simulation with fully developed turbulence Ba0 after inserting a protoplanet with values of the dimensionless parameter $GM_p /( H^3\Omega_p^2) = M_p R^3/(M_* H^3)$ measuring the mass of the protoplanet equal to $0.1, 0.3, 1$ and $2$ respectively."548" In. this section. ©, and are the angular velocity and radius of the centre of the box."," In this section, $\Omega_p$ and $R$ are the angular velocity and radius of the centre of the box."549 Thus simulations Bal ancl Ba2 are directly comparable to the global simulations G2 and G8 in terms, Thus simulations Ba1 and Ba2 are directly comparable to the global simulations G2 and G3 in terms550"The best fit position for3125... found by averaging the OT order data from three IIRC-S datasets. is (CI2000) =he2022POG. the31725'|9""6 with rums Ες of zm6 iu cach COOLinate due to aaspect uncertainties.","The best fit position for, found by averaging the $0^{\rm th}$ order data from the three HRC-S datasets, is (J2000) $\alpha=07^{\rm551h}20^{\rm m}24\fs96$, $\delta=-31\degr25\arcmin49\farcs6$, with rms uncertainty of $\approx 0\farcs6$ in each coordinate due to aspect uncertainties."552 This is cousisteut (171 away) with the optical position (ναι&vauKerkwijk1998)., This is consistent $1\farcs4$ away) with the optical position \citep{kvk98}.553". The N-rav source appears unresolved and its profile is consistent with that of a point source (half-power radius of zz 05),", The X-ray source appears unresolved and its profile is consistent with that of a point source (half-power radius of $\approx 0\farcs5$ ).554 For the IIIRI data. we extracted the events within a circle of radius 145 pixels (2275) coutered ou the source;," For the HRI data, we extracted the events within a circle of radius 45 pixels $22\farcs5$ ) centered on the source."555 We used a circle of radius 200 pixels (100) for the PSPC data., We used a circle of radius 200 pixels $100\arcsec$ ) for the PSPC data.556 These events were barveeutered using the programs aud aud corrected to Barvecutric Dynamical Time (TDB) according to Cox(2000.p.11).., These events were barycentered using the programs and and corrected to Barycentric Dynamical Time (TDB) according to \citet[][p.\ 14]{allen}.557 We extracted the LLECS eveuts within a circle with radius of 25 pixels (200) centered on the source and restricted to those with pulscanvariant (PI) amplitudes that were less than 90 (energies «0.95 keV). m order to maximize the sieual-to-noise.," We extracted the LECS events within a circle with radius of 25 pixels $200\arcsec$ ) centered on the source and restricted to those with pulse-invariant (PI) amplitudes that were less than 90 (energies $< 0.95$ keV), in order to maximize the signal-to-noise."558 Finally. we barvceeutered the events with the toolbaryconv.," Finally, we barycentered the events with the tool."559". For cach dataset, we computed Z? power spectra around the known &.39-8 period."," For each dataset, we computed $Z_{1}^{2}$ power spectra around the known 8.39-s period."560 Specifically. we explored the period range from) 8.3976 s to S.105 s iu steps of7ps (oversampling bv factors of 20S00 relative the nominal step-size of PZ/AT. where Py=8.39 s is the approximate period aud AT is the span of the dataset from Table 1)).," Specifically, we explored the period range from 8.376 s to 8.405 s in steps of $7 \mbox{ }\mu{\rm s}$ (oversampling by factors of 20–800 relative the nominal step-size of $P_{0}^{2}/\Delta561T$, where $P_{0}=8.39$ s is the approximate period and $\Delta T$ is the span of the dataset from Table \ref{tab:sum}) )."562 As can be secu from Figure 1. all but the MURC-S aud IIIRI-2 datasets vielded unambiguous period estimates., As can be seen from Figure \ref{fig:zn2} all but the HRC-S and HRI-2 datasets yielded unambiguous period estimates.563 For the IIRC-S and IIRE-2 sets the period estimates are anbieuous because the large gaps iu the observations result in strong side-lobes., For the HRC-S and HRI-2 sets the period estimates are ambiguous because the large gaps in the observations result in strong side-lobes.564 In Figure 2.. we display the best-fit periods for the munambiguous determünatious as well as possible periods for the ITRC-S aud IIBE-2 datasets.," In Figure \ref{fig:sum}, we display the best-fit periods for the unambiguous determinations as well as possible periods for the HRC-S and HRI-2 datasets."565 As can be seen from Figure 2. the ambieuity of the IIRC-S aud IIRI-2 datasets can be resolved provided we assiune (reasonably) that the period evolves smoothly with time.," As can be seen from Figure \ref{fig:sum}, the ambiguity of the HRC-S and HRI-2 datasets can be resolved provided we assume (reasonably) that the period evolves smoothly with time."566 Our choice of period (for IIRC-S aud HRE2) and the best Gt periods (for the other datasets) are shown in Table 1.., Our choice of period (for HRC-S and HRI-2) and the best fit periods (for the other datasets) are shown in Table \ref{tab:sum}.567 The errors ou the periods were determined using the analytical expression from Ransom(2001)., The errors on the periods were determined using the analytical expression from \citet{ransom01}.568. While that expression was derived for FFT power spectra. Zi power spectra have the same statistics (both are exponcutially distributed) so the same relations should apply (we lave verified this with numerical simulations).," While that expression was derived for FFT power spectra, $Z_{1}^{2}$ power spectra have the same statistics (both are exponentially distributed) so the same relations should apply (we have verified this with numerical simulations)."569 We also show iuTable 1. times-of-arrival (TOAs) for cach of the datasets.," We also show inTable \ref{tab:sum}570 times-of-arrival (TOAs) for each of the datasets."571 The data in Table are consistent with there being no nieasurable P: fitting for a linear spin-down gives Po—SS91115(8) s at NJD 51633 aud, The data in Table \ref{tab:sum} are consistent with there being no measurable $\dot{P}$ : fitting for a linear spin-down gives $P=8.391115(8)$ s at MJD 51633 and572significance level.,significance level.573 Assuming that the jet emission is opticallv thin. this result if true [or I1IBLs. implies that the IIDLs show predominantly longitudinal jet. 2 fields. while the LBLs possess predominantly (ransverse jel D fields.," Assuming that the jet emission is optically thin, this result if true for HBLs, implies that the HBLs show predominantly longitudinal jet $B$ fields, while the LBLs possess predominantly transverse jet $B$ fields."574 Clearly (his bimodality in D field structure needs to be tested with a larger sample of IIBLs., Clearly this bimodality in $B$ field structure needs to be tested with a larger sample of HBLs.575 We note that the jet EVPAs of those IIBLs which have allernatively been classified as IBLs by ?.. occupy the middle of the EVPA range (between 20 - 70°).," We note that the jet EVPAs of those HBLs which have alternatively been classified as IBLs by \citet{Nieppola06}, occupy the middle of the EVPA range (between 20 - $\degr$ )."576 This behaviour also warrants further investigation., This behaviour also warrants further investigation.577 some of the IIDLs show evidence for a ‘spine-sheath’ 2 field structure. with the inner region of the jet having transverse 2 fields and the edges having longitudinal / fields.," Some of the HBLs show evidence for a `spine-sheath' $B$ field structure, with the inner region of the jet having transverse $B$ fields and the edges having longitudinal $B$ fields."578 This tvpe of 2 field structure has been observed in other blazars (727). and it could result from interaction of the jet with the surrounding medium. or due to jet acceleration being a function of the angular distance from the jel axis. producing a velocity. structure (?)..," This type of $B$ field structure has been observed in other blazars \citep{Attridge99,Giroletti04b} and it could result from interaction of the jet with the surrounding medium, or due to jet acceleration being a function of the angular distance from the jet axis, producing a velocity structure \citep{Ghisellini05}."579 Alternativelv. as ? and ? have pointed out. this could be associated with the presence of a helical 2 field associated with the jets of these objects.," Alternatively, as \citet{GabuzdaMurrayCronin04} and \citet{Lyutikov05} have pointed out, this could be associated with the presence of a helical $B$ field associated with the jets of these objects."580" Such fields could come about in a natural wav due to (he ""winding up” of a seed field via the combination of outflow. aud rotation of the central black-holeaccretion-disk system.", Such fields could come about in a natural way due to the “winding up” of a seed field via the combination of outflow and rotation of the central black-hole–accretion-disk system.581 Particularlygood examples of a 'spine-sheath! D [field structure are 1227+255 (Fig. 10)), Particularlygood examples of a `spine-sheath' $B$ field structure are 1227+255 (Fig. \ref{fig:1227}) )582 and 11214502 (Fie. 12))., and 1727+502 (Fig. \ref{fig:1727}) ).583 We were able to derive tentative (wo-epoch apparent speeds for a number of the objects in our sample from the mocdel-fitiing results in Table 5.. either on their own or combined," We were able to derive tentative two-epoch apparent speeds for a number of the objects in our sample from the model-fitting results in Table \ref{modelBLL}, , either on their own or combined"584electronic. form.,electronic form.585onlv.. They are also available [rom the authors., They are also available from the authors.586 For 10 of our 12 sample galaxies. NICMOS imaging with theZ5 is available from theS57 archive.," For 10 of our 12 sample galaxies, NICMOS imaging with the is available from the archive."587 We retrieved the re-reduced FIGOW (comparable to 4-band) images from the archive., We retrieved the re-reduced F160W (comparable to $H$ -band) images from the archive.588 However. we improved the quality of some of these images by doing additional data reduction to remove artifacts.," However, we improved the quality of some of these images by doing additional data reduction to remove artifacts."589 We relied on header. information to place the images on an astrometrically correct. erid., We relied on header information to place the images on an astrometrically correct grid.590 The images are all taken with the NIC2 camera. with a pixel size of 07075.," The images are all taken with the NIC2 camera, with a pixel size of 0.075."591 1n most cases. the image retrieved. from the archive is a combination of several individual exposures.," In most cases, the image retrieved from the archive is a combination of several individual exposures."592 For NGC 3516 and NGC 3982. however. one single exposure was available. and these images in fact improved most due to our additional data reduction.," For NGC 3516 and NGC 3982, however, one single exposure was available, and these images in fact improved most due to our additional data reduction."593 Regan Mulchaey. (1999). published: two of these images (NGC 3516 and NGC 3982)., Regan Mulchaey (1999) published two of these images (NGC 3516 and NGC 3982).594 We show the central areas of all images in bie., We show the central areas of all images in Fig.595 1. with the same scale and orientation.," 1, with the same scale and orientation."596 In most of the objects. a wealth of detail can be seen in the CNR.," In most of the objects, a wealth of detail can be seen in the CNR."597 The emission usually coincides with the location of the SE ring. and most of the individual bright knots are due to regions of current SE.," The emission usually coincides with the location of the SF ring, and most of the individual bright knots are due to regions of current SF."598 Dust lanes and/or SE regions often outline spiral-like patterns. which will be discussed in more detail below. and in Paper LL.," Dust lanes and/or SF regions often outline spiral-like patterns, which will be discussed in more detail below, and in Paper III."599 In this section. we describe some of the results of the NIIt imaging of our sample galaxies. as shown in detail in Fig.," In this section, we describe some of the results of the NIR imaging of our sample galaxies, as shown in detail in Fig."600 1(HST NIR images) and Fig., 1 NIR images) and Fig.601 2 (ground based. multi-band images and. profile fits)., 2 (ground based multi-band images and profile fits).602 A more systematic study of parameters derived. from these data in combination with optical imaging of the complete galaxy dises is forthcoming (Papers LE ane LL)., A more systematic study of parameters derived from these data in combination with optical imaging of the complete galaxy discs is forthcoming (Papers II and III).603 Our broad-band NI images are remarkably smooth. ane do not show any structure in the CN (Fig.," Our broad-band NIR images are remarkably smooth, and do not show any structure in the CNR (Fig."604 2a), 2a).605 The colour index images. however. show a red ring-like structure. possibly outlining a single spiral arm that departs from the," The colour index images, however, show a red ring-like structure, possibly outlining a single spiral arm that departs from the"606Iu real SZ observations. instrumental ioise and primary CMB cause additional errors iu the SZ statistics such as the power spectrum and peak παοι counts.,"In real SZ observations, instrumental noise and primary CMB cause additional errors in the SZ statistics such as the power spectrum and peak number counts."607 We ueed to estimate these ellects to derive optimal observing strategies to ueasure these statistics in the preseuce of noise., We need to estimate these effects to derive optimal observing strategies to measure these statistics in the presence of noise.608 With these observational errors. our methods 2)) to extract 3D eas information is liitec aud we must check their feasibility.," With these observational errors, our methods \ref{sec:application}) ) to extract 3D gas information is limited and we must check their feasibility."609 In this section. we take AMIBA as our target to address tlese Isstles.," In this section, we take AMIBA as our target to address these issues."610 AMIBA is a 19 element interferometer with 1.2 meter dishes., AMIBA is a 19 element interferometer with $1.2$ meter dishes.611 All dishes are closely packed in three concentric rings., All dishes are closely packed in three concentric rings.612 It operates at Ager=90 Ghz with Av=16 Ghz. system noise Z4=100 Is and system ellicieney 10.7.," It operates at $\nu_{\rm center}=90$ Ghz with $\Delta \nu=16$ Ghz, system noise $T_{\rm sys}=100$ K and system efficiency $\eta\sim0.7$."613 At this Lrequeney. O2—1L.6y with Sp(90Chz)0.5.," At this frequency, $\Theta\simeq -1.6y$ with $S_T(90 {\rm Ghz})\simeq0.8$."614 The goal of this experiment is to image maps of the CMB sky with are minute resolution., The goal of this experiment is to image maps of the CMB sky with arc minute resolution.615 We consider observations with fixed integration time aud aim at fiudiug the optimal sky area Q axl sky fractional coverage Fas=OfI5 for a given statistics., We consider observations with fixed integration time and aim at finding the optimal sky area $\Omega$ and sky fractional coverage $f_{\rm sky}=\Omega/4\pi$ for a given statistics.616 For closely packed interferometers observing such weak signals. te erouud fringe can be a major source of noise.," For closely packed interferometers observing such weak signals, the ground fringe can be a major source of noise."617 To eliminate the [n]0‘ound fringe. AMIBA plans to drift scan: the telescope is parked while the sky critts by.," To eliminate the ground fringe, AMIBA plans to drift scan: the telescope is parked while the sky drifts by."618 Thus assures that the grouxd frige renalus constant with time., This assures that the ground fringe remains constant with time.619 The mean value of each fringe is then subtracted [rom the SCall. Cleauly elimiuatlug the erouud.," The mean value of each fringe is then subtracted from the scan, cleanly eliminating the ground."620 A [ield is mosaicked by a series of adjacent scans. and the nost uilorn coverage Is achieved by incrementally offsetting the pointing ceuter ou each sceau to vield a finely samplec 2-D map.," A field is mosaicked by a series of adjacent scans, and the most uniform coverage is achieved by incrementally offsetting the pointing center on each scan to yield a finely sampled 2-D map."621 The raw output of the experiment are correlations. two for eacl baseine. polarizaiol and frequency chanuel correspouding to the real aud. imaginary correlat«Y outjus.," The raw output of the experiment are correlations, two for each baseline, polarization and frequency channel, corresponding to the real and imaginary correlator outputs."622 We ca1 Iüuk of each of these outputs to correspoud to an image of the sky filterec throeh some auisol‘opic beam., We can think of each of these outputs to correspond to an image of the sky filtered through some anisotropic beam.623 As a first step. we cau combine degenerate baselines ancl »olarizatiois. recluciug the 171 baselines to 30 non-degenerate baselines.," As a first step, we can combine degenerate baselines and polarizations, reducing the 171 baselines to 30 non-degenerate baselines."624 Since tle CAMB is expeced to not )e significantly inpolarized. we Call COIDDine the two polarization channels. leadiug to 60 raw inays per [requecy channel.," Since the CMB is expected to not be significantly unpolarized, we can combine the two polarization channels, leading to 60 raw maps per frequency channel."625 These Naps can be mereed optimally 1ito one globa map by couvolviug: each map wit its own beam. txd scalingl each nap to the same noise level. aud coadcding these uaps. resultiny ed ina “Clean map.," These maps can be merged optimally into one global map by convolving each map with its own beam, and scaling each map to the same noise level, and coadding these maps, resulting in a 'clean' map."626 Each of he coustiueut naps lac explicily white noise. so tlie 1olse statistics of te stunmect lap t‘e easily compuable.," Each of the constituent maps had explicitly white noise, so the noise statistics of the summed map are easily computable."627 The ‘clea1 nap can be deconvolved by the uatural beam. resulting in a --atural map.," The 'clean' map can be deconvolved by the natural beam, resulting in a 'natural' map."628 ΤΙis natural ma dIs an image of the sky. couvoved with the natt‘al beam of the telescope plus whie noise., This 'natural' map is an image of the sky convolved with the natural beam of the telescope plus white noise.629 The arele aveaged natural beam is si0wn in fig. 9.., The angle averaged natural beam is shown in fig. \ref{fig:beam}.630" The CMB intensity fluctuation df, uaeasttrec by AMIBA has three components: the primary CMB. te SZ effect aud the instrumental olse."," The CMB intensity fluctuation $\delta I_{\nu}$ measured by AMIBA has three components: the primary CMB, the SZ effect and the instrumental noise."631 I is related to the temperature [Iuctuatjou by, It is related to the temperature fluctuation by632a chain of hvdrostatie stages.,a chain of hydrostatic stages.633 “Phe assumption that TEE correlates with line formation depths can be tested as well., The assumption that TEE correlates with line formation depths can be tested as well.634 We applied our plane.parallel models to compute formation depths of the line cores of the ancl lines., We applied our plane–parallel models to compute formation depths of the line cores of the and lines.635 |t appeared that the core of the strong 4686 line forms much closer to the surface (at. column mass  0.01 ecem 7) than any of the lines., It appeared that the core of the strong 4686 line forms much closer to the surface (at column mass $\sim$ 0.01 $^{-2}$ ) than any of the lines.636 However. this was not the case with the two other lines (5411 and 4541 AY) we used in our study.," However, this was not the case with the two other lines (5411 and 4541 ) we used in our study."637 Similar tests have been carried out for other eroups of lines but assuming an LYE line formation., Similar tests have been carried out for other groups of lines but assuming an LTE line formation.638 These exercises suggest that. before. combining lines in different. groups and computing their average RVs. one has to be sure (of course under the assumption that our planeparallel models are applicable) that their depths of formation are similar.," These exercises suggest that before combining lines in different groups and computing their average RVs, one has to be sure (of course under the assumption that our plane–parallel models are applicable) that their depths of formation are similar."639 The velocity.excitation relationship found for many hot supergiants (Llutchings 1976) exists also in HD. 188209., The velocity–excitation relationship found for many hot supergiants (Hutchings 1976) exists also in HD 188209.640 In Figs., In Figs.641 5 and 6 we present plots of mean RY versus TEE and standard: deviations of the mean RY versus “TEL for the different groups of lines computed. for all dates. (the last two lines in Table 2)., 5 and 6 we present plots of mean RV versus TEE and standard deviations of the mean RV versus TEE for the different groups of lines computed for all dates (the last two lines in Table 2).642 These plots exclude a pure Ixeplerian. motion as the only cause of the ΗΝ variations., These plots exclude a pure Keplerian motion as the only cause of the RV variations.643 Pulsations and stochastic motions (intrinsic wind variations caused by some hyedrodynamical instabilities) in the wind can bring to the RV. variations as well., Pulsations and stochastic motions (intrinsic wind variations caused by some hydrodynamical instabilities) in the wind can bring to the RV variations as well.644 I£ we suppose that stochastic variations are not important. then the existence of a standard deviation-EEI. relationship would suggest that deeper lavers in the atmosphere pulsate with smaller amplitudes.," If we suppose that stochastic variations are not important, then the existence of a standard deviation-TEE relationship would suggest that deeper layers in the atmosphere pulsate with smaller amplitudes."645 “Phe aniplituce of pulsations increases when approaching to the surface., The amplitude of pulsations increases when approaching to the surface.646 The period search was carried out with help of the package (Dhillon Privett 1997) of the software., The period search was carried out with help of the package (Dhillon Privett 1997) of the software.647 The following strategy was applied when looking for a periodic signal in the RY curves of dillerent groups of lines., The following strategy was applied when looking for a periodic signal in the RV curves of different groups of lines.648 Due to the large gaps (especially between runs 5 and. 6) in our observations. we first. decided to study each of the runs 5. 6 and 7 separately.," Due to the large gaps (especially between runs 5 and 6) in our observations, we first decided to study each of the runs 5, 6 and 7 separately."649 The algorithm (Roberts et al., The algorithm (Roberts et al.650 LOST) was emploved. to cover a space of loop gains rom 0.2 to 0.6 and the number of iterations from LO to ew hundreds., 1987) was employed to cover a space of loop gains from 0.2 to 0.6 and the number of iterations from 10 to few hundreds.651 The convergence. of the periodograms was achieved for the majority of eroups of lines in all three runs., The convergence of the periodograms was achieved for the majority of groups of lines in all three runs.652 The mean frequeney suggested by most of the groups in all hree runs is O4440.05 + (2.24 days)., The mean frequency suggested by most of the groups in all three runs is $\pm$ 0.05 $^{-1}$ (2.24 days).653 However. this »eriod is very close to the Nvquist frequency Smallest Data Interval)) of the data and might be misleading.," However, this period is very close to the Nyquist frequency $\times$ Smallest Data Interval)) of the data and might be misleading."654 We have also looked for periodic signals in the combined data of all groups obtained in all runs (Table. 2)., We have also looked for periodic signals in the combined data of all groups obtained in all runs (Table 2).655" The maximum and minimum. frequencies were set to LOO and QO. respectively,"," The maximum and minimum frequencies were set to 100 and 0, respectively."656 A analysis of the time series of the majority of groups revealed a frequency of O.5140.1 days (1.95 days)., A analysis of the time series of the majority of groups revealed a frequency of $\pm$ 0.1 $^{-1}$ (1.95 days).657 The gain factor was 0.1 at the first iteration. hen was decreased. by 15-20 iteration until stabilization.," The gain factor was 0.1 at the first iteration, then was decreased by 15-20 iteration until stabilization."658 The average RY for each date obtained by averaging the Ws of allthe groups revealed a frequency. of 0470.12 lon (2.1 davs)., The average RV for each date obtained by averaging the RVs of allthe groups revealed a frequency of $\pm$ 0.12 $^{-1}$ (2.1 days).659 Again.: both frequencies⋅: are very. close o the Nyquist frequeney ane we should discard them.," Again, both frequencies are very close to the Nyquist frequency and we should discard them."660 We must point out that our periodograms did not show any »aks at frequencies smaller than 0.4., We must point out that our periodograms did not show any peaks at frequencies smaller than 0.4 $^{-1}$.661 The next strongest peak which appeared. in our periodograms was near 0.1564:0.15. + (6.4 days), The next strongest peak which appeared in our periodograms was near $\pm$ 0.15 $^{-1}$ (6.4 days).662 Clearly this period. is not alfected by sampling., Clearly this period is not affected by sampling.663 We have also analysed the RY data using the Lomb-Scargle method (Lomb 1976. Scargle 1982) which allows to compute statistical probability. of peaks in periocdograms.," We have also analysed the RV data using the Lomb-Scargle method (Lomb 1976, Scargle 1982) which allows to compute statistical probability of peaks in periodograms."664 To ensure reliable significance values. the minimum. number of permutations was set. LOO.," To ensure reliable significance values, the minimum number of permutations was set 100."665" The probability that the period is not equal to 6.4 days. was alwavs less than 30 ο,A.", The probability that the period is not equal to 6.4 days was always less than 30 $\%$.666 The peak at 6.4 days appears in all periodograms but given its significance value. we cannot definitely rule out its non-physical nature.," The peak at 6.4 days appears in all periodograms but given its significance value, we cannot definitely rule out its non-physical nature."667 In Figs., In Figs.668 7 and S we show the and the periodogranis and the fitting of a sin curve to folded data. respectively.," 7 and 8 we show the and the periodograms and the fitting of a sin curve to folded data, respectively."669 All hot supergiants have variable profiles in their spectra (Rosendahl 1973)., All hot supergiants have variable profiles in their spectra (Rosendahl 1973).670 The shape of the may vary from P (νο to inverse P €vg. double-peaked.. pure absorption and/or emission (Ebbets 1982) with typical time-scales of the order of davs.," The shape of the may vary from P Cyg to inverse P Cyg, double-peaked, pure absorption and/or emission (Ebbets 1982) with typical time-scales of the order of days."671 The nature of this variability is not vet understood., The nature of this variability is not yet understood.672 The existence of variable asymmetric outllows/infalls of matter ancl some corotating structures related. to. surface. inhomogenitics ancl possible magnetic fields have been proposed. for BA-type (Ixaufer et al., The existence of variable asymmetric outflows/infalls of matter and some corotating structures related to surface inhomogenities and possible magnetic fields have been proposed for BA-type (Kaufer et al.673 1996) and. O-tvpe (Fullerton. et. al., 1996) and O-type (Fullerton et al.674.. 1996: Ixaper. ct al., 1996; Kaper et al.675 1997) supergiants., 1997) supergiants.676 In addition. there have been. detailed: stucdes of the rotating giant loop in 7 Orionis (Ixraelian. Chentsov Musaev 1997) and the corotating spiral structures in LED. 64760 and LID 93521 (Llowarth et al.," In addition, there have been detailed studies of the rotating giant loop in $\beta$ Orionis (Israelian, Chentsov Musaev 1997) and the corotating spiral structures in HD 64760 and HD 93521 (Howarth et al."677 1998: Fullerton et al., 1998; Fullerton et al.678 1997)., 1997).679 Lt is of course very σοι to distinguish. binary svstenms from single stars without understanding the nature of variability., It is of course very difficult to distinguish binary systems from single stars without understanding the nature of variability.680 As Thaller (1907) suggests. the can suller some peculiar variability due to the colliding winds in a binary system.," As Thaller (1997) suggests, the can suffer some peculiar variability due to the colliding winds in a binary system."681 The time evolution of profiles in three cilferent runs is shown in Figure 9., The time evolution of profiles in three different runs is shown in Figure 9.682 The average profile consists of three components. a central emission. accompanied. by blue and red. absorptions.," The average profile consists of three components, a central emission accompanied by blue and red absorptions."683 We have not observed. a single profile without a central reversal., We have not observed a single profile without a central reversal.684 Ehe emission. is not always centered. exactly on the rest wavelength but is varving., The emission is not always centered exactly on the rest wavelength but is varying.685 It may approach the continuum level. go above it ancl clecrease rapidly in strength.," It may approach the continuum level, go above it and decrease rapidly in strength."686 Apparently the time-scale of the variability is at least one day., Apparently the time-scale of the variability is at least one day.687" The 5""! run has been divided into two parts (runs 5a 5b) with four successive nights in each.", The $^{\rm th}$ run has been divided into two parts (runs 5a 5b) with four successive nights in each.688 Ehe variability is observed over a wide range from about 400 to 200 kims, The variability is observed over a wide range from about $-$ 400 to 200 ${\rm km}~{\rm s}^{-1}$ .689 We have already seen in Section 4.2 that our spherical, We have already seen in Section 4.2 that our spherical690As a check on our procedure. we stack the best fits to the individual SEDs for both models.,"As a check on our procedure, we stack the best fits to the individual SEDs for both models."691 The stacks are siuilar to the purple aud orange curves in Figure 3.., The stacks are similar to the purple and orange curves in Figure \ref{fig:sed}.692 Along the same lines. we assess the qualities of the individual fits.," Along the same lines, we assess the qualities of the individual fits."693 All galaxies favor the Druzual&Chazr-lot(2003). models. with median values for (zeus aud of 0.91 and L3. respectively.," All galaxies favor the \cite{bc03} models, with median values for $\chi^2_{\rm BC03}$ and $\chi^2_{\rm M05}$ of 0.91 and 4.3, respectively."694 VaysWhereas both the Brugual&Charlot(2003) and Maraston(2005) SPS models can reproduce the aan ccolors in the selection box. the exact colors at fixed age and star formation timescale are slightlv different.," Whereas both the \cite{bc03} and \cite{ma05} SPS models can reproduce the and colors in the selection box, the exact colors at fixed age and star formation timescale are slightly different."695 Iu order to test whether these πια] differences cause ai bias that favors a particular SPS aodel. we split the post-starburst galaxy sample at το. andrepeatedth canalysis forboth samples.," In order to test whether these small differences cause a bias that favors a particular SPS model, we split the post-starburst galaxy sample at $=0.55$, and repeated the analysis for both sub-samples."696 BothSE Dsaresignificantlybetter fithythe sub BrusulC ο Tite Fulleom po dex.," Both SEDs are significantly better fit by the \cite{bc03} models (with similar fit qualities as for the full composite spectrum), where the redder sample is older by $\sim$ 0.1 dex."697" Additionally, we repeat the analysis for a redder yomndary ViniO.6. gieliingasamplcof-110 ealaxies."," Additionally, we repeat the analysis for a redder boundary $<0.6$, yielding a sample of $\sim$ 110 galaxies."698 The composite spectrum is better fit bv a slightly older stellar population. but stil strongly avors the Brugual&Charlot(2003) models above he Maraston(2005).," The composite spectrum is better fit by a slightly older stellar population, but still strongly favors the \cite{bc03} models above the \cite{ma05}."699.. Altogether. this confirms our biased selection.," Altogether, this confirms our unbiased selection."700 MacArthuretal.(2010) compare the near-infrared Huxes of two spiral galaxies to predictions frou loue-slit spectra. reporting better consistency with the Alaraston(2005) models than with Druzual&Char-ot (2003).," \cite{mac10} compare the near-infrared fluxes of two spiral galaxies to predictions from long-slit spectra, reporting better consistency with the \cite{ma05} models than with \cite{bc03}."701. However. the interpretation of their results is coniplicated by the preseuce of a siguificautlv. older stellar population. which coutributes to the total light. aud the presence of dust. which nav inimuc the effects of a TP-AGB star population.," However, the interpretation of their results is complicated by the presence of a significantly older stellar population, which contributes to the total light, and the presence of dust, which may mimic the effects of a TP-AGB star population."702 Nonetheless. if is possible that the Maraston(2005) uodel indeed provides a better description for the SED shape during the evolution phase of these spiral galaxies.," Nonetheless, it is possible that the \cite{ma05} model indeed provides a better description for the SED shape during the evolution phase of these spiral galaxies."703 Aavastonetal.(2006.2007) use the broadbaud jotonietryv of seven spectroscopically confirmed galaxies ) assess the fit quality of different SPS inodels aud find no overall preference for a particular SPS model.," \cite{ma06,ma07} use the broadband photometry of seven spectroscopically confirmed galaxies to assess the fit quality of different SPS models and find no overall preference for a particular SPS model."704 Ouly one galaxy (ID 3650) of this sample would have entered our selection (see Figure 2))., Only one galaxy (ID 3650) of this sample would have entered our selection (see Figure \ref{fig:sel}) ).705 We have re-fitted this galaxy usine the same method as for the colposite spectruni acl broadly consistent with Marastonetal.(2006) we neither find a strong xeference for a particular SPS model (see Table 1)).," We have re-fitted this galaxy using the same method as for the composite spectrum, and – broadly consistent with \cite{ma06} – we neither find a strong preference for a particular SPS model (see Table \ref{tab:mod}) )."706 Thus. the differences in fitting techniques do not account or the laree discrepancy in X? value for the composite spectrmm.," Thus, the differences in fitting techniques do not account for the large discrepancy in $\chi^2$ value for the composite spectrum."707 Moreover. as several galaxies i our sample. in particular at ligher redshift. are alinost equally well fit bv the Marastou(2005) inodels. our study is uot in disagreement with Marastonetal.(2006).," Moreover, as several galaxies in our sample, in particular at higher redshift, are almost equally well fit by the \cite{ma05} models, our study is not in disagreement with \cite{ma06}."708. This redshift dependence may be caused by the fact hat the metallicity aud dust coutent at fixed stellar nass evolve with redshift (c.e..Exbetal.2006:Nbüolinoetal. 2008).. and thus it may be possible that the contribution from TP-ACGD stars also chanees with time.," This redshift dependence may be caused by the fact that the metallicity and dust content at fixed stellar mass evolve with redshift \cite[e.g.,][]{er06,mai08}, and thus it may be possible that the contribution from TP-AGB stars also changes with time."709 We test this bv splitting our sample at 2=1.56 aud repeating the analyses for both sub-s:uuples., We test this by splitting our sample at $z=1.56$ and repeating the analyses for both sub-samples.710 Although. for both samples the Druzual&Charlot(2003) inodels provide siguificauthy better fits. the relative fit quality of the Maraston(2005) aodels versus Druzual&Char-lot(2003) increases with redshift.," Although, for both samples the \cite{bc03}711 models provide significantly better fits, the relative fit quality of the \cite{ma05} models versus \cite{bc03} increases with redshift."712 Future work might be able to separate these trends and coustrain TP-AGB models as a function of stellar mass aud metallicity., Future work might be able to separate these trends and constrain TP-AGB models as a function of stellar mass and metallicity.713 The difference in fit quality between the Druzual&Charlot(2003). and Marastou(2005) models for the conrposite post-starburst ealaxy spectrum reflects the differcut treatments of the TP-AGD phase.," The difference in fit quality between the \cite{bc03} and \cite{ma05}714 models for the composite post-starburst galaxy spectrum reflects the different treatments of the TP-AGB phase."715 Our results suggest that the treatineut by Druzual&Charlot(2003) Is tore appropriate for our post-starburst galaxy sample than that of the Maraston(2005) models., Our results suggest that the treatment by \cite{bc03} is more appropriate for our post-starburst galaxy sample than that of the \cite{ma05} models.716 We use the flexible (FSPS) models by Conroyetal.(2009.2010) to obtain a more quantitative constraint on the TP-AGB phase. as FSPS allows the modification of the bolometric huuimositv aud effective temperature of the TP-AGB stars.," We use the flexible (FSPS) models by \cite{co09,co10} to obtain a more quantitative constraint on the TP-AGB phase, as FSPS allows the modification of the bolometric luminosity and effective temperature of the TP-AGB stars."717 Werten ho lie ας) conrposite post-starburst galaxy spoectrun. restricting the wavelength region to A«6000 aand assunndug the latest default Padova TP-ACB models (Cdrardietal.2000:AMarigo&Carardi2007:ALarigoetal. 2008).," We start with the best-fit FSPS model to the composite post-starburst galaxy spectrum, restricting the wavelength region to $\lambda<6000$ and assuming the latest default Padova TP-AGB models \citep{gi00,mg07,mar08}."718. Similar to the other models. this is a stellar population with ((f/vr)29.01. ((r/yr)—85.1. aud au oof 0.£ mag (for solar metallicitv).," Similar to the other models, this is a stellar population with $t$ /yr)=9.04, $\tau$ /yr)=8.1, and an of 0.4 mag (for solar metallicity)."719 Next. we fix the age. star formation timescale and dust coutent of the stellar population aud vary both the effective temperature aud bolometric luminosity of the TP-ACB stars. quantified as shifts with respect to the Padova evolutionary tracks. aandL.. respectively.," Next, we fix the age, star formation timescale and dust content of the stellar population and vary both the effective temperature and bolometric luminosity of the TP-AGB stars, quantified as shifts with respect to the Padova evolutionary tracks, and, respectively."720 Thus. we ignore any potential degeneracies betweenT..L.. aud other stellar yopulation properties (Conroyetal.2009).," Thus, we ignore any potential degeneracies between, and other stellar population properties \citep{co09}."721. Figure L illustrates the influence of both parameters on the SED and shows their 47 contours, Figure \ref{fig:fsps} illustrates the influence of both parameters on the SED and shows their $\chi^2$ contours.722 The best fit has a reduced 47 value of 0.75. thus similar to Diruzual&Charlot(2003).," The best fit has a reduced $\chi^2$ value of 0.75, thus similar to \cite{bc03}."723. The composite post-starburst ealaxv spectrun sugeests that the predicted effective eniperatures of TP-AGD stars iu the Padova models are consistent with our observations. but the overall uninositv is ~0.5 dex lower.," The composite post-starburst galaxy spectrum suggests that the predicted effective temperatures of TP-AGB stars in the Padova models are consistent with our observations, but the overall luminosity is $\sim$ 0.5 dex lower."724 Tn this Letter. we define a photometrically selected saluple of 62 post-starburst ealaxics from the NAIBS and use their composite SED to obtain new constraints ou the SED shape during the time that the TP-ACD stars are thought to be most dominaut.," In this Letter, we define a photometrically selected sample of 62 post-starburst galaxies from the NMBS and use their composite SED to obtain new constraints on the SED shape during the time that the TP-AGB stars are thought to be most dominant."725 The SED is well fit by the Druzual&Charlot(2003) SPS models. while the Alaraston(2005) models do not reproduce the rest-frame optical and near-infrared parts of the SED simultancously. implying that these models eive too much weight to TP-AGB stars.," The SED is well fit by the \cite{bc03} SPS models, while the \cite{ma05} models do not reproduce the rest-frame optical and near-infrared parts of the SED simultaneously, implying that these models give too much weight to TP-AGB stars."726" This has previously been found by Conroy&Cuuu(2010) usimg post-starburst ealaxies in the SDSS,", This has previously been found by \cite{cg10} using post-starburst galaxies in the SDSS.727 The high-resolution photometric sampling of the NMDS allows us to derive quantitative constraiuts on the huninositv in the TP-ACGD phase., The high-resolution photometric sampling of the NMBS allows us to derive quantitative constraints on the luminosity in the TP-AGB phase.728 Using the FSPS, Using the FSPS729 (c.e.. (oe.Staneketal.2003:ILorth2003).," \citep[e.g.,][]{tota97, wije98} \citep[e.g.,][]{stan03, hjor03}, \citep[the current record is $z = 8.2$ for GRB~090423;][]{tanv09, salv09}."730. ~O.1 AL. + ," \citep[e.g.,][]{fynb03, lefl03, fruc06} $\sim$ $M_{\odot}$ $^{-1}$ \citep[e.g.,][]{sava09, leve10, sven10}."731than SERs derived from UV. optical. NIR waveleneths (c.g..Dergeretal.2003:LeFloch2006)... (," than SFRs derived from UV, optical, NIR wavelengths \citep[e.g.,][]{berg03, lefl06}. ("7322) Laree hydrogen column deusities (Αα21072 2) are observed along the line of sight to GRBs (e.g.Jakobssouetal.2006:Schady2007:Zhengct 2009)... (,"2) Large hydrogen column densities $N_{\rm H} \gsim 10^{22}$ $^{-2}$ ) are observed along the line of sight to GRBs \citep[e.g.,][]{jako06, scha07, zhen09}. ("7333) About of CRBs are vdark GRBs” (e...FyuboCereineretal. 2011).,"3) About of GRBs are “dark GRBs” \citep[e.g.,][]{fynb01, djor01, fynb09, grei11}."734. The nature of davk GRBs. which are characterized by the faintuess of their optical afterglow compared to their X-ray afterglow (Jakobssonetal.200I:vanderHorstetal. 2009).. is not vet well uuderstood and one possible explanation is due to the large dust extinction along the line of sight to GRBs (e...Perleyetal. 2009).," The nature of dark GRBs, which are characterized by the faintness of their optical afterglow compared to their X-ray afterglow \citep{jako04, vand09}, is not yet well understood and one possible explanation is due to the large dust extinction along the line of sight to GRBs \citep[e.g.,][]{perl09}."735". So far. only a small fraction of CRB hosts have been studied for which ligh obscured star formation is indicated (οιοι,Tauviretal.2001:Priddey20060)."," So far, only a small fraction of GRB hosts have been studied for which high obscured star formation is indicated \citep[e.g.,][]{tanv04, prid06}."736 Whether GRB hosts have obscured star formation is still nucertain because it is difficult to identity them when heir optical afterelows are extincted by dust., Whether GRB hosts have obscured star formation is still uncertain because it is difficult to identify them when their optical afterglows are extincted by dust.737 An alternative approach for understanding star-Oration activity iu CRB hosts is to measure the amount of molecular eas. which is the iugredieut for star orimation.," An alternative approach for understanding star-formation activity in GRB hosts is to measure the amount of molecular gas, which is the ingredient for star formation."738 The CO emission. line observatious provide he information of molecular gas mass. dynamical mass. and star-formation cficiency in CRB hosts without being affected by dust extinction.," The CO emission line observations provide the information of molecular gas mass, dynamical mass, and star-formation efficiency in GRB hosts without being affected by dust extinction."739 Thus far. oulv a few efforts ave been mace to search for 1iolecular eas in GRB hosts (Table 13): CO (10) observations of the CRB 030329 vost (IKolinoetal.2005:Endo2007).. CO (32) observations of the GRB 9850125 host (IIatsukadeetal. 2007).. and CO (32) observatious of the CRB 090123 vost (Staunwayctal.2011).," Thus far, only a few efforts have been made to search for molecular gas in GRB hosts (Table \ref{tab:summary}) ): CO (1–0) observations of the GRB 030329 host \citep{kohn05, endo07}, CO (3–2) observations of the GRB 980425 host \citep{hats07}, and CO (3–2) observations of the GRB 090423 host \citep{stan11}."740.. No CO emission has been detected froin GRB hosts and whether CRBhosts have sufficient molecular gas to παλιταπα their star formation relains unknown., No CO emission has been detected from GRB hosts and whether GRBhosts have sufficient molecular gas to maintain their star formation remains unknown.741 Iu this paper. we report a search for CO line cussion," In this paper, we report a search for CO line emission"742is for halos with mass LO?M.. and the bottom panel for 101ΔΕ. halos.,"is for halos with mass $10^{6} \Msun$, and the bottom panel for $10^{7} \Msun$ halos."743 We separated the halos out by nmiass to delineate the effect. of spin from. that of mass., We separated the halos out by mass to delineate the effect of spin from that of mass.744 We. first computed. the overall correlation function for all halos in the eiven mass range. and then used two sub-samples based on their spin parameter.," We first computed the overall correlation function for all halos in the given mass range, and then used two sub-samples based on their spin parameter."745 The cuts in spin parameter. were chosen so that one third of the halos were in the high and low spin bins respectively., The cuts in spin parameter were chosen so that one third of the halos were in the high and low spin bins respectively.746 The error bars show Poisson errors in DD). When counting halo pairs for the spin cut samples. we employed two methods.," The error bars show Poisson errors in $DD(r)$, When counting halo pairs for the spin cut samples, we employed two methods."747 First. we counted only pairs where roth halos were in the given bin. and these results are shown in Figure 3..," First, we counted only pairs where both halos were in the given bin, and these results are shown in Figure \ref{corr}."748 We also counted the pairs where only one halo was in the high or low spin bin., We also counted the pairs where only one halo was in the high or low spin bin.749 This method of counting oroduced similar results as the first method., This method of counting produced similar results as the first method.750" We find that there is a cistinction in the correlation ""unction when the data are separated by the spin parameter.", We find that there is a distinction in the correlation function when the data are separated by the spin parameter.751 Ligh spin halos are more strongly clustered than low spin 1alos. similar to the result found by Bettetal.(2007) in the Millennium Simulation.," High spin halos are more strongly clustered than low spin halos, similar to the result found by \citet{bett07} in the Millennium Simulation."752 We also find that the dillerence in clustering is preserved over a range of redshifts., We also find that the difference in clustering is preserved over a range of redshifts.753 The excess clustering is due to the fact that in a denser environment. halos feel stronger tidal torques. and thus have larger angular momentum and spin parameters.," The excess clustering is due to the fact that in a denser environment, halos feel stronger tidal torques, and thus have larger angular momentum and spin parameters."754 The correlation function can be Gt to a power-law. €(r)=GB). where BR is the correlation length.," The correlation function can be fit to a power-law, $\xi(r) = (r/R)^\gamma$, where $R$ is the correlation length."755 We find the high spin halos have a correlation length on average 25% larger than the low spin halos over the various mass ancl redshift. slices used. here., We find the high spin halos have a correlation length on average $25\%$ larger than the low spin halos over the various mass and redshift slices used here.756 The slope. 5. did not show any correlation with spin. mass. or redshift.," The slope, $\gamma$, did not show any correlation with spin, mass, or redshift."757 In this paper. we have examined. the angular momentum distribution of simulated high redshift dark matter halos and their correlation functions.," In this paper, we have examined the angular momentum distribution of simulated high redshift dark matter halos and their correlation functions."758 While the angular momentunm. distributions for this population are well fit by log-normal distributions as is the case for lower redshift and more massive halos. we find that the clustering properties of the ugh redshift population depend on the value of spin.," While the angular momentum distributions for this population are well fit by log-normal distributions as is the case for lower redshift and more massive halos, we find that the clustering properties of the high redshift population depend on the value of spin."759 For a given mass bin selecting by spin. we find that the correlation unction is higher for high spin halos.," For a given mass bin selecting by spin, we find that the correlation function is higher for high spin halos."760 This is an important rend and appears to be robust., This is an important trend and appears to be robust.761 Although in this study we aave restricted ourselves to the analysis of dark matter only simulations. the different correlation lengths of high and ow spin halos are likely to have an important impact in eedback from these carly galaxies.," Although in this study we have restricted ourselves to the analysis of dark matter only simulations, the different correlation lengths of high and low spin halos are likely to have an important impact in feedback from these early galaxies."762 Pop LLL stars appear to jwe a large impact on their environment due to radiative (Johnson.Criet.&Bromm2007:Whalenetal.2008). and supernova (Ciriefetal.2007:Whalen2008). feedback.," Pop III stars appear to have a large impact on their environment due to radiative \citep{johnson07,whalen08b} and supernova \citep{grief07,whalen08} feedback."763 We note here that in a recent paper OShea&Norman(2007) tracked the spin parameters of halos that formed the irst stars in 12 cosmological random realizations ancl cid not ind a correlation between halo spin and collapse time., We note here that in a recent paper \citet{oshea07} tracked the spin parameters of halos that formed the first stars in 12 cosmological random realizations and did not find a correlation between halo spin and collapse time.764 The, The765order of he Eddington one. the disc hickuess stavs moderate and a verticalv integrated approximalon iav be retained discs) 21.,"order of the Eddington one, the disc thickness stays moderate and a vertically integrated approximation may be retained ) \cite{abr88}."766" Iu the limit ri21. though. the beliaviou of the disc iux the possible relevance of strong outflows still remain open isstes,"," In the limit $\dot m \gg 1$, though, the behaviour of the disc and the possible relevance of strong outflows still remain open issues."767 Once again. the problem is iulcreutly 2D. aud t1C sinultauneous roles of convection. advection and outflows have to be assessed in order o model pro]xlv the expeced SED.," Once again, the problem is inherently 2D, and the simultaneous roles of convection, advection and outflows have to be assessed in order to model properly the expected SED."768" Uulike for the the optically thin ADAF/C‘DAF cases. he observable catures of these optically thick solutio have heen investigate in onlv a hateful of cases so far σον, thus reducing t general appreciation of their importance for interpreting observations."," Unlike for the the optically thin ADAF/CDAF cases, the observable features of these optically thick solutions have been investigated in only a handful of cases so far \cite{szu96,mine00}, thus reducing the general appreciation of their importance for interpreting observations."769" The ADAF solution has received a ereat deal of interest in the last decade vecause of its potential capabilitv to explain the observajonal data from our Galactic Ceuter 2771,"," The ADAF solution has received a great deal of interest in the last decade because of its potential capability to explain the observational data from our Galactic Center \cite{mf01,n02}."770 On the other laud. ecometrically hick adiabatic flows are ical models to test elobal immerical simulations of pdTWD turbuleut accretion fkws against. without having ο deal with the complicous of radiative ranster needed to simulate thin. radiative cfiicicut disces.," On the other hand, geometrically thick adiabatic flows are ideal models to test global numerical simulations of MHD turbulent accretion flows against, without having to deal with the complications of radiative transfer needed to simulate thin, radiative efficient discs."771" Indec. already when rw 1D apoxoxination of sclfsinulay ADAF theory is abandoned. aud the ""ul 2D liaure of the problem is anavsed. both from the theoretical poiut of VICW: 2277 and from inunuercal smiulatious 26.25 it is clear that radiativelv inefficient flows are prone to strong convective ΠαςταΜος aid/or powerful Olflows."," Indeed, already when the 1D approximation of self-similar ADAF theory is abandoned, and the full 2D nature of the problem is analysed, both from the theoretical point of view \cite{nia00} and from numerical simulations \cite{ia00,hb02}, it is clear that radiatively inefficient flows are prone to strong convective instabilities and/or powerful outflows."772" I1 general σος, convective flows are more likely at low walues of the viscosiv parameter. while stroug outflows are generated or hieh values of ay."," In general \cite{bb99,ia00}, convective flows are more likely at low values of the viscosity parameter, while strong outflows are generated for high values of $\alpha_{\rm v}$."773 Iu he former case (purely coivective flows). accretion is cffocively tow.-ifled. witi Little or no mass inflow or outflow: the euergv extracted 1 the Inner part is couvectively transported outward.," In the former case (purely convective flows), accretion is effectively stifled, with little or no mass inflow or outflow: the energy extracted in the inner part is convectively transported outward."774 Such a redistribution ¢ Xelorgv αλλος fiuid elements in he accreting gas alters the purely advective nature of the flow and modifies the radial profiles of plivsical quantities. as the deusity. with profound implication for the iuterpretation of the observed radiation.," Such a redistribution of energy among fluid elements in the accreting gas alters the purely advective nature of the flow and modifies the radial profiles of physical quantities, as the density, with profound implication for the interpretation of the observed radiation."775" Iu the latter case. svsteniaic outflows remove lass and energy from he flow. with little aceretion outo tle black hole σοι,"," In the latter case, systematic outflows remove mass and energy from the flow, with little accretion onto the black hole \cite{hbs01,hb02}."776" Despite the ie efforts made by several eroups. bot «n the theory aud ou the simulation side. the relative inportance of convectioi ad outflow for acliabatic flows 1s still matter of a vigorous debate 25,56. the controversy being essentially over he capability of any bydrodvuamical model supplemented with a-like viscosity prescriptions to capture the basic plivsical properties of an inherently magueto-lydrodvuamical system."," Despite the big efforts made by several groups, both on the theory and on the simulation side, the relative importance of convection and outflow for adiabatic flows is still matter of a vigorous debate \cite{bh02,nq02}, the controversy being essentially over the capability of any hydrodynamical model supplemented with $\alpha$ -like viscosity prescriptions to capture the basic physical properties of an inherently magneto-hydrodynamical system."777 As usual. it appears likely that such controversy wil oulv be settled with the collection of more constraiius observational data.," As usual, it appears likely that such controversy will only be settled with the collection of more constraining observational data."778 , 779We also note. however. that their simulated galaxy has a virial temperature below 1x10! Ix hence does not possess (he eflicient atomic cooling.,"We also note, however, that their simulated galaxy has a virial temperature below $1\times 10^4~$ K hence does not possess the efficient atomic cooling."780 It is possible that. for galaxies with efficient atomic cooling. star formation ellicieney may be much higher (than what Abel (2002) simulation indicates.," It is possible that, for galaxies with efficient atomic cooling, star formation efficiency may be much higher than what Abel (2002) simulation indicates."781 Detailed simulations will be invaluable., Detailed simulations will be invaluable.782" Finally. we note that. if star lormation in cooling shells produced by exploding massive Pop U1 stus. the ""Pop 11.5"" stars proposed bv Mackey (2003). is efficient. Chev may make a non-neeligible contribution to the pool of ionizing photons."," Finally, we note that, if star formation in cooling shells produced by exploding massive Pop III stars, the “Pop II.5"" stars proposed by Mackey (2003), is efficient, they may make a non-negligible contribution to the pool of ionizing photons."783 These stars might form at oll-center locations aud (hus might possess a relatively larger ionizing photon escape Iraction., These stars might form at off-center locations and thus might possess a relatively larger ionizing photon escape fraction.784 The counteracting factor is that these stars might be substantially less massive than the first eeneralion meltal-Iree stars. since the metallicity of the eas in the cooling shells may be «uite hieh. hence are less efficient ionizing photon emitters.," The counteracting factor is that these stars might be substantially less massive than the first generation metal-free stars, since the metallicity of the gas in the cooling shells may be quite high, hence are less efficient ionizing photon emitters."785" Adopting the best fit standard cold dark matter model with a fixed power-law index by WAIAP observations with O1;= 0.27. Q,= 0.047. A=0.73. Hj,=T2km/s/Mpe. n,=0.99 and o,=0.90 (Spergel 2003) ancl based on the observed Thomson optical depthli due to intergalaetic medium by WMADP (Ixogut 2003).B we are able to craw several relatively secure conclusions will regard to Pop LI star formation processes al very. high redshilt. ("," Adopting the best fit standard cold dark matter model with a fixed power-law index by WMAP observations with $\Omega_M=0.27$ , $\Omega_b=0.047$ , $\Lambda=0.73$, $H_0=72$ km/s/Mpc, $n_s=0.99$ and $\sigma_8=0.90$ (Spergel 2003) and based on the observed Thomson optical depth due to intergalactic medium by WMAP (Kogut 2003), we are able to draw several relatively secure conclusions with regard to Pop III star formation processes at very high redshift. ("7861) The combination of the normal Salpeter IME for Pop III metal-Iree stars and the absence of a dramatic upturn in the star formation efficiency. and/or ionizing photon escape fraction at high redshift ἐς2 6) would produce a Thomson optical depth due to IGA at reionization of z.< 0.09. inconsistent with the observed 7.=0.17£0.04 (6894) (IXogut. 2003) al >26 level. (,1) The combination of the normal Salpeter IMF for Pop III metal-free stars and the absence of a dramatic upturn in the star formation efficiency and/or ionizing photon escape fraction at high redshift $z>6$ ) would produce a Thomson optical depth due to IGM at reionization of $\tau_e \le 0.09$ inconsistent with the observed $\tau_e=0.17\pm 0.04$ $68\%$ ) (Kogut 2003) at $\ge 2\sigma$ level. (7872) A top-heavy IMIF for the Pop III metal-Iree stars and. plausible star formation efficiency and ionizing photon escape. as gauged by the corresponding values for Pop I ealaxies recuired in order (o achieve the second reionization finale al 2~6 vield 7.<0.12: (3) In the event that the metal enrichment elliciency of the intergalactie mediun by Pop HI stars is very low thus Pop II era is prolonged. one may be able to obtain 7.=0.15. (,"2) A top-heavy IMF for the Pop III metal-free stars and plausible star formation efficiency and ionizing photon escape, as gauged by the corresponding values for Pop II galaxies required in order to achieve the second reionization finale at $z\sim 6$ yield $\tau_e \le 0.12$; (3) In the event that the metal enrichment efficiency of the intergalactic medium by Pop III stars is very low thus Pop III era is prolonged, one may be able to obtain $\tau_e = 0.15$. ("7884) It seems quite improbable to reach τ>0.17 even with verv massive Pop III stus. unless (1) Che cosmological model power index » is positively tilted to n>1.03 and/or Gi) Pop HI star formation in minihalos with molecular hwdrogen cooling has an efficiency eH.fff)>0.01 (süll requiring ionizing photon escapefraction greater(han 0.3) or (Gii) alternatively.there may be unknown. non-stellar ionizing sources at very. high,"4) It seems quite improbable to reach $\tau_e \ge 0.17$ even with very massive Pop III metal-free stars, unless (i) the cosmological model power index $n$ is positively tilted to $n\ge 1.03$ and/or (ii) Pop III star formation in minihalos with molecular hydrogen cooling has an efficiency $c_*(H_2,III)>0.01$ (still requiring ionizing photon escapefraction greaterthan $0.3$ ) or (iii) alternatively,there may be unknown, non-stellar ionizing sources at very high"789"of the TLUSTY OSTAR2002 and BSTAR2006 SEDs (Lanz&Hubeny2003,2007) we can interpolate on effective temperature, surface gravity, and metallicity, as we cannot vary abundances individually.","of the TLUSTY OSTAR2002 and BSTAR2006 SEDs \citep{lanz, lanz07} we can interpolate on effective temperature, surface gravity, and metallicity, as we cannot vary abundances individually."790 We used TLUSTY to be consistent with the physical calibration of the spectral classes presented by Heapetal.(2006)., We used TLUSTY to be consistent with the physical calibration of the spectral classes presented by \citet{srh06}.791. The interpolation methods have been generalized and many other grids of stellar SEDs are available., The interpolation methods have been generalized and many other grids of stellar SEDs are available.792 We have developed a domain decomposition method to compute these grids on MPI-aware parallel machines., We have developed a domain decomposition method to compute these grids on MPI-aware parallel machines.793 Each grid point is an independent model calculation and so can be done on separate computer nodes., Each grid point is an independent model calculation and so can be done on separate computer nodes.794 'This results in a speedup that is of the order of the number of available processors., This results in a speedup that is of the order of the number of available processors.795 The capability to compute grids of photoionization models where certain key parameters are incremented in equidistant linear or logarithmic steps was introduced several years ago and has been discussed in Porteretal.(2006).., The capability to compute grids of photoionization models where certain key parameters are incremented in equidistant linear or logarithmic steps was introduced several years ago and has been discussed in \citet{porter}.796 We recently enhanced this capability by parallelizing the algorithm using the Message Passing Interface (MPI) specification., We recently enhanced this capability by parallelizing the algorithm using the Message Passing Interface (MPI) specification.797 This allows much larger grids to be computed in parallel on distributed clusters of computers., This allows much larger grids to be computed in parallel on distributed clusters of computers.798 The calculations are set up in such a way that each core calculates a separate model (domain decomposition) and all the results are gathered when the grid has finished., The calculations are set up in such a way that each core calculates a separate model (domain decomposition) and all the results are gathered when the grid has finished.799 The communication overhead is negligible since the MPI threads only need to communicate when the grid calculation starts and finishes., The communication overhead is negligible since the MPI threads only need to communicate when the grid calculation starts and finishes.800 Hence this algorithm is highly efficient and scales well to high numbers of cores for sufficiently large grids., Hence this algorithm is highly efficient and scales well to high numbers of cores for sufficiently large grids.801SERD since we have not attempted to correct for the contributions of faint sources below our flux. limits.,SFRD since we have not attempted to correct for the contributions of faint sources below our flux limits.802 The SFRD from our submillimeter sources can be estimated under the assumption that star formation domunates ACN coutributions., The SFRD from our submillimeter sources can be estimated under the assumption that star formation dominates AGN contributions.803" We can calenulate the contribution of the c6 nuuJv subinillineter sources at +=1.3 toSu, the SERD using Eq. 135:", We can calculate the contribution of the $S_{850\mu{\rm m}}>6$ mJy submillimeter sources at $z=1-3$ to the SFRD using Eq. \ref{mdot3};804 we find Uulike the nuuber distribution versus redshift. the SFRD needs large corrections for coimpleteuess due to re fact that we are detecting only relatively bright sources here (at about six times the DIunuinositv at which je subiuillimeter background is primarily resolved). aud ie distribution dN/dS mereases rapidly as 5$ decreases.," we find Unlike the number distribution versus redshift, the SFRD needs large corrections for completeness due to the fact that we are detecting only relatively bright sources here (at about six times the luminosity at which the submillimeter background is primarily resolved), and the distribution $dN/dS$ increases rapidly as $S$ decreases."805 To estimate the completeness correction. we assunie rat the ο.” of Noon S and : factorize. NfdSd.=gOSτν," To estimate the completeness correction, we assume that the dependences of $N$ on $S$ and $z$ factorize, $d^2N/dSdz=g(S)h(z)$."806 This is a plausible assuuption iu jo ubnüillimeter where the fluxes are nearly independent of redshift: nonetheless. in view of the Simail et ((1999)) y.udy. this assuniption remains to be confined.," This is a plausible assumption in the submillimeter where the fluxes are nearly independent of redshift; nonetheless, in view of the Smail et (1999b) study, this assumption remains to be confirmed."807 We can determine the completeness correction for the SFRD using the empirical uuuber distribution at juu vorsus 5$ that describes the measured submillimeter counts above nuntyv (Bareer. Cowie. Sanders 1999).," We can determine the completeness correction for the SFRD using the empirical number distribution at $\mu$ m versus $S$ that describes the measured submillimeter counts above mJy (Barger, Cowie, Sanders 1999)."808 We are iaklàiug the assumption that the flux to Ley conversion. based on Arp 220 applies in the low submillimeter flux region: the populationjustification is that even the dominant ~1 nuuJv are near-ULIG sources., We are making the assumption that the flux to $L_{FIR}$ conversion based on Arp 220 applies in the low submillimeter flux region; the justification is that even the dominant $\sim 1$ mJy population are near-ULIG sources.809 The completeness correction over all subuullumeter fluxes is therefore the measured 850 jun extragalactic background light (EBL) divided by the 850 jan light above nuudJy., The completeness correction over all submillimeter fluxes is therefore the measured $850\ \mu$ m extragalactic background light (EBL) divided by the $850\ \mu$ m light above mJy.810 The 850 jan EBL weasurement of 3.1«10+ ddeg7? from Puget et (01996) and L4s10! 3 frou Fixsen et (4905) inplyv. correction factors in the submillimeter of 1l aud 15. respectively.," The $850\ \mu$ m EBL measurement of $3.1\times 10^4$ $^{-2}$ from Puget et (1996) and $4.4\times 10^4$ $^{-2}$ from Fixsen et (1998) imply correction factors in the submillimeter of 11 and 15, respectively."811 Thus. the estimated total submillimeter contribution to the SFRD iu units of hgM.vr+Mpc?n is where we have used the factor of 11 completcucss correction.," Thus, the estimated total submillimeter contribution to the SFRD in units of $h_{65}\ \rm{M_\odot}\ \rm{yr}^{-1}\ {\rm Mpc}^{-3}$ is where we have used the factor of 11 completeness correction."812" More speculatively, we can determine the SFRD from lugher vedshift sources using our two 26 ΙΙ submillimeter sources without radio counterparts."," More speculatively, we can determine the SFRD from higher redshift sources using our two $>6$ mJy submillimeter sources without radio counterparts."813 In this case we use the volune from 2=36 and the actual area surveved in the submillimeter., In this case we use the volume from $z=3-6$ and the actual area surveyed in the submillimeter.814" We fud After including the factor of 11 completeness correction. this becomes II958 used photometric redshift estimates to infor that four of their five 5s,72 nuuJyv sources were imn the redshift range +=2.L."," We find After including the factor of 11 completeness correction, this becomes H98 used photometric redshift estimates to infer that four of their five $S_{850\mu{\rm m}}>2$ mJy sources were in the redshift range $z=2-4$."815 While these source identifications were problematic. it appears likely from the preseut work that the redshifts do lic in this rough redshift ranuec.," While these source identifications were problematic, it appears likely from the present work that the redshifts do lie in this rough redshift range."816 Using our paraincters and a scaled Απρ 220 SED. we Bud that the SERD for their sources with O4=0 is 0.10005Do;M.yr.1Mpe7.," Using our parameters and a scaled Arp 220 SED, we find that the SFRD for their sources with $\Omega_\Lambda=0$ is $0.10^{+0.08}_{-0.05}\ h_{65}\ {\rm M_\odot}\ {\rm yr}^{-1}\ {\rm Mpc}^{-3}$."817 If we make a completeness correction to include the contribution below nuuJy. we obtain SFRD-0.28!απhosM.xr|Mpe iu good agreement with our result in Eq. 21a..," If we make a completeness correction to include the contribution below mJy, we obtain $0.28^{+0.22}_{-0.14}\ h_{65}\ {\rm M_\odot}\ {\rm yr}^{-1}\ {\rm Mpc}^{-3}$, in good agreement with our result in Eq. \ref{eqtruesfrdsmma}."818 The presence of a substantial fraction of ACN-dominated ULIG sources would reduce the above SFRDs., The presence of a substantial fraction of AGN-dominated ULIG sources would reduce the above SFRDs.819 Iu a recent near-infrared spectroscopic study of 61 local ULICs. VVeilleux. Sanders. Jim (1999) found ACN characteristics in 20025 per cent of the sample. which increased to 3550 per ceut for the sample with Lyy>oP Πρ ," In a recent near-infrared spectroscopic study of 64 local ULIGs, \markcite{veilleux99}V Veilleux, Sanders, Kim (1999) found AGN characteristics in $20-25$ per cent of the sample, which increased to $35-50$ per cent for the sample with $L_{IR}>10^{12.3}\ {\rm L}_\odot$ ."820Thus. our 76 uunJy coutributions to the SFRD lav need to be reduced by a factor ~1.52.," Thus, our $>6$ mJy contributions to the SFRD may need to be reduced by a factor $\sim 1.5-2$."821 However. the lower ACN fraction in fainter ULICs seen locally suggests that AGN coutiunination may be less of an issue for the extrapolated SERD of the whole submillimeter population.," However, the lower AGN fraction in fainter ULIGs seen locally suggests that AGN contamination may be less of an issue for the extrapolated SFRD of the whole submillimeter population."822 The determination of the SFRD fron) optical observations has been a subject of inteuse investigation., The determination of the SFRD from optical observations has been a subject of intense investigation.823 Observations first indicated a rather rapid rise in the SFRD from:=01 followed by a sharp decline at higher redshifts with the peak SFRD being :1.5 (Madau ct 11996)., Observations first indicated a rather rapid rise in the SFRD from $z=0-1$ followed by a sharp decline at higher redshifts with the peak SFRD being $z\sim 1.5$ (Madau et 1996).824 A recent modification in the inferred optical SERD at low redshifts was made by CCowie. Songaila. Darger (1999). whose data indicated a more gradual rise in the SFRD than had previously beeu found by LLilly et ((1996).," A recent modification in the inferred optical SFRD at low redshifts was made by \markcite{cowie99}C Cowie, Songaila, Barger (1999), whose data indicated a more gradual rise in the SFRD than had previously been found by \markcite{lilly96}L Lilly et (1996)."825 Tt was realized that dust obscuration effects could result in factors of 3 to 5 (PPettini et 11997: MMoeurer. Heckman. Calzetti 1999) iucreases in the SERD at lugh redshift.," It was realized that dust obscuration effects could result in factors of 3 to 5 \markcite{pettini97}P Pettini et 1997; \markcite{meurer99}M Meurer, Heckman, Calzetti 1999) increases in the SFRD at high redshift."826 With these rather uncertain dust corrections taken iuto account. it has been argued that the SFRD flattous at a coustaut SPRDz0.2ligsM.xr1Mpe jin the O4=0 cosinologv for >=1...5 (Steidel et 11999).," With these rather uncertain dust corrections taken into account, it has been argued that the SFRD flattens at a constant $\rm{SFRD}\approx 0.2\ h_{65}\ \rm{M}_\odot\ \rm{yr}^{-1}\ \rm{Mpc}^{-3}$ in the $\Omega_\Lambda=0$ cosmology for $z=1-5$ (Steidel et 1999)."827 Iu Fig., In Fig.828 Hl we compare the star formation history in the optical (without extinction corrections) with that which we obtain in the submillimeter both before (Eqs., \ref{figsfrdvsz} we compare the star formation history in the optical (without extinction corrections) with that which we obtain in the submillimeter both before (Eqs.829 θα and 22a: solid triangles) aud after (Eqs., \ref{eqsfrdsmma} and \ref{eqhisfrdsmma}; solid triangles) and after (Eqs.830 2la and 23a:: solid circles) correcting for iuconipleteness., \ref{eqtruesfrdsmma} and \ref{eqhitruesfrdsmma}; solid circles) correcting for incompleteness.831 We also iuchide our newly deteriiued radio SFRD lanits (Eqs., We also include our newly determined radio SFRD limits (Eqs.832 17a. aud 18a)) on the figure as solid squares., \ref{eqlowradioa} and \ref{eqhiradioa}) ) on the figure as solid squares.833 The submillimeter contribution to the SERD interred from our 26 nuuJw observations is comparable to the ultravioletfoptical contribution to the SFRD., The submillimeter contribution to the SFRD inferred from our $>6$ mJy observations is comparable to the ultraviolet/optical contribution to the SFRD.834 The two wavelength regimes are Likely sample cdiffercut stages iu ealaxy formation., The two wavelength regimes are likely sampling different stages in galaxy formation.835 The subuullunecter detects the formation, The submillimeter detects the formation836 of the isothermal ,edge of the isothermal plateau.837"Once the planet edgedecouples, it is released inside plateau.the itself a of inward since the plateau,temperature regiongradient vanishes."," Once the planet decouples, it is released inside the plateau, itself a region of inward migration since the temperature gradient vanishes."838" As disk migrationevolution continues, the soon finds itself at the outer of the decoupledisothermal planet and starts migrating outwards."," As disk evolution continues, the decoupled planet soon finds itself at the outer edge of the isothermal plateau, and starts migrating outwards."839"edge For planets ofΜα, plateau,decoupling occurs at rp=1 AAU at MMyr 3bb)."," For planets of, decoupling occurs at $r_p$ AU at Myr b)."840 The planet then rapidly descends the temperature gradient until it reaches the outer equilibrium radius., The planet then rapidly descends the temperature gradient until it reaches the outer equilibrium radius.841" However, this radius too moves inward faster than the planet can migrate, so the planet enters the isothermal outer disk (where T~T;), another region of slow inward migration."," However, this radius too moves inward faster than the planet can migrate, so the planet enters the isothermal outer disk (where $T\simeq{T_b}$ ), another region of slow inward migration."842" At this stage, a planet of still has time to migrate from ry—2.0 AU to ry—1.5 AU before the density drops too low to drive further migration 3dd)."," At this stage, a planet of still has time to migrate from $r_p=2.0$ AU to $r_p=1.5$ AU before the density drops too low to drive further migration d)."843 The of is planetstrongly coupled and would follow the outer equilibrium radius until it hit the inner boundary of our model at AAU., The planet of is strongly coupled and would follow the outer equilibrium radius until it hit the inner boundary of our model at AU.844 The halt at AAU seen in 3ee represents an artificial termination of the simulation., The halt at AU seen in e represents an artificial termination of the simulation.845"Figure At that point, two criteria had been fulfilled."," At that point, two criteria had been fulfilled."846" First, the scale height had become smaller than the Hill radius of the so gap formation should have occurred."," First, the scale height had become smaller than the Hill radius of the planet, so gap formation should have occurred."847" This is not planet,sufficient to terminate the simulation, because the inward motion of the equilibrium radius itself occurs at the timescale of Type II "," This is not sufficient to terminate the simulation, because the inward motion of the equilibrium radius itself occurs at the timescale of Type II migration."848"However, the second criterion was that the mass migration.parameter determining Type II migration, 7? (Mordasinietal. 2009)), had become smaller than the planet's mass."," However, the second criterion was that the mass parameter determining Type II migration, $\varSigma{r^2}$ \citealp{Mordasini}) ), had become smaller than the planet's mass."849" At this Type II becomes planet dominated and we stage,consider that it migrationcomes to a halt."," At this stage, Type II migration becomes planet dominated and we consider that it comes to a halt."850 The smaller planets never carve 5aps., The smaller planets never carve gaps.851"We investigate migration in disks with different values of My and Mo, yet constrained by lifetime of without differences."," We investigate migration in disks with different values of $\dot{M}_{\rm w}$ and $\dot{M_0}$, yet constrained by a lifetime of Myr, without finding qualitative differences."852"a A in MMyr, findingbehavior is qualitativeseen for hotter disks.", A change in migration behavior is only seen for hotter disks.853" changeFor agg=0.1, migrationthe disks show onlyOz:1 throughout."," For $\alpha_{\rm SS}$ =0.1, the disks show $\varTheta \approx 1$ throughout."854 where the [ist term in each of these is (he uncorrelatecl piece that matches what we lind using results [rom our svnthetic survevs.,", where the first term in each of these is the uncorrelated piece that matches what we find using results from our synthetic surveys."855 This also matches what we expect [rom the Fisher matrix for this fit., This also matches what we expect from the Fisher matrix for this fit.856 Furthermore. lor τας=0.1725. we find that Ér220.025.," Furthermore, for $z_{\rm max}=0.1725$, we find that $r\approx 0.025$."857 We find that this value of r is consistent with the statistics of the galaxy velocities in the simulation box. where we estimated using 5.000 random galaxies. One further issue is whether or not it is advantageous to throw away low redshift data points.," We find that this value of $r$ is consistent with the statistics of the galaxy velocities in the simulation box, where we estimated using $5,000$ random galaxies, One further issue is whether or not it is advantageous to throw away low redshift data points."858 To explore this. we add a random intrinsic scatter of 0.1 mag to the SN magnitudes. in addition to the peculiar velocity error.," To explore this, we add a random intrinsic scatter of $0.1$ mag to the SN magnitudes, in addition to the peculiar velocity error."859" We (hen throw away all data points that have a final(observed) redshift below a cutoff 2y4,.", We then throw away all data points that have a final(observed) redshift below a cutoff $z_{\rm min}$.860 The resulting errors are shown in Table 4.. lor AN=500 and τς=0.1725.," The resulting errors are shown in Table \ref{zmin}, for $N=500$ and $z_{\rm max}=0.1725$."861" We thus find that the optimal minimum redshift is z44,20.02. for which we lind a 7% reduction in total error."," We thus find that the optimal minimum redshift is $z_{\rm min}\approx 0.02$, for which we find a $7\%$ reduction in total error."862 We also find. for these survey parameters. that the error due to peculiar velocities is (he same order of magnitude as (he error due to the intrinsic scatter alone.," We also find, for these survey parameters, that the error due to peculiar velocities is the same order of magnitude as the error due to the intrinsic scatter alone."863" We give some of the results of fit Gi). for zi,=0. in Table 5.. where oy is the error in O4."," We give some of the results of fit (ii), for $z_{\rm min}=0$, in Table \ref{3param}, where $\sigma_{\Lambda}$ is the error in $\Omega_{\Lambda}$."864 These errors scale asoctka and(," These errors scale as,, and."86513) This time we find i»=0.036 when τας=0.1725. which isstill consistent with our prior rough estimate [rom galaxy statistics.," This time we find $r=0.036$ when $z_{\rm max}=0.1725$, which isstill consistent with our prior rough estimate from galaxy statistics."866" By adding an intrinsic magnitude scatter of0.1 mag lo a survey with NV=500 and za,=0.1725. we now find the optimal minimum redshift to be tii,= 0.01. this time vielding a total error reduction of 9%."," By adding an intrinsic magnitude scatter of $0.1$ mag to a survey with $N=500$ and $z_{\rm max}=0.1725$, we now find the optimal minimum redshift to be $z_{\rm min}=0.01$ , this time yielding a total error reduction of $9\%$ ."867 We find once again that the, We find once again that the868"Note that as a consequence of the isospin svmmetry of the nucleon-nucleon interactions. we have and A7"" (therefore A1) does not depend on the matter composition but only on the barvon density nmn—om,|ons","Note that as a consequence of the isospin symmetry of the nucleon-nucleon interactions, we have ${\cal K}^{nn}\{n_n,n_p\}={\cal K}^{pp}\{n_p,n_n\}$ and ${\cal K}^{np}$ (therefore $\lambda_1$ ) does not depend on the matter composition but only on the baryon density $n_{\rm b}=n_n+n_p$."869" This means that entrainment effects are not allectecl by the various chemical reactions that may occur inside the core. as discussed in Section Ἐν, "," This means that entrainment effects are not affected by the various chemical reactions that may occur inside the core, as discussed in Section \ref{sect.composition}. ."870"In the high density limit ην3Land anyX1. all the elements of the mobility matrix become equal. AK""mm, "," In the high density limit $\beta_3 n_n \gg 1$ and $\beta_3 n_p \gg 1$, all the elements of the mobility matrix become equal ${\cal K}^{q q^\prime} \rightarrow m/n_{\rm b}$."871As a consequence. the non-relativistic elfective masses tend to m7/m—»nj/nmy.," As a consequence, the non-relativistic effective masses tend to $m^q_\star/m \rightarrow n_q/n_{\rm b}$."872 This asvmptotic limit which corresponds to the strongest entrainment cllects (see the discussion of Section 3)) is never reached in neutron star core for the nucleon-nucleon interactions considered in this work. since m2; is tvpicallvy of the order of I0po (see Table 3)).," This asymptotic limit which corresponds to the strongest entrainment effects (see the discussion of Section \ref{sect.non-rel.hydro}) ) is never reached in neutron star core for the nucleon-nucleon interactions considered in this work, since $m/\beta_3$ is typically of the order of $\sim 10 \rho_0$ (see Table \ref{table.forces.properties}) )."873 We have selected. elective forces according to the following criteria., We have selected effective forces according to the following criteria.874" First of all. the chosen forces have to vield. reasonable values of the ""semi-empirical saturation properties of infinite uniform symmetric nuclear matter. namely the equilibrium or saturation density vy (or the mass density po= nom). the binding energy per nucleon the symmetry energy. coefficient with =tn, nj)/m.. and the incompressibility modulus Global fits to essentially all the available experimental nuclear mass data vield ngo0.16[m. 7.0, o10 MeV. a,c2835 AleV and A220.240 MeV (2).."," First of all, the chosen forces have to yield reasonable values of the “semi-empirical” saturation properties of infinite uniform symmetric nuclear matter, namely the equilibrium or saturation density $n_0$ (or the mass density $\rho_0=n_0 m$ ), the binding energy per nucleon the symmetry energy coefficient with $I= (n_n-n_p)/n_{\rm b}$ , and the incompressibility modulus Global fits to essentially all the available experimental nuclear mass data yield $n_0 \simeq 0.16$ $^{-3}$, $a_v\simeq -16$ MeV, $a_s \simeq 28-35$ MeV and $K_\infty \simeq 220-240$ MeV \citep{lunney-03}."875 Due to the strong interactions. the mass of the individual nucleons in nuclear matter is different from the bare mass and can be written as in which m and m; are the so-called isoscalar ancl isovector effective masses respectively (see for instance 2)).," Due to the strong interactions, the mass of the individual nucleons in nuclear matter is different from the bare mass and can be written as in which $m^*_s$ and $m^*_v$ are the so-called isoscalar and isovector effective masses respectively (see for instance \citealt{farine-01}) )."876 The isovector effective mass is à crucial microscopic input since it controls directly the strength of entrainment cllects in mixtures., The isovector effective mass is a crucial microscopic input since it controls directly the strength of entrainment effects in neutron-proton mixtures.877 Indeed the parameter :2; which determines the mobility matrix. Eqs. (107)).(108))," Indeed the parameter $\beta_3$ which determines the mobility matrix, Eqs. \ref{eq.kappann}) \ref{eq.kappapp}) )"878 and. (109)). is given by In principle. this isovector cllective mass can be determined from measurements of the giant isovector clectric dipole resonance in finite nuclei (consisting of relative motions between neutrons and protons).," and \ref{eq.kappanp}) ), is given by In principle, this isovector effective mass can be determined from measurements of the giant isovector electric dipole resonance in finite nuclei (consisting of relative motions between neutrons and protons)."879 Nevertheless estimates are model dependent providing values mz/m0.7. Lat saturation density (see in particular the ciscussion of 2? in Sect., Nevertheless estimates are model dependent providing values $m^{*}_v/m\sim 0.7-1$ at saturation density (see in particular the discussion of \citealt{lunney-03} in Sect.880 HHI-D-5-0)., III-B-5-e).881 Microscopic many-body calculations in infinite uniform nuclear matter starting from the bare nucleon-nucleon interaction lead to an isovector elfective mass around m/m~0.7 (see for instance 2))., Microscopic many-body calculations in infinite uniform nuclear matter starting from the bare nucleon-nucleon interaction lead to an isovector effective mass around $m^{*}_v/m\sim 0.7$ (see for instance \citealt{zuo-06}) ).882 Besides we consider only those effective forces that have been constrained to fit the uniform infinite neutron matter equation of state., Besides we consider only those effective forces that have been constrained to fit the uniform infinite neutron matter equation of state.883 Otherwise these elective forces could not be reliably extrapolated to the neutron rich matter inside neutron star core., Otherwise these effective forces could not be reliably extrapolated to the neutron rich matter inside neutron star core.884 The main deficiencies of elective forces is the existence of instabilities that are not found by microscopic caleulations (???)..," The main deficiencies of effective forces is the existence of instabilities that are not found by microscopic calculations \citep{margueron-02, agrawal-04,lesinski-06}."885 Especially many Skyrme forces predict a spurious ferromagnetic transition in neutron matter above some critical densities., Especially many Skyrme forces predict a spurious ferromagnetic transition in neutron matter above some critical densities.886 We thus require that no such instabilities occur in the density range of interest p«3po by imposing that the dimensionless Landau parameter. usually noted Cy. be greater than 1 in neutron matter (following the analvsis of 2)).," We thus require that no such instabilities occur in the density range of interest $\rho < 3 \rho_0$ by imposing that the dimensionless Landau parameter, usually noted $G_0$, be greater than $-1$ in neutron matter (following the analysis of \citealt{margueron-02}) )."887 Ht turns out that this criterion is very restrictive., It turns out that this criterion is very restrictive.888 Several forces that reproduce reasonably well both the saturation properties of svmmetrie nuclear matter and the neutron matter equation ofstate do not pass this test., Several forces that reproduce reasonably well both the saturation properties of symmetric nuclear matter and the neutron matter equation of state do not pass this test.889 For instance. the parametrization IUVEP (?).. which was the first attempt to construct an effective force for astrophysical applications. predicts that neutron matter becomes spin polarized slightly above saturation density 20.175 [m7 (the density [or the onset. of instability is obtained by solving Gy= 1).," For instance, the parametrization RATP \citep{ratp-82}, which was the first attempt to construct an effective force for astrophysical applications, predicts that neutron matter becomes spin polarized slightly above saturation density $\simeq 0.175$ $^{-3}$ (the density for the onset of instability is obtained by solving $G_0=-1$ )."890 Likewise the forces SEM. and Skyrme 1. which have been applied to study dense matter in neutron stars and. supernova cores (7277)... vield a ferromagnetic transition density in neutron matter c0.212 (m.? and c0.256 £m.7 respectively.," Likewise the forces SkM and Skyrme $1^{\prime}$, which have been applied to study dense matter in neutron stars and supernova cores \citep{bonche-82,lattimer-85,lassaut-87, lorenz-93}, yield a ferromagnetic transition density in neutron matter $\simeq 0.212$ $^{-3}$ and $\simeq 0.256$ $^{-3}$ respectively."891 We have found that only the forces of the Saclayv-Lyon group (277).and the recent parametrization LNS (?) satisfy all the aboveconditions.," We have found that only the forces of the Saclay-Lyon group \citep{chabanat-97,chabanat-98,chabanat-err-98} and the recent parametrization LNS \citep{cao-06} satisfy all the aboveconditions."892 They. prediet a ferromagnetic instability in neutron matter like the other forces. but at significantly higher densities ~34ρυ which we do not consider in this work.," They predict a ferromagnetic instability in neutron matter like the other forces, but at significantly higher densities $\sim 3-4 \rho_0$ which we do not consider in this work."893 The force LNS seems the most appropriate to describe neutron star core since, The force LNS seems the most appropriate to describe neutron star core since894per solar mass of stars formed. was found to vary between ~10. Laud ~5«10.7 for a side rauge of possible metal-free IMEs.,"per solar mass of stars formed, was found to vary between $\sim 10^{-4}$ and $\sim 5 \times 10^{-3}$ for a wide range of possible metal-free IMFs."895 Note that while our two simple PPSN rate deusities are chosen such that thev can be casily rescaled by the reader. they are nevertheless consistent with the ranec of ;>L values predicted i more sophisticated models. as discussed iu $85.," Note that while our two simple PPSN rate densities are chosen such that they can be easily rescaled by the reader, they are nevertheless consistent with the range of $z \gtrsim 1$ values predicted in more sophisticated models, as discussed in 5."896 Furthermore. the total amount of iietals produced in our simple models is consistent with the element abundances observed in extremely metal-poor Calactic halo stars.," Furthermore, the total amount of metals produced in our simple models is consistent with the element abundances observed in extremely metal-poor Galactic halo stars."897 Asstuuing a typical value of 200 NL. of metals ejected per PPSNaud integrating down to τ=2.5. one obtains values ~6G«10?AD. ? for both of our PPSN rate deusitv models.," Assuming a typical value of 200 $\msun$ of metals ejected per PPSNand integrating down to $z=2.5$, one obtains values $\sim 6 \times 10^5 \msun$ $^{-3}$ for both of our PPSN rate density models."898 This corresponds to a mass fraction of barvous that have been processed by VMS of ~G10ον which is consistent with the 37«10. limits inferred by Oh (2001) to explain the relative abundances in extremely metal-poor Galactic stars.," This corresponds to a mass fraction of baryons that have been processed by VMS of $\sim 6 \times 10^{-5}$, which is consistent with the $3-7 \times 10^{-5}$ limits inferred by Oh (2001) to explain the relative abundances in extremely metal-poor Galactic stars."899 The resulting observed counts for these models are given in Figure { for two liiting magnitudes., The resulting observed counts for these models are given in Figure \ref{fig:Iband} for two limiting magnitudes.900 Iu the upper paucls. we take a fay=26 maguitude lnüt. appropriate for the Iustitute for Astronomy (fA) Deep Survey (Barris 2001). a erouncd-based survey that covered a total of 2.5 deg? frou September 2001 to April 2002.," In the upper panels, we take a $I_{\rm AB} = 26$ magnitude limit, appropriate for the Institute for Astronomy (IfA) Deep Survey (Barris 2004), a ground-based survey that covered a total of 2.5 $^2$ from September 2001 to April 2002."901 As we are interested in rare objects this tvpe of survey is more constraimiues that a more detailed. smaller-area searches such as theZ[ubble Wigher : Supernova Search (Riess 2001: Strolger 2001).," As we are interested in rare objects, this type of survey is more constraining that a more detailed, smaller-area searches such as the Higher $z$ Supernova Search (Riess 2004; Strolger 2004)."902 From this figure we see that existing data sects. if properly analvzed. are casily able to place usefuü constraints on VAIS formation at low redshifts.," From this figure we see that existing data sets, if properly analyzed, are easily able to place useful constraints on VMS formation at low redshifts."903 Given a typical PPSN aiodel like 200-I for example. the already realized TEA survew can be used to place a constraint of <1% of the total star formation rate density out to a redshitt ~1.," Given a typical PPSN model like 200-I for example, the already realized IfA survey can be used to place a constraint of $\lesssim 1 \%$ of the total star formation rate density out to a redshift $\sim 1$."904 Similarly. extreme models such as 250-8 can be probed out to redshifts ~2. all within the coutex of a recent SN search driven dy completely differcu science Goals.," Similarly, extreme models such as 250-S can be probed out to redshifts $\sim 2$, all within the context of a recent SN search driven by completely different science goals."905 Note however that these lits are stronglv dependent ou siguificant mixiug in the SN progenitor or he production of Ni. and thus models such as 150-2. remain largely uuconstrained by the TEA survey.," Note however that these limits are strongly dependent on significant mixing in the SN progenitor or the production of $^{56}$ Ni, and thus models such as 150-W remain largely unconstrained by the IfA survey."906 Iu the bottom panels of Figure Lowe consider a liniting naenitude of νο=27. appropriate for the COSMOSsurvev'. un ongoing project that will cover 2 dee? using he on IST.," In the bottom panels of Figure \ref{fig:Iband} we consider a limiting magnitude of $I_{\rm AB} = 27$, appropriate for the COSMOS, an ongoing project that will cover 2 $^2$ using the on HST."907 Raising the iutiug magnitude from Jap=26 to fap=27 has thexunary effect of extending the sensitivity out to slightly uigher redshifts., Raising the limiting magnitude from $I_{\rm AB} = 26$ to $I_{\rm AB} = 27$ has theprimary effect of extending the sensitivity out to slightly higher redshifts.908 This pushes the probed rauge fro11 2<1 ο τς1.5 in the 200-I case aud frou :xz2 to:<3 in the 250-S case., This pushes the probed range from $z \lesssim 1$ to $z \lesssim 1.5$ in the 200-I case and from $z \lesssim 2$ to $z \lesssim 3$ in the 250-S case.909 Again this is all in the coutext of an ongoing survey., Again this is all in the context of an ongoing survey.910 Even with this fainter limiting magnitude. rowever. low-luuinosity like 150-W are extremely difficult to find. aud remain arecly uucoustrainecd.," Even with this fainter limiting magnitude, however, low-luminosity like 150-W are extremely difficult to find, and remain largely unconstrained."911 This shortcoming ds easily overcome by moving to NIB wavelengths., This shortcoming is easily overcome by moving to NIR wavelengths.912 In Figure 5.. we calculate the PPSN coustraints that would be obtained from three possible realizations of the planned space-based (IDEAL).," In Figure \ref{fig:Hband}, , we calculate the PPSN constraints that would be obtained from three possible realizations of the planned space-based ."913 Iu the upper aud ceutral paucls, In the upper and central panels914closest to the observer.,closest to the observer.915 This curve demonstrates the fact that in addition to the largest erains. (he grains closest to (he source also add much power to the core of the scattering halo.," This curve demonstrates the fact that in addition to the largest grains, the grains closest to the source also add much power to the core of the scattering halo."916 By moving these grains closer to the observer the central scattering peak loses power accordinelv., By moving these grains closer to the observer the central scattering peak loses power accordingly.917 This fit is qualitatively about as good as the fit of the NAIRN curve with a uniform dust distribution., This fit is qualitatively about as good as the fit of the XMRN curve with a uniform dust distribution.918 It could be improved by extending the size distribution to still larger sizes while keeping the dust-lo-gas ratio constant al the original value of 0.0066., It could be improved by extending the size distribution to still larger sizes while keeping the dust-to-gas ratio constant at the original value of 0.0066.919 As demonstrated with the examples of the three uniform line-of-sight. distributions (solid. dotted. and dashed lines). the addition of still larger grains would steepen the dot-dashed profile in the central core and lower the intensity in the outer halo. as required by the observations.," As demonstrated with the examples of the three uniform line-of-sight distributions (solid, dotted, and dashed lines), the addition of still larger grains would steepen the dot-dashed profile in the central core and lower the intensity in the outer halo, as required by the observations."920 The results of our caleulations show that extending the \IRN grain size distribution to larger grain sizes. as characterized bv the NMBRN model. results in a better fit to the X-aay halo of Nova Cyvgni 1992.," The results of our calculations show that extending the MRN grain size distribution to larger grain sizes, as characterized by the XMRN model, results in a better fit to the X-ray halo of Nova Cygni 1992."921 This suggests that particles with sizes larger than 0.25 jou constitute a significant mass fraction of the interstellar dust population along one line of sight through the general ISAT., This suggests that particles with sizes larger than 0.25 $\mu$ m constitute a significant mass fraction of the interstellar dust population along one line of sight through the general ISM.922 Our results are therefore the first extension of the conclusions of Frisch et al. (, Our results are therefore the first extension of the conclusions of Frisch et al. (9231999) bevond the local Galactic neighborhood of the solar svstem.,1999) beyond the local Galactic neighborhood of the solar system.924 ILowever. in contrast to the locally-basecl result of Frisch et al. (," However, in contrast to the locally-based result of Frisch et al. ("9251999). we do not find any evidence that the dust-to-@as mass ratio along the Nova Cvgni 1992 line-ol-sight must be larger (han the canonical interstellar value.,"1999), we do not find any evidence that the dust-to-gas mass ratio along the Nova Cygni 1992 line-of-sight must be larger than the canonical interstellar value."926 We need to examine {ο what extent our conclusions depend on the specilic cust model used in the calewlations., We need to examine to what extent our conclusions depend on the specific dust model used in the calculations.927 It is possible that other functional forms of the grain size distribution. different. dust compositions. or different dust morphology may provide an improved fit to the Nova Cvgni 1992 halo.," It is possible that other functional forms of the grain size distribution, different dust compositions, or different dust morphology may provide an improved fit to the Nova Cygni 1992 halo."928CC 2 1-42 DEC DD - dy.where. rj is the inner boundary of the dise.,C = 1- 4a )^2 D = where $r_{ms}$ is the inner boundary of the disc.929" The equation of conservation of mass remains valid. while hydrostatic equilibrium in the vertical direction leads to a corrected expression for the half thickness of the disc (Riffert Herold 1995). (2)Ver where c,=(p/p) 7. p and p are the total pressure and density of the disk. respectively."," The equation of conservation of mass remains valid, while hydrostatic equilibrium in the vertical direction leads to a corrected expression for the half thickness of the disc (Riffert Herold 1995), H, where $c_{\rm930s}=(p/\rho)^{1/2}$ , $p$ and $\rho$ are the total pressure and density of the disk, respectively."931" The viscous shear 7, 1s also corrected as = OIαρ. and the angular momentum equation can be simplified as (Riffert Herold 1995. Lei et al."," The viscous shear $T_{r \phi}$ is also corrected as = - p, and the angular momentum equation can be simplified as (Riffert Herold 1995, Lei et al."932" 2009) =pepe The equation of state is PP = + habt Petpy. where Peay. Pag. Po. and p, are the gas pressure from nucleons. radiation pressure of photons. degeneracy pressure of electrons. and radiation pressure of neutrinos. respectively (see. e.g. Di Matteo et al."," 2009) = The equation of state is p = + + +, where $p_{\rm gas}$, $p_{\rm rad}$, $p_{\rm e}$, and $p_\nu$ are the gas pressure from nucleons, radiation pressure of photons, degeneracy pressure of electrons, and radiation pressure of neutrinos, respectively (see, e.g. Di Matteo et al."933 2002: Liu et al., 2002; Liu et al.934 2007)., 2007).935" The energy equation is written as = + tQ. where Qu. Quan. Όρμος and Q, are the viscous heating rate. the advective cooling rate. the cooling rate due to photodisintegration of a-particles and the cooling due to the neutrino radiation. respectively (see. e.g. Di Matteo et al."," The energy equation is written as = + +, where $Q_{\rm vis}$, $Q_{\rm adv}$, $Q_{\rm photo}$ and $Q_\nu$ are the viscous heating rate, the advective cooling rate, the cooling rate due to photodisintegration of $\alpha$ -particles and the cooling due to the neutrino radiation, respectively (see, e.g. Di Matteo et al."936 2002: Liu et al., 2002; Liu et al.937 2007)., 2007).938" The heating rate Qi, is expressed as The equation system consisting of Eqs. (", The heating rate $Q_{\rm vis}$ is expressed as = The equation system consisting of Eqs. (9391). (2). (4)-(13) is closed for an unknown precession period P. It can be numerically solved for a given parameter set of M. M. a. and a.,"1), (2), (4)-(13) is closed for an unknown precession period $P$ It can be numerically solved for a given parameter set of $M$ $\dot{M}$ , $a$ , and $\alpha$."940 We show P as a function of M for the parameter sets («à=0.9. M=Μα a= 0.01). (a= 0.9. M=3M. e= 0.1). (a=0.Ι. M2 3M.«= 0.1) and (a=0.1. M=3M. av= 0.01) in Fig.," We show $P$ as a function of $\dot{M}$ for the parameter sets $a=0.9$, $M = 3 M_\odot$, $\alpha=0.01$ ), $a=0.9$ , $M = 3 M_\odot$, $\alpha=0.1$ ), $a=0.1$, $M = 3 M_\odot$, $\alpha=0.1$ ) and $a=0.1$, $M = 3 M_\odot$, $\alpha=0.01$ ) in Fig."941 2., 2.942 It is found that P varies from tens of milliseconds to 10 ks. if M=001~10 Mis. a=0.01~0.1. anda=0.1~0.9.," It is found that $P$ varies from tens of milliseconds to 10 ks, if $\dot{M}=0.01\sim 10$ $M_\odot$ /s, $\alpha=0.01\sim 0.1$, and $a=0.1\sim 0.9$."943 It can approach the timescale of lighteurve or be longer than the accretion timescale whose provide a couple of possibilitiesof lightcurve., It can approach the timescale of lightcurve or be longer than the accretion timescale whose provide a couple of possibilitiesof lightcurve.944 Incollapsar scenario. the centralblack holewould be rapidly rotates. 1.e.. ¢ 0.9.For the compact object mergers.the spinof theblack hole is not strictly as high asthat in the," Incollapsar scenario, the centralblack holewould be rapidly rotates, i.e., $a\gtrsim 0.9$ .For the compact object mergers,the spinof theblack hole is not strictly as high asthat in the"945with a possibly different coustaut C that depend ou 7.,with a possibly different constant $C$ that depend on $T$.946 Iudeed. the terii 7 enters in estimating oyphUU since (3.16)) is now replaced (see again Figure 3)) by This shows the claim.," Indeed, the term $T$ enters in estimating $\<\Psi\tilde{f}\>^{(\g/2)}_{t,\R^{2}}$ since \ref{fin_add}) ) is now replaced (see again Figure \ref{fig3}) ) by This shows the claim."947 oO , $\hfill{\Box}$ 948" Atz~ 5,? reported the UV LF from a combination of HDF and Subaru images, totalling a survey area about 1/9 of ours.","At $z\sim5$ , \citet{iwata07} reported the UV LF from a combination of HDF and Subaru images, totalling a survey area about 1/9 of ours."949? based their study on approximately 100 LBGs from very deep ACS and NICMOS imaging., \citet{oesch07} based their study on approximately 100 LBGs from very deep ACS and NICMOS imaging.950" ? also defined a z~5 sample from their observations, combining Vi'z and Ri’z’ selected objects, as did ?.."," \citet{yoshida06} also defined a $z\sim 5$ sample from their observations, combining $Vi'z'$ and $Ri'z'$ selected objects, as did \citet{ouchi04a}. ."951 ? selected 275 Veo6i775Zg50 LBGs to estimate az~5 UV LE, \citet{giavalisco04} selected 275 $V_{606}i_{775}z_{850}$ LBGs to estimate a $z\sim 5$ UV LF.952" ? also measured a sample of 1416 V-dropouts from their deep HST ACS sample, which resulted in an estimation of the UV LF down to Mj600,48=—17.16."," \citet{bouwens07} also measured a sample of 1416 V-dropouts from their deep HST ACS sample, which resulted in an estimation of the UV LF down to $M_{1600,AB}=-17.16$."953" Similar to the Schechter parameters found for z~4, there is. a large discrepancy. in. the literature. for the Schechter parameters at z~5."," Similar to the Schechter parameters found for $z \sim 4$, there is a large discrepancy in the literature for the Schechter parameters at $z \sim 5$."954 The statistical uncertainties in the Schechter parameters is very small for our r-dropout sample., The statistical uncertainties in the Schechter parameters is very small for our $r$ -dropout sample.955" Note however that several systematic uncertainties are not included in these error ellipses, see Sect. 4.3.."," Note however that several systematic uncertainties are not included in these error ellipses, see Sect. \ref{sec:robust}."956" Our results agree reasonably well, within the 1—o level, with many previous determinations at z~5."," Our results agree reasonably well, within the $1-\sigma$ level, with many previous determinations at $z\sim 5$."957 In Fig., In Fig.958" 14. we compare the SFR density values given in Table 3 to values reported by ?,, who made use of z GALEX data, ? at intermediate z, and ? at high z."," \ref{fig:sfrd} we compare the SFR density values given in Table \ref{tab:sfrd} to values reported by \citet{schiminovich05}, who made use of $z$ GALEX data, \citet{reddy09} at intermediate $z$, and \citet{bouwens09} at high $z$."959 The uncorrected SFRDs are in good agreement with each other and show a smooth redshift evolution., The uncorrected SFRDs are in good agreement with each other and show a smooth redshift evolution.960" However, it is clear that the dust correction is the major uncertainty because of the age-dust degeneracy."," However, it is clear that the dust correction is the major uncertainty because of the age-dust degeneracy."961 We use the same dust correction as ? and also include systematic uncertainties in the error bars., We use the same dust correction as \citet{bouwens09} and also include systematic uncertainties in the error bars.962" In this paper we use the CFHT Legacy Survey Deep fields to estimate the UV Luminosity Functions of the largest u, g-, and r-dropouts samples to date."," In this paper we use the CFHT Legacy Survey Deep fields to estimate the UV Luminosity Functions of the largest $u$, $g$ -, and $r$ -dropouts samples to date."963 As our samples are all extracted from the same dataset this study is ideally suitedto study a timeevolution of the luminosity function in the redshift, As our samples are all extracted from the same dataset this study is ideally suitedto study a timeevolution of the luminosity function in the redshift964respectively the poloidal aud toroidal field components. evaluated at the surface of the filament: The dots. squares. aud x's represent models of types 1. 2 and 3 respectively.,"respectively the poloidal and toroidal field components, evaluated at the surface of the filament: The dots, squares, and x's represent models of types 1, 2, and 3 respectively."965" Note that D.ςD,s is sinall or nanv of our models because the toroidal maeuetic field dominates iu he outer cuvelope. Lear the radius of pressure truncation."," Note that $\ratio$ is small for many of our models because the toroidal magnetic field dominates in the outer envelope, near the radius of pressure truncation."966 The ratio of: D.FB. is substanwally higher iu he interior regions of the filameut., The ratio of $\Bz/\Bphi$ is substantially higher in the interior regions of the filament.967 Au interesting feature of Figure 2 is that the polarization outterus are of he first type for a large portion of our models., An interesting feature of Figure \ref{fig:space} is that the polarization patterns are of the first type for a large portion of our models.968 Thus. may of our 110dels are qualitativedv simular to the Alatthews aud Wilson (2000) map of the Orion filament. discussed ii1 Section [.2..," Thus, many of our models are qualitatively similar to the Matthews and Wilson (2000) map of the Orion filament, discussed in Section \ref{sec:patterns}."969 We Bud this type opattern for most models with B.ςλες~0.1., We find this type of pattern for most models with $\ratio\appleq 0.1$.970 Generally. polarization patterus of the second type occur when Bes/Bos~0.33. and the third type occurs for interiuediate values between abou 0.1 αnd 0.33.," Generally, polarization patterns of the second type occur when $\ratio\appgeq 0.33$, and the third type occurs for intermediate values between about 0.1 and 0.33."971 This may be uuderstood as follows., This may be understood as follows.972" When D.s/D,,s is sua1. the models are dominated by the toroidal field component so that he xoloidal field is ineffective at canceling the polarization due to the toroidal field. as discussed iu Section [.2.."," When $\ratio$ is small, the models are dominated by the toroidal field component so that the poloidal field is ineffective at canceling the polarization due to the toroidal field, as discussed in Section \ref{sec:patterns}."973 Thus. the polarization pattern is of tvpe L.," Thus, the polarization pattern is of type 1."974" However. ax B.s is mereased relative to D,,s. he competition becomes stronger 1util D.« becomes dominant along some line of sight. which first occurs whe1 D.s/D,,«szOL."," However, as $\Bzs$ is increased relative to $\Bphis$, the competition becomes stronger until $\Bzs$ becomes dominant along some line of sight, which first occurs when $\ratio \approx 0.1$."975 This results iu a 907 Hip in the polarization vectors at this position. which we categorizet( as the first Type 5n model.," This results in a $90^\circ$ flip in the polarization vectors at this position, which we categorize as the first Type 3 model."976 The exact opposite occurs when Bogδις is increased past about k:?)ὃν, The exact opposite occurs when $\ratio$ is increased past about $0.33$.977 Past this poiut. the toroidal feld. component becomes too weak compared to the poloidal field to POCuce a flip in the polarization vectors resulΠιο in Type 2 patterns.," Past this point, the toroidal field component becomes too weak compared to the poloidal field to produce a flip in the polarization vectors resulting in Type 2 patterns."978 Figure 3.Mi shows the deeree to which the Cluission is depolarized for all three types of polarizatio- ottern., Figure \ref{fig:depolarized} shows the degree to which the emission is depolarized for all three types of polarization pattern.979" We define the polarization hole dept las (PincaDuiVPna Where Pig, is the masiuuuu volarization percentage iu the map and D, is the local mimi polarization percentage at the localon of the volarization hole with the lowest polarization."," We define the polarization hole depth as $(P_{max}-P_{min})/P_{max}$, where $P_{max}$ is the maximum polarization percentage in the map and $P_{min}$ is the local minimum polarization percentage at the location of the polarization hole with the lowest polarization."980" We find that the polarization hole depth ecucrally Increases. With scatter. as a function of D.DB,« for Type 1 ποσο] from 0 when DB,s/D,s-0 O 1004 when B,s/D,,s=0.1."," We find that the polarization hole depth generally increases, with scatter, as a function of $\ratio$ for Type 1 models from $0\%$ when $\ratio=0$ to $100\%$ when $\ratio=0.1$."981 This is easily iuclerstood by essentially the same argument eiven in thie previous paragraph., This is easily understood by essentially the same argument given in the previous paragraph.982" There is no 5ienificaut poarization hole when D.D,s is πμ because coutributious to the volarization arising frou t16 poloidal field do not effectively cancel the larger coutrilnitions from the toroida| field along anv line of sight.", There is no significant polarization hole when $\ratio$ is small because contributions to the polarization arising from the poloidal field do not effectively cancel the larger contributions from the toroidal field along any line of sight.983" The deph of the polarization hole increases until D..yBosaw0.1. where he first Type 3 pattern οneregcs,"," The depth of the polarization hole increases until $\ratio \approx 0.1$, where the first Type 3 pattern emerges."984" Note that the poarization hole depth is alwavs 1X4 for Type EMi models. since D,;,=0 at the locations where the orieutiou of the polarization vectors flips by 90."," Note that the polarization hole depth is always $100\%$ for Type 3 models, since $P_{min}=0$ at the locations where the oriention of the polarization vectors flips by $90^\circ$."985" Tucreasing B.s/D,s decreases t1e depth of t16 polarization hole for Type 2 models. since the contribution to the polarization froin the toroidal Seld becnues progressively less effective at canceling he polarization due to the dominant pooidal fie"," Increasing $\ratio$ decreases the depth of the polarization hole for Type 2 models, since the contribution to the polarization from the toroidal field becomes progressively less effective at canceling the polarization due to the dominant poloidal field."986 We define the width of the epolarized region as the distance beween the polarization maxima ou either side of the polarization hole., We define the width of the depolarized region as the distance between the polarization maxima on either side of the polarization hole.987 Panel 3b » shows the ratio of this sviIth divided by the filament diameter., Panel \ref{fig:depolarized}b b shows the ratio of this width divided by the filament diameter.988" Generally. this ratio increases with D.ςδι,s for Type 1 models. frou nearly 0 to about 0.1. which occurs at the point where the uodels clauge to Eype 3."," Generally, this ratio increases with $\ratio$ for Type 1 models, from nearly $0$ to about $0.4$, which occurs at the point where the models change to Type 3."989" This fractional widhn continues to increase past this point until B.s/D,,szm0.25. whereiC the poarization width jumps discontinuously to the full width of the fibuneut."," This fractional width continues to increase past this point until $\ratio \approx 0.23$, where the polarization width jumps discontinuously to the full width of the filament."990 This happens OCATISC of a chanec in the qualitative behaviour of the polarization vectors near the οσο of the flament., This happens because of a change in the qualitative behaviour of the polarization vectors near the edge of the filament.991 Note fiat the pol:wization percentage shown in Figure 1 js a πάπα at the outer οσο of the filameit for Type Ll modes. but a αλαπα for Type 2 models.," Note that the polarization percentage shown in Figure \ref{fig:types} is a minimum at the outer edge of the filament for Type 1 models, but a maximum for Type 2 models."992 As we move through a, As we move through a993marked as Gl. G2. G8. G4 and G5 in Fig.,"marked as G1, G2, G3, G4 and G5 in Fig."994 9 fall within the slit., 9 fall within the slit.995 The spectra reveal that they are all emission line galaxies at different z than the quasar., The spectra reveal that they are all emission line galaxies at different $z$ than the quasar.996 The spatial profile of the emission. lines along DPA 115 (Fig., The spatial profile of the emission lines along PA 115 (Fig.997" 13) is dominated by a barely resolved. central component of ISGEO.04"" (vs. 1.600.049.", 13) is dominated by a barely resolved central component of $\pm$ $\arcsec$ (vs. $\pm$ $\arcsec$ ).998 Phe seeing F'WLILM. was very similar at the beginning and. the end. of this object. exposures. so seeing variations during the spectroscopic observations are not Likely to plav a role and the line emission is actually spatially extended.," The seeing FWHM was very similar at the beginning and the end of this object exposures, so seeing variations during the spectroscopic observations are not likely to play a role and the line emission is actually spatially extended."999" The implied. intrinsic size is —1"" or ~5.5 kpc.", The implied intrinsic size is $\sim$ $\arcsec$ or $\sim$ 5.5 kpc.1000 Given the strong contamination by the nuclear emission. it is not possible to isolate the emission from this ELL to analyse the kinematic and ionization properties.," Given the strong contamination by the nuclear emission, it is not possible to isolate the emission from this EELR to analyse the kinematic and ionization properties."1001In addition. very [aint emission is detected. at 37. level towards the West (indicated with ΠΟΙΟ in Fig.,"In addition, very faint emission is detected at $\sim$ $\sigma$ level towards the West (indicated with “EELR” in Fig."1002 13) up to a radial extent of or −∕∕⋅38.5 kpe from⋅ the continuum. centroicd., 13) up to a radial extent of $\arcsec$ or 38.5 kpc from the continuum centroid.1003. ThisTl quasarju (F'ig.àld)(Γιά) appears to |be interacting[ting withwill a companion galaxy (Cil in the figure). although a chance projection cannot be discarded from the image alone.," This quasar (Fig.â14) appears to be interacting with a companion galaxy (G1 in the figure), although a chance projection cannot be discarded from the image alone."1004 The FORS?2 slit was located at PA 65. crossing both nuclei.," The FORS2 slit was located at PA 65, crossing both nuclei."1005 The nuclear spectrum shows strong5 continuum compared with the other quasars in the sample— and a very broad. underlying H2 component (Fig.al5)., The nuclear spectrum shows strong continuum compared with the other quasars in the sample and a very broad underlying $\beta$ component (Fig.â15).1006 Phe flux of this component has not been included in the 111 lux used. to calculate the nuclear line ratios (Table 2)., The flux of this component has not been included in the $\beta$ flux used to calculate the nuclear line ratios (Table 2).1007 Broad underlying Hell might also be present., Broad underlying HeII might also be present.1008 Several FeV] emission lines are detected. CFeVIIA3586.. LABT59. FeVIH]JA5159).," Several [FeVII] emission lines are detected $\lambda$ 3586, $\lambda$ 3759, $\lambda$ 5159)."1009 Forbidden high ionization lines (FILL) have been detected in the spectra of many active galaxies (c.g. Penston ct al. 1984.. ," Forbidden high ionization lines (FHIL) have been detected in the spectra of many active galaxies (e.g. Penston et al. \citeyear{pen84}, ,"1010Mullanev et al. 2009))., Mullaney et al. \citeyear{mul09}) ).1011 Their ionization potential is, Their ionization potential is1012and in Table 3 we present the final abuudances.,and in Table \ref{table:abundances} we present the final abundances.1013 Iun the discussion to follow we express our abundances relative to the solar values of(2006)., In the discussion to follow we express our abundances relative to the solar values of.1014. The abundance dependences ou the stellar parameters are given in Table 1.., The abundance dependences on the stellar parameters are given in Table \ref{table:abundanceUncertainties}.1015 Iu Figure L we present our |Fe/TI| determinations for the two sample regions iu the upper panel of Figure L., In Figure \ref{fig:FeH} we present our [Fe/H] determinations for the two sample regions in the upper panel of Figure \ref{fig:FeH}.1016 Iu the lower panel of Figure | we graphically represent the median |Fe/TII] aud its interquartile rauge as a function of angular distance (A. as defined in (2005))) from the main body of Ser., In the lower panel of Figure \ref{fig:FeH} we graphically represent the median [Fe/H] and its interquartile range as a function of angular distance $\Lambda_{\odot}$ as defined in ) from the main body of Sgr.1017 Ao two-sided Ix-S test is used to determine the probability that the stream samples were drawn from the core sample2005)., A two-sided K-S test is used to determine the probability that the stream samples were drawn from the core sample.1018. The percentages above ch sample in the lower panel of Figure { show the probability that this is the case., The percentages above each sample in the lower panel of Figure \ref{fig:FeH} show the probability that this is the case.1019 Low values of this probability indicate that the assumption that the stream samples are sinülu to that of +i6 core is a poor one., Low values of this probability indicate that the assumption that the stream samples are similar to that of the core is a poor one.1020 More distant material is seen fo be progressively less like the core sunple., More distant material is seen to be progressively less like the core sample.1021" A eradieut of (2.140,3)&10.7 dex/degree is determined from) a least-squares fit to the core. A. =66"" and A.=132"" samples."," A gradient of $-(2.4\pm0.3)\times10^{-3}$ dex/degree is determined from a least-squares fit to the core, $\Lambda_{\odot}$ $^{\circ}$ and $\Lambda_{\odot}$ $^{\circ}$ samples."1022 At a mean distance of 22 kpc this projects to (9.121.1)ς10! dex / kpe., At a mean distance of 22 kpc this projects to $-(9.4\pm1.1)\times10^{-4}$ dex / kpc.1023 The target stars have been taken from the study of aud are selected therein on the basis of their 2\LASS colours as ejut stars., The target stars have been taken from the study of and are selected therein on the basis of their 2MASS colours as M-giant stars.1024 The judicious selection of isolates the upper red giaut brauch (ROB) of Ser with low contamination from the Milky Wav (MW) field., The judicious selection of isolates the upper red giant branch (RGB) of Sgr with low contamination from the Milky Way (MW) field.1025 However. it also imposes a bias towards metalrich stars as detailed in(2003).," However, it also imposes a bias towards metal-rich stars as detailed in."1026. Metallicitfies of [Fe/TI}<1 dex are essentially excluded due to this colour selection., Metallicities of $ < -1$ dex are essentially excluded due to this colour selection.1027 To minimise the effects of this inposed metallicity bias on our fiudiues. the above figures compare our results with literature data that impose identical colour selection of the M-giauts.," To minimise the effects of this imposed metallicity bias on our findings, the above figures compare our results with literature data that impose identical colour selection of the M-giants."1028 Utilisation of ΑΙ. also muposes an age ranee to the sample of stars we study., Utilisation of M-giants also imposes an age range to the sample of stars we study.1029 An M-giant of [Fe/T] NI dex (typical of the Ser core: 20051) possesses an age of 22.5 Cr., An M-giant of [Fe/H] = $-0.4$ dex (typical of the Sgr core; ) possesses an age of 2–2.5 Gyr.1030 At lower metallicities an older age is required to reach the same JJv color (for example a 1M... [Fe/T]| 0.1 star is 0.1 dex younger than a [Fe/II| = -0.7 star at. IW=1.0: 2008))., At lower metallicities an older age is required to reach the same $J$$-$$K$ color (for example a $_{\odot}$ [Fe/H] = -0.4 star is 0.1 dex younger than a [Fe/H] = -0.7 star at $J$$-$$K$ =1.0; ).1031 Qur results mav be compared to the metallicity eracieut observed in the more extcusively studied leading arm material., Our results may be compared to the metallicity gradient observed in the more extensively studied leading arm material.1032 As noted above. the leading ari is more extensively phased mixed.," As noted above, the leading arm is more extensively phased mixed."1033 That is to sav the material lost in successive orbits is not as spatially differentiated as in the trailing arm., That is to say the material lost in successive orbits is not as spatially differentiated as in the trailing arm.1034 This effect would be expected to reduce the apparent imnoetalliitv. &eradicnt aloug the leading arn compared to the trailne ari., This effect would be expected to reduce the apparent metallicity gradient along the leading arm compared to the trailing arm.1035 In their study of the leading aria M. eiauts.(2007).. report the metallicity distribution fiction ((AIDF) in two regions: one centred at A.~230° of around 1007 in extent. and another region at A.30° (proposed to be old leading ari debris displaced ~390° from the main body).," In their study of the leading arm M giants, report the metallicity distribution function (MDF) in two regions; one centred at $\Lambda_{\odot} \sim 230^{\circ}$ of around $^{\circ}$ in extent, and another region at $\Lambda_{\odot} \sim 30^{\circ}$ (proposed to be old leading arm debris displaced $\sim 390^{\circ}$ from the main body)."1036" The mean inetallicities ave found to be 0.7 dex aud l.l dex respectively,", The mean metallicities are found to be $-0.7$ dex and $-1.1$ dex respectively.1037" Taken together with the mean imetalliitv of the core. this equates to a metallicity eradient of 2.2«10"" dex/deeree."," Taken together with the mean metallicity of the core, this equates to a metallicity gradient of $-2.2\times10^{-3}$ dex/degree."1038 This is compatible with the present results for the trailing aru., This is compatible with the present results for the trailing arm.1039 The |Fe/II| eeradient we derive her oes also compatible with the mean metallicity determined. again frou M-giauts. iu the sample of (amarkecd MOT in Figure 1).," The [Fe/H] gradient we derive here is also compatible with the mean metallicity determined, again from M-giants, in the sample of (marked M07 in Figure \ref{fig:FeH}) )."1040" Further. it is noteworthy that our observed |Fe/II| gradient continues to the ""North Galactic Cap positive velocity’ eroup which is ascribed by to au old wrap of the trailing aru."," Further, it is noteworthy that our observed [Fe/H] gradient continues to the 'North Galactic Cap positive velocity' group which is ascribed by to an old wrap of the trailing arm."1041 The North Calactic Cap saluple is not used in our determination of the motallicity eradieut of the trailing arin since there is possible coufusion with other kinematically distinct substructures in the direction of the North Galactic Cap sample., The North Galactic Cap sample is not used in our determination of the metallicity gradient of the trailing arm since there is possible confusion with other kinematically distinct substructures in the direction of the North Galactic Cap sample.1042 The North Galactic Cap suuple occupies au area of the sky oeji which there is both leading aud trailing ari material as well as material from the Vireo Stellar Stream 2009)., The North Galactic Cap sample occupies an area of the sky in which there is both leading and trailing arm material as well as material from the Virgo Stellar Stream .1043. The dynamical models of predict that while the lealues ar uaterial atthe position. of the North Galactic Cap sample will possess uceative velocities. the railing material will possess velocities of 100Vesp<200 |.," The dynamical models of predict that while the leading arm material atthe position of the North Galactic Cap sample will possess negative velocities, the trailing material will possess velocities of $100<V_{GSR}<200$ $^{-1}$."1044 The Vireo Stellar Stream naterial possesses a colder velocity profile ceutred at Ve;sg100 1., The Virgo Stellar Stream material possesses a colder velocity profile centred at $V_{GSR}\sim 100$ $^{-1}$.1045 shows hat considerable overlap iu radial velocity exists vetween the two svstenis and cousequeutlv it is, shows that considerable overlap in radial velocity exists between the two systems and consequently it is1046which do permmte the connected couponcuts of A.,which do permute the connected components of $\tilde{A}$.1047 A connected component Ay of A will be a cover of A with covering eroup Dy: thus Py is isomorphic to the quotient eroup zi)(Ay). aud in partieular it is abelian.," A connected component $\tilde{A}_0$ of $\tilde{A}$ will be a cover of $A$ with covering group $\Gamma_0$; thus $\Gamma_0$ is isomorphic to the quotient group $\pi_1(A)/\pi_1(\tilde{A}_0)$, and in particular it is abelian."1048" We now take the Stein factorization of σιX.»F2, which gives where the ecnerie fibre of o is an abclian surface; such as Ay."," We now take the Stein factorization of $\tilde{\pi}:\tilde{X}\rightarrow\P^2$ , which gives where the generic fibre of $\phi$ is an abelian surface, such as $\tilde{A}_0$."1049 Moreover. τιZ Eds a Calois cover with Galois group T/Ty: the points of τ1(f) correspond to the different connected components of cL and T/Ty acts frecly and transitively on these components.," Moreover, $\tau:Z\rightarrow\P^2$ is a Galois cover with Galois group $\Gamma/\Gamma_0$; the points of $\tau^{-1}(t)$ correspond to the different connected components of $\tilde{A}$, and $\Gamma/\Gamma_0$ acts freely and transitively on these components."1050 In particular. Z>E? is a d/-to-L cover. where d divides d. (," In particular, $Z\rightarrow\P^2$ is a $d^{\prime}$ -to-1 cover, where $d^{\prime}$ divides $d$. ("1051This illustrates the utility of the restrictions that d is one in classes 5 and 6. and one or two in class 3.),"This illustrates the utility of the restrictions that $d$ is one in classes 5 and 6, and one or two in class 3.)"1052 The problem of coustructing examples cau be formulated as follows., The problem of constructing examples can be formulated as follows.1053 Cave X from one of the six classes. we look for a fibration of X by abelian surfaces over a unface Z.," Given $\tilde{X}$ from one of the six classes, we look for a fibration of $\tilde{X}$ by abelian surfaces over a surface $Z$."1054" Wo try to express Z as a Galois cover r:Z>μὲ, with Galois group ΕΤο."," We try to express $Z$ as a Galois cover $\tau:Z\rightarrow\P^2$, with Galois group $\Gamma/\Gamma_0$."1055 Of course τ inst be ramified since I? is simply counected., Of course $\tau$ must be ramified since $\P^2$ is simply connected.1056 There will be a quoticut N/Ty which is also fibved by abelian surfaces overZ., There will be a quotient $\tilde{X}/\Gamma_0$ which is also fibred by abelian surfaces over$Z$.1057 The problem is to extend the action of [/Ty ou Z. which has fixed-points. to a fixed-point free action on N/Ty: for then the quotient is the required four-fold VY. ντος by abelian surfaces over F7.," The problem is to extend the action of $\Gamma/\Gamma_0$ on $Z$, which has fixed-points, to a fixed-point free action on $\tilde{X}/\Gamma_0$; for then the quotient is the required four-fold $X$ , fibred by abelian surfaces over $\P^2$."1058 The following diagram sunumnuauizes this construction., The following diagram summarizes this construction.1059 Tf some clement of [/Ty fixes s€Z. then that element iust act in a free manner on the abelian surface fibre above s.," If some element of $\Gamma/\Gamma_0$ fixes $s\in Z$, then that element must act in a fixed-point free manner on the abelian surface fibre above $s$."1060 Usually the quotieut of this action will again be an abelian surface. aud thus the element should act by a translation.," Usually the quotient of this action will again be an abelian surface, and thus the element should act by a translation."1061 This suggests that P/Ty should be abelian. aud we will keep this as a οπήςπιο principle when coustructing examples.," This suggests that $\Gamma/\Gamma_0$ should be abelian, and we will keep this as a guiding principle when constructing examples."1062 However. there may not be a point sCZ fixed bx the entire eroup 1Τι. so we wont find necessarily find that the entire eroup acts as translations on a single abclian surface.," However, there may not be a point $s\in Z$ fixed by the entire group $\Gamma/\Gamma_0$, so we won't find necessarily find that the entire group acts as translations on a single abelian surface."1063 Moreover. s could lic iu the discriminantlocus of the abelian surface fibration. iiplviug that the fibre above s is a degeneration rather than a simooth abelian surface.," Moreover, $s$ could lie in the discriminantlocus of the abelian surface fibration, implying that the fibre above $s$ is a degeneration rather than a smooth abelian surface."1064 Retumineg tow:NV> TP. we have the followingresults coucerning direct Mages of the structure sheaf.," Returning to $\pi:X\rightarrow\P^2$ , we have the followingresults concerning direct images of the structure sheaf."1065Accurale ages for nearby stellar clusters are the basic observational templates that constrain the formation history of our Galaxy and the Universe.,Accurate ages for nearby stellar clusters are the basic observational templates that constrain the formation history of our Galaxy and the Universe.1066 Unfortunately. theoretical isochrones fit to the upper main sequence provide absolute ages for the most thoroughly studied voung open clusters that are still uncertain by a factor of two (Staulferetal.2000).," Unfortunately, theoretical isochrones fit to the upper main sequence provide absolute ages for the most thoroughly studied young open clusters that are still uncertain by a factor of two \citep{sta00}."1067. The uncertainty niainly results from (he dependence of (he lifetime of massive stars on (hie size ol their convective cores., The uncertainty mainly results from the dependence of the lifetime of massive stars on the size of their convective cores.1068 Convective core overshoot brings fresh hvdiogen-rich material to the core. extending the stellar lifetime on the main sequence.," Convective core overshoot brings fresh hydrogen-rich material to the core, extending the stellar lifetime on the main sequence."1069 As a result. cluster age estimates are «quite sensitive to (he degree of convective core overshoot in (he theoretical calculations.," As a result, cluster age estimates are quite sensitive to the degree of convective core overshoot in the theoretical calculations."1070 There is evidence that the inclusion of convective core overshoot results in an improved agreement between theoretical evolution rates ancl umber counts in the Hertzsprune gap. and also an improved fit to (he width of the main sequence turnolL in open clusters (Andersen.Nordstrom.1990:Demarque.Sarajedini.&Guo 1994).," There is evidence that the inclusion of convective core overshoot results in an improved agreement between theoretical evolution rates and number counts in the Hertzsprung gap, and also an improved fit to the width of the main sequence turnoff in open clusters \citep{and90,dem94}."1071. Thus. theoretical caleulations (hat include convective core overshoot result in an older absolute age scale relative to theoretical calculations (hat do not.," Thus, theoretical calculations that include convective core overshoot result in an older absolute age scale relative to theoretical calculations that do not."1072 Calibrating the older convective core overshoot age scale recquires an independent technique for determining stellar cluster ages., Calibrating the older convective core overshoot age scale requires an independent technique for determining stellar cluster ages.1073 Lithium depletion age dating is one possibility. and in (his paper we discuss the reliability of Chis technique.," Lithium depletion age dating is one possibility, and in this paper we discuss the reliability of this technique."1074 The lithium depletion boundary (LDB) technique is an independent method to determine the age of open clusters with ages (hat range from 20 to 200 Mvr., The lithium depletion boundary (LDB) technique is an independent method to determine the age of open clusters with ages that range from 20 to 200 Myr.1075 Proton reactions destrov Li* near a destruction temperature. Tj~2.5xLO? Ix. easily obtained under stellar conditions.," Proton reactions destroy $^{7}$ near a destruction temperature, $_{D}\sim 2.5\times 10^{6}$ K, easily obtained under stellar conditions."1076 In general. (he presence or absence of photospheric lithium determines whether sullicient lime has passed [for a majoritv of the stellar material to reach depths in the star where T-—Tp.," In general, the presence or absence of photospheric lithium determines whether sufficient time has passed for a majority of the stellar material to reach depths in the star where $_{D}$."1077 For stars that are fully convective during pre-main-sequence contraction (Mz0.4 AL. ). the convective overturn timescale is much less than the evolutionary timescale. and the entire lithium content is rapidly destroved when the stellar core temperature. Το reaches Tp.," For stars that are fully convective during pre-main-sequence contraction $\la 0.4$ $_{\odot}$ ), the convective overturn timescale is much less than the evolutionary timescale, and the entire lithium content is rapidly destroyed when the stellar core temperature, $_{C}$, reaches $_{D}$."1078 Since the rate at which the core temperature increases to the destruction temperature is a strong function of stellar mass. spectral observations of Li* in fully convective stars during pre-anain-sequence contraction is an accurate age diagnostic.," Since the rate at which the core temperature increases to the destruction temperature is a strong function of stellar mass, spectral observations of $^{7}$ in fully convective stars during pre-main-sequence contraction is an accurate age diagnostic."1079 Higher mass stars reach the condition Te =Ty at an earlier age and higher luminosity than lower mass stars. and the lithium abundance decreases by a [ictor of 100 over a very narrow luminosity.," Higher mass stars reach the condition $_{C}=$ $_{D}$ at an earlier age and higher luminosity than lower mass stars, and the lithium abundance decreases by a factor of 100 over a very narrow luminosity."1080 LDB ages have been obtained [or several voung open clusters: the Pleiades. Alpha Per. IC 2391. NGC 2547 (Stauffer.Schultz.&Wirkpatrick1998:Staufferοἱal.1999:Bar-radovNavascués.Statler.&Patten1999:Oliveiraοἱal... 2003).," LDB ages have been obtained for several young open clusters: the Pleiades, Alpha Per, IC 2391, NGC 2547 \citep{sta98,sta99,bar99,oli03}."1081. In an independent analvsis. Jeffries&Navlor(2000) verifiecl (he conclusions of the previous open cluster studies that the LDD ages are ~1.6 times older (han upper mainu-sequence-lilling ages without. convective core overshoot.," In an independent analysis, \citet{jef00} verified the conclusions of the previous open cluster studies that the LDB ages are $\sim$ 1.6 times older than upper main-sequence-fitting ages without convective core overshoot."1082 Jeffries&Navlor(2000). [ind that the observational, \citet{jef00} find that the observational1083rocky planet. (he latter acts as a test particle (to leading order).,"rocky planet, the latter acts as a test particle (to leading order)."1084 If the rocky planet migrates sufficiently slowly. it generally becomes locked. into mean motion resonance with the Hot Jupiter.," If the rocky planet migrates sufficiently slowly, it generally becomes locked into mean motion resonance with the Hot Jupiter."1085 Continued migration of the second body then pushes both planets inward. although {his motion ceases if the second body reaches the inner edge of the disk (and Chis motion becomes ineffective if (he second planet is too small).," Continued migration of the second body then pushes both planets inward, although this motion ceases if the second body reaches the inner edge of the disk (and this motion becomes ineffective if the second planet is too small)."1086 Η migration ceases. (he resulting pair of planets could survive in or near resonance.," If migration ceases, the resulting pair of planets could survive in or near resonance."1087 If the Hot Jupiter can be observed in (ransil. the second body can produce transit timing variations (ASSC).," If the Hot Jupiter can be observed in transit, the second body can produce transit timing variations (ASSC)."1088 If migration occurs too quickly. the second planet passes through mean motion resonance (Quillen 2006. Netchum et al.," If migration occurs too quickly, the second planet passes through mean motion resonance (Quillen 2006, Ketchum et al."1089 2011) and will often experience a close encounter with the Hot Jupiter., 2011) and will often experience a close encounter with the Hot Jupiter.1090 The interaction event can result in either a collision between the planets (and assimilation of the rocky body) or the accretion of one planet (generally the smaller one) by the star., The interaction event can result in either a collision between the planets (and assimilation of the rocky body) or the accretion of one planet (generally the smaller one) by the star.1091 Planets are rarely scattered out of (he solar svstem because the exavitational potential of the star (for a 4-day orbit) is deeper (han that of the Jovian planet (escape thus requires 3-body effects)., Planets are rarely scattered out of the solar system because the gravitational potential of the star (for a $\sim4$ -day orbit) is deeper than that of the Jovian planet (escape thus requires 3-body effects).1092 One goal of this work is (ο determine (he branching ratios for the various outcomes survival. acceretion. scaltering into (he star as a function of (Jovian) planetary. mass aud orbital eccentricity.," One goal of this work is to determine the branching ratios for the various outcomes — survival, accretion, scattering into the star — as a function of (Jovian) planetary mass and orbital eccentricity."1093 We approach this problem by performing direct. numerical integrations of migrating planetary svstems. Le. we integrate the full set of 18 phase space variables for the 3-bodx problem consisting of the star. Hot Jupiter. aud a second migrating planet.," We approach this problem by performing direct numerical integrations of migrating planetary systems, i.e., we integrate the full set of 18 phase space variables for the 3-body problem consisting of the star, Hot Jupiter, and a second migrating planet."1094 These integrations are carried out. using a D-5 integration scheme., These integrations are carried out using a B-S integration scheme.1095 In addition to gravitv. we include forcing terms that represent inward migration ancl eccentricitv damping: these additional effects arise due to the forces exerted on the planet(s) by the circumstellar disk.," In addition to gravity, we include forcing terms that represent inward migration and eccentricity damping; these additional effects arise due to the forces exerted on the planet(s) by the circumstellar disk."1096 However. we cdo not model the disk directly. but rather include forcing terms to model its behavior.," However, we do not model the disk directly, but rather include forcing terms to model its behavior."1097" We consider simple disk models where the surface density. aud temperature distribution are power-laws in radius. ye where X, and 71 are normalization constants."," We consider simple disk models where the surface density and temperature distribution are power-laws in radius, )^p where $\Sigma_1$ and $T_1$ are normalization constants."1098" Here we taker,=1AU. so the coellicients M4 and 7, correspond to values at 1 AU."," Here we take $r_1=1$AU, so the coefficients $\Sigma_1$ and $T_1$ correspond to values at 1 AU."1099 The index p=1—2. where the intermediate value p—3/2 arises for the Minimum Mass Solar Nebula (Weidenschiling 1977) and where recent observations suggest p—0.940.2 (Andrews et al.," The index $p=1-2$, where the intermediate value $p=3/2$ arises for the Minimum Mass Solar Nebula (Weidenschilling 1977) and where recent observations suggest $p=0.9\pm0.2$ (Andrews et al."1100 2010)., 2010).1101 The normalization for the surface density has a range of values. with X4221500—4500 e/cni? (Ixuchner 2004).," The normalization for the surface density has a range of values, with $\Sigma_1\approx1500-4500$ $^2$ (Kuchner 2004)."1102 The power-law index of the temperature profile qzz3/4 for a viscous accretion disk (Pringle 1981) and a flat reprocessing disk (Adams Shu 1936). whereas q221/2 lor a flared reprocessing disk (Chiang Goldreich 1997).," The power-law index of the temperature profile $q\approx3/4$ for a viscous accretion disk (Pringle 1981) and a flat reprocessing disk (Adams Shu 1986), whereas $q\approx1/2$ for a flared reprocessing disk (Chiang Goldreich 1997)."1103 The latter value is often used to describe the early solar nebula (Weidenschilling 1977)., The latter value is often used to describe the early solar nebula (Weidenschilling 1977).1104 The disk scale height //— a5/€. where ay is the sound speed. which is determined by," The disk scale height $H=a_S/\Omega$ , where $a_S$ is the sound speed, which is determined by"1105 e. ο2z G ¢&=wir) p=pr) 0£=0 , $v_c$ $v_c\approx$ $G$ $\psi=\psi(r)$ $\rho=\rho(r)$ $\delta {\mathcal L}=0$ 1106to predict the X-ray emission from the WIIIM.,to predict the X-ray emission from the WHIM.1107 Compared to our previous work (2006).. we exploited the good spatial resolution (on the order of the adopted gravitational softening of 7.5 h.| kpe. compared to the ~195 ! kpe resolution element used by Cen Ostriker 1999) of a Lagrangian simulation to create hieh resolution maps of 1e barvon distribution.," Compared to our previous work \cite{Ursino06}, we exploited the good spatial resolution (on the order of the adopted gravitational softening of $7.5$ $^{-1}$ kpc, compared to the $\sim195$ $^{-1}$ kpc resolution element used by Cen Ostriker 1999) of a Lagrangian simulation to create high resolution maps of the baryon distribution."1108 We locused our attention on the effect of the metallicity model used on the X-ray Mnission., We focused our attention on the effect of the metallicity model used on the X-ray emission.1109 A\letallicity in the filaments is one of (he greatest uncertainties in this tvpe of V.imulations., Metallicity in the filaments is one of the greatest uncertainties in this type of simulations.1110 Observations of the interealactic medium put some limits on metals in the InterGalactic Medium (IGM)., Observations of the intergalactic medium put some limits on metals in the InterGalactic Medium (IGM).1111" At z<0.5 groups and clusters have metallicity Ze0.3 Z.. while Ly-a clouds have Z~0.1 Z. wilh a large scatter (0.01<Z/Z.,«1)."," At $z\lesssim0.5$ groups and clusters have metallicity $\textrm{Z}\sim 0.3$ $_\odot$, while $\alpha$ clouds have $\textrm{Z}\sim0.1$ $_\odot$ with a large scatter $0.01<\textrm{Z/Z}_\odot<1$ )."1112 Going at higher redshifts metallicity becomes lower. possibly by a factor 10 already al 2223 Finoguenov.elProchaskaetal.(2004):Simcoe (2006).," Going at higher redshifts metallicity becomes lower, possibly by a factor 10 already at $z\approx3$ \cite{Finoguenov03, Prochaska04, Simcoe06}."1113. From the analvsis of the low redshift absorbers. colder WIIM structures have Z~0.15 Z. Danforth&Shull(2008).," From the analysis of the low redshift absorbers, colder WHIM structures have $\textrm{Z}\sim0.15$ $_\odot$ \cite{Danforth08}."1114. Although there is à possible correlation between higher metallicities and higher densities. a simple modeling of IGM metallicity is difficult.," Although there is a possible correlation between higher metallicities and higher densities, a simple modeling of IGM metallicity is difficult."1115 At present time it is even uncertain if ihere was an early metal enrichment (22 4). if metals in the IGM are due to the newborn (z« 2) galaxies. or if metal enrichment history is described by a mixture of the two models Aguirre&Schave.(2005).," At present time it is even uncertain if there was an early metal enrichment $z\approx4$ ), if metals in the IGM are due to the newborn $z<2$ ) galaxies, or if metal enrichment history is described by a mixture of the two models \cite{Aguirre05}."1116. Cosmologieal simulations with an acetate physical description (galactic winds. star formation. black hole feedback. and so forth) ean come to an avail in reproducing the proper metallicity Cen&Ostriker(1999b):Borganietal.(2004):Ostriker(2006):Tornatoreetal.(2009):Wiersma (2009b).," Cosmological simulations with an accurate physical description (galactic winds, star formation, black hole feedback, and so forth) can come to an avail in reproducing the proper metallicity \cite{CenOst99b, 1117Borgani04, CenOst06, Tornatore09, Wiersma09b}."1118. These models predict that the average WIIIM metallicity is of the order of 0.1 Z. but the behavior as a function of density changes widely from simulation to simulation., These models predict that the average WHIM metallicity is of the order of $0.1$ $_\odot$ but the behavior as a function of density changes widely from simulation to simulation.1119 Due to the lack of üght constraints on metallicity [rom both observations and simulations. we allowed our code to work with a set ol metallicity models. in addition to the one coming directly [rom the Borgani simulation.," Due to the lack of tight constraints on metallicity from both observations and simulations, we allowed our code to work with a set of metallicity models, in addition to the one coming directly from the Borgani simulation."1120 Thanks to this degree of freeclom we were able to investigate the dependence of the soft X-ray emission on the different metallicity models., Thanks to this degree of freedom we were able to investigate the dependence of the soft X-ray emission on the different metallicity models.1121 The paper is structured as follows., The paper is structured as follows.1122 In 2. we introduce the hydrodvnamic cosmological simulation.in 3 we describe the code we used to simulate the X-ray emission in a selected lied of view. in 4 we show the simulated images and spectra. in 5 we discuss how the emitted spectra depend on (he metallicity models.," In \ref{Model} we introduce the hydrodynamic cosmological simulation, in \ref{Simulation} we describe the code we used to simulate the X-ray emission in a selected field of view, in \ref{Results} we show the simulated images and spectra, in \ref{Metallicity-emission} we discuss how the emitted spectra depend on the metallicity models."1123 The general properties of the cosmological model are described in details in Dorgani et al. (, The general properties of the cosmological model are described in details in Borgani et al. (11242004) and references therein.,2004) and references therein.1125 The simulation uses a flat A cold dark matter CACDM), The simulation uses a flat $\Lambda$ cold dark matter $\Lambda$ CDM)1126simplifying assumption of isotropic rellection ancl write the reflected intensity in the form: In order to calculate the time-varving iron line profiles and the corresponding continuum light curves we used the Following 1) We use a rav-tracing technique to follow the trajectories of photons [from positions (r.y) on the observers image plane to the disc. keeping track of all Jover-Lindequist Coordinates LiGr. y). rGr.gn). Cr.gy). (Cr.y). until the photons either intersect the accretion disc plane or disappear below the event horizon (Phe observer is located. at F=10003. 6= Poand ó=OUS where ? is the inclination).,"simplifying assumption of isotropic reflection and write the reflected intensity in the form: In order to calculate the time-varying iron line profiles and the corresponding continuum light curves we used the following 1) We use a ray-tracing technique to follow the trajectories of photons from positions $(x,y)$ on the observer's image plane to the disc, keeping track of all Boyer-Lindquist coordinates $\tilde{t}_{do}(x,y)$ , $r(x,y)$, $\theta(x,y)$, $\phi(x,y)$, until the photons either intersect the accretion disc plane or disappear below the event horizon (The observer is located at $r=1000m$, $\theta=i$ and $\phi=0^{o}$, where $i$ is the inclination)."1127 We then calculate the redshift factor corresponding to the particular final position of a photon and its arrival time from the disc., We then calculate the redshift factor corresponding to the particular final position of a photon and its arrival time from the disc.1128 We generate an image of approximately 1600| pixels covering roughly an area of 160m«160m. 2) Using the time dependent ionization and illumination pattern described above and albedo eg;(Le.£). we specify the emoergent [ux from the disc as a function of time and energy in the fixed. spectral band. ic. we integrate. all. photons coming [rom regions of equal arrival time regions on the accretion disc at à particular energy.," We generate an image of approximately $1600\times 1600$ pixels covering roughly an area of $160m\times 160m$ 2) Using the time dependent ionization and illumination pattern described above and albedo $a_{R}(E,\xi)$, we specify the emergent flux from the disc as a function of time and energy in the fixed spectral band, i.e. we integrate all photons coming from regions of equal arrival time regions on the accretion disc at a particular energy."1129 In doing so we also take into account the fact that the source changes its position and rotate the illumination and ionization patterns accordingly., In doing so we also take into account the fact that the source changes its position and rotate the illumination and ionization patterns accordingly.1130 This allowed: us to compute the reflected. spectrum as a function of time and thus the reflected component of the light curve., This allowed us to compute the reflected spectrum as a function of time and thus the reflected component of the light curve.1131 We use the following formulae (see appendix € [or additional explanations): where by(1) is the contribution to the flux from the Hare at the n-th position given hy: where gv. is the redshift factor for the clise-to-ohserver case. αμ is the pixel surface area on the observer's image plane. ro is the distance from the black hole svstem and Pato|hte.," We use the following formulae (see appendix C for additional explanations): where $F^{(n)}_{R}(t)$ is the contribution to the flux from the flare at the n-th position given by: where $g_{do}$ is the redshift factor for the disc-to-observer case, $dxdy$ is the pixel surface area on the observer's image plane, $r_{0}$ is the distance from the black hole system and $\tilde{t}=1132\tilde{t}_{sd}+\tilde{t}_{do}$."1133 3) We compute the direct Dux component by propagating photons from the source to the observer., 3) We compute the direct flux component by propagating photons from the source to the observer.1134 We use a formula analogous to that above to calculate this 4) Llaving specified the illumination pattern aud ionization state for a given position of the flare above the accretion disc. we determine the contribution of each. eric clement on the disc surface to the iron line profile from the formula: where fy(9.0) is the integrated. over a fixed. energy banc X-ray flux at the given. position on the clisc.," We use a formula analogous to that above to calculate this 4) Having specified the illumination pattern and ionization state for a given position of the flare above the accretion disc, we determine the contribution of each grid element on the disc surface to the iron line profile from the formula: where $F_{X}(r,\phi)$ is the integrated over a fixed energy band X-ray flux at the given position on the disc."1135 The above function is the Creen’s function. (transfer. function) corresponding to the n-th position of the 5) In the last step we use the transfer functions for single isolated ]ares in order to calculate the observed iron line Hux variations., The above function is the Green's function (transfer function) corresponding to the n-th position of the 5) In the last step we use the transfer functions for single isolated flares in order to calculate the observed iron line flux variations.1136 We use the following expression: where we also take into account the delays due to the revolution of the flare around the black hole., We use the following expression: where we also take into account the delays due to the revolution of the flare around the black hole.1137 As in the case of he reflected Dux. we interpolate the contributions to the Dux rom the isolated [ares and then add the interpolated Luxes.," As in the case of the reflected flux, we interpolate the contributions to the flux from the isolated flares and then add the interpolated fluxes."1138 ote that the binning of the transfer functions in time would introduce a small adcditional (artificial) flux variability. oeause we physically rotate the illumination pattern.," Note that the binning of the transfer functions in time would introduce a small additional (artificial) flux variability, because we physically rotate the illumination pattern."1139 This is because the dillerences between the arrival times [rom he neighbouring disc elements on the approaching side of he dise would be shorter compared to the corresponding dillerences on the opposite sido., This is because the differences between the arrival times from the neighbouring disc elements on the approaching side of the disc would be shorter compared to the corresponding differences on the opposite side.1140 We present iron line [lux variations and the corresponding ight curves lor one full. revolution of the [lare around he black hole with a step-like luminosity variation in the ocal [rame of reference of the Iare., We present iron line flux variations and the corresponding light curves for one full revolution of the flare around the black hole with a step-like luminosity variation in the local frame of reference of the flare.1141 This is for illustrative purposes and we stress that while it is trivial. for example. to eeneralize the code to include arbitrary intrinsic Luminosity variations in the rest frame of the flare. we do not. wish o complicate the interpretation of the results.," This is for illustrative purposes and we stress that while it is trivial, for example, to generalize the code to include arbitrary intrinsic luminosity variations in the rest frame of the flare, we do not wish to complicate the interpretation of the results."1142 Future observations may guide us as to how to introduce additional jpdilications in the computations., Future observations may guide us as to how to introduce additional modifications in the computations.1143 Phe results in the present form can in principle be applied to the case of Isolated Dares or at least strong outbursts accompanied by minor ones., The results in the present form can in principle be applied to the case of isolated flares or at least strong outbursts accompanied by minor ones.1144 In he computations we assume that the source omits a power aw spectrum with energy index a=1., In the computations we assume that the source emits a power law spectrum with energy index $\alpha=1$.1145 Fie and Fig.2 present the light. curves., Fig.1 and Fig.2 present the light curves.1146 The light curves are a superposition of the direct. flux. from the lave and the reflected lux from the disc., The light curves are a superposition of the direct flux from the flare and the reflected flux from the disc.1147 The small olfset oween these (wo. components (note the shift. between initial and final times of the reflected ane direct Dux) is due o the additional time photonsneed to propagate towards he disc and back., The small offset between these two components (note the shift between initial and final times of the reflected and direct flux) is due to the additional time photonsneed to propagate towards the disc and back.1148 Phe small albedo of the cise material, The small albedo of the disc material1149of the source/sky itself.,of the source/sky itself.1150" The zoomed image shows the first 20 DCEs, where DEC=0 corresponds to the sky measurement, DCE-1 the stim, DCE- 2 to 7 to observations in the ""internal dark reference” and DCE=8 is the sky measurement followed by another six DCEs and the next calibration stim (DCE=15)."," The zoomed image shows the first 20 DCEs, where DEC=0 corresponds to the sky measurement, DCE=1 the stim, DCE= 2 to 7 to observations in the ""internal dark reference"" and DCE=8 is the sky measurement followed by another six DCEs and the next calibration stim (DCE=15)."1151" We note that the level of the DCE=7 is essentially zero, because in the data reduction pipeline this is the ""reference"" measurement that is subtracted from each BCD."," We note that the level of the DCE=7 is essentially zero, because in the data reduction pipeline this is the 'reference' measurement that is subtracted from each BCD."1152" We also note that the sky itself (DCE=8) is at ~3 MJy/sr, which is the final TPM measurement."," We also note that the sky itself (DCE=8) is at $\sim3$ MJy/sr, which is the final TPM measurement."1153 The comparison of the TPM with the photometric observation shows that the light contribution of the telescope at 160 um is ~1.3 MJy/sr., The comparison of the TPM with the photometric observation shows that the light contribution of the telescope at 160 $\mu$ m is $\sim 1.3$ MJy/sr.1154" The level of spurious emission due to the telescope background emission at 160 um is 1.0+0.2 The absolute calibration of 160 44m TPM relies on the standard 160 um calibration, which is based on asteroids, that is tied itself to the 24 and 70 um MIPS absolute calibration to be internally consistent (?).."," The level of spurious emission due to the telescope background emission at 160 $\mu$ m is $\pm$ 0.2 The absolute calibration of 160 $\mu$ m TPM relies on the standard 160 $\mu$ m calibration, which is based on asteroids, that is tied itself to the 24 and 70 $\mu$ m MIPS absolute calibration to be internally consistent \citep{2007PASP..119.1038S}."1155" Finally, we stress that a single DCE at 160 uum does not cover the 160 jum beam (40"")), hence the TPM mode was designed to move the scan mirror to cover the beam in one cycle."," Finally, we stress that a single DCE at 160 $\mu$ m does not cover the 160 $\mu$ m beam ), hence the TPM mode was designed to move the scan mirror to cover the beam in one cycle."1156 A standard TPM 160 um observation contains four cycles., A standard TPM 160 $\mu$ m observation contains four cycles.1157" The final product for a single 160 um TPM observation is a 5x5' small mosaic, and for our measurements we calculated the mean over such an image."," The final product for a single 160 $\mu$ m TPM observation is a $\times$ small mosaic, and for our measurements we calculated the mean over such an image."1158" The two ELAIS N1 TPM observations at 160 um took 2386 s with 88 s on source each, while the two photometric observations using the enhanced mode took 671 secs with 54 secs on each source."," The two ELAIS N1 TPM observations at 160 $\mu$ m took 2386 s with 88 s on source each, while the two photometric observations using the enhanced mode took 671 secs with 54 secs on each source."1159" These numbers illustrate the efficiency of the two modes; for every second on source at TPM, about seven seconds woth of data are used for calibration and latency decay."," These numbers illustrate the efficiency of the two modes; for every second on source at TPM, about seven seconds woth of data are used for calibration and latency decay."1160" We used the 25 deg? data cube (x, y, velocities) centered on ELAIS N1."," We used the 25 $^2$ data cube (x, y, velocities) centered on ELAIS N1."1161 These data were obtained in 2006 and 2010 withthe 100-meter Green Bank Telescope (GBT)., These data were obtained in 2006 and 2010 withthe 100-meter Green Bank Telescope (GBT).1162" Spectra were measured over a 5?x5° area centered on (f,b) = (85.5°,+44.3°) every 3.5’ in both coordinates.", Spectra were measured over a $5^o \times 5^o$ area centered on $\ell$ $b$ ) = $^o$ $^o$ ) every $\arcmin$ in both coordinates.1163 Data were taken by in-band frequency switching yielding spectra with a velocity coverage —450<Visa€+355 km s anda velocity resolution of 0.80 km.s~!., Data were taken by in-band frequency switching yielding spectra with a velocity coverage $-450 \leq V_{LSR} \leq +355$ km $^{-1}$ and a velocity resolution of 0.80 $^{-1}$.1164" Spectra were calibrated, corrected for stray radiation, and placed on a brightness temperature (Τη) scale as described in ?) and ?).."," Spectra were calibrated, corrected for stray radiation, and placed on a brightness temperature $T_b$ ) scale as described in \citet{2010ASPC..438..156B} and \citet{2011A&A...536A..81B}."1165 A third-order polynomial was fit to the emission-free regions of the spectra to remove any residual instrumental baseline., A third-order polynomial was fit to the emission-free regions of the spectra to remove any residual instrumental baseline.1166" The final data cube has a root mean square (rms) noise in a single channel of 0.12 K of Ty, and an effective angular resolution of 9.4’x9.1’ in € and b, We distinguish three velocity components in the gas data: the local, intermediate (IVC), and high velocity cloud (HVC)."," The final data cube has a root mean square (rms) noise in a single channel of 0.12 K of $T_b$, and an effective angular resolution of $9.4 \arcmin \times 9.1 \arcmin$ in $\ell$ and $b$, We distinguish three velocity components in the gas data: the local, intermediate (IVC), and high velocity cloud (HVC)."1167 These are shown in Fig. 8.., These are shown in Fig. \ref{fig:GBT}.1168" The HVC is centered around -115 km/s and the IVC around -23 km/s, as illustrated in Fig. 9.."," The HVC is centered around -115 km/s and the IVC around -23 km/s, as illustrated in Fig. \ref{fig:comp_spectra}."1169" This figure shows velocity spectra along three lines of sight, each of which is dominated by one component."," This figure shows velocity spectra along three lines of sight, each of which is dominated by one component."1170 The IVC and the HVC are clearly seen in the middle and bottom panels., The IVC and the HVC are clearly seen in the middle and bottom panels.1171" We used IRIS (re-processed IRAS data) maps at 60 and 100 uum to measure the emissivities of the dust correlated to the components and derive the CIB power spectrum at 100 um. This new generation of IRAS images was processed using a more reliable zodiacal light subtraction, from a calibration and zero level compatible with DIRBE and a more reliable destriping (?).. "," We used IRIS (re-processed IRAS data) maps at 60 and 100 $\mu$ m to measure the emissivities of the dust correlated to the components and derive the CIB power spectrum at 100 $\mu$ m. This new generation of IRAS images was processed using a more reliable zodiacal light subtraction, from a calibration and zero level compatible with DIRBE and a more reliable destriping \citep{2005ApJS..157..302M}. ."1172"At 100 uum, the IRIS product also represents a significant improvement on the ?) maps."," At 100 $\mu$ m, the IRIS product also represents a significant improvement on the \citet{1998ApJ...500..525S} maps."1173 IRIS keeps the full, IRIS keeps the full1174"where Aj,z P4. As#Pa. and Ayz0.","where $A_1\ne P_{g\theta}$ , $A_2\ne P_{\theta\theta}$ , and $A_3\ne0$."1175 The importance of the extra higher order terms was emphasised most recently by Scoccimarro(2004)., The importance of the extra higher order terms was emphasised most recently by \citet{Sco04}.1176. In addition to these redshift-space effects. the linear theory relation between 6 and 8. given in Eq. (69).," In addition to these redshift-space effects, the linear theory relation between $\delta$ and $\theta$, given in Eq. \ref{eq:lin_f}) ),"1177 will break down in the quasi-linear regime. so we should expect the shapes of PL. Pu and Pu to be different.," will break down in the quasi-linear regime, so we should expect the shapes of $P_{gg}$, $P_{g\theta}$ and $P_{\theta\theta}$ to be different."1178 The relationship between Eqns., The relationship between Eqns.1179 (8 I5p can be written where Gtk.po) has the property lim;ροκ40)=I.," \ref{eq:pgs_lin} \ref{eq:pgs_qlin}) ) can be written where $G(k,\mu^2)$ has the property $\lim_{k\to0}G(k,\mu^2)=1$."1180 The standard model for redshift-space distortions includes a component caused by an uncorrelated velocity dispersion that grows on small scales., The standard model for redshift-space distortions includes a component caused by an uncorrelated velocity dispersion that grows on small scales.1181" Such a model is motivated by the idea of ""thermal motion"" of particles in collapsed structures. which causes the Fingers-Of-God (FOG) observed in redshift surveys (Jackson 1972)."," Such a model is motivated by the idea of “thermal motion” of particles in collapsed structures, which causes the Fingers-Of-God (FOG) observed in redshift surveys \citep{Jac72}."1182". An additional component comprising uncorrelated particle motions will dilute both the galaxy overdensity 6,. and the “extra” overdensity term caused by the linear distortions. €."," An additional component comprising uncorrelated particle motions will dilute both the galaxy overdensity $\delta_g$, and the “extra” overdensity term caused by the linear distortions, $\theta$."1183 Motivated by numerical simulations (Sheth&Diaferio2001:Huffetal.2007) and the halo model (White2001:Seljak20013.. we ean assume that the centre of mass of a halo. around which galaxies orbit. still moves according to (quasi-Minear motion.," Motivated by numerical simulations \citep{SheDia01,HSWSW07} and the halo model \citep{Whi01,Sel01}, we can assume that the centre of mass of a halo, around which galaxies orbit, still moves according to (quasi-)linear motion."1184 Such a model leads to the much-used ‘streaming’ models (e.g.Hamilton1998) where with Εμ.) a function that depends on the distribution of random pair velocities in collapsed objects. which is often written as a function of v=Kc. where c is the rms velocity dispersion.," Such a model leads to the much-used `streaming' models \citep[e.g.][]{HamiltonReview} where with $F(k,\mu^2)$ a function that depends on the distribution of random pair velocities in collapsed objects, which is often written as a function of $y=k\sigma$, where $\sigma$ is the rms velocity dispersion."1185 In order to mateh behaviour on large scales. we require lim;»F(k.47)=|.," In order to match behaviour on large scales, we require $\lim_{k\to0}F(k,\mu^2)=1$."1186 We have written the equation in this form to highlight the similarity with Eq. (16)., We have written the equation in this form to highlight the similarity with Eq. \ref{eq:G}) ).1187 Note that this model is constructed by a rather ad-hoc splicing of linear. quasi-linear and non-linear behaviour which ignores the scale-dependence of the mapping between real and redshift space separations (Fisher1995:Scoccimarro2004.andreferences therein)... while Eq. (169) ," Note that this model is constructed by a rather ad-hoc splicing of linear, quasi-linear and non-linear behaviour which ignores the scale-dependence of the mapping between real and redshift space separations \citep[][and references therein]{Fis95,Sco04}, while Eq. \ref{eq:G}) )"1188was based on the analysis of the redshift-space distortions in the linear limit., was based on the analysis of the redshift-space distortions in the quasi-linear limit.1189 In general FOG are difficult to model well. and their amplitude is strongly dependent on the mean halo mass and satellite fraction of the population under consideration (White2001:Seljak2," In general FOG are difficult to model well, and their amplitude is strongly dependent on the mean halo mass and satellite fraction of the population under consideration \citep{Whi01,Sel01}."119000 Previous work has concentrated on models with Gaussian or Exponential distributions (e.g.Coleetal.1995:Peacock&Dodds1996) for the pairwise velocity dispersion in configuration space.," Previous work has concentrated on models with Gaussian or Exponential distributions \citep[e.g.][]{cole95,PeaDod96} for the pairwise velocity dispersion in configuration space."1191 For an Exponential model for the pairwise velocity dispersion in configuration space. weexpeet a Lorentz damping factor for the power spectrum. while the Gaussian dispersion translates to a Gaussian damping of the power spectrum These terms have the same behaviour to first order.," For an Exponential model for the pairwise velocity dispersion in configuration space, weexpect a Lorentz damping factor for the power spectrum, while the Gaussian dispersion translates to a Gaussian damping of the power spectrum These terms have the same behaviour to first order."1192 The exact form of Fk.48). and the value of c is strongly dependent on the galaxy population Jing&Borner2004:Lietal. 2007).," The exact form of $F(k,\mu^2)$, and the value of $\sigma$ is strongly dependent on the galaxy population \citep{Jing04,Li07}. ."1193". An alternative approach would be to try to ""eliminate"" the FOG by applying a halo finding algorithm to the sample and manually moving galaxies either to halo centres. or to a spherically symmetric distribution around these centres (e.g. Tegmark 2004))."," An alternative approach would be to try to “eliminate” the FOG by applying a halo finding algorithm to the sample and manually moving galaxies either to halo centres, or to a spherically symmetric distribution around these centres (e.g. \citealt{tegmark04}) )."1194 Such approaches tend to mask the fact that the radial “compression” is still model dependent. and requires a similar free parameter to 7 in Eq. (20)).," Such approaches tend to mask the fact that the radial “compression” is still model dependent, and requires a similar free parameter to $\sigma$ in Eq. \ref{eq:pgs_combined}) )."1195" This ""parameter"" controls the probability density function for the distortion of any galaxy in redshift space (Reid&Spergel2008).", This “parameter” controls the probability density function for the distortion of any galaxy in redshift space \citep{reid08}.1196. However. FOG compression does have the advantage of including extra information in the analvsis from the phases. which are used to locate the halos.," However, FOG compression does have the advantage of including extra information in the analysis from the phases, which are used to locate the halos."1197" Dealing directly with the FOG is not the same as extending the linear model. and P... P, Pee into the non-linear regime. as discussed in the previous section."," Dealing directly with the FOG is not the same as extending the linear model, and $P_{gg}$, $P_{g\theta}$ $P_{\theta\theta}$ into the non-linear regime, as discussed in the previous section."1198" The real-space effect of random thermal motion of galaxies on small scales would lead P,, to decrease in amplitude. because of the decoherence of density and velocity divergence. while P,, increases."," The real-space effect of random thermal motion of galaxies on small scales would lead $P_{g\theta}$ to decrease in amplitude, because of the decoherence of density and velocity divergence, while $P_{\theta\theta}$ increases."1199 We showed in Eq. (16)), We showed in Eq. \ref{eq:G}) )1200 that a similar function to F(A.47) would be required to include quasi-linear behaviour in the redshift-space power spectrum.," that a similar function to $F(k,\mu^2)$ would be required to include quasi-linear behaviour in the redshift-space power spectrum."

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